actually run Z3 for "SMT_Tests" when "ISABELLE_FULL_TEST" is enabled

--- a/src/HOL/ROOT	Wed Jan 02 09:13:50 2013 +0100
+++ b/src/HOL/ROOT	Wed Jan 02 09:31:25 2013 +0100
@@ -671,12 +671,12 @@
 session "HOL-Word-SMT_Examples" in SMT_Examples = "HOL-Word" +
   options [document = false, quick_and_dirty]
   theories
-    SMT_Tests
     SMT_Examples
     SMT_Word_Examples
+  theories [condition = ISABELLE_FULL_TEST]
+    SMT_Tests
   files
     "SMT_Examples.certs"
-    "SMT_Tests.certs"
     "SMT_Word_Examples.certs"
 
 session "HOL-Boogie" in "Boogie" = "HOL-Word" +

--- a/src/HOL/SMT_Examples/SMT_Examples.thy	Wed Jan 02 09:13:50 2013 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy	Wed Jan 02 09:31:25 2013 +0100
@@ -8,7 +8,6 @@
 imports Complex_Main
 begin
 
-declare [[smt_oracle = false]]
 declare [[smt_certificates = "SMT_Examples.certs"]]
 declare [[smt_read_only_certificates = true]]
 

--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Wed Jan 02 09:13:50 2013 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,53781 +0,0 @@
-23d01cdabb599769b54210e40617eea3d6c91e30 8 0
-#2 := false
-#1 := true
-#7 := (not true)
-#29 := (iff #7 false)
-#30 := [rewrite]: #29
-#28 := [asserted]: #7
-[mp #28 #30]: false
-unsat
-da9cf67daad06e6b55c8a58d39d168a3e68ef149 16 0
-#2 := false
-#7 := (not false)
-#8 := (not #7)
-#37 := (iff #8 false)
-#1 := true
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #8 #32)
-#30 := (iff #7 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #8
-[mp #29 #38]: false
-unsat
-7a1bb52ecd7d9418dd685e581c967efeb26876f4 21 0
-#2 := false
-#1 := true
-#7 := (not true)
-#8 := (not #7)
-#9 := (not #8)
-#42 := (iff #9 false)
-#31 := (iff #7 false)
-#32 := [rewrite]: #31
-#40 := (iff #9 #7)
-#38 := (iff #8 true)
-#33 := (not false)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #8 #33)
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#41 := [monotonicity #39]: #40
-#43 := [trans #41 #32]: #42
-#30 := [asserted]: #9
-[mp #30 #43]: false
-unsat
-6f92ca4f0e1770fcc8e653a3dc6a9a2100ac72fc 16 0
-#2 := false
-#1 := true
-#7 := (and true true)
-#8 := (not #7)
-#37 := (iff #8 false)
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #8 #32)
-#30 := (iff #7 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #8
-[mp #29 #38]: false
-unsat
-8bfe03ac24c5a99989017691842a79e88a05ac7c 16 0
-#2 := false
-#1 := true
-#7 := (or true false)
-#8 := (not #7)
-#37 := (iff #8 false)
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #8 #32)
-#30 := (iff #7 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #8
-[mp #29 #38]: false
-unsat
-5f12d6ee03b980092f8f61fd8d8cfd33a3a3aa1c 16 0
-#2 := false
-#1 := true
-#7 := (implies false true)
-#8 := (not #7)
-#37 := (iff #8 false)
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #8 #32)
-#30 := (iff #7 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #8
-[mp #29 #38]: false
-unsat
-b6f361c6fc132ef6bfb658932ab99e83188e4a5c 24 0
-#2 := false
-#1 := true
-#7 := (iff false true)
-#8 := (not #7)
-#9 := (not #8)
-#45 := (iff #9 false)
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #9 #40)
-#38 := (iff #8 true)
-#33 := (not false)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #8 #33)
-#31 := (iff #7 false)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #9
-[mp #30 #46]: false
-unsat
-22e23526a38d50ce23abbe4dbfb697891cbcd840 22 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (or #8 #9)
-#11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
-unsat
-902f835133cd6a5c2f7f8ebd7c78b25a41552b0b 30 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (and #8 #9)
-#11 := (not #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (not false)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 false)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-e413d2599061059e7509241c4afb58a241792143 49 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (and false #8)
-#12 := (or #11 #8)
-#10 := (not #8)
-#13 := (or #10 #12)
-#1 := true
-#9 := (and true #8)
-#14 := (or #9 #13)
-#15 := (not #14)
-#67 := (iff #15 false)
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #15 #62)
-#60 := (iff #14 true)
-#55 := (or #8 true)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #14 #55)
-#53 := (iff #13 true)
-#48 := (or #10 #8)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #13 #48)
-#46 := (iff #12 #8)
-#41 := (or false #8)
-#44 := (iff #41 #8)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 false)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#50 := [monotonicity #47]: #49
-#54 := [trans #50 #52]: #53
-#37 := (iff #9 #8)
-#38 := [rewrite]: #37
-#57 := [monotonicity #38 #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#36 := [asserted]: #15
-[mp #36 #68]: false
-unsat
-59514aaeba28f26ae6e2aa6e362e2d1af4138910 21 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (implies #8 #8)
-#10 := (not #9)
-#39 := (iff #10 false)
-#1 := true
-#34 := (not true)
-#37 := (iff #34 false)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#32 := (iff #9 true)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#31 := [asserted]: #10
-[mp #31 #40]: false
-unsat
-3c237c6663696e3e9e3813b33e057fd540002911 30 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (and #8 #9)
-#11 := (implies #10 false)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (implies false false)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 false)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-67a6978ea29dd08617f96b717aa6e108001ae5f6 48 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#12 := (and #10 #8)
-#47 := (not #12)
-#68 := (iff #47 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #47 #63)
-#61 := (iff #12 true)
-#56 := (and true true)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #12 #56)
-#52 := (iff #8 true)
-#11 := (and #8 #10)
-#36 := (not #11)
-#37 := (or #36 #12)
-#40 := (not #37)
-#13 := (implies #11 #12)
-#14 := (not #13)
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#35 := [asserted]: #14
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #11
-#44 := [and-elim #43]: #8
-#53 := [iff-true #44]: #52
-#54 := (iff #10 true)
-#46 := [and-elim #43]: #10
-#55 := [iff-true #46]: #54
-#58 := [monotonicity #55 #53]: #57
-#62 := [trans #58 #60]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#48 := [not-or-elim #45]: #47
-[mp #48 #69]: false
-unsat
-f82a7c681aece7ed4681eb3d1ac78d727ad5a702 48 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#71 := (iff #11 false)
-#66 := (or false false)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #11 #66)
-#62 := (iff #10 false)
-#53 := (not #10)
-#36 := (not #11)
-#43 := (or #36 #10 #8)
-#46 := (not #43)
-#12 := (or #10 #8)
-#13 := (implies #11 #12)
-#14 := (not #13)
-#49 := (iff #14 #46)
-#37 := (or #36 #12)
-#40 := (not #37)
-#47 := (iff #40 #46)
-#44 := (iff #37 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#50 := [trans #42 #48]: #49
-#35 := [asserted]: #14
-#51 := [mp #35 #50]: #46
-#54 := [not-or-elim #51]: #53
-#63 := [iff-false #54]: #62
-#64 := (iff #8 false)
-#55 := (not #8)
-#56 := [not-or-elim #51]: #55
-#65 := [iff-false #56]: #64
-#68 := [monotonicity #65 #63]: #67
-#72 := [trans #68 #70]: #71
-#52 := [not-or-elim #51]: #11
-[mp #52 #72]: false
-unsat
-fb29bce93621dffd68841a1b3fb5a13d0bf5c688 46 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#55 := (not #8)
-#71 := (iff #55 false)
-#1 := true
-#66 := (not true)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #55 #66)
-#62 := (iff #8 true)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#11 := (and #8 #10)
-#36 := (not #11)
-#43 := (or #36 #8 #10)
-#46 := (not #43)
-#12 := (or #8 #10)
-#13 := (implies #11 #12)
-#14 := (not #13)
-#49 := (iff #14 #46)
-#37 := (or #36 #12)
-#40 := (not #37)
-#47 := (iff #40 #46)
-#44 := (iff #37 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#50 := [trans #42 #48]: #49
-#35 := [asserted]: #14
-#51 := [mp #35 #50]: #46
-#52 := [not-or-elim #51]: #11
-#53 := [and-elim #52]: #8
-#63 := [iff-true #53]: #62
-#68 := [monotonicity #63]: #67
-#72 := [trans #68 #70]: #71
-#56 := [not-or-elim #51]: #55
-[mp #56 #72]: false
-unsat
-4bc7626ad30ca8d1808bcd7007aadf7e3808f557 35 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#13 := (not #8)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#11 := (or #8 #10)
-#12 := (not #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#52 := (iff #15 false)
-#37 := (or #11 #13)
-#40 := (not #37)
-#50 := (iff #40 false)
-#1 := true
-#45 := (not true)
-#48 := (iff #45 false)
-#49 := [rewrite]: #48
-#46 := (iff #40 #45)
-#43 := (iff #37 true)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#53 := [trans #42 #51]: #52
-#36 := [asserted]: #15
-[mp #36 #53]: false
-unsat
-9765f42e1923ee1286e51e6aaa01fea0147bcc3c 35 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#13 := (not #10)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#12 := (not #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#52 := (iff #15 false)
-#37 := (or #11 #13)
-#40 := (not #37)
-#50 := (iff #40 false)
-#1 := true
-#45 := (not true)
-#48 := (iff #45 false)
-#49 := [rewrite]: #48
-#46 := (iff #40 #45)
-#43 := (iff #37 true)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#53 := [trans #42 #51]: #52
-#36 := [asserted]: #15
-[mp #36 #53]: false
-unsat
-53caf383c23c48b243dad428460d0b2bad5eb2a7 29 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#51 := (iff #8 false)
-#9 := (not #8)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#12 := (and #8 #11)
-#13 := (not #12)
-#37 := (or #8 #13)
-#40 := (not #37)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#36 := [asserted]: #15
-#45 := [mp #36 #42]: #40
-#43 := [not-or-elim #45]: #9
-#52 := [iff-false #43]: #51
-#44 := [not-or-elim #45]: #12
-#46 := [and-elim #44]: #8
-[mp #46 #52]: false
-unsat
-8a6cff36c5c734fbecce18e7f0b86cdc4b398c76 29 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#51 := (iff #8 false)
-#9 := (not #8)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#12 := (and #11 #8)
-#13 := (not #12)
-#37 := (or #8 #13)
-#40 := (not #37)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#36 := [asserted]: #15
-#45 := [mp #36 #42]: #40
-#43 := [not-or-elim #45]: #9
-#52 := [iff-false #43]: #51
-#44 := [not-or-elim #45]: #12
-#47 := [and-elim #44]: #8
-[mp #47 #52]: false
-unsat
-8ed51fcc2c7a7fe92c740f362b331dc69282b7f4 31 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#13 := (not #10)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#12 := (not #8)
-#14 := (or #12 #13)
-#11 := (and #8 #10)
-#40 := (iff #11 #14)
-#43 := (iff #40 false)
-#15 := (not #14)
-#49 := (iff #15 #14)
-#46 := (iff #49 false)
-#47 := [rewrite]: #46
-#50 := (iff #40 #49)
-#16 := (iff #11 #15)
-#48 := [rewrite]: #16
-#51 := [monotonicity #48]: #50
-#45 := [trans #51 #47]: #43
-#17 := (not #16)
-#39 := (iff #17 #40)
-#41 := [rewrite]: #39
-#38 := [asserted]: #17
-#44 := [mp #38 #41]: #40
-[mp #44 #45]: false
-unsat
-40fc055a5f5aa6bfe535236f4ab4452ddc7101b7 53 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#15 := (and #10 #13)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#16 := (and #8 #15)
-#11 := (and #8 #10)
-#14 := (and #11 #13)
-#17 := (implies #14 #16)
-#18 := (not #17)
-#69 := (iff #18 false)
-#40 := (not #14)
-#41 := (or #40 #16)
-#44 := (not #41)
-#67 := (iff #44 false)
-#1 := true
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #44 #62)
-#60 := (iff #41 true)
-#47 := (and #8 #10 #13)
-#50 := (not #47)
-#55 := (or #50 #47)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #41 #55)
-#53 := (iff #16 #47)
-#54 := [rewrite]: #53
-#51 := (iff #40 #50)
-#48 := (iff #14 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#57 := [monotonicity #52 #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#45 := (iff #18 #44)
-#42 := (iff #17 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#70 := [trans #46 #68]: #69
-#39 := [asserted]: #18
-[mp #39 #70]: false
-unsat
-2a514d849c826c123fb15c9d79d484f526c07958 68 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#47 := (or #8 #10 #13)
-#90 := (iff #47 false)
-#85 := (or false false false)
-#88 := (iff #85 false)
-#89 := [rewrite]: #88
-#86 := (iff #47 #85)
-#83 := (iff #13 false)
-#72 := (not #13)
-#50 := (not #47)
-#56 := (or #50 #8 #10 #13)
-#61 := (not #56)
-#15 := (or #10 #13)
-#16 := (or #8 #15)
-#11 := (or #8 #10)
-#14 := (or #11 #13)
-#17 := (implies #14 #16)
-#18 := (not #17)
-#64 := (iff #18 #61)
-#40 := (not #14)
-#41 := (or #40 #16)
-#44 := (not #41)
-#62 := (iff #44 #61)
-#59 := (iff #41 #56)
-#53 := (or #50 #16)
-#57 := (iff #53 #56)
-#58 := [rewrite]: #57
-#54 := (iff #41 #53)
-#51 := (iff #40 #50)
-#48 := (iff #14 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#55 := [monotonicity #52]: #54
-#60 := [trans #55 #58]: #59
-#63 := [monotonicity #60]: #62
-#45 := (iff #18 #44)
-#42 := (iff #17 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#65 := [trans #46 #63]: #64
-#39 := [asserted]: #18
-#66 := [mp #39 #65]: #61
-#73 := [not-or-elim #66]: #72
-#84 := [iff-false #73]: #83
-#81 := (iff #10 false)
-#70 := (not #10)
-#71 := [not-or-elim #66]: #70
-#82 := [iff-false #71]: #81
-#79 := (iff #8 false)
-#68 := (not #8)
-#69 := [not-or-elim #66]: #68
-#80 := [iff-false #69]: #79
-#87 := [monotonicity #80 #82 #84]: #86
-#91 := [trans #87 #89]: #90
-#67 := [not-or-elim #66]: #47
-[mp #67 #91]: false
-unsat
-e0b09cf8a39c11d9d4bee6ec1a6a5b93b2257b06 80 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#15 := (or #8 #13)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#60 := (not #10)
-#59 := (not #8)
-#61 := (or #59 #60)
-#62 := (not #61)
-#85 := (not #13)
-#96 := [hypothesis]: #13
-#86 := (or #15 #85)
-#87 := [def-axiom]: #86
-#97 := [unit-resolution #87 #96]: #15
-#16 := (or #10 #13)
-#92 := (or #16 #85)
-#93 := [def-axiom]: #92
-#98 := [unit-resolution #93 #96]: #16
-#64 := (not #16)
-#63 := (not #15)
-#65 := (or #63 #64)
-#17 := (and #15 #16)
-#49 := (not #17)
-#74 := (iff #49 #65)
-#66 := (not #65)
-#69 := (not #66)
-#72 := (iff #69 #65)
-#73 := [rewrite]: #72
-#70 := (iff #49 #69)
-#67 := (iff #17 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#11 := (and #8 #10)
-#14 := (or #11 #13)
-#41 := (not #14)
-#42 := (or #41 #17)
-#45 := (not #42)
-#18 := (implies #14 #17)
-#19 := (not #18)
-#46 := (iff #19 #45)
-#43 := (iff #18 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#40 := [asserted]: #19
-#50 := [mp #40 #47]: #45
-#51 := [not-or-elim #50]: #49
-#76 := [mp #51 #75]: #65
-#99 := [unit-resolution #76 #98 #97]: false
-#100 := [lemma #99]: #85
-#55 := (or #62 #13)
-#56 := (iff #14 #55)
-#57 := (iff #11 #62)
-#58 := [rewrite]: #57
-#53 := [monotonicity #58]: #56
-#48 := [not-or-elim #50]: #14
-#54 := [mp #48 #53]: #55
-#101 := [unit-resolution #54 #100]: #62
-#77 := (or #61 #8)
-#78 := [def-axiom]: #77
-#102 := [unit-resolution #78 #101]: #8
-#83 := (or #15 #59)
-#84 := [def-axiom]: #83
-#103 := [unit-resolution #84 #102]: #15
-#79 := (or #61 #10)
-#80 := [def-axiom]: #79
-#104 := [unit-resolution #80 #101]: #10
-#90 := (or #16 #60)
-#91 := [def-axiom]: #90
-#105 := [unit-resolution #91 #104]: #16
-[unit-resolution #76 #105 #103]: false
-unsat
-32f6ddd6b17440644504f27b6be1cc3c71634e05 82 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#16 := (and #8 #13)
-#60 := (not #16)
-#101 := (iff #60 false)
-#1 := true
-#71 := (not true)
-#99 := (iff #71 false)
-#100 := [rewrite]: #99
-#72 := (iff #60 #71)
-#96 := (iff #16 true)
-#91 := (and true true)
-#94 := (iff #91 true)
-#95 := [rewrite]: #94
-#92 := (iff #16 #91)
-#70 := (iff #13 true)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#14 := (or #13 #10)
-#80 := (iff #14 #13)
-#75 := (or #13 false)
-#78 := (iff #75 #13)
-#79 := [rewrite]: #78
-#76 := (iff #14 #75)
-#73 := (iff #10 false)
-#62 := (not #10)
-#11 := (or #8 #10)
-#15 := (and #11 #14)
-#41 := (not #15)
-#48 := (or #41 #16 #10)
-#51 := (not #48)
-#17 := (or #16 #10)
-#18 := (implies #15 #17)
-#19 := (not #18)
-#54 := (iff #19 #51)
-#42 := (or #41 #17)
-#45 := (not #42)
-#52 := (iff #45 #51)
-#49 := (iff #42 #48)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#46 := (iff #19 #45)
-#43 := (iff #18 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#55 := [trans #47 #53]: #54
-#40 := [asserted]: #19
-#56 := [mp #40 #55]: #51
-#63 := [not-or-elim #56]: #62
-#74 := [iff-false #63]: #73
-#77 := [monotonicity #74]: #76
-#81 := [trans #77 #79]: #80
-#57 := [not-or-elim #56]: #15
-#59 := [and-elim #57]: #14
-#69 := [mp #59 #81]: #13
-#82 := [iff-true #69]: #70
-#68 := (iff #8 true)
-#88 := (iff #11 #8)
-#83 := (or #8 false)
-#86 := (iff #83 #8)
-#87 := [rewrite]: #86
-#84 := (iff #11 #83)
-#85 := [monotonicity #74]: #84
-#89 := [trans #85 #87]: #88
-#58 := [and-elim #57]: #11
-#67 := [mp #58 #89]: #8
-#90 := [iff-true #67]: #68
-#93 := [monotonicity #90 #82]: #92
-#97 := [trans #93 #95]: #96
-#98 := [monotonicity #97]: #72
-#102 := [trans #98 #100]: #101
-#61 := [not-or-elim #56]: #60
-[mp #61 #102]: false
-unsat
-822dd2da88addcc306ac946c913fcb511aa60583 81 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#102 := (iff #11 false)
-#97 := (or false false)
-#100 := (iff #97 false)
-#101 := [rewrite]: #100
-#98 := (iff #11 #97)
-#95 := (iff #10 false)
-#91 := (not #10)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-#16 := (and #10 #13)
-#62 := (not #16)
-#92 := (iff #62 #91)
-#89 := (iff #16 #10)
-#1 := true
-#84 := (and #10 true)
-#87 := (iff #84 #10)
-#88 := [rewrite]: #87
-#85 := (iff #16 #84)
-#69 := (iff #13 true)
-#14 := (and #11 #13)
-#15 := (and #8 #13)
-#41 := (not #14)
-#48 := (or #41 #15 #16)
-#51 := (not #48)
-#17 := (or #15 #16)
-#18 := (implies #14 #17)
-#19 := (not #18)
-#54 := (iff #19 #51)
-#42 := (or #41 #17)
-#45 := (not #42)
-#52 := (iff #45 #51)
-#49 := (iff #42 #48)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#46 := (iff #19 #45)
-#43 := (iff #18 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#55 := [trans #47 #53]: #54
-#40 := [asserted]: #19
-#56 := [mp #40 #55]: #51
-#57 := [not-or-elim #56]: #14
-#59 := [and-elim #57]: #13
-#70 := [iff-true #59]: #69
-#86 := [monotonicity #70]: #85
-#90 := [trans #86 #88]: #89
-#93 := [monotonicity #90]: #92
-#63 := [not-or-elim #56]: #62
-#94 := [mp #63 #93]: #91
-#96 := [iff-false #94]: #95
-#82 := (iff #8 false)
-#78 := (not #8)
-#60 := (not #15)
-#79 := (iff #60 #78)
-#76 := (iff #15 #8)
-#71 := (and #8 true)
-#74 := (iff #71 #8)
-#75 := [rewrite]: #74
-#72 := (iff #15 #71)
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#80 := [monotonicity #77]: #79
-#61 := [not-or-elim #56]: #60
-#81 := [mp #61 #80]: #78
-#83 := [iff-false #81]: #82
-#99 := [monotonicity #83 #96]: #98
-#103 := [trans #99 #101]: #102
-#58 := [and-elim #57]: #11
-[mp #58 #103]: false
-unsat
-8cc97fc7cc00db3ed62df1f9aee16d60ca0091ad 83 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#60 := (not #10)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#59 := (not #8)
-#61 := (or #59 #60)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-#16 := (or #8 #13)
-#68 := (not #16)
-#99 := [hypothesis]: #60
-#83 := (or #61 #10)
-#84 := [def-axiom]: #83
-#100 := [unit-resolution #84 #99]: #61
-#55 := (not #13)
-#56 := (or #55 #60)
-#89 := (or #56 #10)
-#90 := [def-axiom]: #89
-#101 := [unit-resolution #90 #99]: #56
-#53 := (not #56)
-#62 := (not #61)
-#64 := (or #62 #53)
-#14 := (and #13 #10)
-#11 := (and #8 #10)
-#15 := (or #11 #14)
-#65 := (iff #15 #64)
-#54 := (iff #14 #53)
-#63 := [rewrite]: #54
-#57 := (iff #11 #62)
-#58 := [rewrite]: #57
-#66 := [monotonicity #58 #63]: #65
-#17 := (and #16 #10)
-#41 := (not #15)
-#42 := (or #41 #17)
-#45 := (not #42)
-#18 := (implies #15 #17)
-#19 := (not #18)
-#46 := (iff #19 #45)
-#43 := (iff #18 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#40 := [asserted]: #19
-#50 := [mp #40 #47]: #45
-#48 := [not-or-elim #50]: #15
-#67 := [mp #48 #66]: #64
-#102 := [unit-resolution #67 #101 #100]: false
-#103 := [lemma #102]: #10
-#69 := (or #68 #60)
-#49 := (not #17)
-#78 := (iff #49 #69)
-#70 := (not #69)
-#73 := (not #70)
-#76 := (iff #73 #69)
-#77 := [rewrite]: #76
-#74 := (iff #49 #73)
-#71 := (iff #17 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#51 := [not-or-elim #50]: #49
-#80 := [mp #51 #79]: #69
-#104 := [unit-resolution #80 #103]: #68
-#93 := (or #16 #59)
-#94 := [def-axiom]: #93
-#105 := [unit-resolution #94 #104]: #59
-#81 := (or #61 #8)
-#82 := [def-axiom]: #81
-#106 := [unit-resolution #82 #105]: #61
-#95 := (or #16 #55)
-#96 := [def-axiom]: #95
-#107 := [unit-resolution #96 #104]: #55
-#87 := (or #56 #13)
-#88 := [def-axiom]: #87
-#108 := [unit-resolution #88 #107]: #56
-[unit-resolution #67 #108 #106]: false
-unsat
-52fb5169edaf3c81cfc25b6a7116b0b55c8a28c3 55 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#36 := (not #8)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#37 := (or #36 #10)
-#43 := (not #37)
-#44 := (or #43 #8)
-#52 := (not #44)
-#53 := (or #52 #8)
-#58 := (not #53)
-#11 := (implies #8 #10)
-#12 := (implies #11 #8)
-#13 := (implies #12 #8)
-#14 := (not #13)
-#59 := (iff #14 #58)
-#56 := (iff #13 #53)
-#49 := (implies #44 #8)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #13 #49)
-#47 := (iff #12 #44)
-#40 := (implies #37 #8)
-#45 := (iff #40 #44)
-#46 := [rewrite]: #45
-#41 := (iff #12 #40)
-#38 := (iff #11 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#48 := [trans #42 #46]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#60 := [monotonicity #57]: #59
-#35 := [asserted]: #14
-#63 := [mp #35 #60]: #58
-#62 := [not-or-elim #63]: #36
-#76 := (iff #44 #43)
-#71 := (or #43 false)
-#74 := (iff #71 #43)
-#75 := [rewrite]: #74
-#72 := (iff #44 #71)
-#69 := (iff #8 false)
-#70 := [iff-false #62]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#61 := [not-or-elim #63]: #44
-#67 := [mp #61 #77]: #43
-#65 := [not-or-elim #67]: #8
-[unit-resolution #65 #62]: false
-unsat
-dd980002bd81efbda187ebb6bc06f50928195b21 129 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#16 := (or #8 #13)
-#52 := (not #16)
-#53 := (or #52 #10)
-#45 := (not #13)
-#46 := (or #45 #10)
-#75 := (not #46)
-#41 := (not #8)
-#42 := (or #41 #10)
-#74 := (not #42)
-#76 := (or #74 #75)
-#116 := (not #53)
-#77 := (not #76)
-#128 := [hypothesis]: #77
-#122 := (or #76 #116)
-#83 := (iff #76 #53)
-#49 := (and #42 #46)
-#62 := (not #49)
-#63 := (iff #62 #53)
-#84 := (iff #63 #83)
-#81 := (iff #62 #76)
-#69 := (not #77)
-#79 := (iff #69 #76)
-#80 := [rewrite]: #79
-#71 := (iff #62 #69)
-#72 := (iff #49 #77)
-#73 := [rewrite]: #72
-#78 := [monotonicity #73]: #71
-#82 := [trans #78 #80]: #81
-#85 := [monotonicity #82]: #84
-#17 := (implies #16 #10)
-#14 := (implies #13 #10)
-#11 := (implies #8 #10)
-#15 := (and #11 #14)
-#18 := (iff #15 #17)
-#19 := (not #18)
-#66 := (iff #19 #63)
-#56 := (iff #49 #53)
-#59 := (not #56)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #19 #59)
-#57 := (iff #18 #56)
-#54 := (iff #17 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#48 := [rewrite]: #47
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#51 := [monotonicity #44 #48]: #50
-#58 := [monotonicity #51 #55]: #57
-#61 := [monotonicity #58]: #60
-#67 := [trans #61 #65]: #66
-#40 := [asserted]: #19
-#70 := [mp #40 #67]: #63
-#86 := [mp #70 #85]: #83
-#119 := (not #83)
-#120 := (or #76 #116 #119)
-#121 := [def-axiom]: #120
-#123 := [unit-resolution #121 #86]: #122
-#129 := [unit-resolution #123 #128]: #116
-#112 := (or #53 #16)
-#113 := [def-axiom]: #112
-#130 := [unit-resolution #113 #129]: #16
-#100 := (or #76 #42)
-#101 := [def-axiom]: #100
-#131 := [unit-resolution #101 #128]: #42
-#89 := (not #10)
-#114 := (or #53 #89)
-#115 := [def-axiom]: #114
-#132 := [unit-resolution #115 #129]: #89
-#92 := (or #74 #41 #10)
-#93 := [def-axiom]: #92
-#133 := [unit-resolution #93 #132 #131]: #41
-#102 := (or #76 #46)
-#103 := [def-axiom]: #102
-#134 := [unit-resolution #103 #128]: #46
-#98 := (or #75 #45 #10)
-#99 := [def-axiom]: #98
-#135 := [unit-resolution #99 #132 #134]: #45
-#110 := (or #52 #8 #13)
-#111 := [def-axiom]: #110
-#136 := [unit-resolution #111 #135 #133 #130]: false
-#137 := [lemma #136]: #76
-#126 := (or #77 #53)
-#124 := (or #77 #53 #119)
-#125 := [def-axiom]: #124
-#127 := [unit-resolution #125 #86]: #126
-#138 := [unit-resolution #127 #137]: #53
-#139 := [hypothesis]: #74
-#90 := (or #42 #89)
-#91 := [def-axiom]: #90
-#140 := [unit-resolution #91 #139]: #89
-#87 := (or #42 #8)
-#88 := [def-axiom]: #87
-#141 := [unit-resolution #88 #139]: #8
-#106 := (or #16 #41)
-#107 := [def-axiom]: #106
-#142 := [unit-resolution #107 #141]: #16
-#117 := (or #116 #52 #10)
-#118 := [def-axiom]: #117
-#143 := [unit-resolution #118 #142 #140 #138]: false
-#144 := [lemma #143]: #42
-#104 := (or #77 #74 #75)
-#105 := [def-axiom]: #104
-#145 := [unit-resolution #105 #144 #137]: #75
-#96 := (or #46 #89)
-#97 := [def-axiom]: #96
-#146 := [unit-resolution #97 #145]: #89
-#94 := (or #46 #13)
-#95 := [def-axiom]: #94
-#147 := [unit-resolution #95 #145]: #13
-#108 := (or #16 #45)
-#109 := [def-axiom]: #108
-#148 := [unit-resolution #109 #147]: #16
-[unit-resolution #118 #148 #146 #138]: false
-unsat
-642785ae09fc22b58f15d1ae19762bba0657cc2e 87 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#44 := (not #10)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#51 := (not #8)
-#69 := (or #51 #44 #13)
-#11 := (and #8 #10)
-#40 := (not #11)
-#41 := (or #40 #13)
-#63 := (not #41)
-#72 := (iff #63 #69)
-#105 := (iff #72 false)
-#97 := (not #69)
-#100 := (iff #97 #69)
-#103 := (iff #100 false)
-#104 := [rewrite]: #103
-#101 := (iff #72 #100)
-#98 := (iff #63 #97)
-#95 := (iff #41 #69)
-#83 := (or #51 #44)
-#90 := (or #83 #13)
-#93 := (iff #90 #69)
-#94 := [rewrite]: #93
-#91 := (iff #41 #90)
-#88 := (iff #40 #83)
-#84 := (not #83)
-#81 := (not #84)
-#80 := (iff #81 #83)
-#87 := [rewrite]: #80
-#82 := (iff #40 #81)
-#85 := (iff #11 #84)
-#86 := [rewrite]: #85
-#79 := [monotonicity #86]: #82
-#89 := [trans #79 #87]: #88
-#92 := [monotonicity #89]: #91
-#96 := [trans #92 #94]: #95
-#99 := [monotonicity #96]: #98
-#102 := [monotonicity #99]: #101
-#106 := [trans #102 #104]: #105
-#15 := (implies #10 #13)
-#16 := (implies #8 #15)
-#14 := (implies #11 #13)
-#17 := (iff #14 #16)
-#18 := (not #17)
-#75 := (iff #18 #72)
-#45 := (or #44 #13)
-#52 := (or #51 #45)
-#64 := (iff #63 #52)
-#73 := (iff #64 #72)
-#70 := (iff #52 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#67 := (iff #18 #64)
-#57 := (iff #41 #52)
-#60 := (not #57)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #18 #60)
-#58 := (iff #17 #57)
-#55 := (iff #16 #52)
-#48 := (implies #8 #45)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #16 #48)
-#46 := (iff #15 #45)
-#47 := [rewrite]: #46
-#50 := [monotonicity #47]: #49
-#56 := [trans #50 #54]: #55
-#42 := (iff #14 #41)
-#43 := [rewrite]: #42
-#59 := [monotonicity #43 #56]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#76 := [trans #68 #74]: #75
-#39 := [asserted]: #18
-#77 := [mp #39 #76]: #72
-[mp #77 #106]: false
-unsat
-3cb22aa5593767652961218f5ced2beb102ad8c3 172 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#17 := (and #8 #14)
-#70 := (not #17)
-#191 := (iff #70 false)
-#1 := true
-#126 := (not true)
-#189 := (iff #126 false)
-#190 := [rewrite]: #189
-#136 := (iff #70 #126)
-#186 := (iff #17 true)
-#181 := (and true true)
-#184 := (iff #181 true)
-#185 := [rewrite]: #184
-#182 := (iff #17 #181)
-#124 := (iff #14 true)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#57 := (not #14)
-#58 := (or #57 #10)
-#64 := (not #58)
-#65 := (or #64 #10)
-#156 := (iff #65 #14)
-#151 := (or #14 false)
-#154 := (iff #151 #14)
-#155 := [rewrite]: #154
-#152 := (iff #65 #151)
-#127 := (iff #10 false)
-#116 := (not #10)
-#71 := (or #70 #10)
-#77 := (not #71)
-#86 := (not #65)
-#44 := (not #8)
-#45 := (or #44 #10)
-#51 := (not #45)
-#52 := (or #51 #10)
-#95 := (not #52)
-#104 := (or #95 #86 #77 #10)
-#107 := (not #104)
-#18 := (implies #17 #10)
-#19 := (implies #18 #10)
-#15 := (implies #14 #10)
-#16 := (implies #15 #10)
-#20 := (implies #16 #19)
-#11 := (implies #8 #10)
-#12 := (implies #11 #10)
-#21 := (implies #12 #20)
-#22 := (not #21)
-#110 := (iff #22 #107)
-#78 := (or #77 #10)
-#87 := (or #86 #78)
-#96 := (or #95 #87)
-#101 := (not #96)
-#108 := (iff #101 #107)
-#105 := (iff #96 #104)
-#106 := [rewrite]: #105
-#109 := [monotonicity #106]: #108
-#102 := (iff #22 #101)
-#99 := (iff #21 #96)
-#92 := (implies #52 #87)
-#97 := (iff #92 #96)
-#98 := [rewrite]: #97
-#93 := (iff #21 #92)
-#90 := (iff #20 #87)
-#83 := (implies #65 #78)
-#88 := (iff #83 #87)
-#89 := [rewrite]: #88
-#84 := (iff #20 #83)
-#81 := (iff #19 #78)
-#74 := (implies #71 #10)
-#79 := (iff #74 #78)
-#80 := [rewrite]: #79
-#75 := (iff #19 #74)
-#72 := (iff #18 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [trans #76 #80]: #81
-#68 := (iff #16 #65)
-#61 := (implies #58 #10)
-#66 := (iff #61 #65)
-#67 := [rewrite]: #66
-#62 := (iff #16 #61)
-#59 := (iff #15 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#69 := [trans #63 #67]: #68
-#85 := [monotonicity #69 #82]: #84
-#91 := [trans #85 #89]: #90
-#55 := (iff #12 #52)
-#48 := (implies #45 #10)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #12 #48)
-#46 := (iff #11 #45)
-#47 := [rewrite]: #46
-#50 := [monotonicity #47]: #49
-#56 := [trans #50 #54]: #55
-#94 := [monotonicity #56 #91]: #93
-#100 := [trans #94 #98]: #99
-#103 := [monotonicity #100]: #102
-#111 := [trans #103 #109]: #110
-#43 := [asserted]: #22
-#112 := [mp #43 #111]: #107
-#117 := [not-or-elim #112]: #116
-#128 := [iff-false #117]: #127
-#149 := (iff #64 #14)
-#144 := (not #57)
-#147 := (iff #144 #14)
-#148 := [rewrite]: #147
-#145 := (iff #64 #144)
-#142 := (iff #58 #57)
-#137 := (or #57 false)
-#140 := (iff #137 #57)
-#141 := [rewrite]: #140
-#138 := (iff #58 #137)
-#139 := [monotonicity #128]: #138
-#143 := [trans #139 #141]: #142
-#146 := [monotonicity #143]: #145
-#150 := [trans #146 #148]: #149
-#153 := [monotonicity #150 #128]: #152
-#157 := [trans #153 #155]: #156
-#114 := [not-or-elim #112]: #65
-#123 := [mp #114 #157]: #14
-#158 := [iff-true #123]: #124
-#122 := (iff #8 true)
-#178 := (iff #52 #8)
-#173 := (or #8 false)
-#176 := (iff #173 #8)
-#177 := [rewrite]: #176
-#174 := (iff #52 #173)
-#171 := (iff #51 #8)
-#166 := (not #44)
-#169 := (iff #166 #8)
-#170 := [rewrite]: #169
-#167 := (iff #51 #166)
-#164 := (iff #45 #44)
-#159 := (or #44 false)
-#162 := (iff #159 #44)
-#163 := [rewrite]: #162
-#160 := (iff #45 #159)
-#161 := [monotonicity #128]: #160
-#165 := [trans #161 #163]: #164
-#168 := [monotonicity #165]: #167
-#172 := [trans #168 #170]: #171
-#175 := [monotonicity #172 #128]: #174
-#179 := [trans #175 #177]: #178
-#113 := [not-or-elim #112]: #52
-#121 := [mp #113 #179]: #8
-#180 := [iff-true #121]: #122
-#183 := [monotonicity #180 #158]: #182
-#187 := [trans #183 #185]: #186
-#188 := [monotonicity #187]: #136
-#192 := [trans #188 #190]: #191
-#134 := (iff #71 #70)
-#129 := (or #70 false)
-#132 := (iff #129 #70)
-#133 := [rewrite]: #132
-#130 := (iff #71 #129)
-#131 := [monotonicity #128]: #130
-#135 := [trans #131 #133]: #134
-#115 := [not-or-elim #112]: #71
-#125 := [mp #115 #135]: #70
-[mp #125 #192]: false
-unsat
-2a741b287996e3d5a24eaaf5674ca253bbcd8ef7 107 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#17 := (and #8 #14)
-#58 := (not #17)
-#59 := (or #58 #10)
-#126 := (iff #59 false)
-#121 := (or false false)
-#124 := (iff #121 false)
-#125 := [rewrite]: #124
-#122 := (iff #59 #121)
-#105 := (iff #10 false)
-#95 := (not #10)
-#62 := (not #59)
-#51 := (not #14)
-#44 := (not #8)
-#84 := (or #44 #51 #10 #62)
-#87 := (not #84)
-#18 := (implies #17 #10)
-#19 := (not #18)
-#15 := (implies #14 #10)
-#16 := (not #15)
-#20 := (implies #16 #19)
-#11 := (implies #8 #10)
-#12 := (not #11)
-#21 := (implies #12 #20)
-#22 := (not #21)
-#90 := (iff #22 #87)
-#52 := (or #51 #10)
-#68 := (or #52 #62)
-#45 := (or #44 #10)
-#76 := (or #45 #68)
-#81 := (not #76)
-#88 := (iff #81 #87)
-#85 := (iff #76 #84)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#82 := (iff #22 #81)
-#79 := (iff #21 #76)
-#48 := (not #45)
-#73 := (implies #48 #68)
-#77 := (iff #73 #76)
-#78 := [rewrite]: #77
-#74 := (iff #21 #73)
-#71 := (iff #20 #68)
-#55 := (not #52)
-#65 := (implies #55 #62)
-#69 := (iff #65 #68)
-#70 := [rewrite]: #69
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#56 := (iff #16 #55)
-#53 := (iff #15 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#67 := [monotonicity #57 #64]: #66
-#72 := [trans #67 #70]: #71
-#49 := (iff #12 #48)
-#46 := (iff #11 #45)
-#47 := [rewrite]: #46
-#50 := [monotonicity #47]: #49
-#75 := [monotonicity #50 #72]: #74
-#80 := [trans #75 #78]: #79
-#83 := [monotonicity #80]: #82
-#91 := [trans #83 #89]: #90
-#43 := [asserted]: #22
-#92 := [mp #43 #91]: #87
-#96 := [not-or-elim #92]: #95
-#106 := [iff-false #96]: #105
-#119 := (iff #58 false)
-#1 := true
-#114 := (not true)
-#117 := (iff #114 false)
-#118 := [rewrite]: #117
-#115 := (iff #58 #114)
-#112 := (iff #17 true)
-#107 := (and true true)
-#110 := (iff #107 true)
-#111 := [rewrite]: #110
-#108 := (iff #17 #107)
-#103 := (iff #14 true)
-#94 := [not-or-elim #92]: #14
-#104 := [iff-true #94]: #103
-#101 := (iff #8 true)
-#93 := [not-or-elim #92]: #8
-#102 := [iff-true #93]: #101
-#109 := [monotonicity #102 #104]: #108
-#113 := [trans #109 #111]: #112
-#116 := [monotonicity #113]: #115
-#120 := [trans #116 #118]: #119
-#123 := [monotonicity #120 #106]: #122
-#127 := [trans #123 #125]: #126
-#97 := [not-or-elim #92]: #59
-[mp #97 #127]: false
-unsat
-e5df9c3ac788514d2b7d8d9dabf4974cdc46f887 136 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-#73 := (not #12)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#41 := (not #8)
-#48 := (or #41 #12)
-#81 := (not #48)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#45 := (or #41 #10)
-#80 := (not #45)
-#134 := [hypothesis]: #80
-#107 := (or #45 #8)
-#108 := [def-axiom]: #107
-#135 := [unit-resolution #108 #134]: #8
-#72 := (not #10)
-#74 := (or #72 #73)
-#109 := (or #45 #72)
-#110 := [def-axiom]: #109
-#136 := [unit-resolution #110 #134]: #72
-#95 := (or #74 #10)
-#96 := [def-axiom]: #95
-#137 := [unit-resolution #96 #136]: #74
-#75 := (not #74)
-#67 := (or #41 #75)
-#82 := (or #80 #81)
-#119 := (or #82 #45)
-#120 := [def-axiom]: #119
-#138 := [unit-resolution #120 #134]: #82
-#83 := (not #82)
-#128 := (or #67 #83)
-#89 := (iff #67 #82)
-#51 := (and #45 #48)
-#13 := (and #10 #12)
-#42 := (or #41 #13)
-#60 := (not #42)
-#61 := (iff #60 #51)
-#92 := (iff #61 #89)
-#77 := (not #67)
-#86 := (iff #77 #83)
-#90 := (iff #86 #89)
-#91 := [rewrite]: #90
-#87 := (iff #61 #86)
-#84 := (iff #51 #83)
-#85 := [rewrite]: #84
-#78 := (iff #60 #77)
-#69 := (iff #42 #67)
-#70 := (iff #13 #75)
-#71 := [rewrite]: #70
-#76 := [monotonicity #71]: #69
-#79 := [monotonicity #76]: #78
-#88 := [monotonicity #79 #85]: #87
-#93 := [trans #88 #91]: #92
-#16 := (implies #8 #12)
-#15 := (implies #8 #10)
-#17 := (and #15 #16)
-#14 := (implies #8 #13)
-#18 := (iff #14 #17)
-#19 := (not #18)
-#64 := (iff #19 #61)
-#54 := (iff #42 #51)
-#57 := (not #54)
-#62 := (iff #57 #61)
-#63 := [rewrite]: #62
-#58 := (iff #19 #57)
-#55 := (iff #18 #54)
-#52 := (iff #17 #51)
-#49 := (iff #16 #48)
-#50 := [rewrite]: #49
-#46 := (iff #15 #45)
-#47 := [rewrite]: #46
-#53 := [monotonicity #47 #50]: #52
-#43 := (iff #14 #42)
-#44 := [rewrite]: #43
-#56 := [monotonicity #44 #53]: #55
-#59 := [monotonicity #56]: #58
-#65 := [trans #59 #63]: #64
-#40 := [asserted]: #19
-#68 := [mp #40 #65]: #61
-#94 := [mp #68 #93]: #89
-#125 := (not #89)
-#126 := (or #67 #83 #125)
-#127 := [def-axiom]: #126
-#129 := [unit-resolution #127 #94]: #128
-#139 := [unit-resolution #129 #138]: #67
-#105 := (or #77 #41 #75)
-#106 := [def-axiom]: #105
-#140 := [unit-resolution #106 #139 #137 #135]: false
-#141 := [lemma #140]: #45
-#142 := [hypothesis]: #77
-#101 := (or #67 #8)
-#102 := [def-axiom]: #101
-#143 := [unit-resolution #102 #142]: #8
-#144 := [unit-resolution #129 #142]: #83
-#121 := (or #82 #48)
-#122 := [def-axiom]: #121
-#145 := [unit-resolution #122 #144]: #48
-#103 := (or #67 #74)
-#104 := [def-axiom]: #103
-#146 := [unit-resolution #104 #142]: #74
-#111 := (or #80 #41 #10)
-#112 := [def-axiom]: #111
-#147 := [unit-resolution #112 #143 #141]: #10
-#99 := (or #75 #72 #73)
-#100 := [def-axiom]: #99
-#148 := [unit-resolution #100 #147 #146]: #73
-#117 := (or #81 #41 #12)
-#118 := [def-axiom]: #117
-#149 := [unit-resolution #118 #148 #145 #143]: false
-#150 := [lemma #149]: #67
-#132 := (or #77 #82)
-#130 := (or #77 #82 #125)
-#131 := [def-axiom]: #130
-#133 := [unit-resolution #131 #94]: #132
-#151 := [unit-resolution #133 #150]: #82
-#123 := (or #83 #80 #81)
-#124 := [def-axiom]: #123
-#152 := [unit-resolution #124 #151 #141]: #81
-#115 := (or #48 #73)
-#116 := [def-axiom]: #115
-#153 := [unit-resolution #116 #152]: #73
-#113 := (or #48 #8)
-#114 := [def-axiom]: #113
-#154 := [unit-resolution #114 #152]: #8
-#155 := [unit-resolution #106 #154 #150]: #75
-#97 := (or #74 #12)
-#98 := [def-axiom]: #97
-[unit-resolution #98 #155 #153]: false
-unsat
-2b64d751f48e9ffd90426fd6834e1d0739b8d27d 43 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#11 := (implies #10 #8)
-#12 := (implies #8 #11)
-#13 := (not #12)
-#60 := (iff #13 false)
-#35 := (not #10)
-#36 := (or #35 #8)
-#42 := (not #8)
-#43 := (or #42 #36)
-#48 := (not #43)
-#58 := (iff #48 false)
-#1 := true
-#53 := (not true)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #48 #53)
-#51 := (iff #43 true)
-#52 := [rewrite]: #51
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#49 := (iff #13 #48)
-#46 := (iff #12 #43)
-#39 := (implies #8 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #12 #39)
-#37 := (iff #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#61 := [trans #50 #59]: #60
-#34 := [asserted]: #13
-[mp #34 #61]: false
-unsat
-b8e0ff6234cf196c70abfdfcc191c52116ff14bf 120 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#41 := (not #10)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#48 := (not #8)
-#81 := (or #48 #41 #12)
-#141 := (iff #81 false)
-#136 := (or false false false)
-#139 := (iff #136 false)
-#140 := [rewrite]: #139
-#137 := (iff #81 #136)
-#115 := (iff #12 false)
-#104 := (not #12)
-#54 := (or #48 #10)
-#63 := (not #54)
-#84 := (not #81)
-#90 := (or #84 #63 #48 #12)
-#95 := (not #90)
-#16 := (implies #8 #12)
-#15 := (implies #8 #10)
-#17 := (implies #15 #16)
-#13 := (implies #10 #12)
-#14 := (implies #8 #13)
-#18 := (implies #14 #17)
-#19 := (not #18)
-#98 := (iff #19 #95)
-#57 := (or #48 #12)
-#64 := (or #63 #57)
-#42 := (or #41 #12)
-#49 := (or #48 #42)
-#72 := (not #49)
-#73 := (or #72 #64)
-#78 := (not #73)
-#96 := (iff #78 #95)
-#93 := (iff #73 #90)
-#87 := (or #84 #64)
-#91 := (iff #87 #90)
-#92 := [rewrite]: #91
-#88 := (iff #73 #87)
-#85 := (iff #72 #84)
-#82 := (iff #49 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#89 := [monotonicity #86]: #88
-#94 := [trans #89 #92]: #93
-#97 := [monotonicity #94]: #96
-#79 := (iff #19 #78)
-#76 := (iff #18 #73)
-#69 := (implies #49 #64)
-#74 := (iff #69 #73)
-#75 := [rewrite]: #74
-#70 := (iff #18 #69)
-#67 := (iff #17 #64)
-#60 := (implies #54 #57)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #17 #60)
-#58 := (iff #16 #57)
-#59 := [rewrite]: #58
-#55 := (iff #15 #54)
-#56 := [rewrite]: #55
-#62 := [monotonicity #56 #59]: #61
-#68 := [trans #62 #66]: #67
-#52 := (iff #14 #49)
-#45 := (implies #8 #42)
-#50 := (iff #45 #49)
-#51 := [rewrite]: #50
-#46 := (iff #14 #45)
-#43 := (iff #13 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#53 := [trans #47 #51]: #52
-#71 := [monotonicity #53 #68]: #70
-#77 := [trans #71 #75]: #76
-#80 := [monotonicity #77]: #79
-#99 := [trans #80 #97]: #98
-#40 := [asserted]: #19
-#100 := [mp #40 #99]: #95
-#105 := [not-or-elim #100]: #104
-#116 := [iff-false #105]: #115
-#134 := (iff #41 false)
-#1 := true
-#117 := (not true)
-#120 := (iff #117 false)
-#121 := [rewrite]: #120
-#132 := (iff #41 #117)
-#112 := (iff #10 true)
-#129 := (iff #54 #10)
-#124 := (or false #10)
-#127 := (iff #124 #10)
-#128 := [rewrite]: #127
-#125 := (iff #54 #124)
-#122 := (iff #48 false)
-#118 := (iff #48 #117)
-#113 := (iff #8 true)
-#103 := [not-or-elim #100]: #8
-#114 := [iff-true #103]: #113
-#119 := [monotonicity #114]: #118
-#123 := [trans #119 #121]: #122
-#126 := [monotonicity #123]: #125
-#130 := [trans #126 #128]: #129
-#102 := [not-or-elim #100]: #54
-#111 := [mp #102 #130]: #10
-#131 := [iff-true #111]: #112
-#133 := [monotonicity #131]: #132
-#135 := [trans #133 #121]: #134
-#138 := [monotonicity #123 #135 #116]: #137
-#142 := [trans #138 #140]: #141
-#101 := [not-or-elim #100]: #81
-[mp #101 #142]: false
-unsat
-8a8c56cbbacd73dc988b4e0a6095fc9e6705a6a6 94 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#41 := (not #8)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#66 := (or #10 #41 #13)
-#115 := (iff #66 false)
-#110 := (or false false false)
-#113 := (iff #110 false)
-#114 := [rewrite]: #113
-#111 := (iff #66 #110)
-#101 := (iff #13 false)
-#90 := (not #13)
-#69 := (not #66)
-#75 := (or #69 #41 #10 #13)
-#80 := (not #75)
-#16 := (or #10 #13)
-#17 := (implies #8 #16)
-#14 := (implies #8 #13)
-#11 := (implies #8 #10)
-#15 := (or #11 #14)
-#18 := (implies #15 #17)
-#19 := (not #18)
-#83 := (iff #19 #80)
-#51 := (or #41 #16)
-#45 := (or #41 #13)
-#42 := (or #41 #10)
-#48 := (or #42 #45)
-#57 := (not #48)
-#58 := (or #57 #51)
-#63 := (not #58)
-#81 := (iff #63 #80)
-#78 := (iff #58 #75)
-#72 := (or #69 #51)
-#76 := (iff #72 #75)
-#77 := [rewrite]: #76
-#73 := (iff #58 #72)
-#70 := (iff #57 #69)
-#67 := (iff #48 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#79 := [trans #74 #77]: #78
-#82 := [monotonicity #79]: #81
-#64 := (iff #19 #63)
-#61 := (iff #18 #58)
-#54 := (implies #48 #51)
-#59 := (iff #54 #58)
-#60 := [rewrite]: #59
-#55 := (iff #18 #54)
-#52 := (iff #17 #51)
-#53 := [rewrite]: #52
-#49 := (iff #15 #48)
-#46 := (iff #14 #45)
-#47 := [rewrite]: #46
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#50 := [monotonicity #44 #47]: #49
-#56 := [monotonicity #50 #53]: #55
-#62 := [trans #56 #60]: #61
-#65 := [monotonicity #62]: #64
-#84 := [trans #65 #82]: #83
-#40 := [asserted]: #19
-#85 := [mp #40 #84]: #80
-#91 := [not-or-elim #85]: #90
-#102 := [iff-false #91]: #101
-#108 := (iff #41 false)
-#1 := true
-#103 := (not true)
-#106 := (iff #103 false)
-#107 := [rewrite]: #106
-#104 := (iff #41 #103)
-#97 := (iff #8 true)
-#87 := [not-or-elim #85]: #8
-#98 := [iff-true #87]: #97
-#105 := [monotonicity #98]: #104
-#109 := [trans #105 #107]: #108
-#99 := (iff #10 false)
-#88 := (not #10)
-#89 := [not-or-elim #85]: #88
-#100 := [iff-false #89]: #99
-#112 := [monotonicity #100 #109 #102]: #111
-#116 := [trans #112 #114]: #115
-#86 := [not-or-elim #85]: #66
-[mp #86 #116]: false
-unsat
-58f02564c26046ffbbf0af2951cd5b2669f92e0c 112 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#38 := (not #8)
-#39 := (or #38 #10)
-#45 := (not #39)
-#46 := (or #45 #8)
-#54 := (not #46)
-#55 := (or #54 #8)
-#63 := (not #55)
-#64 := (or #63 #10)
-#134 := (iff #64 false)
-#129 := (or false false)
-#132 := (iff #129 false)
-#133 := [rewrite]: #132
-#130 := (iff #64 #129)
-#90 := (iff #10 false)
-#82 := (not #10)
-#72 := (not #64)
-#73 := (or #72 #10)
-#78 := (not #73)
-#11 := (implies #8 #10)
-#12 := (implies #11 #8)
-#13 := (implies #12 #8)
-#14 := (implies #13 #10)
-#15 := (implies #14 #10)
-#16 := (not #15)
-#79 := (iff #16 #78)
-#76 := (iff #15 #73)
-#69 := (implies #64 #10)
-#74 := (iff #69 #73)
-#75 := [rewrite]: #74
-#70 := (iff #15 #69)
-#67 := (iff #14 #64)
-#60 := (implies #55 #10)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #14 #60)
-#58 := (iff #13 #55)
-#51 := (implies #46 #8)
-#56 := (iff #51 #55)
-#57 := [rewrite]: #56
-#52 := (iff #13 #51)
-#49 := (iff #12 #46)
-#42 := (implies #39 #8)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #12 #42)
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#59 := [trans #53 #57]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#71 := [monotonicity #68]: #70
-#77 := [trans #71 #75]: #76
-#80 := [monotonicity #77]: #79
-#37 := [asserted]: #16
-#83 := [mp #37 #80]: #78
-#84 := [not-or-elim #83]: #82
-#91 := [iff-false #84]: #90
-#127 := (iff #63 false)
-#1 := true
-#122 := (not true)
-#125 := (iff #122 false)
-#126 := [rewrite]: #125
-#123 := (iff #63 #122)
-#120 := (iff #55 true)
-#115 := (or #38 #8)
-#118 := (iff #115 true)
-#119 := [rewrite]: #118
-#116 := (iff #55 #115)
-#113 := (iff #54 #38)
-#111 := (iff #46 #8)
-#106 := (or #8 #8)
-#109 := (iff #106 #8)
-#110 := [rewrite]: #109
-#107 := (iff #46 #106)
-#104 := (iff #45 #8)
-#99 := (not #38)
-#102 := (iff #99 #8)
-#103 := [rewrite]: #102
-#100 := (iff #45 #99)
-#97 := (iff #39 #38)
-#92 := (or #38 false)
-#95 := (iff #92 #38)
-#96 := [rewrite]: #95
-#93 := (iff #39 #92)
-#94 := [monotonicity #91]: #93
-#98 := [trans #94 #96]: #97
-#101 := [monotonicity #98]: #100
-#105 := [trans #101 #103]: #104
-#108 := [monotonicity #105]: #107
-#112 := [trans #108 #110]: #111
-#114 := [monotonicity #112]: #113
-#117 := [monotonicity #114]: #116
-#121 := [trans #117 #119]: #120
-#124 := [monotonicity #121]: #123
-#128 := [trans #124 #126]: #127
-#131 := [monotonicity #128 #91]: #130
-#135 := [trans #131 #133]: #134
-#81 := [not-or-elim #83]: #64
-[mp #81 #135]: false
-unsat
-a7f6ab6ad332f5aded5b2efbf0f5616121d36767 67 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#13 := (not #8)
-#38 := (or #13 #10)
-#89 := (iff #38 false)
-#84 := (or false false)
-#87 := (iff #84 false)
-#88 := [rewrite]: #87
-#85 := (iff #38 #84)
-#73 := (iff #10 false)
-#12 := (not #10)
-#47 := (not #38)
-#56 := (or #47 #10 #13)
-#59 := (not #56)
-#14 := (implies #12 #13)
-#11 := (implies #8 #10)
-#15 := (implies #11 #14)
-#16 := (not #15)
-#62 := (iff #16 #59)
-#41 := (or #10 #13)
-#48 := (or #47 #41)
-#53 := (not #48)
-#60 := (iff #53 #59)
-#57 := (iff #48 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#54 := (iff #16 #53)
-#51 := (iff #15 #48)
-#44 := (implies #38 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #15 #44)
-#42 := (iff #14 #41)
-#43 := [rewrite]: #42
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#46 := [monotonicity #40 #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#63 := [trans #55 #61]: #62
-#37 := [asserted]: #16
-#64 := [mp #37 #63]: #59
-#66 := [not-or-elim #64]: #12
-#74 := [iff-false #66]: #73
-#82 := (iff #13 false)
-#1 := true
-#77 := (not true)
-#80 := (iff #77 false)
-#81 := [rewrite]: #80
-#78 := (iff #13 #77)
-#75 := (iff #8 true)
-#67 := [not-or-elim #64]: #8
-#76 := [iff-true #67]: #75
-#79 := [monotonicity #76]: #78
-#83 := [trans #79 #81]: #82
-#86 := [monotonicity #83 #74]: #85
-#90 := [trans #86 #88]: #89
-#65 := [not-or-elim #64]: #38
-[mp #65 #90]: false
-unsat
-96fa7a8ac0c9f92be5ba4897a13fe923e953299b 94 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#41 := (not #8)
-#66 := (or #41 #10 #12)
-#115 := (iff #66 false)
-#110 := (or false false false)
-#113 := (iff #110 false)
-#114 := [rewrite]: #113
-#111 := (iff #66 #110)
-#101 := (iff #12 false)
-#90 := (not #12)
-#69 := (not #66)
-#75 := (or #69 #10 #41 #12)
-#80 := (not #75)
-#16 := (implies #8 #12)
-#15 := (implies #8 #10)
-#17 := (or #15 #16)
-#13 := (or #10 #12)
-#14 := (implies #8 #13)
-#18 := (implies #14 #17)
-#19 := (not #18)
-#83 := (iff #19 #80)
-#48 := (or #41 #12)
-#45 := (or #41 #10)
-#51 := (or #45 #48)
-#42 := (or #41 #13)
-#57 := (not #42)
-#58 := (or #57 #51)
-#63 := (not #58)
-#81 := (iff #63 #80)
-#78 := (iff #58 #75)
-#72 := (or #69 #51)
-#76 := (iff #72 #75)
-#77 := [rewrite]: #76
-#73 := (iff #58 #72)
-#70 := (iff #57 #69)
-#67 := (iff #42 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#79 := [trans #74 #77]: #78
-#82 := [monotonicity #79]: #81
-#64 := (iff #19 #63)
-#61 := (iff #18 #58)
-#54 := (implies #42 #51)
-#59 := (iff #54 #58)
-#60 := [rewrite]: #59
-#55 := (iff #18 #54)
-#52 := (iff #17 #51)
-#49 := (iff #16 #48)
-#50 := [rewrite]: #49
-#46 := (iff #15 #45)
-#47 := [rewrite]: #46
-#53 := [monotonicity #47 #50]: #52
-#43 := (iff #14 #42)
-#44 := [rewrite]: #43
-#56 := [monotonicity #44 #53]: #55
-#62 := [trans #56 #60]: #61
-#65 := [monotonicity #62]: #64
-#84 := [trans #65 #82]: #83
-#40 := [asserted]: #19
-#85 := [mp #40 #84]: #80
-#91 := [not-or-elim #85]: #90
-#102 := [iff-false #91]: #101
-#97 := (iff #10 false)
-#87 := (not #10)
-#88 := [not-or-elim #85]: #87
-#98 := [iff-false #88]: #97
-#108 := (iff #41 false)
-#1 := true
-#103 := (not true)
-#106 := (iff #103 false)
-#107 := [rewrite]: #106
-#104 := (iff #41 #103)
-#99 := (iff #8 true)
-#89 := [not-or-elim #85]: #8
-#100 := [iff-true #89]: #99
-#105 := [monotonicity #100]: #104
-#109 := [trans #105 #107]: #108
-#112 := [monotonicity #109 #98 #102]: #111
-#116 := [trans #112 #114]: #115
-#86 := [not-or-elim #85]: #66
-[mp #86 #116]: false
-unsat
-470cd9c1962b0613b02378d77ef88475d95420b4 65 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#42 := (not #10)
-#81 := [hypothesis]: #42
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#38 := (not #8)
-#39 := (or #38 #10)
-#43 := (or #42 #8)
-#46 := (and #39 #43)
-#14 := (iff #8 #10)
-#52 := (not #46)
-#53 := (or #52 #14)
-#58 := (not #53)
-#12 := (implies #10 #8)
-#11 := (implies #8 #10)
-#13 := (and #11 #12)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#59 := (iff #16 #58)
-#56 := (iff #15 #53)
-#49 := (implies #46 #14)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #13 #46)
-#44 := (iff #12 #43)
-#45 := [rewrite]: #44
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#48 := [monotonicity #41 #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#60 := [monotonicity #57]: #59
-#37 := [asserted]: #16
-#63 := [mp #37 #60]: #58
-#61 := [not-or-elim #63]: #46
-#62 := [and-elim #61]: #39
-#82 := [unit-resolution #62 #81]: #38
-#69 := (or #8 #10)
-#74 := (iff #38 #10)
-#65 := (not #14)
-#75 := (iff #65 #74)
-#76 := [rewrite]: #75
-#66 := [not-or-elim #63]: #65
-#77 := [mp #66 #76]: #74
-#78 := (not #74)
-#71 := (or #8 #10 #78)
-#68 := [def-axiom]: #71
-#80 := [unit-resolution #68 #77]: #69
-#83 := [unit-resolution #80 #82 #81]: false
-#84 := [lemma #83]: #10
-#64 := [and-elim #61]: #43
-#85 := [unit-resolution #64 #84]: #8
-#73 := (or #38 #42)
-#79 := (or #38 #42 #78)
-#72 := [def-axiom]: #79
-#70 := [unit-resolution #72 #77]: #73
-[unit-resolution #70 #85 #84]: false
-unsat
-3583d404baf1a70621bef42b341cd5ed7f857304 67 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#12 := (iff #10 #8)
-#53 := (not #12)
-#71 := [hypothesis]: #53
-#76 := (or #10 #12)
-#48 := (not #10)
-#72 := [hypothesis]: #48
-#36 := (not #8)
-#37 := (iff #36 #10)
-#47 := (not #37)
-#69 := (or #47 #12)
-#38 := (iff #37 #12)
-#11 := (iff #8 #10)
-#13 := (iff #11 #12)
-#14 := (not #13)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#35 := [asserted]: #14
-#43 := [mp #35 #40]: #38
-#62 := (not #38)
-#67 := (or #47 #12 #62)
-#68 := [def-axiom]: #67
-#70 := [unit-resolution #68 #43]: #69
-#73 := [unit-resolution #70 #71]: #47
-#42 := (or #37 #36 #10)
-#44 := [def-axiom]: #42
-#74 := [unit-resolution #44 #72 #73]: #36
-#58 := (or #12 #10 #8)
-#59 := [def-axiom]: #58
-#75 := [unit-resolution #59 #74 #72 #71]: false
-#77 := [lemma #75]: #76
-#78 := [unit-resolution #77 #71]: #10
-#51 := (or #37 #8 #48)
-#52 := [def-axiom]: #51
-#79 := [unit-resolution #52 #78 #73]: #8
-#60 := (or #12 #48 #36)
-#61 := [def-axiom]: #60
-#80 := [unit-resolution #61 #79 #78 #71]: false
-#81 := [lemma #80]: #12
-#82 := [hypothesis]: #36
-#65 := (or #37 #53)
-#63 := (or #37 #53 #62)
-#64 := [def-axiom]: #63
-#66 := [unit-resolution #64 #43]: #65
-#83 := [unit-resolution #66 #81]: #37
-#45 := (or #47 #8 #10)
-#46 := [def-axiom]: #45
-#84 := [unit-resolution #46 #82 #83]: #10
-#56 := (or #53 #48 #8)
-#57 := [def-axiom]: #56
-#85 := [unit-resolution #57 #84 #82 #81]: false
-#86 := [lemma #85]: #8
-#49 := (or #47 #36 #48)
-#50 := [def-axiom]: #49
-#87 := [unit-resolution #50 #86 #83]: #48
-#54 := (or #53 #10 #36)
-#55 := [def-axiom]: #54
-[unit-resolution #55 #87 #86 #81]: false
-unsat
-25b6de20c7289df4e64dbeeda9c253f854a640a3 30 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (iff #8 #9)
-#11 := (not #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (not false)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 false)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-6c7aa77a3e726f6965e1c58daf22b14f9c6eacb5 68 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#13 := (not #8)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#41 := (or #10 #13)
-#38 := (or #13 #10)
-#68 := (not #41)
-#80 := [hypothesis]: #68
-#78 := (or #38 #41)
-#50 := (not #38)
-#51 := (iff #50 #41)
-#12 := (not #10)
-#14 := (implies #12 #13)
-#11 := (implies #8 #10)
-#15 := (iff #11 #14)
-#16 := (not #15)
-#54 := (iff #16 #51)
-#44 := (iff #38 #41)
-#47 := (not #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #16 #47)
-#45 := (iff #15 #44)
-#42 := (iff #14 #41)
-#43 := [rewrite]: #42
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#46 := [monotonicity #40 #43]: #45
-#49 := [monotonicity #46]: #48
-#55 := [trans #49 #53]: #54
-#37 := [asserted]: #16
-#58 := [mp #37 #55]: #51
-#71 := (not #51)
-#76 := (or #38 #41 #71)
-#77 := [def-axiom]: #76
-#79 := [unit-resolution #77 #58]: #78
-#81 := [unit-resolution #79 #80]: #38
-#57 := (or #41 #12)
-#59 := [def-axiom]: #57
-#82 := [unit-resolution #59 #80]: #12
-#66 := (or #41 #8)
-#67 := [def-axiom]: #66
-#83 := [unit-resolution #67 #80]: #8
-#60 := (or #50 #13 #10)
-#61 := [def-axiom]: #60
-#84 := [unit-resolution #61 #83 #82 #81]: false
-#85 := [lemma #84]: #41
-#74 := (or #50 #68)
-#72 := (or #50 #68 #71)
-#73 := [def-axiom]: #72
-#75 := [unit-resolution #73 #58]: #74
-#86 := [unit-resolution #75 #85]: #50
-#62 := (or #38 #8)
-#63 := [def-axiom]: #62
-#87 := [unit-resolution #63 #86]: #8
-#64 := (or #38 #12)
-#65 := [def-axiom]: #64
-#88 := [unit-resolution #65 #86]: #12
-#69 := (or #68 #10 #13)
-#70 := [def-axiom]: #69
-[unit-resolution #70 #88 #87 #85]: false
-unsat
-ee2587d9af24c00533fd6cc57d8b9c430858d515 64 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (iff #8 #8)
-#10 := (iff #8 #9)
-#11 := (iff #8 #10)
-#12 := (iff #8 #11)
-#13 := (iff #8 #12)
-#14 := (iff #8 #13)
-#15 := (iff #8 #14)
-#16 := (iff #8 #15)
-#17 := (iff #8 #16)
-#18 := (not #17)
-#82 := (iff #18 false)
-#1 := true
-#77 := (not true)
-#80 := (iff #77 false)
-#81 := [rewrite]: #80
-#78 := (iff #18 #77)
-#75 := (iff #17 true)
-#40 := (iff #9 true)
-#41 := [rewrite]: #40
-#73 := (iff #17 #9)
-#71 := (iff #16 #8)
-#42 := (iff #8 true)
-#45 := (iff #42 #8)
-#46 := [rewrite]: #45
-#69 := (iff #16 #42)
-#67 := (iff #15 true)
-#65 := (iff #15 #9)
-#63 := (iff #14 #8)
-#61 := (iff #14 #42)
-#59 := (iff #13 true)
-#57 := (iff #13 #9)
-#55 := (iff #12 #8)
-#53 := (iff #12 #42)
-#51 := (iff #11 true)
-#49 := (iff #11 #9)
-#47 := (iff #10 #8)
-#43 := (iff #10 #42)
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#50 := [monotonicity #48]: #49
-#52 := [trans #50 #41]: #51
-#54 := [monotonicity #52]: #53
-#56 := [trans #54 #46]: #55
-#58 := [monotonicity #56]: #57
-#60 := [trans #58 #41]: #59
-#62 := [monotonicity #60]: #61
-#64 := [trans #62 #46]: #63
-#66 := [monotonicity #64]: #65
-#68 := [trans #66 #41]: #67
-#70 := [monotonicity #68]: #69
-#72 := [trans #70 #46]: #71
-#74 := [monotonicity #72]: #73
-#76 := [trans #74 #41]: #75
-#79 := [monotonicity #76]: #78
-#83 := [trans #79 #81]: #82
-#39 := [asserted]: #18
-[mp #39 #83]: false
-unsat
-37203ec99bf7e03cbb0be72ecadd1ceb545297a3 121 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#13 := (if #8 #10 #12)
-#44 := (or #8 #12)
-#69 := (not #44)
-#15 := (not #8)
-#41 := (or #15 #10)
-#68 := (not #41)
-#70 := (or #68 #69)
-#71 := (not #70)
-#123 := [hypothesis]: #71
-#103 := (or #70 #44)
-#104 := [def-axiom]: #103
-#124 := [unit-resolution #104 #123]: #44
-#56 := (not #13)
-#114 := (or #56 #70)
-#73 := (iff #13 #70)
-#47 := (and #41 #44)
-#57 := (iff #56 #47)
-#76 := (iff #57 #73)
-#63 := (iff #56 #71)
-#74 := (iff #63 #73)
-#75 := [rewrite]: #74
-#65 := (iff #57 #63)
-#66 := (iff #47 #71)
-#67 := [rewrite]: #66
-#72 := [monotonicity #67]: #65
-#77 := [trans #72 #75]: #76
-#16 := (implies #15 #12)
-#14 := (implies #8 #10)
-#17 := (and #14 #16)
-#18 := (iff #13 #17)
-#19 := (not #18)
-#60 := (iff #19 #57)
-#50 := (iff #13 #47)
-#53 := (not #50)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #19 #53)
-#51 := (iff #18 #50)
-#48 := (iff #17 #47)
-#45 := (iff #16 #44)
-#46 := [rewrite]: #45
-#42 := (iff #14 #41)
-#43 := [rewrite]: #42
-#49 := [monotonicity #43 #46]: #48
-#52 := [monotonicity #49]: #51
-#55 := [monotonicity #52]: #54
-#61 := [trans #55 #59]: #60
-#40 := [asserted]: #19
-#64 := [mp #40 #61]: #57
-#78 := [mp #64 #77]: #73
-#107 := (not #73)
-#112 := (or #56 #70 #107)
-#113 := [def-axiom]: #112
-#115 := [unit-resolution #113 #78]: #114
-#125 := [unit-resolution #115 #123]: #56
-#101 := (or #70 #41)
-#102 := [def-axiom]: #101
-#126 := [unit-resolution #102 #123]: #41
-#121 := (or #15 #68 #13)
-#116 := [hypothesis]: #41
-#117 := [hypothesis]: #8
-#83 := (not #10)
-#118 := [hypothesis]: #56
-#84 := (or #13 #15 #83)
-#85 := [def-axiom]: #84
-#119 := [unit-resolution #85 #117 #118]: #83
-#93 := (or #68 #15 #10)
-#94 := [def-axiom]: #93
-#120 := [unit-resolution #94 #119 #117 #116]: false
-#122 := [lemma #120]: #121
-#127 := [unit-resolution #122 #126 #125]: #15
-#86 := (not #12)
-#87 := (or #13 #8 #86)
-#88 := [def-axiom]: #87
-#128 := [unit-resolution #88 #127 #125]: #86
-#99 := (or #69 #8 #12)
-#100 := [def-axiom]: #99
-#129 := [unit-resolution #100 #128 #127 #124]: false
-#130 := [lemma #129]: #70
-#110 := (or #13 #71)
-#108 := (or #13 #71 #107)
-#109 := [def-axiom]: #108
-#111 := [unit-resolution #109 #78]: #110
-#133 := [unit-resolution #111 #130]: #13
-#131 := [hypothesis]: #15
-#89 := (or #41 #8)
-#90 := [def-axiom]: #89
-#132 := [unit-resolution #90 #131]: #41
-#81 := (or #56 #8 #12)
-#82 := [def-axiom]: #81
-#134 := [unit-resolution #82 #131 #133]: #12
-#97 := (or #44 #86)
-#98 := [def-axiom]: #97
-#135 := [unit-resolution #98 #134]: #44
-#105 := (or #71 #68 #69)
-#106 := [def-axiom]: #105
-#136 := [unit-resolution #106 #135 #132 #130]: false
-#137 := [lemma #136]: #8
-#79 := (or #56 #15 #10)
-#80 := [def-axiom]: #79
-#138 := [unit-resolution #80 #137 #133]: #10
-#95 := (or #44 #15)
-#96 := [def-axiom]: #95
-#139 := [unit-resolution #96 #137]: #44
-#140 := [unit-resolution #106 #139 #130]: #68
-#91 := (or #41 #83)
-#92 := [def-axiom]: #91
-[unit-resolution #92 #140 #138]: false
-unsat
-ca9aa750ee4c38be0511c4f7f0526ad22c26b354 50 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#40 := (not #8)
-#74 := [hypothesis]: #8
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#36 := (not #10)
-#37 := (or #36 #8)
-#58 := (or #37 #40)
-#59 := [def-axiom]: #58
-#75 := [unit-resolution #59 #74]: #37
-#54 := (not #37)
-#76 := (or #40 #54)
-#41 := (or #40 #10)
-#44 := (if #8 #37 #41)
-#47 := (not #44)
-#12 := (implies #8 #10)
-#11 := (implies #10 #8)
-#13 := (if #8 #11 #12)
-#14 := (not #13)
-#48 := (iff #14 #47)
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#43 := [rewrite]: #42
-#38 := (iff #11 #37)
-#39 := [rewrite]: #38
-#46 := [monotonicity #39 #43]: #45
-#49 := [monotonicity #46]: #48
-#35 := [asserted]: #14
-#52 := [mp #35 #49]: #47
-#70 := (or #44 #40 #54)
-#71 := [def-axiom]: #70
-#77 := [unit-resolution #71 #52]: #76
-#78 := [unit-resolution #77 #75 #74]: false
-#79 := [lemma #78]: #40
-#53 := (or #41 #8)
-#60 := [def-axiom]: #53
-#80 := [unit-resolution #60 #79]: #41
-#63 := (not #41)
-#81 := (or #8 #63)
-#72 := (or #44 #8 #63)
-#73 := [def-axiom]: #72
-#82 := [unit-resolution #73 #52]: #81
-[unit-resolution #82 #80 #79]: false
-unsat
-22136385e4a040042c56d71f978a5676aac282d0 108 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f6 :: S1
-#14 := f6
-#15 := (= f6 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#16 := (if #11 #13 #15)
-#42 := (not #16)
-#94 := [hypothesis]: #42
-#108 := (or #10 #16)
-#47 := (not #11)
-#52 := (not #8)
-#100 := (or #52 #16)
-#95 := [hypothesis]: #8
-#53 := (or #11 #52)
-#54 := [def-axiom]: #53
-#96 := [unit-resolution #54 #95]: #11
-#17 := (if #10 #13 #15)
-#18 := (if #8 #13 #17)
-#92 := (or #16 #18)
-#43 := (iff #42 #18)
-#19 := (iff #16 #18)
-#20 := (not #19)
-#44 := (iff #20 #43)
-#45 := [rewrite]: #44
-#41 := [asserted]: #20
-#48 := [mp #41 #45]: #43
-#85 := (not #43)
-#90 := (or #16 #18 #85)
-#91 := [def-axiom]: #90
-#93 := [unit-resolution #91 #48]: #92
-#97 := [unit-resolution #93 #94]: #18
-#76 := (not #18)
-#77 := (or #76 #52 #13)
-#78 := [def-axiom]: #77
-#98 := [unit-resolution #78 #95 #97]: #13
-#61 := (not #13)
-#62 := (or #16 #47 #61)
-#63 := [def-axiom]: #62
-#99 := [unit-resolution #63 #98 #96 #94]: false
-#101 := [lemma #99]: #100
-#102 := [unit-resolution #101 #94]: #52
-#55 := (not #10)
-#103 := [hypothesis]: #55
-#49 := (or #47 #8 #10)
-#56 := [def-axiom]: #49
-#104 := [unit-resolution #56 #103 #102]: #47
-#79 := (or #76 #8 #17)
-#80 := [def-axiom]: #79
-#105 := [unit-resolution #80 #102 #97]: #17
-#67 := (not #17)
-#70 := (or #67 #10 #15)
-#71 := [def-axiom]: #70
-#106 := [unit-resolution #71 #103 #105]: #15
-#64 := (not #15)
-#65 := (or #16 #11 #64)
-#66 := [def-axiom]: #65
-#107 := [unit-resolution #66 #106 #104 #94]: false
-#109 := [lemma #107]: #108
-#110 := [unit-resolution #109 #94]: #10
-#50 := (or #11 #55)
-#51 := [def-axiom]: #50
-#111 := [unit-resolution #51 #110]: #11
-#68 := (or #67 #55 #13)
-#69 := [def-axiom]: #68
-#112 := [unit-resolution #69 #110 #105]: #13
-#113 := [unit-resolution #63 #112 #111 #94]: false
-#114 := [lemma #113]: #16
-#115 := [hypothesis]: #47
-#116 := [unit-resolution #51 #115]: #55
-#59 := (or #42 #11 #15)
-#60 := [def-axiom]: #59
-#117 := [unit-resolution #60 #115 #114]: #15
-#88 := (or #42 #76)
-#86 := (or #42 #76 #85)
-#87 := [def-axiom]: #86
-#89 := [unit-resolution #87 #48]: #88
-#118 := [unit-resolution #89 #114]: #76
-#119 := [unit-resolution #54 #115]: #52
-#83 := (or #18 #8 #67)
-#84 := [def-axiom]: #83
-#120 := [unit-resolution #84 #119 #118]: #67
-#74 := (or #17 #10 #64)
-#75 := [def-axiom]: #74
-#121 := [unit-resolution #75 #120 #117 #116]: false
-#122 := [lemma #121]: #11
-#57 := (or #42 #47 #13)
-#58 := [def-axiom]: #57
-#123 := [unit-resolution #58 #122 #114]: #13
-#81 := (or #18 #52 #61)
-#82 := [def-axiom]: #81
-#124 := [unit-resolution #82 #123 #118]: #52
-#125 := [unit-resolution #84 #124 #118]: #67
-#126 := [unit-resolution #56 #124 #122]: #10
-#72 := (or #17 #55 #61)
-#73 := [def-axiom]: #72
-[unit-resolution #73 #126 #125 #123]: false
-unsat
-042cd6410e2120e0a1d26569b905b9483437aab5 126 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f6 :: S1
-#14 := f6
-#15 := (= f6 f1)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#53 := (not #10)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#52 := (not #8)
-#54 := (or #52 #53)
-#57 := (if #54 #15 #13)
-#62 := (not #57)
-#112 := [hypothesis]: #62
-#126 := (or #53 #57)
-#55 := (not #54)
-#118 := (or #8 #57)
-#113 := [hypothesis]: #52
-#69 := (or #54 #8)
-#70 := [def-axiom]: #69
-#114 := [unit-resolution #70 #113]: #54
-#17 := (if #10 #13 #15)
-#18 := (if #8 #17 #15)
-#110 := (or #57 #18)
-#65 := (iff #62 #18)
-#11 := (and #8 #10)
-#16 := (if #11 #13 #15)
-#42 := (not #16)
-#43 := (iff #42 #18)
-#66 := (iff #43 #65)
-#63 := (iff #42 #62)
-#60 := (iff #16 #57)
-#47 := (if #55 #13 #15)
-#58 := (iff #47 #57)
-#59 := [rewrite]: #58
-#49 := (iff #16 #47)
-#50 := (iff #11 #55)
-#51 := [rewrite]: #50
-#56 := [monotonicity #51]: #49
-#61 := [trans #56 #59]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#19 := (iff #16 #18)
-#20 := (not #19)
-#44 := (iff #20 #43)
-#45 := [rewrite]: #44
-#41 := [asserted]: #20
-#48 := [mp #41 #45]: #43
-#68 := [mp #48 #67]: #65
-#103 := (not #65)
-#108 := (or #57 #18 #103)
-#109 := [def-axiom]: #108
-#111 := [unit-resolution #109 #68]: #110
-#115 := [unit-resolution #111 #112]: #18
-#94 := (not #18)
-#97 := (or #94 #8 #15)
-#98 := [def-axiom]: #97
-#116 := [unit-resolution #98 #113 #115]: #15
-#79 := (not #15)
-#80 := (or #57 #55 #79)
-#81 := [def-axiom]: #80
-#117 := [unit-resolution #81 #116 #114 #112]: false
-#119 := [lemma #117]: #118
-#120 := [unit-resolution #119 #112]: #8
-#121 := [hypothesis]: #10
-#73 := (or #55 #52 #53)
-#74 := [def-axiom]: #73
-#122 := [unit-resolution #74 #121 #120]: #55
-#95 := (or #94 #52 #17)
-#96 := [def-axiom]: #95
-#123 := [unit-resolution #96 #120 #115]: #17
-#85 := (not #17)
-#86 := (or #85 #53 #13)
-#87 := [def-axiom]: #86
-#124 := [unit-resolution #87 #121 #123]: #13
-#82 := (not #13)
-#83 := (or #57 #54 #82)
-#84 := [def-axiom]: #83
-#125 := [unit-resolution #84 #124 #122 #112]: false
-#127 := [lemma #125]: #126
-#128 := [unit-resolution #127 #112]: #53
-#71 := (or #54 #10)
-#72 := [def-axiom]: #71
-#129 := [unit-resolution #72 #128]: #54
-#88 := (or #85 #10 #15)
-#89 := [def-axiom]: #88
-#130 := [unit-resolution #89 #128 #123]: #15
-#131 := [unit-resolution #81 #130 #129 #112]: false
-#132 := [lemma #131]: #57
-#133 := [hypothesis]: #55
-#134 := [unit-resolution #72 #133]: #10
-#77 := (or #62 #54 #13)
-#78 := [def-axiom]: #77
-#135 := [unit-resolution #78 #133 #132]: #13
-#106 := (or #62 #94)
-#104 := (or #62 #94 #103)
-#105 := [def-axiom]: #104
-#107 := [unit-resolution #105 #68]: #106
-#136 := [unit-resolution #107 #132]: #94
-#137 := [unit-resolution #70 #133]: #8
-#99 := (or #18 #52 #85)
-#100 := [def-axiom]: #99
-#138 := [unit-resolution #100 #137 #136]: #85
-#90 := (or #17 #53 #82)
-#91 := [def-axiom]: #90
-#139 := [unit-resolution #91 #138 #135 #134]: false
-#140 := [lemma #139]: #54
-#75 := (or #62 #55 #15)
-#76 := [def-axiom]: #75
-#141 := [unit-resolution #76 #140 #132]: #15
-#101 := (or #18 #8 #79)
-#102 := [def-axiom]: #101
-#142 := [unit-resolution #102 #141 #136]: #8
-#143 := [unit-resolution #100 #142 #136]: #85
-#144 := [unit-resolution #74 #142 #140]: #53
-#92 := (or #17 #10 #79)
-#93 := [def-axiom]: #92
-[unit-resolution #93 #144 #143 #141]: false
-unsat
-ef537e4da9516844ed6fad53f93372fb0890ad4d 144 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-decl f6 :: S1
-#13 := f6
-#14 := (= f6 f1)
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#15 := (if #10 #12 #14)
-#44 := (not #8)
-#45 := (or #44 #15)
-#66 := (not #45)
-#54 := (or #44 #14)
-#51 := (or #44 #12)
-#48 := (or #44 #10)
-#57 := (if #48 #51 #54)
-#113 := (not #57)
-#131 := [hypothesis]: #113
-#129 := (or #45 #57)
-#67 := (iff #66 #57)
-#19 := (implies #8 #14)
-#18 := (implies #8 #12)
-#17 := (implies #8 #10)
-#20 := (if #17 #18 #19)
-#16 := (implies #8 #15)
-#21 := (iff #16 #20)
-#22 := (not #21)
-#70 := (iff #22 #67)
-#60 := (iff #45 #57)
-#63 := (not #60)
-#68 := (iff #63 #67)
-#69 := [rewrite]: #68
-#64 := (iff #22 #63)
-#61 := (iff #21 #60)
-#58 := (iff #20 #57)
-#55 := (iff #19 #54)
-#56 := [rewrite]: #55
-#52 := (iff #18 #51)
-#53 := [rewrite]: #52
-#49 := (iff #17 #48)
-#50 := [rewrite]: #49
-#59 := [monotonicity #50 #53 #56]: #58
-#46 := (iff #16 #45)
-#47 := [rewrite]: #46
-#62 := [monotonicity #47 #59]: #61
-#65 := [monotonicity #62]: #64
-#71 := [trans #65 #69]: #70
-#43 := [asserted]: #22
-#74 := [mp #43 #71]: #67
-#122 := (not #67)
-#127 := (or #45 #57 #122)
-#128 := [def-axiom]: #127
-#130 := [unit-resolution #128 #74]: #129
-#132 := [unit-resolution #130 #131]: #45
-#103 := (not #51)
-#142 := (or #54 #57)
-#110 := (not #54)
-#133 := [hypothesis]: #110
-#106 := (or #54 #8)
-#107 := [def-axiom]: #106
-#134 := [unit-resolution #107 #133]: #8
-#90 := (or #66 #44 #15)
-#91 := [def-axiom]: #90
-#135 := [unit-resolution #91 #134 #132]: #15
-#83 := (not #14)
-#108 := (or #54 #83)
-#109 := [def-axiom]: #108
-#136 := [unit-resolution #109 #133]: #83
-#78 := (not #15)
-#76 := (or #78 #10 #14)
-#77 := [def-axiom]: #76
-#137 := [unit-resolution #77 #136 #135]: #10
-#79 := (not #10)
-#94 := (or #48 #79)
-#95 := [def-axiom]: #94
-#138 := [unit-resolution #95 #137]: #48
-#80 := (or #78 #79 #12)
-#81 := [def-axiom]: #80
-#139 := [unit-resolution #81 #137 #135]: #12
-#73 := (not #12)
-#101 := (or #51 #73)
-#102 := [def-axiom]: #101
-#140 := [unit-resolution #102 #139]: #51
-#96 := (not #48)
-#118 := (or #57 #96 #103)
-#119 := [def-axiom]: #118
-#141 := [unit-resolution #119 #140 #138 #131]: false
-#143 := [lemma #141]: #142
-#144 := [unit-resolution #143 #131]: #54
-#120 := (or #57 #48 #110)
-#121 := [def-axiom]: #120
-#145 := [unit-resolution #121 #144 #131]: #48
-#146 := [unit-resolution #119 #145 #131]: #103
-#99 := (or #51 #8)
-#100 := [def-axiom]: #99
-#147 := [unit-resolution #100 #146]: #8
-#148 := [unit-resolution #91 #147 #132]: #15
-#149 := [unit-resolution #102 #146]: #73
-#97 := (or #96 #44 #10)
-#98 := [def-axiom]: #97
-#150 := [unit-resolution #98 #147 #145]: #10
-#151 := [unit-resolution #81 #150 #149 #148]: false
-#152 := [lemma #151]: #57
-#125 := (or #66 #113)
-#123 := (or #66 #113 #122)
-#124 := [def-axiom]: #123
-#126 := [unit-resolution #124 #74]: #125
-#153 := [unit-resolution #126 #152]: #66
-#86 := (or #45 #8)
-#87 := [def-axiom]: #86
-#154 := [unit-resolution #87 #153]: #8
-#88 := (or #45 #78)
-#89 := [def-axiom]: #88
-#157 := [unit-resolution #89 #153]: #78
-#155 := [hypothesis]: #79
-#156 := [unit-resolution #98 #155 #154]: #96
-#84 := (or #15 #10 #83)
-#85 := [def-axiom]: #84
-#158 := [unit-resolution #85 #155 #157]: #83
-#111 := (or #110 #44 #14)
-#112 := [def-axiom]: #111
-#159 := [unit-resolution #112 #158 #154]: #110
-#116 := (or #113 #48 #54)
-#117 := [def-axiom]: #116
-#160 := [unit-resolution #117 #159 #156 #152]: false
-#161 := [lemma #160]: #10
-#75 := (or #15 #79 #73)
-#82 := [def-axiom]: #75
-#162 := [unit-resolution #82 #161 #157]: #73
-#163 := [unit-resolution #95 #161]: #48
-#114 := (or #113 #96 #51)
-#115 := [def-axiom]: #114
-#164 := [unit-resolution #115 #163 #152]: #51
-#104 := (or #103 #44 #12)
-#105 := [def-axiom]: #104
-[unit-resolution #105 #164 #162 #154]: false
-unsat
-78c572bbf37fdaeffbdf327837dfe6e150ab4121 22 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (if #8 #8 #9)
-#11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
-unsat
-7bfe3d6a8ddb1e5cf6b5e7e7e25b7bb8d3947426 22 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (if #9 #9 #8)
-#11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
-unsat
-36cacffa0b357a87bd4cda01a469de9e5b1b6ff9 18 0
-#2 := false
-decl f3 :: S2
-#7 := f3
-#8 := (= f3 f3)
-#9 := (not #8)
-#38 := (iff #9 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
-unsat
-fdbd50a73d75354218917a033ec85c8b60aadac7 28 0
-#2 := false
-decl f3 :: S2
-#7 := f3
-decl f4 :: S2
-#8 := f4
-#10 := (= f4 f3)
-#9 := (= f3 f4)
-#54 := (iff #9 #10)
-#52 := (iff #10 #9)
-#53 := [commutativity]: #52
-#55 := [symm #53]: #54
-#34 := (not #9)
-#35 := (or #34 #10)
-#38 := (not #35)
-#11 := (implies #9 #10)
-#12 := (not #11)
-#39 := (iff #12 #38)
-#36 := (iff #11 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#33 := [asserted]: #12
-#43 := [mp #33 #40]: #38
-#41 := [not-or-elim #43]: #9
-#50 := [mp #41 #55]: #10
-#42 := (not #10)
-#44 := [not-or-elim #43]: #42
-[unit-resolution #44 #50]: false
-unsat
-1e7092f06fe51080cd1f2ff9c767c120dee0f325 34 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f3 :: S2
-#7 := f3
-#13 := (= f3 f5)
-decl f4 :: S2
-#8 := f4
-#11 := (= f4 f5)
-#61 := (iff #11 #13)
-#59 := (iff #13 #11)
-#9 := (= f3 f4)
-#12 := (and #9 #11)
-#37 := (not #12)
-#38 := (or #37 #13)
-#41 := (not #38)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#36 := [asserted]: #15
-#46 := [mp #36 #43]: #41
-#44 := [not-or-elim #46]: #12
-#45 := [and-elim #44]: #9
-#60 := [monotonicity #45]: #59
-#62 := [symm #60]: #61
-#47 := [and-elim #44]: #11
-#57 := [mp #47 #62]: #13
-#48 := (not #13)
-#49 := [not-or-elim #46]: #48
-[unit-resolution #49 #57]: false
-unsat
-dcb560c85ca9bae67a2cc2056cbff42277192208 27 0
-#2 := false
-decl f5 :: (-> S2 S2)
-decl f4 :: S2
-#8 := f4
-#11 := (f5 f4)
-decl f3 :: S2
-#7 := f3
-#10 := (f5 f3)
-#12 := (= #10 #11)
-#9 := (= f3 f4)
-#36 := (not #9)
-#37 := (or #36 #12)
-#40 := (not #37)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#35 := [asserted]: #14
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #9
-#54 := [monotonicity #43]: #12
-#44 := (not #12)
-#46 := [not-or-elim #45]: #44
-[unit-resolution #46 #54]: false
-unsat
-b268f4bef33523b0e58fb79bfaa877e0377ed0fe 31 0
-#2 := false
-decl f5 :: (-> S2 S2 S3)
-decl f3 :: S2
-#7 := f3
-decl f4 :: S2
-#8 := f4
-#11 := (f5 f4 f3)
-#10 := (f5 f3 f4)
-#12 := (= #10 #11)
-#56 := (= #11 #10)
-#9 := (= f3 f4)
-#36 := (not #9)
-#37 := (or #36 #12)
-#40 := (not #37)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#35 := [asserted]: #14
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #9
-#54 := (= f4 f3)
-#55 := [symm #43]: #54
-#57 := [monotonicity #55 #43]: #56
-#52 := [symm #57]: #12
-#44 := (not #12)
-#46 := [not-or-elim #45]: #44
-[unit-resolution #46 #52]: false
-unsat
-c15ed7f86c495f57e47ba25cbe1dd59e25e6cfd8 44 0
-#2 := false
-decl f4 :: S2
-#7 := f4
-decl f3 :: (-> S2 S2)
-#8 := (f3 f4)
-#16 := (= #8 f4)
-#9 := (f3 #8)
-#11 := (f3 #9)
-#12 := (f3 #11)
-#13 := (f3 #12)
-#14 := (= #13 f4)
-#10 := (= #9 f4)
-#15 := (and #10 #14)
-#40 := (not #15)
-#41 := (or #40 #16)
-#44 := (not #41)
-#17 := (implies #15 #16)
-#18 := (not #17)
-#45 := (iff #18 #44)
-#42 := (iff #17 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#39 := [asserted]: #18
-#49 := [mp #39 #46]: #44
-#47 := [not-or-elim #49]: #15
-#50 := [and-elim #47]: #14
-#54 := (= #8 #13)
-#56 := (= f4 #12)
-#58 := (= #9 #12)
-#64 := (= #12 #9)
-#62 := (= #11 #8)
-#48 := [and-elim #47]: #10
-#63 := [monotonicity #48]: #62
-#65 := [monotonicity #63]: #64
-#59 := [symm #65]: #58
-#60 := (= f4 #9)
-#61 := [symm #48]: #60
-#57 := [trans #61 #59]: #56
-#55 := [monotonicity #57]: #54
-#66 := [trans #55 #50]: #16
-#51 := (not #16)
-#52 := [not-or-elim #49]: #51
-[unit-resolution #52 #66]: false
-unsat
-e014a521ad8c0c3dc3dc83f7de12a8ea100eaf98 137 0
-#2 := false
-decl f6 :: S2
-#12 := f6
-decl f5 :: S2
-#10 := f5
-decl f4 :: S2
-#9 := f4
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (if #8 f4 f5)
-#13 := (= #11 f6)
-#17 := (= f5 f6)
-#46 := (or #8 #17)
-#71 := (not #46)
-#14 := (= f4 f6)
-#16 := (not #8)
-#43 := (or #16 #14)
-#70 := (not #43)
-#72 := (or #70 #71)
-#116 := [hypothesis]: #71
-#103 := (or #72 #46)
-#104 := [def-axiom]: #103
-#118 := [unit-resolution #104 #116]: #72
-#73 := (not #72)
-#110 := (or #13 #73)
-#75 := (iff #13 #72)
-#49 := (and #43 #46)
-#58 := (not #13)
-#59 := (iff #58 #49)
-#78 := (iff #59 #75)
-#65 := (iff #58 #73)
-#76 := (iff #65 #75)
-#77 := [rewrite]: #76
-#67 := (iff #59 #65)
-#68 := (iff #49 #73)
-#69 := [rewrite]: #68
-#74 := [monotonicity #69]: #67
-#79 := [trans #74 #77]: #78
-#18 := (implies #16 #17)
-#15 := (implies #8 #14)
-#19 := (and #15 #18)
-#20 := (iff #13 #19)
-#21 := (not #20)
-#62 := (iff #21 #59)
-#52 := (iff #13 #49)
-#55 := (not #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #21 #55)
-#53 := (iff #20 #52)
-#50 := (iff #19 #49)
-#47 := (iff #18 #46)
-#48 := [rewrite]: #47
-#44 := (iff #15 #43)
-#45 := [rewrite]: #44
-#51 := [monotonicity #45 #48]: #50
-#54 := [monotonicity #51]: #53
-#57 := [monotonicity #54]: #56
-#63 := [trans #57 #61]: #62
-#42 := [asserted]: #21
-#66 := [mp #42 #63]: #59
-#80 := [mp #66 #79]: #75
-#107 := (not #75)
-#108 := (or #13 #73 #107)
-#109 := [def-axiom]: #108
-#111 := [unit-resolution #109 #80]: #110
-#119 := [unit-resolution #111 #118]: #13
-#82 := (= f5 #11)
-#94 := (or #46 #16)
-#95 := [def-axiom]: #94
-#120 := [unit-resolution #95 #116]: #16
-#85 := (or #8 #82)
-#86 := [def-axiom]: #85
-#121 := [unit-resolution #86 #120]: #82
-#122 := [trans #121 #119]: #17
-#96 := (not #17)
-#97 := (or #46 #96)
-#98 := [def-axiom]: #97
-#117 := [unit-resolution #98 #116]: #96
-#123 := [unit-resolution #117 #122]: false
-#124 := [lemma #123]: #46
-#133 := (iff #13 #14)
-#131 := (iff #14 #13)
-#81 := (= f4 #11)
-#125 := [hypothesis]: #8
-#83 := (or #16 #81)
-#84 := [def-axiom]: #83
-#130 := [unit-resolution #84 #125]: #81
-#132 := [monotonicity #130]: #131
-#134 := [symm #132]: #133
-#139 := (or #72 #16)
-#89 := (not #14)
-#135 := (iff #58 #89)
-#136 := [monotonicity #134]: #135
-#126 := [hypothesis]: #73
-#114 := (or #58 #72)
-#112 := (or #58 #72 #107)
-#113 := [def-axiom]: #112
-#115 := [unit-resolution #113 #80]: #114
-#129 := [unit-resolution #115 #126]: #58
-#137 := [mp #129 #136]: #89
-#101 := (or #72 #43)
-#102 := [def-axiom]: #101
-#127 := [unit-resolution #102 #126]: #43
-#92 := (or #70 #16 #14)
-#93 := [def-axiom]: #92
-#128 := [unit-resolution #93 #127 #125]: #14
-#138 := [unit-resolution #128 #137]: false
-#140 := [lemma #138]: #139
-#141 := [unit-resolution #140 #125]: #72
-#144 := [unit-resolution #111 #141]: #13
-#145 := [mp #144 #134]: #14
-#105 := (or #73 #70 #71)
-#106 := [def-axiom]: #105
-#142 := [unit-resolution #106 #141 #124]: #70
-#90 := (or #43 #89)
-#91 := [def-axiom]: #90
-#143 := [unit-resolution #91 #142]: #89
-#146 := [unit-resolution #143 #145]: false
-#147 := [lemma #146]: #16
-#99 := (or #71 #8 #17)
-#100 := [def-axiom]: #99
-#152 := [unit-resolution #100 #147 #124]: #17
-#155 := (= #11 f5)
-#151 := [unit-resolution #86 #147]: #82
-#156 := [symm #151]: #155
-#157 := [trans #156 #152]: #13
-#87 := (or #43 #8)
-#88 := [def-axiom]: #87
-#148 := [unit-resolution #88 #147]: #43
-#149 := [unit-resolution #106 #148 #124]: #73
-#150 := [unit-resolution #115 #149]: #58
-[unit-resolution #150 #157]: false
-unsat
-991ba005efd39f0b714631fc764d551ecd33f6bf 25 0
-#2 := false
-#7 := (:var 0 S2)
-#8 := (= #7 #7)
-#9 := (forall (vars (?v0 S2)) #8)
-#10 := (not #9)
-#46 := (iff #10 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #10 #41)
-#39 := (iff #9 true)
-#34 := (forall (vars (?v0 S2)) true)
-#37 := (iff #34 true)
-#38 := [elim-unused]: #37
-#35 := (iff #9 #34)
-#32 := (iff #8 true)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #10
-[mp #31 #47]: false
-unsat
-10c5b2de1ef268e3092f5c3c42ead76ab232f440 23 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (iff #10 #10)
-#12 := (not #11)
-#41 := (iff #12 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (iff #11 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#33 := [asserted]: #12
-[mp #33 #42]: false
-unsat
-3f5721f2d9a816052aac390d06514062d4ac382d 67 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl ?v0!0 :: S2
-#55 := ?v0!0
-#56 := (f3 ?v0!0)
-#57 := (= #56 f1)
-#58 := (not #57)
-decl ?v1!1 :: S2
-#66 := ?v1!1
-#67 := (f3 ?v1!1)
-#68 := (= #67 f1)
-#69 := (or #57 #68)
-#70 := (not #69)
-#86 := (and #57 #70)
-#63 := (not #58)
-#76 := (and #63 #70)
-#87 := (iff #76 #86)
-#84 := (iff #63 #57)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#10 := (:var 1 S2)
-#11 := (f3 #10)
-#12 := (= #11 f1)
-#13 := (or #12 #9)
-#14 := (forall (vars (?v1 S2)) #13)
-#39 := (not #9)
-#40 := (or #39 #14)
-#43 := (forall (vars (?v0 S2)) #40)
-#46 := (not #43)
-#79 := (~ #46 #76)
-#50 := (or #57 #9)
-#52 := (forall (vars (?v1 S2)) #50)
-#59 := (or #58 #52)
-#60 := (not #59)
-#77 := (~ #60 #76)
-#71 := (not #52)
-#72 := (~ #71 #70)
-#73 := [sk]: #72
-#64 := (~ #63 #63)
-#65 := [refl]: #64
-#78 := [nnf-neg #65 #73]: #77
-#61 := (~ #46 #60)
-#62 := [sk]: #61
-#80 := [trans #62 #78]: #79
-#15 := (implies #9 #14)
-#16 := (forall (vars (?v0 S2)) #15)
-#17 := (not #16)
-#47 := (iff #17 #46)
-#44 := (iff #16 #43)
-#41 := (iff #15 #40)
-#42 := [rewrite]: #41
-#45 := [quant-intro #42]: #44
-#48 := [monotonicity #45]: #47
-#38 := [asserted]: #17
-#51 := [mp #38 #48]: #46
-#81 := [mp~ #51 #80]: #76
-#82 := [mp #81 #88]: #86
-#89 := [and-elim #82]: #70
-#90 := [not-or-elim #89]: #58
-#83 := [and-elim #82]: #57
-[unit-resolution #83 #90]: false
-unsat
-700a60c41d4e55e179e3bc8ce3a6f9ff4e4e4db4 235 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl ?v0!2 :: S2
-#87 := ?v0!2
-#88 := (f3 ?v0!2)
-#89 := (= #88 f1)
-#124 := (not #89)
-decl ?v0!0 :: S2
-#50 := ?v0!0
-#51 := (f3 ?v0!0)
-#52 := (= #51 f1)
-#53 := (not #52)
-#216 := [hypothesis]: #53
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#624 := (pattern #8)
-#9 := (= #8 f1)
-#631 := (forall (vars (?v0 S2)) (:pat #624) #9)
-decl f4 :: (-> S2 S1)
-#10 := (f4 #7)
-#625 := (pattern #10)
-#11 := (= #10 f1)
-#639 := (forall (vars (?v0 S2)) (:pat #625) #11)
-#644 := (not #639)
-#636 := (not #631)
-#647 := (or #636 #644)
-#650 := (not #647)
-#56 := (not #11)
-#55 := (not #9)
-#64 := (or #55 #56)
-#65 := (not #64)
-#626 := (forall (vars (?v0 S2)) (:pat #624 #625) #65)
-#618 := (not #626)
-#249 := (f4 ?v0!0)
-#610 := (= #249 f1)
-#608 := (not #610)
-#611 := (or #53 #608)
-#90 := (f4 ?v0!2)
-#91 := (= #90 f1)
-#125 := (not #91)
-#126 := (or #124 #125)
-#127 := (not #126)
-#285 := [hypothesis]: #626
-#273 := (or #127 #618)
-#612 := [hypothesis]: #126
-#274 := (or #618 #127)
-#405 := [quant-inst #87]: #274
-#614 := [unit-resolution #405 #285 #612]: false
-#615 := [lemma #614]: #273
-#598 := [unit-resolution #615 #285]: #127
-#620 := (or #126 #89)
-#621 := [def-axiom]: #620
-#305 := [unit-resolution #621 #598]: #89
-#287 := [hypothesis]: #125
-#286 := (or #126 #91)
-#619 := [def-axiom]: #286
-#280 := [unit-resolution #619 #287]: #126
-#299 := (or #644 #91)
-#298 := [hypothesis]: #639
-#300 := [quant-inst #87]: #299
-#297 := [unit-resolution #300 #298 #287]: false
-#301 := [lemma #297]: #299
-#616 := [unit-resolution #301 #287]: #644
-#209 := (or #647 #639)
-#295 := [def-axiom]: #209
-#622 := [unit-resolution #295 #616]: #647
-#653 := (or #626 #650)
-#15 := (forall (vars (?v0 S2)) #11)
-#61 := (not #15)
-#14 := (forall (vars (?v0 S2)) #9)
-#45 := (not #14)
-#116 := (or #45 #61)
-#117 := (not #116)
-#113 := (forall (vars (?v0 S2)) #65)
-#120 := (or #113 #117)
-#654 := (iff #120 #653)
-#651 := (iff #117 #650)
-#648 := (iff #116 #647)
-#645 := (iff #61 #644)
-#642 := (iff #15 #639)
-#640 := (iff #11 #11)
-#641 := [refl]: #640
-#643 := [quant-intro #641]: #642
-#646 := [monotonicity #643]: #645
-#637 := (iff #45 #636)
-#634 := (iff #14 #631)
-#632 := (iff #9 #9)
-#633 := [refl]: #632
-#635 := [quant-intro #633]: #634
-#638 := [monotonicity #635]: #637
-#649 := [monotonicity #638 #646]: #648
-#652 := [monotonicity #649]: #651
-#629 := (iff #113 #626)
-#627 := (iff #65 #65)
-#628 := [refl]: #627
-#630 := [quant-intro #628]: #629
-#655 := [monotonicity #630 #652]: #654
-#16 := (and #14 #15)
-#12 := (and #9 #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#99 := (or #13 #16)
-#121 := (iff #99 #120)
-#118 := (iff #16 #117)
-#119 := [rewrite]: #118
-#114 := (iff #13 #113)
-#96 := (iff #12 #65)
-#97 := [rewrite]: #96
-#115 := [quant-intro #97]: #114
-#122 := [monotonicity #115 #119]: #121
-decl ?v0!1 :: S2
-#57 := ?v0!1
-#58 := (f4 ?v0!1)
-#59 := (= #58 f1)
-#60 := (not #59)
-#92 := (and #89 #91)
-#93 := (not #92)
-#106 := (or #93 #53 #60)
-#109 := (and #99 #106)
-#66 := (or #53 #60)
-#98 := (or #93 #66)
-#100 := (and #99 #98)
-#110 := (iff #100 #109)
-#107 := (iff #98 #106)
-#108 := [rewrite]: #107
-#111 := [monotonicity #108]: #110
-#40 := (not #13)
-#41 := (iff #40 #16)
-#101 := (~ #41 #100)
-#78 := (~ #16 #16)
-#76 := (~ #15 #15)
-#74 := (~ #11 #11)
-#75 := [refl]: #74
-#77 := [nnf-pos #75]: #76
-#72 := (~ #14 #14)
-#70 := (~ #9 #9)
-#71 := [refl]: #70
-#73 := [nnf-pos #71]: #72
-#79 := [monotonicity #73 #77]: #78
-#67 := (not #16)
-#68 := (~ #67 #66)
-#62 := (~ #61 #60)
-#63 := [sk]: #62
-#47 := (~ #45 #53)
-#54 := [sk]: #47
-#69 := [nnf-neg #54 #63]: #68
-#94 := (~ #40 #93)
-#95 := [sk]: #94
-#84 := (not #40)
-#85 := (~ #84 #13)
-#82 := (~ #13 #13)
-#80 := (~ #12 #12)
-#81 := [refl]: #80
-#83 := [nnf-pos #81]: #82
-#86 := [nnf-neg #83]: #85
-#102 := [nnf-pos #86 #95 #69 #79]: #101
-#17 := (iff #13 #16)
-#18 := (not #17)
-#42 := (iff #18 #41)
-#43 := [rewrite]: #42
-#39 := [asserted]: #18
-#46 := [mp #39 #43]: #41
-#103 := [mp~ #46 #102]: #100
-#104 := [mp #103 #111]: #109
-#105 := [and-elim #104]: #99
-#123 := [mp #105 #122]: #120
-#656 := [mp #123 #655]: #653
-#617 := [unit-resolution #656 #622]: #626
-#623 := [unit-resolution #405 #617 #280]: false
-#613 := [lemma #623]: #91
-#257 := (f3 ?v0!1)
-#599 := (= #257 f1)
-#261 := (not #599)
-#262 := (or #261 #60)
-#263 := (not #262)
-#609 := (or #263 #618)
-#264 := [hypothesis]: #262
-#602 := (or #618 #263)
-#603 := [quant-inst #57]: #602
-#601 := [unit-resolution #603 #285 #264]: false
-#248 := [lemma #601]: #609
-#317 := [unit-resolution #248 #285]: #263
-#600 := (or #262 #59)
-#606 := [def-axiom]: #600
-#591 := [unit-resolution #606 #317]: #59
-#140 := (or #124 #125 #53 #60)
-#143 := (iff #106 #140)
-#137 := (or #126 #53 #60)
-#141 := (iff #137 #140)
-#142 := [rewrite]: #141
-#138 := (iff #106 #137)
-#135 := (iff #93 #126)
-#130 := (not #127)
-#133 := (iff #130 #126)
-#134 := [rewrite]: #133
-#131 := (iff #93 #130)
-#128 := (iff #92 #127)
-#129 := [rewrite]: #128
-#132 := [monotonicity #129]: #131
-#136 := [trans #132 #134]: #135
-#139 := [monotonicity #136]: #138
-#144 := [trans #139 #142]: #143
-#112 := [and-elim #104]: #106
-#145 := [mp #112 #144]: #140
-#595 := [unit-resolution #145 #591 #613 #305]: #53
-#322 := (or #611 #52)
-#323 := [def-axiom]: #322
-#592 := [unit-resolution #323 #595]: #611
-#597 := (not #611)
-#320 := (or #618 #597)
-#321 := [quant-inst #50]: #320
-#596 := [unit-resolution #321 #285 #592]: false
-#306 := [lemma #596]: #618
-#593 := [unit-resolution #656 #306]: #650
-#208 := (or #647 #631)
-#294 := [def-axiom]: #208
-#307 := [unit-resolution #294 #593]: #631
-#594 := (or #636 #52)
-#316 := [quant-inst #50]: #594
-#308 := [unit-resolution #316 #307 #216]: false
-#309 := [lemma #308]: #52
-#587 := [hypothesis]: #60
-#588 := [unit-resolution #295 #593]: #639
-#302 := (or #644 #59)
-#585 := [quant-inst #57]: #302
-#589 := [unit-resolution #585 #588 #587]: false
-#586 := [lemma #589]: #59
-#590 := (or #124 #53 #60)
-#579 := [unit-resolution #145 #613]: #590
-#576 := [unit-resolution #579 #586 #309]: #124
-#580 := (or #636 #89)
-#581 := [quant-inst #87]: #580
-[unit-resolution #581 #307 #576]: false
-unsat
-77c37fe7fae5071b8918f3ac6af902a7b756b568 145 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl ?v0!1 :: S2
-#72 := ?v0!1
-#73 := (f3 ?v0!1)
-#74 := (= #73 f1)
-#75 := (not #74)
-decl f4 :: S1
-#11 := f4
-#12 := (= f4 f1)
-#55 := (or #74 #12)
-#56 := (not #55)
-decl ?v0!0 :: S2
-#49 := ?v0!0
-#50 := (f3 ?v0!0)
-#51 := (= #50 f1)
-#52 := (or #51 #12)
-#247 := (not #51)
-#44 := (not #52)
-#579 := [hypothesis]: #44
-#258 := (or #52 #247)
-#259 := [def-axiom]: #258
-#580 := [unit-resolution #259 #579]: #247
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#584 := (pattern #8)
-#9 := (= #8 f1)
-#14 := (or #9 #12)
-#590 := (forall (vars (?v0 S2)) (:pat #584) #14)
-#81 := (not #12)
-#260 := (or #52 #81)
-#257 := [def-axiom]: #260
-#574 := [unit-resolution #257 #579]: #81
-#585 := (forall (vars (?v0 S2)) (:pat #584) #9)
-#234 := (not #585)
-#365 := (or #234 #51)
-#576 := [hypothesis]: #247
-#578 := [hypothesis]: #585
-#572 := [quant-inst #49]: #365
-#245 := [unit-resolution #572 #578 #576]: false
-#246 := [lemma #245]: #365
-#233 := [unit-resolution #246 #580]: #234
-#595 := (or #585 #12 #590)
-#15 := (forall (vars (?v0 S2)) #14)
-#10 := (forall (vars (?v0 S2)) #9)
-#95 := (or #10 #12 #15)
-#596 := (iff #95 #595)
-#593 := (iff #15 #590)
-#591 := (iff #14 #14)
-#592 := [refl]: #591
-#594 := [quant-intro #592]: #593
-#588 := (iff #10 #585)
-#586 := (iff #9 #9)
-#587 := [refl]: #586
-#589 := [quant-intro #587]: #588
-#597 := [monotonicity #589 #594]: #596
-#84 := (and #75 #81)
-#87 := (or #84 #44)
-#98 := (and #95 #87)
-#13 := (or #10 #12)
-#88 := (or #13 #15)
-#89 := (and #88 #87)
-#99 := (iff #89 #98)
-#96 := (iff #88 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#39 := (not #13)
-#40 := (iff #39 #15)
-#90 := (~ #40 #89)
-#59 := (~ #15 #15)
-#57 := (~ #14 #14)
-#58 := [refl]: #57
-#60 := [nnf-pos #58]: #59
-#46 := (not #15)
-#53 := (~ #46 #44)
-#54 := [sk]: #53
-#85 := (~ #39 #84)
-#82 := (~ #81 #81)
-#83 := [refl]: #82
-#76 := (not #10)
-#77 := (~ #76 #75)
-#78 := [sk]: #77
-#86 := [nnf-neg #78 #83]: #85
-#69 := (not #39)
-#70 := (~ #69 #13)
-#67 := (~ #13 #13)
-#65 := (~ #12 #12)
-#66 := [refl]: #65
-#63 := (~ #10 #10)
-#61 := (~ #9 #9)
-#62 := [refl]: #61
-#64 := [nnf-pos #62]: #63
-#68 := [monotonicity #64 #66]: #67
-#71 := [nnf-neg #68]: #70
-#91 := [nnf-pos #71 #86 #54 #60]: #90
-#16 := (iff #13 #15)
-#17 := (not #16)
-#41 := (iff #17 #40)
-#42 := [rewrite]: #41
-#38 := [asserted]: #17
-#45 := [mp #38 #42]: #40
-#92 := [mp~ #45 #91]: #89
-#93 := [mp #92 #100]: #98
-#94 := [and-elim #93]: #95
-#598 := [mp #94 #597]: #595
-#575 := [unit-resolution #598 #233 #574]: #590
-#581 := (not #590)
-#582 := (or #581 #51 #12)
-#577 := (or #581 #52)
-#573 := (iff #577 #582)
-#232 := [rewrite]: #573
-#583 := [quant-inst #49]: #577
-#237 := [mp #583 #232]: #582
-#217 := [unit-resolution #237 #574 #575 #580]: false
-#559 := [lemma #217]: #52
-#102 := (or #56 #44)
-#103 := (iff #87 #102)
-#79 := (iff #84 #56)
-#80 := [rewrite]: #79
-#104 := [monotonicity #80]: #103
-#101 := [and-elim #93]: #87
-#105 := [mp #101 #104]: #102
-#221 := [unit-resolution #105 #559]: #56
-#168 := (or #55 #75)
-#254 := [def-axiom]: #168
-#222 := [unit-resolution #254 #221]: #75
-#169 := (or #55 #81)
-#255 := [def-axiom]: #169
-#560 := [unit-resolution #255 #221]: #81
-#565 := [hypothesis]: #590
-#223 := (or #581 #74 #12)
-#224 := (or #581 #55)
-#562 := (iff #224 #223)
-#563 := [rewrite]: #562
-#561 := [quant-inst #72]: #224
-#564 := [mp #561 #563]: #223
-#566 := [unit-resolution #564 #560 #565 #222]: false
-#203 := [lemma #566]: #581
-#567 := [unit-resolution #598 #203 #560]: #585
-#208 := (or #234 #74)
-#209 := [quant-inst #72]: #208
-[unit-resolution #209 #567 #222]: false
-unsat
-1936a8c3d8900c4f3411f9f65f9183a1e77d9f6e 34 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S2 S1)
-#8 := (:var 0 S2)
-#12 := (:var 1 S2)
-#13 := (f3 #12 #8)
-#14 := (= #13 f1)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#7 := (:var 2 S2)
-#9 := (f3 #7 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #10)
-#16 := (iff #11 #15)
-#17 := (not #16)
-#52 := (iff #17 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #17 #47)
-#45 := (iff #16 true)
-#40 := (iff #15 #15)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #16 #40)
-#39 := [elim-unused]: #16
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#38 := [asserted]: #17
-[mp #38 #53]: false
-unsat
-0be5cd612b1c80ec2188777514a42f95d455ac60 103 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S2 S1)
-decl f4 :: S2
-#15 := f4
-decl f5 :: S2
-#19 := f5
-#241 := (f3 f5 f4)
-#156 := (= #241 f1)
-#242 := (not #156)
-#20 := (f3 f4 f5)
-#21 := (= #20 f1)
-#80 := (not #21)
-#8 := (:var 0 S2)
-#16 := (f3 #8 f4)
-#17 := (= #16 f1)
-#18 := (forall (vars (?v0 S2)) #17)
-#53 := (not #18)
-#7 := (:var 1 S2)
-#11 := (f3 #8 #7)
-#12 := (= #11 f1)
-#9 := (f3 #7 #8)
-#10 := (= #9 f1)
-#46 := (not #10)
-#47 := (or #46 #12)
-#50 := (forall (vars (?v0 S2) (?v1 S2)) #47)
-#60 := (not #50)
-#69 := (or #60 #53 #21)
-#72 := (not #69)
-#22 := (implies #18 #21)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2) (?v1 S2)) #13)
-#23 := (implies #14 #22)
-#24 := (not #23)
-#75 := (iff #24 #72)
-#54 := (or #53 #21)
-#61 := (or #60 #54)
-#66 := (not #61)
-#73 := (iff #66 #72)
-#70 := (iff #61 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#67 := (iff #24 #66)
-#64 := (iff #23 #61)
-#57 := (implies #50 #54)
-#62 := (iff #57 #61)
-#63 := [rewrite]: #62
-#58 := (iff #23 #57)
-#55 := (iff #22 #54)
-#56 := [rewrite]: #55
-#51 := (iff #14 #50)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#52 := [quant-intro #49]: #51
-#59 := [monotonicity #52 #56]: #58
-#65 := [trans #59 #63]: #64
-#68 := [monotonicity #65]: #67
-#76 := [trans #68 #74]: #75
-#45 := [asserted]: #24
-#77 := [mp #45 #76]: #72
-#81 := [not-or-elim #77]: #80
-#572 := (pattern #11)
-#571 := (pattern #9)
-#573 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #571 #572) #47)
-#576 := (iff #50 #573)
-#574 := (iff #47 #47)
-#575 := [refl]: #574
-#577 := [quant-intro #575]: #576
-#93 := (~ #50 #50)
-#91 := (~ #47 #47)
-#92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
-#78 := [not-or-elim #77]: #50
-#83 := [mp~ #78 #94]: #50
-#578 := [mp #83 #577]: #573
-#245 := (not #573)
-#246 := (or #245 #242 #21)
-#157 := (or #242 #21)
-#247 := (or #245 #157)
-#248 := (iff #247 #246)
-#227 := [rewrite]: #248
-#244 := [quant-inst #19 #15]: #247
-#563 := [mp #244 #227]: #246
-#243 := [unit-resolution #563 #578 #81]: #242
-#579 := (pattern #16)
-#580 := (forall (vars (?v0 S2)) (:pat #579) #17)
-#583 := (iff #18 #580)
-#581 := (iff #17 #17)
-#582 := [refl]: #581
-#584 := [quant-intro #582]: #583
-#85 := (~ #18 #18)
-#84 := (~ #17 #17)
-#95 := [refl]: #84
-#86 := [nnf-pos #95]: #85
-#79 := [not-or-elim #77]: #18
-#96 := [mp~ #79 #86]: #18
-#585 := [mp #96 #584]: #580
-#565 := (not #580)
-#221 := (or #565 #156)
-#352 := [quant-inst #19]: #221
-[unit-resolution #352 #585 #243]: false
-unsat
-ac63a8f94b83c505b675b60053e9418e47f3332d 101 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: (-> S3 S2 S2)
-decl f6 :: S2
-#16 := f6
-decl f5 :: S3
-#10 := f5
-#20 := (f4 f5 f6)
-#21 := (f4 f5 #20)
-#232 := (f3 #21)
-#552 := (= #232 f1)
-#230 := (f3 #20)
-#145 := (= #230 f1)
-#17 := (f3 f6)
-#18 := (= #17 f1)
-#7 := (:var 0 S2)
-#11 := (f4 f5 #7)
-#12 := (f3 #11)
-#13 := (= #12 f1)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#48 := (not #9)
-#49 := (or #48 #13)
-#52 := (forall (vars (?v0 S2)) #49)
-#55 := (and #52 #18)
-#22 := (f4 f5 #21)
-#23 := (f3 #22)
-#24 := (= #23 f1)
-#61 := (not #55)
-#62 := (or #61 #24)
-#67 := (not #62)
-#14 := (implies #9 #13)
-#15 := (forall (vars (?v0 S2)) #14)
-#19 := (and #15 #18)
-#25 := (implies #19 #24)
-#26 := (not #25)
-#68 := (iff #26 #67)
-#65 := (iff #25 #62)
-#58 := (implies #55 #24)
-#63 := (iff #58 #62)
-#64 := [rewrite]: #63
-#59 := (iff #25 #58)
-#56 := (iff #19 #55)
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#54 := [quant-intro #51]: #53
-#57 := [monotonicity #54]: #56
-#60 := [monotonicity #57]: #59
-#66 := [trans #60 #64]: #65
-#69 := [monotonicity #66]: #68
-#47 := [asserted]: #26
-#72 := [mp #47 #69]: #67
-#70 := [not-or-elim #72]: #55
-#73 := [and-elim #70]: #18
-#560 := (pattern #11)
-#561 := (forall (vars (?v0 S2)) (:pat #560) #49)
-#564 := (iff #52 #561)
-#562 := (iff #49 #49)
-#563 := [refl]: #562
-#565 := [quant-intro #563]: #564
-#87 := (~ #52 #52)
-#85 := (~ #49 #49)
-#86 := [refl]: #85
-#88 := [nnf-pos #86]: #87
-#71 := [and-elim #70]: #52
-#77 := [mp~ #71 #88]: #52
-#566 := [mp #77 #565]: #561
-#144 := (not #18)
-#223 := (not #561)
-#234 := (or #223 #144 #145)
-#231 := (or #144 #145)
-#235 := (or #223 #231)
-#233 := (iff #235 #234)
-#237 := [rewrite]: #233
-#236 := [quant-inst #16]: #235
-#216 := [mp #236 #237]: #234
-#558 := [unit-resolution #216 #566 #73]: #145
-#146 := (not #145)
-#548 := (or #223 #146 #552)
-#554 := (or #146 #552)
-#221 := (or #223 #554)
-#555 := (iff #221 #548)
-#556 := [rewrite]: #555
-#222 := [quant-inst #20]: #221
-#557 := [mp #222 #556]: #548
-#553 := [unit-resolution #557 #566 #558]: #552
-#74 := (not #24)
-#75 := [not-or-elim #72]: #74
-#210 := (not #552)
-#559 := (or #223 #210 #24)
-#341 := (or #210 #24)
-#549 := (or #223 #341)
-#213 := (iff #549 #559)
-#550 := [rewrite]: #213
-#208 := [quant-inst #21]: #549
-#209 := [mp #208 #550]: #559
-[unit-resolution #209 #566 #75 #553]: false
-unsat
-f1a3aeaad9840f61d284b110db9d2ac5a6976876 64 0
-#2 := false
-decl f3 :: (-> S2 S2 S3)
-decl f4 :: S2
-#13 := f4
-decl f5 :: S2
-#15 := f5
-#17 := (f3 f5 f4)
-#16 := (f3 f4 f5)
-#18 := (= #16 #17)
-#65 := (not #18)
-#7 := (:var 1 S2)
-#8 := (:var 0 S2)
-#10 := (f3 #8 #7)
-#9 := (f3 #7 #8)
-#11 := (= #9 #10)
-#12 := (forall (vars (?v0 S2) (?v1 S2)) #11)
-#55 := (not #12)
-#56 := (or #55 #18)
-#61 := (not #56)
-#14 := (= f4 f4)
-#19 := (and #14 #18)
-#20 := (implies #12 #19)
-#21 := (not #20)
-#62 := (iff #21 #61)
-#59 := (iff #20 #56)
-#52 := (implies #12 #18)
-#57 := (iff #52 #56)
-#58 := [rewrite]: #57
-#53 := (iff #20 #52)
-#50 := (iff #19 #18)
-#1 := true
-#45 := (and true #18)
-#48 := (iff #45 #18)
-#49 := [rewrite]: #48
-#46 := (iff #19 #45)
-#43 := (iff #14 true)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
-#54 := [monotonicity #51]: #53
-#60 := [trans #54 #58]: #59
-#63 := [monotonicity #60]: #62
-#42 := [asserted]: #21
-#66 := [mp #42 #63]: #61
-#67 := [not-or-elim #66]: #65
-#553 := (pattern #10)
-#552 := (pattern #9)
-#554 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #552 #553) #11)
-#557 := (iff #12 #554)
-#555 := (iff #11 #11)
-#556 := [refl]: #555
-#558 := [quant-intro #556]: #557
-#77 := (~ #12 #12)
-#75 := (~ #11 #11)
-#76 := [refl]: #75
-#78 := [nnf-pos #76]: #77
-#64 := [not-or-elim #66]: #12
-#69 := [mp~ #64 #78]: #12
-#559 := [mp #69 #558]: #554
-#137 := (not #554)
-#223 := (or #137 #18)
-#138 := [quant-inst #13 #15]: #223
-[unit-resolution #138 #559 #67]: false
-unsat
-c37af3173480108eddc4b3a3068306cd906ea03a 203 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl f7 :: S2
-#21 := f7
-#24 := (f3 f7)
-#25 := (= #24 f1)
-decl f5 :: S2
-#14 := f5
-#240 := (f3 f5)
-#327 := (= #240 f1)
-#242 := (not #327)
-decl f4 :: (-> S2 S1)
-#15 := (f4 f5)
-#16 := (= #15 f1)
-#17 := (not #16)
-decl f6 :: (-> S2 S1)
-#22 := (f6 f7)
-#23 := (= #22 f1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#19 := (not #9)
-#10 := (f4 #7)
-#11 := (= #10 f1)
-#18 := (not #11)
-#20 := (and #18 #19)
-#63 := (not #20)
-#88 := (or #63 #23 #25)
-#91 := (forall (vars (?v0 S2)) #88)
-#57 := (or #19 #11)
-#60 := (forall (vars (?v0 S2)) #57)
-#100 := (and #60 #17 #91)
-#31 := (f4 f7)
-#32 := (= #31 f1)
-#105 := (not #100)
-#111 := (or #105 #23 #32)
-#116 := (not #111)
-#33 := (or #23 #32)
-#26 := (or #23 #25)
-#27 := (implies #20 #26)
-#28 := (forall (vars (?v0 S2)) #27)
-#29 := (and #17 #28)
-#12 := (implies #9 #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#30 := (and #13 #29)
-#34 := (implies #30 #33)
-#35 := (not #34)
-#119 := (iff #35 #116)
-#64 := (or #63 #26)
-#67 := (forall (vars (?v0 S2)) #64)
-#70 := (and #17 #67)
-#73 := (and #60 #70)
-#79 := (not #73)
-#80 := (or #79 #33)
-#85 := (not #80)
-#117 := (iff #85 #116)
-#114 := (iff #80 #111)
-#108 := (or #105 #33)
-#112 := (iff #108 #111)
-#113 := [rewrite]: #112
-#109 := (iff #80 #108)
-#106 := (iff #79 #105)
-#103 := (iff #73 #100)
-#94 := (and #17 #91)
-#97 := (and #60 #94)
-#101 := (iff #97 #100)
-#102 := [rewrite]: #101
-#98 := (iff #73 #97)
-#95 := (iff #70 #94)
-#92 := (iff #67 #91)
-#89 := (iff #64 #88)
-#90 := [rewrite]: #89
-#93 := [quant-intro #90]: #92
-#96 := [monotonicity #93]: #95
-#99 := [monotonicity #96]: #98
-#104 := [trans #99 #102]: #103
-#107 := [monotonicity #104]: #106
-#110 := [monotonicity #107]: #109
-#115 := [trans #110 #113]: #114
-#118 := [monotonicity #115]: #117
-#86 := (iff #35 #85)
-#83 := (iff #34 #80)
-#76 := (implies #73 #33)
-#81 := (iff #76 #80)
-#82 := [rewrite]: #81
-#77 := (iff #34 #76)
-#74 := (iff #30 #73)
-#71 := (iff #29 #70)
-#68 := (iff #28 #67)
-#65 := (iff #27 #64)
-#66 := [rewrite]: #65
-#69 := [quant-intro #66]: #68
-#72 := [monotonicity #69]: #71
-#61 := (iff #13 #60)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#62 := [quant-intro #59]: #61
-#75 := [monotonicity #62 #72]: #74
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#87 := [monotonicity #84]: #86
-#120 := [trans #87 #118]: #119
-#56 := [asserted]: #35
-#121 := [mp #56 #120]: #116
-#122 := [not-or-elim #121]: #100
-#124 := [and-elim #122]: #17
-#657 := (pattern #10)
-#656 := (pattern #8)
-#658 := (forall (vars (?v0 S2)) (:pat #656 #657) #57)
-#661 := (iff #60 #658)
-#659 := (iff #57 #57)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#138 := (~ #60 #60)
-#141 := (~ #57 #57)
-#142 := [refl]: #141
-#154 := [nnf-pos #142]: #138
-#123 := [and-elim #122]: #60
-#135 := [mp~ #123 #154]: #60
-#663 := [mp #135 #662]: #658
-#331 := (not #658)
-#332 := (or #331 #242 #16)
-#328 := (or #242 #16)
-#329 := (or #331 #328)
-#312 := (iff #329 #332)
-#648 := [rewrite]: #312
-#333 := [quant-inst #14]: #329
-#650 := [mp #333 #648]: #332
-#654 := [unit-resolution #650 #663 #124]: #242
-#169 := (or #11 #9 #25)
-#664 := (forall (vars (?v0 S2)) (:pat #657 #656) #169)
-#174 := (forall (vars (?v0 S2)) #169)
-#667 := (iff #174 #664)
-#665 := (iff #169 #169)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#146 := (or #63 #25)
-#151 := (forall (vars (?v0 S2)) #146)
-#175 := (iff #151 #174)
-#172 := (iff #146 #169)
-#155 := (or #11 #9)
-#166 := (or #155 #25)
-#170 := (iff #166 #169)
-#171 := [rewrite]: #170
-#167 := (iff #146 #166)
-#164 := (iff #63 #155)
-#156 := (not #155)
-#159 := (not #156)
-#162 := (iff #159 #155)
-#163 := [rewrite]: #162
-#160 := (iff #63 #159)
-#157 := (iff #20 #156)
-#158 := [rewrite]: #157
-#161 := [monotonicity #158]: #160
-#165 := [trans #161 #163]: #164
-#168 := [monotonicity #165]: #167
-#173 := [trans #168 #171]: #172
-#176 := [quant-intro #173]: #175
-#134 := (~ #151 #151)
-#136 := (~ #146 #146)
-#133 := [refl]: #136
-#131 := [nnf-pos #133]: #134
-#152 := (iff #91 #151)
-#149 := (iff #88 #146)
-#143 := (or #63 false #25)
-#147 := (iff #143 #146)
-#148 := [rewrite]: #147
-#144 := (iff #88 #143)
-#139 := (iff #23 false)
-#126 := (not #23)
-#127 := [not-or-elim #121]: #126
-#140 := [iff-false #127]: #139
-#145 := [monotonicity #140]: #144
-#150 := [trans #145 #148]: #149
-#153 := [quant-intro #150]: #152
-#125 := [and-elim #122]: #91
-#137 := [mp #125 #153]: #151
-#132 := [mp~ #137 #131]: #151
-#177 := [mp #132 #176]: #174
-#669 := [mp #177 #668]: #664
-#437 := (not #664)
-#644 := (or #437 #16 #327 #25)
-#319 := (or #16 #327 #25)
-#317 := (or #437 #319)
-#651 := (iff #317 #644)
-#652 := [rewrite]: #651
-#318 := [quant-inst #14]: #317
-#653 := [mp #318 #652]: #644
-#649 := [unit-resolution #653 #124 #669 #654]: #25
-#128 := (not #32)
-#129 := [not-or-elim #121]: #128
-#330 := (not #25)
-#655 := (or #331 #330 #32)
-#306 := (or #330 #32)
-#645 := (or #331 #306)
-#309 := (iff #645 #655)
-#646 := [rewrite]: #309
-#304 := [quant-inst #21]: #645
-#305 := [mp #304 #646]: #655
-[unit-resolution #305 #663 #129 #649]: false
-unsat
-19990be1db50e963aafcc1c9ab3bda9712fc1797 1 0
-unsat
-1cfdaf7cf1764c12b112c06ca51a00830c6fcdde 25 0
-#2 := false
-#7 := (:var 0 S2)
-#8 := (= #7 #7)
-#9 := (exists (vars (?v0 S2)) #8)
-#10 := (not #9)
-#46 := (iff #10 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #10 #41)
-#39 := (iff #9 true)
-#34 := (exists (vars (?v0 S2)) true)
-#37 := (iff #34 true)
-#38 := [elim-unused]: #37
-#35 := (iff #9 #34)
-#32 := (iff #8 true)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #10
-[mp #31 #47]: false
-unsat
-983e6603d4caff6f91195b6f7c23c1ebf8889f75 23 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#10 := (exists (vars (?v0 S2)) #9)
-#11 := (iff #10 #10)
-#12 := (not #11)
-#41 := (iff #12 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (iff #11 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#33 := [asserted]: #12
-[mp #33 #42]: false
-unsat
-a5805ee4c963267c1bf8cb35e86d5702ad58f164 205 0
-#2 := false
-decl f4 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#10 := (f4 #7)
-#600 := (pattern #10)
-decl f1 :: S1
-#3 := f1
-#11 := (= #10 f1)
-#55 := (not #11)
-#614 := (forall (vars (?v0 S2)) (:pat #600) #55)
-#619 := (not #614)
-decl f3 :: (-> S2 S1)
-#8 := (f3 #7)
-#599 := (pattern #8)
-#9 := (= #8 f1)
-#50 := (not #9)
-#606 := (forall (vars (?v0 S2)) (:pat #599) #50)
-#611 := (not #606)
-#622 := (or #611 #619)
-#625 := (not #622)
-#12 := (or #9 #11)
-#96 := (not #12)
-#601 := (forall (vars (?v0 S2)) (:pat #599 #600) #96)
-#275 := (not #601)
-decl ?v0!1 :: S2
-#73 := ?v0!1
-#74 := (f4 ?v0!1)
-#75 := (= #74 f1)
-#579 := (f3 ?v0!1)
-#580 := (= #579 f1)
-#575 := (or #580 #75)
-decl ?v0!2 :: S2
-#83 := ?v0!2
-#86 := (f4 ?v0!2)
-#87 := (= #86 f1)
-#249 := (not #87)
-#84 := (f3 ?v0!2)
-#85 := (= #84 f1)
-#88 := (or #85 #87)
-#262 := (not #88)
-#274 := [hypothesis]: #601
-#595 := (or #262 #275)
-#273 := [hypothesis]: #88
-#272 := (or #275 #262)
-#276 := [quant-inst #83]: #272
-#594 := [unit-resolution #276 #274 #273]: false
-#596 := [lemma #594]: #595
-#218 := [unit-resolution #596 #274]: #262
-#380 := (or #88 #249)
-#587 := [def-axiom]: #380
-#582 := [unit-resolution #587 #218]: #249
-#255 := (not #85)
-#591 := (or #88 #255)
-#593 := [def-axiom]: #591
-#296 := [unit-resolution #593 #218]: #255
-decl ?v0!0 :: S2
-#66 := ?v0!0
-#67 := (f3 ?v0!0)
-#68 := (= #67 f1)
-#590 := (not #68)
-#597 := (f4 ?v0!0)
-#592 := (= #597 f1)
-#598 := (or #68 #592)
-#588 := (not #598)
-#577 := (or #588 #275)
-#247 := [hypothesis]: #598
-#589 := (or #275 #588)
-#248 := [quant-inst #66]: #589
-#252 := [unit-resolution #248 #274 #247]: false
-#578 := [lemma #252]: #577
-#297 := [unit-resolution #578 #274]: #588
-#232 := (or #598 #590)
-#574 := [def-axiom]: #232
-#298 := [unit-resolution #574 #297]: #590
-#110 := (or #85 #87 #68 #75)
-#58 := (forall (vars (?v0 S2)) #55)
-#53 := (forall (vars (?v0 S2)) #50)
-#62 := (and #53 #58)
-#99 := (forall (vars (?v0 S2)) #96)
-#102 := (or #99 #62)
-#113 := (and #110 #102)
-#80 := (or #68 #75)
-#103 := (or #88 #80)
-#104 := (and #103 #102)
-#114 := (iff #104 #113)
-#111 := (iff #103 #110)
-#112 := [rewrite]: #111
-#115 := [monotonicity #112]: #114
-#15 := (exists (vars (?v0 S2)) #11)
-#14 := (exists (vars (?v0 S2)) #9)
-#16 := (or #14 #15)
-#13 := (exists (vars (?v0 S2)) #12)
-#40 := (not #13)
-#41 := (iff #40 #16)
-#105 := (~ #41 #104)
-#81 := (~ #16 #80)
-#76 := (~ #15 #75)
-#77 := [sk]: #76
-#69 := (~ #14 #68)
-#70 := [sk]: #69
-#82 := [monotonicity #70 #77]: #81
-#63 := (not #16)
-#64 := (~ #63 #62)
-#59 := (not #15)
-#60 := (~ #59 #58)
-#56 := (~ #55 #55)
-#57 := [refl]: #56
-#61 := [nnf-neg #57]: #60
-#45 := (not #14)
-#47 := (~ #45 #53)
-#51 := (~ #50 #50)
-#52 := [refl]: #51
-#54 := [nnf-neg #52]: #47
-#65 := [nnf-neg #54 #61]: #64
-#100 := (~ #40 #99)
-#97 := (~ #96 #96)
-#98 := [refl]: #97
-#101 := [nnf-neg #98]: #100
-#93 := (not #40)
-#94 := (~ #93 #88)
-#89 := (~ #13 #88)
-#90 := [sk]: #89
-#95 := [nnf-neg #90]: #94
-#106 := [nnf-pos #95 #101 #65 #82]: #105
-#17 := (iff #13 #16)
-#18 := (not #17)
-#42 := (iff #18 #41)
-#43 := [rewrite]: #42
-#39 := [asserted]: #18
-#46 := [mp #39 #43]: #41
-#107 := [mp~ #46 #106]: #104
-#108 := [mp #107 #115]: #113
-#109 := [and-elim #108]: #110
-#191 := [unit-resolution #109 #298 #296 #582]: #75
-#586 := (not #75)
-#572 := (or #575 #586)
-#573 := [def-axiom]: #572
-#568 := [unit-resolution #573 #191]: #575
-#581 := (not #575)
-#584 := (or #275 #581)
-#223 := [quant-inst #73]: #584
-#569 := [unit-resolution #223 #274 #568]: false
-#291 := [lemma #569]: #275
-#628 := (or #601 #625)
-#72 := (not #58)
-#71 := (not #53)
-#91 := (or #71 #72)
-#92 := (not #91)
-#117 := (or #99 #92)
-#629 := (iff #117 #628)
-#626 := (iff #92 #625)
-#623 := (iff #91 #622)
-#620 := (iff #72 #619)
-#617 := (iff #58 #614)
-#615 := (iff #55 #55)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#621 := [monotonicity #618]: #620
-#612 := (iff #71 #611)
-#609 := (iff #53 #606)
-#607 := (iff #50 #50)
-#608 := [refl]: #607
-#610 := [quant-intro #608]: #609
-#613 := [monotonicity #610]: #612
-#624 := [monotonicity #613 #621]: #623
-#627 := [monotonicity #624]: #626
-#604 := (iff #99 #601)
-#602 := (iff #96 #96)
-#603 := [refl]: #602
-#605 := [quant-intro #603]: #604
-#630 := [monotonicity #605 #627]: #629
-#118 := (iff #102 #117)
-#78 := (iff #62 #92)
-#79 := [rewrite]: #78
-#119 := [monotonicity #79]: #118
-#116 := [and-elim #108]: #102
-#120 := [mp #116 #119]: #117
-#631 := [mp #120 #630]: #628
-#224 := [unit-resolution #631 #291]: #625
-#184 := (or #622 #614)
-#270 := [def-axiom]: #184
-#283 := [unit-resolution #270 #224]: #614
-#183 := (or #622 #606)
-#269 := [def-axiom]: #183
-#585 := [unit-resolution #269 #224]: #606
-#570 := [hypothesis]: #68
-#571 := (or #611 #590)
-#281 := [quant-inst #66]: #571
-#567 := [unit-resolution #281 #570 #585]: false
-#282 := [lemma #567]: #590
-#295 := [hypothesis]: #85
-#583 := (or #611 #255)
-#280 := [quant-inst #83]: #583
-#292 := [unit-resolution #280 #295 #585]: false
-#566 := [lemma #292]: #255
-#284 := [hypothesis]: #87
-#562 := (or #619 #249)
-#563 := [quant-inst #83]: #562
-#277 := [unit-resolution #563 #284 #283]: false
-#560 := [lemma #277]: #249
-#564 := [unit-resolution #109 #560 #566 #282]: #75
-#565 := (or #619 #586)
-#554 := [quant-inst #73]: #565
-[unit-resolution #554 #564 #283]: false
-unsat
-15bd078d1caba7b30476b1f272408346e917c717 173 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#611 := (pattern #8)
-decl f1 :: S1
-#3 := f1
-#9 := (= #8 f1)
-#77 := (not #9)
-#612 := (forall (vars (?v0 S2)) (:pat #611) #77)
-decl f4 :: S1
-#11 := f4
-#12 := (= f4 f1)
-#84 := (not #12)
-decl ?v0!1 :: S2
-#62 := ?v0!1
-#63 := (f3 ?v0!1)
-#64 := (= #63 f1)
-#67 := (not #64)
-#68 := (or #67 #84)
-#267 := [hypothesis]: #84
-#196 := (or #68 #12)
-#282 := [def-axiom]: #196
-#603 := [unit-resolution #282 #267]: #68
-decl ?v0!0 :: S2
-#54 := ?v0!0
-#55 := (f3 ?v0!0)
-#56 := (= #55 f1)
-#106 := (not #56)
-#107 := (or #106 #84)
-#286 := (or #107 #12)
-#287 := [def-axiom]: #286
-#605 := [unit-resolution #287 #267]: #107
-#108 := (not #107)
-#60 := (not #68)
-#111 := (or #60 #108)
-#57 := (and #56 #12)
-#71 := (and #64 #12)
-#91 := (or #71 #57)
-#112 := (iff #91 #111)
-#109 := (iff #57 #108)
-#110 := [rewrite]: #109
-#61 := (iff #71 #60)
-#105 := [rewrite]: #61
-#113 := [monotonicity #105 #110]: #112
-#14 := (and #9 #12)
-#49 := (not #14)
-#52 := (forall (vars (?v0 S2)) #49)
-#80 := (forall (vars (?v0 S2)) #77)
-#98 := (or #80 #84 #52)
-#101 := (and #91 #98)
-#87 := (or #80 #84)
-#90 := (or #87 #52)
-#92 := (and #91 #90)
-#102 := (iff #92 #101)
-#99 := (iff #90 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#15 := (exists (vars (?v0 S2)) #14)
-#10 := (exists (vars (?v0 S2)) #9)
-#13 := (and #10 #12)
-#39 := (not #13)
-#40 := (iff #39 #15)
-#93 := (~ #40 #92)
-#58 := (~ #15 #57)
-#59 := [sk]: #58
-#44 := (not #15)
-#46 := (~ #44 #52)
-#50 := (~ #49 #49)
-#51 := [refl]: #50
-#53 := [nnf-neg #51]: #46
-#88 := (~ #39 #87)
-#85 := (~ #84 #84)
-#86 := [refl]: #85
-#81 := (not #10)
-#82 := (~ #81 #80)
-#78 := (~ #77 #77)
-#79 := [refl]: #78
-#83 := [nnf-neg #79]: #82
-#89 := [nnf-neg #83 #86]: #88
-#74 := (not #39)
-#75 := (~ #74 #71)
-#72 := (~ #13 #71)
-#69 := (~ #12 #12)
-#70 := [refl]: #69
-#65 := (~ #10 #64)
-#66 := [sk]: #65
-#73 := [monotonicity #66 #70]: #72
-#76 := [nnf-neg #73]: #75
-#94 := [nnf-pos #76 #89 #53 #59]: #93
-#16 := (iff #13 #15)
-#17 := (not #16)
-#41 := (iff #17 #40)
-#42 := [rewrite]: #41
-#38 := [asserted]: #17
-#45 := [mp #38 #42]: #40
-#95 := [mp~ #45 #94]: #92
-#96 := [mp #95 #103]: #101
-#97 := [and-elim #96]: #91
-#114 := [mp #97 #113]: #111
-#261 := [unit-resolution #114 #605 #603]: false
-#392 := [lemma #261]: #12
-#115 := (or #77 #84)
-#617 := (forall (vars (?v0 S2)) (:pat #611) #115)
-#600 := (not #617)
-#249 := [hypothesis]: #617
-#273 := (not #612)
-#272 := [hypothesis]: #56
-#606 := (or #273 #106)
-#599 := [hypothesis]: #612
-#607 := [quant-inst #54]: #606
-#608 := [unit-resolution #607 #272 #599]: false
-#609 := [lemma #608]: #606
-#604 := [unit-resolution #609 #272]: #273
-#622 := (or #612 #84 #617)
-#126 := (forall (vars (?v0 S2)) #115)
-#129 := (or #80 #84 #126)
-#623 := (iff #129 #622)
-#620 := (iff #126 #617)
-#618 := (iff #115 #115)
-#619 := [refl]: #618
-#621 := [quant-intro #619]: #620
-#615 := (iff #80 #612)
-#613 := (iff #77 #77)
-#614 := [refl]: #613
-#616 := [quant-intro #614]: #615
-#624 := [monotonicity #616 #621]: #623
-#130 := (iff #98 #129)
-#127 := (iff #52 #126)
-#124 := (iff #49 #115)
-#116 := (not #115)
-#119 := (not #116)
-#122 := (iff #119 #115)
-#123 := [rewrite]: #122
-#120 := (iff #49 #119)
-#117 := (iff #14 #116)
-#118 := [rewrite]: #117
-#121 := [monotonicity #118]: #120
-#125 := [trans #121 #123]: #124
-#128 := [quant-intro #125]: #127
-#131 := [monotonicity #128]: #130
-#104 := [and-elim #96]: #98
-#132 := [mp #104 #131]: #129
-#625 := [mp #132 #624]: #622
-#610 := [unit-resolution #625 #604 #392]: #617
-#259 := (or #600 #106 #84)
-#264 := (or #600 #107)
-#260 := (iff #264 #259)
-#602 := [rewrite]: #260
-#601 := [quant-inst #54]: #264
-#244 := [mp #601 #602]: #259
-#586 := [unit-resolution #244 #392 #272 #610]: false
-#248 := [lemma #586]: #106
-#274 := (or #107 #56)
-#285 := [def-axiom]: #274
-#250 := [unit-resolution #285 #248]: #107
-#587 := [unit-resolution #114 #250]: #60
-#195 := (or #68 #64)
-#281 := [def-axiom]: #195
-#593 := [unit-resolution #281 #587]: #64
-#251 := (or #600 #67 #84)
-#588 := (or #600 #68)
-#590 := (iff #588 #251)
-#591 := [rewrite]: #590
-#589 := [quant-inst #62]: #588
-#592 := [mp #589 #591]: #251
-#230 := [unit-resolution #592 #593 #392 #249]: false
-#594 := [lemma #230]: #600
-#596 := [unit-resolution #625 #594 #392]: #612
-#236 := (or #273 #67)
-#597 := [quant-inst #62]: #236
-[unit-resolution #597 #593 #596]: false
-unsat
-f04d5873e94a5aad7b78e98d30003072c55f70b2 34 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S4 S1)
-#8 := (:var 0 S4)
-#12 := (:var 1 S2)
-#13 := (f3 #12 #8)
-#14 := (= #13 f1)
-#15 := (exists (vars (?v0 S2) (?v1 S4)) #14)
-#7 := (:var 2 S2)
-#9 := (f3 #7 #8)
-#10 := (= #9 f1)
-#11 := (exists (vars (?v0 S2) (?v1 S3) (?v2 S4)) #10)
-#16 := (iff #11 #15)
-#17 := (not #16)
-#52 := (iff #17 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #17 #47)
-#45 := (iff #16 true)
-#40 := (iff #15 #15)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #16 #40)
-#39 := [elim-unused]: #16
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#38 := [asserted]: #17
-[mp #38 #53]: false
-unsat
-859cb38c5f32b7d6ba5f7cb98e20433a77c5ac6e 72 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#568 := (pattern #8)
-decl f1 :: S1
-#3 := f1
-#9 := (= #8 f1)
-#10 := (not #9)
-#569 := (forall (vars (?v0 S2)) (:pat #568) #10)
-#84 := (forall (vars (?v0 S2)) #10)
-#572 := (iff #84 #569)
-#570 := (iff #10 #10)
-#571 := [refl]: #570
-#573 := [quant-intro #571]: #572
-#12 := (exists (vars (?v0 S2)) #9)
-#18 := (not #12)
-#85 := (~ #18 #84)
-#81 := (~ #10 #10)
-#82 := [refl]: #81
-#88 := [nnf-neg #82]: #85
-decl f4 :: (-> S2 S1)
-#13 := (f4 #7)
-#14 := (= #13 f1)
-#15 := (and #9 #14)
-#16 := (exists (vars (?v0 S2)) #15)
-#17 := (or #12 #16)
-#11 := (exists (vars (?v0 S2)) #10)
-#46 := (and #11 #17 #18)
-#19 := (and #17 #18)
-#20 := (and #11 #19)
-#21 := (not #20)
-#22 := (not #21)
-#49 := (iff #22 #46)
-#47 := (iff #20 #46)
-#48 := [rewrite]: #47
-#44 := (iff #22 #20)
-#45 := [rewrite]: #44
-#50 := [trans #45 #48]: #49
-#43 := [asserted]: #22
-#51 := [mp #43 #50]: #46
-#54 := [and-elim #51]: #18
-#89 := [mp~ #54 #88]: #84
-#574 := [mp #89 #573]: #569
-decl ?v0!1 :: S2
-#72 := ?v0!1
-#73 := (f3 ?v0!1)
-#75 := (= #73 f1)
-#76 := (f4 ?v0!1)
-#77 := (= #76 f1)
-#78 := (and #75 #77)
-#79 := (~ #16 #78)
-#80 := [sk]: #79
-#69 := (iff #17 #16)
-#64 := (or false #16)
-#67 := (iff #64 #16)
-#68 := [rewrite]: #67
-#65 := (iff #17 #64)
-#62 := (iff #12 false)
-#63 := [iff-false #54]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#53 := [and-elim #51]: #17
-#60 := [mp #53 #70]: #16
-#83 := [mp~ #60 #80]: #78
-#86 := [and-elim #83]: #75
-#152 := (not #75)
-#239 := (not #569)
-#154 := (or #239 #152)
-#240 := [quant-inst #72]: #154
-[unit-resolution #240 #86 #574]: false
-unsat
-f78c1cf1e21deba8da342bf5b3ccd8619a3acc09 2 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
-unsat
-f78f234620a6b9d63296ecb6ddac45e9775a4139 2 0
-WARNING: For problems containing quantifiers, the model finding capabilities of Z3 work better when the formula does not contain nested quantifiers. You can use PULL_NESTED_QUANTIFIERS=true to eliminate nested quantifiers.
-unsat
-ff5923442190bbdb9015d06b9eb041224ec4aa67 1 0
-unsat
-4c6ce503f607e74ba8e93edccc79946582314947 1 0
-unsat
-12584fda31d4fe9678f56daf5308984bcbc8882b 1 0
-unsat
-3c63947a5d206f9097abc5a6fc0fbae82d2d79e0 1 0
-unsat
-54883b23fe5740347c973de8603dbf0368168608 79 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1 S1)
-decl ?v0!0 :: S1
-#47 := ?v0!0
-decl f4 :: S2
-#7 := f4
-#48 := (f3 f4 ?v0!0)
-#49 := (= #48 f1)
-decl ?v0!1 :: S1
-#61 := ?v0!1
-#62 := (f3 f4 ?v0!1)
-#63 := (= #62 f1)
-#145 := (not #63)
-#231 := [hypothesis]: #63
-#8 := (:var 0 S1)
-#9 := (f3 f4 #8)
-#561 := (pattern #9)
-#10 := (= #9 f1)
-#13 := (not #10)
-#562 := (forall (vars (?v0 S1)) (:pat #561) #13)
-#14 := (forall (vars (?v0 S1)) #13)
-#565 := (iff #14 #562)
-#563 := (iff #13 #13)
-#564 := [refl]: #563
-#566 := [quant-intro #564]: #565
-#80 := (or #63 #49)
-#83 := (and #14 #80)
-#50 := (not #49)
-#42 := (not #50)
-#68 := (or #63 #42)
-#69 := (or #14 #14)
-#70 := (and #69 #68)
-#84 := (iff #70 #83)
-#81 := (iff #68 #80)
-#78 := (iff #42 #49)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#76 := (iff #69 #14)
-#77 := [rewrite]: #76
-#85 := [monotonicity #77 #82]: #84
-#11 := (exists (vars (?v0 S1)) #10)
-#38 := (iff #11 #14)
-#71 := (~ #38 #70)
-#57 := (~ #14 #14)
-#55 := (~ #13 #13)
-#56 := [refl]: #55
-#58 := [nnf-pos #56]: #57
-#44 := (not #14)
-#51 := (~ #44 #42)
-#52 := [sk]: #51
-#64 := (~ #11 #63)
-#65 := [sk]: #64
-#12 := (not #11)
-#59 := (~ #12 #14)
-#60 := [nnf-neg #56]: #59
-#72 := [nnf-pos #60 #65 #52 #58]: #71
-#15 := (iff #12 #14)
-#16 := (not #15)
-#39 := (iff #16 #38)
-#40 := [rewrite]: #39
-#37 := [asserted]: #16
-#43 := [mp #37 #40]: #38
-#73 := [mp~ #43 #72]: #70
-#74 := [mp #73 #85]: #83
-#75 := [and-elim #74]: #14
-#567 := [mp #75 #566]: #562
-#232 := (not #562)
-#147 := (or #232 #145)
-#233 := [quant-inst #61]: #147
-#146 := [unit-resolution #233 #567 #231]: false
-#224 := [lemma #146]: #145
-#86 := [and-elim #74]: #80
-#235 := [unit-resolution #86 #224]: #49
-#237 := (or #232 #50)
-#234 := [quant-inst #47]: #237
-[unit-resolution #234 #567 #235]: false
-unsat
-99b6c9d07fc5dd56e24a241d63a8bd5f333486a2 179 0
-#2 := false
-decl f3 :: (-> S2 S1 S1)
-#8 := (:var 0 S1)
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 #8)
-#607 := (pattern #9)
-decl f1 :: S1
-#3 := f1
-#10 := (= #9 f1)
-#613 := (forall (vars (?v0 S1)) (:pat #607) #10)
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-#618 := (not #613)
-#621 := (or #618 #12)
-#624 := (not #621)
-#40 := (not #10)
-#41 := (or #40 #12)
-#106 := (not #41)
-#608 := (forall (vars (?v0 S1)) (:pat #607) #106)
-#595 := (not #608)
-decl ?v0!1 :: S1
-#94 := ?v0!1
-#95 := (f3 f4 ?v0!1)
-#96 := (= #95 f1)
-#97 := (not #96)
-#98 := (or #97 #12)
-decl ?v0!0 :: S1
-#81 := ?v0!0
-#82 := (f3 f4 ?v0!0)
-#83 := (= #82 f1)
-#84 := (not #83)
-#91 := (or #84 #12)
-#283 := [hypothesis]: #84
-#602 := (or #91 #83)
-#603 := [def-axiom]: #602
-#257 := [unit-resolution #603 #283]: #91
-#280 := (or #618 #83)
-#282 := [hypothesis]: #613
-#284 := [quant-inst #81]: #280
-#263 := [unit-resolution #284 #283 #282]: false
-#599 := [lemma #263]: #280
-#388 := [unit-resolution #599 #283]: #618
-#191 := (or #621 #613)
-#192 := [def-axiom]: #191
-#596 := [unit-resolution #192 #388]: #621
-#627 := (or #608 #624)
-#15 := (forall (vars (?v0 S1)) #10)
-#47 := (not #15)
-#48 := (or #47 #12)
-#78 := (not #48)
-#109 := (forall (vars (?v0 S1)) #106)
-#101 := (or #109 #78)
-#628 := (iff #101 #627)
-#625 := (iff #78 #624)
-#622 := (iff #48 #621)
-#619 := (iff #47 #618)
-#616 := (iff #15 #613)
-#614 := (iff #10 #10)
-#615 := [refl]: #614
-#617 := [quant-intro #615]: #616
-#620 := [monotonicity #617]: #619
-#623 := [monotonicity #620]: #622
-#626 := [monotonicity #623]: #625
-#611 := (iff #109 #608)
-#609 := (iff #106 #106)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#629 := [monotonicity #612 #626]: #628
-#74 := (not #12)
-#77 := (and #15 #74)
-#112 := (or #109 #77)
-#102 := (iff #112 #101)
-#87 := (iff #77 #78)
-#88 := [rewrite]: #87
-#127 := [monotonicity #88]: #102
-#120 := (or #97 #84 #12)
-#123 := (and #120 #112)
-#113 := (or #98 #91)
-#114 := (and #113 #112)
-#124 := (iff #114 #123)
-#121 := (iff #113 #120)
-#122 := [rewrite]: #121
-#125 := [monotonicity #122]: #124
-#44 := (exists (vars (?v0 S1)) #41)
-#57 := (not #44)
-#58 := (iff #57 #48)
-#115 := (~ #58 #114)
-#92 := (~ #48 #91)
-#89 := (~ #12 #12)
-#90 := [refl]: #89
-#85 := (~ #47 #84)
-#86 := [sk]: #85
-#93 := [monotonicity #86 #90]: #92
-#79 := (~ #78 #77)
-#75 := (~ #74 #74)
-#76 := [refl]: #75
-#64 := (not #47)
-#66 := (~ #64 #15)
-#71 := (~ #15 #15)
-#69 := (~ #10 #10)
-#70 := [refl]: #69
-#72 := [nnf-pos #70]: #71
-#73 := [nnf-neg #72]: #66
-#80 := [nnf-neg #73 #76]: #79
-#110 := (~ #57 #109)
-#107 := (~ #106 #106)
-#108 := [refl]: #107
-#111 := [nnf-neg #108]: #110
-#103 := (not #57)
-#104 := (~ #103 #98)
-#99 := (~ #44 #98)
-#100 := [sk]: #99
-#105 := [nnf-neg #100]: #104
-#116 := [nnf-pos #105 #111 #80 #93]: #115
-#16 := (implies #15 #12)
-#13 := (implies #10 #12)
-#14 := (exists (vars (?v0 S1)) #13)
-#17 := (iff #14 #16)
-#18 := (not #17)
-#61 := (iff #18 #58)
-#51 := (iff #44 #48)
-#54 := (not #51)
-#59 := (iff #54 #58)
-#60 := [rewrite]: #59
-#55 := (iff #18 #54)
-#52 := (iff #17 #51)
-#49 := (iff #16 #48)
-#50 := [rewrite]: #49
-#45 := (iff #14 #44)
-#42 := (iff #13 #41)
-#43 := [rewrite]: #42
-#46 := [quant-intro #43]: #45
-#53 := [monotonicity #46 #50]: #52
-#56 := [monotonicity #53]: #55
-#62 := [trans #56 #60]: #61
-#39 := [asserted]: #18
-#65 := [mp #39 #62]: #58
-#117 := [mp~ #65 #116]: #114
-#118 := [mp #117 #125]: #123
-#126 := [and-elim #118]: #112
-#128 := [mp #126 #127]: #101
-#630 := [mp #128 #629]: #627
-#255 := [unit-resolution #630 #596]: #608
-#601 := (not #91)
-#268 := (or #595 #601)
-#269 := [quant-inst #81]: #268
-#260 := [unit-resolution #269 #255 #257]: false
-#597 := [lemma #260]: #83
-#604 := (not #98)
-#586 := [hypothesis]: #604
-#598 := (or #98 #96)
-#240 := [def-axiom]: #598
-#587 := [unit-resolution #240 #586]: #96
-#582 := (or #98 #74)
-#244 := [def-axiom]: #582
-#588 := [unit-resolution #244 #586]: #74
-#119 := [and-elim #118]: #120
-#583 := [unit-resolution #119 #588 #587 #597]: false
-#589 := [lemma #583]: #98
-#584 := (or #604 #595)
-#605 := [hypothesis]: #98
-#600 := [hypothesis]: #608
-#606 := (or #595 #604)
-#256 := [quant-inst #94]: #606
-#247 := [unit-resolution #256 #600 #605]: false
-#585 := [lemma #247]: #584
-#226 := [unit-resolution #585 #589]: #595
-#590 := [unit-resolution #630 #226]: #624
-#232 := [unit-resolution #192 #590]: #613
-#277 := (or #621 #74)
-#278 := [def-axiom]: #277
-#593 := [unit-resolution #278 #590]: #74
-#591 := [unit-resolution #119 #593 #597]: #97
-#592 := (or #618 #96)
-#231 := [quant-inst #94]: #592
-[unit-resolution #231 #591 #232]: false
-unsat
-99ed87e27f19515cee990b0e1501f89b03efe0b8 128 0
-#2 := false
-decl f3 :: (-> S3 S2 S1)
-#10 := (:var 0 S2)
-decl f4 :: (-> S4 S1 S3)
-decl f6 :: S1
-#16 := f6
-decl f5 :: S4
-#7 := f5
-#17 := (f4 f5 f6)
-#18 := (f3 #17 #10)
-#582 := (pattern #18)
-decl f1 :: S1
-#3 := f1
-#19 := (= #18 f1)
-#85 := (not #19)
-#583 := (forall (vars (?v0 S2)) (:pat #582) #85)
-decl f7 :: S2
-#21 := f7
-#22 := (f3 #17 f7)
-#23 := (= #22 f1)
-#159 := (= f6 f1)
-#160 := (iff #23 #159)
-#8 := (:var 1 S1)
-#9 := (f4 f5 #8)
-#11 := (f3 #9 #10)
-#575 := (pattern #11)
-#13 := (= #8 f1)
-#12 := (= #11 f1)
-#14 := (iff #12 #13)
-#576 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #575) #14)
-#15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
-#579 := (iff #15 #576)
-#577 := (iff #14 #14)
-#578 := [refl]: #577
-#580 := [quant-intro #578]: #579
-#62 := (~ #15 #15)
-#69 := (~ #14 #14)
-#70 := [refl]: #69
-#63 := [nnf-pos #70]: #62
-#20 := (exists (vars (?v0 S2)) #19)
-#24 := (iff #20 #23)
-#48 := (not #15)
-#49 := (or #48 #24)
-#52 := (not #49)
-#25 := (implies #15 #24)
-#26 := (not #25)
-#53 := (iff #26 #52)
-#50 := (iff #25 #49)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#47 := [asserted]: #26
-#57 := [mp #47 #54]: #52
-#55 := [not-or-elim #57]: #15
-#60 := [mp~ #55 #63]: #15
-#581 := [mp #60 #580]: #576
-#161 := (not #576)
-#237 := (or #161 #160)
-#570 := [quant-inst #16 #21]: #237
-#246 := [unit-resolution #570 #581]: #160
-decl ?v0!0 :: S2
-#75 := ?v0!0
-#76 := (f3 #17 ?v0!0)
-#77 := (= #76 f1)
-#245 := (iff #77 #159)
-#247 := (or #161 #245)
-#238 := [quant-inst #16 #75]: #247
-#236 := [unit-resolution #238 #581]: #245
-#249 := (not #245)
-#208 := (or #249 #159)
-#61 := (not #23)
-#224 := [hypothesis]: #61
-#92 := (or #77 #23)
-#88 := (forall (vars (?v0 S2)) #85)
-#91 := (or #88 #61)
-#93 := (and #92 #91)
-#64 := (not #20)
-#65 := (iff #64 #23)
-#94 := (~ #65 #93)
-#73 := (~ #23 #23)
-#74 := [refl]: #73
-#71 := (~ #61 #61)
-#72 := [refl]: #71
-#89 := (~ #64 #88)
-#86 := (~ #85 #85)
-#87 := [refl]: #86
-#90 := [nnf-neg #87]: #89
-#82 := (not #64)
-#83 := (~ #82 #77)
-#78 := (~ #20 #77)
-#79 := [sk]: #78
-#84 := [nnf-neg #79]: #83
-#95 := [nnf-pos #84 #90 #72 #74]: #94
-#56 := (not #24)
-#66 := (iff #56 #65)
-#67 := [rewrite]: #66
-#58 := [not-or-elim #57]: #56
-#68 := [mp #58 #67]: #65
-#96 := [mp~ #68 #95]: #93
-#99 := [and-elim #96]: #92
-#566 := [unit-resolution #99 #224]: #77
-#252 := (not #77)
-#231 := (or #249 #252 #159)
-#567 := [def-axiom]: #231
-#550 := [unit-resolution #567 #566]: #208
-#212 := [unit-resolution #550 #236]: #159
-#250 := (not #159)
-#571 := (not #160)
-#213 := (or #571 #250)
-#572 := (or #571 #23 #250)
-#573 := [def-axiom]: #572
-#214 := [unit-resolution #573 #224]: #213
-#215 := [unit-resolution #214 #212 #246]: false
-#552 := [lemma #215]: #23
-#588 := (or #583 #61)
-#589 := (iff #91 #588)
-#586 := (iff #88 #583)
-#584 := (iff #85 #85)
-#585 := [refl]: #584
-#587 := [quant-intro #585]: #586
-#590 := [monotonicity #587]: #589
-#100 := [and-elim #96]: #91
-#591 := [mp #100 #590]: #588
-#251 := [unit-resolution #591 #552]: #583
-#564 := (not #583)
-#223 := (or #564 #61)
-#228 := [quant-inst #21]: #223
-[unit-resolution #228 #552 #251]: false
-unsat
-f269326ea50ac00c82433764ea1a5a8988d23a7e 81 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1 S1)
-decl f5 :: S1
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#10 := (= #9 f1)
-decl f6 :: S1
-#19 := f6
-#20 := (f3 f4 f6)
-#21 := (= #20 f1)
-#46 := (not #10)
-#11 := (:var 0 S1)
-#12 := (f3 f4 #11)
-#13 := (= #12 f1)
-#16 := (not #13)
-#17 := (forall (vars (?v0 S1)) #16)
-#14 := (exists (vars (?v0 S1)) #13)
-#15 := (not #14)
-#18 := (if #10 #15 #17)
-#53 := (not #18)
-#62 := (or #53 #46 #21)
-#65 := (not #62)
-#22 := (implies #10 #21)
-#23 := (implies #18 #22)
-#24 := (not #23)
-#68 := (iff #24 #65)
-#47 := (or #46 #21)
-#54 := (or #53 #47)
-#59 := (not #54)
-#66 := (iff #59 #65)
-#63 := (iff #54 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#60 := (iff #24 #59)
-#57 := (iff #23 #54)
-#50 := (implies #18 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #23 #50)
-#48 := (iff #22 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #58]: #60
-#69 := [trans #61 #67]: #68
-#45 := [asserted]: #24
-#70 := [mp #45 #69]: #65
-#72 := [not-or-elim #70]: #10
-#569 := (pattern #12)
-#570 := (forall (vars (?v0 S1)) (:pat #569) #16)
-#573 := (iff #17 #570)
-#571 := (iff #16 #16)
-#572 := [refl]: #571
-#574 := [quant-intro #572]: #573
-#79 := (~ #15 #17)
-#82 := (~ #16 #16)
-#83 := [refl]: #82
-#91 := [nnf-neg #83]: #79
-#89 := (iff #18 #15)
-#1 := true
-#84 := (if true #15 #17)
-#87 := (iff #84 #15)
-#88 := [rewrite]: #87
-#85 := (iff #18 #84)
-#80 := (iff #10 true)
-#81 := [iff-true #72]: #80
-#86 := [monotonicity #81]: #85
-#90 := [trans #86 #88]: #89
-#71 := [not-or-elim #70]: #18
-#78 := [mp #71 #90]: #15
-#76 := [mp~ #78 #91]: #17
-#575 := [mp #76 #574]: #570
-#154 := (not #570)
-#240 := (or #154 #46)
-#155 := [quant-inst #8]: #240
-[unit-resolution #155 #575 #72]: false
-unsat
-d1f4b96a9786562ebfa2e0c93b66635da8fcf6c8 138 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f7 :: S1
-#26 := f7
-#215 := (= f7 f1)
-decl f3 :: (-> S3 S2 S1)
-decl f6 :: S2
-#20 := f6
-decl f4 :: (-> S4 S1 S3)
-decl f5 :: S4
-#7 := f5
-#27 := (f4 f5 f7)
-#31 := (f3 #27 f6)
-#32 := (= #31 f1)
-#301 := (iff #32 #215)
-#10 := (:var 0 S2)
-#8 := (:var 1 S1)
-#9 := (f4 f5 #8)
-#11 := (f3 #9 #10)
-#631 := (pattern #11)
-#13 := (= #8 f1)
-#12 := (= #11 f1)
-#14 := (iff #12 #13)
-#632 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #631) #14)
-#15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
-#635 := (iff #15 #632)
-#633 := (iff #14 #14)
-#634 := [refl]: #633
-#636 := [quant-intro #634]: #635
-#75 := (~ #15 #15)
-#82 := (~ #14 #14)
-#83 := [refl]: #82
-#76 := [nnf-pos #83]: #75
-#18 := (:var 0 S1)
-#19 := (f4 f5 #18)
-#21 := (f3 #19 f6)
-#22 := (= #21 f1)
-#23 := (forall (vars (?v0 S1)) #22)
-#16 := (exists (vars (?v1 S2)) #12)
-#17 := (forall (vars (?v0 S1)) #16)
-#24 := (iff #17 #23)
-#25 := (and #15 #24)
-#28 := (f3 #27 #10)
-#29 := (= #28 f1)
-#30 := (exists (vars (?v0 S2)) #29)
-#33 := (iff #30 #32)
-#57 := (not #25)
-#58 := (or #57 #33)
-#61 := (not #58)
-#34 := (implies #25 #33)
-#35 := (not #34)
-#62 := (iff #35 #61)
-#59 := (iff #34 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#56 := [asserted]: #35
-#66 := [mp #56 #63]: #61
-#64 := [not-or-elim #66]: #25
-#65 := [and-elim #64]: #15
-#73 := [mp~ #65 #76]: #15
-#637 := [mp #73 #636]: #632
-#304 := (not #632)
-#620 := (or #304 #301)
-#279 := [quant-inst #26 #20]: #620
-#306 := [unit-resolution #279 #637]: #301
-decl ?v0!3 :: S2
-#129 := ?v0!3
-#132 := (f3 #27 ?v0!3)
-#133 := (= #132 f1)
-#305 := (iff #133 #215)
-#308 := (or #304 #305)
-#287 := [quant-inst #26 #129]: #308
-#307 := [unit-resolution #287 #637]: #305
-#623 := (not #305)
-#608 := (or #623 #215)
-#117 := (not #32)
-#663 := (pattern #28)
-#141 := (not #29)
-#664 := (forall (vars (?v0 S2)) (:pat #663) #141)
-#216 := [hypothesis]: #32
-#669 := (or #664 #117)
-#144 := (forall (vars (?v0 S2)) #141)
-#147 := (or #144 #117)
-#670 := (iff #147 #669)
-#667 := (iff #144 #664)
-#665 := (iff #141 #141)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#671 := [monotonicity #668]: #670
-#148 := (or #133 #32)
-#149 := (and #148 #147)
-#77 := (not #30)
-#78 := (iff #77 #32)
-#150 := (~ #78 #149)
-#90 := (~ #32 #32)
-#128 := [refl]: #90
-#118 := (~ #117 #117)
-#89 := [refl]: #118
-#145 := (~ #77 #144)
-#142 := (~ #141 #141)
-#143 := [refl]: #142
-#146 := [nnf-neg #143]: #145
-#138 := (not #77)
-#139 := (~ #138 #133)
-#134 := (~ #30 #133)
-#135 := [sk]: #134
-#140 := [nnf-neg #135]: #139
-#151 := [nnf-pos #140 #146 #89 #128]: #150
-#68 := (not #33)
-#79 := (iff #68 #78)
-#80 := [rewrite]: #79
-#69 := [not-or-elim #66]: #68
-#81 := [mp #69 #80]: #78
-#152 := [mp~ #81 #151]: #149
-#156 := [and-elim #152]: #147
-#672 := [mp #156 #671]: #669
-#302 := [unit-resolution #672 #216]: #664
-#619 := (not #664)
-#292 := (or #619 #117)
-#293 := [quant-inst #20]: #292
-#626 := [unit-resolution #293 #216 #302]: false
-#627 := [lemma #626]: #117
-#155 := [and-elim #152]: #148
-#271 := [unit-resolution #155 #627]: #133
-#217 := (not #133)
-#303 := (or #623 #217 #215)
-#294 := [def-axiom]: #303
-#609 := [unit-resolution #294 #271]: #608
-#610 := [unit-resolution #609 #307]: #215
-#625 := (not #215)
-#284 := (not #301)
-#611 := (or #284 #625)
-#621 := (or #284 #32 #625)
-#280 := [def-axiom]: #621
-#612 := [unit-resolution #280 #627]: #611
-[unit-resolution #612 #610 #306]: false
-unsat
-e3789d696531e28820a0701533dd90dd157ebfb7 66 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-#8 := (:var 0 S3)
-decl ?v0!0 :: S2
-#43 := ?v0!0
-#44 := (f3 ?v0!0 #8)
-#537 := (pattern #44)
-decl f4 :: (-> S5 S2 S3)
-decl f5 :: S5
-#10 := f5
-#45 := (f4 f5 ?v0!0)
-#46 := (f3 ?v0!0 #45)
-#39 := (= #44 #46)
-#50 := (not #39)
-#538 := (forall (vars (?v1 S3)) (:pat #537) #50)
-#199 := (not #538)
-#533 := (= #46 #46)
-#529 := (not #533)
-#528 := (or #199 #529)
-#514 := (iff #528 #199)
-#512 := (or #199 false)
-#176 := (iff #512 #199)
-#177 := [rewrite]: #176
-#174 := (iff #528 #512)
-#527 := (iff #529 false)
-#1 := true
-#530 := (not true)
-#185 := (iff #530 false)
-#190 := [rewrite]: #185
-#536 := (iff #529 #530)
-#534 := (iff #533 true)
-#535 := [rewrite]: #534
-#526 := [monotonicity #535]: #536
-#186 := [trans #526 #190]: #527
-#175 := [monotonicity #186]: #174
-#515 := [trans #175 #177]: #514
-#170 := [quant-inst #45]: #528
-#516 := [mp #170 #515]: #199
-#53 := (forall (vars (?v1 S3)) #50)
-#541 := (iff #53 #538)
-#539 := (iff #50 #50)
-#540 := [refl]: #539
-#542 := [quant-intro #540]: #541
-#7 := (:var 1 S2)
-#11 := (f4 f5 #7)
-#12 := (f3 #7 #11)
-#9 := (f3 #7 #8)
-#13 := (= #9 #12)
-#14 := (exists (vars (?v1 S3)) #13)
-#15 := (forall (vars (?v0 S2)) #14)
-#16 := (not #15)
-#56 := (~ #16 #53)
-#40 := (exists (vars (?v1 S3)) #39)
-#47 := (not #40)
-#54 := (~ #47 #53)
-#51 := (~ #50 #50)
-#52 := [refl]: #51
-#55 := [nnf-neg #52]: #54
-#48 := (~ #16 #47)
-#49 := [sk]: #48
-#57 := [trans #49 #55]: #56
-#37 := [asserted]: #16
-#58 := [mp~ #37 #57]: #53
-#543 := [mp #58 #542]: #538
-[unit-resolution #543 #516]: false
-unsat
-d324903e560baa1595f5a14b9effa96572ff81c3 88 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl ?v0!0 :: S2
-#58 := ?v0!0
-#59 := (f3 ?v0!0)
-#60 := (= #59 f1)
-decl ?v0!1 :: S2
-#71 := ?v0!1
-#72 := (f3 ?v0!1)
-#73 := (= #72 f1)
-#155 := (not #73)
-#241 := [hypothesis]: #73
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#571 := (pattern #8)
-#9 := (= #8 f1)
-#13 := (not #9)
-#572 := (forall (vars (?v0 S2)) (:pat #571) #13)
-#14 := (forall (vars (?v0 S2)) #13)
-#575 := (iff #14 #572)
-#573 := (iff #13 #13)
-#574 := [refl]: #573
-#576 := [quant-intro #574]: #575
-#90 := (or #73 #60)
-#93 := (and #14 #90)
-#61 := (not #60)
-#53 := (not #61)
-#78 := (or #73 #53)
-#79 := (or #14 #14)
-#80 := (and #79 #78)
-#94 := (iff #80 #93)
-#91 := (iff #78 #90)
-#88 := (iff #53 #60)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#86 := (iff #79 #14)
-#87 := [rewrite]: #86
-#95 := [monotonicity #87 #92]: #94
-#10 := (exists (vars (?v0 S2)) #9)
-#47 := (iff #10 #14)
-#81 := (~ #47 #80)
-#67 := (~ #14 #14)
-#65 := (~ #13 #13)
-#66 := [refl]: #65
-#68 := [nnf-pos #66]: #67
-#15 := (not #14)
-#55 := (~ #15 #53)
-#62 := [sk]: #55
-#74 := (~ #10 #73)
-#75 := [sk]: #74
-#11 := (not #10)
-#69 := (~ #11 #14)
-#70 := [nnf-neg #66]: #69
-#82 := [nnf-pos #70 #75 #62 #68]: #81
-#12 := (not #11)
-#16 := (iff #12 #15)
-#17 := (not #16)
-#50 := (iff #17 #47)
-#41 := (iff #10 #15)
-#44 := (not #41)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #17 #44)
-#42 := (iff #16 #41)
-#39 := (iff #12 #10)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#51 := [trans #46 #49]: #50
-#38 := [asserted]: #17
-#54 := [mp #38 #51]: #47
-#83 := [mp~ #54 #82]: #80
-#84 := [mp #83 #95]: #93
-#85 := [and-elim #84]: #14
-#577 := [mp #85 #576]: #572
-#242 := (not #572)
-#157 := (or #242 #155)
-#243 := [quant-inst #71]: #157
-#156 := [unit-resolution #243 #577 #241]: false
-#234 := [lemma #156]: #155
-#96 := [and-elim #84]: #90
-#245 := [unit-resolution #96 #234]: #60
-#247 := (or #242 #61)
-#244 := [quant-inst #58]: #247
-[unit-resolution #244 #577 #245]: false
-unsat
-3de5495059db2c9339efaef2e05436267d6715ae 98 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!16)
-#2 := false
-decl f3 :: (-> S2 S3 S4 S5 S6)
-decl f6 :: (-> S8 S4 S5)
-decl ?v2!1 :: (-> S3 S4)
-#63 := (:var 1 S3)
-#64 := (?v2!1 #63)
-decl f7 :: (-> S9 S2 S8)
-decl ?v0!0 :: S2
-#50 := ?v0!0
-decl f8 :: S9
-#14 := f8
-#53 := (f7 f8 ?v0!0)
-#66 := (f6 #53 #64)
-decl f4 :: (-> S7 S2 S3)
-decl f5 :: S7
-#12 := f5
-#52 := (f4 f5 ?v0!0)
-#67 := (f3 ?v0!0 #52 #64 #66)
-#10 := (:var 0 S5)
-#65 := (f3 ?v0!0 #63 #64 #10)
-#68 := (= #65 #67)
-#61 := (not #68)
-#88 := (forall (vars (?v1 S3) (?v3 S5)) #61)
-#543 := (not #88)
-#541 := (?v2!1 #52)
-#530 := (f6 #53 #541)
-#534 := (f3 ?v0!0 #52 #541 #530)
-#525 := (= #534 #534)
-#520 := (not #525)
-#371 := (or #543 #520)
-#517 := (iff #371 #543)
-#514 := (or #543 false)
-#510 := (iff #514 #543)
-#511 := [rewrite]: #510
-#515 := (iff #371 #514)
-#369 := (iff #520 false)
-#1 := true
-#539 := (not true)
-#522 := (iff #539 false)
-#528 := [rewrite]: #522
-#536 := (iff #520 #539)
-#526 := (iff #525 true)
-#555 := [rewrite]: #526
-#527 := [monotonicity #555]: #536
-#370 := [trans #527 #528]: #369
-#516 := [monotonicity #370]: #515
-#518 := [trans #516 #511]: #517
-#513 := [quant-inst #52 #530]: #371
-#512 := [mp #513 #518]: #543
-#75 := (forall (vars (?v3 S5)) #61)
-#80 := (forall (vars (?v1 S3)) #75)
-#89 := (iff #80 #88)
-#90 := [pull-quant]: #89
-#9 := (:var 1 S4)
-#7 := (:var 3 S2)
-#15 := (f7 f8 #7)
-#16 := (f6 #15 #9)
-#13 := (f4 f5 #7)
-#17 := (f3 #7 #13 #9 #16)
-#8 := (:var 2 S3)
-#11 := (f3 #7 #8 #9 #10)
-#18 := (= #11 #17)
-#19 := (exists (vars (?v3 S5)) #18)
-#20 := (forall (vars (?v2 S4)) #19)
-#21 := (exists (vars (?v1 S3)) #20)
-#22 := (forall (vars (?v0 S2)) #21)
-#23 := (not #22)
-#83 := (~ #23 #80)
-#46 := (f6 #53 #9)
-#47 := (f3 ?v0!0 #52 #9 #46)
-#51 := (f3 ?v0!0 #8 #9 #10)
-#54 := (= #51 #47)
-#55 := (exists (vars (?v3 S5)) #54)
-#56 := (forall (vars (?v2 S4)) #55)
-#57 := (exists (vars (?v1 S3)) #56)
-#58 := (not #57)
-#81 := (~ #58 #80)
-#71 := (not #56)
-#78 := (~ #71 #75)
-#69 := (exists (vars (?v3 S5)) #68)
-#70 := (not #69)
-#76 := (~ #70 #75)
-#62 := (~ #61 #61)
-#74 := [refl]: #62
-#77 := [nnf-neg #74]: #76
-#72 := (~ #71 #70)
-#73 := [sk]: #72
-#79 := [trans #73 #77]: #78
-#82 := [nnf-neg #79]: #81
-#59 := (~ #23 #58)
-#60 := [sk]: #59
-#84 := [trans #60 #82]: #83
-#44 := [asserted]: #23
-#85 := [mp~ #44 #84]: #80
-#86 := [mp #85 #90]: #88
-[unit-resolution #86 #512]: false
-unsat
-c05210ac4c810516250c979692bf95e10f79efbc 67 0
-#2 := false
-decl f4 :: (-> S4 S2 S3)
-#10 := (:var 1 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f6 :: S5
-#16 := f6
-#17 := (f5 f6 #10)
-#18 := (f4 #17 #10)
-#15 := (:var 0 S3)
-#19 := (= #15 #18)
-#20 := (not #19)
-#21 := (or #19 #20)
-#22 := (forall (vars (?v1 S3)) #21)
-#7 := (:var 0 S2)
-#11 := (= #7 #10)
-#12 := (not #11)
-#13 := (or #11 #12)
-#14 := (forall (vars (?v1 S2)) #13)
-decl f3 :: S2
-#8 := f3
-#9 := (= #7 f3)
-#23 := (if #9 #14 #22)
-#24 := (exists (vars (?v0 S2)) #23)
-#25 := (not #24)
-#84 := (iff #25 false)
-#1 := true
-#79 := (not true)
-#82 := (iff #79 false)
-#83 := [rewrite]: #82
-#80 := (iff #25 #79)
-#77 := (iff #24 true)
-#72 := (exists (vars (?v0 S2)) true)
-#75 := (iff #72 true)
-#76 := [elim-unused]: #75
-#73 := (iff #24 #72)
-#70 := (iff #23 true)
-#65 := (if #9 true true)
-#68 := (iff #65 true)
-#69 := [rewrite]: #68
-#66 := (iff #23 #65)
-#63 := (iff #22 true)
-#58 := (forall (vars (?v1 S3)) true)
-#61 := (iff #58 true)
-#62 := [elim-unused]: #61
-#59 := (iff #22 #58)
-#56 := (iff #21 true)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#64 := [trans #60 #62]: #63
-#54 := (iff #14 true)
-#49 := (forall (vars (?v1 S2)) true)
-#52 := (iff #49 true)
-#53 := [elim-unused]: #52
-#50 := (iff #14 #49)
-#47 := (iff #13 true)
-#48 := [rewrite]: #47
-#51 := [quant-intro #48]: #50
-#55 := [trans #51 #53]: #54
-#67 := [monotonicity #55 #64]: #66
-#71 := [trans #67 #69]: #70
-#74 := [quant-intro #71]: #73
-#78 := [trans #74 #76]: #77
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#46 := [asserted]: #25
-[mp #46 #85]: false
-unsat
-954b31fcb23d6bdcc4d8c96fd318c51c72effd7f 64 0
-#2 := false
-decl f4 :: (-> S4 S2 S3)
-#10 := (:var 1 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f6 :: S5
-#16 := f6
-#17 := (f5 f6 #10)
-#18 := (f4 #17 #10)
-#15 := (:var 0 S3)
-#19 := (= #15 #18)
-#20 := (not #19)
-#21 := (or #19 #20)
-#22 := (exists (vars (?v1 S3)) #21)
-#7 := (:var 0 S2)
-#11 := (= #7 #10)
-#12 := (not #11)
-#13 := (or #11 #12)
-#14 := (exists (vars (?v1 S2)) #13)
-decl f3 :: S2
-#8 := f3
-#9 := (= #7 f3)
-#23 := (if #9 #14 #22)
-#24 := (exists (vars (?v0 S2)) #23)
-#25 := (not #24)
-#81 := (iff #25 false)
-#1 := true
-#76 := (not true)
-#79 := (iff #76 false)
-#80 := [rewrite]: #79
-#77 := (iff #25 #76)
-#74 := (iff #24 true)
-#49 := (exists (vars (?v1 S2)) true)
-#52 := (iff #49 true)
-#53 := [elim-unused]: #52
-#72 := (iff #24 #49)
-#70 := (iff #23 true)
-#65 := (if #9 true true)
-#68 := (iff #65 true)
-#69 := [rewrite]: #68
-#66 := (iff #23 #65)
-#63 := (iff #22 true)
-#58 := (exists (vars (?v1 S3)) true)
-#61 := (iff #58 true)
-#62 := [elim-unused]: #61
-#59 := (iff #22 #58)
-#56 := (iff #21 true)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#64 := [trans #60 #62]: #63
-#54 := (iff #14 true)
-#50 := (iff #14 #49)
-#47 := (iff #13 true)
-#48 := [rewrite]: #47
-#51 := [quant-intro #48]: #50
-#55 := [trans #51 #53]: #54
-#67 := [monotonicity #55 #64]: #66
-#71 := [trans #67 #69]: #70
-#73 := [quant-intro #71]: #72
-#75 := [trans #73 #53]: #74
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#46 := [asserted]: #25
-[mp #46 #82]: false
-unsat
-f51403ccc25360b96d5b86de9da670599bc2bdd5 154 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#10 := (:var 0 S2)
-#11 := (f3 #10)
-#583 := (pattern #11)
-decl f1 :: S1
-#3 := f1
-#12 := (= #11 f1)
-#95 := (not #12)
-#599 := (forall (vars (?v0 S2)) (:pat #583) #95)
-decl ?v0!1 :: S2
-#72 := ?v0!1
-#73 := (f3 ?v0!1)
-#74 := (= #73 f1)
-decl ?v0!0 :: S2
-#63 := ?v0!0
-#64 := (f3 ?v0!0)
-#56 := (= #64 f1)
-#167 := (iff #56 #74)
-#572 := (not #167)
-#580 := [hypothesis]: #572
-#57 := (iff #56 #12)
-#584 := (forall (vars (?v1 S2)) (:pat #583) #57)
-#54 := (forall (vars (?v1 S2)) #57)
-#587 := (iff #54 #584)
-#585 := (iff #57 #57)
-#586 := [refl]: #585
-#588 := [quant-intro #586]: #587
-#7 := (:var 1 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#13 := (iff #9 #12)
-#14 := (forall (vars (?v1 S2)) #13)
-#15 := (exists (vars (?v0 S2)) #14)
-#55 := (~ #15 #54)
-#68 := (~ #54 #54)
-#66 := (~ #57 #57)
-#67 := [refl]: #66
-#69 := [nnf-pos #67]: #68
-#65 := [sk]: #55
-#70 := [trans #65 #69]: #55
-#17 := (forall (vars (?v0 S2)) #12)
-#16 := (exists (vars (?v0 S2)) #12)
-#18 := (iff #16 #17)
-#42 := (not #15)
-#43 := (or #42 #18)
-#46 := (not #43)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#47 := (iff #20 #46)
-#44 := (iff #19 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#41 := [asserted]: #20
-#51 := [mp #41 #48]: #46
-#49 := [not-or-elim #51]: #15
-#71 := [mp~ #49 #70]: #54
-#589 := [mp #71 #588]: #584
-#254 := (not #584)
-#576 := (or #254 #167)
-#582 := [quant-inst #72]: #576
-#581 := [unit-resolution #582 #589 #580]: false
-#564 := [lemma #581]: #167
-#559 := (or #572 #74)
-#259 := (not #56)
-#169 := [hypothesis]: #259
-#590 := (forall (vars (?v0 S2)) (:pat #583) #12)
-decl ?v0!2 :: S2
-#85 := ?v0!2
-#86 := (f3 ?v0!2)
-#87 := (= #86 f1)
-#246 := (not #87)
-#255 := (or #56 #246)
-#253 := (iff #56 #87)
-#245 := (not #253)
-#168 := [hypothesis]: #245
-#571 := (or #254 #253)
-#244 := [quant-inst #85]: #571
-#364 := [unit-resolution #244 #589 #168]: false
-#573 := [lemma #364]: #253
-#257 := (or #245 #56 #246)
-#258 := [def-axiom]: #257
-#223 := [unit-resolution #258 #573]: #255
-#560 := [unit-resolution #223 #169]: #246
-#595 := (or #87 #590)
-#102 := (or #87 #17)
-#596 := (iff #102 #595)
-#593 := (iff #17 #590)
-#591 := (iff #12 #12)
-#592 := [refl]: #591
-#594 := [quant-intro #592]: #593
-#597 := [monotonicity #594]: #596
-#75 := (not #74)
-#98 := (forall (vars (?v0 S2)) #95)
-#101 := (or #98 #75)
-#103 := (and #102 #101)
-#58 := (not #16)
-#59 := (iff #58 #17)
-#104 := (~ #59 #103)
-#83 := (~ #17 #17)
-#81 := (~ #12 #12)
-#82 := [refl]: #81
-#84 := [nnf-pos #82]: #83
-#76 := (not #17)
-#77 := (~ #76 #75)
-#78 := [sk]: #77
-#99 := (~ #58 #98)
-#96 := (~ #95 #95)
-#97 := [refl]: #96
-#100 := [nnf-neg #97]: #99
-#92 := (not #58)
-#93 := (~ #92 #87)
-#88 := (~ #16 #87)
-#89 := [sk]: #88
-#94 := [nnf-neg #89]: #93
-#105 := [nnf-pos #94 #100 #78 #84]: #104
-#50 := (not #18)
-#60 := (iff #50 #59)
-#61 := [rewrite]: #60
-#52 := [not-or-elim #51]: #50
-#62 := [mp #52 #61]: #59
-#106 := [mp~ #62 #105]: #103
-#109 := [and-elim #106]: #102
-#598 := [mp #109 #597]: #595
-#561 := [unit-resolution #598 #560]: #590
-#216 := (not #590)
-#558 := (or #216 #56)
-#220 := [quant-inst #63]: #558
-#562 := [unit-resolution #220 #561 #169]: false
-#563 := [lemma #562]: #56
-#232 := (or #572 #259 #74)
-#574 := [def-axiom]: #232
-#565 := [unit-resolution #574 #563]: #559
-#569 := [unit-resolution #565 #564]: #74
-#604 := (or #599 #75)
-#605 := (iff #101 #604)
-#602 := (iff #98 #599)
-#600 := (iff #95 #95)
-#601 := [refl]: #600
-#603 := [quant-intro #601]: #602
-#606 := [monotonicity #603]: #605
-#110 := [and-elim #106]: #101
-#607 := [mp #110 #606]: #604
-#567 := [unit-resolution #607 #569]: #599
-#570 := (or #259 #87)
-#256 := (or #245 #259 #87)
-#260 := [def-axiom]: #256
-#556 := [unit-resolution #260 #573]: #570
-#557 := [unit-resolution #556 #563]: #87
-#202 := (not #599)
-#566 := (or #202 #246)
-#568 := [quant-inst #85]: #566
-[unit-resolution #568 #557 #567]: false
-unsat
-3bee024f02f6d6345f10af17fc9f9efaf0eafdfa 91 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#562 := (pattern #8)
-decl f1 :: S1
-#3 := f1
-decl ?v1!0 :: S2
-#54 := ?v1!0
-#46 := (f3 ?v1!0)
-#48 := (= #46 f1)
-#9 := (= #8 f1)
-#35 := (not #9)
-#59 := (or #35 #48)
-#60 := (not #59)
-#563 := (forall (vars (?v0 S2)) (:pat #562) #60)
-#212 := (not #563)
-#55 := (not #48)
-#343 := (or #55 #48)
-#556 := (not #343)
-#201 := (or #212 #556)
-#538 := (iff #201 #212)
-#539 := (or #212 false)
-#542 := (iff #539 #212)
-#543 := [rewrite]: #542
-#540 := (iff #201 #539)
-#199 := (iff #556 false)
-#1 := true
-#552 := (not true)
-#195 := (iff #552 false)
-#537 := [rewrite]: #195
-#211 := (iff #556 #552)
-#210 := (iff #343 true)
-#215 := [rewrite]: #210
-#553 := [monotonicity #215]: #211
-#200 := [trans #553 #537]: #199
-#541 := [monotonicity #200]: #540
-#544 := [trans #541 #543]: #538
-#202 := [quant-inst #54]: #201
-#181 := [mp #202 #544]: #212
-#80 := (forall (vars (?v0 S2)) #60)
-#566 := (iff #80 #563)
-#564 := (iff #60 #60)
-#565 := [refl]: #564
-#567 := [quant-intro #565]: #566
-#73 := (and #9 #55)
-#76 := (forall (vars (?v0 S2)) #73)
-#81 := (iff #76 #80)
-#70 := (iff #73 #60)
-#79 := [rewrite]: #70
-#82 := [quant-intro #79]: #81
-#51 := (not #35)
-#61 := (and #51 #55)
-#65 := (forall (vars (?v0 S2)) #61)
-#77 := (iff #65 #76)
-#74 := (iff #61 #73)
-#71 := (iff #51 #9)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#78 := [quant-intro #75]: #77
-#10 := (forall (vars (?v1 S2)) #9)
-#36 := (or #35 #10)
-#39 := (exists (vars (?v0 S2)) #36)
-#42 := (not #39)
-#66 := (~ #42 #65)
-#62 := (not #36)
-#63 := (~ #62 #61)
-#56 := (not #10)
-#57 := (~ #56 #55)
-#58 := [sk]: #57
-#52 := (~ #51 #51)
-#53 := [refl]: #52
-#64 := [nnf-neg #53 #58]: #63
-#67 := [nnf-neg #64]: #66
-#11 := (implies #9 #10)
-#12 := (exists (vars (?v0 S2)) #11)
-#13 := (not #12)
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (iff #11 #36)
-#38 := [rewrite]: #37
-#41 := [quant-intro #38]: #40
-#44 := [monotonicity #41]: #43
-#34 := [asserted]: #13
-#47 := [mp #34 #44]: #42
-#68 := [mp~ #47 #67]: #65
-#69 := [mp #68 #78]: #76
-#83 := [mp #69 #82]: #80
-#568 := [mp #83 #567]: #563
-[unit-resolution #568 #181]: false
-unsat
-45134300a71a5bae52258f9afddcfb2800b39351 86 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S3 S2 S1)
-decl ?v0!0 :: S2
-#60 := ?v0!0
-decl ?v0!1 :: S3
-#70 := ?v0!1
-#549 := (f3 ?v0!1 ?v0!0)
-#188 := (= #549 f1)
-#189 := (not #188)
-#14 := (:var 0 S2)
-#71 := (f3 ?v0!1 #14)
-#571 := (pattern #71)
-#72 := (= #71 f1)
-#77 := (not #72)
-#572 := (forall (vars (?v1 S2)) (:pat #571) #77)
-#80 := (forall (vars (?v1 S2)) #77)
-#575 := (iff #80 #572)
-#573 := (iff #77 #77)
-#574 := [refl]: #573
-#576 := [quant-intro #574]: #575
-#13 := (:var 1 S3)
-#15 := (f3 #13 #14)
-#16 := (= #15 f1)
-#17 := (exists (vars (?v1 S2)) #16)
-#18 := (forall (vars (?v0 S3)) #17)
-#50 := (not #18)
-#83 := (~ #50 #80)
-#73 := (exists (vars (?v1 S2)) #72)
-#74 := (not #73)
-#81 := (~ #74 #80)
-#78 := (~ #77 #77)
-#79 := [refl]: #78
-#82 := [nnf-neg #79]: #81
-#75 := (~ #50 #74)
-#76 := [sk]: #75
-#84 := [trans #76 #82]: #83
-#8 := (:var 1 S2)
-#7 := (:var 0 S3)
-#9 := (f3 #7 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v1 S3)) #10)
-#12 := (exists (vars (?v0 S2)) #11)
-#42 := (not #12)
-#43 := (or #42 #18)
-#46 := (not #43)
-#19 := (implies #12 #18)
-#20 := (not #19)
-#47 := (iff #20 #46)
-#44 := (iff #19 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#41 := [asserted]: #20
-#51 := [mp #41 #48]: #46
-#52 := [not-or-elim #51]: #50
-#85 := [mp~ #52 #84]: #80
-#577 := [mp #85 #576]: #572
-#550 := (not #572)
-#548 := (or #550 #189)
-#551 := [quant-inst #60]: #548
-#543 := [unit-resolution #551 #577]: #189
-#61 := (f3 #7 ?v0!0)
-#564 := (pattern #61)
-#62 := (= #61 f1)
-#565 := (forall (vars (?v1 S3)) (:pat #564) #62)
-#63 := (forall (vars (?v1 S3)) #62)
-#568 := (iff #63 #565)
-#566 := (iff #62 #62)
-#567 := [refl]: #566
-#569 := [quant-intro #567]: #568
-#54 := (~ #12 #63)
-#66 := (~ #63 #63)
-#64 := (~ #62 #62)
-#65 := [refl]: #64
-#67 := [nnf-pos #65]: #66
-#55 := [sk]: #54
-#68 := [trans #55 #67]: #54
-#49 := [not-or-elim #51]: #12
-#69 := [mp~ #49 #68]: #63
-#570 := [mp #69 #569]: #565
-#557 := (not #565)
-#537 := (or #557 #188)
-#538 := [quant-inst #70]: #537
-[unit-resolution #538 #570 #543]: false
-unsat
-495d743f85fbd7a7c1dc6d3a6d586246681b024f 86 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#579 := (pattern #8)
-decl f1 :: S1
-#3 := f1
-#9 := (= #8 f1)
-#40 := (not #9)
-#586 := (forall (vars (?v0 S2)) (:pat #579) #40)
-#97 := (forall (vars (?v0 S2)) #40)
-#589 := (iff #97 #586)
-#587 := (iff #40 #40)
-#588 := [refl]: #587
-#590 := [quant-intro #588]: #589
-#16 := (exists (vars (?v0 S2)) #9)
-#66 := (not #16)
-#98 := (~ #66 #97)
-#93 := (~ #40 #40)
-#94 := [refl]: #93
-#99 := [nnf-neg #94]: #98
-#10 := (:var 1 S2)
-#11 := (= #7 #10)
-#41 := (or #40 #11)
-#44 := (forall (vars (?v1 S2)) #41)
-#47 := (and #9 #44)
-#50 := (exists (vars (?v0 S2)) #47)
-#56 := (not #50)
-#57 := (or #56 #16)
-#62 := (not #57)
-#12 := (implies #9 #11)
-#13 := (forall (vars (?v1 S2)) #12)
-#14 := (and #9 #13)
-#15 := (exists (vars (?v0 S2)) #14)
-#17 := (implies #15 #16)
-#18 := (not #17)
-#63 := (iff #18 #62)
-#60 := (iff #17 #57)
-#53 := (implies #50 #16)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #17 #53)
-#51 := (iff #15 #50)
-#48 := (iff #14 #47)
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#43 := [rewrite]: #42
-#46 := [quant-intro #43]: #45
-#49 := [monotonicity #46]: #48
-#52 := [quant-intro #49]: #51
-#55 := [monotonicity #52]: #54
-#61 := [trans #55 #59]: #60
-#64 := [monotonicity #61]: #63
-#39 := [asserted]: #18
-#67 := [mp #39 #64]: #62
-#68 := [not-or-elim #67]: #66
-#100 := [mp~ #68 #99]: #97
-#591 := [mp #100 #590]: #586
-decl ?v0!0 :: S2
-#76 := ?v0!0
-#77 := (f3 ?v0!0)
-#78 := (= #77 f1)
-#79 := (= #7 ?v0!0)
-#70 := (or #40 #79)
-#71 := (forall (vars (?v1 S2)) #70)
-#80 := (and #78 #71)
-#81 := (~ #50 #80)
-#89 := (~ #80 #80)
-#87 := (~ #71 #71)
-#85 := (~ #70 #70)
-#86 := [refl]: #85
-#88 := [nnf-pos #86]: #87
-#83 := (~ #78 #78)
-#84 := [refl]: #83
-#90 := [monotonicity #84 #88]: #89
-#82 := [sk]: #81
-#91 := [trans #82 #90]: #81
-#65 := [not-or-elim #67]: #50
-#92 := [mp~ #65 #91]: #80
-#95 := [and-elim #92]: #78
-#163 := (not #78)
-#250 := (not #586)
-#165 := (or #250 #163)
-#251 := [quant-inst #76]: #165
-[unit-resolution #251 #95 #591]: false
-unsat
-aa5dc2c51501c5229e09c29f21c70d436d198117 362 0
-#2 := false
-decl ?v0!2 :: S2
-#125 := ?v0!2
-decl ?v1!3 :: (-> S2 S2)
-#574 := (?v1!3 ?v0!2)
-#583 := (= #574 ?v0!2)
-#555 := (not #583)
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#570 := (f3 #574)
-#575 := (= #570 f1)
-#582 := (not #575)
-#581 := (or #582 #583)
-#577 := (not #581)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#663 := (pattern #8)
-#146 := (?v1!3 #7)
-#150 := (= #146 #7)
-#147 := (f3 #146)
-#148 := (= #147 f1)
-#149 := (not #148)
-#151 := (or #149 #150)
-#152 := (not #151)
-#9 := (= #8 f1)
-#17 := (not #9)
-#158 := (or #17 #152)
-#696 := (forall (vars (?v0 S2)) (:pat #663) #158)
-decl ?v1!0 :: (-> S2 S2)
-#89 := (?v1!0 #7)
-#82 := (f3 #89)
-#84 := (= #82 f1)
-#91 := (not #84)
-#90 := (= #89 #7)
-#92 := (or #90 #91)
-#93 := (not #92)
-#99 := (or #17 #93)
-#701 := (forall (vars (?v0 S2)) (:pat #663) #99)
-#347 := (not #701)
-#615 := (?v1!0 ?v0!2)
-#599 := (f3 #615)
-#600 := (= #599 f1)
-#602 := (not #600)
-#616 := (= #615 ?v0!2)
-#603 := (or #616 #602)
-#601 := (not #603)
-#591 := [hypothesis]: #601
-#500 := (or #603 #600)
-#501 := [def-axiom]: #500
-#580 := [unit-resolution #501 #591]: #600
-#498 := (not #616)
-#499 := (or #603 #498)
-#492 := [def-axiom]: #499
-#561 := [unit-resolution #492 #591]: #498
-#128 := (= #7 ?v0!2)
-#129 := (or #17 #128)
-#664 := (forall (vars (?v1 S2)) (:pat #663) #129)
-#669 := (not #664)
-#126 := (f3 ?v0!2)
-#127 := (= #126 f1)
-#156 := (not #127)
-#672 := (or #156 #669)
-#675 := (not #672)
-decl ?v0!1 :: S2
-#107 := ?v0!1
-#110 := (= #7 ?v0!1)
-#111 := (or #110 #17)
-#678 := (forall (vars (?v1 S2)) (:pat #663) #111)
-#683 := (not #678)
-#108 := (f3 ?v0!1)
-#109 := (= #108 f1)
-#175 := (not #109)
-#686 := (or #175 #683)
-#633 := (?v1!0 ?v0!1)
-#650 := (f3 #633)
-#636 := (= #650 f1)
-#647 := (not #636)
-#355 := (= #633 ?v0!1)
-#637 := (or #355 #647)
-#344 := (not #637)
-#662 := (not #696)
-#319 := (?v1!3 ?v0!1)
-#444 := (= #319 ?v0!1)
-#655 := (f3 #319)
-#657 := (= #655 f1)
-#313 := (not #657)
-#651 := (or #313 #444)
-#689 := (not #686)
-#606 := [hypothesis]: #689
-#338 := (or #686 #678)
-#339 := [def-axiom]: #338
-#612 := [unit-resolution #339 #606]: #678
-#631 := (or #651 #683)
-#654 := (not #444)
-#324 := (not #651)
-#288 := [hypothesis]: #324
-#296 := (or #651 #654)
-#638 := [def-axiom]: #296
-#649 := [unit-resolution #638 #288]: #654
-#653 := (or #651 #657)
-#312 := [def-axiom]: #653
-#356 := [unit-resolution #312 #288]: #657
-#630 := [hypothesis]: #678
-#303 := (or #683 #444 #313)
-#658 := (or #444 #313)
-#640 := (or #683 #658)
-#642 := (iff #640 #303)
-#643 := [rewrite]: #642
-#641 := [quant-inst #319]: #640
-#644 := [mp #641 #643]: #303
-#634 := [unit-resolution #644 #630 #356 #649]: false
-#635 := [lemma #634]: #631
-#487 := [unit-resolution #635 #612]: #651
-#326 := (or #686 #109)
-#337 := [def-axiom]: #326
-#488 := [unit-resolution #337 #606]: #109
-#661 := (or #662 #175 #324)
-#660 := [hypothesis]: #651
-#656 := [hypothesis]: #696
-#362 := [hypothesis]: #109
-#325 := (or #175 #324)
-#652 := (or #662 #325)
-#316 := (iff #652 #661)
-#360 := [rewrite]: #316
-#311 := [quant-inst #107]: #652
-#361 := [mp #311 #360]: #661
-#255 := [unit-resolution #361 #362 #656 #660]: false
-#632 := [lemma #255]: #661
-#447 := [unit-resolution #632 #488 #487]: #662
-#706 := (or #696 #701)
-#103 := (forall (vars (?v0 S2)) #99)
-#162 := (forall (vars (?v0 S2)) #158)
-#165 := (or #162 #103)
-#707 := (iff #165 #706)
-#704 := (iff #103 #701)
-#702 := (iff #99 #99)
-#703 := [refl]: #702
-#705 := [quant-intro #703]: #704
-#699 := (iff #162 #696)
-#697 := (iff #158 #158)
-#698 := [refl]: #697
-#700 := [quant-intro #698]: #699
-#708 := [monotonicity #700 #705]: #707
-#112 := (forall (vars (?v1 S2)) #111)
-#113 := (and #109 #112)
-#130 := (forall (vars (?v1 S2)) #129)
-#131 := (and #127 #130)
-#166 := (or #131 #113)
-#167 := (and #166 #165)
-#10 := (:var 1 S2)
-#11 := (= #7 #10)
-#57 := (or #11 #17)
-#60 := (forall (vars (?v1 S2)) #57)
-#63 := (and #9 #60)
-#66 := (exists (vars (?v0 S2)) #63)
-#45 := (or #17 #11)
-#48 := (forall (vars (?v1 S2)) #45)
-#51 := (and #9 #48)
-#54 := (exists (vars (?v0 S2)) #51)
-#75 := (not #54)
-#76 := (iff #75 #66)
-#168 := (~ #76 #167)
-#114 := (~ #66 #113)
-#122 := (~ #113 #113)
-#120 := (~ #112 #112)
-#118 := (~ #111 #111)
-#119 := [refl]: #118
-#121 := [nnf-pos #119]: #120
-#116 := (~ #109 #109)
-#117 := [refl]: #116
-#123 := [monotonicity #117 #121]: #122
-#115 := [sk]: #114
-#124 := [trans #115 #123]: #114
-#104 := (not #66)
-#105 := (~ #104 #103)
-#100 := (not #63)
-#101 := (~ #100 #99)
-#94 := (not #60)
-#95 := (~ #94 #93)
-#96 := [sk]: #95
-#87 := (~ #17 #17)
-#88 := [refl]: #87
-#102 := [nnf-neg #88 #96]: #101
-#106 := [nnf-neg #102]: #105
-#163 := (~ #75 #162)
-#159 := (not #51)
-#160 := (~ #159 #158)
-#153 := (not #48)
-#154 := (~ #153 #152)
-#155 := [sk]: #154
-#161 := [nnf-neg #88 #155]: #160
-#164 := [nnf-neg #161]: #163
-#143 := (not #75)
-#144 := (~ #143 #131)
-#132 := (~ #54 #131)
-#140 := (~ #131 #131)
-#138 := (~ #130 #130)
-#136 := (~ #129 #129)
-#137 := [refl]: #136
-#139 := [nnf-pos #137]: #138
-#134 := (~ #127 #127)
-#135 := [refl]: #134
-#141 := [monotonicity #135 #139]: #140
-#133 := [sk]: #132
-#142 := [trans #133 #141]: #132
-#145 := [nnf-neg #142]: #144
-#169 := [nnf-pos #145 #164 #106 #124]: #168
-#16 := (not #11)
-#18 := (implies #16 #17)
-#19 := (forall (vars (?v1 S2)) #18)
-#20 := (and #9 #19)
-#21 := (exists (vars (?v0 S2)) #20)
-#12 := (implies #9 #11)
-#13 := (forall (vars (?v1 S2)) #12)
-#14 := (and #9 #13)
-#15 := (exists (vars (?v0 S2)) #14)
-#22 := (iff #15 #21)
-#23 := (not #22)
-#79 := (iff #23 #76)
-#69 := (iff #54 #66)
-#72 := (not #69)
-#77 := (iff #72 #76)
-#78 := [rewrite]: #77
-#73 := (iff #23 #72)
-#70 := (iff #22 #69)
-#67 := (iff #21 #66)
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#58 := (iff #18 #57)
-#59 := [rewrite]: #58
-#62 := [quant-intro #59]: #61
-#65 := [monotonicity #62]: #64
-#68 := [quant-intro #65]: #67
-#55 := (iff #15 #54)
-#52 := (iff #14 #51)
-#49 := (iff #13 #48)
-#46 := (iff #12 #45)
-#47 := [rewrite]: #46
-#50 := [quant-intro #47]: #49
-#53 := [monotonicity #50]: #52
-#56 := [quant-intro #53]: #55
-#71 := [monotonicity #56 #68]: #70
-#74 := [monotonicity #71]: #73
-#80 := [trans #74 #78]: #79
-#44 := [asserted]: #23
-#83 := [mp #44 #80]: #76
-#170 := [mp~ #83 #169]: #167
-#174 := [and-elim #170]: #165
-#709 := [mp #174 #708]: #706
-#595 := [unit-resolution #709 #447]: #701
-#348 := (or #347 #175 #344)
-#359 := (or #175 #344)
-#626 := (or #347 #359)
-#341 := (iff #626 #348)
-#624 := [rewrite]: #341
-#627 := [quant-inst #107]: #626
-#628 := [mp #627 #624]: #348
-#497 := [unit-resolution #628 #488 #595]: #344
-#619 := (or #637 #636)
-#620 := [def-axiom]: #619
-#592 := [unit-resolution #620 #497]: #636
-#625 := (not #355)
-#629 := (or #637 #625)
-#618 := [def-axiom]: #629
-#593 := [unit-resolution #618 #497]: #625
-#621 := (or #683 #355 #647)
-#622 := (or #683 #637)
-#623 := (iff #622 #621)
-#464 := [rewrite]: #623
-#617 := [quant-inst #633]: #622
-#465 := [mp #617 #464]: #621
-#596 := [unit-resolution #465 #612 #593 #592]: false
-#481 := [lemma #596]: #686
-#692 := (or #675 #689)
-#176 := (not #112)
-#177 := (or #175 #176)
-#178 := (not #177)
-#157 := (not #130)
-#97 := (or #156 #157)
-#98 := (not #97)
-#181 := (or #98 #178)
-#693 := (iff #181 #692)
-#690 := (iff #178 #689)
-#687 := (iff #177 #686)
-#684 := (iff #176 #683)
-#681 := (iff #112 #678)
-#679 := (iff #111 #111)
-#680 := [refl]: #679
-#682 := [quant-intro #680]: #681
-#685 := [monotonicity #682]: #684
-#688 := [monotonicity #685]: #687
-#691 := [monotonicity #688]: #690
-#676 := (iff #98 #675)
-#673 := (iff #97 #672)
-#670 := (iff #157 #669)
-#667 := (iff #130 #664)
-#665 := (iff #129 #129)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#671 := [monotonicity #668]: #670
-#674 := [monotonicity #671]: #673
-#677 := [monotonicity #674]: #676
-#694 := [monotonicity #677 #691]: #693
-#182 := (iff #166 #181)
-#179 := (iff #113 #178)
-#180 := [rewrite]: #179
-#171 := (iff #131 #98)
-#172 := [rewrite]: #171
-#183 := [monotonicity #172 #180]: #182
-#173 := [and-elim #170]: #166
-#184 := [mp #173 #183]: #181
-#695 := [mp #184 #694]: #692
-#562 := [unit-resolution #695 #481]: #675
-#248 := (or #672 #664)
-#334 := [def-axiom]: #248
-#564 := [unit-resolution #334 #562]: #664
-#597 := (or #669 #602 #616)
-#486 := (or #602 #616)
-#594 := (or #669 #486)
-#585 := (iff #594 #597)
-#587 := [rewrite]: #585
-#598 := [quant-inst #615]: #594
-#579 := [mp #598 #587]: #597
-#565 := [unit-resolution #579 #564 #561 #580]: false
-#566 := [lemma #565]: #603
-#613 := [hypothesis]: #701
-#247 := (or #672 #127)
-#333 := [def-axiom]: #247
-#443 := [unit-resolution #333 #562]: #127
-#614 := (or #347 #156 #601)
-#604 := (or #156 #601)
-#445 := (or #347 #604)
-#496 := (iff #445 #614)
-#569 := [rewrite]: #496
-#446 := [quant-inst #125]: #445
-#571 := [mp #446 #569]: #614
-#572 := [unit-resolution #571 #443 #613 #566]: false
-#573 := [lemma #572]: #347
-#528 := [unit-resolution #709 #573]: #696
-#567 := (or #662 #156 #577)
-#584 := (or #156 #577)
-#547 := (or #662 #584)
-#550 := (iff #547 #567)
-#551 := [rewrite]: #550
-#548 := [quant-inst #125]: #547
-#552 := [mp #548 #551]: #567
-#529 := [unit-resolution #552 #443 #528]: #577
-#556 := (or #581 #555)
-#557 := [def-axiom]: #556
-#518 := [unit-resolution #557 #529]: #555
-#553 := (or #581 #575)
-#554 := [def-axiom]: #553
-#523 := [unit-resolution #554 #529]: #575
-#549 := (or #669 #582 #583)
-#560 := (or #669 #581)
-#539 := (iff #560 #549)
-#541 := [rewrite]: #539
-#538 := [quant-inst #574]: #560
-#542 := [mp #538 #541]: #549
-[unit-resolution #542 #564 #523 #518]: false
-unsat
-c5872bdd32bd9e895950d088cbea7b6331bcd87a 148 0
-#2 := false
-decl f4 :: S2
-#7 := f4
-decl ?v1!0 :: (-> S2 S2)
-#189 := (?v1!0 f4)
-#191 := (= #189 f4)
-#267 := (not #191)
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#275 := (f3 #189)
-#190 := (= #275 f1)
-#276 := (not #190)
-#277 := (or #276 #191)
-#268 := (not #277)
-#10 := (:var 0 S2)
-#11 := (f3 #10)
-#605 := (pattern #11)
-#104 := (?v1!0 #10)
-#113 := (= #104 #10)
-#105 := (f3 #104)
-#101 := (= #105 f1)
-#112 := (not #101)
-#114 := (or #112 #113)
-#115 := (not #114)
-#12 := (= #11 f1)
-#46 := (not #12)
-#121 := (or #46 #115)
-#612 := (forall (vars (?v0 S2)) (:pat #605) #121)
-#125 := (forall (vars (?v0 S2)) #121)
-#615 := (iff #125 #612)
-#613 := (iff #121 #121)
-#614 := [refl]: #613
-#616 := [quant-intro #614]: #615
-#16 := (:var 1 S2)
-#17 := (= #10 #16)
-#53 := (or #46 #17)
-#56 := (forall (vars (?v1 S2)) #53)
-#59 := (and #12 #56)
-#62 := (exists (vars (?v0 S2)) #59)
-#97 := (not #62)
-#126 := (~ #97 #125)
-#122 := (not #59)
-#123 := (~ #122 #121)
-#116 := (not #56)
-#117 := (~ #116 #115)
-#118 := [sk]: #117
-#103 := (~ #46 #46)
-#100 := [refl]: #103
-#124 := [nnf-neg #100 #118]: #123
-#127 := [nnf-neg #124]: #126
-#13 := (= #10 f4)
-#47 := (or #46 #13)
-#50 := (forall (vars (?v0 S2)) #47)
-#68 := (not #50)
-#8 := (f3 f4)
-#9 := (= #8 f1)
-#77 := (not #9)
-#86 := (or #77 #68 #62)
-#89 := (not #86)
-#18 := (implies #12 #17)
-#19 := (forall (vars (?v1 S2)) #18)
-#20 := (and #12 #19)
-#21 := (exists (vars (?v0 S2)) #20)
-#14 := (implies #12 #13)
-#15 := (forall (vars (?v0 S2)) #14)
-#22 := (implies #15 #21)
-#23 := (implies #9 #22)
-#24 := (not #23)
-#92 := (iff #24 #89)
-#69 := (or #68 #62)
-#78 := (or #77 #69)
-#83 := (not #78)
-#90 := (iff #83 #89)
-#87 := (iff #78 #86)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#84 := (iff #24 #83)
-#81 := (iff #23 #78)
-#74 := (implies #9 #69)
-#79 := (iff #74 #78)
-#80 := [rewrite]: #79
-#75 := (iff #23 #74)
-#72 := (iff #22 #69)
-#65 := (implies #50 #62)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #22 #65)
-#63 := (iff #21 #62)
-#60 := (iff #20 #59)
-#57 := (iff #19 #56)
-#54 := (iff #18 #53)
-#55 := [rewrite]: #54
-#58 := [quant-intro #55]: #57
-#61 := [monotonicity #58]: #60
-#64 := [quant-intro #61]: #63
-#51 := (iff #15 #50)
-#48 := (iff #14 #47)
-#49 := [rewrite]: #48
-#52 := [quant-intro #49]: #51
-#67 := [monotonicity #52 #64]: #66
-#73 := [trans #67 #71]: #72
-#76 := [monotonicity #73]: #75
-#82 := [trans #76 #80]: #81
-#85 := [monotonicity #82]: #84
-#93 := [trans #85 #91]: #92
-#45 := [asserted]: #24
-#94 := [mp #45 #93]: #89
-#98 := [not-or-elim #94]: #97
-#128 := [mp~ #98 #127]: #125
-#617 := [mp #128 #616]: #612
-#95 := [not-or-elim #94]: #9
-#278 := (not #612)
-#282 := (or #278 #77 #268)
-#279 := (or #77 #268)
-#261 := (or #278 #279)
-#599 := (iff #261 #282)
-#255 := [rewrite]: #599
-#597 := [quant-inst #7]: #261
-#386 := [mp #597 #255]: #282
-#245 := [unit-resolution #386 #95 #617]: #268
-#600 := (or #277 #267)
-#601 := [def-axiom]: #600
-#582 := [unit-resolution #601 #245]: #267
-#593 := (or #277 #190)
-#266 := [def-axiom]: #593
-#592 := [unit-resolution #266 #245]: #190
-#606 := (forall (vars (?v0 S2)) (:pat #605) #47)
-#609 := (iff #50 #606)
-#607 := (iff #47 #47)
-#608 := [refl]: #607
-#610 := [quant-intro #608]: #609
-#110 := (~ #50 #50)
-#108 := (~ #47 #47)
-#109 := [refl]: #108
-#111 := [nnf-pos #109]: #110
-#96 := [not-or-elim #94]: #50
-#102 := [mp~ #96 #111]: #50
-#611 := [mp #102 #610]: #606
-#598 := (not #606)
-#604 := (or #598 #276 #191)
-#594 := (or #598 #277)
-#258 := (iff #594 #604)
-#595 := [rewrite]: #258
-#253 := [quant-inst #189]: #594
-#254 := [mp #253 #595]: #604
-[unit-resolution #254 #611 #592 #582]: false
-unsat
-0d91aeb4f1e5219f5da913cca278e0e7cef9a2ce 170 0
-#2 := false
-decl ?v0!0 :: S2
-#97 := ?v0!0
-decl ?v1!1 :: (-> S2 S2)
-#296 := (?v1!1 ?v0!0)
-#298 := (= #296 ?v0!0)
-#621 := (not #298)
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#211 := (f3 #296)
-#297 := (= #211 f1)
-#212 := (not #297)
-#289 := (or #212 #298)
-#300 := (not #289)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#633 := (pattern #8)
-#93 := (?v1!1 #7)
-#110 := (= #93 #7)
-#94 := (f3 #93)
-#108 := (= #94 f1)
-#109 := (not #108)
-#111 := (or #109 #110)
-#112 := (not #111)
-#9 := (= #8 f1)
-#57 := (not #9)
-#118 := (or #57 #112)
-#634 := (forall (vars (?v0 S2)) (:pat #633) #118)
-#122 := (forall (vars (?v0 S2)) #118)
-#637 := (iff #122 #634)
-#635 := (iff #118 #118)
-#636 := [refl]: #635
-#638 := [quant-intro #636]: #637
-#11 := (:var 1 S2)
-#19 := (= #7 #11)
-#58 := (or #57 #19)
-#61 := (forall (vars (?v1 S2)) #58)
-#64 := (and #9 #61)
-#67 := (exists (vars (?v0 S2)) #64)
-#86 := (not #67)
-#123 := (~ #86 #122)
-#119 := (not #64)
-#120 := (~ #119 #118)
-#113 := (not #61)
-#114 := (~ #113 #112)
-#115 := [sk]: #114
-#106 := (~ #57 #57)
-#107 := [refl]: #106
-#121 := [nnf-neg #107 #115]: #120
-#124 := [nnf-neg #121]: #123
-#15 := (= #11 #7)
-#12 := (f3 #11)
-#13 := (= #12 f1)
-#14 := (and #13 #9)
-#47 := (not #14)
-#48 := (or #47 #15)
-#51 := (forall (vars (?v0 S2) (?v1 S2)) #48)
-#10 := (exists (vars (?v0 S2)) #9)
-#54 := (and #10 #51)
-#73 := (not #54)
-#74 := (or #73 #67)
-#79 := (not #74)
-#20 := (implies #9 #19)
-#21 := (forall (vars (?v1 S2)) #20)
-#22 := (and #9 #21)
-#23 := (exists (vars (?v0 S2)) #22)
-#16 := (implies #14 #15)
-#17 := (forall (vars (?v0 S2) (?v1 S2)) #16)
-#18 := (and #10 #17)
-#24 := (implies #18 #23)
-#25 := (not #24)
-#80 := (iff #25 #79)
-#77 := (iff #24 #74)
-#70 := (implies #54 #67)
-#75 := (iff #70 #74)
-#76 := [rewrite]: #75
-#71 := (iff #24 #70)
-#68 := (iff #23 #67)
-#65 := (iff #22 #64)
-#62 := (iff #21 #61)
-#59 := (iff #20 #58)
-#60 := [rewrite]: #59
-#63 := [quant-intro #60]: #62
-#66 := [monotonicity #63]: #65
-#69 := [quant-intro #66]: #68
-#55 := (iff #18 #54)
-#52 := (iff #17 #51)
-#49 := (iff #16 #48)
-#50 := [rewrite]: #49
-#53 := [quant-intro #50]: #52
-#56 := [monotonicity #53]: #55
-#72 := [monotonicity #56 #69]: #71
-#78 := [trans #72 #76]: #77
-#81 := [monotonicity #78]: #80
-#46 := [asserted]: #25
-#84 := [mp #46 #81]: #79
-#87 := [not-or-elim #84]: #86
-#125 := [mp~ #87 #124]: #122
-#639 := [mp #125 #638]: #634
-#98 := (f3 ?v0!0)
-#99 := (= #98 f1)
-#100 := (~ #10 #99)
-#89 := [sk]: #100
-#82 := [not-or-elim #84]: #54
-#83 := [and-elim #82]: #10
-#102 := [mp~ #83 #89]: #99
-#210 := (not #99)
-#303 := (not #634)
-#282 := (or #303 #210 #300)
-#301 := (or #210 #300)
-#618 := (or #303 #301)
-#276 := (iff #618 #282)
-#407 := [rewrite]: #276
-#620 := [quant-inst #97]: #618
-#614 := [mp #620 #407]: #282
-#600 := [unit-resolution #614 #102 #639]: #300
-#622 := (or #289 #621)
-#623 := [def-axiom]: #622
-#307 := [unit-resolution #623 #600]: #621
-#287 := (or #289 #297)
-#288 := [def-axiom]: #287
-#596 := [unit-resolution #288 #600]: #297
-#626 := (pattern #12 #8)
-#116 := (not #13)
-#139 := (or #116 #57 #15)
-#627 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #626) #139)
-#144 := (forall (vars (?v0 S2) (?v1 S2)) #139)
-#630 := (iff #144 #627)
-#628 := (iff #139 #139)
-#629 := [refl]: #628
-#631 := [quant-intro #629]: #630
-#145 := (iff #51 #144)
-#142 := (iff #48 #139)
-#117 := (or #116 #57)
-#136 := (or #117 #15)
-#140 := (iff #136 #139)
-#141 := [rewrite]: #140
-#137 := (iff #48 #136)
-#134 := (iff #47 #117)
-#126 := (not #117)
-#129 := (not #126)
-#132 := (iff #129 #117)
-#133 := [rewrite]: #132
-#130 := (iff #47 #129)
-#127 := (iff #14 #126)
-#128 := [rewrite]: #127
-#131 := [monotonicity #128]: #130
-#135 := [trans #131 #133]: #134
-#138 := [monotonicity #135]: #137
-#143 := [trans #138 #141]: #142
-#146 := [quant-intro #143]: #145
-#103 := (~ #51 #51)
-#90 := (~ #48 #48)
-#101 := [refl]: #90
-#104 := [nnf-pos #101]: #103
-#85 := [and-elim #82]: #51
-#105 := [mp~ #85 #104]: #51
-#147 := [mp #105 #146]: #144
-#632 := [mp #147 #631]: #627
-#611 := (not #627)
-#250 := (or #611 #212 #210 #298)
-#617 := (or #212 #210 #298)
-#251 := (or #611 #617)
-#610 := (iff #251 #250)
-#613 := [rewrite]: #610
-#612 := [quant-inst #296 #97]: #251
-#599 := [mp #612 #613]: #250
-[unit-resolution #599 #102 #632 #596 #307]: false
-unsat
-142a1362d1a72bfbc8fcd56ed6d2ef4df96159b7 169 0
-#2 := false
-decl ?v0!0 :: S2
-#96 := ?v0!0
-decl ?v1!1 :: (-> S2 S2)
-#292 := (?v1!1 ?v0!0)
-#294 := (= #292 ?v0!0)
-#617 := (not #294)
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#207 := (f3 #292)
-#293 := (= #207 f1)
-#208 := (not #293)
-#285 := (or #208 #294)
-#296 := (not #285)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#622 := (pattern #8)
-#127 := (?v1!1 #7)
-#131 := (= #127 #7)
-#128 := (f3 #127)
-#129 := (= #128 f1)
-#130 := (not #129)
-#132 := (or #130 #131)
-#133 := (not #132)
-#9 := (= #8 f1)
-#44 := (not #9)
-#139 := (or #44 #133)
-#629 := (forall (vars (?v0 S2)) (:pat #622) #139)
-#142 := (forall (vars (?v0 S2)) #139)
-#632 := (iff #142 #629)
-#630 := (iff #139 #139)
-#631 := [refl]: #630
-#633 := [quant-intro #631]: #632
-#10 := (:var 1 S2)
-#11 := (= #7 #10)
-#45 := (or #44 #11)
-#48 := (forall (vars (?v1 S2)) #45)
-#51 := (and #9 #48)
-#60 := (not #51)
-#106 := (forall (vars (?v0 S2)) #60)
-#143 := (~ #106 #142)
-#140 := (~ #60 #139)
-#134 := (not #48)
-#135 := (~ #134 #133)
-#136 := [sk]: #135
-#123 := (~ #44 #44)
-#124 := [refl]: #123
-#141 := [nnf-neg #124 #136]: #140
-#144 := [nnf-pos #141]: #143
-decl f4 :: S1
-#16 := f4
-#17 := (= f4 f1)
-#61 := (or #60 #17)
-#66 := (forall (vars (?v0 S2)) #61)
-#107 := (iff #66 #106)
-#104 := (iff #61 #60)
-#99 := (or #60 false)
-#102 := (iff #99 #60)
-#103 := [rewrite]: #102
-#100 := (iff #61 #99)
-#97 := (iff #17 false)
-#88 := (not #17)
-#54 := (exists (vars (?v0 S2)) #51)
-#69 := (and #54 #66)
-#75 := (not #69)
-#76 := (or #75 #17)
-#81 := (not #76)
-#12 := (implies #9 #11)
-#13 := (forall (vars (?v1 S2)) #12)
-#14 := (and #9 #13)
-#18 := (implies #14 #17)
-#19 := (forall (vars (?v0 S2)) #18)
-#15 := (exists (vars (?v0 S2)) #14)
-#20 := (and #15 #19)
-#21 := (implies #20 #17)
-#22 := (not #21)
-#82 := (iff #22 #81)
-#79 := (iff #21 #76)
-#72 := (implies #69 #17)
-#77 := (iff #72 #76)
-#78 := [rewrite]: #77
-#73 := (iff #21 #72)
-#70 := (iff #20 #69)
-#67 := (iff #19 #66)
-#64 := (iff #18 #61)
-#57 := (implies #51 #17)
-#62 := (iff #57 #61)
-#63 := [rewrite]: #62
-#58 := (iff #18 #57)
-#52 := (iff #14 #51)
-#49 := (iff #13 #48)
-#46 := (iff #12 #45)
-#47 := [rewrite]: #46
-#50 := [quant-intro #47]: #49
-#53 := [monotonicity #50]: #52
-#59 := [monotonicity #53]: #58
-#65 := [trans #59 #63]: #64
-#68 := [quant-intro #65]: #67
-#55 := (iff #15 #54)
-#56 := [quant-intro #53]: #55
-#71 := [monotonicity #56 #68]: #70
-#74 := [monotonicity #71]: #73
-#80 := [trans #74 #78]: #79
-#83 := [monotonicity #80]: #82
-#43 := [asserted]: #22
-#86 := [mp #43 #83]: #81
-#89 := [not-or-elim #86]: #88
-#98 := [iff-false #89]: #97
-#101 := [monotonicity #98]: #100
-#105 := [trans #101 #103]: #104
-#108 := [quant-intro #105]: #107
-#84 := [not-or-elim #86]: #69
-#87 := [and-elim #84]: #66
-#95 := [mp #87 #108]: #106
-#145 := [mp~ #95 #144]: #142
-#634 := [mp #145 #633]: #629
-#109 := (f3 ?v0!0)
-#93 := (= #109 f1)
-#94 := (= #7 ?v0!0)
-#91 := (or #44 #94)
-#92 := (forall (vars (?v1 S2)) #91)
-#110 := (and #93 #92)
-#111 := (~ #54 #110)
-#119 := (~ #110 #110)
-#117 := (~ #92 #92)
-#115 := (~ #91 #91)
-#116 := [refl]: #115
-#118 := [nnf-pos #116]: #117
-#113 := (~ #93 #93)
-#114 := [refl]: #113
-#120 := [monotonicity #114 #118]: #119
-#112 := [sk]: #111
-#121 := [trans #112 #120]: #111
-#85 := [and-elim #84]: #54
-#122 := [mp~ #85 #121]: #110
-#125 := [and-elim #122]: #93
-#206 := (not #93)
-#299 := (not #629)
-#278 := (or #299 #206 #296)
-#297 := (or #206 #296)
-#614 := (or #299 #297)
-#272 := (iff #614 #278)
-#403 := [rewrite]: #272
-#616 := [quant-inst #96]: #614
-#610 := [mp #616 #403]: #278
-#599 := [unit-resolution #610 #125 #634]: #296
-#618 := (or #285 #617)
-#619 := [def-axiom]: #618
-#600 := [unit-resolution #619 #599]: #617
-#283 := (or #285 #293)
-#284 := [def-axiom]: #283
-#595 := [unit-resolution #284 #599]: #293
-#623 := (forall (vars (?v1 S2)) (:pat #622) #91)
-#626 := (iff #92 #623)
-#624 := (iff #91 #91)
-#625 := [refl]: #624
-#627 := [quant-intro #625]: #626
-#126 := [and-elim #122]: #92
-#628 := [mp #126 #627]: #623
-#621 := (not #623)
-#611 := (or #621 #208 #294)
-#270 := (or #621 #285)
-#612 := (iff #270 #611)
-#271 := [rewrite]: #612
-#275 := [quant-inst #292]: #270
-#613 := [mp #275 #271]: #611
-[unit-resolution #613 #628 #595 #600]: false
-unsat
-85de22f5139d27f456b9708b8915cc94f19e85fe 76 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: (-> S2 S1)
-decl f6 :: S2
-#15 := f6
-#19 := (f5 f6)
-#20 := (= #19 f1)
-#70 := (not #20)
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#8 := f4
-#16 := (f3 f6 f4)
-#17 := (= #16 f1)
-#7 := (:var 0 S2)
-#11 := (f5 #7)
-#12 := (= #11 f1)
-#9 := (f3 #7 f4)
-#10 := (= #9 f1)
-#44 := (not #10)
-#45 := (or #44 #12)
-#48 := (forall (vars (?v0 S2)) #45)
-#51 := (and #48 #17)
-#57 := (not #51)
-#58 := (or #57 #20)
-#63 := (not #58)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2)) #13)
-#18 := (and #14 #17)
-#21 := (implies #18 #20)
-#22 := (not #21)
-#64 := (iff #22 #63)
-#61 := (iff #21 #58)
-#54 := (implies #51 #20)
-#59 := (iff #54 #58)
-#60 := [rewrite]: #59
-#55 := (iff #21 #54)
-#52 := (iff #18 #51)
-#49 := (iff #14 #48)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#50 := [quant-intro #47]: #49
-#53 := [monotonicity #50]: #52
-#56 := [monotonicity #53]: #55
-#62 := [trans #56 #60]: #61
-#65 := [monotonicity #62]: #64
-#43 := [asserted]: #22
-#68 := [mp #43 #65]: #63
-#71 := [not-or-elim #68]: #70
-#66 := [not-or-elim #68]: #51
-#69 := [and-elim #66]: #17
-#557 := (pattern #11)
-#556 := (pattern #9)
-#558 := (forall (vars (?v0 S2)) (:pat #556 #557) #45)
-#561 := (iff #48 #558)
-#559 := (iff #45 #45)
-#560 := [refl]: #559
-#562 := [quant-intro #560]: #561
-#83 := (~ #48 #48)
-#81 := (~ #45 #45)
-#82 := [refl]: #81
-#84 := [nnf-pos #82]: #83
-#67 := [and-elim #66]: #48
-#73 := [mp~ #67 #84]: #48
-#563 := [mp #73 #562]: #558
-#140 := (not #17)
-#142 := (not #558)
-#228 := (or #142 #140 #20)
-#226 := (or #140 #20)
-#219 := (or #142 #226)
-#231 := (iff #219 #228)
-#232 := [rewrite]: #231
-#230 := [quant-inst #15]: #219
-#229 := [mp #230 #232]: #228
-[unit-resolution #229 #563 #69 #71]: false
-unsat
-ff730e3fbc712bd1b0cb2a46bedef24362b618c7 74 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#8 := f4
-decl f6 :: S2
-#15 := f6
-#18 := (f3 f6 f4)
-#19 := (= #18 f1)
-decl f5 :: (-> S2 S1)
-#16 := (f5 f6)
-#17 := (= #16 f1)
-#20 := (and #17 #19)
-#21 := (not #20)
-#7 := (:var 0 S2)
-#11 := (f5 #7)
-#12 := (= #11 f1)
-#9 := (f3 #7 f4)
-#10 := (= #9 f1)
-#13 := (and #10 #12)
-#14 := (exists (vars (?v0 S2)) #13)
-#22 := (or #14 #21)
-#23 := (not #22)
-#44 := [asserted]: #23
-#49 := [not-or-elim #44]: #20
-#51 := [and-elim #49]: #19
-#50 := [and-elim #49]: #17
-#556 := (pattern #11)
-#555 := (pattern #9)
-#65 := (not #12)
-#64 := (not #10)
-#66 := (or #64 #65)
-#557 := (forall (vars (?v0 S2)) (:pat #555 #556) #66)
-#73 := (forall (vars (?v0 S2)) #66)
-#560 := (iff #73 #557)
-#558 := (iff #66 #66)
-#559 := [refl]: #558
-#561 := [quant-intro #559]: #560
-#59 := (not #13)
-#62 := (forall (vars (?v0 S2)) #59)
-#74 := (iff #62 #73)
-#71 := (iff #59 #66)
-#67 := (not #66)
-#55 := (not #67)
-#69 := (iff #55 #66)
-#70 := [rewrite]: #69
-#56 := (iff #59 #55)
-#57 := (iff #13 #67)
-#58 := [rewrite]: #57
-#68 := [monotonicity #58]: #56
-#72 := [trans #68 #70]: #71
-#75 := [quant-intro #72]: #74
-#47 := (not #14)
-#46 := (~ #47 #62)
-#60 := (~ #59 #59)
-#61 := [refl]: #60
-#52 := [nnf-neg #61]: #46
-#48 := [not-or-elim #44]: #47
-#63 := [mp~ #48 #52]: #62
-#76 := [mp #63 #75]: #73
-#562 := [mp #76 #561]: #557
-#225 := (not #17)
-#139 := (not #19)
-#227 := (not #557)
-#218 := (or #227 #139 #225)
-#140 := (or #139 #225)
-#229 := (or #227 #140)
-#231 := (iff #229 #218)
-#228 := [rewrite]: #231
-#230 := [quant-inst #15]: #229
-#232 := [mp #230 #228]: #218
-[unit-resolution #232 #562 #50 #51]: false
-unsat
-e9bea58a61d26211f4c51dafc9afee93d49dc96f 26 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#12 := (not #11)
-#13 := (or #11 #12)
-#14 := (not #13)
-#43 := (iff #14 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #14 #38)
-#36 := (iff #13 true)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#35 := [asserted]: #14
-[mp #35 #44]: false
-unsat
-969eb616732d66fd3a59354121995900f8f42332 27 0
-#2 := false
-#1 := true
-#8 := (or false true)
-#7 := (and true false)
-#9 := (implies #7 #8)
-#10 := (not #9)
-#48 := (iff #10 false)
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #10 #43)
-#41 := (iff #9 true)
-#36 := (implies false true)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #9 #36)
-#34 := (iff #8 true)
-#35 := [rewrite]: #34
-#32 := (iff #7 false)
-#33 := [rewrite]: #32
-#38 := [monotonicity #33 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#31 := [asserted]: #10
-[mp #31 #49]: false
-unsat
-0554d9d3c0442590754bd0080e373209e9f303c4 23 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#7 := f4
-#8 := (f3 f4)
-#9 := (= #8 f1)
-#10 := (iff #9 #9)
-#11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
-unsat
-984bba573a128d0d85b1bac615cf60bd7590bfe3 25 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#10 := (= #9 f1)
-#11 := (iff #10 #10)
-#12 := (not #11)
-#41 := (iff #12 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (iff #11 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#33 := [asserted]: #12
-[mp #33 #42]: false
-unsat
-49ae3a9a230a943562434a3318ab9bef51520a37 24 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (not #10)
-#12 := (if #10 #10 #11)
-#13 := (not #12)
-#42 := (iff #13 false)
-#1 := true
-#37 := (not true)
-#40 := (iff #37 false)
-#41 := [rewrite]: #40
-#38 := (iff #13 #37)
-#35 := (iff #12 true)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#43 := [trans #39 #41]: #42
-#34 := [asserted]: #13
-[mp #34 #43]: false
-unsat
-dc53d4d1fa6be018411a9832462fb78b5005d0d6 123 0
-#2 := false
-decl f4 :: S2
-#8 := f4
-decl f3 :: S2
-#7 := f3
-#9 := (= f3 f4)
-decl inj!0 :: (-> S3 S2)
-decl f6 :: (-> S2 S3)
-#28 := (f6 f4)
-#179 := (inj!0 #28)
-#265 := (= #179 f4)
-#18 := (:var 0 S2)
-#19 := (f6 #18)
-#112 := (pattern #19)
-#111 := (inj!0 #19)
-#108 := (= #111 #18)
-#594 := (forall (vars (k!0 S2)) (:pat #112) #108)
-#113 := (forall (vars (k!0 S2)) (:pat #112) #108)
-#595 := (iff #113 #594)
-#597 := (iff #594 #594)
-#598 := [rewrite]: #597
-#596 := [rewrite]: #595
-#599 := [trans #596 #598]: #595
-#16 := (:var 1 S2)
-#21 := (= #18 #16)
-#17 := (f6 #16)
-#20 := (= #17 #19)
-#54 := (not #20)
-#55 := (or #54 #21)
-#58 := (forall (vars (?v0 S2) (?v1 S2)) #55)
-#114 := (iff #58 #113)
-#115 := [rewrite]: #114
-#118 := (~ #58 #58)
-#116 := (~ #55 #55)
-#117 := [refl]: #116
-#119 := [nnf-pos #117]: #118
-decl f5 :: S2
-#11 := f5
-#14 := (= f4 f5)
-#15 := (not #14)
-#12 := (= f3 f5)
-#13 := (not #12)
-#10 := (not #9)
-#82 := (and #10 #13 #15 #58)
-#27 := (f6 f3)
-#29 := (= #27 #28)
-#30 := (not #29)
-#85 := (not #82)
-#88 := (or #85 #30)
-#91 := (not #88)
-#22 := (implies #20 #21)
-#23 := (forall (vars (?v0 S2) (?v1 S2)) #22)
-#24 := (and #15 #23)
-#25 := (and #13 #24)
-#26 := (and #10 #25)
-#31 := (implies #26 #30)
-#32 := (not #31)
-#94 := (iff #32 #91)
-#61 := (and #15 #58)
-#64 := (and #13 #61)
-#67 := (and #10 #64)
-#73 := (not #67)
-#74 := (or #73 #30)
-#79 := (not #74)
-#92 := (iff #79 #91)
-#89 := (iff #74 #88)
-#86 := (iff #73 #85)
-#83 := (iff #67 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#80 := (iff #32 #79)
-#77 := (iff #31 #74)
-#70 := (implies #67 #30)
-#75 := (iff #70 #74)
-#76 := [rewrite]: #75
-#71 := (iff #31 #70)
-#68 := (iff #26 #67)
-#65 := (iff #25 #64)
-#62 := (iff #24 #61)
-#59 := (iff #23 #58)
-#56 := (iff #22 #55)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#63 := [monotonicity #60]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#78 := [trans #72 #76]: #77
-#81 := [monotonicity #78]: #80
-#95 := [trans #81 #93]: #94
-#53 := [asserted]: #32
-#96 := [mp #53 #95]: #91
-#97 := [not-or-elim #96]: #82
-#101 := [and-elim #97]: #58
-#110 := [mp~ #101 #119]: #58
-#109 := [mp #110 #115]: #113
-#600 := [mp #109 #599]: #594
-#180 := (not #594)
-#270 := (or #180 #265)
-#267 := [quant-inst #8]: #270
-#250 := [unit-resolution #267 #600]: #265
-#590 := (= f3 #179)
-#178 := (inj!0 #27)
-#256 := (= #178 #179)
-#244 := (= #179 #178)
-#269 := (= #28 #27)
-#102 := [not-or-elim #96]: #29
-#271 := [symm #102]: #269
-#375 := [monotonicity #271]: #244
-#589 := [symm #375]: #256
-#582 := (= f3 #178)
-#264 := (= #178 f3)
-#266 := (or #180 #264)
-#257 := [quant-inst #7]: #266
-#268 := [unit-resolution #257 #600]: #264
-#255 := [symm #268]: #582
-#591 := [trans #255 #589]: #590
-#592 := [trans #591 #250]: #9
-#98 := [and-elim #97]: #10
-[unit-resolution #98 #592]: false
-unsat
-86ad856b2260c7ba2d06c5558baa33155c591c5a 93 0
-#2 := false
-decl f5 :: S3
-#17 := f5
-decl f4 :: S3
-#16 := f4
-#18 := (= f4 f5)
-decl inj!0 :: (-> S2 S4 S3)
-decl f3 :: (-> S2 S3 S4)
-decl f6 :: S2
-#21 := f6
-#23 := (f3 f6 f5)
-#154 := (inj!0 f6 #23)
-#240 := (= #154 f5)
-#8 := (:var 1 S3)
-#78 := (:var 0 S2)
-#89 := (f3 #78 #8)
-#83 := (pattern #89)
-#79 := (inj!0 #78 #89)
-#80 := (= #79 #8)
-#84 := (forall (vars (k!0 S3) (k!1 S2)) (:pat #83) #80)
-#10 := (:var 0 S3)
-#13 := (= #8 #10)
-#7 := (:var 2 S2)
-#11 := (f3 #7 #10)
-#9 := (f3 #7 #8)
-#12 := (= #9 #11)
-#49 := (not #12)
-#50 := (or #49 #13)
-#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #50)
-#81 := (iff #53 #84)
-#82 := [rewrite]: #81
-#87 := (~ #53 #53)
-#85 := (~ #50 #50)
-#86 := [refl]: #85
-#88 := [nnf-pos #86]: #87
-#19 := (not #18)
-#56 := (and #53 #19)
-#22 := (f3 f6 f4)
-#24 := (= #22 #23)
-#25 := (not #24)
-#62 := (not #56)
-#63 := (or #62 #25)
-#68 := (not #63)
-#14 := (implies #12 #13)
-#15 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #14)
-#20 := (and #15 #19)
-#26 := (implies #20 #25)
-#27 := (not #26)
-#69 := (iff #27 #68)
-#66 := (iff #26 #63)
-#59 := (implies #56 #25)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #26 #59)
-#57 := (iff #20 #56)
-#54 := (iff #15 #53)
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#67 := [trans #61 #65]: #66
-#70 := [monotonicity #67]: #69
-#48 := [asserted]: #27
-#73 := [mp #48 #70]: #68
-#71 := [not-or-elim #73]: #56
-#72 := [and-elim #71]: #53
-#77 := [mp~ #72 #88]: #53
-#90 := [mp #77 #82]: #84
-#155 := (not #84)
-#245 := (or #155 #240)
-#242 := [quant-inst #17 #21]: #245
-#225 := [unit-resolution #242 #90]: #240
-#565 := (= f4 #154)
-#153 := (inj!0 f6 #22)
-#231 := (= #153 #154)
-#219 := (= #154 #153)
-#244 := (= #23 #22)
-#75 := [not-or-elim #73]: #24
-#246 := [symm #75]: #244
-#350 := [monotonicity #246]: #219
-#564 := [symm #350]: #231
-#557 := (= f4 #153)
-#239 := (= #153 f4)
-#241 := (or #155 #239)
-#232 := [quant-inst #16 #21]: #241
-#243 := [unit-resolution #232 #90]: #239
-#230 := [symm #243]: #557
-#566 := [trans #230 #564]: #565
-#567 := [trans #566 #225]: #18
-#74 := [and-elim #71]: #19
-[unit-resolution #74 #567]: false
-unsat
-dbb9fd47289aae1ee4ef07ea6bbb0529555aea58 91 0
-#2 := false
-decl f5 :: S2
-#17 := f5
-decl f4 :: S2
-#16 := f4
-#18 := (= f4 f5)
-decl inj!0 :: (-> S3 S4 S2)
-decl f3 :: (-> S2 S3 S4)
-decl f6 :: S3
-#21 := f6
-#23 := (f3 f5 f6)
-#152 := (inj!0 f6 #23)
-#238 := (= #152 f5)
-#8 := (:var 1 S3)
-#10 := (:var 0 S2)
-#11 := (f3 #10 #8)
-#79 := (pattern #11)
-#78 := (inj!0 #8 #11)
-#89 := (= #78 #10)
-#80 := (forall (vars (k!0 S3) (k!1 S2)) (:pat #79) #89)
-#7 := (:var 2 S2)
-#13 := (= #7 #10)
-#9 := (f3 #7 #8)
-#12 := (= #9 #11)
-#49 := (not #12)
-#50 := (or #49 #13)
-#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #50)
-#83 := (iff #53 #80)
-#84 := [rewrite]: #83
-#87 := (~ #53 #53)
-#85 := (~ #50 #50)
-#86 := [refl]: #85
-#88 := [nnf-pos #86]: #87
-#19 := (not #18)
-#56 := (and #53 #19)
-#22 := (f3 f4 f6)
-#24 := (= #22 #23)
-#25 := (not #24)
-#62 := (not #56)
-#63 := (or #62 #25)
-#68 := (not #63)
-#14 := (implies #12 #13)
-#15 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #14)
-#20 := (and #15 #19)
-#26 := (implies #20 #25)
-#27 := (not #26)
-#69 := (iff #27 #68)
-#66 := (iff #26 #63)
-#59 := (implies #56 #25)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #26 #59)
-#57 := (iff #20 #56)
-#54 := (iff #15 #53)
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#67 := [trans #61 #65]: #66
-#70 := [monotonicity #67]: #69
-#48 := [asserted]: #27
-#73 := [mp #48 #70]: #68
-#71 := [not-or-elim #73]: #56
-#72 := [and-elim #71]: #53
-#77 := [mp~ #72 #88]: #53
-#81 := [mp #77 #84]: #80
-#153 := (not #80)
-#243 := (or #153 #238)
-#240 := [quant-inst #21 #17]: #243
-#223 := [unit-resolution #240 #81]: #238
-#563 := (= f4 #152)
-#151 := (inj!0 f6 #22)
-#229 := (= #151 #152)
-#217 := (= #152 #151)
-#242 := (= #23 #22)
-#75 := [not-or-elim #73]: #24
-#244 := [symm #75]: #242
-#348 := [monotonicity #244]: #217
-#562 := [symm #348]: #229
-#555 := (= f4 #151)
-#237 := (= #151 f4)
-#239 := (or #153 #237)
-#230 := [quant-inst #21 #16]: #239
-#241 := [unit-resolution #230 #81]: #237
-#228 := [symm #241]: #555
-#564 := [trans #228 #562]: #563
-#565 := [trans #564 #223]: #18
-#74 := [and-elim #71]: #19
-[unit-resolution #74 #565]: false
-unsat
-2999a68dda8007862d764357a968ba4d913e9986 26 0
-#2 := false
-decl f5 :: S2
-#13 := f5
-decl f3 :: (-> S3 S2 S2)
-decl f4 :: S3
-#7 := f4
-#14 := (f3 f4 f5)
-#15 := (= #14 f5)
-#16 := (not #15)
-#38 := [asserted]: #16
-#8 := (:var 0 S2)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#11 := (= #9 #8)
-#12 := (forall (vars (?v0 S2)) (:pat #10) #11)
-#48 := (~ #12 #12)
-#46 := (~ #11 #11)
-#47 := [refl]: #46
-#49 := [nnf-pos #47]: #48
-#37 := [asserted]: #12
-#40 := [mp~ #37 #49]: #12
-#193 := (not #12)
-#186 := (or #193 #15)
-#197 := [quant-inst #13]: #186
-[unit-resolution #197 #40 #38]: false
-unsat
-57a110a2a64d6237b6a312b1d9c36299cd964fe9 30 0
-#2 := false
-decl f4 :: (-> S3 S4)
-decl f6 :: S3
-#16 := f6
-#17 := (f4 f6)
-decl f3 :: (-> S2 S4)
-decl f5 :: S2
-#14 := f5
-#15 := (f3 f5)
-#18 := (= #15 #17)
-#19 := (not #18)
-#41 := [asserted]: #19
-#9 := (:var 0 S3)
-#10 := (f4 #9)
-#7 := (:var 1 S2)
-#8 := (f3 #7)
-#11 := (pattern #8 #10)
-#12 := (= #8 #10)
-#13 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #11) #12)
-#51 := (~ #13 #13)
-#49 := (~ #12 #12)
-#50 := [refl]: #49
-#52 := [nnf-pos #50]: #51
-#40 := [asserted]: #13
-#43 := [mp~ #40 #52]: #13
-#111 := (not #13)
-#197 := (or #111 #18)
-#112 := [quant-inst #14 #16]: #197
-[unit-resolution #112 #43 #41]: false
-unsat
-504b592c818b50152d0a32c8e6416d9f077ac9e1 47 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: (-> S2 S1)
-decl f5 :: S2
-#15 := f5
-#18 := (f4 f5)
-#19 := (= #18 f1)
-#20 := (not #19)
-#50 := [asserted]: #20
-decl f3 :: (-> S2 S1)
-#16 := (f3 f5)
-#17 := (= #16 f1)
-#49 := [asserted]: #17
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (pattern #8)
-#11 := (f4 #7)
-#12 := (= #11 f1)
-#10 := (= #8 f1)
-#42 := (not #10)
-#43 := (or #42 #12)
-#46 := (forall (vars (?v0 S2)) (:pat #9) #43)
-#63 := (~ #46 #46)
-#61 := (~ #43 #43)
-#62 := [refl]: #61
-#64 := [nnf-pos #62]: #63
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2)) (:pat #9) #13)
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#45 := [rewrite]: #44
-#48 := [quant-intro #45]: #47
-#41 := [asserted]: #14
-#51 := [mp #41 #48]: #46
-#53 := [mp~ #51 #64]: #46
-#120 := (not #17)
-#122 := (not #46)
-#208 := (or #122 #120 #19)
-#206 := (or #120 #19)
-#199 := (or #122 #206)
-#211 := (iff #199 #208)
-#212 := [rewrite]: #211
-#210 := [quant-inst #15]: #199
-#209 := [mp #210 #212]: #208
-[unit-resolution #209 #53 #49 #50]: false
-unsat
-2f0e1a7b2581f301956cfc589414e25e013c2022 80 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: (-> S2 S1)
-decl f6 :: S2
-#18 := f6
-#23 := (f5 f6)
-#24 := (= #23 f1)
-#25 := (not #24)
-#57 := [asserted]: #25
-decl f4 :: (-> S2 S1)
-#21 := (f4 f6)
-#22 := (= #21 f1)
-#55 := [asserted]: #22
-decl f3 :: (-> S2 S1)
-#19 := (f3 f6)
-#20 := (= #19 f1)
-#54 := [asserted]: #20
-#7 := (:var 0 S2)
-#9 := (f4 #7)
-#8 := (f3 #7)
-#10 := (pattern #8 #9)
-#14 := (f5 #7)
-#15 := (= #14 f1)
-#12 := (= #9 f1)
-#73 := (not #12)
-#11 := (= #8 f1)
-#60 := (not #11)
-#80 := (or #60 #73 #15)
-#85 := (forall (vars (?v0 S2)) (:pat #10) #80)
-#13 := (and #11 #12)
-#47 := (not #13)
-#48 := (or #47 #15)
-#51 := (forall (vars (?v0 S2)) (:pat #10) #48)
-#86 := (iff #51 #85)
-#83 := (iff #48 #80)
-#61 := (or #60 #73)
-#77 := (or #61 #15)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #48 #77)
-#75 := (iff #47 #61)
-#62 := (not #61)
-#65 := (not #62)
-#64 := (iff #65 #61)
-#74 := [rewrite]: #64
-#66 := (iff #47 #65)
-#67 := (iff #13 #62)
-#68 := [rewrite]: #67
-#63 := [monotonicity #68]: #66
-#76 := [trans #63 #74]: #75
-#79 := [monotonicity #76]: #78
-#84 := [trans #79 #82]: #83
-#87 := [quant-intro #84]: #86
-#71 := (~ #51 #51)
-#69 := (~ #48 #48)
-#70 := [refl]: #69
-#72 := [nnf-pos #70]: #71
-#16 := (implies #13 #15)
-#17 := (forall (vars (?v0 S2)) (:pat #10) #16)
-#52 := (iff #17 #51)
-#49 := (iff #16 #48)
-#50 := [rewrite]: #49
-#53 := [quant-intro #50]: #52
-#46 := [asserted]: #17
-#56 := [mp #46 #53]: #51
-#59 := [mp~ #56 #72]: #51
-#88 := [mp #59 #87]: #85
-#237 := (not #22)
-#151 := (not #20)
-#239 := (not #85)
-#230 := (or #239 #151 #237 #24)
-#152 := (or #151 #237 #24)
-#241 := (or #239 #152)
-#243 := (iff #241 #230)
-#240 := [rewrite]: #243
-#242 := [quant-inst #18]: #241
-#244 := [mp #242 #240]: #230
-[unit-resolution #244 #88 #54 #55 #57]: false
-unsat
-7566f2da21c88f266bea2fe10fd785422cefa613 94 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl f6 :: S2
-#20 := f6
-#21 := (f3 f6)
-#22 := (= #21 f1)
-#145 := (not #22)
-decl f5 :: (-> S2 S1)
-#26 := (f5 f6)
-#27 := (= #26 f1)
-#231 := (or #145 #27)
-decl f4 :: (-> S2 S1)
-#23 := (f4 f6)
-#24 := (= #23 f1)
-#232 := (not #24)
-#147 := (or #232 #27)
-#233 := (not #147)
-#146 := (not #231)
-#224 := (or #146 #233)
-#235 := (not #224)
-#236 := [hypothesis]: #224
-#7 := (:var 0 S2)
-#10 := (f4 #7)
-#11 := (pattern #10)
-#8 := (f3 #7)
-#9 := (pattern #8)
-#13 := (f5 #7)
-#14 := (= #13 f1)
-#16 := (= #10 f1)
-#54 := (not #16)
-#55 := (or #54 #14)
-#80 := (not #55)
-#12 := (= #8 f1)
-#50 := (not #12)
-#51 := (or #50 #14)
-#69 := (not #51)
-#70 := (or #69 #80)
-#71 := (not #70)
-#72 := (forall (vars (?v0 S2)) (:pat #9 #11) #71)
-#58 := (and #51 #55)
-#61 := (forall (vars (?v0 S2)) (:pat #9 #11) #58)
-#73 := (iff #61 #72)
-#74 := (iff #58 #71)
-#75 := [rewrite]: #74
-#81 := [quant-intro #75]: #73
-#78 := (~ #61 #61)
-#76 := (~ #58 #58)
-#77 := [refl]: #76
-#79 := [nnf-pos #77]: #78
-#17 := (implies #16 #14)
-#15 := (implies #12 #14)
-#18 := (and #15 #17)
-#19 := (forall (vars (?v0 S2)) (:pat #9 #11) #18)
-#62 := (iff #19 #61)
-#59 := (iff #18 #58)
-#56 := (iff #17 #55)
-#57 := [rewrite]: #56
-#52 := (iff #15 #51)
-#53 := [rewrite]: #52
-#60 := [monotonicity #53 #57]: #59
-#63 := [quant-intro #60]: #62
-#49 := [asserted]: #19
-#66 := [mp #49 #63]: #61
-#68 := [mp~ #66 #79]: #61
-#82 := [mp #68 #81]: #72
-#234 := (not #72)
-#238 := (or #234 #235)
-#217 := [quant-inst #20]: #238
-#237 := [unit-resolution #217 #82 #236]: false
-#552 := [lemma #237]: #235
-#560 := (or #224 #231)
-#550 := [def-axiom]: #560
-#194 := [unit-resolution #550 #552]: #231
-#536 := (or #146 #145)
-#28 := (not #27)
-#65 := [asserted]: #28
-#549 := (or #146 #145 #27)
-#222 := [def-axiom]: #549
-#198 := [unit-resolution #222 #65]: #536
-#199 := [unit-resolution #198 #194]: #145
-#209 := (or #224 #147)
-#214 := [def-axiom]: #209
-#200 := [unit-resolution #214 #552]: #147
-#201 := (or #233 #232)
-#559 := (or #233 #232 #27)
-#554 := [def-axiom]: #559
-#538 := [unit-resolution #554 #65]: #201
-#539 := [unit-resolution #538 #200]: #232
-#25 := (or #22 #24)
-#64 := [asserted]: #25
-[unit-resolution #64 #539 #199]: false
-unsat
-83f372862020f387ac902abe14c65133bfb11c52 47 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: (-> S2 S1)
-decl f5 :: S2
-#16 := f5
-#19 := (f4 f5)
-#20 := (= #19 f1)
-#21 := (not #20)
-#51 := [asserted]: #21
-decl f3 :: (-> S2 S1)
-#17 := (f3 f5)
-#18 := (= #17 f1)
-#50 := [asserted]: #18
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (pattern #8)
-#12 := (f4 #7)
-#13 := (= #12 f1)
-#11 := (= #8 f1)
-#43 := (not #11)
-#44 := (or #43 #13)
-#47 := (forall (vars (?v0 S2)) (:pat #9) #44)
-#64 := (~ #47 #47)
-#62 := (~ #44 #44)
-#63 := [refl]: #62
-#65 := [nnf-pos #63]: #64
-#14 := (implies #11 #13)
-#15 := (forall (vars (?v0 S2)) (:pat #9) #14)
-#48 := (iff #15 #47)
-#45 := (iff #14 #44)
-#46 := [rewrite]: #45
-#49 := [quant-intro #46]: #48
-#42 := [asserted]: #15
-#52 := [mp #42 #49]: #47
-#54 := [mp~ #52 #65]: #47
-#120 := (not #18)
-#122 := (not #47)
-#208 := (or #122 #120 #20)
-#206 := (or #120 #20)
-#199 := (or #122 #206)
-#211 := (iff #199 #208)
-#212 := [rewrite]: #211
-#210 := [quant-inst #16]: #199
-#209 := [mp #210 #212]: #208
-[unit-resolution #209 #54 #50 #51]: false
-unsat
-7f77972298a74beb29a94a34ab2a10ec8952f699 54 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: (-> S2 S1)
-decl f5 :: S2
-#15 := f5
-#18 := (f4 f5)
-#19 := (= #18 f1)
-#20 := (not #19)
-#50 := [asserted]: #20
-decl f3 :: (-> S2 S1)
-#16 := (f3 f5)
-#17 := (= #16 f1)
-#49 := [asserted]: #17
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#536 := (pattern #11)
-#9 := (f3 #8)
-#535 := (pattern #9)
-#12 := (= #11 f1)
-#10 := (= #9 f1)
-#42 := (not #10)
-#43 := (or #42 #12)
-#537 := (forall (vars (?v0 S2)) (:pat #535 #536) #43)
-#46 := (forall (vars (?v0 S2)) #43)
-#540 := (iff #46 #537)
-#538 := (iff #43 #43)
-#539 := [refl]: #538
-#541 := [quant-intro #539]: #540
-#63 := (~ #46 #46)
-#61 := (~ #43 #43)
-#62 := [refl]: #61
-#64 := [nnf-pos #62]: #63
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2)) #13)
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#45 := [rewrite]: #44
-#48 := [quant-intro #45]: #47
-#41 := [asserted]: #14
-#51 := [mp #41 #48]: #46
-#53 := [mp~ #51 #64]: #46
-#542 := [mp #53 #541]: #537
-#119 := (not #17)
-#121 := (not #537)
-#207 := (or #121 #119 #19)
-#205 := (or #119 #19)
-#198 := (or #121 #205)
-#210 := (iff #198 #207)
-#211 := [rewrite]: #210
-#209 := [quant-inst #15]: #198
-#208 := [mp #209 #211]: #207
-[unit-resolution #208 #542 #49 #50]: false
-unsat
-9b5c16c73032091e1ec7375b17805aa94497d6a1 16 0
-#2 := false
-#1 := true
-#7 := (implies true true)
-#8 := (not #7)
-#37 := (iff #8 false)
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #8 #32)
-#30 := (iff #7 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #8
-[mp #29 #38]: false
-unsat
-4c88c1927abd3263418bbec2ea6a27c312c22645 16 0
-#2 := false
-#7 := (implies false false)
-#8 := (not #7)
-#37 := (iff #8 false)
-#1 := true
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #8 #32)
-#30 := (iff #7 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #8
-[mp #29 #38]: false
-unsat
-2947b9fb81e1118b8d74090c78db2d5a21b405bf 23 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#7 := f4
-#8 := (f3 f4)
-#9 := (= #8 f1)
-#10 := (implies #9 #9)
-#11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
-unsat
-d21a861104797656b2243093005bad40c57dc562 34 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#12 := (implies #8 #11)
-#13 := (not #12)
-#51 := (iff #13 false)
-#35 := (not #8)
-#36 := (or #35 #11)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #13 #39)
-#37 := (iff #12 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#34 := [asserted]: #13
-[mp #34 #52]: false
-unsat
-27d2c4925d91cba6878c40dc50ee04811f3ebdce 34 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#11 := (or #10 #8)
-#12 := (implies #8 #11)
-#13 := (not #12)
-#51 := (iff #13 false)
-#35 := (not #8)
-#36 := (or #35 #11)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #13 #39)
-#37 := (iff #12 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#34 := [asserted]: #13
-[mp #34 #52]: false
-unsat
-9cdbc92a317e7d7c328d4e9ec144f4d7f38bfbb4 42 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#12 := (implies #8 #11)
-#9 := (not #8)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#59 := (iff #14 false)
-#36 := (or #9 #11)
-#42 := (or #8 #36)
-#47 := (not #42)
-#57 := (iff #47 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #47 #52)
-#50 := (iff #42 true)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#48 := (iff #14 #47)
-#45 := (iff #13 #42)
-#39 := (implies #9 #36)
-#43 := (iff #39 #42)
-#44 := [rewrite]: #43
-#40 := (iff #13 #39)
-#37 := (iff #12 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#46 := [trans #41 #44]: #45
-#49 := [monotonicity #46]: #48
-#60 := [trans #49 #58]: #59
-#35 := [asserted]: #14
-[mp #35 #60]: false
-unsat
-450b6e38cc400f1592be414b6b28c4b433488131 75 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#38 := (not #8)
-#39 := (or #38 #10)
-#95 := (iff #39 false)
-#90 := (or false false)
-#93 := (iff #90 false)
-#94 := [rewrite]: #93
-#91 := (iff #39 #90)
-#81 := (iff #10 false)
-#11 := (not #10)
-#42 := (not #39)
-#64 := (or #38 #10 #42)
-#67 := (not #64)
-#12 := (implies #8 #10)
-#13 := (not #12)
-#14 := (implies #11 #13)
-#15 := (implies #8 #14)
-#16 := (not #15)
-#70 := (iff #16 #67)
-#48 := (or #10 #42)
-#56 := (or #38 #48)
-#61 := (not #56)
-#68 := (iff #61 #67)
-#65 := (iff #56 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#62 := (iff #16 #61)
-#59 := (iff #15 #56)
-#53 := (implies #8 #48)
-#57 := (iff #53 #56)
-#58 := [rewrite]: #57
-#54 := (iff #15 #53)
-#51 := (iff #14 #48)
-#45 := (implies #11 #42)
-#49 := (iff #45 #48)
-#50 := [rewrite]: #49
-#46 := (iff #14 #45)
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#52 := [trans #47 #50]: #51
-#55 := [monotonicity #52]: #54
-#60 := [trans #55 #58]: #59
-#63 := [monotonicity #60]: #62
-#71 := [trans #63 #69]: #70
-#37 := [asserted]: #16
-#72 := [mp #37 #71]: #67
-#74 := [not-or-elim #72]: #11
-#82 := [iff-false #74]: #81
-#88 := (iff #38 false)
-#1 := true
-#83 := (not true)
-#86 := (iff #83 false)
-#87 := [rewrite]: #86
-#84 := (iff #38 #83)
-#79 := (iff #8 true)
-#73 := [not-or-elim #72]: #8
-#80 := [iff-true #73]: #79
-#85 := [monotonicity #80]: #84
-#89 := [trans #85 #87]: #88
-#92 := [monotonicity #89 #82]: #91
-#96 := [trans #92 #94]: #95
-#75 := [not-or-elim #72]: #39
-[mp #75 #96]: false
-unsat
-5c79202855f7fb0e7df333ffc44048260e2027d9 43 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f5 :: (-> S2 S1)
-decl f4 :: S2
-#7 := f4
-#10 := (f5 f4)
-#11 := (= #10 f1)
-decl f3 :: (-> S2 S1)
-#8 := (f3 f4)
-#9 := (= #8 f1)
-#12 := (iff #9 #11)
-#47 := (not #12)
-#62 := (iff #47 false)
-#1 := true
-#57 := (not true)
-#60 := (iff #57 false)
-#61 := [rewrite]: #60
-#58 := (iff #47 #57)
-#55 := (iff #12 true)
-#36 := (not #9)
-#37 := (iff #36 #11)
-#44 := (not #37)
-#52 := (iff #44 #12)
-#53 := [rewrite]: #52
-#38 := (or #37 #12)
-#41 := (not #38)
-#13 := (implies #12 #12)
-#14 := (not #13)
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#35 := [asserted]: #14
-#46 := [mp #35 #43]: #41
-#45 := [not-or-elim #46]: #44
-#54 := [mp #45 #53]: #12
-#56 := [iff-true #54]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#48 := [not-or-elim #46]: #47
-[mp #48 #63]: false
-unsat
-d9f29ce899862b64fac95c45fd1c9213e07c6a55 50 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f3 :: S2
-#7 := f3
-#12 := (= f3 f5)
-decl f4 :: S2
-#8 := f4
-#11 := (= f4 f5)
-#77 := (iff #11 #12)
-#75 := (iff #12 #11)
-#9 := (= f3 f4)
-#37 := (not #11)
-#44 := (not #9)
-#53 := (or #44 #37 #12)
-#56 := (not #53)
-#13 := (implies #11 #12)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#59 := (iff #15 #56)
-#38 := (or #37 #12)
-#45 := (or #44 #38)
-#50 := (not #45)
-#57 := (iff #50 #56)
-#54 := (iff #45 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#60 := [trans #52 #58]: #59
-#36 := [asserted]: #15
-#61 := [mp #36 #60]: #56
-#62 := [not-or-elim #61]: #9
-#76 := [monotonicity #62]: #75
-#78 := [symm #76]: #77
-#63 := [not-or-elim #61]: #11
-#73 := [mp #63 #78]: #12
-#64 := (not #12)
-#65 := [not-or-elim #61]: #64
-[unit-resolution #65 #73]: false
-unsat
-1ef8c48f30160deabb1afaa941172d3fdc476c91 27 0
-#2 := false
-decl f5 :: (-> S2 S3)
-decl f4 :: S2
-#8 := f4
-#11 := (f5 f4)
-decl f3 :: S2
-#7 := f3
-#10 := (f5 f3)
-#12 := (= #10 #11)
-#9 := (= f3 f4)
-#36 := (not #9)
-#37 := (or #36 #12)
-#40 := (not #37)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#35 := [asserted]: #14
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #9
-#54 := [monotonicity #43]: #12
-#44 := (not #12)
-#46 := [not-or-elim #45]: #44
-[unit-resolution #46 #54]: false
-unsat
-1df4d0f227ca61b0473875213498c8bd2447ee70 55 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1 S1)
-decl f5 :: S1
-#12 := f5
-decl f4 :: S2
-#7 := f4
-#13 := (f3 f4 f5)
-#14 := (= #13 f1)
-#57 := (not #14)
-#15 := (= f5 f1)
-#8 := (:var 0 S1)
-#9 := (f3 f4 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v0 S1)) #10)
-#40 := (not #11)
-#47 := (or #40 #14 #15)
-#50 := (not #47)
-#16 := (or #14 #15)
-#17 := (implies #11 #16)
-#18 := (not #17)
-#53 := (iff #18 #50)
-#41 := (or #40 #16)
-#44 := (not #41)
-#51 := (iff #44 #50)
-#48 := (iff #41 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#45 := (iff #18 #44)
-#42 := (iff #17 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#54 := [trans #46 #52]: #53
-#39 := [asserted]: #18
-#55 := [mp #39 #54]: #50
-#58 := [not-or-elim #55]: #57
-#545 := (pattern #9)
-#546 := (forall (vars (?v0 S1)) (:pat #545) #10)
-#549 := (iff #11 #546)
-#547 := (iff #10 #10)
-#548 := [refl]: #547
-#550 := [quant-intro #548]: #549
-#72 := (~ #11 #11)
-#70 := (~ #10 #10)
-#71 := [refl]: #70
-#73 := [nnf-pos #71]: #72
-#56 := [not-or-elim #55]: #11
-#62 := [mp~ #56 #73]: #11
-#551 := [mp #62 #550]: #546
-#215 := (not #546)
-#216 := (or #215 #14)
-#208 := [quant-inst #12]: #216
-[unit-resolution #208 #551 #58]: false
-unsat
-4d29349a83c88fd119fed66c5796e61d5e6eb4b7 83 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S2 S1)
-decl ?v0!0 :: S2
-#54 := ?v0!0
-#63 := (f3 ?v0!0 ?v0!0)
-#55 := (= #63 f1)
-#56 := (not #55)
-#8 := (:var 0 S2)
-#15 := (f3 #8 #8)
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#49 := (not #17)
-#64 := (~ #49 #56)
-#65 := [sk]: #64
-#7 := (:var 1 S2)
-#11 := (f3 #8 #7)
-#12 := (= #11 f1)
-#9 := (f3 #7 #8)
-#10 := (= #9 f1)
-#13 := (and #10 #12)
-#14 := (forall (vars (?v0 S2) (?v1 S2)) #13)
-#41 := (not #14)
-#42 := (or #41 #17)
-#45 := (not #42)
-#18 := (implies #14 #17)
-#19 := (not #18)
-#46 := (iff #19 #45)
-#43 := (iff #18 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#40 := [asserted]: #19
-#50 := [mp #40 #47]: #45
-#51 := [not-or-elim #50]: #49
-#68 := [mp~ #51 #65]: #56
-#556 := (pattern #11)
-#555 := (pattern #9)
-#67 := (not #12)
-#66 := (not #10)
-#69 := (or #66 #67)
-#70 := (not #69)
-#557 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #555 #556) #70)
-#73 := (forall (vars (?v0 S2) (?v1 S2)) #70)
-#560 := (iff #73 #557)
-#558 := (iff #70 #70)
-#559 := [refl]: #558
-#561 := [quant-intro #559]: #560
-#74 := (iff #14 #73)
-#71 := (iff #13 #70)
-#72 := [rewrite]: #71
-#75 := [quant-intro #72]: #74
-#61 := (~ #14 #14)
-#59 := (~ #13 #13)
-#60 := [refl]: #59
-#62 := [nnf-pos #60]: #61
-#48 := [not-or-elim #50]: #14
-#53 := [mp~ #48 #62]: #14
-#76 := [mp #53 #75]: #73
-#562 := [mp #76 #561]: #557
-#232 := (not #557)
-#211 := (or #232 #55)
-#139 := (or #56 #56)
-#225 := (not #139)
-#547 := (or #232 #225)
-#205 := (iff #547 #211)
-#543 := (iff #211 #211)
-#216 := [rewrite]: #543
-#231 := (iff #225 #55)
-#141 := (not #56)
-#229 := (iff #141 #55)
-#230 := [rewrite]: #229
-#227 := (iff #225 #141)
-#140 := (iff #139 #56)
-#226 := [rewrite]: #140
-#218 := [monotonicity #226]: #227
-#228 := [trans #218 #230]: #231
-#336 := [monotonicity #228]: #205
-#217 := [trans #336 #216]: #205
-#549 := [quant-inst #54 #54]: #547
-#550 := [mp #549 #217]: #211
-[unit-resolution #550 #562 #68]: false
-unsat
-263480c8c5909524c36f6198f60c623fbcfc953d 41 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#64 := (iff #11 false)
-#59 := (or false false)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #11 #59)
-#57 := (iff #10 false)
-#48 := (not #10)
-#12 := (not #8)
-#13 := (and #11 #12)
-#37 := (not #13)
-#38 := (or #37 #10)
-#41 := (not #38)
-#14 := (implies #13 #10)
-#15 := (not #14)
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#36 := [asserted]: #15
-#46 := [mp #36 #43]: #41
-#49 := [not-or-elim #46]: #48
-#58 := [iff-false #49]: #57
-#55 := (iff #8 false)
-#44 := [not-or-elim #46]: #13
-#47 := [and-elim #44]: #12
-#56 := [iff-false #47]: #55
-#61 := [monotonicity #56 #58]: #60
-#65 := [trans #61 #63]: #64
-#45 := [and-elim #44]: #11
-[mp #45 #65]: false
-unsat
-050883983ebe99dc3b7f24a011b1724b1b2c4dd9 33 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f6 :: S1
-#14 := f6
-#15 := (= f6 f1)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-#16 := (and #13 #15)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (and #8 #10)
-#17 := (or #11 #16)
-#18 := (implies #17 #17)
-#19 := (not #18)
-#48 := (iff #19 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #19 #43)
-#41 := (iff #18 true)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#40 := [asserted]: #19
-[mp #40 #49]: false
-unsat
-5826af388cc5a35d2efebb6e51d8775678624a36 21 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#8 := 0::Int
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 0::Int)
-#10 := (= #9 #9)
-#11 := (not #10)
-#56 := (iff #11 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #11 #51)
-#49 := (iff #10 true)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#48 := [asserted]: #11
-[mp #48 #57]: false
-unsat
-5e5769d2d58c1ee052480c0b6f4e0dcef2e67169 21 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#8 := 1::Int
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 1::Int)
-#10 := (= #9 #9)
-#11 := (not #10)
-#57 := (iff #11 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #11 #52)
-#50 := (iff #10 true)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#49 := [asserted]: #11
-[mp #49 #58]: false
-unsat
-789dd368fa77887408c1828978af0572cced1843 18 0
-#2 := false
-#8 := 1::Int
-#7 := 0::Int
-#9 := (< 0::Int 1::Int)
-#10 := (not #9)
-#40 := (iff #10 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (iff #9 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #10
-[mp #30 #41]: false
-unsat
-a9af7c16cc7269b2c7732f50c5ea73bba73088c0 18 0
-#2 := false
-#8 := 1::Int
-#7 := 0::Int
-#9 := (<= 0::Int 1::Int)
-#10 := (not #9)
-#40 := (iff #10 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (iff #9 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #10
-[mp #30 #41]: false
-unsat
-850b27c2d840b86ab5903dbe975b63ba1dab1ea7 18 0
-#2 := false
-#8 := 2345678901::Int
-#7 := 123456789::Int
-#9 := (< 123456789::Int 2345678901::Int)
-#10 := (not #9)
-#41 := (iff #10 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #10 #36)
-#34 := (iff #9 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #10
-[mp #31 #42]: false
-unsat
-9e233efcf15a85c9402b5ed5fea5d2ee7d7da37e 32 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 1::Int
-decl f4 :: S2
-#7 := f4
-#12 := (f3 f4 1::Int)
-#8 := 0::Int
-#10 := (+ 0::Int 1::Int)
-#11 := (f3 f4 #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#67 := (iff #14 false)
-#1 := true
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #14 #62)
-#60 := (iff #13 true)
-#55 := (= #12 #12)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #13 #55)
-#52 := (= #10 1::Int)
-#53 := [rewrite]: #52
-#54 := [monotonicity #53]: #13
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#51 := [asserted]: #14
-[mp #51 #68]: false
-unsat
-abc5d7d63d1192687b6f5ea215db822a41f37207 39 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#11 := 1::Int
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#9 := f7
-decl f6 :: S4
-#8 := f6
-#10 := (f5 f6 f7)
-#12 := (+ #10 1::Int)
-decl f4 :: S2
-#7 := f4
-#13 := (f3 f4 #12)
-#14 := (= #13 #13)
-#15 := (not #14)
-#71 := (iff #15 false)
-#1 := true
-#66 := (not true)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #15 #66)
-#64 := (iff #14 true)
-#53 := (+ 1::Int #10)
-#56 := (f3 f4 #53)
-#59 := (= #56 #56)
-#62 := (iff #59 true)
-#63 := [rewrite]: #62
-#60 := (iff #14 #59)
-#57 := (= #13 #56)
-#54 := (= #12 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58 #58]: #60
-#65 := [trans #61 #63]: #64
-#68 := [monotonicity #65]: #67
-#72 := [trans #68 #70]: #71
-#52 := [asserted]: #15
-[mp #52 #72]: false
-unsat
-4f23e7a09b61a0353f978f0745982e2d205dbdd8 35 0
-#2 := false
-#10 := 1::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#11 := (+ #9 1::Int)
-#12 := (< #9 #11)
-#13 := (not #12)
-#70 := (iff #13 false)
-#52 := (+ 1::Int #9)
-#55 := (< #9 #52)
-#58 := (not #55)
-#68 := (iff #58 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #58 #63)
-#61 := (iff #55 true)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#59 := (iff #13 #58)
-#56 := (iff #12 #55)
-#53 := (= #11 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#60 := [monotonicity #57]: #59
-#71 := [trans #60 #69]: #70
-#51 := [asserted]: #13
-[mp #51 #71]: false
-unsat
-21c805ab7618df702910e81acc19099bb8f38592 435 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-decl f8 :: S3
-#14 := f8
-decl f6 :: S4
-#8 := f6
-#15 := (f5 f6 f8)
-#11 := 1::Int
-#65 := (+ 1::Int #15)
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#59 := (+ 1::Int #10)
-#398 := (= #59 #65)
-#365 := (not #398)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#68 := (f3 f4 #65)
-#62 := (f3 f4 #59)
-#71 := (= #62 #68)
-#627 := (f5 f6 #62)
-#444 := (f3 f4 #627)
-#382 := (= #444 #68)
-#376 := (= #68 #444)
-#372 := (= #65 #627)
-#389 := (= #59 #627)
-#306 := -1::Int
-#266 := (* -1::Int #627)
-#267 := (+ #10 #266)
-#616 := (<= #267 -1::Int)
-#604 := (= #267 -1::Int)
-#618 := (>= #10 -1::Int)
-#27 := 0::Int
-#465 := (>= #10 0::Int)
-#443 := (= #10 0::Int)
-#285 := (f3 f4 #10)
-#458 := (f5 f6 #285)
-#466 := (= #458 0::Int)
-#429 := (not #465)
-#445 := [hypothesis]: #429
-#467 := (or #465 #466)
-#28 := (:var 0 Int)
-#30 := (f3 f4 #28)
-#636 := (pattern #30)
-#31 := (f5 f6 #30)
-#36 := (= #31 0::Int)
-#98 := (>= #28 0::Int)
-#128 := (or #98 #36)
-#643 := (forall (vars (?v0 Int)) (:pat #636) #128)
-#131 := (forall (vars (?v0 Int)) #128)
-#646 := (iff #131 #643)
-#644 := (iff #128 #128)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#144 := (~ #131 #131)
-#152 := (~ #128 #128)
-#153 := [refl]: #152
-#145 := [nnf-pos #153]: #144
-#35 := (< #28 0::Int)
-#37 := (implies #35 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#134 := (iff #38 #131)
-#112 := (not #35)
-#113 := (or #112 #36)
-#116 := (forall (vars (?v0 Int)) #113)
-#132 := (iff #116 #131)
-#129 := (iff #113 #128)
-#126 := (iff #112 #98)
-#99 := (not #98)
-#121 := (not #99)
-#124 := (iff #121 #98)
-#125 := [rewrite]: #124
-#122 := (iff #112 #121)
-#119 := (iff #35 #99)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120]: #122
-#127 := [trans #123 #125]: #126
-#130 := [monotonicity #127]: #129
-#133 := [quant-intro #130]: #132
-#117 := (iff #38 #116)
-#114 := (iff #37 #113)
-#115 := [rewrite]: #114
-#118 := [quant-intro #115]: #117
-#135 := [trans #118 #133]: #134
-#111 := [asserted]: #38
-#136 := [mp #111 #135]: #131
-#154 := [mp~ #136 #145]: #131
-#648 := [mp #154 #647]: #643
-#328 := (not #643)
-#470 := (or #328 #465 #466)
-#563 := (or #328 #467)
-#564 := (iff #563 #470)
-#551 := [rewrite]: #564
-#560 := [quant-inst #10]: #563
-#553 := [mp #560 #551]: #470
-#406 := [unit-resolution #553 #648]: #467
-#407 := [unit-resolution #406 #445]: #466
-#414 := (= #10 #458)
-#472 := (= f7 #285)
-#621 := (= #285 f7)
-#22 := (:var 0 S3)
-#23 := (f5 f6 #22)
-#629 := (pattern #23)
-#24 := (f3 f4 #23)
-#25 := (= #24 #22)
-#630 := (forall (vars (?v0 S3)) (:pat #629) #25)
-#26 := (forall (vars (?v0 S3)) #25)
-#633 := (iff #26 #630)
-#631 := (iff #25 #25)
-#632 := [refl]: #631
-#634 := [quant-intro #632]: #633
-#150 := (~ #26 #26)
-#148 := (~ #25 #25)
-#149 := [refl]: #148
-#151 := [nnf-pos #149]: #150
-#86 := [asserted]: #26
-#140 := [mp~ #86 #151]: #26
-#635 := [mp #140 #634]: #630
-#410 := (not #630)
-#617 := (or #410 #621)
-#290 := [quant-inst #9]: #617
-#451 := [unit-resolution #290 #635]: #621
-#427 := [symm #451]: #472
-#416 := [monotonicity #427]: #414
-#417 := [trans #416 #407]: #443
-#418 := (not #443)
-#420 := (or #418 #465)
-#421 := [th-lemma arith triangle-eq]: #420
-#422 := [unit-resolution #421 #445 #417]: false
-#423 := [lemma #422]: #465
-#394 := (or #429 #618)
-#392 := [th-lemma arith farkas 1 1]: #394
-#395 := [unit-resolution #392 #423]: #618
-#619 := (not #618)
-#269 := (or #619 #604)
-#32 := (= #31 #28)
-#102 := (or #99 #32)
-#637 := (forall (vars (?v0 Int)) (:pat #636) #102)
-#105 := (forall (vars (?v0 Int)) #102)
-#640 := (iff #105 #637)
-#638 := (iff #102 #102)
-#639 := [refl]: #638
-#641 := [quant-intro #639]: #640
-#142 := (~ #105 #105)
-#141 := (~ #102 #102)
-#138 := [refl]: #141
-#143 := [nnf-pos #138]: #142
-#29 := (<= 0::Int #28)
-#33 := (implies #29 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#108 := (iff #34 #105)
-#89 := (not #29)
-#90 := (or #89 #32)
-#93 := (forall (vars (?v0 Int)) #90)
-#106 := (iff #93 #105)
-#103 := (iff #90 #102)
-#100 := (iff #89 #99)
-#96 := (iff #29 #98)
-#97 := [rewrite]: #96
-#101 := [monotonicity #97]: #100
-#104 := [monotonicity #101]: #103
-#107 := [quant-intro #104]: #106
-#94 := (iff #34 #93)
-#91 := (iff #33 #90)
-#92 := [rewrite]: #91
-#95 := [quant-intro #92]: #94
-#109 := [trans #95 #107]: #108
-#87 := [asserted]: #34
-#110 := [mp #87 #109]: #105
-#139 := [mp~ #110 #143]: #105
-#642 := [mp #139 #641]: #637
-#608 := (not #637)
-#609 := (or #608 #619 #604)
-#622 := (= #627 #59)
-#291 := (>= #59 0::Int)
-#624 := (not #291)
-#628 := (or #624 #622)
-#610 := (or #608 #628)
-#254 := (iff #610 #609)
-#611 := (or #608 #269)
-#614 := (iff #611 #609)
-#253 := [rewrite]: #614
-#248 := (iff #610 #611)
-#606 := (iff #628 #269)
-#262 := (iff #622 #604)
-#268 := [rewrite]: #262
-#278 := (iff #624 #619)
-#277 := (iff #291 #618)
-#282 := [rewrite]: #277
-#620 := [monotonicity #282]: #278
-#607 := [monotonicity #620 #268]: #606
-#612 := [monotonicity #607]: #248
-#615 := [trans #612 #253]: #254
-#605 := [quant-inst #59]: #610
-#613 := [mp #605 #615]: #609
-#449 := [unit-resolution #613 #642]: #269
-#383 := [unit-resolution #449 #395]: #604
-#415 := (not #604)
-#446 := (or #415 #616)
-#448 := [th-lemma arith triangle-eq]: #446
-#386 := [unit-resolution #448 #383]: #616
-#602 := (>= #267 -1::Int)
-#457 := (or #415 #602)
-#459 := [th-lemma arith triangle-eq]: #457
-#388 := [unit-resolution #459 #383]: #602
-#385 := [th-lemma arith eq-propagate -1 -1 #388 #386]: #389
-#380 := (= #65 #59)
-#390 := [hypothesis]: #398
-#370 := [symm #390]: #380
-#373 := [trans #370 #385]: #372
-#377 := [monotonicity #373]: #376
-#375 := [symm #377]: #382
-#381 := (= #62 #444)
-#424 := (= #444 #62)
-#426 := (or #410 #424)
-#396 := [quant-inst #62]: #426
-#393 := [unit-resolution #396 #635]: #424
-#374 := [symm #393]: #381
-#378 := [trans #374 #375]: #71
-#80 := (not #71)
-#19 := (= f7 f8)
-#623 := (f3 f4 #15)
-#279 := (= #623 f8)
-#625 := (or #410 #279)
-#626 := [quant-inst #14]: #625
-#514 := [unit-resolution #626 #635]: #279
-#434 := (= f7 #623)
-#428 := (= #285 #623)
-#461 := (= #10 #15)
-#307 := (f5 f6 #68)
-#588 := (* -1::Int #307)
-#583 := (+ #15 #588)
-#411 := (<= #583 -1::Int)
-#587 := (= #583 -1::Int)
-#591 := (>= #15 -1::Int)
-#468 := (>= #15 0::Int)
-#544 := (= #15 0::Int)
-#469 := (f5 f6 #623)
-#545 := (= #469 0::Int)
-#548 := (not #468)
-#549 := [hypothesis]: #548
-#542 := (or #468 #545)
-#555 := (or #328 #468 #545)
-#556 := (or #328 #542)
-#557 := (iff #556 #555)
-#546 := [rewrite]: #557
-#552 := [quant-inst #15]: #556
-#547 := [mp #552 #546]: #555
-#533 := [unit-resolution #547 #648]: #542
-#513 := [unit-resolution #533 #549]: #545
-#518 := (= #15 #469)
-#516 := (= f8 #623)
-#517 := [symm #514]: #516
-#519 := [monotonicity #517]: #518
-#520 := [trans #519 #513]: #544
-#521 := (not #544)
-#522 := (or #521 #468)
-#523 := [th-lemma arith triangle-eq]: #522
-#524 := [unit-resolution #523 #549 #520]: false
-#525 := [lemma #524]: #468
-#511 := (or #548 #591)
-#506 := [th-lemma arith farkas 1 1]: #511
-#512 := [unit-resolution #506 #525]: #591
-#585 := (not #591)
-#430 := (or #585 #587)
-#574 := (or #608 #585 #587)
-#590 := (= #307 #65)
-#592 := (>= #65 0::Int)
-#593 := (not #592)
-#594 := (or #593 #590)
-#575 := (or #608 #594)
-#573 := (iff #575 #574)
-#577 := (or #608 #430)
-#578 := (iff #577 #574)
-#579 := [rewrite]: #578
-#571 := (iff #575 #577)
-#431 := (iff #594 #430)
-#582 := (iff #590 #587)
-#589 := [rewrite]: #582
-#586 := (iff #593 #585)
-#595 := (iff #592 #591)
-#584 := [rewrite]: #595
-#581 := [monotonicity #584]: #586
-#432 := [monotonicity #581 #589]: #431
-#572 := [monotonicity #432]: #571
-#580 := [trans #572 #579]: #573
-#576 := [quant-inst #65]: #575
-#409 := [mp #576 #580]: #574
-#536 := [unit-resolution #409 #642]: #430
-#498 := [unit-resolution #536 #512]: #587
-#527 := (not #587)
-#528 := (or #527 #411)
-#530 := [th-lemma arith triangle-eq]: #528
-#494 := [unit-resolution #530 #498]: #411
-#412 := (>= #583 -1::Int)
-#495 := (or #527 #412)
-#496 := [th-lemma arith triangle-eq]: #495
-#499 := [unit-resolution #496 #498]: #412
-#504 := (+ #307 #266)
-#508 := (<= #504 0::Int)
-#526 := (= #307 #627)
-#501 := (= #627 #307)
-#214 := (not #19)
-#510 := [hypothesis]: #214
-#305 := (or #71 #19)
-#81 := (iff #80 #19)
-#16 := (+ #15 1::Int)
-#17 := (f3 f4 #16)
-#12 := (+ #10 1::Int)
-#13 := (f3 f4 #12)
-#18 := (= #13 #17)
-#20 := (iff #18 #19)
-#21 := (not #20)
-#84 := (iff #21 #81)
-#74 := (iff #71 #19)
-#77 := (not #74)
-#82 := (iff #77 #81)
-#83 := [rewrite]: #82
-#78 := (iff #21 #77)
-#75 := (iff #20 #74)
-#72 := (iff #18 #71)
-#69 := (= #17 #68)
-#66 := (= #16 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#63 := (= #13 #62)
-#60 := (= #12 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#73 := [monotonicity #64 #70]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#85 := [trans #79 #83]: #84
-#58 := [asserted]: #21
-#88 := [mp #58 #85]: #81
-#299 := (not #81)
-#303 := (or #71 #19 #299)
-#304 := [def-axiom]: #303
-#302 := [unit-resolution #304 #88]: #305
-#500 := [unit-resolution #302 #510]: #71
-#502 := [monotonicity #500]: #501
-#497 := [symm #502]: #526
-#503 := (not #526)
-#476 := (or #503 #508)
-#477 := [th-lemma arith triangle-eq]: #476
-#478 := [unit-resolution #477 #497]: #508
-#509 := (>= #504 0::Int)
-#371 := (or #503 #509)
-#482 := [th-lemma arith triangle-eq]: #371
-#483 := [unit-resolution #482 #497]: #509
-#603 := (= #627 0::Int)
-#474 := (not #603)
-#565 := (= #307 0::Int)
-#534 := (not #565)
-#455 := (iff #534 #474)
-#473 := (iff #565 #603)
-#488 := (iff #603 #565)
-#493 := [monotonicity #502]: #488
-#419 := [symm #493]: #473
-#479 := [monotonicity #419]: #455
-#462 := (<= #307 0::Int)
-#484 := (not #462)
-#489 := (not #411)
-#485 := (or #484 #548 #489)
-#486 := [th-lemma arith assign-bounds -1 1]: #485
-#487 := [unit-resolution #486 #494 #525]: #484
-#490 := (or #534 #462)
-#491 := [th-lemma arith triangle-eq]: #490
-#492 := [unit-resolution #491 #487]: #534
-#480 := [mp #492 #479]: #474
-#325 := (or #618 #603)
-#221 := (or #328 #618 #603)
-#310 := (or #291 #603)
-#598 := (or #328 #310)
-#601 := (iff #598 #221)
-#321 := (or #328 #325)
-#600 := (iff #321 #221)
-#597 := [rewrite]: #600
-#322 := (iff #598 #321)
-#326 := (iff #310 #325)
-#327 := [monotonicity #282]: #326
-#596 := [monotonicity #327]: #322
-#311 := [trans #596 #597]: #601
-#599 := [quant-inst #59]: #598
-#312 := [mp #599 #311]: #221
-#475 := [unit-resolution #312 #648]: #325
-#481 := [unit-resolution #475 #480]: #618
-#456 := [unit-resolution #449 #481]: #604
-#450 := [unit-resolution #448 #456]: #616
-#460 := [unit-resolution #459 #456]: #602
-#471 := [th-lemma arith eq-propagate -1 -1 1 1 1 1 #460 #450 #483 #478 #499 #494]: #461
-#433 := [monotonicity #471]: #428
-#435 := [trans #427 #433]: #434
-#436 := [trans #435 #514]: #19
-#437 := [unit-resolution #510 #436]: false
-#438 := [lemma #437]: #19
-#301 := (or #80 #214)
-#215 := (or #80 #214 #299)
-#300 := [def-axiom]: #215
-#292 := [unit-resolution #300 #88]: #301
-#391 := [unit-resolution #292 #438]: #80
-#379 := [unit-resolution #391 #378]: false
-#367 := [lemma #379]: #365
-#399 := (* -1::Int #65)
-#405 := (+ #59 #399)
-#384 := (<= #405 0::Int)
-#439 := (* -1::Int #15)
-#440 := (+ #10 #439)
-#441 := (<= #440 0::Int)
-#368 := [monotonicity #438]: #461
-#366 := (not #461)
-#369 := (or #366 #441)
-#351 := [th-lemma arith triangle-eq]: #369
-#353 := [unit-resolution #351 #368]: #441
-#354 := (not #441)
-#355 := (or #384 #354)
-#356 := [th-lemma arith assign-bounds -1]: #355
-#357 := [unit-resolution #356 #353]: #384
-#387 := (>= #405 0::Int)
-#442 := (>= #440 0::Int)
-#358 := (or #366 #442)
-#359 := [th-lemma arith triangle-eq]: #358
-#360 := [unit-resolution #359 #368]: #442
-#361 := (not #442)
-#362 := (or #387 #361)
-#363 := [th-lemma arith assign-bounds -1]: #362
-#352 := [unit-resolution #363 #360]: #387
-#341 := (not #387)
-#364 := (not #384)
-#343 := (or #398 #364 #341)
-#344 := [th-lemma arith triangle-eq]: #343
-#345 := [unit-resolution #344 #352 #357]: #398
-[unit-resolution #345 #367]: false
-unsat
-acd75482eb0fadad2769b1851e88fa0d92a18b2f 57 0
-#2 := false
-#13 := 1::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#16 := (+ #11 1::Int)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#15 := (+ #9 1::Int)
-#17 := (+ #15 #16)
-#12 := (+ #9 #11)
-#14 := (+ #12 1::Int)
-#18 := (< #14 #17)
-#19 := (not #18)
-#91 := (iff #19 false)
-#70 := 2::Int
-#71 := (+ 2::Int #12)
-#58 := (+ 1::Int #12)
-#76 := (< #58 #71)
-#79 := (not #76)
-#89 := (iff #79 false)
-#1 := true
-#83 := (not true)
-#87 := (iff #83 false)
-#88 := [rewrite]: #87
-#85 := (iff #79 #83)
-#82 := (iff #76 true)
-#84 := [rewrite]: #82
-#86 := [monotonicity #84]: #85
-#90 := [trans #86 #88]: #89
-#80 := (iff #19 #79)
-#77 := (iff #18 #76)
-#74 := (= #17 #71)
-#64 := (+ 1::Int #11)
-#61 := (+ 1::Int #9)
-#67 := (+ #61 #64)
-#72 := (= #67 #71)
-#73 := [rewrite]: #72
-#68 := (= #17 #67)
-#65 := (= #16 #64)
-#66 := [rewrite]: #65
-#62 := (= #15 #61)
-#63 := [rewrite]: #62
-#69 := [monotonicity #63 #66]: #68
-#75 := [trans #69 #73]: #74
-#59 := (= #14 #58)
-#60 := [rewrite]: #59
-#78 := [monotonicity #60 #75]: #77
-#81 := [monotonicity #78]: #80
-#92 := [trans #81 #90]: #91
-#57 := [asserted]: #19
-[mp #57 #92]: false
-unsat
-cafcbe1d613718219fa1714ac3be1c8043d2d395 51 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#16 := (:var 0 S3)
-decl f6 :: S4
-#8 := f6
-#17 := (f5 f6 #16)
-#607 := (pattern #17)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#18 := (f3 f4 #17)
-#19 := (= #18 #16)
-#608 := (forall (vars (?v0 S3)) (:pat #607) #19)
-#20 := (forall (vars (?v0 S3)) #19)
-#611 := (iff #20 #608)
-#609 := (iff #19 #19)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#127 := (~ #20 #20)
-#125 := (~ #19 #19)
-#126 := [refl]: #125
-#128 := [nnf-pos #126]: #127
-#63 := [asserted]: #20
-#117 := [mp~ #63 #128]: #20
-#613 := [mp #117 #612]: #608
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#54 := (f3 f4 #10)
-#57 := (= #54 f7)
-#60 := (not #57)
-#11 := 0::Int
-#12 := (+ #10 0::Int)
-#13 := (f3 f4 #12)
-#14 := (= #13 f7)
-#15 := (not #14)
-#61 := (iff #15 #60)
-#58 := (iff #14 #57)
-#55 := (= #13 #54)
-#52 := (= #12 #10)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#59 := [monotonicity #56]: #58
-#62 := [monotonicity #59]: #61
-#51 := [asserted]: #15
-#65 := [mp #51 #62]: #60
-#278 := (not #608)
-#279 := (or #278 #57)
-#270 := [quant-inst #9]: #279
-[unit-resolution #270 #65 #613]: false
-unsat
-1dfcd4e08e6f8d1a1620a5d9deeafd855aa26e59 51 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#16 := (:var 0 S3)
-decl f6 :: S4
-#9 := f6
-#17 := (f5 f6 #16)
-#607 := (pattern #17)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#18 := (f3 f4 #17)
-#19 := (= #18 #16)
-#608 := (forall (vars (?v0 S3)) (:pat #607) #19)
-#20 := (forall (vars (?v0 S3)) #19)
-#611 := (iff #20 #608)
-#609 := (iff #19 #19)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#127 := (~ #20 #20)
-#125 := (~ #19 #19)
-#126 := [refl]: #125
-#128 := [nnf-pos #126]: #127
-#63 := [asserted]: #20
-#117 := [mp~ #63 #128]: #20
-#613 := [mp #117 #612]: #608
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#54 := (f3 f4 #11)
-#57 := (= #54 f7)
-#60 := (not #57)
-#8 := 0::Int
-#12 := (+ 0::Int #11)
-#13 := (f3 f4 #12)
-#14 := (= #13 f7)
-#15 := (not #14)
-#61 := (iff #15 #60)
-#58 := (iff #14 #57)
-#55 := (= #13 #54)
-#52 := (= #12 #11)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#59 := [monotonicity #56]: #58
-#62 := [monotonicity #59]: #61
-#51 := [asserted]: #15
-#65 := [mp #51 #62]: #60
-#278 := (not #608)
-#279 := (or #278 #57)
-#270 := [quant-inst #10]: #279
-[unit-resolution #270 #65 #613]: false
-unsat
-807ee369d1a6496ab946d19ae1b2533180edb6b7 41 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#9 := f7
-decl f6 :: S4
-#8 := f6
-#10 := (f5 f6 f7)
-decl f8 :: S3
-#11 := f8
-#12 := (f5 f6 f8)
-#15 := (+ #12 #10)
-decl f4 :: S2
-#7 := f4
-#16 := (f3 f4 #15)
-#13 := (+ #10 #12)
-#14 := (f3 f4 #13)
-#17 := (= #14 #16)
-#18 := (not #17)
-#72 := (iff #18 false)
-#1 := true
-#67 := (not true)
-#70 := (iff #67 false)
-#71 := [rewrite]: #70
-#68 := (iff #18 #67)
-#65 := (iff #17 true)
-#60 := (= #14 #14)
-#63 := (iff #60 true)
-#64 := [rewrite]: #63
-#61 := (iff #17 #60)
-#58 := (= #16 #14)
-#56 := (= #15 #13)
-#57 := [rewrite]: #56
-#59 := [monotonicity #57]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#55 := [asserted]: #18
-[mp #55 #73]: false
-unsat
-69a5d92a496670834736208baa7873f48a8b26ef 46 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 S3 Int)
-decl f9 :: S3
-#13 := f9
-decl f6 :: S4
-#8 := f6
-#14 := (f5 f6 f9)
-decl f8 :: S3
-#11 := f8
-#12 := (f5 f6 f8)
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#18 := (+ #10 #12)
-#19 := (+ #18 #14)
-decl f4 :: S2
-#7 := f4
-#20 := (f3 f4 #19)
-#15 := (+ #12 #14)
-#16 := (+ #10 #15)
-#17 := (f3 f4 #16)
-#21 := (= #17 #20)
-#22 := (not #21)
-#76 := (iff #22 false)
-#1 := true
-#71 := (not true)
-#74 := (iff #71 false)
-#75 := [rewrite]: #74
-#72 := (iff #22 #71)
-#69 := (iff #21 true)
-#64 := (= #17 #17)
-#67 := (iff #64 true)
-#68 := [rewrite]: #67
-#65 := (iff #21 #64)
-#62 := (= #20 #17)
-#60 := (= #19 #16)
-#61 := [rewrite]: #60
-#63 := [monotonicity #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#59 := [asserted]: #22
-[mp #59 #77]: false
-unsat
-79c07e1ad7272206c5e814c398f47e58d945d62c 406 0
-#2 := false
-#15 := 0::Int
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#9 := f7
-decl f6 :: S4
-#8 := f6
-#10 := (f5 f6 f7)
-#465 := (= #10 0::Int)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#610 := (f3 f4 #10)
-#405 := (f5 f6 #610)
-#558 := (= #405 0::Int)
-decl f8 :: S3
-#11 := f8
-#12 := (f5 f6 f8)
-#284 := (f3 f4 #12)
-#562 := (f5 f6 #284)
-#554 := (= #562 0::Int)
-#404 := (>= #10 0::Int)
-#429 := (not #558)
-#432 := [hypothesis]: #429
-#559 := (or #404 #558)
-#28 := (:var 0 Int)
-#30 := (f3 f4 #28)
-#629 := (pattern #30)
-#31 := (f5 f6 #30)
-#36 := (= #31 0::Int)
-#75 := (>= #28 0::Int)
-#105 := (or #75 #36)
-#636 := (forall (vars (?v0 Int)) (:pat #629) #105)
-#108 := (forall (vars (?v0 Int)) #105)
-#639 := (iff #108 #636)
-#637 := (iff #105 #105)
-#638 := [refl]: #637
-#640 := [quant-intro #638]: #639
-#121 := (~ #108 #108)
-#129 := (~ #105 #105)
-#130 := [refl]: #129
-#122 := [nnf-pos #130]: #121
-#35 := (< #28 0::Int)
-#37 := (implies #35 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#111 := (iff #38 #108)
-#89 := (not #35)
-#90 := (or #89 #36)
-#93 := (forall (vars (?v0 Int)) #90)
-#109 := (iff #93 #108)
-#106 := (iff #90 #105)
-#103 := (iff #89 #75)
-#76 := (not #75)
-#98 := (not #76)
-#101 := (iff #98 #75)
-#102 := [rewrite]: #101
-#99 := (iff #89 #98)
-#96 := (iff #35 #76)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#104 := [trans #100 #102]: #103
-#107 := [monotonicity #104]: #106
-#110 := [quant-intro #107]: #109
-#94 := (iff #38 #93)
-#91 := (iff #37 #90)
-#92 := [rewrite]: #91
-#95 := [quant-intro #92]: #94
-#112 := [trans #95 #110]: #111
-#88 := [asserted]: #38
-#113 := [mp #88 #112]: #108
-#131 := [mp~ #113 #122]: #108
-#641 := [mp #131 #640]: #636
-#320 := (not #636)
-#560 := (or #320 #404 #558)
-#563 := (or #320 #559)
-#446 := (iff #563 #560)
-#447 := [rewrite]: #446
-#445 := [quant-inst #10]: #563
-#406 := [mp #445 #447]: #560
-#433 := [unit-resolution #406 #641]: #559
-#434 := [unit-resolution #433 #432]: #404
-#493 := (not #404)
-#439 := (or #493 #554)
-#551 := (= #12 0::Int)
-#13 := (+ #10 #12)
-#14 := (f3 f4 #13)
-#275 := (f5 f6 #14)
-#403 := -1::Int
-#260 := (* -1::Int #275)
-#261 := (+ #12 #260)
-#262 := (+ #10 #261)
-#609 := (<= #262 0::Int)
-#597 := (= #262 0::Int)
-#615 := (>= #13 0::Int)
-#561 := (>= #12 0::Int)
-#517 := (not #554)
-#490 := [hypothesis]: #517
-#456 := (or #561 #554)
-#555 := (or #320 #561 #554)
-#440 := (or #320 #456)
-#457 := (iff #440 #555)
-#458 := [rewrite]: #457
-#455 := [quant-inst #12]: #440
-#451 := [mp #455 #458]: #555
-#496 := [unit-resolution #451 #641]: #456
-#469 := [unit-resolution #496 #490]: #561
-#497 := [hypothesis]: #404
-#470 := (not #561)
-#471 := (or #615 #493 #470)
-#364 := [th-lemma arith assign-bounds -1 -1]: #471
-#475 := [unit-resolution #364 #497 #469]: #615
-#621 := (not #615)
-#259 := (or #621 #597)
-#32 := (= #31 #28)
-#79 := (or #76 #32)
-#630 := (forall (vars (?v0 Int)) (:pat #629) #79)
-#82 := (forall (vars (?v0 Int)) #79)
-#633 := (iff #82 #630)
-#631 := (iff #79 #79)
-#632 := [refl]: #631
-#634 := [quant-intro #632]: #633
-#119 := (~ #82 #82)
-#118 := (~ #79 #79)
-#115 := [refl]: #118
-#120 := [nnf-pos #115]: #119
-#29 := (<= 0::Int #28)
-#33 := (implies #29 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#85 := (iff #34 #82)
-#66 := (not #29)
-#67 := (or #66 #32)
-#70 := (forall (vars (?v0 Int)) #67)
-#83 := (iff #70 #82)
-#80 := (iff #67 #79)
-#77 := (iff #66 #76)
-#73 := (iff #29 #75)
-#74 := [rewrite]: #73
-#78 := [monotonicity #74]: #77
-#81 := [monotonicity #78]: #80
-#84 := [quant-intro #81]: #83
-#71 := (iff #34 #70)
-#68 := (iff #33 #67)
-#69 := [rewrite]: #68
-#72 := [quant-intro #69]: #71
-#86 := [trans #72 #84]: #85
-#64 := [asserted]: #34
-#87 := [mp #64 #86]: #82
-#116 := [mp~ #87 #120]: #82
-#635 := [mp #116 #634]: #630
-#601 := (not #630)
-#602 := (or #601 #621 #597)
-#612 := (= #275 #13)
-#271 := (or #621 #612)
-#603 := (or #601 #271)
-#247 := (iff #603 #602)
-#604 := (or #601 #259)
-#607 := (iff #604 #602)
-#246 := [rewrite]: #607
-#241 := (iff #603 #604)
-#599 := (iff #271 #259)
-#255 := (iff #612 #597)
-#613 := [rewrite]: #255
-#600 := [monotonicity #613]: #599
-#605 := [monotonicity #600]: #241
-#608 := [trans #605 #246]: #247
-#598 := [quant-inst #13]: #603
-#606 := [mp #598 #608]: #602
-#476 := [unit-resolution #606 #635]: #259
-#477 := [unit-resolution #476 #475]: #597
-#482 := (not #597)
-#478 := (or #482 #609)
-#479 := [th-lemma arith triangle-eq]: #478
-#480 := [unit-resolution #479 #477]: #609
-#595 := (>= #262 0::Int)
-#589 := (<= #275 0::Int)
-#596 := (= #275 0::Int)
-#16 := (f3 f4 0::Int)
-#590 := (f5 f6 #16)
-#594 := (= #590 0::Int)
-#581 := (or #601 #594)
-#318 := (>= 0::Int 0::Int)
-#319 := (not #318)
-#304 := (or #319 #594)
-#576 := (or #601 #304)
-#423 := (iff #576 #581)
-#425 := (iff #581 #581)
-#567 := [rewrite]: #425
-#575 := (iff #304 #594)
-#588 := (or false #594)
-#579 := (iff #588 #594)
-#574 := [rewrite]: #579
-#577 := (iff #304 #588)
-#587 := (iff #319 false)
-#1 := true
-#307 := (not true)
-#300 := (iff #307 false)
-#583 := [rewrite]: #300
-#585 := (iff #319 #307)
-#305 := (iff #318 true)
-#306 := [rewrite]: #305
-#586 := [monotonicity #306]: #585
-#584 := [trans #586 #583]: #587
-#578 := [monotonicity #584]: #577
-#580 := [trans #578 #574]: #575
-#424 := [monotonicity #580]: #423
-#568 := [trans #424 #567]: #423
-#582 := [quant-inst #15]: #576
-#569 := [mp #582 #568]: #581
-#557 := [unit-resolution #569 #635]: #594
-#503 := (= #275 #590)
-#17 := (= #14 #16)
-#19 := (= f8 #16)
-#133 := (not #19)
-#18 := (= f7 #16)
-#132 := (not #18)
-#123 := (or #132 #133)
-#521 := (= #13 0::Int)
-#534 := (= #13 #590)
-#548 := (= #12 #590)
-#124 := (not #123)
-#556 := [hypothesis]: #124
-#208 := (or #123 #19)
-#293 := [def-axiom]: #208
-#544 := [unit-resolution #293 #556]: #19
-#549 := [monotonicity #544]: #548
-#533 := (= #13 #12)
-#459 := (= #10 #12)
-#537 := (= f7 f8)
-#546 := (= #16 f8)
-#538 := [symm #544]: #546
-#207 := (or #123 #18)
-#292 := [def-axiom]: #207
-#535 := [unit-resolution #292 #556]: #18
-#547 := [trans #535 #538]: #537
-#532 := [monotonicity #547]: #459
-#530 := (= #13 #10)
-#527 := (= #10 #13)
-#552 := (<= #12 0::Int)
-#545 := [trans #549 #557]: #551
-#550 := (not #551)
-#539 := (or #550 #552)
-#540 := [th-lemma arith triangle-eq]: #539
-#541 := [unit-resolution #540 #545]: #552
-#542 := (or #550 #561)
-#536 := [th-lemma arith triangle-eq]: #542
-#543 := [unit-resolution #536 #545]: #561
-#528 := [th-lemma arith eq-propagate -1 -1 #543 #541]: #527
-#531 := [symm #528]: #530
-#529 := [trans #531 #532]: #533
-#520 := [trans #529 #549]: #534
-#523 := [trans #520 #557]: #521
-#524 := [monotonicity #523]: #17
-#59 := (not #17)
-#616 := (or #59 #123)
-#139 := (iff #17 #123)
-#20 := (and #18 #19)
-#60 := (iff #59 #20)
-#142 := (iff #60 #139)
-#136 := (iff #59 #124)
-#140 := (iff #136 #139)
-#141 := [rewrite]: #140
-#137 := (iff #60 #136)
-#134 := (iff #20 #124)
-#135 := [rewrite]: #134
-#138 := [monotonicity #135]: #137
-#143 := [trans #138 #141]: #142
-#21 := (iff #17 #20)
-#22 := (not #21)
-#61 := (iff #22 #60)
-#62 := [rewrite]: #61
-#58 := [asserted]: #22
-#65 := [mp #58 #62]: #60
-#144 := [mp #65 #143]: #139
-#296 := (not #139)
-#278 := (or #59 #123 #296)
-#614 := [def-axiom]: #278
-#272 := [unit-resolution #614 #144]: #616
-#553 := [unit-resolution #272 #556]: #59
-#525 := [unit-resolution #553 #524]: false
-#522 := [lemma #525]: #123
-#295 := (or #17 #124)
-#297 := (or #17 #124 #296)
-#298 := [def-axiom]: #297
-#299 := [unit-resolution #298 #144]: #295
-#502 := [unit-resolution #299 #522]: #17
-#504 := [monotonicity #502]: #503
-#499 := [trans #504 #557]: #596
-#505 := (not #596)
-#491 := (or #505 #589)
-#487 := [th-lemma arith triangle-eq]: #491
-#488 := [unit-resolution #487 #499]: #589
-#483 := (not #589)
-#484 := (or #595 #493 #470 #483)
-#485 := [th-lemma arith assign-bounds -1 -1 1]: #484
-#481 := [unit-resolution #485 #497 #488 #469]: #595
-#593 := (>= #275 0::Int)
-#486 := (or #505 #593)
-#466 := [th-lemma arith triangle-eq]: #486
-#412 := [unit-resolution #466 #499]: #593
-#460 := (* -1::Int #12)
-#461 := (+ #10 #460)
-#519 := (<= #461 0::Int)
-#492 := (not #609)
-#467 := (or #519 #470 #483 #492)
-#448 := [th-lemma arith assign-bounds 1 -1/2 -1/2]: #467
-#472 := [unit-resolution #448 #480 #469 #488]: #519
-#463 := (>= #461 0::Int)
-#494 := (or #463 #492 #493)
-#498 := (not #463)
-#500 := [hypothesis]: #498
-#501 := [hypothesis]: #609
-#489 := [th-lemma arith farkas -1/2 -1/2 -1/2 1 #488 #501 #500 #497]: false
-#495 := [lemma #489]: #494
-#473 := [unit-resolution #495 #480 #497]: #463
-#468 := [th-lemma arith eq-propagate 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #473 #472 #412 #488 #481 #480]: #551
-#474 := (= #562 #12)
-#617 := (= #284 f8)
-#23 := (:var 0 S3)
-#24 := (f5 f6 #23)
-#622 := (pattern #24)
-#25 := (f3 f4 #24)
-#26 := (= #25 #23)
-#623 := (forall (vars (?v0 S3)) (:pat #622) #26)
-#27 := (forall (vars (?v0 S3)) #26)
-#626 := (iff #27 #623)
-#624 := (iff #26 #26)
-#625 := [refl]: #624
-#627 := [quant-intro #625]: #626
-#127 := (~ #27 #27)
-#125 := (~ #26 #26)
-#126 := [refl]: #125
-#128 := [nnf-pos #126]: #127
-#63 := [asserted]: #27
-#117 := [mp~ #63 #128]: #27
-#628 := [mp #117 #627]: #623
-#618 := (not #623)
-#611 := (or #618 #617)
-#270 := [quant-inst #11]: #611
-#506 := [unit-resolution #270 #628]: #617
-#442 := [monotonicity #506]: #474
-#449 := [trans #442 #468]: #554
-#408 := [unit-resolution #490 #449]: false
-#441 := [lemma #408]: #439
-#435 := [unit-resolution #441 #434]: #554
-#418 := (= #405 #562)
-#510 := (= #12 #562)
-#507 := (= f8 #284)
-#509 := [symm #506]: #507
-#511 := [monotonicity #509]: #510
-#416 := (= #405 #12)
-#436 := [trans #511 #435]: #551
-#437 := [unit-resolution #536 #436]: #561
-#422 := [unit-resolution #364 #437 #434]: #615
-#438 := [unit-resolution #476 #422]: #597
-#399 := [unit-resolution #479 #438]: #609
-#400 := [unit-resolution #448 #399 #437 #488]: #519
-#407 := [unit-resolution #495 #399 #434]: #463
-#409 := (not #519)
-#410 := (or #459 #409 #498)
-#411 := [th-lemma arith triangle-eq]: #410
-#413 := [unit-resolution #411 #407 #400]: #459
-#414 := (= #405 #10)
-#283 := (= #610 f7)
-#619 := (or #618 #283)
-#620 := [quant-inst #9]: #619
-#452 := [unit-resolution #620 #628]: #283
-#415 := [monotonicity #452]: #414
-#417 := [trans #415 #413]: #416
-#401 := [trans #417 #511]: #418
-#419 := [trans #401 #435]: #558
-#389 := [unit-resolution #432 #419]: false
-#390 := [lemma #389]: #558
-#464 := (= #10 #405)
-#453 := (= f7 #610)
-#454 := [symm #452]: #453
-#444 := [monotonicity #454]: #464
-#392 := [trans #444 #390]: #465
-#430 := (or #429 #18)
-#421 := (= #610 #16)
-#450 := [hypothesis]: #558
-#420 := [trans #444 #450]: #465
-#426 := [monotonicity #420]: #421
-#427 := [trans #454 #426]: #18
-#443 := [hypothesis]: #132
-#428 := [unit-resolution #443 #427]: false
-#431 := [lemma #428]: #430
-#394 := [unit-resolution #431 #390]: #18
-#294 := (or #124 #132 #133)
-#285 := [def-axiom]: #294
-#395 := [unit-resolution #285 #394 #522]: #133
-#518 := (or #517 #19)
-#513 := (= #284 #16)
-#526 := [hypothesis]: #554
-#512 := [trans #511 #526]: #551
-#514 := [monotonicity #512]: #513
-#515 := [trans #509 #514]: #19
-#462 := [hypothesis]: #133
-#516 := [unit-resolution #462 #515]: false
-#508 := [lemma #516]: #518
-#396 := [unit-resolution #508 #395]: #517
-#238 := [unit-resolution #441 #396]: #493
-#397 := (not #465)
-#393 := (or #397 #404)
-#398 := [th-lemma arith triangle-eq]: #393
-[unit-resolution #398 #238 #392]: false
-unsat
-7309f258a79af4da7f45b6f7385fe1a230a81a14 51 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#16 := (:var 0 S3)
-decl f6 :: S4
-#8 := f6
-#17 := (f5 f6 #16)
-#607 := (pattern #17)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#18 := (f3 f4 #17)
-#19 := (= #18 #16)
-#608 := (forall (vars (?v0 S3)) (:pat #607) #19)
-#20 := (forall (vars (?v0 S3)) #19)
-#611 := (iff #20 #608)
-#609 := (iff #19 #19)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#127 := (~ #20 #20)
-#125 := (~ #19 #19)
-#126 := [refl]: #125
-#128 := [nnf-pos #126]: #127
-#63 := [asserted]: #20
-#117 := [mp~ #63 #128]: #20
-#613 := [mp #117 #612]: #608
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#54 := (f3 f4 #10)
-#57 := (= #54 f7)
-#60 := (not #57)
-#11 := 0::Int
-#12 := (- #10 0::Int)
-#13 := (f3 f4 #12)
-#14 := (= #13 f7)
-#15 := (not #14)
-#61 := (iff #15 #60)
-#58 := (iff #14 #57)
-#55 := (= #13 #54)
-#52 := (= #12 #10)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#59 := [monotonicity #56]: #58
-#62 := [monotonicity #59]: #61
-#51 := [asserted]: #15
-#65 := [mp #51 #62]: #60
-#278 := (not #608)
-#279 := (or #278 #57)
-#270 := [quant-inst #9]: #279
-[unit-resolution #270 #65 #613]: false
-unsat
-a612762a52e0e6c4e482e14565e5fee7610935cc 161 0
-#2 := false
-decl f7 :: (-> S4 Int S3)
-#16 := 0::Int
-decl f8 :: S4
-#13 := f8
-#17 := (f7 f8 0::Int)
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#57 := -1::Int
-#58 := (* -1::Int #11)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#59 := (+ #9 #58)
-#62 := (f7 f8 #59)
-#65 := (= #62 #17)
-#321 := (f3 f4 #62)
-#589 := (f7 f8 #321)
-#575 := (= #589 #17)
-#429 := (= #17 #589)
-#469 := (= 0::Int #321)
-#285 := (= #321 0::Int)
-#26 := (:var 0 Int)
-#28 := (f7 f8 #26)
-#652 := (pattern #28)
-#29 := (f3 f4 #28)
-#34 := (= #29 0::Int)
-#113 := (>= #26 0::Int)
-#144 := (or #113 #34)
-#659 := (forall (vars (?v0 Int)) (:pat #652) #144)
-#147 := (forall (vars (?v0 Int)) #144)
-#662 := (iff #147 #659)
-#660 := (iff #144 #144)
-#661 := [refl]: #660
-#663 := [quant-intro #661]: #662
-#162 := (~ #147 #147)
-#154 := (~ #144 #144)
-#155 := [refl]: #154
-#163 := [nnf-pos #155]: #162
-#33 := (< #26 0::Int)
-#35 := (implies #33 #34)
-#36 := (forall (vars (?v0 Int)) #35)
-#150 := (iff #36 #147)
-#128 := (not #33)
-#129 := (or #128 #34)
-#132 := (forall (vars (?v0 Int)) #129)
-#148 := (iff #132 #147)
-#145 := (iff #129 #144)
-#142 := (iff #128 #113)
-#115 := (not #113)
-#137 := (not #115)
-#140 := (iff #137 #113)
-#141 := [rewrite]: #140
-#138 := (iff #128 #137)
-#135 := (iff #33 #115)
-#136 := [rewrite]: #135
-#139 := [monotonicity #136]: #138
-#143 := [trans #139 #141]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#133 := (iff #36 #132)
-#130 := (iff #35 #129)
-#131 := [rewrite]: #130
-#134 := [quant-intro #131]: #133
-#151 := [trans #134 #149]: #150
-#127 := [asserted]: #36
-#152 := [mp #127 #151]: #147
-#170 := [mp~ #152 #163]: #147
-#664 := [mp #170 #663]: #659
-#81 := (>= #59 0::Int)
-#80 := (not #81)
-#91 := (or #81 #65)
-#94 := (not #91)
-#14 := (- #9 #11)
-#15 := (f7 f8 #14)
-#18 := (= #15 #17)
-#12 := (< #9 #11)
-#19 := (implies #12 #18)
-#20 := (not #19)
-#97 := (iff #20 #94)
-#71 := (not #12)
-#72 := (or #71 #65)
-#77 := (not #72)
-#95 := (iff #77 #94)
-#92 := (iff #72 #91)
-#89 := (iff #71 #81)
-#84 := (not #80)
-#87 := (iff #84 #81)
-#88 := [rewrite]: #87
-#85 := (iff #71 #84)
-#82 := (iff #12 #80)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#90 := [trans #86 #88]: #89
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93]: #95
-#78 := (iff #20 #77)
-#75 := (iff #19 #72)
-#68 := (implies #12 #65)
-#73 := (iff #68 #72)
-#74 := [rewrite]: #73
-#69 := (iff #19 #68)
-#66 := (iff #18 #65)
-#63 := (= #15 #62)
-#60 := (= #14 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#70 := [monotonicity #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [monotonicity #76]: #78
-#98 := [trans #79 #96]: #97
-#56 := [asserted]: #20
-#99 := [mp #56 #98]: #94
-#100 := [not-or-elim #99]: #80
-#624 := (not #659)
-#625 := (or #624 #81 #285)
-#286 := (or #81 #285)
-#626 := (or #624 #286)
-#627 := (iff #626 #625)
-#265 := [rewrite]: #627
-#621 := [quant-inst #59]: #626
-#628 := [mp #621 #265]: #625
-#583 := [unit-resolution #628 #100 #664]: #285
-#470 := [symm #583]: #469
-#577 := [monotonicity #470]: #429
-#578 := [symm #577]: #575
-#479 := (= #62 #589)
-#596 := (= #589 #62)
-#21 := (:var 0 S3)
-#22 := (f3 f4 #21)
-#645 := (pattern #22)
-#23 := (f7 f8 #22)
-#24 := (= #23 #21)
-#646 := (forall (vars (?v0 S3)) (:pat #645) #24)
-#25 := (forall (vars (?v0 S3)) #24)
-#649 := (iff #25 #646)
-#647 := (iff #24 #24)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#168 := (~ #25 #25)
-#166 := (~ #24 #24)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#103 := [asserted]: #25
-#158 := [mp~ #103 #169]: #25
-#651 := [mp #158 #650]: #646
-#318 := (not #646)
-#586 := (or #318 #596)
-#468 := [quant-inst #62]: #586
-#585 := [unit-resolution #468 #651]: #596
-#574 := [symm #585]: #479
-#463 := [trans #574 #578]: #65
-#101 := (not #65)
-#102 := [not-or-elim #99]: #101
-[unit-resolution #102 #463]: false
-unsat
-daef8f790726761d318bc7ef25020f07145aab1a 281 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#15 := 0::Int
-decl f4 :: S2
-#7 := f4
-#16 := (f3 f4 0::Int)
-decl f5 :: (-> S4 S3 Int)
-decl f8 :: S3
-#11 := f8
-decl f6 :: S4
-#8 := f6
-#12 := (f5 f6 f8)
-#59 := -1::Int
-#60 := (* -1::Int #12)
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#61 := (+ #10 #60)
-#64 := (f3 f4 #61)
-#67 := (= #64 #16)
-#290 := (f5 f6 #64)
-#535 := (f3 f4 #290)
-#460 := (= #535 #16)
-#484 := (= #16 #535)
-#459 := (= 0::Int #290)
-#610 := (= #290 0::Int)
-#309 := (>= #61 0::Int)
-#310 := (not #309)
-#70 := (* -1::Int #10)
-#71 := (+ #70 #12)
-#74 := (f3 f4 #71)
-#435 := (f5 f6 #74)
-#546 := (<= #435 0::Int)
-#487 := (not #546)
-#451 := (= #435 0::Int)
-#508 := (not #451)
-#77 := (= #74 #16)
-#542 := (f3 f4 #435)
-#528 := (= #542 #16)
-#524 := (= #16 #542)
-#522 := (= 0::Int #435)
-#518 := [hypothesis]: #451
-#523 := [symm #518]: #522
-#525 := [monotonicity #523]: #524
-#529 := [symm #525]: #528
-#526 := (= #74 #542)
-#543 := (= #542 #74)
-#23 := (:var 0 S3)
-#24 := (f5 f6 #23)
-#633 := (pattern #24)
-#25 := (f3 f4 #24)
-#26 := (= #25 #23)
-#634 := (forall (vars (?v0 S3)) (:pat #633) #26)
-#27 := (forall (vars (?v0 S3)) #26)
-#637 := (iff #27 #634)
-#635 := (iff #26 #26)
-#636 := [refl]: #635
-#638 := [quant-intro #636]: #637
-#156 := (~ #27 #27)
-#154 := (~ #26 #26)
-#155 := [refl]: #154
-#157 := [nnf-pos #155]: #156
-#91 := [asserted]: #27
-#146 := [mp~ #91 #157]: #27
-#639 := [mp #146 #638]: #634
-#306 := (not #634)
-#533 := (or #306 #543)
-#537 := [quant-inst #74]: #533
-#517 := [unit-resolution #537 #639]: #543
-#527 := [symm #517]: #526
-#519 := [trans #527 #529]: #77
-#89 := (not #77)
-#80 := (or #67 #77)
-#83 := (not #80)
-#18 := (- #12 #10)
-#19 := (f3 f4 #18)
-#20 := (= #19 #16)
-#13 := (- #10 #12)
-#14 := (f3 f4 #13)
-#17 := (= #14 #16)
-#21 := (or #17 #20)
-#22 := (not #21)
-#84 := (iff #22 #83)
-#81 := (iff #21 #80)
-#78 := (iff #20 #77)
-#75 := (= #19 #74)
-#72 := (= #18 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#68 := (iff #17 #67)
-#65 := (= #14 #64)
-#62 := (= #13 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#82 := [monotonicity #69 #79]: #81
-#85 := [monotonicity #82]: #84
-#58 := [asserted]: #22
-#88 := [mp #58 #85]: #83
-#90 := [not-or-elim #88]: #89
-#530 := [unit-resolution #90 #519]: false
-#509 := [lemma #530]: #508
-#548 := (>= #435 0::Int)
-#579 := (<= #61 0::Int)
-#468 := (or #579 #451)
-#28 := (:var 0 Int)
-#30 := (f3 f4 #28)
-#640 := (pattern #30)
-#31 := (f5 f6 #30)
-#36 := (= #31 0::Int)
-#101 := (>= #28 0::Int)
-#132 := (or #101 #36)
-#647 := (forall (vars (?v0 Int)) (:pat #640) #132)
-#135 := (forall (vars (?v0 Int)) #132)
-#650 := (iff #135 #647)
-#648 := (iff #132 #132)
-#649 := [refl]: #648
-#651 := [quant-intro #649]: #650
-#150 := (~ #135 #135)
-#142 := (~ #132 #132)
-#143 := [refl]: #142
-#151 := [nnf-pos #143]: #150
-#35 := (< #28 0::Int)
-#37 := (implies #35 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#138 := (iff #38 #135)
-#116 := (not #35)
-#117 := (or #116 #36)
-#120 := (forall (vars (?v0 Int)) #117)
-#136 := (iff #120 #135)
-#133 := (iff #117 #132)
-#130 := (iff #116 #101)
-#103 := (not #101)
-#125 := (not #103)
-#128 := (iff #125 #101)
-#129 := [rewrite]: #128
-#126 := (iff #116 #125)
-#123 := (iff #35 #103)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#134 := [monotonicity #131]: #133
-#137 := [quant-intro #134]: #136
-#121 := (iff #38 #120)
-#118 := (iff #37 #117)
-#119 := [rewrite]: #118
-#122 := [quant-intro #119]: #121
-#139 := [trans #122 #137]: #138
-#115 := [asserted]: #38
-#140 := [mp #115 #139]: #135
-#158 := [mp~ #140 #151]: #135
-#652 := [mp #158 #651]: #647
-#614 := (not #647)
-#470 := (or #614 #579 #451)
-#593 := (>= #71 0::Int)
-#466 := (or #593 #451)
-#471 := (or #614 #466)
-#555 := (iff #471 #470)
-#473 := (or #614 #468)
-#564 := (iff #473 #470)
-#568 := [rewrite]: #564
-#474 := (iff #471 #473)
-#469 := (iff #466 #468)
-#580 := (iff #593 #579)
-#581 := [rewrite]: #580
-#462 := [monotonicity #581]: #469
-#567 := [monotonicity #462]: #474
-#557 := [trans #567 #568]: #555
-#472 := [quant-inst #71]: #471
-#549 := [mp #472 #557]: #470
-#513 := [unit-resolution #549 #652]: #468
-#503 := [unit-resolution #513 #509]: #579
-#583 := (+ #60 #435)
-#577 := (+ #10 #583)
-#566 := (>= #577 0::Int)
-#584 := (= #577 0::Int)
-#575 := (not #579)
-#416 := (or #575 #584)
-#32 := (= #31 #28)
-#106 := (or #103 #32)
-#641 := (forall (vars (?v0 Int)) (:pat #640) #106)
-#109 := (forall (vars (?v0 Int)) #106)
-#644 := (iff #109 #641)
-#642 := (iff #106 #106)
-#643 := [refl]: #642
-#645 := [quant-intro #643]: #644
-#148 := (~ #109 #109)
-#147 := (~ #106 #106)
-#144 := [refl]: #147
-#149 := [nnf-pos #144]: #148
-#29 := (<= 0::Int #28)
-#33 := (implies #29 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#112 := (iff #34 #109)
-#93 := (not #29)
-#94 := (or #93 #32)
-#97 := (forall (vars (?v0 Int)) #94)
-#110 := (iff #97 #109)
-#107 := (iff #94 #106)
-#104 := (iff #93 #103)
-#100 := (iff #29 #101)
-#102 := [rewrite]: #100
-#105 := [monotonicity #102]: #104
-#108 := [monotonicity #105]: #107
-#111 := [quant-intro #108]: #110
-#98 := (iff #34 #97)
-#95 := (iff #33 #94)
-#96 := [rewrite]: #95
-#99 := [quant-intro #96]: #98
-#113 := [trans #99 #111]: #112
-#92 := [asserted]: #34
-#114 := [mp #92 #113]: #109
-#145 := [mp~ #114 #149]: #109
-#646 := [mp #145 #645]: #641
-#626 := (not #641)
-#572 := (or #626 #575 #584)
-#436 := (= #435 #71)
-#434 := (not #593)
-#578 := (or #434 #436)
-#573 := (or #626 #578)
-#565 := (iff #573 #572)
-#574 := (or #626 #416)
-#458 := (iff #574 #572)
-#417 := [rewrite]: #458
-#456 := (iff #573 #574)
-#569 := (iff #578 #416)
-#413 := (iff #436 #584)
-#415 := [rewrite]: #413
-#576 := (iff #434 #575)
-#582 := [monotonicity #581]: #576
-#570 := [monotonicity #582 #415]: #569
-#457 := [monotonicity #570]: #456
-#467 := [trans #457 #417]: #565
-#571 := [quant-inst #71]: #573
-#562 := [mp #571 #467]: #572
-#504 := [unit-resolution #562 #646]: #416
-#505 := [unit-resolution #504 #503]: #584
-#506 := (not #584)
-#501 := (or #506 #566)
-#507 := [th-lemma arith triangle-eq]: #501
-#480 := [unit-resolution #507 #505]: #566
-#481 := (not #566)
-#482 := (or #548 #481 #575)
-#375 := [th-lemma arith assign-bounds 1 -1]: #482
-#486 := [unit-resolution #375 #480 #503]: #548
-#488 := (not #548)
-#493 := (or #451 #487 #488)
-#489 := [th-lemma arith triangle-eq]: #493
-#490 := [unit-resolution #489 #486 #509]: #487
-#563 := (<= #577 0::Int)
-#491 := (or #506 #563)
-#494 := [th-lemma arith triangle-eq]: #491
-#495 := [unit-resolution #494 #505]: #563
-#496 := (not #563)
-#492 := (or #310 #546 #496)
-#497 := [th-lemma arith assign-bounds 1 -1]: #492
-#477 := [unit-resolution #497 #495 #490]: #310
-#611 := (or #309 #610)
-#609 := (or #614 #309 #610)
-#615 := (or #614 #611)
-#616 := (iff #615 #609)
-#618 := [rewrite]: #616
-#253 := [quant-inst #61]: #615
-#258 := [mp #253 #618]: #609
-#423 := [unit-resolution #258 #652]: #611
-#478 := [unit-resolution #423 #477]: #610
-#483 := [symm #478]: #459
-#479 := [monotonicity #483]: #484
-#419 := [symm #479]: #460
-#485 := (= #64 #535)
-#536 := (= #535 #64)
-#499 := (or #306 #536)
-#500 := [quant-inst #64]: #499
-#512 := [unit-resolution #500 #639]: #536
-#453 := [symm #512]: #485
-#450 := [trans #453 #419]: #67
-#86 := (not #67)
-#87 := [not-or-elim #88]: #86
-[unit-resolution #87 #450]: false
-unsat
-b4a6a90393789bf8defbaef4acfd5e61ff77c32f 270 0
-#2 := false
-decl f8 :: S3
-#11 := f8
-decl f7 :: S3
-#9 := f7
-#27 := 0::Int
-decl f5 :: (-> S4 S3 Int)
-decl f6 :: S4
-#8 := f6
-#12 := (f5 f6 f8)
-#59 := -1::Int
-#60 := (* -1::Int #12)
-#10 := (f5 f6 f7)
-#61 := (+ #10 #60)
-#88 := (>= #61 0::Int)
-#94 := (if #88 f7 f8)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#64 := (f3 f4 #61)
-#67 := (f5 f6 #64)
-#73 := (+ #12 #67)
-#78 := (f3 f4 #73)
-#99 := (= #78 #94)
-#321 := (= f8 #94)
-#87 := (not #88)
-#236 := (= f7 #94)
-#489 := [hypothesis]: #88
-#237 := (or #87 #236)
-#322 := [def-axiom]: #237
-#490 := [unit-resolution #322 #489]: #236
-#515 := (= #78 f7)
-#327 := (f3 f4 #10)
-#324 := (= #327 f7)
-#22 := (:var 0 S3)
-#23 := (f5 f6 #22)
-#650 := (pattern #23)
-#24 := (f3 f4 #23)
-#25 := (= #24 #22)
-#651 := (forall (vars (?v0 S3)) (:pat #650) #25)
-#26 := (forall (vars (?v0 S3)) #25)
-#654 := (iff #26 #651)
-#652 := (iff #25 #25)
-#653 := [refl]: #652
-#655 := [quant-intro #653]: #654
-#171 := (~ #26 #26)
-#169 := (~ #25 #25)
-#170 := [refl]: #169
-#172 := [nnf-pos #170]: #171
-#108 := [asserted]: #26
-#161 := [mp~ #108 #172]: #26
-#656 := [mp #161 #655]: #651
-#328 := (not #651)
-#431 := (or #328 #324)
-#638 := [quant-inst #9]: #431
-#576 := [unit-resolution #638 #656]: #324
-#532 := (= #78 #327)
-#549 := (= #73 #10)
-#567 := (= #10 #73)
-#643 := (* -1::Int #67)
-#649 := (+ #60 #643)
-#639 := (+ #10 #649)
-#626 := (<= #639 0::Int)
-#648 := (= #639 0::Int)
-#304 := (or #87 #648)
-#28 := (:var 0 Int)
-#30 := (f3 f4 #28)
-#657 := (pattern #30)
-#31 := (f5 f6 #30)
-#32 := (= #31 #28)
-#118 := (>= #28 0::Int)
-#120 := (not #118)
-#123 := (or #120 #32)
-#658 := (forall (vars (?v0 Int)) (:pat #657) #123)
-#126 := (forall (vars (?v0 Int)) #123)
-#661 := (iff #126 #658)
-#659 := (iff #123 #123)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#163 := (~ #126 #126)
-#162 := (~ #123 #123)
-#159 := [refl]: #162
-#164 := [nnf-pos #159]: #163
-#29 := (<= 0::Int #28)
-#33 := (implies #29 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#129 := (iff #34 #126)
-#110 := (not #29)
-#111 := (or #110 #32)
-#114 := (forall (vars (?v0 Int)) #111)
-#127 := (iff #114 #126)
-#124 := (iff #111 #123)
-#121 := (iff #110 #120)
-#117 := (iff #29 #118)
-#119 := [rewrite]: #117
-#122 := [monotonicity #119]: #121
-#125 := [monotonicity #122]: #124
-#128 := [quant-intro #125]: #127
-#115 := (iff #34 #114)
-#112 := (iff #33 #111)
-#113 := [rewrite]: #112
-#116 := [quant-intro #113]: #115
-#130 := [trans #116 #128]: #129
-#109 := [asserted]: #34
-#131 := [mp #109 #130]: #126
-#160 := [mp~ #131 #164]: #126
-#663 := [mp #160 #662]: #658
-#641 := (not #658)
-#284 := (or #641 #87 #648)
-#312 := (= #67 #61)
-#313 := (or #87 #312)
-#625 := (or #641 #313)
-#629 := (iff #625 #284)
-#289 := (or #641 #304)
-#627 := (iff #289 #284)
-#628 := [rewrite]: #627
-#290 := (iff #625 #289)
-#640 := (iff #313 #304)
-#647 := (iff #312 #648)
-#299 := [rewrite]: #647
-#300 := [monotonicity #299]: #640
-#291 := [monotonicity #300]: #290
-#630 := [trans #291 #628]: #629
-#288 := [quant-inst #61]: #625
-#631 := [mp #288 #630]: #284
-#544 := [unit-resolution #631 #663]: #304
-#545 := [unit-resolution #544 #489]: #648
-#546 := (not #648)
-#536 := (or #546 #626)
-#547 := [th-lemma arith triangle-eq]: #536
-#525 := [unit-resolution #547 #545]: #626
-#632 := (>= #639 0::Int)
-#526 := (or #546 #632)
-#528 := [th-lemma arith triangle-eq]: #526
-#529 := [unit-resolution #528 #545]: #632
-#530 := [th-lemma arith eq-propagate -1 -1 #529 #525]: #567
-#531 := [symm #530]: #549
-#527 := [monotonicity #531]: #532
-#516 := [trans #527 #576]: #515
-#517 := [trans #516 #490]: #99
-#102 := (not #99)
-#18 := (< #10 #12)
-#19 := (if #18 f8 f7)
-#13 := (- #10 #12)
-#14 := (f3 f4 #13)
-#15 := (f5 f6 #14)
-#16 := (+ #15 #12)
-#17 := (f3 f4 #16)
-#20 := (= #17 #19)
-#21 := (not #20)
-#105 := (iff #21 #102)
-#81 := (= #78 #19)
-#84 := (not #81)
-#103 := (iff #84 #102)
-#100 := (iff #81 #99)
-#97 := (= #19 #94)
-#91 := (if #87 f8 f7)
-#95 := (= #91 #94)
-#96 := [rewrite]: #95
-#92 := (= #19 #91)
-#89 := (iff #18 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#98 := [trans #93 #96]: #97
-#101 := [monotonicity #98]: #100
-#104 := [monotonicity #101]: #103
-#85 := (iff #21 #84)
-#82 := (iff #20 #81)
-#79 := (= #17 #78)
-#76 := (= #16 #73)
-#70 := (+ #67 #12)
-#74 := (= #70 #73)
-#75 := [rewrite]: #74
-#71 := (= #16 #70)
-#68 := (= #15 #67)
-#65 := (= #14 #64)
-#62 := (= #13 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#77 := [trans #72 #75]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#106 := [trans #86 #104]: #105
-#58 := [asserted]: #21
-#107 := [mp #58 #106]: #102
-#520 := [unit-resolution #107 #517]: false
-#521 := [lemma #520]: #87
-#323 := (or #88 #321)
-#314 := [def-axiom]: #323
-#542 := [unit-resolution #314 #521]: #321
-#511 := (= #78 f8)
-#325 := (f3 f4 #12)
-#326 := (= #325 f8)
-#307 := (or #328 #326)
-#642 := [quant-inst #11]: #307
-#543 := [unit-resolution #642 #656]: #326
-#510 := (= #78 #325)
-#504 := (= #73 #12)
-#392 := (= #12 #73)
-#347 := (<= #67 0::Int)
-#270 := (= #67 0::Int)
-#633 := (or #88 #270)
-#36 := (= #31 0::Int)
-#149 := (or #118 #36)
-#664 := (forall (vars (?v0 Int)) (:pat #657) #149)
-#152 := (forall (vars (?v0 Int)) #149)
-#667 := (iff #152 #664)
-#665 := (iff #149 #149)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#165 := (~ #152 #152)
-#173 := (~ #149 #149)
-#174 := [refl]: #173
-#166 := [nnf-pos #174]: #165
-#35 := (< #28 0::Int)
-#37 := (implies #35 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#155 := (iff #38 #152)
-#133 := (not #35)
-#134 := (or #133 #36)
-#137 := (forall (vars (?v0 Int)) #134)
-#153 := (iff #137 #152)
-#150 := (iff #134 #149)
-#147 := (iff #133 #118)
-#142 := (not #120)
-#145 := (iff #142 #118)
-#146 := [rewrite]: #145
-#143 := (iff #133 #142)
-#140 := (iff #35 #120)
-#141 := [rewrite]: #140
-#144 := [monotonicity #141]: #143
-#148 := [trans #144 #146]: #147
-#151 := [monotonicity #148]: #150
-#154 := [quant-intro #151]: #153
-#138 := (iff #38 #137)
-#135 := (iff #37 #134)
-#136 := [rewrite]: #135
-#139 := [quant-intro #136]: #138
-#156 := [trans #139 #154]: #155
-#132 := [asserted]: #38
-#157 := [mp #132 #156]: #152
-#175 := [mp~ #157 #166]: #152
-#669 := [mp #175 #668]: #664
-#276 := (not #664)
-#636 := (or #276 #88 #270)
-#634 := (or #276 #633)
-#623 := (iff #634 #636)
-#624 := [rewrite]: #623
-#637 := [quant-inst #61]: #634
-#346 := [mp #637 #624]: #636
-#533 := [unit-resolution #346 #669]: #633
-#519 := [unit-resolution #533 #521]: #270
-#522 := (not #270)
-#523 := (or #522 #347)
-#518 := [th-lemma arith triangle-eq]: #523
-#524 := [unit-resolution #518 #519]: #347
-#348 := (>= #67 0::Int)
-#497 := (or #522 #348)
-#498 := [th-lemma arith triangle-eq]: #497
-#499 := [unit-resolution #498 #519]: #348
-#503 := [th-lemma arith eq-propagate 1 1 #499 #524]: #392
-#505 := [symm #503]: #504
-#506 := [monotonicity #505]: #510
-#512 := [trans #506 #543]: #511
-#513 := [trans #512 #542]: #99
-[unit-resolution #107 #513]: false
-unsat
-fb9388a38938cbf21b6b2ff0332cf8b767f78d03 468 0
-#2 := false
-#30 := 0::Int
-decl f5 :: (-> S4 S3 Int)
-decl f3 :: (-> S2 Int S3)
-decl f8 :: S3
-#11 := f8
-decl f6 :: S4
-#8 := f6
-#12 := (f5 f6 f8)
-#62 := -1::Int
-#63 := (* -1::Int #12)
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#64 := (+ #10 #63)
-decl f4 :: S2
-#7 := f4
-#67 := (f3 f4 #64)
-#70 := (f5 f6 #67)
-#640 := (* -1::Int #70)
-#630 := (+ #63 #640)
-#290 := (+ #10 #630)
-#639 := (= #290 0::Int)
-#491 := (not #639)
-#623 := (>= #290 0::Int)
-#347 := (not #623)
-decl f9 :: S3
-#16 := f9
-#17 := (f5 f6 f9)
-#76 := (* -1::Int #17)
-#85 := (+ #63 #76)
-#86 := (+ #10 #85)
-#581 := (>= #86 0::Int)
-#579 := (not #581)
-#89 := (f3 f4 #86)
-#77 := (+ #76 #70)
-#82 := (f3 f4 #77)
-#92 := (= #82 #89)
-#582 := (f5 f6 #89)
-#510 := (f3 f4 #582)
-#506 := (= #510 #89)
-#25 := (:var 0 S3)
-#26 := (f5 f6 #25)
-#641 := (pattern #26)
-#27 := (f3 f4 #26)
-#28 := (= #27 #25)
-#642 := (forall (vars (?v0 S3)) (:pat #641) #28)
-#29 := (forall (vars (?v0 S3)) #28)
-#645 := (iff #29 #642)
-#643 := (iff #28 #28)
-#644 := [refl]: #643
-#646 := [quant-intro #644]: #645
-#162 := (~ #29 #29)
-#160 := (~ #28 #28)
-#161 := [refl]: #160
-#163 := [nnf-pos #161]: #162
-#98 := [asserted]: #29
-#152 := [mp~ #98 #163]: #29
-#647 := [mp #152 #646]: #642
-#314 := (not #642)
-#463 := (or #314 #506)
-#484 := [quant-inst #89]: #463
-#448 := [unit-resolution #484 #647]: #506
-#441 := (= #82 #510)
-#369 := (= #77 #582)
-#570 := (* -1::Int #582)
-#571 := (+ #76 #570)
-#574 := (+ #63 #571)
-#459 := (+ #10 #574)
-#565 := (<= #459 0::Int)
-#425 := (= #459 0::Int)
-#258 := [hypothesis]: #581
-#475 := (or #579 #425)
-#31 := (:var 0 Int)
-#33 := (f3 f4 #31)
-#648 := (pattern #33)
-#34 := (f5 f6 #33)
-#35 := (= #34 #31)
-#109 := (>= #31 0::Int)
-#111 := (not #109)
-#114 := (or #111 #35)
-#649 := (forall (vars (?v0 Int)) (:pat #648) #114)
-#117 := (forall (vars (?v0 Int)) #114)
-#652 := (iff #117 #649)
-#650 := (iff #114 #114)
-#651 := [refl]: #650
-#653 := [quant-intro #651]: #652
-#154 := (~ #117 #117)
-#153 := (~ #114 #114)
-#150 := [refl]: #153
-#155 := [nnf-pos #150]: #154
-#32 := (<= 0::Int #31)
-#36 := (implies #32 #35)
-#37 := (forall (vars (?v0 Int)) #36)
-#120 := (iff #37 #117)
-#101 := (not #32)
-#102 := (or #101 #35)
-#105 := (forall (vars (?v0 Int)) #102)
-#118 := (iff #105 #117)
-#115 := (iff #102 #114)
-#112 := (iff #101 #111)
-#108 := (iff #32 #109)
-#110 := [rewrite]: #108
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [quant-intro #116]: #118
-#106 := (iff #37 #105)
-#103 := (iff #36 #102)
-#104 := [rewrite]: #103
-#107 := [quant-intro #104]: #106
-#121 := [trans #107 #119]: #120
-#99 := [asserted]: #37
-#122 := [mp #99 #121]: #117
-#151 := [mp~ #122 #155]: #117
-#654 := [mp #151 #653]: #649
-#632 := (not #649)
-#477 := (or #632 #579 #425)
-#464 := (= #582 #86)
-#465 := (or #579 #464)
-#470 := (or #632 #465)
-#572 := (iff #470 #477)
-#479 := (or #632 #475)
-#482 := (iff #479 #477)
-#575 := [rewrite]: #482
-#480 := (iff #470 #479)
-#474 := (iff #465 #475)
-#466 := (iff #464 #425)
-#573 := [rewrite]: #466
-#476 := [monotonicity #573]: #474
-#481 := [monotonicity #476]: #480
-#576 := [trans #481 #575]: #572
-#478 := [quant-inst #86]: #470
-#563 := [mp #478 #576]: #477
-#497 := [unit-resolution #563 #654]: #475
-#389 := [unit-resolution #497 #258]: #425
-#499 := (not #425)
-#434 := (or #499 #565)
-#435 := [th-lemma arith triangle-eq]: #434
-#393 := [unit-resolution #435 #389]: #565
-#557 := (>= #459 0::Int)
-#502 := (or #499 #557)
-#503 := [th-lemma arith triangle-eq]: #502
-#386 := [unit-resolution #503 #389]: #557
-#617 := (<= #290 0::Int)
-#422 := (>= #64 0::Int)
-#555 := (>= #582 0::Int)
-#394 := (not #565)
-#387 := (or #555 #394 #579)
-#390 := [th-lemma arith assign-bounds 1 -1]: #387
-#391 := [unit-resolution #390 #393 #258]: #555
-#485 := (not #557)
-#505 := (not #555)
-#380 := (or #422 #505 #485)
-#566 := (>= #17 0::Int)
-#415 := (= #17 0::Int)
-#227 := (f3 f4 #17)
-#567 := (f5 f6 #227)
-#562 := (= #567 0::Int)
-#405 := (not #566)
-#406 := [hypothesis]: #405
-#546 := (or #566 #562)
-#39 := (= #34 0::Int)
-#140 := (or #109 #39)
-#655 := (forall (vars (?v0 Int)) (:pat #648) #140)
-#143 := (forall (vars (?v0 Int)) #140)
-#658 := (iff #143 #655)
-#656 := (iff #140 #140)
-#657 := [refl]: #656
-#659 := [quant-intro #657]: #658
-#156 := (~ #143 #143)
-#164 := (~ #140 #140)
-#165 := [refl]: #164
-#157 := [nnf-pos #165]: #156
-#38 := (< #31 0::Int)
-#40 := (implies #38 #39)
-#41 := (forall (vars (?v0 Int)) #40)
-#146 := (iff #41 #143)
-#124 := (not #38)
-#125 := (or #124 #39)
-#128 := (forall (vars (?v0 Int)) #125)
-#144 := (iff #128 #143)
-#141 := (iff #125 #140)
-#138 := (iff #124 #109)
-#133 := (not #111)
-#136 := (iff #133 #109)
-#137 := [rewrite]: #136
-#134 := (iff #124 #133)
-#131 := (iff #38 #111)
-#132 := [rewrite]: #131
-#135 := [monotonicity #132]: #134
-#139 := [trans #135 #137]: #138
-#142 := [monotonicity #139]: #141
-#145 := [quant-intro #142]: #144
-#129 := (iff #41 #128)
-#126 := (iff #40 #125)
-#127 := [rewrite]: #126
-#130 := [quant-intro #127]: #129
-#147 := [trans #130 #145]: #146
-#123 := [asserted]: #41
-#148 := [mp #123 #147]: #143
-#166 := [mp~ #148 #157]: #143
-#660 := [mp #166 #659]: #655
-#267 := (not #655)
-#550 := (or #267 #566 #562)
-#551 := (or #267 #546)
-#548 := (iff #551 #550)
-#553 := [rewrite]: #548
-#552 := [quant-inst #17]: #551
-#539 := [mp #552 #553]: #550
-#404 := [unit-resolution #539 #660]: #546
-#407 := [unit-resolution #404 #406]: #562
-#401 := (= #17 #567)
-#398 := (= f9 #227)
-#312 := (= #227 f9)
-#305 := (or #314 #312)
-#316 := [quant-inst #16]: #305
-#395 := [unit-resolution #316 #647]: #312
-#400 := [symm #395]: #398
-#397 := [monotonicity #400]: #401
-#402 := [trans #397 #407]: #415
-#392 := (not #415)
-#382 := (or #392 #566)
-#384 := [th-lemma arith triangle-eq]: #382
-#385 := [unit-resolution #384 #406 #402]: false
-#388 := [lemma #385]: #566
-#377 := (or #405 #422 #505 #485)
-#379 := [th-lemma arith assign-bounds 1 1 1]: #377
-#378 := [unit-resolution #379 #388]: #380
-#381 := [unit-resolution #378 #391 #386]: #422
-#629 := (not #422)
-#295 := (or #629 #639)
-#275 := (or #632 #629 #639)
-#636 := (= #70 #64)
-#637 := (or #629 #636)
-#616 := (or #632 #637)
-#620 := (iff #616 #275)
-#280 := (or #632 #295)
-#618 := (iff #280 #275)
-#619 := [rewrite]: #618
-#281 := (iff #616 #280)
-#631 := (iff #637 #295)
-#638 := (iff #636 #639)
-#634 := [rewrite]: #638
-#291 := [monotonicity #634]: #631
-#282 := [monotonicity #291]: #281
-#621 := [trans #282 #619]: #620
-#279 := [quant-inst #64]: #616
-#622 := [mp #279 #621]: #275
-#461 := [unit-resolution #622 #654]: #295
-#363 := [unit-resolution #461 #381]: #639
-#492 := (or #491 #617)
-#487 := [th-lemma arith triangle-eq]: #492
-#365 := [unit-resolution #487 #363]: #617
-#366 := (or #491 #623)
-#367 := [th-lemma arith triangle-eq]: #366
-#368 := [unit-resolution #367 #363]: #623
-#370 := [th-lemma arith eq-propagate 1 1 -1 -1 #368 #365 #386 #393]: #369
-#371 := [monotonicity #370]: #441
-#372 := [trans #371 #448]: #92
-#95 := (not #92)
-#20 := (+ #12 #17)
-#21 := (- #10 #20)
-#22 := (f3 f4 #21)
-#13 := (- #10 #12)
-#14 := (f3 f4 #13)
-#15 := (f5 f6 #14)
-#18 := (- #15 #17)
-#19 := (f3 f4 #18)
-#23 := (= #19 #22)
-#24 := (not #23)
-#96 := (iff #24 #95)
-#93 := (iff #23 #92)
-#90 := (= #22 #89)
-#87 := (= #21 #86)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#83 := (= #19 #82)
-#80 := (= #18 #77)
-#73 := (- #70 #17)
-#78 := (= #73 #77)
-#79 := [rewrite]: #78
-#74 := (= #18 #73)
-#71 := (= #15 #70)
-#68 := (= #14 #67)
-#65 := (= #13 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#81 := [trans #75 #79]: #80
-#84 := [monotonicity #81]: #83
-#94 := [monotonicity #84 #91]: #93
-#97 := [monotonicity #94]: #96
-#61 := [asserted]: #24
-#100 := [mp #61 #97]: #95
-#373 := [unit-resolution #100 #372]: false
-#374 := [lemma #373]: #579
-#340 := (f5 f6 #82)
-#580 := (>= #340 0::Int)
-#611 := (+ #17 #640)
-#333 := (<= #611 0::Int)
-#554 := (= #582 0::Int)
-#490 := (not #554)
-#443 := (= #340 0::Int)
-#612 := (not #333)
-#489 := [hypothesis]: #612
-#586 := (or #333 #443)
-#589 := (or #267 #333 #443)
-#626 := (>= #77 0::Int)
-#444 := (or #626 #443)
-#583 := (or #267 #444)
-#423 := (iff #583 #589)
-#590 := (or #267 #586)
-#592 := (iff #590 #589)
-#421 := [rewrite]: #592
-#591 := (iff #583 #590)
-#587 := (iff #444 #586)
-#334 := (iff #626 #333)
-#608 := [rewrite]: #334
-#588 := [monotonicity #608]: #587
-#585 := [monotonicity #588]: #591
-#424 := [trans #585 #421]: #423
-#584 := [quant-inst #77]: #583
-#577 := [mp #584 #424]: #589
-#449 := [unit-resolution #577 #660]: #586
-#450 := [unit-resolution #449 #489]: #443
-#426 := (not #443)
-#428 := (or #490 #426)
-#517 := (f3 f4 #340)
-#455 := (= #517 #510)
-#451 := (= #510 #517)
-#446 := (= #582 #340)
-#440 := (= 0::Int #340)
-#514 := [hypothesis]: #443
-#445 := [symm #514]: #440
-#439 := [hypothesis]: #554
-#447 := [trans #439 #445]: #446
-#452 := [monotonicity #447]: #451
-#456 := [symm #452]: #455
-#453 := (= #82 #517)
-#519 := (= #517 #82)
-#507 := (or #314 #519)
-#508 := [quant-inst #82]: #507
-#513 := [unit-resolution #508 #647]: #519
-#454 := [symm #513]: #453
-#457 := [trans #454 #456]: #441
-#418 := [trans #457 #448]: #92
-#419 := [unit-resolution #100 #418]: false
-#429 := [lemma #419]: #428
-#430 := [unit-resolution #429 #450]: #490
-#556 := (or #581 #554)
-#568 := (or #267 #581 #554)
-#564 := (or #267 #556)
-#558 := (iff #564 #568)
-#559 := [rewrite]: #558
-#569 := [quant-inst #86]: #564
-#560 := [mp #569 #559]: #568
-#496 := [unit-resolution #560 #660]: #556
-#432 := [unit-resolution #496 #430]: #581
-#433 := [unit-resolution #497 #432]: #425
-#436 := [unit-resolution #435 #433]: #565
-#561 := (<= #582 0::Int)
-#473 := (or #561 #333)
-#339 := (>= #70 0::Int)
-#261 := (= #70 0::Int)
-#500 := (not #617)
-#511 := (not #561)
-#512 := [hypothesis]: #511
-#509 := (or #555 #561)
-#515 := [th-lemma arith farkas 1 1]: #509
-#488 := [unit-resolution #515 #512]: #555
-#383 := (or #490 #561)
-#494 := [th-lemma arith triangle-eq]: #383
-#495 := [unit-resolution #494 #512]: #490
-#501 := [unit-resolution #496 #495]: #581
-#498 := [unit-resolution #497 #501]: #425
-#504 := [unit-resolution #503 #498]: #557
-#431 := (or #500 #333 #505 #485)
-#486 := [th-lemma arith assign-bounds 1 1 -1]: #431
-#467 := [unit-resolution #486 #504 #489 #488]: #500
-#493 := [unit-resolution #487 #467]: #491
-#468 := [unit-resolution #461 #493]: #629
-#624 := (or #422 #261)
-#627 := (or #267 #422 #261)
-#625 := (or #267 #624)
-#614 := (iff #625 #627)
-#615 := [rewrite]: #614
-#628 := [quant-inst #64]: #625
-#337 := [mp #628 #615]: #627
-#427 := [unit-resolution #337 #660]: #624
-#458 := [unit-resolution #427 #468]: #261
-#460 := (not #261)
-#462 := (or #460 #339)
-#469 := [th-lemma arith triangle-eq]: #462
-#471 := [unit-resolution #469 #458]: #339
-#472 := [th-lemma arith farkas 1 1 1 1 1 #489 #468 #488 #504 #471]: false
-#483 := [lemma #472]: #473
-#437 := [unit-resolution #483 #489]: #561
-#420 := (or #554 #511 #505)
-#438 := [th-lemma arith triangle-eq]: #420
-#408 := [unit-resolution #438 #430 #437]: #505
-#409 := [th-lemma arith farkas 1 -1 1 #408 #432 #436]: false
-#410 := [lemma #409]: #333
-#323 := (+ #640 #340)
-#324 := (+ #17 #323)
-#442 := (>= #324 0::Int)
-#325 := (= #324 0::Int)
-#605 := (or #612 #325)
-#606 := (or #632 #612 #325)
-#234 := (= #340 #77)
-#266 := (not #626)
-#610 := (or #266 #234)
-#603 := (or #632 #610)
-#599 := (iff #603 #606)
-#596 := (or #632 #605)
-#593 := (iff #596 #606)
-#594 := [rewrite]: #593
-#597 := (iff #603 #596)
-#320 := (iff #610 #605)
-#326 := (iff #234 #325)
-#604 := [rewrite]: #326
-#609 := (iff #266 #612)
-#613 := [monotonicity #608]: #609
-#602 := [monotonicity #613 #604]: #320
-#598 := [monotonicity #602]: #597
-#600 := [trans #598 #594]: #599
-#607 := [quant-inst #77]: #603
-#595 := [mp #607 #600]: #606
-#375 := [unit-resolution #595 #654]: #605
-#364 := [unit-resolution #375 #410]: #325
-#376 := (not #325)
-#353 := (or #376 #442)
-#355 := [th-lemma arith triangle-eq]: #353
-#356 := [unit-resolution #355 #364]: #442
-#357 := (not #442)
-#358 := (or #580 #357 #612)
-#359 := [th-lemma arith assign-bounds 1 -1]: #358
-#360 := [unit-resolution #359 #356 #410]: #580
-#601 := (<= #324 0::Int)
-#361 := (or #376 #601)
-#354 := [th-lemma arith triangle-eq]: #361
-#362 := [unit-resolution #354 #364]: #601
-#349 := (not #601)
-#348 := (not #580)
-#351 := (or #347 #581 #348 #349)
-#350 := [th-lemma arith assign-bounds 1 1 -1]: #351
-#352 := [unit-resolution #350 #362 #360 #374]: #347
-#341 := [unit-resolution #367 #352]: #491
-#338 := (<= #70 0::Int)
-#328 := (not #338)
-#578 := (<= #340 0::Int)
-#335 := (not #578)
-#342 := [unit-resolution #496 #374]: #554
-#343 := [unit-resolution #429 #342]: #426
-#336 := (or #443 #335)
-#344 := (or #443 #335 #348)
-#345 := [th-lemma arith triangle-eq]: #344
-#346 := [unit-resolution #345 #360]: #336
-#327 := [unit-resolution #346 #343]: #335
-#329 := (or #328 #405 #578 #349)
-#321 := [th-lemma arith assign-bounds -1 -1 1]: #329
-#330 := [unit-resolution #321 #362 #327 #388]: #328
-#331 := (or #460 #338)
-#322 := [th-lemma arith triangle-eq]: #331
-#332 := [unit-resolution #322 #330]: #460
-#299 := [unit-resolution #427 #332]: #422
-[unit-resolution #461 #299 #341]: false
-unsat
-c3fe9dd07d48c19f169e86364b6e16e6491742af 37 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#11 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#9 := f7
-decl f6 :: S4
-#8 := f6
-#10 := (f5 f6 f7)
-#12 := (* #10 0::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#16 := (not #15)
-#68 := (iff #16 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #16 #63)
-#61 := (iff #15 true)
-#56 := (= #14 #14)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #15 #56)
-#53 := (= #12 0::Int)
-#54 := [rewrite]: #53
-#55 := [monotonicity #54]: #15
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#52 := [asserted]: #16
-[mp #52 #69]: false
-unsat
-77553bfdf91cbdbb4f547370608d4248384211db 37 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#8 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#10 := f7
-decl f6 :: S4
-#9 := f6
-#11 := (f5 f6 f7)
-#12 := (* 0::Int #11)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#16 := (not #15)
-#68 := (iff #16 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #16 #63)
-#61 := (iff #15 true)
-#56 := (= #14 #14)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #15 #56)
-#53 := (= #12 0::Int)
-#54 := [rewrite]: #53
-#55 := [monotonicity #54]: #15
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#52 := [asserted]: #16
-[mp #52 #69]: false
-unsat
-1749d19b84217f6922dc5d71d8e67fefffa1dd3a 51 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#16 := (:var 0 S3)
-decl f6 :: S4
-#8 := f6
-#17 := (f5 f6 #16)
-#607 := (pattern #17)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#18 := (f3 f4 #17)
-#19 := (= #18 #16)
-#608 := (forall (vars (?v0 S3)) (:pat #607) #19)
-#20 := (forall (vars (?v0 S3)) #19)
-#611 := (iff #20 #608)
-#609 := (iff #19 #19)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#128 := (~ #20 #20)
-#126 := (~ #19 #19)
-#127 := [refl]: #126
-#129 := [nnf-pos #127]: #128
-#64 := [asserted]: #20
-#118 := [mp~ #64 #129]: #20
-#613 := [mp #118 #612]: #608
-decl f7 :: S3
-#9 := f7
-#10 := (f5 f6 f7)
-#55 := (f3 f4 #10)
-#58 := (= #55 f7)
-#61 := (not #58)
-#11 := 1::Int
-#12 := (* #10 1::Int)
-#13 := (f3 f4 #12)
-#14 := (= #13 f7)
-#15 := (not #14)
-#62 := (iff #15 #61)
-#59 := (iff #14 #58)
-#56 := (= #13 #55)
-#53 := (= #12 #10)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#60 := [monotonicity #57]: #59
-#63 := [monotonicity #60]: #62
-#52 := [asserted]: #15
-#66 := [mp #52 #63]: #61
-#278 := (not #608)
-#279 := (or #278 #58)
-#270 := [quant-inst #9]: #279
-[unit-resolution #270 #66 #613]: false
-unsat
-67566504424067f67a103ec753b4c58eea51e2b0 51 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#16 := (:var 0 S3)
-decl f6 :: S4
-#9 := f6
-#17 := (f5 f6 #16)
-#607 := (pattern #17)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#18 := (f3 f4 #17)
-#19 := (= #18 #16)
-#608 := (forall (vars (?v0 S3)) (:pat #607) #19)
-#20 := (forall (vars (?v0 S3)) #19)
-#611 := (iff #20 #608)
-#609 := (iff #19 #19)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#128 := (~ #20 #20)
-#126 := (~ #19 #19)
-#127 := [refl]: #126
-#129 := [nnf-pos #127]: #128
-#64 := [asserted]: #20
-#118 := [mp~ #64 #129]: #20
-#613 := [mp #118 #612]: #608
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#55 := (f3 f4 #11)
-#58 := (= #55 f7)
-#61 := (not #58)
-#8 := 1::Int
-#12 := (* 1::Int #11)
-#13 := (f3 f4 #12)
-#14 := (= #13 f7)
-#15 := (not #14)
-#62 := (iff #15 #61)
-#59 := (iff #14 #58)
-#56 := (= #13 #55)
-#53 := (= #12 #11)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#60 := [monotonicity #57]: #59
-#63 := [monotonicity #60]: #62
-#52 := [asserted]: #15
-#66 := [mp #52 #63]: #61
-#278 := (not #608)
-#279 := (or #278 #58)
-#270 := [quant-inst #10]: #279
-[unit-resolution #270 #66 #613]: false
-unsat
-9a8122f90fb878d81c9ec24c34cad517ec0e86e9 39 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#8 := 3::Int
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#10 := f7
-decl f6 :: S4
-#9 := f6
-#11 := (f5 f6 f7)
-#14 := (* #11 3::Int)
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 #14)
-#12 := (* 3::Int #11)
-#13 := (f3 f4 #12)
-#16 := (= #13 #15)
-#17 := (not #16)
-#71 := (iff #17 false)
-#1 := true
-#66 := (not true)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #17 #66)
-#64 := (iff #16 true)
-#59 := (= #13 #13)
-#62 := (iff #59 true)
-#63 := [rewrite]: #62
-#60 := (iff #16 #59)
-#57 := (= #15 #13)
-#55 := (= #14 #12)
-#56 := [rewrite]: #55
-#58 := [monotonicity #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#68 := [monotonicity #65]: #67
-#72 := [trans #68 #70]: #71
-#54 := [asserted]: #17
-[mp #54 #72]: false
-unsat
-04d7d06577757be1339383f753c875196ebaee4b 246 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#7 := f4
-#13 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 0::Int)
-#11 := (f5 #10 0::Int)
-#12 := (f3 f4 #11)
-#14 := (= #12 #13)
-#503 := (= #11 0::Int)
-#22 := (:var 0 Int)
-#33 := (:var 1 Int)
-#34 := (f6 f7 #33)
-#35 := (f5 #34 #22)
-#830 := (pattern #35)
-#135 := -1::Int
-#139 := (* -1::Int #22)
-#136 := (* -1::Int #33)
-#142 := (div #136 #139)
-#308 := (* -1::Int #142)
-#309 := (+ #35 #308)
-#310 := (= #309 0::Int)
-#45 := (div #33 #22)
-#305 := (* -1::Int #45)
-#306 := (+ #35 #305)
-#307 := (= #306 0::Int)
-#161 := (<= #22 0::Int)
-#168 := (>= #33 0::Int)
-#268 := (or #168 #161)
-#269 := (not #268)
-#157 := (<= #33 0::Int)
-#266 := (or #157 #161)
-#267 := (not #266)
-#272 := (or #267 #269)
-#311 := (if #272 #307 #310)
-#304 := (= #35 0::Int)
-#37 := (= #22 0::Int)
-#36 := (= #33 0::Int)
-#38 := (or #36 #37)
-#312 := (if #38 #304 #311)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #312)
-#315 := (forall (vars (?v0 Int) (?v1 Int)) #312)
-#834 := (iff #315 #831)
-#832 := (iff #312 #312)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#275 := (if #272 #45 #142)
-#278 := (if #38 0::Int #275)
-#281 := (= #35 #278)
-#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
-#316 := (iff #284 #315)
-#313 := (iff #281 #312)
-#314 := [rewrite]: #313
-#317 := [quant-intro #314]: #316
-#162 := (not #161)
-#169 := (not #168)
-#172 := (and #169 #162)
-#158 := (not #157)
-#165 := (and #158 #162)
-#175 := (or #165 #172)
-#178 := (if #175 #45 #142)
-#181 := (if #38 0::Int #178)
-#184 := (= #35 #181)
-#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
-#285 := (iff #187 #284)
-#282 := (iff #184 #281)
-#279 := (= #181 #278)
-#276 := (= #178 #275)
-#273 := (iff #175 #272)
-#270 := (iff #172 #269)
-#271 := [rewrite]: #270
-#251 := (iff #165 #267)
-#252 := [rewrite]: #251
-#274 := [monotonicity #252 #271]: #273
-#277 := [monotonicity #274]: #276
-#280 := [monotonicity #277]: #279
-#283 := [monotonicity #280]: #282
-#286 := [quant-intro #283]: #285
-#247 := (~ #187 #187)
-#260 := (~ #184 #184)
-#261 := [refl]: #260
-#248 := [nnf-pos #261]: #247
-#47 := (- #22)
-#46 := (- #33)
-#48 := (div #46 #47)
-#40 := (< 0::Int #22)
-#42 := (< #33 0::Int)
-#43 := (and #42 #40)
-#39 := (< 0::Int #33)
-#41 := (and #39 #40)
-#44 := (or #41 #43)
-#49 := (if #44 #45 #48)
-#50 := (if #38 0::Int #49)
-#51 := (= #35 #50)
-#52 := (forall (vars (?v0 Int) (?v1 Int)) #51)
-#190 := (iff #52 #187)
-#145 := (if #44 #45 #142)
-#148 := (if #38 0::Int #145)
-#151 := (= #35 #148)
-#154 := (forall (vars (?v0 Int) (?v1 Int)) #151)
-#188 := (iff #154 #187)
-#185 := (iff #151 #184)
-#182 := (= #148 #181)
-#179 := (= #145 #178)
-#176 := (iff #44 #175)
-#173 := (iff #43 #172)
-#163 := (iff #40 #162)
-#164 := [rewrite]: #163
-#170 := (iff #42 #169)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171 #164]: #173
-#166 := (iff #41 #165)
-#159 := (iff #39 #158)
-#160 := [rewrite]: #159
-#167 := [monotonicity #160 #164]: #166
-#177 := [monotonicity #167 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [quant-intro #186]: #188
-#155 := (iff #52 #154)
-#152 := (iff #51 #151)
-#149 := (= #50 #148)
-#146 := (= #49 #145)
-#143 := (= #48 #142)
-#140 := (= #47 #139)
-#141 := [rewrite]: #140
-#137 := (= #46 #136)
-#138 := [rewrite]: #137
-#144 := [monotonicity #138 #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [monotonicity #150]: #152
-#156 := [quant-intro #153]: #155
-#191 := [trans #156 #189]: #190
-#134 := [asserted]: #52
-#192 := [mp #134 #191]: #187
-#262 := [mp~ #192 #248]: #187
-#287 := [mp #262 #286]: #284
-#318 := [mp #287 #317]: #315
-#836 := [mp #318 #835]: #831
-#737 := (not #831)
-#733 := (or #737 #503)
-#489 := (* -1::Int 0::Int)
-#771 := (div #489 #489)
-#775 := (* -1::Int #771)
-#772 := (+ #11 #775)
-#776 := (= #772 0::Int)
-#494 := (div 0::Int 0::Int)
-#495 := (* -1::Int #494)
-#773 := (+ #11 #495)
-#774 := (= #773 0::Int)
-#777 := (<= 0::Int 0::Int)
-#591 := (>= 0::Int 0::Int)
-#782 := (or #591 #777)
-#492 := (not #782)
-#781 := (or #777 #777)
-#778 := (not #781)
-#493 := (or #778 #492)
-#765 := (if #493 #774 #776)
-#780 := (= 0::Int 0::Int)
-#502 := (or #780 #780)
-#766 := (if #502 #503 #765)
-#738 := (or #737 #766)
-#728 := (iff #738 #733)
-#730 := (iff #733 #733)
-#724 := [rewrite]: #730
-#735 := (iff #766 #503)
-#1 := true
-#732 := (if true #503 #774)
-#723 := (iff #732 #503)
-#725 := [rewrite]: #723
-#734 := (iff #766 #732)
-#741 := (iff #765 #774)
-#648 := (if false #774 #774)
-#651 := (iff #648 #774)
-#744 := [rewrite]: #651
-#649 := (iff #765 #648)
-#639 := (iff #776 #774)
-#645 := (= #772 #773)
-#628 := (= #775 #495)
-#740 := (= #771 #494)
-#644 := (= #489 0::Int)
-#739 := [rewrite]: #644
-#743 := [monotonicity #739 #739]: #740
-#643 := [monotonicity #743]: #628
-#646 := [monotonicity #643]: #645
-#647 := [monotonicity #646]: #639
-#594 := (iff #493 false)
-#748 := (or false false)
-#634 := (iff #748 false)
-#635 := [rewrite]: #634
-#751 := (iff #493 #748)
-#749 := (iff #492 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#746 := (iff #492 #460)
-#592 := (iff #782 true)
-#763 := (or true true)
-#764 := (iff #763 true)
-#770 := [rewrite]: #764
-#761 := (iff #782 #763)
-#613 := (iff #777 true)
-#755 := [rewrite]: #613
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#590 := [monotonicity #800 #755]: #761
-#593 := [trans #590 #770]: #592
-#747 := [monotonicity #593]: #746
-#750 := [trans #747 #448]: #749
-#760 := (iff #778 false)
-#753 := (iff #778 #460)
-#758 := (iff #781 true)
-#756 := (iff #781 #763)
-#757 := [monotonicity #755 #755]: #756
-#752 := [trans #757 #770]: #758
-#759 := [monotonicity #752]: #753
-#754 := [trans #759 #448]: #760
-#633 := [monotonicity #754 #750]: #751
-#742 := [trans #633 #635]: #594
-#650 := [monotonicity #742 #647]: #649
-#745 := [trans #650 #744]: #741
-#611 := (iff #502 true)
-#768 := (iff #502 #763)
-#767 := (iff #780 true)
-#762 := [rewrite]: #767
-#769 := [monotonicity #762 #762]: #768
-#612 := [trans #769 #770]: #611
-#726 := [monotonicity #612 #745]: #734
-#736 := [trans #726 #725]: #735
-#729 := [monotonicity #736]: #728
-#731 := [trans #729 #724]: #728
-#727 := [quant-inst #9 #9]: #738
-#715 := [mp #727 #731]: #733
-#718 := [unit-resolution #715 #836]: #503
-#719 := [monotonicity #718]: #14
-#15 := (not #14)
-#83 := [asserted]: #15
-[unit-resolution #83 #719]: false
-unsat
-8c194d24ce95c51840adf6b32bc910599b480f95 263 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#13 := 0::Int
-decl f4 :: S2
-#7 := f4
-#16 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#10 := f10
-decl f9 :: S6
-#9 := f9
-#11 := (f8 f9 f10)
-decl f7 :: S5
-#8 := f7
-#12 := (f6 f7 #11)
-#14 := (f5 #12 0::Int)
-#15 := (f3 f4 #14)
-#17 := (= #15 #16)
-#495 := (= #14 0::Int)
-#24 := (:var 0 Int)
-#35 := (:var 1 Int)
-#36 := (f6 f7 #35)
-#37 := (f5 #36 #24)
-#832 := (pattern #37)
-#137 := -1::Int
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #35)
-#144 := (div #138 #141)
-#310 := (* -1::Int #144)
-#311 := (+ #37 #310)
-#312 := (= #311 0::Int)
-#47 := (div #35 #24)
-#307 := (* -1::Int #47)
-#308 := (+ #37 #307)
-#309 := (= #308 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #35 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #35 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#313 := (if #274 #309 #312)
-#306 := (= #37 0::Int)
-#39 := (= #24 0::Int)
-#38 := (= #35 0::Int)
-#40 := (or #38 #39)
-#314 := (if #40 #306 #313)
-#833 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #832) #314)
-#317 := (forall (vars (?v0 Int) (?v1 Int)) #314)
-#836 := (iff #317 #833)
-#834 := (iff #314 #314)
-#835 := [refl]: #834
-#837 := [quant-intro #835]: #836
-#277 := (if #274 #47 #144)
-#280 := (if #40 0::Int #277)
-#283 := (= #37 #280)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#318 := (iff #286 #317)
-#315 := (iff #283 #314)
-#316 := [rewrite]: #315
-#319 := [quant-intro #316]: #318
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#180 := (if #177 #47 #144)
-#183 := (if #40 0::Int #180)
-#186 := (= #37 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#287 := (iff #189 #286)
-#284 := (iff #186 #283)
-#281 := (= #183 #280)
-#278 := (= #180 #277)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#279 := [monotonicity #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [monotonicity #282]: #284
-#288 := [quant-intro #285]: #287
-#249 := (~ #189 #189)
-#262 := (~ #186 #186)
-#263 := [refl]: #262
-#250 := [nnf-pos #263]: #249
-#49 := (- #24)
-#48 := (- #35)
-#50 := (div #48 #49)
-#42 := (< 0::Int #24)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#51 := (if #46 #47 #50)
-#52 := (if #40 0::Int #51)
-#53 := (= #37 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#192 := (iff #54 #189)
-#147 := (if #46 #47 #144)
-#150 := (if #40 0::Int #147)
-#153 := (= #37 #150)
-#156 := (forall (vars (?v0 Int) (?v1 Int)) #153)
-#190 := (iff #156 #189)
-#187 := (iff #153 #186)
-#184 := (= #150 #183)
-#181 := (= #147 #180)
-#178 := (iff #46 #177)
-#175 := (iff #45 #174)
-#165 := (iff #42 #164)
-#166 := [rewrite]: #165
-#172 := (iff #44 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #43 #167)
-#161 := (iff #41 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#157 := (iff #54 #156)
-#154 := (iff #53 #153)
-#151 := (= #52 #150)
-#148 := (= #51 #147)
-#145 := (= #50 #144)
-#142 := (= #49 #141)
-#143 := [rewrite]: #142
-#139 := (= #48 #138)
-#140 := [rewrite]: #139
-#146 := [monotonicity #140 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#193 := [trans #158 #191]: #192
-#136 := [asserted]: #54
-#194 := [mp #136 #193]: #189
-#264 := [mp~ #194 #250]: #189
-#289 := [mp #264 #288]: #286
-#320 := [mp #289 #319]: #317
-#838 := [mp #320 #837]: #833
-#713 := (not #833)
-#714 := (or #713 #495)
-#765 := (* -1::Int 0::Int)
-#764 := (* -1::Int #11)
-#770 := (div #764 #765)
-#771 := (* -1::Int #770)
-#766 := (+ #14 #771)
-#772 := (= #766 0::Int)
-#778 := (div #11 0::Int)
-#767 := (* -1::Int #778)
-#768 := (+ #14 #767)
-#769 := (= #768 0::Int)
-#497 := (<= 0::Int 0::Int)
-#491 := (>= #11 0::Int)
-#773 := (or #491 #497)
-#777 := (not #773)
-#496 := (<= #11 0::Int)
-#775 := (or #496 #497)
-#776 := (not #775)
-#774 := (or #776 #777)
-#613 := (if #774 #769 #772)
-#784 := (= 0::Int 0::Int)
-#780 := (= #11 0::Int)
-#494 := (or #780 #784)
-#614 := (if #494 #495 #613)
-#715 := (or #713 #614)
-#716 := (iff #715 #714)
-#697 := (iff #714 #714)
-#699 := [rewrite]: #697
-#710 := (iff #614 #495)
-#734 := (div #764 0::Int)
-#725 := (* -1::Int #734)
-#738 := (+ #14 #725)
-#740 := (= #738 0::Int)
-#1 := true
-#721 := (if true #495 #740)
-#719 := (iff #721 #495)
-#724 := [rewrite]: #719
-#722 := (iff #614 #721)
-#718 := (iff #613 #740)
-#731 := (if false #769 #740)
-#733 := (iff #731 #740)
-#717 := [rewrite]: #733
-#732 := (iff #613 #731)
-#729 := (iff #772 #740)
-#739 := (= #766 #738)
-#727 := (= #771 #725)
-#736 := (= #770 #734)
-#743 := (= #765 0::Int)
-#747 := [rewrite]: #743
-#728 := [monotonicity #747]: #736
-#737 := [monotonicity #728]: #727
-#735 := [monotonicity #737]: #739
-#730 := [monotonicity #735]: #729
-#653 := (iff #774 false)
-#641 := (or false false)
-#651 := (iff #641 false)
-#652 := [rewrite]: #651
-#649 := (iff #774 #641)
-#647 := (iff #777 false)
-#451 := (not true)
-#789 := (iff #451 false)
-#790 := [rewrite]: #789
-#630 := (iff #777 #451)
-#742 := (iff #773 true)
-#637 := (or #491 true)
-#646 := (iff #637 true)
-#741 := [rewrite]: #646
-#596 := (iff #773 #637)
-#756 := (iff #497 true)
-#763 := [rewrite]: #756
-#744 := [monotonicity #763]: #596
-#745 := [trans #744 #741]: #742
-#645 := [monotonicity #745]: #630
-#648 := [trans #645 #790]: #647
-#635 := (iff #776 false)
-#750 := (iff #776 #451)
-#751 := (iff #775 true)
-#592 := (or #496 true)
-#748 := (iff #592 true)
-#749 := [rewrite]: #748
-#594 := (iff #775 #592)
-#595 := [monotonicity #763]: #594
-#752 := [trans #595 #749]: #751
-#753 := [monotonicity #752]: #750
-#636 := [trans #753 #790]: #635
-#650 := [monotonicity #636 #648]: #649
-#746 := [trans #650 #652]: #653
-#726 := [monotonicity #746 #730]: #732
-#720 := [trans #726 #717]: #718
-#761 := (iff #494 true)
-#758 := (or #780 true)
-#754 := (iff #758 true)
-#755 := [rewrite]: #754
-#759 := (iff #494 #758)
-#615 := (iff #784 true)
-#757 := [rewrite]: #615
-#760 := [monotonicity #757]: #759
-#762 := [trans #760 #755]: #761
-#723 := [monotonicity #762 #720]: #722
-#711 := [trans #723 #724]: #710
-#696 := [monotonicity #711]: #716
-#700 := [trans #696 #699]: #716
-#712 := [quant-inst #11 #13]: #715
-#701 := [mp #712 #700]: #714
-#703 := [unit-resolution #701 #838]: #495
-#704 := [monotonicity #703]: #17
-#18 := (not #17)
-#85 := [asserted]: #18
-[unit-resolution #85 #704]: false
-unsat
-4e4622ee8bc45ab84a91b4f6c078726a6c12f7d8 280 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 0::Int)
-#12 := (f5 #10 1::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#777 := (= #12 0::Int)
-#23 := (:var 0 Int)
-#34 := (:var 1 Int)
-#35 := (f6 f7 #34)
-#36 := (f5 #35 #23)
-#830 := (pattern #36)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #34)
-#143 := (div #137 #140)
-#309 := (* -1::Int #143)
-#310 := (+ #36 #309)
-#311 := (= #310 0::Int)
-#46 := (div #34 #23)
-#306 := (* -1::Int #46)
-#307 := (+ #36 #306)
-#308 := (= #307 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #34 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #34 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#312 := (if #273 #308 #311)
-#305 := (= #36 0::Int)
-#38 := (= #23 0::Int)
-#37 := (= #34 0::Int)
-#39 := (or #37 #38)
-#313 := (if #39 #305 #312)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #313)
-#316 := (forall (vars (?v0 Int) (?v1 Int)) #313)
-#834 := (iff #316 #831)
-#832 := (iff #313 #313)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#276 := (if #273 #46 #143)
-#279 := (if #39 0::Int #276)
-#282 := (= #36 #279)
-#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
-#317 := (iff #285 #316)
-#314 := (iff #282 #313)
-#315 := [rewrite]: #314
-#318 := [quant-intro #315]: #317
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#179 := (if #176 #46 #143)
-#182 := (if #39 0::Int #179)
-#185 := (= #36 #182)
-#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
-#286 := (iff #188 #285)
-#283 := (iff #185 #282)
-#280 := (= #182 #279)
-#277 := (= #179 #276)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#278 := [monotonicity #275]: #277
-#281 := [monotonicity #278]: #280
-#284 := [monotonicity #281]: #283
-#287 := [quant-intro #284]: #286
-#248 := (~ #188 #188)
-#261 := (~ #185 #185)
-#262 := [refl]: #261
-#249 := [nnf-pos #262]: #248
-#48 := (- #23)
-#47 := (- #34)
-#49 := (div #47 #48)
-#41 := (< 0::Int #23)
-#43 := (< #34 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #34)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#50 := (if #45 #46 #49)
-#51 := (if #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#191 := (iff #53 #188)
-#146 := (if #45 #46 #143)
-#149 := (if #39 0::Int #146)
-#152 := (= #36 #149)
-#155 := (forall (vars (?v0 Int) (?v1 Int)) #152)
-#189 := (iff #155 #188)
-#186 := (iff #152 #185)
-#183 := (= #149 #182)
-#180 := (= #146 #179)
-#177 := (iff #45 #176)
-#174 := (iff #44 #173)
-#164 := (iff #41 #163)
-#165 := [rewrite]: #164
-#171 := (iff #43 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #42 #166)
-#160 := (iff #40 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [quant-intro #187]: #189
-#156 := (iff #53 #155)
-#153 := (iff #52 #152)
-#150 := (= #51 #149)
-#147 := (= #50 #146)
-#144 := (= #49 #143)
-#141 := (= #48 #140)
-#142 := [rewrite]: #141
-#138 := (= #47 #137)
-#139 := [rewrite]: #138
-#145 := [monotonicity #139 #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [quant-intro #154]: #156
-#192 := [trans #157 #190]: #191
-#135 := [asserted]: #53
-#193 := [mp #135 #192]: #188
-#263 := [mp~ #193 #249]: #188
-#288 := [mp #263 #287]: #285
-#319 := [mp #288 #318]: #316
-#836 := [mp #319 #835]: #831
-#704 := (not #831)
-#705 := (or #704 #777)
-#772 := (* -1::Int 1::Int)
-#775 := (* -1::Int 0::Int)
-#776 := (div #775 #772)
-#765 := (* -1::Int #776)
-#766 := (+ #12 #765)
-#767 := (= #766 0::Int)
-#773 := (div 0::Int 1::Int)
-#774 := (* -1::Int #773)
-#489 := (+ #12 #774)
-#771 := (= #489 0::Int)
-#778 := (<= 1::Int 0::Int)
-#591 := (>= 0::Int 0::Int)
-#493 := (or #591 #778)
-#494 := (not #493)
-#781 := (<= 0::Int 0::Int)
-#782 := (or #781 #778)
-#492 := (not #782)
-#495 := (or #492 #494)
-#762 := (if #495 #771 #767)
-#502 := (= 1::Int 0::Int)
-#780 := (= 0::Int 0::Int)
-#503 := (or #780 #502)
-#763 := (if #503 #777 #762)
-#706 := (or #704 #763)
-#707 := (iff #706 #705)
-#686 := (iff #705 #705)
-#688 := [rewrite]: #686
-#702 := (iff #763 #777)
-#1 := true
-#697 := (if true #777 #777)
-#700 := (iff #697 #777)
-#701 := [rewrite]: #700
-#698 := (iff #763 #697)
-#694 := (iff #762 #777)
-#711 := (if false #777 #777)
-#710 := (iff #711 #777)
-#714 := [rewrite]: #710
-#712 := (iff #762 #711)
-#708 := (iff #767 #777)
-#717 := (= #766 #12)
-#741 := (+ #12 0::Int)
-#734 := (= #741 #12)
-#726 := [rewrite]: #734
-#720 := (= #766 #741)
-#718 := (= #765 0::Int)
-#649 := (= #775 0::Int)
-#650 := [rewrite]: #649
-#715 := (= #765 #775)
-#724 := (= #776 0::Int)
-#738 := (div 0::Int -1::Int)
-#729 := (= #738 0::Int)
-#730 := [rewrite]: #729
-#727 := (= #776 #738)
-#737 := (= #772 -1::Int)
-#733 := [rewrite]: #737
-#728 := [monotonicity #650 #733]: #727
-#731 := [trans #728 #730]: #724
-#716 := [monotonicity #731]: #715
-#719 := [trans #716 #650]: #718
-#721 := [monotonicity #719]: #720
-#722 := [trans #721 #726]: #717
-#709 := [monotonicity #722]: #708
-#735 := (iff #771 #777)
-#723 := (= #489 #12)
-#745 := (= #489 #741)
-#651 := (= #774 0::Int)
-#647 := (= #774 #775)
-#646 := (= #773 0::Int)
-#639 := [rewrite]: #646
-#648 := [monotonicity #639]: #647
-#744 := [trans #648 #650]: #651
-#732 := [monotonicity #744]: #745
-#725 := [trans #732 #726]: #723
-#736 := [monotonicity #725]: #735
-#643 := (iff #495 false)
-#644 := (or false false)
-#743 := (iff #644 false)
-#628 := [rewrite]: #743
-#739 := (iff #495 #644)
-#594 := (iff #494 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#634 := (iff #494 #460)
-#751 := (iff #493 true)
-#611 := (or true false)
-#755 := (iff #611 true)
-#756 := [rewrite]: #755
-#750 := (iff #493 #611)
-#759 := (iff #778 false)
-#760 := [rewrite]: #759
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#748 := [monotonicity #800 #760]: #750
-#633 := [trans #748 #756]: #751
-#635 := [monotonicity #633]: #634
-#742 := [trans #635 #448]: #594
-#747 := (iff #492 false)
-#593 := (iff #492 #460)
-#590 := (iff #782 true)
-#754 := (iff #782 #611)
-#752 := (iff #781 true)
-#753 := [rewrite]: #752
-#761 := [monotonicity #753 #760]: #754
-#592 := [trans #761 #756]: #590
-#746 := [monotonicity #592]: #593
-#749 := [trans #746 #448]: #747
-#740 := [monotonicity #749 #742]: #739
-#645 := [trans #740 #628]: #643
-#713 := [monotonicity #645 #736 #709]: #712
-#695 := [trans #713 #714]: #694
-#757 := (iff #503 true)
-#612 := (iff #503 #611)
-#764 := (iff #502 false)
-#770 := [rewrite]: #764
-#768 := (iff #780 true)
-#769 := [rewrite]: #768
-#613 := [monotonicity #769 #770]: #612
-#758 := [trans #613 #756]: #757
-#699 := [monotonicity #758 #695]: #698
-#703 := [trans #699 #701]: #702
-#685 := [monotonicity #703]: #707
-#689 := [trans #685 #688]: #707
-#696 := [quant-inst #9 #11]: #706
-#690 := [mp #696 #689]: #705
-#692 := [unit-resolution #690 #836]: #777
-#687 := [monotonicity #692]: #15
-#16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #687]: false
-unsat
-f2d5511489ae0b1083bd6d09fc48e4e14f9df895 283 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 1::Int
-decl f4 :: S2
-#7 := f4
-#13 := (f3 f4 1::Int)
-decl f5 :: (-> S4 Int Int)
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 1::Int)
-#11 := (f5 #10 1::Int)
-#12 := (f3 f4 #11)
-#14 := (= #12 #13)
-#736 := (= #11 1::Int)
-#23 := (:var 0 Int)
-#34 := (:var 1 Int)
-#35 := (f6 f7 #34)
-#36 := (f5 #35 #23)
-#830 := (pattern #36)
-#22 := 0::Int
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #34)
-#143 := (div #137 #140)
-#309 := (* -1::Int #143)
-#310 := (+ #36 #309)
-#311 := (= #310 0::Int)
-#46 := (div #34 #23)
-#306 := (* -1::Int #46)
-#307 := (+ #36 #306)
-#308 := (= #307 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #34 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #34 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#312 := (if #273 #308 #311)
-#305 := (= #36 0::Int)
-#38 := (= #23 0::Int)
-#37 := (= #34 0::Int)
-#39 := (or #37 #38)
-#313 := (if #39 #305 #312)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #313)
-#316 := (forall (vars (?v0 Int) (?v1 Int)) #313)
-#834 := (iff #316 #831)
-#832 := (iff #313 #313)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#276 := (if #273 #46 #143)
-#279 := (if #39 0::Int #276)
-#282 := (= #36 #279)
-#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
-#317 := (iff #285 #316)
-#314 := (iff #282 #313)
-#315 := [rewrite]: #314
-#318 := [quant-intro #315]: #317
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#179 := (if #176 #46 #143)
-#182 := (if #39 0::Int #179)
-#185 := (= #36 #182)
-#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
-#286 := (iff #188 #285)
-#283 := (iff #185 #282)
-#280 := (= #182 #279)
-#277 := (= #179 #276)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#278 := [monotonicity #275]: #277
-#281 := [monotonicity #278]: #280
-#284 := [monotonicity #281]: #283
-#287 := [quant-intro #284]: #286
-#248 := (~ #188 #188)
-#261 := (~ #185 #185)
-#262 := [refl]: #261
-#249 := [nnf-pos #262]: #248
-#48 := (- #23)
-#47 := (- #34)
-#49 := (div #47 #48)
-#41 := (< 0::Int #23)
-#43 := (< #34 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #34)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#50 := (if #45 #46 #49)
-#51 := (if #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#191 := (iff #53 #188)
-#146 := (if #45 #46 #143)
-#149 := (if #39 0::Int #146)
-#152 := (= #36 #149)
-#155 := (forall (vars (?v0 Int) (?v1 Int)) #152)
-#189 := (iff #155 #188)
-#186 := (iff #152 #185)
-#183 := (= #149 #182)
-#180 := (= #146 #179)
-#177 := (iff #45 #176)
-#174 := (iff #44 #173)
-#164 := (iff #41 #163)
-#165 := [rewrite]: #164
-#171 := (iff #43 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #42 #166)
-#160 := (iff #40 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [quant-intro #187]: #189
-#156 := (iff #53 #155)
-#153 := (iff #52 #152)
-#150 := (= #51 #149)
-#147 := (= #50 #146)
-#144 := (= #49 #143)
-#141 := (= #48 #140)
-#142 := [rewrite]: #141
-#138 := (= #47 #137)
-#139 := [rewrite]: #138
-#145 := [monotonicity #139 #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [quant-intro #154]: #156
-#192 := [trans #157 #190]: #191
-#135 := [asserted]: #53
-#193 := [mp #135 #192]: #188
-#263 := [mp~ #193 #249]: #188
-#288 := [mp #263 #287]: #285
-#319 := [mp #288 #318]: #316
-#836 := [mp #319 #835]: #831
-#707 := (not #831)
-#685 := (or #707 #736)
-#771 := (* -1::Int 1::Int)
-#775 := (div #771 #771)
-#772 := (* -1::Int #775)
-#776 := (+ #11 #772)
-#765 := (= #776 0::Int)
-#495 := (div 1::Int 1::Int)
-#773 := (* -1::Int #495)
-#774 := (+ #11 #773)
-#489 := (= #774 0::Int)
-#781 := (<= 1::Int 0::Int)
-#591 := (>= 1::Int 0::Int)
-#492 := (or #591 #781)
-#493 := (not #492)
-#778 := (or #781 #781)
-#782 := (not #778)
-#494 := (or #782 #493)
-#766 := (if #494 #489 #765)
-#777 := (= #11 0::Int)
-#502 := (= 1::Int 0::Int)
-#503 := (or #502 #502)
-#767 := (if #503 #777 #766)
-#686 := (or #707 #767)
-#689 := (iff #686 #685)
-#691 := (iff #685 #685)
-#692 := [rewrite]: #691
-#706 := (iff #767 #736)
-#701 := (if false #777 #736)
-#704 := (iff #701 #736)
-#705 := [rewrite]: #704
-#702 := (iff #767 #701)
-#699 := (iff #766 #736)
-#1 := true
-#714 := (if true #736 #736)
-#697 := (iff #714 #736)
-#698 := [rewrite]: #697
-#694 := (iff #766 #714)
-#713 := (iff #765 #736)
-#741 := (+ -1::Int #11)
-#723 := (= #741 0::Int)
-#737 := (iff #723 #736)
-#733 := [rewrite]: #737
-#711 := (iff #765 #723)
-#708 := (= #776 #741)
-#650 := (+ #11 -1::Int)
-#745 := (= #650 #741)
-#732 := [rewrite]: #745
-#717 := (= #776 #650)
-#720 := (= #772 -1::Int)
-#639 := (= #771 -1::Int)
-#647 := [rewrite]: #639
-#718 := (= #772 #771)
-#715 := (= #775 1::Int)
-#728 := (div -1::Int -1::Int)
-#724 := (= #728 1::Int)
-#731 := [rewrite]: #724
-#729 := (= #775 #728)
-#730 := [monotonicity #647 #647]: #729
-#716 := [trans #730 #731]: #715
-#719 := [monotonicity #716]: #718
-#721 := [trans #719 #647]: #720
-#722 := [monotonicity #721]: #717
-#709 := [trans #722 #732]: #708
-#712 := [monotonicity #709]: #711
-#710 := [trans #712 #733]: #713
-#738 := (iff #489 #736)
-#725 := (iff #489 #723)
-#734 := (= #774 #741)
-#651 := (= #774 #650)
-#648 := (= #773 -1::Int)
-#645 := (= #773 #771)
-#628 := (= #495 1::Int)
-#643 := [rewrite]: #628
-#646 := [monotonicity #643]: #645
-#649 := [trans #646 #647]: #648
-#744 := [monotonicity #649]: #651
-#726 := [trans #744 #732]: #734
-#735 := [monotonicity #726]: #725
-#727 := [trans #735 #733]: #738
-#740 := (iff #494 true)
-#746 := (or true false)
-#750 := (iff #746 true)
-#748 := [rewrite]: #750
-#644 := (iff #494 #746)
-#594 := (iff #493 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#634 := (iff #493 #460)
-#751 := (iff #492 true)
-#747 := (iff #492 #746)
-#755 := (iff #781 false)
-#756 := [rewrite]: #755
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#749 := [monotonicity #800 #756]: #747
-#633 := [trans #749 #748]: #751
-#635 := [monotonicity #633]: #634
-#742 := [trans #635 #448]: #594
-#592 := (iff #782 true)
-#759 := (not false)
-#761 := (iff #759 true)
-#590 := [rewrite]: #761
-#760 := (iff #782 #759)
-#752 := (iff #778 false)
-#768 := (or false false)
-#770 := (iff #768 false)
-#611 := [rewrite]: #770
-#757 := (iff #778 #768)
-#758 := [monotonicity #756 #756]: #757
-#753 := [trans #758 #611]: #752
-#754 := [monotonicity #753]: #760
-#593 := [trans #754 #590]: #592
-#739 := [monotonicity #593 #742]: #644
-#743 := [trans #739 #748]: #740
-#695 := [monotonicity #743 #727 #710]: #694
-#700 := [trans #695 #698]: #699
-#612 := (iff #503 false)
-#769 := (iff #503 #768)
-#762 := (iff #502 false)
-#763 := [rewrite]: #762
-#764 := [monotonicity #763 #763]: #769
-#613 := [trans #764 #611]: #612
-#703 := [monotonicity #613 #700]: #702
-#696 := [trans #703 #705]: #706
-#690 := [monotonicity #696]: #689
-#687 := [trans #690 #692]: #689
-#688 := [quant-inst #9 #9]: #686
-#693 := [mp #688 #687]: #685
-#676 := [unit-resolution #693 #836]: #736
-#677 := [monotonicity #676]: #14
-#15 := (not #14)
-#84 := [asserted]: #15
-[unit-resolution #84 #677]: false
-unsat
-b5e857fcfdcccfc1f8e76abc18cb220c195f28ba 294 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 3::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 3::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 3::Int)
-#12 := (f5 #10 1::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#724 := (= #12 3::Int)
-#24 := (:var 0 Int)
-#35 := (:var 1 Int)
-#36 := (f6 f7 #35)
-#37 := (f5 #36 #24)
-#830 := (pattern #37)
-#23 := 0::Int
-#137 := -1::Int
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #35)
-#144 := (div #138 #141)
-#310 := (* -1::Int #144)
-#311 := (+ #37 #310)
-#312 := (= #311 0::Int)
-#47 := (div #35 #24)
-#307 := (* -1::Int #47)
-#308 := (+ #37 #307)
-#309 := (= #308 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #35 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #35 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#313 := (if #274 #309 #312)
-#306 := (= #37 0::Int)
-#39 := (= #24 0::Int)
-#38 := (= #35 0::Int)
-#40 := (or #38 #39)
-#314 := (if #40 #306 #313)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #314)
-#317 := (forall (vars (?v0 Int) (?v1 Int)) #314)
-#834 := (iff #317 #831)
-#832 := (iff #314 #314)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#277 := (if #274 #47 #144)
-#280 := (if #40 0::Int #277)
-#283 := (= #37 #280)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#318 := (iff #286 #317)
-#315 := (iff #283 #314)
-#316 := [rewrite]: #315
-#319 := [quant-intro #316]: #318
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#180 := (if #177 #47 #144)
-#183 := (if #40 0::Int #180)
-#186 := (= #37 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#287 := (iff #189 #286)
-#284 := (iff #186 #283)
-#281 := (= #183 #280)
-#278 := (= #180 #277)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#279 := [monotonicity #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [monotonicity #282]: #284
-#288 := [quant-intro #285]: #287
-#249 := (~ #189 #189)
-#262 := (~ #186 #186)
-#263 := [refl]: #262
-#250 := [nnf-pos #263]: #249
-#49 := (- #24)
-#48 := (- #35)
-#50 := (div #48 #49)
-#42 := (< 0::Int #24)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#51 := (if #46 #47 #50)
-#52 := (if #40 0::Int #51)
-#53 := (= #37 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#192 := (iff #54 #189)
-#147 := (if #46 #47 #144)
-#150 := (if #40 0::Int #147)
-#153 := (= #37 #150)
-#156 := (forall (vars (?v0 Int) (?v1 Int)) #153)
-#190 := (iff #156 #189)
-#187 := (iff #153 #186)
-#184 := (= #150 #183)
-#181 := (= #147 #180)
-#178 := (iff #46 #177)
-#175 := (iff #45 #174)
-#165 := (iff #42 #164)
-#166 := [rewrite]: #165
-#172 := (iff #44 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #43 #167)
-#161 := (iff #41 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#157 := (iff #54 #156)
-#154 := (iff #53 #153)
-#151 := (= #52 #150)
-#148 := (= #51 #147)
-#145 := (= #50 #144)
-#142 := (= #49 #141)
-#143 := [rewrite]: #142
-#139 := (= #48 #138)
-#140 := [rewrite]: #139
-#146 := [monotonicity #140 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#193 := [trans #158 #191]: #192
-#136 := [asserted]: #54
-#194 := [mp #136 #193]: #189
-#264 := [mp~ #194 #250]: #189
-#289 := [mp #264 #288]: #286
-#320 := [mp #289 #319]: #317
-#836 := [mp #320 #835]: #831
-#679 := (not #831)
-#675 := (or #679 #724)
-#776 := (* -1::Int 1::Int)
-#772 := (* -1::Int 3::Int)
-#765 := (div #772 #776)
-#766 := (* -1::Int #765)
-#767 := (+ #12 #766)
-#762 := (= #767 0::Int)
-#774 := (div 3::Int 1::Int)
-#489 := (* -1::Int #774)
-#771 := (+ #12 #489)
-#775 := (= #771 0::Int)
-#782 := (<= 1::Int 0::Int)
-#591 := (>= 3::Int 0::Int)
-#494 := (or #591 #782)
-#495 := (not #494)
-#778 := (<= 3::Int 0::Int)
-#492 := (or #778 #782)
-#493 := (not #492)
-#773 := (or #493 #495)
-#763 := (if #773 #775 #762)
-#781 := (= #12 0::Int)
-#503 := (= 1::Int 0::Int)
-#502 := (= 3::Int 0::Int)
-#777 := (or #502 #503)
-#768 := (if #777 #781 #763)
-#676 := (or #679 #768)
-#680 := (iff #676 #675)
-#682 := (iff #675 #675)
-#683 := [rewrite]: #682
-#687 := (iff #768 #724)
-#688 := (if false #781 #724)
-#691 := (iff #688 #724)
-#692 := [rewrite]: #691
-#689 := (iff #768 #688)
-#685 := (iff #763 #724)
-#1 := true
-#704 := (if true #724 #724)
-#696 := (iff #704 #724)
-#707 := [rewrite]: #696
-#705 := (iff #763 #704)
-#702 := (iff #762 #724)
-#741 := -3::Int
-#736 := (+ -3::Int #12)
-#728 := (= #736 0::Int)
-#731 := (iff #728 #724)
-#715 := [rewrite]: #731
-#700 := (iff #762 #728)
-#698 := (= #767 #736)
-#723 := (+ #12 -3::Int)
-#737 := (= #723 #736)
-#733 := [rewrite]: #737
-#695 := (= #767 #723)
-#714 := (= #766 -3::Int)
-#745 := (= #772 -3::Int)
-#732 := [rewrite]: #745
-#713 := (= #766 #772)
-#711 := (= #765 3::Int)
-#721 := (div -3::Int -1::Int)
-#708 := (= #721 3::Int)
-#709 := [rewrite]: #708
-#717 := (= #765 #721)
-#719 := (= #776 -1::Int)
-#720 := [rewrite]: #719
-#722 := [monotonicity #732 #720]: #717
-#712 := [trans #722 #709]: #711
-#710 := [monotonicity #712]: #713
-#694 := [trans #710 #732]: #714
-#697 := [monotonicity #694]: #695
-#699 := [trans #697 #733]: #698
-#701 := [monotonicity #699]: #700
-#703 := [trans #701 #715]: #702
-#716 := (iff #775 #724)
-#729 := (iff #775 #728)
-#738 := (= #771 #736)
-#725 := (= #771 #723)
-#734 := (= #489 -3::Int)
-#651 := (= #489 #772)
-#649 := (= #774 3::Int)
-#650 := [rewrite]: #649
-#744 := [monotonicity #650]: #651
-#726 := [trans #744 #732]: #734
-#735 := [monotonicity #726]: #725
-#727 := [trans #735 #733]: #738
-#730 := [monotonicity #727]: #729
-#718 := [trans #730 #715]: #716
-#647 := (iff #773 true)
-#634 := (or true false)
-#742 := (iff #634 true)
-#644 := [rewrite]: #742
-#646 := (iff #773 #634)
-#643 := (iff #495 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#743 := (iff #495 #460)
-#739 := (iff #494 true)
-#635 := (iff #494 #634)
-#760 := (iff #782 false)
-#754 := [rewrite]: #760
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#594 := [monotonicity #800 #754]: #635
-#740 := [trans #594 #644]: #739
-#628 := [monotonicity #740]: #743
-#645 := [trans #628 #448]: #643
-#751 := (iff #493 true)
-#746 := (not false)
-#750 := (iff #746 true)
-#748 := [rewrite]: #750
-#747 := (iff #493 #746)
-#592 := (iff #492 false)
-#612 := (or false false)
-#756 := (iff #612 false)
-#757 := [rewrite]: #756
-#761 := (iff #492 #612)
-#753 := (iff #778 false)
-#759 := [rewrite]: #753
-#590 := [monotonicity #759 #754]: #761
-#593 := [trans #590 #757]: #592
-#749 := [monotonicity #593]: #747
-#633 := [trans #749 #748]: #751
-#639 := [monotonicity #633 #645]: #646
-#648 := [trans #639 #644]: #647
-#706 := [monotonicity #648 #718 #703]: #705
-#686 := [trans #706 #707]: #685
-#758 := (iff #777 false)
-#613 := (iff #777 #612)
-#770 := (iff #503 false)
-#611 := [rewrite]: #770
-#769 := (iff #502 false)
-#764 := [rewrite]: #769
-#755 := [monotonicity #764 #611]: #613
-#752 := [trans #755 #757]: #758
-#690 := [monotonicity #752 #686]: #689
-#693 := [trans #690 #692]: #687
-#681 := [monotonicity #693]: #680
-#678 := [trans #681 #683]: #680
-#677 := [quant-inst #9 #11]: #676
-#684 := [mp #677 #678]: #675
-#659 := [unit-resolution #684 #836]: #724
-#552 := [monotonicity #659]: #15
-#16 := (not #15)
-#85 := [asserted]: #16
-[unit-resolution #85 #552]: false
-unsat
-35f8a4cc325e6764f31a3b4bdaffd9418bbd18c9 343 0
-#2 := false
-decl f10 :: S3
-#10 := f10
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 Int Int)
-#13 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f9 :: S6
-#9 := f9
-#11 := (f8 f9 f10)
-decl f7 :: S5
-#8 := f7
-#12 := (f6 f7 #11)
-#14 := (f5 #12 1::Int)
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 #14)
-#16 := (= #15 f10)
-#398 := (f3 f4 #11)
-#482 := (= #398 f10)
-#18 := (:var 0 S3)
-#19 := (f8 f9 #18)
-#811 := (pattern #19)
-#20 := (f3 f4 #19)
-#21 := (= #20 #18)
-#812 := (forall (vars (?v0 S3)) (:pat #811) #21)
-#22 := (forall (vars (?v0 S3)) #21)
-#815 := (iff #22 #812)
-#813 := (iff #21 #21)
-#814 := [refl]: #813
-#816 := [quant-intro #814]: #815
-#257 := (~ #22 #22)
-#255 := (~ #21 #21)
-#256 := [refl]: #255
-#258 := [nnf-pos #256]: #257
-#86 := [asserted]: #22
-#243 := [mp~ #86 #258]: #22
-#817 := [mp #243 #816]: #812
-#475 := (not #812)
-#486 := (or #475 #482)
-#487 := [quant-inst #10]: #486
-#664 := [unit-resolution #487 #817]: #482
-#638 := (= #15 #398)
-#663 := (= #14 #11)
-#790 := (div #11 1::Int)
-#625 := (= #790 #11)
-#549 := (= #11 #790)
-#23 := 0::Int
-#137 := -1::Int
-#791 := (* -1::Int #790)
-#588 := (+ #11 #791)
-#600 := (<= #588 0::Int)
-#627 := (= #588 0::Int)
-#1 := true
-#83 := [true-axiom]: true
-#555 := (or false #627)
-#558 := [th-lemma arith]: #555
-#559 := [unit-resolution #558 #83]: #627
-#563 := (not #627)
-#556 := (or #563 #600)
-#564 := [th-lemma arith triangle-eq]: #556
-#557 := [unit-resolution #564 #559]: #600
-#602 := (>= #588 0::Int)
-#560 := (or #563 #602)
-#561 := [th-lemma arith triangle-eq]: #560
-#547 := [unit-resolution #561 #559]: #602
-#550 := [th-lemma arith eq-propagate 1 1 #547 #557]: #549
-#533 := [symm #550]: #625
-#552 := (= #14 #790)
-#792 := (+ #14 #791)
-#649 := (<= #792 0::Int)
-#787 := (= #792 0::Int)
-#807 := (= #11 0::Int)
-#728 := (not #807)
-#697 := (= 0::Int #11)
-#665 := [hypothesis]: #807
-#708 := [symm #665]: #697
-#802 := (= #14 0::Int)
-#666 := (or #728 #802)
-#793 := (* -1::Int #11)
-#612 := (div #793 -1::Int)
-#756 := (* -1::Int #612)
-#759 := (+ #14 #756)
-#760 := (= #759 0::Int)
-#451 := (>= #11 0::Int)
-#767 := (not #451)
-#445 := (<= #11 0::Int)
-#495 := (not #445)
-#764 := (or #495 #767)
-#762 := (if #764 #787 #760)
-#594 := (if #807 #802 #762)
-#24 := (:var 0 Int)
-#35 := (:var 1 Int)
-#36 := (f6 f7 #35)
-#37 := (f5 #36 #24)
-#831 := (pattern #37)
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #35)
-#144 := (div #138 #141)
-#310 := (* -1::Int #144)
-#311 := (+ #37 #310)
-#312 := (= #311 0::Int)
-#47 := (div #35 #24)
-#307 := (* -1::Int #47)
-#308 := (+ #37 #307)
-#309 := (= #308 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #35 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #35 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#313 := (if #274 #309 #312)
-#306 := (= #37 0::Int)
-#39 := (= #24 0::Int)
-#38 := (= #35 0::Int)
-#40 := (or #38 #39)
-#314 := (if #40 #306 #313)
-#832 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #831) #314)
-#317 := (forall (vars (?v0 Int) (?v1 Int)) #314)
-#835 := (iff #317 #832)
-#833 := (iff #314 #314)
-#834 := [refl]: #833
-#836 := [quant-intro #834]: #835
-#277 := (if #274 #47 #144)
-#280 := (if #40 0::Int #277)
-#283 := (= #37 #280)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#318 := (iff #286 #317)
-#315 := (iff #283 #314)
-#316 := [rewrite]: #315
-#319 := [quant-intro #316]: #318
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#180 := (if #177 #47 #144)
-#183 := (if #40 0::Int #180)
-#186 := (= #37 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#287 := (iff #189 #286)
-#284 := (iff #186 #283)
-#281 := (= #183 #280)
-#278 := (= #180 #277)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#279 := [monotonicity #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [monotonicity #282]: #284
-#288 := [quant-intro #285]: #287
-#249 := (~ #189 #189)
-#262 := (~ #186 #186)
-#263 := [refl]: #262
-#250 := [nnf-pos #263]: #249
-#49 := (- #24)
-#48 := (- #35)
-#50 := (div #48 #49)
-#42 := (< 0::Int #24)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#51 := (if #46 #47 #50)
-#52 := (if #40 0::Int #51)
-#53 := (= #37 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#192 := (iff #54 #189)
-#147 := (if #46 #47 #144)
-#150 := (if #40 0::Int #147)
-#153 := (= #37 #150)
-#156 := (forall (vars (?v0 Int) (?v1 Int)) #153)
-#190 := (iff #156 #189)
-#187 := (iff #153 #186)
-#184 := (= #150 #183)
-#181 := (= #147 #180)
-#178 := (iff #46 #177)
-#175 := (iff #45 #174)
-#165 := (iff #42 #164)
-#166 := [rewrite]: #165
-#172 := (iff #44 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #43 #167)
-#161 := (iff #41 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#157 := (iff #54 #156)
-#154 := (iff #53 #153)
-#151 := (= #52 #150)
-#148 := (= #51 #147)
-#145 := (= #50 #144)
-#142 := (= #49 #141)
-#143 := [rewrite]: #142
-#139 := (= #48 #138)
-#140 := [rewrite]: #139
-#146 := [monotonicity #140 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#193 := [trans #158 #191]: #192
-#136 := [asserted]: #54
-#194 := [mp #136 #193]: #189
-#264 := [mp~ #194 #250]: #189
-#289 := [mp #264 #288]: #286
-#320 := [mp #289 #319]: #317
-#837 := [mp #320 #836]: #832
-#750 := (not #832)
-#751 := (or #750 #594)
-#431 := (* -1::Int 1::Int)
-#794 := (div #793 #431)
-#796 := (* -1::Int #794)
-#436 := (+ #14 #796)
-#437 := (= #436 0::Int)
-#786 := (<= 1::Int 0::Int)
-#452 := (or #451 #786)
-#788 := (not #452)
-#449 := (or #445 #786)
-#450 := (not #449)
-#789 := (or #450 #788)
-#797 := (if #789 #787 #437)
-#808 := (= 1::Int 0::Int)
-#461 := (or #807 #808)
-#795 := (if #461 #802 #797)
-#749 := (or #750 #795)
-#634 := (iff #749 #751)
-#636 := (iff #751 #751)
-#595 := [rewrite]: #636
-#747 := (iff #795 #594)
-#591 := (iff #797 #762)
-#761 := (iff #437 #760)
-#753 := (= #436 #759)
-#757 := (= #796 #756)
-#613 := (= #794 #612)
-#765 := (= #431 -1::Int)
-#771 := [rewrite]: #765
-#614 := [monotonicity #771]: #613
-#758 := [monotonicity #614]: #757
-#754 := [monotonicity #758]: #753
-#755 := [monotonicity #754]: #761
-#769 := (iff #789 #764)
-#768 := (iff #788 #767)
-#777 := (iff #452 #451)
-#775 := (or #451 false)
-#776 := (iff #775 #451)
-#773 := [rewrite]: #776
-#490 := (iff #452 #775)
-#781 := (iff #786 false)
-#503 := [rewrite]: #781
-#772 := [monotonicity #503]: #490
-#766 := [trans #772 #773]: #777
-#763 := [monotonicity #766]: #768
-#496 := (iff #450 #495)
-#493 := (iff #449 #445)
-#504 := (or #445 false)
-#779 := (iff #504 #445)
-#783 := [rewrite]: #779
-#778 := (iff #449 #504)
-#782 := [monotonicity #503]: #778
-#494 := [trans #782 #783]: #493
-#774 := [monotonicity #494]: #496
-#770 := [monotonicity #774 #763]: #769
-#593 := [monotonicity #770 #755]: #591
-#404 := (iff #461 #807)
-#785 := (or #807 false)
-#509 := (iff #785 #807)
-#510 := [rewrite]: #509
-#507 := (iff #461 #785)
-#798 := (iff #808 false)
-#784 := [rewrite]: #798
-#508 := [monotonicity #784]: #507
-#780 := [trans #508 #510]: #404
-#748 := [monotonicity #780 #593]: #747
-#635 := [monotonicity #748]: #634
-#743 := [trans #635 #595]: #634
-#752 := [quant-inst #11 #13]: #749
-#645 := [mp #752 #743]: #751
-#672 := [unit-resolution #645 #837]: #594
-#739 := (not #594)
-#729 := (or #739 #728 #802)
-#730 := [def-axiom]: #729
-#671 := [unit-resolution #730 #672]: #666
-#667 := [unit-resolution #671 #665]: #802
-#631 := [trans #667 #708]: #663
-#597 := [monotonicity #631]: #638
-#628 := [trans #597 #664]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-#630 := [unit-resolution #85 #628]: false
-#632 := [lemma #630]: #728
-#662 := (or #807 #787)
-#646 := (not #764)
-#724 := (not #787)
-#668 := [hypothesis]: #724
-#669 := [hypothesis]: #728
-#673 := (or #807 #762)
-#731 := (or #739 #807 #762)
-#725 := [def-axiom]: #731
-#674 := [unit-resolution #725 #672]: #673
-#670 := [unit-resolution #674 #669]: #762
-#742 := (not #762)
-#746 := (or #742 #646 #787)
-#733 := [def-axiom]: #746
-#675 := [unit-resolution #733 #670 #668]: #646
-#629 := (or #764 #451)
-#644 := [def-axiom]: #629
-#655 := [unit-resolution #644 #675]: #451
-#741 := (or #764 #445)
-#744 := [def-axiom]: #741
-#601 := [unit-resolution #744 #675]: #445
-#656 := (or #807 #495 #767)
-#637 := [th-lemma arith triangle-eq]: #656
-#661 := [unit-resolution #637 #669 #601 #655]: false
-#657 := [lemma #661]: #662
-#565 := [unit-resolution #657 #632]: #787
-#568 := (or #724 #649)
-#570 := [th-lemma arith triangle-eq]: #568
-#571 := [unit-resolution #570 #565]: #649
-#650 := (>= #792 0::Int)
-#567 := (or #724 #650)
-#572 := [th-lemma arith triangle-eq]: #567
-#562 := [unit-resolution #572 #565]: #650
-#554 := [th-lemma arith eq-propagate 1 1 #562 #571]: #552
-#535 := [trans #554 #533]: #663
-#536 := [monotonicity #535]: #638
-#537 := [trans #536 #664]: #16
-[unit-resolution #85 #537]: false
-unsat
-634d492b81b7e3859d758e0f7fab5f7237c6b80a 281 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 0::Int)
-#12 := (f5 #10 3::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#777 := (= #12 0::Int)
-#23 := (:var 0 Int)
-#34 := (:var 1 Int)
-#35 := (f6 f7 #34)
-#36 := (f5 #35 #23)
-#830 := (pattern #36)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #34)
-#143 := (div #137 #140)
-#309 := (* -1::Int #143)
-#310 := (+ #36 #309)
-#311 := (= #310 0::Int)
-#46 := (div #34 #23)
-#306 := (* -1::Int #46)
-#307 := (+ #36 #306)
-#308 := (= #307 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #34 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #34 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#312 := (if #273 #308 #311)
-#305 := (= #36 0::Int)
-#38 := (= #23 0::Int)
-#37 := (= #34 0::Int)
-#39 := (or #37 #38)
-#313 := (if #39 #305 #312)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #313)
-#316 := (forall (vars (?v0 Int) (?v1 Int)) #313)
-#834 := (iff #316 #831)
-#832 := (iff #313 #313)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#276 := (if #273 #46 #143)
-#279 := (if #39 0::Int #276)
-#282 := (= #36 #279)
-#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
-#317 := (iff #285 #316)
-#314 := (iff #282 #313)
-#315 := [rewrite]: #314
-#318 := [quant-intro #315]: #317
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#179 := (if #176 #46 #143)
-#182 := (if #39 0::Int #179)
-#185 := (= #36 #182)
-#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
-#286 := (iff #188 #285)
-#283 := (iff #185 #282)
-#280 := (= #182 #279)
-#277 := (= #179 #276)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#278 := [monotonicity #275]: #277
-#281 := [monotonicity #278]: #280
-#284 := [monotonicity #281]: #283
-#287 := [quant-intro #284]: #286
-#248 := (~ #188 #188)
-#261 := (~ #185 #185)
-#262 := [refl]: #261
-#249 := [nnf-pos #262]: #248
-#48 := (- #23)
-#47 := (- #34)
-#49 := (div #47 #48)
-#41 := (< 0::Int #23)
-#43 := (< #34 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #34)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#50 := (if #45 #46 #49)
-#51 := (if #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#191 := (iff #53 #188)
-#146 := (if #45 #46 #143)
-#149 := (if #39 0::Int #146)
-#152 := (= #36 #149)
-#155 := (forall (vars (?v0 Int) (?v1 Int)) #152)
-#189 := (iff #155 #188)
-#186 := (iff #152 #185)
-#183 := (= #149 #182)
-#180 := (= #146 #179)
-#177 := (iff #45 #176)
-#174 := (iff #44 #173)
-#164 := (iff #41 #163)
-#165 := [rewrite]: #164
-#171 := (iff #43 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #42 #166)
-#160 := (iff #40 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [quant-intro #187]: #189
-#156 := (iff #53 #155)
-#153 := (iff #52 #152)
-#150 := (= #51 #149)
-#147 := (= #50 #146)
-#144 := (= #49 #143)
-#141 := (= #48 #140)
-#142 := [rewrite]: #141
-#138 := (= #47 #137)
-#139 := [rewrite]: #138
-#145 := [monotonicity #139 #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [quant-intro #154]: #156
-#192 := [trans #157 #190]: #191
-#135 := [asserted]: #53
-#193 := [mp #135 #192]: #188
-#263 := [mp~ #193 #249]: #188
-#288 := [mp #263 #287]: #285
-#319 := [mp #288 #318]: #316
-#836 := [mp #319 #835]: #831
-#705 := (not #831)
-#706 := (or #705 #777)
-#772 := (* -1::Int 3::Int)
-#775 := (* -1::Int 0::Int)
-#776 := (div #775 #772)
-#765 := (* -1::Int #776)
-#766 := (+ #12 #765)
-#767 := (= #766 0::Int)
-#773 := (div 0::Int 3::Int)
-#774 := (* -1::Int #773)
-#489 := (+ #12 #774)
-#771 := (= #489 0::Int)
-#778 := (<= 3::Int 0::Int)
-#591 := (>= 0::Int 0::Int)
-#493 := (or #591 #778)
-#494 := (not #493)
-#781 := (<= 0::Int 0::Int)
-#782 := (or #781 #778)
-#492 := (not #782)
-#495 := (or #492 #494)
-#762 := (if #495 #771 #767)
-#502 := (= 3::Int 0::Int)
-#780 := (= 0::Int 0::Int)
-#503 := (or #780 #502)
-#763 := (if #503 #777 #762)
-#696 := (or #705 #763)
-#685 := (iff #696 #706)
-#688 := (iff #706 #706)
-#689 := [rewrite]: #688
-#703 := (iff #763 #777)
-#1 := true
-#698 := (if true #777 #777)
-#701 := (iff #698 #777)
-#702 := [rewrite]: #701
-#699 := (iff #763 #698)
-#695 := (iff #762 #777)
-#712 := (if false #777 #777)
-#714 := (iff #712 #777)
-#694 := [rewrite]: #714
-#713 := (iff #762 #712)
-#709 := (iff #767 #777)
-#722 := (= #766 #12)
-#741 := (+ #12 0::Int)
-#734 := (= #741 #12)
-#726 := [rewrite]: #734
-#721 := (= #766 #741)
-#719 := (= #765 0::Int)
-#649 := (= #775 0::Int)
-#650 := [rewrite]: #649
-#716 := (= #765 #775)
-#731 := (= #776 0::Int)
-#737 := -3::Int
-#727 := (div 0::Int -3::Int)
-#730 := (= #727 0::Int)
-#724 := [rewrite]: #730
-#728 := (= #776 #727)
-#733 := (= #772 -3::Int)
-#738 := [rewrite]: #733
-#729 := [monotonicity #650 #738]: #728
-#715 := [trans #729 #724]: #731
-#718 := [monotonicity #715]: #716
-#720 := [trans #718 #650]: #719
-#717 := [monotonicity #720]: #721
-#708 := [trans #717 #726]: #722
-#711 := [monotonicity #708]: #709
-#735 := (iff #771 #777)
-#723 := (= #489 #12)
-#745 := (= #489 #741)
-#651 := (= #774 0::Int)
-#647 := (= #774 #775)
-#646 := (= #773 0::Int)
-#639 := [rewrite]: #646
-#648 := [monotonicity #639]: #647
-#744 := [trans #648 #650]: #651
-#732 := [monotonicity #744]: #745
-#725 := [trans #732 #726]: #723
-#736 := [monotonicity #725]: #735
-#643 := (iff #495 false)
-#644 := (or false false)
-#743 := (iff #644 false)
-#628 := [rewrite]: #743
-#739 := (iff #495 #644)
-#594 := (iff #494 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#634 := (iff #494 #460)
-#751 := (iff #493 true)
-#611 := (or true false)
-#755 := (iff #611 true)
-#756 := [rewrite]: #755
-#750 := (iff #493 #611)
-#759 := (iff #778 false)
-#760 := [rewrite]: #759
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#748 := [monotonicity #800 #760]: #750
-#633 := [trans #748 #756]: #751
-#635 := [monotonicity #633]: #634
-#742 := [trans #635 #448]: #594
-#747 := (iff #492 false)
-#593 := (iff #492 #460)
-#590 := (iff #782 true)
-#754 := (iff #782 #611)
-#752 := (iff #781 true)
-#753 := [rewrite]: #752
-#761 := [monotonicity #753 #760]: #754
-#592 := [trans #761 #756]: #590
-#746 := [monotonicity #592]: #593
-#749 := [trans #746 #448]: #747
-#740 := [monotonicity #749 #742]: #739
-#645 := [trans #740 #628]: #643
-#710 := [monotonicity #645 #736 #711]: #713
-#697 := [trans #710 #694]: #695
-#757 := (iff #503 true)
-#612 := (iff #503 #611)
-#764 := (iff #502 false)
-#770 := [rewrite]: #764
-#768 := (iff #780 true)
-#769 := [rewrite]: #768
-#613 := [monotonicity #769 #770]: #612
-#758 := [trans #613 #756]: #757
-#700 := [monotonicity #758 #697]: #699
-#704 := [trans #700 #702]: #703
-#686 := [monotonicity #704]: #685
-#690 := [trans #686 #689]: #685
-#707 := [quant-inst #9 #11]: #696
-#691 := [mp #707 #690]: #706
-#687 := [unit-resolution #691 #836]: #777
-#693 := [monotonicity #687]: #15
-#16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #693]: false
-unsat
-64f54c697dbe7c3319cdf093c32632d4b6ddde2a 298 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#14 := 0::Int
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 3::Int
-decl f6 :: (-> S5 Int S4)
-#9 := 1::Int
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 1::Int)
-#12 := (f5 #10 3::Int)
-#13 := (f3 f4 #12)
-#16 := (= #13 #15)
-#777 := (= #12 0::Int)
-#24 := (:var 0 Int)
-#35 := (:var 1 Int)
-#36 := (f6 f7 #35)
-#37 := (f5 #36 #24)
-#830 := (pattern #37)
-#137 := -1::Int
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #35)
-#144 := (div #138 #141)
-#310 := (* -1::Int #144)
-#311 := (+ #37 #310)
-#312 := (= #311 0::Int)
-#47 := (div #35 #24)
-#307 := (* -1::Int #47)
-#308 := (+ #37 #307)
-#309 := (= #308 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #35 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #35 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#313 := (if #274 #309 #312)
-#306 := (= #37 0::Int)
-#39 := (= #24 0::Int)
-#38 := (= #35 0::Int)
-#40 := (or #38 #39)
-#314 := (if #40 #306 #313)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #314)
-#317 := (forall (vars (?v0 Int) (?v1 Int)) #314)
-#834 := (iff #317 #831)
-#832 := (iff #314 #314)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#277 := (if #274 #47 #144)
-#280 := (if #40 0::Int #277)
-#283 := (= #37 #280)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#318 := (iff #286 #317)
-#315 := (iff #283 #314)
-#316 := [rewrite]: #315
-#319 := [quant-intro #316]: #318
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#180 := (if #177 #47 #144)
-#183 := (if #40 0::Int #180)
-#186 := (= #37 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#287 := (iff #189 #286)
-#284 := (iff #186 #283)
-#281 := (= #183 #280)
-#278 := (= #180 #277)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#279 := [monotonicity #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [monotonicity #282]: #284
-#288 := [quant-intro #285]: #287
-#249 := (~ #189 #189)
-#262 := (~ #186 #186)
-#263 := [refl]: #262
-#250 := [nnf-pos #263]: #249
-#49 := (- #24)
-#48 := (- #35)
-#50 := (div #48 #49)
-#42 := (< 0::Int #24)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#51 := (if #46 #47 #50)
-#52 := (if #40 0::Int #51)
-#53 := (= #37 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#192 := (iff #54 #189)
-#147 := (if #46 #47 #144)
-#150 := (if #40 0::Int #147)
-#153 := (= #37 #150)
-#156 := (forall (vars (?v0 Int) (?v1 Int)) #153)
-#190 := (iff #156 #189)
-#187 := (iff #153 #186)
-#184 := (= #150 #183)
-#181 := (= #147 #180)
-#178 := (iff #46 #177)
-#175 := (iff #45 #174)
-#165 := (iff #42 #164)
-#166 := [rewrite]: #165
-#172 := (iff #44 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #43 #167)
-#161 := (iff #41 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#157 := (iff #54 #156)
-#154 := (iff #53 #153)
-#151 := (= #52 #150)
-#148 := (= #51 #147)
-#145 := (= #50 #144)
-#142 := (= #49 #141)
-#143 := [rewrite]: #142
-#139 := (= #48 #138)
-#140 := [rewrite]: #139
-#146 := [monotonicity #140 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#193 := [trans #158 #191]: #192
-#136 := [asserted]: #54
-#194 := [mp #136 #193]: #189
-#264 := [mp~ #194 #250]: #189
-#289 := [mp #264 #288]: #286
-#320 := [mp #289 #319]: #317
-#836 := [mp #320 #835]: #831
-#682 := (not #831)
-#683 := (or #682 #777)
-#776 := (* -1::Int 3::Int)
-#772 := (* -1::Int 1::Int)
-#765 := (div #772 #776)
-#766 := (* -1::Int #765)
-#767 := (+ #12 #766)
-#762 := (= #767 0::Int)
-#774 := (div 1::Int 3::Int)
-#489 := (* -1::Int #774)
-#771 := (+ #12 #489)
-#775 := (= #771 0::Int)
-#778 := (<= 3::Int 0::Int)
-#493 := (>= 1::Int 0::Int)
-#494 := (or #493 #778)
-#495 := (not #494)
-#781 := (<= 1::Int 0::Int)
-#782 := (or #781 #778)
-#492 := (not #782)
-#773 := (or #492 #495)
-#763 := (if #773 #775 #762)
-#502 := (= 3::Int 0::Int)
-#780 := (= 1::Int 0::Int)
-#503 := (or #780 #502)
-#768 := (if #503 #777 #763)
-#678 := (or #682 #768)
-#657 := (iff #678 #683)
-#659 := (iff #683 #683)
-#552 := [rewrite]: #659
-#680 := (iff #768 #777)
-#693 := (if false #777 #777)
-#676 := (iff #693 #777)
-#677 := [rewrite]: #676
-#679 := (iff #768 #693)
-#692 := (iff #763 #777)
-#705 := (= #12 1::Int)
-#1 := true
-#686 := (if true #777 #705)
-#690 := (iff #686 #777)
-#691 := [rewrite]: #690
-#688 := (iff #763 #686)
-#707 := (iff #762 #705)
-#697 := (+ -1::Int #12)
-#702 := (= #697 0::Int)
-#706 := (iff #702 #705)
-#696 := [rewrite]: #706
-#703 := (iff #762 #702)
-#700 := (= #767 #697)
-#714 := (+ #12 -1::Int)
-#698 := (= #714 #697)
-#699 := [rewrite]: #698
-#694 := (= #767 #714)
-#713 := (= #766 -1::Int)
-#724 := (= #772 -1::Int)
-#731 := [rewrite]: #724
-#711 := (= #766 #772)
-#708 := (= #765 1::Int)
-#715 := -3::Int
-#719 := (div -1::Int -3::Int)
-#717 := (= #719 1::Int)
-#722 := [rewrite]: #717
-#720 := (= #765 #719)
-#716 := (= #776 -3::Int)
-#718 := [rewrite]: #716
-#721 := [monotonicity #731 #718]: #720
-#709 := [trans #721 #722]: #708
-#712 := [monotonicity #709]: #711
-#710 := [trans #712 #731]: #713
-#695 := [monotonicity #710]: #694
-#701 := [trans #695 #699]: #700
-#704 := [monotonicity #701]: #703
-#685 := [trans #704 #696]: #707
-#729 := (iff #775 #777)
-#727 := (= #771 #12)
-#735 := (+ #12 0::Int)
-#733 := (= #735 #12)
-#738 := [rewrite]: #733
-#736 := (= #771 #735)
-#723 := (= #489 0::Int)
-#741 := (* -1::Int 0::Int)
-#734 := (= #741 0::Int)
-#726 := [rewrite]: #734
-#745 := (= #489 #741)
-#651 := (= #774 0::Int)
-#744 := [rewrite]: #651
-#732 := [monotonicity #744]: #745
-#725 := [trans #732 #726]: #723
-#737 := [monotonicity #725]: #736
-#728 := [trans #737 #738]: #727
-#730 := [monotonicity #728]: #729
-#649 := (iff #773 true)
-#594 := (or true false)
-#739 := (iff #594 true)
-#740 := [rewrite]: #739
-#647 := (iff #773 #594)
-#646 := (iff #495 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#643 := (iff #495 #460)
-#743 := (iff #494 true)
-#742 := (iff #494 #594)
-#760 := (iff #778 false)
-#754 := [rewrite]: #760
-#634 := (iff #493 true)
-#635 := [rewrite]: #634
-#644 := [monotonicity #635 #754]: #742
-#628 := [trans #644 #740]: #743
-#645 := [monotonicity #628]: #643
-#639 := [trans #645 #448]: #646
-#751 := (iff #492 true)
-#746 := (not false)
-#750 := (iff #746 true)
-#748 := [rewrite]: #750
-#747 := (iff #492 #746)
-#592 := (iff #782 false)
-#612 := (or false false)
-#756 := (iff #612 false)
-#757 := [rewrite]: #756
-#761 := (iff #782 #612)
-#753 := (iff #781 false)
-#759 := [rewrite]: #753
-#590 := [monotonicity #759 #754]: #761
-#593 := [trans #590 #757]: #592
-#749 := [monotonicity #593]: #747
-#633 := [trans #749 #748]: #751
-#648 := [monotonicity #633 #639]: #647
-#650 := [trans #648 #740]: #649
-#689 := [monotonicity #650 #730 #685]: #688
-#687 := [trans #689 #691]: #692
-#758 := (iff #503 false)
-#613 := (iff #503 #612)
-#770 := (iff #502 false)
-#611 := [rewrite]: #770
-#769 := (iff #780 false)
-#764 := [rewrite]: #769
-#755 := [monotonicity #764 #611]: #613
-#752 := [trans #755 #757]: #758
-#675 := [monotonicity #752 #687]: #679
-#681 := [trans #675 #677]: #680
-#658 := [monotonicity #681]: #657
-#663 := [trans #658 #552]: #657
-#684 := [quant-inst #9 #11]: #678
-#664 := [mp #684 #663]: #683
-#670 := [unit-resolution #664 #836]: #777
-#666 := [monotonicity #670]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #666]: false
-unsat
-d531b5a296176d2110a62307c2de9e0839c802fe 288 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#13 := 1::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 1::Int)
-decl f5 :: (-> S4 Int Int)
-#9 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 3::Int)
-#11 := (f5 #10 3::Int)
-#12 := (f3 f4 #11)
-#15 := (= #12 #14)
-#727 := (= #11 1::Int)
-#24 := (:var 0 Int)
-#35 := (:var 1 Int)
-#36 := (f6 f7 #35)
-#37 := (f5 #36 #24)
-#830 := (pattern #37)
-#23 := 0::Int
-#137 := -1::Int
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #35)
-#144 := (div #138 #141)
-#310 := (* -1::Int #144)
-#311 := (+ #37 #310)
-#312 := (= #311 0::Int)
-#47 := (div #35 #24)
-#307 := (* -1::Int #47)
-#308 := (+ #37 #307)
-#309 := (= #308 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #35 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #35 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#313 := (if #274 #309 #312)
-#306 := (= #37 0::Int)
-#39 := (= #24 0::Int)
-#38 := (= #35 0::Int)
-#40 := (or #38 #39)
-#314 := (if #40 #306 #313)
-#831 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #830) #314)
-#317 := (forall (vars (?v0 Int) (?v1 Int)) #314)
-#834 := (iff #317 #831)
-#832 := (iff #314 #314)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#277 := (if #274 #47 #144)
-#280 := (if #40 0::Int #277)
-#283 := (= #37 #280)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#318 := (iff #286 #317)
-#315 := (iff #283 #314)
-#316 := [rewrite]: #315
-#319 := [quant-intro #316]: #318
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#180 := (if #177 #47 #144)
-#183 := (if #40 0::Int #180)
-#186 := (= #37 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#287 := (iff #189 #286)
-#284 := (iff #186 #283)
-#281 := (= #183 #280)
-#278 := (= #180 #277)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#279 := [monotonicity #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [monotonicity #282]: #284
-#288 := [quant-intro #285]: #287
-#249 := (~ #189 #189)
-#262 := (~ #186 #186)
-#263 := [refl]: #262
-#250 := [nnf-pos #263]: #249
-#49 := (- #24)
-#48 := (- #35)
-#50 := (div #48 #49)
-#42 := (< 0::Int #24)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#51 := (if #46 #47 #50)
-#52 := (if #40 0::Int #51)
-#53 := (= #37 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#192 := (iff #54 #189)
-#147 := (if #46 #47 #144)
-#150 := (if #40 0::Int #147)
-#153 := (= #37 #150)
-#156 := (forall (vars (?v0 Int) (?v1 Int)) #153)
-#190 := (iff #156 #189)
-#187 := (iff #153 #186)
-#184 := (= #150 #183)
-#181 := (= #147 #180)
-#178 := (iff #46 #177)
-#175 := (iff #45 #174)
-#165 := (iff #42 #164)
-#166 := [rewrite]: #165
-#172 := (iff #44 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #43 #167)
-#161 := (iff #41 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#157 := (iff #54 #156)
-#154 := (iff #53 #153)
-#151 := (= #52 #150)
-#148 := (= #51 #147)
-#145 := (= #50 #144)
-#142 := (= #49 #141)
-#143 := [rewrite]: #142
-#139 := (= #48 #138)
-#140 := [rewrite]: #139
-#146 := [monotonicity #140 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#193 := [trans #158 #191]: #192
-#136 := [asserted]: #54
-#194 := [mp #136 #193]: #189
-#264 := [mp~ #194 #250]: #189
-#289 := [mp #264 #288]: #286
-#320 := [mp #289 #319]: #317
-#836 := [mp #320 #835]: #831
-#692 := (not #831)
-#687 := (or #692 #727)
-#775 := (* -1::Int 3::Int)
-#772 := (div #775 #775)
-#776 := (* -1::Int #772)
-#765 := (+ #11 #776)
-#766 := (= #765 0::Int)
-#773 := (div 3::Int 3::Int)
-#774 := (* -1::Int #773)
-#489 := (+ #11 #774)
-#771 := (= #489 0::Int)
-#781 := (<= 3::Int 0::Int)
-#492 := (>= 3::Int 0::Int)
-#493 := (or #492 #781)
-#494 := (not #493)
-#778 := (or #781 #781)
-#782 := (not #778)
-#495 := (or #782 #494)
-#767 := (if #495 #771 #766)
-#777 := (= #11 0::Int)
-#502 := (= 3::Int 0::Int)
-#503 := (or #502 #502)
-#762 := (if #503 #777 #767)
-#693 := (or #692 #762)
-#675 := (iff #693 #687)
-#677 := (iff #687 #687)
-#680 := [rewrite]: #677
-#690 := (iff #762 #727)
-#707 := (if false #777 #727)
-#688 := (iff #707 #727)
-#689 := [rewrite]: #688
-#685 := (iff #762 #707)
-#706 := (iff #767 #727)
-#1 := true
-#701 := (if true #727 #727)
-#704 := (iff #701 #727)
-#705 := [rewrite]: #704
-#702 := (iff #767 #701)
-#699 := (iff #766 #727)
-#726 := (+ -1::Int #11)
-#737 := (= #726 0::Int)
-#728 := (iff #737 #727)
-#729 := [rewrite]: #728
-#697 := (iff #766 #737)
-#694 := (= #765 #726)
-#745 := (+ #11 -1::Int)
-#723 := (= #745 #726)
-#725 := [rewrite]: #723
-#710 := (= #765 #745)
-#712 := (= #776 -1::Int)
-#647 := (* -1::Int 1::Int)
-#650 := (= #647 -1::Int)
-#651 := [rewrite]: #650
-#709 := (= #776 #647)
-#722 := (= #772 1::Int)
-#731 := -3::Int
-#718 := (div -3::Int -3::Int)
-#721 := (= #718 1::Int)
-#717 := [rewrite]: #721
-#719 := (= #772 #718)
-#715 := (= #775 -3::Int)
-#716 := [rewrite]: #715
-#720 := [monotonicity #716 #716]: #719
-#708 := [trans #720 #717]: #722
-#711 := [monotonicity #708]: #709
-#713 := [trans #711 #651]: #712
-#714 := [monotonicity #713]: #710
-#695 := [trans #714 #725]: #694
-#698 := [monotonicity #695]: #697
-#700 := [trans #698 #729]: #699
-#730 := (iff #771 #727)
-#733 := (iff #771 #737)
-#735 := (= #489 #726)
-#732 := (= #489 #745)
-#744 := (= #774 -1::Int)
-#648 := (= #774 #647)
-#646 := (= #773 1::Int)
-#639 := [rewrite]: #646
-#649 := [monotonicity #639]: #648
-#741 := [trans #649 #651]: #744
-#734 := [monotonicity #741]: #732
-#736 := [trans #734 #725]: #735
-#738 := [monotonicity #736]: #733
-#724 := [trans #738 #729]: #730
-#643 := (iff #495 true)
-#750 := (or true false)
-#633 := (iff #750 true)
-#634 := [rewrite]: #633
-#743 := (iff #495 #750)
-#739 := (iff #494 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#742 := (iff #494 #460)
-#635 := (iff #493 true)
-#748 := (iff #493 #750)
-#756 := (iff #781 false)
-#757 := [rewrite]: #756
-#747 := (iff #492 true)
-#749 := [rewrite]: #747
-#751 := [monotonicity #749 #757]: #748
-#594 := [trans #751 #634]: #635
-#644 := [monotonicity #594]: #742
-#740 := [trans #644 #448]: #739
-#593 := (iff #782 true)
-#760 := (not false)
-#590 := (iff #760 true)
-#592 := [rewrite]: #590
-#754 := (iff #782 #760)
-#753 := (iff #778 false)
-#769 := (or false false)
-#611 := (iff #769 false)
-#612 := [rewrite]: #611
-#758 := (iff #778 #769)
-#752 := [monotonicity #757 #757]: #758
-#759 := [trans #752 #612]: #753
-#761 := [monotonicity #759]: #754
-#746 := [trans #761 #592]: #593
-#628 := [monotonicity #746 #740]: #743
-#645 := [trans #628 #634]: #643
-#703 := [monotonicity #645 #724 #700]: #702
-#696 := [trans #703 #705]: #706
-#613 := (iff #503 false)
-#764 := (iff #503 #769)
-#763 := (iff #502 false)
-#768 := [rewrite]: #763
-#770 := [monotonicity #768 #768]: #764
-#755 := [trans #770 #612]: #613
-#686 := [monotonicity #755 #696]: #685
-#691 := [trans #686 #689]: #690
-#676 := [monotonicity #691]: #675
-#681 := [trans #676 #680]: #675
-#679 := [quant-inst #9 #9]: #693
-#682 := [mp #679 #681]: #687
-#684 := [unit-resolution #682 #836]: #727
-#657 := [monotonicity #684]: #15
-#16 := (not #15)
-#85 := [asserted]: #16
-[unit-resolution #85 #657]: false
-unsat
-d789ae3569fe642ed1b603027ce5b8f4594bdee7 409 0
-#2 := false
-#22 := 0::Int
-#12 := 3::Int
-decl f6 :: (-> S4 S5 Int)
-decl f8 :: S5
-#9 := f8
-decl f7 :: S4
-#8 := f7
-#10 := (f6 f7 f8)
-#756 := (mod #10 3::Int)
-#87 := -1::Int
-#730 := (* -1::Int #756)
-#482 := (div #10 3::Int)
-#790 := -3::Int
-#729 := (* -3::Int #482)
-#726 := (+ #729 #730)
-#731 := (+ #10 #726)
-#728 := (= #731 0::Int)
-#1 := true
-#82 := [true-axiom]: true
-#685 := (or false #728)
-#686 := [th-lemma arith]: #685
-#689 := [unit-resolution #686 #82]: #728
-#721 := (>= #731 0::Int)
-#634 := (not #721)
-#722 := (>= #756 0::Int)
-#671 := (or false #722)
-#639 := [th-lemma arith]: #671
-#646 := [unit-resolution #639 #82]: #722
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#7 := f5
-#11 := (f4 f5 #10)
-#13 := (f3 #11 3::Int)
-#90 := (* -1::Int #13)
-#91 := (+ #10 #90)
-#89 := (>= #91 0::Int)
-#93 := (not #89)
-#14 := (<= #13 #10)
-#15 := (not #14)
-#94 := (iff #15 #93)
-#88 := (iff #14 #89)
-#92 := [rewrite]: #88
-#95 := [monotonicity #92]: #94
-#84 := [asserted]: #15
-#96 := [mp #84 #95]: #93
-#814 := (* -1::Int #482)
-#815 := (+ #13 #814)
-#758 := (<= #815 0::Int)
-#816 := (= #815 0::Int)
-#817 := (* -1::Int #10)
-#501 := (div #817 -3::Int)
-#504 := (* -1::Int #501)
-#498 := (+ #13 #504)
-#781 := (= #498 0::Int)
-#470 := (>= #10 0::Int)
-#412 := (not #470)
-#497 := (<= #10 0::Int)
-#445 := (not #497)
-#511 := (or #445 #412)
-#775 := (if #511 #816 #781)
-#491 := (= #10 0::Int)
-#648 := (not #491)
-#762 := (<= #13 0::Int)
-#493 := (= #13 0::Int)
-#701 := [hypothesis]: #491
-#696 := (or #648 #493)
-#772 := (if #491 #493 #775)
-#23 := (:var 0 Int)
-#34 := (:var 1 Int)
-#35 := (f4 f5 #34)
-#36 := (f3 #35 #23)
-#839 := (pattern #36)
-#149 := (* -1::Int #23)
-#146 := (* -1::Int #34)
-#152 := (div #146 #149)
-#318 := (* -1::Int #152)
-#319 := (+ #36 #318)
-#320 := (= #319 0::Int)
-#46 := (div #34 #23)
-#315 := (* -1::Int #46)
-#316 := (+ #36 #315)
-#317 := (= #316 0::Int)
-#171 := (<= #23 0::Int)
-#178 := (>= #34 0::Int)
-#278 := (or #178 #171)
-#279 := (not #278)
-#167 := (<= #34 0::Int)
-#276 := (or #167 #171)
-#277 := (not #276)
-#282 := (or #277 #279)
-#321 := (if #282 #317 #320)
-#314 := (= #36 0::Int)
-#38 := (= #23 0::Int)
-#37 := (= #34 0::Int)
-#39 := (or #37 #38)
-#322 := (if #39 #314 #321)
-#840 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #839) #322)
-#325 := (forall (vars (?v0 Int) (?v1 Int)) #322)
-#843 := (iff #325 #840)
-#841 := (iff #322 #322)
-#842 := [refl]: #841
-#844 := [quant-intro #842]: #843
-#285 := (if #282 #46 #152)
-#288 := (if #39 0::Int #285)
-#291 := (= #36 #288)
-#294 := (forall (vars (?v0 Int) (?v1 Int)) #291)
-#326 := (iff #294 #325)
-#323 := (iff #291 #322)
-#324 := [rewrite]: #323
-#327 := [quant-intro #324]: #326
-#172 := (not #171)
-#179 := (not #178)
-#182 := (and #179 #172)
-#168 := (not #167)
-#175 := (and #168 #172)
-#185 := (or #175 #182)
-#188 := (if #185 #46 #152)
-#191 := (if #39 0::Int #188)
-#194 := (= #36 #191)
-#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
-#295 := (iff #197 #294)
-#292 := (iff #194 #291)
-#289 := (= #191 #288)
-#286 := (= #188 #285)
-#283 := (iff #185 #282)
-#280 := (iff #182 #279)
-#281 := [rewrite]: #280
-#261 := (iff #175 #277)
-#262 := [rewrite]: #261
-#284 := [monotonicity #262 #281]: #283
-#287 := [monotonicity #284]: #286
-#290 := [monotonicity #287]: #289
-#293 := [monotonicity #290]: #292
-#296 := [quant-intro #293]: #295
-#257 := (~ #197 #197)
-#270 := (~ #194 #194)
-#271 := [refl]: #270
-#258 := [nnf-pos #271]: #257
-#48 := (- #23)
-#47 := (- #34)
-#49 := (div #47 #48)
-#41 := (< 0::Int #23)
-#43 := (< #34 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #34)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#50 := (if #45 #46 #49)
-#51 := (if #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#200 := (iff #53 #197)
-#155 := (if #45 #46 #152)
-#158 := (if #39 0::Int #155)
-#161 := (= #36 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#198 := (iff #164 #197)
-#195 := (iff #161 #194)
-#192 := (= #158 #191)
-#189 := (= #155 #188)
-#186 := (iff #45 #185)
-#183 := (iff #44 #182)
-#173 := (iff #41 #172)
-#174 := [rewrite]: #173
-#180 := (iff #43 #179)
-#181 := [rewrite]: #180
-#184 := [monotonicity #181 #174]: #183
-#176 := (iff #42 #175)
-#169 := (iff #40 #168)
-#170 := [rewrite]: #169
-#177 := [monotonicity #170 #174]: #176
-#187 := [monotonicity #177 #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [monotonicity #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [quant-intro #196]: #198
-#165 := (iff #53 #164)
-#162 := (iff #52 #161)
-#159 := (= #51 #158)
-#156 := (= #50 #155)
-#153 := (= #49 #152)
-#150 := (= #48 #149)
-#151 := [rewrite]: #150
-#147 := (= #47 #146)
-#148 := [rewrite]: #147
-#154 := [monotonicity #148 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#201 := [trans #166 #199]: #200
-#145 := [asserted]: #53
-#202 := [mp #145 #201]: #197
-#272 := [mp~ #202 #258]: #197
-#297 := [mp #272 #296]: #294
-#328 := [mp #297 #327]: #325
-#845 := [mp #328 #844]: #840
-#773 := (not #840)
-#779 := (or #773 #772)
-#812 := (* -1::Int 3::Int)
-#818 := (div #817 #812)
-#808 := (* -1::Int #818)
-#468 := (+ #13 #808)
-#473 := (= #468 0::Int)
-#476 := (<= 3::Int 0::Int)
-#600 := (or #470 #476)
-#807 := (not #600)
-#811 := (or #497 #476)
-#813 := (not #811)
-#481 := (or #813 #807)
-#809 := (if #481 #816 #473)
-#492 := (= 3::Int 0::Int)
-#496 := (or #491 #492)
-#469 := (if #496 #493 #809)
-#620 := (or #773 #469)
-#622 := (iff #620 #779)
-#765 := (iff #779 #779)
-#766 := [rewrite]: #765
-#777 := (iff #469 #772)
-#776 := (iff #809 #775)
-#785 := (iff #473 #781)
-#780 := (= #468 #498)
-#782 := (= #808 #504)
-#502 := (= #818 #501)
-#787 := (= #812 -3::Int)
-#791 := [rewrite]: #787
-#503 := [monotonicity #791]: #502
-#783 := [monotonicity #503]: #782
-#784 := [monotonicity #783]: #780
-#774 := [monotonicity #784]: #785
-#512 := (iff #481 #511)
-#788 := (iff #807 #412)
-#517 := (iff #600 #470)
-#806 := (or #470 false)
-#515 := (iff #806 #470)
-#516 := [rewrite]: #515
-#792 := (iff #600 #806)
-#798 := (iff #476 false)
-#799 := [rewrite]: #798
-#793 := [monotonicity #799]: #792
-#518 := [trans #793 #516]: #517
-#789 := [monotonicity #518]: #788
-#805 := (iff #813 #445)
-#804 := (iff #811 #497)
-#800 := (or #497 false)
-#439 := (iff #800 #497)
-#802 := [rewrite]: #439
-#795 := (iff #811 #800)
-#801 := [monotonicity #799]: #795
-#444 := [trans #801 #802]: #804
-#803 := [monotonicity #444]: #805
-#786 := [monotonicity #803 #789]: #512
-#771 := [monotonicity #786 #774]: #776
-#796 := (iff #496 #491)
-#794 := (or #491 false)
-#459 := (iff #794 #491)
-#460 := [rewrite]: #459
-#457 := (iff #496 #794)
-#810 := (iff #492 false)
-#453 := [rewrite]: #810
-#458 := [monotonicity #453]: #457
-#797 := [trans #458 #460]: #796
-#778 := [monotonicity #797 #771]: #777
-#764 := [monotonicity #778]: #622
-#767 := [trans #764 #766]: #622
-#621 := [quant-inst #10 #12]: #620
-#761 := [mp #621 #767]: #779
-#666 := [unit-resolution #761 #845]: #772
-#655 := (not #772)
-#656 := (or #655 #648 #493)
-#657 := [def-axiom]: #656
-#702 := [unit-resolution #657 #666]: #696
-#688 := [unit-resolution #702 #701]: #493
-#660 := (not #493)
-#684 := (or #660 #762)
-#720 := [th-lemma arith triangle-eq]: #684
-#640 := [unit-resolution #720 #688]: #762
-#647 := (or #648 #470)
-#649 := [th-lemma arith triangle-eq]: #647
-#650 := [unit-resolution #649 #701]: #470
-#651 := [th-lemma arith farkas -1 1 1 #650 #96 #640]: false
-#661 := [lemma #651]: #648
-#667 := (or #491 #775)
-#658 := (or #655 #491 #775)
-#659 := [def-axiom]: #658
-#668 := [unit-resolution #659 #666]: #667
-#625 := [unit-resolution #668 #661]: #775
-decl f9 :: (-> S6 Int S5)
-decl f10 :: S6
-#16 := f10
-#406 := (f9 f10 #10)
-#743 := (f6 f7 #406)
-#735 := (= #743 0::Int)
-#609 := (not #735)
-#664 := (iff #648 #609)
-#683 := (iff #491 #735)
-#682 := (iff #735 #491)
-#680 := (= #743 #10)
-#490 := (= #406 f8)
-#17 := (:var 0 S5)
-#18 := (f6 f7 #17)
-#819 := (pattern #18)
-#19 := (f9 f10 #18)
-#20 := (= #19 #17)
-#820 := (forall (vars (?v0 S5)) (:pat #819) #20)
-#21 := (forall (vars (?v0 S5)) #20)
-#823 := (iff #21 #820)
-#821 := (iff #20 #20)
-#822 := [refl]: #821
-#824 := [quant-intro #822]: #823
-#265 := (~ #21 #21)
-#263 := (~ #20 #20)
-#264 := [refl]: #263
-#266 := [nnf-pos #264]: #265
-#85 := [asserted]: #21
-#251 := [mp~ #85 #266]: #21
-#825 := [mp #251 #824]: #820
-#483 := (not #820)
-#494 := (or #483 #490)
-#495 := [quant-inst #9]: #494
-#677 := [unit-resolution #495 #825]: #490
-#681 := [monotonicity #677]: #680
-#678 := [monotonicity #681]: #682
-#663 := [symm #678]: #683
-#645 := [monotonicity #663]: #664
-#626 := [mp #661 #645]: #609
-#732 := (or #470 #735)
-#25 := (f9 f10 #23)
-#826 := (pattern #25)
-#26 := (f6 f7 #25)
-#31 := (= #26 0::Int)
-#105 := (>= #23 0::Int)
-#136 := (or #105 #31)
-#833 := (forall (vars (?v0 Int)) (:pat #826) #136)
-#139 := (forall (vars (?v0 Int)) #136)
-#836 := (iff #139 #833)
-#834 := (iff #136 #136)
-#835 := [refl]: #834
-#837 := [quant-intro #835]: #836
-#255 := (~ #139 #139)
-#267 := (~ #136 #136)
-#268 := [refl]: #267
-#256 := [nnf-pos #268]: #255
-#30 := (< #23 0::Int)
-#32 := (implies #30 #31)
-#33 := (forall (vars (?v0 Int)) #32)
-#142 := (iff #33 #139)
-#120 := (not #30)
-#121 := (or #120 #31)
-#124 := (forall (vars (?v0 Int)) #121)
-#140 := (iff #124 #139)
-#137 := (iff #121 #136)
-#134 := (iff #120 #105)
-#107 := (not #105)
-#129 := (not #107)
-#132 := (iff #129 #105)
-#133 := [rewrite]: #132
-#130 := (iff #120 #129)
-#127 := (iff #30 #107)
-#128 := [rewrite]: #127
-#131 := [monotonicity #128]: #130
-#135 := [trans #131 #133]: #134
-#138 := [monotonicity #135]: #137
-#141 := [quant-intro #138]: #140
-#125 := (iff #33 #124)
-#122 := (iff #32 #121)
-#123 := [rewrite]: #122
-#126 := [quant-intro #123]: #125
-#143 := [trans #126 #141]: #142
-#119 := [asserted]: #33
-#144 := [mp #119 #143]: #139
-#269 := [mp~ #144 #256]: #139
-#838 := [mp #269 #837]: #833
-#745 := (not #833)
-#746 := (or #745 #470 #735)
-#742 := (or #745 #732)
-#736 := (iff #742 #746)
-#737 := [rewrite]: #736
-#747 := [quant-inst #10]: #742
-#738 := [mp #747 #737]: #746
-#670 := [unit-resolution #738 #838]: #732
-#627 := [unit-resolution #670 #626]: #470
-#628 := (or #491 #445 #412)
-#629 := [th-lemma arith triangle-eq]: #628
-#630 := [unit-resolution #629 #627 #661]: #445
-#769 := (or #511 #497)
-#763 := [def-axiom]: #769
-#631 := [unit-resolution #763 #630]: #511
-#601 := (not #511)
-#643 := (not #775)
-#644 := (or #643 #601 #816)
-#603 := [def-axiom]: #644
-#632 := [unit-resolution #603 #631 #625]: #816
-#748 := (not #816)
-#679 := (or #748 #758)
-#675 := [th-lemma arith triangle-eq]: #679
-#633 := [unit-resolution #675 #632]: #758
-#635 := (not #758)
-#619 := (not #722)
-#596 := (or #634 #412 #619 #635 #89)
-#597 := [th-lemma arith assign-bounds 2 1 3 3]: #596
-#604 := [unit-resolution #597 #627 #633 #96 #646]: #634
-#690 := (not #728)
-#691 := (or #690 #721)
-#692 := [th-lemma arith triangle-eq]: #691
-[unit-resolution #692 #604 #689]: false
-unsat
-c5c3c657f3d41eaffb467378e2ecb04b1c7d2a98 559 0
-#2 := false
-decl f10 :: S3
-#10 := f10
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 Int Int)
-#13 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f9 :: S6
-#9 := f9
-#11 := (f8 f9 f10)
-decl f7 :: S5
-#8 := f7
-#12 := (f6 f7 #11)
-#14 := (f5 #12 3::Int)
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 #14)
-#16 := (= #15 f10)
-#17 := 0::Int
-#18 := (f3 f4 0::Int)
-#416 := (= #18 f10)
-#19 := (= f10 #18)
-#476 := (f3 f4 #11)
-#424 := (= #476 #18)
-#437 := (= #18 #476)
-#434 := (= 0::Int #11)
-#482 := (f8 f9 #15)
-#574 := (= #482 #11)
-#462 := (= #11 #482)
-#456 := (= f10 #15)
-#406 := (not #19)
-#534 := [hypothesis]: #406
-#493 := (or #16 #19)
-#89 := (not #16)
-#90 := (iff #89 #19)
-#20 := (iff #16 #19)
-#21 := (not #20)
-#91 := (iff #21 #90)
-#92 := [rewrite]: #91
-#88 := [asserted]: #21
-#95 := [mp #88 #92]: #90
-#490 := (not #90)
-#495 := (or #16 #19 #490)
-#496 := [def-axiom]: #495
-#497 := [unit-resolution #496 #95]: #493
-#536 := [unit-resolution #497 #534]: #16
-#461 := [symm #536]: #456
-#463 := [monotonicity #461]: #462
-#426 := [symm #463]: #574
-#427 := (= 0::Int #482)
-#447 := (= #14 #482)
-#814 := (= #482 #14)
-#813 := (>= #14 0::Int)
-#585 := (or #813 #89)
-#784 := (= #11 0::Int)
-#816 := (= #482 0::Int)
-#581 := (iff #816 #784)
-#595 := [hypothesis]: #16
-#577 := [monotonicity #595]: #574
-#583 := [monotonicity #577]: #581
-#470 := (not #813)
-#586 := [hypothesis]: #470
-#817 := (or #813 #816)
-#27 := (:var 0 Int)
-#29 := (f3 f4 #27)
-#826 := (pattern #29)
-#30 := (f8 f9 #29)
-#35 := (= #30 0::Int)
-#105 := (>= #27 0::Int)
-#135 := (or #105 #35)
-#833 := (forall (vars (?v0 Int)) (:pat #826) #135)
-#138 := (forall (vars (?v0 Int)) #135)
-#836 := (iff #138 #833)
-#834 := (iff #135 #135)
-#835 := [refl]: #834
-#837 := [quant-intro #835]: #836
-#255 := (~ #138 #138)
-#267 := (~ #135 #135)
-#268 := [refl]: #267
-#256 := [nnf-pos #268]: #255
-#34 := (< #27 0::Int)
-#36 := (implies #34 #35)
-#37 := (forall (vars (?v0 Int)) #36)
-#141 := (iff #37 #138)
-#119 := (not #34)
-#120 := (or #119 #35)
-#123 := (forall (vars (?v0 Int)) #120)
-#139 := (iff #123 #138)
-#136 := (iff #120 #135)
-#133 := (iff #119 #105)
-#106 := (not #105)
-#128 := (not #106)
-#131 := (iff #128 #105)
-#132 := [rewrite]: #131
-#129 := (iff #119 #128)
-#126 := (iff #34 #106)
-#127 := [rewrite]: #126
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#137 := [monotonicity #134]: #136
-#140 := [quant-intro #137]: #139
-#124 := (iff #37 #123)
-#121 := (iff #36 #120)
-#122 := [rewrite]: #121
-#125 := [quant-intro #122]: #124
-#142 := [trans #125 #140]: #141
-#118 := [asserted]: #37
-#143 := [mp #118 #142]: #138
-#269 := [mp~ #143 #256]: #138
-#838 := [mp #269 #837]: #833
-#794 := (not #833)
-#457 := (or #794 #813 #816)
-#458 := (or #794 #817)
-#460 := (iff #458 #457)
-#796 := [rewrite]: #460
-#459 := [quant-inst #14]: #458
-#797 := [mp #459 #796]: #457
-#594 := [unit-resolution #797 #838]: #817
-#590 := [unit-resolution #594 #586]: #816
-#584 := [mp #590 #583]: #784
-#690 := (not #784)
-#774 := (= #14 0::Int)
-#666 := (not #774)
-#587 := (or #666 #813)
-#588 := [th-lemma arith triangle-eq]: #587
-#589 := [unit-resolution #588 #586]: #666
-#592 := (or #690 #774)
-#735 := -3::Int
-#145 := -1::Int
-#765 := (* -1::Int #11)
-#744 := (div #765 -3::Int)
-#742 := (* -1::Int #744)
-#737 := (+ #14 #742)
-#733 := (= #737 0::Int)
-#620 := (div #11 3::Int)
-#621 := (* -1::Int #620)
-#622 := (+ #14 #621)
-#764 := (= #622 0::Int)
-#777 := (>= #11 0::Int)
-#660 := (not #777)
-#775 := (<= #11 0::Int)
-#752 := (not #775)
-#754 := (or #752 #660)
-#725 := (if #754 #764 #733)
-#729 := (if #784 #774 #725)
-#38 := (:var 1 Int)
-#39 := (f6 f7 #38)
-#40 := (f5 #39 #27)
-#839 := (pattern #40)
-#149 := (* -1::Int #27)
-#146 := (* -1::Int #38)
-#152 := (div #146 #149)
-#318 := (* -1::Int #152)
-#319 := (+ #40 #318)
-#320 := (= #319 0::Int)
-#50 := (div #38 #27)
-#315 := (* -1::Int #50)
-#316 := (+ #40 #315)
-#317 := (= #316 0::Int)
-#171 := (<= #27 0::Int)
-#178 := (>= #38 0::Int)
-#278 := (or #178 #171)
-#279 := (not #278)
-#167 := (<= #38 0::Int)
-#276 := (or #167 #171)
-#277 := (not #276)
-#282 := (or #277 #279)
-#321 := (if #282 #317 #320)
-#314 := (= #40 0::Int)
-#42 := (= #27 0::Int)
-#41 := (= #38 0::Int)
-#43 := (or #41 #42)
-#322 := (if #43 #314 #321)
-#840 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #839) #322)
-#325 := (forall (vars (?v0 Int) (?v1 Int)) #322)
-#843 := (iff #325 #840)
-#841 := (iff #322 #322)
-#842 := [refl]: #841
-#844 := [quant-intro #842]: #843
-#285 := (if #282 #50 #152)
-#288 := (if #43 0::Int #285)
-#291 := (= #40 #288)
-#294 := (forall (vars (?v0 Int) (?v1 Int)) #291)
-#326 := (iff #294 #325)
-#323 := (iff #291 #322)
-#324 := [rewrite]: #323
-#327 := [quant-intro #324]: #326
-#172 := (not #171)
-#179 := (not #178)
-#182 := (and #179 #172)
-#168 := (not #167)
-#175 := (and #168 #172)
-#185 := (or #175 #182)
-#188 := (if #185 #50 #152)
-#191 := (if #43 0::Int #188)
-#194 := (= #40 #191)
-#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
-#295 := (iff #197 #294)
-#292 := (iff #194 #291)
-#289 := (= #191 #288)
-#286 := (= #188 #285)
-#283 := (iff #185 #282)
-#280 := (iff #182 #279)
-#281 := [rewrite]: #280
-#261 := (iff #175 #277)
-#262 := [rewrite]: #261
-#284 := [monotonicity #262 #281]: #283
-#287 := [monotonicity #284]: #286
-#290 := [monotonicity #287]: #289
-#293 := [monotonicity #290]: #292
-#296 := [quant-intro #293]: #295
-#257 := (~ #197 #197)
-#270 := (~ #194 #194)
-#271 := [refl]: #270
-#258 := [nnf-pos #271]: #257
-#52 := (- #27)
-#51 := (- #38)
-#53 := (div #51 #52)
-#45 := (< 0::Int #27)
-#47 := (< #38 0::Int)
-#48 := (and #47 #45)
-#44 := (< 0::Int #38)
-#46 := (and #44 #45)
-#49 := (or #46 #48)
-#54 := (if #49 #50 #53)
-#55 := (if #43 0::Int #54)
-#56 := (= #40 #55)
-#57 := (forall (vars (?v0 Int) (?v1 Int)) #56)
-#200 := (iff #57 #197)
-#155 := (if #49 #50 #152)
-#158 := (if #43 0::Int #155)
-#161 := (= #40 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#198 := (iff #164 #197)
-#195 := (iff #161 #194)
-#192 := (= #158 #191)
-#189 := (= #155 #188)
-#186 := (iff #49 #185)
-#183 := (iff #48 #182)
-#173 := (iff #45 #172)
-#174 := [rewrite]: #173
-#180 := (iff #47 #179)
-#181 := [rewrite]: #180
-#184 := [monotonicity #181 #174]: #183
-#176 := (iff #46 #175)
-#169 := (iff #44 #168)
-#170 := [rewrite]: #169
-#177 := [monotonicity #170 #174]: #176
-#187 := [monotonicity #177 #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [monotonicity #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [quant-intro #196]: #198
-#165 := (iff #57 #164)
-#162 := (iff #56 #161)
-#159 := (= #55 #158)
-#156 := (= #54 #155)
-#153 := (= #53 #152)
-#150 := (= #52 #149)
-#151 := [rewrite]: #150
-#147 := (= #51 #146)
-#148 := [rewrite]: #147
-#154 := [monotonicity #148 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#201 := [trans #166 #199]: #200
-#144 := [asserted]: #57
-#202 := [mp #144 #201]: #197
-#272 := [mp~ #202 #258]: #197
-#297 := [mp #272 #296]: #294
-#328 := [mp #297 #327]: #325
-#845 := [mp #328 #844]: #840
-#731 := (not #840)
-#717 := (or #731 #729)
-#766 := (* -1::Int 3::Int)
-#767 := (div #765 #766)
-#761 := (* -1::Int #767)
-#762 := (+ #14 #761)
-#768 := (= #762 0::Int)
-#776 := (<= 3::Int 0::Int)
-#778 := (or #777 #776)
-#773 := (not #778)
-#771 := (or #775 #776)
-#772 := (not #771)
-#779 := (or #772 #773)
-#769 := (if #779 #764 #768)
-#781 := (= 3::Int 0::Int)
-#785 := (or #784 #781)
-#763 := (if #785 #774 #769)
-#718 := (or #731 #763)
-#721 := (iff #718 #717)
-#719 := (iff #717 #717)
-#723 := [rewrite]: #719
-#730 := (iff #763 #729)
-#727 := (iff #769 #725)
-#740 := (iff #768 #733)
-#738 := (= #762 #737)
-#747 := (= #761 #742)
-#745 := (= #767 #744)
-#732 := (= #766 -3::Int)
-#734 := [rewrite]: #732
-#746 := [monotonicity #734]: #745
-#736 := [monotonicity #746]: #747
-#739 := [monotonicity #736]: #738
-#724 := [monotonicity #739]: #740
-#741 := (iff #779 #754)
-#753 := (iff #773 #660)
-#658 := (iff #778 #777)
-#654 := (or #777 false)
-#656 := (iff #654 #777)
-#657 := [rewrite]: #656
-#655 := (iff #778 #654)
-#760 := (iff #776 false)
-#642 := [rewrite]: #760
-#648 := [monotonicity #642]: #655
-#659 := [trans #648 #657]: #658
-#750 := [monotonicity #659]: #753
-#637 := (iff #772 #752)
-#748 := (iff #771 #775)
-#643 := (or #775 false)
-#751 := (iff #643 #775)
-#653 := [rewrite]: #751
-#644 := (iff #771 #643)
-#603 := [monotonicity #642]: #644
-#749 := [trans #603 #653]: #748
-#652 := [monotonicity #749]: #637
-#743 := [monotonicity #652 #750]: #741
-#728 := [monotonicity #743 #724]: #727
-#759 := (iff #785 #784)
-#601 := (or #784 false)
-#756 := (iff #601 #784)
-#758 := [rewrite]: #756
-#602 := (iff #785 #601)
-#770 := (iff #781 false)
-#599 := [rewrite]: #770
-#755 := [monotonicity #599]: #602
-#757 := [trans #755 #758]: #759
-#726 := [monotonicity #757 #728]: #730
-#722 := [monotonicity #726]: #721
-#703 := [trans #722 #723]: #721
-#720 := [quant-inst #11 #13]: #718
-#704 := [mp #720 #703]: #717
-#591 := [unit-resolution #704 #845]: #729
-#689 := (not #729)
-#691 := (or #689 #690 #774)
-#692 := [def-axiom]: #691
-#593 := [unit-resolution #692 #591]: #592
-#436 := [unit-resolution #593 #589]: #690
-#582 := [unit-resolution #436 #584]: false
-#573 := [lemma #582]: #585
-#537 := [unit-resolution #573 #536]: #813
-#815 := (or #470 #814)
-#31 := (= #30 #27)
-#109 := (or #106 #31)
-#827 := (forall (vars (?v0 Int)) (:pat #826) #109)
-#112 := (forall (vars (?v0 Int)) #109)
-#830 := (iff #112 #827)
-#828 := (iff #109 #109)
-#829 := [refl]: #828
-#831 := [quant-intro #829]: #830
-#253 := (~ #112 #112)
-#252 := (~ #109 #109)
-#249 := [refl]: #252
-#254 := [nnf-pos #249]: #253
-#28 := (<= 0::Int #27)
-#32 := (implies #28 #31)
-#33 := (forall (vars (?v0 Int)) #32)
-#115 := (iff #33 #112)
-#96 := (not #28)
-#97 := (or #96 #31)
-#100 := (forall (vars (?v0 Int)) #97)
-#113 := (iff #100 #112)
-#110 := (iff #97 #109)
-#107 := (iff #96 #106)
-#103 := (iff #28 #105)
-#104 := [rewrite]: #103
-#108 := [monotonicity #104]: #107
-#111 := [monotonicity #108]: #110
-#114 := [quant-intro #111]: #113
-#101 := (iff #33 #100)
-#98 := (iff #32 #97)
-#99 := [rewrite]: #98
-#102 := [quant-intro #99]: #101
-#116 := [trans #102 #114]: #115
-#94 := [asserted]: #33
-#117 := [mp #94 #116]: #112
-#250 := [mp~ #117 #254]: #112
-#832 := [mp #250 #831]: #827
-#812 := (not #827)
-#818 := (or #812 #470 #814)
-#808 := (or #812 #815)
-#473 := (iff #808 #818)
-#809 := [rewrite]: #473
-#468 := [quant-inst #14]: #808
-#469 := [mp #468 #809]: #818
-#538 := [unit-resolution #469 #832]: #815
-#454 := [unit-resolution #538 #537]: #814
-#422 := [symm #454]: #447
-#446 := (= 0::Int #14)
-#614 := (* -1::Int #14)
-#615 := (+ #11 #614)
-#616 := (>= #615 0::Int)
-#613 := (= #11 #14)
-#464 := [trans #463 #454]: #613
-#465 := (not #613)
-#466 := (or #465 #616)
-#455 := [th-lemma arith triangle-eq]: #466
-#467 := [unit-resolution #455 #464]: #616
-#448 := (not #616)
-#450 := (or #777 #470 #448)
-#451 := [th-lemma arith assign-bounds 1 1]: #450
-#449 := [unit-resolution #451 #537 #467]: #777
-#598 := (<= #615 0::Int)
-#452 := (or #465 #598)
-#440 := [th-lemma arith triangle-eq]: #452
-#442 := [unit-resolution #440 #464]: #598
-#471 := (not #598)
-#474 := (or #774 #471 #660 #470)
-#714 := (mod #11 3::Int)
-#563 := (* -1::Int #714)
-#562 := (* -3::Int #620)
-#566 := (+ #562 #563)
-#567 := (+ #11 #566)
-#560 := (= #567 0::Int)
-#1 := true
-#86 := [true-axiom]: true
-#539 := (or false #560)
-#532 := [th-lemma arith]: #539
-#540 := [unit-resolution #532 #86]: #560
-#565 := (>= #567 0::Int)
-#479 := (not #565)
-#568 := (>= #714 0::Int)
-#525 := (or false #568)
-#526 := [th-lemma arith]: #525
-#527 := [unit-resolution #526 #86]: #568
-#706 := (<= #14 0::Int)
-#530 := (not #706)
-#529 := [hypothesis]: #813
-#528 := [hypothesis]: #666
-#519 := (or #774 #530 #470)
-#520 := [th-lemma arith triangle-eq]: #519
-#521 := [unit-resolution #520 #528 #529]: #530
-#513 := [hypothesis]: #598
-#715 := (<= #622 0::Int)
-#522 := [unit-resolution #593 #528]: #690
-#523 := (or #784 #725)
-#687 := (or #689 #784 #725)
-#693 := [def-axiom]: #687
-#514 := [unit-resolution #693 #591]: #523
-#524 := [unit-resolution #514 #522]: #725
-#505 := [hypothesis]: #777
-#506 := (or #784 #752 #660)
-#507 := [th-lemma arith triangle-eq]: #506
-#499 := [unit-resolution #507 #522 #505]: #752
-#707 := (or #754 #775)
-#708 := [def-axiom]: #707
-#508 := [unit-resolution #708 #499]: #754
-#711 := (not #754)
-#697 := (not #725)
-#698 := (or #697 #711 #764)
-#699 := [def-axiom]: #698
-#509 := [unit-resolution #699 #508 #524]: #764
-#696 := (not #764)
-#500 := (or #696 #715)
-#510 := [th-lemma arith triangle-eq]: #500
-#477 := [unit-resolution #510 #509]: #715
-#484 := (not #715)
-#480 := (not #568)
-#485 := (or #479 #480 #706 #471 #484)
-#486 := [th-lemma arith assign-bounds 1 2 1 3]: #485
-#487 := [unit-resolution #486 #477 #513 #521 #527]: #479
-#488 := (not #560)
-#478 := (or #488 #565)
-#489 := [th-lemma arith triangle-eq]: #478
-#472 := [unit-resolution #489 #487 #540]: false
-#475 := [lemma #472]: #474
-#443 := [unit-resolution #475 #442 #449 #537]: #774
-#441 := [symm #443]: #446
-#432 := [trans #441 #422]: #427
-#435 := [trans #432 #426]: #434
-#433 := [monotonicity #435]: #437
-#425 := [symm #433]: #424
-#438 := (= f10 #476)
-#811 := (= #476 f10)
-#22 := (:var 0 S3)
-#23 := (f8 f9 #22)
-#819 := (pattern #23)
-#24 := (f3 f4 #23)
-#25 := (= #24 #22)
-#820 := (forall (vars (?v0 S3)) (:pat #819) #25)
-#26 := (forall (vars (?v0 S3)) #25)
-#823 := (iff #26 #820)
-#821 := (iff #25 #25)
-#822 := [refl]: #821
-#824 := [quant-intro #822]: #823
-#265 := (~ #26 #26)
-#263 := (~ #25 #25)
-#264 := [refl]: #263
-#266 := [nnf-pos #264]: #265
-#93 := [asserted]: #26
-#251 := [mp~ #93 #266]: #26
-#825 := [mp #251 #824]: #820
-#600 := (not #820)
-#807 := (or #600 #811)
-#481 := [quant-inst #10]: #807
-#535 := [unit-resolution #481 #825]: #811
-#421 := [symm #535]: #438
-#428 := [trans #421 #425]: #19
-#429 := [unit-resolution #534 #428]: false
-#430 := [lemma #429]: #19
-#413 := [symm #430]: #416
-#415 := (= #15 #18)
-#798 := (f8 f9 #18)
-#799 := (= #798 0::Int)
-#412 := (or #812 #799)
-#810 := (>= 0::Int 0::Int)
-#453 := (not #810)
-#800 := (or #453 #799)
-#788 := (or #812 #800)
-#511 := (iff #788 #412)
-#786 := (iff #412 #412)
-#790 := [rewrite]: #786
-#517 := (iff #800 #799)
-#806 := (or false #799)
-#515 := (iff #806 #799)
-#516 := [rewrite]: #515
-#792 := (iff #800 #806)
-#805 := (iff #453 false)
-#439 := (not true)
-#444 := (iff #439 false)
-#445 := [rewrite]: #444
-#802 := (iff #453 #439)
-#795 := (iff #810 true)
-#801 := [rewrite]: #795
-#804 := [monotonicity #801]: #802
-#803 := [trans #804 #445]: #805
-#793 := [monotonicity #803]: #792
-#518 := [trans #793 #516]: #517
-#512 := [monotonicity #518]: #511
-#787 := [trans #512 #790]: #511
-#789 := [quant-inst #17]: #788
-#791 := [mp #789 #787]: #412
-#431 := [unit-resolution #791 #832]: #799
-#414 := (= #11 #798)
-#417 := [monotonicity #430]: #414
-#418 := [trans #417 #431]: #784
-#419 := [unit-resolution #593 #418]: #774
-#420 := [monotonicity #419]: #415
-#407 := [trans #420 #413]: #16
-#483 := (or #89 #406)
-#491 := (or #89 #406 #490)
-#492 := [def-axiom]: #491
-#494 := [unit-resolution #492 #95]: #483
-#423 := [unit-resolution #494 #430]: #89
-[unit-resolution #423 #407]: false
-unsat
-1d2ee8034acef6abcc30ff56f495f5a58955cc18 267 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#7 := f4
-#13 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 0::Int)
-#11 := (f5 #10 0::Int)
-#12 := (f3 f4 #11)
-#14 := (= #12 #13)
-#502 := (= #11 0::Int)
-#22 := (:var 0 Int)
-#34 := (:var 1 Int)
-#54 := (f6 f7 #34)
-#55 := (f5 #54 #22)
-#837 := (pattern #55)
-#135 := -1::Int
-#139 := (* -1::Int #22)
-#136 := (* -1::Int #34)
-#194 := (mod #136 #139)
-#324 := (+ #55 #194)
-#325 := (= #324 0::Int)
-#56 := (mod #34 #22)
-#321 := (* -1::Int #56)
-#322 := (+ #55 #321)
-#323 := (= #322 0::Int)
-#161 := (<= #22 0::Int)
-#168 := (>= #34 0::Int)
-#268 := (or #168 #161)
-#269 := (not #268)
-#157 := (<= #34 0::Int)
-#266 := (or #157 #161)
-#267 := (not #266)
-#272 := (or #267 #269)
-#326 := (if #272 #323 #325)
-#320 := (= #55 0::Int)
-#37 := (= #34 0::Int)
-#327 := (if #37 #320 #326)
-#319 := (= #55 #34)
-#38 := (= #22 0::Int)
-#328 := (if #38 #319 #327)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #328)
-#331 := (forall (vars (?v0 Int) (?v1 Int)) #328)
-#841 := (iff #331 #838)
-#839 := (iff #328 #328)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#200 := (* -1::Int #194)
-#288 := (if #272 #56 #200)
-#291 := (if #37 0::Int #288)
-#294 := (if #38 #34 #291)
-#297 := (= #55 #294)
-#300 := (forall (vars (?v0 Int) (?v1 Int)) #297)
-#332 := (iff #300 #331)
-#329 := (iff #297 #328)
-#330 := [rewrite]: #329
-#333 := [quant-intro #330]: #332
-#162 := (not #161)
-#169 := (not #168)
-#172 := (and #169 #162)
-#158 := (not #157)
-#165 := (and #158 #162)
-#175 := (or #165 #172)
-#220 := (if #175 #56 #200)
-#223 := (if #37 0::Int #220)
-#226 := (if #38 #34 #223)
-#229 := (= #55 #226)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#301 := (iff #232 #300)
-#298 := (iff #229 #297)
-#295 := (= #226 #294)
-#292 := (= #223 #291)
-#289 := (= #220 #288)
-#273 := (iff #175 #272)
-#270 := (iff #172 #269)
-#271 := [rewrite]: #270
-#251 := (iff #165 #267)
-#252 := [rewrite]: #251
-#274 := [monotonicity #252 #271]: #273
-#290 := [monotonicity #274]: #289
-#293 := [monotonicity #290]: #292
-#296 := [monotonicity #293]: #295
-#299 := [monotonicity #296]: #298
-#302 := [quant-intro #299]: #301
-#249 := (~ #232 #232)
-#263 := (~ #229 #229)
-#264 := [refl]: #263
-#250 := [nnf-pos #264]: #249
-#48 := (- #22)
-#47 := (- #34)
-#57 := (mod #47 #48)
-#58 := (- #57)
-#41 := (< 0::Int #22)
-#43 := (< #34 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #34)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#59 := (if #45 #56 #58)
-#60 := (if #37 0::Int #59)
-#61 := (if #38 #34 #60)
-#62 := (= #55 #61)
-#63 := (forall (vars (?v0 Int) (?v1 Int)) #62)
-#235 := (iff #63 #232)
-#205 := (if #45 #56 #200)
-#208 := (if #37 0::Int #205)
-#211 := (if #38 #34 #208)
-#214 := (= #55 #211)
-#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
-#233 := (iff #217 #232)
-#230 := (iff #214 #229)
-#227 := (= #211 #226)
-#224 := (= #208 #223)
-#221 := (= #205 #220)
-#176 := (iff #45 #175)
-#173 := (iff #44 #172)
-#163 := (iff #41 #162)
-#164 := [rewrite]: #163
-#170 := (iff #43 #169)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171 #164]: #173
-#166 := (iff #42 #165)
-#159 := (iff #40 #158)
-#160 := [rewrite]: #159
-#167 := [monotonicity #160 #164]: #166
-#177 := [monotonicity #167 #174]: #176
-#222 := [monotonicity #177]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#218 := (iff #63 #217)
-#215 := (iff #62 #214)
-#212 := (= #61 #211)
-#209 := (= #60 #208)
-#206 := (= #59 #205)
-#203 := (= #58 #200)
-#197 := (- #194)
-#201 := (= #197 #200)
-#202 := [rewrite]: #201
-#198 := (= #58 #197)
-#195 := (= #57 #194)
-#140 := (= #48 #139)
-#141 := [rewrite]: #140
-#137 := (= #47 #136)
-#138 := [rewrite]: #137
-#196 := [monotonicity #138 #141]: #195
-#199 := [monotonicity #196]: #198
-#204 := [trans #199 #202]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [quant-intro #216]: #218
-#236 := [trans #219 #234]: #235
-#193 := [asserted]: #63
-#237 := [mp #193 #236]: #232
-#265 := [mp~ #237 #250]: #232
-#303 := [mp #265 #302]: #300
-#334 := [mp #303 #333]: #331
-#843 := [mp #334 #842]: #838
-#738 := (not #838)
-#727 := (or #738 #502)
-#774 := (* -1::Int 0::Int)
-#489 := (mod #774 #774)
-#771 := (+ #11 #489)
-#775 := (= #771 0::Int)
-#493 := (mod 0::Int 0::Int)
-#494 := (* -1::Int #493)
-#495 := (+ #11 #494)
-#773 := (= #495 0::Int)
-#503 := (<= 0::Int 0::Int)
-#591 := (>= 0::Int 0::Int)
-#778 := (or #591 #503)
-#782 := (not #778)
-#777 := (or #503 #503)
-#781 := (not #777)
-#492 := (or #781 #782)
-#772 := (if #492 #773 #775)
-#780 := (= 0::Int 0::Int)
-#776 := (if #780 #502 #772)
-#765 := (if #780 #502 #776)
-#728 := (or #738 #765)
-#730 := (iff #728 #727)
-#731 := (iff #727 #727)
-#715 := [rewrite]: #731
-#737 := (iff #765 #502)
-#1 := true
-#726 := (if true #502 #502)
-#735 := (iff #726 #502)
-#736 := [rewrite]: #735
-#723 := (iff #765 #726)
-#732 := (iff #776 #502)
-#742 := (+ #11 #493)
-#740 := (= #742 0::Int)
-#650 := (if true #502 #740)
-#741 := (iff #650 #502)
-#745 := [rewrite]: #741
-#651 := (iff #776 #650)
-#648 := (iff #772 #740)
-#643 := (if false #773 #740)
-#639 := (iff #643 #740)
-#647 := [rewrite]: #639
-#645 := (iff #772 #643)
-#743 := (iff #775 #740)
-#644 := (= #771 #742)
-#635 := (= #489 #493)
-#633 := (= #774 0::Int)
-#634 := [rewrite]: #633
-#594 := [monotonicity #634 #634]: #635
-#739 := [monotonicity #594]: #644
-#628 := [monotonicity #739]: #743
-#748 := (iff #492 false)
-#593 := (or false false)
-#749 := (iff #593 false)
-#750 := [rewrite]: #749
-#746 := (iff #492 #593)
-#590 := (iff #782 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#754 := (iff #782 #460)
-#759 := (iff #778 true)
-#768 := (or true true)
-#770 := (iff #768 true)
-#611 := [rewrite]: #770
-#752 := (iff #778 #768)
-#762 := (iff #503 true)
-#763 := [rewrite]: #762
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#753 := [monotonicity #800 #763]: #752
-#760 := [trans #753 #611]: #759
-#761 := [monotonicity #760]: #754
-#592 := [trans #761 #448]: #590
-#757 := (iff #781 false)
-#755 := (iff #781 #460)
-#612 := (iff #777 true)
-#769 := (iff #777 #768)
-#764 := [monotonicity #763 #763]: #769
-#613 := [trans #764 #611]: #612
-#756 := [monotonicity #613]: #755
-#758 := [trans #756 #448]: #757
-#747 := [monotonicity #758 #592]: #746
-#751 := [trans #747 #750]: #748
-#646 := [monotonicity #751 #628]: #645
-#649 := [trans #646 #647]: #648
-#766 := (iff #780 true)
-#767 := [rewrite]: #766
-#744 := [monotonicity #767 #649]: #651
-#734 := [trans #744 #745]: #732
-#725 := [monotonicity #767 #734]: #723
-#733 := [trans #725 #736]: #737
-#724 := [monotonicity #733]: #730
-#716 := [trans #724 #715]: #730
-#729 := [quant-inst #9 #9]: #728
-#718 := [mp #729 #716]: #727
-#720 := [unit-resolution #718 #843]: #502
-#721 := [monotonicity #720]: #14
-#15 := (not #14)
-#83 := [asserted]: #15
-[unit-resolution #83 #721]: false
-unsat
-3423d3f62be3468a179235b7bd3ba97bcbe5bc80 300 0
-#2 := false
-decl f10 :: S3
-#10 := f10
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 Int Int)
-#13 := 0::Int
-decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f9 :: S6
-#9 := f9
-#11 := (f8 f9 f10)
-decl f7 :: S5
-#8 := f7
-#12 := (f6 f7 #11)
-#14 := (f5 #12 0::Int)
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 #14)
-#16 := (= #15 f10)
-#398 := (f3 f4 #11)
-#482 := (= #398 f10)
-#18 := (:var 0 S3)
-#19 := (f8 f9 #18)
-#811 := (pattern #19)
-#20 := (f3 f4 #19)
-#21 := (= #20 #18)
-#812 := (forall (vars (?v0 S3)) (:pat #811) #21)
-#22 := (forall (vars (?v0 S3)) #21)
-#815 := (iff #22 #812)
-#813 := (iff #21 #21)
-#814 := [refl]: #813
-#816 := [quant-intro #814]: #815
-#256 := (~ #22 #22)
-#254 := (~ #21 #21)
-#255 := [refl]: #254
-#257 := [nnf-pos #255]: #256
-#85 := [asserted]: #22
-#242 := [mp~ #85 #257]: #22
-#817 := [mp #242 #816]: #812
-#475 := (not #812)
-#486 := (or #475 #482)
-#487 := [quant-inst #10]: #486
-#650 := [unit-resolution #487 #817]: #482
-#652 := (= #15 #398)
-#808 := (= #14 #11)
-#23 := (:var 0 Int)
-#35 := (:var 1 Int)
-#55 := (f6 f7 #35)
-#56 := (f5 #55 #23)
-#838 := (pattern #56)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #35)
-#195 := (mod #137 #140)
-#325 := (+ #56 #195)
-#326 := (= #325 0::Int)
-#57 := (mod #35 #23)
-#322 := (* -1::Int #57)
-#323 := (+ #56 #322)
-#324 := (= #323 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #35 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #35 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#327 := (if #273 #324 #326)
-#321 := (= #56 0::Int)
-#38 := (= #35 0::Int)
-#328 := (if #38 #321 #327)
-#320 := (= #56 #35)
-#39 := (= #23 0::Int)
-#329 := (if #39 #320 #328)
-#839 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #838) #329)
-#332 := (forall (vars (?v0 Int) (?v1 Int)) #329)
-#842 := (iff #332 #839)
-#840 := (iff #329 #329)
-#841 := [refl]: #840
-#843 := [quant-intro #841]: #842
-#201 := (* -1::Int #195)
-#289 := (if #273 #57 #201)
-#292 := (if #38 0::Int #289)
-#295 := (if #39 #35 #292)
-#298 := (= #56 #295)
-#301 := (forall (vars (?v0 Int) (?v1 Int)) #298)
-#333 := (iff #301 #332)
-#330 := (iff #298 #329)
-#331 := [rewrite]: #330
-#334 := [quant-intro #331]: #333
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#221 := (if #176 #57 #201)
-#224 := (if #38 0::Int #221)
-#227 := (if #39 #35 #224)
-#230 := (= #56 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#302 := (iff #233 #301)
-#299 := (iff #230 #298)
-#296 := (= #227 #295)
-#293 := (= #224 #292)
-#290 := (= #221 #289)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#291 := [monotonicity #275]: #290
-#294 := [monotonicity #291]: #293
-#297 := [monotonicity #294]: #296
-#300 := [monotonicity #297]: #299
-#303 := [quant-intro #300]: #302
-#250 := (~ #233 #233)
-#264 := (~ #230 #230)
-#265 := [refl]: #264
-#251 := [nnf-pos #265]: #250
-#49 := (- #23)
-#48 := (- #35)
-#58 := (mod #48 #49)
-#59 := (- #58)
-#42 := (< 0::Int #23)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#60 := (if #46 #57 #59)
-#61 := (if #38 0::Int #60)
-#62 := (if #39 #35 #61)
-#63 := (= #56 #62)
-#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#236 := (iff #64 #233)
-#206 := (if #46 #57 #201)
-#209 := (if #38 0::Int #206)
-#212 := (if #39 #35 #209)
-#215 := (= #56 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#234 := (iff #218 #233)
-#231 := (iff #215 #230)
-#228 := (= #212 #227)
-#225 := (= #209 #224)
-#222 := (= #206 #221)
-#177 := (iff #46 #176)
-#174 := (iff #45 #173)
-#164 := (iff #42 #163)
-#165 := [rewrite]: #164
-#171 := (iff #44 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #43 #166)
-#160 := (iff #41 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#223 := [monotonicity #178]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#219 := (iff #64 #218)
-#216 := (iff #63 #215)
-#213 := (= #62 #212)
-#210 := (= #61 #209)
-#207 := (= #60 #206)
-#204 := (= #59 #201)
-#198 := (- #195)
-#202 := (= #198 #201)
-#203 := [rewrite]: #202
-#199 := (= #59 #198)
-#196 := (= #58 #195)
-#141 := (= #49 #140)
-#142 := [rewrite]: #141
-#138 := (= #48 #137)
-#139 := [rewrite]: #138
-#197 := [monotonicity #139 #142]: #196
-#200 := [monotonicity #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#237 := [trans #220 #235]: #236
-#194 := [asserted]: #64
-#238 := [mp #194 #237]: #233
-#266 := [mp~ #238 #251]: #233
-#304 := [mp #266 #303]: #301
-#335 := [mp #304 #334]: #332
-#844 := [mp #335 #843]: #839
-#740 := (not #839)
-#741 := (or #740 #808)
-#431 := (* -1::Int 0::Int)
-#793 := (* -1::Int #11)
-#794 := (mod #793 #431)
-#796 := (+ #14 #794)
-#436 := (= #796 0::Int)
-#790 := (mod #11 0::Int)
-#791 := (* -1::Int #790)
-#792 := (+ #14 #791)
-#787 := (= #792 0::Int)
-#786 := (<= 0::Int 0::Int)
-#451 := (>= #11 0::Int)
-#452 := (or #451 #786)
-#788 := (not #452)
-#445 := (<= #11 0::Int)
-#449 := (or #445 #786)
-#450 := (not #449)
-#789 := (or #450 #788)
-#437 := (if #789 #787 #436)
-#802 := (= #14 0::Int)
-#461 := (= #11 0::Int)
-#797 := (if #461 #802 #437)
-#807 := (= 0::Int 0::Int)
-#795 := (if #807 #808 #797)
-#744 := (or #740 #795)
-#644 := (iff #744 #741)
-#647 := (iff #741 #741)
-#640 := [rewrite]: #647
-#743 := (iff #795 #808)
-#614 := (mod #793 0::Int)
-#758 := (+ #14 #614)
-#754 := (= #758 0::Int)
-#750 := (if #461 #802 #754)
-#1 := true
-#752 := (if true #808 #750)
-#636 := (iff #752 #808)
-#595 := [rewrite]: #636
-#634 := (iff #795 #752)
-#751 := (iff #797 #750)
-#747 := (iff #437 #754)
-#755 := (if false #787 #754)
-#593 := (iff #755 #754)
-#594 := [rewrite]: #593
-#762 := (iff #437 #755)
-#760 := (iff #436 #754)
-#759 := (= #796 #758)
-#756 := (= #794 #614)
-#612 := (= #431 0::Int)
-#613 := [rewrite]: #612
-#757 := [monotonicity #613]: #756
-#753 := [monotonicity #757]: #759
-#761 := [monotonicity #753]: #760
-#765 := (iff #789 false)
-#768 := (or false false)
-#769 := (iff #768 false)
-#770 := [rewrite]: #769
-#763 := (iff #789 #768)
-#766 := (iff #788 false)
-#504 := (not true)
-#779 := (iff #504 false)
-#783 := [rewrite]: #779
-#773 := (iff #788 #504)
-#772 := (iff #452 true)
-#495 := (or #451 true)
-#775 := (iff #495 true)
-#490 := [rewrite]: #775
-#496 := (iff #452 #495)
-#785 := (iff #786 true)
-#507 := [rewrite]: #785
-#774 := [monotonicity #507]: #496
-#776 := [trans #774 #490]: #772
-#777 := [monotonicity #776]: #773
-#767 := [trans #777 #783]: #766
-#493 := (iff #450 false)
-#778 := (iff #450 #504)
-#781 := (iff #449 true)
-#508 := (or #445 true)
-#404 := (iff #508 true)
-#780 := [rewrite]: #404
-#509 := (iff #449 #508)
-#510 := [monotonicity #507]: #509
-#503 := [trans #510 #780]: #781
-#782 := [monotonicity #503]: #778
-#494 := [trans #782 #783]: #493
-#764 := [monotonicity #494 #767]: #763
-#771 := [trans #764 #770]: #765
-#591 := [monotonicity #771 #761]: #762
-#748 := [trans #591 #594]: #747
-#749 := [monotonicity #748]: #751
-#798 := (iff #807 true)
-#784 := [rewrite]: #798
-#635 := [monotonicity #784 #749]: #634
-#645 := [trans #635 #595]: #743
-#646 := [monotonicity #645]: #644
-#648 := [trans #646 #640]: #644
-#629 := [quant-inst #11 #13]: #744
-#649 := [mp #629 #648]: #741
-#651 := [unit-resolution #649 #844]: #808
-#745 := [monotonicity #651]: #652
-#742 := [trans #745 #650]: #16
-#17 := (not #16)
-#84 := [asserted]: #17
-[unit-resolution #84 #742]: false
-unsat
-c3011ba0f8d5cd7434b90805d32c60ec6054ba7f 294 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 0::Int)
-#12 := (f5 #10 1::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#502 := (= #12 0::Int)
-#23 := (:var 0 Int)
-#35 := (:var 1 Int)
-#55 := (f6 f7 #35)
-#56 := (f5 #55 #23)
-#837 := (pattern #56)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #35)
-#195 := (mod #137 #140)
-#325 := (+ #56 #195)
-#326 := (= #325 0::Int)
-#57 := (mod #35 #23)
-#322 := (* -1::Int #57)
-#323 := (+ #56 #322)
-#324 := (= #323 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #35 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #35 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#327 := (if #273 #324 #326)
-#321 := (= #56 0::Int)
-#38 := (= #35 0::Int)
-#328 := (if #38 #321 #327)
-#320 := (= #56 #35)
-#39 := (= #23 0::Int)
-#329 := (if #39 #320 #328)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #329)
-#332 := (forall (vars (?v0 Int) (?v1 Int)) #329)
-#841 := (iff #332 #838)
-#839 := (iff #329 #329)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#201 := (* -1::Int #195)
-#289 := (if #273 #57 #201)
-#292 := (if #38 0::Int #289)
-#295 := (if #39 #35 #292)
-#298 := (= #56 #295)
-#301 := (forall (vars (?v0 Int) (?v1 Int)) #298)
-#333 := (iff #301 #332)
-#330 := (iff #298 #329)
-#331 := [rewrite]: #330
-#334 := [quant-intro #331]: #333
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#221 := (if #176 #57 #201)
-#224 := (if #38 0::Int #221)
-#227 := (if #39 #35 #224)
-#230 := (= #56 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#302 := (iff #233 #301)
-#299 := (iff #230 #298)
-#296 := (= #227 #295)
-#293 := (= #224 #292)
-#290 := (= #221 #289)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#291 := [monotonicity #275]: #290
-#294 := [monotonicity #291]: #293
-#297 := [monotonicity #294]: #296
-#300 := [monotonicity #297]: #299
-#303 := [quant-intro #300]: #302
-#250 := (~ #233 #233)
-#264 := (~ #230 #230)
-#265 := [refl]: #264
-#251 := [nnf-pos #265]: #250
-#49 := (- #23)
-#48 := (- #35)
-#58 := (mod #48 #49)
-#59 := (- #58)
-#42 := (< 0::Int #23)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#60 := (if #46 #57 #59)
-#61 := (if #38 0::Int #60)
-#62 := (if #39 #35 #61)
-#63 := (= #56 #62)
-#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#236 := (iff #64 #233)
-#206 := (if #46 #57 #201)
-#209 := (if #38 0::Int #206)
-#212 := (if #39 #35 #209)
-#215 := (= #56 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#234 := (iff #218 #233)
-#231 := (iff #215 #230)
-#228 := (= #212 #227)
-#225 := (= #209 #224)
-#222 := (= #206 #221)
-#177 := (iff #46 #176)
-#174 := (iff #45 #173)
-#164 := (iff #42 #163)
-#165 := [rewrite]: #164
-#171 := (iff #44 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #43 #166)
-#160 := (iff #41 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#223 := [monotonicity #178]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#219 := (iff #64 #218)
-#216 := (iff #63 #215)
-#213 := (= #62 #212)
-#210 := (= #61 #209)
-#207 := (= #60 #206)
-#204 := (= #59 #201)
-#198 := (- #195)
-#202 := (= #198 #201)
-#203 := [rewrite]: #202
-#199 := (= #59 #198)
-#196 := (= #58 #195)
-#141 := (= #49 #140)
-#142 := [rewrite]: #141
-#138 := (= #48 #137)
-#139 := [rewrite]: #138
-#197 := [monotonicity #139 #142]: #196
-#200 := [monotonicity #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#237 := [trans #220 #235]: #236
-#194 := [asserted]: #64
-#238 := [mp #194 #237]: #233
-#266 := [mp~ #238 #251]: #233
-#304 := [mp #266 #303]: #301
-#335 := [mp #304 #334]: #332
-#843 := [mp #335 #842]: #838
-#699 := (not #838)
-#700 := (or #699 #502)
-#775 := (* -1::Int 1::Int)
-#771 := (* -1::Int 0::Int)
-#772 := (mod #771 #775)
-#776 := (+ #12 #772)
-#765 := (= #776 0::Int)
-#495 := (mod 0::Int 1::Int)
-#773 := (* -1::Int #495)
-#774 := (+ #12 #773)
-#489 := (= #774 0::Int)
-#781 := (<= 1::Int 0::Int)
-#591 := (>= 0::Int 0::Int)
-#492 := (or #591 #781)
-#493 := (not #492)
-#777 := (<= 0::Int 0::Int)
-#778 := (or #777 #781)
-#782 := (not #778)
-#494 := (or #782 #493)
-#766 := (if #494 #489 #765)
-#503 := (= 0::Int 0::Int)
-#767 := (if #503 #502 #766)
-#780 := (= 1::Int 0::Int)
-#762 := (if #780 #502 #767)
-#701 := (or #699 #762)
-#703 := (iff #701 #700)
-#705 := (iff #700 #700)
-#706 := [rewrite]: #705
-#697 := (iff #762 #502)
-#716 := (if false #502 #502)
-#720 := (iff #716 #502)
-#721 := [rewrite]: #720
-#694 := (iff #762 #716)
-#710 := (iff #767 #502)
-#1 := true
-#708 := (if true #502 #502)
-#712 := (iff #708 #502)
-#713 := [rewrite]: #712
-#709 := (iff #767 #708)
-#717 := (iff #766 #502)
-#718 := (iff #766 #716)
-#731 := (iff #765 #502)
-#730 := (= #776 #12)
-#648 := (+ #12 0::Int)
-#651 := (= #648 #12)
-#744 := [rewrite]: #651
-#728 := (= #776 #648)
-#738 := (= #772 0::Int)
-#725 := (mod 0::Int -1::Int)
-#737 := (= #725 0::Int)
-#733 := [rewrite]: #737
-#735 := (= #772 #725)
-#726 := (= #775 -1::Int)
-#723 := [rewrite]: #726
-#645 := (= #771 0::Int)
-#646 := [rewrite]: #645
-#736 := [monotonicity #646 #723]: #735
-#727 := [trans #736 #733]: #738
-#729 := [monotonicity #727]: #728
-#724 := [trans #729 #744]: #730
-#715 := [monotonicity #724]: #731
-#732 := (iff #489 #502)
-#741 := (= #774 #12)
-#649 := (= #774 #648)
-#639 := (= #773 0::Int)
-#628 := (= #773 #771)
-#740 := (= #495 0::Int)
-#743 := [rewrite]: #740
-#643 := [monotonicity #743]: #628
-#647 := [trans #643 #646]: #639
-#650 := [monotonicity #647]: #649
-#745 := [trans #650 #744]: #741
-#734 := [monotonicity #745]: #732
-#644 := (iff #494 false)
-#633 := (or false false)
-#594 := (iff #633 false)
-#742 := [rewrite]: #594
-#634 := (iff #494 #633)
-#748 := (iff #493 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#749 := (iff #493 #460)
-#746 := (iff #492 true)
-#755 := (or true false)
-#758 := (iff #755 true)
-#752 := [rewrite]: #758
-#592 := (iff #492 #755)
-#612 := (iff #781 false)
-#613 := [rewrite]: #612
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#593 := [monotonicity #800 #613]: #592
-#747 := [trans #593 #752]: #746
-#750 := [monotonicity #747]: #749
-#751 := [trans #750 #448]: #748
-#761 := (iff #782 false)
-#760 := (iff #782 #460)
-#753 := (iff #778 true)
-#756 := (iff #778 #755)
-#770 := (iff #777 true)
-#611 := [rewrite]: #770
-#757 := [monotonicity #611 #613]: #756
-#759 := [trans #757 #752]: #753
-#754 := [monotonicity #759]: #760
-#590 := [trans #754 #448]: #761
-#635 := [monotonicity #590 #751]: #634
-#739 := [trans #635 #742]: #644
-#719 := [monotonicity #739 #734 #715]: #718
-#722 := [trans #719 #721]: #717
-#769 := (iff #503 true)
-#764 := [rewrite]: #769
-#711 := [monotonicity #764 #722]: #709
-#714 := [trans #711 #713]: #710
-#763 := (iff #780 false)
-#768 := [rewrite]: #763
-#695 := [monotonicity #768 #714]: #694
-#698 := [trans #695 #721]: #697
-#704 := [monotonicity #698]: #703
-#696 := [trans #704 #706]: #703
-#702 := [quant-inst #9 #11]: #701
-#707 := [mp #702 #696]: #700
-#686 := [unit-resolution #707 #843]: #502
-#688 := [monotonicity #686]: #15
-#16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #688]: false
-unsat
-87b099d8145ebeef9dc0d37605a12e1099e37589 295 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#13 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#9 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 1::Int)
-#11 := (f5 #10 1::Int)
-#12 := (f3 f4 #11)
-#15 := (= #12 #14)
-#503 := (= #11 0::Int)
-#23 := (:var 0 Int)
-#35 := (:var 1 Int)
-#55 := (f6 f7 #35)
-#56 := (f5 #55 #23)
-#837 := (pattern #56)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #35)
-#195 := (mod #137 #140)
-#325 := (+ #56 #195)
-#326 := (= #325 0::Int)
-#57 := (mod #35 #23)
-#322 := (* -1::Int #57)
-#323 := (+ #56 #322)
-#324 := (= #323 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #35 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #35 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#327 := (if #273 #324 #326)
-#321 := (= #56 0::Int)
-#38 := (= #35 0::Int)
-#328 := (if #38 #321 #327)
-#320 := (= #56 #35)
-#39 := (= #23 0::Int)
-#329 := (if #39 #320 #328)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #329)
-#332 := (forall (vars (?v0 Int) (?v1 Int)) #329)
-#841 := (iff #332 #838)
-#839 := (iff #329 #329)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#201 := (* -1::Int #195)
-#289 := (if #273 #57 #201)
-#292 := (if #38 0::Int #289)
-#295 := (if #39 #35 #292)
-#298 := (= #56 #295)
-#301 := (forall (vars (?v0 Int) (?v1 Int)) #298)
-#333 := (iff #301 #332)
-#330 := (iff #298 #329)
-#331 := [rewrite]: #330
-#334 := [quant-intro #331]: #333
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#221 := (if #176 #57 #201)
-#224 := (if #38 0::Int #221)
-#227 := (if #39 #35 #224)
-#230 := (= #56 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#302 := (iff #233 #301)
-#299 := (iff #230 #298)
-#296 := (= #227 #295)
-#293 := (= #224 #292)
-#290 := (= #221 #289)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#291 := [monotonicity #275]: #290
-#294 := [monotonicity #291]: #293
-#297 := [monotonicity #294]: #296
-#300 := [monotonicity #297]: #299
-#303 := [quant-intro #300]: #302
-#250 := (~ #233 #233)
-#264 := (~ #230 #230)
-#265 := [refl]: #264
-#251 := [nnf-pos #265]: #250
-#49 := (- #23)
-#48 := (- #35)
-#58 := (mod #48 #49)
-#59 := (- #58)
-#42 := (< 0::Int #23)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#60 := (if #46 #57 #59)
-#61 := (if #38 0::Int #60)
-#62 := (if #39 #35 #61)
-#63 := (= #56 #62)
-#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#236 := (iff #64 #233)
-#206 := (if #46 #57 #201)
-#209 := (if #38 0::Int #206)
-#212 := (if #39 #35 #209)
-#215 := (= #56 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#234 := (iff #218 #233)
-#231 := (iff #215 #230)
-#228 := (= #212 #227)
-#225 := (= #209 #224)
-#222 := (= #206 #221)
-#177 := (iff #46 #176)
-#174 := (iff #45 #173)
-#164 := (iff #42 #163)
-#165 := [rewrite]: #164
-#171 := (iff #44 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #43 #166)
-#160 := (iff #41 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#223 := [monotonicity #178]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#219 := (iff #64 #218)
-#216 := (iff #63 #215)
-#213 := (= #62 #212)
-#210 := (= #61 #209)
-#207 := (= #60 #206)
-#204 := (= #59 #201)
-#198 := (- #195)
-#202 := (= #198 #201)
-#203 := [rewrite]: #202
-#199 := (= #59 #198)
-#196 := (= #58 #195)
-#141 := (= #49 #140)
-#142 := [rewrite]: #141
-#138 := (= #48 #137)
-#139 := [rewrite]: #138
-#197 := [monotonicity #139 #142]: #196
-#200 := [monotonicity #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#237 := [trans #220 #235]: #236
-#194 := [asserted]: #64
-#238 := [mp #194 #237]: #233
-#266 := [mp~ #238 #251]: #233
-#304 := [mp #266 #303]: #301
-#335 := [mp #304 #334]: #332
-#843 := [mp #335 #842]: #838
-#703 := (not #838)
-#704 := (or #703 #503)
-#771 := (* -1::Int 1::Int)
-#775 := (mod #771 #771)
-#772 := (+ #11 #775)
-#776 := (= #772 0::Int)
-#495 := (mod 1::Int 1::Int)
-#773 := (* -1::Int #495)
-#774 := (+ #11 #773)
-#489 := (= #774 0::Int)
-#777 := (<= 1::Int 0::Int)
-#782 := (>= 1::Int 0::Int)
-#492 := (or #782 #777)
-#493 := (not #492)
-#781 := (or #777 #777)
-#778 := (not #781)
-#494 := (or #778 #493)
-#765 := (if #494 #489 #776)
-#780 := (= 1::Int 0::Int)
-#766 := (if #780 #503 #765)
-#502 := (= #11 1::Int)
-#767 := (if #780 #502 #766)
-#705 := (or #703 #767)
-#696 := (iff #705 #704)
-#685 := (iff #704 #704)
-#686 := [rewrite]: #685
-#701 := (iff #767 #503)
-#695 := (if false #502 #503)
-#699 := (iff #695 #503)
-#700 := [rewrite]: #699
-#697 := (iff #767 #695)
-#714 := (iff #766 #503)
-#709 := (if false #503 #503)
-#713 := (iff #709 #503)
-#710 := [rewrite]: #713
-#711 := (iff #766 #709)
-#722 := (iff #765 #503)
-#1 := true
-#718 := (if true #503 #503)
-#721 := (iff #718 #503)
-#717 := [rewrite]: #721
-#719 := (iff #765 #718)
-#715 := (iff #776 #503)
-#724 := (= #772 #11)
-#649 := (+ #11 0::Int)
-#744 := (= #649 #11)
-#741 := [rewrite]: #744
-#729 := (= #772 #649)
-#727 := (= #775 0::Int)
-#735 := (mod -1::Int -1::Int)
-#733 := (= #735 0::Int)
-#738 := [rewrite]: #733
-#736 := (= #775 #735)
-#723 := (= #771 -1::Int)
-#725 := [rewrite]: #723
-#737 := [monotonicity #725 #725]: #736
-#728 := [trans #737 #738]: #727
-#730 := [monotonicity #728]: #729
-#731 := [trans #730 #741]: #724
-#716 := [monotonicity #731]: #715
-#734 := (iff #489 #503)
-#745 := (= #774 #11)
-#650 := (= #774 #649)
-#647 := (= #773 0::Int)
-#628 := (* -1::Int 0::Int)
-#646 := (= #628 0::Int)
-#639 := [rewrite]: #646
-#643 := (= #773 #628)
-#740 := (= #495 0::Int)
-#743 := [rewrite]: #740
-#645 := [monotonicity #743]: #643
-#648 := [trans #645 #639]: #647
-#651 := [monotonicity #648]: #650
-#732 := [trans #651 #741]: #745
-#726 := [monotonicity #732]: #734
-#644 := (iff #494 true)
-#592 := (or true false)
-#747 := (iff #592 true)
-#749 := [rewrite]: #747
-#594 := (iff #494 #592)
-#634 := (iff #493 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#751 := (iff #493 #460)
-#750 := (iff #492 true)
-#593 := (iff #492 #592)
-#768 := (iff #777 false)
-#769 := [rewrite]: #768
-#761 := (iff #782 true)
-#590 := [rewrite]: #761
-#746 := [monotonicity #590 #769]: #593
-#748 := [trans #746 #749]: #750
-#633 := [monotonicity #748]: #751
-#635 := [trans #633 #448]: #634
-#760 := (iff #778 true)
-#757 := (not false)
-#753 := (iff #757 true)
-#759 := [rewrite]: #753
-#758 := (iff #778 #757)
-#755 := (iff #781 false)
-#764 := (or false false)
-#612 := (iff #764 false)
-#613 := [rewrite]: #612
-#770 := (iff #781 #764)
-#611 := [monotonicity #769 #769]: #770
-#756 := [trans #611 #613]: #755
-#752 := [monotonicity #756]: #758
-#754 := [trans #752 #759]: #760
-#742 := [monotonicity #754 #635]: #594
-#739 := [trans #742 #749]: #644
-#720 := [monotonicity #739 #726 #716]: #719
-#708 := [trans #720 #717]: #722
-#762 := (iff #780 false)
-#763 := [rewrite]: #762
-#712 := [monotonicity #763 #708]: #711
-#694 := [trans #712 #710]: #714
-#698 := [monotonicity #763 #694]: #697
-#702 := [trans #698 #700]: #701
-#707 := [monotonicity #702]: #696
-#688 := [trans #707 #686]: #696
-#706 := [quant-inst #9 #9]: #705
-#689 := [mp #706 #688]: #704
-#691 := [unit-resolution #689 #843]: #503
-#692 := [monotonicity #691]: #15
-#16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #692]: false
-unsat
-a614d34cd521f11124f03ffe353f27df43731180 306 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#14 := 0::Int
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 1::Int
-decl f6 :: (-> S5 Int S4)
-#9 := 3::Int
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 3::Int)
-#12 := (f5 #10 1::Int)
-#13 := (f3 f4 #12)
-#16 := (= #13 #15)
-#777 := (= #12 0::Int)
-#24 := (:var 0 Int)
-#36 := (:var 1 Int)
-#56 := (f6 f7 #36)
-#57 := (f5 #56 #24)
-#837 := (pattern #57)
-#137 := -1::Int
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #36)
-#196 := (mod #138 #141)
-#326 := (+ #57 #196)
-#327 := (= #326 0::Int)
-#58 := (mod #36 #24)
-#323 := (* -1::Int #58)
-#324 := (+ #57 #323)
-#325 := (= #324 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #36 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #36 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#328 := (if #274 #325 #327)
-#322 := (= #57 0::Int)
-#39 := (= #36 0::Int)
-#329 := (if #39 #322 #328)
-#321 := (= #57 #36)
-#40 := (= #24 0::Int)
-#330 := (if #40 #321 #329)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #330)
-#333 := (forall (vars (?v0 Int) (?v1 Int)) #330)
-#841 := (iff #333 #838)
-#839 := (iff #330 #330)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#202 := (* -1::Int #196)
-#290 := (if #274 #58 #202)
-#293 := (if #39 0::Int #290)
-#296 := (if #40 #36 #293)
-#299 := (= #57 #296)
-#302 := (forall (vars (?v0 Int) (?v1 Int)) #299)
-#334 := (iff #302 #333)
-#331 := (iff #299 #330)
-#332 := [rewrite]: #331
-#335 := [quant-intro #332]: #334
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#222 := (if #177 #58 #202)
-#225 := (if #39 0::Int #222)
-#228 := (if #40 #36 #225)
-#231 := (= #57 #228)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#303 := (iff #234 #302)
-#300 := (iff #231 #299)
-#297 := (= #228 #296)
-#294 := (= #225 #293)
-#291 := (= #222 #290)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#292 := [monotonicity #276]: #291
-#295 := [monotonicity #292]: #294
-#298 := [monotonicity #295]: #297
-#301 := [monotonicity #298]: #300
-#304 := [quant-intro #301]: #303
-#251 := (~ #234 #234)
-#265 := (~ #231 #231)
-#266 := [refl]: #265
-#252 := [nnf-pos #266]: #251
-#50 := (- #24)
-#49 := (- #36)
-#59 := (mod #49 #50)
-#60 := (- #59)
-#43 := (< 0::Int #24)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#61 := (if #47 #58 #60)
-#62 := (if #39 0::Int #61)
-#63 := (if #40 #36 #62)
-#64 := (= #57 #63)
-#65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#237 := (iff #65 #234)
-#207 := (if #47 #58 #202)
-#210 := (if #39 0::Int #207)
-#213 := (if #40 #36 #210)
-#216 := (= #57 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#235 := (iff #219 #234)
-#232 := (iff #216 #231)
-#229 := (= #213 #228)
-#226 := (= #210 #225)
-#223 := (= #207 #222)
-#178 := (iff #47 #177)
-#175 := (iff #46 #174)
-#165 := (iff #43 #164)
-#166 := [rewrite]: #165
-#172 := (iff #45 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #44 #167)
-#161 := (iff #42 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#224 := [monotonicity #179]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#220 := (iff #65 #219)
-#217 := (iff #64 #216)
-#214 := (= #63 #213)
-#211 := (= #62 #210)
-#208 := (= #61 #207)
-#205 := (= #60 #202)
-#199 := (- #196)
-#203 := (= #199 #202)
-#204 := [rewrite]: #203
-#200 := (= #60 #199)
-#197 := (= #59 #196)
-#142 := (= #50 #141)
-#143 := [rewrite]: #142
-#139 := (= #49 #138)
-#140 := [rewrite]: #139
-#198 := [monotonicity #140 #143]: #197
-#201 := [monotonicity #198]: #200
-#206 := [trans #201 #204]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#238 := [trans #221 #236]: #237
-#195 := [asserted]: #65
-#239 := [mp #195 #238]: #234
-#267 := [mp~ #239 #252]: #234
-#305 := [mp #267 #304]: #302
-#336 := [mp #305 #335]: #333
-#843 := [mp #336 #842]: #838
-#690 := (not #838)
-#691 := (or #690 #777)
-#776 := (* -1::Int 1::Int)
-#772 := (* -1::Int 3::Int)
-#765 := (mod #772 #776)
-#766 := (+ #12 #765)
-#767 := (= #766 0::Int)
-#774 := (mod 3::Int 1::Int)
-#489 := (* -1::Int #774)
-#771 := (+ #12 #489)
-#775 := (= #771 0::Int)
-#778 := (<= 1::Int 0::Int)
-#493 := (>= 3::Int 0::Int)
-#494 := (or #493 #778)
-#495 := (not #494)
-#781 := (<= 3::Int 0::Int)
-#782 := (or #781 #778)
-#492 := (not #782)
-#773 := (or #492 #495)
-#762 := (if #773 #775 #767)
-#503 := (= 3::Int 0::Int)
-#763 := (if #503 #777 #762)
-#502 := (= #12 3::Int)
-#780 := (= 1::Int 0::Int)
-#768 := (if #780 #502 #763)
-#692 := (or #690 #768)
-#693 := (iff #692 #691)
-#675 := (iff #691 #691)
-#676 := [rewrite]: #675
-#688 := (iff #768 #777)
-#706 := (if false #502 #777)
-#685 := (iff #706 #777)
-#686 := [rewrite]: #685
-#696 := (iff #768 #706)
-#704 := (iff #763 #777)
-#699 := (if false #777 #777)
-#702 := (iff #699 #777)
-#703 := [rewrite]: #702
-#700 := (iff #763 #699)
-#697 := (iff #762 #777)
-#1 := true
-#713 := (if true #777 #777)
-#694 := (iff #713 #777)
-#695 := [rewrite]: #694
-#710 := (iff #762 #713)
-#711 := (iff #767 #777)
-#708 := (= #766 #12)
-#734 := (+ #12 0::Int)
-#725 := (= #734 #12)
-#735 := [rewrite]: #725
-#717 := (= #766 #734)
-#720 := (= #765 0::Int)
-#727 := -3::Int
-#731 := (mod -3::Int -1::Int)
-#718 := (= #731 0::Int)
-#719 := [rewrite]: #718
-#715 := (= #765 #731)
-#730 := (= #776 -1::Int)
-#724 := [rewrite]: #730
-#728 := (= #772 -3::Int)
-#729 := [rewrite]: #728
-#716 := [monotonicity #729 #724]: #715
-#721 := [trans #716 #719]: #720
-#722 := [monotonicity #721]: #717
-#709 := [trans #722 #735]: #708
-#712 := [monotonicity #709]: #711
-#733 := (iff #775 #777)
-#736 := (= #771 #12)
-#726 := (= #771 #734)
-#745 := (= #489 0::Int)
-#649 := (* -1::Int 0::Int)
-#744 := (= #649 0::Int)
-#741 := [rewrite]: #744
-#650 := (= #489 #649)
-#647 := (= #774 0::Int)
-#648 := [rewrite]: #647
-#651 := [monotonicity #648]: #650
-#732 := [trans #651 #741]: #745
-#723 := [monotonicity #732]: #726
-#737 := [trans #723 #735]: #736
-#738 := [monotonicity #737]: #733
-#646 := (iff #773 true)
-#751 := (or true false)
-#635 := (iff #751 true)
-#594 := [rewrite]: #635
-#643 := (iff #773 #751)
-#743 := (iff #495 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#739 := (iff #495 #460)
-#742 := (iff #494 true)
-#633 := (iff #494 #751)
-#755 := (iff #778 false)
-#756 := [rewrite]: #755
-#750 := (iff #493 true)
-#748 := [rewrite]: #750
-#634 := [monotonicity #748 #756]: #633
-#644 := [trans #634 #594]: #742
-#740 := [monotonicity #644]: #739
-#628 := [trans #740 #448]: #743
-#747 := (iff #492 true)
-#761 := (not false)
-#593 := (iff #761 true)
-#746 := [rewrite]: #593
-#590 := (iff #492 #761)
-#760 := (iff #782 false)
-#757 := (or false false)
-#753 := (iff #757 false)
-#759 := [rewrite]: #753
-#758 := (iff #782 #757)
-#612 := (iff #781 false)
-#613 := [rewrite]: #612
-#752 := [monotonicity #613 #756]: #758
-#754 := [trans #752 #759]: #760
-#592 := [monotonicity #754]: #590
-#749 := [trans #592 #746]: #747
-#645 := [monotonicity #749 #628]: #643
-#639 := [trans #645 #594]: #646
-#714 := [monotonicity #639 #738 #712]: #710
-#698 := [trans #714 #695]: #697
-#770 := (iff #503 false)
-#611 := [rewrite]: #770
-#701 := [monotonicity #611 #698]: #700
-#705 := [trans #701 #703]: #704
-#769 := (iff #780 false)
-#764 := [rewrite]: #769
-#707 := [monotonicity #764 #705]: #696
-#689 := [trans #707 #686]: #688
-#679 := [monotonicity #689]: #693
-#677 := [trans #679 #676]: #693
-#687 := [quant-inst #9 #11]: #692
-#680 := [mp #687 #677]: #691
-#682 := [unit-resolution #680 #843]: #777
-#683 := [monotonicity #682]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #683]: false
-unsat
-f29683011f680c62d56f5c3422022e33ef78fbc7 309 0
-#2 := false
-#16 := 0::Int
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#10 := f10
-decl f9 :: S6
-#9 := f9
-#11 := (f8 f9 f10)
-#491 := (>= #11 0::Int)
-#636 := (not #491)
-#496 := (<= #11 0::Int)
-#592 := (not #496)
-#744 := (or #592 #636)
-#708 := (not #744)
-decl f5 :: (-> S4 Int Int)
-#13 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#12 := (f6 f7 #11)
-#14 := (f5 #12 1::Int)
-#495 := (= #14 0::Int)
-#689 := (not #495)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#17 := (f3 f4 0::Int)
-#15 := (f3 f4 #14)
-#18 := (= #15 #17)
-#598 := [hypothesis]: #495
-#629 := [monotonicity #598]: #18
-#19 := (not #18)
-#86 := [asserted]: #19
-#631 := [unit-resolution #86 #629]: false
-#633 := [lemma #631]: #689
-#138 := -1::Int
-#764 := (* -1::Int #11)
-#737 := (mod #764 -1::Int)
-#735 := (+ #14 #737)
-#730 := (= #735 0::Int)
-#726 := (if #744 #495 #730)
-#494 := (= #11 0::Int)
-#683 := (not #494)
-#676 := (or #683 #495)
-#718 := (if #494 #495 #726)
-#25 := (:var 0 Int)
-#37 := (:var 1 Int)
-#57 := (f6 f7 #37)
-#58 := (f5 #57 #25)
-#839 := (pattern #58)
-#142 := (* -1::Int #25)
-#139 := (* -1::Int #37)
-#197 := (mod #139 #142)
-#327 := (+ #58 #197)
-#328 := (= #327 0::Int)
-#59 := (mod #37 #25)
-#324 := (* -1::Int #59)
-#325 := (+ #58 #324)
-#326 := (= #325 0::Int)
-#164 := (<= #25 0::Int)
-#171 := (>= #37 0::Int)
-#271 := (or #171 #164)
-#272 := (not #271)
-#160 := (<= #37 0::Int)
-#269 := (or #160 #164)
-#270 := (not #269)
-#275 := (or #270 #272)
-#329 := (if #275 #326 #328)
-#323 := (= #58 0::Int)
-#40 := (= #37 0::Int)
-#330 := (if #40 #323 #329)
-#322 := (= #58 #37)
-#41 := (= #25 0::Int)
-#331 := (if #41 #322 #330)
-#840 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #839) #331)
-#334 := (forall (vars (?v0 Int) (?v1 Int)) #331)
-#843 := (iff #334 #840)
-#841 := (iff #331 #331)
-#842 := [refl]: #841
-#844 := [quant-intro #842]: #843
-#203 := (* -1::Int #197)
-#291 := (if #275 #59 #203)
-#294 := (if #40 0::Int #291)
-#297 := (if #41 #37 #294)
-#300 := (= #58 #297)
-#303 := (forall (vars (?v0 Int) (?v1 Int)) #300)
-#335 := (iff #303 #334)
-#332 := (iff #300 #331)
-#333 := [rewrite]: #332
-#336 := [quant-intro #333]: #335
-#165 := (not #164)
-#172 := (not #171)
-#175 := (and #172 #165)
-#161 := (not #160)
-#168 := (and #161 #165)
-#178 := (or #168 #175)
-#223 := (if #178 #59 #203)
-#226 := (if #40 0::Int #223)
-#229 := (if #41 #37 #226)
-#232 := (= #58 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#304 := (iff #235 #303)
-#301 := (iff #232 #300)
-#298 := (= #229 #297)
-#295 := (= #226 #294)
-#292 := (= #223 #291)
-#276 := (iff #178 #275)
-#273 := (iff #175 #272)
-#274 := [rewrite]: #273
-#254 := (iff #168 #270)
-#255 := [rewrite]: #254
-#277 := [monotonicity #255 #274]: #276
-#293 := [monotonicity #277]: #292
-#296 := [monotonicity #293]: #295
-#299 := [monotonicity #296]: #298
-#302 := [monotonicity #299]: #301
-#305 := [quant-intro #302]: #304
-#252 := (~ #235 #235)
-#266 := (~ #232 #232)
-#267 := [refl]: #266
-#253 := [nnf-pos #267]: #252
-#51 := (- #25)
-#50 := (- #37)
-#60 := (mod #50 #51)
-#61 := (- #60)
-#44 := (< 0::Int #25)
-#46 := (< #37 0::Int)
-#47 := (and #46 #44)
-#43 := (< 0::Int #37)
-#45 := (and #43 #44)
-#48 := (or #45 #47)
-#62 := (if #48 #59 #61)
-#63 := (if #40 0::Int #62)
-#64 := (if #41 #37 #63)
-#65 := (= #58 #64)
-#66 := (forall (vars (?v0 Int) (?v1 Int)) #65)
-#238 := (iff #66 #235)
-#208 := (if #48 #59 #203)
-#211 := (if #40 0::Int #208)
-#214 := (if #41 #37 #211)
-#217 := (= #58 #214)
-#220 := (forall (vars (?v0 Int) (?v1 Int)) #217)
-#236 := (iff #220 #235)
-#233 := (iff #217 #232)
-#230 := (= #214 #229)
-#227 := (= #211 #226)
-#224 := (= #208 #223)
-#179 := (iff #48 #178)
-#176 := (iff #47 #175)
-#166 := (iff #44 #165)
-#167 := [rewrite]: #166
-#173 := (iff #46 #172)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174 #167]: #176
-#169 := (iff #45 #168)
-#162 := (iff #43 #161)
-#163 := [rewrite]: #162
-#170 := [monotonicity #163 #167]: #169
-#180 := [monotonicity #170 #177]: #179
-#225 := [monotonicity #180]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#221 := (iff #66 #220)
-#218 := (iff #65 #217)
-#215 := (= #64 #214)
-#212 := (= #63 #211)
-#209 := (= #62 #208)
-#206 := (= #61 #203)
-#200 := (- #197)
-#204 := (= #200 #203)
-#205 := [rewrite]: #204
-#201 := (= #61 #200)
-#198 := (= #60 #197)
-#143 := (= #51 #142)
-#144 := [rewrite]: #143
-#140 := (= #50 #139)
-#141 := [rewrite]: #140
-#199 := [monotonicity #141 #144]: #198
-#202 := [monotonicity #199]: #201
-#207 := [trans #202 #205]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [monotonicity #216]: #218
-#222 := [quant-intro #219]: #221
-#239 := [trans #222 #237]: #238
-#196 := [asserted]: #66
-#240 := [mp #196 #239]: #235
-#268 := [mp~ #240 #253]: #235
-#306 := [mp #268 #305]: #303
-#337 := [mp #306 #336]: #334
-#845 := [mp #337 #844]: #840
-#714 := (not #840)
-#715 := (or #714 #718)
-#765 := (* -1::Int 1::Int)
-#770 := (mod #764 #765)
-#771 := (+ #14 #770)
-#766 := (= #771 0::Int)
-#778 := (mod #11 1::Int)
-#767 := (* -1::Int #778)
-#768 := (+ #14 #767)
-#769 := (= #768 0::Int)
-#497 := (<= 1::Int 0::Int)
-#773 := (or #491 #497)
-#777 := (not #773)
-#775 := (or #496 #497)
-#776 := (not #775)
-#774 := (or #776 #777)
-#772 := (if #774 #769 #766)
-#613 := (if #494 #495 #772)
-#784 := (= #14 #11)
-#780 := (= 1::Int 0::Int)
-#614 := (if #780 #784 #613)
-#712 := (or #714 #614)
-#696 := (iff #712 #715)
-#699 := (iff #715 #715)
-#700 := [rewrite]: #699
-#711 := (iff #614 #718)
-#722 := (if false #784 #718)
-#724 := (iff #722 #718)
-#710 := [rewrite]: #724
-#723 := (iff #614 #722)
-#720 := (iff #613 #718)
-#733 := (iff #772 #726)
-#731 := (iff #766 #730)
-#740 := (= #771 #735)
-#738 := (= #770 #737)
-#725 := (= #765 -1::Int)
-#727 := [rewrite]: #725
-#739 := [monotonicity #727]: #738
-#729 := [monotonicity #739]: #740
-#732 := [monotonicity #729]: #731
-#736 := (iff #769 #495)
-#747 := (= #768 #14)
-#651 := (+ #14 0::Int)
-#746 := (= #651 #14)
-#743 := [rewrite]: #746
-#652 := (= #768 #651)
-#649 := (= #767 0::Int)
-#630 := (* -1::Int 0::Int)
-#648 := (= #630 0::Int)
-#641 := [rewrite]: #648
-#645 := (= #767 #630)
-#742 := (= #778 0::Int)
-#745 := [rewrite]: #742
-#647 := [monotonicity #745]: #645
-#650 := [trans #647 #641]: #649
-#653 := [monotonicity #650]: #652
-#734 := [trans #653 #743]: #747
-#728 := [monotonicity #734]: #736
-#646 := (iff #774 #744)
-#637 := (iff #777 #636)
-#753 := (iff #773 #491)
-#748 := (or #491 false)
-#752 := (iff #748 #491)
-#750 := [rewrite]: #752
-#749 := (iff #773 #748)
-#758 := (iff #497 false)
-#759 := [rewrite]: #758
-#751 := [monotonicity #759]: #749
-#635 := [trans #751 #750]: #753
-#596 := [monotonicity #635]: #637
-#594 := (iff #776 #592)
-#756 := (iff #775 #496)
-#760 := (or #496 false)
-#761 := (iff #760 #496)
-#762 := [rewrite]: #761
-#754 := (iff #775 #760)
-#755 := [monotonicity #759]: #754
-#763 := [trans #755 #762]: #756
-#595 := [monotonicity #763]: #594
-#741 := [monotonicity #595 #596]: #646
-#717 := [monotonicity #741 #728 #732]: #733
-#721 := [monotonicity #717]: #720
-#615 := (iff #780 false)
-#757 := [rewrite]: #615
-#719 := [monotonicity #757 #721]: #723
-#713 := [trans #719 #710]: #711
-#697 := [monotonicity #713]: #696
-#701 := [trans #697 #700]: #696
-#716 := [quant-inst #11 #13]: #712
-#702 := [mp #716 #701]: #715
-#668 := [unit-resolution #702 #845]: #718
-#682 := (not #718)
-#684 := (or #682 #683 #495)
-#685 := [def-axiom]: #684
-#656 := [unit-resolution #685 #668]: #676
-#583 := [unit-resolution #656 #633]: #683
-#657 := (or #494 #726)
-#680 := (or #682 #494 #726)
-#686 := [def-axiom]: #680
-#638 := [unit-resolution #686 #668]: #657
-#588 := [unit-resolution #638 #583]: #726
-#690 := (not #726)
-#691 := (or #690 #708 #495)
-#692 := [def-axiom]: #691
-#567 := [unit-resolution #692 #588 #633]: #708
-#706 := (or #744 #491)
-#707 := [def-axiom]: #706
-#570 := [unit-resolution #707 #567]: #491
-#704 := (or #744 #496)
-#705 := [def-axiom]: #704
-#574 := [unit-resolution #705 #567]: #496
-#576 := (or #494 #592 #636)
-#577 := [th-lemma arith triangle-eq]: #576
-[unit-resolution #577 #583 #574 #570]: false
-unsat
-f5dee1de42c18302f6c788168a6801f729654264 295 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 0::Int)
-#12 := (f5 #10 3::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#502 := (= #12 0::Int)
-#23 := (:var 0 Int)
-#35 := (:var 1 Int)
-#55 := (f6 f7 #35)
-#56 := (f5 #55 #23)
-#837 := (pattern #56)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #35)
-#195 := (mod #137 #140)
-#325 := (+ #56 #195)
-#326 := (= #325 0::Int)
-#57 := (mod #35 #23)
-#322 := (* -1::Int #57)
-#323 := (+ #56 #322)
-#324 := (= #323 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #35 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #35 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#327 := (if #273 #324 #326)
-#321 := (= #56 0::Int)
-#38 := (= #35 0::Int)
-#328 := (if #38 #321 #327)
-#320 := (= #56 #35)
-#39 := (= #23 0::Int)
-#329 := (if #39 #320 #328)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #329)
-#332 := (forall (vars (?v0 Int) (?v1 Int)) #329)
-#841 := (iff #332 #838)
-#839 := (iff #329 #329)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#201 := (* -1::Int #195)
-#289 := (if #273 #57 #201)
-#292 := (if #38 0::Int #289)
-#295 := (if #39 #35 #292)
-#298 := (= #56 #295)
-#301 := (forall (vars (?v0 Int) (?v1 Int)) #298)
-#333 := (iff #301 #332)
-#330 := (iff #298 #329)
-#331 := [rewrite]: #330
-#334 := [quant-intro #331]: #333
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#221 := (if #176 #57 #201)
-#224 := (if #38 0::Int #221)
-#227 := (if #39 #35 #224)
-#230 := (= #56 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#302 := (iff #233 #301)
-#299 := (iff #230 #298)
-#296 := (= #227 #295)
-#293 := (= #224 #292)
-#290 := (= #221 #289)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#291 := [monotonicity #275]: #290
-#294 := [monotonicity #291]: #293
-#297 := [monotonicity #294]: #296
-#300 := [monotonicity #297]: #299
-#303 := [quant-intro #300]: #302
-#250 := (~ #233 #233)
-#264 := (~ #230 #230)
-#265 := [refl]: #264
-#251 := [nnf-pos #265]: #250
-#49 := (- #23)
-#48 := (- #35)
-#58 := (mod #48 #49)
-#59 := (- #58)
-#42 := (< 0::Int #23)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#60 := (if #46 #57 #59)
-#61 := (if #38 0::Int #60)
-#62 := (if #39 #35 #61)
-#63 := (= #56 #62)
-#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#236 := (iff #64 #233)
-#206 := (if #46 #57 #201)
-#209 := (if #38 0::Int #206)
-#212 := (if #39 #35 #209)
-#215 := (= #56 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#234 := (iff #218 #233)
-#231 := (iff #215 #230)
-#228 := (= #212 #227)
-#225 := (= #209 #224)
-#222 := (= #206 #221)
-#177 := (iff #46 #176)
-#174 := (iff #45 #173)
-#164 := (iff #42 #163)
-#165 := [rewrite]: #164
-#171 := (iff #44 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #43 #166)
-#160 := (iff #41 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#223 := [monotonicity #178]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#219 := (iff #64 #218)
-#216 := (iff #63 #215)
-#213 := (= #62 #212)
-#210 := (= #61 #209)
-#207 := (= #60 #206)
-#204 := (= #59 #201)
-#198 := (- #195)
-#202 := (= #198 #201)
-#203 := [rewrite]: #202
-#199 := (= #59 #198)
-#196 := (= #58 #195)
-#141 := (= #49 #140)
-#142 := [rewrite]: #141
-#138 := (= #48 #137)
-#139 := [rewrite]: #138
-#197 := [monotonicity #139 #142]: #196
-#200 := [monotonicity #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#237 := [trans #220 #235]: #236
-#194 := [asserted]: #64
-#238 := [mp #194 #237]: #233
-#266 := [mp~ #238 #251]: #233
-#304 := [mp #266 #303]: #301
-#335 := [mp #304 #334]: #332
-#843 := [mp #335 #842]: #838
-#700 := (not #838)
-#701 := (or #700 #502)
-#775 := (* -1::Int 3::Int)
-#771 := (* -1::Int 0::Int)
-#772 := (mod #771 #775)
-#776 := (+ #12 #772)
-#765 := (= #776 0::Int)
-#495 := (mod 0::Int 3::Int)
-#773 := (* -1::Int #495)
-#774 := (+ #12 #773)
-#489 := (= #774 0::Int)
-#781 := (<= 3::Int 0::Int)
-#591 := (>= 0::Int 0::Int)
-#492 := (or #591 #781)
-#493 := (not #492)
-#777 := (<= 0::Int 0::Int)
-#778 := (or #777 #781)
-#782 := (not #778)
-#494 := (or #782 #493)
-#766 := (if #494 #489 #765)
-#503 := (= 0::Int 0::Int)
-#767 := (if #503 #502 #766)
-#780 := (= 3::Int 0::Int)
-#762 := (if #780 #502 #767)
-#702 := (or #700 #762)
-#704 := (iff #702 #701)
-#706 := (iff #701 #701)
-#696 := [rewrite]: #706
-#698 := (iff #762 #502)
-#718 := (if false #502 #502)
-#721 := (iff #718 #502)
-#717 := [rewrite]: #721
-#695 := (iff #762 #718)
-#714 := (iff #767 #502)
-#1 := true
-#709 := (if true #502 #502)
-#713 := (iff #709 #502)
-#710 := [rewrite]: #713
-#711 := (iff #767 #709)
-#722 := (iff #766 #502)
-#719 := (iff #766 #718)
-#715 := (iff #765 #502)
-#724 := (= #776 #12)
-#648 := (+ #12 0::Int)
-#651 := (= #648 #12)
-#744 := [rewrite]: #651
-#729 := (= #776 #648)
-#727 := (= #772 0::Int)
-#726 := -3::Int
-#735 := (mod 0::Int -3::Int)
-#733 := (= #735 0::Int)
-#738 := [rewrite]: #733
-#736 := (= #772 #735)
-#723 := (= #775 -3::Int)
-#725 := [rewrite]: #723
-#645 := (= #771 0::Int)
-#646 := [rewrite]: #645
-#737 := [monotonicity #646 #725]: #736
-#728 := [trans #737 #738]: #727
-#730 := [monotonicity #728]: #729
-#731 := [trans #730 #744]: #724
-#716 := [monotonicity #731]: #715
-#732 := (iff #489 #502)
-#741 := (= #774 #12)
-#649 := (= #774 #648)
-#639 := (= #773 0::Int)
-#628 := (= #773 #771)
-#740 := (= #495 0::Int)
-#743 := [rewrite]: #740
-#643 := [monotonicity #743]: #628
-#647 := [trans #643 #646]: #639
-#650 := [monotonicity #647]: #649
-#745 := [trans #650 #744]: #741
-#734 := [monotonicity #745]: #732
-#644 := (iff #494 false)
-#633 := (or false false)
-#594 := (iff #633 false)
-#742 := [rewrite]: #594
-#634 := (iff #494 #633)
-#748 := (iff #493 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#749 := (iff #493 #460)
-#746 := (iff #492 true)
-#755 := (or true false)
-#758 := (iff #755 true)
-#752 := [rewrite]: #758
-#592 := (iff #492 #755)
-#612 := (iff #781 false)
-#613 := [rewrite]: #612
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#593 := [monotonicity #800 #613]: #592
-#747 := [trans #593 #752]: #746
-#750 := [monotonicity #747]: #749
-#751 := [trans #750 #448]: #748
-#761 := (iff #782 false)
-#760 := (iff #782 #460)
-#753 := (iff #778 true)
-#756 := (iff #778 #755)
-#770 := (iff #777 true)
-#611 := [rewrite]: #770
-#757 := [monotonicity #611 #613]: #756
-#759 := [trans #757 #752]: #753
-#754 := [monotonicity #759]: #760
-#590 := [trans #754 #448]: #761
-#635 := [monotonicity #590 #751]: #634
-#739 := [trans #635 #742]: #644
-#720 := [monotonicity #739 #734 #716]: #719
-#708 := [trans #720 #717]: #722
-#769 := (iff #503 true)
-#764 := [rewrite]: #769
-#712 := [monotonicity #764 #708]: #711
-#694 := [trans #712 #710]: #714
-#763 := (iff #780 false)
-#768 := [rewrite]: #763
-#697 := [monotonicity #768 #694]: #695
-#699 := [trans #697 #717]: #698
-#705 := [monotonicity #699]: #704
-#707 := [trans #705 #696]: #704
-#703 := [quant-inst #9 #11]: #702
-#685 := [mp #703 #707]: #701
-#688 := [unit-resolution #685 #843]: #502
-#689 := [monotonicity #688]: #15
-#16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #689]: false
-unsat
-a2a3dbca7e9573eaa0bdadbb6bd04a2c290ad9e4 321 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 1::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 1::Int)
-decl f5 :: (-> S4 Int Int)
-#11 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 1::Int)
-#12 := (f5 #10 3::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#503 := (= #12 1::Int)
-#24 := (:var 0 Int)
-#36 := (:var 1 Int)
-#56 := (f6 f7 #36)
-#57 := (f5 #56 #24)
-#837 := (pattern #57)
-#23 := 0::Int
-#137 := -1::Int
-#141 := (* -1::Int #24)
-#138 := (* -1::Int #36)
-#196 := (mod #138 #141)
-#326 := (+ #57 #196)
-#327 := (= #326 0::Int)
-#58 := (mod #36 #24)
-#323 := (* -1::Int #58)
-#324 := (+ #57 #323)
-#325 := (= #324 0::Int)
-#163 := (<= #24 0::Int)
-#170 := (>= #36 0::Int)
-#270 := (or #170 #163)
-#271 := (not #270)
-#159 := (<= #36 0::Int)
-#268 := (or #159 #163)
-#269 := (not #268)
-#274 := (or #269 #271)
-#328 := (if #274 #325 #327)
-#322 := (= #57 0::Int)
-#39 := (= #36 0::Int)
-#329 := (if #39 #322 #328)
-#321 := (= #57 #36)
-#40 := (= #24 0::Int)
-#330 := (if #40 #321 #329)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #330)
-#333 := (forall (vars (?v0 Int) (?v1 Int)) #330)
-#841 := (iff #333 #838)
-#839 := (iff #330 #330)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#202 := (* -1::Int #196)
-#290 := (if #274 #58 #202)
-#293 := (if #39 0::Int #290)
-#296 := (if #40 #36 #293)
-#299 := (= #57 #296)
-#302 := (forall (vars (?v0 Int) (?v1 Int)) #299)
-#334 := (iff #302 #333)
-#331 := (iff #299 #330)
-#332 := [rewrite]: #331
-#335 := [quant-intro #332]: #334
-#164 := (not #163)
-#171 := (not #170)
-#174 := (and #171 #164)
-#160 := (not #159)
-#167 := (and #160 #164)
-#177 := (or #167 #174)
-#222 := (if #177 #58 #202)
-#225 := (if #39 0::Int #222)
-#228 := (if #40 #36 #225)
-#231 := (= #57 #228)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#303 := (iff #234 #302)
-#300 := (iff #231 #299)
-#297 := (= #228 #296)
-#294 := (= #225 #293)
-#291 := (= #222 #290)
-#275 := (iff #177 #274)
-#272 := (iff #174 #271)
-#273 := [rewrite]: #272
-#253 := (iff #167 #269)
-#254 := [rewrite]: #253
-#276 := [monotonicity #254 #273]: #275
-#292 := [monotonicity #276]: #291
-#295 := [monotonicity #292]: #294
-#298 := [monotonicity #295]: #297
-#301 := [monotonicity #298]: #300
-#304 := [quant-intro #301]: #303
-#251 := (~ #234 #234)
-#265 := (~ #231 #231)
-#266 := [refl]: #265
-#252 := [nnf-pos #266]: #251
-#50 := (- #24)
-#49 := (- #36)
-#59 := (mod #49 #50)
-#60 := (- #59)
-#43 := (< 0::Int #24)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#61 := (if #47 #58 #60)
-#62 := (if #39 0::Int #61)
-#63 := (if #40 #36 #62)
-#64 := (= #57 #63)
-#65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#237 := (iff #65 #234)
-#207 := (if #47 #58 #202)
-#210 := (if #39 0::Int #207)
-#213 := (if #40 #36 #210)
-#216 := (= #57 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#235 := (iff #219 #234)
-#232 := (iff #216 #231)
-#229 := (= #213 #228)
-#226 := (= #210 #225)
-#223 := (= #207 #222)
-#178 := (iff #47 #177)
-#175 := (iff #46 #174)
-#165 := (iff #43 #164)
-#166 := [rewrite]: #165
-#172 := (iff #45 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #166]: #175
-#168 := (iff #44 #167)
-#161 := (iff #42 #160)
-#162 := [rewrite]: #161
-#169 := [monotonicity #162 #166]: #168
-#179 := [monotonicity #169 #176]: #178
-#224 := [monotonicity #179]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#220 := (iff #65 #219)
-#217 := (iff #64 #216)
-#214 := (= #63 #213)
-#211 := (= #62 #210)
-#208 := (= #61 #207)
-#205 := (= #60 #202)
-#199 := (- #196)
-#203 := (= #199 #202)
-#204 := [rewrite]: #203
-#200 := (= #60 #199)
-#197 := (= #59 #196)
-#142 := (= #50 #141)
-#143 := [rewrite]: #142
-#139 := (= #49 #138)
-#140 := [rewrite]: #139
-#198 := [monotonicity #140 #143]: #197
-#201 := [monotonicity #198]: #200
-#206 := [trans #201 #204]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#238 := [trans #221 #236]: #237
-#195 := [asserted]: #65
-#239 := [mp #195 #238]: #234
-#267 := [mp~ #239 #252]: #234
-#305 := [mp #267 #304]: #302
-#336 := [mp #305 #335]: #333
-#843 := [mp #336 #842]: #838
-#683 := (not #838)
-#678 := (or #683 #503)
-#776 := (* -1::Int 3::Int)
-#772 := (* -1::Int 1::Int)
-#765 := (mod #772 #776)
-#766 := (+ #12 #765)
-#767 := (= #766 0::Int)
-#774 := (mod 1::Int 3::Int)
-#489 := (* -1::Int #774)
-#771 := (+ #12 #489)
-#775 := (= #771 0::Int)
-#782 := (<= 3::Int 0::Int)
-#591 := (>= 1::Int 0::Int)
-#494 := (or #591 #782)
-#495 := (not #494)
-#778 := (<= 1::Int 0::Int)
-#492 := (or #778 #782)
-#493 := (not #492)
-#773 := (or #493 #495)
-#762 := (if #773 #775 #767)
-#781 := (= #12 0::Int)
-#777 := (= 1::Int 0::Int)
-#763 := (if #777 #781 #762)
-#502 := (= 3::Int 0::Int)
-#768 := (if #502 #503 #763)
-#684 := (or #683 #768)
-#658 := (iff #684 #678)
-#552 := (iff #678 #678)
-#663 := [rewrite]: #552
-#681 := (iff #768 #503)
-#679 := (if false #503 #503)
-#677 := (iff #679 #503)
-#680 := [rewrite]: #677
-#675 := (iff #768 #679)
-#687 := (iff #763 #503)
-#688 := (if false #781 #503)
-#691 := (iff #688 #503)
-#692 := [rewrite]: #691
-#689 := (iff #763 #688)
-#685 := (iff #762 #503)
-#698 := -2::Int
-#699 := (= #12 -2::Int)
-#1 := true
-#704 := (if true #503 #699)
-#696 := (iff #704 #503)
-#707 := [rewrite]: #696
-#705 := (iff #762 #704)
-#702 := (iff #767 #699)
-#357 := 2::Int
-#711 := (+ 2::Int #12)
-#694 := (= #711 0::Int)
-#700 := (iff #694 #699)
-#701 := [rewrite]: #700
-#695 := (iff #767 #694)
-#710 := (= #766 #711)
-#722 := (+ #12 2::Int)
-#712 := (= #722 #711)
-#713 := [rewrite]: #712
-#708 := (= #766 #722)
-#721 := (= #765 2::Int)
-#730 := -3::Int
-#715 := (mod -1::Int -3::Int)
-#719 := (= #715 2::Int)
-#720 := [rewrite]: #719
-#716 := (= #765 #715)
-#724 := (= #776 -3::Int)
-#731 := [rewrite]: #724
-#649 := (= #772 -1::Int)
-#650 := [rewrite]: #649
-#718 := [monotonicity #650 #731]: #716
-#717 := [trans #718 #720]: #721
-#709 := [monotonicity #717]: #708
-#714 := [trans #709 #713]: #710
-#697 := [monotonicity #714]: #695
-#703 := [trans #697 #701]: #702
-#728 := (iff #775 #503)
-#734 := (+ -1::Int #12)
-#736 := (= #734 0::Int)
-#738 := (iff #736 #503)
-#727 := [rewrite]: #738
-#737 := (iff #775 #736)
-#725 := (= #771 #734)
-#741 := (+ #12 -1::Int)
-#726 := (= #741 #734)
-#723 := [rewrite]: #726
-#745 := (= #771 #741)
-#651 := (= #489 -1::Int)
-#647 := (= #489 #772)
-#646 := (= #774 1::Int)
-#639 := [rewrite]: #646
-#648 := [monotonicity #639]: #647
-#744 := [trans #648 #650]: #651
-#732 := [monotonicity #744]: #745
-#735 := [trans #732 #723]: #725
-#733 := [monotonicity #735]: #737
-#729 := [trans #733 #727]: #728
-#643 := (iff #773 true)
-#750 := (or true false)
-#633 := (iff #750 true)
-#634 := [rewrite]: #633
-#743 := (iff #773 #750)
-#739 := (iff #495 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#742 := (iff #495 #460)
-#635 := (iff #494 true)
-#748 := (iff #494 #750)
-#755 := (iff #782 false)
-#756 := [rewrite]: #755
-#464 := (iff #591 true)
-#800 := [rewrite]: #464
-#751 := [monotonicity #800 #756]: #748
-#594 := [trans #751 #634]: #635
-#644 := [monotonicity #594]: #742
-#740 := [trans #644 #448]: #739
-#747 := (iff #493 true)
-#761 := (not false)
-#593 := (iff #761 true)
-#746 := [rewrite]: #593
-#590 := (iff #493 #761)
-#760 := (iff #492 false)
-#757 := (or false false)
-#753 := (iff #757 false)
-#759 := [rewrite]: #753
-#758 := (iff #492 #757)
-#612 := (iff #778 false)
-#613 := [rewrite]: #612
-#752 := [monotonicity #613 #756]: #758
-#754 := [trans #752 #759]: #760
-#592 := [monotonicity #754]: #590
-#749 := [trans #592 #746]: #747
-#628 := [monotonicity #749 #740]: #743
-#645 := [trans #628 #634]: #643
-#706 := [monotonicity #645 #729 #703]: #705
-#686 := [trans #706 #707]: #685
-#770 := (iff #777 false)
-#611 := [rewrite]: #770
-#690 := [monotonicity #611 #686]: #689
-#693 := [trans #690 #692]: #687
-#769 := (iff #502 false)
-#764 := [rewrite]: #769
-#676 := [monotonicity #764 #693]: #675
-#682 := [trans #676 #680]: #681
-#659 := [monotonicity #682]: #658
-#664 := [trans #659 #663]: #658
-#657 := [quant-inst #9 #11]: #684
-#665 := [mp #657 #664]: #678
-#667 := [unit-resolution #665 #843]: #503
-#668 := [monotonicity #667]: #15
-#16 := (not #15)
-#85 := [asserted]: #16
-[unit-resolution #85 #668]: false
-unsat
-cc3d71be6ab4da3c4f7dfa56b53ad9595e6253f7 296 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#13 := 0::Int
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#9 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#10 := (f6 f7 3::Int)
-#11 := (f5 #10 3::Int)
-#12 := (f3 f4 #11)
-#15 := (= #12 #14)
-#503 := (= #11 0::Int)
-#23 := (:var 0 Int)
-#35 := (:var 1 Int)
-#55 := (f6 f7 #35)
-#56 := (f5 #55 #23)
-#837 := (pattern #56)
-#136 := -1::Int
-#140 := (* -1::Int #23)
-#137 := (* -1::Int #35)
-#195 := (mod #137 #140)
-#325 := (+ #56 #195)
-#326 := (= #325 0::Int)
-#57 := (mod #35 #23)
-#322 := (* -1::Int #57)
-#323 := (+ #56 #322)
-#324 := (= #323 0::Int)
-#162 := (<= #23 0::Int)
-#169 := (>= #35 0::Int)
-#269 := (or #169 #162)
-#270 := (not #269)
-#158 := (<= #35 0::Int)
-#267 := (or #158 #162)
-#268 := (not #267)
-#273 := (or #268 #270)
-#327 := (if #273 #324 #326)
-#321 := (= #56 0::Int)
-#38 := (= #35 0::Int)
-#328 := (if #38 #321 #327)
-#320 := (= #56 #35)
-#39 := (= #23 0::Int)
-#329 := (if #39 #320 #328)
-#838 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #837) #329)
-#332 := (forall (vars (?v0 Int) (?v1 Int)) #329)
-#841 := (iff #332 #838)
-#839 := (iff #329 #329)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#201 := (* -1::Int #195)
-#289 := (if #273 #57 #201)
-#292 := (if #38 0::Int #289)
-#295 := (if #39 #35 #292)
-#298 := (= #56 #295)
-#301 := (forall (vars (?v0 Int) (?v1 Int)) #298)
-#333 := (iff #301 #332)
-#330 := (iff #298 #329)
-#331 := [rewrite]: #330
-#334 := [quant-intro #331]: #333
-#163 := (not #162)
-#170 := (not #169)
-#173 := (and #170 #163)
-#159 := (not #158)
-#166 := (and #159 #163)
-#176 := (or #166 #173)
-#221 := (if #176 #57 #201)
-#224 := (if #38 0::Int #221)
-#227 := (if #39 #35 #224)
-#230 := (= #56 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#302 := (iff #233 #301)
-#299 := (iff #230 #298)
-#296 := (= #227 #295)
-#293 := (= #224 #292)
-#290 := (= #221 #289)
-#274 := (iff #176 #273)
-#271 := (iff #173 #270)
-#272 := [rewrite]: #271
-#252 := (iff #166 #268)
-#253 := [rewrite]: #252
-#275 := [monotonicity #253 #272]: #274
-#291 := [monotonicity #275]: #290
-#294 := [monotonicity #291]: #293
-#297 := [monotonicity #294]: #296
-#300 := [monotonicity #297]: #299
-#303 := [quant-intro #300]: #302
-#250 := (~ #233 #233)
-#264 := (~ #230 #230)
-#265 := [refl]: #264
-#251 := [nnf-pos #265]: #250
-#49 := (- #23)
-#48 := (- #35)
-#58 := (mod #48 #49)
-#59 := (- #58)
-#42 := (< 0::Int #23)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#60 := (if #46 #57 #59)
-#61 := (if #38 0::Int #60)
-#62 := (if #39 #35 #61)
-#63 := (= #56 #62)
-#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#236 := (iff #64 #233)
-#206 := (if #46 #57 #201)
-#209 := (if #38 0::Int #206)
-#212 := (if #39 #35 #209)
-#215 := (= #56 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#234 := (iff #218 #233)
-#231 := (iff #215 #230)
-#228 := (= #212 #227)
-#225 := (= #209 #224)
-#222 := (= #206 #221)
-#177 := (iff #46 #176)
-#174 := (iff #45 #173)
-#164 := (iff #42 #163)
-#165 := [rewrite]: #164
-#171 := (iff #44 #170)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #165]: #174
-#167 := (iff #43 #166)
-#160 := (iff #41 #159)
-#161 := [rewrite]: #160
-#168 := [monotonicity #161 #165]: #167
-#178 := [monotonicity #168 #175]: #177
-#223 := [monotonicity #178]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#219 := (iff #64 #218)
-#216 := (iff #63 #215)
-#213 := (= #62 #212)
-#210 := (= #61 #209)
-#207 := (= #60 #206)
-#204 := (= #59 #201)
-#198 := (- #195)
-#202 := (= #198 #201)
-#203 := [rewrite]: #202
-#199 := (= #59 #198)
-#196 := (= #58 #195)
-#141 := (= #49 #140)
-#142 := [rewrite]: #141
-#138 := (= #48 #137)
-#139 := [rewrite]: #138
-#197 := [monotonicity #139 #142]: #196
-#200 := [monotonicity #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#237 := [trans #220 #235]: #236
-#194 := [asserted]: #64
-#238 := [mp #194 #237]: #233
-#266 := [mp~ #238 #251]: #233
-#304 := [mp #266 #303]: #301
-#335 := [mp #304 #334]: #332
-#843 := [mp #335 #842]: #838
-#704 := (not #838)
-#705 := (or #704 #503)
-#771 := (* -1::Int 3::Int)
-#775 := (mod #771 #771)
-#772 := (+ #11 #775)
-#776 := (= #772 0::Int)
-#495 := (mod 3::Int 3::Int)
-#773 := (* -1::Int #495)
-#774 := (+ #11 #773)
-#489 := (= #774 0::Int)
-#777 := (<= 3::Int 0::Int)
-#782 := (>= 3::Int 0::Int)
-#492 := (or #782 #777)
-#493 := (not #492)
-#781 := (or #777 #777)
-#778 := (not #781)
-#494 := (or #778 #493)
-#765 := (if #494 #489 #776)
-#780 := (= 3::Int 0::Int)
-#766 := (if #780 #503 #765)
-#502 := (= #11 3::Int)
-#767 := (if #780 #502 #766)
-#706 := (or #704 #767)
-#707 := (iff #706 #705)
-#686 := (iff #705 #705)
-#688 := [rewrite]: #686
-#702 := (iff #767 #503)
-#697 := (if false #502 #503)
-#700 := (iff #697 #503)
-#701 := [rewrite]: #700
-#698 := (iff #767 #697)
-#694 := (iff #766 #503)
-#711 := (if false #503 #503)
-#710 := (iff #711 #503)
-#714 := [rewrite]: #710
-#712 := (iff #766 #711)
-#708 := (iff #765 #503)
-#1 := true
-#719 := (if true #503 #503)
-#717 := (iff #719 #503)
-#722 := [rewrite]: #717
-#720 := (iff #765 #719)
-#716 := (iff #776 #503)
-#731 := (= #772 #11)
-#649 := (+ #11 0::Int)
-#744 := (= #649 #11)
-#741 := [rewrite]: #744
-#730 := (= #772 #649)
-#728 := (= #775 0::Int)
-#723 := -3::Int
-#736 := (mod -3::Int -3::Int)
-#738 := (= #736 0::Int)
-#727 := [rewrite]: #738
-#737 := (= #775 #736)
-#725 := (= #771 -3::Int)
-#735 := [rewrite]: #725
-#733 := [monotonicity #735 #735]: #737
-#729 := [trans #733 #727]: #728
-#724 := [monotonicity #729]: #730
-#715 := [trans #724 #741]: #731
-#718 := [monotonicity #715]: #716
-#734 := (iff #489 #503)
-#745 := (= #774 #11)
-#650 := (= #774 #649)
-#647 := (= #773 0::Int)
-#628 := (* -1::Int 0::Int)
-#646 := (= #628 0::Int)
-#639 := [rewrite]: #646
-#643 := (= #773 #628)
-#740 := (= #495 0::Int)
-#743 := [rewrite]: #740
-#645 := [monotonicity #743]: #643
-#648 := [trans #645 #639]: #647
-#651 := [monotonicity #648]: #650
-#732 := [trans #651 #741]: #745
-#726 := [monotonicity #732]: #734
-#644 := (iff #494 true)
-#592 := (or true false)
-#747 := (iff #592 true)
-#749 := [rewrite]: #747
-#594 := (iff #494 #592)
-#634 := (iff #493 false)
-#460 := (not true)
-#785 := (iff #460 false)
-#448 := [rewrite]: #785
-#751 := (iff #493 #460)
-#750 := (iff #492 true)
-#593 := (iff #492 #592)
-#768 := (iff #777 false)
-#769 := [rewrite]: #768
-#761 := (iff #782 true)
-#590 := [rewrite]: #761
-#746 := [monotonicity #590 #769]: #593
-#748 := [trans #746 #749]: #750
-#633 := [monotonicity #748]: #751
-#635 := [trans #633 #448]: #634
-#760 := (iff #778 true)
-#757 := (not false)
-#753 := (iff #757 true)
-#759 := [rewrite]: #753
-#758 := (iff #778 #757)
-#755 := (iff #781 false)
-#764 := (or false false)
-#612 := (iff #764 false)
-#613 := [rewrite]: #612
-#770 := (iff #781 #764)
-#611 := [monotonicity #769 #769]: #770
-#756 := [trans #611 #613]: #755
-#752 := [monotonicity #756]: #758
-#754 := [trans #752 #759]: #760
-#742 := [monotonicity #754 #635]: #594
-#739 := [trans #742 #749]: #644
-#721 := [monotonicity #739 #726 #718]: #720
-#709 := [trans #721 #722]: #708
-#762 := (iff #780 false)
-#763 := [rewrite]: #762
-#713 := [monotonicity #763 #709]: #712
-#695 := [trans #713 #714]: #694
-#699 := [monotonicity #763 #695]: #698
-#703 := [trans #699 #701]: #702
-#685 := [monotonicity #703]: #707
-#689 := [trans #685 #688]: #707
-#696 := [quant-inst #9 #9]: #706
-#690 := [mp #696 #689]: #705
-#692 := [unit-resolution #690 #843]: #503
-#687 := [monotonicity #692]: #15
-#16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #687]: false
-unsat
-1df07385907a71330f107e5e8097355bfe585e4f 407 0
-#2 := false
-#12 := 3::Int
-decl f6 :: (-> S4 S5 Int)
-decl f8 :: S5
-#9 := f8
-decl f7 :: S4
-#8 := f7
-#10 := (f6 f7 f8)
-#485 := (mod #10 3::Int)
-#701 := (>= #485 3::Int)
-#702 := (not #701)
-#1 := true
-#82 := [true-axiom]: true
-#693 := (or false #702)
-#694 := [th-lemma arith]: #693
-#695 := [unit-resolution #694 #82]: #702
-#22 := 0::Int
-#148 := -1::Int
-#817 := (* -1::Int #485)
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#7 := f5
-#11 := (f4 f5 #10)
-#13 := (f3 #11 3::Int)
-#818 := (+ #13 #817)
-#604 := (<= #818 0::Int)
-#819 := (= #818 0::Int)
-#521 := -3::Int
-#820 := (* -1::Int #10)
-#792 := (mod #820 -3::Int)
-#789 := (+ #13 #792)
-#794 := (= #789 0::Int)
-#473 := (>= #10 0::Int)
-#809 := (not #473)
-#500 := (<= #10 0::Int)
-#803 := (not #500)
-#518 := (or #803 #809)
-#506 := (if #518 #819 #794)
-#496 := (= #13 0::Int)
-#499 := (= #10 0::Int)
-#786 := (if #499 #496 #506)
-#23 := (:var 0 Int)
-#35 := (:var 1 Int)
-#55 := (f4 f5 #35)
-#56 := (f3 #55 #23)
-#849 := (pattern #56)
-#152 := (* -1::Int #23)
-#149 := (* -1::Int #35)
-#207 := (mod #149 #152)
-#337 := (+ #56 #207)
-#338 := (= #337 0::Int)
-#57 := (mod #35 #23)
-#334 := (* -1::Int #57)
-#335 := (+ #56 #334)
-#336 := (= #335 0::Int)
-#174 := (<= #23 0::Int)
-#181 := (>= #35 0::Int)
-#281 := (or #181 #174)
-#282 := (not #281)
-#170 := (<= #35 0::Int)
-#279 := (or #170 #174)
-#280 := (not #279)
-#285 := (or #280 #282)
-#339 := (if #285 #336 #338)
-#333 := (= #56 0::Int)
-#38 := (= #35 0::Int)
-#340 := (if #38 #333 #339)
-#332 := (= #56 #35)
-#39 := (= #23 0::Int)
-#341 := (if #39 #332 #340)
-#850 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #849) #341)
-#344 := (forall (vars (?v0 Int) (?v1 Int)) #341)
-#853 := (iff #344 #850)
-#851 := (iff #341 #341)
-#852 := [refl]: #851
-#854 := [quant-intro #852]: #853
-#213 := (* -1::Int #207)
-#301 := (if #285 #57 #213)
-#304 := (if #38 0::Int #301)
-#307 := (if #39 #35 #304)
-#310 := (= #56 #307)
-#313 := (forall (vars (?v0 Int) (?v1 Int)) #310)
-#345 := (iff #313 #344)
-#342 := (iff #310 #341)
-#343 := [rewrite]: #342
-#346 := [quant-intro #343]: #345
-#175 := (not #174)
-#182 := (not #181)
-#185 := (and #182 #175)
-#171 := (not #170)
-#178 := (and #171 #175)
-#188 := (or #178 #185)
-#233 := (if #188 #57 #213)
-#236 := (if #38 0::Int #233)
-#239 := (if #39 #35 #236)
-#242 := (= #56 #239)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#314 := (iff #245 #313)
-#311 := (iff #242 #310)
-#308 := (= #239 #307)
-#305 := (= #236 #304)
-#302 := (= #233 #301)
-#286 := (iff #188 #285)
-#283 := (iff #185 #282)
-#284 := [rewrite]: #283
-#264 := (iff #178 #280)
-#265 := [rewrite]: #264
-#287 := [monotonicity #265 #284]: #286
-#303 := [monotonicity #287]: #302
-#306 := [monotonicity #303]: #305
-#309 := [monotonicity #306]: #308
-#312 := [monotonicity #309]: #311
-#315 := [quant-intro #312]: #314
-#262 := (~ #245 #245)
-#276 := (~ #242 #242)
-#277 := [refl]: #276
-#263 := [nnf-pos #277]: #262
-#49 := (- #23)
-#48 := (- #35)
-#58 := (mod #48 #49)
-#59 := (- #58)
-#42 := (< 0::Int #23)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#60 := (if #46 #57 #59)
-#61 := (if #38 0::Int #60)
-#62 := (if #39 #35 #61)
-#63 := (= #56 #62)
-#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#248 := (iff #64 #245)
-#218 := (if #46 #57 #213)
-#221 := (if #38 0::Int #218)
-#224 := (if #39 #35 #221)
-#227 := (= #56 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#246 := (iff #230 #245)
-#243 := (iff #227 #242)
-#240 := (= #224 #239)
-#237 := (= #221 #236)
-#234 := (= #218 #233)
-#189 := (iff #46 #188)
-#186 := (iff #45 #185)
-#176 := (iff #42 #175)
-#177 := [rewrite]: #176
-#183 := (iff #44 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184 #177]: #186
-#179 := (iff #43 #178)
-#172 := (iff #41 #171)
-#173 := [rewrite]: #172
-#180 := [monotonicity #173 #177]: #179
-#190 := [monotonicity #180 #187]: #189
-#235 := [monotonicity #190]: #234
-#238 := [monotonicity #235]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [quant-intro #244]: #246
-#231 := (iff #64 #230)
-#228 := (iff #63 #227)
-#225 := (= #62 #224)
-#222 := (= #61 #221)
-#219 := (= #60 #218)
-#216 := (= #59 #213)
-#210 := (- #207)
-#214 := (= #210 #213)
-#215 := [rewrite]: #214
-#211 := (= #59 #210)
-#208 := (= #58 #207)
-#153 := (= #49 #152)
-#154 := [rewrite]: #153
-#150 := (= #48 #149)
-#151 := [rewrite]: #150
-#209 := [monotonicity #151 #154]: #208
-#212 := [monotonicity #209]: #211
-#217 := [trans #212 #215]: #216
-#220 := [monotonicity #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#249 := [trans #232 #247]: #248
-#206 := [asserted]: #64
-#250 := [mp #206 #249]: #245
-#278 := [mp~ #250 #263]: #245
-#316 := [mp #278 #315]: #313
-#347 := [mp #316 #346]: #344
-#855 := [mp #347 #854]: #850
-#775 := (not #850)
-#780 := (or #775 #786)
-#815 := (* -1::Int 3::Int)
-#821 := (mod #820 #815)
-#811 := (+ #13 #821)
-#471 := (= #811 0::Int)
-#479 := (<= 3::Int 0::Int)
-#603 := (or #473 #479)
-#810 := (not #603)
-#814 := (or #500 #479)
-#816 := (not #814)
-#484 := (or #816 #810)
-#476 := (if #484 #819 #471)
-#812 := (if #499 #496 #476)
-#495 := (= #13 #10)
-#494 := (= 3::Int 0::Int)
-#472 := (if #494 #495 #812)
-#781 := (or #775 #472)
-#782 := (iff #781 #780)
-#624 := (iff #780 #780)
-#625 := [rewrite]: #624
-#779 := (iff #472 #786)
-#787 := (if false #495 #786)
-#777 := (iff #787 #786)
-#778 := [rewrite]: #777
-#784 := (iff #472 #787)
-#501 := (iff #812 #786)
-#507 := (iff #476 #506)
-#504 := (iff #471 #794)
-#793 := (= #811 #789)
-#514 := (= #821 #792)
-#415 := (= #815 -3::Int)
-#791 := [rewrite]: #415
-#515 := [monotonicity #791]: #514
-#790 := [monotonicity #515]: #793
-#505 := [monotonicity #790]: #504
-#519 := (iff #484 #518)
-#795 := (iff #810 #809)
-#808 := (iff #603 #473)
-#442 := (or #473 false)
-#447 := (iff #442 #473)
-#448 := [rewrite]: #447
-#805 := (iff #603 #442)
-#797 := (iff #479 false)
-#460 := [rewrite]: #797
-#807 := [monotonicity #460]: #805
-#806 := [trans #807 #448]: #808
-#796 := [monotonicity #806]: #795
-#798 := (iff #816 #803)
-#801 := (iff #814 #500)
-#461 := (or #500 false)
-#799 := (iff #461 #500)
-#800 := [rewrite]: #799
-#462 := (iff #814 #461)
-#463 := [monotonicity #460]: #462
-#802 := [trans #463 #800]: #801
-#804 := [monotonicity #802]: #798
-#520 := [monotonicity #804 #796]: #519
-#785 := [monotonicity #520 #505]: #507
-#783 := [monotonicity #785]: #501
-#813 := (iff #494 false)
-#456 := [rewrite]: #813
-#788 := [monotonicity #456 #783]: #784
-#774 := [trans #788 #778]: #779
-#623 := [monotonicity #774]: #782
-#767 := [trans #623 #625]: #782
-#776 := [quant-inst #10 #12]: #781
-#768 := [mp #776 #767]: #780
-#690 := [unit-resolution #768 #855]: #786
-#755 := (not #499)
-#752 := (not #786)
-#677 := (or #752 #755)
-#651 := (not #496)
-#769 := (<= #13 0::Int)
-#696 := (not #769)
-#89 := (>= #13 3::Int)
-#14 := (< #13 3::Int)
-#15 := (not #14)
-#96 := (iff #15 #89)
-#87 := (not #89)
-#91 := (not #87)
-#94 := (iff #91 #89)
-#95 := [rewrite]: #94
-#92 := (iff #15 #91)
-#88 := (iff #14 #87)
-#90 := [rewrite]: #88
-#93 := [monotonicity #90]: #92
-#97 := [trans #93 #95]: #96
-#84 := [asserted]: #15
-#98 := [mp #84 #97]: #89
-#669 := (or #696 #87)
-#670 := [th-lemma arith farkas 1 1]: #669
-#671 := [unit-resolution #670 #98]: #696
-#564 := (or #651 #769)
-#675 := [th-lemma arith triangle-eq]: #564
-#676 := [unit-resolution #675 #671]: #651
-#640 := (or #752 #755 #496)
-#655 := [def-axiom]: #640
-#682 := [unit-resolution #655 #676]: #677
-#678 := [unit-resolution #682 #690]: #755
-#657 := (or #752 #499 #506)
-#658 := [def-axiom]: #657
-#679 := [unit-resolution #658 #678 #690]: #506
-decl f9 :: (-> S6 Int S5)
-decl f10 :: S6
-#16 := f10
-#409 := (f9 f10 #10)
-#663 := (f6 f7 #409)
-#756 := (= #663 0::Int)
-#612 := (not #756)
-#667 := (iff #755 #612)
-#686 := (iff #499 #756)
-#685 := (iff #756 #499)
-#683 := (= #663 #10)
-#493 := (= #409 f8)
-#17 := (:var 0 S5)
-#18 := (f6 f7 #17)
-#822 := (pattern #18)
-#19 := (f9 f10 #18)
-#20 := (= #19 #17)
-#823 := (forall (vars (?v0 S5)) (:pat #822) #20)
-#21 := (forall (vars (?v0 S5)) #20)
-#826 := (iff #21 #823)
-#824 := (iff #20 #20)
-#825 := [refl]: #824
-#827 := [quant-intro #825]: #826
-#268 := (~ #21 #21)
-#266 := (~ #20 #20)
-#267 := [refl]: #266
-#269 := [nnf-pos #267]: #268
-#85 := [asserted]: #21
-#254 := [mp~ #85 #269]: #21
-#828 := [mp #254 #827]: #823
-#486 := (not #823)
-#497 := (or #486 #493)
-#498 := [quant-inst #9]: #497
-#680 := [unit-resolution #498 #828]: #493
-#684 := [monotonicity #680]: #683
-#681 := [monotonicity #684]: #685
-#666 := [symm #681]: #686
-#648 := [monotonicity #666]: #667
-#672 := [mp #678 #648]: #612
-#753 := (or #473 #756)
-#25 := (f9 f10 #23)
-#829 := (pattern #25)
-#26 := (f6 f7 #25)
-#31 := (= #26 0::Int)
-#108 := (>= #23 0::Int)
-#138 := (or #108 #31)
-#836 := (forall (vars (?v0 Int)) (:pat #829) #138)
-#141 := (forall (vars (?v0 Int)) #138)
-#839 := (iff #141 #836)
-#837 := (iff #138 #138)
-#838 := [refl]: #837
-#840 := [quant-intro #838]: #839
-#258 := (~ #141 #141)
-#270 := (~ #138 #138)
-#271 := [refl]: #270
-#259 := [nnf-pos #271]: #258
-#30 := (< #23 0::Int)
-#32 := (implies #30 #31)
-#33 := (forall (vars (?v0 Int)) #32)
-#144 := (iff #33 #141)
-#122 := (not #30)
-#123 := (or #122 #31)
-#126 := (forall (vars (?v0 Int)) #123)
-#142 := (iff #126 #141)
-#139 := (iff #123 #138)
-#136 := (iff #122 #108)
-#109 := (not #108)
-#131 := (not #109)
-#134 := (iff #131 #108)
-#135 := [rewrite]: #134
-#132 := (iff #122 #131)
-#129 := (iff #30 #109)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130]: #132
-#137 := [trans #133 #135]: #136
-#140 := [monotonicity #137]: #139
-#143 := [quant-intro #140]: #142
-#127 := (iff #33 #126)
-#124 := (iff #32 #123)
-#125 := [rewrite]: #124
-#128 := [quant-intro #125]: #127
-#145 := [trans #128 #143]: #144
-#121 := [asserted]: #33
-#146 := [mp #121 #145]: #141
-#272 := [mp~ #146 #259]: #141
-#841 := [mp #272 #840]: #836
-#746 := (not #836)
-#738 := (or #746 #473 #756)
-#735 := (or #746 #753)
-#747 := (iff #735 #738)
-#748 := [rewrite]: #747
-#737 := [quant-inst #10]: #735
-#749 := [mp #737 #748]: #738
-#673 := [unit-resolution #749 #841]: #753
-#668 := [unit-resolution #673 #672]: #473
-#674 := (or #499 #803 #809)
-#642 := [th-lemma arith triangle-eq]: #674
-#649 := [unit-resolution #642 #678]: #518
-#608 := [unit-resolution #649 #668]: #803
-#764 := (or #518 #500)
-#765 := [def-axiom]: #764
-#639 := [unit-resolution #765 #608]: #518
-#766 := (not #518)
-#761 := (not #506)
-#762 := (or #761 #766 #819)
-#760 := [def-axiom]: #762
-#641 := [unit-resolution #760 #639 #679]: #819
-#646 := (not #819)
-#643 := (or #646 #604)
-#650 := [th-lemma arith triangle-eq]: #643
-#652 := [unit-resolution #650 #641]: #604
-[th-lemma arith farkas -1 1 1 #98 #652 #695]: false
-unsat
-1311ced639549b32ffab57e57f403189256df4d9 590 0
-#2 := false
-#13 := 3::Int
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#10 := f10
-decl f9 :: S6
-#9 := f9
-#11 := (f8 f9 f10)
-#458 := (mod #11 3::Int)
-#638 := (>= #458 3::Int)
-#639 := (not #638)
-#1 := true
-#85 := [true-axiom]: true
-#629 := (or false #639)
-#599 := [th-lemma arith]: #629
-#600 := [unit-resolution #599 #85]: #639
-#94 := (>= #11 3::Int)
-#92 := (not #94)
-#522 := [hypothesis]: #92
-#25 := 0::Int
-#706 := (div #11 3::Int)
-#633 := -3::Int
-#696 := (* -3::Int #706)
-#158 := -1::Int
-#818 := (* -1::Int #458)
-#676 := (+ #818 #696)
-#622 := (+ #11 #676)
-#678 := (<= #622 0::Int)
-#691 := (= #622 0::Int)
-#601 := (or false #691)
-#602 := [th-lemma arith]: #601
-#604 := [unit-resolution #602 #85]: #691
-#605 := (not #691)
-#606 := (or #605 #678)
-#449 := [th-lemma arith triangle-eq]: #606
-#607 := [unit-resolution #449 #604]: #678
-decl f5 :: (-> S4 Int Int)
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#8 := f7
-#12 := (f6 f7 #11)
-#14 := (f5 #12 3::Int)
-#816 := (+ #14 #818)
-#767 := (<= #816 0::Int)
-#819 := (= #816 0::Int)
-#810 := (= #11 0::Int)
-#753 := (not #810)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#7 := f4
-#15 := (f3 f4 #14)
-#16 := (= #15 f10)
-#88 := (not #16)
-#509 := (or #88 #94)
-#99 := (iff #16 #94)
-#17 := (< #11 3::Int)
-#18 := (iff #16 #17)
-#19 := (not #18)
-#104 := (iff #19 #99)
-#89 := (iff #88 #17)
-#102 := (iff #89 #99)
-#96 := (iff #88 #92)
-#100 := (iff #96 #99)
-#101 := [rewrite]: #100
-#97 := (iff #89 #96)
-#93 := (iff #17 #92)
-#95 := [rewrite]: #93
-#98 := [monotonicity #95]: #97
-#103 := [trans #98 #101]: #102
-#90 := (iff #19 #89)
-#91 := [rewrite]: #90
-#105 := [trans #91 #103]: #104
-#87 := [asserted]: #19
-#106 := [mp #87 #105]: #99
-#419 := (not #99)
-#507 := (or #88 #94 #419)
-#508 := [def-axiom]: #507
-#506 := [unit-resolution #508 #106]: #509
-#513 := [unit-resolution #506 #522]: #88
-#705 := (or #753 #16)
-#510 := (f3 f4 #11)
-#489 := (= #510 f10)
-#20 := (:var 0 S3)
-#21 := (f8 f9 #20)
-#832 := (pattern #21)
-#22 := (f3 f4 #21)
-#23 := (= #22 #20)
-#833 := (forall (vars (?v0 S3)) (:pat #832) #23)
-#24 := (forall (vars (?v0 S3)) #23)
-#836 := (iff #24 #833)
-#834 := (iff #23 #23)
-#835 := [refl]: #834
-#837 := [quant-intro #835]: #836
-#278 := (~ #24 #24)
-#276 := (~ #23 #23)
-#277 := [refl]: #276
-#279 := [nnf-pos #277]: #278
-#107 := [asserted]: #24
-#264 := [mp~ #107 #279]: #24
-#838 := [mp #264 #837]: #833
-#483 := (not #833)
-#613 := (or #483 #489)
-#820 := [quant-inst #10]: #613
-#712 := [unit-resolution #820 #838]: #489
-#699 := (= #15 #510)
-#823 := (= #14 #11)
-#701 := (= 0::Int #11)
-#713 := [hypothesis]: #810
-#697 := [symm #713]: #701
-#811 := (= #14 0::Int)
-#714 := (or #753 #811)
-#805 := (* -1::Int #11)
-#777 := (mod #805 -3::Int)
-#780 := (+ #14 #777)
-#781 := (= #780 0::Int)
-#452 := (>= #11 0::Int)
-#784 := (not #452)
-#812 := (<= #11 0::Int)
-#795 := (not #812)
-#791 := (or #795 #784)
-#783 := (if #791 #819 #781)
-#615 := (if #810 #811 #783)
-#26 := (:var 0 Int)
-#38 := (:var 1 Int)
-#58 := (f6 f7 #38)
-#59 := (f5 #58 #26)
-#859 := (pattern #59)
-#162 := (* -1::Int #26)
-#159 := (* -1::Int #38)
-#217 := (mod #159 #162)
-#347 := (+ #59 #217)
-#348 := (= #347 0::Int)
-#60 := (mod #38 #26)
-#344 := (* -1::Int #60)
-#345 := (+ #59 #344)
-#346 := (= #345 0::Int)
-#184 := (<= #26 0::Int)
-#191 := (>= #38 0::Int)
-#291 := (or #191 #184)
-#292 := (not #291)
-#180 := (<= #38 0::Int)
-#289 := (or #180 #184)
-#290 := (not #289)
-#295 := (or #290 #292)
-#349 := (if #295 #346 #348)
-#343 := (= #59 0::Int)
-#41 := (= #38 0::Int)
-#350 := (if #41 #343 #349)
-#342 := (= #59 #38)
-#42 := (= #26 0::Int)
-#351 := (if #42 #342 #350)
-#860 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #859) #351)
-#354 := (forall (vars (?v0 Int) (?v1 Int)) #351)
-#863 := (iff #354 #860)
-#861 := (iff #351 #351)
-#862 := [refl]: #861
-#864 := [quant-intro #862]: #863
-#223 := (* -1::Int #217)
-#311 := (if #295 #60 #223)
-#314 := (if #41 0::Int #311)
-#317 := (if #42 #38 #314)
-#320 := (= #59 #317)
-#323 := (forall (vars (?v0 Int) (?v1 Int)) #320)
-#355 := (iff #323 #354)
-#352 := (iff #320 #351)
-#353 := [rewrite]: #352
-#356 := [quant-intro #353]: #355
-#185 := (not #184)
-#192 := (not #191)
-#195 := (and #192 #185)
-#181 := (not #180)
-#188 := (and #181 #185)
-#198 := (or #188 #195)
-#243 := (if #198 #60 #223)
-#246 := (if #41 0::Int #243)
-#249 := (if #42 #38 #246)
-#252 := (= #59 #249)
-#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
-#324 := (iff #255 #323)
-#321 := (iff #252 #320)
-#318 := (= #249 #317)
-#315 := (= #246 #314)
-#312 := (= #243 #311)
-#296 := (iff #198 #295)
-#293 := (iff #195 #292)
-#294 := [rewrite]: #293
-#274 := (iff #188 #290)
-#275 := [rewrite]: #274
-#297 := [monotonicity #275 #294]: #296
-#313 := [monotonicity #297]: #312
-#316 := [monotonicity #313]: #315
-#319 := [monotonicity #316]: #318
-#322 := [monotonicity #319]: #321
-#325 := [quant-intro #322]: #324
-#272 := (~ #255 #255)
-#286 := (~ #252 #252)
-#287 := [refl]: #286
-#273 := [nnf-pos #287]: #272
-#52 := (- #26)
-#51 := (- #38)
-#61 := (mod #51 #52)
-#62 := (- #61)
-#45 := (< 0::Int #26)
-#47 := (< #38 0::Int)
-#48 := (and #47 #45)
-#44 := (< 0::Int #38)
-#46 := (and #44 #45)
-#49 := (or #46 #48)
-#63 := (if #49 #60 #62)
-#64 := (if #41 0::Int #63)
-#65 := (if #42 #38 #64)
-#66 := (= #59 #65)
-#67 := (forall (vars (?v0 Int) (?v1 Int)) #66)
-#258 := (iff #67 #255)
-#228 := (if #49 #60 #223)
-#231 := (if #41 0::Int #228)
-#234 := (if #42 #38 #231)
-#237 := (= #59 #234)
-#240 := (forall (vars (?v0 Int) (?v1 Int)) #237)
-#256 := (iff #240 #255)
-#253 := (iff #237 #252)
-#250 := (= #234 #249)
-#247 := (= #231 #246)
-#244 := (= #228 #243)
-#199 := (iff #49 #198)
-#196 := (iff #48 #195)
-#186 := (iff #45 #185)
-#187 := [rewrite]: #186
-#193 := (iff #47 #192)
-#194 := [rewrite]: #193
-#197 := [monotonicity #194 #187]: #196
-#189 := (iff #46 #188)
-#182 := (iff #44 #181)
-#183 := [rewrite]: #182
-#190 := [monotonicity #183 #187]: #189
-#200 := [monotonicity #190 #197]: #199
-#245 := [monotonicity #200]: #244
-#248 := [monotonicity #245]: #247
-#251 := [monotonicity #248]: #250
-#254 := [monotonicity #251]: #253
-#257 := [quant-intro #254]: #256
-#241 := (iff #67 #240)
-#238 := (iff #66 #237)
-#235 := (= #65 #234)
-#232 := (= #64 #231)
-#229 := (= #63 #228)
-#226 := (= #62 #223)
-#220 := (- #217)
-#224 := (= #220 #223)
-#225 := [rewrite]: #224
-#221 := (= #62 #220)
-#218 := (= #61 #217)
-#163 := (= #52 #162)
-#164 := [rewrite]: #163
-#160 := (= #51 #159)
-#161 := [rewrite]: #160
-#219 := [monotonicity #161 #164]: #218
-#222 := [monotonicity #219]: #221
-#227 := [trans #222 #225]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [quant-intro #239]: #241
-#259 := [trans #242 #257]: #258
-#216 := [asserted]: #67
-#260 := [mp #216 #259]: #255
-#288 := [mp~ #260 #273]: #255
-#326 := [mp #288 #325]: #323
-#357 := [mp #326 #356]: #354
-#865 := [mp #357 #864]: #860
-#616 := (not #860)
-#764 := (or #616 #615)
-#806 := (* -1::Int 3::Int)
-#528 := (mod #805 #806)
-#529 := (+ #14 #528)
-#530 := (= #529 0::Int)
-#813 := (<= 3::Int 0::Int)
-#815 := (or #452 #813)
-#817 := (not #815)
-#808 := (or #812 #813)
-#814 := (not #808)
-#457 := (or #814 #817)
-#531 := (if #457 #819 #530)
-#425 := (if #810 #811 #531)
-#482 := (= 3::Int 0::Int)
-#801 := (if #482 #823 #425)
-#666 := (or #616 #801)
-#762 := (iff #666 #764)
-#650 := (iff #764 #764)
-#665 := [rewrite]: #650
-#656 := (iff #801 #615)
-#771 := (if false #823 #615)
-#773 := (iff #771 #615)
-#655 := [rewrite]: #773
-#772 := (iff #801 #771)
-#768 := (iff #425 #615)
-#612 := (iff #531 #783)
-#782 := (iff #530 #781)
-#774 := (= #529 #780)
-#778 := (= #528 #777)
-#634 := (= #806 -3::Int)
-#635 := [rewrite]: #634
-#779 := [monotonicity #635]: #778
-#775 := [monotonicity #779]: #774
-#776 := [monotonicity #775]: #782
-#786 := (iff #457 #791)
-#785 := (iff #817 #784)
-#788 := (iff #815 #452)
-#793 := (or #452 false)
-#798 := (iff #793 #452)
-#787 := [rewrite]: #798
-#797 := (iff #815 #793)
-#525 := (iff #813 false)
-#799 := [rewrite]: #525
-#794 := [monotonicity #799]: #797
-#789 := [trans #794 #787]: #788
-#790 := [monotonicity #789]: #785
-#796 := (iff #814 #795)
-#516 := (iff #808 #812)
-#803 := (or #812 false)
-#514 := (iff #803 #812)
-#515 := [rewrite]: #514
-#800 := (iff #808 #803)
-#804 := [monotonicity #799]: #800
-#517 := [trans #804 #515]: #516
-#511 := [monotonicity #517]: #796
-#792 := [monotonicity #511 #790]: #786
-#614 := [monotonicity #792 #776]: #612
-#769 := [monotonicity #614]: #768
-#802 := (iff #482 false)
-#524 := [rewrite]: #802
-#770 := [monotonicity #524 #769]: #772
-#657 := [trans #770 #655]: #656
-#765 := [monotonicity #657]: #762
-#667 := [trans #765 #665]: #762
-#761 := [quant-inst #11 #13]: #666
-#668 := [mp #761 #667]: #764
-#722 := [unit-resolution #668 #865]: #615
-#746 := (not #615)
-#737 := (or #746 #753 #811)
-#738 := [def-axiom]: #737
-#709 := [unit-resolution #738 #722]: #714
-#715 := [unit-resolution #709 #713]: #811
-#698 := [trans #715 #697]: #823
-#702 := [monotonicity #698]: #699
-#703 := [trans #702 #712]: #16
-#711 := [hypothesis]: #88
-#704 := [unit-resolution #711 #703]: false
-#700 := [lemma #704]: #705
-#523 := [unit-resolution #700 #513]: #753
-#708 := (or #810 #819)
-#735 := [hypothesis]: #753
-#673 := (not #791)
-#755 := (not #819)
-#732 := [hypothesis]: #755
-#723 := (or #810 #783)
-#740 := (or #746 #810 #783)
-#741 := [def-axiom]: #740
-#724 := [unit-resolution #741 #722]: #723
-#725 := [unit-resolution #724 #735]: #783
-#745 := (not #783)
-#747 := (or #745 #673 #819)
-#757 := [def-axiom]: #747
-#726 := [unit-resolution #757 #725 #732]: #673
-#669 := (or #791 #812)
-#670 := [def-axiom]: #669
-#727 := [unit-resolution #670 #726]: #812
-#671 := (or #791 #452)
-#672 := [def-axiom]: #671
-#728 := [unit-resolution #672 #726]: #452
-#718 := (or #810 #795 #784)
-#729 := [th-lemma arith triangle-eq]: #718
-#707 := [unit-resolution #729 #728 #727 #735]: false
-#710 := [lemma #707]: #708
-#490 := [unit-resolution #710 #523]: #819
-#492 := (or #755 #767)
-#493 := [th-lemma arith triangle-eq]: #492
-#484 := [unit-resolution #493 #490]: #767
-#370 := 1::Int
-#597 := -2::Int
-#526 := (* -2::Int #706)
-#535 := (+ #818 #526)
-#536 := (+ #11 #535)
-#527 := (>= #536 1::Int)
-#609 := (* -1::Int #14)
-#610 := (+ #11 #609)
-#617 := (<= #610 0::Int)
-#502 := (not #617)
-#648 := (= #11 #14)
-#626 := (not #648)
-#627 := (or #626 #16)
-#620 := [hypothesis]: #648
-#621 := [symm #620]: #823
-#623 := [monotonicity #621]: #699
-#624 := [trans #623 #712]: #16
-#625 := [unit-resolution #711 #624]: false
-#628 := [lemma #625]: #627
-#475 := [unit-resolution #628 #513]: #626
-#619 := (>= #610 0::Int)
-#611 := (>= #706 0::Int)
-#731 := (f8 f9 #510)
-#733 := (= #731 0::Int)
-#461 := (not #733)
-#463 := (iff #753 #461)
-#468 := (iff #810 #733)
-#478 := (iff #733 #810)
-#476 := (= #731 #11)
-#477 := [monotonicity #712]: #476
-#479 := [monotonicity #477]: #478
-#480 := [symm #479]: #468
-#464 := [monotonicity #480]: #463
-#462 := [mp #523 #464]: #461
-#734 := (or #452 #733)
-#28 := (f3 f4 #26)
-#839 := (pattern #28)
-#29 := (f8 f9 #28)
-#34 := (= #29 0::Int)
-#118 := (>= #26 0::Int)
-#148 := (or #118 #34)
-#846 := (forall (vars (?v0 Int)) (:pat #839) #148)
-#151 := (forall (vars (?v0 Int)) #148)
-#849 := (iff #151 #846)
-#847 := (iff #148 #148)
-#848 := [refl]: #847
-#850 := [quant-intro #848]: #849
-#268 := (~ #151 #151)
-#280 := (~ #148 #148)
-#281 := [refl]: #280
-#269 := [nnf-pos #281]: #268
-#33 := (< #26 0::Int)
-#35 := (implies #33 #34)
-#36 := (forall (vars (?v0 Int)) #35)
-#154 := (iff #36 #151)
-#132 := (not #33)
-#133 := (or #132 #34)
-#136 := (forall (vars (?v0 Int)) #133)
-#152 := (iff #136 #151)
-#149 := (iff #133 #148)
-#146 := (iff #132 #118)
-#119 := (not #118)
-#141 := (not #119)
-#144 := (iff #141 #118)
-#145 := [rewrite]: #144
-#142 := (iff #132 #141)
-#139 := (iff #33 #119)
-#140 := [rewrite]: #139
-#143 := [monotonicity #140]: #142
-#147 := [trans #143 #145]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
-#137 := (iff #36 #136)
-#134 := (iff #35 #133)
-#135 := [rewrite]: #134
-#138 := [quant-intro #135]: #137
-#155 := [trans #138 #153]: #154
-#131 := [asserted]: #36
-#156 := [mp #131 #155]: #151
-#282 := [mp~ #156 #269]: #151
-#851 := [mp #282 #850]: #846
-#466 := (not #846)
-#736 := (or #466 #452 #733)
-#716 := (or #466 #734)
-#719 := (iff #716 #736)
-#720 := [rewrite]: #719
-#717 := [quant-inst #11]: #716
-#721 := [mp #717 #720]: #736
-#465 := [unit-resolution #721 #851]: #734
-#453 := [unit-resolution #465 #462]: #452
-#594 := (or #611 #784)
-#603 := (not #611)
-#608 := [hypothesis]: #603
-#587 := [hypothesis]: #452
-#590 := [th-lemma arith farkas 1 3 1 1 #587 #608 #607 #600]: false
-#596 := [lemma #590]: #594
-#455 := [unit-resolution #596 #453]: #611
-#557 := (not #767)
-#565 := (or #619 #557 #603)
-#570 := (not #619)
-#571 := [hypothesis]: #570
-#684 := (>= #622 0::Int)
-#560 := (or #605 #684)
-#561 := [th-lemma arith triangle-eq]: #560
-#562 := [unit-resolution #561 #604]: #684
-#563 := [hypothesis]: #611
-#572 := [hypothesis]: #767
-#564 := [th-lemma arith farkas 1 -3 -1 1 #572 #563 #562 #571]: false
-#566 := [lemma #564]: #565
-#456 := [unit-resolution #566 #484 #455]: #619
-#459 := (or #648 #502 #570)
-#454 := [th-lemma arith triangle-eq]: #459
-#460 := [unit-resolution #454 #456 #475]: #502
-#754 := (>= #816 0::Int)
-#435 := (or #755 #754)
-#439 := [th-lemma arith triangle-eq]: #435
-#440 := [unit-resolution #439 #490]: #754
-#467 := (not #754)
-#469 := (or #527 #467 #617)
-#499 := (not #527)
-#491 := [hypothesis]: #499
-#485 := [hypothesis]: #502
-#487 := [hypothesis]: #754
-#488 := [th-lemma arith farkas -1/3 -1/3 -2/3 1 #487 #485 #562 #491]: false
-#474 := [lemma #488]: #469
-#445 := [unit-resolution #474 #440 #460]: #527
-#824 := (>= #14 0::Int)
-#652 := (>= #458 0::Int)
-#447 := (or false #652)
-#448 := [th-lemma arith]: #447
-#450 := [unit-resolution #448 #85]: #652
-#446 := (not #652)
-#451 := (or #824 #446 #467)
-#434 := [th-lemma arith assign-bounds 1 1]: #451
-#437 := [unit-resolution #434 #440 #450]: #824
-#438 := [th-lemma arith farkas -1 -3 1 2 1 #437 #445 #484 #607 #522]: false
-#441 := [lemma #438]: #94
-#494 := (f8 f9 #15)
-#495 := (= #494 #14)
-#423 := (iff #495 #648)
-#420 := (= #494 #11)
-#505 := (or #16 #92)
-#503 := (or #16 #92 #419)
-#504 := [def-axiom]: #503
-#496 := [unit-resolution #504 #106]: #505
-#433 := [unit-resolution #496 #441]: #16
-#422 := [monotonicity #433]: #420
-#421 := [monotonicity #422]: #423
-#442 := (or #795 #92)
-#443 := [th-lemma arith farkas 1 1]: #442
-#436 := [unit-resolution #443 #441]: #795
-#444 := (or #753 #812)
-#429 := [th-lemma arith triangle-eq]: #444
-#426 := [unit-resolution #429 #436]: #753
-#427 := [unit-resolution #710 #426]: #819
-#430 := [unit-resolution #439 #427]: #754
-#431 := [unit-resolution #434 #430 #450]: #824
-#826 := (not #824)
-#827 := (or #826 #495)
-#30 := (= #29 #26)
-#122 := (or #119 #30)
-#840 := (forall (vars (?v0 Int)) (:pat #839) #122)
-#125 := (forall (vars (?v0 Int)) #122)
-#843 := (iff #125 #840)
-#841 := (iff #122 #122)
-#842 := [refl]: #841
-#844 := [quant-intro #842]: #843
-#266 := (~ #125 #125)
-#265 := (~ #122 #122)
-#262 := [refl]: #265
-#267 := [nnf-pos #262]: #266
-#27 := (<= 0::Int #26)
-#31 := (implies #27 #30)
-#32 := (forall (vars (?v0 Int)) #31)
-#128 := (iff #32 #125)
-#109 := (not #27)
-#110 := (or #109 #30)
-#113 := (forall (vars (?v0 Int)) #110)
-#126 := (iff #113 #125)
-#123 := (iff #110 #122)
-#120 := (iff #109 #119)
-#116 := (iff #27 #118)
-#117 := [rewrite]: #116
-#121 := [monotonicity #117]: #120
-#124 := [monotonicity #121]: #123
-#127 := [quant-intro #124]: #126
-#114 := (iff #32 #113)
-#111 := (iff #31 #110)
-#112 := [rewrite]: #111
-#115 := [quant-intro #112]: #114
-#129 := [trans #115 #127]: #128
-#108 := [asserted]: #32
-#130 := [mp #108 #129]: #125
-#263 := [mp~ #130 #267]: #125
-#845 := [mp #263 #844]: #840
-#830 := (not #840)
-#825 := (or #830 #826 #495)
-#831 := (or #830 #827)
-#481 := (iff #831 #825)
-#486 := [rewrite]: #481
-#821 := [quant-inst #14]: #831
-#822 := [mp #821 #486]: #825
-#432 := [unit-resolution #822 #845]: #827
-#428 := [unit-resolution #432 #431]: #495
-#424 := [mp #428 #421]: #648
-#866 := (or #626 #617)
-#867 := [th-lemma arith triangle-eq]: #866
-#868 := [unit-resolution #867 #424]: #617
-#869 := [unit-resolution #493 #427]: #767
-[th-lemma arith farkas 1 1 -1 1 #869 #868 #441 #600]: false
-unsat
-9d3396d381ad41e645649796d61e70c5401ede3a 761 0
-#2 := false
-#28 := 0::Int
-decl f9 :: (-> S6 S2 Int)
-decl f3 :: S2
-#7 := f3
-decl f10 :: S6
-#10 := f10
-#11 := (f9 f10 f3)
-#804 := (>= #11 0::Int)
-#780 := (not #804)
-#816 := (<= #11 0::Int)
-#631 := (not #816)
-#610 := (or #631 #780)
-#753 := (not #610)
-#471 := (= #11 0::Int)
-#730 := (not #471)
-decl f4 :: (-> S3 Int S2)
-decl f6 :: (-> S4 Int Int)
-#13 := 1::Int
-decl f7 :: (-> S5 Int S4)
-decl f11 :: S5
-#16 := f11
-#17 := (f7 f11 #11)
-#18 := (f6 #17 1::Int)
-decl f8 :: S5
-#9 := f8
-#12 := (f7 f8 #11)
-#14 := (f6 #12 1::Int)
-#92 := (+ #14 #18)
-decl f5 :: S3
-#8 := f5
-#95 := (f4 f5 #92)
-#98 := (= f3 #95)
-#507 := (f9 f10 #95)
-#465 := (f4 f5 #507)
-#467 := (= #465 #95)
-#23 := (:var 0 S2)
-#24 := (f9 f10 #23)
-#830 := (pattern #24)
-#25 := (f4 f5 #24)
-#26 := (= #25 #23)
-#831 := (forall (vars (?v0 S2)) (:pat #830) #26)
-#27 := (forall (vars (?v0 S2)) #26)
-#834 := (iff #27 #831)
-#832 := (iff #26 #26)
-#833 := [refl]: #832
-#835 := [quant-intro #833]: #834
-#276 := (~ #27 #27)
-#274 := (~ #26 #26)
-#275 := [refl]: #274
-#277 := [nnf-pos #275]: #276
-#104 := [asserted]: #27
-#262 := [mp~ #104 #277]: #27
-#836 := [mp #262 #835]: #831
-#494 := (not #831)
-#908 := (or #494 #467)
-#909 := [quant-inst #95]: #908
-#952 := [unit-resolution #909 #836]: #467
-#959 := (= f3 #465)
-#417 := (f4 f5 #11)
-#957 := (= #417 #465)
-#955 := (= #465 #417)
-#950 := (= #507 #11)
-#948 := (= 0::Int #11)
-#906 := [hypothesis]: #471
-#949 := [symm #906]: #948
-#469 := (= #507 0::Int)
-#815 := (>= #507 0::Int)
-#673 := (>= #18 0::Int)
-#724 := (= #18 0::Int)
-#907 := (or #730 #724)
-#156 := -1::Int
-#522 := (* -1::Int #11)
-#744 := (mod #522 -1::Int)
-#685 := (+ #18 #744)
-#687 := (= #685 0::Int)
-#692 := (if #610 #724 #687)
-#694 := (if #471 #724 #692)
-#29 := (:var 0 Int)
-#40 := (:var 1 Int)
-#60 := (f7 f11 #40)
-#61 := (f6 #60 #29)
-#857 := (pattern #61)
-#160 := (* -1::Int #29)
-#157 := (* -1::Int #40)
-#215 := (mod #157 #160)
-#345 := (+ #61 #215)
-#346 := (= #345 0::Int)
-#62 := (mod #40 #29)
-#342 := (* -1::Int #62)
-#343 := (+ #61 #342)
-#344 := (= #343 0::Int)
-#182 := (<= #29 0::Int)
-#189 := (>= #40 0::Int)
-#289 := (or #189 #182)
-#290 := (not #289)
-#178 := (<= #40 0::Int)
-#287 := (or #178 #182)
-#288 := (not #287)
-#293 := (or #288 #290)
-#347 := (if #293 #344 #346)
-#341 := (= #61 0::Int)
-#43 := (= #40 0::Int)
-#348 := (if #43 #341 #347)
-#340 := (= #61 #40)
-#44 := (= #29 0::Int)
-#349 := (if #44 #340 #348)
-#858 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #857) #349)
-#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
-#861 := (iff #352 #858)
-#859 := (iff #349 #349)
-#860 := [refl]: #859
-#862 := [quant-intro #860]: #861
-#221 := (* -1::Int #215)
-#309 := (if #293 #62 #221)
-#312 := (if #43 0::Int #309)
-#315 := (if #44 #40 #312)
-#318 := (= #61 #315)
-#321 := (forall (vars (?v0 Int) (?v1 Int)) #318)
-#353 := (iff #321 #352)
-#350 := (iff #318 #349)
-#351 := [rewrite]: #350
-#354 := [quant-intro #351]: #353
-#183 := (not #182)
-#190 := (not #189)
-#193 := (and #190 #183)
-#179 := (not #178)
-#186 := (and #179 #183)
-#196 := (or #186 #193)
-#241 := (if #196 #62 #221)
-#244 := (if #43 0::Int #241)
-#247 := (if #44 #40 #244)
-#250 := (= #61 #247)
-#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
-#322 := (iff #253 #321)
-#319 := (iff #250 #318)
-#316 := (= #247 #315)
-#313 := (= #244 #312)
-#310 := (= #241 #309)
-#294 := (iff #196 #293)
-#291 := (iff #193 #290)
-#292 := [rewrite]: #291
-#272 := (iff #186 #288)
-#273 := [rewrite]: #272
-#295 := [monotonicity #273 #292]: #294
-#311 := [monotonicity #295]: #310
-#314 := [monotonicity #311]: #313
-#317 := [monotonicity #314]: #316
-#320 := [monotonicity #317]: #319
-#323 := [quant-intro #320]: #322
-#270 := (~ #253 #253)
-#284 := (~ #250 #250)
-#285 := [refl]: #284
-#271 := [nnf-pos #285]: #270
-#54 := (- #29)
-#53 := (- #40)
-#63 := (mod #53 #54)
-#64 := (- #63)
-#47 := (< 0::Int #29)
-#49 := (< #40 0::Int)
-#50 := (and #49 #47)
-#46 := (< 0::Int #40)
-#48 := (and #46 #47)
-#51 := (or #48 #50)
-#65 := (if #51 #62 #64)
-#66 := (if #43 0::Int #65)
-#67 := (if #44 #40 #66)
-#68 := (= #61 #67)
-#69 := (forall (vars (?v0 Int) (?v1 Int)) #68)
-#256 := (iff #69 #253)
-#226 := (if #51 #62 #221)
-#229 := (if #43 0::Int #226)
-#232 := (if #44 #40 #229)
-#235 := (= #61 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#254 := (iff #238 #253)
-#251 := (iff #235 #250)
-#248 := (= #232 #247)
-#245 := (= #229 #244)
-#242 := (= #226 #241)
-#197 := (iff #51 #196)
-#194 := (iff #50 #193)
-#184 := (iff #47 #183)
-#185 := [rewrite]: #184
-#191 := (iff #49 #190)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192 #185]: #194
-#187 := (iff #48 #186)
-#180 := (iff #46 #179)
-#181 := [rewrite]: #180
-#188 := [monotonicity #181 #185]: #187
-#198 := [monotonicity #188 #195]: #197
-#243 := [monotonicity #198]: #242
-#246 := [monotonicity #243]: #245
-#249 := [monotonicity #246]: #248
-#252 := [monotonicity #249]: #251
-#255 := [quant-intro #252]: #254
-#239 := (iff #69 #238)
-#236 := (iff #68 #235)
-#233 := (= #67 #232)
-#230 := (= #66 #229)
-#227 := (= #65 #226)
-#224 := (= #64 #221)
-#218 := (- #215)
-#222 := (= #218 #221)
-#223 := [rewrite]: #222
-#219 := (= #64 #218)
-#216 := (= #63 #215)
-#161 := (= #54 #160)
-#162 := [rewrite]: #161
-#158 := (= #53 #157)
-#159 := [rewrite]: #158
-#217 := [monotonicity #159 #162]: #216
-#220 := [monotonicity #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#257 := [trans #240 #255]: #256
-#214 := [asserted]: #69
-#258 := [mp #214 #257]: #253
-#286 := [mp~ #258 #271]: #253
-#324 := [mp #286 #323]: #321
-#355 := [mp #324 #354]: #352
-#863 := [mp #355 #862]: #858
-#657 := (not #858)
-#616 := (or #657 #694)
-#523 := (* -1::Int 1::Int)
-#727 := (mod #522 #523)
-#705 := (+ #18 #727)
-#706 := (= #705 0::Int)
-#748 := (mod #11 1::Int)
-#725 := (* -1::Int #748)
-#726 := (+ #18 #725)
-#716 := (= #726 0::Int)
-#814 := (<= 1::Int 0::Int)
-#526 := (or #804 #814)
-#527 := (not #526)
-#817 := (or #816 #814)
-#803 := (not #817)
-#528 := (or #803 #527)
-#708 := (if #528 #716 #706)
-#709 := (if #471 #724 #708)
-#723 := (= #18 #11)
-#807 := (= 1::Int 0::Int)
-#710 := (if #807 #723 #709)
-#647 := (or #657 #710)
-#651 := (iff #647 #616)
-#660 := (iff #616 #616)
-#661 := [rewrite]: #660
-#682 := (iff #710 #694)
-#675 := (if false #723 #694)
-#681 := (iff #675 #694)
-#676 := [rewrite]: #681
-#656 := (iff #710 #675)
-#674 := (iff #709 #694)
-#693 := (iff #708 #692)
-#688 := (iff #706 #687)
-#690 := (= #705 #685)
-#683 := (= #727 #744)
-#766 := (= #523 -1::Int)
-#767 := [rewrite]: #766
-#684 := [monotonicity #767]: #683
-#686 := [monotonicity #684]: #690
-#691 := [monotonicity #686]: #688
-#679 := (iff #716 #724)
-#677 := (= #726 #18)
-#701 := (+ #18 0::Int)
-#698 := (= #701 #18)
-#704 := [rewrite]: #698
-#702 := (= #726 #701)
-#697 := (= #725 0::Int)
-#707 := (* -1::Int 0::Int)
-#695 := (= #707 0::Int)
-#696 := [rewrite]: #695
-#713 := (= #725 #707)
-#711 := (= #748 0::Int)
-#712 := [rewrite]: #711
-#699 := [monotonicity #712]: #713
-#700 := [trans #699 #696]: #697
-#703 := [monotonicity #700]: #702
-#678 := [trans #703 #704]: #677
-#572 := [monotonicity #678]: #679
-#612 := (iff #528 #610)
-#774 := (iff #527 #780)
-#773 := (iff #526 #804)
-#775 := (or #804 false)
-#778 := (iff #775 #804)
-#772 := [rewrite]: #778
-#776 := (iff #526 #775)
-#785 := (iff #814 false)
-#786 := [rewrite]: #785
-#777 := [monotonicity #786]: #776
-#779 := [trans #777 #772]: #773
-#781 := [monotonicity #779]: #774
-#632 := (iff #803 #631)
-#784 := (iff #817 #816)
-#787 := (or #816 false)
-#788 := (iff #787 #816)
-#789 := [rewrite]: #788
-#782 := (iff #817 #787)
-#783 := [monotonicity #786]: #782
-#790 := [trans #783 #789]: #784
-#633 := [monotonicity #790]: #632
-#613 := [monotonicity #633 #781]: #612
-#689 := [monotonicity #613 #572 #691]: #693
-#620 := [monotonicity #689]: #674
-#514 := (iff #807 false)
-#515 := [rewrite]: #514
-#680 := [monotonicity #515 #620]: #656
-#650 := [trans #680 #676]: #682
-#658 := [monotonicity #650]: #651
-#662 := [trans #658 #661]: #651
-#649 := [quant-inst #11 #13]: #647
-#672 := [mp #649 #662]: #616
-#476 := [unit-resolution #672 #863]: #694
-#645 := (not #694)
-#630 := (or #645 #730 #724)
-#646 := [def-axiom]: #630
-#910 := [unit-resolution #646 #476]: #907
-#881 := [unit-resolution #910 #906]: #724
-#639 := (not #724)
-#463 := (or #639 #673)
-#451 := [th-lemma arith triangle-eq]: #463
-#882 := [unit-resolution #451 #881]: #673
-#743 := (>= #14 0::Int)
-#529 := (div #11 1::Int)
-#423 := (* -1::Int #529)
-#586 := (+ #11 #423)
-#590 := (= #586 0::Int)
-#1 := true
-#87 := [true-axiom]: true
-#565 := (or false #590)
-#542 := [th-lemma arith]: #565
-#544 := [unit-resolution #542 #87]: #590
-#574 := (<= #586 0::Int)
-#495 := (not #574)
-#545 := (not #743)
-#546 := [hypothesis]: #545
-#799 := (+ #14 #423)
-#750 := (>= #799 0::Int)
-#800 := (= #799 0::Int)
-#769 := (div #522 -1::Int)
-#771 := (* -1::Int #769)
-#655 := (+ #14 #771)
-#664 := (= #655 0::Int)
-#763 := (if #610 #800 #664)
-#456 := (= #14 0::Int)
-#718 := (not #456)
-#547 := (or #718 #743)
-#548 := [th-lemma arith triangle-eq]: #547
-#549 := [unit-resolution #548 #546]: #718
-#543 := (or #730 #456)
-#665 := (if #471 #456 #763)
-#41 := (f7 f8 #40)
-#42 := (f6 #41 #29)
-#850 := (pattern #42)
-#163 := (div #157 #160)
-#329 := (* -1::Int #163)
-#330 := (+ #42 #329)
-#331 := (= #330 0::Int)
-#52 := (div #40 #29)
-#326 := (* -1::Int #52)
-#327 := (+ #42 #326)
-#328 := (= #327 0::Int)
-#332 := (if #293 #328 #331)
-#325 := (= #42 0::Int)
-#45 := (or #43 #44)
-#333 := (if #45 #325 #332)
-#851 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #850) #333)
-#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
-#854 := (iff #336 #851)
-#852 := (iff #333 #333)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#296 := (if #293 #52 #163)
-#299 := (if #45 0::Int #296)
-#302 := (= #42 #299)
-#305 := (forall (vars (?v0 Int) (?v1 Int)) #302)
-#337 := (iff #305 #336)
-#334 := (iff #302 #333)
-#335 := [rewrite]: #334
-#338 := [quant-intro #335]: #337
-#199 := (if #196 #52 #163)
-#202 := (if #45 0::Int #199)
-#205 := (= #42 #202)
-#208 := (forall (vars (?v0 Int) (?v1 Int)) #205)
-#306 := (iff #208 #305)
-#303 := (iff #205 #302)
-#300 := (= #202 #299)
-#297 := (= #199 #296)
-#298 := [monotonicity #295]: #297
-#301 := [monotonicity #298]: #300
-#304 := [monotonicity #301]: #303
-#307 := [quant-intro #304]: #306
-#268 := (~ #208 #208)
-#281 := (~ #205 #205)
-#282 := [refl]: #281
-#269 := [nnf-pos #282]: #268
-#55 := (div #53 #54)
-#56 := (if #51 #52 #55)
-#57 := (if #45 0::Int #56)
-#58 := (= #42 #57)
-#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
-#211 := (iff #59 #208)
-#166 := (if #51 #52 #163)
-#169 := (if #45 0::Int #166)
-#172 := (= #42 #169)
-#175 := (forall (vars (?v0 Int) (?v1 Int)) #172)
-#209 := (iff #175 #208)
-#206 := (iff #172 #205)
-#203 := (= #169 #202)
-#200 := (= #166 #199)
-#201 := [monotonicity #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [quant-intro #207]: #209
-#176 := (iff #59 #175)
-#173 := (iff #58 #172)
-#170 := (= #57 #169)
-#167 := (= #56 #166)
-#164 := (= #55 #163)
-#165 := [monotonicity #159 #162]: #164
-#168 := [monotonicity #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [quant-intro #174]: #176
-#212 := [trans #177 #210]: #211
-#155 := [asserted]: #59
-#213 := [mp #155 #212]: #208
-#283 := [mp~ #213 #269]: #208
-#308 := [mp #283 #307]: #305
-#339 := [mp #308 #338]: #336
-#856 := [mp #339 #855]: #851
-#667 := (not #851)
-#668 := (or #667 #665)
-#797 := (div #522 #523)
-#801 := (* -1::Int #797)
-#798 := (+ #14 #801)
-#802 := (= #798 0::Int)
-#512 := (if #528 #800 #802)
-#455 := (or #471 #807)
-#513 := (if #455 #456 #512)
-#669 := (or #667 #513)
-#671 := (iff #669 #668)
-#761 := (iff #668 #668)
-#765 := [rewrite]: #761
-#666 := (iff #513 #665)
-#648 := (iff #512 #763)
-#759 := (iff #802 #664)
-#614 := (= #798 #655)
-#653 := (= #801 #771)
-#770 := (= #797 #769)
-#768 := [monotonicity #767]: #770
-#654 := [monotonicity #768]: #653
-#762 := [monotonicity #654]: #614
-#760 := [monotonicity #762]: #759
-#663 := [monotonicity #613 #760]: #648
-#792 := (iff #455 #471)
-#793 := (or #471 false)
-#791 := (iff #793 #471)
-#795 := [rewrite]: #791
-#794 := (iff #455 #793)
-#509 := [monotonicity #515]: #794
-#796 := [trans #509 #795]: #792
-#659 := [monotonicity #796 #663]: #666
-#764 := [monotonicity #659]: #671
-#752 := [trans #764 #765]: #671
-#670 := [quant-inst #11 #13]: #669
-#754 := [mp #670 #752]: #668
-#550 := [unit-resolution #754 #856]: #665
-#733 := (not #665)
-#734 := (or #733 #730 #456)
-#714 := [def-axiom]: #734
-#551 := [unit-resolution #714 #550]: #543
-#536 := [unit-resolution #551 #549]: #730
-#537 := (or #471 #763)
-#715 := (or #733 #471 #763)
-#717 := [def-axiom]: #715
-#538 := [unit-resolution #717 #550]: #537
-#540 := [unit-resolution #538 #536]: #763
-#621 := (f9 f10 #417)
-#622 := (= #621 0::Int)
-#534 := (not #622)
-#525 := (iff #730 #534)
-#524 := (iff #471 #622)
-#531 := (iff #622 #471)
-#541 := (= #621 #11)
-#501 := (= #417 f3)
-#505 := (or #494 #501)
-#506 := [quant-inst #7]: #505
-#539 := [unit-resolution #506 #836]: #501
-#530 := [monotonicity #539]: #541
-#532 := [monotonicity #530]: #531
-#533 := [symm #532]: #524
-#535 := [monotonicity #533]: #525
-#516 := [mp #536 #535]: #534
-#623 := (or #804 #622)
-#31 := (f4 f5 #29)
-#837 := (pattern #31)
-#32 := (f9 f10 #31)
-#37 := (= #32 0::Int)
-#116 := (>= #29 0::Int)
-#146 := (or #116 #37)
-#844 := (forall (vars (?v0 Int)) (:pat #837) #146)
-#149 := (forall (vars (?v0 Int)) #146)
-#847 := (iff #149 #844)
-#845 := (iff #146 #146)
-#846 := [refl]: #845
-#848 := [quant-intro #846]: #847
-#266 := (~ #149 #149)
-#278 := (~ #146 #146)
-#279 := [refl]: #278
-#267 := [nnf-pos #279]: #266
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#152 := (iff #39 #149)
-#130 := (not #36)
-#131 := (or #130 #37)
-#134 := (forall (vars (?v0 Int)) #131)
-#150 := (iff #134 #149)
-#147 := (iff #131 #146)
-#144 := (iff #130 #116)
-#117 := (not #116)
-#139 := (not #117)
-#142 := (iff #139 #116)
-#143 := [rewrite]: #142
-#140 := (iff #130 #139)
-#137 := (iff #36 #117)
-#138 := [rewrite]: #137
-#141 := [monotonicity #138]: #140
-#145 := [trans #141 #143]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#135 := (iff #39 #134)
-#132 := (iff #38 #131)
-#133 := [rewrite]: #132
-#136 := [quant-intro #133]: #135
-#153 := [trans #136 #151]: #152
-#129 := [asserted]: #39
-#154 := [mp #129 #153]: #149
-#280 := [mp~ #154 #267]: #149
-#849 := [mp #280 #848]: #844
-#808 := (not #844)
-#626 := (or #808 #804 #622)
-#609 := (or #808 #623)
-#597 := (iff #609 #626)
-#598 := [rewrite]: #597
-#627 := [quant-inst #11]: #609
-#599 := [mp #627 #598]: #626
-#517 := [unit-resolution #599 #849]: #623
-#518 := [unit-resolution #517 #516]: #804
-#510 := (or #471 #631 #780)
-#519 := [th-lemma arith triangle-eq]: #510
-#520 := [unit-resolution #519 #536]: #610
-#511 := [unit-resolution #520 #518]: #631
-#745 := (or #610 #816)
-#755 := [def-axiom]: #745
-#521 := [unit-resolution #755 #511]: #610
-#736 := (not #763)
-#738 := (or #736 #753 #800)
-#739 := [def-axiom]: #738
-#488 := [unit-resolution #739 #521 #540]: #800
-#737 := (not #800)
-#490 := (or #737 #750)
-#491 := [th-lemma arith triangle-eq]: #490
-#482 := [unit-resolution #491 #488]: #750
-#496 := (not #750)
-#497 := (or #495 #780 #743 #496)
-#498 := [th-lemma arith assign-bounds 1 1 -1]: #497
-#499 := [unit-resolution #498 #518 #482 #546]: #495
-#489 := (not #590)
-#500 := (or #489 #574)
-#483 := [th-lemma arith triangle-eq]: #500
-#485 := [unit-resolution #483 #499 #544]: false
-#486 := [lemma #485]: #743
-#611 := (* -1::Int #507)
-#818 := (+ #18 #611)
-#492 := (+ #14 #818)
-#805 := (<= #492 0::Int)
-#824 := (= #492 0::Int)
-#502 := (>= #92 0::Int)
-#915 := (not #673)
-#916 := (or #502 #545 #915)
-#917 := [th-lemma arith assign-bounds 1 -1]: #916
-#918 := [unit-resolution #917 #882 #486]: #502
-#503 := (not #502)
-#481 := (or #503 #824)
-#33 := (= #32 #29)
-#120 := (or #117 #33)
-#838 := (forall (vars (?v0 Int)) (:pat #837) #120)
-#123 := (forall (vars (?v0 Int)) #120)
-#841 := (iff #123 #838)
-#839 := (iff #120 #120)
-#840 := [refl]: #839
-#842 := [quant-intro #840]: #841
-#264 := (~ #123 #123)
-#263 := (~ #120 #120)
-#260 := [refl]: #263
-#265 := [nnf-pos #260]: #264
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#126 := (iff #35 #123)
-#107 := (not #30)
-#108 := (or #107 #33)
-#111 := (forall (vars (?v0 Int)) #108)
-#124 := (iff #111 #123)
-#121 := (iff #108 #120)
-#118 := (iff #107 #117)
-#114 := (iff #30 #116)
-#115 := [rewrite]: #114
-#119 := [monotonicity #115]: #118
-#122 := [monotonicity #119]: #121
-#125 := [quant-intro #122]: #124
-#112 := (iff #35 #111)
-#109 := (iff #34 #108)
-#110 := [rewrite]: #109
-#113 := [quant-intro #110]: #112
-#127 := [trans #113 #125]: #126
-#105 := [asserted]: #35
-#128 := [mp #105 #127]: #123
-#261 := [mp~ #128 #265]: #123
-#843 := [mp #261 #842]: #838
-#826 := (not #838)
-#827 := (or #826 #503 #824)
-#504 := (= #507 #92)
-#508 := (or #503 #504)
-#828 := (or #826 #508)
-#480 := (iff #828 #827)
-#829 := (or #826 #481)
-#484 := (iff #829 #827)
-#820 := [rewrite]: #484
-#819 := (iff #828 #829)
-#493 := (iff #508 #481)
-#822 := (iff #504 #824)
-#487 := [rewrite]: #822
-#825 := [monotonicity #487]: #493
-#479 := [monotonicity #825]: #819
-#821 := [trans #479 #820]: #480
-#823 := [quant-inst #92]: #828
-#464 := [mp #823 #821]: #827
-#919 := [unit-resolution #464 #843]: #481
-#920 := [unit-resolution #919 #918]: #824
-#921 := (not #824)
-#922 := (or #921 #805)
-#923 := [th-lemma arith triangle-eq]: #922
-#924 := [unit-resolution #923 #920]: #805
-#925 := (not #805)
-#926 := (or #815 #545 #915 #925)
-#927 := [th-lemma arith assign-bounds 1 -1 1]: #926
-#928 := [unit-resolution #927 #924 #486 #882]: #815
-#813 := (<= #507 0::Int)
-#652 := (<= #18 0::Int)
-#461 := (or #639 #652)
-#462 := [th-lemma arith triangle-eq]: #461
-#929 := [unit-resolution #462 #881]: #652
-#746 := (<= #14 0::Int)
-#930 := [unit-resolution #551 #906]: #456
-#931 := (or #718 #746)
-#932 := [th-lemma arith triangle-eq]: #931
-#933 := [unit-resolution #932 #930]: #746
-#468 := (>= #492 0::Int)
-#934 := (or #921 #468)
-#935 := [th-lemma arith triangle-eq]: #934
-#936 := [unit-resolution #935 #920]: #468
-#939 := (not #468)
-#938 := (not #652)
-#937 := (not #746)
-#940 := (or #813 #937 #938 #939)
-#941 := [th-lemma arith assign-bounds -1 -1 1]: #940
-#942 := [unit-resolution #941 #936 #933 #929]: #813
-#944 := (not #815)
-#943 := (not #813)
-#945 := (or #469 #943 #944)
-#946 := [th-lemma arith triangle-eq]: #945
-#947 := [unit-resolution #946 #942 #928]: #469
-#951 := [trans #947 #949]: #950
-#956 := [monotonicity #951]: #955
-#958 := [symm #956]: #957
-#441 := (= f3 #417)
-#434 := [symm #539]: #441
-#960 := [trans #434 #958]: #959
-#961 := [trans #960 #952]: #98
-#101 := (not #98)
-#15 := (* #14 1::Int)
-#19 := (+ #15 #18)
-#20 := (f4 f5 #19)
-#21 := (= f3 #20)
-#22 := (not #21)
-#102 := (iff #22 #101)
-#99 := (iff #21 #98)
-#96 := (= #20 #95)
-#93 := (= #19 #92)
-#90 := (= #15 #14)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#89 := [asserted]: #22
-#106 := [mp #89 #103]: #101
-#962 := [unit-resolution #106 #961]: false
-#963 := [lemma #962]: #730
-#428 := (or #471 #753)
-#442 := (= #417 #95)
-#439 := (= #11 #92)
-#454 := (= #14 #92)
-#472 := [hypothesis]: #610
-#473 := [hypothesis]: #730
-#477 := (or #471 #692)
-#607 := (or #645 #471 #692)
-#608 := [def-axiom]: #607
-#466 := [unit-resolution #608 #476]: #477
-#478 := [unit-resolution #466 #473]: #692
-#634 := (not #692)
-#635 := (or #634 #753 #724)
-#636 := [def-axiom]: #635
-#459 := [unit-resolution #636 #478 #472]: #724
-#460 := [unit-resolution #462 #459]: #652
-#453 := [unit-resolution #451 #459]: #673
-#457 := [th-lemma arith eq-propagate -1 -1 #453 #460]: #454
-#449 := (= #11 #14)
-#749 := (<= #799 0::Int)
-#452 := [unit-resolution #538 #473]: #763
-#458 := [unit-resolution #739 #452 #472]: #800
-#433 := (or #737 #749)
-#437 := [th-lemma arith triangle-eq]: #433
-#438 := [unit-resolution #437 #458]: #749
-#443 := [unit-resolution #491 #458]: #750
-#445 := [unit-resolution #483 #544]: #574
-#577 := (>= #586 0::Int)
-#446 := (or #489 #577)
-#448 := [th-lemma arith triangle-eq]: #446
-#444 := [unit-resolution #448 #544]: #577
-#432 := [th-lemma arith eq-propagate 1 1 -1 -1 #444 #445 #443 #438]: #449
-#440 := [trans #432 #457]: #439
-#427 := [monotonicity #440]: #442
-#424 := [trans #434 #427]: #98
-#425 := [unit-resolution #106 #424]: false
-#429 := [lemma #425]: #428
-#953 := [unit-resolution #429 #963]: #753
-#913 := (or #471 #780)
-#911 := [hypothesis]: #804
-#474 := [hypothesis]: #631
-#475 := [unit-resolution #755 #474]: #610
-#435 := [unit-resolution #429 #475]: #471
-#436 := (or #730 #816)
-#430 := [th-lemma arith triangle-eq]: #436
-#426 := [unit-resolution #430 #435 #474]: false
-#431 := [lemma #426]: #816
-#912 := [unit-resolution #519 #473 #431 #911]: false
-#914 := [lemma #912]: #913
-#954 := [unit-resolution #914 #963]: #780
-#756 := (or #610 #804)
-#757 := [def-axiom]: #756
-[unit-resolution #757 #954 #953]: false
-unsat
-b88eecece4a97949c3e182a0994557edf8a964b2 816 0
-#2 := false
-#28 := 0::Int
-decl f9 :: (-> S6 S2 Int)
-decl f3 :: S2
-#7 := f3
-decl f10 :: S6
-#10 := f10
-#11 := (f9 f10 f3)
-#805 := (>= #11 0::Int)
-#781 := (not #805)
-#817 := (<= #11 0::Int)
-#632 := (not #817)
-#611 := (or #632 #781)
-#759 := (not #611)
-#472 := (= #11 0::Int)
-#735 := (not #472)
-decl f4 :: (-> S3 Int S2)
-decl f6 :: (-> S4 Int Int)
-#13 := 3::Int
-decl f7 :: (-> S5 Int S4)
-decl f11 :: S5
-#16 := f11
-#17 := (f7 f11 #11)
-#18 := (f6 #17 3::Int)
-decl f8 :: S5
-#9 := f8
-#12 := (f7 f8 #11)
-#14 := (f6 #12 3::Int)
-#90 := (* 3::Int #14)
-#93 := (+ #90 #18)
-decl f5 :: S3
-#8 := f5
-#96 := (f4 f5 #93)
-#99 := (= f3 #96)
-#418 := (f4 f5 #11)
-#997 := (= #418 #96)
-#995 := (= #96 #418)
-#993 := (= #93 #11)
-#989 := (= 0::Int #11)
-#953 := [hypothesis]: #472
-#990 := [symm #953]: #989
-#991 := (= #93 0::Int)
-#508 := (f9 f10 #96)
-#470 := (= #508 0::Int)
-#816 := (>= #508 0::Int)
-#657 := (>= #18 0::Int)
-#726 := (= #18 0::Int)
-#954 := (or #735 #726)
-#767 := -3::Int
-#157 := -1::Int
-#523 := (* -1::Int #11)
-#752 := (mod #523 -3::Int)
-#714 := (+ #18 #752)
-#697 := (= #714 0::Int)
-#750 := (mod #11 3::Int)
-#727 := (* -1::Int #750)
-#717 := (+ #18 #727)
-#728 := (= #717 0::Int)
-#702 := (if #611 #728 #697)
-#699 := (if #472 #726 #702)
-#29 := (:var 0 Int)
-#40 := (:var 1 Int)
-#60 := (f7 f11 #40)
-#61 := (f6 #60 #29)
-#858 := (pattern #61)
-#161 := (* -1::Int #29)
-#158 := (* -1::Int #40)
-#216 := (mod #158 #161)
-#346 := (+ #61 #216)
-#347 := (= #346 0::Int)
-#62 := (mod #40 #29)
-#343 := (* -1::Int #62)
-#344 := (+ #61 #343)
-#345 := (= #344 0::Int)
-#183 := (<= #29 0::Int)
-#190 := (>= #40 0::Int)
-#290 := (or #190 #183)
-#291 := (not #290)
-#179 := (<= #40 0::Int)
-#288 := (or #179 #183)
-#289 := (not #288)
-#294 := (or #289 #291)
-#348 := (if #294 #345 #347)
-#342 := (= #61 0::Int)
-#43 := (= #40 0::Int)
-#349 := (if #43 #342 #348)
-#341 := (= #61 #40)
-#44 := (= #29 0::Int)
-#350 := (if #44 #341 #349)
-#859 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #858) #350)
-#353 := (forall (vars (?v0 Int) (?v1 Int)) #350)
-#862 := (iff #353 #859)
-#860 := (iff #350 #350)
-#861 := [refl]: #860
-#863 := [quant-intro #861]: #862
-#222 := (* -1::Int #216)
-#310 := (if #294 #62 #222)
-#313 := (if #43 0::Int #310)
-#316 := (if #44 #40 #313)
-#319 := (= #61 #316)
-#322 := (forall (vars (?v0 Int) (?v1 Int)) #319)
-#354 := (iff #322 #353)
-#351 := (iff #319 #350)
-#352 := [rewrite]: #351
-#355 := [quant-intro #352]: #354
-#184 := (not #183)
-#191 := (not #190)
-#194 := (and #191 #184)
-#180 := (not #179)
-#187 := (and #180 #184)
-#197 := (or #187 #194)
-#242 := (if #197 #62 #222)
-#245 := (if #43 0::Int #242)
-#248 := (if #44 #40 #245)
-#251 := (= #61 #248)
-#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
-#323 := (iff #254 #322)
-#320 := (iff #251 #319)
-#317 := (= #248 #316)
-#314 := (= #245 #313)
-#311 := (= #242 #310)
-#295 := (iff #197 #294)
-#292 := (iff #194 #291)
-#293 := [rewrite]: #292
-#273 := (iff #187 #289)
-#274 := [rewrite]: #273
-#296 := [monotonicity #274 #293]: #295
-#312 := [monotonicity #296]: #311
-#315 := [monotonicity #312]: #314
-#318 := [monotonicity #315]: #317
-#321 := [monotonicity #318]: #320
-#324 := [quant-intro #321]: #323
-#271 := (~ #254 #254)
-#285 := (~ #251 #251)
-#286 := [refl]: #285
-#272 := [nnf-pos #286]: #271
-#54 := (- #29)
-#53 := (- #40)
-#63 := (mod #53 #54)
-#64 := (- #63)
-#47 := (< 0::Int #29)
-#49 := (< #40 0::Int)
-#50 := (and #49 #47)
-#46 := (< 0::Int #40)
-#48 := (and #46 #47)
-#51 := (or #48 #50)
-#65 := (if #51 #62 #64)
-#66 := (if #43 0::Int #65)
-#67 := (if #44 #40 #66)
-#68 := (= #61 #67)
-#69 := (forall (vars (?v0 Int) (?v1 Int)) #68)
-#257 := (iff #69 #254)
-#227 := (if #51 #62 #222)
-#230 := (if #43 0::Int #227)
-#233 := (if #44 #40 #230)
-#236 := (= #61 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#255 := (iff #239 #254)
-#252 := (iff #236 #251)
-#249 := (= #233 #248)
-#246 := (= #230 #245)
-#243 := (= #227 #242)
-#198 := (iff #51 #197)
-#195 := (iff #50 #194)
-#185 := (iff #47 #184)
-#186 := [rewrite]: #185
-#192 := (iff #49 #191)
-#193 := [rewrite]: #192
-#196 := [monotonicity #193 #186]: #195
-#188 := (iff #48 #187)
-#181 := (iff #46 #180)
-#182 := [rewrite]: #181
-#189 := [monotonicity #182 #186]: #188
-#199 := [monotonicity #189 #196]: #198
-#244 := [monotonicity #199]: #243
-#247 := [monotonicity #244]: #246
-#250 := [monotonicity #247]: #249
-#253 := [monotonicity #250]: #252
-#256 := [quant-intro #253]: #255
-#240 := (iff #69 #239)
-#237 := (iff #68 #236)
-#234 := (= #67 #233)
-#231 := (= #66 #230)
-#228 := (= #65 #227)
-#225 := (= #64 #222)
-#219 := (- #216)
-#223 := (= #219 #222)
-#224 := [rewrite]: #223
-#220 := (= #64 #219)
-#217 := (= #63 #216)
-#162 := (= #54 #161)
-#163 := [rewrite]: #162
-#159 := (= #53 #158)
-#160 := [rewrite]: #159
-#218 := [monotonicity #160 #163]: #217
-#221 := [monotonicity #218]: #220
-#226 := [trans #221 #224]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#258 := [trans #241 #256]: #257
-#215 := [asserted]: #69
-#259 := [mp #215 #258]: #254
-#287 := [mp~ #259 #272]: #254
-#325 := [mp #287 #324]: #322
-#356 := [mp #325 #355]: #353
-#864 := [mp #356 #863]: #859
-#687 := (not #859)
-#688 := (or #687 #699)
-#524 := (* -1::Int 3::Int)
-#706 := (mod #523 #524)
-#707 := (+ #18 #706)
-#709 := (= #707 0::Int)
-#815 := (<= 3::Int 0::Int)
-#527 := (or #805 #815)
-#528 := (not #527)
-#818 := (or #817 #815)
-#804 := (not #818)
-#529 := (or #804 #528)
-#710 := (if #529 #728 #709)
-#711 := (if #472 #726 #710)
-#725 := (= #18 #11)
-#808 := (= 3::Int 0::Int)
-#712 := (if #808 #725 #711)
-#689 := (or #687 #712)
-#693 := (iff #689 #688)
-#690 := (iff #688 #688)
-#695 := [rewrite]: #690
-#686 := (iff #712 #699)
-#679 := (if false #725 #699)
-#684 := (iff #679 #699)
-#685 := [rewrite]: #684
-#680 := (iff #712 #679)
-#705 := (iff #711 #699)
-#703 := (iff #710 #702)
-#698 := (iff #709 #697)
-#700 := (= #707 #714)
-#713 := (= #706 #752)
-#768 := (= #524 -3::Int)
-#770 := [rewrite]: #768
-#708 := [monotonicity #770]: #713
-#696 := [monotonicity #708]: #700
-#701 := [monotonicity #696]: #698
-#613 := (iff #529 #611)
-#775 := (iff #528 #781)
-#774 := (iff #527 #805)
-#776 := (or #805 false)
-#779 := (iff #776 #805)
-#773 := [rewrite]: #779
-#777 := (iff #527 #776)
-#786 := (iff #815 false)
-#787 := [rewrite]: #786
-#778 := [monotonicity #787]: #777
-#780 := [trans #778 #773]: #774
-#782 := [monotonicity #780]: #775
-#633 := (iff #804 #632)
-#785 := (iff #818 #817)
-#788 := (or #817 false)
-#789 := (iff #788 #817)
-#790 := [rewrite]: #789
-#783 := (iff #818 #788)
-#784 := [monotonicity #787]: #783
-#791 := [trans #784 #790]: #785
-#634 := [monotonicity #791]: #633
-#614 := [monotonicity #634 #782]: #613
-#704 := [monotonicity #614 #701]: #703
-#678 := [monotonicity #704]: #705
-#515 := (iff #808 false)
-#516 := [rewrite]: #515
-#573 := [monotonicity #516 #678]: #680
-#691 := [trans #573 #685]: #686
-#694 := [monotonicity #691]: #693
-#675 := [trans #694 #695]: #693
-#692 := [quant-inst #11 #13]: #689
-#621 := [mp #692 #675]: #688
-#421 := [unit-resolution #621 #864]: #699
-#653 := (not #699)
-#674 := (or #653 #735 #726)
-#629 := [def-axiom]: #674
-#955 := [unit-resolution #629 #421]: #954
-#956 := [unit-resolution #955 #953]: #726
-#636 := (not #726)
-#957 := (or #636 #657)
-#928 := [th-lemma arith triangle-eq]: #957
-#929 := [unit-resolution #928 #956]: #657
-#746 := (>= #14 0::Int)
-#530 := (div #11 3::Int)
-#626 := (* -3::Int #530)
-#627 := (+ #626 #727)
-#610 := (+ #11 #627)
-#625 := (= #610 0::Int)
-#1 := true
-#87 := [true-axiom]: true
-#576 := (or false #625)
-#584 := [th-lemma arith]: #576
-#577 := [unit-resolution #584 #87]: #625
-#599 := (<= #610 0::Int)
-#531 := (not #599)
-#590 := (>= #750 3::Int)
-#591 := (not #590)
-#580 := (or false #591)
-#581 := [th-lemma arith]: #580
-#567 := [unit-resolution #581 #87]: #591
-#569 := (not #746)
-#570 := [hypothesis]: #569
-#424 := (* -1::Int #530)
-#800 := (+ #14 #424)
-#745 := (>= #800 0::Int)
-#801 := (= #800 0::Int)
-#771 := (div #523 -3::Int)
-#654 := (* -1::Int #771)
-#615 := (+ #14 #654)
-#760 := (= #615 0::Int)
-#649 := (if #611 #801 #760)
-#457 := (= #14 0::Int)
-#720 := (not #457)
-#568 := (or #720 #746)
-#571 := [th-lemma arith triangle-eq]: #568
-#553 := [unit-resolution #571 #570]: #720
-#556 := (or #735 #457)
-#667 := (if #472 #457 #649)
-#41 := (f7 f8 #40)
-#42 := (f6 #41 #29)
-#851 := (pattern #42)
-#164 := (div #158 #161)
-#330 := (* -1::Int #164)
-#331 := (+ #42 #330)
-#332 := (= #331 0::Int)
-#52 := (div #40 #29)
-#327 := (* -1::Int #52)
-#328 := (+ #42 #327)
-#329 := (= #328 0::Int)
-#333 := (if #294 #329 #332)
-#326 := (= #42 0::Int)
-#45 := (or #43 #44)
-#334 := (if #45 #326 #333)
-#852 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #851) #334)
-#337 := (forall (vars (?v0 Int) (?v1 Int)) #334)
-#855 := (iff #337 #852)
-#853 := (iff #334 #334)
-#854 := [refl]: #853
-#856 := [quant-intro #854]: #855
-#297 := (if #294 #52 #164)
-#300 := (if #45 0::Int #297)
-#303 := (= #42 #300)
-#306 := (forall (vars (?v0 Int) (?v1 Int)) #303)
-#338 := (iff #306 #337)
-#335 := (iff #303 #334)
-#336 := [rewrite]: #335
-#339 := [quant-intro #336]: #338
-#200 := (if #197 #52 #164)
-#203 := (if #45 0::Int #200)
-#206 := (= #42 #203)
-#209 := (forall (vars (?v0 Int) (?v1 Int)) #206)
-#307 := (iff #209 #306)
-#304 := (iff #206 #303)
-#301 := (= #203 #300)
-#298 := (= #200 #297)
-#299 := [monotonicity #296]: #298
-#302 := [monotonicity #299]: #301
-#305 := [monotonicity #302]: #304
-#308 := [quant-intro #305]: #307
-#269 := (~ #209 #209)
-#282 := (~ #206 #206)
-#283 := [refl]: #282
-#270 := [nnf-pos #283]: #269
-#55 := (div #53 #54)
-#56 := (if #51 #52 #55)
-#57 := (if #45 0::Int #56)
-#58 := (= #42 #57)
-#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
-#212 := (iff #59 #209)
-#167 := (if #51 #52 #164)
-#170 := (if #45 0::Int #167)
-#173 := (= #42 #170)
-#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
-#210 := (iff #176 #209)
-#207 := (iff #173 #206)
-#204 := (= #170 #203)
-#201 := (= #167 #200)
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [monotonicity #205]: #207
-#211 := [quant-intro #208]: #210
-#177 := (iff #59 #176)
-#174 := (iff #58 #173)
-#171 := (= #57 #170)
-#168 := (= #56 #167)
-#165 := (= #55 #164)
-#166 := [monotonicity #160 #163]: #165
-#169 := [monotonicity #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [quant-intro #175]: #177
-#213 := [trans #178 #211]: #212
-#156 := [asserted]: #59
-#214 := [mp #156 #213]: #209
-#284 := [mp~ #214 #270]: #209
-#309 := [mp #284 #308]: #306
-#340 := [mp #309 #339]: #337
-#857 := [mp #340 #856]: #852
-#669 := (not #852)
-#670 := (or #669 #667)
-#798 := (div #523 #524)
-#802 := (* -1::Int #798)
-#799 := (+ #14 #802)
-#803 := (= #799 0::Int)
-#513 := (if #529 #801 #803)
-#456 := (or #472 #808)
-#514 := (if #456 #457 #513)
-#671 := (or #669 #514)
-#765 := (iff #671 #670)
-#766 := (iff #670 #670)
-#753 := [rewrite]: #766
-#660 := (iff #514 #667)
-#664 := (iff #513 #649)
-#761 := (iff #803 #760)
-#763 := (= #799 #615)
-#655 := (= #802 #654)
-#769 := (= #798 #771)
-#772 := [monotonicity #770]: #769
-#656 := [monotonicity #772]: #655
-#665 := [monotonicity #656]: #763
-#764 := [monotonicity #665]: #761
-#666 := [monotonicity #614 #764]: #664
-#793 := (iff #456 #472)
-#794 := (or #472 false)
-#792 := (iff #794 #472)
-#796 := [rewrite]: #792
-#795 := (iff #456 #794)
-#510 := [monotonicity #516]: #795
-#797 := [trans #510 #796]: #793
-#668 := [monotonicity #797 #666]: #660
-#762 := [monotonicity #668]: #765
-#755 := [trans #762 #753]: #765
-#672 := [quant-inst #11 #13]: #671
-#747 := [mp #672 #755]: #670
-#555 := [unit-resolution #747 #857]: #667
-#731 := (not #667)
-#715 := (or #731 #735 #457)
-#716 := [def-axiom]: #715
-#557 := [unit-resolution #716 #555]: #556
-#558 := [unit-resolution #557 #553]: #735
-#559 := (or #472 #649)
-#718 := (or #731 #472 #649)
-#719 := [def-axiom]: #718
-#560 := [unit-resolution #719 #555]: #559
-#561 := [unit-resolution #560 #558]: #649
-#641 := (f9 f10 #418)
-#642 := (= #641 0::Int)
-#545 := (not #642)
-#546 := (iff #735 #545)
-#566 := (iff #472 #642)
-#565 := (iff #642 #472)
-#563 := (= #641 #11)
-#502 := (= #418 f3)
-#23 := (:var 0 S2)
-#24 := (f9 f10 #23)
-#831 := (pattern #24)
-#25 := (f4 f5 #24)
-#26 := (= #25 #23)
-#832 := (forall (vars (?v0 S2)) (:pat #831) #26)
-#27 := (forall (vars (?v0 S2)) #26)
-#835 := (iff #27 #832)
-#833 := (iff #26 #26)
-#834 := [refl]: #833
-#836 := [quant-intro #834]: #835
-#277 := (~ #27 #27)
-#275 := (~ #26 #26)
-#276 := [refl]: #275
-#278 := [nnf-pos #276]: #277
-#105 := [asserted]: #27
-#263 := [mp~ #105 #278]: #27
-#837 := [mp #263 #836]: #832
-#495 := (not #832)
-#506 := (or #495 #502)
-#507 := [quant-inst #7]: #506
-#562 := [unit-resolution #507 #837]: #502
-#564 := [monotonicity #562]: #563
-#554 := [monotonicity #564]: #565
-#543 := [symm #554]: #566
-#547 := [monotonicity #543]: #546
-#548 := [mp #558 #547]: #545
-#643 := (or #805 #642)
-#31 := (f4 f5 #29)
-#838 := (pattern #31)
-#32 := (f9 f10 #31)
-#37 := (= #32 0::Int)
-#117 := (>= #29 0::Int)
-#147 := (or #117 #37)
-#845 := (forall (vars (?v0 Int)) (:pat #838) #147)
-#150 := (forall (vars (?v0 Int)) #147)
-#848 := (iff #150 #845)
-#846 := (iff #147 #147)
-#847 := [refl]: #846
-#849 := [quant-intro #847]: #848
-#267 := (~ #150 #150)
-#279 := (~ #147 #147)
-#280 := [refl]: #279
-#268 := [nnf-pos #280]: #267
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#153 := (iff #39 #150)
-#131 := (not #36)
-#132 := (or #131 #37)
-#135 := (forall (vars (?v0 Int)) #132)
-#151 := (iff #135 #150)
-#148 := (iff #132 #147)
-#145 := (iff #131 #117)
-#118 := (not #117)
-#140 := (not #118)
-#143 := (iff #140 #117)
-#144 := [rewrite]: #143
-#141 := (iff #131 #140)
-#138 := (iff #36 #118)
-#139 := [rewrite]: #138
-#142 := [monotonicity #139]: #141
-#146 := [trans #142 #144]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#136 := (iff #39 #135)
-#133 := (iff #38 #132)
-#134 := [rewrite]: #133
-#137 := [quant-intro #134]: #136
-#154 := [trans #137 #152]: #153
-#130 := [asserted]: #39
-#155 := [mp #130 #154]: #150
-#281 := [mp~ #155 #268]: #150
-#850 := [mp #281 #849]: #845
-#809 := (not #845)
-#646 := (or #809 #805 #642)
-#631 := (or #809 #643)
-#608 := (iff #631 #646)
-#609 := [rewrite]: #608
-#647 := [quant-inst #11]: #631
-#616 := [mp #647 #609]: #646
-#549 := [unit-resolution #616 #850]: #643
-#550 := [unit-resolution #549 #548]: #805
-#551 := (or #472 #632 #781)
-#544 := [th-lemma arith triangle-eq]: #551
-#552 := [unit-resolution #544 #558]: #611
-#537 := [unit-resolution #552 #550]: #632
-#756 := (or #611 #817)
-#757 := [def-axiom]: #756
-#538 := [unit-resolution #757 #537]: #611
-#739 := (not #649)
-#740 := (or #739 #759 #801)
-#741 := [def-axiom]: #740
-#539 := [unit-resolution #741 #538 #561]: #801
-#743 := (not #801)
-#541 := (or #743 #745)
-#540 := [th-lemma arith triangle-eq]: #541
-#542 := [unit-resolution #540 #539]: #745
-#532 := (not #745)
-#533 := (or #531 #781 #590 #746 #532)
-#525 := [th-lemma arith assign-bounds 1 1 3 -3]: #533
-#534 := [unit-resolution #525 #550 #542 #570 #567]: #531
-#535 := (not #625)
-#526 := (or #535 #599)
-#536 := [th-lemma arith triangle-eq]: #526
-#517 := [unit-resolution #536 #534 #577]: false
-#518 := [lemma #517]: #746
-#819 := (* -1::Int #508)
-#493 := (+ #18 #819)
-#494 := (+ #90 #493)
-#806 := (<= #494 0::Int)
-#482 := (= #494 0::Int)
-#503 := (>= #93 0::Int)
-#880 := (not #657)
-#881 := (or #503 #569 #880)
-#882 := [th-lemma arith assign-bounds 3 -1]: #881
-#962 := [unit-resolution #882 #929 #518]: #503
-#504 := (not #503)
-#823 := (or #504 #482)
-#33 := (= #32 #29)
-#121 := (or #118 #33)
-#839 := (forall (vars (?v0 Int)) (:pat #838) #121)
-#124 := (forall (vars (?v0 Int)) #121)
-#842 := (iff #124 #839)
-#840 := (iff #121 #121)
-#841 := [refl]: #840
-#843 := [quant-intro #841]: #842
-#265 := (~ #124 #124)
-#264 := (~ #121 #121)
-#261 := [refl]: #264
-#266 := [nnf-pos #261]: #265
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#127 := (iff #35 #124)
-#108 := (not #30)
-#109 := (or #108 #33)
-#112 := (forall (vars (?v0 Int)) #109)
-#125 := (iff #112 #124)
-#122 := (iff #109 #121)
-#119 := (iff #108 #118)
-#115 := (iff #30 #117)
-#116 := [rewrite]: #115
-#120 := [monotonicity #116]: #119
-#123 := [monotonicity #120]: #122
-#126 := [quant-intro #123]: #125
-#113 := (iff #35 #112)
-#110 := (iff #34 #109)
-#111 := [rewrite]: #110
-#114 := [quant-intro #111]: #113
-#128 := [trans #114 #126]: #127
-#106 := [asserted]: #35
-#129 := [mp #106 #128]: #124
-#262 := [mp~ #129 #266]: #124
-#844 := [mp #262 #843]: #839
-#827 := (not #839)
-#828 := (or #827 #504 #482)
-#505 := (= #508 #93)
-#509 := (or #504 #505)
-#829 := (or #827 #509)
-#481 := (iff #829 #828)
-#830 := (or #827 #823)
-#485 := (iff #830 #828)
-#821 := [rewrite]: #485
-#820 := (iff #829 #830)
-#612 := (iff #509 #823)
-#825 := (iff #505 #482)
-#488 := [rewrite]: #825
-#826 := [monotonicity #488]: #612
-#480 := [monotonicity #826]: #820
-#822 := [trans #480 #821]: #481
-#824 := [quant-inst #93]: #829
-#465 := [mp #824 #822]: #828
-#884 := [unit-resolution #465 #844]: #823
-#963 := [unit-resolution #884 #962]: #482
-#886 := (not #482)
-#887 := (or #886 #806)
-#888 := [th-lemma arith triangle-eq]: #887
-#964 := [unit-resolution #888 #963]: #806
-#890 := (not #806)
-#965 := (or #816 #569 #880 #890)
-#966 := [th-lemma arith assign-bounds 3 -1 1]: #965
-#967 := [unit-resolution #966 #964 #518 #929]: #816
-#814 := (<= #508 0::Int)
-#676 := (<= #18 0::Int)
-#968 := (or #636 #676)
-#969 := [th-lemma arith triangle-eq]: #968
-#970 := [unit-resolution #969 #956]: #676
-#744 := (<= #14 0::Int)
-#971 := [unit-resolution #557 #953]: #457
-#972 := (or #720 #744)
-#973 := [th-lemma arith triangle-eq]: #972
-#974 := [unit-resolution #973 #971]: #744
-#469 := (>= #494 0::Int)
-#894 := (or #886 #469)
-#895 := [th-lemma arith triangle-eq]: #894
-#975 := [unit-resolution #895 #963]: #469
-#897 := (not #469)
-#977 := (not #676)
-#976 := (not #744)
-#978 := (or #814 #976 #977 #897)
-#979 := [th-lemma arith assign-bounds -3 -1 1]: #978
-#980 := [unit-resolution #979 #975 #974 #970]: #814
-#982 := (not #816)
-#981 := (not #814)
-#983 := (or #470 #981 #982)
-#984 := [th-lemma arith triangle-eq]: #983
-#985 := [unit-resolution #984 #980 #967]: #470
-#491 := (= #93 #508)
-#492 := (+ #93 #819)
-#490 := (<= #492 0::Int)
-#891 := (or #490 #890)
-#892 := [th-lemma arith assign-bounds -1]: #891
-#986 := [unit-resolution #892 #964]: #490
-#501 := (>= #492 0::Int)
-#898 := (or #501 #897)
-#899 := [th-lemma arith assign-bounds -1]: #898
-#987 := [unit-resolution #899 #975]: #501
-#902 := (not #501)
-#901 := (not #490)
-#903 := (or #491 #901 #902)
-#904 := [th-lemma arith triangle-eq]: #903
-#988 := [unit-resolution #904 #987 #986]: #491
-#992 := [trans #988 #985]: #991
-#994 := [trans #992 #990]: #993
-#996 := [monotonicity #994]: #995
-#998 := [symm #996]: #997
-#450 := (= f3 #418)
-#433 := [symm #562]: #450
-#999 := [trans #433 #998]: #99
-#102 := (not #99)
-#15 := (* #14 3::Int)
-#19 := (+ #15 #18)
-#20 := (f4 f5 #19)
-#21 := (= f3 #20)
-#22 := (not #21)
-#103 := (iff #22 #102)
-#100 := (iff #21 #99)
-#97 := (= #20 #96)
-#94 := (= #19 #93)
-#91 := (= #15 #90)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#104 := [monotonicity #101]: #103
-#89 := [asserted]: #22
-#107 := [mp #89 #104]: #102
-#1000 := [unit-resolution #107 #999]: false
-#1001 := [lemma #1000]: #735
-#907 := (or #472 #759)
-#751 := (<= #800 0::Int)
-#426 := [hypothesis]: #611
-#429 := [hypothesis]: #735
-#430 := [unit-resolution #560 #429]: #649
-#431 := [unit-resolution #741 #430 #426]: #801
-#427 := (or #743 #751)
-#432 := [th-lemma arith triangle-eq]: #427
-#419 := [unit-resolution #432 #431]: #751
-#681 := (<= #717 0::Int)
-#422 := (or #472 #702)
-#630 := (or #653 #472 #702)
-#635 := [def-axiom]: #630
-#420 := [unit-resolution #635 #421]: #422
-#423 := [unit-resolution #420 #429]: #702
-#651 := (not #702)
-#658 := (or #651 #759 #728)
-#617 := [def-axiom]: #658
-#865 := [unit-resolution #617 #423 #426]: #728
-#652 := (not #728)
-#866 := (or #652 #681)
-#867 := [th-lemma arith triangle-eq]: #866
-#868 := [unit-resolution #867 #865]: #681
-#869 := [unit-resolution #540 #431]: #745
-#682 := (>= #717 0::Int)
-#870 := (or #652 #682)
-#871 := [th-lemma arith triangle-eq]: #870
-#872 := [unit-resolution #871 #865]: #682
-#601 := (>= #750 0::Int)
-#873 := (or false #601)
-#874 := [th-lemma arith]: #873
-#875 := [unit-resolution #874 #87]: #601
-#458 := (not #682)
-#876 := (not #601)
-#877 := (or #657 #876 #458)
-#878 := [th-lemma arith assign-bounds 1 1]: #877
-#879 := [unit-resolution #878 #872 #875]: #657
-#883 := [unit-resolution #882 #879 #518]: #503
-#885 := [unit-resolution #884 #883]: #482
-#889 := [unit-resolution #888 #885]: #806
-#893 := [unit-resolution #892 #889]: #490
-#896 := [unit-resolution #895 #885]: #469
-#900 := [unit-resolution #899 #896]: #501
-#905 := [unit-resolution #904 #900 #893]: #491
-#460 := (not #751)
-#462 := (not #681)
-#443 := (not #491)
-#428 := (or #443 #458 #532 #462 #460)
-#519 := (f4 f5 #508)
-#511 := (= #519 #96)
-#512 := (or #495 #511)
-#522 := [quant-inst #96]: #512
-#473 := [unit-resolution #522 #837]: #511
-#440 := (= f3 #519)
-#436 := (= #418 #519)
-#449 := (= #11 #508)
-#474 := [hypothesis]: #491
-#484 := (= #11 #93)
-#486 := (* -1::Int #93)
-#487 := (+ #11 #486)
-#468 := (>= #487 0::Int)
-#475 := [hypothesis]: #751
-#600 := (>= #610 0::Int)
-#476 := (or #535 #600)
-#477 := [th-lemma arith triangle-eq]: #476
-#478 := [unit-resolution #477 #577]: #600
-#467 := [hypothesis]: #681
-#479 := (not #600)
-#463 := (or #468 #479 #460 #462)
-#461 := [th-lemma arith assign-bounds -1 3 1]: #463
-#464 := [unit-resolution #461 #467 #478 #475]: #468
-#466 := (<= #487 0::Int)
-#452 := [hypothesis]: #745
-#454 := [unit-resolution #536 #577]: #599
-#455 := [hypothesis]: #682
-#453 := (or #466 #531 #532 #458)
-#459 := [th-lemma arith assign-bounds -1 3 1]: #453
-#434 := [unit-resolution #459 #455 #454 #452]: #466
-#439 := (not #468)
-#438 := (not #466)
-#444 := (or #484 #438 #439)
-#446 := [th-lemma arith triangle-eq]: #444
-#447 := [unit-resolution #446 #434 #464]: #484
-#445 := [trans #447 #474]: #449
-#437 := [monotonicity #445]: #436
-#441 := [trans #433 #437]: #440
-#442 := [trans #441 #473]: #99
-#435 := [unit-resolution #107 #442]: false
-#425 := [lemma #435]: #428
-#906 := [unit-resolution #425 #905 #872 #869 #868 #419]: false
-#908 := [lemma #906]: #907
-#1002 := [unit-resolution #908 #1001]: #759
-#960 := (or #472 #781)
-#958 := [hypothesis]: #805
-#574 := [hypothesis]: #632
-#575 := [unit-resolution #757 #574]: #611
-#578 := [unit-resolution #908 #575]: #472
-#579 := (or #735 #817)
-#583 := [th-lemma arith triangle-eq]: #579
-#496 := [unit-resolution #583 #578 #574]: false
-#497 := [lemma #496]: #817
-#959 := [unit-resolution #544 #429 #497 #958]: false
-#961 := [lemma #959]: #960
-#1003 := [unit-resolution #961 #1001]: #781
-#758 := (or #611 #805)
-#754 := [def-axiom]: #758
-[unit-resolution #754 #1003 #1002]: false
-unsat
-eda44a5672e0665e25283a25dd7f355a8eaca7e9 62 0
-#2 := false
-#22 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#56 := -1::Int
-#57 := (* -1::Int #11)
-#58 := (+ #9 #57)
-#59 := (<= #58 0::Int)
-#62 := (if #59 #9 #11)
-#70 := (* -1::Int #62)
-#253 := (+ #11 #70)
-#602 := (>= #253 0::Int)
-#290 := (= #11 #62)
-#206 := (not #59)
-#205 := (= #9 #62)
-#598 := (not #205)
-#71 := (+ #9 #70)
-#69 := (>= #71 0::Int)
-#75 := (not #69)
-#12 := (<= #9 #11)
-#13 := (if #12 #9 #11)
-#14 := (<= #13 #9)
-#15 := (not #14)
-#76 := (iff #15 #75)
-#73 := (iff #14 #69)
-#65 := (<= #62 #9)
-#68 := (iff #65 #69)
-#72 := [rewrite]: #68
-#66 := (iff #14 #65)
-#63 := (= #13 #62)
-#60 := (iff #12 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#74 := [trans #67 #72]: #73
-#77 := [monotonicity #74]: #76
-#53 := [asserted]: #15
-#78 := [mp #53 #77]: #75
-#594 := [hypothesis]: #205
-#599 := (or #598 #69)
-#600 := [th-lemma arith triangle-eq]: #599
-#595 := [unit-resolution #600 #594 #78]: false
-#601 := [lemma #595]: #598
-#291 := (or #206 #205)
-#292 := [def-axiom]: #291
-#604 := [unit-resolution #292 #601]: #206
-#283 := (or #59 #290)
-#294 := [def-axiom]: #283
-#244 := [unit-resolution #294 #604]: #290
-#245 := (not #290)
-#605 := (or #245 #602)
-#603 := [th-lemma arith triangle-eq]: #605
-#606 := [unit-resolution #603 #244]: #602
-[th-lemma arith farkas 1 1 1 #78 #604 #606]: false
-unsat
-97b1f19af776d1080cad185bb98c38caf958ba23 62 0
-#2 := false
-#22 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#56 := -1::Int
-#57 := (* -1::Int #11)
-#58 := (+ #9 #57)
-#59 := (<= #58 0::Int)
-#62 := (if #59 #9 #11)
-#69 := (* -1::Int #62)
-#70 := (+ #11 #69)
-#68 := (>= #70 0::Int)
-#75 := (not #68)
-#12 := (<= #9 #11)
-#13 := (if #12 #9 #11)
-#14 := (<= #13 #11)
-#15 := (not #14)
-#76 := (iff #15 #75)
-#73 := (iff #14 #68)
-#65 := (<= #62 #11)
-#71 := (iff #65 #68)
-#72 := [rewrite]: #71
-#66 := (iff #14 #65)
-#63 := (= #13 #62)
-#60 := (iff #12 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#74 := [trans #67 #72]: #73
-#77 := [monotonicity #74]: #76
-#53 := [asserted]: #15
-#78 := [mp #53 #77]: #75
-#290 := (= #11 #62)
-#206 := (not #59)
-#599 := [hypothesis]: #59
-#253 := (+ #9 #69)
-#598 := (>= #253 0::Int)
-#205 := (= #9 #62)
-#291 := (or #206 #205)
-#292 := [def-axiom]: #291
-#600 := [unit-resolution #292 #599]: #205
-#595 := (not #205)
-#601 := (or #595 #598)
-#239 := [th-lemma arith triangle-eq]: #601
-#602 := [unit-resolution #239 #600]: #598
-#604 := [th-lemma arith farkas -1 1 1 #602 #78 #599]: false
-#244 := [lemma #604]: #206
-#283 := (or #59 #290)
-#294 := [def-axiom]: #283
-#245 := [unit-resolution #294 #244]: #290
-#605 := (not #290)
-#603 := (or #605 #68)
-#606 := [th-lemma arith triangle-eq]: #603
-[unit-resolution #606 #245 #78]: false
-unsat
-3471bb506d588114610f4dc57e0a4000d67c30d5 238 0
-#2 := false
-#23 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#57 := -1::Int
-#58 := (* -1::Int #11)
-#59 := (+ #9 #58)
-#60 := (<= #59 0::Int)
-#63 := (if #60 #9 #11)
-#72 := (* -1::Int #63)
-#255 := (+ #9 #72)
-#600 := (>= #255 0::Int)
-#607 := (not #600)
-#617 := (>= #11 0::Int)
-#586 := (= #11 0::Int)
-decl f7 :: (-> S4 Int S3)
-decl f8 :: S4
-#17 := f8
-#295 := (f7 f8 #11)
-#618 := (f3 f4 #295)
-#271 := (= #618 0::Int)
-#592 := (not #617)
-#439 := [hypothesis]: #592
-#612 := (or #617 #271)
-#24 := (:var 0 Int)
-#26 := (f7 f8 #24)
-#628 := (pattern #26)
-#27 := (f3 f4 #26)
-#32 := (= #27 0::Int)
-#89 := (>= #24 0::Int)
-#120 := (or #89 #32)
-#635 := (forall (vars (?v0 Int)) (:pat #628) #120)
-#123 := (forall (vars (?v0 Int)) #120)
-#638 := (iff #123 #635)
-#636 := (iff #120 #120)
-#637 := [refl]: #636
-#639 := [quant-intro #637]: #638
-#136 := (~ #123 #123)
-#144 := (~ #120 #120)
-#145 := [refl]: #144
-#137 := [nnf-pos #145]: #136
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#126 := (iff #34 #123)
-#104 := (not #31)
-#105 := (or #104 #32)
-#108 := (forall (vars (?v0 Int)) #105)
-#124 := (iff #108 #123)
-#121 := (iff #105 #120)
-#118 := (iff #104 #89)
-#91 := (not #89)
-#113 := (not #91)
-#116 := (iff #113 #89)
-#117 := [rewrite]: #116
-#114 := (iff #104 #113)
-#111 := (iff #31 #91)
-#112 := [rewrite]: #111
-#115 := [monotonicity #112]: #114
-#119 := [trans #115 #117]: #118
-#122 := [monotonicity #119]: #121
-#125 := [quant-intro #122]: #124
-#109 := (iff #34 #108)
-#106 := (iff #33 #105)
-#107 := [rewrite]: #106
-#110 := [quant-intro #107]: #109
-#127 := [trans #110 #125]: #126
-#103 := [asserted]: #34
-#128 := [mp #103 #127]: #123
-#146 := [mp~ #128 #137]: #123
-#640 := [mp #146 #639]: #635
-#619 := (not #635)
-#259 := (or #619 #617 #271)
-#260 := (or #619 #612)
-#262 := (iff #260 #259)
-#598 := [rewrite]: #262
-#261 := [quant-inst #11]: #260
-#599 := [mp #261 #598]: #259
-#304 := [unit-resolution #599 #640]: #612
-#454 := [unit-resolution #304 #439]: #271
-#300 := (= #11 #618)
-#584 := (= f6 #295)
-#299 := (= #295 f6)
-#18 := (:var 0 S3)
-#19 := (f3 f4 #18)
-#621 := (pattern #19)
-#20 := (f7 f8 #19)
-#21 := (= #20 #18)
-#622 := (forall (vars (?v0 S3)) (:pat #621) #21)
-#22 := (forall (vars (?v0 S3)) #21)
-#625 := (iff #22 #622)
-#623 := (iff #21 #21)
-#624 := [refl]: #623
-#626 := [quant-intro #624]: #625
-#142 := (~ #22 #22)
-#140 := (~ #21 #21)
-#141 := [refl]: #140
-#143 := [nnf-pos #141]: #142
-#55 := [asserted]: #22
-#132 := [mp~ #55 #143]: #22
-#627 := [mp #132 #626]: #622
-#278 := (not #622)
-#609 := (or #278 #299)
-#283 := [quant-inst #10]: #609
-#306 := [unit-resolution #283 #627]: #299
-#585 := [symm #306]: #584
-#582 := [monotonicity #585]: #300
-#456 := [trans #582 #454]: #586
-#457 := (not #586)
-#450 := (or #457 #617)
-#458 := [th-lemma arith triangle-eq]: #450
-#459 := [unit-resolution #458 #439 #456]: false
-#460 := [lemma #459]: #617
-#555 := (or #592 #607)
-#73 := (+ #11 #72)
-#74 := (+ #9 #73)
-#70 := (>= #74 0::Int)
-#77 := (not #70)
-#14 := (+ #9 #11)
-#12 := (<= #9 #11)
-#13 := (if #12 #9 #11)
-#15 := (<= #13 #14)
-#16 := (not #15)
-#78 := (iff #16 #77)
-#75 := (iff #15 #70)
-#66 := (<= #63 #14)
-#69 := (iff #66 #70)
-#71 := [rewrite]: #69
-#67 := (iff #15 #66)
-#64 := (= #13 #63)
-#61 := (iff #12 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#68 := [monotonicity #65]: #67
-#76 := [trans #68 #71]: #75
-#79 := [monotonicity #76]: #78
-#54 := [asserted]: #16
-#80 := [mp #54 #79]: #77
-#589 := (or #592 #607 #70)
-#593 := [th-lemma arith assign-bounds 1 -1]: #589
-#552 := [unit-resolution #593 #80]: #555
-#556 := [unit-resolution #552 #460]: #607
-#207 := (= #9 #63)
-#297 := (f7 f8 #9)
-#402 := (f3 f4 #297)
-#284 := (= #402 0::Int)
-#405 := (iff #284 #207)
-#445 := (iff #207 #284)
-#562 := (= #63 0::Int)
-#424 := (>= #73 0::Int)
-#292 := (= #11 #63)
-#580 := (iff #284 #292)
-#574 := (iff #292 #284)
-#587 := (= 0::Int #402)
-#578 := (iff #587 #284)
-#573 := [commutativity]: #578
-#576 := (iff #292 #587)
-#314 := (= #63 #402)
-#591 := (= #9 #402)
-#319 := (= f5 #297)
-#298 := (= #297 f5)
-#613 := (or #278 #298)
-#615 := [quant-inst #8]: #613
-#318 := [unit-resolution #615 #627]: #298
-#320 := [symm #318]: #319
-#313 := [monotonicity #320]: #591
-#214 := (= #63 #9)
-#601 := (not #292)
-#602 := [hypothesis]: #601
-#285 := (or #60 #292)
-#296 := [def-axiom]: #285
-#597 := [unit-resolution #296 #602]: #60
-#208 := (not #60)
-#293 := (or #208 #207)
-#294 := [def-axiom]: #293
-#603 := [unit-resolution #294 #597]: #207
-#590 := [symm #603]: #214
-#588 := [trans #590 #313]: #314
-#241 := (not #207)
-#604 := (or #241 #600)
-#606 := [th-lemma arith triangle-eq]: #604
-#246 := [unit-resolution #606 #603]: #600
-#303 := [unit-resolution #593 #246 #80]: #592
-#305 := [unit-resolution #304 #303]: #271
-#583 := [trans #582 #305]: #586
-#577 := [monotonicity #583 #588]: #576
-#579 := [trans #577 #573]: #574
-#575 := [symm #579]: #580
-#272 := (>= #9 0::Int)
-#247 := (not #272)
-#605 := (or #247 #208 #607 #70)
-#608 := [th-lemma arith assign-bounds -1 1 -1]: #605
-#594 := [unit-resolution #608 #597 #80 #246]: #247
-#616 := (or #272 #284)
-#614 := (or #619 #272 #284)
-#620 := (or #619 #616)
-#270 := (iff #620 #614)
-#275 := [rewrite]: #270
-#610 := [quant-inst #9]: #620
-#611 := [mp #610 #275]: #614
-#595 := [unit-resolution #611 #640]: #616
-#317 := [unit-resolution #595 #594]: #284
-#581 := [mp #317 #575]: #292
-#422 := [unit-resolution #602 #581]: false
-#423 := [lemma #422]: #292
-#567 := (or #601 #424)
-#568 := [th-lemma arith triangle-eq]: #567
-#569 := [unit-resolution #568 #423]: #424
-#566 := [hypothesis]: #241
-#572 := [unit-resolution #294 #566]: #208
-#563 := (not #424)
-#401 := (or #592 #563 #60 #70)
-#403 := [th-lemma arith assign-bounds 1 1 1]: #401
-#404 := [unit-resolution #403 #572 #80 #569]: #592
-#557 := [unit-resolution #304 #404]: #271
-#561 := (= #63 #618)
-#558 := (= #63 #11)
-#560 := [symm #423]: #558
-#559 := [trans #560 #582]: #561
-#444 := [trans #559 #557]: #562
-#446 := [monotonicity #313 #444]: #445
-#553 := [symm #446]: #405
-#564 := (or #247 #563 #70)
-#570 := [th-lemma arith assign-bounds 1 -1]: #564
-#571 := [unit-resolution #570 #569 #80]: #247
-#565 := [unit-resolution #595 #571]: #284
-#455 := [mp #565 #553]: #207
-#550 := [unit-resolution #566 #455]: false
-#551 := [lemma #550]: #207
-[unit-resolution #606 #551 #556]: false
-unsat
-fe9dfffa2627f52b211026454fe85b424a23c79e 109 0
-#2 := false
-#28 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#13 := f7
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 f7)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#67 := -1::Int
-#76 := (* -1::Int #14)
-#86 := (+ #11 #76)
-#87 := (<= #86 0::Int)
-#90 := (if #87 #11 #14)
-#98 := (* -1::Int #90)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#99 := (+ #9 #98)
-#97 := (>= #99 0::Int)
-#96 := (not #97)
-#77 := (+ #9 #76)
-#75 := (>= #77 0::Int)
-#74 := (not #75)
-#70 := (* -1::Int #11)
-#71 := (+ #9 #70)
-#69 := (>= #71 0::Int)
-#68 := (not #69)
-#80 := (and #68 #74)
-#83 := (not #80)
-#104 := (or #83 #96)
-#107 := (not #104)
-#17 := (<= #11 #14)
-#18 := (if #17 #11 #14)
-#19 := (< #9 #18)
-#15 := (< #9 #14)
-#12 := (< #9 #11)
-#16 := (and #12 #15)
-#20 := (implies #16 #19)
-#21 := (not #20)
-#110 := (iff #21 #107)
-#60 := (not #16)
-#61 := (or #60 #19)
-#64 := (not #61)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #19 #96)
-#93 := (< #9 #90)
-#100 := (iff #93 #96)
-#101 := [rewrite]: #100
-#94 := (iff #19 #93)
-#91 := (= #18 #90)
-#88 := (iff #17 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#95 := [monotonicity #92]: #94
-#103 := [trans #95 #101]: #102
-#84 := (iff #60 #83)
-#81 := (iff #16 #80)
-#78 := (iff #15 #74)
-#79 := [rewrite]: #78
-#72 := (iff #12 #68)
-#73 := [rewrite]: #72
-#82 := [monotonicity #73 #79]: #81
-#85 := [monotonicity #82]: #84
-#106 := [monotonicity #85 #103]: #105
-#109 := [monotonicity #106]: #108
-#65 := (iff #21 #64)
-#62 := (iff #20 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#111 := [trans #66 #109]: #110
-#59 := [asserted]: #21
-#112 := [mp #59 #111]: #107
-#116 := [not-or-elim #112]: #97
-#113 := [not-or-elim #112]: #80
-#115 := [and-elim #113]: #74
-#633 := (+ #14 #98)
-#630 := (<= #633 0::Int)
-#330 := (= #14 #90)
-#246 := (not #87)
-#245 := (= #11 #90)
-#628 := (not #245)
-#642 := (+ #11 #98)
-#644 := (<= #642 0::Int)
-#357 := (not #644)
-#114 := [and-elim #113]: #68
-#355 := [hypothesis]: #644
-#356 := [th-lemma arith farkas -1 -1 1 #355 #114 #116]: false
-#358 := [lemma #356]: #357
-#252 := [hypothesis]: #245
-#629 := (or #628 #644)
-#351 := [th-lemma arith triangle-eq]: #629
-#352 := [unit-resolution #351 #252 #358]: false
-#626 := [lemma #352]: #628
-#331 := (or #246 #245)
-#332 := [def-axiom]: #331
-#631 := [unit-resolution #332 #626]: #246
-#323 := (or #87 #330)
-#334 := [def-axiom]: #323
-#341 := [unit-resolution #334 #631]: #330
-#342 := (not #330)
-#343 := (or #342 #630)
-#344 := [th-lemma arith triangle-eq]: #343
-#622 := [unit-resolution #344 #341]: #630
-[th-lemma arith farkas -1 -1 1 #622 #115 #116]: false
-unsat
-5cb55092de9089ed8a3391dc81cfc498bef42803 151 0
-#2 := false
-decl f5 :: S3
-#8 := f5
-decl f6 :: S3
-#10 := f6
-#24 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#58 := -1::Int
-#59 := (* -1::Int #11)
-#9 := (f3 f4 f5)
-#60 := (+ #9 #59)
-#68 := (>= #60 0::Int)
-#70 := (if #68 f6 f5)
-#61 := (<= #60 0::Int)
-#64 := (if #61 f5 f6)
-#73 := (= #64 #70)
-#296 := (= f6 #70)
-#560 := (iff #296 #73)
-#557 := (iff #73 #296)
-#607 := (= #64 f6)
-#291 := (= f6 #64)
-#207 := (not #61)
-#206 := (= f5 #64)
-#563 := (not #206)
-#566 := (iff #206 #73)
-#423 := (iff #73 #206)
-#579 := (= #64 f5)
-#421 := (iff #579 #206)
-#422 := [commutativity]: #421
-#574 := (iff #73 #579)
-#304 := (= #70 f5)
-#297 := (= f5 #70)
-#598 := (not #297)
-#599 := [hypothesis]: #598
-#612 := (or #68 #297)
-#614 := [def-axiom]: #612
-#245 := [unit-resolution #614 #599]: #68
-#294 := (not #68)
-#298 := (or #294 #296)
-#277 := [def-axiom]: #298
-#246 := [unit-resolution #277 #245]: #296
-#575 := (= f5 f6)
-decl f7 :: (-> S4 Int S3)
-decl f8 :: S4
-#18 := f8
-#608 := (f7 f8 #11)
-#282 := (= #608 f6)
-#19 := (:var 0 S3)
-#20 := (f3 f4 #19)
-#620 := (pattern #20)
-#21 := (f7 f8 #20)
-#22 := (= #21 #19)
-#621 := (forall (vars (?v0 S3)) (:pat #620) #22)
-#23 := (forall (vars (?v0 S3)) #22)
-#624 := (iff #23 #621)
-#622 := (iff #22 #22)
-#623 := [refl]: #622
-#625 := [quant-intro #623]: #624
-#141 := (~ #23 #23)
-#139 := (~ #22 #22)
-#140 := [refl]: #139
-#142 := [nnf-pos #140]: #141
-#56 := [asserted]: #23
-#131 := [mp~ #56 #142]: #23
-#626 := [mp #131 #625]: #621
-#283 := (not #621)
-#613 := (or #283 #282)
-#619 := [quant-inst #10]: #613
-#302 := [unit-resolution #619 #626]: #282
-#582 := (= f5 #608)
-#271 := (f7 f8 #9)
-#581 := (= #271 #608)
-#305 := (= #608 #271)
-#588 := (= #11 #9)
-#587 := (= #9 #11)
-#213 := (not #291)
-#76 := (not #73)
-#589 := (iff #76 #213)
-#318 := (iff #73 #291)
-#316 := (iff #607 #291)
-#317 := [commutativity]: #316
-#593 := (iff #73 #607)
-#606 := (= #70 f6)
-#604 := [symm #246]: #606
-#594 := [monotonicity #604]: #593
-#319 := [trans #594 #317]: #318
-#590 := [monotonicity #319]: #589
-#14 := (<= #11 #9)
-#15 := (if #14 f6 f5)
-#12 := (<= #9 #11)
-#13 := (if #12 f5 f6)
-#16 := (= #13 #15)
-#17 := (not #16)
-#77 := (iff #17 #76)
-#74 := (iff #16 #73)
-#71 := (= #15 #70)
-#67 := (iff #14 #68)
-#69 := [rewrite]: #67
-#72 := [monotonicity #69]: #71
-#65 := (= #13 #64)
-#62 := (iff #12 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#75 := [monotonicity #66 #72]: #74
-#78 := [monotonicity #75]: #77
-#55 := [asserted]: #17
-#79 := [mp #55 #78]: #76
-#312 := [mp #79 #590]: #213
-#284 := (or #61 #291)
-#295 := [def-axiom]: #284
-#313 := [unit-resolution #295 #312]: #61
-#591 := [th-lemma arith eq-propagate 1 1 #245 #313]: #587
-#592 := [symm #591]: #588
-#583 := [monotonicity #592]: #305
-#585 := [symm #583]: #581
-#584 := (= f5 #271)
-#401 := (= #271 f5)
-#615 := (or #283 #401)
-#616 := [quant-inst #8]: #615
-#605 := [unit-resolution #616 #626]: #401
-#299 := [symm #605]: #584
-#586 := [trans #299 #585]: #582
-#576 := [trans #586 #302]: #575
-#577 := [trans #576 #246]: #297
-#572 := [unit-resolution #599 #577]: false
-#573 := [lemma #572]: #297
-#578 := [symm #573]: #304
-#580 := [monotonicity #578]: #574
-#565 := [trans #580 #422]: #423
-#567 := [symm #565]: #566
-#303 := [hypothesis]: #206
-#568 := [mp #303 #567]: #73
-#562 := [unit-resolution #79 #568]: false
-#569 := [lemma #562]: #563
-#292 := (or #207 #206)
-#293 := [def-axiom]: #292
-#570 := [unit-resolution #293 #569]: #207
-#403 := [unit-resolution #295 #570]: #291
-#556 := [symm #403]: #607
-#559 := [monotonicity #556]: #557
-#558 := [symm #559]: #560
-#564 := (or #68 #61)
-#571 := [th-lemma arith farkas 1 1]: #564
-#400 := [unit-resolution #571 #570]: #68
-#402 := [unit-resolution #277 #400]: #296
-#561 := [mp #402 #558]: #73
-[unit-resolution #79 #561]: false
-unsat
-dfbdf9498a779cc07990188555d390512d351434 141 0
-#2 := false
-#10 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: (-> S4 Int S3)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-decl f7 :: S4
-#12 := f7
-#272 := (f6 f7 #9)
-#570 := (f3 f4 #272)
-#277 := (= #570 0::Int)
-#543 := (= #9 0::Int)
-#11 := (<= #9 0::Int)
-#13 := (f6 f7 0::Int)
-#14 := (if #11 f5 #13)
-#266 := (= #13 #14)
-#567 := (not #266)
-#15 := (= #14 #13)
-#16 := (not #15)
-#564 := (iff #16 #567)
-#293 := (iff #15 #266)
-#294 := [commutativity]: #293
-#568 := [monotonicity #294]: #564
-#52 := [asserted]: #16
-#278 := [mp #52 #568]: #567
-#259 := (or #11 #266)
-#270 := [def-axiom]: #259
-#279 := [unit-resolution #270 #278]: #11
-#569 := (>= #9 0::Int)
-#541 := (not #277)
-#181 := (= f5 #14)
-#182 := (not #11)
-#267 := (or #182 #181)
-#268 := [def-axiom]: #267
-#280 := [unit-resolution #268 #279]: #181
-#556 := (= #13 f5)
-#269 := (= #272 f5)
-#17 := (:var 0 S3)
-#18 := (f3 f4 #17)
-#596 := (pattern #18)
-#19 := (f6 f7 #18)
-#20 := (= #19 #17)
-#597 := (forall (vars (?v0 S3)) (:pat #596) #20)
-#21 := (forall (vars (?v0 S3)) #20)
-#600 := (iff #21 #597)
-#598 := (iff #20 #20)
-#599 := [refl]: #598
-#601 := [quant-intro #599]: #600
-#116 := (~ #21 #21)
-#114 := (~ #20 #20)
-#115 := [refl]: #114
-#117 := [nnf-pos #115]: #116
-#53 := [asserted]: #21
-#106 := [mp~ #53 #117]: #21
-#602 := [mp #106 #601]: #597
-#588 := (not #597)
-#590 := (or #588 #269)
-#246 := [quant-inst #8]: #590
-#281 := [unit-resolution #246 #602]: #269
-#549 := (= #13 #272)
-#553 := (= 0::Int #9)
-#551 := (= #570 #9)
-#557 := (= #9 #570)
-#560 := (= f5 #272)
-#274 := [symm #281]: #560
-#561 := [monotonicity #274]: #557
-#552 := [symm #561]: #551
-#558 := (= 0::Int #570)
-#559 := [hypothesis]: #277
-#562 := [symm #559]: #558
-#548 := [trans #562 #552]: #553
-#554 := [monotonicity #548]: #549
-#397 := [trans #554 #281]: #556
-#398 := [trans #397 #280]: #266
-#399 := [unit-resolution #278 #398]: false
-#542 := [lemma #399]: #541
-#292 := (or #569 #277)
-#22 := (:var 0 Int)
-#24 := (f6 f7 #22)
-#603 := (pattern #24)
-#25 := (f3 f4 #24)
-#30 := (= #25 0::Int)
-#64 := (>= #22 0::Int)
-#94 := (or #64 #30)
-#610 := (forall (vars (?v0 Int)) (:pat #603) #94)
-#97 := (forall (vars (?v0 Int)) #94)
-#613 := (iff #97 #610)
-#611 := (iff #94 #94)
-#612 := [refl]: #611
-#614 := [quant-intro #612]: #613
-#110 := (~ #97 #97)
-#118 := (~ #94 #94)
-#119 := [refl]: #118
-#111 := [nnf-pos #119]: #110
-#29 := (< #22 0::Int)
-#31 := (implies #29 #30)
-#32 := (forall (vars (?v0 Int)) #31)
-#100 := (iff #32 #97)
-#78 := (not #29)
-#79 := (or #78 #30)
-#82 := (forall (vars (?v0 Int)) #79)
-#98 := (iff #82 #97)
-#95 := (iff #79 #94)
-#92 := (iff #78 #64)
-#65 := (not #64)
-#87 := (not #65)
-#90 := (iff #87 #64)
-#91 := [rewrite]: #90
-#88 := (iff #78 #87)
-#85 := (iff #29 #65)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#93 := [trans #89 #91]: #92
-#96 := [monotonicity #93]: #95
-#99 := [quant-intro #96]: #98
-#83 := (iff #32 #82)
-#80 := (iff #31 #79)
-#81 := [rewrite]: #80
-#84 := [quant-intro #81]: #83
-#101 := [trans #84 #99]: #100
-#77 := [asserted]: #32
-#102 := [mp #77 #101]: #97
-#120 := [mp~ #102 #111]: #97
-#615 := [mp #120 #614]: #610
-#295 := (not #610)
-#188 := (or #295 #569 #277)
-#565 := (or #295 #292)
-#288 := (iff #565 #188)
-#289 := [rewrite]: #288
-#566 := [quant-inst #9]: #565
-#563 := [mp #566 #289]: #188
-#555 := [unit-resolution #563 #615]: #292
-#550 := [unit-resolution #555 #542]: #569
-#544 := [th-lemma arith eq-propagate 0 0 #550 #279]: #543
-#538 := [monotonicity #281]: #551
-#539 := [trans #538 #544]: #277
-[unit-resolution #542 #539]: false
-unsat
-812e594047adacc8648774584661958380724a55 62 0
-#2 := false
-#22 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#56 := -1::Int
-#57 := (* -1::Int #11)
-#58 := (+ #9 #57)
-#59 := (<= #58 0::Int)
-#62 := (if #59 #11 #9)
-#68 := (* -1::Int #62)
-#69 := (+ #9 #68)
-#70 := (<= #69 0::Int)
-#75 := (not #70)
-#12 := (<= #9 #11)
-#13 := (if #12 #11 #9)
-#14 := (<= #9 #13)
-#15 := (not #14)
-#76 := (iff #15 #75)
-#73 := (iff #14 #70)
-#65 := (<= #9 #62)
-#71 := (iff #65 #70)
-#72 := [rewrite]: #71
-#66 := (iff #14 #65)
-#63 := (= #13 #62)
-#60 := (iff #12 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#74 := [trans #67 #72]: #73
-#77 := [monotonicity #74]: #76
-#53 := [asserted]: #15
-#78 := [mp #53 #77]: #75
-#290 := (= #9 #62)
-#206 := (not #59)
-#599 := [hypothesis]: #59
-#253 := (+ #11 #68)
-#594 := (<= #253 0::Int)
-#205 := (= #11 #62)
-#291 := (or #206 #205)
-#292 := [def-axiom]: #291
-#600 := [unit-resolution #292 #599]: #205
-#595 := (not #205)
-#601 := (or #595 #594)
-#239 := [th-lemma arith triangle-eq]: #601
-#602 := [unit-resolution #239 #600]: #594
-#604 := [th-lemma arith farkas 1 -1 1 #602 #78 #599]: false
-#244 := [lemma #604]: #206
-#283 := (or #59 #290)
-#294 := [def-axiom]: #283
-#245 := [unit-resolution #294 #244]: #290
-#605 := (not #290)
-#603 := (or #605 #70)
-#606 := [th-lemma arith triangle-eq]: #603
-[unit-resolution #606 #245 #78]: false
-unsat
-4d3aa2ede700d1c10ea9ca78d1cd42eb1d9ac7f6 62 0
-#2 := false
-#22 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#56 := -1::Int
-#59 := (* -1::Int #11)
-#60 := (+ #9 #59)
-#58 := (>= #60 0::Int)
-#62 := (if #58 #9 #11)
-#68 := (* -1::Int #62)
-#253 := (+ #11 #68)
-#239 := (<= #253 0::Int)
-#290 := (= #11 #62)
-#206 := (not #58)
-#205 := (= #9 #62)
-#598 := (not #205)
-#69 := (+ #9 #68)
-#70 := (<= #69 0::Int)
-#75 := (not #70)
-#12 := (<= #11 #9)
-#13 := (if #12 #9 #11)
-#14 := (<= #9 #13)
-#15 := (not #14)
-#76 := (iff #15 #75)
-#73 := (iff #14 #70)
-#65 := (<= #9 #62)
-#71 := (iff #65 #70)
-#72 := [rewrite]: #71
-#66 := (iff #14 #65)
-#63 := (= #13 #62)
-#57 := (iff #12 #58)
-#61 := [rewrite]: #57
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#74 := [trans #67 #72]: #73
-#77 := [monotonicity #74]: #76
-#53 := [asserted]: #15
-#78 := [mp #53 #77]: #75
-#594 := [hypothesis]: #205
-#599 := (or #598 #70)
-#600 := [th-lemma arith triangle-eq]: #599
-#595 := [unit-resolution #600 #594 #78]: false
-#601 := [lemma #595]: #598
-#291 := (or #206 #205)
-#292 := [def-axiom]: #291
-#604 := [unit-resolution #292 #601]: #206
-#283 := (or #58 #290)
-#294 := [def-axiom]: #283
-#244 := [unit-resolution #294 #604]: #290
-#245 := (not #290)
-#605 := (or #245 #239)
-#603 := [th-lemma arith triangle-eq]: #605
-#606 := [unit-resolution #603 #244]: #239
-[th-lemma arith farkas 1 1 1 #78 #604 #606]: false
-unsat
-231f97166ce8df86a8011ff98d1fa9f68fa8398e 409 0
-#2 := false
-#29 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: (-> S4 Int S3)
-decl f8 :: S3
-#11 := f8
-decl f4 :: S2
-#7 := f4
-#12 := (f3 f4 f8)
-decl f7 :: S3
-#9 := f7
-#10 := (f3 f4 f7)
-#61 := -1::Int
-#72 := (* -1::Int #10)
-#73 := (+ #72 #12)
-decl f6 :: S4
-#8 := f6
-#76 := (f5 f6 #73)
-#79 := (f3 f4 #76)
-#62 := (* -1::Int #12)
-#341 := (+ #62 #79)
-#619 := (+ #10 #341)
-#459 := (<= #619 0::Int)
-#620 := (= #619 0::Int)
-#63 := (+ #10 #62)
-#91 := (<= #63 0::Int)
-#94 := (if #91 #12 #10)
-#100 := (* -1::Int #94)
-#564 := (+ #10 #100)
-#540 := (<= #564 0::Int)
-#521 := (not #540)
-#594 := (<= #79 0::Int)
-#602 := (= #79 0::Int)
-#243 := (not #91)
-#487 := [hypothesis]: #243
-#604 := (or #91 #602)
-#30 := (:var 0 Int)
-#32 := (f5 f6 #30)
-#663 := (pattern #32)
-#33 := (f3 f4 #32)
-#38 := (= #33 0::Int)
-#124 := (>= #30 0::Int)
-#155 := (or #124 #38)
-#670 := (forall (vars (?v0 Int)) (:pat #663) #155)
-#158 := (forall (vars (?v0 Int)) #155)
-#673 := (iff #158 #670)
-#671 := (iff #155 #155)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#171 := (~ #158 #158)
-#179 := (~ #155 #155)
-#180 := [refl]: #179
-#172 := [nnf-pos #180]: #171
-#37 := (< #30 0::Int)
-#39 := (implies #37 #38)
-#40 := (forall (vars (?v0 Int)) #39)
-#161 := (iff #40 #158)
-#139 := (not #37)
-#140 := (or #139 #38)
-#143 := (forall (vars (?v0 Int)) #140)
-#159 := (iff #143 #158)
-#156 := (iff #140 #155)
-#153 := (iff #139 #124)
-#126 := (not #124)
-#148 := (not #126)
-#151 := (iff #148 #124)
-#152 := [rewrite]: #151
-#149 := (iff #139 #148)
-#146 := (iff #37 #126)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#154 := [trans #150 #152]: #153
-#157 := [monotonicity #154]: #156
-#160 := [quant-intro #157]: #159
-#144 := (iff #40 #143)
-#141 := (iff #39 #140)
-#142 := [rewrite]: #141
-#145 := [quant-intro #142]: #144
-#162 := [trans #145 #160]: #161
-#138 := [asserted]: #40
-#163 := [mp #138 #162]: #158
-#181 := [mp~ #163 #172]: #158
-#675 := [mp #181 #674]: #670
-#353 := (not #670)
-#605 := (or #353 #91 #602)
-#630 := (>= #73 0::Int)
-#603 := (or #630 #602)
-#606 := (or #353 #603)
-#593 := (iff #606 #605)
-#607 := (or #353 #604)
-#439 := (iff #607 #605)
-#592 := [rewrite]: #439
-#436 := (iff #606 #607)
-#598 := (iff #603 #604)
-#628 := (iff #630 #91)
-#338 := [rewrite]: #628
-#599 := [monotonicity #338]: #598
-#438 := [monotonicity #599]: #436
-#595 := [trans #438 #592]: #593
-#600 := [quant-inst #73]: #606
-#596 := [mp #600 #595]: #605
-#488 := [unit-resolution #596 #675]: #604
-#498 := [unit-resolution #488 #487]: #602
-#478 := (not #602)
-#499 := (or #478 #594)
-#454 := [th-lemma arith triangle-eq]: #499
-#455 := [unit-resolution #454 #498]: #594
-#539 := (not #594)
-#466 := (or #539 #521)
-#66 := (f5 f6 #63)
-#69 := (f3 f4 #66)
-#647 := (* -1::Int #69)
-#290 := (+ #62 #647)
-#631 := (+ #10 #290)
-#640 := (>= #631 0::Int)
-#646 := (= #631 0::Int)
-#654 := (>= #63 0::Int)
-#573 := (+ #12 #100)
-#574 := (<= #573 0::Int)
-#558 := (not #574)
-#349 := (<= #69 0::Int)
-#643 := (= #69 0::Int)
-#649 := (not #654)
-#527 := [hypothesis]: #649
-#629 := (or #654 #643)
-#354 := (or #353 #654 #643)
-#355 := (or #353 #629)
-#625 := (iff #355 #354)
-#626 := [rewrite]: #625
-#249 := [quant-inst #63]: #355
-#348 := [mp #249 #626]: #354
-#514 := [unit-resolution #348 #675]: #629
-#517 := [unit-resolution #514 #527]: #643
-#518 := (not #643)
-#519 := (or #518 #349)
-#515 := [th-lemma arith triangle-eq]: #519
-#520 := [unit-resolution #515 #517]: #349
-#479 := (>= #10 0::Int)
-#560 := (= #10 0::Int)
-#332 := (f5 f6 #10)
-#480 := (f3 f4 #332)
-#481 := (= #480 0::Int)
-#554 := (not #479)
-#541 := [hypothesis]: #554
-#440 := (or #479 #481)
-#585 := (or #353 #479 #481)
-#586 := (or #353 #440)
-#474 := (iff #586 #585)
-#489 := [rewrite]: #474
-#589 := [quant-inst #10]: #586
-#491 := [mp #589 #489]: #585
-#543 := [unit-resolution #491 #675]: #440
-#544 := [unit-resolution #543 #541]: #481
-#548 := (= #10 #480)
-#546 := (= f7 #332)
-#333 := (= #332 f7)
-#24 := (:var 0 S3)
-#25 := (f3 f4 #24)
-#656 := (pattern #25)
-#26 := (f5 f6 #25)
-#27 := (= #26 #24)
-#657 := (forall (vars (?v0 S3)) (:pat #656) #27)
-#28 := (forall (vars (?v0 S3)) #27)
-#660 := (iff #28 #657)
-#658 := (iff #27 #27)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#177 := (~ #28 #28)
-#175 := (~ #27 #27)
-#176 := [refl]: #175
-#178 := [nnf-pos #176]: #177
-#114 := [asserted]: #28
-#167 := [mp~ #114 #178]: #28
-#662 := [mp #167 #661]: #657
-#313 := (not #657)
-#648 := (or #313 #333)
-#650 := [quant-inst #9]: #648
-#545 := [unit-resolution #650 #662]: #333
-#547 := [symm #545]: #546
-#549 := [monotonicity #547]: #548
-#550 := [trans #549 #544]: #560
-#551 := (not #560)
-#552 := (or #551 #479)
-#542 := [th-lemma arith triangle-eq]: #552
-#553 := [unit-resolution #542 #541 #550]: false
-#531 := [lemma #553]: #479
-#500 := (or #654 #91)
-#446 := [th-lemma arith farkas 1 1]: #500
-#501 := [unit-resolution #446 #527]: #91
-#621 := (or #243 #620)
-#34 := (= #33 #30)
-#129 := (or #126 #34)
-#664 := (forall (vars (?v0 Int)) (:pat #663) #129)
-#132 := (forall (vars (?v0 Int)) #129)
-#667 := (iff #132 #664)
-#665 := (iff #129 #129)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#169 := (~ #132 #132)
-#168 := (~ #129 #129)
-#165 := [refl]: #168
-#170 := [nnf-pos #165]: #169
-#31 := (<= 0::Int #30)
-#35 := (implies #31 #34)
-#36 := (forall (vars (?v0 Int)) #35)
-#135 := (iff #36 #132)
-#116 := (not #31)
-#117 := (or #116 #34)
-#120 := (forall (vars (?v0 Int)) #117)
-#133 := (iff #120 #132)
-#130 := (iff #117 #129)
-#127 := (iff #116 #126)
-#123 := (iff #31 #124)
-#125 := [rewrite]: #123
-#128 := [monotonicity #125]: #127
-#131 := [monotonicity #128]: #130
-#134 := [quant-intro #131]: #133
-#121 := (iff #36 #120)
-#118 := (iff #35 #117)
-#119 := [rewrite]: #118
-#122 := [quant-intro #119]: #121
-#136 := [trans #122 #134]: #135
-#115 := [asserted]: #36
-#137 := [mp #115 #136]: #132
-#166 := [mp~ #137 #170]: #132
-#669 := [mp #166 #668]: #664
-#633 := (not #664)
-#611 := (or #633 #243 #620)
-#627 := (= #79 #73)
-#352 := (not #630)
-#624 := (or #352 #627)
-#612 := (or #633 #624)
-#616 := (iff #612 #611)
-#608 := (or #633 #621)
-#615 := (iff #608 #611)
-#610 := [rewrite]: #615
-#609 := (iff #612 #608)
-#618 := (iff #624 #621)
-#335 := (iff #627 #620)
-#617 := [rewrite]: #335
-#339 := (iff #352 #243)
-#340 := [monotonicity #338]: #339
-#622 := [monotonicity #340 #617]: #618
-#614 := [monotonicity #622]: #609
-#457 := [trans #614 #610]: #616
-#613 := [quant-inst #73]: #612
-#458 := [mp #613 #457]: #611
-#482 := [unit-resolution #458 #669]: #621
-#506 := [unit-resolution #482 #501]: #620
-#507 := (not #620)
-#502 := (or #507 #459)
-#508 := [th-lemma arith triangle-eq]: #502
-#476 := [unit-resolution #508 #506]: #459
-#557 := (not #459)
-#555 := (not #349)
-#559 := (or #554 #555 #557 #558)
-#565 := [hypothesis]: #574
-#566 := [hypothesis]: #479
-#567 := [hypothesis]: #459
-#101 := (+ #79 #100)
-#102 := (+ #69 #101)
-#103 := (<= #102 0::Int)
-#108 := (not #103)
-#20 := (<= #10 #12)
-#21 := (if #20 #12 #10)
-#16 := (- #12 #10)
-#17 := (f5 f6 #16)
-#18 := (f3 f4 #17)
-#13 := (- #10 #12)
-#14 := (f5 f6 #13)
-#15 := (f3 f4 #14)
-#19 := (+ #15 #18)
-#22 := (<= #19 #21)
-#23 := (not #22)
-#111 := (iff #23 #108)
-#82 := (+ #69 #79)
-#85 := (<= #82 #21)
-#88 := (not #85)
-#109 := (iff #88 #108)
-#106 := (iff #85 #103)
-#97 := (<= #82 #94)
-#104 := (iff #97 #103)
-#105 := [rewrite]: #104
-#98 := (iff #85 #97)
-#95 := (= #21 #94)
-#92 := (iff #20 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#99 := [monotonicity #96]: #98
-#107 := [trans #99 #105]: #106
-#110 := [monotonicity #107]: #109
-#89 := (iff #23 #88)
-#86 := (iff #22 #85)
-#83 := (= #19 #82)
-#80 := (= #18 #79)
-#77 := (= #17 #76)
-#74 := (= #16 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#70 := (= #15 #69)
-#67 := (= #14 #66)
-#64 := (= #13 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#84 := [monotonicity #71 #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [monotonicity #87]: #89
-#112 := [trans #90 #110]: #111
-#60 := [asserted]: #23
-#113 := [mp #60 #112]: #108
-#563 := [hypothesis]: #349
-#568 := [th-lemma arith farkas 1 -1 1 -1 1 #563 #113 #567 #566 #565]: false
-#556 := [lemma #568]: #559
-#483 := [unit-resolution #556 #476 #531 #520]: #558
-#242 := (= #12 #94)
-#328 := (or #243 #242)
-#329 := [def-axiom]: #328
-#442 := [unit-resolution #329 #501]: #242
-#473 := (not #242)
-#475 := (or #473 #574)
-#477 := [th-lemma arith triangle-eq]: #475
-#484 := [unit-resolution #477 #442 #483]: false
-#486 := [lemma #484]: #654
-#295 := (or #649 #646)
-#634 := (or #633 #649 #646)
-#305 := (= #69 #63)
-#310 := (or #649 #305)
-#635 := (or #633 #310)
-#641 := (iff #635 #634)
-#637 := (or #633 #295)
-#276 := (iff #637 #634)
-#639 := [rewrite]: #276
-#632 := (iff #635 #637)
-#296 := (iff #310 #295)
-#306 := (iff #305 #646)
-#294 := [rewrite]: #306
-#297 := [monotonicity #294]: #296
-#638 := [monotonicity #297]: #632
-#281 := [trans #638 #639]: #641
-#636 := [quant-inst #63]: #635
-#282 := [mp #636 #281]: #634
-#460 := [unit-resolution #282 #669]: #295
-#461 := [unit-resolution #460 #486]: #646
-#462 := (not #646)
-#463 := (or #462 #640)
-#464 := [th-lemma arith triangle-eq]: #463
-#465 := [unit-resolution #464 #461]: #640
-#588 := (>= #12 0::Int)
-#526 := (= #12 0::Int)
-#330 := (f5 f6 #12)
-#490 := (f3 f4 #330)
-#492 := (= #490 0::Int)
-#533 := (not #588)
-#528 := [hypothesis]: #533
-#485 := (or #588 #492)
-#495 := (or #353 #588 #492)
-#496 := (or #353 #485)
-#590 := (iff #496 #495)
-#587 := [rewrite]: #590
-#497 := [quant-inst #12]: #496
-#591 := [mp #497 #587]: #495
-#529 := [unit-resolution #591 #675]: #485
-#524 := [unit-resolution #529 #528]: #492
-#505 := (= #12 #490)
-#503 := (= f8 #330)
-#334 := (= #330 f8)
-#644 := (or #313 #334)
-#318 := [quant-inst #11]: #644
-#530 := [unit-resolution #318 #662]: #334
-#504 := [symm #530]: #503
-#398 := [monotonicity #504]: #505
-#509 := [trans #398 #524]: #526
-#510 := (not #526)
-#511 := (or #510 #588)
-#516 := [th-lemma arith triangle-eq]: #511
-#512 := [unit-resolution #516 #528 #509]: false
-#513 := [lemma #512]: #588
-#525 := (not #640)
-#522 := (or #533 #539 #525 #521)
-#534 := [hypothesis]: #540
-#535 := [hypothesis]: #588
-#536 := [hypothesis]: #640
-#537 := [hypothesis]: #594
-#538 := [th-lemma arith farkas -1 1 -1 -1 1 #113 #537 #536 #535 #534]: false
-#523 := [lemma #538]: #522
-#467 := [unit-resolution #523 #513 #465]: #466
-#468 := [unit-resolution #467 #455]: #521
-#327 := (= #10 #94)
-#320 := (or #91 #327)
-#331 := [def-axiom]: #320
-#469 := [unit-resolution #331 #487]: #327
-#470 := (not #327)
-#471 := (or #470 #540)
-#456 := [th-lemma arith triangle-eq]: #471
-#472 := [unit-resolution #456 #469 #468]: false
-#433 := [lemma #472]: #91
-#434 := [unit-resolution #482 #433]: #620
-#441 := [unit-resolution #508 #434]: #459
-#443 := [unit-resolution #329 #433]: #242
-#444 := [unit-resolution #477 #443]: #574
-#445 := (or #349 #525 #243)
-#447 := [th-lemma arith assign-bounds 1 -1]: #445
-#448 := [unit-resolution #447 #465 #433]: #349
-#449 := (or #555 #557 #558)
-#450 := [unit-resolution #556 #531]: #449
-[unit-resolution #450 #448 #444 #441]: false
-unsat
-f2081c9ce72ee506fa1abe41bc9504adb41b6a70 109 0
-#2 := false
-#28 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-decl f7 :: S3
-#13 := f7
-#14 := (f3 f4 f7)
-#67 := -1::Int
-#74 := (* -1::Int #14)
-#86 := (+ #9 #74)
-#87 := (<= #86 0::Int)
-#90 := (if #87 #14 #9)
-#96 := (* -1::Int #90)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#97 := (+ #11 #96)
-#98 := (<= #97 0::Int)
-#99 := (not #98)
-#75 := (+ #11 #74)
-#76 := (<= #75 0::Int)
-#77 := (not #76)
-#70 := (* -1::Int #11)
-#71 := (+ #9 #70)
-#69 := (>= #71 0::Int)
-#68 := (not #69)
-#80 := (and #68 #77)
-#83 := (not #80)
-#104 := (or #83 #99)
-#107 := (not #104)
-#17 := (<= #9 #14)
-#18 := (if #17 #14 #9)
-#19 := (< #18 #11)
-#15 := (< #14 #11)
-#12 := (< #9 #11)
-#16 := (and #12 #15)
-#20 := (implies #16 #19)
-#21 := (not #20)
-#110 := (iff #21 #107)
-#60 := (not #16)
-#61 := (or #60 #19)
-#64 := (not #61)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #19 #99)
-#93 := (< #90 #11)
-#100 := (iff #93 #99)
-#101 := [rewrite]: #100
-#94 := (iff #19 #93)
-#91 := (= #18 #90)
-#88 := (iff #17 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#95 := [monotonicity #92]: #94
-#103 := [trans #95 #101]: #102
-#84 := (iff #60 #83)
-#81 := (iff #16 #80)
-#78 := (iff #15 #77)
-#79 := [rewrite]: #78
-#72 := (iff #12 #68)
-#73 := [rewrite]: #72
-#82 := [monotonicity #73 #79]: #81
-#85 := [monotonicity #82]: #84
-#106 := [monotonicity #85 #103]: #105
-#109 := [monotonicity #106]: #108
-#65 := (iff #21 #64)
-#62 := (iff #20 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#111 := [trans #66 #109]: #110
-#59 := [asserted]: #21
-#112 := [mp #59 #111]: #107
-#116 := [not-or-elim #112]: #98
-#113 := [not-or-elim #112]: #80
-#114 := [and-elim #113]: #68
-#644 := (+ #9 #96)
-#627 := (>= #644 0::Int)
-#330 := (= #9 #90)
-#246 := (not #87)
-#245 := (= #14 #90)
-#628 := (not #245)
-#642 := (+ #14 #96)
-#633 := (>= #642 0::Int)
-#357 := (not #633)
-#115 := [and-elim #113]: #77
-#355 := [hypothesis]: #633
-#356 := [th-lemma arith farkas -1 -1 1 #355 #115 #116]: false
-#358 := [lemma #356]: #357
-#252 := [hypothesis]: #245
-#629 := (or #628 #633)
-#351 := [th-lemma arith triangle-eq]: #629
-#352 := [unit-resolution #351 #252 #358]: false
-#626 := [lemma #352]: #628
-#331 := (or #246 #245)
-#332 := [def-axiom]: #331
-#631 := [unit-resolution #332 #626]: #246
-#323 := (or #87 #330)
-#334 := [def-axiom]: #323
-#341 := [unit-resolution #334 #631]: #330
-#342 := (not #330)
-#343 := (or #342 #627)
-#344 := [th-lemma arith triangle-eq]: #343
-#622 := [unit-resolution #344 #341]: #627
-[th-lemma arith farkas -1 1 1 #622 #114 #116]: false
-unsat
-173bb4f0b36bcf659115903eaed06f43d1cc4af2 149 0
-#2 := false
-decl f6 :: S3
-#10 := f6
-decl f5 :: S3
-#8 := f5
-#24 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#58 := -1::Int
-#59 := (* -1::Int #11)
-#9 := (f3 f4 f5)
-#60 := (+ #9 #59)
-#68 := (>= #60 0::Int)
-#70 := (if #68 f5 f6)
-#61 := (<= #60 0::Int)
-#64 := (if #61 f6 f5)
-#73 := (= #64 #70)
-#296 := (= f5 #70)
-#557 := (iff #296 #73)
-#403 := (iff #73 #296)
-#607 := (= #64 f5)
-#291 := (= f5 #64)
-#207 := (not #61)
-#206 := (= f6 #64)
-#568 := (not #206)
-#423 := (iff #206 #73)
-#421 := (iff #73 #206)
-#573 := (= #64 f6)
-#574 := (iff #573 #206)
-#580 := [commutativity]: #574
-#578 := (iff #73 #573)
-#577 := (= #70 f6)
-#297 := (= f6 #70)
-#598 := (not #297)
-#599 := [hypothesis]: #598
-#612 := (or #68 #297)
-#614 := [def-axiom]: #612
-#605 := [unit-resolution #614 #599]: #68
-#294 := (not #68)
-#298 := (or #294 #296)
-#277 := [def-axiom]: #298
-#245 := [unit-resolution #277 #605]: #296
-#581 := (= f6 f5)
-decl f7 :: (-> S4 Int S3)
-decl f8 :: S4
-#18 := f8
-#271 := (f7 f8 #9)
-#401 := (= #271 f5)
-#19 := (:var 0 S3)
-#20 := (f3 f4 #19)
-#620 := (pattern #20)
-#21 := (f7 f8 #20)
-#22 := (= #21 #19)
-#621 := (forall (vars (?v0 S3)) (:pat #620) #22)
-#23 := (forall (vars (?v0 S3)) #22)
-#624 := (iff #23 #621)
-#622 := (iff #22 #22)
-#623 := [refl]: #622
-#625 := [quant-intro #623]: #624
-#141 := (~ #23 #23)
-#139 := (~ #22 #22)
-#140 := [refl]: #139
-#142 := [nnf-pos #140]: #141
-#56 := [asserted]: #23
-#131 := [mp~ #56 #142]: #23
-#626 := [mp #131 #625]: #621
-#283 := (not #621)
-#615 := (or #283 #401)
-#616 := [quant-inst #8]: #615
-#246 := [unit-resolution #616 #626]: #401
-#584 := (= f6 #271)
-#608 := (f7 f8 #11)
-#305 := (= #608 #271)
-#588 := (= #11 #9)
-#587 := (= #9 #11)
-#213 := (not #291)
-#76 := (not #73)
-#589 := (iff #76 #213)
-#318 := (iff #73 #291)
-#316 := (iff #607 #291)
-#317 := [commutativity]: #316
-#593 := (iff #73 #607)
-#606 := (= #70 f5)
-#604 := [symm #245]: #606
-#594 := [monotonicity #604]: #593
-#319 := [trans #594 #317]: #318
-#590 := [monotonicity #319]: #589
-#14 := (<= #11 #9)
-#15 := (if #14 f5 f6)
-#12 := (<= #9 #11)
-#13 := (if #12 f6 f5)
-#16 := (= #13 #15)
-#17 := (not #16)
-#77 := (iff #17 #76)
-#74 := (iff #16 #73)
-#71 := (= #15 #70)
-#67 := (iff #14 #68)
-#69 := [rewrite]: #67
-#72 := [monotonicity #69]: #71
-#65 := (= #13 #64)
-#62 := (iff #12 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#75 := [monotonicity #66 #72]: #74
-#78 := [monotonicity #75]: #77
-#55 := [asserted]: #17
-#79 := [mp #55 #78]: #76
-#312 := [mp #79 #590]: #213
-#284 := (or #61 #291)
-#295 := [def-axiom]: #284
-#313 := [unit-resolution #295 #312]: #61
-#591 := [th-lemma arith eq-propagate 1 1 #605 #313]: #587
-#592 := [symm #591]: #588
-#583 := [monotonicity #592]: #305
-#303 := (= f6 #608)
-#282 := (= #608 f6)
-#613 := (or #283 #282)
-#619 := [quant-inst #10]: #613
-#302 := [unit-resolution #619 #626]: #282
-#304 := [symm #302]: #303
-#299 := [trans #304 #583]: #584
-#585 := [trans #299 #246]: #581
-#582 := [trans #585 #245]: #297
-#586 := [unit-resolution #599 #582]: false
-#575 := [lemma #586]: #297
-#572 := [symm #575]: #577
-#579 := [monotonicity #572]: #578
-#422 := [trans #579 #580]: #421
-#565 := [symm #422]: #423
-#576 := [hypothesis]: #206
-#566 := [mp #576 #565]: #73
-#567 := [unit-resolution #79 #566]: false
-#562 := [lemma #567]: #568
-#292 := (or #207 #206)
-#293 := [def-axiom]: #292
-#563 := [unit-resolution #293 #562]: #207
-#400 := [unit-resolution #295 #563]: #291
-#402 := [symm #400]: #607
-#556 := [monotonicity #402]: #403
-#559 := [symm #556]: #557
-#569 := (or #68 #61)
-#570 := [th-lemma arith farkas 1 1]: #569
-#564 := [unit-resolution #570 #563]: #68
-#571 := [unit-resolution #277 #564]: #296
-#560 := [mp #571 #559]: #73
-[unit-resolution #79 #560]: false
-unsat
-c843701a69b18945f314fe27c203badcfa31d469 137 0
-#2 := false
-decl f5 :: S3
-#8 := f5
-decl f6 :: (-> S4 Int S3)
-#10 := 0::Int
-decl f7 :: S4
-#12 := f7
-#13 := (f6 f7 0::Int)
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#11 := (<= #9 0::Int)
-#14 := (if #11 #13 f5)
-#266 := (= f5 #14)
-#181 := (= #13 #14)
-#568 := (not #266)
-#15 := (= #14 f5)
-#16 := (not #15)
-#278 := (iff #16 #568)
-#567 := (iff #15 #266)
-#564 := [commutativity]: #567
-#279 := [monotonicity #564]: #278
-#52 := [asserted]: #16
-#280 := [mp #52 #279]: #568
-#259 := (or #11 #266)
-#270 := [def-axiom]: #259
-#281 := [unit-resolution #270 #280]: #11
-#182 := (not #11)
-#267 := (or #182 #181)
-#268 := [def-axiom]: #267
-#548 := [unit-resolution #268 #281]: #181
-#399 := (= f5 #13)
-#272 := (f6 f7 #9)
-#397 := (= #272 #13)
-#274 := (= #9 0::Int)
-#252 := (f3 f4 #272)
-#377 := (= #252 0::Int)
-#273 := (>= #9 0::Int)
-#289 := (not #377)
-#563 := [hypothesis]: #289
-#584 := (or #273 #377)
-#22 := (:var 0 Int)
-#24 := (f6 f7 #22)
-#603 := (pattern #24)
-#25 := (f3 f4 #24)
-#30 := (= #25 0::Int)
-#64 := (>= #22 0::Int)
-#94 := (or #64 #30)
-#610 := (forall (vars (?v0 Int)) (:pat #603) #94)
-#97 := (forall (vars (?v0 Int)) #94)
-#613 := (iff #97 #610)
-#611 := (iff #94 #94)
-#612 := [refl]: #611
-#614 := [quant-intro #612]: #613
-#110 := (~ #97 #97)
-#118 := (~ #94 #94)
-#119 := [refl]: #118
-#111 := [nnf-pos #119]: #110
-#29 := (< #22 0::Int)
-#31 := (implies #29 #30)
-#32 := (forall (vars (?v0 Int)) #31)
-#100 := (iff #32 #97)
-#78 := (not #29)
-#79 := (or #78 #30)
-#82 := (forall (vars (?v0 Int)) #79)
-#98 := (iff #82 #97)
-#95 := (iff #79 #94)
-#92 := (iff #78 #64)
-#65 := (not #64)
-#87 := (not #65)
-#90 := (iff #87 #64)
-#91 := [rewrite]: #90
-#88 := (iff #78 #87)
-#85 := (iff #29 #65)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#93 := [trans #89 #91]: #92
-#96 := [monotonicity #93]: #95
-#99 := [quant-intro #96]: #98
-#83 := (iff #32 #82)
-#80 := (iff #31 #79)
-#81 := [rewrite]: #80
-#84 := [quant-intro #81]: #83
-#101 := [trans #84 #99]: #100
-#77 := [asserted]: #32
-#102 := [mp #77 #101]: #97
-#120 := [mp~ #102 #111]: #97
-#615 := [mp #120 #614]: #610
-#591 := (not #610)
-#592 := (or #591 #273 #377)
-#593 := (or #591 #584)
-#589 := (iff #593 #592)
-#595 := [rewrite]: #589
-#594 := [quant-inst #9]: #593
-#585 := [mp #594 #595]: #592
-#559 := [unit-resolution #585 #615]: #584
-#560 := [unit-resolution #559 #563]: #273
-#557 := [th-lemma arith eq-propagate 0 0 #560 #281]: #274
-#558 := (= #252 #9)
-#269 := (= #272 f5)
-#17 := (:var 0 S3)
-#18 := (f3 f4 #17)
-#596 := (pattern #18)
-#19 := (f6 f7 #18)
-#20 := (= #19 #17)
-#597 := (forall (vars (?v0 S3)) (:pat #596) #20)
-#21 := (forall (vars (?v0 S3)) #20)
-#600 := (iff #21 #597)
-#598 := (iff #20 #20)
-#599 := [refl]: #598
-#601 := [quant-intro #599]: #600
-#116 := (~ #21 #21)
-#114 := (~ #20 #20)
-#115 := [refl]: #114
-#117 := [nnf-pos #115]: #116
-#53 := [asserted]: #21
-#106 := [mp~ #53 #117]: #21
-#602 := [mp #106 #601]: #597
-#588 := (not #597)
-#590 := (or #588 #269)
-#246 := [quant-inst #8]: #590
-#561 := [unit-resolution #246 #602]: #269
-#562 := [monotonicity #561]: #558
-#551 := [trans #562 #557]: #377
-#552 := [unit-resolution #563 #551]: false
-#553 := [lemma #552]: #377
-#555 := (= #9 #252)
-#549 := (= f5 #272)
-#554 := [symm #561]: #549
-#550 := [monotonicity #554]: #555
-#556 := [trans #550 #553]: #274
-#398 := [monotonicity #556]: #397
-#541 := [trans #554 #398]: #399
-#542 := [trans #541 #548]: #266
-[unit-resolution #280 #542]: false
-unsat
-39efecfe038f83ab2d1aa99967fadc5bc10be8c6 114 0
-#2 := false
-#7 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#273 := (= #10 0::Int)
-decl f6 :: (-> S4 Int S3)
-decl f7 :: S4
-#13 := f7
-#270 := (f6 f7 #10)
-#271 := (f3 f4 #270)
-#272 := (= #271 0::Int)
-#19 := (:var 0 Int)
-#21 := (f6 f7 #19)
-#607 := (pattern #21)
-#22 := (f3 f4 #21)
-#27 := (= #22 0::Int)
-#68 := (>= #19 0::Int)
-#98 := (or #68 #27)
-#614 := (forall (vars (?v0 Int)) (:pat #607) #98)
-#101 := (forall (vars (?v0 Int)) #98)
-#617 := (iff #101 #614)
-#615 := (iff #98 #98)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#114 := (~ #101 #101)
-#122 := (~ #98 #98)
-#123 := [refl]: #122
-#115 := [nnf-pos #123]: #114
-#26 := (< #19 0::Int)
-#28 := (implies #26 #27)
-#29 := (forall (vars (?v0 Int)) #28)
-#104 := (iff #29 #101)
-#82 := (not #26)
-#83 := (or #82 #27)
-#86 := (forall (vars (?v0 Int)) #83)
-#102 := (iff #86 #101)
-#99 := (iff #83 #98)
-#96 := (iff #82 #68)
-#69 := (not #68)
-#91 := (not #69)
-#94 := (iff #91 #68)
-#95 := [rewrite]: #94
-#92 := (iff #82 #91)
-#89 := (iff #26 #69)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#97 := [trans #93 #95]: #96
-#100 := [monotonicity #97]: #99
-#103 := [quant-intro #100]: #102
-#87 := (iff #29 #86)
-#84 := (iff #28 #83)
-#85 := [rewrite]: #84
-#88 := [quant-intro #85]: #87
-#105 := [trans #88 #103]: #104
-#81 := [asserted]: #29
-#106 := [mp #81 #105]: #101
-#124 := [mp~ #106 #115]: #101
-#619 := [mp #124 #618]: #614
-#54 := (>= #10 0::Int)
-#55 := (not #54)
-#11 := (<= 0::Int #10)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#52 := (iff #11 #54)
-#53 := [rewrite]: #52
-#57 := [monotonicity #53]: #56
-#49 := [asserted]: #12
-#58 := [mp #49 #57]: #55
-#256 := (not #614)
-#592 := (or #256 #54 #272)
-#276 := (or #54 #272)
-#594 := (or #256 #276)
-#381 := (iff #594 #592)
-#588 := [rewrite]: #381
-#250 := [quant-inst #10]: #594
-#261 := [mp #250 #588]: #592
-#262 := [unit-resolution #261 #58 #619]: #272
-#598 := (= #10 #271)
-#596 := (= f5 #270)
-#186 := (= #270 f5)
-#14 := (:var 0 S3)
-#15 := (f3 f4 #14)
-#600 := (pattern #15)
-#16 := (f6 f7 #15)
-#17 := (= #16 #14)
-#601 := (forall (vars (?v0 S3)) (:pat #600) #17)
-#18 := (forall (vars (?v0 S3)) #17)
-#604 := (iff #18 #601)
-#602 := (iff #17 #17)
-#603 := [refl]: #602
-#605 := [quant-intro #603]: #604
-#120 := (~ #18 #18)
-#118 := (~ #17 #17)
-#119 := [refl]: #118
-#121 := [nnf-pos #119]: #120
-#50 := [asserted]: #18
-#110 := [mp~ #50 #121]: #18
-#606 := [mp #110 #605]: #601
-#263 := (not #601)
-#274 := (or #263 #186)
-#275 := [quant-inst #9]: #274
-#595 := [unit-resolution #275 #606]: #186
-#597 := [symm #595]: #596
-#593 := [monotonicity #597]: #598
-#599 := [trans #593 #262]: #273
-#589 := (not #273)
-#248 := (or #589 #54)
-#253 := [th-lemma arith triangle-eq]: #248
-[unit-resolution #253 #58 #599]: false
-unsat
-f7e768909a7c1b933ad0d893349ffd5af448126c 88 0
-#2 := false
-decl f6 :: (-> S4 Int S3)
-#12 := 1::Int
-decl f7 :: S4
-#15 := f7
-#16 := (f6 f7 1::Int)
-decl f5 :: S3
-#9 := f5
-#17 := (= f5 #16)
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#299 := (f6 f7 #10)
-#325 := (= #299 #16)
-#616 := (= #16 #299)
-#615 := (= 1::Int #10)
-#253 := (= #10 1::Int)
-#13 := (<= #10 1::Int)
-#7 := 0::Int
-#63 := (<= #10 0::Int)
-#64 := (not #63)
-#67 := (and #64 #13)
-#70 := (not #67)
-#73 := (or #70 #17)
-#76 := (not #73)
-#11 := (< 0::Int #10)
-#14 := (and #11 #13)
-#18 := (implies #14 #17)
-#19 := (not #18)
-#79 := (iff #19 #76)
-#56 := (not #14)
-#57 := (or #56 #17)
-#60 := (not #57)
-#77 := (iff #60 #76)
-#74 := (iff #57 #73)
-#71 := (iff #56 #70)
-#68 := (iff #14 #67)
-#65 := (iff #11 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#61 := (iff #19 #60)
-#58 := (iff #18 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#80 := [trans #62 #78]: #79
-#55 := [asserted]: #19
-#81 := [mp #55 #80]: #76
-#82 := [not-or-elim #81]: #67
-#84 := [and-elim #82]: #13
-#83 := [and-elim #82]: #64
-#254 := [th-lemma arith eq-propagate 0 0 #83 #84]: #253
-#613 := [symm #254]: #615
-#602 := [monotonicity #613]: #616
-#326 := [symm #602]: #325
-#603 := (= f5 #299)
-#215 := (= #299 f5)
-#20 := (:var 0 S3)
-#21 := (f3 f4 #20)
-#629 := (pattern #21)
-#22 := (f6 f7 #21)
-#23 := (= #22 #20)
-#630 := (forall (vars (?v0 S3)) (:pat #629) #23)
-#24 := (forall (vars (?v0 S3)) #23)
-#633 := (iff #24 #630)
-#631 := (iff #23 #23)
-#632 := [refl]: #631
-#634 := [quant-intro #632]: #633
-#154 := (~ #24 #24)
-#152 := (~ #23 #23)
-#153 := [refl]: #152
-#155 := [nnf-pos #153]: #154
-#87 := [asserted]: #24
-#144 := [mp~ #87 #155]: #24
-#635 := [mp #144 #634]: #630
-#292 := (not #630)
-#303 := (or #292 #215)
-#304 := [quant-inst #9]: #303
-#614 := [unit-resolution #304 #635]: #215
-#310 := [symm #614]: #603
-#327 := [trans #310 #326]: #17
-#85 := (not #17)
-#86 := [not-or-elim #81]: #85
-[unit-resolution #86 #327]: false
-unsat
-e9599784ae48c0a76ee6ce769530275315a7c306 22 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#10 := (<= #9 #9)
-#11 := (not #10)
-#59 := (iff #11 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #11 #54)
-#52 := (iff #10 true)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#49 := [asserted]: #11
-[mp #49 #60]: false
-unsat
-bc3dab857c3b884433a23e55254b9c450e3d29a1 56 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#13 := 3::Int
-#15 := (* 3::Int #11)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#14 := (* 3::Int #9)
-#16 := (<= #14 #15)
-#12 := (<= #9 #11)
-#17 := (implies #12 #16)
-#18 := (not #17)
-#89 := (iff #18 false)
-#57 := (not #12)
-#58 := (or #57 #16)
-#61 := (not #58)
-#87 := (iff #61 false)
-#1 := true
-#82 := (not true)
-#85 := (iff #82 false)
-#86 := [rewrite]: #85
-#83 := (iff #61 #82)
-#80 := (iff #58 true)
-#25 := 0::Int
-#64 := -1::Int
-#65 := (* -1::Int #11)
-#66 := (+ #9 #65)
-#67 := (<= #66 0::Int)
-#70 := (not #67)
-#75 := (or #70 #67)
-#78 := (iff #75 true)
-#79 := [rewrite]: #78
-#76 := (iff #58 #75)
-#73 := (iff #16 #67)
-#74 := [rewrite]: #73
-#71 := (iff #57 #70)
-#68 := (iff #12 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#77 := [monotonicity #72 #74]: #76
-#81 := [trans #77 #79]: #80
-#84 := [monotonicity #81]: #83
-#88 := [trans #84 #86]: #87
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#90 := [trans #63 #88]: #89
-#56 := [asserted]: #18
-[mp #56 #90]: false
-unsat
-782e867b2e6b539b485b3c801c1684af80e8e4eb 61 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#13 := 3::Int
-#15 := (* 3::Int #11)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#14 := (* 3::Int #9)
-#16 := (< #14 #15)
-#12 := (< #9 #11)
-#17 := (implies #12 #16)
-#18 := (not #17)
-#94 := (iff #18 false)
-#57 := (not #12)
-#58 := (or #57 #16)
-#61 := (not #58)
-#92 := (iff #61 false)
-#1 := true
-#87 := (not true)
-#90 := (iff #87 false)
-#91 := [rewrite]: #90
-#88 := (iff #61 #87)
-#85 := (iff #58 true)
-#25 := 0::Int
-#64 := -1::Int
-#67 := (* -1::Int #11)
-#68 := (+ #9 #67)
-#66 := (>= #68 0::Int)
-#65 := (not #66)
-#79 := (or #66 #65)
-#83 := (iff #79 true)
-#84 := [rewrite]: #83
-#81 := (iff #58 #79)
-#80 := (iff #16 #65)
-#78 := [rewrite]: #80
-#76 := (iff #57 #66)
-#71 := (not #65)
-#74 := (iff #71 #66)
-#75 := [rewrite]: #74
-#72 := (iff #57 #71)
-#69 := (iff #12 #65)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#82 := [monotonicity #77 #78]: #81
-#86 := [trans #82 #84]: #85
-#89 := [monotonicity #86]: #88
-#93 := [trans #89 #91]: #92
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#95 := [trans #63 #93]: #94
-#56 := [asserted]: #18
-[mp #56 #95]: false
-unsat
-94669687013e4a07eb52cc8d3181b4486a98fb64 57 0
-#2 := false
-#22 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#61 := -1::Int
-#64 := (* -1::Int #11)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#65 := (+ #9 #64)
-#75 := (<= #65 0::Int)
-#88 := (not #75)
-#63 := (>= #65 0::Int)
-#78 := (or #63 #75)
-#81 := (not #78)
-#13 := (<= #9 #11)
-#12 := (< #9 #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#84 := (iff #15 #81)
-#54 := (not #12)
-#55 := (or #54 #13)
-#58 := (not #55)
-#82 := (iff #58 #81)
-#79 := (iff #55 #78)
-#76 := (iff #13 #75)
-#77 := [rewrite]: #76
-#73 := (iff #54 #63)
-#62 := (not #63)
-#68 := (not #62)
-#71 := (iff #68 #63)
-#72 := [rewrite]: #71
-#69 := (iff #54 #68)
-#66 := (iff #12 #62)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80]: #82
-#59 := (iff #15 #58)
-#56 := (iff #14 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#85 := [trans #60 #83]: #84
-#53 := [asserted]: #15
-#86 := [mp #53 #85]: #81
-#89 := [not-or-elim #86]: #88
-#87 := [not-or-elim #86]: #62
-#218 := (or #75 #63)
-#303 := [th-lemma arith farkas 1 1]: #218
-#219 := [unit-resolution #303 #87]: #75
-[unit-resolution #219 #89]: false
-unsat
-7c33b6e5c3b47260d57df088f1707958b9c6cfb4 78 0
-#2 := false
-#74 := -1::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#7 := f4
-#11 := (f3 f4 f6)
-#77 := (* -1::Int #11)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#78 := (+ #9 #77)
-#88 := (<= #78 -1::Int)
-#24 := 0::Int
-#76 := (>= #78 0::Int)
-#75 := (not #76)
-#224 := (not #88)
-#277 := [hypothesis]: #224
-#315 := (or #75 #88)
-#91 := (iff #76 #88)
-#13 := 1::Int
-#14 := (+ #9 1::Int)
-#15 := (<= #14 #11)
-#12 := (< #9 #11)
-#16 := (iff #12 #15)
-#17 := (not #16)
-#94 := (iff #17 #91)
-#56 := (+ 1::Int #9)
-#59 := (<= #56 #11)
-#68 := (not #12)
-#69 := (iff #68 #59)
-#92 := (iff #69 #91)
-#89 := (iff #59 #88)
-#90 := [rewrite]: #89
-#86 := (iff #68 #76)
-#81 := (not #75)
-#84 := (iff #81 #76)
-#85 := [rewrite]: #84
-#82 := (iff #68 #81)
-#79 := (iff #12 #75)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#87 := [trans #83 #85]: #86
-#93 := [monotonicity #87 #90]: #92
-#72 := (iff #17 #69)
-#62 := (iff #12 #59)
-#65 := (not #62)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #17 #65)
-#63 := (iff #16 #62)
-#60 := (iff #15 #59)
-#57 := (= #14 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#73 := [trans #67 #71]: #72
-#95 := [trans #73 #93]: #94
-#55 := [asserted]: #17
-#96 := [mp #55 #95]: #91
-#309 := (not #91)
-#313 := (or #75 #88 #309)
-#314 := [def-axiom]: #313
-#312 := [unit-resolution #314 #96]: #315
-#278 := [unit-resolution #312 #277]: #75
-#614 := [th-lemma arith farkas 1 1 #277 #278]: false
-#620 := [lemma #614]: #88
-#258 := (or #224 #75)
-#621 := [th-lemma arith farkas 1 1]: #258
-#623 := [unit-resolution #621 #620]: #75
-#311 := (or #76 #224)
-#225 := (or #76 #224 #309)
-#310 := [def-axiom]: #225
-#302 := [unit-resolution #310 #96]: #311
-[unit-resolution #302 #623 #620]: false
-unsat
-1ddff06a9124711b00597d9f7f79edb1f5ac02da 19 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#10 := (< #9 #9)
-#11 := (not #10)
-#12 := (not #11)
-#55 := (iff #12 false)
-#53 := (iff #10 false)
-#54 := [rewrite]: #53
-#51 := (iff #12 #10)
-#52 := [rewrite]: #51
-#56 := [trans #52 #54]: #55
-#50 := [asserted]: #12
-[mp #50 #56]: false
-unsat
-34a197030d596a851cfea7401235747df59a05b3 81 0
-#2 := false
-#26 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#13 := f7
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 f7)
-#74 := -1::Int
-#75 := (* -1::Int #14)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#76 := (+ #11 #75)
-#77 := (<= #76 0::Int)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#83 := (+ #9 #75)
-#84 := (<= #83 0::Int)
-#80 := (not #77)
-#87 := (* -1::Int #11)
-#88 := (+ #9 #87)
-#89 := (<= #88 0::Int)
-#92 := (not #89)
-#101 := (or #92 #80 #84)
-#106 := (not #101)
-#16 := (<= #9 #14)
-#15 := (<= #11 #14)
-#17 := (implies #15 #16)
-#12 := (<= #9 #11)
-#18 := (implies #12 #17)
-#19 := (not #18)
-#109 := (iff #19 #106)
-#58 := (not #15)
-#59 := (or #58 #16)
-#65 := (not #12)
-#66 := (or #65 #59)
-#71 := (not #66)
-#107 := (iff #71 #106)
-#104 := (iff #66 #101)
-#95 := (or #80 #84)
-#98 := (or #92 #95)
-#102 := (iff #98 #101)
-#103 := [rewrite]: #102
-#99 := (iff #66 #98)
-#96 := (iff #59 #95)
-#85 := (iff #16 #84)
-#86 := [rewrite]: #85
-#81 := (iff #58 #80)
-#78 := (iff #15 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#97 := [monotonicity #82 #86]: #96
-#93 := (iff #65 #92)
-#90 := (iff #12 #89)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#100 := [monotonicity #94 #97]: #99
-#105 := [trans #100 #103]: #104
-#108 := [monotonicity #105]: #107
-#72 := (iff #19 #71)
-#69 := (iff #18 #66)
-#62 := (implies #12 #59)
-#67 := (iff #62 #66)
-#68 := [rewrite]: #67
-#63 := (iff #18 #62)
-#60 := (iff #17 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#70 := [trans #64 #68]: #69
-#73 := [monotonicity #70]: #72
-#110 := [trans #73 #108]: #109
-#57 := [asserted]: #19
-#111 := [mp #57 #110]: #106
-#113 := [not-or-elim #111]: #77
-#114 := (not #84)
-#115 := [not-or-elim #111]: #114
-#112 := [not-or-elim #111]: #89
-[th-lemma arith farkas 1 -1 1 #112 #115 #113]: false
-unsat
-7b0882598adc749ae782704cbf82bc84a198ea68 86 0
-#2 := false
-#26 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#13 := f7
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 f7)
-#74 := -1::Int
-#75 := (* -1::Int #14)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#76 := (+ #11 #75)
-#77 := (<= #76 0::Int)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#83 := (+ #9 #75)
-#84 := (<= #83 0::Int)
-#80 := (not #77)
-#89 := (* -1::Int #11)
-#90 := (+ #9 #89)
-#88 := (>= #90 0::Int)
-#106 := (or #88 #80 #84)
-#111 := (not #106)
-#16 := (<= #9 #14)
-#15 := (<= #11 #14)
-#17 := (implies #15 #16)
-#12 := (< #9 #11)
-#18 := (implies #12 #17)
-#19 := (not #18)
-#114 := (iff #19 #111)
-#58 := (not #15)
-#59 := (or #58 #16)
-#65 := (not #12)
-#66 := (or #65 #59)
-#71 := (not #66)
-#112 := (iff #71 #111)
-#109 := (iff #66 #106)
-#100 := (or #80 #84)
-#103 := (or #88 #100)
-#107 := (iff #103 #106)
-#108 := [rewrite]: #107
-#104 := (iff #66 #103)
-#101 := (iff #59 #100)
-#85 := (iff #16 #84)
-#86 := [rewrite]: #85
-#81 := (iff #58 #80)
-#78 := (iff #15 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#102 := [monotonicity #82 #86]: #101
-#98 := (iff #65 #88)
-#87 := (not #88)
-#93 := (not #87)
-#96 := (iff #93 #88)
-#97 := [rewrite]: #96
-#94 := (iff #65 #93)
-#91 := (iff #12 #87)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#99 := [trans #95 #97]: #98
-#105 := [monotonicity #99 #102]: #104
-#110 := [trans #105 #108]: #109
-#113 := [monotonicity #110]: #112
-#72 := (iff #19 #71)
-#69 := (iff #18 #66)
-#62 := (implies #12 #59)
-#67 := (iff #62 #66)
-#68 := [rewrite]: #67
-#63 := (iff #18 #62)
-#60 := (iff #17 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#70 := [trans #64 #68]: #69
-#73 := [monotonicity #70]: #72
-#115 := [trans #73 #113]: #114
-#57 := [asserted]: #19
-#116 := [mp #57 #115]: #111
-#118 := [not-or-elim #116]: #77
-#117 := [not-or-elim #116]: #87
-#119 := (not #84)
-#120 := [not-or-elim #116]: #119
-[th-lemma arith farkas 1 1 1 #120 #117 #118]: false
-unsat
-d78e40f60c9b56c29d89cfe670baf3737ca499b3 86 0
-#2 := false
-#26 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#13 := f7
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 f7)
-#74 := -1::Int
-#77 := (* -1::Int #14)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#88 := (+ #9 #77)
-#89 := (<= #88 0::Int)
-#119 := (not #89)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#78 := (+ #11 #77)
-#76 := (>= #78 0::Int)
-#92 := (* -1::Int #11)
-#93 := (+ #9 #92)
-#94 := (<= #93 0::Int)
-#97 := (not #94)
-#106 := (or #97 #76 #89)
-#111 := (not #106)
-#16 := (<= #9 #14)
-#15 := (< #11 #14)
-#17 := (implies #15 #16)
-#12 := (<= #9 #11)
-#18 := (implies #12 #17)
-#19 := (not #18)
-#114 := (iff #19 #111)
-#58 := (not #15)
-#59 := (or #58 #16)
-#65 := (not #12)
-#66 := (or #65 #59)
-#71 := (not #66)
-#112 := (iff #71 #111)
-#109 := (iff #66 #106)
-#100 := (or #76 #89)
-#103 := (or #97 #100)
-#107 := (iff #103 #106)
-#108 := [rewrite]: #107
-#104 := (iff #66 #103)
-#101 := (iff #59 #100)
-#90 := (iff #16 #89)
-#91 := [rewrite]: #90
-#86 := (iff #58 #76)
-#75 := (not #76)
-#81 := (not #75)
-#84 := (iff #81 #76)
-#85 := [rewrite]: #84
-#82 := (iff #58 #81)
-#79 := (iff #15 #75)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#87 := [trans #83 #85]: #86
-#102 := [monotonicity #87 #91]: #101
-#98 := (iff #65 #97)
-#95 := (iff #12 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#105 := [monotonicity #99 #102]: #104
-#110 := [trans #105 #108]: #109
-#113 := [monotonicity #110]: #112
-#72 := (iff #19 #71)
-#69 := (iff #18 #66)
-#62 := (implies #12 #59)
-#67 := (iff #62 #66)
-#68 := [rewrite]: #67
-#63 := (iff #18 #62)
-#60 := (iff #17 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#70 := [trans #64 #68]: #69
-#73 := [monotonicity #70]: #72
-#115 := [trans #73 #113]: #114
-#57 := [asserted]: #19
-#116 := [mp #57 #115]: #111
-#120 := [not-or-elim #116]: #119
-#118 := [not-or-elim #116]: #75
-#117 := [not-or-elim #116]: #94
-[th-lemma arith farkas 1 1 1 #117 #118 #120]: false
-unsat
-355ace00757b4951a8f0a007e56528f29f4c829d 91 0
-#2 := false
-#26 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#13 := f7
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 f7)
-#74 := -1::Int
-#77 := (* -1::Int #14)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#90 := (+ #9 #77)
-#89 := (>= #90 0::Int)
-#88 := (not #89)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#78 := (+ #11 #77)
-#76 := (>= #78 0::Int)
-#95 := (* -1::Int #11)
-#96 := (+ #9 #95)
-#94 := (>= #96 0::Int)
-#112 := (or #94 #76 #88)
-#117 := (not #112)
-#16 := (< #9 #14)
-#15 := (< #11 #14)
-#17 := (implies #15 #16)
-#12 := (< #9 #11)
-#18 := (implies #12 #17)
-#19 := (not #18)
-#120 := (iff #19 #117)
-#58 := (not #15)
-#59 := (or #58 #16)
-#65 := (not #12)
-#66 := (or #65 #59)
-#71 := (not #66)
-#118 := (iff #71 #117)
-#115 := (iff #66 #112)
-#106 := (or #76 #88)
-#109 := (or #94 #106)
-#113 := (iff #109 #112)
-#114 := [rewrite]: #113
-#110 := (iff #66 #109)
-#107 := (iff #59 #106)
-#91 := (iff #16 #88)
-#92 := [rewrite]: #91
-#86 := (iff #58 #76)
-#75 := (not #76)
-#81 := (not #75)
-#84 := (iff #81 #76)
-#85 := [rewrite]: #84
-#82 := (iff #58 #81)
-#79 := (iff #15 #75)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#87 := [trans #83 #85]: #86
-#108 := [monotonicity #87 #92]: #107
-#104 := (iff #65 #94)
-#93 := (not #94)
-#99 := (not #93)
-#102 := (iff #99 #94)
-#103 := [rewrite]: #102
-#100 := (iff #65 #99)
-#97 := (iff #12 #93)
-#98 := [rewrite]: #97
-#101 := [monotonicity #98]: #100
-#105 := [trans #101 #103]: #104
-#111 := [monotonicity #105 #108]: #110
-#116 := [trans #111 #114]: #115
-#119 := [monotonicity #116]: #118
-#72 := (iff #19 #71)
-#69 := (iff #18 #66)
-#62 := (implies #12 #59)
-#67 := (iff #62 #66)
-#68 := [rewrite]: #67
-#63 := (iff #18 #62)
-#60 := (iff #17 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#70 := [trans #64 #68]: #69
-#73 := [monotonicity #70]: #72
-#121 := [trans #73 #119]: #120
-#57 := [asserted]: #19
-#122 := [mp #57 #121]: #117
-#125 := [not-or-elim #122]: #89
-#124 := [not-or-elim #122]: #75
-#123 := [not-or-elim #122]: #93
-[th-lemma arith farkas 1 1 1 #123 #124 #125]: false
-unsat
-c6e2a76c11802bc1dbc13937c0da68298caebc2d 75 0
-#2 := false
-#27 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#13 := f7
-decl f4 :: S2
-#7 := f4
-#14 := (f3 f4 f7)
-#66 := -1::Int
-#74 := (* -1::Int #14)
-decl f5 :: S3
-#8 := f5
-#9 := (f3 f4 f5)
-#85 := (+ #9 #74)
-#86 := (<= #85 0::Int)
-#87 := (not #86)
-decl f6 :: S3
-#10 := f6
-#11 := (f3 f4 f6)
-#75 := (+ #11 #74)
-#73 := (>= #75 0::Int)
-#76 := (not #73)
-#69 := (* -1::Int #11)
-#70 := (+ #9 #69)
-#68 := (>= #70 0::Int)
-#67 := (not #68)
-#79 := (and #67 #76)
-#82 := (not #79)
-#97 := (or #82 #86)
-#100 := (not #97)
-#17 := (< #14 #9)
-#18 := (not #17)
-#15 := (< #11 #14)
-#12 := (< #9 #11)
-#16 := (and #12 #15)
-#19 := (implies #16 #18)
-#20 := (not #19)
-#103 := (iff #20 #100)
-#59 := (not #16)
-#60 := (or #59 #18)
-#63 := (not #60)
-#101 := (iff #63 #100)
-#98 := (iff #60 #97)
-#95 := (iff #18 #86)
-#90 := (not #87)
-#93 := (iff #90 #86)
-#94 := [rewrite]: #93
-#91 := (iff #18 #90)
-#88 := (iff #17 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#96 := [trans #92 #94]: #95
-#83 := (iff #59 #82)
-#80 := (iff #16 #79)
-#77 := (iff #15 #76)
-#78 := [rewrite]: #77
-#71 := (iff #12 #67)
-#72 := [rewrite]: #71
-#81 := [monotonicity #72 #78]: #80
-#84 := [monotonicity #81]: #83
-#99 := [monotonicity #84 #96]: #98
-#102 := [monotonicity #99]: #101
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#104 := [trans #65 #102]: #103
-#58 := [asserted]: #20
-#105 := [mp #58 #104]: #100
-#109 := [not-or-elim #105]: #87
-#106 := [not-or-elim #105]: #79
-#108 := [and-elim #106]: #76
-#107 := [and-elim #106]: #67
-[th-lemma arith farkas 1 1 1 #107 #108 #109]: false
-unsat
-f1af9130b40233478fdc7662d2e61597d0d0c162 17 0
-#2 := false
-#7 := 0::Int
-#8 := (= 0::Int 0::Int)
-#9 := (not #8)
-#37 := (iff #9 false)
-#1 := true
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
-[mp #29 #38]: false
-unsat
-df5bd564889a3a421a410f30957cfbf7950c8d24 25 0
-#2 := false
-#7 := 0::Int
-#8 := (- 0::Int)
-#9 := (= 0::Int #8)
-#10 := (not #9)
-#45 := (iff #10 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #10 #40)
-#38 := (iff #9 true)
-#33 := (= 0::Int 0::Int)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (= #8 0::Int)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #10
-[mp #30 #46]: false
-unsat
-7bb6bad9020ee08bca9f57f4097fba1ccde7a752 17 0
-#2 := false
-#7 := 1::Int
-#8 := (= 1::Int 1::Int)
-#9 := (not #8)
-#38 := (iff #9 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
-unsat
-e358808f536492e400da2798c38454f7a31ee728 34 0
-#2 := false
-#7 := 1::Int
-#8 := (- 1::Int)
-#9 := (= #8 1::Int)
-#10 := (not #9)
-#11 := (not #10)
-#55 := (iff #11 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #11 #50)
-#48 := (iff #10 true)
-#43 := (not false)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #10 #43)
-#41 := (iff #9 false)
-#33 := -1::Int
-#36 := (= -1::Int 1::Int)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #9 #36)
-#34 := (= #8 -1::Int)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#32 := [asserted]: #11
-[mp #32 #56]: false
-unsat
-289258b061b6c2ab7d0444f514f156a31ab808a5 40 0
-#2 := false
-#11 := 567::Int
-#9 := 345::Int
-#7 := 123::Int
-#8 := (- 123::Int)
-#10 := (+ #8 345::Int)
-#12 := (< #10 567::Int)
-#13 := (not #12)
-#61 := (iff #13 false)
-#41 := 222::Int
-#46 := (< 222::Int 567::Int)
-#49 := (not #46)
-#59 := (iff #49 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #49 #54)
-#52 := (iff #46 true)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#50 := (iff #13 #49)
-#47 := (iff #12 #46)
-#44 := (= #10 222::Int)
-#35 := -123::Int
-#38 := (+ -123::Int 345::Int)
-#42 := (= #38 222::Int)
-#43 := [rewrite]: #42
-#39 := (= #10 #38)
-#36 := (= #8 -123::Int)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#62 := [trans #51 #60]: #61
-#34 := [asserted]: #13
-[mp #34 #62]: false
-unsat
-ec3d9bd94c80cde36f0de69695b202f9ddf0b4fa 30 0
-#2 := false
-#9 := 2345678901::Int
-#7 := 123456789::Int
-#8 := (- 123456789::Int)
-#10 := (< #8 2345678901::Int)
-#11 := (not #10)
-#51 := (iff #11 false)
-#33 := -123456789::Int
-#36 := (< -123456789::Int 2345678901::Int)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #11 #39)
-#37 := (iff #10 #36)
-#34 := (= #8 -123456789::Int)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#32 := [asserted]: #11
-[mp #32 #52]: false
-unsat
-e691c4b38a0343c2894ab60a09c5cabe20925699 26 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#8 := 0::Int
-#9 := (+ f3 0::Int)
-#10 := (= #9 f3)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= f3 f3)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-5c4b8f51c8c77bd1a261a8ed01b60034ae255cfc 26 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#7 := 0::Int
-#9 := (+ 0::Int f3)
-#10 := (= #9 f3)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= f3 f3)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-01d4aea8f66d97bfd6d4aa17e6a8adfadb01a40a 29 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-decl f4 :: Int
-#8 := f4
-#10 := (+ f4 f3)
-#9 := (+ f3 f4)
-#11 := (= #9 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (= #9 #9)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (= #10 #9)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-7c37cd9f2beeef1c65d4ffd557883d8830a3d5c8 33 0
-#2 := false
-decl f5 :: Int
-#9 := f5
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#12 := (+ f3 f4)
-#13 := (+ #12 f5)
-#10 := (+ f4 f5)
-#11 := (+ f3 #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#51 := (iff #15 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #15 #46)
-#44 := (iff #14 true)
-#39 := (= #11 #11)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #14 #39)
-#37 := (= #13 #11)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#36 := [asserted]: #15
-[mp #36 #52]: false
-unsat
-f7b791c457a131b93a9eb5502d849317ab54ee47 45 0
-#2 := false
-decl f4 :: Int
-#8 := f4
-#12 := (- f4)
-decl f3 :: Int
-#7 := f3
-#13 := (= f3 #12)
-#10 := 0::Int
-#9 := (+ f3 f4)
-#11 := (= #9 0::Int)
-#14 := (iff #11 #13)
-#15 := (not #14)
-#64 := (iff #15 false)
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#40 := (= f3 #37)
-#49 := (not #11)
-#50 := (iff #49 #40)
-#62 := (iff #50 false)
-#57 := (iff #49 #11)
-#60 := (iff #57 false)
-#61 := [rewrite]: #60
-#58 := (iff #50 #57)
-#55 := (iff #40 #11)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#53 := (iff #15 #50)
-#43 := (iff #11 #40)
-#46 := (not #43)
-#51 := (iff #46 #50)
-#52 := [rewrite]: #51
-#47 := (iff #15 #46)
-#44 := (iff #14 #43)
-#41 := (iff #13 #40)
-#38 := (= #12 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#54 := [trans #48 #52]: #53
-#65 := [trans #54 #63]: #64
-#35 := [asserted]: #15
-[mp #35 #65]: false
-unsat
-310dcc34c35fac2a90c97769561f401f5711a5cb 26 0
-#2 := false
-#7 := 1::Int
-#8 := (- 1::Int)
-#9 := (= #8 #8)
-#10 := (not #9)
-#47 := (iff #10 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #10 #42)
-#40 := (iff #9 true)
-#32 := -1::Int
-#35 := (= -1::Int -1::Int)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #9 #35)
-#33 := (= #8 -1::Int)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #10
-[mp #31 #48]: false
-unsat
-cec035ee1776e184f791b0a4756799d613e13376 26 0
-#2 := false
-#7 := 3::Int
-#8 := (- 3::Int)
-#9 := (= #8 #8)
-#10 := (not #9)
-#47 := (iff #10 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #10 #42)
-#40 := (iff #9 true)
-#32 := -3::Int
-#35 := (= -3::Int -3::Int)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #9 #35)
-#33 := (= #8 -3::Int)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #10
-[mp #31 #48]: false
-unsat
-3815df4ff70adc684db4806205e34634fa08e24e 53 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#9 := 0::Int
-#11 := (< 0::Int f3)
-#8 := (- f3)
-#10 := (< #8 0::Int)
-#12 := (iff #10 #11)
-#13 := (not #12)
-#73 := (iff #13 false)
-#34 := -1::Int
-#35 := (* -1::Int f3)
-#38 := (< #35 0::Int)
-#47 := (not #38)
-#48 := (iff #47 #11)
-#71 := (iff #48 false)
-#53 := (<= f3 0::Int)
-#54 := (not #53)
-#66 := (iff #53 #54)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #48 #66)
-#64 := (iff #11 #54)
-#65 := [rewrite]: #64
-#62 := (iff #47 #53)
-#57 := (not #54)
-#60 := (iff #57 #53)
-#61 := [rewrite]: #60
-#58 := (iff #47 #57)
-#55 := (iff #38 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#72 := [trans #68 #70]: #71
-#51 := (iff #13 #48)
-#41 := (iff #38 #11)
-#44 := (not #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#39 := (iff #10 #38)
-#36 := (= #8 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#74 := [trans #52 #72]: #73
-#33 := [asserted]: #13
-[mp #33 #74]: false
-unsat
-0a4435dcf9c2c38efb971e8501cc52dde8c28b6b 61 0
-#2 := false
-#7 := 0::Int
-decl f3 :: Int
-#8 := f3
-#10 := (- f3)
-#11 := (< #10 0::Int)
-#9 := (< 0::Int f3)
-#12 := (implies #9 #11)
-#13 := (not #12)
-#80 := (iff #13 false)
-#34 := -1::Int
-#35 := (* -1::Int f3)
-#38 := (< #35 0::Int)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#78 := (iff #50 false)
-#1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #50 #73)
-#71 := (iff #45 true)
-#53 := (<= f3 0::Int)
-#54 := (not #53)
-#66 := (or #53 #54)
-#69 := (iff #66 true)
-#70 := [rewrite]: #69
-#67 := (iff #45 #66)
-#64 := (iff #38 #54)
-#65 := [rewrite]: #64
-#62 := (iff #44 #53)
-#57 := (not #54)
-#60 := (iff #57 #53)
-#61 := [rewrite]: #60
-#58 := (iff #44 #57)
-#55 := (iff #9 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#72 := [trans #68 #70]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#51 := (iff #13 #50)
-#48 := (iff #12 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#81 := [trans #52 #79]: #80
-#33 := [asserted]: #13
-[mp #33 #81]: false
-unsat
-ff6b944415a61fef8e7066737bb3f4071effee41 61 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#10 := (- f3)
-#8 := 0::Int
-#11 := (< 0::Int #10)
-#9 := (< f3 0::Int)
-#12 := (implies #9 #11)
-#13 := (not #12)
-#80 := (iff #13 false)
-#34 := -1::Int
-#35 := (* -1::Int f3)
-#38 := (< 0::Int #35)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#78 := (iff #50 false)
-#1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #50 #73)
-#71 := (iff #45 true)
-#53 := (>= f3 0::Int)
-#54 := (not #53)
-#66 := (or #53 #54)
-#69 := (iff #66 true)
-#70 := [rewrite]: #69
-#67 := (iff #45 #66)
-#64 := (iff #38 #54)
-#65 := [rewrite]: #64
-#62 := (iff #44 #53)
-#57 := (not #54)
-#60 := (iff #57 #53)
-#61 := [rewrite]: #60
-#58 := (iff #44 #57)
-#55 := (iff #9 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#72 := [trans #68 #70]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#51 := (iff #13 #50)
-#48 := (iff #12 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#81 := [trans #52 #79]: #80
-#33 := [asserted]: #13
-[mp #33 #81]: false
-unsat
-1edbd3da42c4e3944ae42bd9887fadb3437e96a1 26 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#8 := 0::Int
-#9 := (- f3 0::Int)
-#10 := (= #9 f3)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= f3 f3)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-b83a075b345830e9b6e6ce14a816684d0ce48153 32 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#10 := (- f3)
-#7 := 0::Int
-#9 := (- 0::Int f3)
-#11 := (= #9 #10)
-#12 := (not #11)
-#51 := (iff #12 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (iff #11 true)
-#33 := -1::Int
-#34 := (* -1::Int f3)
-#39 := (= #34 #34)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#37 := (= #10 #34)
-#38 := [rewrite]: #37
-#35 := (= #9 #34)
-#36 := [rewrite]: #35
-#41 := [monotonicity #36 #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-cd3e641f4c63603b28155ba6239b2f0c22391251 64 0
-#2 := false
-#11 := 0::Int
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#10 := (- f3 f4)
-#12 := (< #10 0::Int)
-#9 := (< f3 f4)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#82 := (iff #14 false)
-#35 := -1::Int
-#36 := (* -1::Int f4)
-#37 := (+ f3 #36)
-#40 := (< #37 0::Int)
-#46 := (not #9)
-#47 := (or #46 #40)
-#52 := (not #47)
-#80 := (iff #52 false)
-#1 := true
-#75 := (not true)
-#78 := (iff #75 false)
-#79 := [rewrite]: #78
-#76 := (iff #52 #75)
-#73 := (iff #47 true)
-#56 := (>= #37 0::Int)
-#55 := (not #56)
-#68 := (or #56 #55)
-#71 := (iff #68 true)
-#72 := [rewrite]: #71
-#69 := (iff #47 #68)
-#66 := (iff #40 #55)
-#67 := [rewrite]: #66
-#64 := (iff #46 #56)
-#59 := (not #55)
-#62 := (iff #59 #56)
-#63 := [rewrite]: #62
-#60 := (iff #46 #59)
-#57 := (iff #9 #55)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#70 := [monotonicity #65 #67]: #69
-#74 := [trans #70 #72]: #73
-#77 := [monotonicity #74]: #76
-#81 := [trans #77 #79]: #80
-#53 := (iff #14 #52)
-#50 := (iff #13 #47)
-#43 := (implies #9 #40)
-#48 := (iff #43 #47)
-#49 := [rewrite]: #48
-#44 := (iff #13 #43)
-#41 := (iff #12 #40)
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#51 := [trans #45 #49]: #50
-#54 := [monotonicity #51]: #53
-#83 := [trans #54 #81]: #82
-#34 := [asserted]: #14
-[mp #34 #83]: false
-unsat
-61cdc1fc5eb0d0636c10956aeb832369d0478262 44 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-decl f4 :: Int
-#8 := f4
-#10 := (- f4 f3)
-#11 := (- #10)
-#9 := (- f3 f4)
-#12 := (= #9 #11)
-#13 := (not #12)
-#63 := (iff #13 false)
-#1 := true
-#58 := (not true)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #13 #58)
-#56 := (iff #12 true)
-#35 := -1::Int
-#36 := (* -1::Int f4)
-#37 := (+ f3 #36)
-#51 := (= #37 #37)
-#54 := (iff #51 true)
-#55 := [rewrite]: #54
-#52 := (iff #12 #51)
-#49 := (= #11 #37)
-#40 := (* -1::Int f3)
-#41 := (+ #40 f4)
-#44 := (- #41)
-#47 := (= #44 #37)
-#48 := [rewrite]: #47
-#45 := (= #11 #44)
-#42 := (= #10 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#38 := (= #9 #37)
-#39 := [rewrite]: #38
-#53 := [monotonicity #39 #50]: #52
-#57 := [trans #53 #55]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#34 := [asserted]: #13
-[mp #34 #64]: false
-unsat
-1f1c398b527ff7ee3d1a5967ff2a131100a56323 42 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-decl f4 :: Int
-#8 := f4
-#10 := (- f4)
-#11 := (+ #10 f3)
-#9 := (- f3 f4)
-#12 := (= #9 #11)
-#13 := (not #12)
-#61 := (iff #13 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #13 #56)
-#54 := (iff #12 true)
-#35 := -1::Int
-#36 := (* -1::Int f4)
-#37 := (+ f3 #36)
-#49 := (= #37 #37)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #12 #49)
-#47 := (= #11 #37)
-#42 := (+ #36 f3)
-#45 := (= #42 #37)
-#46 := [rewrite]: #45
-#43 := (= #11 #42)
-#40 := (= #10 #36)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#38 := (= #9 #37)
-#39 := [rewrite]: #38
-#51 := [monotonicity #39 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#34 := [asserted]: #13
-[mp #34 #62]: false
-unsat
-d180958823e52c24cdf709d7b779e581a5146a9d 48 0
-#2 := false
-decl f5 :: Int
-#10 := f5
-decl f4 :: Int
-#8 := f4
-#12 := (+ f4 f5)
-decl f3 :: Int
-#7 := f3
-#13 := (- f3 #12)
-#9 := (- f3 f4)
-#11 := (- #9 f5)
-#14 := (= #11 #13)
-#15 := (not #14)
-#66 := (iff #15 false)
-#1 := true
-#61 := (not true)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #15 #61)
-#59 := (iff #14 true)
-#37 := -1::Int
-#45 := (* -1::Int f5)
-#38 := (* -1::Int f4)
-#46 := (+ #38 #45)
-#47 := (+ f3 #46)
-#54 := (= #47 #47)
-#57 := (iff #54 true)
-#58 := [rewrite]: #57
-#55 := (iff #14 #54)
-#52 := (= #13 #47)
-#53 := [rewrite]: #52
-#50 := (= #11 #47)
-#39 := (+ f3 #38)
-#42 := (- #39 f5)
-#48 := (= #42 #47)
-#49 := [rewrite]: #48
-#43 := (= #11 #42)
-#40 := (= #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#51 := [trans #44 #49]: #50
-#56 := [monotonicity #51 #53]: #55
-#60 := [trans #56 #58]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#36 := [asserted]: #15
-[mp #36 #67]: false
-unsat
-e52eb52be8591bb795a077857670e69de11af1da 26 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#7 := f3
-#9 := (* f3 0::Int)
-#10 := (= #9 0::Int)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= 0::Int 0::Int)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-44b181d9f3d713df94663408b08cd9af6cbe23f9 26 0
-#2 := false
-#7 := 0::Int
-decl f3 :: Int
-#8 := f3
-#9 := (* 0::Int f3)
-#10 := (= #9 0::Int)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= 0::Int 0::Int)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-723479197e5c26fbfd35522ce4cd26d5915d7119 26 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#8 := 1::Int
-#9 := (* f3 1::Int)
-#10 := (= #9 f3)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
-unsat
-07b026f7999300309ad1aa93f8da68492163aa1d 26 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#7 := 1::Int
-#9 := (* 1::Int f3)
-#10 := (= #9 f3)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
-unsat
-e5021087f8c15699d6bd7188a85d3d91458b6e0f 40 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#11 := (- f3)
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := (* f3 #9)
-#12 := (= #10 #11)
-#13 := (not #12)
-#60 := (iff #13 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #13 #55)
-#53 := (iff #12 true)
-#35 := -1::Int
-#41 := (* -1::Int f3)
-#48 := (= #41 #41)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #12 #48)
-#46 := (= #11 #41)
-#47 := [rewrite]: #46
-#44 := (= #10 #41)
-#38 := (* f3 -1::Int)
-#42 := (= #38 #41)
-#43 := [rewrite]: #42
-#39 := (= #10 #38)
-#36 := (= #9 -1::Int)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#50 := [monotonicity #45 #47]: #49
-#54 := [trans #50 #52]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#34 := [asserted]: #13
-[mp #34 #61]: false
-unsat
-92512c29655e3be3ef6191609f8fa8665ffb186f 35 0
-#2 := false
-decl f3 :: Int
-#9 := f3
-#11 := (- f3)
-#7 := 1::Int
-#8 := (- 1::Int)
-#10 := (* #8 f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#55 := (iff #13 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #13 #50)
-#48 := (iff #12 true)
-#35 := -1::Int
-#38 := (* -1::Int f3)
-#43 := (= #38 #38)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (= #11 #38)
-#42 := [rewrite]: #41
-#39 := (= #10 #38)
-#36 := (= #8 -1::Int)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [monotonicity #40 #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#34 := [asserted]: #13
-[mp #34 #56]: false
-unsat
-63a5902a5fc3cd2e10705ba8b00e69639073cd3f 28 0
-#2 := false
-#7 := 3::Int
-decl f3 :: Int
-#8 := f3
-#10 := (* f3 3::Int)
-#9 := (* 3::Int f3)
-#11 := (= #9 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (= #9 #9)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (= #10 #9)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-238cf59caa00b771da8649f78ab90d7b2fb747c2 238 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#15 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#13 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#14 := (f4 f5 #13)
-#16 := (f3 #14 #15)
-#726 := (pattern #16)
-#8 := 0::Int
-#66 := -1::Int
-#70 := (* -1::Int #15)
-#67 := (* -1::Int #13)
-#73 := (div #67 #70)
-#224 := (* -1::Int #73)
-#225 := (+ #16 #224)
-#226 := (= #225 0::Int)
-#26 := (div #13 #15)
-#221 := (* -1::Int #26)
-#222 := (+ #16 #221)
-#223 := (= #222 0::Int)
-#92 := (<= #15 0::Int)
-#99 := (>= #13 0::Int)
-#184 := (or #99 #92)
-#185 := (not #184)
-#88 := (<= #13 0::Int)
-#182 := (or #88 #92)
-#183 := (not #182)
-#188 := (or #183 #185)
-#227 := (if #188 #223 #226)
-#220 := (= #16 0::Int)
-#18 := (= #15 0::Int)
-#17 := (= #13 0::Int)
-#19 := (or #17 #18)
-#228 := (if #19 #220 #227)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #228)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#730 := (iff #231 #727)
-#728 := (iff #228 #228)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#191 := (if #188 #26 #73)
-#194 := (if #19 0::Int #191)
-#197 := (= #16 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#232 := (iff #200 #231)
-#229 := (iff #197 #228)
-#230 := [rewrite]: #229
-#233 := [quant-intro #230]: #232
-#93 := (not #92)
-#100 := (not #99)
-#103 := (and #100 #93)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (if #106 #26 #73)
-#112 := (if #19 0::Int #109)
-#115 := (= #16 #112)
-#118 := (forall (vars (?v0 Int) (?v1 Int)) #115)
-#201 := (iff #118 #200)
-#198 := (iff #115 #197)
-#195 := (= #112 #194)
-#192 := (= #109 #191)
-#189 := (iff #106 #188)
-#186 := (iff #103 #185)
-#187 := [rewrite]: #186
-#176 := (iff #96 #183)
-#177 := [rewrite]: #176
-#190 := [monotonicity #177 #187]: #189
-#193 := [monotonicity #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#180 := (~ #118 #118)
-#178 := (~ #115 #115)
-#179 := [refl]: #178
-#181 := [nnf-pos #179]: #180
-#28 := (- #15)
-#27 := (- #13)
-#29 := (div #27 #28)
-#21 := (< 0::Int #15)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (if #25 #26 #29)
-#31 := (if #19 0::Int #30)
-#32 := (= #16 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#121 := (iff #33 #118)
-#76 := (if #25 #26 #73)
-#79 := (if #19 0::Int #76)
-#82 := (= #16 #79)
-#85 := (forall (vars (?v0 Int) (?v1 Int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #25 #106)
-#104 := (iff #24 #103)
-#94 := (iff #21 #93)
-#95 := [rewrite]: #94
-#101 := (iff #23 #100)
-#102 := [rewrite]: #101
-#105 := [monotonicity #102 #95]: #104
-#97 := (iff #22 #96)
-#90 := (iff #20 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #33 #85)
-#83 := (iff #32 #82)
-#80 := (= #31 #79)
-#77 := (= #30 #76)
-#74 := (= #29 #73)
-#71 := (= #28 #70)
-#72 := [rewrite]: #71
-#68 := (= #27 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#65 := [asserted]: #33
-#123 := [mp #65 #122]: #118
-#172 := [mp~ #123 #181]: #118
-#203 := [mp #172 #202]: #200
-#234 := [mp #203 #233]: #231
-#732 := [mp #234 #731]: #727
-#9 := (f4 f5 0::Int)
-#10 := (f3 #9 0::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#64 := [asserted]: #12
-#685 := (not #727)
-#680 := (or #685 #11)
-#377 := (* -1::Int 0::Int)
-#507 := (div #377 #377)
-#714 := (* -1::Int #507)
-#388 := (+ #10 #714)
-#389 := (= #388 0::Int)
-#404 := (div 0::Int 0::Int)
-#383 := (* -1::Int #404)
-#718 := (+ #10 #383)
-#720 := (= #718 0::Int)
-#398 := (<= 0::Int 0::Int)
-#401 := (>= 0::Int 0::Int)
-#402 := (or #401 #398)
-#403 := (not #402)
-#399 := (or #398 #398)
-#390 := (not #399)
-#400 := (or #390 #403)
-#721 := (if #400 #720 #389)
-#313 := (= 0::Int 0::Int)
-#397 := (or #313 #313)
-#722 := (if #397 #11 #721)
-#686 := (or #685 #722)
-#528 := (iff #686 #680)
-#671 := (iff #680 #680)
-#672 := [rewrite]: #671
-#679 := (iff #722 #11)
-#1 := true
-#692 := (if true #11 #720)
-#683 := (iff #692 #11)
-#678 := [rewrite]: #683
-#681 := (iff #722 #692)
-#691 := (iff #721 #720)
-#411 := (if false #720 #720)
-#405 := (iff #411 #720)
-#687 := [rewrite]: #405
-#689 := (iff #721 #411)
-#409 := (iff #389 #720)
-#698 := (= #388 #718)
-#697 := (= #714 #383)
-#419 := (= #507 #404)
-#696 := (= #377 0::Int)
-#418 := [rewrite]: #696
-#693 := [monotonicity #418 #418]: #419
-#694 := [monotonicity #693]: #697
-#408 := [monotonicity #694]: #698
-#410 := [monotonicity #408]: #409
-#319 := (iff #400 false)
-#700 := (or false false)
-#424 := (iff #700 false)
-#425 := [rewrite]: #424
-#422 := (iff #400 #700)
-#713 := (iff #403 false)
-#367 := (not true)
-#705 := (iff #367 false)
-#706 := [rewrite]: #705
-#712 := (iff #403 #367)
-#351 := (iff #402 true)
-#719 := (or true true)
-#375 := (iff #719 true)
-#380 := [rewrite]: #375
-#709 := (iff #402 #719)
-#717 := (iff #398 true)
-#360 := [rewrite]: #717
-#708 := (iff #401 true)
-#346 := [rewrite]: #708
-#711 := [monotonicity #346 #360]: #709
-#352 := [trans #711 #380]: #351
-#710 := [monotonicity #352]: #712
-#699 := [trans #710 #706]: #713
-#707 := (iff #390 false)
-#703 := (iff #390 #367)
-#365 := (iff #399 true)
-#701 := (iff #399 #719)
-#364 := [monotonicity #360 #360]: #701
-#366 := [trans #364 #380]: #365
-#704 := [monotonicity #366]: #703
-#702 := [trans #704 #706]: #707
-#423 := [monotonicity #702 #699]: #422
-#695 := [trans #423 #425]: #319
-#690 := [monotonicity #695 #410]: #689
-#688 := [trans #690 #687]: #691
-#716 := (iff #397 true)
-#725 := (iff #397 #719)
-#723 := (iff #313 true)
-#724 := [rewrite]: #723
-#715 := [monotonicity #724 #724]: #725
-#376 := [trans #715 #380]: #716
-#682 := [monotonicity #376 #688]: #681
-#684 := [trans #682 #678]: #679
-#529 := [monotonicity #684]: #528
-#673 := [trans #529 #672]: #528
-#527 := [quant-inst #8 #8]: #686
-#674 := [mp #527 #673]: #680
-[unit-resolution #674 #64 #732]: false
-unsat
-6309bf780f2ba9dd55b826441e74066dc2c9aa9e 251 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#727 := (pattern #17)
-#10 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #16)
-#68 := (* -1::Int #14)
-#74 := (div #68 #71)
-#225 := (* -1::Int #74)
-#226 := (+ #17 #225)
-#227 := (= #226 0::Int)
-#27 := (div #14 #16)
-#222 := (* -1::Int #27)
-#223 := (+ #17 #222)
-#224 := (= #223 0::Int)
-#93 := (<= #16 0::Int)
-#100 := (>= #14 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #14 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#228 := (if #189 #224 #227)
-#221 := (= #17 0::Int)
-#19 := (= #16 0::Int)
-#18 := (= #14 0::Int)
-#20 := (or #18 #19)
-#229 := (if #20 #221 #228)
-#728 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #727) #229)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#731 := (iff #232 #728)
-#729 := (iff #229 #229)
-#730 := [refl]: #729
-#732 := [quant-intro #730]: #731
-#192 := (if #189 #27 #74)
-#195 := (if #20 0::Int #192)
-#198 := (= #17 #195)
-#201 := (forall (vars (?v0 Int) (?v1 Int)) #198)
-#233 := (iff #201 #232)
-#230 := (iff #198 #229)
-#231 := [rewrite]: #230
-#234 := [quant-intro #231]: #233
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (if #107 #27 #74)
-#113 := (if #20 0::Int #110)
-#116 := (= #17 #113)
-#119 := (forall (vars (?v0 Int) (?v1 Int)) #116)
-#202 := (iff #119 #201)
-#199 := (iff #116 #198)
-#196 := (= #113 #195)
-#193 := (= #110 #192)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [quant-intro #200]: #202
-#181 := (~ #119 #119)
-#179 := (~ #116 #116)
-#180 := [refl]: #179
-#182 := [nnf-pos #180]: #181
-#29 := (- #16)
-#28 := (- #14)
-#30 := (div #28 #29)
-#22 := (< 0::Int #16)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (if #26 #27 #30)
-#32 := (if #20 0::Int #31)
-#33 := (= #17 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#122 := (iff #34 #119)
-#77 := (if #26 #27 #74)
-#80 := (if #20 0::Int #77)
-#83 := (= #17 #80)
-#86 := (forall (vars (?v0 Int) (?v1 Int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #26 #107)
-#105 := (iff #25 #104)
-#95 := (iff #22 #94)
-#96 := [rewrite]: #95
-#102 := (iff #24 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #23 #97)
-#91 := (iff #21 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #34 #86)
-#84 := (iff #33 #83)
-#81 := (= #32 #80)
-#78 := (= #31 #77)
-#75 := (= #30 #74)
-#72 := (= #29 #71)
-#73 := [rewrite]: #72
-#69 := (= #28 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#66 := [asserted]: #34
-#124 := [mp #66 #123]: #119
-#173 := [mp~ #124 #182]: #119
-#204 := [mp #173 #203]: #201
-#235 := [mp #204 #234]: #232
-#733 := [mp #235 #732]: #728
-decl f6 :: Int
-#8 := f6
-#9 := (f4 f5 f6)
-#11 := (f3 #9 0::Int)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#670 := (not #728)
-#676 := (or #670 #12)
-#389 := (* -1::Int 0::Int)
-#715 := (* -1::Int f6)
-#390 := (div #715 #389)
-#722 := (* -1::Int #390)
-#723 := (+ #11 #722)
-#724 := (= #723 0::Int)
-#719 := (div f6 0::Int)
-#721 := (* -1::Int #719)
-#378 := (+ #11 #721)
-#508 := (= #378 0::Int)
-#391 := (<= 0::Int 0::Int)
-#404 := (>= f6 0::Int)
-#401 := (or #404 #391)
-#405 := (not #401)
-#400 := (<= f6 0::Int)
-#402 := (or #400 #391)
-#403 := (not #402)
-#384 := (or #403 #405)
-#725 := (if #384 #508 #724)
-#398 := (= 0::Int 0::Int)
-#314 := (= f6 0::Int)
-#399 := (or #314 #398)
-#720 := (if #399 #12 #725)
-#677 := (or #670 #720)
-#678 := (iff #677 #676)
-#509 := (iff #676 #676)
-#510 := [rewrite]: #509
-#675 := (iff #720 #12)
-#411 := (div #715 0::Int)
-#691 := (* -1::Int #411)
-#692 := (+ #11 #691)
-#682 := (= #692 0::Int)
-#1 := true
-#529 := (if true #12 #682)
-#673 := (iff #529 #12)
-#674 := [rewrite]: #673
-#530 := (iff #720 #529)
-#687 := (iff #725 #682)
-#679 := (if false #508 #682)
-#686 := (iff #679 #682)
-#681 := [rewrite]: #686
-#680 := (iff #725 #679)
-#683 := (iff #724 #682)
-#689 := (= #723 #692)
-#406 := (= #722 #691)
-#412 := (= #390 #411)
-#409 := (= #389 0::Int)
-#410 := [rewrite]: #409
-#690 := [monotonicity #410]: #412
-#688 := [monotonicity #690]: #406
-#693 := [monotonicity #688]: #689
-#684 := [monotonicity #693]: #683
-#695 := (iff #384 false)
-#697 := (or false false)
-#694 := (iff #697 false)
-#698 := [rewrite]: #694
-#419 := (iff #384 #697)
-#320 := (iff #405 false)
-#703 := (not true)
-#710 := (iff #703 false)
-#712 := [rewrite]: #710
-#425 := (iff #405 #703)
-#423 := (iff #401 true)
-#713 := (or #404 true)
-#700 := (iff #713 true)
-#701 := [rewrite]: #700
-#711 := (iff #401 #713)
-#365 := (iff #391 true)
-#366 := [rewrite]: #365
-#714 := [monotonicity #366]: #711
-#424 := [trans #714 #701]: #423
-#426 := [monotonicity #424]: #425
-#696 := [trans #426 #712]: #320
-#352 := (iff #403 false)
-#709 := (iff #403 #703)
-#707 := (iff #402 true)
-#367 := (or #400 true)
-#705 := (iff #367 true)
-#706 := [rewrite]: #705
-#368 := (iff #402 #367)
-#704 := [monotonicity #366]: #368
-#708 := [trans #704 #706]: #707
-#347 := [monotonicity #708]: #709
-#353 := [trans #347 #712]: #352
-#420 := [monotonicity #353 #696]: #419
-#699 := [trans #420 #698]: #695
-#685 := [monotonicity #699 #684]: #680
-#528 := [trans #685 #681]: #687
-#361 := (iff #399 true)
-#376 := (or #314 true)
-#377 := (iff #376 true)
-#718 := [rewrite]: #377
-#381 := (iff #399 #376)
-#726 := (iff #398 true)
-#716 := [rewrite]: #726
-#717 := [monotonicity #716]: #381
-#702 := [trans #717 #718]: #361
-#672 := [monotonicity #702 #528]: #530
-#669 := [trans #672 #674]: #675
-#507 := [monotonicity #669]: #678
-#663 := [trans #507 #510]: #678
-#671 := [quant-inst #8 #10]: #677
-#664 := [mp #671 #663]: #676
-[unit-resolution #664 #65 #733]: false
-unsat
-06fdbb5d35836ddf21804a31fcb1c796b637cebe 272 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#726 := (pattern #17)
-#8 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #16)
-#68 := (* -1::Int #14)
-#74 := (div #68 #71)
-#225 := (* -1::Int #74)
-#226 := (+ #17 #225)
-#227 := (= #226 0::Int)
-#27 := (div #14 #16)
-#222 := (* -1::Int #27)
-#223 := (+ #17 #222)
-#224 := (= #223 0::Int)
-#93 := (<= #16 0::Int)
-#100 := (>= #14 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #14 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#228 := (if #189 #224 #227)
-#221 := (= #17 0::Int)
-#19 := (= #16 0::Int)
-#18 := (= #14 0::Int)
-#20 := (or #18 #19)
-#229 := (if #20 #221 #228)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #229)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#730 := (iff #232 #727)
-#728 := (iff #229 #229)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#192 := (if #189 #27 #74)
-#195 := (if #20 0::Int #192)
-#198 := (= #17 #195)
-#201 := (forall (vars (?v0 Int) (?v1 Int)) #198)
-#233 := (iff #201 #232)
-#230 := (iff #198 #229)
-#231 := [rewrite]: #230
-#234 := [quant-intro #231]: #233
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (if #107 #27 #74)
-#113 := (if #20 0::Int #110)
-#116 := (= #17 #113)
-#119 := (forall (vars (?v0 Int) (?v1 Int)) #116)
-#202 := (iff #119 #201)
-#199 := (iff #116 #198)
-#196 := (= #113 #195)
-#193 := (= #110 #192)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [quant-intro #200]: #202
-#181 := (~ #119 #119)
-#179 := (~ #116 #116)
-#180 := [refl]: #179
-#182 := [nnf-pos #180]: #181
-#29 := (- #16)
-#28 := (- #14)
-#30 := (div #28 #29)
-#22 := (< 0::Int #16)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (if #26 #27 #30)
-#32 := (if #20 0::Int #31)
-#33 := (= #17 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#122 := (iff #34 #119)
-#77 := (if #26 #27 #74)
-#80 := (if #20 0::Int #77)
-#83 := (= #17 #80)
-#86 := (forall (vars (?v0 Int) (?v1 Int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #26 #107)
-#105 := (iff #25 #104)
-#95 := (iff #22 #94)
-#96 := [rewrite]: #95
-#102 := (iff #24 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #23 #97)
-#91 := (iff #21 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #34 #86)
-#84 := (iff #33 #83)
-#81 := (= #32 #80)
-#78 := (= #31 #77)
-#75 := (= #30 #74)
-#72 := (= #29 #71)
-#73 := [rewrite]: #72
-#69 := (= #28 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#66 := [asserted]: #34
-#124 := [mp #66 #123]: #119
-#173 := [mp~ #124 #182]: #119
-#204 := [mp #173 #203]: #201
-#235 := [mp #204 #234]: #232
-#732 := [mp #235 #731]: #727
-#10 := 1::Int
-#9 := (f4 f5 0::Int)
-#11 := (f3 #9 1::Int)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#659 := (not #727)
-#544 := (or #659 #12)
-#388 := (* -1::Int 1::Int)
-#714 := (* -1::Int 0::Int)
-#389 := (div #714 #388)
-#721 := (* -1::Int #389)
-#722 := (+ #11 #721)
-#723 := (= #722 0::Int)
-#718 := (div 0::Int 1::Int)
-#720 := (* -1::Int #718)
-#377 := (+ #11 #720)
-#507 := (= #377 0::Int)
-#390 := (<= 1::Int 0::Int)
-#403 := (>= 0::Int 0::Int)
-#400 := (or #403 #390)
-#404 := (not #400)
-#399 := (<= 0::Int 0::Int)
-#401 := (or #399 #390)
-#402 := (not #401)
-#383 := (or #402 #404)
-#724 := (if #383 #507 #723)
-#397 := (= 1::Int 0::Int)
-#313 := (= 0::Int 0::Int)
-#398 := (or #313 #397)
-#719 := (if #398 #12 #724)
-#559 := (or #659 #719)
-#562 := (iff #559 #544)
-#563 := (iff #544 #544)
-#564 := [rewrite]: #563
-#655 := (iff #719 #12)
-#1 := true
-#550 := (if true #12 #12)
-#658 := (iff #550 #12)
-#560 := [rewrite]: #658
-#551 := (iff #719 #550)
-#667 := (iff #724 #12)
-#662 := (if false #12 #12)
-#666 := (iff #662 #12)
-#664 := [rewrite]: #666
-#663 := (iff #724 #662)
-#508 := (iff #723 #12)
-#677 := (= #722 #11)
-#691 := (+ #11 0::Int)
-#681 := (= #691 #11)
-#682 := [rewrite]: #681
-#676 := (= #722 #691)
-#669 := (= #721 0::Int)
-#689 := (= #714 0::Int)
-#690 := [rewrite]: #689
-#674 := (= #721 #714)
-#672 := (= #389 0::Int)
-#686 := (div 0::Int -1::Int)
-#529 := (= #686 0::Int)
-#671 := [rewrite]: #529
-#527 := (= #389 #686)
-#685 := (= #388 -1::Int)
-#680 := [rewrite]: #685
-#528 := [monotonicity #690 #680]: #527
-#673 := [trans #528 #671]: #672
-#668 := [monotonicity #673]: #674
-#675 := [trans #668 #690]: #669
-#670 := [monotonicity #675]: #676
-#506 := [trans #670 #682]: #677
-#509 := [monotonicity #506]: #508
-#679 := (iff #507 #12)
-#683 := (= #377 #11)
-#688 := (= #377 #691)
-#405 := (= #720 0::Int)
-#410 := (= #720 #714)
-#408 := (= #718 0::Int)
-#409 := [rewrite]: #408
-#411 := [monotonicity #409]: #410
-#687 := [trans #411 #690]: #405
-#692 := [monotonicity #687]: #688
-#678 := [trans #692 #682]: #683
-#684 := [monotonicity #678]: #679
-#694 := (iff #383 false)
-#696 := (or false false)
-#693 := (iff #696 false)
-#697 := [rewrite]: #693
-#418 := (iff #383 #696)
-#319 := (iff #404 false)
-#708 := (not true)
-#711 := (iff #708 false)
-#351 := [rewrite]: #711
-#424 := (iff #404 #708)
-#422 := (iff #400 true)
-#716 := (or true false)
-#360 := (iff #716 true)
-#701 := [rewrite]: #360
-#699 := (iff #400 #716)
-#703 := (iff #390 false)
-#704 := [rewrite]: #703
-#710 := (iff #403 true)
-#713 := [rewrite]: #710
-#700 := [monotonicity #713 #704]: #699
-#423 := [trans #700 #701]: #422
-#425 := [monotonicity #423]: #424
-#695 := [trans #425 #351]: #319
-#352 := (iff #402 false)
-#346 := (iff #402 #708)
-#707 := (iff #401 true)
-#705 := (iff #401 #716)
-#366 := (iff #399 true)
-#367 := [rewrite]: #366
-#706 := [monotonicity #367 #704]: #705
-#702 := [trans #706 #701]: #707
-#709 := [monotonicity #702]: #346
-#712 := [trans #709 #351]: #352
-#419 := [monotonicity #712 #695]: #418
-#698 := [trans #419 #697]: #694
-#665 := [monotonicity #698 #684 #509]: #663
-#549 := [trans #665 #664]: #667
-#364 := (iff #398 true)
-#376 := (iff #398 #716)
-#375 := (iff #397 false)
-#380 := [rewrite]: #375
-#725 := (iff #313 true)
-#715 := [rewrite]: #725
-#717 := [monotonicity #715 #380]: #376
-#365 := [trans #717 #701]: #364
-#510 := [monotonicity #365 #549]: #551
-#656 := [trans #510 #560]: #655
-#555 := [monotonicity #656]: #562
-#565 := [trans #555 #564]: #562
-#561 := [quant-inst #8 #10]: #559
-#566 := [mp #561 #565]: #544
-[unit-resolution #566 #65 #732]: false
-unsat
-fe9044a7983d603398b14459325449d5e84b7012 275 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#15 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#13 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#14 := (f4 f5 #13)
-#16 := (f3 #14 #15)
-#726 := (pattern #16)
-#17 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #15)
-#68 := (* -1::Int #13)
-#74 := (div #68 #71)
-#225 := (* -1::Int #74)
-#226 := (+ #16 #225)
-#227 := (= #226 0::Int)
-#27 := (div #13 #15)
-#222 := (* -1::Int #27)
-#223 := (+ #16 #222)
-#224 := (= #223 0::Int)
-#93 := (<= #15 0::Int)
-#100 := (>= #13 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #13 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#228 := (if #189 #224 #227)
-#221 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#18 := (= #13 0::Int)
-#20 := (or #18 #19)
-#229 := (if #20 #221 #228)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #229)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#730 := (iff #232 #727)
-#728 := (iff #229 #229)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#192 := (if #189 #27 #74)
-#195 := (if #20 0::Int #192)
-#198 := (= #16 #195)
-#201 := (forall (vars (?v0 Int) (?v1 Int)) #198)
-#233 := (iff #201 #232)
-#230 := (iff #198 #229)
-#231 := [rewrite]: #230
-#234 := [quant-intro #231]: #233
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (if #107 #27 #74)
-#113 := (if #20 0::Int #110)
-#116 := (= #16 #113)
-#119 := (forall (vars (?v0 Int) (?v1 Int)) #116)
-#202 := (iff #119 #201)
-#199 := (iff #116 #198)
-#196 := (= #113 #195)
-#193 := (= #110 #192)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [quant-intro #200]: #202
-#181 := (~ #119 #119)
-#179 := (~ #116 #116)
-#180 := [refl]: #179
-#182 := [nnf-pos #180]: #181
-#29 := (- #15)
-#28 := (- #13)
-#30 := (div #28 #29)
-#22 := (< 0::Int #15)
-#24 := (< #13 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #13)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (if #26 #27 #30)
-#32 := (if #20 0::Int #31)
-#33 := (= #16 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#122 := (iff #34 #119)
-#77 := (if #26 #27 #74)
-#80 := (if #20 0::Int #77)
-#83 := (= #16 #80)
-#86 := (forall (vars (?v0 Int) (?v1 Int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #26 #107)
-#105 := (iff #25 #104)
-#95 := (iff #22 #94)
-#96 := [rewrite]: #95
-#102 := (iff #24 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #23 #97)
-#91 := (iff #21 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #34 #86)
-#84 := (iff #33 #83)
-#81 := (= #32 #80)
-#78 := (= #31 #77)
-#75 := (= #30 #74)
-#72 := (= #29 #71)
-#73 := [rewrite]: #72
-#69 := (= #28 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#66 := [asserted]: #34
-#124 := [mp #66 #123]: #119
-#173 := [mp~ #124 #182]: #119
-#204 := [mp #173 #203]: #201
-#235 := [mp #204 #234]: #232
-#732 := [mp #235 #731]: #727
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#10 := (f3 #9 1::Int)
-#11 := (= #10 1::Int)
-#12 := (not #11)
-#65 := [asserted]: #12
-#561 := (not #727)
-#562 := (or #561 #11)
-#507 := (* -1::Int 1::Int)
-#714 := (div #507 #507)
-#388 := (* -1::Int #714)
-#389 := (+ #10 #388)
-#721 := (= #389 0::Int)
-#383 := (div 1::Int 1::Int)
-#718 := (* -1::Int #383)
-#720 := (+ #10 #718)
-#377 := (= #720 0::Int)
-#399 := (<= 1::Int 0::Int)
-#402 := (>= 1::Int 0::Int)
-#403 := (or #402 #399)
-#400 := (not #403)
-#390 := (or #399 #399)
-#401 := (not #390)
-#404 := (or #401 #400)
-#722 := (if #404 #377 #721)
-#398 := (= #10 0::Int)
-#313 := (= 1::Int 0::Int)
-#397 := (or #313 #313)
-#723 := (if #397 #398 #722)
-#555 := (or #561 #723)
-#564 := (iff #555 #562)
-#566 := (iff #562 #562)
-#567 := [rewrite]: #566
-#544 := (iff #723 #11)
-#658 := (if false #398 #11)
-#656 := (iff #658 #11)
-#659 := [rewrite]: #656
-#560 := (iff #723 #658)
-#551 := (iff #722 #11)
-#1 := true
-#666 := (if true #11 #11)
-#549 := (iff #666 #11)
-#550 := [rewrite]: #549
-#664 := (iff #722 #666)
-#663 := (iff #721 #11)
-#691 := (+ -1::Int #10)
-#683 := (= #691 0::Int)
-#684 := (iff #683 #11)
-#685 := [rewrite]: #684
-#509 := (iff #721 #683)
-#506 := (= #389 #691)
-#690 := (+ #10 -1::Int)
-#688 := (= #690 #691)
-#692 := [rewrite]: #688
-#670 := (= #389 #690)
-#675 := (= #388 -1::Int)
-#409 := (= #507 -1::Int)
-#410 := [rewrite]: #409
-#668 := (= #388 #507)
-#673 := (= #714 1::Int)
-#527 := (div -1::Int -1::Int)
-#671 := (= #527 1::Int)
-#672 := [rewrite]: #671
-#528 := (= #714 #527)
-#529 := [monotonicity #410 #410]: #528
-#674 := [trans #529 #672]: #673
-#669 := [monotonicity #674]: #668
-#676 := [trans #669 #410]: #675
-#677 := [monotonicity #676]: #670
-#508 := [trans #677 #692]: #506
-#662 := [monotonicity #508]: #509
-#665 := [trans #662 #685]: #663
-#680 := (iff #377 #11)
-#678 := (iff #377 #683)
-#681 := (= #720 #691)
-#405 := (= #720 #690)
-#411 := (= #718 -1::Int)
-#698 := (= #718 #507)
-#697 := (= #383 1::Int)
-#694 := [rewrite]: #697
-#408 := [monotonicity #694]: #698
-#689 := [trans #408 #410]: #411
-#687 := [monotonicity #689]: #405
-#682 := [trans #687 #692]: #681
-#679 := [monotonicity #682]: #678
-#686 := [trans #679 #685]: #680
-#419 := (iff #404 true)
-#711 := (or true false)
-#712 := (iff #711 true)
-#710 := [rewrite]: #712
-#696 := (iff #404 #711)
-#319 := (iff #400 false)
-#700 := (not true)
-#424 := (iff #700 false)
-#425 := [rewrite]: #424
-#422 := (iff #400 #700)
-#713 := (iff #403 true)
-#351 := (iff #403 #711)
-#360 := (iff #399 false)
-#701 := [rewrite]: #360
-#346 := (iff #402 true)
-#709 := [rewrite]: #346
-#352 := [monotonicity #709 #701]: #351
-#699 := [trans #352 #710]: #713
-#423 := [monotonicity #699]: #422
-#695 := [trans #423 #425]: #319
-#702 := (iff #401 true)
-#703 := (not false)
-#706 := (iff #703 true)
-#707 := [rewrite]: #706
-#704 := (iff #401 #703)
-#366 := (iff #390 false)
-#725 := (or false false)
-#380 := (iff #725 false)
-#716 := [rewrite]: #380
-#364 := (iff #390 #725)
-#365 := [monotonicity #701 #701]: #364
-#367 := [trans #365 #716]: #366
-#705 := [monotonicity #367]: #704
-#708 := [trans #705 #707]: #702
-#418 := [monotonicity #708 #695]: #696
-#693 := [trans #418 #710]: #419
-#667 := [monotonicity #693 #686 #665]: #664
-#510 := [trans #667 #550]: #551
-#376 := (iff #397 false)
-#715 := (iff #397 #725)
-#724 := (iff #313 false)
-#719 := [rewrite]: #724
-#375 := [monotonicity #719 #719]: #715
-#717 := [trans #375 #716]: #376
-#655 := [monotonicity #717 #510]: #560
-#559 := [trans #655 #659]: #544
-#565 := [monotonicity #559]: #564
-#660 := [trans #565 #567]: #564
-#563 := [quant-inst #8 #8]: #555
-#657 := [mp #563 #660]: #562
-[unit-resolution #657 #65 #732]: false
-unsat
-2afe6ba8054e3b6ca9e599e36f01a50ef2fd9772 286 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#726 := (pattern #17)
-#18 := 0::Int
-#68 := -1::Int
-#72 := (* -1::Int #16)
-#69 := (* -1::Int #14)
-#75 := (div #69 #72)
-#226 := (* -1::Int #75)
-#227 := (+ #17 #226)
-#228 := (= #227 0::Int)
-#28 := (div #14 #16)
-#223 := (* -1::Int #28)
-#224 := (+ #17 #223)
-#225 := (= #224 0::Int)
-#94 := (<= #16 0::Int)
-#101 := (>= #14 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #14 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#229 := (if #190 #225 #228)
-#222 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #14 0::Int)
-#21 := (or #19 #20)
-#230 := (if #21 #222 #229)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #230)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#730 := (iff #233 #727)
-#728 := (iff #230 #230)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#193 := (if #190 #28 #75)
-#196 := (if #21 0::Int #193)
-#199 := (= #17 #196)
-#202 := (forall (vars (?v0 Int) (?v1 Int)) #199)
-#234 := (iff #202 #233)
-#231 := (iff #199 #230)
-#232 := [rewrite]: #231
-#235 := [quant-intro #232]: #234
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (if #108 #28 #75)
-#114 := (if #21 0::Int #111)
-#117 := (= #17 #114)
-#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#197 := (= #114 #196)
-#194 := (= #111 #193)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [quant-intro #201]: #203
-#182 := (~ #120 #120)
-#180 := (~ #117 #117)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#30 := (- #16)
-#29 := (- #14)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #14 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #14)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#123 := (iff #35 #120)
-#78 := (if #27 #28 #75)
-#81 := (if #21 0::Int #78)
-#84 := (= #17 #81)
-#87 := (forall (vars (?v0 Int) (?v1 Int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #27 #108)
-#106 := (iff #26 #105)
-#96 := (iff #23 #95)
-#97 := [rewrite]: #96
-#103 := (iff #25 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #24 #98)
-#92 := (iff #22 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #35 #87)
-#85 := (iff #34 #84)
-#82 := (= #33 #81)
-#79 := (= #32 #78)
-#76 := (= #31 #75)
-#73 := (= #30 #72)
-#74 := [rewrite]: #73
-#70 := (= #29 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#67 := [asserted]: #35
-#125 := [mp #67 #124]: #120
-#174 := [mp~ #125 #183]: #120
-#205 := [mp #174 #204]: #202
-#236 := [mp #205 #235]: #233
-#732 := [mp #236 #731]: #727
-#8 := 3::Int
-#10 := 1::Int
-#9 := (f4 f5 3::Int)
-#11 := (f3 #9 1::Int)
-#12 := (= #11 3::Int)
-#13 := (not #12)
-#66 := [asserted]: #13
-#661 := (not #727)
-#648 := (or #661 #12)
-#389 := (* -1::Int 1::Int)
-#388 := (* -1::Int 3::Int)
-#721 := (div #388 #389)
-#722 := (* -1::Int #721)
-#723 := (+ #11 #722)
-#724 := (= #723 0::Int)
-#720 := (div 3::Int 1::Int)
-#377 := (* -1::Int #720)
-#507 := (+ #11 #377)
-#714 := (= #507 0::Int)
-#401 := (<= 1::Int 0::Int)
-#400 := (>= 3::Int 0::Int)
-#404 := (or #400 #401)
-#383 := (not #404)
-#390 := (<= 3::Int 0::Int)
-#402 := (or #390 #401)
-#403 := (not #402)
-#718 := (or #403 #383)
-#719 := (if #718 #714 #724)
-#399 := (= #11 0::Int)
-#397 := (= 1::Int 0::Int)
-#313 := (= 3::Int 0::Int)
-#398 := (or #313 #397)
-#725 := (if #398 #399 #719)
-#650 := (or #661 #725)
-#639 := (iff #650 #648)
-#651 := (iff #648 #648)
-#652 := [rewrite]: #651
-#660 := (iff #725 #12)
-#563 := (if false #399 #12)
-#566 := (iff #563 #12)
-#567 := [rewrite]: #566
-#564 := (iff #725 #563)
-#562 := (iff #719 #12)
-#1 := true
-#656 := (if true #12 #12)
-#559 := (iff #656 #12)
-#561 := [rewrite]: #559
-#659 := (iff #719 #656)
-#560 := (iff #724 #12)
-#691 := -3::Int
-#684 := (+ -3::Int #11)
-#528 := (= #684 0::Int)
-#672 := (iff #528 #12)
-#673 := [rewrite]: #672
-#510 := (iff #724 #528)
-#550 := (= #723 #684)
-#683 := (+ #11 -3::Int)
-#685 := (= #683 #684)
-#680 := [rewrite]: #685
-#667 := (= #723 #683)
-#666 := (= #722 -3::Int)
-#688 := (= #388 -3::Int)
-#692 := [rewrite]: #688
-#663 := (= #722 #388)
-#509 := (= #721 3::Int)
-#676 := (div -3::Int -1::Int)
-#506 := (= #676 3::Int)
-#508 := [rewrite]: #506
-#670 := (= #721 #676)
-#669 := (= #389 -1::Int)
-#675 := [rewrite]: #669
-#677 := [monotonicity #692 #675]: #670
-#662 := [trans #677 #508]: #509
-#665 := [monotonicity #662]: #663
-#664 := [trans #665 #692]: #666
-#549 := [monotonicity #664]: #667
-#551 := [trans #549 #680]: #550
-#658 := [monotonicity #551]: #510
-#655 := [trans #658 #673]: #560
-#674 := (iff #714 #12)
-#529 := (iff #714 #528)
-#686 := (= #507 #684)
-#678 := (= #507 #683)
-#681 := (= #377 -3::Int)
-#405 := (= #377 #388)
-#689 := (= #720 3::Int)
-#690 := [rewrite]: #689
-#687 := [monotonicity #690]: #405
-#682 := [trans #687 #692]: #681
-#679 := [monotonicity #682]: #678
-#527 := [trans #679 #680]: #686
-#671 := [monotonicity #527]: #529
-#668 := [trans #671 #673]: #674
-#410 := (iff #718 true)
-#700 := (or true false)
-#424 := (iff #700 true)
-#425 := [rewrite]: #424
-#408 := (iff #718 #700)
-#694 := (iff #383 false)
-#696 := (not true)
-#693 := (iff #696 false)
-#697 := [rewrite]: #693
-#418 := (iff #383 #696)
-#319 := (iff #404 true)
-#422 := (iff #404 #700)
-#704 := (iff #401 false)
-#705 := [rewrite]: #704
-#713 := (iff #400 true)
-#699 := [rewrite]: #713
-#423 := [monotonicity #699 #705]: #422
-#695 := [trans #423 #425]: #319
-#419 := [monotonicity #695]: #418
-#698 := [trans #419 #697]: #694
-#712 := (iff #403 true)
-#346 := (not false)
-#351 := (iff #346 true)
-#352 := [rewrite]: #351
-#709 := (iff #403 #346)
-#702 := (iff #402 false)
-#376 := (or false false)
-#701 := (iff #376 false)
-#364 := [rewrite]: #701
-#706 := (iff #402 #376)
-#367 := (iff #390 false)
-#703 := [rewrite]: #367
-#707 := [monotonicity #703 #705]: #706
-#708 := [trans #707 #364]: #702
-#711 := [monotonicity #708]: #709
-#710 := [trans #711 #352]: #712
-#409 := [monotonicity #710 #698]: #408
-#411 := [trans #409 #425]: #410
-#544 := [monotonicity #411 #668 #655]: #659
-#555 := [trans #544 #561]: #562
-#365 := (iff #398 false)
-#717 := (iff #398 #376)
-#380 := (iff #397 false)
-#716 := [rewrite]: #380
-#715 := (iff #313 false)
-#375 := [rewrite]: #715
-#360 := [monotonicity #375 #716]: #717
-#366 := [trans #360 #364]: #365
-#565 := [monotonicity #366 #555]: #564
-#657 := [trans #565 #567]: #660
-#641 := [monotonicity #657]: #639
-#653 := [trans #641 #652]: #639
-#642 := [quant-inst #8 #10]: #650
-#649 := [mp #642 #653]: #648
-[unit-resolution #649 #66 #732]: false
-unsat
-bc025623c048399a2cbdaaab334a8777f197552e 314 0
-#2 := false
-#18 := 0::Int
-decl f3 :: (-> S2 Int Int)
-#10 := 1::Int
-decl f4 :: (-> S3 Int S2)
-decl f6 :: Int
-#8 := f6
-decl f5 :: S3
-#7 := f5
-#9 := (f4 f5 f6)
-#11 := (f3 #9 1::Int)
-#400 := (= #11 0::Int)
-#560 := (not #400)
-#12 := (= #11 f6)
-#13 := (not #12)
-#532 := (iff #13 #560)
-#526 := (iff #12 #400)
-#570 := (iff #400 #12)
-#569 := (= 0::Int f6)
-#314 := (= f6 0::Int)
-#721 := (div f6 1::Int)
-#68 := -1::Int
-#378 := (* -1::Int #721)
-#508 := (+ #11 #378)
-#715 := (= #508 0::Int)
-#665 := (not #715)
-#629 := (= #721 f6)
-#572 := (= f6 #721)
-#611 := (+ f6 #378)
-#617 := (<= #611 0::Int)
-#631 := (= #611 0::Int)
-#1 := true
-#64 := [true-axiom]: true
-#583 := (or false #631)
-#584 := [th-lemma arith]: #583
-#585 := [unit-resolution #584 #64]: #631
-#588 := (not #631)
-#589 := (or #588 #617)
-#590 := [th-lemma arith triangle-eq]: #589
-#586 := [unit-resolution #590 #585]: #617
-#618 := (>= #611 0::Int)
-#591 := (or #588 #618)
-#571 := [th-lemma arith triangle-eq]: #591
-#517 := [unit-resolution #571 #585]: #618
-#553 := [th-lemma arith eq-propagate 1 1 #517 #586]: #572
-#573 := [symm #553]: #629
-#582 := (= #11 #721)
-#677 := (<= #508 0::Int)
-#601 := [hypothesis]: #715
-#574 := (or #665 #677)
-#575 := [th-lemma arith triangle-eq]: #574
-#576 := [unit-resolution #575 #601]: #677
-#671 := (>= #508 0::Int)
-#469 := (or #665 #671)
-#580 := [th-lemma arith triangle-eq]: #469
-#581 := [unit-resolution #580 #601]: #671
-#587 := [th-lemma arith eq-propagate 1 1 #581 #576]: #582
-#579 := [trans #587 #573]: #12
-#66 := [asserted]: #13
-#547 := [unit-resolution #66 #579]: false
-#554 := [lemma #547]: #665
-#389 := (* -1::Int f6)
-#419 := (div #389 -1::Int)
-#698 := (* -1::Int #419)
-#409 := (+ #11 #698)
-#412 := (= #409 0::Int)
-#401 := (>= f6 0::Int)
-#701 := (not #401)
-#391 := (<= f6 0::Int)
-#709 := (not #391)
-#425 := (or #709 #701)
-#406 := (if #425 #715 #412)
-#561 := (not #314)
-#651 := [hypothesis]: #561
-#578 := (or #314 #406)
-#689 := (if #314 #400 #406)
-#16 := (:var 0 Int)
-#14 := (:var 1 Int)
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#727 := (pattern #17)
-#72 := (* -1::Int #16)
-#69 := (* -1::Int #14)
-#75 := (div #69 #72)
-#226 := (* -1::Int #75)
-#227 := (+ #17 #226)
-#228 := (= #227 0::Int)
-#28 := (div #14 #16)
-#223 := (* -1::Int #28)
-#224 := (+ #17 #223)
-#225 := (= #224 0::Int)
-#94 := (<= #16 0::Int)
-#101 := (>= #14 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #14 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#229 := (if #190 #225 #228)
-#222 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #14 0::Int)
-#21 := (or #19 #20)
-#230 := (if #21 #222 #229)
-#728 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #727) #230)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#731 := (iff #233 #728)
-#729 := (iff #230 #230)
-#730 := [refl]: #729
-#732 := [quant-intro #730]: #731
-#193 := (if #190 #28 #75)
-#196 := (if #21 0::Int #193)
-#199 := (= #17 #196)
-#202 := (forall (vars (?v0 Int) (?v1 Int)) #199)
-#234 := (iff #202 #233)
-#231 := (iff #199 #230)
-#232 := [rewrite]: #231
-#235 := [quant-intro #232]: #234
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (if #108 #28 #75)
-#114 := (if #21 0::Int #111)
-#117 := (= #17 #114)
-#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#197 := (= #114 #196)
-#194 := (= #111 #193)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [quant-intro #201]: #203
-#182 := (~ #120 #120)
-#180 := (~ #117 #117)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#30 := (- #16)
-#29 := (- #14)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #14 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #14)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#123 := (iff #35 #120)
-#78 := (if #27 #28 #75)
-#81 := (if #21 0::Int #78)
-#84 := (= #17 #81)
-#87 := (forall (vars (?v0 Int) (?v1 Int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #27 #108)
-#106 := (iff #26 #105)
-#96 := (iff #23 #95)
-#97 := [rewrite]: #96
-#103 := (iff #25 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #24 #98)
-#92 := (iff #22 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #35 #87)
-#85 := (iff #34 #84)
-#82 := (= #33 #81)
-#79 := (= #32 #78)
-#76 := (= #31 #75)
-#73 := (= #30 #72)
-#74 := [rewrite]: #73
-#70 := (= #29 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#67 := [asserted]: #35
-#125 := [mp #67 #124]: #120
-#174 := [mp~ #125 #183]: #120
-#205 := [mp #174 #204]: #202
-#236 := [mp #205 #235]: #233
-#733 := [mp #236 #732]: #728
-#683 := (not #728)
-#684 := (or #683 #689)
-#390 := (* -1::Int 1::Int)
-#722 := (div #389 #390)
-#723 := (* -1::Int #722)
-#724 := (+ #11 #723)
-#725 := (= #724 0::Int)
-#402 := (<= 1::Int 0::Int)
-#405 := (or #401 #402)
-#384 := (not #405)
-#403 := (or #391 #402)
-#404 := (not #403)
-#719 := (or #404 #384)
-#720 := (if #719 #715 #725)
-#398 := (= 1::Int 0::Int)
-#399 := (or #314 #398)
-#726 := (if #399 #400 #720)
-#679 := (or #683 #726)
-#685 := (iff #679 #684)
-#681 := (iff #684 #684)
-#687 := [rewrite]: #681
-#693 := (iff #726 #689)
-#688 := (iff #720 #406)
-#690 := (iff #725 #412)
-#410 := (= #724 #409)
-#695 := (= #723 #698)
-#420 := (= #722 #419)
-#696 := (= #390 -1::Int)
-#697 := [rewrite]: #696
-#694 := [monotonicity #697]: #420
-#699 := [monotonicity #694]: #695
-#411 := [monotonicity #699]: #410
-#691 := [monotonicity #411]: #690
-#426 := (iff #719 #425)
-#423 := (iff #384 #701)
-#714 := (iff #405 #401)
-#712 := (or #401 false)
-#713 := (iff #712 #401)
-#711 := [rewrite]: #713
-#352 := (iff #405 #712)
-#366 := (iff #402 false)
-#367 := [rewrite]: #366
-#353 := [monotonicity #367]: #352
-#700 := [trans #353 #711]: #714
-#424 := [monotonicity #700]: #423
-#347 := (iff #404 #709)
-#708 := (iff #403 #391)
-#368 := (or #391 false)
-#706 := (iff #368 #391)
-#707 := [rewrite]: #706
-#704 := (iff #403 #368)
-#705 := [monotonicity #367]: #704
-#703 := [trans #705 #707]: #708
-#710 := [monotonicity #703]: #347
-#320 := [monotonicity #710 #424]: #426
-#692 := [monotonicity #320 #691]: #688
-#702 := (iff #399 #314)
-#381 := (or #314 false)
-#718 := (iff #381 #314)
-#361 := [rewrite]: #718
-#717 := (iff #399 #381)
-#716 := (iff #398 false)
-#376 := [rewrite]: #716
-#377 := [monotonicity #376]: #717
-#365 := [trans #377 #361]: #702
-#682 := [monotonicity #365 #692]: #693
-#686 := [monotonicity #682]: #685
-#528 := [trans #686 #687]: #685
-#680 := [quant-inst #8 #10]: #679
-#529 := [mp #680 #528]: #684
-#577 := [unit-resolution #529 #733]: #689
-#659 := (not #689)
-#660 := (or #659 #314 #406)
-#545 := [def-axiom]: #660
-#513 := [unit-resolution #545 #577]: #578
-#544 := [unit-resolution #513 #651]: #406
-#653 := (or #425 #314)
-#675 := (not #425)
-#658 := [hypothesis]: #675
-#530 := (or #425 #391)
-#672 := [def-axiom]: #530
-#662 := [unit-resolution #672 #658]: #391
-#673 := (or #425 #401)
-#674 := [def-axiom]: #673
-#649 := [unit-resolution #674 #658]: #401
-#643 := (or #314 #709 #701)
-#640 := [th-lemma arith triangle-eq]: #643
-#642 := [unit-resolution #640 #651]: #425
-#652 := [unit-resolution #642 #649 #662]: false
-#654 := [lemma #652]: #653
-#546 := [unit-resolution #654 #651]: #425
-#510 := (not #406)
-#663 := (or #510 #675 #715)
-#664 := [def-axiom]: #663
-#548 := [unit-resolution #664 #546 #544 #554]: false
-#555 := [lemma #548]: #314
-#549 := [symm #555]: #569
-#525 := [monotonicity #549]: #570
-#531 := [symm #525]: #526
-#533 := [monotonicity #531]: #532
-#534 := [mp #66 #533]: #560
-#557 := (or #561 #400)
-#656 := (or #659 #561 #400)
-#657 := [def-axiom]: #656
-#558 := [unit-resolution #657 #577]: #557
-#559 := [unit-resolution #558 #555]: #400
-[unit-resolution #559 #534]: false
-unsat
-54537fcadbc5f87e29d49193f557c51ef593586b 288 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#739 := (pattern #18)
-#8 := 0::Int
-#67 := -1::Int
-#84 := (* -1::Int #17)
-#80 := (* -1::Int #15)
-#87 := (div #80 #84)
-#238 := (* -1::Int #87)
-#239 := (+ #18 #238)
-#240 := (= #239 0::Int)
-#28 := (div #15 #17)
-#235 := (* -1::Int #28)
-#236 := (+ #18 #235)
-#237 := (= #236 0::Int)
-#106 := (<= #17 0::Int)
-#113 := (>= #15 0::Int)
-#198 := (or #113 #106)
-#199 := (not #198)
-#102 := (<= #15 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#241 := (if #202 #237 #240)
-#234 := (= #18 0::Int)
-#20 := (= #17 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#242 := (if #21 #234 #241)
-#740 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #739) #242)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#743 := (iff #245 #740)
-#741 := (iff #242 #242)
-#742 := [refl]: #741
-#744 := [quant-intro #742]: #743
-#205 := (if #202 #28 #87)
-#208 := (if #21 0::Int #205)
-#211 := (= #18 #208)
-#214 := (forall (vars (?v0 Int) (?v1 Int)) #211)
-#246 := (iff #214 #245)
-#243 := (iff #211 #242)
-#244 := [rewrite]: #243
-#247 := [quant-intro #244]: #246
-#107 := (not #106)
-#114 := (not #113)
-#117 := (and #114 #107)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#123 := (if #120 #28 #87)
-#126 := (if #21 0::Int #123)
-#129 := (= #18 #126)
-#132 := (forall (vars (?v0 Int) (?v1 Int)) #129)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#209 := (= #126 #208)
-#206 := (= #123 #205)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [quant-intro #213]: #215
-#194 := (~ #132 #132)
-#192 := (~ #129 #129)
-#193 := [refl]: #192
-#195 := [nnf-pos #193]: #194
-#30 := (- #17)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #18 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#135 := (iff #35 #132)
-#90 := (if #27 #28 #87)
-#93 := (if #21 0::Int #90)
-#96 := (= #18 #93)
-#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
-#133 := (iff #99 #132)
-#130 := (iff #96 #129)
-#127 := (= #93 #126)
-#124 := (= #90 #123)
-#121 := (iff #27 #120)
-#118 := (iff #26 #117)
-#108 := (iff #23 #107)
-#109 := [rewrite]: #108
-#115 := (iff #25 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116 #109]: #118
-#111 := (iff #24 #110)
-#104 := (iff #22 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#125 := [monotonicity #122]: #124
-#128 := [monotonicity #125]: #127
-#131 := [monotonicity #128]: #130
-#134 := [quant-intro #131]: #133
-#100 := (iff #35 #99)
-#97 := (iff #34 #96)
-#94 := (= #33 #93)
-#91 := (= #32 #90)
-#88 := (= #31 #87)
-#85 := (= #30 #84)
-#86 := [rewrite]: #85
-#82 := (= #29 #80)
-#83 := [rewrite]: #82
-#89 := [monotonicity #83 #86]: #88
-#92 := [monotonicity #89]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [quant-intro #98]: #100
-#136 := [trans #101 #134]: #135
-#79 := [asserted]: #35
-#137 := [mp #79 #136]: #132
-#186 := [mp~ #137 #195]: #132
-#217 := [mp #186 #216]: #214
-#248 := [mp #217 #247]: #245
-#745 := [mp #248 #744]: #740
-#9 := (f4 f5 0::Int)
-#70 := (f3 #9 -1::Int)
-#73 := (= #70 0::Int)
-#76 := (not #73)
-#10 := 1::Int
-#11 := (- 1::Int)
-#12 := (f3 #9 #11)
-#13 := (= #12 0::Int)
-#14 := (not #13)
-#77 := (iff #14 #76)
-#74 := (iff #13 #73)
-#71 := (= #12 #70)
-#68 := (= #11 -1::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #14
-#81 := [mp #66 #78]: #76
-#574 := (not #740)
-#575 := (or #574 #73)
-#401 := (* -1::Int -1::Int)
-#727 := (* -1::Int 0::Int)
-#402 := (div #727 #401)
-#734 := (* -1::Int #402)
-#735 := (+ #70 #734)
-#736 := (= #735 0::Int)
-#731 := (div 0::Int -1::Int)
-#733 := (* -1::Int #731)
-#390 := (+ #70 #733)
-#520 := (= #390 0::Int)
-#403 := (<= -1::Int 0::Int)
-#416 := (>= 0::Int 0::Int)
-#413 := (or #416 #403)
-#417 := (not #413)
-#412 := (<= 0::Int 0::Int)
-#414 := (or #412 #403)
-#415 := (not #414)
-#396 := (or #415 #417)
-#737 := (if #396 #520 #736)
-#410 := (= -1::Int 0::Int)
-#326 := (= 0::Int 0::Int)
-#411 := (or #326 #410)
-#732 := (if #411 #73 #737)
-#568 := (or #574 #732)
-#577 := (iff #568 #575)
-#579 := (iff #575 #575)
-#580 := [rewrite]: #579
-#557 := (iff #732 #73)
-#1 := true
-#671 := (if true #73 #73)
-#669 := (iff #671 #73)
-#672 := [rewrite]: #669
-#573 := (iff #732 #671)
-#564 := (iff #737 #73)
-#679 := (if false #73 #73)
-#562 := (iff #679 #73)
-#563 := [rewrite]: #562
-#677 := (iff #737 #679)
-#676 := (iff #736 #73)
-#522 := (= #735 #70)
-#694 := (+ #70 0::Int)
-#691 := (= #694 #70)
-#692 := [rewrite]: #691
-#519 := (= #735 #694)
-#683 := (= #734 0::Int)
-#700 := (= #727 0::Int)
-#704 := [rewrite]: #700
-#688 := (= #734 #727)
-#681 := (= #402 0::Int)
-#542 := (div 0::Int 1::Int)
-#686 := (= #542 0::Int)
-#687 := [rewrite]: #686
-#684 := (= #402 #542)
-#540 := (= #401 1::Int)
-#541 := [rewrite]: #540
-#685 := [monotonicity #704 #541]: #684
-#682 := [trans #685 #687]: #681
-#689 := [monotonicity #682]: #688
-#690 := [trans #689 #704]: #683
-#521 := [monotonicity #690]: #519
-#675 := [trans #521 #692]: #522
-#678 := [monotonicity #675]: #676
-#693 := (iff #520 #73)
-#697 := (= #390 #70)
-#695 := (= #390 #694)
-#701 := (= #733 0::Int)
-#703 := (= #733 #727)
-#424 := (= #731 0::Int)
-#702 := [rewrite]: #424
-#418 := [monotonicity #702]: #703
-#705 := [trans #418 #704]: #701
-#696 := [monotonicity #705]: #695
-#698 := [trans #696 #692]: #697
-#699 := [monotonicity #698]: #693
-#422 := (iff #396 false)
-#706 := (or false false)
-#711 := (iff #706 false)
-#421 := [rewrite]: #711
-#710 := (iff #396 #706)
-#431 := (iff #417 false)
-#724 := (not true)
-#725 := (iff #724 false)
-#723 := [rewrite]: #725
-#708 := (iff #417 #724)
-#438 := (iff #413 true)
-#718 := (or true true)
-#715 := (iff #718 true)
-#721 := [rewrite]: #715
-#436 := (iff #413 #718)
-#716 := (iff #403 true)
-#717 := [rewrite]: #716
-#713 := (iff #416 true)
-#435 := [rewrite]: #713
-#437 := [monotonicity #435 #717]: #436
-#332 := [trans #437 #721]: #438
-#709 := [monotonicity #332]: #708
-#432 := [trans #709 #723]: #431
-#726 := (iff #415 false)
-#364 := (iff #415 #724)
-#359 := (iff #414 true)
-#719 := (iff #414 #718)
-#379 := (iff #412 true)
-#380 := [rewrite]: #379
-#720 := [monotonicity #380 #717]: #719
-#722 := [trans #720 #721]: #359
-#365 := [monotonicity #722]: #364
-#712 := [trans #365 #723]: #726
-#707 := [monotonicity #712 #432]: #710
-#423 := [trans #707 #421]: #422
-#680 := [monotonicity #423 #699 #678]: #677
-#523 := [trans #680 #563]: #564
-#377 := (iff #411 true)
-#729 := (or true false)
-#373 := (iff #729 true)
-#714 := [rewrite]: #373
-#389 := (iff #411 #729)
-#388 := (iff #410 false)
-#393 := [rewrite]: #388
-#738 := (iff #326 true)
-#728 := [rewrite]: #738
-#730 := [monotonicity #728 #393]: #389
-#378 := [trans #730 #714]: #377
-#668 := [monotonicity #378 #523]: #573
-#572 := [trans #668 #672]: #557
-#578 := [monotonicity #572]: #577
-#673 := [trans #578 #580]: #577
-#576 := [quant-inst #8 #67]: #568
-#670 := [mp #576 #673]: #575
-[unit-resolution #670 #81 #745]: false
-unsat
-1919ef46c663d3b5ae90ef3cb3a4aa4abba7ea65 297 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#739 := (pattern #17)
-#18 := 0::Int
-#67 := -1::Int
-#84 := (* -1::Int #16)
-#80 := (* -1::Int #14)
-#87 := (div #80 #84)
-#238 := (* -1::Int #87)
-#239 := (+ #17 #238)
-#240 := (= #239 0::Int)
-#28 := (div #14 #16)
-#235 := (* -1::Int #28)
-#236 := (+ #17 #235)
-#237 := (= #236 0::Int)
-#106 := (<= #16 0::Int)
-#113 := (>= #14 0::Int)
-#198 := (or #113 #106)
-#199 := (not #198)
-#102 := (<= #14 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#241 := (if #202 #237 #240)
-#234 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #14 0::Int)
-#21 := (or #19 #20)
-#242 := (if #21 #234 #241)
-#740 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #739) #242)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#743 := (iff #245 #740)
-#741 := (iff #242 #242)
-#742 := [refl]: #741
-#744 := [quant-intro #742]: #743
-#205 := (if #202 #28 #87)
-#208 := (if #21 0::Int #205)
-#211 := (= #17 #208)
-#214 := (forall (vars (?v0 Int) (?v1 Int)) #211)
-#246 := (iff #214 #245)
-#243 := (iff #211 #242)
-#244 := [rewrite]: #243
-#247 := [quant-intro #244]: #246
-#107 := (not #106)
-#114 := (not #113)
-#117 := (and #114 #107)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#123 := (if #120 #28 #87)
-#126 := (if #21 0::Int #123)
-#129 := (= #17 #126)
-#132 := (forall (vars (?v0 Int) (?v1 Int)) #129)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#209 := (= #126 #208)
-#206 := (= #123 #205)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [quant-intro #213]: #215
-#194 := (~ #132 #132)
-#192 := (~ #129 #129)
-#193 := [refl]: #192
-#195 := [nnf-pos #193]: #194
-#30 := (- #16)
-#29 := (- #14)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #14 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #14)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#135 := (iff #35 #132)
-#90 := (if #27 #28 #87)
-#93 := (if #21 0::Int #90)
-#96 := (= #17 #93)
-#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
-#133 := (iff #99 #132)
-#130 := (iff #96 #129)
-#127 := (= #93 #126)
-#124 := (= #90 #123)
-#121 := (iff #27 #120)
-#118 := (iff #26 #117)
-#108 := (iff #23 #107)
-#109 := [rewrite]: #108
-#115 := (iff #25 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116 #109]: #118
-#111 := (iff #24 #110)
-#104 := (iff #22 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#125 := [monotonicity #122]: #124
-#128 := [monotonicity #125]: #127
-#131 := [monotonicity #128]: #130
-#134 := [quant-intro #131]: #133
-#100 := (iff #35 #99)
-#97 := (iff #34 #96)
-#94 := (= #33 #93)
-#91 := (= #32 #90)
-#88 := (= #31 #87)
-#85 := (= #30 #84)
-#86 := [rewrite]: #85
-#82 := (= #29 #80)
-#83 := [rewrite]: #82
-#89 := [monotonicity #83 #86]: #88
-#92 := [monotonicity #89]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [quant-intro #98]: #100
-#136 := [trans #101 #134]: #135
-#79 := [asserted]: #35
-#137 := [mp #79 #136]: #132
-#186 := [mp~ #137 #195]: #132
-#217 := [mp #186 #216]: #214
-#248 := [mp #217 #247]: #245
-#745 := [mp #248 #744]: #740
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#70 := (f3 #9 -1::Int)
-#73 := (= #70 -1::Int)
-#76 := (not #73)
-#10 := (- 1::Int)
-#11 := (f3 #9 #10)
-#12 := (= #11 #10)
-#13 := (not #12)
-#77 := (iff #13 #76)
-#74 := (iff #12 #73)
-#68 := (= #10 -1::Int)
-#69 := [rewrite]: #68
-#71 := (= #11 #70)
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72 #69]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #13
-#81 := [mp #66 #78]: #76
-#670 := (not #740)
-#674 := (or #670 #73)
-#402 := (* -1::Int -1::Int)
-#401 := (* -1::Int 1::Int)
-#734 := (div #401 #402)
-#735 := (* -1::Int #734)
-#736 := (+ #70 #735)
-#737 := (= #736 0::Int)
-#733 := (div 1::Int -1::Int)
-#390 := (* -1::Int #733)
-#520 := (+ #70 #390)
-#727 := (= #520 0::Int)
-#414 := (<= -1::Int 0::Int)
-#413 := (>= 1::Int 0::Int)
-#417 := (or #413 #414)
-#396 := (not #417)
-#403 := (<= 1::Int 0::Int)
-#415 := (or #403 #414)
-#416 := (not #415)
-#731 := (or #416 #396)
-#732 := (if #731 #727 #737)
-#412 := (= #70 0::Int)
-#410 := (= -1::Int 0::Int)
-#326 := (= 1::Int 0::Int)
-#411 := (or #326 #410)
-#738 := (if #411 #412 #732)
-#661 := (or #670 #738)
-#655 := (iff #661 #674)
-#654 := (iff #674 #674)
-#664 := [rewrite]: #654
-#580 := (iff #738 #73)
-#568 := (if false #412 #73)
-#578 := (iff #568 #73)
-#579 := [rewrite]: #578
-#576 := (iff #738 #568)
-#574 := (iff #732 #73)
-#668 := (if false #73 #73)
-#557 := (iff #668 #73)
-#572 := [rewrite]: #557
-#669 := (iff #732 #668)
-#671 := (iff #737 #73)
-#692 := (+ 1::Int #70)
-#540 := (= #692 0::Int)
-#684 := (iff #540 #73)
-#685 := [rewrite]: #684
-#564 := (iff #737 #540)
-#562 := (= #736 #692)
-#695 := (+ #70 1::Int)
-#697 := (= #695 #692)
-#698 := [rewrite]: #697
-#677 := (= #736 #695)
-#678 := (= #735 1::Int)
-#704 := (= #402 1::Int)
-#701 := [rewrite]: #704
-#675 := (= #735 #402)
-#521 := (= #734 -1::Int)
-#688 := (div -1::Int 1::Int)
-#690 := (= #688 -1::Int)
-#519 := [rewrite]: #690
-#689 := (= #734 #688)
-#681 := (= #401 -1::Int)
-#682 := [rewrite]: #681
-#683 := [monotonicity #682 #701]: #689
-#522 := [trans #683 #519]: #521
-#676 := [monotonicity #522]: #675
-#679 := [trans #676 #701]: #678
-#680 := [monotonicity #679]: #677
-#563 := [trans #680 #698]: #562
-#523 := [monotonicity #563]: #564
-#573 := [trans #523 #685]: #671
-#686 := (iff #727 #73)
-#541 := (iff #727 #540)
-#693 := (= #520 #692)
-#696 := (= #520 #695)
-#705 := (= #390 1::Int)
-#418 := (= #390 #402)
-#702 := (= #733 -1::Int)
-#703 := [rewrite]: #702
-#700 := [monotonicity #703]: #418
-#694 := [trans #700 #701]: #705
-#691 := [monotonicity #694]: #696
-#699 := [trans #691 #698]: #693
-#542 := [monotonicity #699]: #541
-#687 := [trans #542 #685]: #686
-#423 := (iff #731 false)
-#389 := (or false false)
-#714 := (iff #389 false)
-#377 := [rewrite]: #714
-#421 := (iff #731 #389)
-#707 := (iff #396 false)
-#1 := true
-#364 := (not true)
-#723 := (iff #364 false)
-#726 := [rewrite]: #723
-#706 := (iff #396 #364)
-#431 := (iff #417 true)
-#437 := (or true true)
-#708 := (iff #437 true)
-#709 := [rewrite]: #708
-#438 := (iff #417 #437)
-#717 := (iff #414 true)
-#718 := [rewrite]: #717
-#435 := (iff #413 true)
-#436 := [rewrite]: #435
-#332 := [monotonicity #436 #718]: #438
-#432 := [trans #332 #709]: #431
-#710 := [monotonicity #432]: #706
-#711 := [trans #710 #726]: #707
-#712 := (iff #416 false)
-#365 := (iff #416 #364)
-#722 := (iff #415 true)
-#719 := (or false true)
-#721 := (iff #719 true)
-#359 := [rewrite]: #721
-#720 := (iff #415 #719)
-#380 := (iff #403 false)
-#716 := [rewrite]: #380
-#715 := [monotonicity #716 #718]: #720
-#724 := [trans #715 #359]: #722
-#725 := [monotonicity #724]: #365
-#713 := [trans #725 #726]: #712
-#422 := [monotonicity #713 #711]: #421
-#424 := [trans #422 #377]: #423
-#672 := [monotonicity #424 #687 #573]: #669
-#575 := [trans #672 #572]: #574
-#378 := (iff #411 false)
-#730 := (iff #411 #389)
-#393 := (iff #410 false)
-#729 := [rewrite]: #393
-#728 := (iff #326 false)
-#388 := [rewrite]: #728
-#373 := [monotonicity #388 #729]: #730
-#379 := [trans #373 #377]: #378
-#577 := [monotonicity #379 #575]: #576
-#673 := [trans #577 #579]: #580
-#652 := [monotonicity #673]: #655
-#665 := [trans #652 #664]: #655
-#663 := [quant-inst #8 #67]: #661
-#666 := [mp #663 #665]: #674
-[unit-resolution #666 #81 #745]: false
-unsat
-baa666ada000b9422ae7630b704989505cee3646 305 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#743 := (pattern #19)
-#20 := 0::Int
-#69 := -1::Int
-#89 := (* -1::Int #18)
-#85 := (* -1::Int #16)
-#92 := (div #85 #89)
-#243 := (* -1::Int #92)
-#244 := (+ #19 #243)
-#245 := (= #244 0::Int)
-#30 := (div #16 #18)
-#240 := (* -1::Int #30)
-#241 := (+ #19 #240)
-#242 := (= #241 0::Int)
-#111 := (<= #18 0::Int)
-#118 := (>= #16 0::Int)
-#203 := (or #118 #111)
-#204 := (not #203)
-#107 := (<= #16 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#246 := (if #207 #242 #245)
-#239 := (= #19 0::Int)
-#22 := (= #18 0::Int)
-#21 := (= #16 0::Int)
-#23 := (or #21 #22)
-#247 := (if #23 #239 #246)
-#744 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #743) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#747 := (iff #250 #744)
-#745 := (iff #247 #247)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#210 := (if #207 #30 #92)
-#213 := (if #23 0::Int #210)
-#216 := (= #19 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#112 := (not #111)
-#119 := (not #118)
-#122 := (and #119 #112)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#128 := (if #125 #30 #92)
-#131 := (if #23 0::Int #128)
-#134 := (= #19 #131)
-#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#214 := (= #131 #213)
-#211 := (= #128 #210)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#199 := (~ #137 #137)
-#197 := (~ #134 #134)
-#198 := [refl]: #197
-#200 := [nnf-pos #198]: #199
-#32 := (- #18)
-#31 := (- #16)
-#33 := (div #31 #32)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#34 := (if #29 #30 #33)
-#35 := (if #23 0::Int #34)
-#36 := (= #19 #35)
-#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#140 := (iff #37 #137)
-#95 := (if #29 #30 #92)
-#98 := (if #23 0::Int #95)
-#101 := (= #19 #98)
-#104 := (forall (vars (?v0 Int) (?v1 Int)) #101)
-#138 := (iff #104 #137)
-#135 := (iff #101 #134)
-#132 := (= #98 #131)
-#129 := (= #95 #128)
-#126 := (iff #29 #125)
-#123 := (iff #28 #122)
-#113 := (iff #25 #112)
-#114 := [rewrite]: #113
-#120 := (iff #27 #119)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121 #114]: #123
-#116 := (iff #26 #115)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [quant-intro #136]: #138
-#105 := (iff #37 #104)
-#102 := (iff #36 #101)
-#99 := (= #35 #98)
-#96 := (= #34 #95)
-#93 := (= #33 #92)
-#90 := (= #32 #89)
-#91 := [rewrite]: #90
-#87 := (= #31 #85)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [quant-intro #103]: #105
-#141 := [trans #106 #139]: #140
-#84 := [asserted]: #37
-#142 := [mp #84 #141]: #137
-#191 := [mp~ #142 #200]: #137
-#222 := [mp #191 #221]: #219
-#253 := [mp #222 #252]: #250
-#749 := [mp #253 #748]: #744
-#75 := -3::Int
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#72 := (f3 #9 -1::Int)
-#78 := (= #72 -3::Int)
-#81 := (not #78)
-#13 := (- 3::Int)
-#10 := 1::Int
-#11 := (- 1::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#82 := (iff #15 #81)
-#79 := (iff #14 #78)
-#76 := (= #13 -3::Int)
-#77 := [rewrite]: #76
-#73 := (= #12 #72)
-#70 := (= #11 -1::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80]: #82
-#68 := [asserted]: #15
-#86 := [mp #68 #83]: #81
-#667 := (not #744)
-#659 := (or #667 #78)
-#406 := (* -1::Int -1::Int)
-#405 := (* -1::Int 3::Int)
-#738 := (div #405 #406)
-#739 := (* -1::Int #738)
-#740 := (+ #72 #739)
-#741 := (= #740 0::Int)
-#737 := (div 3::Int -1::Int)
-#394 := (* -1::Int #737)
-#524 := (+ #72 #394)
-#731 := (= #524 0::Int)
-#418 := (<= -1::Int 0::Int)
-#417 := (>= 3::Int 0::Int)
-#421 := (or #417 #418)
-#400 := (not #421)
-#407 := (<= 3::Int 0::Int)
-#419 := (or #407 #418)
-#420 := (not #419)
-#735 := (or #420 #400)
-#736 := (if #735 #731 #741)
-#416 := (= #72 0::Int)
-#414 := (= -1::Int 0::Int)
-#330 := (= 3::Int 0::Int)
-#415 := (or #330 #414)
-#742 := (if #415 #416 #736)
-#656 := (or #667 #742)
-#668 := (iff #656 #659)
-#670 := (iff #659 #659)
-#666 := [rewrite]: #670
-#678 := (iff #742 #78)
-#582 := (if false #416 #78)
-#677 := (iff #582 #78)
-#674 := [rewrite]: #677
-#583 := (iff #742 #582)
-#580 := (iff #736 #78)
-#561 := (if false #78 #78)
-#579 := (iff #561 #78)
-#572 := [rewrite]: #579
-#576 := (iff #736 #561)
-#673 := (iff #741 #78)
-#701 := (+ 3::Int #72)
-#545 := (= #701 0::Int)
-#689 := (iff #545 #78)
-#690 := [rewrite]: #689
-#577 := (iff #741 #545)
-#527 := (= #740 #701)
-#700 := (+ #72 3::Int)
-#702 := (= #700 #701)
-#697 := [rewrite]: #702
-#567 := (= #740 #700)
-#684 := (= #739 3::Int)
-#422 := (* -1::Int -3::Int)
-#705 := (= #422 3::Int)
-#709 := [rewrite]: #705
-#683 := (= #739 #422)
-#680 := (= #738 -3::Int)
-#694 := (div -3::Int 1::Int)
-#526 := (= #694 -3::Int)
-#679 := [rewrite]: #526
-#523 := (= #738 #694)
-#693 := (= #406 1::Int)
-#687 := [rewrite]: #693
-#686 := (= #405 -3::Int)
-#692 := [rewrite]: #686
-#525 := [monotonicity #692 #687]: #523
-#682 := [trans #525 #679]: #680
-#681 := [monotonicity #682]: #683
-#566 := [trans #681 #709]: #684
-#568 := [monotonicity #566]: #567
-#675 := [trans #568 #697]: #527
-#672 := [monotonicity #675]: #577
-#676 := [trans #672 #690]: #673
-#691 := (iff #731 #78)
-#546 := (iff #731 #545)
-#703 := (= #524 #701)
-#695 := (= #524 #700)
-#698 := (= #394 3::Int)
-#704 := (= #394 #422)
-#706 := (= #737 -3::Int)
-#707 := [rewrite]: #706
-#708 := [monotonicity #707]: #704
-#699 := [trans #708 #709]: #698
-#696 := [monotonicity #699]: #695
-#544 := [trans #696 #697]: #703
-#688 := [monotonicity #544]: #546
-#685 := [trans #688 #690]: #691
-#427 := (iff #735 false)
-#393 := (or false false)
-#718 := (iff #393 false)
-#381 := [rewrite]: #718
-#425 := (iff #735 #393)
-#711 := (iff #400 false)
-#1 := true
-#368 := (not true)
-#727 := (iff #368 false)
-#730 := [rewrite]: #727
-#710 := (iff #400 #368)
-#435 := (iff #421 true)
-#441 := (or true true)
-#712 := (iff #441 true)
-#713 := [rewrite]: #712
-#442 := (iff #421 #441)
-#721 := (iff #418 true)
-#722 := [rewrite]: #721
-#439 := (iff #417 true)
-#440 := [rewrite]: #439
-#336 := [monotonicity #440 #722]: #442
-#436 := [trans #336 #713]: #435
-#714 := [monotonicity #436]: #710
-#715 := [trans #714 #730]: #711
-#716 := (iff #420 false)
-#369 := (iff #420 #368)
-#726 := (iff #419 true)
-#723 := (or false true)
-#725 := (iff #723 true)
-#363 := [rewrite]: #725
-#724 := (iff #419 #723)
-#384 := (iff #407 false)
-#720 := [rewrite]: #384
-#719 := [monotonicity #720 #722]: #724
-#728 := [trans #719 #363]: #726
-#729 := [monotonicity #728]: #369
-#717 := [trans #729 #730]: #716
-#426 := [monotonicity #717 #715]: #425
-#428 := [trans #426 #381]: #427
-#578 := [monotonicity #428 #685 #676]: #576
-#581 := [trans #578 #572]: #580
-#382 := (iff #415 false)
-#734 := (iff #415 #393)
-#397 := (iff #414 false)
-#733 := [rewrite]: #397
-#732 := (iff #330 false)
-#392 := [rewrite]: #732
-#377 := [monotonicity #392 #733]: #734
-#383 := [trans #377 #381]: #382
-#584 := [monotonicity #383 #581]: #583
-#665 := [trans #584 #674]: #678
-#669 := [monotonicity #665]: #668
-#671 := [trans #669 #666]: #668
-#658 := [quant-inst #8 #69]: #656
-#660 := [mp #658 #671]: #659
-[unit-resolution #660 #86 #749]: false
-unsat
-b30615473f23884eeaa7af098b5437e95d4b87b1 349 0
-#2 := false
-#20 := 0::Int
-#10 := 1::Int
-decl f6 :: Int
-#8 := f6
-#69 := -1::Int
-#75 := (* -1::Int f6)
-#716 := (div #75 1::Int)
-#714 := (* -1::Int #716)
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#7 := f5
-#9 := (f4 f5 f6)
-#72 := (f3 #9 -1::Int)
-#719 := (+ #72 #714)
-#693 := (<= #719 0::Int)
-#710 := (= #719 0::Int)
-#425 := (= f6 0::Int)
-#576 := (not #425)
-#429 := (<= f6 0::Int)
-#617 := [hypothesis]: #425
-#597 := (or #576 #429)
-#543 := [th-lemma arith triangle-eq]: #597
-#598 := [unit-resolution #543 #617]: #429
-#84 := (+ f6 #72)
-#340 := (<= #84 0::Int)
-#579 := (not #340)
-#424 := (>= #84 0::Int)
-#410 := (>= f6 0::Int)
-#686 := (not #710)
-#691 := (>= #719 0::Int)
-#623 := (not #691)
-#632 := (not #424)
-#633 := [hypothesis]: #632
-#624 := (or #623 #424)
-#631 := [hypothesis]: #691
-#667 := (+ f6 #716)
-#664 := (>= #667 0::Int)
-#674 := (= #667 0::Int)
-#1 := true
-#66 := [true-axiom]: true
-#634 := (or false #674)
-#635 := [th-lemma arith]: #634
-#630 := [unit-resolution #635 #66]: #674
-#636 := (not #674)
-#622 := (or #636 #664)
-#618 := [th-lemma arith triangle-eq]: #622
-#619 := [unit-resolution #618 #630]: #664
-#620 := [th-lemma arith farkas 1 -1 1 #619 #633 #631]: false
-#625 := [lemma #620]: #624
-#663 := [unit-resolution #625 #633]: #623
-#626 := (or #686 #691)
-#621 := [th-lemma arith triangle-eq]: #626
-#627 := [unit-resolution #621 #663]: #686
-#601 := (or #425 #710)
-#428 := (= #72 0::Int)
-#698 := (if #425 #428 #710)
-#18 := (:var 0 Int)
-#16 := (:var 1 Int)
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#753 := (pattern #19)
-#98 := (* -1::Int #18)
-#95 := (* -1::Int #16)
-#101 := (div #95 #98)
-#252 := (* -1::Int #101)
-#253 := (+ #19 #252)
-#254 := (= #253 0::Int)
-#30 := (div #16 #18)
-#249 := (* -1::Int #30)
-#250 := (+ #19 #249)
-#251 := (= #250 0::Int)
-#120 := (<= #18 0::Int)
-#127 := (>= #16 0::Int)
-#212 := (or #127 #120)
-#213 := (not #212)
-#116 := (<= #16 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#255 := (if #216 #251 #254)
-#248 := (= #19 0::Int)
-#22 := (= #18 0::Int)
-#21 := (= #16 0::Int)
-#23 := (or #21 #22)
-#256 := (if #23 #248 #255)
-#754 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #753) #256)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#757 := (iff #259 #754)
-#755 := (iff #256 #256)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#219 := (if #216 #30 #101)
-#222 := (if #23 0::Int #219)
-#225 := (= #19 #222)
-#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#121 := (not #120)
-#128 := (not #127)
-#131 := (and #128 #121)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#137 := (if #134 #30 #101)
-#140 := (if #23 0::Int #137)
-#143 := (= #19 #140)
-#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#223 := (= #140 #222)
-#220 := (= #137 #219)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#208 := (~ #146 #146)
-#206 := (~ #143 #143)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#32 := (- #18)
-#31 := (- #16)
-#33 := (div #31 #32)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#34 := (if #29 #30 #33)
-#35 := (if #23 0::Int #34)
-#36 := (= #19 #35)
-#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#149 := (iff #37 #146)
-#104 := (if #29 #30 #101)
-#107 := (if #23 0::Int #104)
-#110 := (= #19 #107)
-#113 := (forall (vars (?v0 Int) (?v1 Int)) #110)
-#147 := (iff #113 #146)
-#144 := (iff #110 #143)
-#141 := (= #107 #140)
-#138 := (= #104 #137)
-#135 := (iff #29 #134)
-#132 := (iff #28 #131)
-#122 := (iff #25 #121)
-#123 := [rewrite]: #122
-#129 := (iff #27 #128)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130 #123]: #132
-#125 := (iff #26 #124)
-#118 := (iff #24 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#114 := (iff #37 #113)
-#111 := (iff #36 #110)
-#108 := (= #35 #107)
-#105 := (= #34 #104)
-#102 := (= #33 #101)
-#99 := (= #32 #98)
-#100 := [rewrite]: #99
-#96 := (= #31 #95)
-#97 := [rewrite]: #96
-#103 := [monotonicity #97 #100]: #102
-#106 := [monotonicity #103]: #105
-#109 := [monotonicity #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [quant-intro #112]: #114
-#150 := [trans #115 #148]: #149
-#94 := [asserted]: #37
-#151 := [mp #94 #150]: #146
-#200 := [mp~ #151 #209]: #146
-#231 := [mp #200 #230]: #228
-#262 := [mp #231 #261]: #259
-#759 := [mp #262 #758]: #754
-#701 := (not #754)
-#695 := (or #701 #698)
-#748 := (* -1::Int -1::Int)
-#749 := (div #75 #748)
-#750 := (* -1::Int #749)
-#751 := (+ #72 #750)
-#746 := (= #751 0::Int)
-#534 := (div f6 -1::Int)
-#741 := (* -1::Int #534)
-#415 := (+ #72 #741)
-#416 := (= #415 0::Int)
-#430 := (<= -1::Int 0::Int)
-#745 := (or #410 #430)
-#747 := (not #745)
-#427 := (or #429 #430)
-#431 := (not #427)
-#404 := (or #431 #747)
-#752 := (if #404 #416 #746)
-#426 := (= -1::Int 0::Int)
-#417 := (or #425 #426)
-#742 := (if #417 #428 #752)
-#696 := (or #701 #742)
-#703 := (iff #696 #695)
-#704 := (iff #695 #695)
-#533 := [rewrite]: #704
-#699 := (iff #742 #698)
-#555 := (iff #752 #710)
-#711 := (if false #416 #710)
-#713 := (iff #711 #710)
-#554 := [rewrite]: #713
-#712 := (iff #752 #711)
-#705 := (iff #746 #710)
-#708 := (= #751 #719)
-#718 := (= #750 #714)
-#717 := (= #749 #716)
-#437 := (= #748 1::Int)
-#438 := [rewrite]: #437
-#432 := [monotonicity #438]: #717
-#715 := [monotonicity #432]: #718
-#709 := [monotonicity #715]: #708
-#706 := [monotonicity #709]: #705
-#435 := (iff #404 false)
-#446 := (or false false)
-#721 := (iff #446 false)
-#725 := [rewrite]: #721
-#720 := (iff #404 #446)
-#723 := (iff #747 false)
-#373 := (not true)
-#378 := (iff #373 false)
-#379 := [rewrite]: #378
-#346 := (iff #747 #373)
-#451 := (iff #745 true)
-#740 := (or #410 true)
-#449 := (iff #740 true)
-#450 := [rewrite]: #449
-#726 := (iff #745 #740)
-#393 := (iff #430 true)
-#394 := [rewrite]: #393
-#727 := [monotonicity #394]: #726
-#452 := [trans #727 #450]: #451
-#722 := [monotonicity #452]: #346
-#445 := [trans #722 #379]: #723
-#739 := (iff #431 false)
-#736 := (iff #431 #373)
-#729 := (iff #427 true)
-#730 := (or #429 true)
-#733 := (iff #730 true)
-#734 := [rewrite]: #733
-#731 := (iff #427 #730)
-#732 := [monotonicity #394]: #731
-#735 := [trans #732 #734]: #729
-#738 := [monotonicity #735]: #736
-#737 := [trans #738 #379]: #739
-#724 := [monotonicity #737 #445]: #720
-#436 := [trans #724 #725]: #435
-#707 := [monotonicity #436 #706]: #712
-#556 := [trans #707 #554]: #555
-#391 := (iff #417 #425)
-#743 := (or #425 false)
-#387 := (iff #743 #425)
-#728 := [rewrite]: #387
-#403 := (iff #417 #743)
-#402 := (iff #426 false)
-#407 := [rewrite]: #402
-#744 := [monotonicity #407]: #403
-#392 := [trans #744 #728]: #391
-#700 := [monotonicity #392 #556]: #699
-#697 := [monotonicity #700]: #703
-#535 := [trans #697 #533]: #703
-#702 := [quant-inst #8 #69]: #696
-#536 := [mp #702 #535]: #695
-#600 := [unit-resolution #536 #759]: #698
-#694 := (not #698)
-#537 := (or #694 #425 #710)
-#685 := [def-axiom]: #537
-#602 := [unit-resolution #685 #600]: #601
-#495 := [unit-resolution #602 #627]: #425
-#606 := (or #576 #410)
-#607 := [th-lemma arith triangle-eq]: #606
-#608 := [unit-resolution #607 #495]: #410
-#690 := (>= #72 0::Int)
-#613 := (or #576 #428)
-#577 := (or #694 #576 #428)
-#578 := [def-axiom]: #577
-#609 := [unit-resolution #578 #600]: #613
-#610 := [unit-resolution #609 #495]: #428
-#587 := (not #428)
-#611 := (or #587 #690)
-#614 := [th-lemma arith triangle-eq]: #611
-#615 := [unit-resolution #614 #610]: #690
-#616 := [th-lemma arith farkas 1 -1 1 #615 #633 #608]: false
-#612 := [lemma #616]: #424
-#599 := (or #579 #632)
-#85 := (= #84 0::Int)
-#88 := (not #85)
-#13 := (- f6)
-#11 := (- 1::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#91 := (iff #15 #88)
-#78 := (= #72 #75)
-#81 := (not #78)
-#89 := (iff #81 #88)
-#86 := (iff #78 #85)
-#87 := [rewrite]: #86
-#90 := [monotonicity #87]: #89
-#82 := (iff #15 #81)
-#79 := (iff #14 #78)
-#76 := (= #13 #75)
-#77 := [rewrite]: #76
-#73 := (= #12 #72)
-#70 := (= #11 -1::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80]: #82
-#92 := [trans #83 #90]: #91
-#68 := [asserted]: #15
-#93 := [mp #68 #92]: #88
-#603 := (or #85 #579 #632)
-#604 := [th-lemma arith triangle-eq]: #603
-#605 := [unit-resolution #604 #93]: #599
-#573 := [unit-resolution #605 #612]: #579
-#689 := (<= #72 0::Int)
-#580 := [unit-resolution #609 #617]: #428
-#539 := (or #587 #689)
-#570 := [th-lemma arith triangle-eq]: #539
-#572 := [unit-resolution #570 #580]: #689
-#574 := [th-lemma arith farkas 1 -1 1 #572 #573 #598]: false
-#581 := [lemma #574]: #576
-#584 := [unit-resolution #602 #581]: #710
-#585 := (or #686 #693)
-#595 := [th-lemma arith triangle-eq]: #585
-#575 := [unit-resolution #595 #584]: #693
-#583 := (<= #667 0::Int)
-#596 := (or #636 #583)
-#551 := [th-lemma arith triangle-eq]: #596
-#552 := [unit-resolution #551 #630]: #583
-[th-lemma arith farkas 1 -1 1 #552 #573 #575]: false
-unsat
-f75a5bc3547a7074f0c9531c7810228e69e7b130 273 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#726 := (pattern #17)
-#8 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #16)
-#68 := (* -1::Int #14)
-#74 := (div #68 #71)
-#225 := (* -1::Int #74)
-#226 := (+ #17 #225)
-#227 := (= #226 0::Int)
-#27 := (div #14 #16)
-#222 := (* -1::Int #27)
-#223 := (+ #17 #222)
-#224 := (= #223 0::Int)
-#93 := (<= #16 0::Int)
-#100 := (>= #14 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #14 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#228 := (if #189 #224 #227)
-#221 := (= #17 0::Int)
-#19 := (= #16 0::Int)
-#18 := (= #14 0::Int)
-#20 := (or #18 #19)
-#229 := (if #20 #221 #228)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #229)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#730 := (iff #232 #727)
-#728 := (iff #229 #229)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#192 := (if #189 #27 #74)
-#195 := (if #20 0::Int #192)
-#198 := (= #17 #195)
-#201 := (forall (vars (?v0 Int) (?v1 Int)) #198)
-#233 := (iff #201 #232)
-#230 := (iff #198 #229)
-#231 := [rewrite]: #230
-#234 := [quant-intro #231]: #233
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (if #107 #27 #74)
-#113 := (if #20 0::Int #110)
-#116 := (= #17 #113)
-#119 := (forall (vars (?v0 Int) (?v1 Int)) #116)
-#202 := (iff #119 #201)
-#199 := (iff #116 #198)
-#196 := (= #113 #195)
-#193 := (= #110 #192)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [quant-intro #200]: #202
-#181 := (~ #119 #119)
-#179 := (~ #116 #116)
-#180 := [refl]: #179
-#182 := [nnf-pos #180]: #181
-#29 := (- #16)
-#28 := (- #14)
-#30 := (div #28 #29)
-#22 := (< 0::Int #16)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (if #26 #27 #30)
-#32 := (if #20 0::Int #31)
-#33 := (= #17 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#122 := (iff #34 #119)
-#77 := (if #26 #27 #74)
-#80 := (if #20 0::Int #77)
-#83 := (= #17 #80)
-#86 := (forall (vars (?v0 Int) (?v1 Int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #26 #107)
-#105 := (iff #25 #104)
-#95 := (iff #22 #94)
-#96 := [rewrite]: #95
-#102 := (iff #24 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #23 #97)
-#91 := (iff #21 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #34 #86)
-#84 := (iff #33 #83)
-#81 := (= #32 #80)
-#78 := (= #31 #77)
-#75 := (= #30 #74)
-#72 := (= #29 #71)
-#73 := [rewrite]: #72
-#69 := (= #28 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#66 := [asserted]: #34
-#124 := [mp #66 #123]: #119
-#173 := [mp~ #124 #182]: #119
-#204 := [mp #173 #203]: #201
-#235 := [mp #204 #234]: #232
-#732 := [mp #235 #731]: #727
-#10 := 3::Int
-#9 := (f4 f5 0::Int)
-#11 := (f3 #9 3::Int)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#544 := (not #727)
-#559 := (or #544 #12)
-#388 := (* -1::Int 3::Int)
-#714 := (* -1::Int 0::Int)
-#389 := (div #714 #388)
-#721 := (* -1::Int #389)
-#722 := (+ #11 #721)
-#723 := (= #722 0::Int)
-#718 := (div 0::Int 3::Int)
-#720 := (* -1::Int #718)
-#377 := (+ #11 #720)
-#507 := (= #377 0::Int)
-#390 := (<= 3::Int 0::Int)
-#403 := (>= 0::Int 0::Int)
-#400 := (or #403 #390)
-#404 := (not #400)
-#399 := (<= 0::Int 0::Int)
-#401 := (or #399 #390)
-#402 := (not #401)
-#383 := (or #402 #404)
-#724 := (if #383 #507 #723)
-#397 := (= 3::Int 0::Int)
-#313 := (= 0::Int 0::Int)
-#398 := (or #313 #397)
-#719 := (if #398 #12 #724)
-#561 := (or #544 #719)
-#555 := (iff #561 #559)
-#564 := (iff #559 #559)
-#565 := [rewrite]: #564
-#656 := (iff #719 #12)
-#1 := true
-#551 := (if true #12 #12)
-#560 := (iff #551 #12)
-#655 := [rewrite]: #560
-#510 := (iff #719 #551)
-#549 := (iff #724 #12)
-#663 := (if false #12 #12)
-#664 := (iff #663 #12)
-#667 := [rewrite]: #664
-#665 := (iff #724 #663)
-#509 := (iff #723 #12)
-#506 := (= #722 #11)
-#691 := (+ #11 0::Int)
-#681 := (= #691 #11)
-#682 := [rewrite]: #681
-#670 := (= #722 #691)
-#675 := (= #721 0::Int)
-#689 := (= #714 0::Int)
-#690 := [rewrite]: #689
-#668 := (= #721 #714)
-#673 := (= #389 0::Int)
-#685 := -3::Int
-#527 := (div 0::Int -3::Int)
-#671 := (= #527 0::Int)
-#672 := [rewrite]: #671
-#528 := (= #389 #527)
-#680 := (= #388 -3::Int)
-#686 := [rewrite]: #680
-#529 := [monotonicity #690 #686]: #528
-#674 := [trans #529 #672]: #673
-#669 := [monotonicity #674]: #668
-#676 := [trans #669 #690]: #675
-#677 := [monotonicity #676]: #670
-#508 := [trans #677 #682]: #506
-#662 := [monotonicity #508]: #509
-#679 := (iff #507 #12)
-#683 := (= #377 #11)
-#688 := (= #377 #691)
-#405 := (= #720 0::Int)
-#410 := (= #720 #714)
-#408 := (= #718 0::Int)
-#409 := [rewrite]: #408
-#411 := [monotonicity #409]: #410
-#687 := [trans #411 #690]: #405
-#692 := [monotonicity #687]: #688
-#678 := [trans #692 #682]: #683
-#684 := [monotonicity #678]: #679
-#694 := (iff #383 false)
-#696 := (or false false)
-#693 := (iff #696 false)
-#697 := [rewrite]: #693
-#418 := (iff #383 #696)
-#319 := (iff #404 false)
-#708 := (not true)
-#711 := (iff #708 false)
-#351 := [rewrite]: #711
-#424 := (iff #404 #708)
-#422 := (iff #400 true)
-#716 := (or true false)
-#360 := (iff #716 true)
-#701 := [rewrite]: #360
-#699 := (iff #400 #716)
-#703 := (iff #390 false)
-#704 := [rewrite]: #703
-#710 := (iff #403 true)
-#713 := [rewrite]: #710
-#700 := [monotonicity #713 #704]: #699
-#423 := [trans #700 #701]: #422
-#425 := [monotonicity #423]: #424
-#695 := [trans #425 #351]: #319
-#352 := (iff #402 false)
-#346 := (iff #402 #708)
-#707 := (iff #401 true)
-#705 := (iff #401 #716)
-#366 := (iff #399 true)
-#367 := [rewrite]: #366
-#706 := [monotonicity #367 #704]: #705
-#702 := [trans #706 #701]: #707
-#709 := [monotonicity #702]: #346
-#712 := [trans #709 #351]: #352
-#419 := [monotonicity #712 #695]: #418
-#698 := [trans #419 #697]: #694
-#666 := [monotonicity #698 #684 #662]: #665
-#550 := [trans #666 #667]: #549
-#364 := (iff #398 true)
-#376 := (iff #398 #716)
-#375 := (iff #397 false)
-#380 := [rewrite]: #375
-#725 := (iff #313 true)
-#715 := [rewrite]: #725
-#717 := [monotonicity #715 #380]: #376
-#365 := [trans #717 #701]: #364
-#658 := [monotonicity #365 #550]: #510
-#659 := [trans #658 #655]: #656
-#563 := [monotonicity #659]: #555
-#566 := [trans #563 #565]: #555
-#562 := [quant-inst #8 #10]: #561
-#567 := [mp #562 #566]: #559
-[unit-resolution #567 #65 #732]: false
-unsat
-3a037a6da2a34725e2878597eed3b279d726e286 289 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#740 := (pattern #18)
-#8 := 0::Int
-#80 := -1::Int
-#85 := (* -1::Int #17)
-#82 := (* -1::Int #15)
-#88 := (div #82 #85)
-#239 := (* -1::Int #88)
-#240 := (+ #18 #239)
-#241 := (= #240 0::Int)
-#28 := (div #15 #17)
-#236 := (* -1::Int #28)
-#237 := (+ #18 #236)
-#238 := (= #237 0::Int)
-#107 := (<= #17 0::Int)
-#114 := (>= #15 0::Int)
-#199 := (or #114 #107)
-#200 := (not #199)
-#103 := (<= #15 0::Int)
-#197 := (or #103 #107)
-#198 := (not #197)
-#203 := (or #198 #200)
-#242 := (if #203 #238 #241)
-#235 := (= #18 0::Int)
-#20 := (= #17 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#243 := (if #21 #235 #242)
-#741 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #740) #243)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#744 := (iff #246 #741)
-#742 := (iff #243 #243)
-#743 := [refl]: #742
-#745 := [quant-intro #743]: #744
-#206 := (if #203 #28 #88)
-#209 := (if #21 0::Int #206)
-#212 := (= #18 #209)
-#215 := (forall (vars (?v0 Int) (?v1 Int)) #212)
-#247 := (iff #215 #246)
-#244 := (iff #212 #243)
-#245 := [rewrite]: #244
-#248 := [quant-intro #245]: #247
-#108 := (not #107)
-#115 := (not #114)
-#118 := (and #115 #108)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#124 := (if #121 #28 #88)
-#127 := (if #21 0::Int #124)
-#130 := (= #18 #127)
-#133 := (forall (vars (?v0 Int) (?v1 Int)) #130)
-#216 := (iff #133 #215)
-#213 := (iff #130 #212)
-#210 := (= #127 #209)
-#207 := (= #124 #206)
-#204 := (iff #121 #203)
-#201 := (iff #118 #200)
-#202 := [rewrite]: #201
-#191 := (iff #111 #198)
-#192 := [rewrite]: #191
-#205 := [monotonicity #192 #202]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [quant-intro #214]: #216
-#195 := (~ #133 #133)
-#193 := (~ #130 #130)
-#194 := [refl]: #193
-#196 := [nnf-pos #194]: #195
-#30 := (- #17)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #18 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#136 := (iff #35 #133)
-#91 := (if #27 #28 #88)
-#94 := (if #21 0::Int #91)
-#97 := (= #18 #94)
-#100 := (forall (vars (?v0 Int) (?v1 Int)) #97)
-#134 := (iff #100 #133)
-#131 := (iff #97 #130)
-#128 := (= #94 #127)
-#125 := (= #91 #124)
-#122 := (iff #27 #121)
-#119 := (iff #26 #118)
-#109 := (iff #23 #108)
-#110 := [rewrite]: #109
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117 #110]: #119
-#112 := (iff #24 #111)
-#105 := (iff #22 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#126 := [monotonicity #123]: #125
-#129 := [monotonicity #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [quant-intro #132]: #134
-#101 := (iff #35 #100)
-#98 := (iff #34 #97)
-#95 := (= #33 #94)
-#92 := (= #32 #91)
-#89 := (= #31 #88)
-#86 := (= #30 #85)
-#87 := [rewrite]: #86
-#83 := (= #29 #82)
-#84 := [rewrite]: #83
-#90 := [monotonicity #84 #87]: #89
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93]: #95
-#99 := [monotonicity #96]: #98
-#102 := [quant-intro #99]: #101
-#137 := [trans #102 #135]: #136
-#79 := [asserted]: #35
-#138 := [mp #79 #137]: #133
-#187 := [mp~ #138 #196]: #133
-#218 := [mp #187 #217]: #215
-#249 := [mp #218 #248]: #246
-#746 := [mp #249 #745]: #741
-#67 := -3::Int
-#9 := (f4 f5 0::Int)
-#70 := (f3 #9 -3::Int)
-#73 := (= #70 0::Int)
-#76 := (not #73)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#13 := (= #12 0::Int)
-#14 := (not #13)
-#77 := (iff #14 #76)
-#74 := (iff #13 #73)
-#71 := (= #12 #70)
-#68 := (= #11 -3::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #14
-#81 := [mp #66 #78]: #76
-#575 := (not #741)
-#576 := (or #575 #73)
-#402 := (* -1::Int -3::Int)
-#728 := (* -1::Int 0::Int)
-#403 := (div #728 #402)
-#735 := (* -1::Int #403)
-#736 := (+ #70 #735)
-#737 := (= #736 0::Int)
-#732 := (div 0::Int -3::Int)
-#734 := (* -1::Int #732)
-#391 := (+ #70 #734)
-#521 := (= #391 0::Int)
-#404 := (<= -3::Int 0::Int)
-#417 := (>= 0::Int 0::Int)
-#414 := (or #417 #404)
-#418 := (not #414)
-#413 := (<= 0::Int 0::Int)
-#415 := (or #413 #404)
-#416 := (not #415)
-#397 := (or #416 #418)
-#738 := (if #397 #521 #737)
-#411 := (= -3::Int 0::Int)
-#327 := (= 0::Int 0::Int)
-#412 := (or #327 #411)
-#733 := (if #412 #73 #738)
-#569 := (or #575 #733)
-#578 := (iff #569 #576)
-#580 := (iff #576 #576)
-#581 := [rewrite]: #580
-#558 := (iff #733 #73)
-#1 := true
-#672 := (if true #73 #73)
-#670 := (iff #672 #73)
-#673 := [rewrite]: #670
-#574 := (iff #733 #672)
-#565 := (iff #738 #73)
-#680 := (if false #73 #73)
-#563 := (iff #680 #73)
-#564 := [rewrite]: #563
-#678 := (iff #738 #680)
-#677 := (iff #737 #73)
-#523 := (= #736 #70)
-#695 := (+ #70 0::Int)
-#692 := (= #695 #70)
-#693 := [rewrite]: #692
-#520 := (= #736 #695)
-#684 := (= #735 0::Int)
-#701 := (= #728 0::Int)
-#705 := [rewrite]: #701
-#689 := (= #735 #728)
-#682 := (= #403 0::Int)
-#543 := (div 0::Int 3::Int)
-#687 := (= #543 0::Int)
-#688 := [rewrite]: #687
-#685 := (= #403 #543)
-#541 := (= #402 3::Int)
-#542 := [rewrite]: #541
-#686 := [monotonicity #705 #542]: #685
-#683 := [trans #686 #688]: #682
-#690 := [monotonicity #683]: #689
-#691 := [trans #690 #705]: #684
-#522 := [monotonicity #691]: #520
-#676 := [trans #522 #693]: #523
-#679 := [monotonicity #676]: #677
-#694 := (iff #521 #73)
-#698 := (= #391 #70)
-#696 := (= #391 #695)
-#702 := (= #734 0::Int)
-#704 := (= #734 #728)
-#425 := (= #732 0::Int)
-#703 := [rewrite]: #425
-#419 := [monotonicity #703]: #704
-#706 := [trans #419 #705]: #702
-#697 := [monotonicity #706]: #696
-#699 := [trans #697 #693]: #698
-#700 := [monotonicity #699]: #694
-#423 := (iff #397 false)
-#707 := (or false false)
-#712 := (iff #707 false)
-#422 := [rewrite]: #712
-#711 := (iff #397 #707)
-#432 := (iff #418 false)
-#725 := (not true)
-#726 := (iff #725 false)
-#724 := [rewrite]: #726
-#709 := (iff #418 #725)
-#439 := (iff #414 true)
-#719 := (or true true)
-#716 := (iff #719 true)
-#722 := [rewrite]: #716
-#437 := (iff #414 #719)
-#717 := (iff #404 true)
-#718 := [rewrite]: #717
-#714 := (iff #417 true)
-#436 := [rewrite]: #714
-#438 := [monotonicity #436 #718]: #437
-#333 := [trans #438 #722]: #439
-#710 := [monotonicity #333]: #709
-#433 := [trans #710 #724]: #432
-#727 := (iff #416 false)
-#365 := (iff #416 #725)
-#360 := (iff #415 true)
-#720 := (iff #415 #719)
-#380 := (iff #413 true)
-#381 := [rewrite]: #380
-#721 := [monotonicity #381 #718]: #720
-#723 := [trans #721 #722]: #360
-#366 := [monotonicity #723]: #365
-#713 := [trans #366 #724]: #727
-#708 := [monotonicity #713 #433]: #711
-#424 := [trans #708 #422]: #423
-#681 := [monotonicity #424 #700 #679]: #678
-#524 := [trans #681 #564]: #565
-#378 := (iff #412 true)
-#730 := (or true false)
-#374 := (iff #730 true)
-#715 := [rewrite]: #374
-#390 := (iff #412 #730)
-#389 := (iff #411 false)
-#394 := [rewrite]: #389
-#739 := (iff #327 true)
-#729 := [rewrite]: #739
-#731 := [monotonicity #729 #394]: #390
-#379 := [trans #731 #715]: #378
-#669 := [monotonicity #379 #524]: #574
-#573 := [trans #669 #673]: #558
-#579 := [monotonicity #573]: #578
-#674 := [trans #579 #581]: #578
-#577 := [quant-inst #8 #67]: #569
-#671 := [mp #577 #674]: #576
-[unit-resolution #671 #81 #746]: false
-unsat
-58560b4c08322ae7fbfadc81b6f10d1874a37205 290 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#726 := (pattern #18)
-#12 := 0::Int
-#68 := -1::Int
-#72 := (* -1::Int #17)
-#69 := (* -1::Int #15)
-#75 := (div #69 #72)
-#226 := (* -1::Int #75)
-#227 := (+ #18 #226)
-#228 := (= #227 0::Int)
-#28 := (div #15 #17)
-#223 := (* -1::Int #28)
-#224 := (+ #18 #223)
-#225 := (= #224 0::Int)
-#94 := (<= #17 0::Int)
-#101 := (>= #15 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #15 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#229 := (if #190 #225 #228)
-#222 := (= #18 0::Int)
-#20 := (= #17 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#230 := (if #21 #222 #229)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #230)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#730 := (iff #233 #727)
-#728 := (iff #230 #230)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#193 := (if #190 #28 #75)
-#196 := (if #21 0::Int #193)
-#199 := (= #18 #196)
-#202 := (forall (vars (?v0 Int) (?v1 Int)) #199)
-#234 := (iff #202 #233)
-#231 := (iff #199 #230)
-#232 := [rewrite]: #231
-#235 := [quant-intro #232]: #234
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (if #108 #28 #75)
-#114 := (if #21 0::Int #111)
-#117 := (= #18 #114)
-#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#197 := (= #114 #196)
-#194 := (= #111 #193)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [quant-intro #201]: #203
-#182 := (~ #120 #120)
-#180 := (~ #117 #117)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#30 := (- #17)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #18 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#123 := (iff #35 #120)
-#78 := (if #27 #28 #75)
-#81 := (if #21 0::Int #78)
-#84 := (= #18 #81)
-#87 := (forall (vars (?v0 Int) (?v1 Int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #27 #108)
-#106 := (iff #26 #105)
-#96 := (iff #23 #95)
-#97 := [rewrite]: #96
-#103 := (iff #25 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #24 #98)
-#92 := (iff #22 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #35 #87)
-#85 := (iff #34 #84)
-#82 := (= #33 #81)
-#79 := (= #32 #78)
-#76 := (= #31 #75)
-#73 := (= #30 #72)
-#74 := [rewrite]: #73
-#70 := (= #29 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#67 := [asserted]: #35
-#125 := [mp #67 #124]: #120
-#174 := [mp~ #125 #183]: #120
-#205 := [mp #174 #204]: #202
-#236 := [mp #205 #235]: #233
-#732 := [mp #236 #731]: #727
-#10 := 3::Int
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#11 := (f3 #9 3::Int)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#66 := [asserted]: #14
-#639 := (not #727)
-#641 := (or #639 #13)
-#388 := (* -1::Int 3::Int)
-#714 := (* -1::Int 1::Int)
-#389 := (div #714 #388)
-#721 := (* -1::Int #389)
-#722 := (+ #11 #721)
-#723 := (= #722 0::Int)
-#718 := (div 1::Int 3::Int)
-#720 := (* -1::Int #718)
-#377 := (+ #11 #720)
-#507 := (= #377 0::Int)
-#390 := (<= 3::Int 0::Int)
-#403 := (>= 1::Int 0::Int)
-#400 := (or #403 #390)
-#404 := (not #400)
-#399 := (<= 1::Int 0::Int)
-#401 := (or #399 #390)
-#402 := (not #401)
-#383 := (or #402 #404)
-#724 := (if #383 #507 #723)
-#397 := (= 3::Int 0::Int)
-#313 := (= 1::Int 0::Int)
-#398 := (or #313 #397)
-#719 := (if #398 #13 #724)
-#651 := (or #639 #719)
-#653 := (iff #651 #641)
-#654 := (iff #641 #641)
-#643 := [rewrite]: #654
-#650 := (iff #719 #13)
-#567 := (if false #13 #13)
-#661 := (iff #567 #13)
-#648 := [rewrite]: #661
-#660 := (iff #719 #567)
-#565 := (iff #724 #13)
-#655 := (= #11 1::Int)
-#1 := true
-#561 := (if true #13 #655)
-#563 := (iff #561 #13)
-#564 := [rewrite]: #563
-#562 := (iff #724 #561)
-#544 := (iff #723 #655)
-#664 := (+ -1::Int #11)
-#510 := (= #664 0::Int)
-#656 := (iff #510 #655)
-#659 := [rewrite]: #656
-#658 := (iff #723 #510)
-#550 := (= #722 #664)
-#663 := (+ #11 -1::Int)
-#667 := (= #663 #664)
-#549 := [rewrite]: #667
-#665 := (= #722 #663)
-#509 := (= #721 -1::Int)
-#528 := (= #714 -1::Int)
-#529 := [rewrite]: #528
-#506 := (= #721 #714)
-#670 := (= #389 1::Int)
-#671 := -3::Int
-#674 := (div -1::Int -3::Int)
-#675 := (= #674 1::Int)
-#676 := [rewrite]: #675
-#668 := (= #389 #674)
-#672 := (= #388 -3::Int)
-#673 := [rewrite]: #672
-#669 := [monotonicity #529 #673]: #668
-#677 := [trans #669 #676]: #670
-#508 := [monotonicity #677]: #506
-#662 := [trans #508 #529]: #509
-#666 := [monotonicity #662]: #665
-#551 := [trans #666 #549]: #550
-#560 := [monotonicity #551]: #658
-#559 := [trans #560 #659]: #544
-#686 := (iff #507 #13)
-#685 := (= #377 #11)
-#682 := (+ #11 0::Int)
-#679 := (= #682 #11)
-#684 := [rewrite]: #679
-#683 := (= #377 #682)
-#692 := (= #720 0::Int)
-#690 := (* -1::Int 0::Int)
-#691 := (= #690 0::Int)
-#688 := [rewrite]: #691
-#405 := (= #720 #690)
-#411 := (= #718 0::Int)
-#689 := [rewrite]: #411
-#687 := [monotonicity #689]: #405
-#681 := [trans #687 #688]: #692
-#678 := [monotonicity #681]: #683
-#680 := [trans #678 #684]: #685
-#527 := [monotonicity #680]: #686
-#409 := (iff #383 true)
-#699 := (or true false)
-#423 := (iff #699 true)
-#424 := [rewrite]: #423
-#698 := (iff #383 #699)
-#697 := (iff #404 false)
-#695 := (not true)
-#419 := (iff #695 false)
-#693 := [rewrite]: #419
-#696 := (iff #404 #695)
-#425 := (iff #400 true)
-#700 := (iff #400 #699)
-#703 := (iff #390 false)
-#704 := [rewrite]: #703
-#710 := (iff #403 true)
-#713 := [rewrite]: #710
-#422 := [monotonicity #713 #704]: #700
-#319 := [trans #422 #424]: #425
-#418 := [monotonicity #319]: #696
-#694 := [trans #418 #693]: #697
-#352 := (iff #402 true)
-#708 := (not false)
-#711 := (iff #708 true)
-#351 := [rewrite]: #711
-#346 := (iff #402 #708)
-#707 := (iff #401 false)
-#716 := (or false false)
-#360 := (iff #716 false)
-#701 := [rewrite]: #360
-#705 := (iff #401 #716)
-#366 := (iff #399 false)
-#367 := [rewrite]: #366
-#706 := [monotonicity #367 #704]: #705
-#702 := [trans #706 #701]: #707
-#709 := [monotonicity #702]: #346
-#712 := [trans #709 #351]: #352
-#408 := [monotonicity #712 #694]: #698
-#410 := [trans #408 #424]: #409
-#555 := [monotonicity #410 #527 #559]: #562
-#566 := [trans #555 #564]: #565
-#364 := (iff #398 false)
-#376 := (iff #398 #716)
-#375 := (iff #397 false)
-#380 := [rewrite]: #375
-#725 := (iff #313 false)
-#715 := [rewrite]: #725
-#717 := [monotonicity #715 #380]: #376
-#365 := [trans #717 #701]: #364
-#657 := [monotonicity #365 #566]: #660
-#642 := [trans #657 #648]: #650
-#649 := [monotonicity #642]: #653
-#644 := [trans #649 #643]: #653
-#652 := [quant-inst #8 #10]: #651
-#645 := [mp #652 #644]: #641
-[unit-resolution #645 #66 #732]: false
-unsat
-a76887b4238113dd2f0fd0fc574d57f879ea15c2 280 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#15 := (f4 f5 #14)
-#17 := (f3 #15 #16)
-#726 := (pattern #17)
-#18 := 0::Int
-#68 := -1::Int
-#72 := (* -1::Int #16)
-#69 := (* -1::Int #14)
-#75 := (div #69 #72)
-#226 := (* -1::Int #75)
-#227 := (+ #17 #226)
-#228 := (= #227 0::Int)
-#28 := (div #14 #16)
-#223 := (* -1::Int #28)
-#224 := (+ #17 #223)
-#225 := (= #224 0::Int)
-#94 := (<= #16 0::Int)
-#101 := (>= #14 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #14 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#229 := (if #190 #225 #228)
-#222 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #14 0::Int)
-#21 := (or #19 #20)
-#230 := (if #21 #222 #229)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #230)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#730 := (iff #233 #727)
-#728 := (iff #230 #230)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#193 := (if #190 #28 #75)
-#196 := (if #21 0::Int #193)
-#199 := (= #17 #196)
-#202 := (forall (vars (?v0 Int) (?v1 Int)) #199)
-#234 := (iff #202 #233)
-#231 := (iff #199 #230)
-#232 := [rewrite]: #231
-#235 := [quant-intro #232]: #234
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (if #108 #28 #75)
-#114 := (if #21 0::Int #111)
-#117 := (= #17 #114)
-#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#197 := (= #114 #196)
-#194 := (= #111 #193)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [quant-intro #201]: #203
-#182 := (~ #120 #120)
-#180 := (~ #117 #117)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#30 := (- #16)
-#29 := (- #14)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #14 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #14)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (if #27 #28 #31)
-#33 := (if #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#123 := (iff #35 #120)
-#78 := (if #27 #28 #75)
-#81 := (if #21 0::Int #78)
-#84 := (= #17 #81)
-#87 := (forall (vars (?v0 Int) (?v1 Int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #27 #108)
-#106 := (iff #26 #105)
-#96 := (iff #23 #95)
-#97 := [rewrite]: #96
-#103 := (iff #25 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #24 #98)
-#92 := (iff #22 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #35 #87)
-#85 := (iff #34 #84)
-#82 := (= #33 #81)
-#79 := (= #32 #78)
-#76 := (= #31 #75)
-#73 := (= #30 #72)
-#74 := [rewrite]: #73
-#70 := (= #29 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#67 := [asserted]: #35
-#125 := [mp #67 #124]: #120
-#174 := [mp~ #125 #183]: #120
-#205 := [mp #174 #204]: #202
-#236 := [mp #205 #235]: #233
-#732 := [mp #236 #731]: #727
-#11 := 1::Int
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#10 := (f3 #9 3::Int)
-#12 := (= #10 1::Int)
-#13 := (not #12)
-#66 := [asserted]: #13
-#564 := (not #727)
-#565 := (or #564 #12)
-#507 := (* -1::Int 3::Int)
-#714 := (div #507 #507)
-#388 := (* -1::Int #714)
-#389 := (+ #10 #388)
-#721 := (= #389 0::Int)
-#383 := (div 3::Int 3::Int)
-#718 := (* -1::Int #383)
-#720 := (+ #10 #718)
-#377 := (= #720 0::Int)
-#399 := (<= 3::Int 0::Int)
-#402 := (>= 3::Int 0::Int)
-#403 := (or #402 #399)
-#400 := (not #403)
-#390 := (or #399 #399)
-#401 := (not #390)
-#404 := (or #401 #400)
-#722 := (if #404 #377 #721)
-#398 := (= #10 0::Int)
-#313 := (= 3::Int 0::Int)
-#397 := (or #313 #313)
-#723 := (if #397 #398 #722)
-#566 := (or #564 #723)
-#660 := (iff #566 #565)
-#661 := (iff #565 #565)
-#648 := [rewrite]: #661
-#555 := (iff #723 #12)
-#659 := (if false #398 #12)
-#561 := (iff #659 #12)
-#562 := [rewrite]: #561
-#544 := (iff #723 #659)
-#655 := (iff #722 #12)
-#1 := true
-#550 := (if true #12 #12)
-#658 := (iff #550 #12)
-#560 := [rewrite]: #658
-#551 := (iff #722 #550)
-#667 := (iff #721 #12)
-#688 := (+ -1::Int #10)
-#678 := (= #688 0::Int)
-#685 := (iff #678 #12)
-#680 := [rewrite]: #685
-#666 := (iff #721 #678)
-#663 := (= #389 #688)
-#405 := (+ #10 -1::Int)
-#692 := (= #405 #688)
-#681 := [rewrite]: #692
-#509 := (= #389 #405)
-#506 := (= #388 -1::Int)
-#698 := (* -1::Int 1::Int)
-#410 := (= #698 -1::Int)
-#411 := [rewrite]: #410
-#670 := (= #388 #698)
-#675 := (= #714 1::Int)
-#528 := -3::Int
-#672 := (div -3::Int -3::Int)
-#668 := (= #672 1::Int)
-#669 := [rewrite]: #668
-#673 := (= #714 #672)
-#529 := (= #507 -3::Int)
-#671 := [rewrite]: #529
-#674 := [monotonicity #671 #671]: #673
-#676 := [trans #674 #669]: #675
-#677 := [monotonicity #676]: #670
-#508 := [trans #677 #411]: #506
-#662 := [monotonicity #508]: #509
-#665 := [trans #662 #681]: #663
-#664 := [monotonicity #665]: #666
-#549 := [trans #664 #680]: #667
-#686 := (iff #377 #12)
-#679 := (iff #377 #678)
-#682 := (= #720 #688)
-#687 := (= #720 #405)
-#689 := (= #718 -1::Int)
-#408 := (= #718 #698)
-#697 := (= #383 1::Int)
-#694 := [rewrite]: #697
-#409 := [monotonicity #694]: #408
-#690 := [trans #409 #411]: #689
-#691 := [monotonicity #690]: #687
-#683 := [trans #691 #681]: #682
-#684 := [monotonicity #683]: #679
-#527 := [trans #684 #680]: #686
-#419 := (iff #404 true)
-#711 := (or true false)
-#712 := (iff #711 true)
-#710 := [rewrite]: #712
-#696 := (iff #404 #711)
-#319 := (iff #400 false)
-#700 := (not true)
-#424 := (iff #700 false)
-#425 := [rewrite]: #424
-#422 := (iff #400 #700)
-#713 := (iff #403 true)
-#351 := (iff #403 #711)
-#360 := (iff #399 false)
-#701 := [rewrite]: #360
-#346 := (iff #402 true)
-#709 := [rewrite]: #346
-#352 := [monotonicity #709 #701]: #351
-#699 := [trans #352 #710]: #713
-#423 := [monotonicity #699]: #422
-#695 := [trans #423 #425]: #319
-#702 := (iff #401 true)
-#703 := (not false)
-#706 := (iff #703 true)
-#707 := [rewrite]: #706
-#704 := (iff #401 #703)
-#366 := (iff #390 false)
-#725 := (or false false)
-#380 := (iff #725 false)
-#716 := [rewrite]: #380
-#364 := (iff #390 #725)
-#365 := [monotonicity #701 #701]: #364
-#367 := [trans #365 #716]: #366
-#705 := [monotonicity #367]: #704
-#708 := [trans #705 #707]: #702
-#418 := [monotonicity #708 #695]: #696
-#693 := [trans #418 #710]: #419
-#510 := [monotonicity #693 #527 #549]: #551
-#656 := [trans #510 #560]: #655
-#376 := (iff #397 false)
-#715 := (iff #397 #725)
-#724 := (iff #313 false)
-#719 := [rewrite]: #724
-#375 := [monotonicity #719 #719]: #715
-#717 := [trans #375 #716]: #376
-#559 := [monotonicity #717 #656]: #544
-#563 := [trans #559 #562]: #555
-#657 := [monotonicity #563]: #660
-#650 := [trans #657 #648]: #660
-#567 := [quant-inst #8 #8]: #566
-#642 := [mp #567 #650]: #565
-[unit-resolution #642 #66 #732]: false
-unsat
-3e19a3704b0d883148b4ca12556acf9eedeb8436 304 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#726 := (pattern #18)
-#19 := 0::Int
-#69 := -1::Int
-#73 := (* -1::Int #17)
-#70 := (* -1::Int #15)
-#76 := (div #70 #73)
-#227 := (* -1::Int #76)
-#228 := (+ #18 #227)
-#229 := (= #228 0::Int)
-#29 := (div #15 #17)
-#224 := (* -1::Int #29)
-#225 := (+ #18 #224)
-#226 := (= #225 0::Int)
-#95 := (<= #17 0::Int)
-#102 := (>= #15 0::Int)
-#187 := (or #102 #95)
-#188 := (not #187)
-#91 := (<= #15 0::Int)
-#185 := (or #91 #95)
-#186 := (not #185)
-#191 := (or #186 #188)
-#230 := (if #191 #226 #229)
-#223 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #15 0::Int)
-#22 := (or #20 #21)
-#231 := (if #22 #223 #230)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #231)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#730 := (iff #234 #727)
-#728 := (iff #231 #231)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#194 := (if #191 #29 #76)
-#197 := (if #22 0::Int #194)
-#200 := (= #18 #197)
-#203 := (forall (vars (?v0 Int) (?v1 Int)) #200)
-#235 := (iff #203 #234)
-#232 := (iff #200 #231)
-#233 := [rewrite]: #232
-#236 := [quant-intro #233]: #235
-#96 := (not #95)
-#103 := (not #102)
-#106 := (and #103 #96)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (if #109 #29 #76)
-#115 := (if #22 0::Int #112)
-#118 := (= #18 #115)
-#121 := (forall (vars (?v0 Int) (?v1 Int)) #118)
-#204 := (iff #121 #203)
-#201 := (iff #118 #200)
-#198 := (= #115 #197)
-#195 := (= #112 #194)
-#192 := (iff #109 #191)
-#189 := (iff #106 #188)
-#190 := [rewrite]: #189
-#179 := (iff #99 #186)
-#180 := [rewrite]: #179
-#193 := [monotonicity #180 #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [monotonicity #199]: #201
-#205 := [quant-intro #202]: #204
-#183 := (~ #121 #121)
-#181 := (~ #118 #118)
-#182 := [refl]: #181
-#184 := [nnf-pos #182]: #183
-#31 := (- #17)
-#30 := (- #15)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (if #28 #29 #32)
-#34 := (if #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#124 := (iff #36 #121)
-#79 := (if #28 #29 #76)
-#82 := (if #22 0::Int #79)
-#85 := (= #18 #82)
-#88 := (forall (vars (?v0 Int) (?v1 Int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #28 #109)
-#107 := (iff #27 #106)
-#97 := (iff #24 #96)
-#98 := [rewrite]: #97
-#104 := (iff #26 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105 #98]: #107
-#100 := (iff #25 #99)
-#93 := (iff #23 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #36 #88)
-#86 := (iff #35 #85)
-#83 := (= #34 #82)
-#80 := (= #33 #79)
-#77 := (= #32 #76)
-#74 := (= #31 #73)
-#75 := [rewrite]: #74
-#71 := (= #30 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#68 := [asserted]: #36
-#126 := [mp #68 #125]: #121
-#175 := [mp~ #126 #184]: #121
-#206 := [mp #175 #205]: #203
-#237 := [mp #206 #236]: #234
-#732 := [mp #237 #731]: #727
-#12 := 1::Int
-#10 := 3::Int
-#8 := 5::Int
-#9 := (f4 f5 5::Int)
-#11 := (f3 #9 3::Int)
-#13 := (= #11 1::Int)
-#14 := (not #13)
-#67 := [asserted]: #14
-#647 := (not #727)
-#631 := (or #647 #13)
-#389 := (* -1::Int 3::Int)
-#388 := (* -1::Int 5::Int)
-#721 := (div #388 #389)
-#722 := (* -1::Int #721)
-#723 := (+ #11 #722)
-#724 := (= #723 0::Int)
-#720 := (div 5::Int 3::Int)
-#377 := (* -1::Int #720)
-#507 := (+ #11 #377)
-#714 := (= #507 0::Int)
-#401 := (<= 3::Int 0::Int)
-#400 := (>= 5::Int 0::Int)
-#404 := (or #400 #401)
-#383 := (not #404)
-#390 := (<= 5::Int 0::Int)
-#402 := (or #390 #401)
-#403 := (not #402)
-#718 := (or #403 #383)
-#719 := (if #718 #714 #724)
-#399 := (= #11 0::Int)
-#397 := (= 3::Int 0::Int)
-#313 := (= 5::Int 0::Int)
-#398 := (or #313 #397)
-#725 := (if #398 #399 #719)
-#632 := (or #647 #725)
-#635 := (iff #632 #631)
-#637 := (iff #631 #631)
-#633 := [rewrite]: #637
-#646 := (iff #725 #13)
-#649 := (if false #399 #13)
-#644 := (iff #649 #13)
-#645 := [rewrite]: #644
-#654 := (iff #725 #649)
-#652 := (iff #719 #13)
-#274 := 2::Int
-#567 := (= #11 2::Int)
-#1 := true
-#650 := (if true #13 #567)
-#641 := (iff #650 #13)
-#651 := [rewrite]: #641
-#642 := (iff #719 #650)
-#661 := (iff #724 #567)
-#551 := -2::Int
-#559 := (+ -2::Int #11)
-#564 := (= #559 0::Int)
-#660 := (iff #564 #567)
-#657 := [rewrite]: #660
-#565 := (iff #724 #564)
-#555 := (= #723 #559)
-#656 := (+ #11 -2::Int)
-#561 := (= #656 #559)
-#562 := [rewrite]: #561
-#659 := (= #723 #656)
-#560 := (= #722 -2::Int)
-#667 := (* -1::Int 2::Int)
-#510 := (= #667 -2::Int)
-#658 := [rewrite]: #510
-#549 := (= #722 #667)
-#666 := (= #721 2::Int)
-#670 := -3::Int
-#669 := -5::Int
-#508 := (div -5::Int -3::Int)
-#663 := (= #508 2::Int)
-#665 := [rewrite]: #663
-#509 := (= #721 #508)
-#677 := (= #389 -3::Int)
-#506 := [rewrite]: #677
-#675 := (= #388 -5::Int)
-#676 := [rewrite]: #675
-#662 := [monotonicity #676 #506]: #509
-#664 := [trans #662 #665]: #666
-#550 := [monotonicity #664]: #549
-#655 := [trans #550 #658]: #560
-#544 := [monotonicity #655]: #659
-#563 := [trans #544 #562]: #555
-#566 := [monotonicity #563]: #565
-#648 := [trans #566 #657]: #661
-#674 := (iff #714 #13)
-#684 := (+ -1::Int #11)
-#528 := (= #684 0::Int)
-#672 := (iff #528 #13)
-#673 := [rewrite]: #672
-#529 := (iff #714 #528)
-#686 := (= #507 #684)
-#683 := (+ #11 -1::Int)
-#685 := (= #683 #684)
-#680 := [rewrite]: #685
-#678 := (= #507 #683)
-#681 := (= #377 -1::Int)
-#405 := (* -1::Int 1::Int)
-#688 := (= #405 -1::Int)
-#692 := [rewrite]: #688
-#687 := (= #377 #405)
-#689 := (= #720 1::Int)
-#690 := [rewrite]: #689
-#691 := [monotonicity #690]: #687
-#682 := [trans #691 #692]: #681
-#679 := [monotonicity #682]: #678
-#527 := [trans #679 #680]: #686
-#671 := [monotonicity #527]: #529
-#668 := [trans #671 #673]: #674
-#410 := (iff #718 true)
-#700 := (or true false)
-#424 := (iff #700 true)
-#425 := [rewrite]: #424
-#408 := (iff #718 #700)
-#694 := (iff #383 false)
-#696 := (not true)
-#693 := (iff #696 false)
-#697 := [rewrite]: #693
-#418 := (iff #383 #696)
-#319 := (iff #404 true)
-#422 := (iff #404 #700)
-#704 := (iff #401 false)
-#705 := [rewrite]: #704
-#713 := (iff #400 true)
-#699 := [rewrite]: #713
-#423 := [monotonicity #699 #705]: #422
-#695 := [trans #423 #425]: #319
-#419 := [monotonicity #695]: #418
-#698 := [trans #419 #697]: #694
-#712 := (iff #403 true)
-#346 := (not false)
-#351 := (iff #346 true)
-#352 := [rewrite]: #351
-#709 := (iff #403 #346)
-#702 := (iff #402 false)
-#376 := (or false false)
-#701 := (iff #376 false)
-#364 := [rewrite]: #701
-#706 := (iff #402 #376)
-#367 := (iff #390 false)
-#703 := [rewrite]: #367
-#707 := [monotonicity #703 #705]: #706
-#708 := [trans #707 #364]: #702
-#711 := [monotonicity #708]: #709
-#710 := [trans #711 #352]: #712
-#409 := [monotonicity #710 #698]: #408
-#411 := [trans #409 #425]: #410
-#639 := [monotonicity #411 #668 #648]: #642
-#653 := [trans #639 #651]: #652
-#365 := (iff #398 false)
-#717 := (iff #398 #376)
-#380 := (iff #397 false)
-#716 := [rewrite]: #380
-#715 := (iff #313 false)
-#375 := [rewrite]: #715
-#360 := [monotonicity #375 #716]: #717
-#366 := [trans #360 #364]: #365
-#643 := [monotonicity #366 #653]: #654
-#640 := [trans #643 #645]: #646
-#636 := [monotonicity #640]: #635
-#638 := [trans #636 #633]: #635
-#634 := [quant-inst #8 #10]: #632
-#624 := [mp #634 #638]: #631
-[unit-resolution #624 #67 #732]: false
-unsat
-5e68ab43f3201baeb2a0c0f495119aa80de32eb9 306 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#743 := (pattern #19)
-#20 := 0::Int
-#75 := -1::Int
-#89 := (* -1::Int #18)
-#85 := (* -1::Int #16)
-#92 := (div #85 #89)
-#243 := (* -1::Int #92)
-#244 := (+ #19 #243)
-#245 := (= #244 0::Int)
-#30 := (div #16 #18)
-#240 := (* -1::Int #30)
-#241 := (+ #19 #240)
-#242 := (= #241 0::Int)
-#111 := (<= #18 0::Int)
-#118 := (>= #16 0::Int)
-#203 := (or #118 #111)
-#204 := (not #203)
-#107 := (<= #16 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#246 := (if #207 #242 #245)
-#239 := (= #19 0::Int)
-#22 := (= #18 0::Int)
-#21 := (= #16 0::Int)
-#23 := (or #21 #22)
-#247 := (if #23 #239 #246)
-#744 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #743) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#747 := (iff #250 #744)
-#745 := (iff #247 #247)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#210 := (if #207 #30 #92)
-#213 := (if #23 0::Int #210)
-#216 := (= #19 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#112 := (not #111)
-#119 := (not #118)
-#122 := (and #119 #112)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#128 := (if #125 #30 #92)
-#131 := (if #23 0::Int #128)
-#134 := (= #19 #131)
-#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#214 := (= #131 #213)
-#211 := (= #128 #210)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#199 := (~ #137 #137)
-#197 := (~ #134 #134)
-#198 := [refl]: #197
-#200 := [nnf-pos #198]: #199
-#32 := (- #18)
-#31 := (- #16)
-#33 := (div #31 #32)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#34 := (if #29 #30 #33)
-#35 := (if #23 0::Int #34)
-#36 := (= #19 #35)
-#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#140 := (iff #37 #137)
-#95 := (if #29 #30 #92)
-#98 := (if #23 0::Int #95)
-#101 := (= #19 #98)
-#104 := (forall (vars (?v0 Int) (?v1 Int)) #101)
-#138 := (iff #104 #137)
-#135 := (iff #101 #134)
-#132 := (= #98 #131)
-#129 := (= #95 #128)
-#126 := (iff #29 #125)
-#123 := (iff #28 #122)
-#113 := (iff #25 #112)
-#114 := [rewrite]: #113
-#120 := (iff #27 #119)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121 #114]: #123
-#116 := (iff #26 #115)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [quant-intro #136]: #138
-#105 := (iff #37 #104)
-#102 := (iff #36 #101)
-#99 := (= #35 #98)
-#96 := (= #34 #95)
-#93 := (= #33 #92)
-#90 := (= #32 #89)
-#91 := [rewrite]: #90
-#87 := (= #31 #85)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [quant-intro #103]: #105
-#141 := [trans #106 #139]: #140
-#84 := [asserted]: #37
-#142 := [mp #84 #141]: #137
-#191 := [mp~ #142 #200]: #137
-#222 := [mp #191 #221]: #219
-#253 := [mp #222 #252]: #250
-#749 := [mp #253 #748]: #744
-#69 := -3::Int
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#72 := (f3 #9 -3::Int)
-#78 := (= #72 -1::Int)
-#81 := (not #78)
-#13 := (- 1::Int)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#82 := (iff #15 #81)
-#79 := (iff #14 #78)
-#76 := (= #13 -1::Int)
-#77 := [rewrite]: #76
-#73 := (= #12 #72)
-#70 := (= #11 -3::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80]: #82
-#68 := [asserted]: #15
-#86 := [mp #68 #83]: #81
-#659 := (not #744)
-#656 := (or #659 #78)
-#406 := (* -1::Int -3::Int)
-#405 := (* -1::Int 1::Int)
-#738 := (div #405 #406)
-#739 := (* -1::Int #738)
-#740 := (+ #72 #739)
-#741 := (= #740 0::Int)
-#737 := (div 1::Int -3::Int)
-#394 := (* -1::Int #737)
-#524 := (+ #72 #394)
-#731 := (= #524 0::Int)
-#418 := (<= -3::Int 0::Int)
-#417 := (>= 1::Int 0::Int)
-#421 := (or #417 #418)
-#400 := (not #421)
-#407 := (<= 1::Int 0::Int)
-#419 := (or #407 #418)
-#420 := (not #419)
-#735 := (or #420 #400)
-#736 := (if #735 #731 #741)
-#416 := (= #72 0::Int)
-#414 := (= -3::Int 0::Int)
-#330 := (= 1::Int 0::Int)
-#415 := (or #330 #414)
-#742 := (if #415 #416 #736)
-#658 := (or #659 #742)
-#669 := (iff #658 #656)
-#666 := (iff #656 #656)
-#671 := [rewrite]: #666
-#665 := (iff #742 #78)
-#572 := (if false #416 #78)
-#582 := (iff #572 #78)
-#583 := [rewrite]: #582
-#674 := (iff #742 #572)
-#584 := (iff #736 #78)
-#580 := (iff #736 #572)
-#578 := (iff #741 #78)
-#567 := (+ 1::Int #72)
-#672 := (= #567 0::Int)
-#561 := (iff #672 #78)
-#576 := [rewrite]: #561
-#673 := (iff #741 #672)
-#675 := (= #740 #567)
-#681 := (+ #72 1::Int)
-#568 := (= #681 #567)
-#527 := [rewrite]: #568
-#684 := (= #740 #681)
-#682 := (= #739 1::Int)
-#523 := (* -1::Int -1::Int)
-#679 := (= #523 1::Int)
-#680 := [rewrite]: #679
-#525 := (= #739 #523)
-#687 := (= #738 -1::Int)
-#691 := (div -1::Int 3::Int)
-#692 := (= #691 -1::Int)
-#693 := [rewrite]: #692
-#685 := (= #738 #691)
-#689 := (= #406 3::Int)
-#690 := [rewrite]: #689
-#546 := (= #405 -1::Int)
-#688 := [rewrite]: #546
-#686 := [monotonicity #688 #690]: #685
-#694 := [trans #686 #693]: #687
-#526 := [monotonicity #694]: #525
-#683 := [trans #526 #680]: #682
-#566 := [monotonicity #683]: #684
-#577 := [trans #566 #527]: #675
-#676 := [monotonicity #577]: #673
-#579 := [trans #676 #576]: #578
-#544 := (iff #731 #416)
-#697 := (= #524 #72)
-#700 := (+ #72 0::Int)
-#701 := (= #700 #72)
-#702 := [rewrite]: #701
-#695 := (= #524 #700)
-#698 := (= #394 0::Int)
-#422 := (* -1::Int 0::Int)
-#705 := (= #422 0::Int)
-#709 := [rewrite]: #705
-#704 := (= #394 #422)
-#706 := (= #737 0::Int)
-#707 := [rewrite]: #706
-#708 := [monotonicity #707]: #704
-#699 := [trans #708 #709]: #698
-#696 := [monotonicity #699]: #695
-#703 := [trans #696 #702]: #697
-#545 := [monotonicity #703]: #544
-#427 := (iff #735 false)
-#393 := (or false false)
-#718 := (iff #393 false)
-#381 := [rewrite]: #718
-#425 := (iff #735 #393)
-#711 := (iff #400 false)
-#1 := true
-#368 := (not true)
-#727 := (iff #368 false)
-#730 := [rewrite]: #727
-#710 := (iff #400 #368)
-#435 := (iff #421 true)
-#441 := (or true true)
-#712 := (iff #441 true)
-#713 := [rewrite]: #712
-#442 := (iff #421 #441)
-#721 := (iff #418 true)
-#722 := [rewrite]: #721
-#439 := (iff #417 true)
-#440 := [rewrite]: #439
-#336 := [monotonicity #440 #722]: #442
-#436 := [trans #336 #713]: #435
-#714 := [monotonicity #436]: #710
-#715 := [trans #714 #730]: #711
-#716 := (iff #420 false)
-#369 := (iff #420 #368)
-#726 := (iff #419 true)
-#723 := (or false true)
-#725 := (iff #723 true)
-#363 := [rewrite]: #725
-#724 := (iff #419 #723)
-#384 := (iff #407 false)
-#720 := [rewrite]: #384
-#719 := [monotonicity #720 #722]: #724
-#728 := [trans #719 #363]: #726
-#729 := [monotonicity #728]: #369
-#717 := [trans #729 #730]: #716
-#426 := [monotonicity #717 #715]: #425
-#428 := [trans #426 #381]: #427
-#581 := [monotonicity #428 #545 #579]: #580
-#677 := [trans #581 #583]: #584
-#382 := (iff #415 false)
-#734 := (iff #415 #393)
-#397 := (iff #414 false)
-#733 := [rewrite]: #397
-#732 := (iff #330 false)
-#392 := [rewrite]: #732
-#377 := [monotonicity #392 #733]: #734
-#383 := [trans #377 #381]: #382
-#678 := [monotonicity #383 #677]: #674
-#667 := [trans #678 #583]: #665
-#670 := [monotonicity #667]: #669
-#660 := [trans #670 #671]: #669
-#668 := [quant-inst #8 #69]: #658
-#661 := [mp #668 #660]: #656
-[unit-resolution #661 #86 #749]: false
-unsat
-96a820c8e0e11b411d8512a13b417469ec37ea05 305 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#743 := (pattern #19)
-#20 := 0::Int
-#75 := -1::Int
-#89 := (* -1::Int #18)
-#85 := (* -1::Int #16)
-#92 := (div #85 #89)
-#243 := (* -1::Int #92)
-#244 := (+ #19 #243)
-#245 := (= #244 0::Int)
-#30 := (div #16 #18)
-#240 := (* -1::Int #30)
-#241 := (+ #19 #240)
-#242 := (= #241 0::Int)
-#111 := (<= #18 0::Int)
-#118 := (>= #16 0::Int)
-#203 := (or #118 #111)
-#204 := (not #203)
-#107 := (<= #16 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#246 := (if #207 #242 #245)
-#239 := (= #19 0::Int)
-#22 := (= #18 0::Int)
-#21 := (= #16 0::Int)
-#23 := (or #21 #22)
-#247 := (if #23 #239 #246)
-#744 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #743) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#747 := (iff #250 #744)
-#745 := (iff #247 #247)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#210 := (if #207 #30 #92)
-#213 := (if #23 0::Int #210)
-#216 := (= #19 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#112 := (not #111)
-#119 := (not #118)
-#122 := (and #119 #112)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#128 := (if #125 #30 #92)
-#131 := (if #23 0::Int #128)
-#134 := (= #19 #131)
-#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#214 := (= #131 #213)
-#211 := (= #128 #210)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#199 := (~ #137 #137)
-#197 := (~ #134 #134)
-#198 := [refl]: #197
-#200 := [nnf-pos #198]: #199
-#32 := (- #18)
-#31 := (- #16)
-#33 := (div #31 #32)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#34 := (if #29 #30 #33)
-#35 := (if #23 0::Int #34)
-#36 := (= #19 #35)
-#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#140 := (iff #37 #137)
-#95 := (if #29 #30 #92)
-#98 := (if #23 0::Int #95)
-#101 := (= #19 #98)
-#104 := (forall (vars (?v0 Int) (?v1 Int)) #101)
-#138 := (iff #104 #137)
-#135 := (iff #101 #134)
-#132 := (= #98 #131)
-#129 := (= #95 #128)
-#126 := (iff #29 #125)
-#123 := (iff #28 #122)
-#113 := (iff #25 #112)
-#114 := [rewrite]: #113
-#120 := (iff #27 #119)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121 #114]: #123
-#116 := (iff #26 #115)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [quant-intro #136]: #138
-#105 := (iff #37 #104)
-#102 := (iff #36 #101)
-#99 := (= #35 #98)
-#96 := (= #34 #95)
-#93 := (= #33 #92)
-#90 := (= #32 #89)
-#91 := [rewrite]: #90
-#87 := (= #31 #85)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [quant-intro #103]: #105
-#141 := [trans #106 #139]: #140
-#84 := [asserted]: #37
-#142 := [mp #84 #141]: #137
-#191 := [mp~ #142 #200]: #137
-#222 := [mp #191 #221]: #219
-#253 := [mp #222 #252]: #250
-#749 := [mp #253 #748]: #744
-#69 := -3::Int
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#72 := (f3 #9 -3::Int)
-#78 := (= #72 -1::Int)
-#81 := (not #78)
-#12 := 1::Int
-#13 := (- 1::Int)
-#10 := (- 3::Int)
-#11 := (f3 #9 #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#82 := (iff #15 #81)
-#79 := (iff #14 #78)
-#76 := (= #13 -1::Int)
-#77 := [rewrite]: #76
-#73 := (= #11 #72)
-#70 := (= #10 -3::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80]: #82
-#68 := [asserted]: #15
-#86 := [mp #68 #83]: #81
-#667 := (not #744)
-#659 := (or #667 #78)
-#406 := (* -1::Int -3::Int)
-#405 := (* -1::Int 3::Int)
-#738 := (div #405 #406)
-#739 := (* -1::Int #738)
-#740 := (+ #72 #739)
-#741 := (= #740 0::Int)
-#737 := (div 3::Int -3::Int)
-#394 := (* -1::Int #737)
-#524 := (+ #72 #394)
-#731 := (= #524 0::Int)
-#418 := (<= -3::Int 0::Int)
-#417 := (>= 3::Int 0::Int)
-#421 := (or #417 #418)
-#400 := (not #421)
-#407 := (<= 3::Int 0::Int)
-#419 := (or #407 #418)
-#420 := (not #419)
-#735 := (or #420 #400)
-#736 := (if #735 #731 #741)
-#416 := (= #72 0::Int)
-#414 := (= -3::Int 0::Int)
-#330 := (= 3::Int 0::Int)
-#415 := (or #330 #414)
-#742 := (if #415 #416 #736)
-#656 := (or #667 #742)
-#668 := (iff #656 #659)
-#670 := (iff #659 #659)
-#666 := [rewrite]: #670
-#678 := (iff #742 #78)
-#582 := (if false #416 #78)
-#677 := (iff #582 #78)
-#674 := [rewrite]: #677
-#583 := (iff #742 #582)
-#580 := (iff #736 #78)
-#561 := (if false #78 #78)
-#579 := (iff #561 #78)
-#572 := [rewrite]: #579
-#576 := (iff #736 #561)
-#673 := (iff #741 #78)
-#701 := (+ 1::Int #72)
-#545 := (= #701 0::Int)
-#689 := (iff #545 #78)
-#690 := [rewrite]: #689
-#577 := (iff #741 #545)
-#527 := (= #740 #701)
-#700 := (+ #72 1::Int)
-#702 := (= #700 #701)
-#697 := [rewrite]: #702
-#567 := (= #740 #700)
-#684 := (= #739 1::Int)
-#422 := (* -1::Int -1::Int)
-#705 := (= #422 1::Int)
-#709 := [rewrite]: #705
-#683 := (= #739 #422)
-#680 := (= #738 -1::Int)
-#694 := (div -3::Int 3::Int)
-#526 := (= #694 -1::Int)
-#679 := [rewrite]: #526
-#523 := (= #738 #694)
-#693 := (= #406 3::Int)
-#687 := [rewrite]: #693
-#686 := (= #405 -3::Int)
-#692 := [rewrite]: #686
-#525 := [monotonicity #692 #687]: #523
-#682 := [trans #525 #679]: #680
-#681 := [monotonicity #682]: #683
-#566 := [trans #681 #709]: #684
-#568 := [monotonicity #566]: #567
-#675 := [trans #568 #697]: #527
-#672 := [monotonicity #675]: #577
-#676 := [trans #672 #690]: #673
-#691 := (iff #731 #78)
-#546 := (iff #731 #545)
-#703 := (= #524 #701)
-#695 := (= #524 #700)
-#698 := (= #394 1::Int)
-#704 := (= #394 #422)
-#706 := (= #737 -1::Int)
-#707 := [rewrite]: #706
-#708 := [monotonicity #707]: #704
-#699 := [trans #708 #709]: #698
-#696 := [monotonicity #699]: #695
-#544 := [trans #696 #697]: #703
-#688 := [monotonicity #544]: #546
-#685 := [trans #688 #690]: #691
-#427 := (iff #735 false)
-#393 := (or false false)
-#718 := (iff #393 false)
-#381 := [rewrite]: #718
-#425 := (iff #735 #393)
-#711 := (iff #400 false)
-#1 := true
-#368 := (not true)
-#727 := (iff #368 false)
-#730 := [rewrite]: #727
-#710 := (iff #400 #368)
-#435 := (iff #421 true)
-#441 := (or true true)
-#712 := (iff #441 true)
-#713 := [rewrite]: #712
-#442 := (iff #421 #441)
-#721 := (iff #418 true)
-#722 := [rewrite]: #721
-#439 := (iff #417 true)
-#440 := [rewrite]: #439
-#336 := [monotonicity #440 #722]: #442
-#436 := [trans #336 #713]: #435
-#714 := [monotonicity #436]: #710
-#715 := [trans #714 #730]: #711
-#716 := (iff #420 false)
-#369 := (iff #420 #368)
-#726 := (iff #419 true)
-#723 := (or false true)
-#725 := (iff #723 true)
-#363 := [rewrite]: #725
-#724 := (iff #419 #723)
-#384 := (iff #407 false)
-#720 := [rewrite]: #384
-#719 := [monotonicity #720 #722]: #724
-#728 := [trans #719 #363]: #726
-#729 := [monotonicity #728]: #369
-#717 := [trans #729 #730]: #716
-#426 := [monotonicity #717 #715]: #425
-#428 := [trans #426 #381]: #427
-#578 := [monotonicity #428 #685 #676]: #576
-#581 := [trans #578 #572]: #580
-#382 := (iff #415 false)
-#734 := (iff #415 #393)
-#397 := (iff #414 false)
-#733 := [rewrite]: #397
-#732 := (iff #330 false)
-#392 := [rewrite]: #732
-#377 := [monotonicity #392 #733]: #734
-#383 := [trans #377 #381]: #382
-#584 := [monotonicity #383 #581]: #583
-#665 := [trans #584 #674]: #678
-#669 := [monotonicity #665]: #668
-#671 := [trans #669 #666]: #668
-#658 := [quant-inst #8 #69]: #656
-#660 := [mp #658 #671]: #659
-[unit-resolution #660 #86 #749]: false
-unsat
-2a80a49785a4b459138949d07841039c329934c0 320 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#744 := (pattern #20)
-#21 := 0::Int
-#86 := -1::Int
-#91 := (* -1::Int #19)
-#88 := (* -1::Int #17)
-#94 := (div #88 #91)
-#245 := (* -1::Int #94)
-#246 := (+ #20 #245)
-#247 := (= #246 0::Int)
-#31 := (div #17 #19)
-#242 := (* -1::Int #31)
-#243 := (+ #20 #242)
-#244 := (= #243 0::Int)
-#113 := (<= #19 0::Int)
-#120 := (>= #17 0::Int)
-#205 := (or #120 #113)
-#206 := (not #205)
-#109 := (<= #17 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#248 := (if #209 #244 #247)
-#241 := (= #20 0::Int)
-#23 := (= #19 0::Int)
-#22 := (= #17 0::Int)
-#24 := (or #22 #23)
-#249 := (if #24 #241 #248)
-#745 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #744) #249)
-#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
-#748 := (iff #252 #745)
-#746 := (iff #249 #249)
-#747 := [refl]: #746
-#749 := [quant-intro #747]: #748
-#212 := (if #209 #31 #94)
-#215 := (if #24 0::Int #212)
-#218 := (= #20 #215)
-#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
-#253 := (iff #221 #252)
-#250 := (iff #218 #249)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#114 := (not #113)
-#121 := (not #120)
-#124 := (and #121 #114)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#130 := (if #127 #31 #94)
-#133 := (if #24 0::Int #130)
-#136 := (= #20 #133)
-#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#216 := (= #133 #215)
-#213 := (= #130 #212)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [quant-intro #220]: #222
-#201 := (~ #139 #139)
-#199 := (~ #136 #136)
-#200 := [refl]: #199
-#202 := [nnf-pos #200]: #201
-#33 := (- #19)
-#32 := (- #17)
-#34 := (div #32 #33)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (if #30 #31 #34)
-#36 := (if #24 0::Int #35)
-#37 := (= #20 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#142 := (iff #38 #139)
-#97 := (if #30 #31 #94)
-#100 := (if #24 0::Int #97)
-#103 := (= #20 #100)
-#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
-#140 := (iff #106 #139)
-#137 := (iff #103 #136)
-#134 := (= #100 #133)
-#131 := (= #97 #130)
-#128 := (iff #30 #127)
-#125 := (iff #29 #124)
-#115 := (iff #26 #114)
-#116 := [rewrite]: #115
-#122 := (iff #28 #121)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123 #116]: #125
-#118 := (iff #27 #117)
-#111 := (iff #25 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [quant-intro #138]: #140
-#107 := (iff #38 #106)
-#104 := (iff #37 #103)
-#101 := (= #36 #100)
-#98 := (= #35 #97)
-#95 := (= #34 #94)
-#92 := (= #33 #91)
-#93 := [rewrite]: #92
-#89 := (= #32 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#99 := [monotonicity #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [quant-intro #105]: #107
-#143 := [trans #108 #141]: #142
-#85 := [asserted]: #38
-#144 := [mp #85 #143]: #139
-#193 := [mp~ #144 #202]: #139
-#224 := [mp #193 #223]: #221
-#255 := [mp #224 #254]: #252
-#750 := [mp #255 #749]: #745
-#76 := -2::Int
-#70 := -3::Int
-#8 := 5::Int
-#9 := (f4 f5 5::Int)
-#73 := (f3 #9 -3::Int)
-#79 := (= #73 -2::Int)
-#82 := (not #79)
-#13 := 2::Int
-#14 := (- 2::Int)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -2::Int)
-#78 := [rewrite]: #77
-#74 := (= #12 #73)
-#71 := (= #11 -3::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#69 := [asserted]: #16
-#87 := [mp #69 #84]: #82
-#664 := (not #745)
-#658 := (or #664 #79)
-#407 := (* -1::Int -3::Int)
-#406 := (* -1::Int 5::Int)
-#739 := (div #406 #407)
-#740 := (* -1::Int #739)
-#741 := (+ #73 #740)
-#742 := (= #741 0::Int)
-#738 := (div 5::Int -3::Int)
-#395 := (* -1::Int #738)
-#525 := (+ #73 #395)
-#732 := (= #525 0::Int)
-#419 := (<= -3::Int 0::Int)
-#418 := (>= 5::Int 0::Int)
-#422 := (or #418 #419)
-#401 := (not #422)
-#408 := (<= 5::Int 0::Int)
-#420 := (or #408 #419)
-#421 := (not #420)
-#736 := (or #421 #401)
-#737 := (if #736 #732 #742)
-#417 := (= #73 0::Int)
-#415 := (= -3::Int 0::Int)
-#331 := (= 5::Int 0::Int)
-#416 := (or #331 #415)
-#743 := (if #416 #417 #737)
-#665 := (or #664 #743)
-#650 := (iff #665 #658)
-#653 := (iff #658 #658)
-#654 := [rewrite]: #653
-#662 := (iff #743 #79)
-#670 := (if false #417 #79)
-#672 := (iff #670 #79)
-#661 := [rewrite]: #672
-#671 := (iff #743 #670)
-#659 := (iff #737 #79)
-#690 := (= #73 -1::Int)
-#679 := (if false #690 #79)
-#660 := (iff #679 #79)
-#657 := [rewrite]: #660
-#666 := (iff #737 #679)
-#678 := (iff #742 #79)
-#562 := (+ 2::Int #73)
-#581 := (= #562 0::Int)
-#584 := (iff #581 #79)
-#585 := [rewrite]: #584
-#582 := (iff #742 #581)
-#580 := (= #741 #562)
-#673 := (+ #73 2::Int)
-#577 := (= #673 #562)
-#579 := [rewrite]: #577
-#674 := (= #741 #673)
-#676 := (= #740 2::Int)
-#685 := (* -1::Int -2::Int)
-#569 := (= #685 2::Int)
-#528 := [rewrite]: #569
-#567 := (= #740 #685)
-#684 := (= #739 -2::Int)
-#693 := -5::Int
-#526 := (div -5::Int 3::Int)
-#681 := (= #526 -2::Int)
-#683 := [rewrite]: #681
-#527 := (= #739 #526)
-#695 := (= #407 3::Int)
-#524 := [rewrite]: #695
-#694 := (= #406 -5::Int)
-#688 := [rewrite]: #694
-#680 := [monotonicity #688 #524]: #527
-#682 := [trans #680 #683]: #684
-#568 := [monotonicity #682]: #567
-#578 := [trans #568 #528]: #676
-#677 := [monotonicity #578]: #674
-#573 := [trans #677 #579]: #580
-#583 := [monotonicity #573]: #582
-#675 := [trans #583 #585]: #678
-#686 := (iff #732 #690)
-#284 := 1::Int
-#702 := (+ 1::Int #73)
-#546 := (= #702 0::Int)
-#691 := (iff #546 #690)
-#692 := [rewrite]: #691
-#547 := (iff #732 #546)
-#704 := (= #525 #702)
-#701 := (+ #73 1::Int)
-#703 := (= #701 #702)
-#698 := [rewrite]: #703
-#696 := (= #525 #701)
-#699 := (= #395 1::Int)
-#423 := (* -1::Int -1::Int)
-#706 := (= #423 1::Int)
-#710 := [rewrite]: #706
-#705 := (= #395 #423)
-#707 := (= #738 -1::Int)
-#708 := [rewrite]: #707
-#709 := [monotonicity #708]: #705
-#700 := [trans #709 #710]: #699
-#697 := [monotonicity #700]: #696
-#545 := [trans #697 #698]: #704
-#689 := [monotonicity #545]: #547
-#687 := [trans #689 #692]: #686
-#428 := (iff #736 false)
-#394 := (or false false)
-#719 := (iff #394 false)
-#382 := [rewrite]: #719
-#426 := (iff #736 #394)
-#712 := (iff #401 false)
-#1 := true
-#369 := (not true)
-#728 := (iff #369 false)
-#731 := [rewrite]: #728
-#711 := (iff #401 #369)
-#436 := (iff #422 true)
-#442 := (or true true)
-#713 := (iff #442 true)
-#714 := [rewrite]: #713
-#443 := (iff #422 #442)
-#722 := (iff #419 true)
-#723 := [rewrite]: #722
-#440 := (iff #418 true)
-#441 := [rewrite]: #440
-#337 := [monotonicity #441 #723]: #443
-#437 := [trans #337 #714]: #436
-#715 := [monotonicity #437]: #711
-#716 := [trans #715 #731]: #712
-#717 := (iff #421 false)
-#370 := (iff #421 #369)
-#727 := (iff #420 true)
-#724 := (or false true)
-#726 := (iff #724 true)
-#364 := [rewrite]: #726
-#725 := (iff #420 #724)
-#385 := (iff #408 false)
-#721 := [rewrite]: #385
-#720 := [monotonicity #721 #723]: #725
-#729 := [trans #720 #364]: #727
-#730 := [monotonicity #729]: #370
-#718 := [trans #730 #731]: #717
-#427 := [monotonicity #718 #716]: #426
-#429 := [trans #427 #382]: #428
-#668 := [monotonicity #429 #687 #675]: #666
-#669 := [trans #668 #657]: #659
-#383 := (iff #416 false)
-#735 := (iff #416 #394)
-#398 := (iff #415 false)
-#734 := [rewrite]: #398
-#733 := (iff #331 false)
-#393 := [rewrite]: #733
-#378 := [monotonicity #393 #734]: #735
-#384 := [trans #378 #382]: #383
-#667 := [monotonicity #384 #669]: #671
-#663 := [trans #667 #661]: #662
-#652 := [monotonicity #663]: #650
-#655 := [trans #652 #654]: #650
-#649 := [quant-inst #8 #70]: #665
-#651 := [mp #649 #655]: #658
-[unit-resolution #651 #87 #750]: false
-unsat
-77ef498d73e559a8192af9250d4abc98f525f4cc 309 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#742 := (pattern #18)
-#19 := 0::Int
-#68 := -1::Int
-#88 := (* -1::Int #17)
-#84 := (* -1::Int #15)
-#91 := (div #84 #88)
-#242 := (* -1::Int #91)
-#243 := (+ #18 #242)
-#244 := (= #243 0::Int)
-#29 := (div #15 #17)
-#239 := (* -1::Int #29)
-#240 := (+ #18 #239)
-#241 := (= #240 0::Int)
-#110 := (<= #17 0::Int)
-#117 := (>= #15 0::Int)
-#202 := (or #117 #110)
-#203 := (not #202)
-#106 := (<= #15 0::Int)
-#200 := (or #106 #110)
-#201 := (not #200)
-#206 := (or #201 #203)
-#245 := (if #206 #241 #244)
-#238 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #15 0::Int)
-#22 := (or #20 #21)
-#246 := (if #22 #238 #245)
-#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #246)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#746 := (iff #249 #743)
-#744 := (iff #246 #246)
-#745 := [refl]: #744
-#747 := [quant-intro #745]: #746
-#209 := (if #206 #29 #91)
-#212 := (if #22 0::Int #209)
-#215 := (= #18 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#250 := (iff #218 #249)
-#247 := (iff #215 #246)
-#248 := [rewrite]: #247
-#251 := [quant-intro #248]: #250
-#111 := (not #110)
-#118 := (not #117)
-#121 := (and #118 #111)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#127 := (if #124 #29 #91)
-#130 := (if #22 0::Int #127)
-#133 := (= #18 #130)
-#136 := (forall (vars (?v0 Int) (?v1 Int)) #133)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#213 := (= #130 #212)
-#210 := (= #127 #209)
-#207 := (iff #124 #206)
-#204 := (iff #121 #203)
-#205 := [rewrite]: #204
-#194 := (iff #114 #201)
-#195 := [rewrite]: #194
-#208 := [monotonicity #195 #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#198 := (~ #136 #136)
-#196 := (~ #133 #133)
-#197 := [refl]: #196
-#199 := [nnf-pos #197]: #198
-#31 := (- #17)
-#30 := (- #15)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (if #28 #29 #32)
-#34 := (if #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#139 := (iff #36 #136)
-#94 := (if #28 #29 #91)
-#97 := (if #22 0::Int #94)
-#100 := (= #18 #97)
-#103 := (forall (vars (?v0 Int) (?v1 Int)) #100)
-#137 := (iff #103 #136)
-#134 := (iff #100 #133)
-#131 := (= #97 #130)
-#128 := (= #94 #127)
-#125 := (iff #28 #124)
-#122 := (iff #27 #121)
-#112 := (iff #24 #111)
-#113 := [rewrite]: #112
-#119 := (iff #26 #118)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120 #113]: #122
-#115 := (iff #25 #114)
-#108 := (iff #23 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#129 := [monotonicity #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [quant-intro #135]: #137
-#104 := (iff #36 #103)
-#101 := (iff #35 #100)
-#98 := (= #34 #97)
-#95 := (= #33 #94)
-#92 := (= #32 #91)
-#89 := (= #31 #88)
-#90 := [rewrite]: #89
-#86 := (= #30 #84)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#96 := [monotonicity #93]: #95
-#99 := [monotonicity #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [quant-intro #102]: #104
-#140 := [trans #105 #138]: #139
-#83 := [asserted]: #36
-#141 := [mp #83 #140]: #136
-#190 := [mp~ #141 #199]: #136
-#221 := [mp #190 #220]: #218
-#252 := [mp #221 #251]: #249
-#748 := [mp #252 #747]: #743
-#11 := 3::Int
-#71 := (f4 f5 -1::Int)
-#74 := (f3 #71 3::Int)
-#77 := (= #74 -1::Int)
-#80 := (not #77)
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 3::Int)
-#13 := (= #12 #9)
-#14 := (not #13)
-#81 := (iff #14 #80)
-#78 := (iff #13 #77)
-#69 := (= #9 -1::Int)
-#70 := [rewrite]: #69
-#75 := (= #12 #74)
-#72 := (= #10 #71)
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76 #70]: #78
-#82 := [monotonicity #79]: #81
-#67 := [asserted]: #14
-#85 := [mp #67 #82]: #80
-#668 := (not #743)
-#669 := (or #668 #77)
-#405 := (* -1::Int 3::Int)
-#404 := (* -1::Int -1::Int)
-#737 := (div #404 #405)
-#738 := (* -1::Int #737)
-#739 := (+ #74 #738)
-#740 := (= #739 0::Int)
-#736 := (div -1::Int 3::Int)
-#393 := (* -1::Int #736)
-#523 := (+ #74 #393)
-#730 := (= #523 0::Int)
-#417 := (<= 3::Int 0::Int)
-#416 := (>= -1::Int 0::Int)
-#420 := (or #416 #417)
-#399 := (not #420)
-#406 := (<= -1::Int 0::Int)
-#418 := (or #406 #417)
-#419 := (not #418)
-#734 := (or #419 #399)
-#735 := (if #734 #730 #740)
-#415 := (= #74 0::Int)
-#413 := (= 3::Int 0::Int)
-#329 := (= -1::Int 0::Int)
-#414 := (or #329 #413)
-#741 := (if #414 #415 #735)
-#665 := (or #668 #741)
-#659 := (iff #665 #669)
-#661 := (iff #669 #669)
-#662 := [rewrite]: #661
-#657 := (iff #741 #77)
-#677 := (if false #415 #77)
-#658 := (iff #677 #77)
-#655 := [rewrite]: #658
-#664 := (iff #741 #677)
-#676 := (iff #735 #77)
-#1 := true
-#579 := (if true #77 #415)
-#582 := (iff #579 #77)
-#583 := [rewrite]: #582
-#580 := (iff #735 #579)
-#578 := (iff #740 #415)
-#575 := (= #739 #74)
-#576 := (+ #74 0::Int)
-#675 := (= #576 #74)
-#560 := [rewrite]: #675
-#671 := (= #739 #576)
-#526 := (= #738 0::Int)
-#680 := (* -1::Int 0::Int)
-#566 := (= #680 0::Int)
-#567 := [rewrite]: #566
-#683 := (= #738 #680)
-#681 := (= #737 0::Int)
-#692 := -3::Int
-#522 := (div 1::Int -3::Int)
-#678 := (= #522 0::Int)
-#679 := [rewrite]: #678
-#524 := (= #737 #522)
-#686 := (= #405 -3::Int)
-#693 := [rewrite]: #686
-#697 := (= #404 1::Int)
-#698 := [rewrite]: #697
-#525 := [monotonicity #698 #693]: #524
-#682 := [trans #525 #679]: #681
-#565 := [monotonicity #682]: #683
-#674 := [trans #565 #567]: #526
-#672 := [monotonicity #674]: #671
-#577 := [trans #672 #560]: #575
-#571 := [monotonicity #577]: #578
-#685 := (iff #730 #77)
-#696 := (+ 1::Int #74)
-#687 := (= #696 0::Int)
-#690 := (iff #687 #77)
-#684 := [rewrite]: #690
-#688 := (iff #730 #687)
-#544 := (= #523 #696)
-#695 := (+ #74 1::Int)
-#702 := (= #695 #696)
-#543 := [rewrite]: #702
-#700 := (= #523 #695)
-#699 := (= #393 1::Int)
-#704 := (= #393 #404)
-#703 := (= #736 -1::Int)
-#707 := [rewrite]: #703
-#708 := [monotonicity #707]: #704
-#694 := [trans #708 #698]: #699
-#701 := [monotonicity #694]: #700
-#545 := [trans #701 #543]: #544
-#689 := [monotonicity #545]: #688
-#691 := [trans #689 #684]: #685
-#706 := (iff #734 true)
-#424 := (or false true)
-#427 := (iff #424 true)
-#705 := [rewrite]: #427
-#425 := (iff #734 #424)
-#710 := (iff #399 true)
-#712 := (not false)
-#709 := (iff #712 true)
-#713 := [rewrite]: #709
-#434 := (iff #399 #712)
-#335 := (iff #420 false)
-#392 := (or false false)
-#717 := (iff #392 false)
-#380 := [rewrite]: #717
-#440 := (iff #420 #392)
-#720 := (iff #417 false)
-#721 := [rewrite]: #720
-#438 := (iff #416 false)
-#439 := [rewrite]: #438
-#441 := [monotonicity #439 #721]: #440
-#711 := [trans #441 #380]: #335
-#435 := [monotonicity #711]: #434
-#714 := [trans #435 #713]: #710
-#715 := (iff #419 false)
-#367 := (not true)
-#726 := (iff #367 false)
-#729 := [rewrite]: #726
-#368 := (iff #419 #367)
-#725 := (iff #418 true)
-#722 := (or true false)
-#724 := (iff #722 true)
-#362 := [rewrite]: #724
-#723 := (iff #418 #722)
-#383 := (iff #406 true)
-#719 := [rewrite]: #383
-#718 := [monotonicity #719 #721]: #723
-#727 := [trans #718 #362]: #725
-#728 := [monotonicity #727]: #368
-#716 := [trans #728 #729]: #715
-#426 := [monotonicity #716 #714]: #425
-#421 := [trans #426 #705]: #706
-#581 := [monotonicity #421 #691 #571]: #580
-#673 := [trans #581 #583]: #676
-#381 := (iff #414 false)
-#733 := (iff #414 #392)
-#396 := (iff #413 false)
-#732 := [rewrite]: #396
-#731 := (iff #329 false)
-#391 := [rewrite]: #731
-#376 := [monotonicity #391 #732]: #733
-#382 := [trans #376 #380]: #381
-#666 := [monotonicity #382 #673]: #664
-#667 := [trans #666 #655]: #657
-#660 := [monotonicity #667]: #659
-#656 := [trans #660 #662]: #659
-#670 := [quant-inst #68 #11]: #665
-#663 := [mp #670 #656]: #669
-[unit-resolution #663 #85 #748]: false
-unsat
-71da820ba222aeb0476106e772b16e56642782f7 311 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#746 := (pattern #19)
-#20 := 0::Int
-#78 := -1::Int
-#92 := (* -1::Int #18)
-#88 := (* -1::Int #16)
-#95 := (div #88 #92)
-#246 := (* -1::Int #95)
-#247 := (+ #19 #246)
-#248 := (= #247 0::Int)
-#30 := (div #16 #18)
-#243 := (* -1::Int #30)
-#244 := (+ #19 #243)
-#245 := (= #244 0::Int)
-#114 := (<= #18 0::Int)
-#121 := (>= #16 0::Int)
-#206 := (or #121 #114)
-#207 := (not #206)
-#110 := (<= #16 0::Int)
-#204 := (or #110 #114)
-#205 := (not #204)
-#210 := (or #205 #207)
-#249 := (if #210 #245 #248)
-#242 := (= #19 0::Int)
-#22 := (= #18 0::Int)
-#21 := (= #16 0::Int)
-#23 := (or #21 #22)
-#250 := (if #23 #242 #249)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #250)
-#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
-#750 := (iff #253 #747)
-#748 := (iff #250 #250)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#213 := (if #210 #30 #95)
-#216 := (if #23 0::Int #213)
-#219 := (= #19 #216)
-#222 := (forall (vars (?v0 Int) (?v1 Int)) #219)
-#254 := (iff #222 #253)
-#251 := (iff #219 #250)
-#252 := [rewrite]: #251
-#255 := [quant-intro #252]: #254
-#115 := (not #114)
-#122 := (not #121)
-#125 := (and #122 #115)
-#111 := (not #110)
-#118 := (and #111 #115)
-#128 := (or #118 #125)
-#131 := (if #128 #30 #95)
-#134 := (if #23 0::Int #131)
-#137 := (= #19 #134)
-#140 := (forall (vars (?v0 Int) (?v1 Int)) #137)
-#223 := (iff #140 #222)
-#220 := (iff #137 #219)
-#217 := (= #134 #216)
-#214 := (= #131 #213)
-#211 := (iff #128 #210)
-#208 := (iff #125 #207)
-#209 := [rewrite]: #208
-#198 := (iff #118 #205)
-#199 := [rewrite]: #198
-#212 := [monotonicity #199 #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [quant-intro #221]: #223
-#202 := (~ #140 #140)
-#200 := (~ #137 #137)
-#201 := [refl]: #200
-#203 := [nnf-pos #201]: #202
-#32 := (- #18)
-#31 := (- #16)
-#33 := (div #31 #32)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#34 := (if #29 #30 #33)
-#35 := (if #23 0::Int #34)
-#36 := (= #19 #35)
-#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#143 := (iff #37 #140)
-#98 := (if #29 #30 #95)
-#101 := (if #23 0::Int #98)
-#104 := (= #19 #101)
-#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
-#141 := (iff #107 #140)
-#138 := (iff #104 #137)
-#135 := (= #101 #134)
-#132 := (= #98 #131)
-#129 := (iff #29 #128)
-#126 := (iff #28 #125)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#123 := (iff #27 #122)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124 #117]: #126
-#119 := (iff #26 #118)
-#112 := (iff #24 #111)
-#113 := [rewrite]: #112
-#120 := [monotonicity #113 #117]: #119
-#130 := [monotonicity #120 #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [quant-intro #139]: #141
-#108 := (iff #37 #107)
-#105 := (iff #36 #104)
-#102 := (= #35 #101)
-#99 := (= #34 #98)
-#96 := (= #33 #95)
-#93 := (= #32 #92)
-#94 := [rewrite]: #93
-#90 := (= #31 #88)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [monotonicity #103]: #105
-#109 := [quant-intro #106]: #108
-#144 := [trans #109 #142]: #143
-#87 := [asserted]: #37
-#145 := [mp #87 #144]: #140
-#194 := [mp~ #145 #203]: #140
-#225 := [mp #194 #224]: #222
-#256 := [mp #225 #255]: #253
-#752 := [mp #256 #751]: #747
-#8 := 3::Int
-#69 := -3::Int
-#72 := (f4 f5 -3::Int)
-#75 := (f3 #72 3::Int)
-#81 := (= #75 -1::Int)
-#84 := (not #81)
-#12 := 1::Int
-#13 := (- 1::Int)
-#9 := (- 3::Int)
-#10 := (f4 f5 #9)
-#11 := (f3 #10 3::Int)
-#14 := (= #11 #13)
-#15 := (not #14)
-#85 := (iff #15 #84)
-#82 := (iff #14 #81)
-#79 := (= #13 -1::Int)
-#80 := [rewrite]: #79
-#76 := (= #11 #75)
-#73 := (= #10 #72)
-#70 := (= #9 -3::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [monotonicity #77 #80]: #82
-#86 := [monotonicity #83]: #85
-#68 := [asserted]: #15
-#89 := [mp #68 #86]: #84
-#661 := (not #747)
-#671 := (or #661 #81)
-#409 := (* -1::Int 3::Int)
-#408 := (* -1::Int -3::Int)
-#741 := (div #408 #409)
-#742 := (* -1::Int #741)
-#743 := (+ #75 #742)
-#744 := (= #743 0::Int)
-#740 := (div -3::Int 3::Int)
-#397 := (* -1::Int #740)
-#527 := (+ #75 #397)
-#734 := (= #527 0::Int)
-#421 := (<= 3::Int 0::Int)
-#420 := (>= -3::Int 0::Int)
-#424 := (or #420 #421)
-#403 := (not #424)
-#410 := (<= -3::Int 0::Int)
-#422 := (or #410 #421)
-#423 := (not #422)
-#738 := (or #423 #403)
-#739 := (if #738 #734 #744)
-#419 := (= #75 0::Int)
-#417 := (= 3::Int 0::Int)
-#333 := (= -3::Int 0::Int)
-#418 := (or #333 #417)
-#745 := (if #418 #419 #739)
-#672 := (or #661 #745)
-#669 := (iff #672 #671)
-#663 := (iff #671 #671)
-#664 := [rewrite]: #663
-#662 := (iff #745 #81)
-#680 := (if false #419 #81)
-#668 := (iff #680 #81)
-#670 := [rewrite]: #668
-#677 := (iff #745 #680)
-#586 := (iff #739 #81)
-#1 := true
-#582 := (if true #81 #81)
-#584 := (iff #582 #81)
-#585 := [rewrite]: #584
-#575 := (iff #739 #582)
-#579 := (iff #744 #81)
-#706 := (+ 1::Int #75)
-#692 := (= #706 0::Int)
-#688 := (iff #692 #81)
-#689 := [rewrite]: #688
-#679 := (iff #744 #692)
-#675 := (= #743 #706)
-#704 := (+ #75 1::Int)
-#547 := (= #704 #706)
-#548 := [rewrite]: #547
-#678 := (= #743 #704)
-#571 := (= #742 1::Int)
-#708 := (* -1::Int -1::Int)
-#702 := (= #708 1::Int)
-#703 := [rewrite]: #702
-#569 := (= #742 #708)
-#684 := (= #741 -1::Int)
-#529 := (div 3::Int -3::Int)
-#685 := (= #529 -1::Int)
-#686 := [rewrite]: #685
-#682 := (= #741 #529)
-#526 := (= #409 -3::Int)
-#528 := [rewrite]: #526
-#690 := (= #408 3::Int)
-#697 := [rewrite]: #690
-#683 := [monotonicity #697 #528]: #682
-#687 := [trans #683 #686]: #684
-#570 := [monotonicity #687]: #569
-#530 := [trans #570 #703]: #571
-#580 := [monotonicity #530]: #678
-#676 := [trans #580 #548]: #675
-#564 := [monotonicity #676]: #679
-#581 := [trans #564 #689]: #579
-#695 := (iff #734 #81)
-#693 := (iff #734 #692)
-#549 := (= #527 #706)
-#705 := (= #527 #704)
-#698 := (= #397 1::Int)
-#712 := (= #397 #708)
-#707 := (= #740 -1::Int)
-#711 := [rewrite]: #707
-#701 := [monotonicity #711]: #712
-#699 := [trans #701 #703]: #698
-#700 := [monotonicity #699]: #705
-#691 := [trans #700 #548]: #549
-#694 := [monotonicity #691]: #693
-#696 := [trans #694 #689]: #695
-#710 := (iff #738 true)
-#428 := (or false true)
-#431 := (iff #428 true)
-#709 := [rewrite]: #431
-#429 := (iff #738 #428)
-#714 := (iff #403 true)
-#716 := (not false)
-#713 := (iff #716 true)
-#717 := [rewrite]: #713
-#438 := (iff #403 #716)
-#339 := (iff #424 false)
-#396 := (or false false)
-#721 := (iff #396 false)
-#384 := [rewrite]: #721
-#444 := (iff #424 #396)
-#724 := (iff #421 false)
-#725 := [rewrite]: #724
-#442 := (iff #420 false)
-#443 := [rewrite]: #442
-#445 := [monotonicity #443 #725]: #444
-#715 := [trans #445 #384]: #339
-#439 := [monotonicity #715]: #438
-#718 := [trans #439 #717]: #714
-#719 := (iff #423 false)
-#371 := (not true)
-#730 := (iff #371 false)
-#733 := [rewrite]: #730
-#372 := (iff #423 #371)
-#729 := (iff #422 true)
-#726 := (or true false)
-#728 := (iff #726 true)
-#366 := [rewrite]: #728
-#727 := (iff #422 #726)
-#387 := (iff #410 true)
-#723 := [rewrite]: #387
-#722 := [monotonicity #723 #725]: #727
-#731 := [trans #722 #366]: #729
-#732 := [monotonicity #731]: #372
-#720 := [trans #732 #733]: #719
-#430 := [monotonicity #720 #718]: #429
-#425 := [trans #430 #709]: #710
-#583 := [monotonicity #425 #696 #581]: #575
-#587 := [trans #583 #585]: #586
-#385 := (iff #418 false)
-#737 := (iff #418 #396)
-#400 := (iff #417 false)
-#736 := [rewrite]: #400
-#735 := (iff #333 false)
-#395 := [rewrite]: #735
-#380 := [monotonicity #395 #736]: #737
-#386 := [trans #380 #384]: #385
-#681 := [monotonicity #386 #587]: #677
-#659 := [trans #681 #670]: #662
-#674 := [monotonicity #659]: #669
-#665 := [trans #674 #664]: #669
-#673 := [quant-inst #69 #8]: #672
-#666 := [mp #673 #665]: #671
-[unit-resolution #666 #89 #752]: false
-unsat
-7926b7bb56c2a95b0f37b98542d8e6b331cd48e9 326 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#747 := (pattern #20)
-#21 := 0::Int
-#89 := -1::Int
-#94 := (* -1::Int #19)
-#91 := (* -1::Int #17)
-#97 := (div #91 #94)
-#248 := (* -1::Int #97)
-#249 := (+ #20 #248)
-#250 := (= #249 0::Int)
-#31 := (div #17 #19)
-#245 := (* -1::Int #31)
-#246 := (+ #20 #245)
-#247 := (= #246 0::Int)
-#116 := (<= #19 0::Int)
-#123 := (>= #17 0::Int)
-#208 := (or #123 #116)
-#209 := (not #208)
-#112 := (<= #17 0::Int)
-#206 := (or #112 #116)
-#207 := (not #206)
-#212 := (or #207 #209)
-#251 := (if #212 #247 #250)
-#244 := (= #20 0::Int)
-#23 := (= #19 0::Int)
-#22 := (= #17 0::Int)
-#24 := (or #22 #23)
-#252 := (if #24 #244 #251)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #252)
-#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
-#751 := (iff #255 #748)
-#749 := (iff #252 #252)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#215 := (if #212 #31 #97)
-#218 := (if #24 0::Int #215)
-#221 := (= #20 #218)
-#224 := (forall (vars (?v0 Int) (?v1 Int)) #221)
-#256 := (iff #224 #255)
-#253 := (iff #221 #252)
-#254 := [rewrite]: #253
-#257 := [quant-intro #254]: #256
-#117 := (not #116)
-#124 := (not #123)
-#127 := (and #124 #117)
-#113 := (not #112)
-#120 := (and #113 #117)
-#130 := (or #120 #127)
-#133 := (if #130 #31 #97)
-#136 := (if #24 0::Int #133)
-#139 := (= #20 #136)
-#142 := (forall (vars (?v0 Int) (?v1 Int)) #139)
-#225 := (iff #142 #224)
-#222 := (iff #139 #221)
-#219 := (= #136 #218)
-#216 := (= #133 #215)
-#213 := (iff #130 #212)
-#210 := (iff #127 #209)
-#211 := [rewrite]: #210
-#200 := (iff #120 #207)
-#201 := [rewrite]: #200
-#214 := [monotonicity #201 #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [quant-intro #223]: #225
-#204 := (~ #142 #142)
-#202 := (~ #139 #139)
-#203 := [refl]: #202
-#205 := [nnf-pos #203]: #204
-#33 := (- #19)
-#32 := (- #17)
-#34 := (div #32 #33)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (if #30 #31 #34)
-#36 := (if #24 0::Int #35)
-#37 := (= #20 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#145 := (iff #38 #142)
-#100 := (if #30 #31 #97)
-#103 := (if #24 0::Int #100)
-#106 := (= #20 #103)
-#109 := (forall (vars (?v0 Int) (?v1 Int)) #106)
-#143 := (iff #109 #142)
-#140 := (iff #106 #139)
-#137 := (= #103 #136)
-#134 := (= #100 #133)
-#131 := (iff #30 #130)
-#128 := (iff #29 #127)
-#118 := (iff #26 #117)
-#119 := [rewrite]: #118
-#125 := (iff #28 #124)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126 #119]: #128
-#121 := (iff #27 #120)
-#114 := (iff #25 #113)
-#115 := [rewrite]: #114
-#122 := [monotonicity #115 #119]: #121
-#132 := [monotonicity #122 #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [quant-intro #141]: #143
-#110 := (iff #38 #109)
-#107 := (iff #37 #106)
-#104 := (= #36 #103)
-#101 := (= #35 #100)
-#98 := (= #34 #97)
-#95 := (= #33 #94)
-#96 := [rewrite]: #95
-#92 := (= #32 #91)
-#93 := [rewrite]: #92
-#99 := [monotonicity #93 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [monotonicity #105]: #107
-#111 := [quant-intro #108]: #110
-#146 := [trans #111 #144]: #145
-#88 := [asserted]: #38
-#147 := [mp #88 #146]: #142
-#196 := [mp~ #147 #205]: #142
-#227 := [mp #196 #226]: #224
-#258 := [mp #227 #257]: #255
-#753 := [mp #258 #752]: #748
-#79 := -2::Int
-#11 := 3::Int
-#70 := -5::Int
-#73 := (f4 f5 -5::Int)
-#76 := (f3 #73 3::Int)
-#82 := (= #76 -2::Int)
-#85 := (not #82)
-#13 := 2::Int
-#14 := (- 2::Int)
-#8 := 5::Int
-#9 := (- 5::Int)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 3::Int)
-#15 := (= #12 #14)
-#16 := (not #15)
-#86 := (iff #16 #85)
-#83 := (iff #15 #82)
-#80 := (= #14 -2::Int)
-#81 := [rewrite]: #80
-#77 := (= #12 #76)
-#74 := (= #10 #73)
-#71 := (= #9 -5::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#84 := [monotonicity #78 #81]: #83
-#87 := [monotonicity #84]: #86
-#69 := [asserted]: #16
-#90 := [mp #69 #87]: #85
-#652 := (not #748)
-#653 := (or #652 #82)
-#410 := (* -1::Int 3::Int)
-#409 := (* -1::Int -5::Int)
-#742 := (div #409 #410)
-#743 := (* -1::Int #742)
-#744 := (+ #76 #743)
-#745 := (= #744 0::Int)
-#741 := (div -5::Int 3::Int)
-#398 := (* -1::Int #741)
-#528 := (+ #76 #398)
-#735 := (= #528 0::Int)
-#422 := (<= 3::Int 0::Int)
-#421 := (>= -5::Int 0::Int)
-#425 := (or #421 #422)
-#404 := (not #425)
-#411 := (<= -5::Int 0::Int)
-#423 := (or #411 #422)
-#424 := (not #423)
-#739 := (or #424 #404)
-#740 := (if #739 #735 #745)
-#420 := (= #76 0::Int)
-#418 := (= 3::Int 0::Int)
-#334 := (= -5::Int 0::Int)
-#419 := (or #334 #418)
-#746 := (if #419 #420 #740)
-#655 := (or #652 #746)
-#657 := (iff #655 #653)
-#654 := (iff #653 #653)
-#659 := [rewrite]: #654
-#661 := (iff #746 #82)
-#675 := (if false #420 #82)
-#666 := (iff #675 #82)
-#667 := [rewrite]: #666
-#664 := (iff #746 #675)
-#674 := (iff #740 #82)
-#681 := (= #76 -1::Int)
-#1 := true
-#663 := (if true #82 #681)
-#672 := (iff #663 #82)
-#673 := [rewrite]: #672
-#660 := (iff #740 #663)
-#669 := (iff #745 #681)
-#287 := 1::Int
-#582 := (+ 1::Int #76)
-#586 := (= #582 0::Int)
-#678 := (iff #586 #681)
-#682 := [rewrite]: #678
-#587 := (iff #745 #586)
-#584 := (= #744 #582)
-#680 := (+ #76 1::Int)
-#583 := (= #680 #582)
-#576 := [rewrite]: #583
-#565 := (= #744 #680)
-#676 := (= #743 1::Int)
-#571 := (* -1::Int -1::Int)
-#679 := (= #571 1::Int)
-#581 := [rewrite]: #679
-#572 := (= #743 #571)
-#688 := (= #742 -1::Int)
-#527 := -3::Int
-#683 := (div 5::Int -3::Int)
-#687 := (= #683 -1::Int)
-#685 := [rewrite]: #687
-#684 := (= #742 #683)
-#529 := (= #410 -3::Int)
-#530 := [rewrite]: #529
-#691 := (= #409 5::Int)
-#698 := [rewrite]: #691
-#686 := [monotonicity #698 #530]: #684
-#570 := [trans #686 #685]: #688
-#531 := [monotonicity #570]: #572
-#677 := [trans #531 #581]: #676
-#580 := [monotonicity #677]: #565
-#585 := [trans #580 #576]: #584
-#588 := [monotonicity #585]: #587
-#671 := [trans #588 #682]: #669
-#696 := (iff #735 #82)
-#707 := (+ 2::Int #76)
-#693 := (= #707 0::Int)
-#689 := (iff #693 #82)
-#690 := [rewrite]: #689
-#694 := (iff #735 #693)
-#550 := (= #528 #707)
-#705 := (+ #76 2::Int)
-#548 := (= #705 #707)
-#549 := [rewrite]: #548
-#706 := (= #528 #705)
-#699 := (= #398 2::Int)
-#709 := (* -1::Int -2::Int)
-#703 := (= #709 2::Int)
-#704 := [rewrite]: #703
-#713 := (= #398 #709)
-#708 := (= #741 -2::Int)
-#712 := [rewrite]: #708
-#702 := [monotonicity #712]: #713
-#700 := [trans #702 #704]: #699
-#701 := [monotonicity #700]: #706
-#692 := [trans #701 #549]: #550
-#695 := [monotonicity #692]: #694
-#697 := [trans #695 #690]: #696
-#711 := (iff #739 true)
-#429 := (or false true)
-#432 := (iff #429 true)
-#710 := [rewrite]: #432
-#430 := (iff #739 #429)
-#715 := (iff #404 true)
-#717 := (not false)
-#714 := (iff #717 true)
-#718 := [rewrite]: #714
-#439 := (iff #404 #717)
-#340 := (iff #425 false)
-#397 := (or false false)
-#722 := (iff #397 false)
-#385 := [rewrite]: #722
-#445 := (iff #425 #397)
-#725 := (iff #422 false)
-#726 := [rewrite]: #725
-#443 := (iff #421 false)
-#444 := [rewrite]: #443
-#446 := [monotonicity #444 #726]: #445
-#716 := [trans #446 #385]: #340
-#440 := [monotonicity #716]: #439
-#719 := [trans #440 #718]: #715
-#720 := (iff #424 false)
-#372 := (not true)
-#731 := (iff #372 false)
-#734 := [rewrite]: #731
-#373 := (iff #424 #372)
-#730 := (iff #423 true)
-#727 := (or true false)
-#729 := (iff #727 true)
-#367 := [rewrite]: #729
-#728 := (iff #423 #727)
-#388 := (iff #411 true)
-#724 := [rewrite]: #388
-#723 := [monotonicity #724 #726]: #728
-#732 := [trans #723 #367]: #730
-#733 := [monotonicity #732]: #373
-#721 := [trans #733 #734]: #720
-#431 := [monotonicity #721 #719]: #430
-#426 := [trans #431 #710]: #711
-#662 := [monotonicity #426 #697 #671]: #660
-#670 := [trans #662 #673]: #674
-#386 := (iff #419 false)
-#738 := (iff #419 #397)
-#401 := (iff #418 false)
-#737 := [rewrite]: #401
-#736 := (iff #334 false)
-#396 := [rewrite]: #736
-#381 := [monotonicity #396 #737]: #738
-#387 := [trans #381 #385]: #386
-#665 := [monotonicity #387 #670]: #664
-#668 := [trans #665 #667]: #661
-#658 := [monotonicity #668]: #657
-#645 := [trans #658 #659]: #657
-#656 := [quant-inst #70 #11]: #655
-#646 := [mp #656 #645]: #653
-[unit-resolution #646 #90 #753]: false
-unsat
-8fedb44b144cd0bde283f4741a534807a56eb96d 312 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#746 := (pattern #20)
-#14 := 0::Int
-#69 := -1::Int
-#92 := (* -1::Int #19)
-#88 := (* -1::Int #17)
-#95 := (div #88 #92)
-#246 := (* -1::Int #95)
-#247 := (+ #20 #246)
-#248 := (= #247 0::Int)
-#30 := (div #17 #19)
-#243 := (* -1::Int #30)
-#244 := (+ #20 #243)
-#245 := (= #244 0::Int)
-#114 := (<= #19 0::Int)
-#121 := (>= #17 0::Int)
-#206 := (or #121 #114)
-#207 := (not #206)
-#110 := (<= #17 0::Int)
-#204 := (or #110 #114)
-#205 := (not #204)
-#210 := (or #205 #207)
-#249 := (if #210 #245 #248)
-#242 := (= #20 0::Int)
-#22 := (= #19 0::Int)
-#21 := (= #17 0::Int)
-#23 := (or #21 #22)
-#250 := (if #23 #242 #249)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #250)
-#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
-#750 := (iff #253 #747)
-#748 := (iff #250 #250)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#213 := (if #210 #30 #95)
-#216 := (if #23 0::Int #213)
-#219 := (= #20 #216)
-#222 := (forall (vars (?v0 Int) (?v1 Int)) #219)
-#254 := (iff #222 #253)
-#251 := (iff #219 #250)
-#252 := [rewrite]: #251
-#255 := [quant-intro #252]: #254
-#115 := (not #114)
-#122 := (not #121)
-#125 := (and #122 #115)
-#111 := (not #110)
-#118 := (and #111 #115)
-#128 := (or #118 #125)
-#131 := (if #128 #30 #95)
-#134 := (if #23 0::Int #131)
-#137 := (= #20 #134)
-#140 := (forall (vars (?v0 Int) (?v1 Int)) #137)
-#223 := (iff #140 #222)
-#220 := (iff #137 #219)
-#217 := (= #134 #216)
-#214 := (= #131 #213)
-#211 := (iff #128 #210)
-#208 := (iff #125 #207)
-#209 := [rewrite]: #208
-#198 := (iff #118 #205)
-#199 := [rewrite]: #198
-#212 := [monotonicity #199 #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [quant-intro #221]: #223
-#202 := (~ #140 #140)
-#200 := (~ #137 #137)
-#201 := [refl]: #200
-#203 := [nnf-pos #201]: #202
-#32 := (- #19)
-#31 := (- #17)
-#33 := (div #31 #32)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#34 := (if #29 #30 #33)
-#35 := (if #23 0::Int #34)
-#36 := (= #20 #35)
-#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#143 := (iff #37 #140)
-#98 := (if #29 #30 #95)
-#101 := (if #23 0::Int #98)
-#104 := (= #20 #101)
-#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
-#141 := (iff #107 #140)
-#138 := (iff #104 #137)
-#135 := (= #101 #134)
-#132 := (= #98 #131)
-#129 := (iff #29 #128)
-#126 := (iff #28 #125)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#123 := (iff #27 #122)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124 #117]: #126
-#119 := (iff #26 #118)
-#112 := (iff #24 #111)
-#113 := [rewrite]: #112
-#120 := [monotonicity #113 #117]: #119
-#130 := [monotonicity #120 #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [quant-intro #139]: #141
-#108 := (iff #37 #107)
-#105 := (iff #36 #104)
-#102 := (= #35 #101)
-#99 := (= #34 #98)
-#96 := (= #33 #95)
-#93 := (= #32 #92)
-#94 := [rewrite]: #93
-#90 := (= #31 #88)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [monotonicity #103]: #105
-#109 := [quant-intro #106]: #108
-#144 := [trans #109 #142]: #143
-#87 := [asserted]: #37
-#145 := [mp #87 #144]: #140
-#194 := [mp~ #145 #203]: #140
-#225 := [mp #194 #224]: #222
-#256 := [mp #225 #255]: #253
-#752 := [mp #256 #751]: #747
-#75 := -3::Int
-#72 := (f4 f5 -1::Int)
-#78 := (f3 #72 -3::Int)
-#81 := (= #78 0::Int)
-#84 := (not #81)
-#11 := 3::Int
-#12 := (- 3::Int)
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := (f4 f5 #9)
-#13 := (f3 #10 #12)
-#15 := (= #13 0::Int)
-#16 := (not #15)
-#85 := (iff #16 #84)
-#82 := (iff #15 #81)
-#79 := (= #13 #78)
-#76 := (= #12 -3::Int)
-#77 := [rewrite]: #76
-#73 := (= #10 #72)
-#70 := (= #9 -1::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#68 := [asserted]: #16
-#89 := [mp #68 #86]: #84
-#671 := (not #747)
-#672 := (or #671 #81)
-#408 := (* -1::Int -3::Int)
-#734 := (* -1::Int -1::Int)
-#409 := (div #734 #408)
-#741 := (* -1::Int #409)
-#742 := (+ #78 #741)
-#743 := (= #742 0::Int)
-#738 := (div -1::Int -3::Int)
-#740 := (* -1::Int #738)
-#397 := (+ #78 #740)
-#527 := (= #397 0::Int)
-#410 := (<= -3::Int 0::Int)
-#423 := (>= -1::Int 0::Int)
-#420 := (or #423 #410)
-#424 := (not #420)
-#419 := (<= -1::Int 0::Int)
-#421 := (or #419 #410)
-#422 := (not #421)
-#403 := (or #422 #424)
-#744 := (if #403 #527 #743)
-#417 := (= -3::Int 0::Int)
-#333 := (= -1::Int 0::Int)
-#418 := (or #333 #417)
-#739 := (if #418 #81 #744)
-#673 := (or #671 #739)
-#674 := (iff #673 #672)
-#664 := (iff #672 #672)
-#665 := [rewrite]: #664
-#659 := (iff #739 #81)
-#677 := (if false #81 #81)
-#670 := (iff #677 #81)
-#662 := [rewrite]: #670
-#681 := (iff #739 #677)
-#587 := (iff #744 #81)
-#691 := (= #78 1::Int)
-#575 := (if false #691 #81)
-#585 := (iff #575 #81)
-#586 := [rewrite]: #585
-#583 := (iff #744 #575)
-#581 := (iff #743 #81)
-#564 := (= #742 #78)
-#678 := (+ #78 0::Int)
-#676 := (= #678 #78)
-#679 := [rewrite]: #676
-#580 := (= #742 #678)
-#571 := (= #741 0::Int)
-#686 := (* -1::Int 0::Int)
-#569 := (= #686 0::Int)
-#570 := [rewrite]: #569
-#684 := (= #741 #686)
-#683 := (= #409 0::Int)
-#697 := (div 1::Int 3::Int)
-#529 := (= #697 0::Int)
-#682 := [rewrite]: #529
-#526 := (= #409 #697)
-#696 := (= #408 3::Int)
-#690 := [rewrite]: #696
-#689 := (= #734 1::Int)
-#695 := [rewrite]: #689
-#528 := [monotonicity #695 #690]: #526
-#685 := [trans #528 #682]: #683
-#687 := [monotonicity #685]: #684
-#530 := [trans #687 #570]: #571
-#675 := [monotonicity #530]: #580
-#579 := [trans #675 #679]: #564
-#582 := [monotonicity #579]: #581
-#694 := (iff #527 #691)
-#699 := (+ -1::Int #78)
-#547 := (= #699 0::Int)
-#692 := (iff #547 #691)
-#693 := [rewrite]: #692
-#548 := (iff #527 #547)
-#700 := (= #397 #699)
-#702 := (+ #78 -1::Int)
-#704 := (= #702 #699)
-#705 := [rewrite]: #704
-#703 := (= #397 #702)
-#712 := (= #740 -1::Int)
-#710 := (* -1::Int 1::Int)
-#711 := (= #710 -1::Int)
-#708 := [rewrite]: #711
-#425 := (= #740 #710)
-#431 := (= #738 1::Int)
-#709 := [rewrite]: #431
-#707 := [monotonicity #709]: #425
-#701 := [trans #707 #708]: #712
-#698 := [monotonicity #701]: #703
-#706 := [trans #698 #705]: #700
-#549 := [monotonicity #706]: #548
-#688 := [trans #549 #693]: #694
-#429 := (iff #403 false)
-#736 := (or false false)
-#380 := (iff #736 false)
-#721 := [rewrite]: #380
-#718 := (iff #403 #736)
-#717 := (iff #424 false)
-#1 := true
-#731 := (not true)
-#732 := (iff #731 false)
-#730 := [rewrite]: #732
-#439 := (iff #424 #731)
-#716 := (iff #420 true)
-#443 := (or false true)
-#339 := (iff #443 true)
-#715 := [rewrite]: #339
-#444 := (iff #420 #443)
-#723 := (iff #410 true)
-#724 := [rewrite]: #723
-#720 := (iff #423 false)
-#442 := [rewrite]: #720
-#445 := [monotonicity #442 #724]: #444
-#438 := [trans #445 #715]: #716
-#713 := [monotonicity #438]: #439
-#714 := [trans #713 #730]: #717
-#733 := (iff #422 false)
-#371 := (iff #422 #731)
-#366 := (iff #421 true)
-#725 := (or true true)
-#722 := (iff #725 true)
-#728 := [rewrite]: #722
-#726 := (iff #421 #725)
-#386 := (iff #419 true)
-#387 := [rewrite]: #386
-#727 := [monotonicity #387 #724]: #726
-#729 := [trans #727 #728]: #366
-#372 := [monotonicity #729]: #371
-#719 := [trans #372 #730]: #733
-#428 := [monotonicity #719 #714]: #718
-#430 := [trans #428 #721]: #429
-#584 := [monotonicity #430 #688 #582]: #583
-#680 := [trans #584 #586]: #587
-#384 := (iff #418 false)
-#396 := (iff #418 #736)
-#395 := (iff #417 false)
-#400 := [rewrite]: #395
-#745 := (iff #333 false)
-#735 := [rewrite]: #745
-#737 := [monotonicity #735 #400]: #396
-#385 := [trans #737 #721]: #384
-#668 := [monotonicity #385 #680]: #681
-#661 := [trans #668 #662]: #659
-#663 := [monotonicity #661]: #674
-#666 := [trans #663 #665]: #674
-#669 := [quant-inst #69 #75]: #673
-#660 := [mp #669 #666]: #672
-[unit-resolution #660 #89 #752]: false
-unsat
-bb462ec316170c69257cf123bc5b6d6575fb0bf4 296 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#743 := (pattern #18)
-#19 := 0::Int
-#84 := -1::Int
-#89 := (* -1::Int #17)
-#86 := (* -1::Int #15)
-#92 := (div #86 #89)
-#243 := (* -1::Int #92)
-#244 := (+ #18 #243)
-#245 := (= #244 0::Int)
-#29 := (div #15 #17)
-#240 := (* -1::Int #29)
-#241 := (+ #18 #240)
-#242 := (= #241 0::Int)
-#111 := (<= #17 0::Int)
-#118 := (>= #15 0::Int)
-#203 := (or #118 #111)
-#204 := (not #203)
-#107 := (<= #15 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#246 := (if #207 #242 #245)
-#239 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #15 0::Int)
-#22 := (or #20 #21)
-#247 := (if #22 #239 #246)
-#744 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #743) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#747 := (iff #250 #744)
-#745 := (iff #247 #247)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#210 := (if #207 #29 #92)
-#213 := (if #22 0::Int #210)
-#216 := (= #18 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#112 := (not #111)
-#119 := (not #118)
-#122 := (and #119 #112)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#128 := (if #125 #29 #92)
-#131 := (if #22 0::Int #128)
-#134 := (= #18 #131)
-#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#214 := (= #131 #213)
-#211 := (= #128 #210)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#199 := (~ #137 #137)
-#197 := (~ #134 #134)
-#198 := [refl]: #197
-#200 := [nnf-pos #198]: #199
-#31 := (- #17)
-#30 := (- #15)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (if #28 #29 #32)
-#34 := (if #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#140 := (iff #36 #137)
-#95 := (if #28 #29 #92)
-#98 := (if #22 0::Int #95)
-#101 := (= #18 #98)
-#104 := (forall (vars (?v0 Int) (?v1 Int)) #101)
-#138 := (iff #104 #137)
-#135 := (iff #101 #134)
-#132 := (= #98 #131)
-#129 := (= #95 #128)
-#126 := (iff #28 #125)
-#123 := (iff #27 #122)
-#113 := (iff #24 #112)
-#114 := [rewrite]: #113
-#120 := (iff #26 #119)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121 #114]: #123
-#116 := (iff #25 #115)
-#109 := (iff #23 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [quant-intro #136]: #138
-#105 := (iff #36 #104)
-#102 := (iff #35 #101)
-#99 := (= #34 #98)
-#96 := (= #33 #95)
-#93 := (= #32 #92)
-#90 := (= #31 #89)
-#91 := [rewrite]: #90
-#87 := (= #30 #86)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [quant-intro #103]: #105
-#141 := [trans #106 #139]: #140
-#83 := [asserted]: #36
-#142 := [mp #83 #141]: #137
-#191 := [mp~ #142 #200]: #137
-#222 := [mp #191 #221]: #219
-#253 := [mp #222 #252]: #250
-#749 := [mp #253 #748]: #744
-#12 := 1::Int
-#68 := -3::Int
-#71 := (f4 f5 -3::Int)
-#74 := (f3 #71 -3::Int)
-#77 := (= #74 1::Int)
-#80 := (not #77)
-#8 := 3::Int
-#9 := (- 3::Int)
-#10 := (f4 f5 #9)
-#11 := (f3 #10 #9)
-#13 := (= #11 1::Int)
-#14 := (not #13)
-#81 := (iff #14 #80)
-#78 := (iff #13 #77)
-#75 := (= #11 #74)
-#69 := (= #9 -3::Int)
-#70 := [rewrite]: #69
-#72 := (= #10 #71)
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73 #70]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#67 := [asserted]: #14
-#85 := [mp #67 #82]: #80
-#580 := (not #744)
-#581 := (or #580 #77)
-#524 := (* -1::Int -3::Int)
-#731 := (div #524 #524)
-#405 := (* -1::Int #731)
-#406 := (+ #74 #405)
-#738 := (= #406 0::Int)
-#400 := (div -3::Int -3::Int)
-#735 := (* -1::Int #400)
-#737 := (+ #74 #735)
-#394 := (= #737 0::Int)
-#416 := (<= -3::Int 0::Int)
-#419 := (>= -3::Int 0::Int)
-#420 := (or #419 #416)
-#417 := (not #420)
-#407 := (or #416 #416)
-#418 := (not #407)
-#421 := (or #418 #417)
-#739 := (if #421 #394 #738)
-#415 := (= #74 0::Int)
-#330 := (= -3::Int 0::Int)
-#414 := (or #330 #330)
-#740 := (if #414 #415 #739)
-#582 := (or #580 #740)
-#584 := (iff #582 #581)
-#674 := (iff #581 #581)
-#678 := [rewrite]: #674
-#579 := (iff #740 #77)
-#673 := (if false #415 #77)
-#576 := (iff #673 #77)
-#578 := [rewrite]: #576
-#676 := (iff #740 #673)
-#577 := (iff #739 #77)
-#566 := (if false #77 #77)
-#527 := (iff #566 #77)
-#675 := [rewrite]: #527
-#567 := (iff #739 #566)
-#681 := (iff #738 #77)
-#705 := (+ -1::Int #74)
-#695 := (= #705 0::Int)
-#702 := (iff #695 #77)
-#697 := [rewrite]: #702
-#682 := (iff #738 #695)
-#679 := (= #406 #705)
-#422 := (+ #74 -1::Int)
-#709 := (= #422 #705)
-#698 := [rewrite]: #709
-#525 := (= #406 #422)
-#694 := (= #405 -1::Int)
-#715 := (* -1::Int 1::Int)
-#427 := (= #715 -1::Int)
-#428 := [rewrite]: #427
-#693 := (= #405 #715)
-#686 := (= #731 1::Int)
-#688 := (div 3::Int 3::Int)
-#691 := (= #688 1::Int)
-#685 := [rewrite]: #691
-#689 := (= #731 #688)
-#545 := (= #524 3::Int)
-#546 := [rewrite]: #545
-#690 := [monotonicity #546 #546]: #689
-#692 := [trans #690 #685]: #686
-#687 := [monotonicity #692]: #693
-#523 := [trans #687 #428]: #694
-#526 := [monotonicity #523]: #525
-#680 := [trans #526 #698]: #679
-#683 := [monotonicity #680]: #682
-#684 := [trans #683 #697]: #681
-#703 := (iff #394 #77)
-#696 := (iff #394 #695)
-#699 := (= #737 #705)
-#704 := (= #737 #422)
-#706 := (= #735 -1::Int)
-#425 := (= #735 #715)
-#714 := (= #400 1::Int)
-#711 := [rewrite]: #714
-#426 := [monotonicity #711]: #425
-#707 := [trans #426 #428]: #706
-#708 := [monotonicity #707]: #704
-#700 := [trans #708 #698]: #699
-#701 := [monotonicity #700]: #696
-#544 := [trans #701 #697]: #703
-#436 := (iff #421 false)
-#742 := (or false false)
-#397 := (iff #742 false)
-#733 := [rewrite]: #397
-#713 := (iff #421 #742)
-#336 := (iff #417 false)
-#1 := true
-#723 := (not true)
-#725 := (iff #723 false)
-#363 := [rewrite]: #725
-#441 := (iff #417 #723)
-#439 := (iff #420 true)
-#729 := (or false true)
-#716 := (iff #729 true)
-#717 := [rewrite]: #716
-#727 := (iff #420 #729)
-#377 := (iff #416 true)
-#718 := [rewrite]: #377
-#368 := (iff #419 false)
-#369 := [rewrite]: #368
-#730 := [monotonicity #369 #718]: #727
-#440 := [trans #730 #717]: #439
-#442 := [monotonicity #440]: #441
-#712 := [trans #442 #363]: #336
-#726 := (iff #418 false)
-#724 := (iff #418 #723)
-#721 := (iff #407 true)
-#381 := (or true true)
-#384 := (iff #381 true)
-#720 := [rewrite]: #384
-#382 := (iff #407 #381)
-#383 := [monotonicity #718 #718]: #382
-#722 := [trans #383 #720]: #721
-#719 := [monotonicity #722]: #724
-#728 := [trans #719 #363]: #726
-#435 := [monotonicity #728 #712]: #713
-#710 := [trans #435 #733]: #436
-#568 := [monotonicity #710 #544 #684]: #567
-#672 := [trans #568 #675]: #577
-#393 := (iff #414 false)
-#732 := (iff #414 #742)
-#741 := (iff #330 false)
-#736 := [rewrite]: #741
-#392 := [monotonicity #736 #736]: #732
-#734 := [trans #392 #733]: #393
-#561 := [monotonicity #734 #672]: #676
-#572 := [trans #561 #578]: #579
-#677 := [monotonicity #572]: #584
-#665 := [trans #677 #678]: #584
-#583 := [quant-inst #68 #68]: #582
-#667 := [mp #583 #665]: #581
-[unit-resolution #667 #85 #749]: false
-unsat
-0b3a009851b606e94e7b0991d7f83ada2f7a2088 323 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#747 := (pattern #20)
-#21 := 0::Int
-#89 := -1::Int
-#94 := (* -1::Int #19)
-#91 := (* -1::Int #17)
-#97 := (div #91 #94)
-#248 := (* -1::Int #97)
-#249 := (+ #20 #248)
-#250 := (= #249 0::Int)
-#31 := (div #17 #19)
-#245 := (* -1::Int #31)
-#246 := (+ #20 #245)
-#247 := (= #246 0::Int)
-#116 := (<= #19 0::Int)
-#123 := (>= #17 0::Int)
-#208 := (or #123 #116)
-#209 := (not #208)
-#112 := (<= #17 0::Int)
-#206 := (or #112 #116)
-#207 := (not #206)
-#212 := (or #207 #209)
-#251 := (if #212 #247 #250)
-#244 := (= #20 0::Int)
-#23 := (= #19 0::Int)
-#22 := (= #17 0::Int)
-#24 := (or #22 #23)
-#252 := (if #24 #244 #251)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #252)
-#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
-#751 := (iff #255 #748)
-#749 := (iff #252 #252)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#215 := (if #212 #31 #97)
-#218 := (if #24 0::Int #215)
-#221 := (= #20 #218)
-#224 := (forall (vars (?v0 Int) (?v1 Int)) #221)
-#256 := (iff #224 #255)
-#253 := (iff #221 #252)
-#254 := [rewrite]: #253
-#257 := [quant-intro #254]: #256
-#117 := (not #116)
-#124 := (not #123)
-#127 := (and #124 #117)
-#113 := (not #112)
-#120 := (and #113 #117)
-#130 := (or #120 #127)
-#133 := (if #130 #31 #97)
-#136 := (if #24 0::Int #133)
-#139 := (= #20 #136)
-#142 := (forall (vars (?v0 Int) (?v1 Int)) #139)
-#225 := (iff #142 #224)
-#222 := (iff #139 #221)
-#219 := (= #136 #218)
-#216 := (= #133 #215)
-#213 := (iff #130 #212)
-#210 := (iff #127 #209)
-#211 := [rewrite]: #210
-#200 := (iff #120 #207)
-#201 := [rewrite]: #200
-#214 := [monotonicity #201 #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [quant-intro #223]: #225
-#204 := (~ #142 #142)
-#202 := (~ #139 #139)
-#203 := [refl]: #202
-#205 := [nnf-pos #203]: #204
-#33 := (- #19)
-#32 := (- #17)
-#34 := (div #32 #33)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (if #30 #31 #34)
-#36 := (if #24 0::Int #35)
-#37 := (= #20 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#145 := (iff #38 #142)
-#100 := (if #30 #31 #97)
-#103 := (if #24 0::Int #100)
-#106 := (= #20 #103)
-#109 := (forall (vars (?v0 Int) (?v1 Int)) #106)
-#143 := (iff #109 #142)
-#140 := (iff #106 #139)
-#137 := (= #103 #136)
-#134 := (= #100 #133)
-#131 := (iff #30 #130)
-#128 := (iff #29 #127)
-#118 := (iff #26 #117)
-#119 := [rewrite]: #118
-#125 := (iff #28 #124)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126 #119]: #128
-#121 := (iff #27 #120)
-#114 := (iff #25 #113)
-#115 := [rewrite]: #114
-#122 := [monotonicity #115 #119]: #121
-#132 := [monotonicity #122 #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [quant-intro #141]: #143
-#110 := (iff #38 #109)
-#107 := (iff #37 #106)
-#104 := (= #36 #103)
-#101 := (= #35 #100)
-#98 := (= #34 #97)
-#95 := (= #33 #94)
-#96 := [rewrite]: #95
-#92 := (= #32 #91)
-#93 := [rewrite]: #92
-#99 := [monotonicity #93 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [monotonicity #105]: #107
-#111 := [quant-intro #108]: #110
-#146 := [trans #111 #144]: #145
-#88 := [asserted]: #38
-#147 := [mp #88 #146]: #142
-#196 := [mp~ #147 #205]: #142
-#227 := [mp #196 #226]: #224
-#258 := [mp #227 #257]: #255
-#753 := [mp #258 #752]: #748
-#14 := 1::Int
-#76 := -3::Int
-#70 := -5::Int
-#73 := (f4 f5 -5::Int)
-#79 := (f3 #73 -3::Int)
-#82 := (= #79 1::Int)
-#85 := (not #82)
-#11 := 3::Int
-#12 := (- 3::Int)
-#8 := 5::Int
-#9 := (- 5::Int)
-#10 := (f4 f5 #9)
-#13 := (f3 #10 #12)
-#15 := (= #13 1::Int)
-#16 := (not #15)
-#86 := (iff #16 #85)
-#83 := (iff #15 #82)
-#80 := (= #13 #79)
-#77 := (= #12 -3::Int)
-#78 := [rewrite]: #77
-#74 := (= #10 #73)
-#71 := (= #9 -5::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#69 := [asserted]: #16
-#90 := [mp #69 #87]: #85
-#667 := (not #748)
-#661 := (or #667 #82)
-#410 := (* -1::Int -3::Int)
-#409 := (* -1::Int -5::Int)
-#742 := (div #409 #410)
-#743 := (* -1::Int #742)
-#744 := (+ #79 #743)
-#745 := (= #744 0::Int)
-#741 := (div -5::Int -3::Int)
-#398 := (* -1::Int #741)
-#528 := (+ #79 #398)
-#735 := (= #528 0::Int)
-#422 := (<= -3::Int 0::Int)
-#421 := (>= -5::Int 0::Int)
-#425 := (or #421 #422)
-#404 := (not #425)
-#411 := (<= -5::Int 0::Int)
-#423 := (or #411 #422)
-#424 := (not #423)
-#739 := (or #424 #404)
-#740 := (if #739 #735 #745)
-#420 := (= #79 0::Int)
-#418 := (= -3::Int 0::Int)
-#334 := (= -5::Int 0::Int)
-#419 := (or #334 #418)
-#746 := (if #419 #420 #740)
-#668 := (or #667 #746)
-#653 := (iff #668 #661)
-#656 := (iff #661 #661)
-#657 := [rewrite]: #656
-#665 := (iff #746 #82)
-#673 := (if false #420 #82)
-#675 := (iff #673 #82)
-#664 := [rewrite]: #675
-#674 := (iff #746 #673)
-#662 := (iff #740 #82)
-#295 := 2::Int
-#694 := (= #79 2::Int)
-#682 := (if false #694 #82)
-#663 := (iff #682 #82)
-#660 := [rewrite]: #663
-#669 := (iff #740 #682)
-#681 := (iff #745 #82)
-#565 := (+ -1::Int #79)
-#584 := (= #565 0::Int)
-#587 := (iff #584 #82)
-#588 := [rewrite]: #587
-#585 := (iff #745 #584)
-#583 := (= #744 #565)
-#676 := (+ #79 -1::Int)
-#580 := (= #676 #565)
-#582 := [rewrite]: #580
-#677 := (= #744 #676)
-#679 := (= #743 -1::Int)
-#688 := (* -1::Int 1::Int)
-#572 := (= #688 -1::Int)
-#531 := [rewrite]: #572
-#570 := (= #743 #688)
-#687 := (= #742 1::Int)
-#529 := (div 5::Int 3::Int)
-#684 := (= #529 1::Int)
-#686 := [rewrite]: #684
-#530 := (= #742 #529)
-#698 := (= #410 3::Int)
-#527 := [rewrite]: #698
-#697 := (= #409 5::Int)
-#691 := [rewrite]: #697
-#683 := [monotonicity #691 #527]: #530
-#685 := [trans #683 #686]: #687
-#571 := [monotonicity #685]: #570
-#581 := [trans #571 #531]: #679
-#680 := [monotonicity #581]: #677
-#576 := [trans #680 #582]: #583
-#586 := [monotonicity #576]: #585
-#678 := [trans #586 #588]: #681
-#690 := (iff #735 #694)
-#709 := -2::Int
-#706 := (+ -2::Int #79)
-#550 := (= #706 0::Int)
-#695 := (iff #550 #694)
-#689 := [rewrite]: #695
-#692 := (iff #735 #550)
-#548 := (= #528 #706)
-#699 := (+ #79 -2::Int)
-#701 := (= #699 #706)
-#707 := [rewrite]: #701
-#700 := (= #528 #699)
-#703 := (= #398 -2::Int)
-#426 := (* -1::Int 2::Int)
-#713 := (= #426 -2::Int)
-#702 := [rewrite]: #713
-#708 := (= #398 #426)
-#710 := (= #741 2::Int)
-#711 := [rewrite]: #710
-#712 := [monotonicity #711]: #708
-#704 := [trans #712 #702]: #703
-#705 := [monotonicity #704]: #700
-#549 := [trans #705 #707]: #548
-#693 := [monotonicity #549]: #692
-#696 := [trans #693 #689]: #690
-#431 := (iff #739 false)
-#397 := (or false false)
-#722 := (iff #397 false)
-#385 := [rewrite]: #722
-#429 := (iff #739 #397)
-#715 := (iff #404 false)
-#1 := true
-#372 := (not true)
-#731 := (iff #372 false)
-#734 := [rewrite]: #731
-#714 := (iff #404 #372)
-#439 := (iff #425 true)
-#445 := (or false true)
-#716 := (iff #445 true)
-#717 := [rewrite]: #716
-#446 := (iff #425 #445)
-#725 := (iff #422 true)
-#726 := [rewrite]: #725
-#443 := (iff #421 false)
-#444 := [rewrite]: #443
-#340 := [monotonicity #444 #726]: #446
-#440 := [trans #340 #717]: #439
-#718 := [monotonicity #440]: #714
-#719 := [trans #718 #734]: #715
-#720 := (iff #424 false)
-#373 := (iff #424 #372)
-#730 := (iff #423 true)
-#727 := (or true true)
-#729 := (iff #727 true)
-#367 := [rewrite]: #729
-#728 := (iff #423 #727)
-#388 := (iff #411 true)
-#724 := [rewrite]: #388
-#723 := [monotonicity #724 #726]: #728
-#732 := [trans #723 #367]: #730
-#733 := [monotonicity #732]: #373
-#721 := [trans #733 #734]: #720
-#430 := [monotonicity #721 #719]: #429
-#432 := [trans #430 #385]: #431
-#671 := [monotonicity #432 #696 #678]: #669
-#672 := [trans #671 #660]: #662
-#386 := (iff #419 false)
-#738 := (iff #419 #397)
-#401 := (iff #418 false)
-#737 := [rewrite]: #401
-#736 := (iff #334 false)
-#396 := [rewrite]: #736
-#381 := [monotonicity #396 #737]: #738
-#387 := [trans #381 #385]: #386
-#670 := [monotonicity #387 #672]: #674
-#666 := [trans #670 #664]: #665
-#655 := [monotonicity #666]: #653
-#658 := [trans #655 #657]: #653
-#652 := [quant-inst #70 #76]: #668
-#654 := [mp #652 #658]: #661
-[unit-resolution #654 #90 #753]: false
-unsat
-634111a9ccc777d6dea9f04f2dd68647c6110ae6 259 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#16 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#14 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#35 := (f4 f5 #14)
-#36 := (f3 #35 #16)
-#733 := (pattern #36)
-#8 := 0::Int
-#66 := -1::Int
-#70 := (* -1::Int #16)
-#67 := (* -1::Int #14)
-#125 := (mod #67 #70)
-#240 := (+ #36 #125)
-#241 := (= #240 0::Int)
-#37 := (mod #14 #16)
-#237 := (* -1::Int #37)
-#238 := (+ #36 #237)
-#239 := (= #238 0::Int)
-#92 := (<= #16 0::Int)
-#99 := (>= #14 0::Int)
-#184 := (or #99 #92)
-#185 := (not #184)
-#88 := (<= #14 0::Int)
-#182 := (or #88 #92)
-#183 := (not #182)
-#188 := (or #183 #185)
-#242 := (if #188 #239 #241)
-#236 := (= #36 0::Int)
-#18 := (= #14 0::Int)
-#243 := (if #18 #236 #242)
-#235 := (= #36 #14)
-#19 := (= #16 0::Int)
-#244 := (if #19 #235 #243)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #244)
-#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
-#737 := (iff #247 #734)
-#735 := (iff #244 #244)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#131 := (* -1::Int #125)
-#204 := (if #188 #37 #131)
-#207 := (if #18 0::Int #204)
-#210 := (if #19 #14 #207)
-#213 := (= #36 #210)
-#216 := (forall (vars (?v0 Int) (?v1 Int)) #213)
-#248 := (iff #216 #247)
-#245 := (iff #213 #244)
-#246 := [rewrite]: #245
-#249 := [quant-intro #246]: #248
-#93 := (not #92)
-#100 := (not #99)
-#103 := (and #100 #93)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (if #106 #37 #131)
-#154 := (if #18 0::Int #151)
-#157 := (if #19 #14 #154)
-#160 := (= #36 #157)
-#163 := (forall (vars (?v0 Int) (?v1 Int)) #160)
-#217 := (iff #163 #216)
-#214 := (iff #160 #213)
-#211 := (= #157 #210)
-#208 := (= #154 #207)
-#205 := (= #151 #204)
-#189 := (iff #106 #188)
-#186 := (iff #103 #185)
-#187 := [rewrite]: #186
-#176 := (iff #96 #183)
-#177 := [rewrite]: #176
-#190 := [monotonicity #177 #187]: #189
-#206 := [monotonicity #190]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [quant-intro #215]: #217
-#174 := (~ #163 #163)
-#173 := (~ #160 #160)
-#170 := [refl]: #173
-#175 := [nnf-pos #170]: #174
-#29 := (- #16)
-#28 := (- #14)
-#38 := (mod #28 #29)
-#39 := (- #38)
-#22 := (< 0::Int #16)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#40 := (if #26 #37 #39)
-#41 := (if #18 0::Int #40)
-#42 := (if #19 #14 #41)
-#43 := (= #36 #42)
-#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
-#166 := (iff #44 #163)
-#136 := (if #26 #37 #131)
-#139 := (if #18 0::Int #136)
-#142 := (if #19 #14 #139)
-#145 := (= #36 #142)
-#148 := (forall (vars (?v0 Int) (?v1 Int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #26 #106)
-#104 := (iff #25 #103)
-#94 := (iff #22 #93)
-#95 := [rewrite]: #94
-#101 := (iff #24 #100)
-#102 := [rewrite]: #101
-#105 := [monotonicity #102 #95]: #104
-#97 := (iff #23 #96)
-#90 := (iff #21 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #44 #148)
-#146 := (iff #43 #145)
-#143 := (= #42 #142)
-#140 := (= #41 #139)
-#137 := (= #40 #136)
-#134 := (= #39 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #39 #128)
-#126 := (= #38 #125)
-#71 := (= #29 #70)
-#72 := [rewrite]: #71
-#68 := (= #28 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#138 := [monotonicity #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #44
-#168 := [mp #124 #167]: #163
-#171 := [mp~ #168 #175]: #163
-#219 := [mp #171 #218]: #216
-#250 := [mp #219 #249]: #247
-#739 := [mp #250 #738]: #734
-#9 := (f4 f5 0::Int)
-#10 := (f3 #9 0::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#64 := [asserted]: #12
-#686 := (not #734)
-#527 := (or #686 #11)
-#720 := (* -1::Int 0::Int)
-#377 := (mod #720 #720)
-#507 := (+ #10 #377)
-#714 := (= #507 0::Int)
-#400 := (mod 0::Int 0::Int)
-#404 := (* -1::Int #400)
-#383 := (+ #10 #404)
-#718 := (= #383 0::Int)
-#397 := (<= 0::Int 0::Int)
-#390 := (>= 0::Int 0::Int)
-#401 := (or #390 #397)
-#402 := (not #401)
-#398 := (or #397 #397)
-#399 := (not #398)
-#403 := (or #399 #402)
-#388 := (if #403 #718 #714)
-#313 := (= 0::Int 0::Int)
-#389 := (if #313 #11 #388)
-#721 := (if #313 #11 #389)
-#528 := (or #686 #721)
-#671 := (iff #528 #527)
-#673 := (iff #527 #527)
-#674 := [rewrite]: #673
-#685 := (iff #721 #11)
-#1 := true
-#682 := (if true #11 #11)
-#679 := (iff #682 #11)
-#684 := [rewrite]: #679
-#683 := (iff #721 #682)
-#692 := (iff #389 #11)
-#695 := (+ #10 #400)
-#419 := (= #695 0::Int)
-#690 := (if true #11 #419)
-#691 := (iff #690 #11)
-#688 := [rewrite]: #691
-#405 := (iff #389 #690)
-#411 := (iff #388 #419)
-#694 := (if false #718 #419)
-#409 := (iff #694 #419)
-#410 := [rewrite]: #409
-#698 := (iff #388 #694)
-#693 := (iff #714 #419)
-#696 := (= #507 #695)
-#425 := (= #377 #400)
-#423 := (= #720 0::Int)
-#424 := [rewrite]: #423
-#319 := [monotonicity #424 #424]: #425
-#418 := [monotonicity #319]: #696
-#697 := [monotonicity #418]: #693
-#700 := (iff #403 false)
-#352 := (or false false)
-#713 := (iff #352 false)
-#699 := [rewrite]: #713
-#712 := (iff #403 #352)
-#711 := (iff #402 false)
-#360 := (not true)
-#365 := (iff #360 false)
-#366 := [rewrite]: #365
-#346 := (iff #402 #360)
-#702 := (iff #401 true)
-#725 := (or true true)
-#380 := (iff #725 true)
-#716 := [rewrite]: #380
-#706 := (iff #401 #725)
-#724 := (iff #397 true)
-#719 := [rewrite]: #724
-#704 := (iff #390 true)
-#705 := [rewrite]: #704
-#707 := [monotonicity #705 #719]: #706
-#708 := [trans #707 #716]: #702
-#709 := [monotonicity #708]: #346
-#351 := [trans #709 #366]: #711
-#367 := (iff #399 false)
-#701 := (iff #399 #360)
-#376 := (iff #398 true)
-#715 := (iff #398 #725)
-#375 := [monotonicity #719 #719]: #715
-#717 := [trans #375 #716]: #376
-#364 := [monotonicity #717]: #701
-#703 := [trans #364 #366]: #367
-#710 := [monotonicity #703 #351]: #712
-#422 := [trans #710 #699]: #700
-#408 := [monotonicity #422 #697]: #698
-#689 := [trans #408 #410]: #411
-#722 := (iff #313 true)
-#723 := [rewrite]: #722
-#687 := [monotonicity #723 #689]: #405
-#681 := [trans #687 #688]: #692
-#678 := [monotonicity #723 #681]: #683
-#680 := [trans #678 #684]: #685
-#672 := [monotonicity #680]: #671
-#668 := [trans #672 #674]: #671
-#529 := [quant-inst #8 #8]: #528
-#669 := [mp #529 #668]: #527
-[unit-resolution #669 #64 #739]: false
-unsat
-9b96f7ce486ea51d67fd20479a535702ca914b66 263 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#36 := (f4 f5 #15)
-#37 := (f3 #36 #17)
-#734 := (pattern #37)
-#10 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #17)
-#68 := (* -1::Int #15)
-#126 := (mod #68 #71)
-#241 := (+ #37 #126)
-#242 := (= #241 0::Int)
-#38 := (mod #15 #17)
-#238 := (* -1::Int #38)
-#239 := (+ #37 #238)
-#240 := (= #239 0::Int)
-#93 := (<= #17 0::Int)
-#100 := (>= #15 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #15 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#243 := (if #189 #240 #242)
-#237 := (= #37 0::Int)
-#19 := (= #15 0::Int)
-#244 := (if #19 #237 #243)
-#236 := (= #37 #15)
-#20 := (= #17 0::Int)
-#245 := (if #20 #236 #244)
-#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #245)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#738 := (iff #248 #735)
-#736 := (iff #245 #245)
-#737 := [refl]: #736
-#739 := [quant-intro #737]: #738
-#132 := (* -1::Int #126)
-#205 := (if #189 #38 #132)
-#208 := (if #19 0::Int #205)
-#211 := (if #20 #15 #208)
-#214 := (= #37 #211)
-#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
-#249 := (iff #217 #248)
-#246 := (iff #214 #245)
-#247 := [rewrite]: #246
-#250 := [quant-intro #247]: #249
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#152 := (if #107 #38 #132)
-#155 := (if #19 0::Int #152)
-#158 := (if #20 #15 #155)
-#161 := (= #37 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#218 := (iff #164 #217)
-#215 := (iff #161 #214)
-#212 := (= #158 #211)
-#209 := (= #155 #208)
-#206 := (= #152 #205)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#207 := [monotonicity #191]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [quant-intro #216]: #218
-#175 := (~ #164 #164)
-#174 := (~ #161 #161)
-#171 := [refl]: #174
-#176 := [nnf-pos #171]: #175
-#30 := (- #17)
-#29 := (- #15)
-#39 := (mod #29 #30)
-#40 := (- #39)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#41 := (if #27 #38 #40)
-#42 := (if #19 0::Int #41)
-#43 := (if #20 #15 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#167 := (iff #45 #164)
-#137 := (if #27 #38 #132)
-#140 := (if #19 0::Int #137)
-#143 := (if #20 #15 #140)
-#146 := (= #37 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#165 := (iff #149 #164)
-#162 := (iff #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#108 := (iff #27 #107)
-#105 := (iff #26 #104)
-#95 := (iff #23 #94)
-#96 := [rewrite]: #95
-#102 := (iff #25 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #24 #97)
-#91 := (iff #22 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#154 := [monotonicity #109]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#150 := (iff #45 #149)
-#147 := (iff #44 #146)
-#144 := (= #43 #143)
-#141 := (= #42 #140)
-#138 := (= #41 #137)
-#135 := (= #40 #132)
-#129 := (- #126)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #40 #129)
-#127 := (= #39 #126)
-#72 := (= #30 #71)
-#73 := [rewrite]: #72
-#69 := (= #29 #68)
-#70 := [rewrite]: #69
-#128 := [monotonicity #70 #73]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#168 := [trans #151 #166]: #167
-#125 := [asserted]: #45
-#169 := [mp #125 #168]: #164
-#172 := [mp~ #169 #176]: #164
-#220 := [mp #172 #219]: #217
-#251 := [mp #220 #250]: #248
-#740 := [mp #251 #739]: #735
-decl f6 :: Int
-#8 := f6
-#9 := (f4 f5 f6)
-#11 := (f3 #9 0::Int)
-#12 := (= #11 f6)
-#13 := (not #12)
-#65 := [asserted]: #13
-#529 := (not #735)
-#530 := (or #529 #12)
-#389 := (* -1::Int 0::Int)
-#715 := (* -1::Int f6)
-#390 := (mod #715 #389)
-#722 := (+ #11 #390)
-#723 := (= #722 0::Int)
-#719 := (mod f6 0::Int)
-#721 := (* -1::Int #719)
-#378 := (+ #11 #721)
-#508 := (= #378 0::Int)
-#391 := (<= 0::Int 0::Int)
-#404 := (>= f6 0::Int)
-#401 := (or #404 #391)
-#405 := (not #401)
-#400 := (<= f6 0::Int)
-#402 := (or #400 #391)
-#403 := (not #402)
-#384 := (or #403 #405)
-#724 := (if #384 #508 #723)
-#399 := (= #11 0::Int)
-#398 := (= f6 0::Int)
-#725 := (if #398 #399 #724)
-#314 := (= 0::Int 0::Int)
-#720 := (if #314 #12 #725)
-#672 := (or #529 #720)
-#674 := (iff #672 #530)
-#669 := (iff #530 #530)
-#670 := [rewrite]: #669
-#687 := (iff #720 #12)
-#420 := (mod #715 0::Int)
-#695 := (+ #11 #420)
-#410 := (= #695 0::Int)
-#682 := (if #398 #399 #410)
-#1 := true
-#679 := (if true #12 #682)
-#686 := (iff #679 #12)
-#681 := [rewrite]: #686
-#680 := (iff #720 #679)
-#683 := (iff #725 #682)
-#689 := (iff #724 #410)
-#690 := (if false #508 #410)
-#688 := (iff #690 #410)
-#692 := [rewrite]: #688
-#691 := (iff #724 #690)
-#411 := (iff #723 #410)
-#699 := (= #722 #695)
-#694 := (= #390 #420)
-#697 := (= #389 0::Int)
-#419 := [rewrite]: #697
-#698 := [monotonicity #419]: #694
-#409 := [monotonicity #698]: #699
-#412 := [monotonicity #409]: #411
-#320 := (iff #384 false)
-#701 := (or false false)
-#425 := (iff #701 false)
-#426 := [rewrite]: #425
-#423 := (iff #384 #701)
-#714 := (iff #405 false)
-#367 := (not true)
-#705 := (iff #367 false)
-#706 := [rewrite]: #705
-#713 := (iff #405 #367)
-#352 := (iff #401 true)
-#703 := (or #404 true)
-#710 := (iff #703 true)
-#712 := [rewrite]: #710
-#709 := (iff #401 #703)
-#376 := (iff #391 true)
-#381 := [rewrite]: #376
-#347 := [monotonicity #381]: #709
-#353 := [trans #347 #712]: #352
-#711 := [monotonicity #353]: #713
-#700 := [trans #711 #706]: #714
-#707 := (iff #403 false)
-#368 := (iff #403 #367)
-#365 := (iff #402 true)
-#717 := (or #400 true)
-#361 := (iff #717 true)
-#702 := [rewrite]: #361
-#377 := (iff #402 #717)
-#718 := [monotonicity #381]: #377
-#366 := [trans #718 #702]: #365
-#704 := [monotonicity #366]: #368
-#708 := [trans #704 #706]: #707
-#424 := [monotonicity #708 #700]: #423
-#696 := [trans #424 #426]: #320
-#406 := [monotonicity #696 #412]: #691
-#693 := [trans #406 #692]: #689
-#684 := [monotonicity #693]: #683
-#726 := (iff #314 true)
-#716 := [rewrite]: #726
-#685 := [monotonicity #716 #684]: #680
-#528 := [trans #685 #681]: #687
-#675 := [monotonicity #528]: #674
-#676 := [trans #675 #670]: #674
-#673 := [quant-inst #8 #10]: #672
-#677 := [mp #673 #676]: #530
-[unit-resolution #677 #65 #740]: false
-unsat
-2c958a27762c93737a9d33717a5efe8ed61ac548 286 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#36 := (f4 f5 #15)
-#37 := (f3 #36 #17)
-#733 := (pattern #37)
-#8 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #17)
-#68 := (* -1::Int #15)
-#126 := (mod #68 #71)
-#241 := (+ #37 #126)
-#242 := (= #241 0::Int)
-#38 := (mod #15 #17)
-#238 := (* -1::Int #38)
-#239 := (+ #37 #238)
-#240 := (= #239 0::Int)
-#93 := (<= #17 0::Int)
-#100 := (>= #15 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #15 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#243 := (if #189 #240 #242)
-#237 := (= #37 0::Int)
-#19 := (= #15 0::Int)
-#244 := (if #19 #237 #243)
-#236 := (= #37 #15)
-#20 := (= #17 0::Int)
-#245 := (if #20 #236 #244)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #245)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#737 := (iff #248 #734)
-#735 := (iff #245 #245)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#132 := (* -1::Int #126)
-#205 := (if #189 #38 #132)
-#208 := (if #19 0::Int #205)
-#211 := (if #20 #15 #208)
-#214 := (= #37 #211)
-#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
-#249 := (iff #217 #248)
-#246 := (iff #214 #245)
-#247 := [rewrite]: #246
-#250 := [quant-intro #247]: #249
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#152 := (if #107 #38 #132)
-#155 := (if #19 0::Int #152)
-#158 := (if #20 #15 #155)
-#161 := (= #37 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#218 := (iff #164 #217)
-#215 := (iff #161 #214)
-#212 := (= #158 #211)
-#209 := (= #155 #208)
-#206 := (= #152 #205)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#207 := [monotonicity #191]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [quant-intro #216]: #218
-#175 := (~ #164 #164)
-#174 := (~ #161 #161)
-#171 := [refl]: #174
-#176 := [nnf-pos #171]: #175
-#30 := (- #17)
-#29 := (- #15)
-#39 := (mod #29 #30)
-#40 := (- #39)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#41 := (if #27 #38 #40)
-#42 := (if #19 0::Int #41)
-#43 := (if #20 #15 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#167 := (iff #45 #164)
-#137 := (if #27 #38 #132)
-#140 := (if #19 0::Int #137)
-#143 := (if #20 #15 #140)
-#146 := (= #37 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#165 := (iff #149 #164)
-#162 := (iff #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#108 := (iff #27 #107)
-#105 := (iff #26 #104)
-#95 := (iff #23 #94)
-#96 := [rewrite]: #95
-#102 := (iff #25 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #24 #97)
-#91 := (iff #22 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#154 := [monotonicity #109]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#150 := (iff #45 #149)
-#147 := (iff #44 #146)
-#144 := (= #43 #143)
-#141 := (= #42 #140)
-#138 := (= #41 #137)
-#135 := (= #40 #132)
-#129 := (- #126)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #40 #129)
-#127 := (= #39 #126)
-#72 := (= #30 #71)
-#73 := [rewrite]: #72
-#69 := (= #29 #68)
-#70 := [rewrite]: #69
-#128 := [monotonicity #70 #73]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#168 := [trans #151 #166]: #167
-#125 := [asserted]: #45
-#169 := [mp #125 #168]: #164
-#172 := [mp~ #169 #176]: #164
-#220 := [mp #172 #219]: #217
-#251 := [mp #220 #250]: #248
-#739 := [mp #251 #738]: #734
-#10 := 1::Int
-#9 := (f4 f5 0::Int)
-#11 := (f3 #9 1::Int)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#510 := (not #734)
-#658 := (or #510 #12)
-#714 := (* -1::Int 1::Int)
-#507 := (* -1::Int 0::Int)
-#388 := (mod #507 #714)
-#389 := (+ #11 #388)
-#721 := (= #389 0::Int)
-#383 := (mod 0::Int 1::Int)
-#718 := (* -1::Int #383)
-#720 := (+ #11 #718)
-#377 := (= #720 0::Int)
-#399 := (<= 1::Int 0::Int)
-#402 := (>= 0::Int 0::Int)
-#403 := (or #402 #399)
-#400 := (not #403)
-#398 := (<= 0::Int 0::Int)
-#390 := (or #398 #399)
-#401 := (not #390)
-#404 := (or #401 #400)
-#722 := (if #404 #377 #721)
-#397 := (= 0::Int 0::Int)
-#723 := (if #397 #12 #722)
-#313 := (= 1::Int 0::Int)
-#724 := (if #313 #12 #723)
-#560 := (or #510 #724)
-#656 := (iff #560 #658)
-#544 := (iff #658 #658)
-#559 := [rewrite]: #544
-#550 := (iff #724 #12)
-#668 := (if false #12 #12)
-#676 := (iff #668 #12)
-#670 := [rewrite]: #676
-#667 := (iff #724 #668)
-#666 := (iff #723 #12)
-#1 := true
-#508 := (if true #12 #12)
-#663 := (iff #508 #12)
-#665 := [rewrite]: #663
-#509 := (iff #723 #508)
-#677 := (iff #722 #12)
-#669 := (iff #722 #668)
-#673 := (iff #721 #12)
-#671 := (= #389 #11)
-#411 := (+ #11 0::Int)
-#405 := (= #411 #11)
-#687 := [rewrite]: #405
-#528 := (= #389 #411)
-#686 := (= #388 0::Int)
-#678 := (mod 0::Int -1::Int)
-#685 := (= #678 0::Int)
-#680 := [rewrite]: #685
-#679 := (= #388 #678)
-#682 := (= #714 -1::Int)
-#683 := [rewrite]: #682
-#698 := (= #507 0::Int)
-#408 := [rewrite]: #698
-#684 := [monotonicity #408 #683]: #679
-#527 := [trans #684 #680]: #686
-#529 := [monotonicity #527]: #528
-#672 := [trans #529 #687]: #671
-#674 := [monotonicity #672]: #673
-#692 := (iff #377 #12)
-#691 := (= #720 #11)
-#689 := (= #720 #411)
-#409 := (= #718 0::Int)
-#697 := (= #718 #507)
-#419 := (= #383 0::Int)
-#693 := [rewrite]: #419
-#694 := [monotonicity #693]: #697
-#410 := [trans #694 #408]: #409
-#690 := [monotonicity #410]: #689
-#688 := [trans #690 #687]: #691
-#681 := [monotonicity #688]: #692
-#696 := (iff #404 false)
-#423 := (or false false)
-#319 := (iff #423 false)
-#695 := [rewrite]: #319
-#424 := (iff #404 #423)
-#700 := (iff #400 false)
-#704 := (not true)
-#707 := (iff #704 false)
-#702 := [rewrite]: #707
-#713 := (iff #400 #704)
-#712 := (iff #403 true)
-#360 := (or true false)
-#365 := (iff #360 true)
-#366 := [rewrite]: #365
-#351 := (iff #403 #360)
-#376 := (iff #399 false)
-#717 := [rewrite]: #376
-#709 := (iff #402 true)
-#711 := [rewrite]: #709
-#352 := [monotonicity #711 #717]: #351
-#710 := [trans #352 #366]: #712
-#699 := [monotonicity #710]: #713
-#422 := [trans #699 #702]: #700
-#708 := (iff #401 false)
-#705 := (iff #401 #704)
-#367 := (iff #390 true)
-#701 := (iff #390 #360)
-#380 := (iff #398 true)
-#716 := [rewrite]: #380
-#364 := [monotonicity #716 #717]: #701
-#703 := [trans #364 #366]: #367
-#706 := [monotonicity #703]: #705
-#346 := [trans #706 #702]: #708
-#425 := [monotonicity #346 #422]: #424
-#418 := [trans #425 #695]: #696
-#675 := [monotonicity #418 #681 #674]: #669
-#506 := [trans #675 #670]: #677
-#715 := (iff #397 true)
-#375 := [rewrite]: #715
-#662 := [monotonicity #375 #506]: #509
-#664 := [trans #662 #665]: #666
-#719 := (iff #313 false)
-#725 := [rewrite]: #719
-#549 := [monotonicity #725 #664]: #667
-#551 := [trans #549 #670]: #550
-#659 := [monotonicity #551]: #656
-#561 := [trans #659 #559]: #656
-#655 := [quant-inst #8 #10]: #560
-#562 := [mp #655 #561]: #658
-[unit-resolution #562 #65 #739]: false
-unsat
-364c5b9098e4b9b582f9064cb2808c3e5b97f78c 287 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#36 := (f4 f5 #15)
-#37 := (f3 #36 #17)
-#733 := (pattern #37)
-#11 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #17)
-#68 := (* -1::Int #15)
-#126 := (mod #68 #71)
-#241 := (+ #37 #126)
-#242 := (= #241 0::Int)
-#38 := (mod #15 #17)
-#238 := (* -1::Int #38)
-#239 := (+ #37 #238)
-#240 := (= #239 0::Int)
-#93 := (<= #17 0::Int)
-#100 := (>= #15 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #15 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#243 := (if #189 #240 #242)
-#237 := (= #37 0::Int)
-#19 := (= #15 0::Int)
-#244 := (if #19 #237 #243)
-#236 := (= #37 #15)
-#20 := (= #17 0::Int)
-#245 := (if #20 #236 #244)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #245)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#737 := (iff #248 #734)
-#735 := (iff #245 #245)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#132 := (* -1::Int #126)
-#205 := (if #189 #38 #132)
-#208 := (if #19 0::Int #205)
-#211 := (if #20 #15 #208)
-#214 := (= #37 #211)
-#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
-#249 := (iff #217 #248)
-#246 := (iff #214 #245)
-#247 := [rewrite]: #246
-#250 := [quant-intro #247]: #249
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#152 := (if #107 #38 #132)
-#155 := (if #19 0::Int #152)
-#158 := (if #20 #15 #155)
-#161 := (= #37 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#218 := (iff #164 #217)
-#215 := (iff #161 #214)
-#212 := (= #158 #211)
-#209 := (= #155 #208)
-#206 := (= #152 #205)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#207 := [monotonicity #191]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [quant-intro #216]: #218
-#175 := (~ #164 #164)
-#174 := (~ #161 #161)
-#171 := [refl]: #174
-#176 := [nnf-pos #171]: #175
-#30 := (- #17)
-#29 := (- #15)
-#39 := (mod #29 #30)
-#40 := (- #39)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#41 := (if #27 #38 #40)
-#42 := (if #19 0::Int #41)
-#43 := (if #20 #15 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#167 := (iff #45 #164)
-#137 := (if #27 #38 #132)
-#140 := (if #19 0::Int #137)
-#143 := (if #20 #15 #140)
-#146 := (= #37 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#165 := (iff #149 #164)
-#162 := (iff #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#108 := (iff #27 #107)
-#105 := (iff #26 #104)
-#95 := (iff #23 #94)
-#96 := [rewrite]: #95
-#102 := (iff #25 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #24 #97)
-#91 := (iff #22 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#154 := [monotonicity #109]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#150 := (iff #45 #149)
-#147 := (iff #44 #146)
-#144 := (= #43 #143)
-#141 := (= #42 #140)
-#138 := (= #41 #137)
-#135 := (= #40 #132)
-#129 := (- #126)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #40 #129)
-#127 := (= #39 #126)
-#72 := (= #30 #71)
-#73 := [rewrite]: #72
-#69 := (= #29 #68)
-#70 := [rewrite]: #69
-#128 := [monotonicity #70 #73]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#168 := [trans #151 #166]: #167
-#125 := [asserted]: #45
-#169 := [mp #125 #168]: #164
-#172 := [mp~ #169 #176]: #164
-#220 := [mp #172 #219]: #217
-#251 := [mp #220 #250]: #248
-#739 := [mp #251 #738]: #734
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#10 := (f3 #9 1::Int)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#658 := (not #734)
-#560 := (or #658 #12)
-#377 := (* -1::Int 1::Int)
-#507 := (mod #377 #377)
-#714 := (+ #10 #507)
-#388 := (= #714 0::Int)
-#404 := (mod 1::Int 1::Int)
-#383 := (* -1::Int #404)
-#718 := (+ #10 #383)
-#720 := (= #718 0::Int)
-#398 := (<= 1::Int 0::Int)
-#401 := (>= 1::Int 0::Int)
-#402 := (or #401 #398)
-#403 := (not #402)
-#399 := (or #398 #398)
-#390 := (not #399)
-#400 := (or #390 #403)
-#389 := (if #400 #720 #388)
-#313 := (= 1::Int 0::Int)
-#721 := (if #313 #12 #389)
-#397 := (= #10 1::Int)
-#722 := (if #313 #397 #721)
-#655 := (or #658 #722)
-#659 := (iff #655 #560)
-#559 := (iff #560 #560)
-#561 := [rewrite]: #559
-#551 := (iff #722 #12)
-#666 := (if false #397 #12)
-#549 := (iff #666 #12)
-#550 := [rewrite]: #549
-#664 := (iff #722 #666)
-#663 := (iff #721 #12)
-#677 := (if false #12 #12)
-#509 := (iff #677 #12)
-#662 := [rewrite]: #509
-#506 := (iff #721 #677)
-#676 := (iff #389 #12)
-#1 := true
-#673 := (if true #12 #12)
-#669 := (iff #673 #12)
-#675 := [rewrite]: #669
-#674 := (iff #389 #673)
-#671 := (iff #388 #12)
-#528 := (= #714 #10)
-#409 := (+ #10 0::Int)
-#689 := (= #409 #10)
-#690 := [rewrite]: #689
-#686 := (= #714 #409)
-#685 := (= #507 0::Int)
-#682 := (mod -1::Int -1::Int)
-#679 := (= #682 0::Int)
-#684 := [rewrite]: #679
-#683 := (= #507 #682)
-#692 := (= #377 -1::Int)
-#681 := [rewrite]: #692
-#678 := [monotonicity #681 #681]: #683
-#680 := [trans #678 #684]: #685
-#527 := [monotonicity #680]: #686
-#529 := [trans #527 #690]: #528
-#672 := [monotonicity #529]: #671
-#691 := (iff #720 #12)
-#405 := (= #718 #10)
-#410 := (= #718 #409)
-#698 := (= #383 0::Int)
-#418 := (* -1::Int 0::Int)
-#697 := (= #418 0::Int)
-#694 := [rewrite]: #697
-#419 := (= #383 #418)
-#695 := (= #404 0::Int)
-#696 := [rewrite]: #695
-#693 := [monotonicity #696]: #419
-#408 := [trans #693 #694]: #698
-#411 := [monotonicity #408]: #410
-#687 := [trans #411 #690]: #405
-#688 := [monotonicity #687]: #691
-#425 := (iff #400 true)
-#707 := (or true false)
-#346 := (iff #707 true)
-#709 := [rewrite]: #346
-#423 := (iff #400 #707)
-#700 := (iff #403 false)
-#352 := (not true)
-#713 := (iff #352 false)
-#699 := [rewrite]: #713
-#712 := (iff #403 #352)
-#711 := (iff #402 true)
-#702 := (iff #402 #707)
-#719 := (iff #398 false)
-#725 := [rewrite]: #719
-#705 := (iff #401 true)
-#706 := [rewrite]: #705
-#708 := [monotonicity #706 #725]: #702
-#351 := [trans #708 #709]: #711
-#710 := [monotonicity #351]: #712
-#422 := [trans #710 #699]: #700
-#703 := (iff #390 true)
-#701 := (not false)
-#366 := (iff #701 true)
-#367 := [rewrite]: #366
-#364 := (iff #390 #701)
-#717 := (iff #399 false)
-#715 := (or false false)
-#716 := (iff #715 false)
-#376 := [rewrite]: #716
-#375 := (iff #399 #715)
-#380 := [monotonicity #725 #725]: #375
-#360 := [trans #380 #376]: #717
-#365 := [monotonicity #360]: #364
-#704 := [trans #365 #367]: #703
-#424 := [monotonicity #704 #422]: #423
-#319 := [trans #424 #709]: #425
-#668 := [monotonicity #319 #688 #672]: #674
-#670 := [trans #668 #675]: #676
-#723 := (iff #313 false)
-#724 := [rewrite]: #723
-#508 := [monotonicity #724 #670]: #506
-#665 := [trans #508 #662]: #663
-#667 := [monotonicity #724 #665]: #664
-#510 := [trans #667 #550]: #551
-#544 := [monotonicity #510]: #659
-#562 := [trans #544 #561]: #659
-#656 := [quant-inst #8 #8]: #655
-#555 := [mp #656 #562]: #560
-[unit-resolution #555 #65 #739]: false
-unsat
-0efd40b813a31e70f41afd259192cc78d55d0047 298 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#733 := (pattern #38)
-#12 := 0::Int
-#68 := -1::Int
-#72 := (* -1::Int #18)
-#69 := (* -1::Int #16)
-#127 := (mod #69 #72)
-#242 := (+ #38 #127)
-#243 := (= #242 0::Int)
-#39 := (mod #16 #18)
-#239 := (* -1::Int #39)
-#240 := (+ #38 #239)
-#241 := (= #240 0::Int)
-#94 := (<= #18 0::Int)
-#101 := (>= #16 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #16 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#244 := (if #190 #241 #243)
-#238 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#245 := (if #20 #238 #244)
-#237 := (= #38 #16)
-#21 := (= #18 0::Int)
-#246 := (if #21 #237 #245)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #246)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#737 := (iff #249 #734)
-#735 := (iff #246 #246)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#133 := (* -1::Int #127)
-#206 := (if #190 #39 #133)
-#209 := (if #20 0::Int #206)
-#212 := (if #21 #16 #209)
-#215 := (= #38 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#250 := (iff #218 #249)
-#247 := (iff #215 #246)
-#248 := [rewrite]: #247
-#251 := [quant-intro #248]: #250
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (if #108 #39 #133)
-#156 := (if #20 0::Int #153)
-#159 := (if #21 #16 #156)
-#162 := (= #38 #159)
-#165 := (forall (vars (?v0 Int) (?v1 Int)) #162)
-#219 := (iff #165 #218)
-#216 := (iff #162 #215)
-#213 := (= #159 #212)
-#210 := (= #156 #209)
-#207 := (= #153 #206)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#208 := [monotonicity #192]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#176 := (~ #165 #165)
-#175 := (~ #162 #162)
-#172 := [refl]: #175
-#177 := [nnf-pos #172]: #176
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#168 := (iff #46 #165)
-#138 := (if #28 #39 #133)
-#141 := (if #20 0::Int #138)
-#144 := (if #21 #16 #141)
-#147 := (= #38 #144)
-#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #28 #108)
-#106 := (iff #27 #105)
-#96 := (iff #24 #95)
-#97 := [rewrite]: #96
-#103 := (iff #26 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #25 #98)
-#92 := (iff #23 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #46 #150)
-#148 := (iff #45 #147)
-#145 := (= #44 #144)
-#142 := (= #43 #141)
-#139 := (= #42 #138)
-#136 := (= #41 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #41 #130)
-#128 := (= #40 #127)
-#73 := (= #31 #72)
-#74 := [rewrite]: #73
-#70 := (= #30 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #46
-#170 := [mp #126 #169]: #165
-#173 := [mp~ #170 #177]: #165
-#221 := [mp #173 #220]: #218
-#252 := [mp #221 #251]: #249
-#739 := [mp #252 #738]: #734
-#10 := 1::Int
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#11 := (f3 #9 1::Int)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#66 := [asserted]: #14
-#563 := (not #734)
-#564 := (or #563 #13)
-#388 := (* -1::Int 1::Int)
-#714 := (* -1::Int 3::Int)
-#389 := (mod #714 #388)
-#721 := (+ #11 #389)
-#722 := (= #721 0::Int)
-#718 := (mod 3::Int 1::Int)
-#720 := (* -1::Int #718)
-#377 := (+ #11 #720)
-#507 := (= #377 0::Int)
-#390 := (<= 1::Int 0::Int)
-#403 := (>= 3::Int 0::Int)
-#400 := (or #403 #390)
-#404 := (not #400)
-#399 := (<= 3::Int 0::Int)
-#401 := (or #399 #390)
-#402 := (not #401)
-#383 := (or #402 #404)
-#723 := (if #383 #507 #722)
-#398 := (= 3::Int 0::Int)
-#724 := (if #398 #13 #723)
-#397 := (= #11 3::Int)
-#313 := (= 1::Int 0::Int)
-#719 := (if #313 #397 #724)
-#565 := (or #563 #719)
-#567 := (iff #565 #564)
-#657 := (iff #564 #564)
-#661 := [rewrite]: #657
-#562 := (iff #719 #13)
-#656 := (if false #397 #13)
-#559 := (iff #656 #13)
-#561 := [rewrite]: #559
-#659 := (iff #719 #656)
-#560 := (iff #724 #13)
-#549 := (if false #13 #13)
-#510 := (iff #549 #13)
-#658 := [rewrite]: #510
-#550 := (iff #724 #549)
-#664 := (iff #723 #13)
-#1 := true
-#509 := (if true #13 #13)
-#665 := (iff #509 #13)
-#666 := [rewrite]: #665
-#662 := (iff #723 #509)
-#506 := (iff #722 #13)
-#670 := (= #721 #11)
-#691 := (+ #11 0::Int)
-#681 := (= #691 #11)
-#682 := [rewrite]: #681
-#675 := (= #721 #691)
-#668 := (= #389 0::Int)
-#685 := -3::Int
-#529 := (mod -3::Int -1::Int)
-#673 := (= #529 0::Int)
-#674 := [rewrite]: #673
-#671 := (= #389 #529)
-#527 := (= #388 -1::Int)
-#528 := [rewrite]: #527
-#680 := (= #714 -3::Int)
-#686 := [rewrite]: #680
-#672 := [monotonicity #686 #528]: #671
-#669 := [trans #672 #674]: #668
-#676 := [monotonicity #669]: #675
-#677 := [trans #676 #682]: #670
-#508 := [monotonicity #677]: #506
-#679 := (iff #507 #13)
-#683 := (= #377 #11)
-#688 := (= #377 #691)
-#405 := (= #720 0::Int)
-#409 := (* -1::Int 0::Int)
-#689 := (= #409 0::Int)
-#690 := [rewrite]: #689
-#410 := (= #720 #409)
-#698 := (= #718 0::Int)
-#408 := [rewrite]: #698
-#411 := [monotonicity #408]: #410
-#687 := [trans #411 #690]: #405
-#692 := [monotonicity #687]: #688
-#678 := [trans #692 #682]: #683
-#684 := [monotonicity #678]: #679
-#697 := (iff #383 true)
-#352 := (or true false)
-#713 := (iff #352 true)
-#699 := [rewrite]: #713
-#419 := (iff #383 #352)
-#696 := (iff #404 false)
-#423 := (not true)
-#319 := (iff #423 false)
-#695 := [rewrite]: #319
-#424 := (iff #404 #423)
-#700 := (iff #400 true)
-#712 := (iff #400 #352)
-#717 := (iff #390 false)
-#360 := [rewrite]: #717
-#711 := (iff #403 true)
-#351 := [rewrite]: #711
-#710 := [monotonicity #351 #360]: #712
-#422 := [trans #710 #699]: #700
-#425 := [monotonicity #422]: #424
-#418 := [trans #425 #695]: #696
-#346 := (iff #402 true)
-#705 := (not false)
-#702 := (iff #705 true)
-#708 := [rewrite]: #702
-#706 := (iff #402 #705)
-#703 := (iff #401 false)
-#701 := (or false false)
-#366 := (iff #701 false)
-#367 := [rewrite]: #366
-#364 := (iff #401 #701)
-#716 := (iff #399 false)
-#376 := [rewrite]: #716
-#365 := [monotonicity #376 #360]: #364
-#704 := [trans #365 #367]: #703
-#707 := [monotonicity #704]: #706
-#709 := [trans #707 #708]: #346
-#693 := [monotonicity #709 #418]: #419
-#694 := [trans #693 #699]: #697
-#663 := [monotonicity #694 #684 #508]: #662
-#667 := [trans #663 #666]: #664
-#375 := (iff #398 false)
-#380 := [rewrite]: #375
-#551 := [monotonicity #380 #667]: #550
-#655 := [trans #551 #658]: #560
-#725 := (iff #313 false)
-#715 := [rewrite]: #725
-#544 := [monotonicity #715 #655]: #659
-#555 := [trans #544 #561]: #562
-#660 := [monotonicity #555]: #567
-#648 := [trans #660 #661]: #567
-#566 := [quant-inst #8 #10]: #565
-#650 := [mp #566 #648]: #564
-[unit-resolution #650 #66 #739]: false
-unsat
-1cff7727da7921a7ced79f03edcd1b205ac8b4b2 294 0
-#2 := false
-#12 := 0::Int
-decl f6 :: Int
-#8 := f6
-#404 := (>= f6 0::Int)
-#710 := (not #404)
-#400 := (<= f6 0::Int)
-#367 := (not #400)
-#353 := (or #367 #710)
-#665 := (not #353)
-#68 := -1::Int
-#715 := (* -1::Int f6)
-#690 := (mod #715 -1::Int)
-decl f3 :: (-> S2 Int Int)
-#10 := 1::Int
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#7 := f5
-#9 := (f4 f5 f6)
-#11 := (f3 #9 1::Int)
-#688 := (+ #11 #690)
-#693 := (= #688 0::Int)
-#13 := (= #11 0::Int)
-#684 := (if #353 #13 #693)
-#399 := (= f6 0::Int)
-#685 := (if #399 #13 #684)
-#18 := (:var 0 Int)
-#16 := (:var 1 Int)
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#734 := (pattern #38)
-#72 := (* -1::Int #18)
-#69 := (* -1::Int #16)
-#127 := (mod #69 #72)
-#242 := (+ #38 #127)
-#243 := (= #242 0::Int)
-#39 := (mod #16 #18)
-#239 := (* -1::Int #39)
-#240 := (+ #38 #239)
-#241 := (= #240 0::Int)
-#94 := (<= #18 0::Int)
-#101 := (>= #16 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #16 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#244 := (if #190 #241 #243)
-#238 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#245 := (if #20 #238 #244)
-#237 := (= #38 #16)
-#21 := (= #18 0::Int)
-#246 := (if #21 #237 #245)
-#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #246)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#738 := (iff #249 #735)
-#736 := (iff #246 #246)
-#737 := [refl]: #736
-#739 := [quant-intro #737]: #738
-#133 := (* -1::Int #127)
-#206 := (if #190 #39 #133)
-#209 := (if #20 0::Int #206)
-#212 := (if #21 #16 #209)
-#215 := (= #38 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#250 := (iff #218 #249)
-#247 := (iff #215 #246)
-#248 := [rewrite]: #247
-#251 := [quant-intro #248]: #250
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (if #108 #39 #133)
-#156 := (if #20 0::Int #153)
-#159 := (if #21 #16 #156)
-#162 := (= #38 #159)
-#165 := (forall (vars (?v0 Int) (?v1 Int)) #162)
-#219 := (iff #165 #218)
-#216 := (iff #162 #215)
-#213 := (= #159 #212)
-#210 := (= #156 #209)
-#207 := (= #153 #206)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#208 := [monotonicity #192]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#176 := (~ #165 #165)
-#175 := (~ #162 #162)
-#172 := [refl]: #175
-#177 := [nnf-pos #172]: #176
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#168 := (iff #46 #165)
-#138 := (if #28 #39 #133)
-#141 := (if #20 0::Int #138)
-#144 := (if #21 #16 #141)
-#147 := (= #38 #144)
-#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #28 #108)
-#106 := (iff #27 #105)
-#96 := (iff #24 #95)
-#97 := [rewrite]: #96
-#103 := (iff #26 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #25 #98)
-#92 := (iff #23 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #46 #150)
-#148 := (iff #45 #147)
-#145 := (= #44 #144)
-#142 := (= #43 #141)
-#139 := (= #42 #138)
-#136 := (= #41 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #41 #130)
-#128 := (= #40 #127)
-#73 := (= #31 #72)
-#74 := [rewrite]: #73
-#70 := (= #30 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #46
-#170 := [mp #126 #169]: #165
-#173 := [mp~ #170 #177]: #165
-#221 := [mp #173 #220]: #218
-#252 := [mp #221 #251]: #249
-#740 := [mp #252 #739]: #735
-#675 := (not #735)
-#669 := (or #675 #685)
-#389 := (* -1::Int 1::Int)
-#390 := (mod #715 #389)
-#722 := (+ #11 #390)
-#723 := (= #722 0::Int)
-#719 := (mod f6 1::Int)
-#721 := (* -1::Int #719)
-#378 := (+ #11 #721)
-#508 := (= #378 0::Int)
-#391 := (<= 1::Int 0::Int)
-#401 := (or #404 #391)
-#405 := (not #401)
-#402 := (or #400 #391)
-#403 := (not #402)
-#384 := (or #403 #405)
-#724 := (if #384 #508 #723)
-#725 := (if #399 #13 #724)
-#398 := (= #11 f6)
-#314 := (= 1::Int 0::Int)
-#720 := (if #314 #398 #725)
-#670 := (or #675 #720)
-#677 := (iff #670 #669)
-#678 := (iff #669 #669)
-#507 := [rewrite]: #678
-#673 := (iff #720 #685)
-#687 := (if false #398 #685)
-#530 := (iff #687 #685)
-#672 := [rewrite]: #530
-#528 := (iff #720 #687)
-#686 := (iff #725 #685)
-#679 := (iff #724 #684)
-#682 := (iff #723 #693)
-#692 := (= #722 #688)
-#691 := (= #390 #690)
-#411 := (= #389 -1::Int)
-#412 := [rewrite]: #411
-#406 := [monotonicity #412]: #691
-#689 := [monotonicity #406]: #692
-#683 := [monotonicity #689]: #682
-#409 := (iff #508 #13)
-#695 := (= #378 #11)
-#697 := (+ #11 0::Int)
-#694 := (= #697 #11)
-#698 := [rewrite]: #694
-#419 := (= #378 #697)
-#320 := (= #721 0::Int)
-#701 := (* -1::Int 0::Int)
-#425 := (= #701 0::Int)
-#426 := [rewrite]: #425
-#423 := (= #721 #701)
-#714 := (= #719 0::Int)
-#700 := [rewrite]: #714
-#424 := [monotonicity #700]: #423
-#696 := [trans #424 #426]: #320
-#420 := [monotonicity #696]: #419
-#699 := [trans #420 #698]: #695
-#410 := [monotonicity #699]: #409
-#713 := (iff #384 #353)
-#712 := (iff #405 #710)
-#709 := (iff #401 #404)
-#705 := (or #404 false)
-#708 := (iff #705 #404)
-#703 := [rewrite]: #708
-#706 := (iff #401 #705)
-#376 := (iff #391 false)
-#381 := [rewrite]: #376
-#707 := [monotonicity #381]: #706
-#347 := [trans #707 #703]: #709
-#352 := [monotonicity #347]: #712
-#368 := (iff #403 #367)
-#365 := (iff #402 #400)
-#717 := (or #400 false)
-#361 := (iff #717 #400)
-#702 := [rewrite]: #361
-#377 := (iff #402 #717)
-#718 := [monotonicity #381]: #377
-#366 := [trans #718 #702]: #365
-#704 := [monotonicity #366]: #368
-#711 := [monotonicity #704 #352]: #713
-#680 := [monotonicity #711 #410 #683]: #679
-#681 := [monotonicity #680]: #686
-#726 := (iff #314 false)
-#716 := [rewrite]: #726
-#529 := [monotonicity #716 #681]: #528
-#674 := [trans #529 #672]: #673
-#671 := [monotonicity #674]: #677
-#509 := [trans #671 #507]: #677
-#676 := [quant-inst #8 #10]: #670
-#510 := [mp #676 #509]: #669
-#607 := [unit-resolution #510 #740]: #685
-#564 := (not #399)
-#556 := (not #685)
-#608 := (or #556 #564)
-#14 := (not #13)
-#66 := [asserted]: #14
-#565 := (or #556 #564 #13)
-#566 := [def-axiom]: #565
-#609 := [unit-resolution #566 #66]: #608
-#604 := [unit-resolution #609 #607]: #564
-#567 := (or #556 #399 #684)
-#568 := [def-axiom]: #567
-#610 := [unit-resolution #568 #604 #607]: #684
-#511 := (not #684)
-#596 := (or #511 #665)
-#659 := (or #511 #665 #13)
-#561 := [def-axiom]: #659
-#592 := [unit-resolution #561 #66]: #596
-#593 := [unit-resolution #592 #610]: #665
-#666 := (or #353 #404)
-#667 := [def-axiom]: #666
-#594 := [unit-resolution #667 #593]: #404
-#663 := (or #353 #400)
-#664 := [def-axiom]: #663
-#597 := [unit-resolution #664 #593]: #400
-#598 := (or #399 #367 #710)
-#599 := [th-lemma arith triangle-eq]: #598
-[unit-resolution #599 #604 #597 #594]: false
-unsat
-d419bb3e51a007e8e5acdc900beee4c77bd2d9be 299 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#746 := (pattern #38)
-#8 := 0::Int
-#67 := -1::Int
-#84 := (* -1::Int #18)
-#80 := (* -1::Int #16)
-#139 := (mod #80 #84)
-#254 := (+ #38 #139)
-#255 := (= #254 0::Int)
-#39 := (mod #16 #18)
-#251 := (* -1::Int #39)
-#252 := (+ #38 #251)
-#253 := (= #252 0::Int)
-#106 := (<= #18 0::Int)
-#113 := (>= #16 0::Int)
-#198 := (or #113 #106)
-#199 := (not #198)
-#102 := (<= #16 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#256 := (if #202 #253 #255)
-#250 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#257 := (if #20 #250 #256)
-#249 := (= #38 #16)
-#21 := (= #18 0::Int)
-#258 := (if #21 #249 #257)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#750 := (iff #261 #747)
-#748 := (iff #258 #258)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#145 := (* -1::Int #139)
-#218 := (if #202 #39 #145)
-#221 := (if #20 0::Int #218)
-#224 := (if #21 #16 #221)
-#227 := (= #38 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#107 := (not #106)
-#114 := (not #113)
-#117 := (and #114 #107)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#165 := (if #120 #39 #145)
-#168 := (if #20 0::Int #165)
-#171 := (if #21 #16 #168)
-#174 := (= #38 #171)
-#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
-#231 := (iff #177 #230)
-#228 := (iff #174 #227)
-#225 := (= #171 #224)
-#222 := (= #168 #221)
-#219 := (= #165 #218)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#220 := [monotonicity #204]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#188 := (~ #177 #177)
-#187 := (~ #174 #174)
-#184 := [refl]: #187
-#189 := [nnf-pos #184]: #188
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#180 := (iff #46 #177)
-#150 := (if #28 #39 #145)
-#153 := (if #20 0::Int #150)
-#156 := (if #21 #16 #153)
-#159 := (= #38 #156)
-#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
-#178 := (iff #162 #177)
-#175 := (iff #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#166 := (= #150 #165)
-#121 := (iff #28 #120)
-#118 := (iff #27 #117)
-#108 := (iff #24 #107)
-#109 := [rewrite]: #108
-#115 := (iff #26 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116 #109]: #118
-#111 := (iff #25 #110)
-#104 := (iff #23 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#167 := [monotonicity #122]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [quant-intro #176]: #178
-#163 := (iff #46 #162)
-#160 := (iff #45 #159)
-#157 := (= #44 #156)
-#154 := (= #43 #153)
-#151 := (= #42 #150)
-#148 := (= #41 #145)
-#142 := (- #139)
-#146 := (= #142 #145)
-#147 := [rewrite]: #146
-#143 := (= #41 #142)
-#140 := (= #40 #139)
-#85 := (= #31 #84)
-#86 := [rewrite]: #85
-#82 := (= #30 #80)
-#83 := [rewrite]: #82
-#141 := [monotonicity #83 #86]: #140
-#144 := [monotonicity #141]: #143
-#149 := [trans #144 #147]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#181 := [trans #164 #179]: #180
-#138 := [asserted]: #46
-#182 := [mp #138 #181]: #177
-#185 := [mp~ #182 #189]: #177
-#233 := [mp #185 #232]: #230
-#264 := [mp #233 #263]: #261
-#752 := [mp #264 #751]: #747
-#9 := (f4 f5 0::Int)
-#70 := (f3 #9 -1::Int)
-#73 := (= #70 0::Int)
-#76 := (not #73)
-#10 := 1::Int
-#11 := (- 1::Int)
-#12 := (f3 #9 #11)
-#13 := (= #12 0::Int)
-#14 := (not #13)
-#77 := (iff #14 #76)
-#74 := (iff #13 #73)
-#71 := (= #12 #70)
-#68 := (= #11 -1::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #14
-#81 := [mp #66 #78]: #76
-#523 := (not #747)
-#671 := (or #523 #73)
-#727 := (* -1::Int -1::Int)
-#520 := (* -1::Int 0::Int)
-#401 := (mod #520 #727)
-#402 := (+ #70 #401)
-#734 := (= #402 0::Int)
-#396 := (mod 0::Int -1::Int)
-#731 := (* -1::Int #396)
-#733 := (+ #70 #731)
-#390 := (= #733 0::Int)
-#412 := (<= -1::Int 0::Int)
-#415 := (>= 0::Int 0::Int)
-#416 := (or #415 #412)
-#413 := (not #416)
-#411 := (<= 0::Int 0::Int)
-#403 := (or #411 #412)
-#414 := (not #403)
-#417 := (or #414 #413)
-#735 := (if #417 #390 #734)
-#410 := (= 0::Int 0::Int)
-#736 := (if #410 #73 #735)
-#326 := (= -1::Int 0::Int)
-#737 := (if #326 #73 #736)
-#573 := (or #523 #737)
-#669 := (iff #573 #671)
-#557 := (iff #671 #671)
-#572 := [rewrite]: #557
-#563 := (iff #737 #73)
-#681 := (if false #73 #73)
-#689 := (iff #681 #73)
-#683 := [rewrite]: #689
-#680 := (iff #737 #681)
-#679 := (iff #736 #73)
-#1 := true
-#521 := (if true #73 #73)
-#676 := (iff #521 #73)
-#678 := [rewrite]: #676
-#522 := (iff #736 #521)
-#690 := (iff #735 #73)
-#682 := (iff #735 #681)
-#686 := (iff #734 #73)
-#684 := (= #402 #70)
-#424 := (+ #70 0::Int)
-#418 := (= #424 #70)
-#700 := [rewrite]: #418
-#541 := (= #402 #424)
-#699 := (= #401 0::Int)
-#691 := (mod 0::Int 1::Int)
-#698 := (= #691 0::Int)
-#693 := [rewrite]: #698
-#692 := (= #401 #691)
-#695 := (= #727 1::Int)
-#696 := [rewrite]: #695
-#711 := (= #520 0::Int)
-#421 := [rewrite]: #711
-#697 := [monotonicity #421 #696]: #692
-#540 := [trans #697 #693]: #699
-#542 := [monotonicity #540]: #541
-#685 := [trans #542 #700]: #684
-#687 := [monotonicity #685]: #686
-#705 := (iff #390 #73)
-#704 := (= #733 #70)
-#702 := (= #733 #424)
-#422 := (= #731 0::Int)
-#710 := (= #731 #520)
-#432 := (= #396 0::Int)
-#706 := [rewrite]: #432
-#707 := [monotonicity #706]: #710
-#423 := [trans #707 #421]: #422
-#703 := [monotonicity #423]: #702
-#701 := [trans #703 #700]: #704
-#694 := [monotonicity #701]: #705
-#709 := (iff #417 false)
-#436 := (or false false)
-#332 := (iff #436 false)
-#708 := [rewrite]: #332
-#437 := (iff #417 #436)
-#713 := (iff #413 false)
-#717 := (not true)
-#720 := (iff #717 false)
-#715 := [rewrite]: #720
-#726 := (iff #413 #717)
-#725 := (iff #416 true)
-#373 := (or true true)
-#378 := (iff #373 true)
-#379 := [rewrite]: #378
-#364 := (iff #416 #373)
-#389 := (iff #412 true)
-#730 := [rewrite]: #389
-#722 := (iff #415 true)
-#724 := [rewrite]: #722
-#365 := [monotonicity #724 #730]: #364
-#723 := [trans #365 #379]: #725
-#712 := [monotonicity #723]: #726
-#435 := [trans #712 #715]: #713
-#721 := (iff #414 false)
-#718 := (iff #414 #717)
-#380 := (iff #403 true)
-#714 := (iff #403 #373)
-#393 := (iff #411 true)
-#729 := [rewrite]: #393
-#377 := [monotonicity #729 #730]: #714
-#716 := [trans #377 #379]: #380
-#719 := [monotonicity #716]: #718
-#359 := [trans #719 #715]: #721
-#438 := [monotonicity #359 #435]: #437
-#431 := [trans #438 #708]: #709
-#688 := [monotonicity #431 #694 #687]: #682
-#519 := [trans #688 #683]: #690
-#728 := (iff #410 true)
-#388 := [rewrite]: #728
-#675 := [monotonicity #388 #519]: #522
-#677 := [trans #675 #678]: #679
-#732 := (iff #326 false)
-#738 := [rewrite]: #732
-#562 := [monotonicity #738 #677]: #680
-#564 := [trans #562 #683]: #563
-#672 := [monotonicity #564]: #669
-#574 := [trans #672 #572]: #669
-#668 := [quant-inst #8 #67]: #573
-#575 := [mp #668 #574]: #671
-[unit-resolution #575 #81 #752]: false
-unsat
-4af2a0ea6f463e71e2c4b38fde6ef00565f6fb9f 306 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#746 := (pattern #38)
-#12 := 0::Int
-#67 := -1::Int
-#84 := (* -1::Int #18)
-#80 := (* -1::Int #16)
-#139 := (mod #80 #84)
-#254 := (+ #38 #139)
-#255 := (= #254 0::Int)
-#39 := (mod #16 #18)
-#251 := (* -1::Int #39)
-#252 := (+ #38 #251)
-#253 := (= #252 0::Int)
-#106 := (<= #18 0::Int)
-#113 := (>= #16 0::Int)
-#198 := (or #113 #106)
-#199 := (not #198)
-#102 := (<= #16 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#256 := (if #202 #253 #255)
-#250 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#257 := (if #20 #250 #256)
-#249 := (= #38 #16)
-#21 := (= #18 0::Int)
-#258 := (if #21 #249 #257)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#750 := (iff #261 #747)
-#748 := (iff #258 #258)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#145 := (* -1::Int #139)
-#218 := (if #202 #39 #145)
-#221 := (if #20 0::Int #218)
-#224 := (if #21 #16 #221)
-#227 := (= #38 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#107 := (not #106)
-#114 := (not #113)
-#117 := (and #114 #107)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#165 := (if #120 #39 #145)
-#168 := (if #20 0::Int #165)
-#171 := (if #21 #16 #168)
-#174 := (= #38 #171)
-#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
-#231 := (iff #177 #230)
-#228 := (iff #174 #227)
-#225 := (= #171 #224)
-#222 := (= #168 #221)
-#219 := (= #165 #218)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#220 := [monotonicity #204]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#188 := (~ #177 #177)
-#187 := (~ #174 #174)
-#184 := [refl]: #187
-#189 := [nnf-pos #184]: #188
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#180 := (iff #46 #177)
-#150 := (if #28 #39 #145)
-#153 := (if #20 0::Int #150)
-#156 := (if #21 #16 #153)
-#159 := (= #38 #156)
-#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
-#178 := (iff #162 #177)
-#175 := (iff #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#166 := (= #150 #165)
-#121 := (iff #28 #120)
-#118 := (iff #27 #117)
-#108 := (iff #24 #107)
-#109 := [rewrite]: #108
-#115 := (iff #26 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116 #109]: #118
-#111 := (iff #25 #110)
-#104 := (iff #23 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#167 := [monotonicity #122]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [quant-intro #176]: #178
-#163 := (iff #46 #162)
-#160 := (iff #45 #159)
-#157 := (= #44 #156)
-#154 := (= #43 #153)
-#151 := (= #42 #150)
-#148 := (= #41 #145)
-#142 := (- #139)
-#146 := (= #142 #145)
-#147 := [rewrite]: #146
-#143 := (= #41 #142)
-#140 := (= #40 #139)
-#85 := (= #31 #84)
-#86 := [rewrite]: #85
-#82 := (= #30 #80)
-#83 := [rewrite]: #82
-#141 := [monotonicity #83 #86]: #140
-#144 := [monotonicity #141]: #143
-#149 := [trans #144 #147]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#181 := [trans #164 #179]: #180
-#138 := [asserted]: #46
-#182 := [mp #138 #181]: #177
-#185 := [mp~ #182 #189]: #177
-#233 := [mp #185 #232]: #230
-#264 := [mp #233 #263]: #261
-#752 := [mp #264 #751]: #747
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#70 := (f3 #9 -1::Int)
-#73 := (= #70 0::Int)
-#76 := (not #73)
-#10 := (- 1::Int)
-#11 := (f3 #9 #10)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#77 := (iff #14 #76)
-#74 := (iff #13 #73)
-#71 := (= #11 #70)
-#68 := (= #10 -1::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #14
-#81 := [mp #66 #78]: #76
-#572 := (not #747)
-#574 := (or #572 #73)
-#401 := (* -1::Int -1::Int)
-#727 := (* -1::Int 1::Int)
-#402 := (mod #727 #401)
-#734 := (+ #70 #402)
-#735 := (= #734 0::Int)
-#731 := (mod 1::Int -1::Int)
-#733 := (* -1::Int #731)
-#390 := (+ #70 #733)
-#520 := (= #390 0::Int)
-#403 := (<= -1::Int 0::Int)
-#416 := (>= 1::Int 0::Int)
-#413 := (or #416 #403)
-#417 := (not #413)
-#412 := (<= 1::Int 0::Int)
-#414 := (or #412 #403)
-#415 := (not #414)
-#396 := (or #415 #417)
-#736 := (if #396 #520 #735)
-#411 := (= 1::Int 0::Int)
-#737 := (if #411 #73 #736)
-#410 := (= #70 1::Int)
-#326 := (= -1::Int 0::Int)
-#732 := (if #326 #410 #737)
-#575 := (or #572 #732)
-#576 := (iff #575 #574)
-#578 := (iff #574 #574)
-#579 := [rewrite]: #578
-#672 := (iff #732 #73)
-#523 := (if false #410 #73)
-#668 := (iff #523 #73)
-#669 := [rewrite]: #668
-#671 := (iff #732 #523)
-#563 := (iff #737 #73)
-#521 := (if false #73 #73)
-#676 := (iff #521 #73)
-#678 := [rewrite]: #676
-#680 := (iff #737 #521)
-#679 := (iff #736 #73)
-#522 := (iff #736 #521)
-#690 := (iff #735 #73)
-#689 := (= #734 #70)
-#704 := (+ #70 0::Int)
-#694 := (= #704 #70)
-#695 := [rewrite]: #694
-#682 := (= #734 #704)
-#687 := (= #402 0::Int)
-#541 := (mod -1::Int 1::Int)
-#685 := (= #541 0::Int)
-#686 := [rewrite]: #685
-#542 := (= #402 #541)
-#699 := (= #401 1::Int)
-#540 := [rewrite]: #699
-#698 := (= #727 -1::Int)
-#693 := [rewrite]: #698
-#684 := [monotonicity #693 #540]: #542
-#681 := [trans #684 #686]: #687
-#688 := [monotonicity #681]: #682
-#683 := [trans #688 #695]: #689
-#519 := [monotonicity #683]: #690
-#692 := (iff #520 #73)
-#696 := (= #390 #70)
-#701 := (= #390 #704)
-#418 := (= #733 0::Int)
-#422 := (* -1::Int 0::Int)
-#702 := (= #422 0::Int)
-#703 := [rewrite]: #702
-#423 := (= #733 #422)
-#711 := (= #731 0::Int)
-#421 := [rewrite]: #711
-#424 := [monotonicity #421]: #423
-#700 := [trans #424 #703]: #418
-#705 := [monotonicity #700]: #701
-#691 := [trans #705 #695]: #696
-#697 := [monotonicity #691]: #692
-#710 := (iff #396 false)
-#708 := (or false false)
-#432 := (iff #708 false)
-#706 := [rewrite]: #432
-#709 := (iff #396 #708)
-#438 := (iff #417 false)
-#1 := true
-#718 := (not true)
-#715 := (iff #718 false)
-#721 := [rewrite]: #715
-#436 := (iff #417 #718)
-#713 := (iff #413 true)
-#365 := (or true true)
-#726 := (iff #365 true)
-#712 := [rewrite]: #726
-#725 := (iff #413 #365)
-#730 := (iff #403 true)
-#373 := [rewrite]: #730
-#724 := (iff #416 true)
-#364 := [rewrite]: #724
-#723 := [monotonicity #364 #373]: #725
-#435 := [trans #723 #712]: #713
-#437 := [monotonicity #435]: #436
-#332 := [trans #437 #721]: #438
-#359 := (iff #415 false)
-#719 := (iff #415 #718)
-#716 := (iff #414 true)
-#714 := (or false true)
-#379 := (iff #714 true)
-#380 := [rewrite]: #379
-#377 := (iff #414 #714)
-#729 := (iff #412 false)
-#389 := [rewrite]: #729
-#378 := [monotonicity #389 #373]: #377
-#717 := [trans #378 #380]: #716
-#720 := [monotonicity #717]: #719
-#722 := [trans #720 #721]: #359
-#431 := [monotonicity #722 #332]: #709
-#707 := [trans #431 #706]: #710
-#675 := [monotonicity #707 #697 #519]: #522
-#677 := [trans #675 #678]: #679
-#388 := (iff #411 false)
-#393 := [rewrite]: #388
-#562 := [monotonicity #393 #677]: #680
-#564 := [trans #562 #678]: #563
-#738 := (iff #326 false)
-#728 := [rewrite]: #738
-#573 := [monotonicity #728 #564]: #671
-#557 := [trans #573 #669]: #672
-#577 := [monotonicity #557]: #576
-#580 := [trans #577 #579]: #576
-#568 := [quant-inst #8 #67]: #575
-#673 := [mp #568 #580]: #574
-[unit-resolution #673 #81 #752]: false
-unsat
-6e0487fe9c651d71e634cf8c64acf5989f144ad3 308 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#746 := (pattern #39)
-#13 := 0::Int
-#68 := -1::Int
-#85 := (* -1::Int #19)
-#81 := (* -1::Int #17)
-#140 := (mod #81 #85)
-#255 := (+ #39 #140)
-#256 := (= #255 0::Int)
-#40 := (mod #17 #19)
-#252 := (* -1::Int #40)
-#253 := (+ #39 #252)
-#254 := (= #253 0::Int)
-#107 := (<= #19 0::Int)
-#114 := (>= #17 0::Int)
-#199 := (or #114 #107)
-#200 := (not #199)
-#103 := (<= #17 0::Int)
-#197 := (or #103 #107)
-#198 := (not #197)
-#203 := (or #198 #200)
-#257 := (if #203 #254 #256)
-#251 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#258 := (if #21 #251 #257)
-#250 := (= #39 #17)
-#22 := (= #19 0::Int)
-#259 := (if #22 #250 #258)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #259)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#750 := (iff #262 #747)
-#748 := (iff #259 #259)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#146 := (* -1::Int #140)
-#219 := (if #203 #40 #146)
-#222 := (if #21 0::Int #219)
-#225 := (if #22 #17 #222)
-#228 := (= #39 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#108 := (not #107)
-#115 := (not #114)
-#118 := (and #115 #108)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#166 := (if #121 #40 #146)
-#169 := (if #21 0::Int #166)
-#172 := (if #22 #17 #169)
-#175 := (= #39 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#232 := (iff #178 #231)
-#229 := (iff #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#220 := (= #166 #219)
-#204 := (iff #121 #203)
-#201 := (iff #118 #200)
-#202 := [rewrite]: #201
-#191 := (iff #111 #198)
-#192 := [rewrite]: #191
-#205 := [monotonicity #192 #202]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#189 := (~ #178 #178)
-#188 := (~ #175 #175)
-#185 := [refl]: #188
-#190 := [nnf-pos #185]: #189
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (if #29 #40 #42)
-#44 := (if #21 0::Int #43)
-#45 := (if #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#181 := (iff #47 #178)
-#151 := (if #29 #40 #146)
-#154 := (if #21 0::Int #151)
-#157 := (if #22 #17 #154)
-#160 := (= #39 #157)
-#163 := (forall (vars (?v0 Int) (?v1 Int)) #160)
-#179 := (iff #163 #178)
-#176 := (iff #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#167 := (= #151 #166)
-#122 := (iff #29 #121)
-#119 := (iff #28 #118)
-#109 := (iff #25 #108)
-#110 := [rewrite]: #109
-#116 := (iff #27 #115)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117 #110]: #119
-#112 := (iff #26 #111)
-#105 := (iff #24 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#168 := [monotonicity #123]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#164 := (iff #47 #163)
-#161 := (iff #46 #160)
-#158 := (= #45 #157)
-#155 := (= #44 #154)
-#152 := (= #43 #151)
-#149 := (= #42 #146)
-#143 := (- #140)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #42 #143)
-#141 := (= #41 #140)
-#86 := (= #32 #85)
-#87 := [rewrite]: #86
-#83 := (= #31 #81)
-#84 := [rewrite]: #83
-#142 := [monotonicity #84 #87]: #141
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#182 := [trans #165 #180]: #181
-#139 := [asserted]: #47
-#183 := [mp #139 #182]: #178
-#186 := [mp~ #183 #190]: #178
-#234 := [mp #186 #233]: #231
-#265 := [mp #234 #264]: #262
-#752 := [mp #265 #751]: #747
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#71 := (f3 #9 -1::Int)
-#74 := (= #71 0::Int)
-#77 := (not #74)
-#10 := 1::Int
-#11 := (- 1::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#78 := (iff #15 #77)
-#75 := (iff #14 #74)
-#72 := (= #12 #71)
-#69 := (= #11 -1::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#67 := [asserted]: #15
-#82 := [mp #67 #79]: #77
-#574 := (not #747)
-#575 := (or #574 #74)
-#401 := (* -1::Int -1::Int)
-#727 := (* -1::Int 3::Int)
-#402 := (mod #727 #401)
-#734 := (+ #71 #402)
-#735 := (= #734 0::Int)
-#731 := (mod 3::Int -1::Int)
-#733 := (* -1::Int #731)
-#390 := (+ #71 #733)
-#520 := (= #390 0::Int)
-#403 := (<= -1::Int 0::Int)
-#416 := (>= 3::Int 0::Int)
-#413 := (or #416 #403)
-#417 := (not #413)
-#412 := (<= 3::Int 0::Int)
-#414 := (or #412 #403)
-#415 := (not #414)
-#396 := (or #415 #417)
-#736 := (if #396 #520 #735)
-#411 := (= 3::Int 0::Int)
-#737 := (if #411 #74 #736)
-#410 := (= #71 3::Int)
-#326 := (= -1::Int 0::Int)
-#732 := (if #326 #410 #737)
-#568 := (or #574 #732)
-#577 := (iff #568 #575)
-#579 := (iff #575 #575)
-#580 := [rewrite]: #579
-#557 := (iff #732 #74)
-#671 := (if false #410 #74)
-#669 := (iff #671 #74)
-#672 := [rewrite]: #669
-#573 := (iff #732 #671)
-#564 := (iff #737 #74)
-#522 := (if false #74 #74)
-#678 := (iff #522 #74)
-#679 := [rewrite]: #678
-#562 := (iff #737 #522)
-#677 := (iff #736 #74)
-#675 := (iff #736 #522)
-#519 := (iff #735 #74)
-#683 := (= #734 #71)
-#704 := (+ #71 0::Int)
-#694 := (= #704 #71)
-#695 := [rewrite]: #694
-#688 := (= #734 #704)
-#681 := (= #402 0::Int)
-#698 := -3::Int
-#542 := (mod -3::Int 1::Int)
-#686 := (= #542 0::Int)
-#687 := [rewrite]: #686
-#684 := (= #402 #542)
-#540 := (= #401 1::Int)
-#541 := [rewrite]: #540
-#693 := (= #727 -3::Int)
-#699 := [rewrite]: #693
-#685 := [monotonicity #699 #541]: #684
-#682 := [trans #685 #687]: #681
-#689 := [monotonicity #682]: #688
-#690 := [trans #689 #695]: #683
-#521 := [monotonicity #690]: #519
-#692 := (iff #520 #74)
-#696 := (= #390 #71)
-#701 := (= #390 #704)
-#418 := (= #733 0::Int)
-#422 := (* -1::Int 0::Int)
-#702 := (= #422 0::Int)
-#703 := [rewrite]: #702
-#423 := (= #733 #422)
-#711 := (= #731 0::Int)
-#421 := [rewrite]: #711
-#424 := [monotonicity #421]: #423
-#700 := [trans #424 #703]: #418
-#705 := [monotonicity #700]: #701
-#691 := [trans #705 #695]: #696
-#697 := [monotonicity #691]: #692
-#710 := (iff #396 false)
-#708 := (or false false)
-#432 := (iff #708 false)
-#706 := [rewrite]: #432
-#709 := (iff #396 #708)
-#438 := (iff #417 false)
-#1 := true
-#718 := (not true)
-#715 := (iff #718 false)
-#721 := [rewrite]: #715
-#436 := (iff #417 #718)
-#713 := (iff #413 true)
-#365 := (or true true)
-#726 := (iff #365 true)
-#712 := [rewrite]: #726
-#725 := (iff #413 #365)
-#730 := (iff #403 true)
-#373 := [rewrite]: #730
-#724 := (iff #416 true)
-#364 := [rewrite]: #724
-#723 := [monotonicity #364 #373]: #725
-#435 := [trans #723 #712]: #713
-#437 := [monotonicity #435]: #436
-#332 := [trans #437 #721]: #438
-#359 := (iff #415 false)
-#719 := (iff #415 #718)
-#716 := (iff #414 true)
-#714 := (or false true)
-#379 := (iff #714 true)
-#380 := [rewrite]: #379
-#377 := (iff #414 #714)
-#729 := (iff #412 false)
-#389 := [rewrite]: #729
-#378 := [monotonicity #389 #373]: #377
-#717 := [trans #378 #380]: #716
-#720 := [monotonicity #717]: #719
-#722 := [trans #720 #721]: #359
-#431 := [monotonicity #722 #332]: #709
-#707 := [trans #431 #706]: #710
-#676 := [monotonicity #707 #697 #521]: #675
-#680 := [trans #676 #679]: #677
-#388 := (iff #411 false)
-#393 := [rewrite]: #388
-#563 := [monotonicity #393 #680]: #562
-#523 := [trans #563 #679]: #564
-#738 := (iff #326 false)
-#728 := [rewrite]: #738
-#668 := [monotonicity #728 #523]: #573
-#572 := [trans #668 #672]: #557
-#578 := [monotonicity #572]: #577
-#673 := [trans #578 #580]: #577
-#576 := [quant-inst #8 #68]: #568
-#670 := [mp #576 #673]: #575
-[unit-resolution #670 #82 #752]: false
-unsat
-cc50be1af933c0c97044d9c6c3e09dc4fd354986 288 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#747 := (pattern #39)
-#13 := 0::Int
-#68 := -1::Int
-#85 := (* -1::Int #19)
-#81 := (* -1::Int #17)
-#140 := (mod #81 #85)
-#255 := (+ #39 #140)
-#256 := (= #255 0::Int)
-#40 := (mod #17 #19)
-#252 := (* -1::Int #40)
-#253 := (+ #39 #252)
-#254 := (= #253 0::Int)
-#107 := (<= #19 0::Int)
-#114 := (>= #17 0::Int)
-#199 := (or #114 #107)
-#200 := (not #199)
-#103 := (<= #17 0::Int)
-#197 := (or #103 #107)
-#198 := (not #197)
-#203 := (or #198 #200)
-#257 := (if #203 #254 #256)
-#251 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#258 := (if #21 #251 #257)
-#250 := (= #39 #17)
-#22 := (= #19 0::Int)
-#259 := (if #22 #250 #258)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #259)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#751 := (iff #262 #748)
-#749 := (iff #259 #259)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#146 := (* -1::Int #140)
-#219 := (if #203 #40 #146)
-#222 := (if #21 0::Int #219)
-#225 := (if #22 #17 #222)
-#228 := (= #39 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#108 := (not #107)
-#115 := (not #114)
-#118 := (and #115 #108)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#166 := (if #121 #40 #146)
-#169 := (if #21 0::Int #166)
-#172 := (if #22 #17 #169)
-#175 := (= #39 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#232 := (iff #178 #231)
-#229 := (iff #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#220 := (= #166 #219)
-#204 := (iff #121 #203)
-#201 := (iff #118 #200)
-#202 := [rewrite]: #201
-#191 := (iff #111 #198)
-#192 := [rewrite]: #191
-#205 := [monotonicity #192 #202]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#189 := (~ #178 #178)
-#188 := (~ #175 #175)
-#185 := [refl]: #188
-#190 := [nnf-pos #185]: #189
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (if #29 #40 #42)
-#44 := (if #21 0::Int #43)
-#45 := (if #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#181 := (iff #47 #178)
-#151 := (if #29 #40 #146)
-#154 := (if #21 0::Int #151)
-#157 := (if #22 #17 #154)
-#160 := (= #39 #157)
-#163 := (forall (vars (?v0 Int) (?v1 Int)) #160)
-#179 := (iff #163 #178)
-#176 := (iff #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#167 := (= #151 #166)
-#122 := (iff #29 #121)
-#119 := (iff #28 #118)
-#109 := (iff #25 #108)
-#110 := [rewrite]: #109
-#116 := (iff #27 #115)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117 #110]: #119
-#112 := (iff #26 #111)
-#105 := (iff #24 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#168 := [monotonicity #123]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#164 := (iff #47 #163)
-#161 := (iff #46 #160)
-#158 := (= #45 #157)
-#155 := (= #44 #154)
-#152 := (= #43 #151)
-#149 := (= #42 #146)
-#143 := (- #140)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #42 #143)
-#141 := (= #41 #140)
-#86 := (= #32 #85)
-#87 := [rewrite]: #86
-#83 := (= #31 #81)
-#84 := [rewrite]: #83
-#142 := [monotonicity #84 #87]: #141
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#182 := [trans #165 #180]: #181
-#139 := [asserted]: #47
-#183 := [mp #139 #182]: #178
-#186 := [mp~ #183 #190]: #178
-#234 := [mp #186 #233]: #231
-#265 := [mp #234 #264]: #262
-#753 := [mp #265 #752]: #748
-decl f6 :: Int
-#8 := f6
-#9 := (f4 f5 f6)
-#71 := (f3 #9 -1::Int)
-#74 := (= #71 0::Int)
-#77 := (not #74)
-#10 := 1::Int
-#11 := (- 1::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#78 := (iff #15 #77)
-#75 := (iff #14 #74)
-#72 := (= #12 #71)
-#69 := (= #11 -1::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#67 := [asserted]: #15
-#82 := [mp #67 #79]: #77
-#691 := (not #748)
-#520 := (or #691 #74)
-#402 := (* -1::Int -1::Int)
-#728 := (* -1::Int f6)
-#403 := (mod #728 #402)
-#735 := (+ #71 #403)
-#736 := (= #735 0::Int)
-#732 := (mod f6 -1::Int)
-#734 := (* -1::Int #732)
-#391 := (+ #71 #734)
-#521 := (= #391 0::Int)
-#404 := (<= -1::Int 0::Int)
-#417 := (>= f6 0::Int)
-#414 := (or #417 #404)
-#418 := (not #414)
-#413 := (<= f6 0::Int)
-#415 := (or #413 #404)
-#416 := (not #415)
-#397 := (or #416 #418)
-#737 := (if #397 #521 #736)
-#412 := (= f6 0::Int)
-#738 := (if #412 #74 #737)
-#411 := (= #71 f6)
-#327 := (= -1::Int 0::Int)
-#733 := (if #327 #411 #738)
-#522 := (or #691 #733)
-#676 := (iff #522 #520)
-#679 := (iff #520 #520)
-#680 := [rewrite]: #679
-#690 := (iff #733 #74)
-#687 := (if false #411 #74)
-#683 := (iff #687 #74)
-#689 := [rewrite]: #683
-#688 := (iff #733 #687)
-#685 := (iff #738 #74)
-#694 := (if #412 #74 #74)
-#542 := (iff #694 #74)
-#543 := [rewrite]: #542
-#700 := (iff #738 #694)
-#698 := (iff #737 #74)
-#695 := (if false #521 #74)
-#692 := (iff #695 #74)
-#693 := [rewrite]: #692
-#696 := (iff #737 #695)
-#702 := (iff #736 #74)
-#701 := (= #735 #71)
-#424 := (+ #71 0::Int)
-#704 := (= #424 #71)
-#419 := [rewrite]: #704
-#425 := (= #735 #424)
-#422 := (= #403 0::Int)
-#433 := (mod #728 1::Int)
-#708 := (= #433 0::Int)
-#712 := [rewrite]: #708
-#707 := (= #403 #433)
-#710 := (= #402 1::Int)
-#432 := [rewrite]: #710
-#711 := [monotonicity #432]: #707
-#423 := [trans #711 #712]: #422
-#703 := [monotonicity #423]: #425
-#705 := [trans #703 #419]: #701
-#706 := [monotonicity #705]: #702
-#333 := (iff #397 false)
-#714 := (or false false)
-#438 := (iff #714 false)
-#439 := [rewrite]: #438
-#436 := (iff #397 #714)
-#727 := (iff #418 false)
-#1 := true
-#380 := (not true)
-#718 := (iff #380 false)
-#719 := [rewrite]: #718
-#726 := (iff #418 #380)
-#365 := (iff #414 true)
-#716 := (or #417 true)
-#723 := (iff #716 true)
-#725 := [rewrite]: #723
-#722 := (iff #414 #716)
-#389 := (iff #404 true)
-#394 := [rewrite]: #389
-#360 := [monotonicity #394]: #722
-#366 := [trans #360 #725]: #365
-#724 := [monotonicity #366]: #726
-#713 := [trans #724 #719]: #727
-#720 := (iff #416 false)
-#381 := (iff #416 #380)
-#378 := (iff #415 true)
-#730 := (or #413 true)
-#374 := (iff #730 true)
-#715 := [rewrite]: #374
-#390 := (iff #415 #730)
-#731 := [monotonicity #394]: #390
-#379 := [trans #731 #715]: #378
-#717 := [monotonicity #379]: #381
-#721 := [trans #717 #719]: #720
-#437 := [monotonicity #721 #713]: #436
-#709 := [trans #437 #439]: #333
-#697 := [monotonicity #709 #706]: #696
-#699 := [trans #697 #693]: #698
-#541 := [monotonicity #699]: #700
-#686 := [trans #541 #543]: #685
-#739 := (iff #327 false)
-#729 := [rewrite]: #739
-#682 := [monotonicity #729 #686]: #688
-#684 := [trans #682 #689]: #690
-#677 := [monotonicity #684]: #676
-#678 := [trans #677 #680]: #676
-#523 := [quant-inst #8 #68]: #522
-#681 := [mp #523 #678]: #520
-[unit-resolution #681 #82 #753]: false
-unsat
-7b2dc6ed2136e8f88a408eac485e7ff01d341877 287 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#36 := (f4 f5 #15)
-#37 := (f3 #36 #17)
-#733 := (pattern #37)
-#8 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #17)
-#68 := (* -1::Int #15)
-#126 := (mod #68 #71)
-#241 := (+ #37 #126)
-#242 := (= #241 0::Int)
-#38 := (mod #15 #17)
-#238 := (* -1::Int #38)
-#239 := (+ #37 #238)
-#240 := (= #239 0::Int)
-#93 := (<= #17 0::Int)
-#100 := (>= #15 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #15 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#243 := (if #189 #240 #242)
-#237 := (= #37 0::Int)
-#19 := (= #15 0::Int)
-#244 := (if #19 #237 #243)
-#236 := (= #37 #15)
-#20 := (= #17 0::Int)
-#245 := (if #20 #236 #244)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #245)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#737 := (iff #248 #734)
-#735 := (iff #245 #245)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#132 := (* -1::Int #126)
-#205 := (if #189 #38 #132)
-#208 := (if #19 0::Int #205)
-#211 := (if #20 #15 #208)
-#214 := (= #37 #211)
-#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
-#249 := (iff #217 #248)
-#246 := (iff #214 #245)
-#247 := [rewrite]: #246
-#250 := [quant-intro #247]: #249
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#152 := (if #107 #38 #132)
-#155 := (if #19 0::Int #152)
-#158 := (if #20 #15 #155)
-#161 := (= #37 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#218 := (iff #164 #217)
-#215 := (iff #161 #214)
-#212 := (= #158 #211)
-#209 := (= #155 #208)
-#206 := (= #152 #205)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#207 := [monotonicity #191]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [quant-intro #216]: #218
-#175 := (~ #164 #164)
-#174 := (~ #161 #161)
-#171 := [refl]: #174
-#176 := [nnf-pos #171]: #175
-#30 := (- #17)
-#29 := (- #15)
-#39 := (mod #29 #30)
-#40 := (- #39)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#41 := (if #27 #38 #40)
-#42 := (if #19 0::Int #41)
-#43 := (if #20 #15 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#167 := (iff #45 #164)
-#137 := (if #27 #38 #132)
-#140 := (if #19 0::Int #137)
-#143 := (if #20 #15 #140)
-#146 := (= #37 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#165 := (iff #149 #164)
-#162 := (iff #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#108 := (iff #27 #107)
-#105 := (iff #26 #104)
-#95 := (iff #23 #94)
-#96 := [rewrite]: #95
-#102 := (iff #25 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #24 #97)
-#91 := (iff #22 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#154 := [monotonicity #109]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#150 := (iff #45 #149)
-#147 := (iff #44 #146)
-#144 := (= #43 #143)
-#141 := (= #42 #140)
-#138 := (= #41 #137)
-#135 := (= #40 #132)
-#129 := (- #126)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #40 #129)
-#127 := (= #39 #126)
-#72 := (= #30 #71)
-#73 := [rewrite]: #72
-#69 := (= #29 #68)
-#70 := [rewrite]: #69
-#128 := [monotonicity #70 #73]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#168 := [trans #151 #166]: #167
-#125 := [asserted]: #45
-#169 := [mp #125 #168]: #164
-#172 := [mp~ #169 #176]: #164
-#220 := [mp #172 #219]: #217
-#251 := [mp #220 #250]: #248
-#739 := [mp #251 #738]: #734
-#10 := 3::Int
-#9 := (f4 f5 0::Int)
-#11 := (f3 #9 3::Int)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#658 := (not #734)
-#560 := (or #658 #12)
-#714 := (* -1::Int 3::Int)
-#507 := (* -1::Int 0::Int)
-#388 := (mod #507 #714)
-#389 := (+ #11 #388)
-#721 := (= #389 0::Int)
-#383 := (mod 0::Int 3::Int)
-#718 := (* -1::Int #383)
-#720 := (+ #11 #718)
-#377 := (= #720 0::Int)
-#399 := (<= 3::Int 0::Int)
-#402 := (>= 0::Int 0::Int)
-#403 := (or #402 #399)
-#400 := (not #403)
-#398 := (<= 0::Int 0::Int)
-#390 := (or #398 #399)
-#401 := (not #390)
-#404 := (or #401 #400)
-#722 := (if #404 #377 #721)
-#397 := (= 0::Int 0::Int)
-#723 := (if #397 #12 #722)
-#313 := (= 3::Int 0::Int)
-#724 := (if #313 #12 #723)
-#655 := (or #658 #724)
-#659 := (iff #655 #560)
-#559 := (iff #560 #560)
-#561 := [rewrite]: #559
-#551 := (iff #724 #12)
-#669 := (if false #12 #12)
-#670 := (iff #669 #12)
-#677 := [rewrite]: #670
-#549 := (iff #724 #669)
-#664 := (iff #723 #12)
-#1 := true
-#509 := (if true #12 #12)
-#665 := (iff #509 #12)
-#666 := [rewrite]: #665
-#662 := (iff #723 #509)
-#506 := (iff #722 #12)
-#675 := (iff #722 #669)
-#674 := (iff #721 #12)
-#672 := (= #389 #11)
-#411 := (+ #11 0::Int)
-#405 := (= #411 #11)
-#687 := [rewrite]: #405
-#529 := (= #389 #411)
-#527 := (= #388 0::Int)
-#682 := -3::Int
-#679 := (mod 0::Int -3::Int)
-#680 := (= #679 0::Int)
-#686 := [rewrite]: #680
-#684 := (= #388 #679)
-#683 := (= #714 -3::Int)
-#678 := [rewrite]: #683
-#698 := (= #507 0::Int)
-#408 := [rewrite]: #698
-#685 := [monotonicity #408 #678]: #684
-#528 := [trans #685 #686]: #527
-#671 := [monotonicity #528]: #529
-#673 := [trans #671 #687]: #672
-#668 := [monotonicity #673]: #674
-#692 := (iff #377 #12)
-#691 := (= #720 #11)
-#689 := (= #720 #411)
-#409 := (= #718 0::Int)
-#697 := (= #718 #507)
-#419 := (= #383 0::Int)
-#693 := [rewrite]: #419
-#694 := [monotonicity #693]: #697
-#410 := [trans #694 #408]: #409
-#690 := [monotonicity #410]: #689
-#688 := [trans #690 #687]: #691
-#681 := [monotonicity #688]: #692
-#696 := (iff #404 false)
-#423 := (or false false)
-#319 := (iff #423 false)
-#695 := [rewrite]: #319
-#424 := (iff #404 #423)
-#700 := (iff #400 false)
-#704 := (not true)
-#707 := (iff #704 false)
-#702 := [rewrite]: #707
-#713 := (iff #400 #704)
-#712 := (iff #403 true)
-#360 := (or true false)
-#365 := (iff #360 true)
-#366 := [rewrite]: #365
-#351 := (iff #403 #360)
-#376 := (iff #399 false)
-#717 := [rewrite]: #376
-#709 := (iff #402 true)
-#711 := [rewrite]: #709
-#352 := [monotonicity #711 #717]: #351
-#710 := [trans #352 #366]: #712
-#699 := [monotonicity #710]: #713
-#422 := [trans #699 #702]: #700
-#708 := (iff #401 false)
-#705 := (iff #401 #704)
-#367 := (iff #390 true)
-#701 := (iff #390 #360)
-#380 := (iff #398 true)
-#716 := [rewrite]: #380
-#364 := [monotonicity #716 #717]: #701
-#703 := [trans #364 #366]: #367
-#706 := [monotonicity #703]: #705
-#346 := [trans #706 #702]: #708
-#425 := [monotonicity #346 #422]: #424
-#418 := [trans #425 #695]: #696
-#676 := [monotonicity #418 #681 #668]: #675
-#508 := [trans #676 #677]: #506
-#715 := (iff #397 true)
-#375 := [rewrite]: #715
-#663 := [monotonicity #375 #508]: #662
-#667 := [trans #663 #666]: #664
-#719 := (iff #313 false)
-#725 := [rewrite]: #719
-#550 := [monotonicity #725 #667]: #549
-#510 := [trans #550 #677]: #551
-#544 := [monotonicity #510]: #659
-#562 := [trans #544 #561]: #659
-#656 := [quant-inst #8 #10]: #655
-#555 := [mp #656 #562]: #560
-[unit-resolution #555 #65 #739]: false
-unsat
-022cbf4beb2e566dadff63f0d8408936ecfe6766 300 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#747 := (pattern #38)
-#8 := 0::Int
-#80 := -1::Int
-#85 := (* -1::Int #18)
-#82 := (* -1::Int #16)
-#140 := (mod #82 #85)
-#255 := (+ #38 #140)
-#256 := (= #255 0::Int)
-#39 := (mod #16 #18)
-#252 := (* -1::Int #39)
-#253 := (+ #38 #252)
-#254 := (= #253 0::Int)
-#107 := (<= #18 0::Int)
-#114 := (>= #16 0::Int)
-#199 := (or #114 #107)
-#200 := (not #199)
-#103 := (<= #16 0::Int)
-#197 := (or #103 #107)
-#198 := (not #197)
-#203 := (or #198 #200)
-#257 := (if #203 #254 #256)
-#251 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#258 := (if #20 #251 #257)
-#250 := (= #38 #16)
-#21 := (= #18 0::Int)
-#259 := (if #21 #250 #258)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #259)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#751 := (iff #262 #748)
-#749 := (iff #259 #259)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#146 := (* -1::Int #140)
-#219 := (if #203 #39 #146)
-#222 := (if #20 0::Int #219)
-#225 := (if #21 #16 #222)
-#228 := (= #38 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#108 := (not #107)
-#115 := (not #114)
-#118 := (and #115 #108)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#166 := (if #121 #39 #146)
-#169 := (if #20 0::Int #166)
-#172 := (if #21 #16 #169)
-#175 := (= #38 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#232 := (iff #178 #231)
-#229 := (iff #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#220 := (= #166 #219)
-#204 := (iff #121 #203)
-#201 := (iff #118 #200)
-#202 := [rewrite]: #201
-#191 := (iff #111 #198)
-#192 := [rewrite]: #191
-#205 := [monotonicity #192 #202]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#189 := (~ #178 #178)
-#188 := (~ #175 #175)
-#185 := [refl]: #188
-#190 := [nnf-pos #185]: #189
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#181 := (iff #46 #178)
-#151 := (if #28 #39 #146)
-#154 := (if #20 0::Int #151)
-#157 := (if #21 #16 #154)
-#160 := (= #38 #157)
-#163 := (forall (vars (?v0 Int) (?v1 Int)) #160)
-#179 := (iff #163 #178)
-#176 := (iff #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#167 := (= #151 #166)
-#122 := (iff #28 #121)
-#119 := (iff #27 #118)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#116 := (iff #26 #115)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117 #110]: #119
-#112 := (iff #25 #111)
-#105 := (iff #23 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#168 := [monotonicity #123]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#164 := (iff #46 #163)
-#161 := (iff #45 #160)
-#158 := (= #44 #157)
-#155 := (= #43 #154)
-#152 := (= #42 #151)
-#149 := (= #41 #146)
-#143 := (- #140)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #41 #143)
-#141 := (= #40 #140)
-#86 := (= #31 #85)
-#87 := [rewrite]: #86
-#83 := (= #30 #82)
-#84 := [rewrite]: #83
-#142 := [monotonicity #84 #87]: #141
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#182 := [trans #165 #180]: #181
-#139 := [asserted]: #46
-#183 := [mp #139 #182]: #178
-#186 := [mp~ #183 #190]: #178
-#234 := [mp #186 #233]: #231
-#265 := [mp #234 #264]: #262
-#753 := [mp #265 #752]: #748
-#67 := -3::Int
-#9 := (f4 f5 0::Int)
-#70 := (f3 #9 -3::Int)
-#73 := (= #70 0::Int)
-#76 := (not #73)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#13 := (= #12 0::Int)
-#14 := (not #13)
-#77 := (iff #14 #76)
-#74 := (iff #13 #73)
-#71 := (= #12 #70)
-#68 := (= #11 -3::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #14
-#81 := [mp #66 #78]: #76
-#524 := (not #748)
-#672 := (or #524 #73)
-#728 := (* -1::Int -3::Int)
-#521 := (* -1::Int 0::Int)
-#402 := (mod #521 #728)
-#403 := (+ #70 #402)
-#735 := (= #403 0::Int)
-#397 := (mod 0::Int -3::Int)
-#732 := (* -1::Int #397)
-#734 := (+ #70 #732)
-#391 := (= #734 0::Int)
-#413 := (<= -3::Int 0::Int)
-#416 := (>= 0::Int 0::Int)
-#417 := (or #416 #413)
-#414 := (not #417)
-#412 := (<= 0::Int 0::Int)
-#404 := (or #412 #413)
-#415 := (not #404)
-#418 := (or #415 #414)
-#736 := (if #418 #391 #735)
-#411 := (= 0::Int 0::Int)
-#737 := (if #411 #73 #736)
-#327 := (= -3::Int 0::Int)
-#738 := (if #327 #73 #737)
-#574 := (or #524 #738)
-#670 := (iff #574 #672)
-#558 := (iff #672 #672)
-#573 := [rewrite]: #558
-#564 := (iff #738 #73)
-#682 := (if false #73 #73)
-#690 := (iff #682 #73)
-#684 := [rewrite]: #690
-#681 := (iff #738 #682)
-#680 := (iff #737 #73)
-#1 := true
-#522 := (if true #73 #73)
-#677 := (iff #522 #73)
-#679 := [rewrite]: #677
-#523 := (iff #737 #522)
-#691 := (iff #736 #73)
-#683 := (iff #736 #682)
-#687 := (iff #735 #73)
-#685 := (= #403 #70)
-#425 := (+ #70 0::Int)
-#419 := (= #425 #70)
-#701 := [rewrite]: #419
-#542 := (= #403 #425)
-#700 := (= #402 0::Int)
-#692 := (mod 0::Int 3::Int)
-#699 := (= #692 0::Int)
-#694 := [rewrite]: #699
-#693 := (= #402 #692)
-#696 := (= #728 3::Int)
-#697 := [rewrite]: #696
-#712 := (= #521 0::Int)
-#422 := [rewrite]: #712
-#698 := [monotonicity #422 #697]: #693
-#541 := [trans #698 #694]: #700
-#543 := [monotonicity #541]: #542
-#686 := [trans #543 #701]: #685
-#688 := [monotonicity #686]: #687
-#706 := (iff #391 #73)
-#705 := (= #734 #70)
-#703 := (= #734 #425)
-#423 := (= #732 0::Int)
-#711 := (= #732 #521)
-#433 := (= #397 0::Int)
-#707 := [rewrite]: #433
-#708 := [monotonicity #707]: #711
-#424 := [trans #708 #422]: #423
-#704 := [monotonicity #424]: #703
-#702 := [trans #704 #701]: #705
-#695 := [monotonicity #702]: #706
-#710 := (iff #418 false)
-#437 := (or false false)
-#333 := (iff #437 false)
-#709 := [rewrite]: #333
-#438 := (iff #418 #437)
-#714 := (iff #414 false)
-#718 := (not true)
-#721 := (iff #718 false)
-#716 := [rewrite]: #721
-#727 := (iff #414 #718)
-#726 := (iff #417 true)
-#374 := (or true true)
-#379 := (iff #374 true)
-#380 := [rewrite]: #379
-#365 := (iff #417 #374)
-#390 := (iff #413 true)
-#731 := [rewrite]: #390
-#723 := (iff #416 true)
-#725 := [rewrite]: #723
-#366 := [monotonicity #725 #731]: #365
-#724 := [trans #366 #380]: #726
-#713 := [monotonicity #724]: #727
-#436 := [trans #713 #716]: #714
-#722 := (iff #415 false)
-#719 := (iff #415 #718)
-#381 := (iff #404 true)
-#715 := (iff #404 #374)
-#394 := (iff #412 true)
-#730 := [rewrite]: #394
-#378 := [monotonicity #730 #731]: #715
-#717 := [trans #378 #380]: #381
-#720 := [monotonicity #717]: #719
-#360 := [trans #720 #716]: #722
-#439 := [monotonicity #360 #436]: #438
-#432 := [trans #439 #709]: #710
-#689 := [monotonicity #432 #695 #688]: #683
-#520 := [trans #689 #684]: #691
-#729 := (iff #411 true)
-#389 := [rewrite]: #729
-#676 := [monotonicity #389 #520]: #523
-#678 := [trans #676 #679]: #680
-#733 := (iff #327 false)
-#739 := [rewrite]: #733
-#563 := [monotonicity #739 #678]: #681
-#565 := [trans #563 #684]: #564
-#673 := [monotonicity #565]: #670
-#575 := [trans #673 #573]: #670
-#669 := [quant-inst #8 #67]: #574
-#576 := [mp #669 #575]: #672
-[unit-resolution #576 #81 #753]: false
-unsat
-2fdc36e59c59da56b5dc6125f7d3f633e77a3d9e 313 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #15)
-#38 := (f3 #37 #17)
-#733 := (pattern #38)
-#19 := 0::Int
-#68 := -1::Int
-#72 := (* -1::Int #17)
-#69 := (* -1::Int #15)
-#127 := (mod #69 #72)
-#242 := (+ #38 #127)
-#243 := (= #242 0::Int)
-#39 := (mod #15 #17)
-#239 := (* -1::Int #39)
-#240 := (+ #38 #239)
-#241 := (= #240 0::Int)
-#94 := (<= #17 0::Int)
-#101 := (>= #15 0::Int)
-#186 := (or #101 #94)
-#187 := (not #186)
-#90 := (<= #15 0::Int)
-#184 := (or #90 #94)
-#185 := (not #184)
-#190 := (or #185 #187)
-#244 := (if #190 #241 #243)
-#238 := (= #38 0::Int)
-#20 := (= #15 0::Int)
-#245 := (if #20 #238 #244)
-#237 := (= #38 #15)
-#21 := (= #17 0::Int)
-#246 := (if #21 #237 #245)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #246)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#737 := (iff #249 #734)
-#735 := (iff #246 #246)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#133 := (* -1::Int #127)
-#206 := (if #190 #39 #133)
-#209 := (if #20 0::Int #206)
-#212 := (if #21 #15 #209)
-#215 := (= #38 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#250 := (iff #218 #249)
-#247 := (iff #215 #246)
-#248 := [rewrite]: #247
-#251 := [quant-intro #248]: #250
-#95 := (not #94)
-#102 := (not #101)
-#105 := (and #102 #95)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (if #108 #39 #133)
-#156 := (if #20 0::Int #153)
-#159 := (if #21 #15 #156)
-#162 := (= #38 #159)
-#165 := (forall (vars (?v0 Int) (?v1 Int)) #162)
-#219 := (iff #165 #218)
-#216 := (iff #162 #215)
-#213 := (= #159 #212)
-#210 := (= #156 #209)
-#207 := (= #153 #206)
-#191 := (iff #108 #190)
-#188 := (iff #105 #187)
-#189 := [rewrite]: #188
-#178 := (iff #98 #185)
-#179 := [rewrite]: #178
-#192 := [monotonicity #179 #189]: #191
-#208 := [monotonicity #192]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#176 := (~ #165 #165)
-#175 := (~ #162 #162)
-#172 := [refl]: #175
-#177 := [nnf-pos #172]: #176
-#31 := (- #17)
-#30 := (- #15)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #15 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#168 := (iff #46 #165)
-#138 := (if #28 #39 #133)
-#141 := (if #20 0::Int #138)
-#144 := (if #21 #15 #141)
-#147 := (= #38 #144)
-#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #28 #108)
-#106 := (iff #27 #105)
-#96 := (iff #24 #95)
-#97 := [rewrite]: #96
-#103 := (iff #26 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104 #97]: #106
-#99 := (iff #25 #98)
-#92 := (iff #23 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #46 #150)
-#148 := (iff #45 #147)
-#145 := (= #44 #144)
-#142 := (= #43 #141)
-#139 := (= #42 #138)
-#136 := (= #41 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #41 #130)
-#128 := (= #40 #127)
-#73 := (= #31 #72)
-#74 := [rewrite]: #73
-#70 := (= #30 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #46
-#170 := [mp #126 #169]: #165
-#173 := [mp~ #170 #177]: #165
-#221 := [mp #173 #220]: #218
-#252 := [mp #221 #251]: #249
-#739 := [mp #252 #738]: #734
-#8 := 1::Int
-#10 := 3::Int
-#9 := (f4 f5 1::Int)
-#11 := (f3 #9 3::Int)
-#12 := (= #11 1::Int)
-#13 := (not #12)
-#66 := [asserted]: #13
-#652 := (not #734)
-#653 := (or #652 #12)
-#388 := (* -1::Int 3::Int)
-#714 := (* -1::Int 1::Int)
-#389 := (mod #714 #388)
-#721 := (+ #11 #389)
-#722 := (= #721 0::Int)
-#718 := (mod 1::Int 3::Int)
-#720 := (* -1::Int #718)
-#377 := (+ #11 #720)
-#507 := (= #377 0::Int)
-#390 := (<= 3::Int 0::Int)
-#403 := (>= 1::Int 0::Int)
-#400 := (or #403 #390)
-#404 := (not #400)
-#399 := (<= 1::Int 0::Int)
-#401 := (or #399 #390)
-#402 := (not #401)
-#383 := (or #402 #404)
-#723 := (if #383 #507 #722)
-#398 := (= #11 0::Int)
-#397 := (= 1::Int 0::Int)
-#724 := (if #397 #398 #723)
-#313 := (= 3::Int 0::Int)
-#719 := (if #313 #12 #724)
-#649 := (or #652 #719)
-#643 := (iff #649 #653)
-#645 := (iff #653 #653)
-#646 := [rewrite]: #645
-#641 := (iff #719 #12)
-#661 := (if false #12 #12)
-#642 := (iff #661 #12)
-#639 := [rewrite]: #642
-#648 := (iff #719 #661)
-#660 := (iff #724 #12)
-#563 := (if false #398 #12)
-#566 := (iff #563 #12)
-#567 := [rewrite]: #566
-#564 := (iff #724 #563)
-#562 := (iff #723 #12)
-#550 := -2::Int
-#551 := (= #11 -2::Int)
-#1 := true
-#656 := (if true #12 #551)
-#559 := (iff #656 #12)
-#561 := [rewrite]: #559
-#659 := (iff #723 #656)
-#560 := (iff #722 #551)
-#273 := 2::Int
-#509 := (+ 2::Int #11)
-#664 := (= #509 0::Int)
-#510 := (iff #664 #551)
-#658 := [rewrite]: #510
-#667 := (iff #722 #664)
-#665 := (= #721 #509)
-#677 := (+ #11 2::Int)
-#662 := (= #677 #509)
-#663 := [rewrite]: #662
-#506 := (= #721 #677)
-#676 := (= #389 2::Int)
-#529 := -3::Int
-#673 := (mod -1::Int -3::Int)
-#669 := (= #673 2::Int)
-#675 := [rewrite]: #669
-#674 := (= #389 #673)
-#671 := (= #388 -3::Int)
-#672 := [rewrite]: #671
-#411 := (= #714 -1::Int)
-#689 := [rewrite]: #411
-#668 := [monotonicity #689 #672]: #674
-#670 := [trans #668 #675]: #676
-#508 := [monotonicity #670]: #506
-#666 := [trans #508 #663]: #665
-#549 := [monotonicity #666]: #667
-#655 := [trans #549 #658]: #560
-#527 := (iff #507 #12)
-#692 := (+ -1::Int #11)
-#679 := (= #692 0::Int)
-#680 := (iff #679 #12)
-#686 := [rewrite]: #680
-#684 := (iff #507 #679)
-#683 := (= #377 #692)
-#687 := (+ #11 -1::Int)
-#681 := (= #687 #692)
-#682 := [rewrite]: #681
-#691 := (= #377 #687)
-#690 := (= #720 -1::Int)
-#409 := (= #720 #714)
-#698 := (= #718 1::Int)
-#408 := [rewrite]: #698
-#410 := [monotonicity #408]: #409
-#405 := [trans #410 #689]: #690
-#688 := [monotonicity #405]: #691
-#678 := [trans #688 #682]: #683
-#685 := [monotonicity #678]: #684
-#528 := [trans #685 #686]: #527
-#697 := (iff #383 true)
-#352 := (or true false)
-#713 := (iff #352 true)
-#699 := [rewrite]: #713
-#419 := (iff #383 #352)
-#696 := (iff #404 false)
-#423 := (not true)
-#319 := (iff #423 false)
-#695 := [rewrite]: #319
-#424 := (iff #404 #423)
-#700 := (iff #400 true)
-#712 := (iff #400 #352)
-#717 := (iff #390 false)
-#360 := [rewrite]: #717
-#711 := (iff #403 true)
-#351 := [rewrite]: #711
-#710 := [monotonicity #351 #360]: #712
-#422 := [trans #710 #699]: #700
-#425 := [monotonicity #422]: #424
-#418 := [trans #425 #695]: #696
-#346 := (iff #402 true)
-#705 := (not false)
-#702 := (iff #705 true)
-#708 := [rewrite]: #702
-#706 := (iff #402 #705)
-#703 := (iff #401 false)
-#701 := (or false false)
-#366 := (iff #701 false)
-#367 := [rewrite]: #366
-#364 := (iff #401 #701)
-#716 := (iff #399 false)
-#376 := [rewrite]: #716
-#365 := [monotonicity #376 #360]: #364
-#704 := [trans #365 #367]: #703
-#707 := [monotonicity #704]: #706
-#709 := [trans #707 #708]: #346
-#693 := [monotonicity #709 #418]: #419
-#694 := [trans #693 #699]: #697
-#544 := [monotonicity #694 #528 #655]: #659
-#555 := [trans #544 #561]: #562
-#375 := (iff #397 false)
-#380 := [rewrite]: #375
-#565 := [monotonicity #380 #555]: #564
-#657 := [trans #565 #567]: #660
-#725 := (iff #313 false)
-#715 := [rewrite]: #725
-#650 := [monotonicity #715 #657]: #648
-#651 := [trans #650 #639]: #641
-#644 := [monotonicity #651]: #643
-#640 := [trans #644 #646]: #643
-#654 := [quant-inst #8 #10]: #649
-#647 := [mp #654 #640]: #653
-[unit-resolution #647 #66 #739]: false
-unsat
-4ee9cc2bcab1ec5264a5fe09246eabd52d90f088 288 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#36 := (f4 f5 #15)
-#37 := (f3 #36 #17)
-#733 := (pattern #37)
-#11 := 0::Int
-#67 := -1::Int
-#71 := (* -1::Int #17)
-#68 := (* -1::Int #15)
-#126 := (mod #68 #71)
-#241 := (+ #37 #126)
-#242 := (= #241 0::Int)
-#38 := (mod #15 #17)
-#238 := (* -1::Int #38)
-#239 := (+ #37 #238)
-#240 := (= #239 0::Int)
-#93 := (<= #17 0::Int)
-#100 := (>= #15 0::Int)
-#185 := (or #100 #93)
-#186 := (not #185)
-#89 := (<= #15 0::Int)
-#183 := (or #89 #93)
-#184 := (not #183)
-#189 := (or #184 #186)
-#243 := (if #189 #240 #242)
-#237 := (= #37 0::Int)
-#19 := (= #15 0::Int)
-#244 := (if #19 #237 #243)
-#236 := (= #37 #15)
-#20 := (= #17 0::Int)
-#245 := (if #20 #236 #244)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #245)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#737 := (iff #248 #734)
-#735 := (iff #245 #245)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#132 := (* -1::Int #126)
-#205 := (if #189 #38 #132)
-#208 := (if #19 0::Int #205)
-#211 := (if #20 #15 #208)
-#214 := (= #37 #211)
-#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
-#249 := (iff #217 #248)
-#246 := (iff #214 #245)
-#247 := [rewrite]: #246
-#250 := [quant-intro #247]: #249
-#94 := (not #93)
-#101 := (not #100)
-#104 := (and #101 #94)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#152 := (if #107 #38 #132)
-#155 := (if #19 0::Int #152)
-#158 := (if #20 #15 #155)
-#161 := (= #37 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#218 := (iff #164 #217)
-#215 := (iff #161 #214)
-#212 := (= #158 #211)
-#209 := (= #155 #208)
-#206 := (= #152 #205)
-#190 := (iff #107 #189)
-#187 := (iff #104 #186)
-#188 := [rewrite]: #187
-#177 := (iff #97 #184)
-#178 := [rewrite]: #177
-#191 := [monotonicity #178 #188]: #190
-#207 := [monotonicity #191]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [quant-intro #216]: #218
-#175 := (~ #164 #164)
-#174 := (~ #161 #161)
-#171 := [refl]: #174
-#176 := [nnf-pos #171]: #175
-#30 := (- #17)
-#29 := (- #15)
-#39 := (mod #29 #30)
-#40 := (- #39)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#41 := (if #27 #38 #40)
-#42 := (if #19 0::Int #41)
-#43 := (if #20 #15 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#167 := (iff #45 #164)
-#137 := (if #27 #38 #132)
-#140 := (if #19 0::Int #137)
-#143 := (if #20 #15 #140)
-#146 := (= #37 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#165 := (iff #149 #164)
-#162 := (iff #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#108 := (iff #27 #107)
-#105 := (iff #26 #104)
-#95 := (iff #23 #94)
-#96 := [rewrite]: #95
-#102 := (iff #25 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103 #96]: #105
-#98 := (iff #24 #97)
-#91 := (iff #22 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#154 := [monotonicity #109]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#150 := (iff #45 #149)
-#147 := (iff #44 #146)
-#144 := (= #43 #143)
-#141 := (= #42 #140)
-#138 := (= #41 #137)
-#135 := (= #40 #132)
-#129 := (- #126)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #40 #129)
-#127 := (= #39 #126)
-#72 := (= #30 #71)
-#73 := [rewrite]: #72
-#69 := (= #29 #68)
-#70 := [rewrite]: #69
-#128 := [monotonicity #70 #73]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#168 := [trans #151 #166]: #167
-#125 := [asserted]: #45
-#169 := [mp #125 #168]: #164
-#172 := [mp~ #169 #176]: #164
-#220 := [mp #172 #219]: #217
-#251 := [mp #220 #250]: #248
-#739 := [mp #251 #738]: #734
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#10 := (f3 #9 3::Int)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#65 := [asserted]: #13
-#560 := (not #734)
-#655 := (or #560 #12)
-#377 := (* -1::Int 3::Int)
-#507 := (mod #377 #377)
-#714 := (+ #10 #507)
-#388 := (= #714 0::Int)
-#404 := (mod 3::Int 3::Int)
-#383 := (* -1::Int #404)
-#718 := (+ #10 #383)
-#720 := (= #718 0::Int)
-#398 := (<= 3::Int 0::Int)
-#401 := (>= 3::Int 0::Int)
-#402 := (or #401 #398)
-#403 := (not #402)
-#399 := (or #398 #398)
-#390 := (not #399)
-#400 := (or #390 #403)
-#389 := (if #400 #720 #388)
-#313 := (= 3::Int 0::Int)
-#721 := (if #313 #12 #389)
-#397 := (= #10 3::Int)
-#722 := (if #313 #397 #721)
-#656 := (or #560 #722)
-#544 := (iff #656 #655)
-#561 := (iff #655 #655)
-#562 := [rewrite]: #561
-#510 := (iff #722 #12)
-#664 := (if false #397 #12)
-#550 := (iff #664 #12)
-#551 := [rewrite]: #550
-#667 := (iff #722 #664)
-#665 := (iff #721 #12)
-#506 := (if false #12 #12)
-#662 := (iff #506 #12)
-#663 := [rewrite]: #662
-#508 := (iff #721 #506)
-#670 := (iff #389 #12)
-#1 := true
-#674 := (if true #12 #12)
-#675 := (iff #674 #12)
-#676 := [rewrite]: #675
-#668 := (iff #389 #674)
-#672 := (iff #388 #12)
-#529 := (= #714 #10)
-#409 := (+ #10 0::Int)
-#689 := (= #409 #10)
-#690 := [rewrite]: #689
-#527 := (= #714 #409)
-#680 := (= #507 0::Int)
-#692 := -3::Int
-#683 := (mod -3::Int -3::Int)
-#684 := (= #683 0::Int)
-#685 := [rewrite]: #684
-#678 := (= #507 #683)
-#681 := (= #377 -3::Int)
-#682 := [rewrite]: #681
-#679 := [monotonicity #682 #682]: #678
-#686 := [trans #679 #685]: #680
-#528 := [monotonicity #686]: #527
-#671 := [trans #528 #690]: #529
-#673 := [monotonicity #671]: #672
-#691 := (iff #720 #12)
-#405 := (= #718 #10)
-#410 := (= #718 #409)
-#698 := (= #383 0::Int)
-#418 := (* -1::Int 0::Int)
-#697 := (= #418 0::Int)
-#694 := [rewrite]: #697
-#419 := (= #383 #418)
-#695 := (= #404 0::Int)
-#696 := [rewrite]: #695
-#693 := [monotonicity #696]: #419
-#408 := [trans #693 #694]: #698
-#411 := [monotonicity #408]: #410
-#687 := [trans #411 #690]: #405
-#688 := [monotonicity #687]: #691
-#425 := (iff #400 true)
-#707 := (or true false)
-#346 := (iff #707 true)
-#709 := [rewrite]: #346
-#423 := (iff #400 #707)
-#700 := (iff #403 false)
-#352 := (not true)
-#713 := (iff #352 false)
-#699 := [rewrite]: #713
-#712 := (iff #403 #352)
-#711 := (iff #402 true)
-#702 := (iff #402 #707)
-#719 := (iff #398 false)
-#725 := [rewrite]: #719
-#705 := (iff #401 true)
-#706 := [rewrite]: #705
-#708 := [monotonicity #706 #725]: #702
-#351 := [trans #708 #709]: #711
-#710 := [monotonicity #351]: #712
-#422 := [trans #710 #699]: #700
-#703 := (iff #390 true)
-#701 := (not false)
-#366 := (iff #701 true)
-#367 := [rewrite]: #366
-#364 := (iff #390 #701)
-#717 := (iff #399 false)
-#715 := (or false false)
-#716 := (iff #715 false)
-#376 := [rewrite]: #716
-#375 := (iff #399 #715)
-#380 := [monotonicity #725 #725]: #375
-#360 := [trans #380 #376]: #717
-#365 := [monotonicity #360]: #364
-#704 := [trans #365 #367]: #703
-#424 := [monotonicity #704 #422]: #423
-#319 := [trans #424 #709]: #425
-#669 := [monotonicity #319 #688 #673]: #668
-#677 := [trans #669 #676]: #670
-#723 := (iff #313 false)
-#724 := [rewrite]: #723
-#509 := [monotonicity #724 #677]: #508
-#666 := [trans #509 #663]: #665
-#549 := [monotonicity #724 #666]: #667
-#658 := [trans #549 #551]: #510
-#559 := [monotonicity #658]: #544
-#555 := [trans #559 #562]: #544
-#659 := [quant-inst #8 #8]: #656
-#563 := [mp #659 #555]: #655
-[unit-resolution #563 #65 #739]: false
-unsat
-fcf9d10e8b8381a23681610013bef54bc4a13a37 319 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#38 := (f4 f5 #16)
-#39 := (f3 #38 #18)
-#733 := (pattern #39)
-#20 := 0::Int
-#69 := -1::Int
-#73 := (* -1::Int #18)
-#70 := (* -1::Int #16)
-#128 := (mod #70 #73)
-#243 := (+ #39 #128)
-#244 := (= #243 0::Int)
-#40 := (mod #16 #18)
-#240 := (* -1::Int #40)
-#241 := (+ #39 #240)
-#242 := (= #241 0::Int)
-#95 := (<= #18 0::Int)
-#102 := (>= #16 0::Int)
-#187 := (or #102 #95)
-#188 := (not #187)
-#91 := (<= #16 0::Int)
-#185 := (or #91 #95)
-#186 := (not #185)
-#191 := (or #186 #188)
-#245 := (if #191 #242 #244)
-#239 := (= #39 0::Int)
-#21 := (= #16 0::Int)
-#246 := (if #21 #239 #245)
-#238 := (= #39 #16)
-#22 := (= #18 0::Int)
-#247 := (if #22 #238 #246)
-#734 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #733) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#737 := (iff #250 #734)
-#735 := (iff #247 #247)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#134 := (* -1::Int #128)
-#207 := (if #191 #40 #134)
-#210 := (if #21 0::Int #207)
-#213 := (if #22 #16 #210)
-#216 := (= #39 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#96 := (not #95)
-#103 := (not #102)
-#106 := (and #103 #96)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#154 := (if #109 #40 #134)
-#157 := (if #21 0::Int #154)
-#160 := (if #22 #16 #157)
-#163 := (= #39 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#220 := (iff #166 #219)
-#217 := (iff #163 #216)
-#214 := (= #160 #213)
-#211 := (= #157 #210)
-#208 := (= #154 #207)
-#192 := (iff #109 #191)
-#189 := (iff #106 #188)
-#190 := [rewrite]: #189
-#179 := (iff #99 #186)
-#180 := [rewrite]: #179
-#193 := [monotonicity #180 #190]: #192
-#209 := [monotonicity #193]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#177 := (~ #166 #166)
-#176 := (~ #163 #163)
-#173 := [refl]: #176
-#178 := [nnf-pos #173]: #177
-#32 := (- #18)
-#31 := (- #16)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (if #29 #40 #42)
-#44 := (if #21 0::Int #43)
-#45 := (if #22 #16 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#169 := (iff #47 #166)
-#139 := (if #29 #40 #134)
-#142 := (if #21 0::Int #139)
-#145 := (if #22 #16 #142)
-#148 := (= #39 #145)
-#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
-#167 := (iff #151 #166)
-#164 := (iff #148 #163)
-#161 := (= #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#110 := (iff #29 #109)
-#107 := (iff #28 #106)
-#97 := (iff #25 #96)
-#98 := [rewrite]: #97
-#104 := (iff #27 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105 #98]: #107
-#100 := (iff #26 #99)
-#93 := (iff #24 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#156 := [monotonicity #111]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#152 := (iff #47 #151)
-#149 := (iff #46 #148)
-#146 := (= #45 #145)
-#143 := (= #44 #142)
-#140 := (= #43 #139)
-#137 := (= #42 #134)
-#131 := (- #128)
-#135 := (= #131 #134)
-#136 := [rewrite]: #135
-#132 := (= #42 #131)
-#129 := (= #41 #128)
-#74 := (= #32 #73)
-#75 := [rewrite]: #74
-#71 := (= #31 #70)
-#72 := [rewrite]: #71
-#130 := [monotonicity #72 #75]: #129
-#133 := [monotonicity #130]: #132
-#138 := [trans #133 #136]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
-#170 := [trans #153 #168]: #169
-#127 := [asserted]: #47
-#171 := [mp #127 #170]: #166
-#174 := [mp~ #171 #178]: #166
-#222 := [mp #174 #221]: #219
-#253 := [mp #222 #252]: #250
-#739 := [mp #253 #738]: #734
-#12 := 2::Int
-#10 := 3::Int
-#8 := 5::Int
-#9 := (f4 f5 5::Int)
-#11 := (f3 #9 3::Int)
-#13 := (= #11 2::Int)
-#14 := (not #13)
-#67 := [asserted]: #14
-#644 := (not #734)
-#645 := (or #644 #13)
-#389 := (* -1::Int 3::Int)
-#388 := (* -1::Int 5::Int)
-#721 := (mod #388 #389)
-#722 := (+ #11 #721)
-#723 := (= #722 0::Int)
-#720 := (mod 5::Int 3::Int)
-#377 := (* -1::Int #720)
-#507 := (+ #11 #377)
-#714 := (= #507 0::Int)
-#401 := (<= 3::Int 0::Int)
-#400 := (>= 5::Int 0::Int)
-#404 := (or #400 #401)
-#383 := (not #404)
-#390 := (<= 5::Int 0::Int)
-#402 := (or #390 #401)
-#403 := (not #402)
-#718 := (or #403 #383)
-#724 := (if #718 #714 #723)
-#399 := (= #11 0::Int)
-#398 := (= 5::Int 0::Int)
-#719 := (if #398 #399 #724)
-#397 := (= #11 5::Int)
-#313 := (= 3::Int 0::Int)
-#725 := (if #313 #397 #719)
-#646 := (or #644 #725)
-#647 := (iff #646 #645)
-#632 := (iff #645 #645)
-#634 := [rewrite]: #632
-#654 := (iff #725 #13)
-#641 := (if false #397 #13)
-#653 := (iff #641 #13)
-#649 := [rewrite]: #653
-#651 := (iff #725 #641)
-#642 := (iff #719 #13)
-#660 := (if false #399 #13)
-#648 := (iff #660 #13)
-#650 := [rewrite]: #648
-#657 := (iff #719 #660)
-#566 := (iff #724 #13)
-#656 := (= #11 -1::Int)
-#1 := true
-#562 := (if true #13 #656)
-#564 := (iff #562 #13)
-#565 := [rewrite]: #564
-#555 := (iff #724 #562)
-#559 := (iff #723 #656)
-#266 := 1::Int
-#667 := (+ 1::Int #11)
-#658 := (= #667 0::Int)
-#659 := (iff #658 #656)
-#544 := [rewrite]: #659
-#560 := (iff #723 #658)
-#551 := (= #722 #667)
-#665 := (+ #11 1::Int)
-#549 := (= #665 #667)
-#550 := [rewrite]: #549
-#666 := (= #722 #665)
-#662 := (= #721 1::Int)
-#669 := -3::Int
-#673 := -5::Int
-#670 := (mod -5::Int -3::Int)
-#508 := (= #670 1::Int)
-#509 := [rewrite]: #508
-#677 := (= #721 #670)
-#675 := (= #389 -3::Int)
-#676 := [rewrite]: #675
-#674 := (= #388 -5::Int)
-#668 := [rewrite]: #674
-#506 := [monotonicity #668 #676]: #677
-#663 := [trans #506 #509]: #662
-#664 := [monotonicity #663]: #666
-#510 := [trans #664 #550]: #551
-#655 := [monotonicity #510]: #560
-#561 := [trans #655 #544]: #559
-#671 := (iff #714 #13)
-#690 := -2::Int
-#683 := (+ -2::Int #11)
-#680 := (= #683 0::Int)
-#528 := (iff #680 #13)
-#529 := [rewrite]: #528
-#686 := (iff #714 #680)
-#684 := (= #507 #683)
-#692 := (+ #11 -2::Int)
-#678 := (= #692 #683)
-#679 := [rewrite]: #678
-#681 := (= #507 #692)
-#691 := (= #377 -2::Int)
-#410 := (* -1::Int 2::Int)
-#405 := (= #410 -2::Int)
-#687 := [rewrite]: #405
-#411 := (= #377 #410)
-#408 := (= #720 2::Int)
-#409 := [rewrite]: #408
-#689 := [monotonicity #409]: #411
-#688 := [trans #689 #687]: #691
-#682 := [monotonicity #688]: #681
-#685 := [trans #682 #679]: #684
-#527 := [monotonicity #685]: #686
-#672 := [trans #527 #529]: #671
-#694 := (iff #718 true)
-#712 := (or true false)
-#699 := (iff #712 true)
-#700 := [rewrite]: #699
-#693 := (iff #718 #712)
-#418 := (iff #383 false)
-#424 := (not true)
-#695 := (iff #424 false)
-#696 := [rewrite]: #695
-#425 := (iff #383 #424)
-#422 := (iff #404 true)
-#710 := (iff #404 #712)
-#360 := (iff #401 false)
-#701 := [rewrite]: #360
-#351 := (iff #400 true)
-#352 := [rewrite]: #351
-#713 := [monotonicity #352 #701]: #710
-#423 := [trans #713 #700]: #422
-#319 := [monotonicity #423]: #425
-#419 := [trans #319 #696]: #418
-#709 := (iff #403 true)
-#706 := (not false)
-#708 := (iff #706 true)
-#346 := [rewrite]: #708
-#707 := (iff #403 #706)
-#704 := (iff #402 false)
-#364 := (or false false)
-#367 := (iff #364 false)
-#703 := [rewrite]: #367
-#365 := (iff #402 #364)
-#376 := (iff #390 false)
-#717 := [rewrite]: #376
-#366 := [monotonicity #717 #701]: #365
-#705 := [trans #366 #703]: #704
-#702 := [monotonicity #705]: #707
-#711 := [trans #702 #346]: #709
-#697 := [monotonicity #711 #419]: #693
-#698 := [trans #697 #700]: #694
-#563 := [monotonicity #698 #672 #561]: #555
-#567 := [trans #563 #565]: #566
-#380 := (iff #398 false)
-#716 := [rewrite]: #380
-#661 := [monotonicity #716 #567]: #657
-#639 := [trans #661 #650]: #642
-#715 := (iff #313 false)
-#375 := [rewrite]: #715
-#652 := [monotonicity #375 #639]: #651
-#643 := [trans #652 #649]: #654
-#631 := [monotonicity #643]: #647
-#635 := [trans #631 #634]: #647
-#640 := [quant-inst #8 #10]: #646
-#636 := [mp #640 #635]: #645
-[unit-resolution #636 #67 #739]: false
-unsat
-c497ff275eec9dfc0af1251e4c8516213924660f 326 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#40 := (f4 f5 #18)
-#41 := (f3 #40 #20)
-#751 := (pattern #41)
-#22 := 0::Int
-#86 := -1::Int
-#91 := (* -1::Int #20)
-#88 := (* -1::Int #18)
-#146 := (mod #88 #91)
-#261 := (+ #41 #146)
-#262 := (= #261 0::Int)
-#42 := (mod #18 #20)
-#258 := (* -1::Int #42)
-#259 := (+ #41 #258)
-#260 := (= #259 0::Int)
-#113 := (<= #20 0::Int)
-#120 := (>= #18 0::Int)
-#205 := (or #120 #113)
-#206 := (not #205)
-#109 := (<= #18 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#263 := (if #209 #260 #262)
-#257 := (= #41 0::Int)
-#23 := (= #18 0::Int)
-#264 := (if #23 #257 #263)
-#256 := (= #41 #18)
-#24 := (= #20 0::Int)
-#265 := (if #24 #256 #264)
-#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #265)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#755 := (iff #268 #752)
-#753 := (iff #265 #265)
-#754 := [refl]: #753
-#756 := [quant-intro #754]: #755
-#152 := (* -1::Int #146)
-#225 := (if #209 #42 #152)
-#228 := (if #23 0::Int #225)
-#231 := (if #24 #18 #228)
-#234 := (= #41 #231)
-#237 := (forall (vars (?v0 Int) (?v1 Int)) #234)
-#269 := (iff #237 #268)
-#266 := (iff #234 #265)
-#267 := [rewrite]: #266
-#270 := [quant-intro #267]: #269
-#114 := (not #113)
-#121 := (not #120)
-#124 := (and #121 #114)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#172 := (if #127 #42 #152)
-#175 := (if #23 0::Int #172)
-#178 := (if #24 #18 #175)
-#181 := (= #41 #178)
-#184 := (forall (vars (?v0 Int) (?v1 Int)) #181)
-#238 := (iff #184 #237)
-#235 := (iff #181 #234)
-#232 := (= #178 #231)
-#229 := (= #175 #228)
-#226 := (= #172 #225)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#227 := [monotonicity #211]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#195 := (~ #184 #184)
-#194 := (~ #181 #181)
-#191 := [refl]: #194
-#196 := [nnf-pos #191]: #195
-#34 := (- #20)
-#33 := (- #18)
-#43 := (mod #33 #34)
-#44 := (- #43)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#45 := (if #31 #42 #44)
-#46 := (if #23 0::Int #45)
-#47 := (if #24 #18 #46)
-#48 := (= #41 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#187 := (iff #49 #184)
-#157 := (if #31 #42 #152)
-#160 := (if #23 0::Int #157)
-#163 := (if #24 #18 #160)
-#166 := (= #41 #163)
-#169 := (forall (vars (?v0 Int) (?v1 Int)) #166)
-#185 := (iff #169 #184)
-#182 := (iff #166 #181)
-#179 := (= #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#128 := (iff #31 #127)
-#125 := (iff #30 #124)
-#115 := (iff #27 #114)
-#116 := [rewrite]: #115
-#122 := (iff #29 #121)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123 #116]: #125
-#118 := (iff #28 #117)
-#111 := (iff #26 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#174 := [monotonicity #129]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [monotonicity #180]: #182
-#186 := [quant-intro #183]: #185
-#170 := (iff #49 #169)
-#167 := (iff #48 #166)
-#164 := (= #47 #163)
-#161 := (= #46 #160)
-#158 := (= #45 #157)
-#155 := (= #44 #152)
-#149 := (- #146)
-#153 := (= #149 #152)
-#154 := [rewrite]: #153
-#150 := (= #44 #149)
-#147 := (= #43 #146)
-#92 := (= #34 #91)
-#93 := [rewrite]: #92
-#89 := (= #33 #88)
-#90 := [rewrite]: #89
-#148 := [monotonicity #90 #93]: #147
-#151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [monotonicity #165]: #167
-#171 := [quant-intro #168]: #170
-#188 := [trans #171 #186]: #187
-#145 := [asserted]: #49
-#189 := [mp #145 #188]: #184
-#192 := [mp~ #189 #196]: #184
-#240 := [mp #192 #239]: #237
-#271 := [mp #240 #270]: #268
-#757 := [mp #271 #756]: #752
-#76 := -2::Int
-#70 := -3::Int
-#8 := 1::Int
-#9 := (f4 f5 1::Int)
-#73 := (f3 #9 -3::Int)
-#79 := (= #73 -2::Int)
-#82 := (not #79)
-#13 := 2::Int
-#14 := (- 2::Int)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -2::Int)
-#78 := [rewrite]: #77
-#74 := (= #12 #73)
-#71 := (= #11 -3::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#69 := [asserted]: #16
-#87 := [mp #69 #84]: #82
-#668 := (not #752)
-#660 := (or #668 #79)
-#407 := (* -1::Int -3::Int)
-#406 := (* -1::Int 1::Int)
-#739 := (mod #406 #407)
-#740 := (+ #73 #739)
-#741 := (= #740 0::Int)
-#738 := (mod 1::Int -3::Int)
-#395 := (* -1::Int #738)
-#525 := (+ #73 #395)
-#732 := (= #525 0::Int)
-#419 := (<= -3::Int 0::Int)
-#418 := (>= 1::Int 0::Int)
-#422 := (or #418 #419)
-#401 := (not #422)
-#408 := (<= 1::Int 0::Int)
-#420 := (or #408 #419)
-#421 := (not #420)
-#736 := (or #421 #401)
-#742 := (if #736 #732 #741)
-#417 := (= #73 0::Int)
-#416 := (= 1::Int 0::Int)
-#737 := (if #416 #417 #742)
-#415 := (= #73 1::Int)
-#331 := (= -3::Int 0::Int)
-#743 := (if #331 #415 #737)
-#657 := (or #668 #743)
-#669 := (iff #657 #660)
-#671 := (iff #660 #660)
-#667 := [rewrite]: #671
-#679 := (iff #743 #79)
-#578 := (if false #415 #79)
-#677 := (iff #578 #79)
-#562 := [rewrite]: #677
-#678 := (iff #743 #578)
-#584 := (iff #737 #79)
-#580 := (if false #417 #79)
-#582 := (iff #580 #79)
-#583 := [rewrite]: #582
-#573 := (iff #737 #580)
-#577 := (iff #742 #79)
-#673 := (iff #742 #578)
-#528 := (iff #741 #79)
-#527 := (+ 2::Int #73)
-#682 := (= #527 0::Int)
-#568 := (iff #682 #79)
-#569 := [rewrite]: #568
-#685 := (iff #741 #682)
-#683 := (= #740 #527)
-#695 := (+ #73 2::Int)
-#680 := (= #695 #527)
-#681 := [rewrite]: #680
-#524 := (= #740 #695)
-#694 := (= #739 2::Int)
-#691 := (mod -1::Int 3::Int)
-#687 := (= #691 2::Int)
-#693 := [rewrite]: #687
-#692 := (= #739 #691)
-#689 := (= #407 3::Int)
-#690 := [rewrite]: #689
-#707 := (= #406 -1::Int)
-#708 := [rewrite]: #707
-#686 := [monotonicity #708 #690]: #692
-#688 := [trans #686 #693]: #694
-#526 := [monotonicity #688]: #524
-#684 := [trans #526 #681]: #683
-#567 := [monotonicity #684]: #685
-#676 := [trans #567 #569]: #528
-#546 := (iff #732 #415)
-#699 := (+ -1::Int #73)
-#702 := (= #699 0::Int)
-#704 := (iff #702 #415)
-#545 := [rewrite]: #704
-#703 := (iff #732 #702)
-#696 := (= #525 #699)
-#709 := (+ #73 -1::Int)
-#700 := (= #709 #699)
-#701 := [rewrite]: #700
-#706 := (= #525 #709)
-#423 := (= #395 -1::Int)
-#428 := (= #395 #406)
-#426 := (= #738 1::Int)
-#427 := [rewrite]: #426
-#429 := [monotonicity #427]: #428
-#705 := [trans #429 #708]: #423
-#710 := [monotonicity #705]: #706
-#697 := [trans #710 #701]: #696
-#698 := [monotonicity #697]: #703
-#547 := [trans #698 #545]: #546
-#712 := (iff #736 false)
-#714 := (or false false)
-#711 := (iff #714 false)
-#715 := [rewrite]: #711
-#436 := (iff #736 #714)
-#337 := (iff #401 false)
-#1 := true
-#724 := (not true)
-#726 := (iff #724 false)
-#364 := [rewrite]: #726
-#442 := (iff #401 #724)
-#440 := (iff #422 true)
-#730 := (or true true)
-#717 := (iff #730 true)
-#718 := [rewrite]: #717
-#728 := (iff #422 #730)
-#378 := (iff #419 true)
-#719 := [rewrite]: #378
-#369 := (iff #418 true)
-#370 := [rewrite]: #369
-#731 := [monotonicity #370 #719]: #728
-#441 := [trans #731 #718]: #440
-#443 := [monotonicity #441]: #442
-#713 := [trans #443 #364]: #337
-#727 := (iff #421 false)
-#725 := (iff #421 #724)
-#722 := (iff #420 true)
-#382 := (or false true)
-#385 := (iff #382 true)
-#721 := [rewrite]: #385
-#383 := (iff #420 #382)
-#394 := (iff #408 false)
-#735 := [rewrite]: #394
-#384 := [monotonicity #735 #719]: #383
-#723 := [trans #384 #721]: #722
-#720 := [monotonicity #723]: #725
-#729 := [trans #720 #364]: #727
-#437 := [monotonicity #729 #713]: #436
-#716 := [trans #437 #715]: #712
-#674 := [monotonicity #716 #547 #676]: #673
-#579 := [trans #674 #562]: #577
-#398 := (iff #416 false)
-#734 := [rewrite]: #398
-#581 := [monotonicity #734 #579]: #573
-#585 := [trans #581 #583]: #584
-#733 := (iff #331 false)
-#393 := [rewrite]: #733
-#675 := [monotonicity #393 #585]: #678
-#666 := [trans #675 #562]: #679
-#670 := [monotonicity #666]: #669
-#672 := [trans #670 #667]: #669
-#659 := [quant-inst #8 #70]: #657
-#661 := [mp #659 #672]: #660
-[unit-resolution #661 #87 #757]: false
-unsat
-a3271abc9f2ec03bd2af23f7e77d6fec07008813 307 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#747 := (pattern #38)
-#12 := 0::Int
-#80 := -1::Int
-#85 := (* -1::Int #18)
-#82 := (* -1::Int #16)
-#140 := (mod #82 #85)
-#255 := (+ #38 #140)
-#256 := (= #255 0::Int)
-#39 := (mod #16 #18)
-#252 := (* -1::Int #39)
-#253 := (+ #38 #252)
-#254 := (= #253 0::Int)
-#107 := (<= #18 0::Int)
-#114 := (>= #16 0::Int)
-#199 := (or #114 #107)
-#200 := (not #199)
-#103 := (<= #16 0::Int)
-#197 := (or #103 #107)
-#198 := (not #197)
-#203 := (or #198 #200)
-#257 := (if #203 #254 #256)
-#251 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#258 := (if #20 #251 #257)
-#250 := (= #38 #16)
-#21 := (= #18 0::Int)
-#259 := (if #21 #250 #258)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #259)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#751 := (iff #262 #748)
-#749 := (iff #259 #259)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#146 := (* -1::Int #140)
-#219 := (if #203 #39 #146)
-#222 := (if #20 0::Int #219)
-#225 := (if #21 #16 #222)
-#228 := (= #38 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#108 := (not #107)
-#115 := (not #114)
-#118 := (and #115 #108)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#166 := (if #121 #39 #146)
-#169 := (if #20 0::Int #166)
-#172 := (if #21 #16 #169)
-#175 := (= #38 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#232 := (iff #178 #231)
-#229 := (iff #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#220 := (= #166 #219)
-#204 := (iff #121 #203)
-#201 := (iff #118 #200)
-#202 := [rewrite]: #201
-#191 := (iff #111 #198)
-#192 := [rewrite]: #191
-#205 := [monotonicity #192 #202]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#189 := (~ #178 #178)
-#188 := (~ #175 #175)
-#185 := [refl]: #188
-#190 := [nnf-pos #185]: #189
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#181 := (iff #46 #178)
-#151 := (if #28 #39 #146)
-#154 := (if #20 0::Int #151)
-#157 := (if #21 #16 #154)
-#160 := (= #38 #157)
-#163 := (forall (vars (?v0 Int) (?v1 Int)) #160)
-#179 := (iff #163 #178)
-#176 := (iff #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#167 := (= #151 #166)
-#122 := (iff #28 #121)
-#119 := (iff #27 #118)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#116 := (iff #26 #115)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117 #110]: #119
-#112 := (iff #25 #111)
-#105 := (iff #23 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#168 := [monotonicity #123]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#164 := (iff #46 #163)
-#161 := (iff #45 #160)
-#158 := (= #44 #157)
-#155 := (= #43 #154)
-#152 := (= #42 #151)
-#149 := (= #41 #146)
-#143 := (- #140)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #41 #143)
-#141 := (= #40 #140)
-#86 := (= #31 #85)
-#87 := [rewrite]: #86
-#83 := (= #30 #82)
-#84 := [rewrite]: #83
-#142 := [monotonicity #84 #87]: #141
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#182 := [trans #165 #180]: #181
-#139 := [asserted]: #46
-#183 := [mp #139 #182]: #178
-#186 := [mp~ #183 #190]: #178
-#234 := [mp #186 #233]: #231
-#265 := [mp #234 #264]: #262
-#753 := [mp #265 #752]: #748
-#67 := -3::Int
-#8 := 3::Int
-#9 := (f4 f5 3::Int)
-#70 := (f3 #9 -3::Int)
-#73 := (= #70 0::Int)
-#76 := (not #73)
-#10 := (- 3::Int)
-#11 := (f3 #9 #10)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#77 := (iff #14 #76)
-#74 := (iff #13 #73)
-#71 := (= #11 #70)
-#68 := (= #10 -3::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#66 := [asserted]: #14
-#81 := [mp #66 #78]: #76
-#573 := (not #748)
-#575 := (or #573 #73)
-#402 := (* -1::Int -3::Int)
-#728 := (* -1::Int 3::Int)
-#403 := (mod #728 #402)
-#735 := (+ #70 #403)
-#736 := (= #735 0::Int)
-#732 := (mod 3::Int -3::Int)
-#734 := (* -1::Int #732)
-#391 := (+ #70 #734)
-#521 := (= #391 0::Int)
-#404 := (<= -3::Int 0::Int)
-#417 := (>= 3::Int 0::Int)
-#414 := (or #417 #404)
-#418 := (not #414)
-#413 := (<= 3::Int 0::Int)
-#415 := (or #413 #404)
-#416 := (not #415)
-#397 := (or #416 #418)
-#737 := (if #397 #521 #736)
-#412 := (= 3::Int 0::Int)
-#738 := (if #412 #73 #737)
-#411 := (= #70 3::Int)
-#327 := (= -3::Int 0::Int)
-#733 := (if #327 #411 #738)
-#576 := (or #573 #733)
-#577 := (iff #576 #575)
-#579 := (iff #575 #575)
-#580 := [rewrite]: #579
-#673 := (iff #733 #73)
-#524 := (if false #411 #73)
-#669 := (iff #524 #73)
-#670 := [rewrite]: #669
-#672 := (iff #733 #524)
-#564 := (iff #738 #73)
-#522 := (if false #73 #73)
-#677 := (iff #522 #73)
-#679 := [rewrite]: #677
-#681 := (iff #738 #522)
-#680 := (iff #737 #73)
-#523 := (iff #737 #522)
-#691 := (iff #736 #73)
-#690 := (= #735 #70)
-#705 := (+ #70 0::Int)
-#695 := (= #705 #70)
-#696 := [rewrite]: #695
-#683 := (= #735 #705)
-#688 := (= #403 0::Int)
-#542 := (mod -3::Int 3::Int)
-#686 := (= #542 0::Int)
-#687 := [rewrite]: #686
-#543 := (= #403 #542)
-#700 := (= #402 3::Int)
-#541 := [rewrite]: #700
-#699 := (= #728 -3::Int)
-#694 := [rewrite]: #699
-#685 := [monotonicity #694 #541]: #543
-#682 := [trans #685 #687]: #688
-#689 := [monotonicity #682]: #683
-#684 := [trans #689 #696]: #690
-#520 := [monotonicity #684]: #691
-#693 := (iff #521 #73)
-#697 := (= #391 #70)
-#702 := (= #391 #705)
-#419 := (= #734 0::Int)
-#423 := (* -1::Int 0::Int)
-#703 := (= #423 0::Int)
-#704 := [rewrite]: #703
-#424 := (= #734 #423)
-#712 := (= #732 0::Int)
-#422 := [rewrite]: #712
-#425 := [monotonicity #422]: #424
-#701 := [trans #425 #704]: #419
-#706 := [monotonicity #701]: #702
-#692 := [trans #706 #696]: #697
-#698 := [monotonicity #692]: #693
-#711 := (iff #397 false)
-#709 := (or false false)
-#433 := (iff #709 false)
-#707 := [rewrite]: #433
-#710 := (iff #397 #709)
-#439 := (iff #418 false)
-#1 := true
-#719 := (not true)
-#716 := (iff #719 false)
-#722 := [rewrite]: #716
-#437 := (iff #418 #719)
-#714 := (iff #414 true)
-#366 := (or true true)
-#727 := (iff #366 true)
-#713 := [rewrite]: #727
-#726 := (iff #414 #366)
-#731 := (iff #404 true)
-#374 := [rewrite]: #731
-#725 := (iff #417 true)
-#365 := [rewrite]: #725
-#724 := [monotonicity #365 #374]: #726
-#436 := [trans #724 #713]: #714
-#438 := [monotonicity #436]: #437
-#333 := [trans #438 #722]: #439
-#360 := (iff #416 false)
-#720 := (iff #416 #719)
-#717 := (iff #415 true)
-#715 := (or false true)
-#380 := (iff #715 true)
-#381 := [rewrite]: #380
-#378 := (iff #415 #715)
-#730 := (iff #413 false)
-#390 := [rewrite]: #730
-#379 := [monotonicity #390 #374]: #378
-#718 := [trans #379 #381]: #717
-#721 := [monotonicity #718]: #720
-#723 := [trans #721 #722]: #360
-#432 := [monotonicity #723 #333]: #710
-#708 := [trans #432 #707]: #711
-#676 := [monotonicity #708 #698 #520]: #523
-#678 := [trans #676 #679]: #680
-#389 := (iff #412 false)
-#394 := [rewrite]: #389
-#563 := [monotonicity #394 #678]: #681
-#565 := [trans #563 #679]: #564
-#739 := (iff #327 false)
-#729 := [rewrite]: #739
-#574 := [monotonicity #729 #565]: #672
-#558 := [trans #574 #670]: #673
-#578 := [monotonicity #558]: #577
-#581 := [trans #578 #580]: #577
-#569 := [quant-inst #8 #67]: #576
-#674 := [mp #569 #581]: #575
-[unit-resolution #674 #81 #753]: false
-unsat
-19af39eefe155fd5ea4a9cb81efe6bb66ad7e60b 335 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#40 := (f4 f5 #18)
-#41 := (f3 #40 #20)
-#750 := (pattern #41)
-#22 := 0::Int
-#76 := -1::Int
-#90 := (* -1::Int #20)
-#86 := (* -1::Int #18)
-#145 := (mod #86 #90)
-#260 := (+ #41 #145)
-#261 := (= #260 0::Int)
-#42 := (mod #18 #20)
-#257 := (* -1::Int #42)
-#258 := (+ #41 #257)
-#259 := (= #258 0::Int)
-#112 := (<= #20 0::Int)
-#119 := (>= #18 0::Int)
-#204 := (or #119 #112)
-#205 := (not #204)
-#108 := (<= #18 0::Int)
-#202 := (or #108 #112)
-#203 := (not #202)
-#208 := (or #203 #205)
-#262 := (if #208 #259 #261)
-#256 := (= #41 0::Int)
-#23 := (= #18 0::Int)
-#263 := (if #23 #256 #262)
-#255 := (= #41 #18)
-#24 := (= #20 0::Int)
-#264 := (if #24 #255 #263)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #264)
-#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
-#754 := (iff #267 #751)
-#752 := (iff #264 #264)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#151 := (* -1::Int #145)
-#224 := (if #208 #42 #151)
-#227 := (if #23 0::Int #224)
-#230 := (if #24 #18 #227)
-#233 := (= #41 #230)
-#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
-#268 := (iff #236 #267)
-#265 := (iff #233 #264)
-#266 := [rewrite]: #265
-#269 := [quant-intro #266]: #268
-#113 := (not #112)
-#120 := (not #119)
-#123 := (and #120 #113)
-#109 := (not #108)
-#116 := (and #109 #113)
-#126 := (or #116 #123)
-#171 := (if #126 #42 #151)
-#174 := (if #23 0::Int #171)
-#177 := (if #24 #18 #174)
-#180 := (= #41 #177)
-#183 := (forall (vars (?v0 Int) (?v1 Int)) #180)
-#237 := (iff #183 #236)
-#234 := (iff #180 #233)
-#231 := (= #177 #230)
-#228 := (= #174 #227)
-#225 := (= #171 #224)
-#209 := (iff #126 #208)
-#206 := (iff #123 #205)
-#207 := [rewrite]: #206
-#196 := (iff #116 #203)
-#197 := [rewrite]: #196
-#210 := [monotonicity #197 #207]: #209
-#226 := [monotonicity #210]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [quant-intro #235]: #237
-#194 := (~ #183 #183)
-#193 := (~ #180 #180)
-#190 := [refl]: #193
-#195 := [nnf-pos #190]: #194
-#34 := (- #20)
-#33 := (- #18)
-#43 := (mod #33 #34)
-#44 := (- #43)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#45 := (if #31 #42 #44)
-#46 := (if #23 0::Int #45)
-#47 := (if #24 #18 #46)
-#48 := (= #41 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#186 := (iff #49 #183)
-#156 := (if #31 #42 #151)
-#159 := (if #23 0::Int #156)
-#162 := (if #24 #18 #159)
-#165 := (= #41 #162)
-#168 := (forall (vars (?v0 Int) (?v1 Int)) #165)
-#184 := (iff #168 #183)
-#181 := (iff #165 #180)
-#178 := (= #162 #177)
-#175 := (= #159 #174)
-#172 := (= #156 #171)
-#127 := (iff #31 #126)
-#124 := (iff #30 #123)
-#114 := (iff #27 #113)
-#115 := [rewrite]: #114
-#121 := (iff #29 #120)
-#122 := [rewrite]: #121
-#125 := [monotonicity #122 #115]: #124
-#117 := (iff #28 #116)
-#110 := (iff #26 #109)
-#111 := [rewrite]: #110
-#118 := [monotonicity #111 #115]: #117
-#128 := [monotonicity #118 #125]: #127
-#173 := [monotonicity #128]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [quant-intro #182]: #184
-#169 := (iff #49 #168)
-#166 := (iff #48 #165)
-#163 := (= #47 #162)
-#160 := (= #46 #159)
-#157 := (= #45 #156)
-#154 := (= #44 #151)
-#148 := (- #145)
-#152 := (= #148 #151)
-#153 := [rewrite]: #152
-#149 := (= #44 #148)
-#146 := (= #43 #145)
-#91 := (= #34 #90)
-#92 := [rewrite]: #91
-#88 := (= #33 #86)
-#89 := [rewrite]: #88
-#147 := [monotonicity #89 #92]: #146
-#150 := [monotonicity #147]: #149
-#155 := [trans #150 #153]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [monotonicity #164]: #166
-#170 := [quant-intro #167]: #169
-#187 := [trans #170 #185]: #186
-#144 := [asserted]: #49
-#188 := [mp #144 #187]: #183
-#191 := [mp~ #188 #195]: #183
-#239 := [mp #191 #238]: #236
-#270 := [mp #239 #269]: #267
-#756 := [mp #270 #755]: #751
-#70 := -3::Int
-#8 := 5::Int
-#9 := (f4 f5 5::Int)
-#73 := (f3 #9 -3::Int)
-#79 := (= #73 -1::Int)
-#82 := (not #79)
-#13 := 1::Int
-#14 := (- 1::Int)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -1::Int)
-#78 := [rewrite]: #77
-#74 := (= #12 #73)
-#71 := (= #11 -3::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#69 := [asserted]: #16
-#87 := [mp #69 #84]: #82
-#660 := (not #751)
-#661 := (or #660 #79)
-#406 := (* -1::Int -3::Int)
-#405 := (* -1::Int 5::Int)
-#738 := (mod #405 #406)
-#739 := (+ #73 #738)
-#740 := (= #739 0::Int)
-#737 := (mod 5::Int -3::Int)
-#394 := (* -1::Int #737)
-#524 := (+ #73 #394)
-#731 := (= #524 0::Int)
-#418 := (<= -3::Int 0::Int)
-#417 := (>= 5::Int 0::Int)
-#421 := (or #417 #418)
-#400 := (not #421)
-#407 := (<= 5::Int 0::Int)
-#419 := (or #407 #418)
-#420 := (not #419)
-#735 := (or #420 #400)
-#741 := (if #735 #731 #740)
-#416 := (= #73 0::Int)
-#415 := (= 5::Int 0::Int)
-#736 := (if #415 #416 #741)
-#414 := (= #73 5::Int)
-#330 := (= -3::Int 0::Int)
-#742 := (if #330 #414 #736)
-#662 := (or #660 #742)
-#657 := (iff #662 #661)
-#648 := (iff #661 #661)
-#649 := [rewrite]: #648
-#666 := (iff #742 #79)
-#656 := (if false #414 #79)
-#669 := (iff #656 #79)
-#670 := [rewrite]: #669
-#658 := (iff #742 #656)
-#667 := (iff #736 #79)
-#584 := (if false #416 #79)
-#678 := (iff #584 #79)
-#665 := [rewrite]: #678
-#677 := (iff #736 #584)
-#582 := (iff #741 #79)
-#291 := 2::Int
-#545 := (= #73 2::Int)
-#578 := (if false #545 #79)
-#580 := (iff #578 #79)
-#581 := [rewrite]: #580
-#579 := (iff #741 #578)
-#561 := (iff #740 #79)
-#684 := (+ 1::Int #73)
-#675 := (= #684 0::Int)
-#673 := (iff #675 #79)
-#676 := [rewrite]: #673
-#577 := (iff #740 #675)
-#568 := (= #739 #684)
-#682 := (+ #73 1::Int)
-#566 := (= #682 #684)
-#567 := [rewrite]: #566
-#683 := (= #739 #682)
-#679 := (= #738 1::Int)
-#691 := -5::Int
-#687 := (mod -5::Int 3::Int)
-#525 := (= #687 1::Int)
-#526 := [rewrite]: #525
-#694 := (= #738 #687)
-#692 := (= #406 3::Int)
-#693 := [rewrite]: #692
-#685 := (= #405 -5::Int)
-#686 := [rewrite]: #685
-#523 := [monotonicity #686 #693]: #694
-#680 := [trans #523 #526]: #679
-#681 := [monotonicity #680]: #683
-#527 := [trans #681 #567]: #568
-#672 := [monotonicity #527]: #577
-#576 := [trans #672 #676]: #561
-#689 := (iff #731 #545)
-#707 := -2::Int
-#700 := (+ -2::Int #73)
-#697 := (= #700 0::Int)
-#546 := (iff #697 #545)
-#688 := [rewrite]: #546
-#703 := (iff #731 #697)
-#701 := (= #524 #700)
-#709 := (+ #73 -2::Int)
-#695 := (= #709 #700)
-#696 := [rewrite]: #695
-#698 := (= #524 #709)
-#708 := (= #394 -2::Int)
-#427 := (* -1::Int 2::Int)
-#422 := (= #427 -2::Int)
-#704 := [rewrite]: #422
-#428 := (= #394 #427)
-#425 := (= #737 2::Int)
-#426 := [rewrite]: #425
-#706 := [monotonicity #426]: #428
-#705 := [trans #706 #704]: #708
-#699 := [monotonicity #705]: #698
-#702 := [trans #699 #696]: #701
-#544 := [monotonicity #702]: #703
-#690 := [trans #544 #688]: #689
-#711 := (iff #735 false)
-#713 := (or false false)
-#710 := (iff #713 false)
-#714 := [rewrite]: #710
-#435 := (iff #735 #713)
-#336 := (iff #400 false)
-#1 := true
-#723 := (not true)
-#725 := (iff #723 false)
-#363 := [rewrite]: #725
-#441 := (iff #400 #723)
-#439 := (iff #421 true)
-#729 := (or true true)
-#716 := (iff #729 true)
-#717 := [rewrite]: #716
-#727 := (iff #421 #729)
-#377 := (iff #418 true)
-#718 := [rewrite]: #377
-#368 := (iff #417 true)
-#369 := [rewrite]: #368
-#730 := [monotonicity #369 #718]: #727
-#440 := [trans #730 #717]: #439
-#442 := [monotonicity #440]: #441
-#712 := [trans #442 #363]: #336
-#726 := (iff #420 false)
-#724 := (iff #420 #723)
-#721 := (iff #419 true)
-#381 := (or false true)
-#384 := (iff #381 true)
-#720 := [rewrite]: #384
-#382 := (iff #419 #381)
-#393 := (iff #407 false)
-#734 := [rewrite]: #393
-#383 := [monotonicity #734 #718]: #382
-#722 := [trans #383 #720]: #721
-#719 := [monotonicity #722]: #724
-#728 := [trans #719 #363]: #726
-#436 := [monotonicity #728 #712]: #435
-#715 := [trans #436 #714]: #711
-#572 := [monotonicity #715 #690 #576]: #579
-#583 := [trans #572 #581]: #582
-#397 := (iff #415 false)
-#733 := [rewrite]: #397
-#674 := [monotonicity #733 #583]: #677
-#659 := [trans #674 #665]: #667
-#732 := (iff #330 false)
-#392 := [rewrite]: #732
-#668 := [monotonicity #392 #659]: #658
-#671 := [trans #668 #670]: #666
-#664 := [monotonicity #671]: #657
-#651 := [trans #664 #649]: #657
-#663 := [quant-inst #8 #70]: #662
-#652 := [mp #663 #651]: #661
-[unit-resolution #652 #87 #756]: false
-unsat
-a7fdbc0f19f952e6755be949d9ee0ea28b9c032d 335 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#39 := (f4 f5 #17)
-#40 := (f3 #39 #19)
-#749 := (pattern #40)
-#21 := 0::Int
-#69 := -1::Int
-#89 := (* -1::Int #19)
-#85 := (* -1::Int #17)
-#144 := (mod #85 #89)
-#259 := (+ #40 #144)
-#260 := (= #259 0::Int)
-#41 := (mod #17 #19)
-#256 := (* -1::Int #41)
-#257 := (+ #40 #256)
-#258 := (= #257 0::Int)
-#111 := (<= #19 0::Int)
-#118 := (>= #17 0::Int)
-#203 := (or #118 #111)
-#204 := (not #203)
-#107 := (<= #17 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#261 := (if #207 #258 #260)
-#255 := (= #40 0::Int)
-#22 := (= #17 0::Int)
-#262 := (if #22 #255 #261)
-#254 := (= #40 #17)
-#23 := (= #19 0::Int)
-#263 := (if #23 #254 #262)
-#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #263)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#753 := (iff #266 #750)
-#751 := (iff #263 #263)
-#752 := [refl]: #751
-#754 := [quant-intro #752]: #753
-#150 := (* -1::Int #144)
-#223 := (if #207 #41 #150)
-#226 := (if #22 0::Int #223)
-#229 := (if #23 #17 #226)
-#232 := (= #40 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#112 := (not #111)
-#119 := (not #118)
-#122 := (and #119 #112)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#170 := (if #125 #41 #150)
-#173 := (if #22 0::Int #170)
-#176 := (if #23 #17 #173)
-#179 := (= #40 #176)
-#182 := (forall (vars (?v0 Int) (?v1 Int)) #179)
-#236 := (iff #182 #235)
-#233 := (iff #179 #232)
-#230 := (= #176 #229)
-#227 := (= #173 #226)
-#224 := (= #170 #223)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#225 := [monotonicity #209]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#193 := (~ #182 #182)
-#192 := (~ #179 #179)
-#189 := [refl]: #192
-#194 := [nnf-pos #189]: #193
-#33 := (- #19)
-#32 := (- #17)
-#42 := (mod #32 #33)
-#43 := (- #42)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#44 := (if #30 #41 #43)
-#45 := (if #22 0::Int #44)
-#46 := (if #23 #17 #45)
-#47 := (= #40 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#185 := (iff #48 #182)
-#155 := (if #30 #41 #150)
-#158 := (if #22 0::Int #155)
-#161 := (if #23 #17 #158)
-#164 := (= #40 #161)
-#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
-#183 := (iff #167 #182)
-#180 := (iff #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#126 := (iff #30 #125)
-#123 := (iff #29 #122)
-#113 := (iff #26 #112)
-#114 := [rewrite]: #113
-#120 := (iff #28 #119)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121 #114]: #123
-#116 := (iff #27 #115)
-#109 := (iff #25 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#172 := [monotonicity #127]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [quant-intro #181]: #183
-#168 := (iff #48 #167)
-#165 := (iff #47 #164)
-#162 := (= #46 #161)
-#159 := (= #45 #158)
-#156 := (= #44 #155)
-#153 := (= #43 #150)
-#147 := (- #144)
-#151 := (= #147 #150)
-#152 := [rewrite]: #151
-#148 := (= #43 #147)
-#145 := (= #42 #144)
-#90 := (= #33 #89)
-#91 := [rewrite]: #90
-#87 := (= #32 #85)
-#88 := [rewrite]: #87
-#146 := [monotonicity #88 #91]: #145
-#149 := [monotonicity #146]: #148
-#154 := [trans #149 #152]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#186 := [trans #169 #184]: #185
-#143 := [asserted]: #48
-#187 := [mp #143 #186]: #182
-#190 := [mp~ #187 #194]: #182
-#238 := [mp #190 #237]: #235
-#269 := [mp #238 #268]: #266
-#755 := [mp #269 #754]: #750
-#13 := 2::Int
-#11 := 3::Int
-#72 := (f4 f5 -1::Int)
-#75 := (f3 #72 3::Int)
-#78 := (= #75 2::Int)
-#81 := (not #78)
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 3::Int)
-#14 := (= #12 2::Int)
-#15 := (not #14)
-#82 := (iff #15 #81)
-#79 := (iff #14 #78)
-#76 := (= #12 #75)
-#73 := (= #10 #72)
-#70 := (= #9 -1::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#68 := [asserted]: #15
-#86 := [mp #68 #83]: #81
-#661 := (not #750)
-#662 := (or #661 #78)
-#405 := (* -1::Int 3::Int)
-#404 := (* -1::Int -1::Int)
-#737 := (mod #404 #405)
-#738 := (+ #75 #737)
-#739 := (= #738 0::Int)
-#736 := (mod -1::Int 3::Int)
-#393 := (* -1::Int #736)
-#523 := (+ #75 #393)
-#730 := (= #523 0::Int)
-#417 := (<= 3::Int 0::Int)
-#416 := (>= -1::Int 0::Int)
-#420 := (or #416 #417)
-#399 := (not #420)
-#406 := (<= -1::Int 0::Int)
-#418 := (or #406 #417)
-#419 := (not #418)
-#734 := (or #419 #399)
-#740 := (if #734 #730 #739)
-#415 := (= #75 0::Int)
-#414 := (= -1::Int 0::Int)
-#735 := (if #414 #415 #740)
-#413 := (= #75 -1::Int)
-#329 := (= 3::Int 0::Int)
-#741 := (if #329 #413 #735)
-#656 := (or #661 #741)
-#647 := (iff #656 #662)
-#650 := (iff #662 #662)
-#651 := [rewrite]: #650
-#659 := (iff #741 #78)
-#667 := (if false #413 #78)
-#665 := (iff #667 #78)
-#670 := [rewrite]: #665
-#668 := (iff #741 #667)
-#655 := (iff #735 #78)
-#673 := (if false #415 #78)
-#666 := (iff #673 #78)
-#658 := [rewrite]: #666
-#677 := (iff #735 #673)
-#583 := (iff #740 #78)
-#1 := true
-#571 := (if true #78 #413)
-#581 := (iff #571 #78)
-#582 := [rewrite]: #581
-#579 := (iff #740 #571)
-#577 := (iff #739 #413)
-#566 := (+ 1::Int #75)
-#671 := (= #566 0::Int)
-#560 := (iff #671 #413)
-#575 := [rewrite]: #560
-#672 := (iff #739 #671)
-#674 := (= #738 #566)
-#680 := (+ #75 1::Int)
-#567 := (= #680 #566)
-#526 := [rewrite]: #567
-#683 := (= #738 #680)
-#681 := (= #737 1::Int)
-#692 := -3::Int
-#522 := (mod 1::Int -3::Int)
-#678 := (= #522 1::Int)
-#679 := [rewrite]: #678
-#524 := (= #737 #522)
-#686 := (= #405 -3::Int)
-#693 := [rewrite]: #686
-#685 := (= #404 1::Int)
-#691 := [rewrite]: #685
-#525 := [monotonicity #691 #693]: #524
-#682 := [trans #525 #679]: #681
-#565 := [monotonicity #682]: #683
-#576 := [trans #565 #526]: #674
-#675 := [monotonicity #576]: #672
-#578 := [trans #675 #575]: #577
-#690 := (iff #730 #78)
-#707 := -2::Int
-#700 := (+ -2::Int #75)
-#544 := (= #700 0::Int)
-#688 := (iff #544 #78)
-#689 := [rewrite]: #688
-#545 := (iff #730 #544)
-#702 := (= #523 #700)
-#699 := (+ #75 -2::Int)
-#701 := (= #699 #700)
-#696 := [rewrite]: #701
-#694 := (= #523 #699)
-#697 := (= #393 -2::Int)
-#706 := (* -1::Int 2::Int)
-#704 := (= #706 -2::Int)
-#708 := [rewrite]: #704
-#421 := (= #393 #706)
-#427 := (= #736 2::Int)
-#705 := [rewrite]: #427
-#703 := [monotonicity #705]: #421
-#698 := [trans #703 #708]: #697
-#695 := [monotonicity #698]: #694
-#543 := [trans #695 #696]: #702
-#687 := [monotonicity #543]: #545
-#684 := [trans #687 #689]: #690
-#425 := (iff #734 true)
-#709 := (or false true)
-#714 := (iff #709 true)
-#424 := [rewrite]: #714
-#713 := (iff #734 #709)
-#434 := (iff #399 true)
-#440 := (not false)
-#711 := (iff #440 true)
-#712 := [rewrite]: #711
-#441 := (iff #399 #440)
-#438 := (iff #420 false)
-#728 := (or false false)
-#715 := (iff #728 false)
-#716 := [rewrite]: #715
-#726 := (iff #420 #728)
-#376 := (iff #417 false)
-#717 := [rewrite]: #376
-#367 := (iff #416 false)
-#368 := [rewrite]: #367
-#729 := [monotonicity #368 #717]: #726
-#439 := [trans #729 #716]: #438
-#335 := [monotonicity #439]: #441
-#435 := [trans #335 #712]: #434
-#725 := (iff #419 false)
-#722 := (not true)
-#724 := (iff #722 false)
-#362 := [rewrite]: #724
-#723 := (iff #419 #722)
-#720 := (iff #418 true)
-#380 := (or true false)
-#383 := (iff #380 true)
-#719 := [rewrite]: #383
-#381 := (iff #418 #380)
-#392 := (iff #406 true)
-#733 := [rewrite]: #392
-#382 := [monotonicity #733 #717]: #381
-#721 := [trans #382 #719]: #720
-#718 := [monotonicity #721]: #723
-#727 := [trans #718 #362]: #725
-#710 := [monotonicity #727 #435]: #713
-#426 := [trans #710 #424]: #425
-#580 := [monotonicity #426 #684 #578]: #579
-#676 := [trans #580 #582]: #583
-#396 := (iff #414 false)
-#732 := [rewrite]: #396
-#664 := [monotonicity #732 #676]: #677
-#657 := [trans #664 #658]: #655
-#731 := (iff #329 false)
-#391 := [rewrite]: #731
-#669 := [monotonicity #391 #657]: #668
-#660 := [trans #669 #670]: #659
-#648 := [monotonicity #660]: #647
-#652 := [trans #648 #651]: #647
-#663 := [quant-inst #69 #11]: #656
-#653 := [mp #663 #652]: #662
-[unit-resolution #653 #86 #755]: false
-unsat
-e5eb6ef756ed3738c8596e457b2e9e48f554cfa6 316 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#750 := (pattern #38)
-#12 := 0::Int
-#83 := -1::Int
-#88 := (* -1::Int #18)
-#85 := (* -1::Int #16)
-#143 := (mod #85 #88)
-#258 := (+ #38 #143)
-#259 := (= #258 0::Int)
-#39 := (mod #16 #18)
-#255 := (* -1::Int #39)
-#256 := (+ #38 #255)
-#257 := (= #256 0::Int)
-#110 := (<= #18 0::Int)
-#117 := (>= #16 0::Int)
-#202 := (or #117 #110)
-#203 := (not #202)
-#106 := (<= #16 0::Int)
-#200 := (or #106 #110)
-#201 := (not #200)
-#206 := (or #201 #203)
-#260 := (if #206 #257 #259)
-#254 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#261 := (if #20 #254 #260)
-#253 := (= #38 #16)
-#21 := (= #18 0::Int)
-#262 := (if #21 #253 #261)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #262)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#754 := (iff #265 #751)
-#752 := (iff #262 #262)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#149 := (* -1::Int #143)
-#222 := (if #206 #39 #149)
-#225 := (if #20 0::Int #222)
-#228 := (if #21 #16 #225)
-#231 := (= #38 #228)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#266 := (iff #234 #265)
-#263 := (iff #231 #262)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#111 := (not #110)
-#118 := (not #117)
-#121 := (and #118 #111)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (if #124 #39 #149)
-#172 := (if #20 0::Int #169)
-#175 := (if #21 #16 #172)
-#178 := (= #38 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#235 := (iff #181 #234)
-#232 := (iff #178 #231)
-#229 := (= #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#207 := (iff #124 #206)
-#204 := (iff #121 #203)
-#205 := [rewrite]: #204
-#194 := (iff #114 #201)
-#195 := [rewrite]: #194
-#208 := [monotonicity #195 #205]: #207
-#224 := [monotonicity #208]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#192 := (~ #181 #181)
-#191 := (~ #178 #178)
-#188 := [refl]: #191
-#193 := [nnf-pos #188]: #192
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#184 := (iff #46 #181)
-#154 := (if #28 #39 #149)
-#157 := (if #20 0::Int #154)
-#160 := (if #21 #16 #157)
-#163 := (= #38 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #28 #124)
-#122 := (iff #27 #121)
-#112 := (iff #24 #111)
-#113 := [rewrite]: #112
-#119 := (iff #26 #118)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120 #113]: #122
-#115 := (iff #25 #114)
-#108 := (iff #23 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #46 #166)
-#164 := (iff #45 #163)
-#161 := (= #44 #160)
-#158 := (= #43 #157)
-#155 := (= #42 #154)
-#152 := (= #41 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #41 #146)
-#144 := (= #40 #143)
-#89 := (= #31 #88)
-#90 := [rewrite]: #89
-#86 := (= #30 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #46
-#186 := [mp #142 #185]: #181
-#189 := [mp~ #186 #193]: #181
-#237 := [mp #189 #236]: #234
-#268 := [mp #237 #267]: #265
-#756 := [mp #268 #755]: #751
-#8 := 3::Int
-#67 := -3::Int
-#70 := (f4 f5 -3::Int)
-#73 := (f3 #70 3::Int)
-#76 := (= #73 0::Int)
-#79 := (not #76)
-#9 := (- 3::Int)
-#10 := (f4 f5 #9)
-#11 := (f3 #10 3::Int)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#80 := (iff #14 #79)
-#77 := (iff #13 #76)
-#74 := (= #11 #73)
-#71 := (= #10 #70)
-#68 := (= #9 -3::Int)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#66 := [asserted]: #14
-#84 := [mp #66 #81]: #79
-#582 := (not #751)
-#583 := (or #582 #76)
-#405 := (* -1::Int 3::Int)
-#731 := (* -1::Int -3::Int)
-#406 := (mod #731 #405)
-#738 := (+ #73 #406)
-#739 := (= #738 0::Int)
-#735 := (mod -3::Int 3::Int)
-#737 := (* -1::Int #735)
-#394 := (+ #73 #737)
-#524 := (= #394 0::Int)
-#407 := (<= 3::Int 0::Int)
-#420 := (>= -3::Int 0::Int)
-#417 := (or #420 #407)
-#421 := (not #417)
-#416 := (<= -3::Int 0::Int)
-#418 := (or #416 #407)
-#419 := (not #418)
-#400 := (or #419 #421)
-#740 := (if #400 #524 #739)
-#415 := (= -3::Int 0::Int)
-#741 := (if #415 #76 #740)
-#414 := (= #73 -3::Int)
-#330 := (= 3::Int 0::Int)
-#736 := (if #330 #414 #741)
-#584 := (or #582 #736)
-#674 := (iff #584 #583)
-#665 := (iff #583 #583)
-#667 := [rewrite]: #665
-#580 := (iff #736 #76)
-#561 := (if false #414 #76)
-#579 := (iff #561 #76)
-#572 := [rewrite]: #579
-#576 := (iff #736 #561)
-#673 := (iff #741 #76)
-#568 := (if false #76 #76)
-#577 := (iff #568 #76)
-#672 := [rewrite]: #577
-#527 := (iff #741 #568)
-#566 := (iff #740 #76)
-#1 := true
-#680 := (if true #76 #76)
-#681 := (iff #680 #76)
-#684 := [rewrite]: #681
-#682 := (iff #740 #680)
-#526 := (iff #739 #76)
-#523 := (= #738 #73)
-#698 := (+ #73 0::Int)
-#695 := (= #698 #73)
-#696 := [rewrite]: #695
-#687 := (= #738 #698)
-#692 := (= #406 0::Int)
-#689 := (mod 3::Int -3::Int)
-#685 := (= #689 0::Int)
-#686 := [rewrite]: #685
-#690 := (= #406 #689)
-#546 := (= #405 -3::Int)
-#688 := [rewrite]: #546
-#544 := (= #731 3::Int)
-#545 := [rewrite]: #544
-#691 := [monotonicity #545 #688]: #690
-#693 := [trans #691 #686]: #692
-#694 := [monotonicity #693]: #687
-#525 := [trans #694 #696]: #523
-#679 := [monotonicity #525]: #526
-#697 := (iff #524 #76)
-#701 := (= #394 #73)
-#699 := (= #394 #698)
-#705 := (= #737 0::Int)
-#706 := (* -1::Int 0::Int)
-#704 := (= #706 0::Int)
-#708 := [rewrite]: #704
-#707 := (= #737 #706)
-#427 := (= #735 0::Int)
-#428 := [rewrite]: #427
-#422 := [monotonicity #428]: #707
-#709 := [trans #422 #708]: #705
-#700 := [monotonicity #709]: #699
-#702 := [trans #700 #696]: #701
-#703 := [monotonicity #702]: #697
-#425 := (iff #400 true)
-#436 := (or false true)
-#711 := (iff #436 true)
-#715 := [rewrite]: #711
-#710 := (iff #400 #436)
-#713 := (iff #421 true)
-#440 := (not false)
-#336 := (iff #440 true)
-#712 := [rewrite]: #336
-#441 := (iff #421 #440)
-#717 := (iff #417 false)
-#369 := (or false false)
-#730 := (iff #369 false)
-#716 := [rewrite]: #730
-#729 := (iff #417 #369)
-#734 := (iff #407 false)
-#377 := [rewrite]: #734
-#728 := (iff #420 false)
-#368 := [rewrite]: #728
-#727 := [monotonicity #368 #377]: #729
-#439 := [trans #727 #716]: #717
-#442 := [monotonicity #439]: #441
-#435 := [trans #442 #712]: #713
-#363 := (iff #419 false)
-#722 := (not true)
-#719 := (iff #722 false)
-#725 := [rewrite]: #719
-#723 := (iff #419 #722)
-#720 := (iff #418 true)
-#718 := (or true false)
-#383 := (iff #718 true)
-#384 := [rewrite]: #383
-#381 := (iff #418 #718)
-#733 := (iff #416 true)
-#393 := [rewrite]: #733
-#382 := [monotonicity #393 #377]: #381
-#721 := [trans #382 #384]: #720
-#724 := [monotonicity #721]: #723
-#726 := [trans #724 #725]: #363
-#714 := [monotonicity #726 #435]: #710
-#426 := [trans #714 #715]: #425
-#683 := [monotonicity #426 #703 #679]: #682
-#567 := [trans #683 #684]: #566
-#392 := (iff #415 false)
-#397 := [rewrite]: #392
-#675 := [monotonicity #397 #567]: #527
-#676 := [trans #675 #672]: #673
-#742 := (iff #330 false)
-#732 := [rewrite]: #742
-#578 := [monotonicity #732 #676]: #576
-#581 := [trans #578 #572]: #580
-#678 := [monotonicity #581]: #674
-#659 := [trans #678 #667]: #674
-#677 := [quant-inst #67 #8]: #584
-#656 := [mp #677 #659]: #583
-[unit-resolution #656 #84 #756]: false
-unsat
-2c8de94340a3f1759be7a084199a7b69b2a47b6e 338 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#39 := (f4 f5 #17)
-#40 := (f3 #39 #19)
-#750 := (pattern #40)
-#21 := 0::Int
-#85 := -1::Int
-#90 := (* -1::Int #19)
-#87 := (* -1::Int #17)
-#145 := (mod #87 #90)
-#260 := (+ #40 #145)
-#261 := (= #260 0::Int)
-#41 := (mod #17 #19)
-#257 := (* -1::Int #41)
-#258 := (+ #40 #257)
-#259 := (= #258 0::Int)
-#112 := (<= #19 0::Int)
-#119 := (>= #17 0::Int)
-#204 := (or #119 #112)
-#205 := (not #204)
-#108 := (<= #17 0::Int)
-#202 := (or #108 #112)
-#203 := (not #202)
-#208 := (or #203 #205)
-#262 := (if #208 #259 #261)
-#256 := (= #40 0::Int)
-#22 := (= #17 0::Int)
-#263 := (if #22 #256 #262)
-#255 := (= #40 #17)
-#23 := (= #19 0::Int)
-#264 := (if #23 #255 #263)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #264)
-#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
-#754 := (iff #267 #751)
-#752 := (iff #264 #264)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#151 := (* -1::Int #145)
-#224 := (if #208 #41 #151)
-#227 := (if #22 0::Int #224)
-#230 := (if #23 #17 #227)
-#233 := (= #40 #230)
-#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
-#268 := (iff #236 #267)
-#265 := (iff #233 #264)
-#266 := [rewrite]: #265
-#269 := [quant-intro #266]: #268
-#113 := (not #112)
-#120 := (not #119)
-#123 := (and #120 #113)
-#109 := (not #108)
-#116 := (and #109 #113)
-#126 := (or #116 #123)
-#171 := (if #126 #41 #151)
-#174 := (if #22 0::Int #171)
-#177 := (if #23 #17 #174)
-#180 := (= #40 #177)
-#183 := (forall (vars (?v0 Int) (?v1 Int)) #180)
-#237 := (iff #183 #236)
-#234 := (iff #180 #233)
-#231 := (= #177 #230)
-#228 := (= #174 #227)
-#225 := (= #171 #224)
-#209 := (iff #126 #208)
-#206 := (iff #123 #205)
-#207 := [rewrite]: #206
-#196 := (iff #116 #203)
-#197 := [rewrite]: #196
-#210 := [monotonicity #197 #207]: #209
-#226 := [monotonicity #210]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [quant-intro #235]: #237
-#194 := (~ #183 #183)
-#193 := (~ #180 #180)
-#190 := [refl]: #193
-#195 := [nnf-pos #190]: #194
-#33 := (- #19)
-#32 := (- #17)
-#42 := (mod #32 #33)
-#43 := (- #42)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#44 := (if #30 #41 #43)
-#45 := (if #22 0::Int #44)
-#46 := (if #23 #17 #45)
-#47 := (= #40 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#186 := (iff #48 #183)
-#156 := (if #30 #41 #151)
-#159 := (if #22 0::Int #156)
-#162 := (if #23 #17 #159)
-#165 := (= #40 #162)
-#168 := (forall (vars (?v0 Int) (?v1 Int)) #165)
-#184 := (iff #168 #183)
-#181 := (iff #165 #180)
-#178 := (= #162 #177)
-#175 := (= #159 #174)
-#172 := (= #156 #171)
-#127 := (iff #30 #126)
-#124 := (iff #29 #123)
-#114 := (iff #26 #113)
-#115 := [rewrite]: #114
-#121 := (iff #28 #120)
-#122 := [rewrite]: #121
-#125 := [monotonicity #122 #115]: #124
-#117 := (iff #27 #116)
-#110 := (iff #25 #109)
-#111 := [rewrite]: #110
-#118 := [monotonicity #111 #115]: #117
-#128 := [monotonicity #118 #125]: #127
-#173 := [monotonicity #128]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [quant-intro #182]: #184
-#169 := (iff #48 #168)
-#166 := (iff #47 #165)
-#163 := (= #46 #162)
-#160 := (= #45 #159)
-#157 := (= #44 #156)
-#154 := (= #43 #151)
-#148 := (- #145)
-#152 := (= #148 #151)
-#153 := [rewrite]: #152
-#149 := (= #43 #148)
-#146 := (= #42 #145)
-#91 := (= #33 #90)
-#92 := [rewrite]: #91
-#88 := (= #32 #87)
-#89 := [rewrite]: #88
-#147 := [monotonicity #89 #92]: #146
-#150 := [monotonicity #147]: #149
-#155 := [trans #150 #153]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [monotonicity #164]: #166
-#170 := [quant-intro #167]: #169
-#187 := [trans #170 #185]: #186
-#144 := [asserted]: #48
-#188 := [mp #144 #187]: #183
-#191 := [mp~ #188 #195]: #183
-#239 := [mp #191 #238]: #236
-#270 := [mp #239 #269]: #267
-#756 := [mp #270 #755]: #751
-#13 := 1::Int
-#11 := 3::Int
-#69 := -5::Int
-#72 := (f4 f5 -5::Int)
-#75 := (f3 #72 3::Int)
-#78 := (= #75 1::Int)
-#81 := (not #78)
-#8 := 5::Int
-#9 := (- 5::Int)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 3::Int)
-#14 := (= #12 1::Int)
-#15 := (not #14)
-#82 := (iff #15 #81)
-#79 := (iff #14 #78)
-#76 := (= #12 #75)
-#73 := (= #10 #72)
-#70 := (= #9 -5::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#68 := [asserted]: #15
-#86 := [mp #68 #83]: #81
-#663 := (not #751)
-#657 := (or #663 #78)
-#406 := (* -1::Int 3::Int)
-#405 := (* -1::Int -5::Int)
-#738 := (mod #405 #406)
-#739 := (+ #75 #738)
-#740 := (= #739 0::Int)
-#737 := (mod -5::Int 3::Int)
-#394 := (* -1::Int #737)
-#524 := (+ #75 #394)
-#731 := (= #524 0::Int)
-#418 := (<= 3::Int 0::Int)
-#417 := (>= -5::Int 0::Int)
-#421 := (or #417 #418)
-#400 := (not #421)
-#407 := (<= -5::Int 0::Int)
-#419 := (or #407 #418)
-#420 := (not #419)
-#735 := (or #420 #400)
-#741 := (if #735 #731 #740)
-#416 := (= #75 0::Int)
-#415 := (= -5::Int 0::Int)
-#736 := (if #415 #416 #741)
-#414 := (= #75 -5::Int)
-#330 := (= 3::Int 0::Int)
-#742 := (if #330 #414 #736)
-#664 := (or #663 #742)
-#649 := (iff #664 #657)
-#652 := (iff #657 #657)
-#653 := [rewrite]: #652
-#661 := (iff #742 #78)
-#669 := (if false #414 #78)
-#671 := (iff #669 #78)
-#660 := [rewrite]: #671
-#670 := (iff #742 #669)
-#658 := (iff #736 #78)
-#678 := (if false #416 #78)
-#659 := (iff #678 #78)
-#656 := [rewrite]: #659
-#665 := (iff #736 #678)
-#677 := (iff #741 #78)
-#676 := -2::Int
-#561 := (= #75 -2::Int)
-#1 := true
-#580 := (if true #78 #561)
-#583 := (iff #580 #78)
-#584 := [rewrite]: #583
-#581 := (iff #741 #580)
-#579 := (iff #740 #561)
-#291 := 2::Int
-#566 := (+ 2::Int #75)
-#577 := (= #566 0::Int)
-#576 := (iff #577 #561)
-#578 := [rewrite]: #576
-#672 := (iff #740 #577)
-#527 := (= #739 #566)
-#683 := (+ #75 2::Int)
-#567 := (= #683 #566)
-#568 := [rewrite]: #567
-#681 := (= #739 #683)
-#680 := (= #738 2::Int)
-#692 := -3::Int
-#694 := (mod 5::Int -3::Int)
-#526 := (= #694 2::Int)
-#679 := [rewrite]: #526
-#523 := (= #738 #694)
-#693 := (= #406 -3::Int)
-#687 := [rewrite]: #693
-#685 := (= #405 5::Int)
-#686 := [rewrite]: #685
-#525 := [monotonicity #686 #687]: #523
-#682 := [trans #525 #679]: #680
-#684 := [monotonicity #682]: #681
-#675 := [trans #684 #568]: #527
-#673 := [monotonicity #675]: #672
-#572 := [trans #673 #578]: #579
-#690 := (iff #731 #78)
-#696 := (+ -1::Int #75)
-#544 := (= #696 0::Int)
-#688 := (iff #544 #78)
-#689 := [rewrite]: #688
-#545 := (iff #731 #544)
-#697 := (= #524 #696)
-#699 := (+ #75 -1::Int)
-#701 := (= #699 #696)
-#702 := [rewrite]: #701
-#700 := (= #524 #699)
-#709 := (= #394 -1::Int)
-#707 := (* -1::Int 1::Int)
-#708 := (= #707 -1::Int)
-#705 := [rewrite]: #708
-#422 := (= #394 #707)
-#428 := (= #737 1::Int)
-#706 := [rewrite]: #428
-#704 := [monotonicity #706]: #422
-#698 := [trans #704 #705]: #709
-#695 := [monotonicity #698]: #700
-#703 := [trans #695 #702]: #697
-#546 := [monotonicity #703]: #545
-#691 := [trans #546 #689]: #690
-#426 := (iff #735 true)
-#710 := (or false true)
-#715 := (iff #710 true)
-#425 := [rewrite]: #715
-#714 := (iff #735 #710)
-#435 := (iff #400 true)
-#441 := (not false)
-#712 := (iff #441 true)
-#713 := [rewrite]: #712
-#442 := (iff #400 #441)
-#439 := (iff #421 false)
-#729 := (or false false)
-#716 := (iff #729 false)
-#717 := [rewrite]: #716
-#727 := (iff #421 #729)
-#377 := (iff #418 false)
-#718 := [rewrite]: #377
-#368 := (iff #417 false)
-#369 := [rewrite]: #368
-#730 := [monotonicity #369 #718]: #727
-#440 := [trans #730 #717]: #439
-#336 := [monotonicity #440]: #442
-#436 := [trans #336 #713]: #435
-#726 := (iff #420 false)
-#723 := (not true)
-#725 := (iff #723 false)
-#363 := [rewrite]: #725
-#724 := (iff #420 #723)
-#721 := (iff #419 true)
-#381 := (or true false)
-#384 := (iff #381 true)
-#720 := [rewrite]: #384
-#382 := (iff #419 #381)
-#393 := (iff #407 true)
-#734 := [rewrite]: #393
-#383 := [monotonicity #734 #718]: #382
-#722 := [trans #383 #720]: #721
-#719 := [monotonicity #722]: #724
-#728 := [trans #719 #363]: #726
-#711 := [monotonicity #728 #436]: #714
-#427 := [trans #711 #425]: #426
-#582 := [monotonicity #427 #691 #572]: #581
-#674 := [trans #582 #584]: #677
-#397 := (iff #415 false)
-#733 := [rewrite]: #397
-#667 := [monotonicity #733 #674]: #665
-#668 := [trans #667 #656]: #658
-#732 := (iff #330 false)
-#392 := [rewrite]: #732
-#666 := [monotonicity #392 #668]: #670
-#662 := [trans #666 #660]: #661
-#651 := [monotonicity #662]: #649
-#654 := [trans #651 #653]: #649
-#648 := [quant-inst #69 #11]: #664
-#650 := [mp #648 #654]: #657
-[unit-resolution #650 #86 #756]: false
-unsat
-8ff94171ae81c6acb1105939644d44501cb6f57a 335 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#39 := (f4 f5 #17)
-#40 := (f3 #39 #19)
-#753 := (pattern #40)
-#21 := 0::Int
-#69 := -1::Int
-#92 := (* -1::Int #19)
-#88 := (* -1::Int #17)
-#147 := (mod #88 #92)
-#262 := (+ #40 #147)
-#263 := (= #262 0::Int)
-#41 := (mod #17 #19)
-#259 := (* -1::Int #41)
-#260 := (+ #40 #259)
-#261 := (= #260 0::Int)
-#114 := (<= #19 0::Int)
-#121 := (>= #17 0::Int)
-#206 := (or #121 #114)
-#207 := (not #206)
-#110 := (<= #17 0::Int)
-#204 := (or #110 #114)
-#205 := (not #204)
-#210 := (or #205 #207)
-#264 := (if #210 #261 #263)
-#258 := (= #40 0::Int)
-#22 := (= #17 0::Int)
-#265 := (if #22 #258 #264)
-#257 := (= #40 #17)
-#23 := (= #19 0::Int)
-#266 := (if #23 #257 #265)
-#754 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #753) #266)
-#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
-#757 := (iff #269 #754)
-#755 := (iff #266 #266)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#153 := (* -1::Int #147)
-#226 := (if #210 #41 #153)
-#229 := (if #22 0::Int #226)
-#232 := (if #23 #17 #229)
-#235 := (= #40 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#270 := (iff #238 #269)
-#267 := (iff #235 #266)
-#268 := [rewrite]: #267
-#271 := [quant-intro #268]: #270
-#115 := (not #114)
-#122 := (not #121)
-#125 := (and #122 #115)
-#111 := (not #110)
-#118 := (and #111 #115)
-#128 := (or #118 #125)
-#173 := (if #128 #41 #153)
-#176 := (if #22 0::Int #173)
-#179 := (if #23 #17 #176)
-#182 := (= #40 #179)
-#185 := (forall (vars (?v0 Int) (?v1 Int)) #182)
-#239 := (iff #185 #238)
-#236 := (iff #182 #235)
-#233 := (= #179 #232)
-#230 := (= #176 #229)
-#227 := (= #173 #226)
-#211 := (iff #128 #210)
-#208 := (iff #125 #207)
-#209 := [rewrite]: #208
-#198 := (iff #118 #205)
-#199 := [rewrite]: #198
-#212 := [monotonicity #199 #209]: #211
-#228 := [monotonicity #212]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#196 := (~ #185 #185)
-#195 := (~ #182 #182)
-#192 := [refl]: #195
-#197 := [nnf-pos #192]: #196
-#33 := (- #19)
-#32 := (- #17)
-#42 := (mod #32 #33)
-#43 := (- #42)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#44 := (if #30 #41 #43)
-#45 := (if #22 0::Int #44)
-#46 := (if #23 #17 #45)
-#47 := (= #40 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#188 := (iff #48 #185)
-#158 := (if #30 #41 #153)
-#161 := (if #22 0::Int #158)
-#164 := (if #23 #17 #161)
-#167 := (= #40 #164)
-#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
-#186 := (iff #170 #185)
-#183 := (iff #167 #182)
-#180 := (= #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#129 := (iff #30 #128)
-#126 := (iff #29 #125)
-#116 := (iff #26 #115)
-#117 := [rewrite]: #116
-#123 := (iff #28 #122)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124 #117]: #126
-#119 := (iff #27 #118)
-#112 := (iff #25 #111)
-#113 := [rewrite]: #112
-#120 := [monotonicity #113 #117]: #119
-#130 := [monotonicity #120 #127]: #129
-#175 := [monotonicity #130]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [quant-intro #184]: #186
-#171 := (iff #48 #170)
-#168 := (iff #47 #167)
-#165 := (= #46 #164)
-#162 := (= #45 #161)
-#159 := (= #44 #158)
-#156 := (= #43 #153)
-#150 := (- #147)
-#154 := (= #150 #153)
-#155 := [rewrite]: #154
-#151 := (= #43 #150)
-#148 := (= #42 #147)
-#93 := (= #33 #92)
-#94 := [rewrite]: #93
-#90 := (= #32 #88)
-#91 := [rewrite]: #90
-#149 := [monotonicity #91 #94]: #148
-#152 := [monotonicity #149]: #151
-#157 := [trans #152 #155]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [monotonicity #166]: #168
-#172 := [quant-intro #169]: #171
-#189 := [trans #172 #187]: #188
-#146 := [asserted]: #48
-#190 := [mp #146 #189]: #185
-#193 := [mp~ #190 #197]: #185
-#241 := [mp #193 #240]: #238
-#272 := [mp #241 #271]: #269
-#759 := [mp #272 #758]: #754
-#75 := -3::Int
-#72 := (f4 f5 -1::Int)
-#78 := (f3 #72 -3::Int)
-#81 := (= #78 -1::Int)
-#84 := (not #81)
-#8 := 1::Int
-#9 := (- 1::Int)
-#11 := 3::Int
-#12 := (- 3::Int)
-#10 := (f4 f5 #9)
-#13 := (f3 #10 #12)
-#14 := (= #13 #9)
-#15 := (not #14)
-#85 := (iff #15 #84)
-#82 := (iff #14 #81)
-#70 := (= #9 -1::Int)
-#71 := [rewrite]: #70
-#79 := (= #13 #78)
-#76 := (= #12 -3::Int)
-#77 := [rewrite]: #76
-#73 := (= #10 #72)
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #80 #71]: #82
-#86 := [monotonicity #83]: #85
-#68 := [asserted]: #15
-#89 := [mp #68 #86]: #84
-#669 := (not #754)
-#674 := (or #669 #81)
-#408 := (* -1::Int -3::Int)
-#734 := (* -1::Int -1::Int)
-#409 := (mod #734 #408)
-#741 := (+ #78 #409)
-#742 := (= #741 0::Int)
-#738 := (mod -1::Int -3::Int)
-#740 := (* -1::Int #738)
-#397 := (+ #78 #740)
-#527 := (= #397 0::Int)
-#410 := (<= -3::Int 0::Int)
-#423 := (>= -1::Int 0::Int)
-#420 := (or #423 #410)
-#424 := (not #420)
-#419 := (<= -1::Int 0::Int)
-#421 := (or #419 #410)
-#422 := (not #421)
-#403 := (or #422 #424)
-#743 := (if #403 #527 #742)
-#418 := (= #78 0::Int)
-#417 := (= -1::Int 0::Int)
-#744 := (if #417 #418 #743)
-#333 := (= -3::Int 0::Int)
-#739 := (if #333 #81 #744)
-#663 := (or #669 #739)
-#665 := (iff #663 #674)
-#660 := (iff #674 #674)
-#667 := [rewrite]: #660
-#672 := (iff #739 #81)
-#670 := (if false #81 #81)
-#661 := (iff #670 #81)
-#671 := [rewrite]: #661
-#662 := (iff #739 #670)
-#681 := (iff #744 #81)
-#585 := (if false #418 #81)
-#680 := (iff #585 #81)
-#677 := [rewrite]: #680
-#586 := (iff #744 #585)
-#583 := (iff #743 #81)
-#293 := 2::Int
-#547 := (= #78 2::Int)
-#564 := (if false #547 #81)
-#582 := (iff #564 #81)
-#575 := [rewrite]: #582
-#579 := (iff #743 #564)
-#676 := (iff #742 #81)
-#686 := (+ 1::Int #78)
-#571 := (= #686 0::Int)
-#580 := (iff #571 #81)
-#675 := [rewrite]: #580
-#530 := (iff #742 #571)
-#569 := (= #741 #686)
-#682 := (+ #78 1::Int)
-#684 := (= #682 #686)
-#687 := [rewrite]: #684
-#683 := (= #741 #682)
-#528 := (= #409 1::Int)
-#695 := (mod 1::Int 3::Int)
-#697 := (= #695 1::Int)
-#526 := [rewrite]: #697
-#696 := (= #409 #695)
-#688 := (= #408 3::Int)
-#689 := [rewrite]: #688
-#693 := (= #734 1::Int)
-#694 := [rewrite]: #693
-#690 := [monotonicity #694 #689]: #696
-#529 := [trans #690 #526]: #528
-#685 := [monotonicity #529]: #683
-#570 := [trans #685 #687]: #569
-#678 := [monotonicity #570]: #530
-#679 := [trans #678 #675]: #676
-#691 := (iff #527 #547)
-#709 := -2::Int
-#702 := (+ -2::Int #78)
-#705 := (= #702 0::Int)
-#548 := (iff #705 #547)
-#549 := [rewrite]: #548
-#700 := (iff #527 #705)
-#699 := (= #397 #702)
-#708 := (+ #78 -2::Int)
-#703 := (= #708 #702)
-#698 := [rewrite]: #703
-#712 := (= #397 #708)
-#707 := (= #740 -2::Int)
-#429 := (* -1::Int 2::Int)
-#710 := (= #429 -2::Int)
-#425 := [rewrite]: #710
-#430 := (= #740 #429)
-#718 := (= #738 2::Int)
-#428 := [rewrite]: #718
-#431 := [monotonicity #428]: #430
-#711 := [trans #431 #425]: #707
-#701 := [monotonicity #711]: #712
-#704 := [trans #701 #698]: #699
-#706 := [monotonicity #704]: #700
-#692 := [trans #706 #549]: #691
-#717 := (iff #403 false)
-#715 := (or false false)
-#439 := (iff #715 false)
-#713 := [rewrite]: #439
-#716 := (iff #403 #715)
-#445 := (iff #424 false)
-#1 := true
-#725 := (not true)
-#722 := (iff #725 false)
-#728 := [rewrite]: #722
-#443 := (iff #424 #725)
-#720 := (iff #420 true)
-#372 := (or false true)
-#733 := (iff #372 true)
-#719 := [rewrite]: #733
-#732 := (iff #420 #372)
-#737 := (iff #410 true)
-#380 := [rewrite]: #737
-#731 := (iff #423 false)
-#371 := [rewrite]: #731
-#730 := [monotonicity #371 #380]: #732
-#442 := [trans #730 #719]: #720
-#444 := [monotonicity #442]: #443
-#339 := [trans #444 #728]: #445
-#366 := (iff #422 false)
-#726 := (iff #422 #725)
-#723 := (iff #421 true)
-#721 := (or true true)
-#386 := (iff #721 true)
-#387 := [rewrite]: #386
-#384 := (iff #421 #721)
-#736 := (iff #419 true)
-#396 := [rewrite]: #736
-#385 := [monotonicity #396 #380]: #384
-#724 := [trans #385 #387]: #723
-#727 := [monotonicity #724]: #726
-#729 := [trans #727 #728]: #366
-#438 := [monotonicity #729 #339]: #716
-#714 := [trans #438 #713]: #717
-#581 := [monotonicity #714 #692 #679]: #579
-#584 := [trans #581 #575]: #583
-#395 := (iff #417 false)
-#400 := [rewrite]: #395
-#587 := [monotonicity #400 #584]: #586
-#668 := [trans #587 #677]: #681
-#745 := (iff #333 false)
-#735 := [rewrite]: #745
-#659 := [monotonicity #735 #668]: #662
-#673 := [trans #659 #671]: #672
-#666 := [monotonicity #673]: #665
-#651 := [trans #666 #667]: #665
-#664 := [quant-inst #69 #75]: #663
-#652 := [mp #664 #651]: #674
-[unit-resolution #652 #89 #759]: false
-unsat
-fa0f3c13527e84e33e9431394773a66086612292 301 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#37 := (f4 f5 #16)
-#38 := (f3 #37 #18)
-#750 := (pattern #38)
-#12 := 0::Int
-#83 := -1::Int
-#88 := (* -1::Int #18)
-#85 := (* -1::Int #16)
-#143 := (mod #85 #88)
-#258 := (+ #38 #143)
-#259 := (= #258 0::Int)
-#39 := (mod #16 #18)
-#255 := (* -1::Int #39)
-#256 := (+ #38 #255)
-#257 := (= #256 0::Int)
-#110 := (<= #18 0::Int)
-#117 := (>= #16 0::Int)
-#202 := (or #117 #110)
-#203 := (not #202)
-#106 := (<= #16 0::Int)
-#200 := (or #106 #110)
-#201 := (not #200)
-#206 := (or #201 #203)
-#260 := (if #206 #257 #259)
-#254 := (= #38 0::Int)
-#20 := (= #16 0::Int)
-#261 := (if #20 #254 #260)
-#253 := (= #38 #16)
-#21 := (= #18 0::Int)
-#262 := (if #21 #253 #261)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #262)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#754 := (iff #265 #751)
-#752 := (iff #262 #262)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#149 := (* -1::Int #143)
-#222 := (if #206 #39 #149)
-#225 := (if #20 0::Int #222)
-#228 := (if #21 #16 #225)
-#231 := (= #38 #228)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#266 := (iff #234 #265)
-#263 := (iff #231 #262)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#111 := (not #110)
-#118 := (not #117)
-#121 := (and #118 #111)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (if #124 #39 #149)
-#172 := (if #20 0::Int #169)
-#175 := (if #21 #16 #172)
-#178 := (= #38 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#235 := (iff #181 #234)
-#232 := (iff #178 #231)
-#229 := (= #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#207 := (iff #124 #206)
-#204 := (iff #121 #203)
-#205 := [rewrite]: #204
-#194 := (iff #114 #201)
-#195 := [rewrite]: #194
-#208 := [monotonicity #195 #205]: #207
-#224 := [monotonicity #208]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#192 := (~ #181 #181)
-#191 := (~ #178 #178)
-#188 := [refl]: #191
-#193 := [nnf-pos #188]: #192
-#31 := (- #18)
-#30 := (- #16)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #16 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#184 := (iff #46 #181)
-#154 := (if #28 #39 #149)
-#157 := (if #20 0::Int #154)
-#160 := (if #21 #16 #157)
-#163 := (= #38 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #28 #124)
-#122 := (iff #27 #121)
-#112 := (iff #24 #111)
-#113 := [rewrite]: #112
-#119 := (iff #26 #118)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120 #113]: #122
-#115 := (iff #25 #114)
-#108 := (iff #23 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #46 #166)
-#164 := (iff #45 #163)
-#161 := (= #44 #160)
-#158 := (= #43 #157)
-#155 := (= #42 #154)
-#152 := (= #41 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #41 #146)
-#144 := (= #40 #143)
-#89 := (= #31 #88)
-#90 := [rewrite]: #89
-#86 := (= #30 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #46
-#186 := [mp #142 #185]: #181
-#189 := [mp~ #186 #193]: #181
-#237 := [mp #189 #236]: #234
-#268 := [mp #237 #267]: #265
-#756 := [mp #268 #755]: #751
-#67 := -3::Int
-#70 := (f4 f5 -3::Int)
-#73 := (f3 #70 -3::Int)
-#76 := (= #73 0::Int)
-#79 := (not #76)
-#8 := 3::Int
-#9 := (- 3::Int)
-#10 := (f4 f5 #9)
-#11 := (f3 #10 #9)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#80 := (iff #14 #79)
-#77 := (iff #13 #76)
-#74 := (= #11 #73)
-#68 := (= #9 -3::Int)
-#69 := [rewrite]: #68
-#71 := (= #10 #70)
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72 #69]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#66 := [asserted]: #14
-#84 := [mp #66 #81]: #79
-#567 := (not #751)
-#568 := (or #567 #76)
-#394 := (* -1::Int -3::Int)
-#524 := (mod #394 #394)
-#731 := (+ #73 #524)
-#405 := (= #731 0::Int)
-#421 := (mod -3::Int -3::Int)
-#400 := (* -1::Int #421)
-#735 := (+ #73 #400)
-#737 := (= #735 0::Int)
-#415 := (<= -3::Int 0::Int)
-#418 := (>= -3::Int 0::Int)
-#419 := (or #418 #415)
-#420 := (not #419)
-#416 := (or #415 #415)
-#407 := (not #416)
-#417 := (or #407 #420)
-#406 := (if #417 #737 #405)
-#330 := (= -3::Int 0::Int)
-#738 := (if #330 #76 #406)
-#414 := (= #73 -3::Int)
-#739 := (if #330 #414 #738)
-#527 := (or #567 #739)
-#577 := (iff #527 #568)
-#673 := (iff #568 #568)
-#676 := [rewrite]: #673
-#684 := (iff #739 #76)
-#679 := (if false #414 #76)
-#683 := (iff #679 #76)
-#681 := [rewrite]: #683
-#680 := (iff #739 #679)
-#525 := (iff #738 #76)
-#690 := (if false #76 #76)
-#686 := (iff #690 #76)
-#692 := [rewrite]: #686
-#694 := (iff #738 #690)
-#693 := (iff #406 #76)
-#691 := (iff #406 #690)
-#688 := (iff #405 #76)
-#545 := (= #731 #73)
-#426 := (+ #73 0::Int)
-#706 := (= #426 #73)
-#707 := [rewrite]: #706
-#703 := (= #731 #426)
-#702 := (= #524 0::Int)
-#699 := (mod 3::Int 3::Int)
-#696 := (= #699 0::Int)
-#701 := [rewrite]: #696
-#700 := (= #524 #699)
-#709 := (= #394 3::Int)
-#698 := [rewrite]: #709
-#695 := [monotonicity #698 #698]: #700
-#697 := [trans #695 #701]: #702
-#544 := [monotonicity #697]: #703
-#546 := [trans #544 #707]: #545
-#689 := [monotonicity #546]: #688
-#708 := (iff #737 #76)
-#422 := (= #735 #73)
-#427 := (= #735 #426)
-#715 := (= #400 0::Int)
-#435 := (* -1::Int 0::Int)
-#714 := (= #435 0::Int)
-#711 := [rewrite]: #714
-#436 := (= #400 #435)
-#712 := (= #421 0::Int)
-#713 := [rewrite]: #712
-#710 := [monotonicity #713]: #436
-#425 := [trans #710 #711]: #715
-#428 := [monotonicity #425]: #427
-#704 := [trans #428 #707]: #422
-#705 := [monotonicity #704]: #708
-#442 := (iff #417 false)
-#716 := (or false false)
-#440 := (iff #716 false)
-#441 := [rewrite]: #440
-#717 := (iff #417 #716)
-#727 := (iff #420 false)
-#1 := true
-#718 := (not true)
-#383 := (iff #718 false)
-#384 := [rewrite]: #383
-#369 := (iff #420 #718)
-#728 := (iff #419 true)
-#724 := (or false true)
-#363 := (iff #724 true)
-#726 := [rewrite]: #363
-#719 := (iff #419 #724)
-#736 := (iff #415 true)
-#742 := [rewrite]: #736
-#722 := (iff #418 false)
-#723 := [rewrite]: #722
-#725 := [monotonicity #723 #742]: #719
-#368 := [trans #725 #726]: #728
-#729 := [monotonicity #368]: #369
-#730 := [trans #729 #384]: #727
-#720 := (iff #407 false)
-#381 := (iff #407 #718)
-#734 := (iff #416 true)
-#732 := (or true true)
-#733 := (iff #732 true)
-#393 := [rewrite]: #733
-#392 := (iff #416 #732)
-#397 := [monotonicity #742 #742]: #392
-#377 := [trans #397 #393]: #734
-#382 := [monotonicity #377]: #381
-#721 := [trans #382 #384]: #720
-#439 := [monotonicity #721 #730]: #717
-#336 := [trans #439 #441]: #442
-#685 := [monotonicity #336 #705 #689]: #691
-#687 := [trans #685 #692]: #693
-#740 := (iff #330 false)
-#741 := [rewrite]: #740
-#523 := [monotonicity #741 #687]: #694
-#526 := [trans #523 #692]: #525
-#682 := [monotonicity #741 #526]: #680
-#566 := [trans #682 #681]: #684
-#672 := [monotonicity #566]: #577
-#561 := [trans #672 #676]: #577
-#675 := [quant-inst #67 #67]: #527
-#576 := [mp #675 #561]: #568
-[unit-resolution #576 #84 #756]: false
-unsat
-78e98b360474b07bbe43f0216b8f59ecf8adcdd9 341 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#21 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#19 := (:var 1 Int)
-decl f5 :: S3
-#7 := f5
-#41 := (f4 f5 #19)
-#42 := (f3 #41 #21)
-#758 := (pattern #42)
-#23 := 0::Int
-#93 := -1::Int
-#98 := (* -1::Int #21)
-#95 := (* -1::Int #19)
-#153 := (mod #95 #98)
-#268 := (+ #42 #153)
-#269 := (= #268 0::Int)
-#43 := (mod #19 #21)
-#265 := (* -1::Int #43)
-#266 := (+ #42 #265)
-#267 := (= #266 0::Int)
-#120 := (<= #21 0::Int)
-#127 := (>= #19 0::Int)
-#212 := (or #127 #120)
-#213 := (not #212)
-#116 := (<= #19 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#270 := (if #216 #267 #269)
-#264 := (= #42 0::Int)
-#24 := (= #19 0::Int)
-#271 := (if #24 #264 #270)
-#263 := (= #42 #19)
-#25 := (= #21 0::Int)
-#272 := (if #25 #263 #271)
-#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #272)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#762 := (iff #275 #759)
-#760 := (iff #272 #272)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#159 := (* -1::Int #153)
-#232 := (if #216 #43 #159)
-#235 := (if #24 0::Int #232)
-#238 := (if #25 #19 #235)
-#241 := (= #42 #238)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#276 := (iff #244 #275)
-#273 := (iff #241 #272)
-#274 := [rewrite]: #273
-#277 := [quant-intro #274]: #276
-#121 := (not #120)
-#128 := (not #127)
-#131 := (and #128 #121)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#179 := (if #134 #43 #159)
-#182 := (if #24 0::Int #179)
-#185 := (if #25 #19 #182)
-#188 := (= #42 #185)
-#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
-#245 := (iff #191 #244)
-#242 := (iff #188 #241)
-#239 := (= #185 #238)
-#236 := (= #182 #235)
-#233 := (= #179 #232)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#234 := [monotonicity #218]: #233
-#237 := [monotonicity #234]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [quant-intro #243]: #245
-#202 := (~ #191 #191)
-#201 := (~ #188 #188)
-#198 := [refl]: #201
-#203 := [nnf-pos #198]: #202
-#35 := (- #21)
-#34 := (- #19)
-#44 := (mod #34 #35)
-#45 := (- #44)
-#28 := (< 0::Int #21)
-#30 := (< #19 0::Int)
-#31 := (and #30 #28)
-#27 := (< 0::Int #19)
-#29 := (and #27 #28)
-#32 := (or #29 #31)
-#46 := (if #32 #43 #45)
-#47 := (if #24 0::Int #46)
-#48 := (if #25 #19 #47)
-#49 := (= #42 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#194 := (iff #50 #191)
-#164 := (if #32 #43 #159)
-#167 := (if #24 0::Int #164)
-#170 := (if #25 #19 #167)
-#173 := (= #42 #170)
-#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
-#192 := (iff #176 #191)
-#189 := (iff #173 #188)
-#186 := (= #170 #185)
-#183 := (= #167 #182)
-#180 := (= #164 #179)
-#135 := (iff #32 #134)
-#132 := (iff #31 #131)
-#122 := (iff #28 #121)
-#123 := [rewrite]: #122
-#129 := (iff #30 #128)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130 #123]: #132
-#125 := (iff #29 #124)
-#118 := (iff #27 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#181 := [monotonicity #136]: #180
-#184 := [monotonicity #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [quant-intro #190]: #192
-#177 := (iff #50 #176)
-#174 := (iff #49 #173)
-#171 := (= #48 #170)
-#168 := (= #47 #167)
-#165 := (= #46 #164)
-#162 := (= #45 #159)
-#156 := (- #153)
-#160 := (= #156 #159)
-#161 := [rewrite]: #160
-#157 := (= #45 #156)
-#154 := (= #44 #153)
-#99 := (= #35 #98)
-#100 := [rewrite]: #99
-#96 := (= #34 #95)
-#97 := [rewrite]: #96
-#155 := [monotonicity #97 #100]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#166 := [monotonicity #163]: #165
-#169 := [monotonicity #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [quant-intro #175]: #177
-#195 := [trans #178 #193]: #194
-#152 := [asserted]: #50
-#196 := [mp #152 #195]: #191
-#199 := [mp~ #196 #203]: #191
-#247 := [mp #199 #246]: #244
-#278 := [mp #247 #277]: #275
-#764 := [mp #278 #763]: #759
-#83 := -2::Int
-#77 := -3::Int
-#71 := -5::Int
-#74 := (f4 f5 -5::Int)
-#80 := (f3 #74 -3::Int)
-#86 := (= #80 -2::Int)
-#89 := (not #86)
-#14 := 2::Int
-#15 := (- 2::Int)
-#11 := 3::Int
-#12 := (- 3::Int)
-#8 := 5::Int
-#9 := (- 5::Int)
-#10 := (f4 f5 #9)
-#13 := (f3 #10 #12)
-#16 := (= #13 #15)
-#17 := (not #16)
-#90 := (iff #17 #89)
-#87 := (iff #16 #86)
-#84 := (= #15 -2::Int)
-#85 := [rewrite]: #84
-#81 := (= #13 #80)
-#78 := (= #12 -3::Int)
-#79 := [rewrite]: #78
-#75 := (= #10 #74)
-#72 := (= #9 -5::Int)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#88 := [monotonicity #82 #85]: #87
-#91 := [monotonicity #88]: #90
-#70 := [asserted]: #17
-#94 := [mp #70 #91]: #89
-#674 := (not #759)
-#679 := (or #674 #86)
-#414 := (* -1::Int -3::Int)
-#413 := (* -1::Int -5::Int)
-#746 := (mod #413 #414)
-#747 := (+ #80 #746)
-#748 := (= #747 0::Int)
-#745 := (mod -5::Int -3::Int)
-#402 := (* -1::Int #745)
-#532 := (+ #80 #402)
-#739 := (= #532 0::Int)
-#426 := (<= -3::Int 0::Int)
-#425 := (>= -5::Int 0::Int)
-#429 := (or #425 #426)
-#408 := (not #429)
-#415 := (<= -5::Int 0::Int)
-#427 := (or #415 #426)
-#428 := (not #427)
-#743 := (or #428 #408)
-#749 := (if #743 #739 #748)
-#424 := (= #80 0::Int)
-#423 := (= -5::Int 0::Int)
-#744 := (if #423 #424 #749)
-#422 := (= #80 -5::Int)
-#338 := (= -3::Int 0::Int)
-#750 := (if #338 #422 #744)
-#668 := (or #674 #750)
-#670 := (iff #668 #679)
-#665 := (iff #679 #679)
-#672 := [rewrite]: #665
-#677 := (iff #750 #86)
-#675 := (if false #422 #86)
-#666 := (iff #675 #86)
-#676 := [rewrite]: #666
-#667 := (iff #750 #675)
-#686 := (iff #744 #86)
-#590 := (if false #424 #86)
-#685 := (iff #590 #86)
-#682 := [rewrite]: #685
-#591 := (iff #744 #590)
-#588 := (iff #749 #86)
-#291 := 1::Int
-#552 := (= #80 1::Int)
-#569 := (if false #552 #86)
-#587 := (iff #569 #86)
-#580 := [rewrite]: #587
-#584 := (iff #749 #569)
-#681 := (iff #748 #86)
-#691 := (+ 2::Int #80)
-#576 := (= #691 0::Int)
-#585 := (iff #576 #86)
-#680 := [rewrite]: #585
-#535 := (iff #748 #576)
-#574 := (= #747 #691)
-#687 := (+ #80 2::Int)
-#689 := (= #687 #691)
-#692 := [rewrite]: #689
-#688 := (= #747 #687)
-#533 := (= #746 2::Int)
-#700 := (mod 5::Int 3::Int)
-#702 := (= #700 2::Int)
-#531 := [rewrite]: #702
-#701 := (= #746 #700)
-#693 := (= #414 3::Int)
-#694 := [rewrite]: #693
-#698 := (= #413 5::Int)
-#699 := [rewrite]: #698
-#695 := [monotonicity #699 #694]: #701
-#534 := [trans #695 #531]: #533
-#690 := [monotonicity #534]: #688
-#575 := [trans #690 #692]: #574
-#683 := [monotonicity #575]: #535
-#684 := [trans #683 #680]: #681
-#696 := (iff #739 #552)
-#707 := (+ -1::Int #80)
-#710 := (= #707 0::Int)
-#553 := (iff #710 #552)
-#554 := [rewrite]: #553
-#705 := (iff #739 #710)
-#704 := (= #532 #707)
-#713 := (+ #80 -1::Int)
-#708 := (= #713 #707)
-#703 := [rewrite]: #708
-#717 := (= #532 #713)
-#712 := (= #402 -1::Int)
-#435 := (* -1::Int 1::Int)
-#715 := (= #435 -1::Int)
-#430 := [rewrite]: #715
-#436 := (= #402 #435)
-#433 := (= #745 1::Int)
-#434 := [rewrite]: #433
-#714 := [monotonicity #434]: #436
-#716 := [trans #714 #430]: #712
-#706 := [monotonicity #716]: #717
-#709 := [trans #706 #703]: #704
-#711 := [monotonicity #709]: #705
-#697 := [trans #711 #554]: #696
-#719 := (iff #743 false)
-#721 := (or false false)
-#718 := (iff #721 false)
-#722 := [rewrite]: #718
-#443 := (iff #743 #721)
-#344 := (iff #408 false)
-#1 := true
-#731 := (not true)
-#733 := (iff #731 false)
-#371 := [rewrite]: #733
-#449 := (iff #408 #731)
-#447 := (iff #429 true)
-#737 := (or false true)
-#724 := (iff #737 true)
-#725 := [rewrite]: #724
-#735 := (iff #429 #737)
-#385 := (iff #426 true)
-#726 := [rewrite]: #385
-#376 := (iff #425 false)
-#377 := [rewrite]: #376
-#738 := [monotonicity #377 #726]: #735
-#448 := [trans #738 #725]: #447
-#450 := [monotonicity #448]: #449
-#720 := [trans #450 #371]: #344
-#734 := (iff #428 false)
-#732 := (iff #428 #731)
-#729 := (iff #427 true)
-#389 := (or true true)
-#392 := (iff #389 true)
-#728 := [rewrite]: #392
-#390 := (iff #427 #389)
-#401 := (iff #415 true)
-#742 := [rewrite]: #401
-#391 := [monotonicity #742 #726]: #390
-#730 := [trans #391 #728]: #729
-#727 := [monotonicity #730]: #732
-#736 := [trans #727 #371]: #734
-#444 := [monotonicity #736 #720]: #443
-#723 := [trans #444 #722]: #719
-#586 := [monotonicity #723 #697 #684]: #584
-#589 := [trans #586 #580]: #588
-#405 := (iff #423 false)
-#741 := [rewrite]: #405
-#592 := [monotonicity #741 #589]: #591
-#673 := [trans #592 #682]: #686
-#740 := (iff #338 false)
-#400 := [rewrite]: #740
-#664 := [monotonicity #400 #673]: #667
-#678 := [trans #664 #676]: #677
-#671 := [monotonicity #678]: #670
-#656 := [trans #671 #672]: #670
-#669 := [quant-inst #71 #77]: #668
-#657 := [mp #669 #656]: #679
-[unit-resolution #657 #94 #764]: false
-unsat
-f7f6dba4a50481c109b9d852231cbc0e5bd8ffbf 316 0
-#2 := false
-#19 := 0::Int
-decl f6 :: Int
-#8 := f6
-#403 := (<= f6 0::Int)
-#413 := (>= f6 0::Int)
-#724 := (not #413)
-#380 := (not #403)
-#725 := (or #380 #724)
-#687 := (not #725)
-#10 := 3::Int
-#733 := (mod f6 3::Int)
-#68 := -1::Int
-#390 := (* -1::Int #733)
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#7 := f5
-#9 := (f4 f5 f6)
-#11 := (f3 #9 3::Int)
-#520 := (+ #11 #390)
-#727 := (= #520 0::Int)
-#678 := (not #727)
-#688 := (<= #520 0::Int)
-#634 := (not #688)
-#638 := (>= #733 3::Int)
-#640 := (not #638)
-#1 := true
-#64 := [true-axiom]: true
-#629 := (or false #640)
-#630 := [th-lemma arith]: #629
-#631 := [unit-resolution #630 #64]: #640
-#632 := [hypothesis]: #688
-#71 := (>= #11 3::Int)
-#12 := (< #11 3::Int)
-#13 := (not #12)
-#78 := (iff #13 #71)
-#69 := (not #71)
-#73 := (not #69)
-#76 := (iff #73 #71)
-#77 := [rewrite]: #76
-#74 := (iff #13 #73)
-#70 := (iff #12 #69)
-#72 := [rewrite]: #70
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#66 := [asserted]: #13
-#80 := [mp #66 #79]: #71
-#633 := [th-lemma arith farkas -1 1 1 #80 #632 #631]: false
-#635 := [lemma #633]: #634
-#623 := (or #678 #688)
-#624 := [th-lemma arith triangle-eq]: #623
-#626 := [unit-resolution #624 #635]: #678
-#621 := (or #687 #727)
-#712 := -3::Int
-#401 := (* -1::Int f6)
-#436 := (mod #401 -3::Int)
-#332 := (+ #11 #436)
-#431 := (= #332 0::Int)
-#710 := (if #725 #727 #431)
-#412 := (= #11 0::Int)
-#411 := (= f6 0::Int)
-#421 := (if #411 #412 #710)
-#17 := (:var 0 Int)
-#15 := (:var 1 Int)
-#37 := (f4 f5 #15)
-#38 := (f3 #37 #17)
-#746 := (pattern #38)
-#84 := (* -1::Int #17)
-#81 := (* -1::Int #15)
-#139 := (mod #81 #84)
-#254 := (+ #38 #139)
-#255 := (= #254 0::Int)
-#39 := (mod #15 #17)
-#251 := (* -1::Int #39)
-#252 := (+ #38 #251)
-#253 := (= #252 0::Int)
-#106 := (<= #17 0::Int)
-#113 := (>= #15 0::Int)
-#198 := (or #113 #106)
-#199 := (not #198)
-#102 := (<= #15 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#256 := (if #202 #253 #255)
-#250 := (= #38 0::Int)
-#20 := (= #15 0::Int)
-#257 := (if #20 #250 #256)
-#249 := (= #38 #15)
-#21 := (= #17 0::Int)
-#258 := (if #21 #249 #257)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#750 := (iff #261 #747)
-#748 := (iff #258 #258)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#145 := (* -1::Int #139)
-#218 := (if #202 #39 #145)
-#221 := (if #20 0::Int #218)
-#224 := (if #21 #15 #221)
-#227 := (= #38 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#107 := (not #106)
-#114 := (not #113)
-#117 := (and #114 #107)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#165 := (if #120 #39 #145)
-#168 := (if #20 0::Int #165)
-#171 := (if #21 #15 #168)
-#174 := (= #38 #171)
-#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
-#231 := (iff #177 #230)
-#228 := (iff #174 #227)
-#225 := (= #171 #224)
-#222 := (= #168 #221)
-#219 := (= #165 #218)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#220 := [monotonicity #204]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#188 := (~ #177 #177)
-#187 := (~ #174 #174)
-#184 := [refl]: #187
-#189 := [nnf-pos #184]: #188
-#31 := (- #17)
-#30 := (- #15)
-#40 := (mod #30 #31)
-#41 := (- #40)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#42 := (if #28 #39 #41)
-#43 := (if #20 0::Int #42)
-#44 := (if #21 #15 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#180 := (iff #46 #177)
-#150 := (if #28 #39 #145)
-#153 := (if #20 0::Int #150)
-#156 := (if #21 #15 #153)
-#159 := (= #38 #156)
-#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
-#178 := (iff #162 #177)
-#175 := (iff #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#166 := (= #150 #165)
-#121 := (iff #28 #120)
-#118 := (iff #27 #117)
-#108 := (iff #24 #107)
-#109 := [rewrite]: #108
-#115 := (iff #26 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116 #109]: #118
-#111 := (iff #25 #110)
-#104 := (iff #23 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#167 := [monotonicity #122]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [quant-intro #176]: #178
-#163 := (iff #46 #162)
-#160 := (iff #45 #159)
-#157 := (= #44 #156)
-#154 := (= #43 #153)
-#151 := (= #42 #150)
-#148 := (= #41 #145)
-#142 := (- #139)
-#146 := (= #142 #145)
-#147 := [rewrite]: #146
-#143 := (= #41 #142)
-#140 := (= #40 #139)
-#85 := (= #31 #84)
-#86 := [rewrite]: #85
-#82 := (= #30 #81)
-#83 := [rewrite]: #82
-#141 := [monotonicity #83 #86]: #140
-#144 := [monotonicity #141]: #143
-#149 := [trans #144 #147]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#181 := [trans #164 #179]: #180
-#138 := [asserted]: #46
-#182 := [mp #138 #181]: #177
-#185 := [mp~ #182 #189]: #177
-#233 := [mp #185 #232]: #230
-#264 := [mp #233 #263]: #261
-#752 := [mp #264 #751]: #747
-#705 := (not #747)
-#694 := (or #705 #421)
-#402 := (* -1::Int 3::Int)
-#734 := (mod #401 #402)
-#735 := (+ #11 #734)
-#736 := (= #735 0::Int)
-#414 := (<= 3::Int 0::Int)
-#417 := (or #413 #414)
-#396 := (not #417)
-#415 := (or #403 #414)
-#416 := (not #415)
-#731 := (or #416 #396)
-#737 := (if #731 #727 #736)
-#732 := (if #411 #412 #737)
-#410 := (= #11 f6)
-#326 := (= 3::Int 0::Int)
-#738 := (if #326 #410 #732)
-#695 := (or #705 #738)
-#691 := (iff #695 #694)
-#697 := (iff #694 #694)
-#698 := [rewrite]: #697
-#704 := (iff #738 #421)
-#424 := (if false #410 #421)
-#418 := (iff #424 #421)
-#700 := [rewrite]: #418
-#702 := (iff #738 #424)
-#422 := (iff #732 #421)
-#707 := (iff #737 #710)
-#432 := (iff #736 #431)
-#708 := (= #735 #332)
-#437 := (= #734 #436)
-#713 := (= #402 -3::Int)
-#435 := [rewrite]: #713
-#438 := [monotonicity #435]: #437
-#709 := [monotonicity #438]: #708
-#706 := [monotonicity #709]: #432
-#723 := (iff #731 #725)
-#364 := (iff #396 #724)
-#359 := (iff #417 #413)
-#718 := (or #413 false)
-#715 := (iff #718 #413)
-#721 := [rewrite]: #715
-#719 := (iff #417 #718)
-#393 := (iff #414 false)
-#729 := [rewrite]: #393
-#720 := [monotonicity #729]: #719
-#722 := [trans #720 #721]: #359
-#365 := [monotonicity #722]: #364
-#716 := (iff #416 #380)
-#378 := (iff #415 #403)
-#389 := (or #403 false)
-#714 := (iff #389 #403)
-#377 := [rewrite]: #714
-#730 := (iff #415 #389)
-#373 := [monotonicity #729]: #730
-#379 := [trans #373 #377]: #378
-#717 := [monotonicity #379]: #716
-#726 := [monotonicity #717 #365]: #723
-#711 := [monotonicity #726 #706]: #707
-#423 := [monotonicity #711]: #422
-#728 := (iff #326 false)
-#388 := [rewrite]: #728
-#703 := [monotonicity #388 #423]: #702
-#701 := [trans #703 #700]: #704
-#692 := [monotonicity #701]: #691
-#693 := [trans #692 #698]: #691
-#696 := [quant-inst #8 #10]: #695
-#699 := [mp #696 #693]: #694
-#627 := [unit-resolution #699 #752]: #421
-#523 := (not #411)
-#564 := (not #421)
-#617 := (or #564 #523)
-#672 := (not #412)
-#540 := (<= #11 0::Int)
-#628 := (not #540)
-#665 := (or #628 #69)
-#666 := [th-lemma arith farkas 1 1]: #665
-#625 := [unit-resolution #666 #80]: #628
-#636 := (or #672 #540)
-#614 := [th-lemma arith triangle-eq]: #636
-#615 := [unit-resolution #614 #625]: #672
-#671 := (or #564 #523 #412)
-#573 := [def-axiom]: #671
-#618 := [unit-resolution #573 #615]: #617
-#619 := [unit-resolution #618 #627]: #523
-#668 := (or #564 #411 #710)
-#669 := [def-axiom]: #668
-#620 := [unit-resolution #669 #619 #627]: #710
-#519 := (not #710)
-#521 := (or #519 #687 #727)
-#522 := [def-axiom]: #521
-#616 := [unit-resolution #522 #620]: #621
-#622 := [unit-resolution #616 #626]: #687
-#542 := (or #725 #403)
-#684 := [def-axiom]: #542
-#608 := [unit-resolution #684 #622]: #403
-#685 := (or #725 #413)
-#686 := [def-axiom]: #685
-#604 := [unit-resolution #686 #622]: #413
-#605 := (or #411 #380 #724)
-#606 := [th-lemma arith triangle-eq]: #605
-#609 := [unit-resolution #606 #619]: #725
-[unit-resolution #609 #604 #608]: false
-unsat
-cbbba807c2c13814c06e13ca075bfb5d6e46a98c 320 0
-#2 := false
-#10 := 3::Int
-decl f6 :: Int
-#8 := f6
-#743 := (mod f6 3::Int)
-#658 := (>= #743 3::Int)
-#663 := (not #658)
-#1 := true
-#66 := [true-axiom]: true
-#645 := (or false #663)
-#646 := [th-lemma arith]: #645
-#647 := [unit-resolution #646 #66]: #663
-#21 := 0::Int
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#7 := f5
-#9 := (f4 f5 f6)
-#11 := (f3 #9 3::Int)
-#92 := -1::Int
-#639 := (* -1::Int #11)
-#640 := (+ f6 #639)
-#641 := (<= #640 0::Int)
-#638 := (= f6 #11)
-#12 := (= #11 f6)
-#78 := (>= f6 3::Int)
-#76 := (not #78)
-#69 := (not #12)
-#80 := (or #69 #76)
-#83 := (not #80)
-#13 := (< f6 3::Int)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#86 := (iff #15 #83)
-#70 := (or #69 #13)
-#73 := (not #70)
-#84 := (iff #73 #83)
-#81 := (iff #70 #80)
-#77 := (iff #13 #76)
-#79 := [rewrite]: #77
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#74 := (iff #15 #73)
-#71 := (iff #14 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#87 := [trans #75 #85]: #86
-#68 := [asserted]: #15
-#88 := [mp #68 #87]: #83
-#89 := [not-or-elim #88]: #12
-#637 := [symm #89]: #638
-#648 := (not #638)
-#626 := (or #648 #641)
-#627 := [th-lemma arith triangle-eq]: #626
-#629 := [unit-resolution #627 #637]: #641
-#90 := [not-or-elim #88]: #78
-#745 := (* -1::Int #743)
-#402 := (+ #11 #745)
-#699 := (<= #402 0::Int)
-#532 := (= #402 0::Int)
-#738 := -3::Int
-#739 := (* -1::Int f6)
-#447 := (mod #739 -3::Int)
-#450 := (+ #11 #447)
-#721 := (= #450 0::Int)
-#428 := (>= f6 0::Int)
-#734 := (not #428)
-#424 := (<= f6 0::Int)
-#391 := (not #424)
-#377 := (or #391 #734)
-#718 := (if #377 #532 #721)
-#423 := (= #11 0::Int)
-#422 := (= f6 0::Int)
-#723 := (if #422 #423 #718)
-#19 := (:var 0 Int)
-#17 := (:var 1 Int)
-#39 := (f4 f5 #17)
-#40 := (f3 #39 #19)
-#758 := (pattern #40)
-#96 := (* -1::Int #19)
-#93 := (* -1::Int #17)
-#151 := (mod #93 #96)
-#266 := (+ #40 #151)
-#267 := (= #266 0::Int)
-#41 := (mod #17 #19)
-#263 := (* -1::Int #41)
-#264 := (+ #40 #263)
-#265 := (= #264 0::Int)
-#118 := (<= #19 0::Int)
-#125 := (>= #17 0::Int)
-#210 := (or #125 #118)
-#211 := (not #210)
-#114 := (<= #17 0::Int)
-#196 := (or #114 #118)
-#197 := (not #196)
-#214 := (or #197 #211)
-#268 := (if #214 #265 #267)
-#262 := (= #40 0::Int)
-#22 := (= #17 0::Int)
-#269 := (if #22 #262 #268)
-#261 := (= #40 #17)
-#23 := (= #19 0::Int)
-#270 := (if #23 #261 #269)
-#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #270)
-#273 := (forall (vars (?v0 Int) (?v1 Int)) #270)
-#762 := (iff #273 #759)
-#760 := (iff #270 #270)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#157 := (* -1::Int #151)
-#230 := (if #214 #41 #157)
-#233 := (if #22 0::Int #230)
-#236 := (if #23 #17 #233)
-#239 := (= #40 #236)
-#242 := (forall (vars (?v0 Int) (?v1 Int)) #239)
-#274 := (iff #242 #273)
-#271 := (iff #239 #270)
-#272 := [rewrite]: #271
-#275 := [quant-intro #272]: #274
-#119 := (not #118)
-#126 := (not #125)
-#129 := (and #126 #119)
-#115 := (not #114)
-#122 := (and #115 #119)
-#132 := (or #122 #129)
-#177 := (if #132 #41 #157)
-#180 := (if #22 0::Int #177)
-#183 := (if #23 #17 #180)
-#186 := (= #40 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#243 := (iff #189 #242)
-#240 := (iff #186 #239)
-#237 := (= #183 #236)
-#234 := (= #180 #233)
-#231 := (= #177 #230)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#213 := [rewrite]: #212
-#204 := (iff #122 #197)
-#205 := [rewrite]: #204
-#216 := [monotonicity #205 #213]: #215
-#232 := [monotonicity #216]: #231
-#235 := [monotonicity #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [monotonicity #238]: #240
-#244 := [quant-intro #241]: #243
-#202 := (~ #189 #189)
-#201 := (~ #186 #186)
-#198 := [refl]: #201
-#203 := [nnf-pos #198]: #202
-#33 := (- #19)
-#32 := (- #17)
-#42 := (mod #32 #33)
-#43 := (- #42)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#44 := (if #30 #41 #43)
-#45 := (if #22 0::Int #44)
-#46 := (if #23 #17 #45)
-#47 := (= #40 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#192 := (iff #48 #189)
-#162 := (if #30 #41 #157)
-#165 := (if #22 0::Int #162)
-#168 := (if #23 #17 #165)
-#171 := (= #40 #168)
-#174 := (forall (vars (?v0 Int) (?v1 Int)) #171)
-#190 := (iff #174 #189)
-#187 := (iff #171 #186)
-#184 := (= #168 #183)
-#181 := (= #165 #180)
-#178 := (= #162 #177)
-#133 := (iff #30 #132)
-#130 := (iff #29 #129)
-#120 := (iff #26 #119)
-#121 := [rewrite]: #120
-#127 := (iff #28 #126)
-#128 := [rewrite]: #127
-#131 := [monotonicity #128 #121]: #130
-#123 := (iff #27 #122)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#124 := [monotonicity #117 #121]: #123
-#134 := [monotonicity #124 #131]: #133
-#179 := [monotonicity #134]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#175 := (iff #48 #174)
-#172 := (iff #47 #171)
-#169 := (= #46 #168)
-#166 := (= #45 #165)
-#163 := (= #44 #162)
-#160 := (= #43 #157)
-#154 := (- #151)
-#158 := (= #154 #157)
-#159 := [rewrite]: #158
-#155 := (= #43 #154)
-#152 := (= #42 #151)
-#97 := (= #33 #96)
-#98 := [rewrite]: #97
-#94 := (= #32 #93)
-#95 := [rewrite]: #94
-#153 := [monotonicity #95 #98]: #152
-#156 := [monotonicity #153]: #155
-#161 := [trans #156 #159]: #160
-#164 := [monotonicity #161]: #163
-#167 := [monotonicity #164]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [quant-intro #173]: #175
-#193 := [trans #176 #191]: #192
-#150 := [asserted]: #48
-#194 := [mp #150 #193]: #189
-#199 := [mp~ #194 #203]: #189
-#245 := [mp #199 #244]: #242
-#276 := [mp #245 #275]: #273
-#764 := [mp #276 #763]: #759
-#713 := (not #759)
-#717 := (or #713 #723)
-#413 := (* -1::Int 3::Int)
-#414 := (mod #739 #413)
-#746 := (+ #11 #414)
-#747 := (= #746 0::Int)
-#415 := (<= 3::Int 0::Int)
-#425 := (or #428 #415)
-#429 := (not #425)
-#426 := (or #424 #415)
-#427 := (not #426)
-#408 := (or #427 #429)
-#748 := (if #408 #532 #747)
-#749 := (if #422 #423 #748)
-#338 := (= 3::Int 0::Int)
-#744 := (if #338 #12 #749)
-#706 := (or #713 #744)
-#708 := (iff #706 #717)
-#704 := (iff #717 #717)
-#709 := [rewrite]: #704
-#712 := (iff #744 #723)
-#435 := (if false #12 #723)
-#715 := (iff #435 #723)
-#430 := [rewrite]: #715
-#436 := (iff #744 #435)
-#433 := (iff #749 #723)
-#722 := (iff #748 #718)
-#443 := (iff #747 #721)
-#344 := (= #746 #450)
-#448 := (= #414 #447)
-#724 := (= #413 -3::Int)
-#725 := [rewrite]: #724
-#449 := [monotonicity #725]: #448
-#720 := [monotonicity #449]: #344
-#444 := [monotonicity #720]: #443
-#737 := (iff #408 #377)
-#736 := (iff #429 #734)
-#733 := (iff #425 #428)
-#729 := (or #428 false)
-#732 := (iff #729 #428)
-#727 := [rewrite]: #732
-#730 := (iff #425 #729)
-#400 := (iff #415 false)
-#405 := [rewrite]: #400
-#731 := [monotonicity #405]: #730
-#371 := [trans #731 #727]: #733
-#376 := [monotonicity #371]: #736
-#392 := (iff #427 #391)
-#389 := (iff #426 #424)
-#741 := (or #424 false)
-#385 := (iff #741 #424)
-#726 := [rewrite]: #385
-#401 := (iff #426 #741)
-#742 := [monotonicity #405]: #401
-#390 := [trans #742 #726]: #389
-#728 := [monotonicity #390]: #392
-#735 := [monotonicity #728 #376]: #737
-#719 := [monotonicity #735 #444]: #722
-#434 := [monotonicity #719]: #433
-#750 := (iff #338 false)
-#740 := [rewrite]: #750
-#714 := [monotonicity #740 #434]: #436
-#716 := [trans #714 #430]: #712
-#703 := [monotonicity #716]: #708
-#710 := [trans #703 #709]: #708
-#707 := [quant-inst #8 #10]: #706
-#705 := [mp #707 #710]: #717
-#630 := [unit-resolution #705 #764]: #723
-#692 := (not #723)
-#616 := (or #692 #718)
-#574 := (not #422)
-#631 := (or #391 #76)
-#632 := [th-lemma arith farkas 1 1]: #631
-#633 := [unit-resolution #632 #90]: #391
-#628 := (or #574 #424)
-#634 := [th-lemma arith triangle-eq]: #628
-#620 := [unit-resolution #634 #633]: #574
-#535 := (or #692 #422 #718)
-#683 := [def-axiom]: #535
-#617 := [unit-resolution #683 #620]: #616
-#618 := [unit-resolution #617 #630]: #718
-#701 := (not #718)
-#622 := (or #701 #532)
-#711 := (or #377 #424)
-#552 := [def-axiom]: #711
-#621 := [unit-resolution #552 #633]: #377
-#696 := (not #377)
-#695 := (or #701 #696 #532)
-#702 := [def-axiom]: #695
-#623 := [unit-resolution #702 #621]: #622
-#624 := [unit-resolution #623 #618]: #532
-#534 := (not #532)
-#619 := (or #534 #699)
-#625 := [th-lemma arith triangle-eq]: #619
-#598 := [unit-resolution #625 #624]: #699
-[th-lemma arith farkas 1 -1 1 1 #598 #90 #629 #647]: false
-unsat
-2f21051636feadbefcb468a259b1c1e30b5de4ad 556 0
-#2 := false
-#23 := 0::Int
-decl f4 :: (-> S2 Int Int)
-#10 := 1::Int
-decl f5 :: (-> S3 Int S2)
-decl f3 :: Int
-#7 := f3
-decl f7 :: S3
-#13 := f7
-#14 := (f5 f7 f3)
-#15 := (f4 #14 1::Int)
-#82 := -1::Int
-#84 := (* -1::Int #15)
-decl f6 :: S3
-#8 := f6
-#9 := (f5 f6 f3)
-#11 := (f4 #9 1::Int)
-#83 := (* -1::Int #11)
-#85 := (+ #83 #84)
-#86 := (+ f3 #85)
-#426 := (>= #86 0::Int)
-#622 := (<= #15 0::Int)
-#686 := (= #15 0::Int)
-#427 := (= f3 0::Int)
-#573 := (not #427)
-#604 := (not #686)
-#545 := [hypothesis]: #604
-#581 := (or #573 #686)
-#750 := (* -1::Int f3)
-#691 := (mod #750 -1::Int)
-#658 := (+ #15 #691)
-#639 := (= #658 0::Int)
-#412 := (>= f3 0::Int)
-#452 := (not #412)
-#431 := (<= f3 0::Int)
-#738 := (not #431)
-#348 := (or #738 #452)
-#643 := (if #348 #686 #639)
-#646 := (if #427 #686 #643)
-#21 := (:var 0 Int)
-#19 := (:var 1 Int)
-#41 := (f5 f7 #19)
-#42 := (f4 #41 #21)
-#762 := (pattern #42)
-#100 := (* -1::Int #21)
-#97 := (* -1::Int #19)
-#155 := (mod #97 #100)
-#270 := (+ #42 #155)
-#271 := (= #270 0::Int)
-#43 := (mod #19 #21)
-#267 := (* -1::Int #43)
-#268 := (+ #42 #267)
-#269 := (= #268 0::Int)
-#122 := (<= #21 0::Int)
-#129 := (>= #19 0::Int)
-#214 := (or #129 #122)
-#215 := (not #214)
-#118 := (<= #19 0::Int)
-#212 := (or #118 #122)
-#213 := (not #212)
-#218 := (or #213 #215)
-#272 := (if #218 #269 #271)
-#266 := (= #42 0::Int)
-#24 := (= #19 0::Int)
-#273 := (if #24 #266 #272)
-#265 := (= #42 #19)
-#25 := (= #21 0::Int)
-#274 := (if #25 #265 #273)
-#763 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #762) #274)
-#277 := (forall (vars (?v0 Int) (?v1 Int)) #274)
-#766 := (iff #277 #763)
-#764 := (iff #274 #274)
-#765 := [refl]: #764
-#767 := [quant-intro #765]: #766
-#161 := (* -1::Int #155)
-#234 := (if #218 #43 #161)
-#237 := (if #24 0::Int #234)
-#240 := (if #25 #19 #237)
-#243 := (= #42 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#278 := (iff #246 #277)
-#275 := (iff #243 #274)
-#276 := [rewrite]: #275
-#279 := [quant-intro #276]: #278
-#123 := (not #122)
-#130 := (not #129)
-#133 := (and #130 #123)
-#119 := (not #118)
-#126 := (and #119 #123)
-#136 := (or #126 #133)
-#181 := (if #136 #43 #161)
-#184 := (if #24 0::Int #181)
-#187 := (if #25 #19 #184)
-#190 := (= #42 #187)
-#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
-#247 := (iff #193 #246)
-#244 := (iff #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#235 := (= #181 #234)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#217 := [rewrite]: #216
-#206 := (iff #126 #213)
-#207 := [rewrite]: #206
-#220 := [monotonicity #207 #217]: #219
-#236 := [monotonicity #220]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#204 := (~ #193 #193)
-#203 := (~ #190 #190)
-#200 := [refl]: #203
-#205 := [nnf-pos #200]: #204
-#35 := (- #21)
-#34 := (- #19)
-#44 := (mod #34 #35)
-#45 := (- #44)
-#28 := (< 0::Int #21)
-#30 := (< #19 0::Int)
-#31 := (and #30 #28)
-#27 := (< 0::Int #19)
-#29 := (and #27 #28)
-#32 := (or #29 #31)
-#46 := (if #32 #43 #45)
-#47 := (if #24 0::Int #46)
-#48 := (if #25 #19 #47)
-#49 := (= #42 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#196 := (iff #50 #193)
-#166 := (if #32 #43 #161)
-#169 := (if #24 0::Int #166)
-#172 := (if #25 #19 #169)
-#175 := (= #42 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#194 := (iff #178 #193)
-#191 := (iff #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#182 := (= #166 #181)
-#137 := (iff #32 #136)
-#134 := (iff #31 #133)
-#124 := (iff #28 #123)
-#125 := [rewrite]: #124
-#131 := (iff #30 #130)
-#132 := [rewrite]: #131
-#135 := [monotonicity #132 #125]: #134
-#127 := (iff #29 #126)
-#120 := (iff #27 #119)
-#121 := [rewrite]: #120
-#128 := [monotonicity #121 #125]: #127
-#138 := [monotonicity #128 #135]: #137
-#183 := [monotonicity #138]: #182
-#186 := [monotonicity #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [monotonicity #189]: #191
-#195 := [quant-intro #192]: #194
-#179 := (iff #50 #178)
-#176 := (iff #49 #175)
-#173 := (= #48 #172)
-#170 := (= #47 #169)
-#167 := (= #46 #166)
-#164 := (= #45 #161)
-#158 := (- #155)
-#162 := (= #158 #161)
-#163 := [rewrite]: #162
-#159 := (= #45 #158)
-#156 := (= #44 #155)
-#101 := (= #35 #100)
-#102 := [rewrite]: #101
-#98 := (= #34 #97)
-#99 := [rewrite]: #98
-#157 := [monotonicity #99 #102]: #156
-#160 := [monotonicity #157]: #159
-#165 := [trans #160 #163]: #164
-#168 := [monotonicity #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#197 := [trans #180 #195]: #196
-#154 := [asserted]: #50
-#198 := [mp #154 #197]: #193
-#201 := [mp~ #198 #205]: #193
-#249 := [mp #201 #248]: #246
-#280 := [mp #249 #279]: #277
-#768 := [mp #280 #767]: #763
-#633 := (not #763)
-#634 := (or #633 #646)
-#751 := (* -1::Int 1::Int)
-#671 := (mod #750 #751)
-#668 := (+ #15 #671)
-#670 := (= #668 0::Int)
-#535 := (mod f3 1::Int)
-#690 := (* -1::Int #535)
-#677 := (+ #15 #690)
-#679 := (= #677 0::Int)
-#432 := (<= 1::Int 0::Int)
-#747 := (or #412 #432)
-#749 := (not #747)
-#429 := (or #431 #432)
-#433 := (not #429)
-#406 := (or #433 #749)
-#680 := (if #406 #679 #670)
-#681 := (if #427 #686 #680)
-#689 := (= #15 f3)
-#428 := (= 1::Int 0::Int)
-#682 := (if #428 #689 #681)
-#635 := (or #633 #682)
-#637 := (iff #635 #634)
-#638 := (iff #634 #634)
-#624 := [rewrite]: #638
-#630 := (iff #682 #646)
-#649 := (if false #689 #646)
-#641 := (iff #649 #646)
-#652 := [rewrite]: #641
-#650 := (iff #682 #649)
-#647 := (iff #681 #646)
-#644 := (iff #680 #643)
-#640 := (iff #670 #639)
-#655 := (= #668 #658)
-#656 := (= #671 #691)
-#447 := (= #751 -1::Int)
-#448 := [rewrite]: #447
-#657 := [monotonicity #448]: #656
-#659 := [monotonicity #657]: #655
-#642 := [monotonicity #659]: #640
-#653 := (iff #679 #686)
-#662 := (= #677 #15)
-#661 := (+ #15 0::Int)
-#665 := (= #661 #15)
-#666 := [rewrite]: #665
-#663 := (= #677 #661)
-#676 := (= #690 0::Int)
-#672 := (* -1::Int 0::Int)
-#675 := (= #672 0::Int)
-#669 := [rewrite]: #675
-#673 := (= #690 #672)
-#678 := (= #535 0::Int)
-#683 := [rewrite]: #678
-#674 := [monotonicity #683]: #673
-#660 := [trans #674 #669]: #676
-#664 := [monotonicity #660]: #663
-#667 := [trans #664 #666]: #662
-#654 := [monotonicity #667]: #653
-#724 := (iff #406 #348)
-#453 := (iff #749 #452)
-#729 := (iff #747 #412)
-#381 := (or #412 false)
-#742 := (iff #381 #412)
-#728 := [rewrite]: #742
-#741 := (iff #747 #381)
-#396 := (iff #432 false)
-#732 := [rewrite]: #396
-#739 := [monotonicity #732]: #741
-#451 := [trans #739 #728]: #729
-#454 := [monotonicity #451]: #453
-#740 := (iff #433 #738)
-#737 := (iff #429 #431)
-#733 := (or #431 false)
-#736 := (iff #733 #431)
-#731 := [rewrite]: #736
-#734 := (iff #429 #733)
-#735 := [monotonicity #732]: #734
-#375 := [trans #735 #731]: #737
-#380 := [monotonicity #375]: #740
-#725 := [monotonicity #380 #454]: #724
-#645 := [monotonicity #725 #654 #642]: #644
-#648 := [monotonicity #645]: #647
-#409 := (iff #428 false)
-#745 := [rewrite]: #409
-#651 := [monotonicity #745 #648]: #650
-#631 := [trans #651 #652]: #630
-#632 := [monotonicity #631]: #637
-#620 := [trans #632 #624]: #637
-#636 := [quant-inst #7 #10]: #635
-#621 := [mp #636 #620]: #634
-#600 := [unit-resolution #621 #768]: #646
-#611 := (not #646)
-#612 := (or #611 #573 #686)
-#613 := [def-axiom]: #612
-#605 := [unit-resolution #613 #600]: #581
-#606 := [unit-resolution #605 #545]: #573
-#705 := (not #348)
-#601 := (or #427 #643)
-#616 := (or #611 #427 #643)
-#617 := [def-axiom]: #616
-#607 := [unit-resolution #617 #600]: #601
-#575 := [unit-resolution #607 #606]: #643
-#628 := (not #643)
-#623 := (or #628 #705 #686)
-#629 := [def-axiom]: #623
-#582 := [unit-resolution #629 #575 #545]: #705
-#703 := (or #348 #431)
-#697 := [def-axiom]: #703
-#541 := [unit-resolution #697 #582]: #431
-#698 := (or #348 #412)
-#704 := [def-axiom]: #698
-#572 := [unit-resolution #704 #582]: #412
-#574 := (or #427 #738 #452)
-#576 := [th-lemma arith triangle-eq]: #574
-#583 := [unit-resolution #576 #572 #541 #606]: false
-#585 := [lemma #583]: #686
-#496 := (or #604 #622)
-#498 := [th-lemma arith triangle-eq]: #496
-#499 := [unit-resolution #498 #585]: #622
-#701 := (<= #11 0::Int)
-#430 := (= #11 0::Int)
-#474 := [hypothesis]: #573
-#536 := (div f3 1::Int)
-#743 := (* -1::Int #536)
-#417 := (+ #11 #743)
-#418 := (= #417 0::Int)
-#580 := (not #418)
-#532 := (+ f3 #743)
-#546 := (>= #532 0::Int)
-#571 := (= #532 0::Int)
-#1 := true
-#68 := [true-axiom]: true
-#509 := (or false #571)
-#512 := [th-lemma arith]: #509
-#514 := [unit-resolution #512 #68]: #571
-#515 := (not #571)
-#511 := (or #515 #546)
-#516 := [th-lemma arith triangle-eq]: #511
-#506 := [unit-resolution #516 #514]: #546
-#537 := (<= #417 0::Int)
-#502 := [hypothesis]: #418
-#503 := (or #580 #537)
-#507 := [th-lemma arith triangle-eq]: #503
-#500 := [unit-resolution #507 #502]: #537
-#504 := (not #546)
-#501 := (not #537)
-#508 := (not #622)
-#505 := (or #426 #508 #501 #504)
-#491 := [th-lemma arith assign-bounds 1 1 -1]: #505
-#493 := [unit-resolution #491 #500 #499 #506]: #426
-#342 := (<= #86 0::Int)
-#544 := (<= #532 0::Int)
-#494 := (or #515 #544)
-#492 := [th-lemma arith triangle-eq]: #494
-#495 := [unit-resolution #492 #514]: #544
-#625 := (>= #15 0::Int)
-#477 := (or #604 #625)
-#479 := [th-lemma arith triangle-eq]: #477
-#480 := [unit-resolution #479 #585]: #625
-#538 := (>= #417 0::Int)
-#481 := (or #580 #538)
-#482 := [th-lemma arith triangle-eq]: #481
-#483 := [unit-resolution #482 #502]: #538
-#486 := (not #544)
-#485 := (not #538)
-#484 := (not #625)
-#487 := (or #342 #484 #485 #486)
-#488 := [th-lemma arith assign-bounds 1 1 -1]: #487
-#489 := [unit-resolution #488 #483 #480 #495]: #342
-#490 := (not #426)
-#478 := (not #342)
-#470 := (or #478 #490)
-#87 := (= #86 0::Int)
-#90 := (not #87)
-#12 := (* #11 1::Int)
-#16 := (+ #12 #15)
-#17 := (= f3 #16)
-#18 := (not #17)
-#93 := (iff #18 #90)
-#73 := (+ #11 #15)
-#76 := (= f3 #73)
-#79 := (not #76)
-#91 := (iff #79 #90)
-#88 := (iff #76 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#80 := (iff #18 #79)
-#77 := (iff #17 #76)
-#74 := (= #16 #73)
-#71 := (= #12 #11)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#94 := [trans #81 #92]: #93
-#70 := [asserted]: #18
-#95 := [mp #70 #94]: #90
-#467 := (or #87 #478 #490)
-#469 := [th-lemma arith triangle-eq]: #467
-#471 := [unit-resolution #469 #95]: #470
-#472 := [unit-resolution #471 #489 #493]: false
-#473 := [lemma #472]: #580
-#722 := (div #750 -1::Int)
-#727 := (* -1::Int #722)
-#439 := (+ #11 #727)
-#719 := (= #439 0::Int)
-#720 := (if #348 #418 #719)
-#468 := (or #427 #720)
-#710 := (if #427 #430 #720)
-#20 := (f5 f6 #19)
-#22 := (f4 #20 #21)
-#755 := (pattern #22)
-#103 := (div #97 #100)
-#254 := (* -1::Int #103)
-#255 := (+ #22 #254)
-#256 := (= #255 0::Int)
-#33 := (div #19 #21)
-#251 := (* -1::Int #33)
-#252 := (+ #22 #251)
-#253 := (= #252 0::Int)
-#257 := (if #218 #253 #256)
-#250 := (= #22 0::Int)
-#26 := (or #24 #25)
-#258 := (if #26 #250 #257)
-#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#759 := (iff #261 #756)
-#757 := (iff #258 #258)
-#758 := [refl]: #757
-#760 := [quant-intro #758]: #759
-#221 := (if #218 #33 #103)
-#224 := (if #26 0::Int #221)
-#227 := (= #22 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#139 := (if #136 #33 #103)
-#142 := (if #26 0::Int #139)
-#145 := (= #22 #142)
-#148 := (forall (vars (?v0 Int) (?v1 Int)) #145)
-#231 := (iff #148 #230)
-#228 := (iff #145 #227)
-#225 := (= #142 #224)
-#222 := (= #139 #221)
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#210 := (~ #148 #148)
-#208 := (~ #145 #145)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#36 := (div #34 #35)
-#37 := (if #32 #33 #36)
-#38 := (if #26 0::Int #37)
-#39 := (= #22 #38)
-#40 := (forall (vars (?v0 Int) (?v1 Int)) #39)
-#151 := (iff #40 #148)
-#106 := (if #32 #33 #103)
-#109 := (if #26 0::Int #106)
-#112 := (= #22 #109)
-#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
-#149 := (iff #115 #148)
-#146 := (iff #112 #145)
-#143 := (= #109 #142)
-#140 := (= #106 #139)
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#116 := (iff #40 #115)
-#113 := (iff #39 #112)
-#110 := (= #38 #109)
-#107 := (= #37 #106)
-#104 := (= #36 #103)
-#105 := [monotonicity #99 #102]: #104
-#108 := [monotonicity #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [quant-intro #114]: #116
-#152 := [trans #117 #150]: #151
-#96 := [asserted]: #40
-#153 := [mp #96 #152]: #148
-#202 := [mp~ #153 #211]: #148
-#233 := [mp #202 #232]: #230
-#264 := [mp #233 #263]: #261
-#761 := [mp #264 #760]: #756
-#707 := (not #756)
-#708 := (or #707 #710)
-#752 := (div #750 #751)
-#753 := (* -1::Int #752)
-#748 := (+ #11 #753)
-#754 := (= #748 0::Int)
-#744 := (if #406 #418 #754)
-#419 := (or #427 #428)
-#404 := (if #419 #430 #744)
-#713 := (or #707 #404)
-#709 := (iff #713 #708)
-#556 := (iff #708 #708)
-#557 := [rewrite]: #556
-#711 := (iff #404 #710)
-#717 := (iff #744 #720)
-#434 := (iff #754 #719)
-#440 := (= #748 #439)
-#437 := (= #753 #727)
-#726 := (= #752 #722)
-#723 := [monotonicity #448]: #726
-#438 := [monotonicity #723]: #437
-#718 := [monotonicity #438]: #440
-#716 := [monotonicity #718]: #434
-#721 := [monotonicity #725 #716]: #717
-#394 := (iff #419 #427)
-#405 := (or #427 false)
-#730 := (iff #405 #427)
-#393 := [rewrite]: #730
-#746 := (iff #419 #405)
-#389 := [monotonicity #745]: #746
-#395 := [trans #389 #393]: #394
-#712 := [monotonicity #395 #721]: #711
-#715 := [monotonicity #712]: #709
-#558 := [trans #715 #557]: #709
-#714 := [quant-inst #7 #10]: #713
-#700 := [mp #714 #558]: #708
-#475 := [unit-resolution #700 #761]: #710
-#688 := (not #710)
-#591 := (or #688 #427 #720)
-#584 := [def-axiom]: #591
-#476 := [unit-resolution #584 #475]: #468
-#461 := [unit-resolution #476 #474]: #720
-#695 := (not #720)
-#693 := (or #695 #705 #418)
-#696 := [def-axiom]: #693
-#462 := [unit-resolution #696 #461 #473]: #705
-#463 := [unit-resolution #697 #462]: #431
-#465 := [unit-resolution #704 #462]: #412
-#464 := [unit-resolution #576 #465 #463 #474]: false
-#466 := [lemma #464]: #427
-#455 := (or #573 #430)
-#588 := (or #688 #573 #430)
-#590 := [def-axiom]: #588
-#456 := [unit-resolution #590 #475]: #455
-#457 := [unit-resolution #456 #466]: #430
-#592 := (not #430)
-#449 := (or #592 #701)
-#458 := [th-lemma arith triangle-eq]: #449
-#459 := [unit-resolution #458 #457]: #701
-#450 := (or #573 #412)
-#460 := [th-lemma arith triangle-eq]: #450
-#441 := [unit-resolution #460 #466]: #412
-#442 := (not #701)
-#443 := (or #426 #442 #508 #452)
-#435 := [th-lemma arith assign-bounds 1 1 -1]: #443
-#444 := [unit-resolution #435 #441 #459 #499]: #426
-#702 := (>= #11 0::Int)
-#445 := (or #592 #702)
-#436 := [th-lemma arith triangle-eq]: #445
-#446 := [unit-resolution #436 #457]: #702
-#413 := (or #573 #431)
-#415 := [th-lemma arith triangle-eq]: #413
-#416 := [unit-resolution #415 #466]: #431
-#407 := (not #702)
-#420 := (or #342 #407 #484 #738)
-#421 := [th-lemma arith assign-bounds 1 1 -1]: #420
-#422 := [unit-resolution #421 #416 #446 #480]: #342
-[unit-resolution #471 #422 #444]: false
-unsat
-d22602bbee9e57cff02bea0b44e81e206f8f757f 546 0
-#2 := false
-#23 := 0::Int
-decl f4 :: (-> S2 Int Int)
-#10 := 3::Int
-decl f5 :: (-> S3 Int S2)
-decl f3 :: Int
-#7 := f3
-decl f6 :: S3
-#8 := f6
-#9 := (f5 f6 f3)
-#11 := (f4 #9 3::Int)
-#704 := (>= #11 0::Int)
-#432 := (= #11 0::Int)
-#429 := (= f3 0::Int)
-#575 := (not #429)
-#571 := [hypothesis]: #575
-#433 := (<= f3 0::Int)
-#414 := (>= f3 0::Int)
-#454 := (not #414)
-#740 := (not #433)
-#350 := (or #740 #454)
-#707 := (not #350)
-#83 := -3::Int
-#85 := -1::Int
-#752 := (* -1::Int f3)
-#724 := (div #752 -3::Int)
-#729 := (* -1::Int #724)
-#441 := (+ #11 #729)
-#721 := (= #441 0::Int)
-#538 := (div f3 3::Int)
-#745 := (* -1::Int #538)
-#419 := (+ #11 #745)
-#420 := (= #419 0::Int)
-#722 := (if #350 #420 #721)
-#557 := (or #429 #722)
-#712 := (if #429 #432 #722)
-#21 := (:var 0 Int)
-#19 := (:var 1 Int)
-#20 := (f5 f6 #19)
-#22 := (f4 #20 #21)
-#757 := (pattern #22)
-#102 := (* -1::Int #21)
-#99 := (* -1::Int #19)
-#105 := (div #99 #102)
-#256 := (* -1::Int #105)
-#257 := (+ #22 #256)
-#258 := (= #257 0::Int)
-#33 := (div #19 #21)
-#253 := (* -1::Int #33)
-#254 := (+ #22 #253)
-#255 := (= #254 0::Int)
-#124 := (<= #21 0::Int)
-#131 := (>= #19 0::Int)
-#216 := (or #131 #124)
-#217 := (not #216)
-#120 := (<= #19 0::Int)
-#214 := (or #120 #124)
-#215 := (not #214)
-#220 := (or #215 #217)
-#259 := (if #220 #255 #258)
-#252 := (= #22 0::Int)
-#25 := (= #21 0::Int)
-#24 := (= #19 0::Int)
-#26 := (or #24 #25)
-#260 := (if #26 #252 #259)
-#758 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #757) #260)
-#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
-#761 := (iff #263 #758)
-#759 := (iff #260 #260)
-#760 := [refl]: #759
-#762 := [quant-intro #760]: #761
-#223 := (if #220 #33 #105)
-#226 := (if #26 0::Int #223)
-#229 := (= #22 #226)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#125 := (not #124)
-#132 := (not #131)
-#135 := (and #132 #125)
-#121 := (not #120)
-#128 := (and #121 #125)
-#138 := (or #128 #135)
-#141 := (if #138 #33 #105)
-#144 := (if #26 0::Int #141)
-#147 := (= #22 #144)
-#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#227 := (= #144 #226)
-#224 := (= #141 #223)
-#221 := (iff #138 #220)
-#218 := (iff #135 #217)
-#219 := [rewrite]: #218
-#208 := (iff #128 #215)
-#209 := [rewrite]: #208
-#222 := [monotonicity #209 #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#212 := (~ #150 #150)
-#210 := (~ #147 #147)
-#211 := [refl]: #210
-#213 := [nnf-pos #211]: #212
-#35 := (- #21)
-#34 := (- #19)
-#36 := (div #34 #35)
-#28 := (< 0::Int #21)
-#30 := (< #19 0::Int)
-#31 := (and #30 #28)
-#27 := (< 0::Int #19)
-#29 := (and #27 #28)
-#32 := (or #29 #31)
-#37 := (if #32 #33 #36)
-#38 := (if #26 0::Int #37)
-#39 := (= #22 #38)
-#40 := (forall (vars (?v0 Int) (?v1 Int)) #39)
-#153 := (iff #40 #150)
-#108 := (if #32 #33 #105)
-#111 := (if #26 0::Int #108)
-#114 := (= #22 #111)
-#117 := (forall (vars (?v0 Int) (?v1 Int)) #114)
-#151 := (iff #117 #150)
-#148 := (iff #114 #147)
-#145 := (= #111 #144)
-#142 := (= #108 #141)
-#139 := (iff #32 #138)
-#136 := (iff #31 #135)
-#126 := (iff #28 #125)
-#127 := [rewrite]: #126
-#133 := (iff #30 #132)
-#134 := [rewrite]: #133
-#137 := [monotonicity #134 #127]: #136
-#129 := (iff #29 #128)
-#122 := (iff #27 #121)
-#123 := [rewrite]: #122
-#130 := [monotonicity #123 #127]: #129
-#140 := [monotonicity #130 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#118 := (iff #40 #117)
-#115 := (iff #39 #114)
-#112 := (= #38 #111)
-#109 := (= #37 #108)
-#106 := (= #36 #105)
-#103 := (= #35 #102)
-#104 := [rewrite]: #103
-#100 := (= #34 #99)
-#101 := [rewrite]: #100
-#107 := [monotonicity #101 #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [quant-intro #116]: #118
-#154 := [trans #119 #152]: #153
-#98 := [asserted]: #40
-#155 := [mp #98 #154]: #150
-#204 := [mp~ #155 #213]: #150
-#235 := [mp #204 #234]: #232
-#266 := [mp #235 #265]: #263
-#763 := [mp #266 #762]: #758
-#709 := (not #758)
-#710 := (or #709 #712)
-#753 := (* -1::Int 3::Int)
-#754 := (div #752 #753)
-#755 := (* -1::Int #754)
-#750 := (+ #11 #755)
-#756 := (= #750 0::Int)
-#434 := (<= 3::Int 0::Int)
-#749 := (or #414 #434)
-#751 := (not #749)
-#431 := (or #433 #434)
-#435 := (not #431)
-#408 := (or #435 #751)
-#746 := (if #408 #420 #756)
-#430 := (= 3::Int 0::Int)
-#421 := (or #429 #430)
-#406 := (if #421 #432 #746)
-#715 := (or #709 #406)
-#711 := (iff #715 #710)
-#558 := (iff #710 #710)
-#559 := [rewrite]: #558
-#713 := (iff #406 #712)
-#719 := (iff #746 #722)
-#436 := (iff #756 #721)
-#442 := (= #750 #441)
-#439 := (= #755 #729)
-#728 := (= #754 #724)
-#449 := (= #753 -3::Int)
-#450 := [rewrite]: #449
-#725 := [monotonicity #450]: #728
-#440 := [monotonicity #725]: #439
-#720 := [monotonicity #440]: #442
-#718 := [monotonicity #720]: #436
-#726 := (iff #408 #350)
-#455 := (iff #751 #454)
-#731 := (iff #749 #414)
-#383 := (or #414 false)
-#744 := (iff #383 #414)
-#730 := [rewrite]: #744
-#743 := (iff #749 #383)
-#398 := (iff #434 false)
-#734 := [rewrite]: #398
-#741 := [monotonicity #734]: #743
-#453 := [trans #741 #730]: #731
-#456 := [monotonicity #453]: #455
-#742 := (iff #435 #740)
-#739 := (iff #431 #433)
-#735 := (or #433 false)
-#738 := (iff #735 #433)
-#733 := [rewrite]: #738
-#736 := (iff #431 #735)
-#737 := [monotonicity #734]: #736
-#377 := [trans #737 #733]: #739
-#382 := [monotonicity #377]: #742
-#727 := [monotonicity #382 #456]: #726
-#723 := [monotonicity #727 #718]: #719
-#396 := (iff #421 #429)
-#407 := (or #429 false)
-#732 := (iff #407 #429)
-#395 := [rewrite]: #732
-#748 := (iff #421 #407)
-#411 := (iff #430 false)
-#747 := [rewrite]: #411
-#391 := [monotonicity #747]: #748
-#397 := [trans #391 #395]: #396
-#714 := [monotonicity #397 #723]: #713
-#717 := [monotonicity #714]: #711
-#560 := [trans #717 #559]: #711
-#716 := [quant-inst #7 #10]: #715
-#702 := [mp #716 #560]: #710
-#572 := [unit-resolution #702 #763]: #712
-#690 := (not #712)
-#593 := (or #690 #429 #722)
-#586 := [def-axiom]: #593
-#573 := [unit-resolution #586 #572]: #557
-#534 := [unit-resolution #573 #571]: #722
-#693 := (mod #752 -3::Int)
-decl f7 :: S3
-#13 := f7
-#14 := (f5 f7 f3)
-#15 := (f4 #14 3::Int)
-#674 := (+ #15 #693)
-#677 := (= #674 0::Int)
-#537 := (mod f3 3::Int)
-#692 := (* -1::Int #537)
-#679 := (+ #15 #692)
-#681 := (= #679 0::Int)
-#662 := (if #350 #681 #677)
-#533 := (or #429 #662)
-#688 := (= #15 0::Int)
-#666 := (if #429 #688 #662)
-#41 := (f5 f7 #19)
-#42 := (f4 #41 #21)
-#764 := (pattern #42)
-#157 := (mod #99 #102)
-#272 := (+ #42 #157)
-#273 := (= #272 0::Int)
-#43 := (mod #19 #21)
-#269 := (* -1::Int #43)
-#270 := (+ #42 #269)
-#271 := (= #270 0::Int)
-#274 := (if #220 #271 #273)
-#268 := (= #42 0::Int)
-#275 := (if #24 #268 #274)
-#267 := (= #42 #19)
-#276 := (if #25 #267 #275)
-#765 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #764) #276)
-#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
-#768 := (iff #279 #765)
-#766 := (iff #276 #276)
-#767 := [refl]: #766
-#769 := [quant-intro #767]: #768
-#163 := (* -1::Int #157)
-#236 := (if #220 #43 #163)
-#239 := (if #24 0::Int #236)
-#242 := (if #25 #19 #239)
-#245 := (= #42 #242)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#280 := (iff #248 #279)
-#277 := (iff #245 #276)
-#278 := [rewrite]: #277
-#281 := [quant-intro #278]: #280
-#183 := (if #138 #43 #163)
-#186 := (if #24 0::Int #183)
-#189 := (if #25 #19 #186)
-#192 := (= #42 #189)
-#195 := (forall (vars (?v0 Int) (?v1 Int)) #192)
-#249 := (iff #195 #248)
-#246 := (iff #192 #245)
-#243 := (= #189 #242)
-#240 := (= #186 #239)
-#237 := (= #183 #236)
-#238 := [monotonicity #222]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [quant-intro #247]: #249
-#206 := (~ #195 #195)
-#205 := (~ #192 #192)
-#202 := [refl]: #205
-#207 := [nnf-pos #202]: #206
-#44 := (mod #34 #35)
-#45 := (- #44)
-#46 := (if #32 #43 #45)
-#47 := (if #24 0::Int #46)
-#48 := (if #25 #19 #47)
-#49 := (= #42 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#198 := (iff #50 #195)
-#168 := (if #32 #43 #163)
-#171 := (if #24 0::Int #168)
-#174 := (if #25 #19 #171)
-#177 := (= #42 #174)
-#180 := (forall (vars (?v0 Int) (?v1 Int)) #177)
-#196 := (iff #180 #195)
-#193 := (iff #177 #192)
-#190 := (= #174 #189)
-#187 := (= #171 #186)
-#184 := (= #168 #183)
-#185 := [monotonicity #140]: #184
-#188 := [monotonicity #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [quant-intro #194]: #196
-#181 := (iff #50 #180)
-#178 := (iff #49 #177)
-#175 := (= #48 #174)
-#172 := (= #47 #171)
-#169 := (= #46 #168)
-#166 := (= #45 #163)
-#160 := (- #157)
-#164 := (= #160 #163)
-#165 := [rewrite]: #164
-#161 := (= #45 #160)
-#158 := (= #44 #157)
-#159 := [monotonicity #101 #104]: #158
-#162 := [monotonicity #159]: #161
-#167 := [trans #162 #165]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [quant-intro #179]: #181
-#199 := [trans #182 #197]: #198
-#156 := [asserted]: #50
-#200 := [mp #156 #199]: #195
-#203 := [mp~ #200 #207]: #195
-#251 := [mp #203 #250]: #248
-#282 := [mp #251 #281]: #279
-#770 := [mp #282 #769]: #765
-#657 := (not #765)
-#661 := (or #657 #666)
-#673 := (mod #752 #753)
-#670 := (+ #15 #673)
-#672 := (= #670 0::Int)
-#682 := (if #408 #681 #672)
-#683 := (if #429 #688 #682)
-#691 := (= #15 f3)
-#684 := (if #430 #691 #683)
-#641 := (or #657 #684)
-#644 := (iff #641 #661)
-#646 := (iff #661 #661)
-#647 := [rewrite]: #646
-#659 := (iff #684 #666)
-#664 := (if false #691 #666)
-#656 := (iff #664 #666)
-#658 := [rewrite]: #656
-#669 := (iff #684 #664)
-#667 := (iff #683 #666)
-#663 := (iff #682 #662)
-#671 := (iff #672 #677)
-#675 := (= #670 #674)
-#680 := (= #673 #693)
-#685 := [monotonicity #450]: #680
-#676 := [monotonicity #685]: #675
-#678 := [monotonicity #676]: #671
-#665 := [monotonicity #727 #678]: #663
-#668 := [monotonicity #665]: #667
-#655 := [monotonicity #747 #668]: #669
-#660 := [trans #655 #658]: #659
-#645 := [monotonicity #660]: #644
-#648 := [trans #645 #647]: #644
-#642 := [quant-inst #7 #10]: #641
-#649 := [mp #642 #648]: #661
-#577 := [unit-resolution #649 #770]: #666
-#623 := (not #666)
-#628 := (or #623 #429 #662)
-#629 := [def-axiom]: #628
-#512 := [unit-resolution #629 #577]: #533
-#515 := [unit-resolution #512 #571]: #662
-#697 := (not #722)
-#632 := (not #662)
-#476 := (or #707 #632 #697)
-#653 := (>= #679 0::Int)
-#535 := [hypothesis]: #662
-#542 := [hypothesis]: #350
-#633 := (or #632 #707 #681)
-#635 := [def-axiom]: #633
-#544 := [unit-resolution #635 #542 #535]: #681
-#638 := (not #681)
-#484 := (or #638 #653)
-#485 := [th-lemma arith triangle-eq]: #484
-#486 := [unit-resolution #485 #544]: #653
-#540 := (>= #419 0::Int)
-#526 := [hypothesis]: #722
-#695 := (or #697 #707 #420)
-#698 := [def-axiom]: #695
-#527 := [unit-resolution #698 #542 #526]: #420
-#582 := (not #420)
-#487 := (or #582 #540)
-#488 := [th-lemma arith triangle-eq]: #487
-#489 := [unit-resolution #488 #527]: #540
-#86 := (* -1::Int #15)
-#84 := (* -3::Int #11)
-#87 := (+ #84 #86)
-#88 := (+ f3 #87)
-#344 := (<= #88 0::Int)
-#490 := (not #344)
-#428 := (>= #88 0::Int)
-#549 := (not #428)
-#550 := [hypothesis]: #549
-#514 := (or #429 #428)
-#532 := (or #707 #428 #632 #697)
-#652 := (<= #679 0::Int)
-#545 := (or #638 #652)
-#546 := [th-lemma arith triangle-eq]: #545
-#548 := [unit-resolution #546 #544]: #652
-#547 := (* -3::Int #538)
-#602 := (+ #692 #547)
-#583 := (+ f3 #602)
-#584 := (>= #583 0::Int)
-#601 := (= #583 0::Int)
-#1 := true
-#68 := [true-axiom]: true
-#551 := (or false #601)
-#552 := [th-lemma arith]: #551
-#553 := [unit-resolution #552 #68]: #601
-#536 := (not #601)
-#554 := (or #536 #584)
-#524 := [th-lemma arith triangle-eq]: #554
-#525 := [unit-resolution #524 #553]: #584
-#539 := (<= #419 0::Int)
-#529 := (or #582 #539)
-#530 := [th-lemma arith triangle-eq]: #529
-#531 := [unit-resolution #530 #527]: #539
-#374 := [th-lemma arith farkas 3 -1 1 1 #531 #525 #550 #548]: false
-#528 := [lemma #374]: #532
-#519 := [unit-resolution #528 #515 #550 #534]: #707
-#705 := (or #350 #433)
-#699 := [def-axiom]: #705
-#521 := [unit-resolution #699 #519]: #433
-#700 := (or #350 #414)
-#706 := [def-axiom]: #700
-#522 := [unit-resolution #706 #519]: #414
-#520 := (or #429 #740 #454)
-#523 := [th-lemma arith triangle-eq]: #520
-#511 := [unit-resolution #523 #522 #521 #571]: false
-#516 := [lemma #511]: #514
-#517 := [unit-resolution #516 #550]: #429
-#513 := (or #575 #414)
-#518 := [th-lemma arith triangle-eq]: #513
-#508 := [unit-resolution #518 #517]: #414
-#650 := (<= #15 0::Int)
-#498 := (or #575 #688)
-#624 := (or #623 #575 #688)
-#627 := [def-axiom]: #624
-#500 := [unit-resolution #627 #577]: #498
-#501 := [unit-resolution #500 #517]: #688
-#630 := (not #688)
-#504 := (or #630 #650)
-#505 := [th-lemma arith triangle-eq]: #504
-#509 := [unit-resolution #505 #501]: #650
-#703 := (<= #11 0::Int)
-#502 := (or #575 #432)
-#590 := (or #690 #575 #432)
-#592 := [def-axiom]: #590
-#510 := [unit-resolution #592 #572]: #502
-#503 := [unit-resolution #510 #517]: #432
-#594 := (not #432)
-#506 := (or #594 #703)
-#507 := [th-lemma arith triangle-eq]: #506
-#493 := [unit-resolution #507 #503]: #703
-#495 := [th-lemma arith farkas -3 -1 -1 1 #493 #509 #550 #508]: false
-#496 := [lemma #495]: #428
-#492 := (or #490 #549)
-#89 := (= #88 0::Int)
-#92 := (not #89)
-#12 := (* #11 3::Int)
-#16 := (+ #12 #15)
-#17 := (= f3 #16)
-#18 := (not #17)
-#95 := (iff #18 #92)
-#71 := (* 3::Int #11)
-#74 := (+ #71 #15)
-#77 := (= f3 #74)
-#80 := (not #77)
-#93 := (iff #80 #92)
-#90 := (iff #77 #89)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#81 := (iff #18 #80)
-#78 := (iff #17 #77)
-#75 := (= #16 #74)
-#72 := (= #12 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#96 := [trans #82 #94]: #95
-#70 := [asserted]: #18
-#97 := [mp #70 #96]: #92
-#491 := (or #89 #490 #549)
-#480 := [th-lemma arith triangle-eq]: #491
-#469 := [unit-resolution #480 #97]: #492
-#471 := [unit-resolution #469 #496]: #490
-#494 := (<= #583 0::Int)
-#472 := (or #536 #494)
-#473 := [th-lemma arith triangle-eq]: #472
-#474 := [unit-resolution #473 #553]: #494
-#475 := [th-lemma arith farkas -1 1 3 1 #474 #471 #489 #486]: false
-#477 := [lemma #475]: #476
-#497 := [unit-resolution #477 #515 #534]: #707
-#479 := [unit-resolution #699 #497]: #433
-#481 := [unit-resolution #706 #497]: #414
-#482 := [unit-resolution #523 #481 #479 #571]: false
-#483 := [lemma #482]: #429
-#470 := [unit-resolution #510 #483]: #432
-#478 := (or #594 #704)
-#463 := [th-lemma arith triangle-eq]: #478
-#464 := [unit-resolution #463 #470]: #704
-#651 := (>= #15 0::Int)
-#465 := [unit-resolution #500 #483]: #688
-#467 := (or #630 #651)
-#466 := [th-lemma arith triangle-eq]: #467
-#468 := [unit-resolution #466 #465]: #651
-#457 := (or #575 #433)
-#458 := [th-lemma arith triangle-eq]: #457
-#459 := [unit-resolution #458 #483]: #433
-[th-lemma arith farkas -1/3 1/3 1/3 1 #459 #468 #471 #464]: false
-unsat
-c91002b99b758c3ccb28f44af2851bf6d5b6b3b9 75 0
-#2 := false
-#7 := 0::Int
-decl f3 :: Int
-#8 := f3
-#34 := -1::Int
-#35 := (* -1::Int f3)
-#47 := (>= f3 0::Int)
-#54 := (if #47 f3 #35)
-#74 := (* -1::Int #54)
-#83 := (+ #35 #74)
-#92 := (<= #83 0::Int)
-#79 := (= #35 #54)
-#48 := (not #47)
-#75 := (+ f3 #74)
-#82 := (<= #75 0::Int)
-#78 := (= f3 #54)
-#84 := [hypothesis]: #47
-#80 := (or #48 #78)
-#81 := [def-axiom]: #80
-#85 := [unit-resolution #81 #84]: #78
-#86 := (not #78)
-#87 := (or #86 #82)
-#88 := [th-lemma arith triangle-eq]: #87
-#89 := [unit-resolution #88 #85]: #82
-#63 := (>= #54 0::Int)
-#67 := (not #63)
-#10 := (- f3)
-#9 := (< f3 0::Int)
-#11 := (if #9 #10 f3)
-#12 := (<= 0::Int #11)
-#13 := (not #12)
-#70 := (iff #13 #67)
-#38 := (if #9 #35 f3)
-#41 := (<= 0::Int #38)
-#44 := (not #41)
-#68 := (iff #44 #67)
-#65 := (iff #41 #63)
-#59 := (<= 0::Int #54)
-#62 := (iff #59 #63)
-#64 := [rewrite]: #62
-#60 := (iff #41 #59)
-#57 := (= #38 #54)
-#51 := (if #48 #35 f3)
-#55 := (= #51 #54)
-#56 := [rewrite]: #55
-#52 := (= #38 #51)
-#49 := (iff #9 #48)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#58 := [trans #53 #56]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#39 := (= #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#71 := [trans #46 #69]: #70
-#33 := [asserted]: #13
-#72 := [mp #33 #71]: #67
-#90 := [th-lemma arith farkas -1 1 1 #84 #72 #89]: false
-#91 := [lemma #90]: #48
-#76 := (or #47 #79)
-#77 := [def-axiom]: #76
-#94 := [unit-resolution #77 #91]: #79
-#95 := (not #79)
-#96 := (or #95 #92)
-#97 := [th-lemma arith triangle-eq]: #96
-#98 := [unit-resolution #97 #94]: #92
-[th-lemma arith farkas 1 1 1 #72 #91 #98]: false
-unsat
-f7d5d4604fbbb605eaa83e4616aa639b578e2c1f 103 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#7 := f3
-#36 := -1::Int
-#37 := (* -1::Int f3)
-#58 := (>= f3 0::Int)
-#65 := (if #58 f3 #37)
-#70 := (= #65 0::Int)
-#13 := (= f3 0::Int)
-#118 := (iff #13 #70)
-#87 := (= f3 #65)
-#101 := (<= #37 0::Int)
-#100 := (= #37 0::Int)
-#84 := (not #13)
-#59 := (not #58)
-#103 := [hypothesis]: #59
-#104 := (or #84 #58)
-#105 := [th-lemma arith triangle-eq]: #104
-#106 := [unit-resolution #105 #103]: #84
-#98 := (or #70 #13)
-#73 := (not #70)
-#76 := (iff #73 #13)
-#10 := (- f3)
-#9 := (< f3 0::Int)
-#11 := (if #9 #10 f3)
-#12 := (= #11 0::Int)
-#14 := (iff #12 #13)
-#15 := (not #14)
-#79 := (iff #15 #76)
-#40 := (if #9 #37 f3)
-#43 := (= #40 0::Int)
-#52 := (not #43)
-#53 := (iff #52 #13)
-#77 := (iff #53 #76)
-#74 := (iff #52 #73)
-#71 := (iff #43 #70)
-#68 := (= #40 #65)
-#62 := (if #59 #37 f3)
-#66 := (= #62 #65)
-#67 := [rewrite]: #66
-#63 := (= #40 #62)
-#60 := (iff #9 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#69 := [trans #64 #67]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#56 := (iff #15 #53)
-#46 := (iff #43 #13)
-#49 := (not #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#80 := [trans #57 #78]: #79
-#35 := [asserted]: #15
-#81 := [mp #35 #80]: #76
-#91 := (not #76)
-#96 := (or #70 #13 #91)
-#97 := [def-axiom]: #96
-#99 := [unit-resolution #97 #81]: #98
-#107 := [unit-resolution #99 #106]: #70
-#88 := (= #37 #65)
-#85 := (or #58 #88)
-#86 := [def-axiom]: #85
-#108 := [unit-resolution #86 #103]: #88
-#109 := [trans #108 #107]: #100
-#110 := (not #100)
-#111 := (or #110 #101)
-#112 := [th-lemma arith triangle-eq]: #111
-#113 := [unit-resolution #112 #109]: #101
-#114 := [th-lemma arith farkas 1 1 #103 #113]: false
-#115 := [lemma #114]: #58
-#89 := (or #59 #87)
-#90 := [def-axiom]: #89
-#117 := [unit-resolution #90 #115]: #87
-#119 := [monotonicity #117]: #118
-#120 := (iff #84 #73)
-#121 := [monotonicity #119]: #120
-#102 := [hypothesis]: #84
-#122 := [mp #102 #121]: #73
-#116 := [unit-resolution #99 #102]: #70
-#123 := [unit-resolution #116 #122]: false
-#124 := [lemma #123]: #13
-#126 := [mp #124 #119]: #70
-#94 := (or #73 #84)
-#92 := (or #73 #84 #91)
-#93 := [def-axiom]: #92
-#95 := [unit-resolution #93 #81]: #94
-#125 := [unit-resolution #95 #124]: #73
-[unit-resolution #125 #126]: false
-unsat
-a86d5276873d6d3bf936c62241af1fdd8cbbc24a 102 0
-#2 := false
-#7 := 0::Int
-decl f3 :: Int
-#8 := f3
-#36 := -1::Int
-#37 := (* -1::Int f3)
-#112 := (* -1::Int #37)
-#113 := (+ f3 #112)
-#115 := (>= #113 0::Int)
-#111 := (= f3 #37)
-#58 := (>= f3 0::Int)
-#69 := (if #58 f3 #37)
-#119 := (= #69 #37)
-#89 := (= #37 #69)
-#61 := (not #58)
-#74 := (= #69 f3)
-#88 := (= f3 #69)
-#105 := (not #88)
-#84 := (not #74)
-#106 := (iff #84 #105)
-#103 := (iff #74 #88)
-#104 := [commutativity]: #103
-#107 := [monotonicity #104]: #106
-#100 := [hypothesis]: #84
-#108 := [mp #100 #107]: #105
-#98 := (or #58 #74)
-#77 := (iff #61 #74)
-#11 := (- f3)
-#10 := (< f3 0::Int)
-#12 := (if #10 #11 f3)
-#13 := (= #12 f3)
-#9 := (<= 0::Int f3)
-#14 := (iff #9 #13)
-#15 := (not #14)
-#80 := (iff #15 #77)
-#40 := (if #10 #37 f3)
-#43 := (= #40 f3)
-#52 := (not #9)
-#53 := (iff #52 #43)
-#78 := (iff #53 #77)
-#75 := (iff #43 #74)
-#72 := (= #40 #69)
-#66 := (if #61 #37 f3)
-#70 := (= #66 #69)
-#71 := [rewrite]: #70
-#67 := (= #40 #66)
-#64 := (iff #10 #61)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#76 := [monotonicity #73]: #75
-#62 := (iff #52 #61)
-#59 := (iff #9 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#79 := [monotonicity #63 #76]: #78
-#56 := (iff #15 #53)
-#46 := (iff #9 #43)
-#49 := (not #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#41 := (= #12 #40)
-#38 := (= #11 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#81 := [trans #57 #79]: #80
-#35 := [asserted]: #15
-#82 := [mp #35 #81]: #77
-#85 := (not #77)
-#96 := (or #58 #74 #85)
-#97 := [def-axiom]: #96
-#99 := [unit-resolution #97 #82]: #98
-#101 := [unit-resolution #99 #100]: #58
-#90 := (or #61 #88)
-#91 := [def-axiom]: #90
-#102 := [unit-resolution #91 #101]: #88
-#109 := [unit-resolution #102 #108]: false
-#110 := [lemma #109]: #74
-#94 := (or #61 #84)
-#92 := (or #61 #84 #85)
-#93 := [def-axiom]: #92
-#95 := [unit-resolution #93 #82]: #94
-#116 := [unit-resolution #95 #110]: #61
-#86 := (or #58 #89)
-#87 := [def-axiom]: #86
-#117 := [unit-resolution #87 #116]: #89
-#120 := [symm #117]: #119
-#118 := [symm #110]: #88
-#121 := [trans #118 #120]: #111
-#122 := (not #111)
-#123 := (or #122 #115)
-#124 := [th-lemma arith triangle-eq]: #123
-#125 := [unit-resolution #124 #121]: #115
-[th-lemma arith farkas 2 1 #116 #125]: false
-unsat
-1d4370f4d13676652ec1fdf0e92ac69e5f27e6bc 143 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#7 := f3
-#36 := -1::Int
-#37 := (* -1::Int f3)
-#58 := (>= f3 0::Int)
-#65 := (if #58 f3 #37)
-#104 := (* -1::Int #65)
-#154 := (+ f3 #104)
-#155 := (<= #154 0::Int)
-#90 := (= f3 #65)
-#105 := (+ #37 #104)
-#107 := (>= #105 0::Int)
-#91 := (= #37 #65)
-#59 := (not #58)
-#139 := [hypothesis]: #59
-#88 := (or #58 #91)
-#89 := [def-axiom]: #88
-#140 := [unit-resolution #89 #139]: #91
-#133 := (not #91)
-#141 := (or #133 #107)
-#142 := [th-lemma arith triangle-eq]: #141
-#143 := [unit-resolution #142 #140]: #107
-#73 := (+ f3 #65)
-#86 := (<= #73 0::Int)
-#148 := (not #86)
-#87 := (>= #73 0::Int)
-#106 := (<= #105 0::Int)
-#74 := (= #73 0::Int)
-#94 := (not #74)
-#126 := (not #87)
-#127 := [hypothesis]: #126
-#128 := (or #94 #87)
-#129 := [th-lemma arith triangle-eq]: #128
-#130 := [unit-resolution #129 #127]: #94
-#124 := (or #59 #74)
-#111 := (= f3 0::Int)
-#9 := (<= f3 0::Int)
-#108 := [hypothesis]: #94
-#102 := (or #9 #74)
-#52 := (not #9)
-#79 := (iff #52 #74)
-#11 := (- f3)
-#10 := (< f3 0::Int)
-#12 := (if #10 #11 f3)
-#13 := (= #12 #11)
-#14 := (iff #9 #13)
-#15 := (not #14)
-#82 := (iff #15 #79)
-#40 := (if #10 #37 f3)
-#43 := (= #40 #37)
-#53 := (iff #52 #43)
-#80 := (iff #53 #79)
-#77 := (iff #43 #74)
-#70 := (= #65 #37)
-#75 := (iff #70 #74)
-#76 := [rewrite]: #75
-#71 := (iff #43 #70)
-#68 := (= #40 #65)
-#62 := (if #59 #37 f3)
-#66 := (= #62 #65)
-#67 := [rewrite]: #66
-#63 := (= #40 #62)
-#60 := (iff #10 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#69 := [trans #64 #67]: #68
-#72 := [monotonicity #69]: #71
-#78 := [trans #72 #76]: #77
-#81 := [monotonicity #78]: #80
-#56 := (iff #15 #53)
-#46 := (iff #9 #43)
-#49 := (not #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#38 := (= #11 #37)
-#39 := [rewrite]: #38
-#41 := (= #12 #40)
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42 #39]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#83 := [trans #57 #81]: #82
-#35 := [asserted]: #15
-#84 := [mp #35 #83]: #79
-#95 := (not #79)
-#100 := (or #9 #74 #95)
-#101 := [def-axiom]: #100
-#103 := [unit-resolution #101 #84]: #102
-#109 := [unit-resolution #103 #108]: #9
-#110 := [hypothesis]: #58
-#112 := [th-lemma arith eq-propagate 0 0 #110 #109]: #111
-#120 := (= #73 f3)
-#118 := (= #65 f3)
-#92 := (or #59 #90)
-#93 := [def-axiom]: #92
-#113 := [unit-resolution #93 #110]: #90
-#119 := [symm #113]: #118
-#116 := (= #73 #65)
-#114 := (= #65 #73)
-#115 := [th-lemma arith eq-propagate 1 1 #110 #109]: #114
-#117 := [symm #115]: #116
-#121 := [trans #117 #119]: #120
-#122 := [trans #121 #112]: #74
-#123 := [unit-resolution #108 #122]: false
-#125 := [lemma #123]: #124
-#131 := [unit-resolution #125 #130]: #59
-#132 := [unit-resolution #89 #131]: #91
-#134 := (or #133 #106)
-#135 := [th-lemma arith triangle-eq]: #134
-#136 := [unit-resolution #135 #132]: #106
-#137 := [th-lemma arith farkas 1 1 #127 #136]: false
-#138 := [lemma #137]: #87
-#144 := (or #58 #9)
-#145 := [th-lemma arith farkas 1 1]: #144
-#146 := [unit-resolution #145 #139]: #9
-#98 := (or #52 #94)
-#96 := (or #52 #94 #95)
-#97 := [def-axiom]: #96
-#99 := [unit-resolution #97 #84]: #98
-#147 := [unit-resolution #99 #146]: #94
-#149 := (or #74 #148 #126)
-#150 := [th-lemma arith triangle-eq]: #149
-#151 := [unit-resolution #150 #147 #138]: #148
-#152 := [th-lemma arith farkas 1 1 #151 #143]: false
-#153 := [lemma #152]: #58
-#157 := [unit-resolution #93 #153]: #90
-#158 := (not #90)
-#159 := (or #158 #155)
-#160 := [th-lemma arith triangle-eq]: #159
-#161 := [unit-resolution #160 #157]: #155
-#162 := [unit-resolution #125 #153]: #74
-#163 := (or #94 #86)
-#164 := [th-lemma arith triangle-eq]: #163
-#165 := [unit-resolution #164 #162]: #86
-#166 := [unit-resolution #99 #162]: #52
-[th-lemma arith farkas 2 1 1 #166 #165 #161]: false
-unsat
-2b84e732fcc2714735cd598d8c722a6eb6af2d0d 116 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#7 := f3
-#37 := -1::Int
-#38 := (* -1::Int f3)
-#64 := (>= f3 0::Int)
-#71 := (if #64 f3 #38)
-#85 := (* -1::Int #71)
-#125 := (+ #38 #85)
-#141 := (<= #125 0::Int)
-#113 := (= #38 #71)
-#65 := (not #64)
-#123 := (+ f3 #85)
-#124 := (<= #123 0::Int)
-#112 := (= f3 #71)
-#126 := [hypothesis]: #64
-#108 := (or #65 #112)
-#109 := [def-axiom]: #108
-#127 := [unit-resolution #109 #126]: #112
-#128 := (not #112)
-#129 := (or #128 #124)
-#130 := [th-lemma arith triangle-eq]: #129
-#131 := [unit-resolution #130 #127]: #124
-#80 := (>= #71 0::Int)
-#79 := (not #80)
-#91 := (if #80 #71 #85)
-#110 := (= #71 #91)
-#134 := (not #110)
-#96 := (= #91 #71)
-#99 := (not #96)
-#135 := (iff #99 #134)
-#132 := (iff #96 #110)
-#133 := [commutativity]: #132
-#136 := [monotonicity #133]: #135
-#10 := (- f3)
-#9 := (< f3 0::Int)
-#11 := (if #9 #10 f3)
-#13 := (- #11)
-#12 := (< #11 0::Int)
-#14 := (if #12 #13 #11)
-#15 := (= #14 #11)
-#16 := (not #15)
-#102 := (iff #16 #99)
-#41 := (if #9 #38 f3)
-#50 := (* -1::Int #41)
-#44 := (< #41 0::Int)
-#55 := (if #44 #50 #41)
-#58 := (= #55 #41)
-#61 := (not #58)
-#100 := (iff #61 #99)
-#97 := (iff #58 #96)
-#74 := (= #41 #71)
-#68 := (if #65 #38 f3)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #41 #68)
-#66 := (iff #9 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#94 := (= #55 #91)
-#88 := (if #79 #85 #71)
-#92 := (= #88 #91)
-#93 := [rewrite]: #92
-#89 := (= #55 #88)
-#86 := (= #50 #85)
-#87 := [monotonicity #75]: #86
-#83 := (iff #44 #79)
-#76 := (< #71 0::Int)
-#81 := (iff #76 #79)
-#82 := [rewrite]: #81
-#77 := (iff #44 #76)
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#90 := [monotonicity #84 #87 #75]: #89
-#95 := [trans #90 #93]: #94
-#98 := [monotonicity #95 #75]: #97
-#101 := [monotonicity #98]: #100
-#62 := (iff #16 #61)
-#59 := (iff #15 #58)
-#42 := (= #11 #41)
-#39 := (= #10 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#56 := (= #14 #55)
-#53 := (= #13 #50)
-#47 := (- #41)
-#51 := (= #47 #50)
-#52 := [rewrite]: #51
-#48 := (= #13 #47)
-#49 := [monotonicity #43]: #48
-#54 := [trans #49 #52]: #53
-#45 := (iff #12 #44)
-#46 := [monotonicity #43]: #45
-#57 := [monotonicity #46 #54 #43]: #56
-#60 := [monotonicity #57 #43]: #59
-#63 := [monotonicity #60]: #62
-#103 := [trans #63 #101]: #102
-#36 := [asserted]: #16
-#104 := [mp #36 #103]: #99
-#137 := [mp #104 #136]: #134
-#114 := (or #79 #110)
-#115 := [def-axiom]: #114
-#138 := [unit-resolution #115 #137]: #79
-#139 := [th-lemma arith farkas -1 1 1 #126 #138 #131]: false
-#140 := [lemma #139]: #65
-#106 := (or #64 #113)
-#107 := [def-axiom]: #106
-#143 := [unit-resolution #107 #140]: #113
-#144 := (not #113)
-#145 := (or #144 #141)
-#146 := [th-lemma arith triangle-eq]: #145
-#147 := [unit-resolution #146 #143]: #141
-[th-lemma arith farkas 1 1 1 #140 #138 #147]: false
-unsat
-9936c013aaffef1779de3d0aed544f8c88008f68 57 0
-#2 := false
-#14 := 0::Int
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#39 := (<= #38 0::Int)
-#42 := (if #39 f3 f4)
-#50 := (* -1::Int #42)
-#59 := (+ f4 #50)
-#73 := (>= #59 0::Int)
-#63 := (= f4 #42)
-#64 := (not #39)
-#62 := (= f3 #42)
-#67 := (not #62)
-#51 := (+ f3 #50)
-#49 := (>= #51 0::Int)
-#55 := (not #49)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#11 := (<= #10 f3)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #49)
-#45 := (<= #42 f3)
-#48 := (iff #45 #49)
-#52 := [rewrite]: #48
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#66 := [hypothesis]: #62
-#68 := (or #67 #49)
-#69 := [th-lemma arith triangle-eq]: #68
-#70 := [unit-resolution #69 #66 #58]: false
-#71 := [lemma #70]: #67
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#74 := [unit-resolution #60 #71]: #64
-#61 := (or #39 #63)
-#35 := [def-axiom]: #61
-#75 := [unit-resolution #35 #74]: #63
-#76 := (not #63)
-#77 := (or #76 #73)
-#78 := [th-lemma arith triangle-eq]: #77
-#79 := [unit-resolution #78 #75]: #73
-[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
-unsat
-92b8d5040546ba1e7f64484d25bbbd4c81b10ebb 57 0
-#2 := false
-#14 := 0::Int
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#39 := (<= #38 0::Int)
-#42 := (if #39 f3 f4)
-#49 := (* -1::Int #42)
-#50 := (+ f4 #49)
-#48 := (>= #50 0::Int)
-#55 := (not #48)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#11 := (<= #10 f4)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #48)
-#45 := (<= #42 f4)
-#51 := (iff #45 #48)
-#52 := [rewrite]: #51
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#63 := (= f4 #42)
-#64 := (not #39)
-#68 := [hypothesis]: #39
-#59 := (+ f3 #49)
-#67 := (>= #59 0::Int)
-#62 := (= f3 #42)
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#69 := [unit-resolution #60 #68]: #62
-#70 := (not #62)
-#71 := (or #70 #67)
-#72 := [th-lemma arith triangle-eq]: #71
-#73 := [unit-resolution #72 #69]: #67
-#74 := [th-lemma arith farkas -1 1 1 #73 #58 #68]: false
-#75 := [lemma #74]: #64
-#61 := (or #39 #63)
-#35 := [def-axiom]: #61
-#76 := [unit-resolution #35 #75]: #63
-#77 := (not #63)
-#78 := (or #77 #48)
-#79 := [th-lemma arith triangle-eq]: #78
-[unit-resolution #79 #76 #58]: false
-unsat
-4790a8f58d0e5e129b7570eac05a8802b41105cc 103 0
-#2 := false
-#19 := 0::Int
-decl f5 :: Int
-#10 := f5
-decl f4 :: Int
-#8 := f4
-#46 := -1::Int
-#55 := (* -1::Int f5)
-#65 := (+ f4 #55)
-#66 := (<= #65 0::Int)
-#69 := (if #66 f4 f5)
-#77 := (* -1::Int #69)
-decl f3 :: Int
-#7 := f3
-#78 := (+ f3 #77)
-#76 := (>= #78 0::Int)
-#75 := (not #76)
-#56 := (+ f3 #55)
-#54 := (>= #56 0::Int)
-#53 := (not #54)
-#49 := (* -1::Int f4)
-#50 := (+ f3 #49)
-#48 := (>= #50 0::Int)
-#47 := (not #48)
-#59 := (and #47 #53)
-#62 := (not #59)
-#83 := (or #62 #75)
-#86 := (not #83)
-#13 := (<= f4 f5)
-#14 := (if #13 f4 f5)
-#15 := (< f3 #14)
-#11 := (< f3 f5)
-#9 := (< f3 f4)
-#12 := (and #9 #11)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#89 := (iff #17 #86)
-#39 := (not #12)
-#40 := (or #39 #15)
-#43 := (not #40)
-#87 := (iff #43 #86)
-#84 := (iff #40 #83)
-#81 := (iff #15 #75)
-#72 := (< f3 #69)
-#79 := (iff #72 #75)
-#80 := [rewrite]: #79
-#73 := (iff #15 #72)
-#70 := (= #14 #69)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#82 := [trans #74 #80]: #81
-#63 := (iff #39 #62)
-#60 := (iff #12 #59)
-#57 := (iff #11 #53)
-#58 := [rewrite]: #57
-#51 := (iff #9 #47)
-#52 := [rewrite]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#85 := [monotonicity #64 #82]: #84
-#88 := [monotonicity #85]: #87
-#44 := (iff #17 #43)
-#41 := (iff #16 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#90 := [trans #45 #88]: #89
-#38 := [asserted]: #17
-#91 := [mp #38 #90]: #86
-#95 := [not-or-elim #91]: #76
-#92 := [not-or-elim #91]: #59
-#94 := [and-elim #92]: #53
-#100 := (+ f5 #77)
-#117 := (<= #100 0::Int)
-#106 := (= f5 #69)
-#107 := (not #66)
-#105 := (= f4 #69)
-#112 := (not #105)
-#102 := (+ f4 #77)
-#99 := (<= #102 0::Int)
-#109 := (not #99)
-#93 := [and-elim #92]: #47
-#97 := [hypothesis]: #99
-#98 := [th-lemma arith farkas -1 -1 1 #97 #93 #95]: false
-#110 := [lemma #98]: #109
-#111 := [hypothesis]: #105
-#113 := (or #112 #99)
-#114 := [th-lemma arith triangle-eq]: #113
-#115 := [unit-resolution #114 #111 #110]: false
-#116 := [lemma #115]: #112
-#108 := (or #107 #105)
-#103 := [def-axiom]: #108
-#119 := [unit-resolution #103 #116]: #107
-#104 := (or #66 #106)
-#101 := [def-axiom]: #104
-#120 := [unit-resolution #101 #119]: #106
-#121 := (not #106)
-#122 := (or #121 #117)
-#123 := [th-lemma arith triangle-eq]: #122
-#124 := [unit-resolution #123 #120]: #117
-[th-lemma arith farkas -1 -1 1 #124 #94 #95]: false
-unsat
-3023c6408a65f8e0a7c485f4d2c4804457e87603 94 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-decl f4 :: Int
-#8 := f4
-#16 := 0::Int
-#38 := -1::Int
-#39 := (* -1::Int f4)
-#40 := (+ f3 #39)
-#48 := (>= #40 0::Int)
-#50 := (if #48 f4 f3)
-#41 := (<= #40 0::Int)
-#44 := (if #41 f3 f4)
-#53 := (= #44 #50)
-#60 := (= f4 #50)
-#65 := (not #41)
-#63 := (= f3 #44)
-#105 := (not #63)
-#67 := (= f3 #50)
-#74 := (not #67)
-#75 := [hypothesis]: #74
-#71 := (or #48 #67)
-#72 := [def-axiom]: #71
-#76 := [unit-resolution #72 #75]: #48
-#68 := (not #48)
-#69 := (or #68 #60)
-#70 := [def-axiom]: #69
-#77 := [unit-resolution #70 #76]: #60
-#73 := (= f3 f4)
-#64 := (= f4 #44)
-#87 := (not #64)
-#56 := (not #53)
-#88 := (iff #56 #87)
-#85 := (iff #53 #64)
-#83 := (iff #64 #53)
-#78 := (= #50 #44)
-#81 := (iff #78 #53)
-#82 := [commutativity]: #81
-#79 := (iff #64 #78)
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#86 := [symm #84]: #85
-#89 := [monotonicity #86]: #88
-#11 := (<= f4 f3)
-#12 := (if #11 f4 f3)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#13 := (= #10 #12)
-#14 := (not #13)
-#57 := (iff #14 #56)
-#54 := (iff #13 #53)
-#51 := (= #12 #50)
-#47 := (iff #11 #48)
-#49 := [rewrite]: #47
-#52 := [monotonicity #49]: #51
-#45 := (= #10 #44)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#55 := [monotonicity #46 #52]: #54
-#58 := [monotonicity #55]: #57
-#35 := [asserted]: #14
-#59 := [mp #35 #58]: #56
-#90 := [mp #59 #89]: #87
-#62 := (or #41 #64)
-#37 := [def-axiom]: #62
-#91 := [unit-resolution #37 #90]: #41
-#94 := (or #73 #65)
-#92 := (or #73 #65 #68)
-#93 := [th-lemma arith triangle-eq]: #92
-#95 := [unit-resolution #93 #76]: #94
-#96 := [unit-resolution #95 #91]: #73
-#97 := [trans #96 #77]: #67
-#98 := [unit-resolution #75 #97]: false
-#99 := [lemma #98]: #67
-#101 := (= #44 f3)
-#100 := [hypothesis]: #63
-#102 := [symm #100]: #101
-#103 := [trans #102 #99]: #53
-#104 := [unit-resolution #59 #103]: false
-#106 := [lemma #104]: #105
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#107 := [unit-resolution #61 #106]: #65
-#109 := (or #48 #41)
-#110 := [th-lemma arith farkas 1 1]: #109
-#111 := [unit-resolution #110 #107]: #48
-#112 := [unit-resolution #70 #111]: #60
-#115 := (= #44 f4)
-#108 := [unit-resolution #37 #107]: #64
-#116 := [symm #108]: #115
-#117 := [trans #116 #112]: #53
-[unit-resolution #59 #117]: false
-unsat
-578d0e90251e6cdccfeca9dee8a741fa13906118 53 0
-#2 := false
-#7 := 0::Int
-decl f3 :: Int
-#8 := f3
-#10 := (<= f3 0::Int)
-#11 := (if #10 f3 0::Int)
-#12 := (= #11 0::Int)
-#63 := (= f3 0::Int)
-#58 := (not #12)
-#44 := (>= f3 0::Int)
-#45 := (not #44)
-#48 := (or #45 #12)
-#51 := (not #48)
-#9 := (<= 0::Int f3)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#54 := (iff #14 #51)
-#35 := (not #9)
-#36 := (or #35 #12)
-#39 := (not #36)
-#52 := (iff #39 #51)
-#49 := (iff #36 #48)
-#46 := (iff #35 #45)
-#42 := (iff #9 #44)
-#43 := [rewrite]: #42
-#47 := [monotonicity #43]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#55 := [trans #41 #53]: #54
-#34 := [asserted]: #14
-#56 := [mp #34 #55]: #51
-#59 := [not-or-elim #56]: #58
-#65 := (or #10 #12)
-#66 := [def-axiom]: #65
-#64 := [unit-resolution #66 #59]: #10
-#57 := [not-or-elim #56]: #44
-#68 := (not #10)
-#61 := (or #63 #68 #45)
-#62 := [th-lemma arith triangle-eq]: #61
-#71 := [unit-resolution #62 #57 #64]: #63
-#73 := (= #11 f3)
-#67 := (= f3 #11)
-#69 := (or #68 #67)
-#70 := [def-axiom]: #69
-#72 := [unit-resolution #70 #64]: #67
-#74 := [symm #72]: #73
-#75 := [trans #74 #71]: #12
-[unit-resolution #59 #75]: false
-unsat
-269e3d24017640dc0306b86823b964d47dcf1328 124 0
-#2 := false
-#12 := 0::Int
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#38 := -1::Int
-#40 := (* -1::Int f4)
-#53 := (+ f3 #40)
-#54 := (<= #53 0::Int)
-#57 := (if #54 f3 f4)
-#105 := (* -1::Int #57)
-#106 := (+ f3 #105)
-#108 := (>= #106 0::Int)
-#93 := (= f3 #57)
-#107 := (+ f4 #105)
-#125 := (>= #107 0::Int)
-#94 := (= f4 #57)
-#95 := (not #54)
-#136 := [hypothesis]: #95
-#92 := (or #54 #94)
-#89 := [def-axiom]: #92
-#137 := [unit-resolution #89 #136]: #94
-#128 := (not #94)
-#129 := (or #128 #125)
-#130 := [th-lemma arith triangle-eq]: #129
-#138 := [unit-resolution #130 #137]: #125
-#39 := (* -1::Int f3)
-#41 := (+ #39 #40)
-#11 := (+ f3 f4)
-#60 := (>= #11 0::Int)
-#67 := (if #60 #11 #41)
-#75 := (* -1::Int #67)
-#104 := (+ #41 #75)
-#124 := (<= #104 0::Int)
-#97 := (= #41 #67)
-#61 := (not #60)
-#109 := [hypothesis]: #60
-#76 := (+ #57 #75)
-#77 := (<= #76 0::Int)
-#82 := (not #77)
-#14 := (- #11)
-#13 := (< #11 0::Int)
-#15 := (if #13 #14 #11)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#16 := (<= #10 #15)
-#17 := (not #16)
-#85 := (iff #17 #82)
-#44 := (if #13 #41 #11)
-#47 := (<= #10 #44)
-#50 := (not #47)
-#83 := (iff #50 #82)
-#80 := (iff #47 #77)
-#72 := (<= #57 #67)
-#78 := (iff #72 #77)
-#79 := [rewrite]: #78
-#73 := (iff #47 #72)
-#70 := (= #44 #67)
-#64 := (if #61 #41 #11)
-#68 := (= #64 #67)
-#69 := [rewrite]: #68
-#65 := (= #44 #64)
-#62 := (iff #13 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#71 := [trans #66 #69]: #70
-#58 := (= #10 #57)
-#55 := (iff #9 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#74 := [monotonicity #59 #71]: #73
-#81 := [trans #74 #79]: #80
-#84 := [monotonicity #81]: #83
-#51 := (iff #17 #50)
-#48 := (iff #16 #47)
-#45 := (= #15 #44)
-#42 := (= #14 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#86 := [trans #52 #84]: #85
-#37 := [asserted]: #17
-#87 := [mp #37 #86]: #82
-#122 := (or #95 #61)
-#110 := [hypothesis]: #54
-#96 := (or #95 #93)
-#91 := [def-axiom]: #96
-#111 := [unit-resolution #91 #110]: #93
-#112 := (not #93)
-#113 := (or #112 #108)
-#114 := [th-lemma arith triangle-eq]: #113
-#115 := [unit-resolution #114 #111]: #108
-#102 := (+ #11 #75)
-#103 := (<= #102 0::Int)
-#90 := (= #11 #67)
-#98 := (or #61 #90)
-#99 := [def-axiom]: #98
-#116 := [unit-resolution #99 #109]: #90
-#117 := (not #90)
-#118 := (or #117 #103)
-#119 := [th-lemma arith triangle-eq]: #118
-#120 := [unit-resolution #119 #116]: #103
-#121 := [th-lemma arith farkas 2 2 2 1 1 #120 #115 #87 #110 #109]: false
-#123 := [lemma #121]: #122
-#126 := [unit-resolution #123 #109]: #95
-#127 := [unit-resolution #89 #126]: #94
-#131 := [unit-resolution #130 #127]: #125
-#132 := [th-lemma arith farkas 2 2 1 2 1 #120 #131 #126 #87 #109]: false
-#133 := [lemma #132]: #61
-#100 := (or #60 #97)
-#101 := [def-axiom]: #100
-#139 := [unit-resolution #101 #133]: #97
-#140 := (not #97)
-#141 := (or #140 #124)
-#142 := [th-lemma arith triangle-eq]: #141
-#143 := [unit-resolution #142 #139]: #124
-#144 := [th-lemma arith farkas 3/2 1/2 1 1 1 #133 #136 #87 #143 #138]: false
-#145 := [lemma #144]: #54
-#146 := [unit-resolution #91 #145]: #93
-#147 := [unit-resolution #114 #146]: #108
-[th-lemma arith farkas 1/2 3/2 1 1 1 #145 #133 #87 #143 #147]: false
-unsat
-1d8c0a442e62239de5b308a0ab90a7e051e0c053 57 0
-#2 := false
-#14 := 0::Int
-decl f3 :: Int
-#7 := f3
-decl f4 :: Int
-#8 := f4
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#39 := (<= #38 0::Int)
-#42 := (if #39 f4 f3)
-#48 := (* -1::Int #42)
-#49 := (+ f3 #48)
-#50 := (<= #49 0::Int)
-#55 := (not #50)
-#9 := (<= f3 f4)
-#10 := (if #9 f4 f3)
-#11 := (<= f3 #10)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #50)
-#45 := (<= f3 #42)
-#51 := (iff #45 #50)
-#52 := [rewrite]: #51
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#63 := (= f3 #42)
-#64 := (not #39)
-#68 := [hypothesis]: #39
-#59 := (+ f4 #48)
-#66 := (<= #59 0::Int)
-#62 := (= f4 #42)
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#69 := [unit-resolution #60 #68]: #62
-#70 := (not #62)
-#71 := (or #70 #66)
-#72 := [th-lemma arith triangle-eq]: #71
-#73 := [unit-resolution #72 #69]: #66
-#74 := [th-lemma arith farkas 1 -1 1 #73 #58 #68]: false
-#75 := [lemma #74]: #64
-#61 := (or #39 #63)
-#35 := [def-axiom]: #61
-#76 := [unit-resolution #35 #75]: #63
-#77 := (not #63)
-#78 := (or #77 #50)
-#79 := [th-lemma arith triangle-eq]: #78
-[unit-resolution #79 #76 #58]: false
-unsat
-33356681256058514a33561c44762f0ba6ed5330 57 0
-#2 := false
-#14 := 0::Int
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#36 := -1::Int
-#39 := (* -1::Int f4)
-#40 := (+ f3 #39)
-#38 := (>= #40 0::Int)
-#42 := (if #38 f3 f4)
-#48 := (* -1::Int #42)
-#59 := (+ f4 #48)
-#72 := (<= #59 0::Int)
-#63 := (= f4 #42)
-#64 := (not #38)
-#62 := (= f3 #42)
-#67 := (not #62)
-#49 := (+ f3 #48)
-#50 := (<= #49 0::Int)
-#55 := (not #50)
-#9 := (<= f4 f3)
-#10 := (if #9 f3 f4)
-#11 := (<= f3 #10)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #50)
-#45 := (<= f3 #42)
-#51 := (iff #45 #50)
-#52 := [rewrite]: #51
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#37 := (iff #9 #38)
-#41 := [rewrite]: #37
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#66 := [hypothesis]: #62
-#68 := (or #67 #50)
-#69 := [th-lemma arith triangle-eq]: #68
-#70 := [unit-resolution #69 #66 #58]: false
-#71 := [lemma #70]: #67
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#74 := [unit-resolution #60 #71]: #64
-#61 := (or #38 #63)
-#35 := [def-axiom]: #61
-#75 := [unit-resolution #35 #74]: #63
-#76 := (not #63)
-#77 := (or #76 #72)
-#78 := [th-lemma arith triangle-eq]: #77
-#79 := [unit-resolution #78 #75]: #72
-[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
-unsat
-f450c8992954aa7e8354d82bf2535ed9619b8684 103 0
-#2 := false
-#19 := 0::Int
-decl f3 :: Int
-#7 := f3
-decl f5 :: Int
-#10 := f5
-#46 := -1::Int
-#53 := (* -1::Int f5)
-#65 := (+ f3 #53)
-#66 := (<= #65 0::Int)
-#69 := (if #66 f5 f3)
-#75 := (* -1::Int #69)
-decl f4 :: Int
-#8 := f4
-#76 := (+ f4 #75)
-#77 := (<= #76 0::Int)
-#78 := (not #77)
-#54 := (+ f4 #53)
-#55 := (<= #54 0::Int)
-#56 := (not #55)
-#49 := (* -1::Int f4)
-#50 := (+ f3 #49)
-#48 := (>= #50 0::Int)
-#47 := (not #48)
-#59 := (and #47 #56)
-#62 := (not #59)
-#83 := (or #62 #78)
-#86 := (not #83)
-#13 := (<= f3 f5)
-#14 := (if #13 f5 f3)
-#15 := (< #14 f4)
-#11 := (< f5 f4)
-#9 := (< f3 f4)
-#12 := (and #9 #11)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#89 := (iff #17 #86)
-#39 := (not #12)
-#40 := (or #39 #15)
-#43 := (not #40)
-#87 := (iff #43 #86)
-#84 := (iff #40 #83)
-#81 := (iff #15 #78)
-#72 := (< #69 f4)
-#79 := (iff #72 #78)
-#80 := [rewrite]: #79
-#73 := (iff #15 #72)
-#70 := (= #14 #69)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#82 := [trans #74 #80]: #81
-#63 := (iff #39 #62)
-#60 := (iff #12 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#51 := (iff #9 #47)
-#52 := [rewrite]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#85 := [monotonicity #64 #82]: #84
-#88 := [monotonicity #85]: #87
-#44 := (iff #17 #43)
-#41 := (iff #16 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#90 := [trans #45 #88]: #89
-#38 := [asserted]: #17
-#91 := [mp #38 #90]: #86
-#95 := [not-or-elim #91]: #77
-#92 := [not-or-elim #91]: #59
-#93 := [and-elim #92]: #47
-#99 := (+ f3 #75)
-#118 := (>= #99 0::Int)
-#106 := (= f3 #69)
-#107 := (not #66)
-#105 := (= f5 #69)
-#112 := (not #105)
-#102 := (+ f5 #75)
-#100 := (>= #102 0::Int)
-#109 := (not #100)
-#94 := [and-elim #92]: #56
-#97 := [hypothesis]: #100
-#98 := [th-lemma arith farkas -1 -1 1 #97 #94 #95]: false
-#110 := [lemma #98]: #109
-#111 := [hypothesis]: #105
-#113 := (or #112 #100)
-#114 := [th-lemma arith triangle-eq]: #113
-#115 := [unit-resolution #114 #111 #110]: false
-#116 := [lemma #115]: #112
-#108 := (or #107 #105)
-#103 := [def-axiom]: #108
-#119 := [unit-resolution #103 #116]: #107
-#104 := (or #66 #106)
-#101 := [def-axiom]: #104
-#120 := [unit-resolution #101 #119]: #106
-#121 := (not #106)
-#122 := (or #121 #118)
-#123 := [th-lemma arith triangle-eq]: #122
-#124 := [unit-resolution #123 #120]: #118
-[th-lemma arith farkas -1 1 1 #124 #93 #95]: false
-unsat
-dc09c2944521a51fac5d926e6bf8729bfa0f3e92 96 0
-#2 := false
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#16 := 0::Int
-#38 := -1::Int
-#39 := (* -1::Int f4)
-#40 := (+ f3 #39)
-#48 := (>= #40 0::Int)
-#50 := (if #48 f3 f4)
-#41 := (<= #40 0::Int)
-#44 := (if #41 f4 f3)
-#53 := (= #44 #50)
-#60 := (= f3 #50)
-#65 := (not #41)
-#63 := (= f4 #44)
-#107 := (not #63)
-#67 := (= f4 #50)
-#74 := (not #67)
-#75 := [hypothesis]: #74
-#71 := (or #48 #67)
-#72 := [def-axiom]: #71
-#76 := [unit-resolution #72 #75]: #48
-#68 := (not #48)
-#69 := (or #68 #60)
-#70 := [def-axiom]: #69
-#77 := [unit-resolution #70 #76]: #60
-#97 := (= f4 f3)
-#73 := (= f3 f4)
-#64 := (= f3 #44)
-#87 := (not #64)
-#56 := (not #53)
-#88 := (iff #56 #87)
-#85 := (iff #53 #64)
-#83 := (iff #64 #53)
-#78 := (= #50 #44)
-#81 := (iff #78 #53)
-#82 := [commutativity]: #81
-#79 := (iff #64 #78)
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#86 := [symm #84]: #85
-#89 := [monotonicity #86]: #88
-#11 := (<= f4 f3)
-#12 := (if #11 f3 f4)
-#9 := (<= f3 f4)
-#10 := (if #9 f4 f3)
-#13 := (= #10 #12)
-#14 := (not #13)
-#57 := (iff #14 #56)
-#54 := (iff #13 #53)
-#51 := (= #12 #50)
-#47 := (iff #11 #48)
-#49 := [rewrite]: #47
-#52 := [monotonicity #49]: #51
-#45 := (= #10 #44)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#55 := [monotonicity #46 #52]: #54
-#58 := [monotonicity #55]: #57
-#35 := [asserted]: #14
-#59 := [mp #35 #58]: #56
-#90 := [mp #59 #89]: #87
-#62 := (or #41 #64)
-#37 := [def-axiom]: #62
-#91 := [unit-resolution #37 #90]: #41
-#94 := (or #73 #65)
-#92 := (or #73 #65 #68)
-#93 := [th-lemma arith triangle-eq]: #92
-#95 := [unit-resolution #93 #76]: #94
-#96 := [unit-resolution #95 #91]: #73
-#98 := [symm #96]: #97
-#99 := [trans #98 #77]: #67
-#100 := [unit-resolution #75 #99]: false
-#101 := [lemma #100]: #67
-#103 := (= #44 f4)
-#102 := [hypothesis]: #63
-#104 := [symm #102]: #103
-#105 := [trans #104 #101]: #53
-#106 := [unit-resolution #59 #105]: false
-#108 := [lemma #106]: #107
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#109 := [unit-resolution #61 #108]: #65
-#111 := (or #48 #41)
-#112 := [th-lemma arith farkas 1 1]: #111
-#113 := [unit-resolution #112 #109]: #48
-#114 := [unit-resolution #70 #113]: #60
-#117 := (= #44 f3)
-#110 := [unit-resolution #37 #109]: #64
-#118 := [symm #110]: #117
-#119 := [trans #118 #114]: #53
-[unit-resolution #59 #119]: false
-unsat
-3742caaf5383415a6af8d6cc983e20de965a2c95 60 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#7 := 0::Int
-#10 := (<= f3 0::Int)
-#11 := (if #10 0::Int f3)
-#68 := (= f3 #11)
-#80 := (= 0::Int #11)
-#67 := (= #11 0::Int)
-#71 := (not #68)
-#12 := (= #11 f3)
-#58 := (not #12)
-#72 := (iff #58 #71)
-#61 := (iff #12 #68)
-#62 := [commutativity]: #61
-#73 := [monotonicity #62]: #72
-#44 := (>= f3 0::Int)
-#45 := (not #44)
-#48 := (or #45 #12)
-#51 := (not #48)
-#9 := (<= 0::Int f3)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#54 := (iff #14 #51)
-#35 := (not #9)
-#36 := (or #35 #12)
-#39 := (not #36)
-#52 := (iff #39 #51)
-#49 := (iff #36 #48)
-#46 := (iff #35 #45)
-#42 := (iff #9 #44)
-#43 := [rewrite]: #42
-#47 := [monotonicity #43]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#55 := [trans #41 #53]: #54
-#34 := [asserted]: #14
-#56 := [mp #34 #55]: #51
-#59 := [not-or-elim #56]: #58
-#74 := [mp #59 #73]: #71
-#66 := (or #10 #68)
-#63 := [def-axiom]: #66
-#75 := [unit-resolution #63 #74]: #10
-#69 := (not #10)
-#70 := (or #69 #67)
-#65 := [def-axiom]: #70
-#76 := [unit-resolution #65 #75]: #67
-#81 := [symm #76]: #80
-#64 := (= f3 0::Int)
-#57 := [not-or-elim #56]: #44
-#77 := (or #64 #69 #45)
-#78 := [th-lemma arith triangle-eq]: #77
-#79 := [unit-resolution #78 #57 #75]: #64
-#82 := [trans #79 #81]: #68
-[unit-resolution #74 #82]: false
-unsat
-2fb3cafc864ef15c2b5fc68d255cca5586a02215 214 0
-#2 := false
-#8 := 0::Int
-decl f4 :: Int
-#13 := f4
-#42 := -1::Int
-#57 := (* -1::Int f4)
-#93 := (>= f4 0::Int)
-#100 := (if #93 f4 #57)
-#105 := (* -1::Int #100)
-#160 := (+ #57 #105)
-#182 := (<= #160 0::Int)
-#136 := (= #57 #100)
-#94 := (not #93)
-decl f3 :: Int
-#7 := f3
-#111 := (+ f3 #57)
-#112 := (<= #111 0::Int)
-#115 := (if #112 f4 f3)
-#154 := (* -1::Int #115)
-#155 := (+ f4 #154)
-#156 := (<= #155 0::Int)
-#157 := (+ f3 #154)
-#192 := (<= #157 0::Int)
-#148 := (= f3 #115)
-#149 := (not #112)
-#147 := (= f4 #115)
-#194 := [hypothesis]: #112
-#150 := (or #149 #147)
-#151 := [def-axiom]: #150
-#195 := [unit-resolution #151 #194]: #147
-#196 := (not #147)
-#197 := (or #196 #156)
-#198 := [th-lemma arith triangle-eq]: #197
-#199 := [unit-resolution #198 #195]: #156
-#178 := (not #156)
-#190 := (or #94 #178)
-#158 := (+ f4 #105)
-#159 := (<= #158 0::Int)
-#135 := (= f4 #100)
-#164 := [hypothesis]: #93
-#143 := (or #94 #135)
-#144 := [def-axiom]: #143
-#165 := [unit-resolution #144 #164]: #135
-#166 := (not #135)
-#167 := (or #166 #159)
-#168 := [th-lemma arith triangle-eq]: #167
-#169 := [unit-resolution #168 #165]: #159
-#78 := (>= f3 0::Int)
-#79 := (not #78)
-#176 := [hypothesis]: #156
-#179 := (or #79 #94 #178)
-#124 := (+ #100 #115)
-#43 := (* -1::Int f3)
-#85 := (if #78 f3 #43)
-#125 := (+ #85 #124)
-#122 := (>= #125 0::Int)
-#128 := (not #122)
-#18 := (<= f3 f4)
-#19 := (if #18 f4 f3)
-#15 := (- f4)
-#14 := (< f4 0::Int)
-#16 := (if #14 #15 f4)
-#10 := (- f3)
-#9 := (< f3 0::Int)
-#11 := (if #9 #10 f3)
-#12 := (- #11)
-#17 := (- #12 #16)
-#20 := (<= #17 #19)
-#21 := (not #20)
-#131 := (iff #21 #128)
-#60 := (if #14 #57 f4)
-#66 := (* -1::Int #60)
-#46 := (if #9 #43 f3)
-#52 := (* -1::Int #46)
-#67 := (+ #52 #66)
-#72 := (<= #67 #19)
-#75 := (not #72)
-#129 := (iff #75 #128)
-#126 := (iff #72 #122)
-#90 := (* -1::Int #85)
-#108 := (+ #90 #105)
-#118 := (<= #108 #115)
-#121 := (iff #118 #122)
-#123 := [rewrite]: #121
-#119 := (iff #72 #118)
-#116 := (= #19 #115)
-#113 := (iff #18 #112)
-#114 := [rewrite]: #113
-#117 := [monotonicity #114]: #116
-#109 := (= #67 #108)
-#106 := (= #66 #105)
-#103 := (= #60 #100)
-#97 := (if #94 #57 f4)
-#101 := (= #97 #100)
-#102 := [rewrite]: #101
-#98 := (= #60 #97)
-#95 := (iff #14 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#104 := [trans #99 #102]: #103
-#107 := [monotonicity #104]: #106
-#91 := (= #52 #90)
-#88 := (= #46 #85)
-#82 := (if #79 #43 f3)
-#86 := (= #82 #85)
-#87 := [rewrite]: #86
-#83 := (= #46 #82)
-#80 := (iff #9 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#110 := [monotonicity #92 #107]: #109
-#120 := [monotonicity #110 #117]: #119
-#127 := [trans #120 #123]: #126
-#130 := [monotonicity #127]: #129
-#76 := (iff #21 #75)
-#73 := (iff #20 #72)
-#70 := (= #17 #67)
-#63 := (- #52 #60)
-#68 := (= #63 #67)
-#69 := [rewrite]: #68
-#64 := (= #17 #63)
-#61 := (= #16 #60)
-#58 := (= #15 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#55 := (= #12 #52)
-#49 := (- #46)
-#53 := (= #49 #52)
-#54 := [rewrite]: #53
-#50 := (= #12 #49)
-#47 := (= #11 #46)
-#44 := (= #10 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#56 := [trans #51 #54]: #55
-#65 := [monotonicity #56 #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#132 := [trans #77 #130]: #131
-#41 := [asserted]: #21
-#133 := [mp #41 #132]: #128
-#161 := (+ f3 #90)
-#162 := (<= #161 0::Int)
-#139 := (= f3 #85)
-#170 := [hypothesis]: #78
-#141 := (or #79 #139)
-#142 := [def-axiom]: #141
-#171 := [unit-resolution #142 #170]: #139
-#172 := (not #139)
-#173 := (or #172 #162)
-#174 := [th-lemma arith triangle-eq]: #173
-#175 := [unit-resolution #174 #171]: #162
-#177 := [th-lemma arith farkas -2 1 -1 1 1 1 #164 #176 #170 #175 #133 #169]: false
-#180 := [lemma #177]: #179
-#183 := [unit-resolution #180 #164 #176]: #79
-#163 := (+ #43 #90)
-#181 := (<= #163 0::Int)
-#140 := (= #43 #85)
-#137 := (or #78 #140)
-#138 := [def-axiom]: #137
-#184 := [unit-resolution #138 #183]: #140
-#185 := (not #140)
-#186 := (or #185 #181)
-#187 := [th-lemma arith triangle-eq]: #186
-#188 := [unit-resolution #187 #184]: #181
-#189 := [th-lemma arith farkas 2 1 1 1 1 1 #164 #176 #133 #188 #183 #169]: false
-#191 := [lemma #189]: #190
-#200 := [unit-resolution #191 #199]: #94
-#145 := (or #93 #136)
-#146 := [def-axiom]: #145
-#201 := [unit-resolution #146 #200]: #136
-#202 := (not #136)
-#203 := (or #202 #182)
-#204 := [th-lemma arith triangle-eq]: #203
-#205 := [unit-resolution #204 #201]: #182
-#206 := (or #79 #149 #93)
-#207 := [th-lemma arith assign-bounds 1 1]: #206
-#208 := [unit-resolution #207 #200 #194]: #79
-#209 := [unit-resolution #138 #208]: #140
-#210 := [unit-resolution #187 #209]: #181
-#211 := [th-lemma arith farkas 1 1 1 1 1 #199 #133 #210 #208 #205]: false
-#212 := [lemma #211]: #149
-#152 := (or #112 #148)
-#153 := [def-axiom]: #152
-#223 := [unit-resolution #153 #212]: #148
-#224 := (not #148)
-#225 := (or #224 #192)
-#226 := [th-lemma arith triangle-eq]: #225
-#227 := [unit-resolution #226 #223]: #192
-#230 := (not #192)
-#231 := (or #156 #112 #230)
-#232 := [th-lemma arith assign-bounds 1 1]: #231
-#233 := [unit-resolution #232 #212 #227]: #156
-#234 := [unit-resolution #191 #233]: #94
-#235 := [unit-resolution #146 #234]: #136
-#236 := [unit-resolution #204 #235]: #182
-#215 := [hypothesis]: #79
-#216 := (or #94 #78 #112)
-#217 := [th-lemma arith assign-bounds 1 1]: #216
-#218 := [unit-resolution #217 #215 #212]: #94
-#219 := [unit-resolution #146 #218]: #136
-#220 := [unit-resolution #204 #219]: #182
-#221 := [unit-resolution #138 #215]: #140
-#222 := [unit-resolution #187 #221]: #181
-#228 := [th-lemma arith farkas 1 1 1 1 1 1 #215 #212 #227 #133 #222 #220]: false
-#229 := [lemma #228]: #78
-#237 := [unit-resolution #142 #229]: #139
-#238 := [unit-resolution #174 #237]: #162
-[th-lemma arith farkas 1 1 1 1 1 1 #212 #227 #133 #229 #238 #236]: false
-unsat
-6d267e11bf9368fb47a07436e29a6e62106843a6 53 0
-#2 := false
-#10 := 1::Int
-decl f3 :: Int
-#8 := f3
-#76 := (>= f3 1::Int)
-#78 := (not #76)
-#13 := (= f3 1::Int)
-#65 := (not #13)
-#11 := (<= f3 1::Int)
-#7 := 0::Int
-#43 := (<= f3 0::Int)
-#44 := (not #43)
-#47 := (and #44 #11)
-#50 := (not #47)
-#53 := (or #50 #13)
-#56 := (not #53)
-#9 := (< 0::Int f3)
-#12 := (and #9 #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#59 := (iff #15 #56)
-#36 := (not #12)
-#37 := (or #36 #13)
-#40 := (not #37)
-#57 := (iff #40 #56)
-#54 := (iff #37 #53)
-#51 := (iff #36 #50)
-#48 := (iff #12 #47)
-#45 := (iff #9 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#55 := [monotonicity #52]: #54
-#58 := [monotonicity #55]: #57
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#60 := [trans #42 #58]: #59
-#35 := [asserted]: #15
-#61 := [mp #35 #60]: #56
-#66 := [not-or-elim #61]: #65
-#75 := (or #13 #78)
-#62 := [not-or-elim #61]: #47
-#64 := [and-elim #62]: #11
-#77 := (not #11)
-#79 := (or #13 #77 #78)
-#74 := [th-lemma arith triangle-eq]: #79
-#72 := [unit-resolution #74 #64]: #75
-#73 := [unit-resolution #72 #66]: #78
-#63 := [and-elim #62]: #44
-[th-lemma arith farkas 1 1 #63 #73]: false
-unsat
-fa8bb7c26f623612658531ec8179e791dc02e2b0 18 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#8 := (<= f3 f3)
-#9 := (not #8)
-#40 := (iff #9 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #9 #35)
-#33 := (iff #8 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #9
-[mp #30 #41]: false
-unsat
-c500db7a265d55897d1b4a11d5a17d5998ebe9ba 51 0
-#2 := false
-decl f4 :: Int
-#8 := f4
-#10 := 3::Int
-#12 := (* 3::Int f4)
-decl f3 :: Int
-#7 := f3
-#11 := (* 3::Int f3)
-#13 := (<= #11 #12)
-#9 := (<= f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#69 := (iff #15 false)
-#37 := (not #9)
-#38 := (or #37 #13)
-#41 := (not #38)
-#67 := (iff #41 false)
-#1 := true
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #41 #62)
-#60 := (iff #38 true)
-#17 := 0::Int
-#44 := -1::Int
-#45 := (* -1::Int f4)
-#46 := (+ f3 #45)
-#47 := (<= #46 0::Int)
-#50 := (not #47)
-#55 := (or #50 #47)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #38 #55)
-#53 := (iff #13 #47)
-#54 := [rewrite]: #53
-#51 := (iff #37 #50)
-#48 := (iff #9 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#57 := [monotonicity #52 #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#70 := [trans #43 #68]: #69
-#36 := [asserted]: #15
-[mp #36 #70]: false
-unsat
-9ac1771d791a430d0a7637ac3d9b4ab1780df97b 56 0
-#2 := false
-decl f4 :: Int
-#8 := f4
-#10 := 3::Int
-#12 := (* 3::Int f4)
-decl f3 :: Int
-#7 := f3
-#11 := (* 3::Int f3)
-#13 := (< #11 #12)
-#9 := (< f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#74 := (iff #15 false)
-#37 := (not #9)
-#38 := (or #37 #13)
-#41 := (not #38)
-#72 := (iff #41 false)
-#1 := true
-#67 := (not true)
-#70 := (iff #67 false)
-#71 := [rewrite]: #70
-#68 := (iff #41 #67)
-#65 := (iff #38 true)
-#17 := 0::Int
-#44 := -1::Int
-#47 := (* -1::Int f4)
-#48 := (+ f3 #47)
-#46 := (>= #48 0::Int)
-#45 := (not #46)
-#59 := (or #46 #45)
-#63 := (iff #59 true)
-#64 := [rewrite]: #63
-#61 := (iff #38 #59)
-#60 := (iff #13 #45)
-#58 := [rewrite]: #60
-#56 := (iff #37 #46)
-#51 := (not #45)
-#54 := (iff #51 #46)
-#55 := [rewrite]: #54
-#52 := (iff #37 #51)
-#49 := (iff #9 #45)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#62 := [monotonicity #57 #58]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#75 := [trans #43 #73]: #74
-#36 := [asserted]: #15
-[mp #36 #75]: false
-unsat
-0d0dc16c86e745f503bac8f1609551cac0dec35b 52 0
-#2 := false
-#14 := 0::Int
-decl f4 :: Int
-#8 := f4
-#41 := -1::Int
-#44 := (* -1::Int f4)
-decl f3 :: Int
-#7 := f3
-#45 := (+ f3 #44)
-#55 := (<= #45 0::Int)
-#68 := (not #55)
-#43 := (>= #45 0::Int)
-#58 := (or #43 #55)
-#61 := (not #58)
-#10 := (<= f3 f4)
-#9 := (< f3 f4)
-#11 := (implies #9 #10)
-#12 := (not #11)
-#64 := (iff #12 #61)
-#34 := (not #9)
-#35 := (or #34 #10)
-#38 := (not #35)
-#62 := (iff #38 #61)
-#59 := (iff #35 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#53 := (iff #34 #43)
-#42 := (not #43)
-#48 := (not #42)
-#51 := (iff #48 #43)
-#52 := [rewrite]: #51
-#49 := (iff #34 #48)
-#46 := (iff #9 #42)
-#47 := [rewrite]: #46
-#50 := [monotonicity #47]: #49
-#54 := [trans #50 #52]: #53
-#60 := [monotonicity #54 #57]: #59
-#63 := [monotonicity #60]: #62
-#39 := (iff #12 #38)
-#36 := (iff #11 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#65 := [trans #40 #63]: #64
-#33 := [asserted]: #12
-#66 := [mp #33 #65]: #61
-#69 := [not-or-elim #66]: #68
-#67 := [not-or-elim #66]: #42
-#77 := (or #55 #43)
-#78 := [th-lemma arith farkas 1 1]: #77
-#79 := [unit-resolution #78 #67]: #55
-[unit-resolution #79 #69]: false
-unsat
-e17223976134e90d22d663b546f65c41ad005eb7 73 0
-#2 := false
-#54 := -1::Int
-decl f4 :: Int
-#8 := f4
-#57 := (* -1::Int f4)
-decl f3 :: Int
-#7 := f3
-#58 := (+ f3 #57)
-#68 := (<= #58 -1::Int)
-#16 := 0::Int
-#56 := (>= #58 0::Int)
-#55 := (not #56)
-#82 := (not #68)
-#88 := [hypothesis]: #82
-#86 := (or #55 #68)
-#71 := (iff #56 #68)
-#10 := 1::Int
-#11 := (+ f3 1::Int)
-#12 := (<= #11 f4)
-#9 := (< f3 f4)
-#13 := (iff #9 #12)
-#14 := (not #13)
-#74 := (iff #14 #71)
-#36 := (+ 1::Int f3)
-#39 := (<= #36 f4)
-#48 := (not #9)
-#49 := (iff #48 #39)
-#72 := (iff #49 #71)
-#69 := (iff #39 #68)
-#70 := [rewrite]: #69
-#66 := (iff #48 #56)
-#61 := (not #55)
-#64 := (iff #61 #56)
-#65 := [rewrite]: #64
-#62 := (iff #48 #61)
-#59 := (iff #9 #55)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#73 := [monotonicity #67 #70]: #72
-#52 := (iff #14 #49)
-#42 := (iff #9 #39)
-#45 := (not #42)
-#50 := (iff #45 #49)
-#51 := [rewrite]: #50
-#46 := (iff #14 #45)
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#53 := [trans #47 #51]: #52
-#75 := [trans #53 #73]: #74
-#35 := [asserted]: #14
-#76 := [mp #35 #75]: #71
-#83 := (not #71)
-#78 := (or #55 #68 #83)
-#79 := [def-axiom]: #78
-#87 := [unit-resolution #79 #76]: #86
-#89 := [unit-resolution #87 #88]: #55
-#90 := [th-lemma arith farkas 1 1 #88 #89]: false
-#91 := [lemma #90]: #68
-#92 := (or #82 #55)
-#93 := [th-lemma arith farkas 1 1]: #92
-#94 := [unit-resolution #93 #91]: #55
-#80 := (or #56 #82)
-#84 := (or #56 #82 #83)
-#85 := [def-axiom]: #84
-#81 := [unit-resolution #85 #76]: #80
-[unit-resolution #81 #94 #91]: false
-unsat
-c2029d4b6a4d4114a4b031b834e2a253b97e4371 15 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-#8 := (< f3 f3)
-#9 := (not #8)
-#10 := (not #9)
-#36 := (iff #10 false)
-#34 := (iff #8 false)
-#35 := [rewrite]: #34
-#32 := (iff #10 #8)
-#33 := [rewrite]: #32
-#37 := [trans #33 #35]: #36
-#31 := [asserted]: #10
-[mp #31 #37]: false
-unsat
-28e1620c910a232c81f0832f349f8c958506720d 75 0
-#2 := false
-#17 := 0::Int
-decl f5 :: Int
-#10 := f5
-#53 := -1::Int
-#54 := (* -1::Int f5)
-decl f4 :: Int
-#8 := f4
-#55 := (+ f4 #54)
-#56 := (<= #55 0::Int)
-decl f3 :: Int
-#7 := f3
-#62 := (+ f3 #54)
-#63 := (<= #62 0::Int)
-#59 := (not #56)
-#66 := (* -1::Int f4)
-#67 := (+ f3 #66)
-#68 := (<= #67 0::Int)
-#71 := (not #68)
-#80 := (or #71 #59 #63)
-#85 := (not #80)
-#12 := (<= f3 f5)
-#11 := (<= f4 f5)
-#13 := (implies #11 #12)
-#9 := (<= f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#88 := (iff #15 #85)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#86 := (iff #50 #85)
-#83 := (iff #45 #80)
-#74 := (or #59 #63)
-#77 := (or #71 #74)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #45 #77)
-#75 := (iff #38 #74)
-#64 := (iff #12 #63)
-#65 := [rewrite]: #64
-#60 := (iff #37 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#76 := [monotonicity #61 #65]: #75
-#72 := (iff #44 #71)
-#69 := (iff #9 #68)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#79 := [monotonicity #73 #76]: #78
-#84 := [trans #79 #82]: #83
-#87 := [monotonicity #84]: #86
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#89 := [trans #52 #87]: #88
-#36 := [asserted]: #15
-#90 := [mp #36 #89]: #85
-#92 := [not-or-elim #90]: #56
-#93 := (not #63)
-#94 := [not-or-elim #90]: #93
-#91 := [not-or-elim #90]: #68
-[th-lemma arith farkas 1 -1 1 #91 #94 #92]: false
-unsat
-dac056ed6e93880024b69dbec647c1c9343924fe 80 0
-#2 := false
-#17 := 0::Int
-decl f5 :: Int
-#10 := f5
-#53 := -1::Int
-#54 := (* -1::Int f5)
-decl f4 :: Int
-#8 := f4
-#55 := (+ f4 #54)
-#56 := (<= #55 0::Int)
-decl f3 :: Int
-#7 := f3
-#62 := (+ f3 #54)
-#63 := (<= #62 0::Int)
-#59 := (not #56)
-#68 := (* -1::Int f4)
-#69 := (+ f3 #68)
-#67 := (>= #69 0::Int)
-#85 := (or #67 #59 #63)
-#90 := (not #85)
-#12 := (<= f3 f5)
-#11 := (<= f4 f5)
-#13 := (implies #11 #12)
-#9 := (< f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#93 := (iff #15 #90)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#91 := (iff #50 #90)
-#88 := (iff #45 #85)
-#79 := (or #59 #63)
-#82 := (or #67 #79)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #45 #82)
-#80 := (iff #38 #79)
-#64 := (iff #12 #63)
-#65 := [rewrite]: #64
-#60 := (iff #37 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#81 := [monotonicity #61 #65]: #80
-#77 := (iff #44 #67)
-#66 := (not #67)
-#72 := (not #66)
-#75 := (iff #72 #67)
-#76 := [rewrite]: #75
-#73 := (iff #44 #72)
-#70 := (iff #9 #66)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#84 := [monotonicity #78 #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#94 := [trans #52 #92]: #93
-#36 := [asserted]: #15
-#95 := [mp #36 #94]: #90
-#97 := [not-or-elim #95]: #56
-#96 := [not-or-elim #95]: #66
-#98 := (not #63)
-#99 := [not-or-elim #95]: #98
-[th-lemma arith farkas 1 1 1 #99 #96 #97]: false
-unsat
-a8974893df200f396c634d964eb984c48eec55db 80 0
-#2 := false
-#17 := 0::Int
-decl f5 :: Int
-#10 := f5
-#53 := -1::Int
-#56 := (* -1::Int f5)
-decl f3 :: Int
-#7 := f3
-#67 := (+ f3 #56)
-#68 := (<= #67 0::Int)
-#98 := (not #68)
-decl f4 :: Int
-#8 := f4
-#57 := (+ f4 #56)
-#55 := (>= #57 0::Int)
-#71 := (* -1::Int f4)
-#72 := (+ f3 #71)
-#73 := (<= #72 0::Int)
-#76 := (not #73)
-#85 := (or #76 #55 #68)
-#90 := (not #85)
-#12 := (<= f3 f5)
-#11 := (< f4 f5)
-#13 := (implies #11 #12)
-#9 := (<= f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#93 := (iff #15 #90)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#91 := (iff #50 #90)
-#88 := (iff #45 #85)
-#79 := (or #55 #68)
-#82 := (or #76 #79)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #45 #82)
-#80 := (iff #38 #79)
-#69 := (iff #12 #68)
-#70 := [rewrite]: #69
-#65 := (iff #37 #55)
-#54 := (not #55)
-#60 := (not #54)
-#63 := (iff #60 #55)
-#64 := [rewrite]: #63
-#61 := (iff #37 #60)
-#58 := (iff #11 #54)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#81 := [monotonicity #66 #70]: #80
-#77 := (iff #44 #76)
-#74 := (iff #9 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#84 := [monotonicity #78 #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#94 := [trans #52 #92]: #93
-#36 := [asserted]: #15
-#95 := [mp #36 #94]: #90
-#99 := [not-or-elim #95]: #98
-#97 := [not-or-elim #95]: #54
-#96 := [not-or-elim #95]: #73
-[th-lemma arith farkas 1 1 1 #96 #97 #99]: false
-unsat
-b7e0a4eabb9a618e1df287bffee02d5551032ee6 85 0
-#2 := false
-#17 := 0::Int
-decl f5 :: Int
-#10 := f5
-#53 := -1::Int
-#56 := (* -1::Int f5)
-decl f3 :: Int
-#7 := f3
-#69 := (+ f3 #56)
-#68 := (>= #69 0::Int)
-#67 := (not #68)
-decl f4 :: Int
-#8 := f4
-#57 := (+ f4 #56)
-#55 := (>= #57 0::Int)
-#74 := (* -1::Int f4)
-#75 := (+ f3 #74)
-#73 := (>= #75 0::Int)
-#91 := (or #73 #55 #67)
-#96 := (not #91)
-#12 := (< f3 f5)
-#11 := (< f4 f5)
-#13 := (implies #11 #12)
-#9 := (< f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#99 := (iff #15 #96)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#97 := (iff #50 #96)
-#94 := (iff #45 #91)
-#85 := (or #55 #67)
-#88 := (or #73 #85)
-#92 := (iff #88 #91)
-#93 := [rewrite]: #92
-#89 := (iff #45 #88)
-#86 := (iff #38 #85)
-#70 := (iff #12 #67)
-#71 := [rewrite]: #70
-#65 := (iff #37 #55)
-#54 := (not #55)
-#60 := (not #54)
-#63 := (iff #60 #55)
-#64 := [rewrite]: #63
-#61 := (iff #37 #60)
-#58 := (iff #11 #54)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#87 := [monotonicity #66 #71]: #86
-#83 := (iff #44 #73)
-#72 := (not #73)
-#78 := (not #72)
-#81 := (iff #78 #73)
-#82 := [rewrite]: #81
-#79 := (iff #44 #78)
-#76 := (iff #9 #72)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#90 := [monotonicity #84 #87]: #89
-#95 := [trans #90 #93]: #94
-#98 := [monotonicity #95]: #97
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#100 := [trans #52 #98]: #99
-#36 := [asserted]: #15
-#101 := [mp #36 #100]: #96
-#104 := [not-or-elim #101]: #68
-#103 := [not-or-elim #101]: #54
-#102 := [not-or-elim #101]: #72
-[th-lemma arith farkas 1 1 1 #102 #103 #104]: false
-unsat
-0d64561170d5f7666bfabd32ae1c1b5265d931e6 69 0
-#2 := false
-#18 := 0::Int
-decl f5 :: Int
-#10 := f5
-#45 := -1::Int
-#53 := (* -1::Int f5)
-decl f3 :: Int
-#7 := f3
-#64 := (+ f3 #53)
-#65 := (<= #64 0::Int)
-#66 := (not #65)
-decl f4 :: Int
-#8 := f4
-#54 := (+ f4 #53)
-#52 := (>= #54 0::Int)
-#55 := (not #52)
-#48 := (* -1::Int f4)
-#49 := (+ f3 #48)
-#47 := (>= #49 0::Int)
-#46 := (not #47)
-#58 := (and #46 #55)
-#61 := (not #58)
-#76 := (or #61 #65)
-#79 := (not #76)
-#13 := (< f5 f3)
-#14 := (not #13)
-#11 := (< f4 f5)
-#9 := (< f3 f4)
-#12 := (and #9 #11)
-#15 := (implies #12 #14)
-#16 := (not #15)
-#82 := (iff #16 #79)
-#38 := (not #12)
-#39 := (or #38 #14)
-#42 := (not #39)
-#80 := (iff #42 #79)
-#77 := (iff #39 #76)
-#74 := (iff #14 #65)
-#69 := (not #66)
-#72 := (iff #69 #65)
-#73 := [rewrite]: #72
-#70 := (iff #14 #69)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#62 := (iff #38 #61)
-#59 := (iff #12 #58)
-#56 := (iff #11 #55)
-#57 := [rewrite]: #56
-#50 := (iff #9 #46)
-#51 := [rewrite]: #50
-#60 := [monotonicity #51 #57]: #59
-#63 := [monotonicity #60]: #62
-#78 := [monotonicity #63 #75]: #77
-#81 := [monotonicity #78]: #80
-#43 := (iff #16 #42)
-#40 := (iff #15 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#83 := [trans #44 #81]: #82
-#37 := [asserted]: #16
-#84 := [mp #37 #83]: #79
-#88 := [not-or-elim #84]: #66
-#85 := [not-or-elim #84]: #58
-#87 := [and-elim #85]: #55
-#86 := [and-elim #85]: #46
-[th-lemma arith farkas 1 1 1 #86 #87 #88]: false
-unsat
-af0350f575bb011825d92c6b725b23ef78ce1fa1 17 0
-#2 := false
-#7 := 0::Real
-#8 := (= 0::Real 0::Real)
-#9 := (not #8)
-#37 := (iff #9 false)
-#1 := true
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
-[mp #29 #38]: false
-unsat
-1ef636a83dafea60626dc36221ab0791106b1afd 25 0
-#2 := false
-#7 := 0::Real
-#8 := (- 0::Real)
-#9 := (= 0::Real #8)
-#10 := (not #9)
-#45 := (iff #10 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #10 #40)
-#38 := (iff #9 true)
-#33 := (= 0::Real 0::Real)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (= #8 0::Real)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #10
-[mp #30 #46]: false
-unsat
-40be88f85c9e0db481ad8ec82bd95178d7fea9fc 17 0
-#2 := false
-#7 := 1::Real
-#8 := (= 1::Real 1::Real)
-#9 := (not #8)
-#38 := (iff #9 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
-unsat
-158b50cd7a5340c24e2fc62138c985348713654b 34 0
-#2 := false
-#7 := 1::Real
-#8 := (- 1::Real)
-#9 := (= #8 1::Real)
-#10 := (not #9)
-#11 := (not #10)
-#55 := (iff #11 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #11 #50)
-#48 := (iff #10 true)
-#43 := (not false)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #10 #43)
-#41 := (iff #9 false)
-#33 := -1::Real
-#36 := (= -1::Real 1::Real)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #9 #36)
-#34 := (= #8 -1::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#32 := [asserted]: #11
-[mp #32 #56]: false
-unsat
-6f5d484ec7cfad7af7977254dc019939ebd214cc 18 0
-#2 := false
-#8 := 1::Real
-#7 := 0::Real
-#9 := (< 0::Real 1::Real)
-#10 := (not #9)
-#40 := (iff #10 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (iff #9 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #10
-[mp #30 #41]: false
-unsat
-e4647906bb792263dfef92dd4a04fd86cf8efa48 18 0
-#2 := false
-#8 := 1::Real
-#7 := 0::Real
-#9 := (<= 0::Real 1::Real)
-#10 := (not #9)
-#40 := (iff #10 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (iff #9 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #10
-[mp #30 #41]: false
-unsat
-6c6a35c4c4c8290ce89a1005e8de2a68e38ab9f1 40 0
-#2 := false
-#11 := 567::Real
-#9 := 345::Real
-#7 := 123::Real
-#8 := (- 123::Real)
-#10 := (+ #8 345::Real)
-#12 := (< #10 567::Real)
-#13 := (not #12)
-#61 := (iff #13 false)
-#41 := 222::Real
-#46 := (< 222::Real 567::Real)
-#49 := (not #46)
-#59 := (iff #49 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #49 #54)
-#52 := (iff #46 true)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#50 := (iff #13 #49)
-#47 := (iff #12 #46)
-#44 := (= #10 222::Real)
-#35 := -123::Real
-#38 := (+ -123::Real 345::Real)
-#42 := (= #38 222::Real)
-#43 := [rewrite]: #42
-#39 := (= #10 #38)
-#36 := (= #8 -123::Real)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#62 := [trans #51 #60]: #61
-#34 := [asserted]: #13
-[mp #34 #62]: false
-unsat
-6cd7f01d0158fe1b48c671f1634290b4c3d0362e 18 0
-#2 := false
-#8 := 2345678901::Real
-#7 := 123456789::Real
-#9 := (< 123456789::Real 2345678901::Real)
-#10 := (not #9)
-#41 := (iff #10 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #10 #36)
-#34 := (iff #9 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #10
-[mp #31 #42]: false
-unsat
-bd73a6ae0433b55288108717d8c4076884cd2760 30 0
-#2 := false
-#9 := 2345678901::Real
-#7 := 123456789::Real
-#8 := (- 123456789::Real)
-#10 := (< #8 2345678901::Real)
-#11 := (not #10)
-#51 := (iff #11 false)
-#33 := -123456789::Real
-#36 := (< -123456789::Real 2345678901::Real)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #11 #39)
-#37 := (iff #10 #36)
-#34 := (= #8 -123456789::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#32 := [asserted]: #11
-[mp #32 #52]: false
-unsat
-cb2f1c021f02a4a0896a377a14007ceda9f3dfef 26 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := 0::Real
-#9 := (+ f3 0::Real)
-#10 := (= #9 f3)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= f3 f3)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-df95853dfdf63ff909e7c1d6374a552556297148 26 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#7 := 0::Real
-#9 := (+ 0::Real f3)
-#10 := (= #9 f3)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= f3 f3)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-38e4ae2664df97269d895a97d6a0913820867eda 29 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-decl f4 :: Real
-#8 := f4
-#10 := (+ f4 f3)
-#9 := (+ f3 f4)
-#11 := (= #9 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (= #9 #9)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (= #10 #9)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-fdc6d9651e9ea1edb706f73f48fa04bf1897ffad 33 0
-#2 := false
-decl f5 :: Real
-#9 := f5
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#12 := (+ f3 f4)
-#13 := (+ #12 f5)
-#10 := (+ f4 f5)
-#11 := (+ f3 #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#51 := (iff #15 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #15 #46)
-#44 := (iff #14 true)
-#39 := (= #11 #11)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #14 #39)
-#37 := (= #13 #11)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#36 := [asserted]: #15
-[mp #36 #52]: false
-unsat
-b90b5c8c12f8e63f42b7158cdc22e7616d773fed 45 0
-#2 := false
-decl f4 :: Real
-#8 := f4
-#12 := (- f4)
-decl f3 :: Real
-#7 := f3
-#13 := (= f3 #12)
-#10 := 0::Real
-#9 := (+ f3 f4)
-#11 := (= #9 0::Real)
-#14 := (iff #11 #13)
-#15 := (not #14)
-#64 := (iff #15 false)
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#40 := (= f3 #37)
-#49 := (not #11)
-#50 := (iff #49 #40)
-#62 := (iff #50 false)
-#57 := (iff #49 #11)
-#60 := (iff #57 false)
-#61 := [rewrite]: #60
-#58 := (iff #50 #57)
-#55 := (iff #40 #11)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#53 := (iff #15 #50)
-#43 := (iff #11 #40)
-#46 := (not #43)
-#51 := (iff #46 #50)
-#52 := [rewrite]: #51
-#47 := (iff #15 #46)
-#44 := (iff #14 #43)
-#41 := (iff #13 #40)
-#38 := (= #12 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#54 := [trans #48 #52]: #53
-#65 := [trans #54 #63]: #64
-#35 := [asserted]: #15
-[mp #35 #65]: false
-unsat
-44508c3b99ed3ca47c812dcb3cd063b1955bb40d 26 0
-#2 := false
-#7 := 1::Real
-#8 := (- 1::Real)
-#9 := (= #8 #8)
-#10 := (not #9)
-#47 := (iff #10 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #10 #42)
-#40 := (iff #9 true)
-#32 := -1::Real
-#35 := (= -1::Real -1::Real)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #9 #35)
-#33 := (= #8 -1::Real)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #10
-[mp #31 #48]: false
-unsat
-fce41356fa222cd0ad9967bcbb1e367080f22540 26 0
-#2 := false
-#7 := 3::Real
-#8 := (- 3::Real)
-#9 := (= #8 #8)
-#10 := (not #9)
-#47 := (iff #10 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #10 #42)
-#40 := (iff #9 true)
-#32 := -3::Real
-#35 := (= -3::Real -3::Real)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #9 #35)
-#33 := (= #8 -3::Real)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #10
-[mp #31 #48]: false
-unsat
-f92b0a53b26261788a99f1f102e26adc2affa71b 53 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#9 := 0::Real
-#11 := (< 0::Real f3)
-#8 := (- f3)
-#10 := (< #8 0::Real)
-#12 := (iff #10 #11)
-#13 := (not #12)
-#73 := (iff #13 false)
-#34 := -1::Real
-#35 := (* -1::Real f3)
-#38 := (< #35 0::Real)
-#47 := (not #38)
-#48 := (iff #47 #11)
-#71 := (iff #48 false)
-#53 := (<= f3 0::Real)
-#54 := (not #53)
-#66 := (iff #53 #54)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #48 #66)
-#64 := (iff #11 #54)
-#65 := [rewrite]: #64
-#62 := (iff #47 #53)
-#57 := (not #54)
-#60 := (iff #57 #53)
-#61 := [rewrite]: #60
-#58 := (iff #47 #57)
-#55 := (iff #38 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#72 := [trans #68 #70]: #71
-#51 := (iff #13 #48)
-#41 := (iff #38 #11)
-#44 := (not #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#39 := (iff #10 #38)
-#36 := (= #8 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#74 := [trans #52 #72]: #73
-#33 := [asserted]: #13
-[mp #33 #74]: false
-unsat
-947dbc99dc836af0697bbc290f76c877a29a0775 61 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#10 := (- f3)
-#11 := (< #10 0::Real)
-#9 := (< 0::Real f3)
-#12 := (implies #9 #11)
-#13 := (not #12)
-#80 := (iff #13 false)
-#34 := -1::Real
-#35 := (* -1::Real f3)
-#38 := (< #35 0::Real)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#78 := (iff #50 false)
-#1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #50 #73)
-#71 := (iff #45 true)
-#53 := (<= f3 0::Real)
-#54 := (not #53)
-#66 := (or #53 #54)
-#69 := (iff #66 true)
-#70 := [rewrite]: #69
-#67 := (iff #45 #66)
-#64 := (iff #38 #54)
-#65 := [rewrite]: #64
-#62 := (iff #44 #53)
-#57 := (not #54)
-#60 := (iff #57 #53)
-#61 := [rewrite]: #60
-#58 := (iff #44 #57)
-#55 := (iff #9 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#72 := [trans #68 #70]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#51 := (iff #13 #50)
-#48 := (iff #12 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#81 := [trans #52 #79]: #80
-#33 := [asserted]: #13
-[mp #33 #81]: false
-unsat
-f85f7c93404a45994b3d3e795113b1a47ef37a6c 61 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#10 := (- f3)
-#8 := 0::Real
-#11 := (< 0::Real #10)
-#9 := (< f3 0::Real)
-#12 := (implies #9 #11)
-#13 := (not #12)
-#80 := (iff #13 false)
-#34 := -1::Real
-#35 := (* -1::Real f3)
-#38 := (< 0::Real #35)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#78 := (iff #50 false)
-#1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #50 #73)
-#71 := (iff #45 true)
-#53 := (>= f3 0::Real)
-#54 := (not #53)
-#66 := (or #53 #54)
-#69 := (iff #66 true)
-#70 := [rewrite]: #69
-#67 := (iff #45 #66)
-#64 := (iff #38 #54)
-#65 := [rewrite]: #64
-#62 := (iff #44 #53)
-#57 := (not #54)
-#60 := (iff #57 #53)
-#61 := [rewrite]: #60
-#58 := (iff #44 #57)
-#55 := (iff #9 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#72 := [trans #68 #70]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#51 := (iff #13 #50)
-#48 := (iff #12 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#81 := [trans #52 #79]: #80
-#33 := [asserted]: #13
-[mp #33 #81]: false
-unsat
-d1707afef5a1121f793c4ae15ea4d8dd324a2ebb 26 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := 0::Real
-#9 := (- f3 0::Real)
-#10 := (= #9 f3)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= f3 f3)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-4d2d9e6632b13b50703c8241c824ac4bc60fa851 32 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#10 := (- f3)
-#7 := 0::Real
-#9 := (- 0::Real f3)
-#11 := (= #9 #10)
-#12 := (not #11)
-#51 := (iff #12 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (iff #11 true)
-#33 := -1::Real
-#34 := (* -1::Real f3)
-#39 := (= #34 #34)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#37 := (= #10 #34)
-#38 := [rewrite]: #37
-#35 := (= #9 #34)
-#36 := [rewrite]: #35
-#41 := [monotonicity #36 #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-f26054cf9e6e46ab9f14eb8b4fa90c23c83e1e20 64 0
-#2 := false
-#11 := 0::Real
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#10 := (- f3 f4)
-#12 := (< #10 0::Real)
-#9 := (< f3 f4)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#82 := (iff #14 false)
-#35 := -1::Real
-#36 := (* -1::Real f4)
-#37 := (+ f3 #36)
-#40 := (< #37 0::Real)
-#46 := (not #9)
-#47 := (or #46 #40)
-#52 := (not #47)
-#80 := (iff #52 false)
-#1 := true
-#75 := (not true)
-#78 := (iff #75 false)
-#79 := [rewrite]: #78
-#76 := (iff #52 #75)
-#73 := (iff #47 true)
-#56 := (>= #37 0::Real)
-#55 := (not #56)
-#68 := (or #56 #55)
-#71 := (iff #68 true)
-#72 := [rewrite]: #71
-#69 := (iff #47 #68)
-#66 := (iff #40 #55)
-#67 := [rewrite]: #66
-#64 := (iff #46 #56)
-#59 := (not #55)
-#62 := (iff #59 #56)
-#63 := [rewrite]: #62
-#60 := (iff #46 #59)
-#57 := (iff #9 #55)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#70 := [monotonicity #65 #67]: #69
-#74 := [trans #70 #72]: #73
-#77 := [monotonicity #74]: #76
-#81 := [trans #77 #79]: #80
-#53 := (iff #14 #52)
-#50 := (iff #13 #47)
-#43 := (implies #9 #40)
-#48 := (iff #43 #47)
-#49 := [rewrite]: #48
-#44 := (iff #13 #43)
-#41 := (iff #12 #40)
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#51 := [trans #45 #49]: #50
-#54 := [monotonicity #51]: #53
-#83 := [trans #54 #81]: #82
-#34 := [asserted]: #14
-[mp #34 #83]: false
-unsat
-34a1de7290f4c8a36751d89b547f21ddb0c0cada 44 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-decl f4 :: Real
-#8 := f4
-#10 := (- f4 f3)
-#11 := (- #10)
-#9 := (- f3 f4)
-#12 := (= #9 #11)
-#13 := (not #12)
-#63 := (iff #13 false)
-#1 := true
-#58 := (not true)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #13 #58)
-#56 := (iff #12 true)
-#35 := -1::Real
-#36 := (* -1::Real f4)
-#37 := (+ f3 #36)
-#51 := (= #37 #37)
-#54 := (iff #51 true)
-#55 := [rewrite]: #54
-#52 := (iff #12 #51)
-#49 := (= #11 #37)
-#40 := (* -1::Real f3)
-#41 := (+ #40 f4)
-#44 := (- #41)
-#47 := (= #44 #37)
-#48 := [rewrite]: #47
-#45 := (= #11 #44)
-#42 := (= #10 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#38 := (= #9 #37)
-#39 := [rewrite]: #38
-#53 := [monotonicity #39 #50]: #52
-#57 := [trans #53 #55]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#34 := [asserted]: #13
-[mp #34 #64]: false
-unsat
-431807e85783cee305c53c73752025f626bba5f5 42 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-decl f4 :: Real
-#8 := f4
-#10 := (- f4)
-#11 := (+ #10 f3)
-#9 := (- f3 f4)
-#12 := (= #9 #11)
-#13 := (not #12)
-#61 := (iff #13 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #13 #56)
-#54 := (iff #12 true)
-#35 := -1::Real
-#36 := (* -1::Real f4)
-#37 := (+ f3 #36)
-#49 := (= #37 #37)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #12 #49)
-#47 := (= #11 #37)
-#42 := (+ #36 f3)
-#45 := (= #42 #37)
-#46 := [rewrite]: #45
-#43 := (= #11 #42)
-#40 := (= #10 #36)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#38 := (= #9 #37)
-#39 := [rewrite]: #38
-#51 := [monotonicity #39 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#34 := [asserted]: #13
-[mp #34 #62]: false
-unsat
-8531d27b75ee018ed4f78df6ab158a7dfda20b74 48 0
-#2 := false
-decl f5 :: Real
-#10 := f5
-decl f4 :: Real
-#8 := f4
-#12 := (+ f4 f5)
-decl f3 :: Real
-#7 := f3
-#13 := (- f3 #12)
-#9 := (- f3 f4)
-#11 := (- #9 f5)
-#14 := (= #11 #13)
-#15 := (not #14)
-#66 := (iff #15 false)
-#1 := true
-#61 := (not true)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #15 #61)
-#59 := (iff #14 true)
-#37 := -1::Real
-#45 := (* -1::Real f5)
-#38 := (* -1::Real f4)
-#46 := (+ #38 #45)
-#47 := (+ f3 #46)
-#54 := (= #47 #47)
-#57 := (iff #54 true)
-#58 := [rewrite]: #57
-#55 := (iff #14 #54)
-#52 := (= #13 #47)
-#53 := [rewrite]: #52
-#50 := (= #11 #47)
-#39 := (+ f3 #38)
-#42 := (- #39 f5)
-#48 := (= #42 #47)
-#49 := [rewrite]: #48
-#43 := (= #11 #42)
-#40 := (= #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#51 := [trans #44 #49]: #50
-#56 := [monotonicity #51 #53]: #55
-#60 := [trans #56 #58]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#36 := [asserted]: #15
-[mp #36 #67]: false
-unsat
-091bb9dd524578370d5c755a79bf57f30adc2896 26 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#9 := (* f3 0::Real)
-#10 := (= #9 0::Real)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= 0::Real 0::Real)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-11ee5f34d2e69fbb83f75a1ce8b20231b0b9ee4e 26 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#9 := (* 0::Real f3)
-#10 := (= #9 0::Real)
-#11 := (not #10)
-#45 := (iff #11 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 true)
-#33 := (= 0::Real 0::Real)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#32 := [rewrite]: #10
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#31 := [asserted]: #11
-[mp #31 #46]: false
-unsat
-c3a72c0601b8cbc5a12b6de3f04815e4023a22d9 26 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := 1::Real
-#9 := (* f3 1::Real)
-#10 := (= #9 f3)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
-unsat
-d67f22dcf49dbce534730cc3548cbd6548413fe9 26 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#7 := 1::Real
-#9 := (* 1::Real f3)
-#10 := (= #9 f3)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
-unsat
-da0267c834e2691ae6adb35657dd447f07a5ddb0 40 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#11 := (- f3)
-#8 := 1::Real
-#9 := (- 1::Real)
-#10 := (* f3 #9)
-#12 := (= #10 #11)
-#13 := (not #12)
-#60 := (iff #13 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #13 #55)
-#53 := (iff #12 true)
-#35 := -1::Real
-#41 := (* -1::Real f3)
-#48 := (= #41 #41)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #12 #48)
-#46 := (= #11 #41)
-#47 := [rewrite]: #46
-#44 := (= #10 #41)
-#38 := (* f3 -1::Real)
-#42 := (= #38 #41)
-#43 := [rewrite]: #42
-#39 := (= #10 #38)
-#36 := (= #9 -1::Real)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#50 := [monotonicity #45 #47]: #49
-#54 := [trans #50 #52]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#34 := [asserted]: #13
-[mp #34 #61]: false
-unsat
-64b057a096fc36168819ce708a4a964a21d4a714 35 0
-#2 := false
-decl f3 :: Real
-#9 := f3
-#11 := (- f3)
-#7 := 1::Real
-#8 := (- 1::Real)
-#10 := (* #8 f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#55 := (iff #13 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #13 #50)
-#48 := (iff #12 true)
-#35 := -1::Real
-#38 := (* -1::Real f3)
-#43 := (= #38 #38)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (= #11 #38)
-#42 := [rewrite]: #41
-#39 := (= #10 #38)
-#36 := (= #8 -1::Real)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [monotonicity #40 #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#34 := [asserted]: #13
-[mp #34 #56]: false
-unsat
-c3e2eae4d4e8a5d34e7872b606228eba3fbea719 28 0
-#2 := false
-#7 := 3::Real
-decl f3 :: Real
-#8 := f3
-#10 := (* f3 3::Real)
-#9 := (* 3::Real f3)
-#11 := (= #9 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#36 := (= #9 #9)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (= #10 #9)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #12
-[mp #33 #49]: false
-unsat
-5e33e92f4c8750528f60b2e66569586bf0f0bb45 30 0
-#2 := false
-#7 := 1::Real
-#8 := 2::Real
-#9 := (/ 1::Real 2::Real)
-#10 := (< #9 1::Real)
-#11 := (not #10)
-#51 := (iff #11 false)
-#33 := 1/2::Real
-#36 := (< 1/2::Real 1::Real)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #11 #39)
-#37 := (iff #10 #36)
-#34 := (= #9 1/2::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#32 := [asserted]: #11
-[mp #32 #52]: false
-unsat
-e08ba17aff2428243af5cf67f75ce9241dfd2567 27 0
-#2 := false
-#8 := 3::Real
-#7 := 1::Real
-#9 := (/ 1::Real 3::Real)
-#10 := (= #9 #9)
-#11 := (not #10)
-#48 := (iff #11 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #11 #43)
-#41 := (iff #10 true)
-#33 := 1/3::Real
-#36 := (= 1/3::Real 1/3::Real)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #10 #36)
-#34 := (= #9 1/3::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#32 := [asserted]: #11
-[mp #32 #49]: false
-unsat
-c23e6b58a553359eacf5eb208af7f8150bf293f2 48 0
-#2 := false
-#8 := 3::Real
-#7 := 1::Real
-#11 := (- 1::Real)
-#12 := (/ #11 3::Real)
-#9 := (- 3::Real)
-#10 := (/ 1::Real #9)
-#13 := (= #10 #12)
-#14 := (not #13)
-#69 := (iff #14 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #14 #64)
-#62 := (iff #13 true)
-#42 := -1/3::Real
-#57 := (= -1/3::Real -1/3::Real)
-#60 := (iff #57 true)
-#61 := [rewrite]: #60
-#58 := (iff #13 #57)
-#55 := (= #12 -1/3::Real)
-#47 := -1::Real
-#50 := (/ -1::Real 3::Real)
-#53 := (= #50 -1/3::Real)
-#54 := [rewrite]: #53
-#51 := (= #12 #50)
-#48 := (= #11 -1::Real)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#45 := (= #10 -1/3::Real)
-#36 := -3::Real
-#39 := (/ 1::Real -3::Real)
-#43 := (= #39 -1/3::Real)
-#44 := [rewrite]: #43
-#40 := (= #10 #39)
-#37 := (= #9 -3::Real)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#46 := [trans #41 #44]: #45
-#59 := [monotonicity #46 #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#35 := [asserted]: #14
-[mp #35 #70]: false
-unsat
-a1da7a34684e1a5bd561f100c0fa893afb3b7a5d 36 0
-#2 := false
-#9 := 3::Real
-#7 := 1::Real
-#8 := (- 1::Real)
-#10 := (/ #8 3::Real)
-#11 := (= #10 #10)
-#12 := (not #11)
-#57 := (iff #12 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #12 #52)
-#50 := (iff #11 true)
-#40 := -1/3::Real
-#45 := (= -1/3::Real -1/3::Real)
-#48 := (iff #45 true)
-#49 := [rewrite]: #48
-#46 := (iff #11 #45)
-#43 := (= #10 -1/3::Real)
-#34 := -1::Real
-#37 := (/ -1::Real 3::Real)
-#41 := (= #37 -1/3::Real)
-#42 := [rewrite]: #41
-#38 := (= #10 #37)
-#35 := (= #8 -1::Real)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#44 := [trans #39 #42]: #43
-#47 := [monotonicity #44 #44]: #46
-#51 := [trans #47 #49]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#33 := [asserted]: #12
-[mp #33 #58]: false
-unsat
-a0d33d56932085d413a998104b0ae2bb7b556dd3 43 0
-#2 := false
-#9 := 3::Real
-#7 := 1::Real
-#12 := (/ 1::Real 3::Real)
-#10 := (- 3::Real)
-#8 := (- 1::Real)
-#11 := (/ #8 #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#64 := (iff #14 false)
-#1 := true
-#59 := (not true)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #14 #59)
-#57 := (iff #13 true)
-#45 := 1/3::Real
-#52 := (= 1/3::Real 1/3::Real)
-#55 := (iff #52 true)
-#56 := [rewrite]: #55
-#53 := (iff #13 #52)
-#50 := (= #12 1/3::Real)
-#51 := [rewrite]: #50
-#48 := (= #11 1/3::Real)
-#39 := -3::Real
-#36 := -1::Real
-#42 := (/ -1::Real -3::Real)
-#46 := (= #42 1/3::Real)
-#47 := [rewrite]: #46
-#43 := (= #11 #42)
-#40 := (= #10 -3::Real)
-#41 := [rewrite]: #40
-#37 := (= #8 -1::Real)
-#38 := [rewrite]: #37
-#44 := [monotonicity #38 #41]: #43
-#49 := [trans #44 #47]: #48
-#54 := [monotonicity #49 #51]: #53
-#58 := [trans #54 #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#35 := [asserted]: #14
-[mp #35 #65]: false
-unsat
-960788d4730f7f2adca59dd014a913eb2be28d68 26 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := 1::Real
-#9 := (/ f3 1::Real)
-#10 := (= #9 f3)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
-unsat
-20774a51f9bccf7108652ad949f64111f5847f42 60 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#67 := 2/3::Real
-#68 := (* 2/3::Real f3)
-#69 := (<= #68 0::Real)
-#65 := (not #69)
-#54 := (<= f3 0::Real)
-#71 := (or #54 #65)
-#74 := (not #71)
-#10 := 3::Real
-#11 := (/ f3 3::Real)
-#12 := (< #11 f3)
-#9 := (< 0::Real f3)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#77 := (iff #14 #74)
-#35 := 1/3::Real
-#36 := (* 1/3::Real f3)
-#39 := (< #36 f3)
-#45 := (not #9)
-#46 := (or #45 #39)
-#51 := (not #46)
-#75 := (iff #51 #74)
-#72 := (iff #46 #71)
-#66 := (iff #39 #65)
-#70 := [rewrite]: #66
-#63 := (iff #45 #54)
-#55 := (not #54)
-#58 := (not #55)
-#61 := (iff #58 #54)
-#62 := [rewrite]: #61
-#59 := (iff #45 #58)
-#56 := (iff #9 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#73 := [monotonicity #64 #70]: #72
-#76 := [monotonicity #73]: #75
-#52 := (iff #14 #51)
-#49 := (iff #13 #46)
-#42 := (implies #9 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#78 := [trans #53 #76]: #77
-#34 := [asserted]: #14
-#79 := [mp #34 #78]: #74
-#81 := [not-or-elim #79]: #69
-#80 := [not-or-elim #79]: #55
-[th-lemma arith farkas -2/3 1 #80 #81]: false
-unsat
-59ae2373184f370c17621f32898c84257dcf4466 60 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#69 := 2/3::Real
-#70 := (* 2/3::Real f3)
-#67 := (>= #70 0::Real)
-#65 := (not #67)
-#56 := (>= f3 0::Real)
-#71 := (or #56 #65)
-#74 := (not #71)
-#10 := 3::Real
-#11 := (/ f3 3::Real)
-#12 := (< f3 #11)
-#9 := (< f3 0::Real)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#77 := (iff #14 #74)
-#35 := 1/3::Real
-#36 := (* 1/3::Real f3)
-#39 := (< f3 #36)
-#45 := (not #9)
-#46 := (or #45 #39)
-#51 := (not #46)
-#75 := (iff #51 #74)
-#72 := (iff #46 #71)
-#66 := (iff #39 #65)
-#68 := [rewrite]: #66
-#63 := (iff #45 #56)
-#54 := (not #56)
-#58 := (not #54)
-#61 := (iff #58 #56)
-#62 := [rewrite]: #61
-#59 := (iff #45 #58)
-#55 := (iff #9 #54)
-#57 := [rewrite]: #55
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#73 := [monotonicity #64 #68]: #72
-#76 := [monotonicity #73]: #75
-#52 := (iff #14 #51)
-#49 := (iff #13 #46)
-#42 := (implies #9 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#78 := [trans #53 #76]: #77
-#34 := [asserted]: #14
-#79 := [mp #34 #78]: #74
-#81 := [not-or-elim #79]: #67
-#80 := [not-or-elim #79]: #54
-[th-lemma arith farkas -2/3 1 #80 #81]: false
-unsat
-588ad60f0eef06c7d10b05e810713f52bae9fbac 36 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#7 := 3::Real
-#9 := (/ f3 3::Real)
-#10 := (* 3::Real #9)
-#11 := (= #10 f3)
-#12 := (not #11)
-#56 := (iff #12 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #12 #51)
-#49 := (iff #11 true)
-#44 := (= f3 f3)
-#47 := (iff #44 true)
-#48 := [rewrite]: #47
-#45 := (iff #11 #44)
-#34 := 1/3::Real
-#35 := (* 1/3::Real f3)
-#38 := (* 3::Real #35)
-#41 := (= #38 f3)
-#42 := [rewrite]: #41
-#39 := (= #10 #38)
-#36 := (= #9 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [trans #40 #42]: #11
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#33 := [asserted]: #12
-[mp #33 #57]: false
-unsat
-87491d527606c77b68ab29c99a67d25340955342 35 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := 3::Real
-#9 := (* f3 3::Real)
-#10 := (/ #9 3::Real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#55 := (iff #12 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #12 #50)
-#48 := (iff #11 true)
-#43 := (= f3 f3)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #11 #43)
-#34 := (* 3::Real f3)
-#37 := (/ #34 3::Real)
-#40 := (= #37 f3)
-#41 := [rewrite]: #40
-#38 := (= #10 #37)
-#35 := (= #9 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [trans #39 #41]: #11
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#33 := [asserted]: #12
-[mp #33 #56]: false
-unsat
-fb3e7bcac57bdcb4f4b6e119fa415b4a8bf5c9e7 62 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#69 := 1/3::Real
-#70 := (* 1/3::Real f3)
-#71 := (<= #70 0::Real)
-#67 := (not #71)
-#56 := (<= f3 0::Real)
-#73 := (or #56 #67)
-#76 := (not #73)
-#12 := 3::Real
-#10 := 2::Real
-#11 := (* 2::Real f3)
-#13 := (/ #11 3::Real)
-#14 := (< #13 f3)
-#9 := (< 0::Real f3)
-#15 := (implies #9 #14)
-#16 := (not #15)
-#79 := (iff #16 #76)
-#38 := 2/3::Real
-#39 := (* 2/3::Real f3)
-#41 := (< #39 f3)
-#47 := (not #9)
-#48 := (or #47 #41)
-#53 := (not #48)
-#77 := (iff #53 #76)
-#74 := (iff #48 #73)
-#68 := (iff #41 #67)
-#72 := [rewrite]: #68
-#65 := (iff #47 #56)
-#57 := (not #56)
-#60 := (not #57)
-#63 := (iff #60 #56)
-#64 := [rewrite]: #63
-#61 := (iff #47 #60)
-#58 := (iff #9 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#75 := [monotonicity #66 #72]: #74
-#78 := [monotonicity #75]: #77
-#54 := (iff #16 #53)
-#51 := (iff #15 #48)
-#44 := (implies #9 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #15 #44)
-#42 := (iff #14 #41)
-#37 := (= #13 #39)
-#40 := [rewrite]: #37
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#80 := [trans #55 #78]: #79
-#36 := [asserted]: #16
-#81 := [mp #36 #80]: #76
-#83 := [not-or-elim #81]: #71
-#82 := [not-or-elim #81]: #57
-[th-lemma arith farkas -1/3 1 #82 #83]: false
-unsat
-953412704db979090a4ca7b4441938d5b81412e0 62 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#71 := 1/3::Real
-#72 := (* 1/3::Real f3)
-#69 := (>= #72 0::Real)
-#67 := (not #69)
-#58 := (>= f3 0::Real)
-#73 := (or #58 #67)
-#76 := (not #73)
-#12 := 3::Real
-#10 := 2::Real
-#11 := (* 2::Real f3)
-#13 := (/ #11 3::Real)
-#14 := (< f3 #13)
-#9 := (< f3 0::Real)
-#15 := (implies #9 #14)
-#16 := (not #15)
-#79 := (iff #16 #76)
-#38 := 2/3::Real
-#39 := (* 2/3::Real f3)
-#41 := (< f3 #39)
-#47 := (not #9)
-#48 := (or #47 #41)
-#53 := (not #48)
-#77 := (iff #53 #76)
-#74 := (iff #48 #73)
-#68 := (iff #41 #67)
-#70 := [rewrite]: #68
-#65 := (iff #47 #58)
-#56 := (not #58)
-#60 := (not #56)
-#63 := (iff #60 #58)
-#64 := [rewrite]: #63
-#61 := (iff #47 #60)
-#57 := (iff #9 #56)
-#59 := [rewrite]: #57
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#75 := [monotonicity #66 #70]: #74
-#78 := [monotonicity #75]: #77
-#54 := (iff #16 #53)
-#51 := (iff #15 #48)
-#44 := (implies #9 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #15 #44)
-#42 := (iff #14 #41)
-#37 := (= #13 #39)
-#40 := [rewrite]: #37
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#80 := [trans #55 #78]: #79
-#36 := [asserted]: #16
-#81 := [mp #36 #80]: #76
-#83 := [not-or-elim #81]: #69
-#82 := [not-or-elim #81]: #56
-[th-lemma arith farkas -1/3 1 #82 #83]: false
-unsat
-1de1767601decde5f6a984aff8700035d237f520 75 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#34 := -1::Real
-#35 := (* -1::Real f3)
-#47 := (>= f3 0::Real)
-#54 := (if #47 f3 #35)
-#74 := (* -1::Real #54)
-#83 := (+ #35 #74)
-#92 := (<= #83 0::Real)
-#79 := (= #35 #54)
-#48 := (not #47)
-#75 := (+ f3 #74)
-#82 := (<= #75 0::Real)
-#78 := (= f3 #54)
-#84 := [hypothesis]: #47
-#80 := (or #48 #78)
-#81 := [def-axiom]: #80
-#85 := [unit-resolution #81 #84]: #78
-#86 := (not #78)
-#87 := (or #86 #82)
-#88 := [th-lemma arith triangle-eq]: #87
-#89 := [unit-resolution #88 #85]: #82
-#63 := (>= #54 0::Real)
-#67 := (not #63)
-#10 := (- f3)
-#9 := (< f3 0::Real)
-#11 := (if #9 #10 f3)
-#12 := (<= 0::Real #11)
-#13 := (not #12)
-#70 := (iff #13 #67)
-#38 := (if #9 #35 f3)
-#41 := (<= 0::Real #38)
-#44 := (not #41)
-#68 := (iff #44 #67)
-#65 := (iff #41 #63)
-#59 := (<= 0::Real #54)
-#62 := (iff #59 #63)
-#64 := [rewrite]: #62
-#60 := (iff #41 #59)
-#57 := (= #38 #54)
-#51 := (if #48 #35 f3)
-#55 := (= #51 #54)
-#56 := [rewrite]: #55
-#52 := (= #38 #51)
-#49 := (iff #9 #48)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#58 := [trans #53 #56]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#39 := (= #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#71 := [trans #46 #69]: #70
-#33 := [asserted]: #13
-#72 := [mp #33 #71]: #67
-#90 := [th-lemma arith farkas -1 1 1 #84 #72 #89]: false
-#91 := [lemma #90]: #48
-#76 := (or #47 #79)
-#77 := [def-axiom]: #76
-#94 := [unit-resolution #77 #91]: #79
-#95 := (not #79)
-#96 := (or #95 #92)
-#97 := [th-lemma arith triangle-eq]: #96
-#98 := [unit-resolution #97 #94]: #92
-[th-lemma arith farkas 1 1 1 #72 #91 #98]: false
-unsat
-97a92254fa3e068ea924e98693ea55400493d4bb 103 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#36 := -1::Real
-#37 := (* -1::Real f3)
-#58 := (>= f3 0::Real)
-#65 := (if #58 f3 #37)
-#70 := (= #65 0::Real)
-#13 := (= f3 0::Real)
-#118 := (iff #13 #70)
-#87 := (= f3 #65)
-#101 := (<= #37 0::Real)
-#100 := (= #37 0::Real)
-#84 := (not #13)
-#59 := (not #58)
-#103 := [hypothesis]: #59
-#104 := (or #84 #58)
-#105 := [th-lemma arith triangle-eq]: #104
-#106 := [unit-resolution #105 #103]: #84
-#98 := (or #70 #13)
-#73 := (not #70)
-#76 := (iff #73 #13)
-#10 := (- f3)
-#9 := (< f3 0::Real)
-#11 := (if #9 #10 f3)
-#12 := (= #11 0::Real)
-#14 := (iff #12 #13)
-#15 := (not #14)
-#79 := (iff #15 #76)
-#40 := (if #9 #37 f3)
-#43 := (= #40 0::Real)
-#52 := (not #43)
-#53 := (iff #52 #13)
-#77 := (iff #53 #76)
-#74 := (iff #52 #73)
-#71 := (iff #43 #70)
-#68 := (= #40 #65)
-#62 := (if #59 #37 f3)
-#66 := (= #62 #65)
-#67 := [rewrite]: #66
-#63 := (= #40 #62)
-#60 := (iff #9 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#69 := [trans #64 #67]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#56 := (iff #15 #53)
-#46 := (iff #43 #13)
-#49 := (not #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#80 := [trans #57 #78]: #79
-#35 := [asserted]: #15
-#81 := [mp #35 #80]: #76
-#91 := (not #76)
-#96 := (or #70 #13 #91)
-#97 := [def-axiom]: #96
-#99 := [unit-resolution #97 #81]: #98
-#107 := [unit-resolution #99 #106]: #70
-#88 := (= #37 #65)
-#85 := (or #58 #88)
-#86 := [def-axiom]: #85
-#108 := [unit-resolution #86 #103]: #88
-#109 := [trans #108 #107]: #100
-#110 := (not #100)
-#111 := (or #110 #101)
-#112 := [th-lemma arith triangle-eq]: #111
-#113 := [unit-resolution #112 #109]: #101
-#114 := [th-lemma arith farkas 1 1 #103 #113]: false
-#115 := [lemma #114]: #58
-#89 := (or #59 #87)
-#90 := [def-axiom]: #89
-#117 := [unit-resolution #90 #115]: #87
-#119 := [monotonicity #117]: #118
-#120 := (iff #84 #73)
-#121 := [monotonicity #119]: #120
-#102 := [hypothesis]: #84
-#122 := [mp #102 #121]: #73
-#116 := [unit-resolution #99 #102]: #70
-#123 := [unit-resolution #116 #122]: false
-#124 := [lemma #123]: #13
-#126 := [mp #124 #119]: #70
-#94 := (or #73 #84)
-#92 := (or #73 #84 #91)
-#93 := [def-axiom]: #92
-#95 := [unit-resolution #93 #81]: #94
-#125 := [unit-resolution #95 #124]: #73
-[unit-resolution #125 #126]: false
-unsat
-5eef55215a56f315e0597001f70244e2d6cbad2b 102 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#36 := -1::Real
-#37 := (* -1::Real f3)
-#112 := (* -1::Real #37)
-#113 := (+ f3 #112)
-#115 := (>= #113 0::Real)
-#111 := (= f3 #37)
-#58 := (>= f3 0::Real)
-#69 := (if #58 f3 #37)
-#119 := (= #69 #37)
-#89 := (= #37 #69)
-#61 := (not #58)
-#74 := (= #69 f3)
-#88 := (= f3 #69)
-#105 := (not #88)
-#84 := (not #74)
-#106 := (iff #84 #105)
-#103 := (iff #74 #88)
-#104 := [commutativity]: #103
-#107 := [monotonicity #104]: #106
-#100 := [hypothesis]: #84
-#108 := [mp #100 #107]: #105
-#98 := (or #58 #74)
-#77 := (iff #61 #74)
-#11 := (- f3)
-#10 := (< f3 0::Real)
-#12 := (if #10 #11 f3)
-#13 := (= #12 f3)
-#9 := (<= 0::Real f3)
-#14 := (iff #9 #13)
-#15 := (not #14)
-#80 := (iff #15 #77)
-#40 := (if #10 #37 f3)
-#43 := (= #40 f3)
-#52 := (not #9)
-#53 := (iff #52 #43)
-#78 := (iff #53 #77)
-#75 := (iff #43 #74)
-#72 := (= #40 #69)
-#66 := (if #61 #37 f3)
-#70 := (= #66 #69)
-#71 := [rewrite]: #70
-#67 := (= #40 #66)
-#64 := (iff #10 #61)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#76 := [monotonicity #73]: #75
-#62 := (iff #52 #61)
-#59 := (iff #9 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#79 := [monotonicity #63 #76]: #78
-#56 := (iff #15 #53)
-#46 := (iff #9 #43)
-#49 := (not #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#41 := (= #12 #40)
-#38 := (= #11 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#81 := [trans #57 #79]: #80
-#35 := [asserted]: #15
-#82 := [mp #35 #81]: #77
-#85 := (not #77)
-#96 := (or #58 #74 #85)
-#97 := [def-axiom]: #96
-#99 := [unit-resolution #97 #82]: #98
-#101 := [unit-resolution #99 #100]: #58
-#90 := (or #61 #88)
-#91 := [def-axiom]: #90
-#102 := [unit-resolution #91 #101]: #88
-#109 := [unit-resolution #102 #108]: false
-#110 := [lemma #109]: #74
-#94 := (or #61 #84)
-#92 := (or #61 #84 #85)
-#93 := [def-axiom]: #92
-#95 := [unit-resolution #93 #82]: #94
-#116 := [unit-resolution #95 #110]: #61
-#86 := (or #58 #89)
-#87 := [def-axiom]: #86
-#117 := [unit-resolution #87 #116]: #89
-#120 := [symm #117]: #119
-#118 := [symm #110]: #88
-#121 := [trans #118 #120]: #111
-#122 := (not #111)
-#123 := (or #122 #115)
-#124 := [th-lemma arith triangle-eq]: #123
-#125 := [unit-resolution #124 #121]: #115
-[th-lemma arith farkas 2 1 #116 #125]: false
-unsat
-45b14df2d2322e566d02d0db8c4a9bcfe19ad7c5 143 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#36 := -1::Real
-#37 := (* -1::Real f3)
-#58 := (>= f3 0::Real)
-#65 := (if #58 f3 #37)
-#104 := (* -1::Real #65)
-#154 := (+ f3 #104)
-#155 := (<= #154 0::Real)
-#90 := (= f3 #65)
-#105 := (+ #37 #104)
-#107 := (>= #105 0::Real)
-#91 := (= #37 #65)
-#59 := (not #58)
-#139 := [hypothesis]: #59
-#88 := (or #58 #91)
-#89 := [def-axiom]: #88
-#140 := [unit-resolution #89 #139]: #91
-#133 := (not #91)
-#141 := (or #133 #107)
-#142 := [th-lemma arith triangle-eq]: #141
-#143 := [unit-resolution #142 #140]: #107
-#73 := (+ f3 #65)
-#86 := (<= #73 0::Real)
-#148 := (not #86)
-#87 := (>= #73 0::Real)
-#106 := (<= #105 0::Real)
-#74 := (= #73 0::Real)
-#94 := (not #74)
-#126 := (not #87)
-#127 := [hypothesis]: #126
-#128 := (or #94 #87)
-#129 := [th-lemma arith triangle-eq]: #128
-#130 := [unit-resolution #129 #127]: #94
-#124 := (or #59 #74)
-#111 := (= f3 0::Real)
-#9 := (<= f3 0::Real)
-#108 := [hypothesis]: #94
-#102 := (or #9 #74)
-#52 := (not #9)
-#79 := (iff #52 #74)
-#11 := (- f3)
-#10 := (< f3 0::Real)
-#12 := (if #10 #11 f3)
-#13 := (= #12 #11)
-#14 := (iff #9 #13)
-#15 := (not #14)
-#82 := (iff #15 #79)
-#40 := (if #10 #37 f3)
-#43 := (= #40 #37)
-#53 := (iff #52 #43)
-#80 := (iff #53 #79)
-#77 := (iff #43 #74)
-#70 := (= #65 #37)
-#75 := (iff #70 #74)
-#76 := [rewrite]: #75
-#71 := (iff #43 #70)
-#68 := (= #40 #65)
-#62 := (if #59 #37 f3)
-#66 := (= #62 #65)
-#67 := [rewrite]: #66
-#63 := (= #40 #62)
-#60 := (iff #10 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#69 := [trans #64 #67]: #68
-#72 := [monotonicity #69]: #71
-#78 := [trans #72 #76]: #77
-#81 := [monotonicity #78]: #80
-#56 := (iff #15 #53)
-#46 := (iff #9 #43)
-#49 := (not #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #15 #49)
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#38 := (= #11 #37)
-#39 := [rewrite]: #38
-#41 := (= #12 #40)
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42 #39]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#83 := [trans #57 #81]: #82
-#35 := [asserted]: #15
-#84 := [mp #35 #83]: #79
-#95 := (not #79)
-#100 := (or #9 #74 #95)
-#101 := [def-axiom]: #100
-#103 := [unit-resolution #101 #84]: #102
-#109 := [unit-resolution #103 #108]: #9
-#110 := [hypothesis]: #58
-#112 := [th-lemma arith eq-propagate 0 0 #110 #109]: #111
-#120 := (= #73 f3)
-#118 := (= #65 f3)
-#92 := (or #59 #90)
-#93 := [def-axiom]: #92
-#113 := [unit-resolution #93 #110]: #90
-#119 := [symm #113]: #118
-#116 := (= #73 #65)
-#114 := (= #65 #73)
-#115 := [th-lemma arith eq-propagate 1 1 #110 #109]: #114
-#117 := [symm #115]: #116
-#121 := [trans #117 #119]: #120
-#122 := [trans #121 #112]: #74
-#123 := [unit-resolution #108 #122]: false
-#125 := [lemma #123]: #124
-#131 := [unit-resolution #125 #130]: #59
-#132 := [unit-resolution #89 #131]: #91
-#134 := (or #133 #106)
-#135 := [th-lemma arith triangle-eq]: #134
-#136 := [unit-resolution #135 #132]: #106
-#137 := [th-lemma arith farkas 1 1 #127 #136]: false
-#138 := [lemma #137]: #87
-#144 := (or #58 #9)
-#145 := [th-lemma arith farkas 1 1]: #144
-#146 := [unit-resolution #145 #139]: #9
-#98 := (or #52 #94)
-#96 := (or #52 #94 #95)
-#97 := [def-axiom]: #96
-#99 := [unit-resolution #97 #84]: #98
-#147 := [unit-resolution #99 #146]: #94
-#149 := (or #74 #148 #126)
-#150 := [th-lemma arith triangle-eq]: #149
-#151 := [unit-resolution #150 #147 #138]: #148
-#152 := [th-lemma arith farkas 1 1 #151 #143]: false
-#153 := [lemma #152]: #58
-#157 := [unit-resolution #93 #153]: #90
-#158 := (not #90)
-#159 := (or #158 #155)
-#160 := [th-lemma arith triangle-eq]: #159
-#161 := [unit-resolution #160 #157]: #155
-#162 := [unit-resolution #125 #153]: #74
-#163 := (or #94 #86)
-#164 := [th-lemma arith triangle-eq]: #163
-#165 := [unit-resolution #164 #162]: #86
-#166 := [unit-resolution #99 #162]: #52
-[th-lemma arith farkas 2 1 1 #166 #165 #161]: false
-unsat
-5eef8e7d84fcda85aa27c59747fcf3f71dac1fdf 116 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#37 := -1::Real
-#38 := (* -1::Real f3)
-#64 := (>= f3 0::Real)
-#71 := (if #64 f3 #38)
-#85 := (* -1::Real #71)
-#125 := (+ #38 #85)
-#141 := (<= #125 0::Real)
-#113 := (= #38 #71)
-#65 := (not #64)
-#123 := (+ f3 #85)
-#124 := (<= #123 0::Real)
-#112 := (= f3 #71)
-#126 := [hypothesis]: #64
-#108 := (or #65 #112)
-#109 := [def-axiom]: #108
-#127 := [unit-resolution #109 #126]: #112
-#128 := (not #112)
-#129 := (or #128 #124)
-#130 := [th-lemma arith triangle-eq]: #129
-#131 := [unit-resolution #130 #127]: #124
-#80 := (>= #71 0::Real)
-#79 := (not #80)
-#91 := (if #80 #71 #85)
-#110 := (= #71 #91)
-#134 := (not #110)
-#96 := (= #91 #71)
-#99 := (not #96)
-#135 := (iff #99 #134)
-#132 := (iff #96 #110)
-#133 := [commutativity]: #132
-#136 := [monotonicity #133]: #135
-#10 := (- f3)
-#9 := (< f3 0::Real)
-#11 := (if #9 #10 f3)
-#13 := (- #11)
-#12 := (< #11 0::Real)
-#14 := (if #12 #13 #11)
-#15 := (= #14 #11)
-#16 := (not #15)
-#102 := (iff #16 #99)
-#41 := (if #9 #38 f3)
-#50 := (* -1::Real #41)
-#44 := (< #41 0::Real)
-#55 := (if #44 #50 #41)
-#58 := (= #55 #41)
-#61 := (not #58)
-#100 := (iff #61 #99)
-#97 := (iff #58 #96)
-#74 := (= #41 #71)
-#68 := (if #65 #38 f3)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #41 #68)
-#66 := (iff #9 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#94 := (= #55 #91)
-#88 := (if #79 #85 #71)
-#92 := (= #88 #91)
-#93 := [rewrite]: #92
-#89 := (= #55 #88)
-#86 := (= #50 #85)
-#87 := [monotonicity #75]: #86
-#83 := (iff #44 #79)
-#76 := (< #71 0::Real)
-#81 := (iff #76 #79)
-#82 := [rewrite]: #81
-#77 := (iff #44 #76)
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#90 := [monotonicity #84 #87 #75]: #89
-#95 := [trans #90 #93]: #94
-#98 := [monotonicity #95 #75]: #97
-#101 := [monotonicity #98]: #100
-#62 := (iff #16 #61)
-#59 := (iff #15 #58)
-#42 := (= #11 #41)
-#39 := (= #10 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#56 := (= #14 #55)
-#53 := (= #13 #50)
-#47 := (- #41)
-#51 := (= #47 #50)
-#52 := [rewrite]: #51
-#48 := (= #13 #47)
-#49 := [monotonicity #43]: #48
-#54 := [trans #49 #52]: #53
-#45 := (iff #12 #44)
-#46 := [monotonicity #43]: #45
-#57 := [monotonicity #46 #54 #43]: #56
-#60 := [monotonicity #57 #43]: #59
-#63 := [monotonicity #60]: #62
-#103 := [trans #63 #101]: #102
-#36 := [asserted]: #16
-#104 := [mp #36 #103]: #99
-#137 := [mp #104 #136]: #134
-#114 := (or #79 #110)
-#115 := [def-axiom]: #114
-#138 := [unit-resolution #115 #137]: #79
-#139 := [th-lemma arith farkas -1 1 1 #126 #138 #131]: false
-#140 := [lemma #139]: #65
-#106 := (or #64 #113)
-#107 := [def-axiom]: #106
-#143 := [unit-resolution #107 #140]: #113
-#144 := (not #113)
-#145 := (or #144 #141)
-#146 := [th-lemma arith triangle-eq]: #145
-#147 := [unit-resolution #146 #143]: #141
-[th-lemma arith farkas 1 1 1 #140 #138 #147]: false
-unsat
-55bb89c7c767723007ed5956fcfa12830981af6f 57 0
-#2 := false
-#15 := 0::Real
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#39 := (<= #38 0::Real)
-#42 := (if #39 f3 f4)
-#50 := (* -1::Real #42)
-#59 := (+ f4 #50)
-#73 := (>= #59 0::Real)
-#63 := (= f4 #42)
-#64 := (not #39)
-#62 := (= f3 #42)
-#67 := (not #62)
-#51 := (+ f3 #50)
-#49 := (>= #51 0::Real)
-#55 := (not #49)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#11 := (<= #10 f3)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #49)
-#45 := (<= #42 f3)
-#48 := (iff #45 #49)
-#52 := [rewrite]: #48
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#66 := [hypothesis]: #62
-#68 := (or #67 #49)
-#69 := [th-lemma arith triangle-eq]: #68
-#70 := [unit-resolution #69 #66 #58]: false
-#71 := [lemma #70]: #67
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#74 := [unit-resolution #60 #71]: #64
-#61 := (or #39 #63)
-#35 := [def-axiom]: #61
-#75 := [unit-resolution #35 #74]: #63
-#76 := (not #63)
-#77 := (or #76 #73)
-#78 := [th-lemma arith triangle-eq]: #77
-#79 := [unit-resolution #78 #75]: #73
-[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
-unsat
-792a7271106d55b993c9a30193c5dc7ee046972f 57 0
-#2 := false
-#15 := 0::Real
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#39 := (<= #38 0::Real)
-#42 := (if #39 f3 f4)
-#49 := (* -1::Real #42)
-#50 := (+ f4 #49)
-#48 := (>= #50 0::Real)
-#55 := (not #48)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#11 := (<= #10 f4)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #48)
-#45 := (<= #42 f4)
-#51 := (iff #45 #48)
-#52 := [rewrite]: #51
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#63 := (= f4 #42)
-#64 := (not #39)
-#68 := [hypothesis]: #39
-#59 := (+ f3 #49)
-#67 := (>= #59 0::Real)
-#62 := (= f3 #42)
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#69 := [unit-resolution #60 #68]: #62
-#70 := (not #62)
-#71 := (or #70 #67)
-#72 := [th-lemma arith triangle-eq]: #71
-#73 := [unit-resolution #72 #69]: #67
-#74 := [th-lemma arith farkas -1 1 1 #73 #58 #68]: false
-#75 := [lemma #74]: #64
-#61 := (or #39 #63)
-#35 := [def-axiom]: #61
-#76 := [unit-resolution #35 #75]: #63
-#77 := (not #63)
-#78 := (or #77 #48)
-#79 := [th-lemma arith triangle-eq]: #78
-[unit-resolution #79 #76 #58]: false
-unsat
-83b40ab4216a9b2572384a8e1f6d8b0f58fd50bf 103 0
-#2 := false
-#20 := 0::Real
-decl f5 :: Real
-#10 := f5
-decl f4 :: Real
-#8 := f4
-#46 := -1::Real
-#55 := (* -1::Real f5)
-#65 := (+ f4 #55)
-#66 := (<= #65 0::Real)
-#69 := (if #66 f4 f5)
-#77 := (* -1::Real #69)
-decl f3 :: Real
-#7 := f3
-#78 := (+ f3 #77)
-#76 := (>= #78 0::Real)
-#75 := (not #76)
-#56 := (+ f3 #55)
-#54 := (>= #56 0::Real)
-#53 := (not #54)
-#49 := (* -1::Real f4)
-#50 := (+ f3 #49)
-#48 := (>= #50 0::Real)
-#47 := (not #48)
-#59 := (and #47 #53)
-#62 := (not #59)
-#83 := (or #62 #75)
-#86 := (not #83)
-#13 := (<= f4 f5)
-#14 := (if #13 f4 f5)
-#15 := (< f3 #14)
-#11 := (< f3 f5)
-#9 := (< f3 f4)
-#12 := (and #9 #11)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#89 := (iff #17 #86)
-#39 := (not #12)
-#40 := (or #39 #15)
-#43 := (not #40)
-#87 := (iff #43 #86)
-#84 := (iff #40 #83)
-#81 := (iff #15 #75)
-#72 := (< f3 #69)
-#79 := (iff #72 #75)
-#80 := [rewrite]: #79
-#73 := (iff #15 #72)
-#70 := (= #14 #69)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#82 := [trans #74 #80]: #81
-#63 := (iff #39 #62)
-#60 := (iff #12 #59)
-#57 := (iff #11 #53)
-#58 := [rewrite]: #57
-#51 := (iff #9 #47)
-#52 := [rewrite]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#85 := [monotonicity #64 #82]: #84
-#88 := [monotonicity #85]: #87
-#44 := (iff #17 #43)
-#41 := (iff #16 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#90 := [trans #45 #88]: #89
-#38 := [asserted]: #17
-#91 := [mp #38 #90]: #86
-#95 := [not-or-elim #91]: #76
-#92 := [not-or-elim #91]: #59
-#94 := [and-elim #92]: #53
-#100 := (+ f5 #77)
-#117 := (<= #100 0::Real)
-#106 := (= f5 #69)
-#107 := (not #66)
-#105 := (= f4 #69)
-#112 := (not #105)
-#102 := (+ f4 #77)
-#99 := (<= #102 0::Real)
-#109 := (not #99)
-#93 := [and-elim #92]: #47
-#97 := [hypothesis]: #99
-#98 := [th-lemma arith farkas -1 -1 1 #97 #93 #95]: false
-#110 := [lemma #98]: #109
-#111 := [hypothesis]: #105
-#113 := (or #112 #99)
-#114 := [th-lemma arith triangle-eq]: #113
-#115 := [unit-resolution #114 #111 #110]: false
-#116 := [lemma #115]: #112
-#108 := (or #107 #105)
-#103 := [def-axiom]: #108
-#119 := [unit-resolution #103 #116]: #107
-#104 := (or #66 #106)
-#101 := [def-axiom]: #104
-#120 := [unit-resolution #101 #119]: #106
-#121 := (not #106)
-#122 := (or #121 #117)
-#123 := [th-lemma arith triangle-eq]: #122
-#124 := [unit-resolution #123 #120]: #117
-[th-lemma arith farkas -1 -1 1 #124 #94 #95]: false
-unsat
-c0fd50acd23f3d8d8def07a171c9f6d478ae387a 94 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-decl f4 :: Real
-#8 := f4
-#17 := 0::Real
-#38 := -1::Real
-#39 := (* -1::Real f4)
-#40 := (+ f3 #39)
-#48 := (>= #40 0::Real)
-#50 := (if #48 f4 f3)
-#41 := (<= #40 0::Real)
-#44 := (if #41 f3 f4)
-#53 := (= #44 #50)
-#60 := (= f4 #50)
-#65 := (not #41)
-#63 := (= f3 #44)
-#105 := (not #63)
-#67 := (= f3 #50)
-#74 := (not #67)
-#75 := [hypothesis]: #74
-#71 := (or #48 #67)
-#72 := [def-axiom]: #71
-#76 := [unit-resolution #72 #75]: #48
-#68 := (not #48)
-#69 := (or #68 #60)
-#70 := [def-axiom]: #69
-#77 := [unit-resolution #70 #76]: #60
-#73 := (= f3 f4)
-#64 := (= f4 #44)
-#87 := (not #64)
-#56 := (not #53)
-#88 := (iff #56 #87)
-#85 := (iff #53 #64)
-#83 := (iff #64 #53)
-#78 := (= #50 #44)
-#81 := (iff #78 #53)
-#82 := [commutativity]: #81
-#79 := (iff #64 #78)
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#86 := [symm #84]: #85
-#89 := [monotonicity #86]: #88
-#11 := (<= f4 f3)
-#12 := (if #11 f4 f3)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#13 := (= #10 #12)
-#14 := (not #13)
-#57 := (iff #14 #56)
-#54 := (iff #13 #53)
-#51 := (= #12 #50)
-#47 := (iff #11 #48)
-#49 := [rewrite]: #47
-#52 := [monotonicity #49]: #51
-#45 := (= #10 #44)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#55 := [monotonicity #46 #52]: #54
-#58 := [monotonicity #55]: #57
-#35 := [asserted]: #14
-#59 := [mp #35 #58]: #56
-#90 := [mp #59 #89]: #87
-#62 := (or #41 #64)
-#37 := [def-axiom]: #62
-#91 := [unit-resolution #37 #90]: #41
-#94 := (or #73 #65)
-#92 := (or #73 #65 #68)
-#93 := [th-lemma arith triangle-eq]: #92
-#95 := [unit-resolution #93 #76]: #94
-#96 := [unit-resolution #95 #91]: #73
-#97 := [trans #96 #77]: #67
-#98 := [unit-resolution #75 #97]: false
-#99 := [lemma #98]: #67
-#101 := (= #44 f3)
-#100 := [hypothesis]: #63
-#102 := [symm #100]: #101
-#103 := [trans #102 #99]: #53
-#104 := [unit-resolution #59 #103]: false
-#106 := [lemma #104]: #105
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#107 := [unit-resolution #61 #106]: #65
-#109 := (or #48 #41)
-#110 := [th-lemma arith farkas 1 1]: #109
-#111 := [unit-resolution #110 #107]: #48
-#112 := [unit-resolution #70 #111]: #60
-#115 := (= #44 f4)
-#108 := [unit-resolution #37 #107]: #64
-#116 := [symm #108]: #115
-#117 := [trans #116 #112]: #53
-[unit-resolution #59 #117]: false
-unsat
-fb76c2d56cf2f934220975a9ef3ad26d44e0bbfc 53 0
-#2 := false
-#7 := 0::Real
-decl f3 :: Real
-#8 := f3
-#10 := (<= f3 0::Real)
-#11 := (if #10 f3 0::Real)
-#12 := (= #11 0::Real)
-#63 := (= f3 0::Real)
-#58 := (not #12)
-#44 := (>= f3 0::Real)
-#45 := (not #44)
-#48 := (or #45 #12)
-#51 := (not #48)
-#9 := (<= 0::Real f3)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#54 := (iff #14 #51)
-#35 := (not #9)
-#36 := (or #35 #12)
-#39 := (not #36)
-#52 := (iff #39 #51)
-#49 := (iff #36 #48)
-#46 := (iff #35 #45)
-#42 := (iff #9 #44)
-#43 := [rewrite]: #42
-#47 := [monotonicity #43]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#55 := [trans #41 #53]: #54
-#34 := [asserted]: #14
-#56 := [mp #34 #55]: #51
-#59 := [not-or-elim #56]: #58
-#65 := (or #10 #12)
-#66 := [def-axiom]: #65
-#64 := [unit-resolution #66 #59]: #10
-#57 := [not-or-elim #56]: #44
-#68 := (not #10)
-#61 := (or #63 #68 #45)
-#62 := [th-lemma arith triangle-eq]: #61
-#71 := [unit-resolution #62 #57 #64]: #63
-#73 := (= #11 f3)
-#67 := (= f3 #11)
-#69 := (or #68 #67)
-#70 := [def-axiom]: #69
-#72 := [unit-resolution #70 #64]: #67
-#74 := [symm #72]: #73
-#75 := [trans #74 #71]: #12
-[unit-resolution #59 #75]: false
-unsat
-7237d883d9dd118244bec827b23fdc7f1b72fdce 124 0
-#2 := false
-#12 := 0::Real
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#38 := -1::Real
-#40 := (* -1::Real f4)
-#53 := (+ f3 #40)
-#54 := (<= #53 0::Real)
-#57 := (if #54 f3 f4)
-#105 := (* -1::Real #57)
-#106 := (+ f3 #105)
-#108 := (>= #106 0::Real)
-#93 := (= f3 #57)
-#107 := (+ f4 #105)
-#125 := (>= #107 0::Real)
-#94 := (= f4 #57)
-#95 := (not #54)
-#136 := [hypothesis]: #95
-#92 := (or #54 #94)
-#89 := [def-axiom]: #92
-#137 := [unit-resolution #89 #136]: #94
-#128 := (not #94)
-#129 := (or #128 #125)
-#130 := [th-lemma arith triangle-eq]: #129
-#138 := [unit-resolution #130 #137]: #125
-#39 := (* -1::Real f3)
-#41 := (+ #39 #40)
-#11 := (+ f3 f4)
-#60 := (>= #11 0::Real)
-#67 := (if #60 #11 #41)
-#75 := (* -1::Real #67)
-#104 := (+ #41 #75)
-#124 := (<= #104 0::Real)
-#97 := (= #41 #67)
-#61 := (not #60)
-#109 := [hypothesis]: #60
-#76 := (+ #57 #75)
-#77 := (<= #76 0::Real)
-#82 := (not #77)
-#14 := (- #11)
-#13 := (< #11 0::Real)
-#15 := (if #13 #14 #11)
-#9 := (<= f3 f4)
-#10 := (if #9 f3 f4)
-#16 := (<= #10 #15)
-#17 := (not #16)
-#85 := (iff #17 #82)
-#44 := (if #13 #41 #11)
-#47 := (<= #10 #44)
-#50 := (not #47)
-#83 := (iff #50 #82)
-#80 := (iff #47 #77)
-#72 := (<= #57 #67)
-#78 := (iff #72 #77)
-#79 := [rewrite]: #78
-#73 := (iff #47 #72)
-#70 := (= #44 #67)
-#64 := (if #61 #41 #11)
-#68 := (= #64 #67)
-#69 := [rewrite]: #68
-#65 := (= #44 #64)
-#62 := (iff #13 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#71 := [trans #66 #69]: #70
-#58 := (= #10 #57)
-#55 := (iff #9 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#74 := [monotonicity #59 #71]: #73
-#81 := [trans #74 #79]: #80
-#84 := [monotonicity #81]: #83
-#51 := (iff #17 #50)
-#48 := (iff #16 #47)
-#45 := (= #15 #44)
-#42 := (= #14 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#86 := [trans #52 #84]: #85
-#37 := [asserted]: #17
-#87 := [mp #37 #86]: #82
-#122 := (or #95 #61)
-#110 := [hypothesis]: #54
-#96 := (or #95 #93)
-#91 := [def-axiom]: #96
-#111 := [unit-resolution #91 #110]: #93
-#112 := (not #93)
-#113 := (or #112 #108)
-#114 := [th-lemma arith triangle-eq]: #113
-#115 := [unit-resolution #114 #111]: #108
-#102 := (+ #11 #75)
-#103 := (<= #102 0::Real)
-#90 := (= #11 #67)
-#98 := (or #61 #90)
-#99 := [def-axiom]: #98
-#116 := [unit-resolution #99 #109]: #90
-#117 := (not #90)
-#118 := (or #117 #103)
-#119 := [th-lemma arith triangle-eq]: #118
-#120 := [unit-resolution #119 #116]: #103
-#121 := [th-lemma arith farkas 2 2 2 1 1 #120 #115 #87 #110 #109]: false
-#123 := [lemma #121]: #122
-#126 := [unit-resolution #123 #109]: #95
-#127 := [unit-resolution #89 #126]: #94
-#131 := [unit-resolution #130 #127]: #125
-#132 := [th-lemma arith farkas 2 2 1 2 1 #120 #131 #126 #87 #109]: false
-#133 := [lemma #132]: #61
-#100 := (or #60 #97)
-#101 := [def-axiom]: #100
-#139 := [unit-resolution #101 #133]: #97
-#140 := (not #97)
-#141 := (or #140 #124)
-#142 := [th-lemma arith triangle-eq]: #141
-#143 := [unit-resolution #142 #139]: #124
-#144 := [th-lemma arith farkas 3/2 1/2 1 1 1 #133 #136 #87 #143 #138]: false
-#145 := [lemma #144]: #54
-#146 := [unit-resolution #91 #145]: #93
-#147 := [unit-resolution #114 #146]: #108
-[th-lemma arith farkas 1/2 3/2 1 1 1 #145 #133 #87 #143 #147]: false
-unsat
-20b2c8eb46b2776c1fa0854f9d43594550f591a7 57 0
-#2 := false
-#15 := 0::Real
-decl f3 :: Real
-#7 := f3
-decl f4 :: Real
-#8 := f4
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#39 := (<= #38 0::Real)
-#42 := (if #39 f4 f3)
-#48 := (* -1::Real #42)
-#49 := (+ f3 #48)
-#50 := (<= #49 0::Real)
-#55 := (not #50)
-#9 := (<= f3 f4)
-#10 := (if #9 f4 f3)
-#11 := (<= f3 #10)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #50)
-#45 := (<= f3 #42)
-#51 := (iff #45 #50)
-#52 := [rewrite]: #51
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#63 := (= f3 #42)
-#64 := (not #39)
-#68 := [hypothesis]: #39
-#59 := (+ f4 #48)
-#66 := (<= #59 0::Real)
-#62 := (= f4 #42)
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#69 := [unit-resolution #60 #68]: #62
-#70 := (not #62)
-#71 := (or #70 #66)
-#72 := [th-lemma arith triangle-eq]: #71
-#73 := [unit-resolution #72 #69]: #66
-#74 := [th-lemma arith farkas 1 -1 1 #73 #58 #68]: false
-#75 := [lemma #74]: #64
-#61 := (or #39 #63)
-#35 := [def-axiom]: #61
-#76 := [unit-resolution #35 #75]: #63
-#77 := (not #63)
-#78 := (or #77 #50)
-#79 := [th-lemma arith triangle-eq]: #78
-[unit-resolution #79 #76 #58]: false
-unsat
-9b77594e0c04af6813ea9fe3eb19b0eebd98140f 57 0
-#2 := false
-#15 := 0::Real
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#36 := -1::Real
-#39 := (* -1::Real f4)
-#40 := (+ f3 #39)
-#38 := (>= #40 0::Real)
-#42 := (if #38 f3 f4)
-#48 := (* -1::Real #42)
-#59 := (+ f4 #48)
-#72 := (<= #59 0::Real)
-#63 := (= f4 #42)
-#64 := (not #38)
-#62 := (= f3 #42)
-#67 := (not #62)
-#49 := (+ f3 #48)
-#50 := (<= #49 0::Real)
-#55 := (not #50)
-#9 := (<= f4 f3)
-#10 := (if #9 f3 f4)
-#11 := (<= f3 #10)
-#12 := (not #11)
-#56 := (iff #12 #55)
-#53 := (iff #11 #50)
-#45 := (<= f3 #42)
-#51 := (iff #45 #50)
-#52 := [rewrite]: #51
-#46 := (iff #11 #45)
-#43 := (= #10 #42)
-#37 := (iff #9 #38)
-#41 := [rewrite]: #37
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#33 := [asserted]: #12
-#58 := [mp #33 #57]: #55
-#66 := [hypothesis]: #62
-#68 := (or #67 #50)
-#69 := [th-lemma arith triangle-eq]: #68
-#70 := [unit-resolution #69 #66 #58]: false
-#71 := [lemma #70]: #67
-#65 := (or #64 #62)
-#60 := [def-axiom]: #65
-#74 := [unit-resolution #60 #71]: #64
-#61 := (or #38 #63)
-#35 := [def-axiom]: #61
-#75 := [unit-resolution #35 #74]: #63
-#76 := (not #63)
-#77 := (or #76 #72)
-#78 := [th-lemma arith triangle-eq]: #77
-#79 := [unit-resolution #78 #75]: #72
-[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
-unsat
-93b3508f44b6322ae09524c5a254ca2b1a5b26c3 103 0
-#2 := false
-#20 := 0::Real
-decl f3 :: Real
-#7 := f3
-decl f5 :: Real
-#10 := f5
-#46 := -1::Real
-#53 := (* -1::Real f5)
-#65 := (+ f3 #53)
-#66 := (<= #65 0::Real)
-#69 := (if #66 f5 f3)
-#75 := (* -1::Real #69)
-decl f4 :: Real
-#8 := f4
-#76 := (+ f4 #75)
-#77 := (<= #76 0::Real)
-#78 := (not #77)
-#54 := (+ f4 #53)
-#55 := (<= #54 0::Real)
-#56 := (not #55)
-#49 := (* -1::Real f4)
-#50 := (+ f3 #49)
-#48 := (>= #50 0::Real)
-#47 := (not #48)
-#59 := (and #47 #56)
-#62 := (not #59)
-#83 := (or #62 #78)
-#86 := (not #83)
-#13 := (<= f3 f5)
-#14 := (if #13 f5 f3)
-#15 := (< #14 f4)
-#11 := (< f5 f4)
-#9 := (< f3 f4)
-#12 := (and #9 #11)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#89 := (iff #17 #86)
-#39 := (not #12)
-#40 := (or #39 #15)
-#43 := (not #40)
-#87 := (iff #43 #86)
-#84 := (iff #40 #83)
-#81 := (iff #15 #78)
-#72 := (< #69 f4)
-#79 := (iff #72 #78)
-#80 := [rewrite]: #79
-#73 := (iff #15 #72)
-#70 := (= #14 #69)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#82 := [trans #74 #80]: #81
-#63 := (iff #39 #62)
-#60 := (iff #12 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#51 := (iff #9 #47)
-#52 := [rewrite]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#85 := [monotonicity #64 #82]: #84
-#88 := [monotonicity #85]: #87
-#44 := (iff #17 #43)
-#41 := (iff #16 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#90 := [trans #45 #88]: #89
-#38 := [asserted]: #17
-#91 := [mp #38 #90]: #86
-#95 := [not-or-elim #91]: #77
-#92 := [not-or-elim #91]: #59
-#93 := [and-elim #92]: #47
-#99 := (+ f3 #75)
-#118 := (>= #99 0::Real)
-#106 := (= f3 #69)
-#107 := (not #66)
-#105 := (= f5 #69)
-#112 := (not #105)
-#102 := (+ f5 #75)
-#100 := (>= #102 0::Real)
-#109 := (not #100)
-#94 := [and-elim #92]: #56
-#97 := [hypothesis]: #100
-#98 := [th-lemma arith farkas -1 -1 1 #97 #94 #95]: false
-#110 := [lemma #98]: #109
-#111 := [hypothesis]: #105
-#113 := (or #112 #100)
-#114 := [th-lemma arith triangle-eq]: #113
-#115 := [unit-resolution #114 #111 #110]: false
-#116 := [lemma #115]: #112
-#108 := (or #107 #105)
-#103 := [def-axiom]: #108
-#119 := [unit-resolution #103 #116]: #107
-#104 := (or #66 #106)
-#101 := [def-axiom]: #104
-#120 := [unit-resolution #101 #119]: #106
-#121 := (not #106)
-#122 := (or #121 #118)
-#123 := [th-lemma arith triangle-eq]: #122
-#124 := [unit-resolution #123 #120]: #118
-[th-lemma arith farkas -1 1 1 #124 #93 #95]: false
-unsat
-7b686f77e111467a15fb3e7ff5fcf4bbb1a56717 96 0
-#2 := false
-decl f4 :: Real
-#8 := f4
-decl f3 :: Real
-#7 := f3
-#17 := 0::Real
-#38 := -1::Real
-#39 := (* -1::Real f4)
-#40 := (+ f3 #39)
-#48 := (>= #40 0::Real)
-#50 := (if #48 f3 f4)
-#41 := (<= #40 0::Real)
-#44 := (if #41 f4 f3)
-#53 := (= #44 #50)
-#60 := (= f3 #50)
-#65 := (not #41)
-#63 := (= f4 #44)
-#107 := (not #63)
-#67 := (= f4 #50)
-#74 := (not #67)
-#75 := [hypothesis]: #74
-#71 := (or #48 #67)
-#72 := [def-axiom]: #71
-#76 := [unit-resolution #72 #75]: #48
-#68 := (not #48)
-#69 := (or #68 #60)
-#70 := [def-axiom]: #69
-#77 := [unit-resolution #70 #76]: #60
-#97 := (= f4 f3)
-#73 := (= f3 f4)
-#64 := (= f3 #44)
-#87 := (not #64)
-#56 := (not #53)
-#88 := (iff #56 #87)
-#85 := (iff #53 #64)
-#83 := (iff #64 #53)
-#78 := (= #50 #44)
-#81 := (iff #78 #53)
-#82 := [commutativity]: #81
-#79 := (iff #64 #78)
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#86 := [symm #84]: #85
-#89 := [monotonicity #86]: #88
-#11 := (<= f4 f3)
-#12 := (if #11 f3 f4)
-#9 := (<= f3 f4)
-#10 := (if #9 f4 f3)
-#13 := (= #10 #12)
-#14 := (not #13)
-#57 := (iff #14 #56)
-#54 := (iff #13 #53)
-#51 := (= #12 #50)
-#47 := (iff #11 #48)
-#49 := [rewrite]: #47
-#52 := [monotonicity #49]: #51
-#45 := (= #10 #44)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#55 := [monotonicity #46 #52]: #54
-#58 := [monotonicity #55]: #57
-#35 := [asserted]: #14
-#59 := [mp #35 #58]: #56
-#90 := [mp #59 #89]: #87
-#62 := (or #41 #64)
-#37 := [def-axiom]: #62
-#91 := [unit-resolution #37 #90]: #41
-#94 := (or #73 #65)
-#92 := (or #73 #65 #68)
-#93 := [th-lemma arith triangle-eq]: #92
-#95 := [unit-resolution #93 #76]: #94
-#96 := [unit-resolution #95 #91]: #73
-#98 := [symm #96]: #97
-#99 := [trans #98 #77]: #67
-#100 := [unit-resolution #75 #99]: false
-#101 := [lemma #100]: #67
-#103 := (= #44 f4)
-#102 := [hypothesis]: #63
-#104 := [symm #102]: #103
-#105 := [trans #104 #101]: #53
-#106 := [unit-resolution #59 #105]: false
-#108 := [lemma #106]: #107
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#109 := [unit-resolution #61 #108]: #65
-#111 := (or #48 #41)
-#112 := [th-lemma arith farkas 1 1]: #111
-#113 := [unit-resolution #112 #109]: #48
-#114 := [unit-resolution #70 #113]: #60
-#117 := (= #44 f3)
-#110 := [unit-resolution #37 #109]: #64
-#118 := [symm #110]: #117
-#119 := [trans #118 #114]: #53
-[unit-resolution #59 #119]: false
-unsat
-e7ef38b396887508c5c85846a0548164638b9e8d 60 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#7 := 0::Real
-#10 := (<= f3 0::Real)
-#11 := (if #10 0::Real f3)
-#68 := (= f3 #11)
-#80 := (= 0::Real #11)
-#67 := (= #11 0::Real)
-#71 := (not #68)
-#12 := (= #11 f3)
-#58 := (not #12)
-#72 := (iff #58 #71)
-#61 := (iff #12 #68)
-#62 := [commutativity]: #61
-#73 := [monotonicity #62]: #72
-#44 := (>= f3 0::Real)
-#45 := (not #44)
-#48 := (or #45 #12)
-#51 := (not #48)
-#9 := (<= 0::Real f3)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#54 := (iff #14 #51)
-#35 := (not #9)
-#36 := (or #35 #12)
-#39 := (not #36)
-#52 := (iff #39 #51)
-#49 := (iff #36 #48)
-#46 := (iff #35 #45)
-#42 := (iff #9 #44)
-#43 := [rewrite]: #42
-#47 := [monotonicity #43]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#55 := [trans #41 #53]: #54
-#34 := [asserted]: #14
-#56 := [mp #34 #55]: #51
-#59 := [not-or-elim #56]: #58
-#74 := [mp #59 #73]: #71
-#66 := (or #10 #68)
-#63 := [def-axiom]: #66
-#75 := [unit-resolution #63 #74]: #10
-#69 := (not #10)
-#70 := (or #69 #67)
-#65 := [def-axiom]: #70
-#76 := [unit-resolution #65 #75]: #67
-#81 := [symm #76]: #80
-#64 := (= f3 0::Real)
-#57 := [not-or-elim #56]: #44
-#77 := (or #64 #69 #45)
-#78 := [th-lemma arith triangle-eq]: #77
-#79 := [unit-resolution #78 #57 #75]: #64
-#82 := [trans #79 #81]: #68
-[unit-resolution #74 #82]: false
-unsat
-af8ce155afa78bf936e9e665a7def6acf5b7d81b 214 0
-#2 := false
-#8 := 0::Real
-decl f4 :: Real
-#13 := f4
-#42 := -1::Real
-#57 := (* -1::Real f4)
-#93 := (>= f4 0::Real)
-#100 := (if #93 f4 #57)
-#105 := (* -1::Real #100)
-#160 := (+ #57 #105)
-#182 := (<= #160 0::Real)
-#136 := (= #57 #100)
-#94 := (not #93)
-decl f3 :: Real
-#7 := f3
-#111 := (+ f3 #57)
-#112 := (<= #111 0::Real)
-#115 := (if #112 f4 f3)
-#154 := (* -1::Real #115)
-#155 := (+ f4 #154)
-#156 := (<= #155 0::Real)
-#157 := (+ f3 #154)
-#192 := (<= #157 0::Real)
-#148 := (= f3 #115)
-#149 := (not #112)
-#147 := (= f4 #115)
-#194 := [hypothesis]: #112
-#150 := (or #149 #147)
-#151 := [def-axiom]: #150
-#195 := [unit-resolution #151 #194]: #147
-#196 := (not #147)
-#197 := (or #196 #156)
-#198 := [th-lemma arith triangle-eq]: #197
-#199 := [unit-resolution #198 #195]: #156
-#178 := (not #156)
-#190 := (or #94 #178)
-#158 := (+ f4 #105)
-#159 := (<= #158 0::Real)
-#135 := (= f4 #100)
-#164 := [hypothesis]: #93
-#143 := (or #94 #135)
-#144 := [def-axiom]: #143
-#165 := [unit-resolution #144 #164]: #135
-#166 := (not #135)
-#167 := (or #166 #159)
-#168 := [th-lemma arith triangle-eq]: #167
-#169 := [unit-resolution #168 #165]: #159
-#78 := (>= f3 0::Real)
-#79 := (not #78)
-#176 := [hypothesis]: #156
-#179 := (or #79 #94 #178)
-#124 := (+ #100 #115)
-#43 := (* -1::Real f3)
-#85 := (if #78 f3 #43)
-#125 := (+ #85 #124)
-#122 := (>= #125 0::Real)
-#128 := (not #122)
-#18 := (<= f3 f4)
-#19 := (if #18 f4 f3)
-#15 := (- f4)
-#14 := (< f4 0::Real)
-#16 := (if #14 #15 f4)
-#10 := (- f3)
-#9 := (< f3 0::Real)
-#11 := (if #9 #10 f3)
-#12 := (- #11)
-#17 := (- #12 #16)
-#20 := (<= #17 #19)
-#21 := (not #20)
-#131 := (iff #21 #128)
-#60 := (if #14 #57 f4)
-#66 := (* -1::Real #60)
-#46 := (if #9 #43 f3)
-#52 := (* -1::Real #46)
-#67 := (+ #52 #66)
-#72 := (<= #67 #19)
-#75 := (not #72)
-#129 := (iff #75 #128)
-#126 := (iff #72 #122)
-#90 := (* -1::Real #85)
-#108 := (+ #90 #105)
-#118 := (<= #108 #115)
-#121 := (iff #118 #122)
-#123 := [rewrite]: #121
-#119 := (iff #72 #118)
-#116 := (= #19 #115)
-#113 := (iff #18 #112)
-#114 := [rewrite]: #113
-#117 := [monotonicity #114]: #116
-#109 := (= #67 #108)
-#106 := (= #66 #105)
-#103 := (= #60 #100)
-#97 := (if #94 #57 f4)
-#101 := (= #97 #100)
-#102 := [rewrite]: #101
-#98 := (= #60 #97)
-#95 := (iff #14 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#104 := [trans #99 #102]: #103
-#107 := [monotonicity #104]: #106
-#91 := (= #52 #90)
-#88 := (= #46 #85)
-#82 := (if #79 #43 f3)
-#86 := (= #82 #85)
-#87 := [rewrite]: #86
-#83 := (= #46 #82)
-#80 := (iff #9 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#110 := [monotonicity #92 #107]: #109
-#120 := [monotonicity #110 #117]: #119
-#127 := [trans #120 #123]: #126
-#130 := [monotonicity #127]: #129
-#76 := (iff #21 #75)
-#73 := (iff #20 #72)
-#70 := (= #17 #67)
-#63 := (- #52 #60)
-#68 := (= #63 #67)
-#69 := [rewrite]: #68
-#64 := (= #17 #63)
-#61 := (= #16 #60)
-#58 := (= #15 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#55 := (= #12 #52)
-#49 := (- #46)
-#53 := (= #49 #52)
-#54 := [rewrite]: #53
-#50 := (= #12 #49)
-#47 := (= #11 #46)
-#44 := (= #10 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#56 := [trans #51 #54]: #55
-#65 := [monotonicity #56 #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#132 := [trans #77 #130]: #131
-#41 := [asserted]: #21
-#133 := [mp #41 #132]: #128
-#161 := (+ f3 #90)
-#162 := (<= #161 0::Real)
-#139 := (= f3 #85)
-#170 := [hypothesis]: #78
-#141 := (or #79 #139)
-#142 := [def-axiom]: #141
-#171 := [unit-resolution #142 #170]: #139
-#172 := (not #139)
-#173 := (or #172 #162)
-#174 := [th-lemma arith triangle-eq]: #173
-#175 := [unit-resolution #174 #171]: #162
-#177 := [th-lemma arith farkas -2 1 -1 1 1 1 #164 #176 #170 #175 #133 #169]: false
-#180 := [lemma #177]: #179
-#183 := [unit-resolution #180 #164 #176]: #79
-#163 := (+ #43 #90)
-#181 := (<= #163 0::Real)
-#140 := (= #43 #85)
-#137 := (or #78 #140)
-#138 := [def-axiom]: #137
-#184 := [unit-resolution #138 #183]: #140
-#185 := (not #140)
-#186 := (or #185 #181)
-#187 := [th-lemma arith triangle-eq]: #186
-#188 := [unit-resolution #187 #184]: #181
-#189 := [th-lemma arith farkas 2 1 1 1 1 1 #164 #176 #133 #188 #183 #169]: false
-#191 := [lemma #189]: #190
-#200 := [unit-resolution #191 #199]: #94
-#145 := (or #93 #136)
-#146 := [def-axiom]: #145
-#201 := [unit-resolution #146 #200]: #136
-#202 := (not #136)
-#203 := (or #202 #182)
-#204 := [th-lemma arith triangle-eq]: #203
-#205 := [unit-resolution #204 #201]: #182
-#206 := (or #79 #149 #93)
-#207 := [th-lemma arith assign-bounds 1 1]: #206
-#208 := [unit-resolution #207 #200 #194]: #79
-#209 := [unit-resolution #138 #208]: #140
-#210 := [unit-resolution #187 #209]: #181
-#211 := [th-lemma arith farkas 1 1 1 1 1 #199 #133 #210 #208 #205]: false
-#212 := [lemma #211]: #149
-#152 := (or #112 #148)
-#153 := [def-axiom]: #152
-#223 := [unit-resolution #153 #212]: #148
-#224 := (not #148)
-#225 := (or #224 #192)
-#226 := [th-lemma arith triangle-eq]: #225
-#227 := [unit-resolution #226 #223]: #192
-#230 := (not #192)
-#231 := (or #156 #112 #230)
-#232 := [th-lemma arith assign-bounds 1 1]: #231
-#233 := [unit-resolution #232 #212 #227]: #156
-#234 := [unit-resolution #191 #233]: #94
-#235 := [unit-resolution #146 #234]: #136
-#236 := [unit-resolution #204 #235]: #182
-#215 := [hypothesis]: #79
-#216 := (or #94 #78 #112)
-#217 := [th-lemma arith assign-bounds 1 1]: #216
-#218 := [unit-resolution #217 #215 #212]: #94
-#219 := [unit-resolution #146 #218]: #136
-#220 := [unit-resolution #204 #219]: #182
-#221 := [unit-resolution #138 #215]: #140
-#222 := [unit-resolution #187 #221]: #181
-#228 := [th-lemma arith farkas 1 1 1 1 1 1 #215 #212 #227 #133 #222 #220]: false
-#229 := [lemma #228]: #78
-#237 := [unit-resolution #142 #229]: #139
-#238 := [unit-resolution #174 #237]: #162
-[th-lemma arith farkas 1 1 1 1 1 1 #212 #227 #133 #229 #238 #236]: false
-unsat
-e807c28ea702b232e7c32bfa79cb58b47a16c570 18 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := (<= f3 f3)
-#9 := (not #8)
-#40 := (iff #9 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #9 #35)
-#33 := (iff #8 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #9
-[mp #30 #41]: false
-unsat
-4cad11a2b8747d7e662d4f469d31b851aa375cfb 50 0
-#2 := false
-#18 := 0::Real
-decl f4 :: Real
-#8 := f4
-#44 := -1::Real
-#45 := (* -1::Real f4)
-decl f3 :: Real
-#7 := f3
-#46 := (+ f3 #45)
-#47 := (<= #46 0::Real)
-#53 := -3::Real
-#54 := (* -3::Real f4)
-#10 := 3::Real
-#11 := (* 3::Real f3)
-#55 := (+ #11 #54)
-#56 := (<= #55 0::Real)
-#50 := (not #47)
-#59 := (or #50 #56)
-#62 := (not #59)
-#12 := (* 3::Real f4)
-#13 := (<= #11 #12)
-#9 := (<= f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#65 := (iff #15 #62)
-#37 := (not #9)
-#38 := (or #37 #13)
-#41 := (not #38)
-#63 := (iff #41 #62)
-#60 := (iff #38 #59)
-#57 := (iff #13 #56)
-#58 := [rewrite]: #57
-#51 := (iff #37 #50)
-#48 := (iff #9 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#66 := [trans #43 #64]: #65
-#36 := [asserted]: #15
-#67 := [mp #36 #66]: #62
-#68 := [not-or-elim #67]: #47
-#69 := (not #56)
-#70 := [not-or-elim #67]: #69
-[th-lemma arith farkas -1/3 1 #70 #68]: false
-unsat
-092a6f5d63ab793d33d43f7284b78642e74e2334 55 0
-#2 := false
-#18 := 0::Real
-decl f4 :: Real
-#8 := f4
-#58 := -3::Real
-#61 := (* -3::Real f4)
-decl f3 :: Real
-#7 := f3
-#10 := 3::Real
-#11 := (* 3::Real f3)
-#62 := (+ #11 #61)
-#60 := (>= #62 0::Real)
-#59 := (not #60)
-#44 := -1::Real
-#47 := (* -1::Real f4)
-#48 := (+ f3 #47)
-#46 := (>= #48 0::Real)
-#65 := (or #46 #59)
-#68 := (not #65)
-#12 := (* 3::Real f4)
-#13 := (< #11 #12)
-#9 := (< f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#71 := (iff #15 #68)
-#37 := (not #9)
-#38 := (or #37 #13)
-#41 := (not #38)
-#69 := (iff #41 #68)
-#66 := (iff #38 #65)
-#63 := (iff #13 #59)
-#64 := [rewrite]: #63
-#56 := (iff #37 #46)
-#45 := (not #46)
-#51 := (not #45)
-#54 := (iff #51 #46)
-#55 := [rewrite]: #54
-#52 := (iff #37 #51)
-#49 := (iff #9 #45)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#67 := [monotonicity #57 #64]: #66
-#70 := [monotonicity #67]: #69
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#72 := [trans #43 #70]: #71
-#36 := [asserted]: #15
-#73 := [mp #36 #72]: #68
-#75 := [not-or-elim #73]: #60
-#74 := [not-or-elim #73]: #45
-[th-lemma arith farkas 3 1 #74 #75]: false
-unsat
-775858e4a5147699bba8b0137f62c6a4d4ac7293 52 0
-#2 := false
-#15 := 0::Real
-decl f4 :: Real
-#8 := f4
-#41 := -1::Real
-#44 := (* -1::Real f4)
-decl f3 :: Real
-#7 := f3
-#45 := (+ f3 #44)
-#55 := (<= #45 0::Real)
-#68 := (not #55)
-#43 := (>= #45 0::Real)
-#58 := (or #43 #55)
-#61 := (not #58)
-#10 := (<= f3 f4)
-#9 := (< f3 f4)
-#11 := (implies #9 #10)
-#12 := (not #11)
-#64 := (iff #12 #61)
-#34 := (not #9)
-#35 := (or #34 #10)
-#38 := (not #35)
-#62 := (iff #38 #61)
-#59 := (iff #35 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#53 := (iff #34 #43)
-#42 := (not #43)
-#48 := (not #42)
-#51 := (iff #48 #43)
-#52 := [rewrite]: #51
-#49 := (iff #34 #48)
-#46 := (iff #9 #42)
-#47 := [rewrite]: #46
-#50 := [monotonicity #47]: #49
-#54 := [trans #50 #52]: #53
-#60 := [monotonicity #54 #57]: #59
-#63 := [monotonicity #60]: #62
-#39 := (iff #12 #38)
-#36 := (iff #11 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#65 := [trans #40 #63]: #64
-#33 := [asserted]: #12
-#66 := [mp #33 #65]: #61
-#69 := [not-or-elim #66]: #68
-#67 := [not-or-elim #66]: #42
-#77 := (or #55 #43)
-#78 := [th-lemma arith farkas 1 1]: #77
-#79 := [unit-resolution #78 #67]: #55
-[unit-resolution #79 #69]: false
-unsat
-49cc2e53f2afe91d793e2317f4c575f413ada734 15 0
-#2 := false
-decl f3 :: Real
-#7 := f3
-#8 := (< f3 f3)
-#9 := (not #8)
-#10 := (not #9)
-#36 := (iff #10 false)
-#34 := (iff #8 false)
-#35 := [rewrite]: #34
-#32 := (iff #10 #8)
-#33 := [rewrite]: #32
-#37 := [trans #33 #35]: #36
-#31 := [asserted]: #10
-[mp #31 #37]: false
-unsat
-eb730fdf8b63348f25dbf613b5bd139042a0fc61 75 0
-#2 := false
-#18 := 0::Real
-decl f5 :: Real
-#10 := f5
-#53 := -1::Real
-#54 := (* -1::Real f5)
-decl f4 :: Real
-#8 := f4
-#55 := (+ f4 #54)
-#56 := (<= #55 0::Real)
-decl f3 :: Real
-#7 := f3
-#62 := (+ f3 #54)
-#63 := (<= #62 0::Real)
-#59 := (not #56)
-#66 := (* -1::Real f4)
-#67 := (+ f3 #66)
-#68 := (<= #67 0::Real)
-#71 := (not #68)
-#80 := (or #71 #59 #63)
-#85 := (not #80)
-#12 := (<= f3 f5)
-#11 := (<= f4 f5)
-#13 := (implies #11 #12)
-#9 := (<= f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#88 := (iff #15 #85)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#86 := (iff #50 #85)
-#83 := (iff #45 #80)
-#74 := (or #59 #63)
-#77 := (or #71 #74)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #45 #77)
-#75 := (iff #38 #74)
-#64 := (iff #12 #63)
-#65 := [rewrite]: #64
-#60 := (iff #37 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#76 := [monotonicity #61 #65]: #75
-#72 := (iff #44 #71)
-#69 := (iff #9 #68)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#79 := [monotonicity #73 #76]: #78
-#84 := [trans #79 #82]: #83
-#87 := [monotonicity #84]: #86
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#89 := [trans #52 #87]: #88
-#36 := [asserted]: #15
-#90 := [mp #36 #89]: #85
-#92 := [not-or-elim #90]: #56
-#93 := (not #63)
-#94 := [not-or-elim #90]: #93
-#91 := [not-or-elim #90]: #68
-[th-lemma arith farkas 1 -1 1 #91 #94 #92]: false
-unsat
-c4e1cef39d74ef1da60772d29906445a2b8051f6 80 0
-#2 := false
-#18 := 0::Real
-decl f5 :: Real
-#10 := f5
-#53 := -1::Real
-#54 := (* -1::Real f5)
-decl f4 :: Real
-#8 := f4
-#55 := (+ f4 #54)
-#56 := (<= #55 0::Real)
-decl f3 :: Real
-#7 := f3
-#62 := (+ f3 #54)
-#63 := (<= #62 0::Real)
-#59 := (not #56)
-#68 := (* -1::Real f4)
-#69 := (+ f3 #68)
-#67 := (>= #69 0::Real)
-#85 := (or #67 #59 #63)
-#90 := (not #85)
-#12 := (<= f3 f5)
-#11 := (<= f4 f5)
-#13 := (implies #11 #12)
-#9 := (< f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#93 := (iff #15 #90)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#91 := (iff #50 #90)
-#88 := (iff #45 #85)
-#79 := (or #59 #63)
-#82 := (or #67 #79)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #45 #82)
-#80 := (iff #38 #79)
-#64 := (iff #12 #63)
-#65 := [rewrite]: #64
-#60 := (iff #37 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#81 := [monotonicity #61 #65]: #80
-#77 := (iff #44 #67)
-#66 := (not #67)
-#72 := (not #66)
-#75 := (iff #72 #67)
-#76 := [rewrite]: #75
-#73 := (iff #44 #72)
-#70 := (iff #9 #66)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#84 := [monotonicity #78 #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#94 := [trans #52 #92]: #93
-#36 := [asserted]: #15
-#95 := [mp #36 #94]: #90
-#97 := [not-or-elim #95]: #56
-#96 := [not-or-elim #95]: #66
-#98 := (not #63)
-#99 := [not-or-elim #95]: #98
-[th-lemma arith farkas 1 1 1 #99 #96 #97]: false
-unsat
-ee1c33aaa657ed33c96d59b6dc6de0701ab6de06 80 0
-#2 := false
-#18 := 0::Real
-decl f5 :: Real
-#10 := f5
-#53 := -1::Real
-#56 := (* -1::Real f5)
-decl f3 :: Real
-#7 := f3
-#67 := (+ f3 #56)
-#68 := (<= #67 0::Real)
-#98 := (not #68)
-decl f4 :: Real
-#8 := f4
-#57 := (+ f4 #56)
-#55 := (>= #57 0::Real)
-#71 := (* -1::Real f4)
-#72 := (+ f3 #71)
-#73 := (<= #72 0::Real)
-#76 := (not #73)
-#85 := (or #76 #55 #68)
-#90 := (not #85)
-#12 := (<= f3 f5)
-#11 := (< f4 f5)
-#13 := (implies #11 #12)
-#9 := (<= f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#93 := (iff #15 #90)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#91 := (iff #50 #90)
-#88 := (iff #45 #85)
-#79 := (or #55 #68)
-#82 := (or #76 #79)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #45 #82)
-#80 := (iff #38 #79)
-#69 := (iff #12 #68)
-#70 := [rewrite]: #69
-#65 := (iff #37 #55)
-#54 := (not #55)
-#60 := (not #54)
-#63 := (iff #60 #55)
-#64 := [rewrite]: #63
-#61 := (iff #37 #60)
-#58 := (iff #11 #54)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#81 := [monotonicity #66 #70]: #80
-#77 := (iff #44 #76)
-#74 := (iff #9 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#84 := [monotonicity #78 #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#94 := [trans #52 #92]: #93
-#36 := [asserted]: #15
-#95 := [mp #36 #94]: #90
-#99 := [not-or-elim #95]: #98
-#97 := [not-or-elim #95]: #54
-#96 := [not-or-elim #95]: #73
-[th-lemma arith farkas 1 1 1 #96 #97 #99]: false
-unsat
-f87b387d325f83aeb1ec75660e6d181565616c1a 85 0
-#2 := false
-#18 := 0::Real
-decl f5 :: Real
-#10 := f5
-#53 := -1::Real
-#56 := (* -1::Real f5)
-decl f3 :: Real
-#7 := f3
-#69 := (+ f3 #56)
-#68 := (>= #69 0::Real)
-#67 := (not #68)
-decl f4 :: Real
-#8 := f4
-#57 := (+ f4 #56)
-#55 := (>= #57 0::Real)
-#74 := (* -1::Real f4)
-#75 := (+ f3 #74)
-#73 := (>= #75 0::Real)
-#91 := (or #73 #55 #67)
-#96 := (not #91)
-#12 := (< f3 f5)
-#11 := (< f4 f5)
-#13 := (implies #11 #12)
-#9 := (< f3 f4)
-#14 := (implies #9 #13)
-#15 := (not #14)
-#99 := (iff #15 #96)
-#37 := (not #11)
-#38 := (or #37 #12)
-#44 := (not #9)
-#45 := (or #44 #38)
-#50 := (not #45)
-#97 := (iff #50 #96)
-#94 := (iff #45 #91)
-#85 := (or #55 #67)
-#88 := (or #73 #85)
-#92 := (iff #88 #91)
-#93 := [rewrite]: #92
-#89 := (iff #45 #88)
-#86 := (iff #38 #85)
-#70 := (iff #12 #67)
-#71 := [rewrite]: #70
-#65 := (iff #37 #55)
-#54 := (not #55)
-#60 := (not #54)
-#63 := (iff #60 #55)
-#64 := [rewrite]: #63
-#61 := (iff #37 #60)
-#58 := (iff #11 #54)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#87 := [monotonicity #66 #71]: #86
-#83 := (iff #44 #73)
-#72 := (not #73)
-#78 := (not #72)
-#81 := (iff #78 #73)
-#82 := [rewrite]: #81
-#79 := (iff #44 #78)
-#76 := (iff #9 #72)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#90 := [monotonicity #84 #87]: #89
-#95 := [trans #90 #93]: #94
-#98 := [monotonicity #95]: #97
-#51 := (iff #15 #50)
-#48 := (iff #14 #45)
-#41 := (implies #9 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #14 #41)
-#39 := (iff #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#100 := [trans #52 #98]: #99
-#36 := [asserted]: #15
-#101 := [mp #36 #100]: #96
-#104 := [not-or-elim #101]: #68
-#103 := [not-or-elim #101]: #54
-#102 := [not-or-elim #101]: #72
-[th-lemma arith farkas 1 1 1 #102 #103 #104]: false
-unsat
-cb8792748fe4720134d96a488ba91a6116c7639a 69 0
-#2 := false
-#19 := 0::Real
-decl f5 :: Real
-#10 := f5
-#45 := -1::Real
-#53 := (* -1::Real f5)
-decl f3 :: Real
-#7 := f3
-#64 := (+ f3 #53)
-#65 := (<= #64 0::Real)
-#66 := (not #65)
-decl f4 :: Real
-#8 := f4
-#54 := (+ f4 #53)
-#52 := (>= #54 0::Real)
-#55 := (not #52)
-#48 := (* -1::Real f4)
-#49 := (+ f3 #48)
-#47 := (>= #49 0::Real)
-#46 := (not #47)
-#58 := (and #46 #55)
-#61 := (not #58)
-#76 := (or #61 #65)
-#79 := (not #76)
-#13 := (< f5 f3)
-#14 := (not #13)
-#11 := (< f4 f5)
-#9 := (< f3 f4)
-#12 := (and #9 #11)
-#15 := (implies #12 #14)
-#16 := (not #15)
-#82 := (iff #16 #79)
-#38 := (not #12)
-#39 := (or #38 #14)
-#42 := (not #39)
-#80 := (iff #42 #79)
-#77 := (iff #39 #76)
-#74 := (iff #14 #65)
-#69 := (not #66)
-#72 := (iff #69 #65)
-#73 := [rewrite]: #72
-#70 := (iff #14 #69)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#62 := (iff #38 #61)
-#59 := (iff #12 #58)
-#56 := (iff #11 #55)
-#57 := [rewrite]: #56
-#50 := (iff #9 #46)
-#51 := [rewrite]: #50
-#60 := [monotonicity #51 #57]: #59
-#63 := [monotonicity #60]: #62
-#78 := [monotonicity #63 #75]: #77
-#81 := [monotonicity #78]: #80
-#43 := (iff #16 #42)
-#40 := (iff #15 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#83 := [trans #44 #81]: #82
-#37 := [asserted]: #16
-#84 := [mp #37 #83]: #79
-#88 := [not-or-elim #84]: #66
-#85 := [not-or-elim #84]: #58
-#87 := [and-elim #85]: #55
-#86 := [and-elim #85]: #46
-[th-lemma arith farkas 1 1 1 #86 #87 #88]: false
-unsat
-f50e567111580fcf350e8f08b1127378c6cf44c1 46 0
-#2 := false
-decl f3 :: (-> S3 S4 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f10 :: S2
-#29 := f10
-decl f6 :: (-> S6 S2 S5)
-decl f9 :: S2
-#27 := f9
-decl f7 :: S6
-#8 := f7
-#28 := (f6 f7 f9)
-#30 := (f5 #28 f10)
-decl f4 :: S3
-#7 := f4
-#31 := (f3 f4 #30)
-#32 := (= f9 #31)
-#136 := (= #31 f9)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#552 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#553 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #552) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#556 := (iff #15 #553)
-#554 := (iff #14 #14)
-#555 := [refl]: #554
-#557 := [quant-intro #555]: #556
-#71 := (~ #15 #15)
-#69 := (~ #14 #14)
-#70 := [refl]: #69
-#72 := [nnf-pos #70]: #71
-#54 := [asserted]: #15
-#59 := [mp~ #54 #72]: #15
-#558 := [mp #59 #557]: #553
-#223 := (not #553)
-#138 := (or #223 #136)
-#224 := [quant-inst #27 #29]: #138
-#208 := [unit-resolution #224 #558]: #136
-#544 := [symm #208]: #32
-#33 := (not #32)
-#57 := [asserted]: #33
-[unit-resolution #57 #544]: false
-unsat
-e847b4eb330cb98ec19557ff4729a4ee5eac5c07 46 0
-#2 := false
-decl f3 :: (-> S3 S4 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f9 :: S2
-#27 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f10 :: S2
-#28 := f10
-decl f7 :: S6
-#8 := f7
-#29 := (f6 f7 f10)
-#30 := (f5 #29 f9)
-decl f8 :: S3
-#16 := f8
-#31 := (f3 f8 #30)
-#32 := (= f9 #31)
-#137 := (= #31 f9)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#552 := (pattern #12)
-#17 := (f3 f8 #12)
-#18 := (= #17 #11)
-#559 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #552) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#562 := (iff #19 #559)
-#560 := (iff #18 #18)
-#561 := [refl]: #560
-#563 := [quant-intro #561]: #562
-#61 := (~ #19 #19)
-#60 := (~ #18 #18)
-#73 := [refl]: #60
-#62 := [nnf-pos #73]: #61
-#55 := [asserted]: #19
-#74 := [mp~ #55 #62]: #19
-#564 := [mp #74 #563]: #559
-#227 := (not #559)
-#228 := (or #227 #137)
-#225 := [quant-inst #28 #27]: #228
-#208 := [unit-resolution #225 #564]: #137
-#544 := [symm #208]: #32
-#33 := (not #32)
-#57 := [asserted]: #33
-[unit-resolution #57 #544]: false
-unsat
-e15e69027875c204e11039aff6e36cce009f63f3 86 0
-#2 := false
-decl f5 :: (-> S5 S2 S4)
-decl f9 :: S2
-#27 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f10 :: S2
-#29 := f10
-decl f7 :: S6
-#8 := f7
-#31 := (f6 f7 f10)
-#32 := (f5 #31 f9)
-#28 := (f6 f7 f9)
-#30 := (f5 #28 f10)
-#33 := (= #30 #32)
-#541 := (= f10 f9)
-#34 := (= f9 f10)
-decl f3 :: (-> S3 S4 S2)
-decl f4 :: S3
-#7 := f4
-#548 := (f3 f4 #32)
-#221 := (= #548 f10)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#560 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#561 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #560) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#564 := (iff #15 #561)
-#562 := (iff #14 #14)
-#563 := [refl]: #562
-#565 := [quant-intro #563]: #564
-#79 := (~ #15 #15)
-#77 := (~ #14 #14)
-#78 := [refl]: #77
-#80 := [nnf-pos #78]: #79
-#57 := [asserted]: #15
-#66 := [mp~ #57 #80]: #15
-#566 := [mp #66 #565]: #561
-#554 := (not #561)
-#553 := (or #554 #221)
-#559 := [quant-inst #29 #27]: #553
-#208 := [unit-resolution #559 #566]: #221
-#199 := (= f9 #548)
-#233 := (f3 f4 #30)
-#197 := (= #233 #548)
-#144 := (not #34)
-#549 := [hypothesis]: #144
-#235 := (or #33 #34)
-#61 := (not #33)
-#62 := (iff #61 #34)
-#35 := (iff #33 #34)
-#36 := (not #35)
-#63 := (iff #36 #62)
-#64 := [rewrite]: #63
-#60 := [asserted]: #36
-#67 := [mp #60 #64]: #62
-#230 := (not #62)
-#223 := (or #33 #34 #230)
-#234 := [def-axiom]: #223
-#236 := [unit-resolution #234 #67]: #235
-#209 := [unit-resolution #236 #549]: #33
-#198 := [monotonicity #209]: #197
-#193 := (= f9 #233)
-#237 := (= #233 f9)
-#210 := (or #554 #237)
-#341 := [quant-inst #27 #29]: #210
-#551 := [unit-resolution #341 #566]: #237
-#535 := [symm #551]: #193
-#200 := [trans #535 #198]: #199
-#537 := [trans #200 #208]: #34
-#538 := [unit-resolution #549 #537]: false
-#539 := [lemma #538]: #34
-#536 := [symm #539]: #541
-#542 := (= #28 #31)
-#179 := [monotonicity #539]: #542
-#543 := [monotonicity #179 #536]: #33
-#146 := (or #61 #144)
-#145 := (or #61 #144 #230)
-#231 := [def-axiom]: #145
-#232 := [unit-resolution #231 #67]: #146
-#540 := [unit-resolution #232 #539]: #61
-[unit-resolution #540 #543]: false
-unsat
-072ec5311fec3c6e1f5e2d99691fb9ed86302245 147 0
-#2 := false
-decl f12 :: S2
-#33 := f12
-decl f10 :: S2
-#29 := f10
-#37 := (= f10 f12)
-#91 := (not #37)
-decl f11 :: S2
-#31 := f11
-decl f9 :: S2
-#27 := f9
-#36 := (= f9 f11)
-#90 := (not #36)
-#77 := (or #90 #91)
-decl f5 :: (-> S5 S2 S4)
-decl f6 :: (-> S6 S2 S5)
-decl f7 :: S6
-#8 := f7
-#32 := (f6 f7 f11)
-#34 := (f5 #32 f12)
-#28 := (f6 f7 f9)
-#30 := (f5 #28 f10)
-#35 := (= #30 #34)
-#78 := (not #77)
-#570 := [hypothesis]: #78
-#164 := (or #77 #37)
-#250 := [def-axiom]: #164
-#217 := [unit-resolution #250 #570]: #37
-#219 := (= #28 #32)
-#163 := (or #77 #36)
-#249 := [def-axiom]: #163
-#218 := [unit-resolution #249 #570]: #36
-#556 := [monotonicity #218]: #219
-#557 := [monotonicity #556 #217]: #35
-#65 := (not #35)
-#571 := (or #65 #77)
-#95 := (iff #35 #77)
-#38 := (and #36 #37)
-#66 := (iff #65 #38)
-#98 := (iff #66 #95)
-#92 := (iff #65 #78)
-#96 := (iff #92 #95)
-#97 := [rewrite]: #96
-#93 := (iff #66 #92)
-#79 := (iff #38 #78)
-#80 := [rewrite]: #79
-#94 := [monotonicity #80]: #93
-#99 := [trans #94 #97]: #98
-#39 := (iff #35 #38)
-#40 := (not #39)
-#67 := (iff #40 #66)
-#68 := [rewrite]: #67
-#64 := [asserted]: #40
-#71 := [mp #64 #68]: #66
-#100 := [mp #71 #99]: #95
-#242 := (not #95)
-#256 := (or #65 #77 #242)
-#235 := [def-axiom]: #256
-#573 := [unit-resolution #235 #100]: #571
-#212 := [unit-resolution #573 #570]: #65
-#558 := [unit-resolution #212 #557]: false
-#559 := [lemma #558]: #77
-decl f3 :: (-> S3 S4 S2)
-decl f4 :: S3
-#7 := f4
-#576 := (f3 f4 #34)
-#577 := (= #576 f11)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#579 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#580 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #579) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#583 := (iff #15 #580)
-#581 := (iff #14 #14)
-#582 := [refl]: #581
-#584 := [quant-intro #582]: #583
-#83 := (~ #15 #15)
-#81 := (~ #14 #14)
-#82 := [refl]: #81
-#84 := [nnf-pos #82]: #83
-#61 := [asserted]: #15
-#70 := [mp~ #61 #84]: #15
-#585 := [mp #70 #584]: #580
-#241 := (not #580)
-#569 := (or #241 #577)
-#228 := [quant-inst #31 #33]: #569
-#560 := [unit-resolution #228 #585]: #577
-#204 := (= f9 #576)
-#229 := (f3 f4 #30)
-#564 := (= #229 #576)
-#255 := (or #35 #78)
-#253 := (or #35 #78 #242)
-#254 := [def-axiom]: #253
-#252 := [unit-resolution #254 #100]: #255
-#555 := [unit-resolution #252 #559]: #35
-#203 := [monotonicity #555]: #564
-#198 := (= f9 #229)
-#360 := (= #229 f9)
-#574 := (or #241 #360)
-#575 := [quant-inst #27 #29]: #574
-#561 := [unit-resolution #575 #585]: #360
-#562 := [symm #561]: #198
-#565 := [trans #562 #203]: #204
-#563 := [trans #565 #560]: #36
-decl f8 :: S3
-#16 := f8
-#227 := (f3 f8 #34)
-#232 := (= #227 f12)
-#17 := (f3 f8 #12)
-#18 := (= #17 #11)
-#586 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #579) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#589 := (iff #19 #586)
-#587 := (iff #18 #18)
-#588 := [refl]: #587
-#590 := [quant-intro #588]: #589
-#73 := (~ #19 #19)
-#72 := (~ #18 #18)
-#85 := [refl]: #72
-#74 := [nnf-pos #85]: #73
-#62 := [asserted]: #19
-#86 := [mp~ #62 #74]: #19
-#591 := [mp #86 #590]: #586
-#572 := (not #586)
-#554 := (or #572 #232)
-#216 := [quant-inst #31 #33]: #554
-#566 := [unit-resolution #216 #591]: #232
-#277 := (= f10 #227)
-#567 := (f3 f8 #30)
-#275 := (= #567 #227)
-#276 := [monotonicity #555]: #275
-#553 := (= f10 #567)
-#240 := (= #567 f10)
-#578 := (or #572 #240)
-#568 := [quant-inst #27 #29]: #578
-#552 := [unit-resolution #568 #591]: #240
-#260 := [symm #552]: #553
-#278 := [trans #260 #276]: #277
-#171 := [trans #278 #566]: #37
-#165 := (or #78 #90 #91)
-#251 := [def-axiom]: #165
-[unit-resolution #251 #171 #563 #559]: false
-unsat
-2e4e9225ab02683d5a755c820a7cd4a4252a5720 97 0
-#2 := false
-decl f8 :: (-> S8 S9 S2)
-decl f10 :: (-> S10 S5 S9)
-decl f5 :: (-> S6 S3 S5)
-decl f22 :: S3
-#57 := f22
-decl f6 :: (-> S7 S2 S6)
-decl f21 :: S2
-#55 := f21
-decl f7 :: S7
-#8 := f7
-#56 := (f6 f7 f21)
-#58 := (f5 #56 f22)
-decl f11 :: (-> S11 S2 S10)
-decl f20 :: S2
-#53 := f20
-decl f12 :: S11
-#17 := f12
-#54 := (f11 f12 f20)
-#59 := (f10 #54 #58)
-decl f9 :: S8
-#16 := f9
-#60 := (f8 f9 #59)
-decl f19 :: S3
-#49 := f19
-decl f18 :: S2
-#47 := f18
-#48 := (f6 f7 f18)
-#50 := (f5 #48 f19)
-decl f17 :: S2
-#45 := f17
-#46 := (f11 f12 f17)
-#51 := (f10 #46 #50)
-#52 := (f8 f9 #51)
-#61 := (= #52 #60)
-#62 := (= f17 f20)
-#198 := (iff #62 #61)
-#63 := (iff #61 #62)
-#243 := (= #60 f20)
-#19 := (:var 0 S5)
-#9 := (:var 1 S2)
-#18 := (f11 f12 #9)
-#20 := (f10 #18 #19)
-#613 := (pattern #20)
-#21 := (f8 f9 #20)
-#22 := (= #21 #9)
-#614 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #613) #22)
-#23 := (forall (vars (?v0 S2) (?v1 S5)) #22)
-#617 := (iff #23 #614)
-#615 := (iff #22 #22)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#100 := (~ #23 #23)
-#99 := (~ #22 #22)
-#118 := [refl]: #99
-#101 := [nnf-pos #118]: #100
-#86 := [asserted]: #23
-#119 := [mp~ #86 #101]: #23
-#619 := [mp #119 #618]: #614
-#597 := (not #614)
-#585 := (or #597 #243)
-#586 := [quant-inst #53 #58]: #585
-#303 := [unit-resolution #586 #619]: #243
-#595 := (= #52 f17)
-#239 := (or #597 #595)
-#581 := [quant-inst #45 #50]: #239
-#304 := [unit-resolution #581 #619]: #595
-#305 := [monotonicity #304 #303]: #63
-#575 := [symm #305]: #198
-#92 := (not #61)
-#190 := (not #62)
-#576 := (iff #190 #92)
-#298 := [monotonicity #575]: #576
-#579 := [hypothesis]: #190
-#299 := [mp #579 #298]: #92
-#281 := (or #61 #62)
-#93 := (iff #92 #62)
-#64 := (not #63)
-#94 := (iff #64 #93)
-#95 := [rewrite]: #94
-#91 := [asserted]: #64
-#98 := [mp #91 #95]: #93
-#276 := (not #93)
-#269 := (or #61 #62 #276)
-#280 := [def-axiom]: #269
-#282 := [unit-resolution #280 #98]: #281
-#580 := [unit-resolution #282 #579]: #61
-#573 := [unit-resolution #580 #299]: false
-#577 := [lemma #573]: #62
-#578 := [mp #577 #575]: #61
-#192 := (or #92 #190)
-#191 := (or #92 #190 #276)
-#277 := [def-axiom]: #191
-#278 := [unit-resolution #277 #98]: #192
-#574 := [unit-resolution #278 #577]: #92
-[unit-resolution #574 #578]: false
-unsat
-326c3cc9171e09e8a8be6ed6bdcf7e348fc9488e 204 0
-#2 := false
-decl f22 :: S8
-#57 := f22
-decl f19 :: S8
-#49 := f19
-#63 := (= f19 f22)
-#135 := (not #63)
-decl f21 :: S2
-#55 := f21
-decl f18 :: S2
-#47 := f18
-#62 := (= f18 f21)
-#134 := (not #62)
-#112 := (or #134 #135)
-decl f15 :: (-> S13 S5 S3)
-decl f5 :: (-> S6 S3 S5)
-decl f10 :: (-> S10 S8 S3)
-decl f11 :: (-> S11 S2 S10)
-decl f12 :: S11
-#17 := f12
-#56 := (f11 f12 f21)
-#58 := (f10 #56 f22)
-decl f6 :: (-> S7 S2 S6)
-decl f20 :: S2
-#53 := f20
-decl f7 :: S7
-#8 := f7
-#54 := (f6 f7 f20)
-#59 := (f5 #54 #58)
-decl f16 :: S13
-#28 := f16
-#60 := (f15 f16 #59)
-#48 := (f11 f12 f18)
-#50 := (f10 #48 f19)
-decl f17 :: S2
-#45 := f17
-#46 := (f6 f7 f17)
-#51 := (f5 #46 #50)
-#52 := (f15 f16 #51)
-#61 := (= #52 #60)
-#306 := (= #58 #60)
-#612 := (= #60 #58)
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#623 := (pattern #12)
-#29 := (f15 f16 #12)
-#30 := (= #29 #11)
-#643 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #623) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3)) #30)
-#646 := (iff #31 #643)
-#644 := (iff #30 #30)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#106 := (~ #31 #31)
-#125 := (~ #30 #30)
-#126 := [refl]: #125
-#107 := [nnf-pos #126]: #106
-#90 := [asserted]: #31
-#127 := [mp~ #90 #107]: #31
-#648 := [mp #127 #647]: #643
-#621 := (not #643)
-#614 := (or #621 #612)
-#256 := [quant-inst #53 #58]: #614
-#593 := [unit-resolution #256 #648]: #612
-#307 := [symm #593]: #306
-#308 := (= #52 #58)
-#595 := (= #50 #58)
-#113 := (not #112)
-#321 := [hypothesis]: #113
-#208 := (or #112 #63)
-#294 := [def-axiom]: #208
-#315 := [unit-resolution #294 #321]: #63
-#590 := (= #48 #56)
-#207 := (or #112 #62)
-#293 := [def-axiom]: #207
-#316 := [unit-resolution #293 #321]: #62
-#594 := [monotonicity #316]: #590
-#305 := [monotonicity #594 #315]: #595
-#611 := (= #52 #50)
-#616 := (or #621 #611)
-#622 := [quant-inst #45 #50]: #616
-#591 := [unit-resolution #622 #648]: #611
-#586 := [trans #591 #305]: #308
-#587 := [trans #586 #307]: #61
-#94 := (not #61)
-#615 := (or #94 #112)
-#139 := (iff #61 #112)
-#64 := (and #62 #63)
-#95 := (iff #94 #64)
-#142 := (iff #95 #139)
-#136 := (iff #94 #113)
-#140 := (iff #136 #139)
-#141 := [rewrite]: #140
-#137 := (iff #95 #136)
-#114 := (iff #64 #113)
-#115 := [rewrite]: #114
-#138 := [monotonicity #115]: #137
-#143 := [trans #138 #141]: #142
-#65 := (iff #61 #64)
-#66 := (not #65)
-#96 := (iff #66 #95)
-#97 := [rewrite]: #96
-#93 := [asserted]: #66
-#100 := [mp #93 #97]: #95
-#144 := [mp #100 #143]: #139
-#286 := (not #139)
-#300 := (or #94 #112 #286)
-#279 := [def-axiom]: #300
-#617 := [unit-resolution #279 #144]: #615
-#322 := [unit-resolution #617 #321]: #94
-#301 := [unit-resolution #322 #587]: false
-#584 := [lemma #301]: #112
-decl f8 :: (-> S9 S3 S2)
-decl f9 :: S9
-#16 := f9
-#600 := (f8 f9 #58)
-#601 := (= #600 f21)
-#19 := (:var 0 S8)
-#18 := (f11 f12 #9)
-#20 := (f10 #18 #19)
-#630 := (pattern #20)
-#21 := (f8 f9 #20)
-#22 := (= #21 #9)
-#631 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #630) #22)
-#23 := (forall (vars (?v0 S2) (?v1 S8)) #22)
-#634 := (iff #23 #631)
-#632 := (iff #22 #22)
-#633 := [refl]: #632
-#635 := [quant-intro #633]: #634
-#102 := (~ #23 #23)
-#101 := (~ #22 #22)
-#120 := [refl]: #101
-#103 := [nnf-pos #120]: #102
-#88 := [asserted]: #23
-#121 := [mp~ #88 #103]: #23
-#636 := [mp #121 #635]: #631
-#261 := (not #631)
-#242 := (or #261 #601)
-#606 := [quant-inst #55 #57]: #242
-#588 := [unit-resolution #606 #636]: #601
-#424 := (= f18 #600)
-#271 := (f8 f9 #50)
-#577 := (= #271 #600)
-#579 := (= #50 #60)
-#299 := (or #61 #113)
-#297 := (or #61 #113 #286)
-#298 := [def-axiom]: #297
-#296 := [unit-resolution #298 #144]: #299
-#585 := [unit-resolution #296 #584]: #61
-#589 := (= #50 #52)
-#578 := [symm #591]: #589
-#580 := [trans #578 #585]: #579
-#575 := [trans #580 #593]: #595
-#583 := [monotonicity #575]: #577
-#581 := (= f18 #271)
-#272 := (= #271 f18)
-#262 := (or #261 #272)
-#263 := [quant-inst #47 #49]: #262
-#576 := [unit-resolution #263 #636]: #272
-#582 := [symm #576]: #581
-#425 := [trans #582 #583]: #424
-#426 := [trans #425 #588]: #62
-decl f13 :: (-> S12 S3 S8)
-decl f14 :: S12
-#24 := f14
-#599 := (f13 f14 #58)
-#605 := (= #599 f22)
-#25 := (f13 f14 #20)
-#26 := (= #25 #19)
-#637 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #630) #26)
-#27 := (forall (vars (?v0 S2) (?v1 S8)) #26)
-#640 := (iff #27 #637)
-#638 := (iff #26 #26)
-#639 := [refl]: #638
-#641 := [quant-intro #639]: #640
-#104 := (~ #27 #27)
-#122 := (~ #26 #26)
-#123 := [refl]: #122
-#105 := [nnf-pos #123]: #104
-#89 := [asserted]: #27
-#124 := [mp~ #89 #105]: #27
-#642 := [mp #124 #641]: #637
-#602 := (not #637)
-#248 := (or #602 #605)
-#609 := [quant-inst #55 #57]: #248
-#568 := [unit-resolution #609 #642]: #605
-#572 := (= f19 #599)
-#598 := (f13 f14 #50)
-#565 := (= #598 #599)
-#566 := [monotonicity #575]: #565
-#570 := (= f19 #598)
-#260 := (= #598 f19)
-#603 := (or #602 #260)
-#604 := [quant-inst #47 #49]: #603
-#569 := [unit-resolution #604 #642]: #260
-#571 := [symm #569]: #570
-#573 := [trans #571 #566]: #572
-#567 := [trans #573 #568]: #63
-#209 := (or #113 #134 #135)
-#295 := [def-axiom]: #209
-[unit-resolution #295 #567 #426 #584]: false
-unsat
-bf4839d9633981e506c1be855f13b8a26192da1d 140 0
-#2 := false
-decl f8 :: (-> S9 S3 S2)
-decl f15 :: (-> S13 S5 S3)
-decl f5 :: (-> S6 S3 S5)
-decl f10 :: (-> S10 S8 S3)
-decl f22 :: S8
-#58 := f22
-decl f11 :: (-> S11 S2 S10)
-decl f21 :: S2
-#56 := f21
-decl f12 :: S11
-#17 := f12
-#57 := (f11 f12 f21)
-#59 := (f10 #57 f22)
-decl f6 :: (-> S7 S2 S6)
-decl f20 :: S2
-#54 := f20
-decl f7 :: S7
-#8 := f7
-#55 := (f6 f7 f20)
-#60 := (f5 #55 #59)
-decl f16 :: S13
-#28 := f16
-#61 := (f15 f16 #60)
-decl f9 :: S9
-#16 := f9
-#62 := (f8 f9 #61)
-decl f19 :: S8
-#49 := f19
-decl f18 :: S2
-#47 := f18
-#48 := (f11 f12 f18)
-#50 := (f10 #48 f19)
-decl f17 :: S2
-#45 := f17
-#46 := (f6 f7 f17)
-#51 := (f5 #46 #50)
-#52 := (f15 f16 #51)
-#53 := (f8 f9 #52)
-#63 := (= #53 #62)
-#64 := (= f18 f21)
-#560 := (iff #64 #63)
-#65 := (iff #63 #64)
-#572 := (= #62 f21)
-#583 := (f8 f9 #59)
-#245 := (= #583 f21)
-#19 := (:var 0 S8)
-#9 := (:var 1 S2)
-#18 := (f11 f12 #9)
-#20 := (f10 #18 #19)
-#615 := (pattern #20)
-#21 := (f8 f9 #20)
-#22 := (= #21 #9)
-#616 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #615) #22)
-#23 := (forall (vars (?v0 S2) (?v1 S8)) #22)
-#619 := (iff #23 #616)
-#617 := (iff #22 #22)
-#618 := [refl]: #617
-#620 := [quant-intro #618]: #619
-#102 := (~ #23 #23)
-#101 := (~ #22 #22)
-#120 := [refl]: #101
-#103 := [nnf-pos #120]: #102
-#88 := [asserted]: #23
-#121 := [mp~ #88 #103]: #23
-#621 := [mp #121 #620]: #616
-#257 := (not #616)
-#587 := (or #257 #245)
-#588 := [quant-inst #56 #58]: #587
-#291 := [unit-resolution #588 #621]: #245
-#293 := (= #62 #583)
-#604 := (= #61 #59)
-#11 := (:var 0 S3)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#608 := (pattern #12)
-#29 := (f15 f16 #12)
-#30 := (= #29 #11)
-#628 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #608) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3)) #30)
-#631 := (iff #31 #628)
-#629 := (iff #30 #30)
-#630 := [refl]: #629
-#632 := [quant-intro #630]: #631
-#106 := (~ #31 #31)
-#125 := (~ #30 #30)
-#126 := [refl]: #125
-#107 := [nnf-pos #126]: #106
-#90 := [asserted]: #31
-#127 := [mp~ #90 #107]: #31
-#633 := [mp #127 #632]: #628
-#269 := (not #628)
-#597 := (or #269 #604)
-#256 := [quant-inst #54 #59]: #597
-#292 := [unit-resolution #256 #633]: #604
-#571 := [monotonicity #292]: #293
-#286 := [trans #571 #291]: #572
-#563 := (= #53 f18)
-#605 := (f8 f9 #50)
-#607 := (= #605 f18)
-#599 := (or #257 #607)
-#241 := [quant-inst #47 #49]: #599
-#569 := [unit-resolution #241 #621]: #607
-#570 := (= #53 #605)
-#264 := (= #52 #50)
-#270 := (or #269 #264)
-#603 := [quant-inst #45 #50]: #270
-#573 := [unit-resolution #603 #633]: #264
-#574 := [monotonicity #573]: #570
-#564 := [trans #574 #569]: #563
-#565 := [monotonicity #564 #286]: #65
-#561 := [symm #565]: #560
-#94 := (not #63)
-#192 := (not #64)
-#566 := (iff #192 #94)
-#567 := [monotonicity #561]: #566
-#579 := [hypothesis]: #192
-#562 := [mp #579 #567]: #94
-#283 := (or #63 #64)
-#95 := (iff #94 #64)
-#66 := (not #65)
-#96 := (iff #66 #95)
-#97 := [rewrite]: #96
-#93 := [asserted]: #66
-#100 := [mp #93 #97]: #95
-#278 := (not #95)
-#271 := (or #63 #64 #278)
-#282 := [def-axiom]: #271
-#284 := [unit-resolution #282 #100]: #283
-#576 := [unit-resolution #284 #579]: #63
-#568 := [unit-resolution #576 #562]: false
-#409 := [lemma #568]: #64
-#411 := [mp #409 #561]: #63
-#194 := (or #94 #192)
-#193 := (or #94 #192 #278)
-#279 := [def-axiom]: #193
-#280 := [unit-resolution #279 #100]: #194
-#410 := [unit-resolution #280 #409]: #94
-[unit-resolution #410 #411]: false
-unsat
-cf1f4336502ff8e78cd5bc19dd27179c762eaf09 140 0
-#2 := false
-decl f13 :: (-> S12 S3 S8)
-decl f15 :: (-> S13 S5 S3)
-decl f5 :: (-> S6 S3 S5)
-decl f10 :: (-> S10 S8 S3)
-decl f22 :: S8
-#58 := f22
-decl f11 :: (-> S11 S2 S10)
-decl f21 :: S2
-#56 := f21
-decl f12 :: S11
-#17 := f12
-#57 := (f11 f12 f21)
-#59 := (f10 #57 f22)
-decl f6 :: (-> S7 S2 S6)
-decl f20 :: S2
-#54 := f20
-decl f7 :: S7
-#8 := f7
-#55 := (f6 f7 f20)
-#60 := (f5 #55 #59)
-decl f16 :: S13
-#28 := f16
-#61 := (f15 f16 #60)
-decl f14 :: S12
-#24 := f14
-#62 := (f13 f14 #61)
-decl f19 :: S8
-#49 := f19
-decl f18 :: S2
-#47 := f18
-#48 := (f11 f12 f18)
-#50 := (f10 #48 f19)
-decl f17 :: S2
-#45 := f17
-#46 := (f6 f7 f17)
-#51 := (f5 #46 #50)
-#52 := (f15 f16 #51)
-#53 := (f13 f14 #52)
-#63 := (= #53 #62)
-#64 := (= f19 f22)
-#560 := (iff #64 #63)
-#65 := (iff #63 #64)
-#572 := (= #62 f22)
-#585 := (f13 f14 #59)
-#586 := (= #585 f22)
-#19 := (:var 0 S8)
-#9 := (:var 1 S2)
-#18 := (f11 f12 #9)
-#20 := (f10 #18 #19)
-#615 := (pattern #20)
-#25 := (f13 f14 #20)
-#26 := (= #25 #19)
-#622 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #615) #26)
-#27 := (forall (vars (?v0 S2) (?v1 S8)) #26)
-#625 := (iff #27 #622)
-#623 := (iff #26 #26)
-#624 := [refl]: #623
-#626 := [quant-intro #624]: #625
-#104 := (~ #27 #27)
-#122 := (~ #26 #26)
-#123 := [refl]: #122
-#105 := [nnf-pos #123]: #104
-#89 := [asserted]: #27
-#124 := [mp~ #89 #105]: #27
-#627 := [mp #124 #626]: #622
-#246 := (not #622)
-#590 := (or #246 #586)
-#227 := [quant-inst #56 #58]: #590
-#291 := [unit-resolution #227 #627]: #586
-#293 := (= #62 #585)
-#604 := (= #61 #59)
-#11 := (:var 0 S3)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#608 := (pattern #12)
-#29 := (f15 f16 #12)
-#30 := (= #29 #11)
-#628 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #608) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3)) #30)
-#631 := (iff #31 #628)
-#629 := (iff #30 #30)
-#630 := [refl]: #629
-#632 := [quant-intro #630]: #631
-#106 := (~ #31 #31)
-#125 := (~ #30 #30)
-#126 := [refl]: #125
-#107 := [nnf-pos #126]: #106
-#90 := [asserted]: #31
-#127 := [mp~ #90 #107]: #31
-#633 := [mp #127 #632]: #628
-#269 := (not #628)
-#597 := (or #269 #604)
-#256 := [quant-inst #54 #59]: #597
-#292 := [unit-resolution #256 #633]: #604
-#571 := [monotonicity #292]: #293
-#286 := [trans #571 #291]: #572
-#563 := (= #53 f19)
-#261 := (f13 f14 #50)
-#598 := (= #261 f19)
-#247 := (or #246 #598)
-#248 := [quant-inst #47 #49]: #247
-#569 := [unit-resolution #248 #627]: #598
-#570 := (= #53 #261)
-#264 := (= #52 #50)
-#270 := (or #269 #264)
-#603 := [quant-inst #45 #50]: #270
-#573 := [unit-resolution #603 #633]: #264
-#574 := [monotonicity #573]: #570
-#564 := [trans #574 #569]: #563
-#565 := [monotonicity #564 #286]: #65
-#561 := [symm #565]: #560
-#94 := (not #63)
-#192 := (not #64)
-#566 := (iff #192 #94)
-#567 := [monotonicity #561]: #566
-#579 := [hypothesis]: #192
-#562 := [mp #579 #567]: #94
-#283 := (or #63 #64)
-#95 := (iff #94 #64)
-#66 := (not #65)
-#96 := (iff #66 #95)
-#97 := [rewrite]: #96
-#93 := [asserted]: #66
-#100 := [mp #93 #97]: #95
-#278 := (not #95)
-#271 := (or #63 #64 #278)
-#282 := [def-axiom]: #271
-#284 := [unit-resolution #282 #100]: #283
-#576 := [unit-resolution #284 #579]: #63
-#568 := [unit-resolution #576 #562]: false
-#409 := [lemma #568]: #64
-#411 := [mp #409 #561]: #63
-#194 := (or #94 #192)
-#193 := (or #94 #192 #278)
-#279 := [def-axiom]: #193
-#280 := [unit-resolution #279 #100]: #194
-#410 := [unit-resolution #280 #409]: #94
-[unit-resolution #410 #411]: false
-unsat
-b698de6114c960aedd429b35adfc1493851107e0 97 0
-#2 := false
-decl f3 :: (-> S3 S4 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f10 :: S2
-#29 := f10
-decl f6 :: (-> S6 S2 S5)
-decl f9 :: S2
-#27 := f9
-decl f7 :: S6
-#8 := f7
-#28 := (f6 f7 f9)
-#30 := (f5 #28 f10)
-decl f8 :: S3
-#16 := f8
-#32 := (f3 f8 #30)
-decl f4 :: S3
-#7 := f4
-#31 := (f3 f4 #30)
-#33 := (= #31 #32)
-#34 := (= f9 f10)
-#550 := (iff #34 #33)
-#35 := (iff #33 #34)
-#237 := (= #32 f10)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#560 := (pattern #12)
-#17 := (f3 f8 #12)
-#18 := (= #17 #11)
-#567 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #560) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#570 := (iff #19 #567)
-#568 := (iff #18 #18)
-#569 := [refl]: #568
-#571 := [quant-intro #569]: #570
-#69 := (~ #19 #19)
-#68 := (~ #18 #18)
-#81 := [refl]: #68
-#70 := [nnf-pos #81]: #69
-#58 := [asserted]: #19
-#82 := [mp~ #58 #70]: #19
-#572 := [mp #82 #571]: #567
-#548 := (not #567)
-#221 := (or #548 #237)
-#222 := [quant-inst #27 #29]: #221
-#549 := [unit-resolution #222 #572]: #237
-#233 := (= #31 f9)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#561 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #560) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#564 := (iff #15 #561)
-#562 := (iff #14 #14)
-#563 := [refl]: #562
-#565 := [quant-intro #563]: #564
-#79 := (~ #15 #15)
-#77 := (~ #14 #14)
-#78 := [refl]: #77
-#80 := [nnf-pos #78]: #79
-#57 := [asserted]: #15
-#66 := [mp~ #57 #80]: #15
-#566 := [mp #66 #565]: #561
-#552 := (not #561)
-#554 := (or #552 #233)
-#210 := [quant-inst #27 #29]: #554
-#208 := [unit-resolution #210 #566]: #233
-#213 := [monotonicity #208 #549]: #35
-#209 := [symm #213]: #550
-#61 := (not #33)
-#144 := (not #34)
-#551 := (iff #144 #61)
-#193 := [monotonicity #209]: #551
-#556 := [hypothesis]: #144
-#535 := [mp #556 #193]: #61
-#235 := (or #33 #34)
-#62 := (iff #61 #34)
-#36 := (not #35)
-#63 := (iff #36 #62)
-#64 := [rewrite]: #63
-#60 := [asserted]: #36
-#67 := [mp #60 #64]: #62
-#230 := (not #62)
-#223 := (or #33 #34 #230)
-#234 := [def-axiom]: #223
-#236 := [unit-resolution #234 #67]: #235
-#557 := [unit-resolution #236 #556]: #33
-#197 := [unit-resolution #557 #535]: false
-#198 := [lemma #197]: #34
-#200 := [mp #198 #209]: #33
-#146 := (or #61 #144)
-#145 := (or #61 #144 #230)
-#231 := [def-axiom]: #145
-#232 := [unit-resolution #231 #67]: #146
-#199 := [unit-resolution #232 #198]: #61
-[unit-resolution #199 #200]: false
-unsat
-6474d219388775f06b6327aa11f8df4ad2448f55 106 0
-#2 := false
-decl f3 :: (-> S3 S4 S2)
-decl f12 :: S4
-#33 := f12
-decl f8 :: S3
-#16 := f8
-#39 := (f3 f8 f12)
-decl f9 :: S4
-#27 := f9
-decl f4 :: S3
-#7 := f4
-#38 := (f3 f4 f9)
-#40 := (= #38 #39)
-decl f5 :: (-> S5 S2 S4)
-decl f10 :: S2
-#28 := f10
-decl f6 :: (-> S6 S2 S5)
-decl f11 :: S2
-#30 := f11
-decl f7 :: S6
-#8 := f7
-#34 := (f6 f7 f11)
-#35 := (f5 #34 f10)
-#230 := (f3 f8 #35)
-#214 := (= #230 #39)
-#549 := (= #39 #230)
-#36 := (= f12 #35)
-#29 := (f6 f7 f10)
-#31 := (f5 #29 f11)
-#32 := (= f9 #31)
-#37 := (and #32 #36)
-#67 := (not #37)
-#68 := (or #67 #40)
-#71 := (not #68)
-#41 := (implies #37 #40)
-#42 := (not #41)
-#72 := (iff #42 #71)
-#69 := (iff #41 #68)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#66 := [asserted]: #42
-#76 := [mp #66 #73]: #71
-#74 := [not-or-elim #76]: #37
-#77 := [and-elim #74]: #36
-#211 := [monotonicity #77]: #549
-#551 := [symm #211]: #214
-#554 := (= #38 #230)
-#212 := (= f10 #230)
-#566 := (= #230 f10)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#574 := (pattern #12)
-#17 := (f3 f8 #12)
-#18 := (= #17 #11)
-#581 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #574) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#584 := (iff #19 #581)
-#582 := (iff #18 #18)
-#583 := [refl]: #582
-#585 := [quant-intro #583]: #584
-#83 := (~ #19 #19)
-#82 := (~ #18 #18)
-#99 := [refl]: #82
-#84 := [nnf-pos #99]: #83
-#64 := [asserted]: #19
-#100 := [mp~ #64 #84]: #19
-#586 := [mp #100 #585]: #581
-#250 := (not #581)
-#235 := (or #250 #566)
-#236 := [quant-inst #30 #28]: #235
-#222 := [unit-resolution #236 #586]: #566
-#213 := [symm #222]: #212
-#552 := (= #38 f10)
-#158 := (f3 f4 #31)
-#244 := (= #158 f10)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#575 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #574) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#578 := (iff #15 #575)
-#576 := (iff #14 #14)
-#577 := [refl]: #576
-#579 := [quant-intro #577]: #578
-#97 := (~ #15 #15)
-#95 := (~ #14 #14)
-#96 := [refl]: #95
-#98 := [nnf-pos #96]: #97
-#63 := [asserted]: #15
-#81 := [mp~ #63 #98]: #15
-#580 := [mp #81 #579]: #575
-#160 := (not #575)
-#246 := (or #160 #244)
-#237 := [quant-inst #28 #30]: #246
-#227 := [unit-resolution #237 #580]: #244
-#565 := (= #38 #158)
-#75 := [and-elim #74]: #32
-#207 := [monotonicity #75]: #565
-#553 := [trans #207 #227]: #552
-#555 := [trans #553 #213]: #554
-#550 := [trans #555 #551]: #40
-#78 := (not #40)
-#79 := [not-or-elim #76]: #78
-[unit-resolution #79 #550]: false
-unsat
-4ebcb713a96f25289faf5874caac5699de053d9a 115 0
-#2 := false
-decl f3 :: (-> S3 S4 S2)
-decl f9 :: S4
-#27 := f9
-decl f8 :: S3
-#16 := f8
-#29 := (f3 f8 f9)
-decl f4 :: S3
-#7 := f4
-#28 := (f3 f4 f9)
-#30 := (= #28 #29)
-decl f5 :: (-> S5 S2 S4)
-decl f6 :: (-> S6 S2 S5)
-decl f7 :: S6
-#8 := f7
-#31 := (f6 f7 #29)
-#32 := (f5 #31 #28)
-#232 := (f3 f4 #32)
-#236 := (= #232 #29)
-#11 := (:var 0 S2)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#559 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#560 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #559) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#563 := (iff #15 #560)
-#561 := (iff #14 #14)
-#562 := [refl]: #561
-#564 := [quant-intro #562]: #563
-#78 := (~ #15 #15)
-#76 := (~ #14 #14)
-#77 := [refl]: #76
-#79 := [nnf-pos #77]: #78
-#56 := [asserted]: #15
-#65 := [mp~ #56 #79]: #15
-#565 := [mp #65 #564]: #560
-#553 := (not #560)
-#209 := (or #553 #236)
-#340 := [quant-inst #29 #28]: #209
-#178 := [unit-resolution #340 #565]: #236
-#545 := (= #28 #232)
-#183 := (= #232 #28)
-#535 := (= #32 f9)
-#33 := (= f9 #32)
-#547 := (f6 f7 #28)
-#220 := (f5 #547 #29)
-#199 := (= #220 #32)
-#534 := (= #32 #220)
-#143 := (not #33)
-#557 := [hypothesis]: #143
-#234 := (or #30 #33)
-#60 := (not #30)
-#61 := (iff #60 #33)
-#34 := (iff #30 #33)
-#35 := (not #34)
-#62 := (iff #35 #61)
-#63 := [rewrite]: #62
-#59 := [asserted]: #35
-#66 := [mp #59 #63]: #61
-#229 := (not #61)
-#222 := (or #30 #33 #229)
-#233 := [def-axiom]: #222
-#235 := [unit-resolution #233 #66]: #234
-#212 := [unit-resolution #235 #557]: #30
-#550 := (= #31 #547)
-#549 := (= #547 #31)
-#208 := [monotonicity #212]: #549
-#192 := [symm #208]: #550
-#196 := [monotonicity #192 #212]: #534
-#536 := [symm #196]: #199
-#197 := (= f9 #220)
-#556 := (= #220 f9)
-#20 := (:var 0 S4)
-#23 := (f3 f8 #20)
-#573 := (pattern #23)
-#21 := (f3 f4 #20)
-#572 := (pattern #21)
-#22 := (f6 f7 #21)
-#24 := (f5 #22 #23)
-#25 := (= #24 #20)
-#574 := (forall (vars (?v0 S4)) (:pat #572 #573) #25)
-#26 := (forall (vars (?v0 S4)) #25)
-#577 := (iff #26 #574)
-#575 := (iff #25 #25)
-#576 := [refl]: #575
-#578 := [quant-intro #576]: #577
-#70 := (~ #26 #26)
-#82 := (~ #25 #25)
-#83 := [refl]: #82
-#71 := [nnf-pos #83]: #70
-#58 := [asserted]: #26
-#84 := [mp~ #58 #71]: #26
-#579 := [mp #84 #578]: #574
-#558 := (not #574)
-#548 := (or #558 #556)
-#207 := [quant-inst #27]: #548
-#552 := [unit-resolution #207 #579]: #556
-#198 := [symm #552]: #197
-#537 := [trans #198 #536]: #33
-#538 := [unit-resolution #557 #537]: false
-#539 := [lemma #538]: #33
-#541 := [symm #539]: #535
-#184 := [monotonicity #541]: #183
-#543 := [symm #184]: #545
-#546 := [trans #543 #178]: #30
-#145 := (or #60 #143)
-#144 := (or #60 #143 #229)
-#230 := [def-axiom]: #144
-#231 := [unit-resolution #230 #66]: #145
-#540 := [unit-resolution #231 #539]: #60
-[unit-resolution #540 #546]: false
-unsat
-d463916fdbeb11527763c4fc4e327a5494ff68cb 43 0
-#2 := false
-decl f9 :: S3
-#30 := f9
-decl f5 :: (-> S5 S3 S3)
-decl f6 :: (-> S6 S2 S5)
-decl f21 :: S2
-#71 := f21
-decl f7 :: S6
-#8 := f7
-#72 := (f6 f7 f21)
-#73 := (f5 #72 f9)
-#74 := (= #73 f9)
-#75 := (not #74)
-#76 := (not #75)
-#107 := (iff #76 #74)
-#108 := [rewrite]: #107
-#106 := [asserted]: #76
-#111 := [mp #106 #108]: #74
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#647 := (pattern #12)
-#34 := (= #12 f9)
-#35 := (not #34)
-#673 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #647) #35)
-#36 := (forall (vars (?v0 S2) (?v1 S3)) #35)
-#676 := (iff #36 #673)
-#674 := (iff #35 #35)
-#675 := [refl]: #674
-#677 := [quant-intro #675]: #676
-#119 := (~ #36 #36)
-#145 := (~ #35 #35)
-#146 := [refl]: #145
-#120 := [nnf-pos #146]: #119
-#101 := [asserted]: #36
-#147 := [mp~ #101 #120]: #36
-#678 := [mp #147 #677]: #673
-#232 := (not #673)
-#318 := (or #232 #75)
-#233 := [quant-inst #71 #30]: #318
-[unit-resolution #233 #678 #111]: false
-unsat
-a60f866ab8b0e8fbdd294bcb1172f7ffdcef9940 47 0
-#2 := false
-decl f9 :: S3
-#30 := f9
-decl f5 :: (-> S5 S3 S3)
-decl f6 :: (-> S6 S2 S5)
-decl f22 :: S2
-#73 := f22
-decl f7 :: S6
-#8 := f7
-#74 := (f6 f7 f22)
-#75 := (f5 #74 f9)
-decl f21 :: S2
-#71 := f21
-#72 := (f6 f7 f21)
-#76 := (f5 #72 #75)
-#77 := (= #76 f9)
-#78 := (not #77)
-#79 := (not #78)
-#110 := (iff #79 #77)
-#111 := [rewrite]: #110
-#109 := [asserted]: #79
-#114 := [mp #109 #111]: #77
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#650 := (pattern #12)
-#34 := (= #12 f9)
-#35 := (not #34)
-#676 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #650) #35)
-#36 := (forall (vars (?v0 S2) (?v1 S3)) #35)
-#679 := (iff #36 #676)
-#677 := (iff #35 #35)
-#678 := [refl]: #677
-#680 := [quant-intro #678]: #679
-#122 := (~ #36 #36)
-#148 := (~ #35 #35)
-#149 := [refl]: #148
-#123 := [nnf-pos #149]: #122
-#104 := [asserted]: #36
-#150 := [mp~ #104 #123]: #36
-#681 := [mp #150 #680]: #676
-#236 := (not #676)
-#311 := (or #236 #78)
-#312 := [quant-inst #71 #75]: #311
-[unit-resolution #312 #681 #114]: false
-unsat
-fd1fe80b67edb2604eeb6ac16a3ead94827c31fa 119 0
-#2 := false
-decl f22 :: S2
-#72 := f22
-decl f21 :: S2
-#71 := f21
-#73 := (= f21 f22)
-decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#30 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f7 :: S6
-#8 := f7
-#77 := (f6 f7 f22)
-#78 := (f5 #77 f9)
-#75 := (f6 f7 f21)
-#76 := (f5 #75 f9)
-#79 := (= #76 #78)
-#634 := (iff #79 #73)
-#642 := (not #634)
-#80 := (not #79)
-#113 := (or #73 #80)
-#116 := (not #113)
-#74 := (not #73)
-#81 := (implies #74 #80)
-#82 := (not #81)
-#117 := (iff #82 #116)
-#114 := (iff #81 #113)
-#115 := [rewrite]: #114
-#118 := [monotonicity #115]: #117
-#112 := [asserted]: #82
-#121 := [mp #112 #118]: #116
-#120 := [not-or-elim #121]: #79
-#119 := [not-or-elim #121]: #74
-#284 := (or #642 #80 #73)
-#645 := [def-axiom]: #284
-#484 := [unit-resolution #645 #119 #120]: #642
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#22 := (:var 2 S3)
-#20 := (:var 3 S2)
-#21 := (f6 f7 #20)
-#23 := (f5 #21 #22)
-#672 := (pattern #23 #12)
-#26 := (= #22 #11)
-#175 := (not #26)
-#25 := (= #20 #9)
-#174 := (not #25)
-#141 := (or #174 #175)
-#142 := (not #141)
-#24 := (= #23 #12)
-#143 := (iff #24 #142)
-#673 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) (:pat #672) #143)
-#177 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #143)
-#676 := (iff #177 #673)
-#674 := (iff #143 #143)
-#675 := [refl]: #674
-#677 := [quant-intro #675]: #676
-#27 := (and #25 #26)
-#28 := (iff #24 #27)
-#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #28)
-#178 := (iff #29 #177)
-#144 := (iff #28 #143)
-#145 := (iff #27 #142)
-#146 := [rewrite]: #145
-#176 := [monotonicity #146]: #144
-#179 := [quant-intro #176]: #178
-#127 := (~ #29 #29)
-#153 := (~ #28 #28)
-#154 := [refl]: #153
-#128 := [nnf-pos #154]: #127
-#105 := [asserted]: #29
-#155 := [mp~ #105 #128]: #29
-#180 := [mp #155 #179]: #177
-#678 := [mp #180 #677]: #673
-#298 := (not #673)
-#299 := (or #298 #634)
-#244 := (= f9 f9)
-#330 := (not #244)
-#333 := (or #74 #330)
-#334 := (not #333)
-#335 := (iff #79 #334)
-#636 := (or #298 #335)
-#638 := (iff #636 #299)
-#640 := (iff #299 #299)
-#635 := [rewrite]: #640
-#296 := (iff #335 #634)
-#650 := (iff #334 #73)
-#648 := (not #74)
-#649 := (iff #648 #73)
-#308 := [rewrite]: #649
-#307 := (iff #334 #648)
-#652 := (iff #333 #74)
-#321 := (or #74 false)
-#656 := (iff #321 #74)
-#657 := [rewrite]: #656
-#654 := (iff #333 #321)
-#647 := (iff #330 false)
-#1 := true
-#315 := (not true)
-#309 := (iff #315 false)
-#440 := [rewrite]: #309
-#651 := (iff #330 #315)
-#332 := (iff #244 true)
-#336 := [rewrite]: #332
-#653 := [monotonicity #336]: #651
-#320 := [trans #653 #440]: #647
-#655 := [monotonicity #320]: #654
-#658 := [trans #655 #657]: #652
-#312 := [monotonicity #658]: #307
-#292 := [trans #312 #308]: #650
-#297 := [monotonicity #292]: #296
-#639 := [monotonicity #297]: #638
-#641 := [trans #639 #635]: #638
-#637 := [quant-inst #71 #30 #72 #30]: #636
-#278 := [mp #637 #641]: #299
-[unit-resolution #278 #678 #484]: false
-unsat
-fe733bec7d455e3d40da889cac8d554d86dc35a2 43 0
-#2 := false
-decl f21 :: S2
-#71 := f21
-decl f3 :: (-> S4 S3 S2)
-decl f5 :: (-> S5 S3 S3)
-decl f22 :: S3
-#73 := f22
-decl f6 :: (-> S6 S2 S5)
-decl f7 :: S6
-#8 := f7
-#72 := (f6 f7 f21)
-#74 := (f5 #72 f22)
-decl f4 :: S4
-#7 := f4
-#75 := (f3 f4 #74)
-#76 := (= #75 f21)
-#77 := (not #76)
-#107 := [asserted]: #77
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#645 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#646 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #645) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
-#649 := (iff #15 #646)
-#647 := (iff #14 #14)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#133 := (~ #15 #15)
-#131 := (~ #14 #14)
-#132 := [refl]: #131
-#134 := [nnf-pos #132]: #133
-#98 := [asserted]: #15
-#109 := [mp~ #98 #134]: #15
-#651 := [mp #109 #650]: #646
-#320 := (not #646)
-#321 := (or #320 #76)
-#318 := [quant-inst #71 #73]: #321
-[unit-resolution #318 #651 #107]: false
-unsat
-94935c8887f8b6d443c5b2bd496a539d3a28c865 42 0
-#2 := false
-decl f22 :: S3
-#73 := f22
-decl f5 :: (-> S5 S3 S3)
-decl f6 :: (-> S6 S2 S5)
-decl f21 :: S2
-#71 := f21
-decl f7 :: S6
-#8 := f7
-#72 := (f6 f7 f21)
-#74 := (f5 #72 f22)
-decl f8 :: S5
-#16 := f8
-#75 := (f5 f8 #74)
-#76 := (= #75 f22)
-#77 := (not #76)
-#107 := [asserted]: #77
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#645 := (pattern #12)
-#17 := (f5 f8 #12)
-#18 := (= #17 #11)
-#652 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #645) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
-#655 := (iff #19 #652)
-#653 := (iff #18 #18)
-#654 := [refl]: #653
-#656 := [quant-intro #654]: #655
-#111 := (~ #19 #19)
-#110 := (~ #18 #18)
-#135 := [refl]: #110
-#112 := [nnf-pos #135]: #111
-#99 := [asserted]: #19
-#136 := [mp~ #99 #112]: #19
-#657 := [mp #136 #656]: #652
-#637 := (not #652)
-#639 := (or #637 #76)
-#295 := [quant-inst #71 #73]: #639
-[unit-resolution #295 #657 #107]: false
-unsat
-6669da017744eefc6b42f0dcbe1d3e77a37840bc 51 0
-#2 := false
-decl f21 :: S2
-#71 := f21
-decl f3 :: (-> S4 S3 S2)
-decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#30 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f23 :: S2
-#75 := f23
-decl f7 :: S6
-#8 := f7
-#76 := (f6 f7 f23)
-#77 := (f5 #76 f9)
-decl f22 :: S2
-#73 := f22
-#74 := (f6 f7 f22)
-#78 := (f5 #74 #77)
-#72 := (f6 f7 f21)
-#79 := (f5 #72 #78)
-decl f4 :: S4
-#7 := f4
-#80 := (f3 f4 #79)
-#81 := (= #80 f21)
-#82 := (not #81)
-#112 := [asserted]: #82
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#650 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#651 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #650) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
-#654 := (iff #15 #651)
-#652 := (iff #14 #14)
-#653 := [refl]: #652
-#655 := [quant-intro #653]: #654
-#138 := (~ #15 #15)
-#136 := (~ #14 #14)
-#137 := [refl]: #136
-#139 := [nnf-pos #137]: #138
-#103 := [asserted]: #15
-#114 := [mp~ #103 #139]: #15
-#656 := [mp #114 #655]: #651
-#620 := (not #651)
-#527 := (or #620 #81)
-#533 := [quant-inst #71 #78]: #527
-[unit-resolution #533 #656 #112]: false
-unsat
-6ba377e7ca086c9c3b645a03c4012a7ef2a8cbb4 50 0
-#2 := false
-decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#30 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f23 :: S2
-#75 := f23
-decl f7 :: S6
-#8 := f7
-#76 := (f6 f7 f23)
-#77 := (f5 #76 f9)
-decl f22 :: S2
-#73 := f22
-#74 := (f6 f7 f22)
-#78 := (f5 #74 #77)
-decl f21 :: S2
-#71 := f21
-#72 := (f6 f7 f21)
-#79 := (f5 #72 #78)
-decl f8 :: S5
-#16 := f8
-#80 := (f5 f8 #79)
-#81 := (= #80 #78)
-#82 := (not #81)
-#112 := [asserted]: #82
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#650 := (pattern #12)
-#17 := (f5 f8 #12)
-#18 := (= #17 #11)
-#657 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #650) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
-#660 := (iff #19 #657)
-#658 := (iff #18 #18)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#116 := (~ #19 #19)
-#115 := (~ #18 #18)
-#140 := [refl]: #115
-#117 := [nnf-pos #140]: #116
-#104 := [asserted]: #19
-#141 := [mp~ #104 #117]: #19
-#662 := [mp #141 #661]: #657
-#618 := (not #657)
-#516 := (or #618 #81)
-#517 := [quant-inst #71 #78]: #516
-[unit-resolution #517 #662 #112]: false
-unsat
-657f931be01b08a5325b20b63a8ffb0654fcebb2 80 0
-#2 := false
-decl f22 :: S2
-#73 := f22
-decl f3 :: (-> S4 S3 S2)
-decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#30 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f23 :: S2
-#75 := f23
-decl f7 :: S6
-#8 := f7
-#76 := (f6 f7 f23)
-#77 := (f5 #76 f9)
-#74 := (f6 f7 f22)
-#78 := (f5 #74 #77)
-decl f21 :: S2
-#71 := f21
-#72 := (f6 f7 f21)
-#79 := (f5 #72 #78)
-decl f8 :: S5
-#16 := f8
-#80 := (f5 f8 #79)
-decl f4 :: S4
-#7 := f4
-#81 := (f3 f4 #80)
-#82 := (= #81 f22)
-#587 := (f3 f4 #78)
-#588 := (= #587 f22)
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#651 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#652 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #651) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
-#655 := (iff #15 #652)
-#653 := (iff #14 #14)
-#654 := [refl]: #653
-#656 := [quant-intro #654]: #655
-#139 := (~ #15 #15)
-#137 := (~ #14 #14)
-#138 := [refl]: #137
-#140 := [nnf-pos #138]: #139
-#104 := [asserted]: #15
-#115 := [mp~ #104 #140]: #15
-#657 := [mp #115 #656]: #652
-#621 := (not #652)
-#490 := (or #621 #588)
-#491 := [quant-inst #73 #77]: #490
-#534 := [unit-resolution #491 #657]: #588
-#522 := (= #81 #587)
-#528 := (= #80 #78)
-#17 := (f5 f8 #12)
-#18 := (= #17 #11)
-#658 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #651) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
-#661 := (iff #19 #658)
-#659 := (iff #18 #18)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#117 := (~ #19 #19)
-#116 := (~ #18 #18)
-#141 := [refl]: #116
-#118 := [nnf-pos #141]: #117
-#105 := [asserted]: #19
-#142 := [mp~ #105 #118]: #19
-#663 := [mp #142 #662]: #658
-#619 := (not #658)
-#518 := (or #619 #528)
-#521 := [quant-inst #71 #78]: #518
-#517 := [unit-resolution #521 #663]: #528
-#523 := [monotonicity #517]: #522
-#524 := [trans #523 #534]: #82
-#83 := (not #82)
-#113 := [asserted]: #83
-[unit-resolution #113 #524]: false
-unsat
-6920dfa78509845f35572b72b18b16e15101305a 61 0
-#2 := false
-decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#30 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f23 :: S2
-#75 := f23
-decl f7 :: S6
-#8 := f7
-#76 := (f6 f7 f23)
-#77 := (f5 #76 f9)
-decl f22 :: S2
-#73 := f22
-#74 := (f6 f7 f22)
-#78 := (f5 #74 #77)
-decl f21 :: S2
-#71 := f21
-#72 := (f6 f7 f21)
-#79 := (f5 #72 #78)
-decl f8 :: S5
-#16 := f8
-#80 := (f5 f8 #79)
-#81 := (f5 f8 #80)
-#82 := (= #81 #77)
-#488 := (f5 f8 #78)
-#489 := (= #488 #77)
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#651 := (pattern #12)
-#17 := (f5 f8 #12)
-#18 := (= #17 #11)
-#658 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #651) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
-#661 := (iff #19 #658)
-#659 := (iff #18 #18)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#117 := (~ #19 #19)
-#116 := (~ #18 #18)
-#141 := [refl]: #116
-#118 := [nnf-pos #141]: #117
-#105 := [asserted]: #19
-#142 := [mp~ #105 #118]: #19
-#663 := [mp #142 #662]: #658
-#619 := (not #658)
-#582 := (or #619 #489)
-#586 := [quant-inst #73 #77]: #582
-#534 := [unit-resolution #586 #663]: #489
-#522 := (= #81 #488)
-#528 := (= #80 #78)
-#518 := (or #619 #528)
-#521 := [quant-inst #71 #78]: #518
-#517 := [unit-resolution #521 #663]: #528
-#523 := [monotonicity #517]: #522
-#524 := [trans #523 #534]: #82
-#83 := (not #82)
-#113 := [asserted]: #83
-[unit-resolution #113 #524]: false
-unsat
-67bfe0df82f77831c5b5d717df54021f63993553 86 0
-#2 := false
-decl f28 :: S2
-#91 := f28
-decl f3 :: (-> S4 S5 S2)
-decl f10 :: (-> S10 S9 S5)
-decl f12 :: (-> S11 S9 S9)
-decl f16 :: S9
-#50 := f16
-decl f13 :: (-> S12 S5 S11)
-decl f5 :: (-> S6 S3 S5)
-decl f29 :: S3
-#93 := f29
-decl f6 :: (-> S7 S2 S6)
-decl f7 :: S7
-#8 := f7
-#92 := (f6 f7 f28)
-#94 := (f5 #92 f29)
-decl f14 :: S12
-#28 := f14
-#95 := (f13 f14 #94)
-#96 := (f12 #95 f16)
-decl f11 :: S10
-#27 := f11
-#97 := (f10 f11 #96)
-decl f4 :: S4
-#7 := f4
-#98 := (f3 f4 #97)
-#99 := (= #98 f28)
-#270 := (f3 f4 #94)
-#356 := (= #270 f28)
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#686 := (pattern #12)
-#13 := (f3 f4 #12)
-#14 := (= #13 #9)
-#687 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #686) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
-#690 := (iff #15 #687)
-#688 := (iff #14 #14)
-#689 := [refl]: #688
-#691 := [quant-intro #689]: #690
-#165 := (~ #15 #15)
-#163 := (~ #14 #14)
-#164 := [refl]: #163
-#166 := [nnf-pos #164]: #165
-#121 := [asserted]: #15
-#135 := [mp~ #121 #166]: #15
-#692 := [mp #135 #691]: #687
-#272 := (not #687)
-#358 := (or #272 #356)
-#349 := [quant-inst #91 #93]: #358
-#339 := [unit-resolution #349 #692]: #356
-#324 := (= #98 #270)
-#348 := (= #97 #94)
-#31 := (:var 0 S9)
-#29 := (:var 1 S5)
-#30 := (f13 f14 #29)
-#32 := (f12 #30 #31)
-#707 := (pattern #32)
-#33 := (f10 f11 #32)
-#34 := (= #33 #29)
-#708 := (forall (vars (?v0 S5) (?v1 S9)) (:pat #707) #34)
-#35 := (forall (vars (?v0 S5) (?v1 S9)) #34)
-#711 := (iff #35 #708)
-#709 := (iff #34 #34)
-#710 := [refl]: #709
-#712 := [quant-intro #710]: #711
-#141 := (~ #35 #35)
-#172 := (~ #34 #34)
-#173 := [refl]: #172
-#142 := [nnf-pos #173]: #141
-#124 := [asserted]: #35
-#174 := [mp~ #124 #142]: #35
-#713 := [mp #174 #712]: #708
-#685 := (not #708)
-#675 := (or #685 #348)
-#334 := [quant-inst #94 #50]: #675
-#676 := [unit-resolution #334 #713]: #348
-#325 := [monotonicity #676]: #324
-#326 := [trans #325 #339]: #99
-#100 := (not #99)
-#133 := [asserted]: #100
-[unit-resolution #133 #326]: false
-unsat
-bc229616226a7711a5d4d576e0d0f4d5a078be1a 86 0
-#2 := false
-decl f29 :: S3
-#93 := f29
-decl f8 :: (-> S8 S5 S3)
-decl f10 :: (-> S10 S9 S5)
-decl f12 :: (-> S11 S9 S9)
-decl f16 :: S9
-#50 := f16
-decl f13 :: (-> S12 S5 S11)
-decl f5 :: (-> S6 S3 S5)
-decl f6 :: (-> S7 S2 S6)
-decl f28 :: S2
-#91 := f28
-decl f7 :: S7
-#8 := f7
-#92 := (f6 f7 f28)
-#94 := (f5 #92 f29)
-decl f14 :: S12
-#28 := f14
-#95 := (f13 f14 #94)
-#96 := (f12 #95 f16)
-decl f11 :: S10
-#27 := f11
-#97 := (f10 f11 #96)
-decl f9 :: S8
-#16 := f9
-#98 := (f8 f9 #97)
-#99 := (= #98 f29)
-#271 := (f8 f9 #94)
-#357 := (= #271 f29)
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#686 := (pattern #12)
-#17 := (f8 f9 #12)
-#18 := (= #17 #11)
-#693 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #686) #18)
-#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
-#696 := (iff #19 #693)
-#694 := (iff #18 #18)
-#695 := [refl]: #694
-#697 := [quant-intro #695]: #696
-#137 := (~ #19 #19)
-#136 := (~ #18 #18)
-#167 := [refl]: #136
-#138 := [nnf-pos #167]: #137
-#122 := [asserted]: #19
-#168 := [mp~ #122 #138]: #19
-#698 := [mp #168 #697]: #693
-#362 := (not #693)
-#359 := (or #362 #357)
-#363 := [quant-inst #91 #93]: #359
-#339 := [unit-resolution #363 #698]: #357
-#324 := (= #98 #271)
-#348 := (= #97 #94)
-#31 := (:var 0 S9)
-#29 := (:var 1 S5)
-#30 := (f13 f14 #29)
-#32 := (f12 #30 #31)
-#707 := (pattern #32)
-#33 := (f10 f11 #32)
-#34 := (= #33 #29)
-#708 := (forall (vars (?v0 S5) (?v1 S9)) (:pat #707) #34)
-#35 := (forall (vars (?v0 S5) (?v1 S9)) #34)
-#711 := (iff #35 #708)
-#709 := (iff #34 #34)
-#710 := [refl]: #709
-#712 := [quant-intro #710]: #711
-#141 := (~ #35 #35)
-#172 := (~ #34 #34)
-#173 := [refl]: #172
-#142 := [nnf-pos #173]: #141
-#124 := [asserted]: #35
-#174 := [mp~ #124 #142]: #35
-#713 := [mp #174 #712]: #708
-#685 := (not #708)
-#675 := (or #685 #348)
-#334 := [quant-inst #94 #50]: #675
-#676 := [unit-resolution #334 #713]: #348
-#325 := [monotonicity #676]: #324
-#326 := [trans #325 #339]: #99
-#100 := (not #99)
-#133 := [asserted]: #100
-[unit-resolution #133 #326]: false
-unsat
-d3a42b698bae47402c814f1b2f6f58cd7ebe4316 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f15 :: S4
-#41 := f15
-decl f4 :: S3
-#7 := f4
-#44 := (f3 f4 f15)
-decl f14 :: S4
-#40 := f14
-#43 := (f3 f4 f14)
-#45 := (= #43 #44)
-#42 := (= f14 f15)
-#75 := (not #42)
-#76 := (or #75 #45)
-#79 := (not #76)
-#46 := (implies #42 #45)
-#47 := (not #46)
-#80 := (iff #47 #79)
-#77 := (iff #46 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#74 := [asserted]: #47
-#84 := [mp #74 #81]: #79
-#82 := [not-or-elim #84]: #42
-#263 := [monotonicity #82]: #45
-#83 := (not #45)
-#85 := [not-or-elim #84]: #83
-[unit-resolution #85 #263]: false
-unsat
-f8f306e974a6666087b450cae3e82e5cd03defda 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f15 :: S4
-#41 := f15
-decl f6 :: S3
-#15 := f6
-#44 := (f3 f6 f15)
-decl f14 :: S4
-#40 := f14
-#43 := (f3 f6 f14)
-#45 := (= #43 #44)
-#42 := (= f14 f15)
-#75 := (not #42)
-#76 := (or #75 #45)
-#79 := (not #76)
-#46 := (implies #42 #45)
-#47 := (not #46)
-#80 := (iff #47 #79)
-#77 := (iff #46 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#74 := [asserted]: #47
-#84 := [mp #74 #81]: #79
-#82 := [not-or-elim #84]: #42
-#263 := [monotonicity #82]: #45
-#83 := (not #45)
-#85 := [not-or-elim #84]: #83
-[unit-resolution #85 #263]: false
-unsat
-c01d80ea8f25cbcdb60031023ba4082a204411e5 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f15 :: S4
-#42 := f15
-decl f4 :: S3
-#7 := f4
-#43 := (f3 f4 f15)
-decl f14 :: S4
-#40 := f14
-#41 := (f3 f4 f14)
-#44 := (= #41 #43)
-#46 := (= f14 f15)
-#47 := (not #46)
-#77 := (or #44 #47)
-#80 := (not #77)
-#45 := (not #44)
-#48 := (implies #45 #47)
-#49 := (not #48)
-#81 := (iff #49 #80)
-#78 := (iff #48 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#76 := [asserted]: #49
-#85 := [mp #76 #82]: #80
-#84 := [not-or-elim #85]: #46
-#263 := [monotonicity #84]: #44
-#83 := [not-or-elim #85]: #45
-[unit-resolution #83 #263]: false
-unsat
-290727ed1ecffbc64e78f5a8cac18f251acb752f 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f15 :: S4
-#42 := f15
-decl f6 :: S3
-#15 := f6
-#43 := (f3 f6 f15)
-decl f14 :: S4
-#40 := f14
-#41 := (f3 f6 f14)
-#44 := (= #41 #43)
-#46 := (= f14 f15)
-#47 := (not #46)
-#77 := (or #44 #47)
-#80 := (not #77)
-#45 := (not #44)
-#48 := (implies #45 #47)
-#49 := (not #48)
-#81 := (iff #49 #80)
-#78 := (iff #48 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#76 := [asserted]: #49
-#85 := [mp #76 #82]: #80
-#84 := [not-or-elim #85]: #46
-#263 := [monotonicity #84]: #44
-#83 := [not-or-elim #85]: #45
-[unit-resolution #83 #263]: false
-unsat
-d178969acccf74676532ed1f0d7dc4526faab060 39 0
-#2 := false
-#40 := 3::Int
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f14 :: S2
-#42 := f14
-#41 := 4::Int
-#43 := (f5 3::Int 4::Int f14)
-decl f4 :: S3
-#7 := f4
-#44 := (f3 f4 #43)
-#45 := (= #44 3::Int)
-#46 := (not #45)
-#73 := [asserted]: #46
-#10 := (:var 0 S2)
-#9 := (:var 1 Int)
-#8 := (:var 2 Int)
-#11 := (f5 #8 #9 #10)
-#165 := (pattern #11)
-#12 := (f3 f4 #11)
-#13 := (= #12 #8)
-#166 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #165) #13)
-#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
-#169 := (iff #14 #166)
-#167 := (iff #13 #13)
-#168 := [refl]: #167
-#170 := [quant-intro #168]: #169
-#77 := (~ #14 #14)
-#75 := (~ #13 #13)
-#76 := [refl]: #75
-#78 := [nnf-pos #76]: #77
-#67 := [asserted]: #14
-#79 := [mp~ #67 #78]: #14
-#171 := [mp #79 #170]: #166
-#215 := (not #166)
-#216 := (or #215 #45)
-#217 := [quant-inst #40 #41 #42]: #216
-[unit-resolution #217 #171 #73]: false
-unsat
-3eb6c851edd6fd9da06cca67794a3b348ac3058b 39 0
-#2 := false
-#41 := 4::Int
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f14 :: S2
-#42 := f14
-#40 := 3::Int
-#43 := (f5 3::Int 4::Int f14)
-decl f6 :: S3
-#15 := f6
-#44 := (f3 f6 #43)
-#45 := (= #44 4::Int)
-#46 := (not #45)
-#73 := [asserted]: #46
-#10 := (:var 0 S2)
-#9 := (:var 1 Int)
-#8 := (:var 2 Int)
-#11 := (f5 #8 #9 #10)
-#165 := (pattern #11)
-#16 := (f3 f6 #11)
-#17 := (= #16 #9)
-#172 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #165) #17)
-#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
-#175 := (iff #18 #172)
-#173 := (iff #17 #17)
-#174 := [refl]: #173
-#176 := [quant-intro #174]: #175
-#82 := (~ #18 #18)
-#80 := (~ #17 #17)
-#81 := [refl]: #80
-#83 := [nnf-pos #81]: #82
-#68 := [asserted]: #18
-#84 := [mp~ #68 #83]: #18
-#177 := [mp #84 #176]: #172
-#220 := (not #172)
-#221 := (or #220 #45)
-#222 := [quant-inst #40 #41 #42]: #221
-[unit-resolution #222 #177 #73]: false
-unsat
-81324eb3e1a2baf8f2353f71658e6c45eca7efde 78 0
-#2 := false
-#41 := 4::Int
-#40 := 3::Int
-#234 := (= 3::Int 4::Int)
-#236 := (iff #234 false)
-#237 := [rewrite]: #236
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f14 :: S2
-#42 := f14
-#43 := (f5 3::Int 4::Int f14)
-decl f6 :: S3
-#15 := f6
-#45 := (f3 f6 #43)
-#216 := (= #45 4::Int)
-#10 := (:var 0 S2)
-#9 := (:var 1 Int)
-#8 := (:var 2 Int)
-#11 := (f5 #8 #9 #10)
-#170 := (pattern #11)
-#16 := (f3 f6 #11)
-#17 := (= #16 #9)
-#177 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #170) #17)
-#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
-#180 := (iff #18 #177)
-#178 := (iff #17 #17)
-#179 := [refl]: #178
-#181 := [quant-intro #179]: #180
-#87 := (~ #18 #18)
-#85 := (~ #17 #17)
-#86 := [refl]: #85
-#88 := [nnf-pos #86]: #87
-#70 := [asserted]: #18
-#89 := [mp~ #70 #88]: #18
-#182 := [mp #89 #181]: #177
-#225 := (not #177)
-#226 := (or #225 #216)
-#227 := [quant-inst #40 #41 #42]: #226
-#220 := [unit-resolution #227 #182]: #216
-#232 := (= 3::Int #45)
-#230 := (= #45 3::Int)
-decl f4 :: S3
-#7 := f4
-#44 := (f3 f4 #43)
-#215 := (= #44 3::Int)
-#12 := (f3 f4 #11)
-#13 := (= #12 #8)
-#171 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #170) #13)
-#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
-#174 := (iff #14 #171)
-#172 := (iff #13 #13)
-#173 := [refl]: #172
-#175 := [quant-intro #173]: #174
-#82 := (~ #14 #14)
-#79 := (~ #13 #13)
-#81 := [refl]: #79
-#83 := [nnf-pos #81]: #82
-#69 := [asserted]: #14
-#84 := [mp~ #69 #83]: #14
-#176 := [mp #84 #175]: #171
-#221 := (not #171)
-#222 := (or #221 #215)
-#223 := [quant-inst #40 #41 #42]: #222
-#224 := [unit-resolution #223 #176]: #215
-#228 := (= #45 #44)
-#46 := (= #44 #45)
-#47 := (not #46)
-#48 := (not #47)
-#76 := (iff #48 #46)
-#77 := [rewrite]: #76
-#75 := [asserted]: #48
-#80 := [mp #75 #77]: #46
-#229 := [symm #80]: #228
-#231 := [trans #229 #224]: #230
-#233 := [symm #231]: #232
-#235 := [trans #233 #220]: #234
-[mp #235 #237]: false
-unsat
-778cf00b027f7cbc8557b11fe4d2c6d98c19dbcf 73 0
-#2 := false
-decl f7 :: (-> Int Int S3 S5)
-decl f15 :: S3
-#49 := f15
-#48 := 4::Int
-#11 := 5::Int
-#52 := (f7 5::Int 4::Int f15)
-decl f11 :: (-> S2 S5 S5)
-#47 := 3::Int
-#50 := (f7 3::Int 4::Int f15)
-decl f4 :: S2
-#7 := f4
-#51 := (f11 f4 #50)
-#53 := (= #51 #52)
-decl f3 :: (-> S2 Int Int)
-#248 := (f3 f4 3::Int)
-#249 := (f7 #248 4::Int f15)
-#278 := (= #249 #52)
-#276 := (= #52 #249)
-#270 := (= 5::Int #248)
-#266 := (= #248 5::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 5::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#86 := (~ #13 #13)
-#84 := (~ #12 #12)
-#85 := [refl]: #84
-#87 := [nnf-pos #85]: #86
-#75 := [asserted]: #13
-#88 := [mp~ #75 #87]: #13
-#271 := (not #13)
-#272 := (or #271 #266)
-#273 := [quant-inst #47]: #272
-#267 := [unit-resolution #273 #88]: #266
-#274 := [symm #267]: #270
-#277 := [monotonicity #274]: #276
-#279 := [symm #277]: #278
-#252 := (= #51 #249)
-#17 := (:var 0 S3)
-#16 := (:var 1 Int)
-#15 := (:var 2 Int)
-#30 := (:var 3 S2)
-#32 := (f3 #30 #15)
-#33 := (f7 #32 #16 #17)
-#198 := (pattern #33)
-#18 := (f7 #15 #16 #17)
-#31 := (f11 #30 #18)
-#197 := (pattern #31)
-#34 := (= #31 #33)
-#199 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #197 #198) #34)
-#35 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #34)
-#202 := (iff #35 #199)
-#200 := (iff #34 #34)
-#201 := [refl]: #200
-#203 := [quant-intro #201]: #202
-#106 := (~ #35 #35)
-#104 := (~ #34 #34)
-#105 := [refl]: #104
-#107 := [nnf-pos #105]: #106
-#79 := [asserted]: #35
-#108 := [mp~ #79 #107]: #35
-#204 := [mp #108 #203]: #199
-#255 := (not #199)
-#256 := (or #255 #252)
-#257 := [quant-inst #7 #47 #48 #49]: #256
-#275 := [unit-resolution #257 #204]: #252
-#280 := [trans #275 #279]: #53
-#54 := (not #53)
-#82 := [asserted]: #54
-[unit-resolution #82 #280]: false
-unsat
-55dc0c2cede66f579f8fb4205f494991679ed411 73 0
-#2 := false
-decl f7 :: (-> Int Int S3 S5)
-decl f15 :: S3
-#49 := f15
-#11 := 6::Int
-#47 := 3::Int
-#52 := (f7 3::Int 6::Int f15)
-decl f12 :: (-> S2 S5 S5)
-#48 := 4::Int
-#50 := (f7 3::Int 4::Int f15)
-decl f4 :: S2
-#7 := f4
-#51 := (f12 f4 #50)
-#53 := (= #51 #52)
-decl f3 :: (-> S2 Int Int)
-#249 := (f3 f4 4::Int)
-#250 := (f7 3::Int #249 f15)
-#279 := (= #250 #52)
-#277 := (= #52 #250)
-#271 := (= 6::Int #249)
-#267 := (= #249 6::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 6::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#86 := (~ #13 #13)
-#84 := (~ #12 #12)
-#85 := [refl]: #84
-#87 := [nnf-pos #85]: #86
-#75 := [asserted]: #13
-#88 := [mp~ #75 #87]: #13
-#272 := (not #13)
-#273 := (or #272 #267)
-#274 := [quant-inst #48]: #273
-#268 := [unit-resolution #274 #88]: #267
-#275 := [symm #268]: #271
-#278 := [monotonicity #275]: #277
-#280 := [symm #278]: #279
-#253 := (= #51 #250)
-#17 := (:var 0 S3)
-#16 := (:var 1 Int)
-#30 := (:var 3 S2)
-#37 := (f3 #30 #16)
-#15 := (:var 2 Int)
-#38 := (f7 #15 #37 #17)
-#207 := (pattern #38)
-#18 := (f7 #15 #16 #17)
-#36 := (f12 #30 #18)
-#206 := (pattern #36)
-#39 := (= #36 #38)
-#208 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #206 #207) #39)
-#40 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #39)
-#211 := (iff #40 #208)
-#209 := (iff #39 #39)
-#210 := [refl]: #209
-#212 := [quant-intro #210]: #211
-#111 := (~ #40 #40)
-#109 := (~ #39 #39)
-#110 := [refl]: #109
-#112 := [nnf-pos #110]: #111
-#80 := [asserted]: #40
-#113 := [mp~ #80 #112]: #40
-#213 := [mp #113 #212]: #208
-#256 := (not #208)
-#257 := (or #256 #253)
-#258 := [quant-inst #7 #47 #48 #49]: #257
-#276 := [unit-resolution #258 #213]: #253
-#281 := [trans #276 #280]: #53
-#54 := (not #53)
-#82 := [asserted]: #54
-[unit-resolution #82 #281]: false
-unsat
-da8cf7e5a8bc928fda4951f71c6fd4dffe39e0c9 141 0
-#2 := false
-decl f16 :: S5
-#53 := f16
-decl f13 :: (-> S2 S5 S5)
-decl f12 :: (-> S2 S5 S5)
-decl f5 :: S2
-#14 := f5
-#57 := (f12 f5 f16)
-decl f4 :: S2
-#7 := f4
-#58 := (f13 f4 #57)
-#59 := (= #58 f16)
-decl f8 :: (-> Int Int S3 S5)
-decl f17 :: S3
-#54 := f17
-#11 := 4::Int
-#17 := 3::Int
-#55 := (f8 3::Int 4::Int f17)
-#327 := (= #55 f16)
-#56 := (= f16 #55)
-#91 := (not #56)
-#92 := (or #91 #59)
-#95 := (not #92)
-#60 := (implies #56 #59)
-#61 := (not #60)
-#96 := (iff #61 #95)
-#93 := (iff #60 #92)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#90 := [asserted]: #61
-#100 := [mp #90 #97]: #95
-#98 := [not-or-elim #100]: #56
-#328 := [symm #98]: #327
-#331 := (= #58 #55)
-decl f3 :: (-> S2 Int Int)
-#285 := (f3 f4 4::Int)
-#247 := (f3 f5 3::Int)
-#289 := (f8 #247 #285 f17)
-#325 := (= #289 #55)
-#309 := (= #285 4::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 4::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#105 := (~ #13 #13)
-#103 := (~ #12 #12)
-#104 := [refl]: #103
-#106 := [nnf-pos #104]: #105
-#82 := [asserted]: #13
-#107 := [mp~ #82 #106]: #13
-#314 := (not #13)
-#315 := (or #314 #309)
-#316 := [quant-inst #11]: #315
-#310 := [unit-resolution #316 #107]: #309
-#281 := (= #247 3::Int)
-#15 := (f3 f5 #8)
-#16 := (pattern #15)
-#18 := (= #15 3::Int)
-#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
-#110 := (~ #19 #19)
-#108 := (~ #18 #18)
-#109 := [refl]: #108
-#111 := [nnf-pos #109]: #110
-#83 := [asserted]: #19
-#112 := [mp~ #83 #111]: #19
-#286 := (not #19)
-#287 := (or #286 #281)
-#288 := [quant-inst #17]: #287
-#313 := [unit-resolution #288 #112]: #281
-#326 := [monotonicity #313 #310]: #325
-#329 := (= #58 #289)
-#248 := (f8 #247 4::Int f17)
-#282 := (f13 f4 #248)
-#290 := (= #282 #289)
-#23 := (:var 0 S3)
-#22 := (:var 1 Int)
-#36 := (:var 3 S2)
-#43 := (f3 #36 #22)
-#21 := (:var 2 Int)
-#44 := (f8 #21 #43 #23)
-#231 := (pattern #44)
-#24 := (f8 #21 #22 #23)
-#42 := (f13 #36 #24)
-#230 := (pattern #42)
-#45 := (= #42 #44)
-#232 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #230 #231) #45)
-#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #45)
-#235 := (iff #46 #232)
-#233 := (iff #45 #45)
-#234 := [refl]: #233
-#236 := [quant-intro #234]: #235
-#135 := (~ #46 #46)
-#133 := (~ #45 #45)
-#134 := [refl]: #133
-#136 := [nnf-pos #134]: #135
-#88 := [asserted]: #46
-#137 := [mp~ #88 #136]: #46
-#237 := [mp #137 #236]: #232
-#293 := (not #232)
-#294 := (or #293 #290)
-#295 := [quant-inst #7 #247 #11 #54]: #294
-#317 := [unit-resolution #295 #237]: #290
-#323 := (= #58 #282)
-#321 := (= #57 #248)
-#246 := (f12 f5 #55)
-#252 := (= #246 #248)
-#38 := (f3 #36 #21)
-#39 := (f8 #38 #22 #23)
-#223 := (pattern #39)
-#37 := (f12 #36 #24)
-#222 := (pattern #37)
-#40 := (= #37 #39)
-#224 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #222 #223) #40)
-#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #40)
-#227 := (iff #41 #224)
-#225 := (iff #40 #40)
-#226 := [refl]: #225
-#228 := [quant-intro #226]: #227
-#130 := (~ #41 #41)
-#128 := (~ #40 #40)
-#129 := [refl]: #128
-#131 := [nnf-pos #129]: #130
-#87 := [asserted]: #41
-#132 := [mp~ #87 #131]: #41
-#229 := [mp #132 #228]: #224
-#255 := (not #224)
-#256 := (or #255 #252)
-#257 := [quant-inst #14 #17 #11 #54]: #256
-#318 := [unit-resolution #257 #229]: #252
-#319 := (= #57 #246)
-#320 := [monotonicity #98]: #319
-#322 := [trans #320 #318]: #321
-#324 := [monotonicity #322]: #323
-#330 := [trans #324 #317]: #329
-#332 := [trans #330 #326]: #331
-#333 := [trans #332 #328]: #59
-#99 := (not #59)
-#101 := [not-or-elim #100]: #99
-[unit-resolution #101 #333]: false
-unsat
-d0a240ecffa93b4cb78f7dba7d0cec224dce11ff 141 0
-#2 := false
-decl f16 :: S5
-#53 := f16
-decl f12 :: (-> S2 S5 S5)
-decl f13 :: (-> S2 S5 S5)
-decl f4 :: S2
-#7 := f4
-#57 := (f13 f4 f16)
-decl f5 :: S2
-#14 := f5
-#58 := (f12 f5 #57)
-#59 := (= #58 f16)
-decl f8 :: (-> Int Int S3 S5)
-decl f17 :: S3
-#54 := f17
-#11 := 4::Int
-#17 := 3::Int
-#55 := (f8 3::Int 4::Int f17)
-#327 := (= #55 f16)
-#56 := (= f16 #55)
-#91 := (not #56)
-#92 := (or #91 #59)
-#95 := (not #92)
-#60 := (implies #56 #59)
-#61 := (not #60)
-#96 := (iff #61 #95)
-#93 := (iff #60 #92)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#90 := [asserted]: #61
-#100 := [mp #90 #97]: #95
-#98 := [not-or-elim #100]: #56
-#328 := [symm #98]: #327
-#331 := (= #58 #55)
-decl f3 :: (-> S2 Int Int)
-#247 := (f3 f4 4::Int)
-#285 := (f3 f5 3::Int)
-#289 := (f8 #285 #247 f17)
-#325 := (= #289 #55)
-#281 := (= #247 4::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 4::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#105 := (~ #13 #13)
-#103 := (~ #12 #12)
-#104 := [refl]: #103
-#106 := [nnf-pos #104]: #105
-#82 := [asserted]: #13
-#107 := [mp~ #82 #106]: #13
-#286 := (not #13)
-#287 := (or #286 #281)
-#288 := [quant-inst #11]: #287
-#310 := [unit-resolution #288 #107]: #281
-#309 := (= #285 3::Int)
-#15 := (f3 f5 #8)
-#16 := (pattern #15)
-#18 := (= #15 3::Int)
-#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
-#110 := (~ #19 #19)
-#108 := (~ #18 #18)
-#109 := [refl]: #108
-#111 := [nnf-pos #109]: #110
-#83 := [asserted]: #19
-#112 := [mp~ #83 #111]: #19
-#314 := (not #19)
-#315 := (or #314 #309)
-#316 := [quant-inst #17]: #315
-#313 := [unit-resolution #316 #112]: #309
-#326 := [monotonicity #313 #310]: #325
-#329 := (= #58 #289)
-#248 := (f8 3::Int #247 f17)
-#282 := (f12 f5 #248)
-#290 := (= #282 #289)
-#23 := (:var 0 S3)
-#22 := (:var 1 Int)
-#21 := (:var 2 Int)
-#36 := (:var 3 S2)
-#38 := (f3 #36 #21)
-#39 := (f8 #38 #22 #23)
-#223 := (pattern #39)
-#24 := (f8 #21 #22 #23)
-#37 := (f12 #36 #24)
-#222 := (pattern #37)
-#40 := (= #37 #39)
-#224 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #222 #223) #40)
-#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #40)
-#227 := (iff #41 #224)
-#225 := (iff #40 #40)
-#226 := [refl]: #225
-#228 := [quant-intro #226]: #227
-#130 := (~ #41 #41)
-#128 := (~ #40 #40)
-#129 := [refl]: #128
-#131 := [nnf-pos #129]: #130
-#87 := [asserted]: #41
-#132 := [mp~ #87 #131]: #41
-#229 := [mp #132 #228]: #224
-#293 := (not #224)
-#294 := (or #293 #290)
-#295 := [quant-inst #14 #17 #247 #54]: #294
-#317 := [unit-resolution #295 #229]: #290
-#323 := (= #58 #282)
-#321 := (= #57 #248)
-#246 := (f13 f4 #55)
-#252 := (= #246 #248)
-#43 := (f3 #36 #22)
-#44 := (f8 #21 #43 #23)
-#231 := (pattern #44)
-#42 := (f13 #36 #24)
-#230 := (pattern #42)
-#45 := (= #42 #44)
-#232 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #230 #231) #45)
-#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #45)
-#235 := (iff #46 #232)
-#233 := (iff #45 #45)
-#234 := [refl]: #233
-#236 := [quant-intro #234]: #235
-#135 := (~ #46 #46)
-#133 := (~ #45 #45)
-#134 := [refl]: #133
-#136 := [nnf-pos #134]: #135
-#88 := [asserted]: #46
-#137 := [mp~ #88 #136]: #46
-#237 := [mp #137 #236]: #232
-#255 := (not #232)
-#256 := (or #255 #252)
-#257 := [quant-inst #7 #17 #11 #54]: #256
-#318 := [unit-resolution #257 #237]: #252
-#319 := (= #57 #246)
-#320 := [monotonicity #98]: #319
-#322 := [trans #320 #318]: #321
-#324 := [monotonicity #322]: #323
-#330 := [trans #324 #317]: #329
-#332 := [trans #330 #326]: #331
-#333 := [trans #332 #328]: #59
-#99 := (not #59)
-#101 := [not-or-elim #100]: #99
-[unit-resolution #101 #333]: false
-unsat
-4836e6abfc464cb08dddd05f1d512ded74175de4 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f26 :: S4
-#73 := f26
-decl f4 :: S3
-#7 := f4
-#76 := (f3 f4 f26)
-decl f25 :: S4
-#72 := f25
-#75 := (f3 f4 f25)
-#77 := (= #75 #76)
-#74 := (= f25 f26)
-#111 := (not #74)
-#112 := (or #111 #77)
-#115 := (not #112)
-#78 := (implies #74 #77)
-#79 := (not #78)
-#116 := (iff #79 #115)
-#113 := (iff #78 #112)
-#114 := [rewrite]: #113
-#117 := [monotonicity #114]: #116
-#110 := [asserted]: #79
-#120 := [mp #110 #117]: #115
-#118 := [not-or-elim #120]: #74
-#318 := [monotonicity #118]: #77
-#119 := (not #77)
-#121 := [not-or-elim #120]: #119
-[unit-resolution #121 #318]: false
-unsat
-f99b4650b4bda1046395cb9c27fb7acec91a2f4f 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f26 :: S4
-#73 := f26
-decl f6 :: S3
-#15 := f6
-#76 := (f3 f6 f26)
-decl f25 :: S4
-#72 := f25
-#75 := (f3 f6 f25)
-#77 := (= #75 #76)
-#74 := (= f25 f26)
-#111 := (not #74)
-#112 := (or #111 #77)
-#115 := (not #112)
-#78 := (implies #74 #77)
-#79 := (not #78)
-#116 := (iff #79 #115)
-#113 := (iff #78 #112)
-#114 := [rewrite]: #113
-#117 := [monotonicity #114]: #116
-#110 := [asserted]: #79
-#120 := [mp #110 #117]: #115
-#118 := [not-or-elim #120]: #74
-#318 := [monotonicity #118]: #77
-#119 := (not #77)
-#121 := [not-or-elim #120]: #119
-[unit-resolution #121 #318]: false
-unsat
-1b3a7b1fc51d4c34ff662c61cf90322ecc09e078 61 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f14 :: (-> S9 S4 S1)
-decl f25 :: S4
-#72 := f25
-decl f15 :: S9
-#40 := f15
-#75 := (f14 f15 f25)
-#76 := (= #75 f1)
-decl f26 :: S4
-#73 := f26
-#77 := (f14 f15 f26)
-#78 := (= #77 f1)
-#643 := (iff #78 #76)
-#79 := (iff #76 #78)
-#649 := (= #75 #77)
-#74 := (= f25 f26)
-#113 := (not #74)
-#114 := (or #113 #79)
-#117 := (not #114)
-#80 := (implies #74 #79)
-#81 := (not #80)
-#118 := (iff #81 #117)
-#115 := (iff #80 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116]: #118
-#112 := [asserted]: #81
-#122 := [mp #112 #119]: #117
-#120 := [not-or-elim #122]: #74
-#305 := [monotonicity #120]: #649
-#436 := [monotonicity #305]: #79
-#316 := [symm #436]: #643
-#149 := (not #76)
-#325 := (not #78)
-#317 := (iff #325 #149)
-#650 := [monotonicity #316]: #317
-#311 := [hypothesis]: #325
-#651 := [mp #311 #650]: #149
-#328 := (or #76 #78)
-#150 := (iff #149 #78)
-#121 := (not #79)
-#151 := (iff #121 #150)
-#152 := [rewrite]: #151
-#123 := [not-or-elim #122]: #121
-#153 := [mp #123 #152]: #150
-#326 := (not #150)
-#330 := (or #76 #78 #326)
-#331 := [def-axiom]: #330
-#332 := [unit-resolution #331 #153]: #328
-#647 := [unit-resolution #332 #311]: #76
-#652 := [unit-resolution #647 #651]: false
-#653 := [lemma #652]: #78
-#654 := [mp #653 #316]: #76
-#318 := (or #149 #325)
-#242 := (or #149 #325 #326)
-#327 := [def-axiom]: #242
-#329 := [unit-resolution #327 #153]: #318
-#648 := [unit-resolution #329 #653]: #149
-[unit-resolution #648 #654]: false
-unsat
-58757bb2c94bdd593c9d8b0fbe00db43524398ac 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f26 :: S4
-#74 := f26
-decl f4 :: S3
-#7 := f4
-#75 := (f3 f4 f26)
-decl f25 :: S4
-#72 := f25
-#73 := (f3 f4 f25)
-#76 := (= #73 #75)
-#78 := (= f25 f26)
-#79 := (not #78)
-#113 := (or #76 #79)
-#116 := (not #113)
-#77 := (not #76)
-#80 := (implies #77 #79)
-#81 := (not #80)
-#117 := (iff #81 #116)
-#114 := (iff #80 #113)
-#115 := [rewrite]: #114
-#118 := [monotonicity #115]: #117
-#112 := [asserted]: #81
-#121 := [mp #112 #118]: #116
-#120 := [not-or-elim #121]: #78
-#318 := [monotonicity #120]: #76
-#119 := [not-or-elim #121]: #77
-[unit-resolution #119 #318]: false
-unsat
-ef9a1a3fd0640f615d1a4ca50416456c2aafb0a5 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f26 :: S4
-#74 := f26
-decl f6 :: S3
-#15 := f6
-#75 := (f3 f6 f26)
-decl f25 :: S4
-#72 := f25
-#73 := (f3 f6 f25)
-#76 := (= #73 #75)
-#78 := (= f25 f26)
-#79 := (not #78)
-#113 := (or #76 #79)
-#116 := (not #113)
-#77 := (not #76)
-#80 := (implies #77 #79)
-#81 := (not #80)
-#117 := (iff #81 #116)
-#114 := (iff #80 #113)
-#115 := [rewrite]: #114
-#118 := [monotonicity #115]: #117
-#112 := [asserted]: #81
-#121 := [mp #112 #118]: #116
-#120 := [not-or-elim #121]: #78
-#318 := [monotonicity #120]: #76
-#119 := [not-or-elim #121]: #77
-[unit-resolution #119 #318]: false
-unsat
-a0e1cfb251466df6713d328d9fc59e2beb3ff57a 66 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f14 :: (-> S9 S4 S1)
-decl f25 :: S4
-#72 := f25
-decl f15 :: S9
-#40 := f15
-#73 := (f14 f15 f25)
-#74 := (= #73 f1)
-decl f26 :: S4
-#75 := f26
-#76 := (f14 f15 f26)
-#77 := (= #76 f1)
-#648 := (iff #77 #74)
-#78 := (iff #74 #77)
-#654 := (= #73 #76)
-#80 := (= f25 f26)
-#81 := (not #80)
-#122 := (or #78 #81)
-#127 := (not #122)
-#79 := (not #78)
-#82 := (implies #79 #81)
-#83 := (not #82)
-#128 := (iff #83 #127)
-#125 := (iff #82 #122)
-#115 := (not #74)
-#116 := (iff #115 #77)
-#119 := (implies #116 #81)
-#123 := (iff #119 #122)
-#124 := [rewrite]: #123
-#120 := (iff #82 #119)
-#117 := (iff #79 #116)
-#118 := [rewrite]: #117
-#121 := [monotonicity #118]: #120
-#126 := [trans #121 #124]: #125
-#129 := [monotonicity #126]: #128
-#114 := [asserted]: #83
-#132 := [mp #114 #129]: #127
-#131 := [not-or-elim #132]: #80
-#310 := [monotonicity #131]: #654
-#441 := [monotonicity #310]: #78
-#321 := [symm #441]: #648
-#330 := (not #77)
-#322 := (iff #330 #115)
-#655 := [monotonicity #321]: #322
-#316 := [hypothesis]: #330
-#656 := [mp #316 #655]: #115
-#333 := (or #74 #77)
-#130 := [not-or-elim #132]: #79
-#156 := [mp #130 #118]: #116
-#331 := (not #116)
-#335 := (or #74 #77 #331)
-#336 := [def-axiom]: #335
-#337 := [unit-resolution #336 #156]: #333
-#652 := [unit-resolution #337 #316]: #74
-#657 := [unit-resolution #652 #656]: false
-#658 := [lemma #657]: #77
-#659 := [mp #658 #321]: #74
-#323 := (or #115 #330)
-#247 := (or #115 #330 #331)
-#332 := [def-axiom]: #247
-#334 := [unit-resolution #332 #156]: #323
-#653 := [unit-resolution #334 #658]: #115
-[unit-resolution #653 #659]: false
-unsat
-3008f68b045e8512a78630fd63e36767a288b498 47 0
-#2 := false
-#72 := 3::Int
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f16 :: (-> S10 S8 S2)
-decl f26 :: S8
-#76 := f26
-decl f17 :: (-> S11 S1 S10)
-decl f25 :: S1
-#74 := f25
-decl f18 :: S11
-#42 := f18
-#75 := (f17 f18 f25)
-#77 := (f16 #75 f26)
-#73 := 4::Int
-#78 := (f5 3::Int 4::Int #77)
-decl f4 :: S3
-#7 := f4
-#79 := (f3 f4 #78)
-#80 := (= #79 3::Int)
-#81 := (not #80)
-#112 := [asserted]: #81
-#10 := (:var 0 S2)
-#9 := (:var 1 Int)
-#8 := (:var 2 Int)
-#11 := (f5 #8 #9 #10)
-#224 := (pattern #11)
-#12 := (f3 f4 #11)
-#13 := (= #12 #8)
-#225 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #224) #13)
-#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
-#228 := (iff #14 #225)
-#226 := (iff #13 #13)
-#227 := [refl]: #226
-#229 := [quant-intro #227]: #228
-#116 := (~ #14 #14)
-#114 := (~ #13 #13)
-#115 := [refl]: #114
-#117 := [nnf-pos #115]: #116
-#102 := [asserted]: #14
-#118 := [mp~ #102 #117]: #14
-#230 := [mp #118 #229]: #225
-#326 := (not #225)
-#327 := (or #326 #80)
-#328 := [quant-inst #72 #73 #77]: #327
-[unit-resolution #328 #230 #112]: false
-unsat
-1c291f66407b060abd6570e3561e84cb6802694a 47 0
-#2 := false
-#73 := 4::Int
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f16 :: (-> S10 S8 S2)
-decl f26 :: S8
-#76 := f26
-decl f17 :: (-> S11 S1 S10)
-decl f25 :: S1
-#74 := f25
-decl f18 :: S11
-#42 := f18
-#75 := (f17 f18 f25)
-#77 := (f16 #75 f26)
-#72 := 3::Int
-#78 := (f5 3::Int 4::Int #77)
-decl f6 :: S3
-#15 := f6
-#79 := (f3 f6 #78)
-#80 := (= #79 4::Int)
-#81 := (not #80)
-#112 := [asserted]: #81
-#10 := (:var 0 S2)
-#9 := (:var 1 Int)
-#8 := (:var 2 Int)
-#11 := (f5 #8 #9 #10)
-#224 := (pattern #11)
-#16 := (f3 f6 #11)
-#17 := (= #16 #9)
-#231 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #224) #17)
-#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
-#234 := (iff #18 #231)
-#232 := (iff #17 #17)
-#233 := [refl]: #232
-#235 := [quant-intro #233]: #234
-#121 := (~ #18 #18)
-#119 := (~ #17 #17)
-#120 := [refl]: #119
-#122 := [nnf-pos #120]: #121
-#103 := [asserted]: #18
-#123 := [mp~ #103 #122]: #18
-#236 := [mp #123 #235]: #231
-#331 := (not #231)
-#332 := (or #331 #80)
-#333 := [quant-inst #72 #73 #77]: #332
-[unit-resolution #333 #236 #112]: false
-unsat
-5e951d88ba01a5b65915e3cf99e633951609c993 85 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f25 :: S1
-#74 := f25
-#81 := (= f25 f1)
-#303 := (not #81)
-#341 := [hypothesis]: #303
-decl f14 :: (-> S9 S4 S1)
-decl f5 :: (-> Int Int S2 S4)
-decl f16 :: (-> S10 S8 S2)
-decl f26 :: S8
-#76 := f26
-decl f17 :: (-> S11 S1 S10)
-decl f18 :: S11
-#42 := f18
-#75 := (f17 f18 f25)
-#77 := (f16 #75 f26)
-#73 := 4::Int
-#72 := 3::Int
-#78 := (f5 3::Int 4::Int #77)
-decl f15 :: S9
-#40 := f15
-#79 := (f14 f15 #78)
-#80 := (= #79 f1)
-#311 := (or #80 #81)
-#115 := (not #80)
-#116 := (iff #115 #81)
-#82 := (iff #80 #81)
-#83 := (not #82)
-#117 := (iff #83 #116)
-#118 := [rewrite]: #117
-#114 := [asserted]: #83
-#121 := [mp #114 #118]: #116
-#304 := (not #116)
-#309 := (or #80 #81 #304)
-#310 := [def-axiom]: #309
-#312 := [unit-resolution #310 #121]: #311
-#342 := [unit-resolution #312 #341]: #80
-#347 := (or #115 #81)
-#45 := (:var 0 S8)
-#43 := (:var 1 S1)
-#44 := (f17 f18 #43)
-#46 := (f16 #44 #45)
-#8 := (:var 2 Int)
-#41 := (:var 3 Int)
-#47 := (f5 #41 #8 #46)
-#274 := (pattern #47)
-#50 := (= #43 f1)
-#48 := (f14 f15 #47)
-#49 := (= #48 f1)
-#51 := (iff #49 #50)
-#275 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) (:pat #274) #51)
-#52 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) #51)
-#278 := (iff #52 #275)
-#276 := (iff #51 #51)
-#277 := [refl]: #276
-#279 := [quant-intro #277]: #278
-#153 := (~ #52 #52)
-#151 := (~ #51 #51)
-#152 := [refl]: #151
-#154 := [nnf-pos #152]: #153
-#110 := [asserted]: #52
-#155 := [mp~ #110 #154]: #52
-#280 := [mp #155 #279]: #275
-#315 := (not #275)
-#316 := (or #315 #82)
-#317 := [quant-inst #72 #73 #74 #76]: #316
-#346 := [unit-resolution #317 #280]: #82
-#320 := (or #83 #115 #81)
-#321 := [def-axiom]: #320
-#348 := [unit-resolution #321 #346]: #347
-#349 := [unit-resolution #348 #342 #341]: false
-#350 := [lemma #349]: #81
-#307 := (or #115 #303)
-#305 := (or #115 #303 #304)
-#306 := [def-axiom]: #305
-#308 := [unit-resolution #306 #121]: #307
-#351 := [unit-resolution #308 #350]: #115
-#352 := (or #80 #303)
-#318 := (or #83 #80 #303)
-#319 := [def-axiom]: #318
-#353 := [unit-resolution #319 #346]: #352
-[unit-resolution #353 #351 #350]: false
-unsat
-812476a17a9a2871c9ebf2cc9391e374a71250ed 86 0
-#2 := false
-#73 := 4::Int
-#72 := 3::Int
-#345 := (= 3::Int 4::Int)
-#347 := (iff #345 false)
-#348 := [rewrite]: #347
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f16 :: (-> S10 S8 S2)
-decl f26 :: S8
-#76 := f26
-decl f17 :: (-> S11 S1 S10)
-decl f25 :: S1
-#74 := f25
-decl f18 :: S11
-#42 := f18
-#75 := (f17 f18 f25)
-#77 := (f16 #75 f26)
-#78 := (f5 3::Int 4::Int #77)
-decl f6 :: S3
-#15 := f6
-#80 := (f3 f6 #78)
-#327 := (= #80 4::Int)
-#10 := (:var 0 S2)
-#9 := (:var 1 Int)
-#8 := (:var 2 Int)
-#11 := (f5 #8 #9 #10)
-#229 := (pattern #11)
-#16 := (f3 f6 #11)
-#17 := (= #16 #9)
-#236 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #229) #17)
-#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
-#239 := (iff #18 #236)
-#237 := (iff #17 #17)
-#238 := [refl]: #237
-#240 := [quant-intro #238]: #239
-#126 := (~ #18 #18)
-#124 := (~ #17 #17)
-#125 := [refl]: #124
-#127 := [nnf-pos #125]: #126
-#105 := [asserted]: #18
-#128 := [mp~ #105 #127]: #18
-#241 := [mp #128 #240]: #236
-#336 := (not #236)
-#337 := (or #336 #327)
-#338 := [quant-inst #72 #73 #77]: #337
-#331 := [unit-resolution #338 #241]: #327
-#343 := (= 3::Int #80)
-#341 := (= #80 3::Int)
-decl f4 :: S3
-#7 := f4
-#79 := (f3 f4 #78)
-#326 := (= #79 3::Int)
-#12 := (f3 f4 #11)
-#13 := (= #12 #8)
-#230 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #229) #13)
-#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
-#233 := (iff #14 #230)
-#231 := (iff #13 #13)
-#232 := [refl]: #231
-#234 := [quant-intro #232]: #233
-#121 := (~ #14 #14)
-#118 := (~ #13 #13)
-#120 := [refl]: #118
-#122 := [nnf-pos #120]: #121
-#104 := [asserted]: #14
-#123 := [mp~ #104 #122]: #14
-#235 := [mp #123 #234]: #230
-#332 := (not #230)
-#333 := (or #332 #326)
-#334 := [quant-inst #72 #73 #77]: #333
-#335 := [unit-resolution #334 #235]: #326
-#339 := (= #80 #79)
-#81 := (= #79 #80)
-#82 := (not #81)
-#83 := (not #82)
-#115 := (iff #83 #81)
-#116 := [rewrite]: #115
-#114 := [asserted]: #83
-#119 := [mp #114 #116]: #81
-#340 := [symm #119]: #339
-#342 := [trans #340 #335]: #341
-#344 := [symm #342]: #343
-#346 := [trans #344 #331]: #345
-[mp #346 #348]: false
-unsat
-fb3b468a9e0e9229a2ed6b6592a5795d32e0cbbf 81 0
-#2 := false
-decl f7 :: (-> Int Int S3 S5)
-decl f17 :: (-> S10 S8 S3)
-decl f27 :: S8
-#83 := f27
-decl f18 :: (-> S11 S1 S10)
-decl f26 :: S1
-#81 := f26
-decl f19 :: S11
-#49 := f19
-#82 := (f18 f19 f26)
-#84 := (f17 #82 f27)
-#80 := 4::Int
-#11 := 5::Int
-#87 := (f7 5::Int 4::Int #84)
-decl f11 :: (-> S2 S5 S5)
-#79 := 3::Int
-#85 := (f7 3::Int 4::Int #84)
-decl f4 :: S2
-#7 := f4
-#86 := (f11 f4 #85)
-#88 := (= #86 #87)
-decl f3 :: (-> S2 Int Int)
-#378 := (f3 f4 3::Int)
-#379 := (f7 #378 4::Int #84)
-#427 := (= #379 #87)
-#425 := (= #87 #379)
-#419 := (= 5::Int #378)
-#415 := (= #378 5::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 5::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#125 := (~ #13 #13)
-#123 := (~ #12 #12)
-#124 := [refl]: #123
-#126 := [nnf-pos #124]: #125
-#110 := [asserted]: #13
-#127 := [mp~ #110 #126]: #13
-#420 := (not #13)
-#421 := (or #420 #415)
-#422 := [quant-inst #79]: #421
-#416 := [unit-resolution #422 #127]: #415
-#423 := [symm #416]: #419
-#426 := [monotonicity #423]: #425
-#428 := [symm #426]: #427
-#382 := (= #86 #379)
-#17 := (:var 0 S3)
-#16 := (:var 1 Int)
-#15 := (:var 2 Int)
-#30 := (:var 3 S2)
-#32 := (f3 #30 #15)
-#33 := (f7 #32 #16 #17)
-#257 := (pattern #33)
-#18 := (f7 #15 #16 #17)
-#31 := (f11 #30 #18)
-#256 := (pattern #31)
-#34 := (= #31 #33)
-#258 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #256 #257) #34)
-#35 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #34)
-#261 := (iff #35 #258)
-#259 := (iff #34 #34)
-#260 := [refl]: #259
-#262 := [quant-intro #260]: #261
-#145 := (~ #35 #35)
-#143 := (~ #34 #34)
-#144 := [refl]: #143
-#146 := [nnf-pos #144]: #145
-#114 := [asserted]: #35
-#147 := [mp~ #114 #146]: #35
-#263 := [mp #147 #262]: #258
-#385 := (not #258)
-#386 := (or #385 #382)
-#387 := [quant-inst #7 #79 #80 #84]: #386
-#424 := [unit-resolution #387 #263]: #382
-#429 := [trans #424 #428]: #88
-#89 := (not #88)
-#121 := [asserted]: #89
-[unit-resolution #121 #429]: false
-unsat
-66c49b5e837d7faf6a74356e58d3b2fd5529a3d1 81 0
-#2 := false
-decl f7 :: (-> Int Int S3 S5)
-decl f17 :: (-> S10 S8 S3)
-decl f27 :: S8
-#83 := f27
-decl f18 :: (-> S11 S1 S10)
-decl f26 :: S1
-#81 := f26
-decl f19 :: S11
-#49 := f19
-#82 := (f18 f19 f26)
-#84 := (f17 #82 f27)
-#11 := 6::Int
-#79 := 3::Int
-#87 := (f7 3::Int 6::Int #84)
-decl f12 :: (-> S2 S5 S5)
-#80 := 4::Int
-#85 := (f7 3::Int 4::Int #84)
-decl f4 :: S2
-#7 := f4
-#86 := (f12 f4 #85)
-#88 := (= #86 #87)
-decl f3 :: (-> S2 Int Int)
-#379 := (f3 f4 4::Int)
-#380 := (f7 3::Int #379 #84)
-#428 := (= #380 #87)
-#426 := (= #87 #380)
-#420 := (= 6::Int #379)
-#416 := (= #379 6::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 6::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#125 := (~ #13 #13)
-#123 := (~ #12 #12)
-#124 := [refl]: #123
-#126 := [nnf-pos #124]: #125
-#110 := [asserted]: #13
-#127 := [mp~ #110 #126]: #13
-#421 := (not #13)
-#422 := (or #421 #416)
-#423 := [quant-inst #80]: #422
-#417 := [unit-resolution #423 #127]: #416
-#424 := [symm #417]: #420
-#427 := [monotonicity #424]: #426
-#429 := [symm #427]: #428
-#383 := (= #86 #380)
-#17 := (:var 0 S3)
-#16 := (:var 1 Int)
-#30 := (:var 3 S2)
-#37 := (f3 #30 #16)
-#15 := (:var 2 Int)
-#38 := (f7 #15 #37 #17)
-#266 := (pattern #38)
-#18 := (f7 #15 #16 #17)
-#36 := (f12 #30 #18)
-#265 := (pattern #36)
-#39 := (= #36 #38)
-#267 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #265 #266) #39)
-#40 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #39)
-#270 := (iff #40 #267)
-#268 := (iff #39 #39)
-#269 := [refl]: #268
-#271 := [quant-intro #269]: #270
-#150 := (~ #40 #40)
-#148 := (~ #39 #39)
-#149 := [refl]: #148
-#151 := [nnf-pos #149]: #150
-#115 := [asserted]: #40
-#152 := [mp~ #115 #151]: #40
-#272 := [mp #152 #271]: #267
-#386 := (not #267)
-#387 := (or #386 #383)
-#388 := [quant-inst #7 #79 #80 #84]: #387
-#425 := [unit-resolution #388 #272]: #383
-#430 := [trans #425 #429]: #88
-#89 := (not #88)
-#121 := [asserted]: #89
-[unit-resolution #121 #430]: false
-unsat
-9aa89ca1a2dffdf92e4644072316fccd998c9605 233 0
-#2 := false
-decl f28 :: S6
-#92 := f28
-decl f25 :: (-> S3 S6 S6)
-decl f15 :: (-> S2 S6 S6)
-decl f14 :: (-> S2 S6 S6)
-decl f5 :: S2
-#14 := f5
-#98 := (f14 f5 f28)
-decl f4 :: S2
-#7 := f4
-#99 := (f15 f4 #98)
-decl f7 :: S3
-#20 := f7
-#100 := (f25 f7 #99)
-#101 := (= #100 f28)
-decl f10 :: (-> Int Int S4 S6)
-decl f20 :: (-> S11 S9 S4)
-decl f29 :: S9
-#94 := f29
-decl f21 :: (-> S12 S1 S11)
-decl f1 :: S1
-#3 := f1
-decl f22 :: S12
-#62 := f22
-#93 := (f21 f22 f1)
-#95 := (f20 #93 f29)
-#11 := 4::Int
-#17 := 3::Int
-#96 := (f10 3::Int 4::Int #95)
-#583 := (= #96 f28)
-#97 := (= f28 #96)
-#144 := (not #97)
-#145 := (or #144 #101)
-#148 := (not #145)
-#102 := (implies #97 #101)
-#103 := (not #102)
-#149 := (iff #103 #148)
-#146 := (iff #102 #145)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#143 := [asserted]: #103
-#153 := [mp #143 #150]: #148
-#151 := [not-or-elim #153]: #97
-#584 := [symm #151]: #583
-#587 := (= #100 #96)
-decl f6 :: (-> S3 S1 S1)
-#496 := (f6 f7 f1)
-#500 := (f21 f22 #496)
-#501 := (f20 #500 f29)
-decl f3 :: (-> S2 Int Int)
-#445 := (f3 f4 4::Int)
-#502 := (f10 3::Int #445 #501)
-#581 := (= #502 #96)
-#556 := (= #501 #95)
-#549 := (= #500 #93)
-#510 := (= #496 f1)
-#21 := (:var 0 S1)
-#22 := (f6 f7 #21)
-#23 := (pattern #22)
-#24 := (= #22 f1)
-#129 := (forall (vars (?v0 S1)) (:pat #23) #24)
-#168 := (~ #129 #129)
-#166 := (~ #24 #24)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#1 := true
-#25 := (iff #24 true)
-#26 := (forall (vars (?v0 S1)) (:pat #23) #25)
-#130 := (iff #26 #129)
-#127 := (iff #25 #24)
-#128 := [rewrite]: #127
-#131 := [quant-intro #128]: #130
-#126 := [asserted]: #26
-#134 := [mp #126 #131]: #129
-#170 := [mp~ #134 #169]: #129
-#552 := (not #129)
-#553 := (or #552 #510)
-#554 := [quant-inst #3]: #553
-#548 := [unit-resolution #554 #170]: #510
-#555 := [monotonicity #548]: #549
-#557 := [monotonicity #555]: #556
-#492 := (= #445 4::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 4::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#158 := (~ #13 #13)
-#156 := (~ #12 #12)
-#157 := [refl]: #156
-#159 := [nnf-pos #157]: #158
-#124 := [asserted]: #13
-#160 := [mp~ #124 #159]: #13
-#497 := (not #13)
-#498 := (or #497 #492)
-#499 := [quant-inst #11]: #498
-#558 := [unit-resolution #499 #160]: #492
-#582 := [monotonicity #558 #557]: #581
-#585 := (= #100 #502)
-#451 := (f10 3::Int #445 #95)
-#493 := (f25 f7 #451)
-#503 := (= #493 #502)
-#65 := (:var 0 S9)
-#63 := (:var 1 S1)
-#77 := (:var 4 S3)
-#79 := (f6 #77 #63)
-#80 := (f21 f22 #79)
-#81 := (f20 #80 #65)
-#28 := (:var 2 Int)
-#61 := (:var 3 Int)
-#82 := (f10 #61 #28 #81)
-#338 := (pattern #82)
-#64 := (f21 f22 #63)
-#66 := (f20 #64 #65)
-#67 := (f10 #61 #28 #66)
-#78 := (f25 #77 #67)
-#337 := (pattern #78)
-#83 := (= #78 #82)
-#339 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #337 #338) #83)
-#84 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #83)
-#342 := (iff #84 #339)
-#340 := (iff #83 #83)
-#341 := [refl]: #340
-#343 := [quant-intro #341]: #342
-#213 := (~ #84 #84)
-#211 := (~ #83 #83)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#141 := [asserted]: #84
-#215 := [mp~ #141 #214]: #84
-#344 := [mp #215 #343]: #339
-#506 := (not #339)
-#507 := (or #506 #503)
-#508 := [quant-inst #20 #17 #445 #3 #94]: #507
-#559 := [unit-resolution #508 #344]: #503
-#579 := (= #100 #493)
-#577 := (= #99 #451)
-#355 := (f3 f5 3::Int)
-#449 := (f10 #355 #445 #95)
-#573 := (= #449 #451)
-#571 := (= #451 #449)
-#561 := (= 3::Int #355)
-#441 := (= #355 3::Int)
-#15 := (f3 f5 #8)
-#16 := (pattern #15)
-#18 := (= #15 3::Int)
-#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
-#163 := (~ #19 #19)
-#161 := (~ #18 #18)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#125 := [asserted]: #19
-#165 := [mp~ #125 #164]: #19
-#446 := (not #19)
-#447 := (or #446 #441)
-#448 := [quant-inst #17]: #447
-#560 := [unit-resolution #448 #165]: #441
-#562 := [symm #560]: #561
-#572 := [monotonicity #562]: #571
-#574 := [symm #572]: #573
-#575 := (= #99 #449)
-#354 := (f10 #355 4::Int #95)
-#442 := (f15 f4 #354)
-#450 := (= #442 #449)
-#30 := (:var 0 S4)
-#29 := (:var 1 Int)
-#43 := (:var 3 S2)
-#50 := (f3 #43 #29)
-#51 := (f10 #28 #50 #30)
-#309 := (pattern #51)
-#31 := (f10 #28 #29 #30)
-#49 := (f15 #43 #31)
-#308 := (pattern #49)
-#52 := (= #49 #51)
-#310 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #308 #309) #52)
-#53 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #52)
-#313 := (iff #53 #310)
-#311 := (iff #52 #52)
-#312 := [refl]: #311
-#314 := [quant-intro #312]: #313
-#193 := (~ #53 #53)
-#191 := (~ #52 #52)
-#192 := [refl]: #191
-#194 := [nnf-pos #192]: #193
-#137 := [asserted]: #53
-#195 := [mp~ #137 #194]: #53
-#315 := [mp #195 #314]: #310
-#453 := (not #310)
-#454 := (or #453 #450)
-#455 := [quant-inst #7 #355 #11 #95]: #454
-#563 := [unit-resolution #455 #315]: #450
-#569 := (= #99 #442)
-#567 := (= #98 #354)
-#353 := (f14 f5 #96)
-#361 := (= #353 #354)
-#45 := (f3 #43 #28)
-#46 := (f10 #45 #29 #30)
-#301 := (pattern #46)
-#44 := (f14 #43 #31)
-#300 := (pattern #44)
-#47 := (= #44 #46)
-#302 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #300 #301) #47)
-#48 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #47)
-#305 := (iff #48 #302)
-#303 := (iff #47 #47)
-#304 := [refl]: #303
-#306 := [quant-intro #304]: #305
-#188 := (~ #48 #48)
-#186 := (~ #47 #47)
-#187 := [refl]: #186
-#189 := [nnf-pos #187]: #188
-#136 := [asserted]: #48
-#190 := [mp~ #136 #189]: #48
-#307 := [mp #190 #306]: #302
-#364 := (not #302)
-#365 := (or #364 #361)
-#366 := [quant-inst #14 #17 #11 #95]: #365
-#564 := [unit-resolution #366 #307]: #361
-#565 := (= #98 #353)
-#566 := [monotonicity #151]: #565
-#568 := [trans #566 #564]: #567
-#570 := [monotonicity #568]: #569
-#576 := [trans #570 #563]: #575
-#578 := [trans #576 #574]: #577
-#580 := [monotonicity #578]: #579
-#586 := [trans #580 #559]: #585
-#588 := [trans #586 #582]: #587
-#589 := [trans #588 #584]: #101
-#152 := (not #101)
-#154 := [not-or-elim #153]: #152
-[unit-resolution #154 #589]: false
-unsat
-b7ee8e1470156257eed64bf3397227c8530efee0 233 0
-#2 := false
-decl f28 :: S6
-#92 := f28
-decl f14 :: (-> S2 S6 S6)
-decl f25 :: (-> S3 S6 S6)
-decl f15 :: (-> S2 S6 S6)
-decl f4 :: S2
-#7 := f4
-#98 := (f15 f4 f28)
-decl f7 :: S3
-#20 := f7
-#99 := (f25 f7 #98)
-decl f5 :: S2
-#14 := f5
-#100 := (f14 f5 #99)
-#101 := (= #100 f28)
-decl f10 :: (-> Int Int S4 S6)
-decl f20 :: (-> S11 S9 S4)
-decl f29 :: S9
-#94 := f29
-decl f21 :: (-> S12 S1 S11)
-decl f1 :: S1
-#3 := f1
-decl f22 :: S12
-#62 := f22
-#93 := (f21 f22 f1)
-#95 := (f20 #93 f29)
-#11 := 4::Int
-#17 := 3::Int
-#96 := (f10 3::Int 4::Int #95)
-#583 := (= #96 f28)
-#97 := (= f28 #96)
-#144 := (not #97)
-#145 := (or #144 #101)
-#148 := (not #145)
-#102 := (implies #97 #101)
-#103 := (not #102)
-#149 := (iff #103 #148)
-#146 := (iff #102 #145)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#143 := [asserted]: #103
-#153 := [mp #143 #150]: #148
-#151 := [not-or-elim #153]: #97
-#584 := [symm #151]: #583
-#587 := (= #100 #96)
-decl f6 :: (-> S3 S1 S1)
-#445 := (f6 f7 f1)
-#449 := (f21 f22 #445)
-#450 := (f20 #449 f29)
-decl f3 :: (-> S2 Int Int)
-#493 := (f3 f5 3::Int)
-#499 := (f10 #493 4::Int #450)
-#581 := (= #499 #96)
-#556 := (= #450 #95)
-#551 := (= #449 #93)
-#459 := (= #445 f1)
-#21 := (:var 0 S1)
-#22 := (f6 f7 #21)
-#23 := (pattern #22)
-#24 := (= #22 f1)
-#129 := (forall (vars (?v0 S1)) (:pat #23) #24)
-#168 := (~ #129 #129)
-#166 := (~ #24 #24)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#1 := true
-#25 := (iff #24 true)
-#26 := (forall (vars (?v0 S1)) (:pat #23) #25)
-#130 := (iff #26 #129)
-#127 := (iff #25 #24)
-#128 := [rewrite]: #127
-#131 := [quant-intro #128]: #130
-#126 := [asserted]: #26
-#134 := [mp #126 #131]: #129
-#170 := [mp~ #134 #169]: #129
-#496 := (not #129)
-#497 := (or #496 #459)
-#498 := [quant-inst #3]: #497
-#548 := [unit-resolution #498 #170]: #459
-#555 := [monotonicity #548]: #551
-#557 := [monotonicity #555]: #556
-#547 := (= #493 3::Int)
-#8 := (:var 0 Int)
-#15 := (f3 f5 #8)
-#16 := (pattern #15)
-#18 := (= #15 3::Int)
-#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
-#163 := (~ #19 #19)
-#161 := (~ #18 #18)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#125 := [asserted]: #19
-#165 := [mp~ #125 #164]: #19
-#552 := (not #19)
-#553 := (or #552 #547)
-#554 := [quant-inst #17]: #553
-#558 := [unit-resolution #554 #165]: #547
-#582 := [monotonicity #558 #557]: #581
-#585 := (= #100 #499)
-#453 := (f10 3::Int 4::Int #450)
-#492 := (f14 f5 #453)
-#500 := (= #492 #499)
-#30 := (:var 0 S4)
-#29 := (:var 1 Int)
-#28 := (:var 2 Int)
-#43 := (:var 3 S2)
-#45 := (f3 #43 #28)
-#46 := (f10 #45 #29 #30)
-#301 := (pattern #46)
-#31 := (f10 #28 #29 #30)
-#44 := (f14 #43 #31)
-#300 := (pattern #44)
-#47 := (= #44 #46)
-#302 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #300 #301) #47)
-#48 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #47)
-#305 := (iff #48 #302)
-#303 := (iff #47 #47)
-#304 := [refl]: #303
-#306 := [quant-intro #304]: #305
-#188 := (~ #48 #48)
-#186 := (~ #47 #47)
-#187 := [refl]: #186
-#189 := [nnf-pos #187]: #188
-#136 := [asserted]: #48
-#190 := [mp~ #136 #189]: #48
-#307 := [mp #190 #306]: #302
-#503 := (not #302)
-#504 := (or #503 #500)
-#505 := [quant-inst #14 #17 #11 #450]: #504
-#559 := [unit-resolution #505 #307]: #500
-#579 := (= #100 #492)
-#577 := (= #99 #453)
-#355 := (f3 f4 4::Int)
-#451 := (f10 3::Int #355 #450)
-#573 := (= #451 #453)
-#571 := (= #453 #451)
-#561 := (= 4::Int #355)
-#441 := (= #355 4::Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 4::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#158 := (~ #13 #13)
-#156 := (~ #12 #12)
-#157 := [refl]: #156
-#159 := [nnf-pos #157]: #158
-#124 := [asserted]: #13
-#160 := [mp~ #124 #159]: #13
-#446 := (not #13)
-#447 := (or #446 #441)
-#448 := [quant-inst #11]: #447
-#560 := [unit-resolution #448 #160]: #441
-#562 := [symm #560]: #561
-#572 := [monotonicity #562]: #571
-#574 := [symm #572]: #573
-#575 := (= #99 #451)
-#354 := (f10 3::Int #355 #95)
-#442 := (f25 f7 #354)
-#452 := (= #442 #451)
-#65 := (:var 0 S9)
-#63 := (:var 1 S1)
-#77 := (:var 4 S3)
-#79 := (f6 #77 #63)
-#80 := (f21 f22 #79)
-#81 := (f20 #80 #65)
-#61 := (:var 3 Int)
-#82 := (f10 #61 #28 #81)
-#338 := (pattern #82)
-#64 := (f21 f22 #63)
-#66 := (f20 #64 #65)
-#67 := (f10 #61 #28 #66)
-#78 := (f25 #77 #67)
-#337 := (pattern #78)
-#83 := (= #78 #82)
-#339 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #337 #338) #83)
-#84 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #83)
-#342 := (iff #84 #339)
-#340 := (iff #83 #83)
-#341 := [refl]: #340
-#343 := [quant-intro #341]: #342
-#213 := (~ #84 #84)
-#211 := (~ #83 #83)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#141 := [asserted]: #84
-#215 := [mp~ #141 #214]: #84
-#344 := [mp #215 #343]: #339
-#455 := (not #339)
-#456 := (or #455 #452)
-#457 := [quant-inst #20 #17 #355 #3 #94]: #456
-#563 := [unit-resolution #457 #344]: #452
-#569 := (= #99 #442)
-#567 := (= #98 #354)
-#353 := (f15 f4 #96)
-#361 := (= #353 #354)
-#50 := (f3 #43 #29)
-#51 := (f10 #28 #50 #30)
-#309 := (pattern #51)
-#49 := (f15 #43 #31)
-#308 := (pattern #49)
-#52 := (= #49 #51)
-#310 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #308 #309) #52)
-#53 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #52)
-#313 := (iff #53 #310)
-#311 := (iff #52 #52)
-#312 := [refl]: #311
-#314 := [quant-intro #312]: #313
-#193 := (~ #53 #53)
-#191 := (~ #52 #52)
-#192 := [refl]: #191
-#194 := [nnf-pos #192]: #193
-#137 := [asserted]: #53
-#195 := [mp~ #137 #194]: #53
-#315 := [mp #195 #314]: #310
-#364 := (not #310)
-#365 := (or #364 #361)
-#366 := [quant-inst #7 #17 #11 #95]: #365
-#564 := [unit-resolution #366 #315]: #361
-#565 := (= #98 #353)
-#566 := [monotonicity #151]: #565
-#568 := [trans #566 #564]: #567
-#570 := [monotonicity #568]: #569
-#576 := [trans #570 #563]: #575
-#578 := [trans #576 #574]: #577
-#580 := [monotonicity #578]: #579
-#586 := [trans #580 #559]: #585
-#588 := [trans #586 #582]: #587
-#589 := [trans #588 #584]: #101
-#152 := (not #101)
-#154 := [not-or-elim #153]: #152
-[unit-resolution #154 #589]: false
-unsat
-41083c23e36988c33cc02e1eff5234558acdcb86 233 0
-#2 := false
-decl f28 :: S6
-#92 := f28
-decl f15 :: (-> S2 S6 S6)
-decl f14 :: (-> S2 S6 S6)
-decl f25 :: (-> S3 S6 S6)
-decl f7 :: S3
-#20 := f7
-#98 := (f25 f7 f28)
-decl f5 :: S2
-#14 := f5
-#99 := (f14 f5 #98)
-decl f4 :: S2
-#7 := f4
-#100 := (f15 f4 #99)
-#101 := (= #100 f28)
-decl f10 :: (-> Int Int S4 S6)
-decl f20 :: (-> S11 S9 S4)
-decl f29 :: S9
-#94 := f29
-decl f21 :: (-> S12 S1 S11)
-decl f1 :: S1
-#3 := f1
-decl f22 :: S12
-#62 := f22
-#93 := (f21 f22 f1)
-#95 := (f20 #93 f29)
-#11 := 4::Int
-#17 := 3::Int
-#96 := (f10 3::Int 4::Int #95)
-#583 := (= #96 f28)
-#97 := (= f28 #96)
-#144 := (not #97)
-#145 := (or #144 #101)
-#148 := (not #145)
-#102 := (implies #97 #101)
-#103 := (not #102)
-#149 := (iff #103 #148)
-#146 := (iff #102 #145)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#143 := [asserted]: #103
-#153 := [mp #143 #150]: #148
-#151 := [not-or-elim #153]: #97
-#584 := [symm #151]: #583
-#587 := (= #100 #96)
-decl f3 :: (-> S2 Int Int)
-#495 := (f3 f4 4::Int)
-#442 := (f3 f5 3::Int)
-#499 := (f10 #442 #495 #95)
-#581 := (= #499 #96)
-#547 := (= #495 4::Int)
-#8 := (:var 0 Int)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#12 := (= #9 4::Int)
-#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
-#158 := (~ #13 #13)
-#156 := (~ #12 #12)
-#157 := [refl]: #156
-#159 := [nnf-pos #157]: #158
-#124 := [asserted]: #13
-#160 := [mp~ #124 #159]: #13
-#552 := (not #13)
-#553 := (or #552 #547)
-#554 := [quant-inst #11]: #553
-#548 := [unit-resolution #554 #160]: #547
-#491 := (= #442 3::Int)
-#15 := (f3 f5 #8)
-#16 := (pattern #15)
-#18 := (= #15 3::Int)
-#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
-#163 := (~ #19 #19)
-#161 := (~ #18 #18)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#125 := [asserted]: #19
-#165 := [mp~ #125 #164]: #19
-#496 := (not #19)
-#497 := (or #496 #491)
-#498 := [quant-inst #17]: #497
-#551 := [unit-resolution #498 #165]: #491
-#582 := [monotonicity #551 #548]: #581
-#585 := (= #100 #499)
-#450 := (f10 #442 4::Int #95)
-#492 := (f15 f4 #450)
-#500 := (= #492 #499)
-#30 := (:var 0 S4)
-#29 := (:var 1 Int)
-#43 := (:var 3 S2)
-#50 := (f3 #43 #29)
-#28 := (:var 2 Int)
-#51 := (f10 #28 #50 #30)
-#309 := (pattern #51)
-#31 := (f10 #28 #29 #30)
-#49 := (f15 #43 #31)
-#308 := (pattern #49)
-#52 := (= #49 #51)
-#310 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #308 #309) #52)
-#53 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #52)
-#313 := (iff #53 #310)
-#311 := (iff #52 #52)
-#312 := [refl]: #311
-#314 := [quant-intro #312]: #313
-#193 := (~ #53 #53)
-#191 := (~ #52 #52)
-#192 := [refl]: #191
-#194 := [nnf-pos #192]: #193
-#137 := [asserted]: #53
-#195 := [mp~ #137 #194]: #53
-#315 := [mp #195 #314]: #310
-#503 := (not #310)
-#504 := (or #503 #500)
-#505 := [quant-inst #7 #442 #11 #95]: #504
-#555 := [unit-resolution #505 #315]: #500
-#579 := (= #100 #492)
-#577 := (= #99 #450)
-decl f6 :: (-> S3 S1 S1)
-#355 := (f6 f7 f1)
-#354 := (f21 f22 #355)
-#361 := (f20 #354 f29)
-#448 := (f10 #442 4::Int #361)
-#573 := (= #448 #450)
-#571 := (= #450 #448)
-#561 := (= #95 #361)
-#559 := (= #361 #95)
-#557 := (= #354 #93)
-#412 := (= #355 f1)
-#21 := (:var 0 S1)
-#22 := (f6 f7 #21)
-#23 := (pattern #22)
-#24 := (= #22 f1)
-#129 := (forall (vars (?v0 S1)) (:pat #23) #24)
-#168 := (~ #129 #129)
-#166 := (~ #24 #24)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#1 := true
-#25 := (iff #24 true)
-#26 := (forall (vars (?v0 S1)) (:pat #23) #25)
-#130 := (iff #26 #129)
-#127 := (iff #25 #24)
-#128 := [rewrite]: #127
-#131 := [quant-intro #128]: #130
-#126 := [asserted]: #26
-#134 := [mp #126 #131]: #129
-#170 := [mp~ #134 #169]: #129
-#445 := (not #129)
-#446 := (or #445 #412)
-#447 := [quant-inst #3]: #446
-#556 := [unit-resolution #447 #170]: #412
-#558 := [monotonicity #556]: #557
-#560 := [monotonicity #558]: #559
-#562 := [symm #560]: #561
-#572 := [monotonicity #562]: #571
-#574 := [symm #572]: #573
-#575 := (= #99 #448)
-#362 := (f10 3::Int 4::Int #361)
-#441 := (f14 f5 #362)
-#449 := (= #441 #448)
-#45 := (f3 #43 #28)
-#46 := (f10 #45 #29 #30)
-#301 := (pattern #46)
-#44 := (f14 #43 #31)
-#300 := (pattern #44)
-#47 := (= #44 #46)
-#302 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #300 #301) #47)
-#48 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #47)
-#305 := (iff #48 #302)
-#303 := (iff #47 #47)
-#304 := [refl]: #303
-#306 := [quant-intro #304]: #305
-#188 := (~ #48 #48)
-#186 := (~ #47 #47)
-#187 := [refl]: #186
-#189 := [nnf-pos #187]: #188
-#136 := [asserted]: #48
-#190 := [mp~ #136 #189]: #48
-#307 := [mp #190 #306]: #302
-#452 := (not #302)
-#453 := (or #452 #449)
-#454 := [quant-inst #14 #17 #11 #361]: #453
-#563 := [unit-resolution #454 #307]: #449
-#569 := (= #99 #441)
-#567 := (= #98 #362)
-#353 := (f25 f7 #96)
-#363 := (= #353 #362)
-#65 := (:var 0 S9)
-#63 := (:var 1 S1)
-#77 := (:var 4 S3)
-#79 := (f6 #77 #63)
-#80 := (f21 f22 #79)
-#81 := (f20 #80 #65)
-#61 := (:var 3 Int)
-#82 := (f10 #61 #28 #81)
-#338 := (pattern #82)
-#64 := (f21 f22 #63)
-#66 := (f20 #64 #65)
-#67 := (f10 #61 #28 #66)
-#78 := (f25 #77 #67)
-#337 := (pattern #78)
-#83 := (= #78 #82)
-#339 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #337 #338) #83)
-#84 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #83)
-#342 := (iff #84 #339)
-#340 := (iff #83 #83)
-#341 := [refl]: #340
-#343 := [quant-intro #341]: #342
-#213 := (~ #84 #84)
-#211 := (~ #83 #83)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#141 := [asserted]: #84
-#215 := [mp~ #141 #214]: #84
-#344 := [mp #215 #343]: #339
-#366 := (not #339)
-#367 := (or #366 #363)
-#368 := [quant-inst #20 #17 #11 #3 #94]: #367
-#564 := [unit-resolution #368 #344]: #363
-#565 := (= #98 #353)
-#566 := [monotonicity #151]: #565
-#568 := [trans #566 #564]: #567
-#570 := [monotonicity #568]: #569
-#576 := [trans #570 #563]: #575
-#578 := [trans #576 #574]: #577
-#580 := [monotonicity #578]: #579
-#586 := [trans #580 #555]: #585
-#588 := [trans #586 #582]: #587
-#589 := [trans #588 #584]: #101
-#152 := (not #101)
-#154 := [not-or-elim #153]: #152
-[unit-resolution #154 #589]: false
-unsat
-1dd70ea57d3666cb5aaa01a8ef0d758d0e424162 18 0
-#2 := false
-decl f3 :: S2
-#7 := f3
-#51 := (= f3 f3)
-#52 := (not #51)
-#106 := (iff #52 false)
-#1 := true
-#101 := (not true)
-#104 := (iff #101 false)
-#105 := [rewrite]: #104
-#102 := (iff #52 #101)
-#98 := (iff #51 true)
-#100 := [rewrite]: #98
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#97 := [asserted]: #52
-[mp #97 #107]: false
-unsat
-bdeca06ba44784eaf57a202bbea41e9cc79df1f4 18 0
-#2 := false
-decl f6 :: S2
-#12 := f6
-#51 := (= f6 f6)
-#52 := (not #51)
-#106 := (iff #52 false)
-#1 := true
-#101 := (not true)
-#104 := (iff #101 false)
-#105 := [rewrite]: #104
-#102 := (iff #52 #101)
-#98 := (iff #51 true)
-#100 := [rewrite]: #98
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#97 := [asserted]: #52
-[mp #97 #107]: false
-unsat
-1d9cdf8282138ea38f1106fe994e0979fa86c7e4 213 0
-#2 := false
-#13 := 2::Int
-#9 := 1::Int
-#243 := (= 1::Int 2::Int)
-#255 := (iff #243 false)
-#256 := [rewrite]: #255
-decl f11 :: (-> S6 S2 Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#8 := f5
-#14 := (f4 f5 2::Int)
-decl f12 :: S6
-#25 := f12
-#227 := (f11 f12 #14)
-#228 := (= #227 2::Int)
-decl f1 :: S1
-#3 := f1
-decl f13 :: (-> Int S7 S1)
-decl f14 :: S7
-#33 := f14
-#217 := (f13 2::Int f14)
-#218 := (= #217 f1)
-#226 := (not #218)
-#366 := [hypothesis]: #226
-#32 := (:var 0 Int)
-#34 := (f13 #32 f14)
-#190 := (pattern #34)
-#17 := 3::Int
-#38 := (= #32 3::Int)
-#37 := (= #32 2::Int)
-#36 := (= #32 1::Int)
-#81 := (or #36 #37 #38)
-#35 := (= #34 f1)
-#84 := (iff #35 #81)
-#191 := (forall (vars (?v0 Int)) (:pat #190) #84)
-#87 := (forall (vars (?v0 Int)) #84)
-#194 := (iff #87 #191)
-#192 := (iff #84 #84)
-#193 := [refl]: #192
-#195 := [quant-intro #193]: #194
-#111 := (~ #87 #87)
-#109 := (~ #84 #84)
-#110 := [refl]: #109
-#112 := [nnf-pos #110]: #111
-#39 := (or #37 #38)
-#40 := (or #36 #39)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#88 := (iff #42 #87)
-#85 := (iff #41 #84)
-#82 := (iff #40 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#78 := [asserted]: #42
-#90 := [mp #78 #89]: #87
-#113 := [mp~ #90 #112]: #87
-#196 := [mp #113 #195]: #191
-#273 := (not #191)
-#357 := (or #273 #218)
-#334 := (= 2::Int 3::Int)
-#331 := (= 2::Int 2::Int)
-#330 := (= 2::Int 1::Int)
-#335 := (or #330 #331 #334)
-#336 := (iff #218 #335)
-#358 := (or #273 #336)
-#360 := (iff #358 #357)
-#362 := (iff #357 #357)
-#363 := [rewrite]: #362
-#355 := (iff #336 #218)
-#1 := true
-#350 := (iff #218 true)
-#353 := (iff #350 #218)
-#354 := [rewrite]: #353
-#351 := (iff #336 #350)
-#348 := (iff #335 true)
-#343 := (or false true false)
-#346 := (iff #343 true)
-#347 := [rewrite]: #346
-#344 := (iff #335 #343)
-#341 := (iff #334 false)
-#342 := [rewrite]: #341
-#339 := (iff #331 true)
-#340 := [rewrite]: #339
-#337 := (iff #330 false)
-#338 := [rewrite]: #337
-#345 := [monotonicity #338 #340 #342]: #344
-#349 := [trans #345 #347]: #348
-#352 := [monotonicity #349]: #351
-#356 := [trans #352 #354]: #355
-#361 := [monotonicity #356]: #360
-#364 := [trans #361 #363]: #360
-#359 := [quant-inst #13]: #358
-#365 := [mp #359 #364]: #357
-#367 := [unit-resolution #365 #196 #366]: false
-#368 := [lemma #367]: #218
-#229 := (or #226 #228)
-#46 := (f4 f5 #32)
-#204 := (pattern #46)
-#47 := (f11 f12 #46)
-#48 := (= #47 #32)
-#91 := (not #35)
-#92 := (or #91 #48)
-#205 := (forall (vars (?v0 Int)) (:pat #190 #204) #92)
-#95 := (forall (vars (?v0 Int)) #92)
-#208 := (iff #95 #205)
-#206 := (iff #92 #92)
-#207 := [refl]: #206
-#209 := [quant-intro #207]: #208
-#121 := (~ #95 #95)
-#119 := (~ #92 #92)
-#120 := [refl]: #119
-#122 := [nnf-pos #120]: #121
-#49 := (implies #35 #48)
-#50 := (forall (vars (?v0 Int)) #49)
-#96 := (iff #50 #95)
-#93 := (iff #49 #92)
-#94 := [rewrite]: #93
-#97 := [quant-intro #94]: #96
-#80 := [asserted]: #50
-#100 := [mp #80 #97]: #95
-#123 := [mp~ #100 #122]: #95
-#210 := [mp #123 #209]: #205
-#219 := (not #205)
-#232 := (or #219 #226 #228)
-#233 := (or #219 #229)
-#235 := (iff #233 #232)
-#236 := [rewrite]: #235
-#234 := [quant-inst #13]: #233
-#237 := [mp #234 #236]: #232
-#369 := [unit-resolution #237 #210]: #229
-#370 := [unit-resolution #369 #368]: #228
-#387 := (= 1::Int #227)
-#385 := (= #227 1::Int)
-#10 := (f4 f5 1::Int)
-#214 := (f11 f12 #10)
-#215 := (= #214 1::Int)
-#211 := (f13 1::Int f14)
-#212 := (= #211 f1)
-#213 := (not #212)
-#283 := [hypothesis]: #213
-#274 := (or #273 #212)
-#250 := (= 1::Int 3::Int)
-#242 := (= 1::Int 1::Int)
-#251 := (or #242 #243 #250)
-#252 := (iff #212 #251)
-#275 := (or #273 #252)
-#277 := (iff #275 #274)
-#279 := (iff #274 #274)
-#280 := [rewrite]: #279
-#271 := (iff #252 #212)
-#266 := (iff #212 true)
-#269 := (iff #266 #212)
-#270 := [rewrite]: #269
-#267 := (iff #252 #266)
-#264 := (iff #251 true)
-#259 := (or true false false)
-#262 := (iff #259 true)
-#263 := [rewrite]: #262
-#260 := (iff #251 #259)
-#257 := (iff #250 false)
-#258 := [rewrite]: #257
-#253 := (iff #242 true)
-#254 := [rewrite]: #253
-#261 := [monotonicity #254 #256 #258]: #260
-#265 := [trans #261 #263]: #264
-#268 := [monotonicity #265]: #267
-#272 := [trans #268 #270]: #271
-#278 := [monotonicity #272]: #277
-#281 := [trans #278 #280]: #277
-#276 := [quant-inst #9]: #275
-#282 := [mp #276 #281]: #274
-#284 := [unit-resolution #282 #196 #283]: false
-#285 := [lemma #284]: #212
-#216 := (or #213 #215)
-#220 := (or #219 #213 #215)
-#221 := (or #219 #216)
-#223 := (iff #221 #220)
-#224 := [rewrite]: #223
-#222 := [quant-inst #9]: #221
-#225 := [mp #222 #224]: #220
-#371 := [unit-resolution #225 #210]: #216
-#372 := [unit-resolution #371 #285]: #215
-#383 := (= #227 #214)
-#381 := (= #14 #10)
-decl f3 :: S2
-#7 := f3
-#11 := (= f3 #10)
-#74 := [asserted]: #11
-#379 := (= #14 f3)
-decl f6 :: S2
-#12 := f6
-#377 := (= f6 f3)
-#51 := (= f3 f6)
-#52 := (not #51)
-#53 := (not #52)
-#99 := (iff #53 #51)
-#101 := [rewrite]: #99
-#98 := [asserted]: #53
-#104 := [mp #98 #101]: #51
-#378 := [symm #104]: #377
-#375 := (= #14 f6)
-#15 := (= f6 #14)
-#75 := [asserted]: #15
-#376 := [symm #75]: #375
-#380 := [trans #376 #378]: #379
-#382 := [trans #380 #74]: #381
-#384 := [monotonicity #382]: #383
-#386 := [trans #384 #372]: #385
-#388 := [symm #386]: #387
-#389 := [trans #388 #370]: #243
-[mp #389 #256]: false
-unsat
-0fc3293c114d86e86e5fda166c582f7031eda038 229 0
-#2 := false
-decl f6 :: S2
-#12 := f6
-decl f8 :: (-> S4 S2 S2)
-decl f3 :: S2
-#7 := f3
-decl f9 :: (-> S5 S2 S4)
-decl f10 :: S5
-#20 := f10
-#51 := (f9 f10 f3)
-#52 := (f8 #51 f3)
-#53 := (= #52 f6)
-decl f4 :: (-> S3 Int S2)
-#13 := 2::Int
-decl f5 :: S3
-#8 := f5
-#14 := (f4 f5 2::Int)
-#435 := (= #14 f6)
-#15 := (= f6 #14)
-#76 := [asserted]: #15
-#436 := [symm #76]: #435
-#439 := (= #52 #14)
-decl f11 :: (-> S6 S2 Int)
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-decl f12 :: S6
-#25 := f12
-#211 := (f11 f12 #10)
-#215 := (* 2::Int #211)
-#218 := (f4 f5 #215)
-#433 := (= #218 #14)
-#431 := (= #14 #218)
-#420 := (= 2::Int #215)
-#418 := (= #215 2::Int)
-#248 := (<= #211 1::Int)
-#237 := (= #211 1::Int)
-decl f1 :: S1
-#3 := f1
-decl f13 :: (-> Int S7 S1)
-decl f14 :: S7
-#33 := f14
-#234 := (f13 1::Int f14)
-#235 := (= #234 f1)
-#236 := (not #235)
-#409 := [hypothesis]: #236
-#32 := (:var 0 Int)
-#34 := (f13 #32 f14)
-#188 := (pattern #34)
-#17 := 3::Int
-#38 := (= #32 3::Int)
-#37 := (= #32 2::Int)
-#36 := (= #32 1::Int)
-#82 := (or #36 #37 #38)
-#35 := (= #34 f1)
-#85 := (iff #35 #82)
-#189 := (forall (vars (?v0 Int)) (:pat #188) #85)
-#88 := (forall (vars (?v0 Int)) #85)
-#192 := (iff #88 #189)
-#190 := (iff #85 #85)
-#191 := [refl]: #190
-#193 := [quant-intro #191]: #192
-#109 := (~ #88 #88)
-#107 := (~ #85 #85)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#39 := (or #37 #38)
-#40 := (or #36 #39)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#89 := (iff #42 #88)
-#86 := (iff #41 #85)
-#83 := (iff #40 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#79 := [asserted]: #42
-#91 := [mp #79 #90]: #88
-#111 := [mp~ #91 #110]: #88
-#194 := [mp #111 #193]: #189
-#311 := (not #189)
-#400 := (or #311 #235)
-#377 := (= 1::Int 3::Int)
-#376 := (= 1::Int 2::Int)
-#375 := (= 1::Int 1::Int)
-#378 := (or #375 #376 #377)
-#379 := (iff #235 #378)
-#401 := (or #311 #379)
-#403 := (iff #401 #400)
-#405 := (iff #400 #400)
-#406 := [rewrite]: #405
-#398 := (iff #379 #235)
-#1 := true
-#393 := (iff #235 true)
-#396 := (iff #393 #235)
-#397 := [rewrite]: #396
-#394 := (iff #379 #393)
-#391 := (iff #378 true)
-#386 := (or true false false)
-#389 := (iff #386 true)
-#390 := [rewrite]: #389
-#387 := (iff #378 #386)
-#384 := (iff #377 false)
-#385 := [rewrite]: #384
-#382 := (iff #376 false)
-#383 := [rewrite]: #382
-#380 := (iff #375 true)
-#381 := [rewrite]: #380
-#388 := [monotonicity #381 #383 #385]: #387
-#392 := [trans #388 #390]: #391
-#395 := [monotonicity #392]: #394
-#399 := [trans #395 #397]: #398
-#404 := [monotonicity #399]: #403
-#407 := [trans #404 #406]: #403
-#402 := [quant-inst #9]: #401
-#408 := [mp #402 #407]: #400
-#410 := [unit-resolution #408 #194 #409]: false
-#411 := [lemma #410]: #235
-#238 := (or #236 #237)
-#46 := (f4 f5 #32)
-#202 := (pattern #46)
-#47 := (f11 f12 #46)
-#48 := (= #47 #32)
-#92 := (not #35)
-#93 := (or #92 #48)
-#203 := (forall (vars (?v0 Int)) (:pat #188 #202) #93)
-#96 := (forall (vars (?v0 Int)) #93)
-#206 := (iff #96 #203)
-#204 := (iff #93 #93)
-#205 := [refl]: #204
-#207 := [quant-intro #205]: #206
-#119 := (~ #96 #96)
-#117 := (~ #93 #93)
-#118 := [refl]: #117
-#120 := [nnf-pos #118]: #119
-#49 := (implies #35 #48)
-#50 := (forall (vars (?v0 Int)) #49)
-#97 := (iff #50 #96)
-#94 := (iff #49 #93)
-#95 := [rewrite]: #94
-#98 := [quant-intro #95]: #97
-#81 := [asserted]: #50
-#101 := [mp #81 #98]: #96
-#121 := [mp~ #101 #120]: #96
-#208 := [mp #121 #207]: #203
-#241 := (not #203)
-#242 := (or #241 #236 #237)
-#243 := (or #241 #238)
-#245 := (iff #243 #242)
-#246 := [rewrite]: #245
-#244 := [quant-inst #9]: #243
-#247 := [mp #244 #246]: #242
-#412 := [unit-resolution #247 #208]: #238
-#413 := [unit-resolution #412 #411]: #237
-#318 := (not #237)
-#357 := (or #318 #248)
-#358 := [th-lemma arith triangle-eq]: #357
-#414 := [unit-resolution #358 #413]: #248
-#249 := (>= #211 1::Int)
-#415 := (or #318 #249)
-#416 := [th-lemma arith triangle-eq]: #415
-#417 := [unit-resolution #416 #413]: #249
-#419 := [th-lemma arith eq-propagate -2 -2 #417 #414]: #418
-#421 := [symm #419]: #420
-#432 := [monotonicity #421]: #431
-#434 := [symm #432]: #433
-#437 := (= #52 #218)
-#209 := (f9 f10 #10)
-#210 := (f8 #209 #10)
-#221 := (= #210 #218)
-#23 := (:var 0 S2)
-#21 := (:var 1 S2)
-#22 := (f9 f10 #21)
-#24 := (f8 #22 #23)
-#181 := (pattern #24)
-#27 := (f11 f12 #23)
-#26 := (f11 f12 #21)
-#28 := (+ #26 #27)
-#29 := (f4 f5 #28)
-#30 := (= #24 #29)
-#182 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #181) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S2)) #30)
-#185 := (iff #31 #182)
-#183 := (iff #30 #30)
-#184 := [refl]: #183
-#186 := [quant-intro #184]: #185
-#104 := (~ #31 #31)
-#102 := (~ #30 #30)
-#103 := [refl]: #102
-#105 := [nnf-pos #103]: #104
-#78 := [asserted]: #31
-#106 := [mp~ #78 #105]: #31
-#187 := [mp #106 #186]: #182
-#224 := (not #182)
-#225 := (or #224 #221)
-#212 := (+ #211 #211)
-#213 := (f4 f5 #212)
-#214 := (= #210 #213)
-#226 := (or #224 #214)
-#228 := (iff #226 #225)
-#230 := (iff #225 #225)
-#231 := [rewrite]: #230
-#222 := (iff #214 #221)
-#219 := (= #213 #218)
-#216 := (= #212 #215)
-#217 := [rewrite]: #216
-#220 := [monotonicity #217]: #219
-#223 := [monotonicity #220]: #222
-#229 := [monotonicity #223]: #228
-#232 := [trans #229 #231]: #228
-#227 := [quant-inst #10 #10]: #226
-#233 := [mp #227 #232]: #225
-#422 := [unit-resolution #233 #187]: #221
-#429 := (= #52 #210)
-#11 := (= f3 #10)
-#75 := [asserted]: #11
-#427 := (= #51 #209)
-#425 := (= #209 #51)
-#423 := (= #10 f3)
-#424 := [symm #75]: #423
-#426 := [monotonicity #424]: #425
-#428 := [symm #426]: #427
-#430 := [monotonicity #428 #75]: #429
-#438 := [trans #430 #422]: #437
-#440 := [trans #438 #434]: #439
-#441 := [trans #440 #436]: #53
-#54 := (not #53)
-#99 := [asserted]: #54
-[unit-resolution #99 #441]: false
-unsat
-e8662cdc68a4df85a63b9e4b41418ecf449034b2 340 0
-#2 := false
-decl f7 :: S2
-#16 := f7
-decl f8 :: (-> S4 S2 S2)
-decl f6 :: S2
-#12 := f6
-decl f9 :: (-> S5 S2 S4)
-decl f3 :: S2
-#7 := f3
-decl f10 :: S5
-#20 := f10
-#51 := (f9 f10 f3)
-#52 := (f8 #51 f6)
-#53 := (= #52 f7)
-decl f4 :: (-> S3 Int S2)
-#17 := 3::Int
-decl f5 :: S3
-#8 := f5
-#18 := (f4 f5 3::Int)
-#522 := (= #18 f7)
-#19 := (= f7 #18)
-#77 := [asserted]: #19
-#523 := [symm #77]: #522
-#526 := (= #52 #18)
-decl f11 :: (-> S6 S2 Int)
-#13 := 2::Int
-#14 := (f4 f5 2::Int)
-decl f12 :: S6
-#25 := f12
-#212 := (f11 f12 #14)
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#211 := (f11 f12 #10)
-#213 := (+ #211 #212)
-#214 := (f4 f5 #213)
-#520 := (= #214 #18)
-#518 := (= #18 #214)
-#474 := (= 3::Int #213)
-#383 := (= #213 3::Int)
-#246 := (<= #212 2::Int)
-#236 := (= #212 2::Int)
-decl f1 :: S1
-#3 := f1
-decl f13 :: (-> Int S7 S1)
-decl f14 :: S7
-#33 := f14
-#224 := (f13 2::Int f14)
-#225 := (= #224 f1)
-#235 := (not #225)
-#513 := [hypothesis]: #235
-#32 := (:var 0 Int)
-#34 := (f13 #32 f14)
-#188 := (pattern #34)
-#38 := (= #32 3::Int)
-#37 := (= #32 2::Int)
-#36 := (= #32 1::Int)
-#82 := (or #36 #37 #38)
-#35 := (= #34 f1)
-#85 := (iff #35 #82)
-#189 := (forall (vars (?v0 Int)) (:pat #188) #85)
-#88 := (forall (vars (?v0 Int)) #85)
-#192 := (iff #88 #189)
-#190 := (iff #85 #85)
-#191 := [refl]: #190
-#193 := [quant-intro #191]: #192
-#109 := (~ #88 #88)
-#107 := (~ #85 #85)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#39 := (or #37 #38)
-#40 := (or #36 #39)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#89 := (iff #42 #88)
-#86 := (iff #41 #85)
-#83 := (iff #40 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#79 := [asserted]: #42
-#91 := [mp #79 #90]: #88
-#111 := [mp~ #91 #110]: #88
-#194 := [mp #111 #193]: #189
-#302 := (not #189)
-#504 := (or #302 #225)
-#481 := (= 2::Int 3::Int)
-#451 := (= 2::Int 2::Int)
-#450 := (= 2::Int 1::Int)
-#482 := (or #450 #451 #481)
-#483 := (iff #225 #482)
-#505 := (or #302 #483)
-#507 := (iff #505 #504)
-#509 := (iff #504 #504)
-#510 := [rewrite]: #509
-#502 := (iff #483 #225)
-#1 := true
-#497 := (iff #225 true)
-#500 := (iff #497 #225)
-#501 := [rewrite]: #500
-#498 := (iff #483 #497)
-#495 := (iff #482 true)
-#490 := (or false true false)
-#493 := (iff #490 true)
-#494 := [rewrite]: #493
-#491 := (iff #482 #490)
-#488 := (iff #481 false)
-#489 := [rewrite]: #488
-#486 := (iff #451 true)
-#487 := [rewrite]: #486
-#484 := (iff #450 false)
-#485 := [rewrite]: #484
-#492 := [monotonicity #485 #487 #489]: #491
-#496 := [trans #492 #494]: #495
-#499 := [monotonicity #496]: #498
-#503 := [trans #499 #501]: #502
-#508 := [monotonicity #503]: #507
-#511 := [trans #508 #510]: #507
-#506 := [quant-inst #13]: #505
-#512 := [mp #506 #511]: #504
-#514 := [unit-resolution #512 #194 #513]: false
-#515 := [lemma #514]: #225
-#237 := (or #235 #236)
-#46 := (f4 f5 #32)
-#202 := (pattern #46)
-#47 := (f11 f12 #46)
-#48 := (= #47 #32)
-#92 := (not #35)
-#93 := (or #92 #48)
-#203 := (forall (vars (?v0 Int)) (:pat #188 #202) #93)
-#96 := (forall (vars (?v0 Int)) #93)
-#206 := (iff #96 #203)
-#204 := (iff #93 #93)
-#205 := [refl]: #204
-#207 := [quant-intro #205]: #206
-#119 := (~ #96 #96)
-#117 := (~ #93 #93)
-#118 := [refl]: #117
-#120 := [nnf-pos #118]: #119
-#49 := (implies #35 #48)
-#50 := (forall (vars (?v0 Int)) #49)
-#97 := (iff #50 #96)
-#94 := (iff #49 #93)
-#95 := [rewrite]: #94
-#98 := [quant-intro #95]: #97
-#81 := [asserted]: #50
-#101 := [mp #81 #98]: #96
-#121 := [mp~ #101 #120]: #96
-#208 := [mp #121 #207]: #203
-#226 := (not #203)
-#240 := (or #226 #235 #236)
-#241 := (or #226 #237)
-#243 := (iff #241 #240)
-#244 := [rewrite]: #243
-#242 := [quant-inst #13]: #241
-#245 := [mp #242 #244]: #240
-#460 := [unit-resolution #245 #208]: #237
-#461 := [unit-resolution #460 #515]: #236
-#312 := (not #236)
-#462 := (or #312 #246)
-#463 := [th-lemma arith triangle-eq]: #462
-#464 := [unit-resolution #463 #461]: #246
-#247 := (>= #212 2::Int)
-#465 := (or #312 #247)
-#466 := [th-lemma arith triangle-eq]: #465
-#467 := [unit-resolution #466 #461]: #247
-#233 := (<= #211 1::Int)
-#222 := (= #211 1::Int)
-#216 := (f13 1::Int f14)
-#217 := (= #216 f1)
-#221 := (not #217)
-#447 := [hypothesis]: #221
-#392 := (or #302 #217)
-#398 := (= 1::Int 3::Int)
-#397 := (= 1::Int 2::Int)
-#396 := (= 1::Int 1::Int)
-#399 := (or #396 #397 #398)
-#400 := (iff #217 #399)
-#393 := (or #302 #400)
-#395 := (iff #393 #392)
-#443 := (iff #392 #392)
-#444 := [rewrite]: #443
-#390 := (iff #400 #217)
-#414 := (iff #217 true)
-#388 := (iff #414 #217)
-#389 := [rewrite]: #388
-#415 := (iff #400 #414)
-#412 := (iff #399 true)
-#407 := (or true false false)
-#410 := (iff #407 true)
-#411 := [rewrite]: #410
-#408 := (iff #399 #407)
-#405 := (iff #398 false)
-#406 := [rewrite]: #405
-#403 := (iff #397 false)
-#404 := [rewrite]: #403
-#401 := (iff #396 true)
-#402 := [rewrite]: #401
-#409 := [monotonicity #402 #404 #406]: #408
-#413 := [trans #409 #411]: #412
-#416 := [monotonicity #413]: #415
-#391 := [trans #416 #389]: #390
-#442 := [monotonicity #391]: #395
-#445 := [trans #442 #444]: #395
-#394 := [quant-inst #9]: #393
-#446 := [mp #394 #445]: #392
-#448 := [unit-resolution #446 #194 #447]: false
-#449 := [lemma #448]: #217
-#223 := (or #221 #222)
-#227 := (or #226 #221 #222)
-#228 := (or #226 #223)
-#230 := (iff #228 #227)
-#231 := [rewrite]: #230
-#229 := [quant-inst #9]: #228
-#232 := [mp #229 #231]: #227
-#468 := [unit-resolution #232 #208]: #223
-#469 := [unit-resolution #468 #449]: #222
-#351 := (not #222)
-#470 := (or #351 #233)
-#471 := [th-lemma arith triangle-eq]: #470
-#472 := [unit-resolution #471 #469]: #233
-#234 := (>= #211 1::Int)
-#386 := (not #234)
-#387 := [hypothesis]: #386
-#417 := (or #351 #234)
-#418 := [th-lemma arith triangle-eq]: #417
-#419 := [unit-resolution #418 #387]: #351
-#333 := (= #211 2::Int)
-#354 := (not #333)
-#348 := (>= #211 2::Int)
-#420 := (not #348)
-#421 := (or #420 #234)
-#422 := [th-lemma arith farkas 1 1]: #421
-#423 := [unit-resolution #422 #387]: #420
-#424 := (or #354 #348)
-#425 := [th-lemma arith triangle-eq]: #424
-#426 := [unit-resolution #425 #423]: #354
-#334 := (= #211 3::Int)
-#357 := (not #334)
-#350 := (>= #211 3::Int)
-#427 := (not #350)
-#428 := (or #427 #234)
-#429 := [th-lemma arith farkas 1 1]: #428
-#430 := [unit-resolution #429 #387]: #427
-#431 := (or #357 #350)
-#432 := [th-lemma arith triangle-eq]: #431
-#433 := [unit-resolution #432 #430]: #357
-#341 := (or #222 #333 #334)
-#289 := (f13 #211 f14)
-#290 := (= #289 f1)
-#342 := (iff #290 #341)
-#345 := (or #302 #342)
-#346 := [quant-inst #211]: #345
-#434 := [unit-resolution #346 #194]: #342
-#363 := (not #342)
-#436 := (or #363 #341)
-#23 := (:var 0 S2)
-#27 := (f11 f12 #23)
-#195 := (pattern #27)
-#43 := (f13 #27 f14)
-#44 := (= #43 f1)
-#196 := (forall (vars (?v0 S2)) (:pat #195) #44)
-#45 := (forall (vars (?v0 S2)) #44)
-#199 := (iff #45 #196)
-#197 := (iff #44 #44)
-#198 := [refl]: #197
-#200 := [quant-intro #198]: #199
-#114 := (~ #45 #45)
-#112 := (~ #44 #44)
-#113 := [refl]: #112
-#115 := [nnf-pos #113]: #114
-#80 := [asserted]: #45
-#116 := [mp~ #80 #115]: #45
-#201 := [mp #116 #200]: #196
-#291 := (not #196)
-#296 := (or #291 #290)
-#297 := [quant-inst #10]: #296
-#435 := [unit-resolution #297 #201]: #290
-#366 := (not #290)
-#367 := (or #363 #366 #341)
-#368 := [def-axiom]: #367
-#437 := [unit-resolution #368 #435]: #436
-#438 := [unit-resolution #437 #434]: #341
-#360 := (not #341)
-#361 := (or #360 #222 #333 #334)
-#362 := [def-axiom]: #361
-#439 := [unit-resolution #362 #438]: #341
-#440 := [unit-resolution #439 #433 #426 #419]: false
-#441 := [lemma #440]: #234
-#473 := [th-lemma arith eq-propagate -1 -1 -1 -1 #441 #472 #467 #464]: #383
-#475 := [symm #473]: #474
-#519 := [monotonicity #475]: #518
-#521 := [symm #519]: #520
-#524 := (= #52 #214)
-#209 := (f9 f10 #10)
-#210 := (f8 #209 #14)
-#215 := (= #210 #214)
-#21 := (:var 1 S2)
-#22 := (f9 f10 #21)
-#24 := (f8 #22 #23)
-#181 := (pattern #24)
-#26 := (f11 f12 #21)
-#28 := (+ #26 #27)
-#29 := (f4 f5 #28)
-#30 := (= #24 #29)
-#182 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #181) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S2)) #30)
-#185 := (iff #31 #182)
-#183 := (iff #30 #30)
-#184 := [refl]: #183
-#186 := [quant-intro #184]: #185
-#104 := (~ #31 #31)
-#102 := (~ #30 #30)
-#103 := [refl]: #102
-#105 := [nnf-pos #103]: #104
-#78 := [asserted]: #31
-#106 := [mp~ #78 #105]: #31
-#187 := [mp #106 #186]: #182
-#218 := (not #182)
-#219 := (or #218 #215)
-#220 := [quant-inst #10 #14]: #219
-#476 := [unit-resolution #220 #187]: #215
-#516 := (= #52 #210)
-#15 := (= f6 #14)
-#76 := [asserted]: #15
-#452 := (= #51 #209)
-#479 := (= #209 #51)
-#477 := (= #10 f3)
-#11 := (= f3 #10)
-#75 := [asserted]: #11
-#478 := [symm #75]: #477
-#480 := [monotonicity #478]: #479
-#453 := [symm #480]: #452
-#517 := [monotonicity #453 #76]: #516
-#525 := [trans #517 #476]: #524
-#527 := [trans #525 #521]: #526
-#528 := [trans #527 #523]: #53
-#54 := (not #53)
-#99 := [asserted]: #54
-[unit-resolution #99 #528]: false
-unsat
-114113d4c28c25e534c670f47fca087183a5f8c8 1 0
-unsat
-494b946d69182e62cf2adb59a4908bcd2cc3c25f 1 0
-unsat
-846610dc3de8c529329029964342bed155b928be 1 0
-unsat
-c78972c2be9e010d564c219e8371a1e07b95e81b 1 0
-unsat
-6ebffc1a9d53b928532f7c058a376cb3c0716d92 1 0
-unsat
-bfcbce0fd0c787695b2cb81657f53a4e946de0f7 1 0
-unsat
-87c04d689bac52cec8b0c1a08d098942fd70d466 1 0
-unsat
-c290166c6fcbece0c64059bd0622a1d9dbb1c5e8 1 0
-unsat
-a2e1430a221557099dbbfaea91575c18c640d29c 1 0
-unsat
-2a17166993a82e94f975eebec87d116c80957ca3 1 0
-unsat
-59e681af5117de8711365345306b7aa17a425e95 1 0
-unsat
-5bc354c4cba9fa390e5a5b4fff48e724cd6a4ebf 1 0
-unsat
-0b4eaebaa1c7da0e8aacfa5a2eba079ece06e131 1 0
-unsat
-048b4d112d6dd41a60f998755f2db6b8efd86231 1 0
-unsat
-44b17af9b9a91745590d6ecb19c7206d98ab139a 1 0
-unsat
-3523e8d2bd307bbba5a32002f0ec6e28e5894143 1 0
-unsat
-6e8b6413930418b08c3489ea4eb22477eb9fad98 1 0
-unsat
-2ff6320af6e3da1595c21bde8e3d60f9f793b05e 1 0
-unsat
-c903ab15e32b62af335654e8c9787041ccb90f1d 1 0
-unsat
-626bc827bc367e9c39a2fe8c6f7c8a2681e74bce 1 0
-unsat
-8ef64ff3e519412fcade8a4d9a8bec98415d6a06 1 0
-unsat
-0e110597ee5fd59c05d2cfca519aa8eb04251546 1 0
-unsat
-7fd213cb5e600482169baaba3e41c80ffd02c436 1 0
-unsat
-885bfcca057c7a00c20747d601df50ad8423656f 1 0
-unsat
-a89a8374bf2ed246a6005542713c5d935dd6dfdc 1 0
-unsat
-876ed7294bbfc54103308ef6b14723c1148733bd 1 0
-unsat
-41d31522928c508669072711001a529f38867652 1 0
-unsat
-207ccab8c5caaba7048ab574dcdb91f4c1e73815 1 0
-unsat
-863ce4ac998f8311e2b7a27eadc176786183347f 1 0
-unsat
-0c7f2686d2381d34ae33481937606b55c3351e5e 1 0
-unsat
-c8c2c45b649fbbacff8b9a61badac4db22cb46c2 1 0
-unsat
-63761ff981670944c18e6dd437cfe4578c88fb15 1 0
-unsat
-55f1f6079a3e9b28fa8aecfb53cd816993999074 1 0
-unsat
-dd27e03a481e9d6d9ad7c5b84a5137b699e90735 1 0
-unsat
-d6059b26d228981814c293de9adcac3c10e56c06 1 0
-unsat
-4f91be474d91f53d29f3f2258bb7d273880ef8e6 1 0
-unsat
-fe0f4adcbca31458a44c9fa7c3a70eef3159899a 1 0
-unsat
-8a88bb45199657d7b93fb63596b175087ccee5b6 1 0
-unsat
-e9444ef1965eaddfc7689e8ddd3c142533cf3405 1 0
-unsat
-1cb7dac6ffcfcf174de9b93048f0d7b2e6695b47 1 0
-unsat
-bbaaddd8f857f1563ff57dbef0644812cb6b7217 1 0
-unsat
-bc866ccbb68526e04dbee31bfbf06c3c0c136997 1 0
-unsat
-a8a33441caa49095c09744f40e851e338d32aab0 1 0
-unsat
-69389e184ca843a40e122fe630100028f5d0dfe2 1 0
-unsat
-59f2b64f5b2d655f8fd50a111cc1bf73a7e32876 1 0
-unsat
-561b779e14608d5bf4b63c02d41e6f6e5d7bac92 1 0
-unsat
-197371e9402d0d463d6f937ba339cf72a8abf07b 1 0
-unsat
-702df5d383bb67100b0fc3f930d58d64c9e9a02d 1 0
-unsat
-edeb3362e6db1fa2b6f5bd97e4c1a396396f2282 1 0
-unsat
-bad693fed8d87da59fb794363aef6ae36b19bcf7 1 0
-unsat
-97fc736b0a2fffdd9e35ec8d6b184e53c9636024 1 0
-unsat
-38010eaae88cc69a2c26a2defbead948aaabd4f4 1 0
-unsat
-4cbb5558bd3975388e0fb974eb0c218f0d9e4a94 1 0
-unsat
-0f4d9605278da9fff8a3d692d173824bfbaa11e8 1 0
-unsat
-581ce35318bef5f170a152cb14de30b8e6da4277 1 0
-unsat
-476ae2a77ea015b7c4b5fa427ba5703e48cebd80 1 0
-unsat
-f8308b4ecb3d87177c35dbad8eba7c049e0cfc96 1 0
-unsat
-4f6185d7afc5cdb6870999c7155dd06a4abca6db 47 0
-#2 := false
-decl f10 :: S4
-#34 := f10
-decl f3 :: (-> S2 S3 S4)
-decl f9 :: S3
-#32 := f9
-decl f4 :: (-> S5 S4 S2)
-decl f5 :: (-> S6 S3 S5)
-decl f6 :: (-> S7 S2 S6)
-decl f8 :: S2
-#30 := f8
-decl f7 :: S7
-#7 := f7
-#31 := (f6 f7 f8)
-#33 := (f5 #31 f9)
-#35 := (f4 #33 f10)
-#36 := (f3 #35 f9)
-#37 := (= #36 f10)
-#38 := (not #37)
-#61 := [asserted]: #38
-#12 := (:var 0 S4)
-#10 := (:var 1 S3)
-#8 := (:var 2 S2)
-#9 := (f6 f7 #8)
-#11 := (f5 #9 #10)
-#13 := (f4 #11 #12)
-#560 := (pattern #13)
-#14 := (f3 #13 #10)
-#15 := (= #14 #12)
-#561 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #560) #15)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
-#564 := (iff #16 #561)
-#562 := (iff #15 #15)
-#563 := [refl]: #562
-#565 := [quant-intro #563]: #564
-#73 := (~ #16 #16)
-#71 := (~ #15 #15)
-#72 := [refl]: #71
-#74 := [nnf-pos #72]: #73
-#59 := [asserted]: #16
-#63 := [mp~ #59 #74]: #16
-#566 := [mp #63 #565]: #561
-#145 := (not #561)
-#231 := (or #145 #37)
-#146 := [quant-inst #30 #32 #34]: #231
-[unit-resolution #146 #566 #61]: false
-unsat
-5bafbb97f7efbe2d659f283d3886a5959ca6e520 87 0
-#2 := false
-decl f9 :: S3
-#31 := f9
-decl f8 :: S3
-#30 := f8
-#32 := (= f8 f9)
-#160 := (= f9 f8)
-decl f3 :: (-> S2 S3 S4)
-decl f10 :: S2
-#34 := f10
-#40 := (f3 f10 f9)
-decl f4 :: (-> S5 S4 S2)
-decl f11 :: S4
-#37 := f11
-decl f5 :: (-> S6 S3 S5)
-decl f6 :: (-> S7 S2 S6)
-decl f7 :: S7
-#7 := f7
-#35 := (f6 f7 f10)
-#36 := (f5 #35 f8)
-#38 := (f4 #36 f11)
-#39 := (f3 #38 f9)
-#41 := (= #39 #40)
-#246 := (= #39 f11)
-#249 := (if #160 #246 #41)
-#23 := (:var 0 S3)
-#21 := (:var 1 S4)
-#19 := (:var 2 S3)
-#17 := (:var 3 S2)
-#18 := (f6 f7 #17)
-#20 := (f5 #18 #19)
-#22 := (f4 #20 #21)
-#24 := (f3 #22 #23)
-#582 := (pattern #24)
-#26 := (f3 #17 #23)
-#95 := (= #24 #26)
-#94 := (= #24 #21)
-#25 := (= #23 #19)
-#82 := (if #25 #94 #95)
-#583 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #582) #82)
-#87 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #82)
-#586 := (iff #87 #583)
-#584 := (iff #82 #82)
-#585 := [refl]: #584
-#587 := [quant-intro #585]: #586
-#27 := (if #25 #21 #26)
-#28 := (= #24 #27)
-#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
-#84 := (iff #29 #87)
-#83 := (iff #28 #82)
-#86 := [rewrite]: #83
-#85 := [quant-intro #86]: #84
-#80 := (~ #29 #29)
-#79 := (~ #28 #28)
-#92 := [refl]: #79
-#81 := [nnf-pos #92]: #80
-#65 := [asserted]: #29
-#93 := [mp~ #65 #81]: #29
-#96 := [mp #93 #85]: #87
-#588 := [mp #96 #587]: #583
-#248 := (not #583)
-#252 := (or #248 #249)
-#231 := [quant-inst #34 #30 #37 #31]: #252
-#250 := [unit-resolution #231 #588]: #249
-#567 := (not #249)
-#251 := (or #567 #160)
-#74 := (not #41)
-#67 := (or #32 #41)
-#70 := (not #67)
-#33 := (not #32)
-#42 := (implies #33 #41)
-#43 := (not #42)
-#71 := (iff #43 #70)
-#68 := (iff #42 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#66 := [asserted]: #43
-#75 := [mp #66 #72]: #70
-#76 := [not-or-elim #75]: #74
-#563 := (or #567 #160 #41)
-#236 := [def-axiom]: #563
-#568 := [unit-resolution #236 #76]: #251
-#574 := [unit-resolution #568 #250]: #160
-#564 := [symm #574]: #32
-#73 := [not-or-elim #75]: #33
-[unit-resolution #73 #564]: false
-unsat
-84690766f80a9a99468eed8a8759374419b173e1 119 0
-#2 := false
-decl f11 :: S4
-#37 := f11
-decl f3 :: (-> S2 S3 S4)
-decl f8 :: S3
-#30 := f8
-decl f4 :: (-> S5 S4 S2)
-decl f12 :: S4
-#41 := f12
-decl f5 :: (-> S6 S3 S5)
-decl f9 :: S3
-#31 := f9
-decl f6 :: (-> S7 S2 S6)
-decl f10 :: S2
-#34 := f10
-decl f7 :: S7
-#7 := f7
-#35 := (f6 f7 f10)
-#36 := (f5 #35 f8)
-#38 := (f4 #36 f11)
-#39 := (f6 f7 #38)
-#40 := (f5 #39 f9)
-#42 := (f4 #40 f12)
-#43 := (f3 #42 f8)
-#44 := (= #43 f11)
-#162 := (f3 #38 f8)
-#248 := (= #162 f11)
-#12 := (:var 0 S4)
-#10 := (:var 1 S3)
-#8 := (:var 2 S2)
-#9 := (f6 f7 #8)
-#11 := (f5 #9 #10)
-#13 := (f4 #11 #12)
-#578 := (pattern #13)
-#14 := (f3 #13 #10)
-#15 := (= #14 #12)
-#579 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #578) #15)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
-#582 := (iff #16 #579)
-#580 := (iff #15 #15)
-#581 := [refl]: #580
-#583 := [quant-intro #581]: #582
-#93 := (~ #16 #16)
-#91 := (~ #15 #15)
-#92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
-#67 := [asserted]: #16
-#81 := [mp~ #67 #94]: #16
-#584 := [mp #81 #583]: #579
-#164 := (not #579)
-#250 := (or #164 #248)
-#241 := [quant-inst #34 #30 #37]: #250
-#234 := [unit-resolution #241 #584]: #248
-#253 := (= #43 #162)
-#252 := (= #43 f12)
-#32 := (= f8 f9)
-#255 := (if #32 #252 #253)
-#23 := (:var 0 S3)
-#21 := (:var 1 S4)
-#19 := (:var 2 S3)
-#17 := (:var 3 S2)
-#18 := (f6 f7 #17)
-#20 := (f5 #18 #19)
-#22 := (f4 #20 #21)
-#24 := (f3 #22 #23)
-#585 := (pattern #24)
-#26 := (f3 #17 #23)
-#98 := (= #24 #26)
-#97 := (= #24 #21)
-#25 := (= #23 #19)
-#85 := (if #25 #97 #98)
-#586 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #585) #85)
-#90 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #85)
-#589 := (iff #90 #586)
-#587 := (iff #85 #85)
-#588 := [refl]: #587
-#590 := [quant-intro #588]: #589
-#27 := (if #25 #21 #26)
-#28 := (= #24 #27)
-#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
-#87 := (iff #29 #90)
-#86 := (iff #28 #85)
-#89 := [rewrite]: #86
-#88 := [quant-intro #89]: #87
-#83 := (~ #29 #29)
-#82 := (~ #28 #28)
-#95 := [refl]: #82
-#84 := [nnf-pos #95]: #83
-#68 := [asserted]: #29
-#96 := [mp~ #68 #84]: #29
-#99 := [mp #96 #88]: #90
-#591 := [mp #99 #590]: #586
-#572 := (not #586)
-#228 := (or #572 #255)
-#359 := [quant-inst #38 #31 #41 #30]: #228
-#570 := [unit-resolution #359 #591]: #255
-#566 := (not #255)
-#231 := (or #566 #253)
-#33 := (not #32)
-#70 := (or #32 #44)
-#73 := (not #70)
-#45 := (implies #33 #44)
-#46 := (not #45)
-#74 := (iff #46 #73)
-#71 := (iff #45 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#69 := [asserted]: #46
-#78 := [mp #69 #75]: #73
-#76 := [not-or-elim #78]: #33
-#573 := (or #566 #32 #253)
-#574 := [def-axiom]: #573
-#568 := [unit-resolution #574 #76]: #231
-#227 := [unit-resolution #568 #570]: #253
-#569 := [trans #227 #234]: #44
-#77 := (not #44)
-#79 := [not-or-elim #78]: #77
-[unit-resolution #79 #569]: false
-unsat
-d65e508e9f0986a9cadbe07239acdf7dea9f9cdd 66 0
-#2 := false
-decl f12 :: S4
-#41 := f12
-decl f3 :: (-> S2 S3 S4)
-decl f9 :: S3
-#31 := f9
-decl f4 :: (-> S5 S4 S2)
-decl f5 :: (-> S6 S3 S5)
-decl f6 :: (-> S7 S2 S6)
-decl f11 :: S4
-#37 := f11
-decl f8 :: S3
-#30 := f8
-decl f10 :: S2
-#34 := f10
-decl f7 :: S7
-#7 := f7
-#35 := (f6 f7 f10)
-#36 := (f5 #35 f8)
-#38 := (f4 #36 f11)
-#39 := (f6 f7 #38)
-#40 := (f5 #39 f9)
-#42 := (f4 #40 f12)
-#43 := (f3 #42 f9)
-#44 := (= #43 f12)
-#77 := (not #44)
-#32 := (= f8 f9)
-#70 := (or #32 #44)
-#73 := (not #70)
-#33 := (not #32)
-#45 := (implies #33 #44)
-#46 := (not #45)
-#74 := (iff #46 #73)
-#71 := (iff #45 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#69 := [asserted]: #46
-#78 := [mp #69 #75]: #73
-#79 := [not-or-elim #78]: #77
-#12 := (:var 0 S4)
-#10 := (:var 1 S3)
-#8 := (:var 2 S2)
-#9 := (f6 f7 #8)
-#11 := (f5 #9 #10)
-#13 := (f4 #11 #12)
-#578 := (pattern #13)
-#14 := (f3 #13 #10)
-#15 := (= #14 #12)
-#579 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #578) #15)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
-#582 := (iff #16 #579)
-#580 := (iff #15 #15)
-#581 := [refl]: #580
-#583 := [quant-intro #581]: #582
-#93 := (~ #16 #16)
-#91 := (~ #15 #15)
-#92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
-#67 := [asserted]: #16
-#81 := [mp~ #67 #94]: #16
-#584 := [mp #81 #583]: #579
-#164 := (not #579)
-#252 := (or #164 #44)
-#253 := [quant-inst #38 #31 #41]: #252
-[unit-resolution #253 #584 #79]: false
-unsat
-0f758203e0be215aacd00c651e831f3fd6369edd 73 0
-#2 := false
-decl f12 :: S4
-#40 := f12
-decl f3 :: (-> S2 S3 S4)
-decl f8 :: S3
-#30 := f8
-decl f4 :: (-> S5 S4 S2)
-decl f5 :: (-> S6 S3 S5)
-decl f9 :: S3
-#31 := f9
-decl f6 :: (-> S7 S2 S6)
-decl f11 :: S4
-#36 := f11
-decl f10 :: S2
-#33 := f10
-decl f7 :: S7
-#7 := f7
-#34 := (f6 f7 f10)
-#35 := (f5 #34 f8)
-#37 := (f4 #35 f11)
-#38 := (f6 f7 #37)
-#39 := (f5 #38 f9)
-#41 := (f4 #39 f12)
-#42 := (f3 #41 f8)
-#43 := (= #42 f12)
-#164 := (f3 #41 f9)
-#250 := (= #164 f12)
-#12 := (:var 0 S4)
-#10 := (:var 1 S3)
-#8 := (:var 2 S2)
-#9 := (f6 f7 #8)
-#11 := (f5 #9 #10)
-#13 := (f4 #11 #12)
-#578 := (pattern #13)
-#14 := (f3 #13 #10)
-#15 := (= #14 #12)
-#579 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #578) #15)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
-#582 := (iff #16 #579)
-#580 := (iff #15 #15)
-#581 := [refl]: #580
-#583 := [quant-intro #581]: #582
-#93 := (~ #16 #16)
-#91 := (~ #15 #15)
-#92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
-#66 := [asserted]: #16
-#81 := [mp~ #66 #94]: #16
-#584 := [mp #81 #583]: #579
-#241 := (not #579)
-#255 := (or #241 #250)
-#234 := [quant-inst #37 #31 #40]: #255
-#215 := [unit-resolution #234 #584]: #250
-#216 := (= #42 #164)
-#32 := (= f8 f9)
-#69 := (not #32)
-#70 := (or #69 #43)
-#73 := (not #70)
-#44 := (implies #32 #43)
-#45 := (not #44)
-#74 := (iff #45 #73)
-#71 := (iff #44 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#68 := [asserted]: #45
-#78 := [mp #68 #75]: #73
-#76 := [not-or-elim #78]: #32
-#217 := [monotonicity #76]: #216
-#218 := [trans #217 #215]: #43
-#77 := (not #43)
-#79 := [not-or-elim #78]: #77
-[unit-resolution #79 #218]: false
-unsat
-147fa7b416ea80f4d0db2b821e5b7f09e2dd6767 152 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f10 :: S3
-#34 := f10
-decl f11 :: S2
-#41 := f11
-#51 := (f3 f11 f10)
-decl f4 :: (-> S5 S4 S2)
-decl f12 :: S4
-#44 := f12
-decl f5 :: (-> S6 S3 S5)
-decl f8 :: S3
-#30 := f8
-decl f6 :: (-> S7 S2 S6)
-decl f7 :: S7
-#7 := f7
-#42 := (f6 f7 f11)
-#43 := (f5 #42 f8)
-#45 := (f4 #43 f12)
-#281 := (f3 #45 f10)
-#282 := (= #281 #51)
-#568 := (= #281 f12)
-#567 := (= f10 f8)
-#565 := (if #567 #568 #282)
-#23 := (:var 0 S3)
-#21 := (:var 1 S4)
-#19 := (:var 2 S3)
-#17 := (:var 3 S2)
-#18 := (f6 f7 #17)
-#20 := (f5 #18 #19)
-#22 := (f4 #20 #21)
-#24 := (f3 #22 #23)
-#611 := (pattern #24)
-#26 := (f3 #17 #23)
-#128 := (= #24 #26)
-#127 := (= #24 #21)
-#25 := (= #23 #19)
-#111 := (if #25 #127 #128)
-#612 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #611) #111)
-#120 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #111)
-#615 := (iff #120 #612)
-#613 := (iff #111 #111)
-#614 := [refl]: #613
-#616 := [quant-intro #614]: #615
-#27 := (if #25 #21 #26)
-#28 := (= #24 #27)
-#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
-#117 := (iff #29 #120)
-#112 := (iff #28 #111)
-#119 := [rewrite]: #112
-#118 := [quant-intro #119]: #117
-#109 := (~ #29 #29)
-#108 := (~ #28 #28)
-#125 := [refl]: #108
-#110 := [nnf-pos #125]: #109
-#76 := [asserted]: #29
-#126 := [mp~ #76 #110]: #29
-#115 := [mp #126 #118]: #120
-#617 := [mp #115 #616]: #612
-#385 := (not #612)
-#570 := (or #385 #565)
-#559 := [quant-inst #41 #30 #44 #34]: #570
-#569 := [unit-resolution #559 #617]: #565
-#561 := (not #567)
-#35 := (= f8 f10)
-#36 := (not #35)
-#546 := (iff #36 #561)
-#551 := (iff #35 #567)
-#566 := (iff #567 #35)
-#550 := [commutativity]: #566
-#552 := [symm #550]: #551
-#547 := [monotonicity #552]: #546
-decl f9 :: S3
-#31 := f9
-#37 := (= f9 f10)
-#38 := (not #37)
-#32 := (= f8 f9)
-#33 := (not #32)
-#85 := (and #33 #36 #38)
-decl f13 :: S4
-#48 := f13
-#46 := (f6 f7 #45)
-#47 := (f5 #46 f9)
-#49 := (f4 #47 f13)
-#50 := (f3 #49 f10)
-#52 := (= #50 #51)
-#88 := (not #85)
-#91 := (or #88 #52)
-#94 := (not #91)
-#39 := (and #36 #38)
-#40 := (and #33 #39)
-#53 := (implies #40 #52)
-#54 := (not #53)
-#97 := (iff #54 #94)
-#78 := (not #40)
-#79 := (or #78 #52)
-#82 := (not #79)
-#95 := (iff #82 #94)
-#92 := (iff #79 #91)
-#89 := (iff #78 #88)
-#86 := (iff #40 #85)
-#87 := [rewrite]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93]: #95
-#83 := (iff #54 #82)
-#80 := (iff #53 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#98 := [trans #84 #96]: #97
-#77 := [asserted]: #54
-#99 := [mp #77 #98]: #94
-#100 := [not-or-elim #99]: #85
-#102 := [and-elim #100]: #36
-#553 := [mp #102 #547]: #561
-#406 := (not #282)
-#104 := (not #52)
-#388 := (iff #104 #406)
-#428 := (iff #52 #282)
-#545 := (iff #282 #52)
-#544 := (= #281 #50)
-#260 := (= #50 #281)
-#279 := (= #50 f13)
-#278 := (= f10 f9)
-#596 := (if #278 #279 #260)
-#592 := (or #385 #596)
-#265 := [quant-inst #45 #31 #48 #34]: #592
-#554 := [unit-resolution #265 #617]: #596
-#599 := (not #278)
-#387 := (iff #38 #599)
-#384 := (iff #37 #278)
-#548 := (iff #278 #37)
-#555 := [commutativity]: #548
-#386 := [symm #555]: #384
-#540 := [monotonicity #386]: #387
-#103 := [and-elim #100]: #38
-#541 := [mp #103 #540]: #599
-#266 := (not #596)
-#602 := (or #266 #278 #260)
-#597 := [def-axiom]: #602
-#543 := [unit-resolution #597 #541 #554]: #260
-#542 := [symm #543]: #544
-#427 := [monotonicity #542]: #545
-#429 := [symm #427]: #428
-#536 := [monotonicity #429]: #388
-#105 := [not-or-elim #99]: #104
-#438 := [mp #105 #536]: #406
-#560 := (not #565)
-#562 := (or #560 #567 #282)
-#563 := [def-axiom]: #562
-[unit-resolution #563 #438 #553 #569]: false
-unsat
-36b249aecd736f13331480916c503eb6e5909c98 39 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#8 := f4
-decl f10 :: S2
-#40 := f10
-#41 := (f3 f10 f4)
-#42 := (= #41 f1)
-#43 := (not #42)
-#44 := (not #43)
-#70 := (iff #44 #42)
-#71 := [rewrite]: #70
-#69 := [asserted]: #44
-#74 := [mp #69 #71]: #42
-#7 := (:var 0 S2)
-#9 := (f3 #7 f4)
-#585 := (pattern #9)
-#10 := (= #9 f1)
-#11 := (not #10)
-#586 := (forall (vars (?v0 S2)) (:pat #585) #11)
-#12 := (forall (vars (?v0 S2)) #11)
-#589 := (iff #12 #586)
-#587 := (iff #11 #11)
-#588 := [refl]: #587
-#590 := [quant-intro #588]: #589
-#88 := (~ #12 #12)
-#86 := (~ #11 #11)
-#87 := [refl]: #86
-#89 := [nnf-pos #87]: #88
-#65 := [asserted]: #12
-#73 := [mp~ #65 #89]: #12
-#591 := [mp #73 #590]: #586
-#256 := (not #586)
-#171 := (or #256 #43)
-#257 := [quant-inst #40]: #171
-[unit-resolution #257 #591 #74]: false
-unsat
-ab0a0cb55145e0e555c965d2dc39dc477d5c1fea 34 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#13 := f5
-decl f10 :: S2
-#40 := f10
-#41 := (f3 f10 f5)
-#42 := (= #41 f1)
-#43 := (not #42)
-#68 := [asserted]: #43
-#7 := (:var 0 S2)
-#14 := (f3 #7 f5)
-#588 := (pattern #14)
-#15 := (= #14 f1)
-#589 := (forall (vars (?v0 S2)) (:pat #588) #15)
-#16 := (forall (vars (?v0 S2)) #15)
-#592 := (iff #16 #589)
-#590 := (iff #15 #15)
-#591 := [refl]: #590
-#593 := [quant-intro #591]: #592
-#72 := (~ #16 #16)
-#71 := (~ #15 #15)
-#86 := [refl]: #71
-#73 := [nnf-pos #86]: #72
-#65 := [asserted]: #16
-#87 := [mp~ #65 #73]: #16
-#594 := [mp #87 #593]: #589
-#252 := (not #589)
-#167 := (or #252 #42)
-#253 := [quant-inst #40]: #167
-[unit-resolution #253 #594 #68]: false
-unsat
-23c20a3f015d52f4e5090d65fc402473d21c2ff7 87 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#43 := f12
-decl f10 :: S2
-#40 := f10
-#49 := (f3 f10 f12)
-#50 := (= #49 f1)
-decl f11 :: S3
-#41 := f11
-#47 := (f3 f10 f11)
-#48 := (= #47 f1)
-#51 := (or #48 #50)
-#270 := (not #51)
-#258 := [hypothesis]: #270
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#18 := f8
-#42 := (f7 f8 f11)
-#44 := (f6 #42 f12)
-#45 := (f3 f10 #44)
-#46 := (= #45 f1)
-#584 := (or #46 #51)
-#79 := (not #46)
-#80 := (iff #79 #51)
-#52 := (iff #46 #51)
-#53 := (not #52)
-#81 := (iff #53 #80)
-#82 := [rewrite]: #81
-#78 := [asserted]: #53
-#85 := [mp #78 #82]: #80
-#269 := (not #80)
-#246 := (or #46 #51 #269)
-#377 := [def-axiom]: #246
-#257 := [unit-resolution #377 #85]: #584
-#591 := [unit-resolution #257 #258]: #46
-#571 := (or #79 #51)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 f8 #19)
-#22 := (f6 #20 #21)
-#17 := (:var 2 S2)
-#23 := (f3 #17 #22)
-#610 := (pattern #23)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#611 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #610) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#614 := (iff #31 #611)
-#612 := (iff #30 #30)
-#613 := [refl]: #612
-#615 := [quant-intro #613]: #614
-#89 := (~ #31 #31)
-#103 := (~ #30 #30)
-#104 := [refl]: #103
-#90 := [nnf-pos #104]: #89
-#76 := [asserted]: #31
-#105 := [mp~ #76 #90]: #31
-#616 := [mp #105 #615]: #611
-#592 := (not #611)
-#593 := (or #592 #52)
-#594 := [quant-inst #40 #41 #43]: #593
-#229 := [unit-resolution #594 #616]: #52
-#585 := (or #53 #79 #51)
-#244 := [def-axiom]: #585
-#233 := [unit-resolution #244 #229]: #571
-#234 := [unit-resolution #233 #591 #258]: false
-#235 := [lemma #234]: #51
-#588 := (or #79 #270)
-#273 := (or #79 #270 #269)
-#252 := [def-axiom]: #273
-#590 := [unit-resolution #252 #85]: #588
-#236 := [unit-resolution #590 #235]: #79
-#573 := (or #46 #270)
-#589 := (or #53 #46 #270)
-#595 := [def-axiom]: #589
-#574 := [unit-resolution #595 #229]: #573
-[unit-resolution #574 #236 #235]: false
-unsat
-64da68860ea07cde955340b27fa12fa5f09a1695 121 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f4 :: S3
-#8 := f4
-decl f7 :: (-> S5 S3 S4)
-decl f11 :: S3
-#41 := f11
-decl f8 :: S5
-#18 := f8
-#42 := (f7 f8 f11)
-#43 := (f6 #42 f4)
-decl f10 :: S2
-#40 := f10
-#44 := (f3 f10 #43)
-#45 := (= #44 f1)
-#75 := (not #45)
-#46 := (f3 f10 f11)
-#47 := (= #46 f1)
-#262 := (not #47)
-#572 := [hypothesis]: #262
-#268 := (or #45 #47)
-#76 := (iff #75 #47)
-#48 := (iff #45 #47)
-#49 := (not #48)
-#77 := (iff #49 #76)
-#78 := [rewrite]: #77
-#74 := [asserted]: #49
-#81 := [mp #74 #78]: #76
-#177 := (not #76)
-#266 := (or #45 #47 #177)
-#267 := [def-axiom]: #266
-#265 := [unit-resolution #267 #81]: #268
-#573 := [unit-resolution #265 #572]: #45
-#269 := (f3 f10 f4)
-#248 := (= #269 f1)
-#584 := (or #47 #248)
-#591 := (not #584)
-#589 := (not #248)
-#242 := [hypothesis]: #248
-#7 := (:var 0 S2)
-#9 := (f3 #7 f4)
-#592 := (pattern #9)
-#10 := (= #9 f1)
-#11 := (not #10)
-#593 := (forall (vars (?v0 S2)) (:pat #592) #11)
-#12 := (forall (vars (?v0 S2)) #11)
-#596 := (iff #12 #593)
-#594 := (iff #11 #11)
-#595 := [refl]: #594
-#597 := [quant-intro #595]: #596
-#95 := (~ #12 #12)
-#93 := (~ #11 #11)
-#94 := [refl]: #93
-#96 := [nnf-pos #94]: #95
-#70 := [asserted]: #12
-#80 := [mp~ #70 #96]: #12
-#598 := [mp #80 #597]: #593
-#232 := (not #593)
-#569 := (or #232 #589)
-#570 := [quant-inst #40]: #569
-#373 := [unit-resolution #570 #598 #242]: false
-#571 := [lemma #373]: #589
-#581 := (or #591 #47 #248)
-#240 := [def-axiom]: #581
-#568 := [unit-resolution #240 #572 #571]: #591
-#211 := (or #75 #584)
-#586 := (iff #45 #584)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 f8 #19)
-#22 := (f6 #20 #21)
-#17 := (:var 2 S2)
-#23 := (f3 #17 #22)
-#606 := (pattern #23)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#607 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #606) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#610 := (iff #31 #607)
-#608 := (iff #30 #30)
-#609 := [refl]: #608
-#611 := [quant-intro #609]: #610
-#85 := (~ #31 #31)
-#99 := (~ #30 #30)
-#100 := [refl]: #99
-#86 := [nnf-pos #100]: #85
-#72 := [asserted]: #31
-#101 := [mp~ #72 #86]: #31
-#612 := [mp #101 #611]: #607
-#580 := (not #607)
-#253 := (or #580 #586)
-#254 := [quant-inst #40 #41 #8]: #253
-#574 := [unit-resolution #254 #612]: #586
-#245 := (not #586)
-#583 := (or #245 #75 #584)
-#225 := [def-axiom]: #583
-#575 := [unit-resolution #225 #574]: #211
-#577 := [unit-resolution #575 #568 #573]: false
-#216 := [lemma #577]: #47
-#264 := (or #75 #262)
-#263 := (or #75 #262 #177)
-#178 := [def-axiom]: #263
-#255 := [unit-resolution #178 #81]: #264
-#217 := [unit-resolution #255 #216]: #75
-#587 := (or #584 #262)
-#588 := [def-axiom]: #587
-#578 := [unit-resolution #588 #216]: #584
-#576 := (or #45 #591)
-#582 := (or #245 #45 #591)
-#241 := [def-axiom]: #582
-#579 := [unit-resolution #241 #574]: #576
-[unit-resolution #579 #578 #217]: false
-unsat
-5d2b2bd5b82e9b686873c91fbf34494378daa8ce 90 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#13 := f5
-decl f10 :: S2
-#40 := f10
-#255 := (f3 f10 f5)
-#170 := (= #255 f1)
-#234 := (not #170)
-decl f11 :: S3
-#41 := f11
-#254 := (f3 f10 f11)
-#169 := (= #254 f1)
-#256 := (or #169 #170)
-#245 := (not #256)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#18 := f8
-#42 := (f7 f8 f11)
-#43 := (f6 #42 f5)
-#44 := (f3 f10 #43)
-#45 := (= #44 f1)
-#247 := (iff #45 #256)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 f8 #19)
-#22 := (f6 #20 #21)
-#17 := (:var 2 S2)
-#23 := (f3 #17 #22)
-#598 := (pattern #23)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#599 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #598) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#602 := (iff #31 #599)
-#600 := (iff #30 #30)
-#601 := [refl]: #600
-#603 := [quant-intro #601]: #602
-#77 := (~ #31 #31)
-#91 := (~ #30 #30)
-#92 := [refl]: #91
-#78 := [nnf-pos #92]: #77
-#69 := [asserted]: #31
-#93 := [mp~ #69 #78]: #31
-#604 := [mp #93 #603]: #599
-#260 := (not #599)
-#257 := (or #260 #247)
-#261 := [quant-inst #40 #41 #13]: #257
-#258 := [unit-resolution #261 #604]: #247
-#580 := (not #247)
-#259 := (or #580 #245)
-#46 := (not #45)
-#71 := [asserted]: #46
-#581 := (or #580 #45 #245)
-#582 := [def-axiom]: #581
-#559 := [unit-resolution #582 #71]: #259
-#221 := [unit-resolution #559 #258]: #245
-#365 := (or #256 #234)
-#572 := [def-axiom]: #365
-#222 := [unit-resolution #572 #221]: #234
-#7 := (:var 0 S2)
-#14 := (f3 #7 f5)
-#591 := (pattern #14)
-#15 := (= #14 f1)
-#592 := (forall (vars (?v0 S2)) (:pat #591) #15)
-#16 := (forall (vars (?v0 S2)) #15)
-#595 := (iff #16 #592)
-#593 := (iff #15 #15)
-#594 := [refl]: #593
-#596 := [quant-intro #594]: #595
-#75 := (~ #16 #16)
-#74 := (~ #15 #15)
-#89 := [refl]: #74
-#76 := [nnf-pos #89]: #75
-#68 := [asserted]: #16
-#90 := [mp~ #68 #76]: #16
-#597 := [mp #90 #596]: #592
-#233 := (not #592)
-#575 := (or #233 #170)
-#217 := [quant-inst #40]: #575
-[unit-resolution #217 #597 #222]: false
-unsat
-ede3dbc56e22f5b2950d014509e65a43a920f4de 131 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#41 := f11
-decl f10 :: S2
-#40 := f10
-#272 := (f3 f10 f11)
-#251 := (= #272 f1)
-decl f12 :: S3
-#43 := f12
-#587 := (f3 f10 f12)
-#589 := (= #587 f1)
-#583 := (or #589 #251)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#18 := f8
-#47 := (f7 f8 f12)
-#48 := (f6 #47 f11)
-#49 := (f3 f10 #48)
-#50 := (= #49 f1)
-#245 := (or #251 #589)
-#42 := (f7 f8 f11)
-#44 := (f6 #42 f12)
-#45 := (f3 f10 #44)
-#46 := (= #45 f1)
-#265 := (not #50)
-#574 := [hypothesis]: #265
-#271 := (or #46 #50)
-#78 := (not #46)
-#79 := (iff #78 #50)
-#51 := (iff #46 #50)
-#52 := (not #51)
-#80 := (iff #52 #79)
-#81 := [rewrite]: #80
-#77 := [asserted]: #52
-#84 := [mp #77 #81]: #79
-#180 := (not #79)
-#269 := (or #46 #50 #180)
-#270 := [def-axiom]: #269
-#268 := [unit-resolution #270 #84]: #271
-#575 := [unit-resolution #268 #574]: #46
-#564 := (or #78 #245)
-#376 := (iff #46 #245)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 f8 #19)
-#22 := (f6 #20 #21)
-#17 := (:var 2 S2)
-#23 := (f3 #17 #22)
-#609 := (pattern #23)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#610 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #609) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#613 := (iff #31 #610)
-#611 := (iff #30 #30)
-#612 := [refl]: #611
-#614 := [quant-intro #612]: #613
-#88 := (~ #31 #31)
-#102 := (~ #30 #30)
-#103 := [refl]: #102
-#89 := [nnf-pos #103]: #88
-#75 := [asserted]: #31
-#104 := [mp~ #75 #89]: #31
-#615 := [mp #104 #614]: #610
-#257 := (not #610)
-#590 := (or #257 #376)
-#591 := [quant-inst #40 #41 #43]: #590
-#187 := [unit-resolution #591 #615]: #376
-#586 := (not #376)
-#232 := (or #586 #78 #245)
-#233 := [def-axiom]: #232
-#565 := [unit-resolution #233 #187]: #564
-#287 := [unit-resolution #565 #575]: #245
-#594 := (not #589)
-#219 := (not #583)
-#562 := (or #50 #219)
-#256 := (iff #50 #583)
-#576 := (or #257 #256)
-#571 := [quant-inst #40 #43 #41]: #576
-#288 := [unit-resolution #571 #615]: #256
-#579 := (not #256)
-#582 := (or #579 #50 #219)
-#568 := [def-axiom]: #582
-#566 := [unit-resolution #568 #288]: #562
-#563 := [unit-resolution #566 #574]: #219
-#577 := (or #583 #594)
-#214 := [def-axiom]: #577
-#567 := [unit-resolution #214 #563]: #594
-#592 := (not #251)
-#578 := (or #583 #592)
-#580 := [def-axiom]: #578
-#277 := [unit-resolution #580 #563]: #592
-#248 := (not #245)
-#585 := (or #248 #251 #589)
-#244 := [def-axiom]: #585
-#278 := [unit-resolution #244 #277 #567 #287]: false
-#279 := [lemma #278]: #50
-#280 := (or #265 #583)
-#569 := (or #579 #265 #583)
-#276 := [def-axiom]: #569
-#558 := [unit-resolution #276 #288]: #280
-#559 := [unit-resolution #558 #279]: #583
-#267 := (or #78 #265)
-#266 := (or #78 #265 #180)
-#181 := [def-axiom]: #266
-#258 := [unit-resolution #181 #84]: #267
-#273 := [unit-resolution #258 #279]: #78
-#556 := (or #46 #248)
-#228 := (or #586 #46 #248)
-#570 := [def-axiom]: #228
-#560 := [unit-resolution #570 #187]: #556
-#557 := [unit-resolution #560 #273]: #248
-#593 := (or #245 #592)
-#588 := [def-axiom]: #593
-#561 := [unit-resolution #588 #557]: #592
-#584 := (or #245 #594)
-#243 := [def-axiom]: #584
-#550 := [unit-resolution #243 #557]: #594
-#220 := (or #219 #589 #251)
-#581 := [def-axiom]: #220
-[unit-resolution #581 #550 #561 #559]: false
-unsat
-36bb986beabfd5d2f2f59f2f22497a8981eb9126 95 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#41 := f11
-decl f10 :: S2
-#40 := f10
-#46 := (f3 f10 f11)
-#47 := (= #46 f1)
-#262 := (not #47)
-#230 := [hypothesis]: #262
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#18 := f8
-#42 := (f7 f8 f11)
-#43 := (f6 #42 f11)
-#44 := (f3 f10 #43)
-#45 := (= #44 f1)
-#268 := (or #45 #47)
-#75 := (not #45)
-#76 := (iff #75 #47)
-#48 := (iff #45 #47)
-#49 := (not #48)
-#77 := (iff #49 #76)
-#78 := [rewrite]: #77
-#74 := [asserted]: #49
-#81 := [mp #74 #78]: #76
-#177 := (not #76)
-#266 := (or #45 #47 #177)
-#267 := [def-axiom]: #266
-#265 := [unit-resolution #267 #81]: #268
-#231 := [unit-resolution #265 #230]: #45
-#569 := (or #75 #47)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 f8 #19)
-#22 := (f6 #20 #21)
-#17 := (:var 2 S2)
-#23 := (f3 #17 #22)
-#606 := (pattern #23)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#607 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #606) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#610 := (iff #31 #607)
-#608 := (iff #30 #30)
-#609 := [refl]: #608
-#611 := [quant-intro #609]: #610
-#85 := (~ #31 #31)
-#99 := (~ #30 #30)
-#100 := [refl]: #99
-#86 := [nnf-pos #100]: #85
-#72 := [asserted]: #31
-#101 := [mp~ #72 #86]: #31
-#612 := [mp #101 #611]: #607
-#580 := (not #607)
-#253 := (or #580 #48)
-#269 := (or #47 #47)
-#248 := (iff #45 #269)
-#254 := (or #580 #248)
-#588 := (iff #254 #253)
-#590 := (iff #253 #253)
-#585 := [rewrite]: #590
-#242 := (iff #248 #48)
-#584 := (iff #269 #47)
-#586 := [rewrite]: #584
-#373 := [monotonicity #586]: #242
-#589 := [monotonicity #373]: #588
-#591 := [trans #589 #585]: #588
-#587 := [quant-inst #40 #41 #41]: #254
-#581 := [mp #587 #591]: #253
-#232 := [unit-resolution #581 #612]: #48
-#582 := (or #49 #75 #47)
-#241 := [def-axiom]: #582
-#570 := [unit-resolution #241 #232]: #569
-#571 := [unit-resolution #570 #231 #230]: false
-#572 := [lemma #571]: #47
-#264 := (or #75 #262)
-#263 := (or #75 #262 #177)
-#178 := [def-axiom]: #263
-#255 := [unit-resolution #178 #81]: #264
-#573 := [unit-resolution #255 #572]: #75
-#568 := (or #45 #262)
-#240 := (or #49 #45 #262)
-#245 := [def-axiom]: #240
-#574 := [unit-resolution #245 #232]: #568
-[unit-resolution #574 #573 #572]: false
-unsat
-8bc88e5edfbcc5ec1dd0cfb089d9a4802a822e0a 194 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#43 := f12
-decl f10 :: S2
-#40 := f10
-#581 := (f3 f10 f12)
-#218 := (= #581 f1)
-decl f11 :: S3
-#41 := f11
-#276 := (f3 f10 f11)
-#255 := (= #276 f1)
-#570 := (or #255 #218)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#18 := f8
-#42 := (f7 f8 f11)
-#50 := (f6 #42 f12)
-#587 := (f3 f10 #50)
-#260 := (= #587 f1)
-#567 := (iff #260 #570)
-#379 := (not #567)
-#548 := (not #570)
-#284 := (not #218)
-decl f13 :: S3
-#45 := f13
-#578 := (f3 f10 f13)
-#579 := (= #578 f1)
-#571 := (or #218 #579)
-#564 := (not #571)
-#44 := (f7 f8 f12)
-#46 := (f6 #44 f13)
-#591 := (f3 f10 #46)
-#593 := (= #591 f1)
-#281 := (iff #593 #571)
-#543 := (not #281)
-#400 := [hypothesis]: #543
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 f8 #19)
-#22 := (f6 #20 #21)
-#17 := (:var 2 S2)
-#23 := (f3 #17 #22)
-#613 := (pattern #23)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#614 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #613) #30)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#617 := (iff #31 #614)
-#615 := (iff #30 #30)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#92 := (~ #31 #31)
-#106 := (~ #30 #30)
-#107 := [refl]: #106
-#93 := [nnf-pos #107]: #92
-#79 := [asserted]: #31
-#108 := [mp~ #79 #93]: #31
-#619 := [mp #108 #618]: #614
-#261 := (not #614)
-#402 := (or #261 #281)
-#544 := [quant-inst #40 #43 #45]: #402
-#401 := [unit-resolution #544 #619 #400]: false
-#537 := [lemma #401]: #281
-#598 := (not #593)
-#249 := (or #255 #593)
-#252 := (not #249)
-#47 := (f6 #42 #46)
-#48 := (f3 f10 #47)
-#49 := (= #48 f1)
-#82 := (not #49)
-#51 := (f7 f8 #50)
-#52 := (f6 #51 f13)
-#53 := (f3 f10 #52)
-#54 := (= #53 f1)
-#269 := (not #54)
-#559 := [hypothesis]: #269
-#275 := (or #49 #54)
-#83 := (iff #82 #54)
-#55 := (iff #49 #54)
-#56 := (not #55)
-#84 := (iff #56 #83)
-#85 := [rewrite]: #84
-#81 := [asserted]: #56
-#88 := [mp #81 #85]: #83
-#184 := (not #83)
-#273 := (or #49 #54 #184)
-#274 := [def-axiom]: #273
-#272 := [unit-resolution #274 #88]: #275
-#282 := [unit-resolution #272 #559]: #49
-#424 := (or #82 #249)
-#380 := (iff #49 #249)
-#594 := (or #261 #380)
-#595 := [quant-inst #40 #41 #46]: #594
-#423 := [unit-resolution #595 #619]: #380
-#590 := (not #380)
-#236 := (or #590 #82 #249)
-#237 := [def-axiom]: #236
-#383 := [unit-resolution #237 #423]: #424
-#531 := [unit-resolution #383 #282]: #249
-#596 := (not #255)
-#283 := (or #261 #567)
-#545 := [quant-inst #40 #41 #43]: #283
-#433 := [unit-resolution #545 #619]: #567
-#434 := (or #379 #548)
-#223 := (not #260)
-#580 := (or #260 #579)
-#573 := (not #580)
-#529 := (or #54 #573)
-#575 := (iff #54 #580)
-#582 := (or #261 #575)
-#584 := [quant-inst #40 #50 #45]: #582
-#528 := [unit-resolution #584 #619]: #575
-#296 := (not #575)
-#297 := (or #296 #54 #573)
-#298 := [def-axiom]: #297
-#532 := [unit-resolution #298 #528]: #529
-#417 := [unit-resolution #532 #559]: #573
-#224 := (or #580 #223)
-#585 := [def-axiom]: #224
-#432 := [unit-resolution #585 #417]: #223
-#381 := (or #379 #260 #548)
-#382 := [def-axiom]: #381
-#435 := [unit-resolution #382 #432]: #434
-#428 := [unit-resolution #435 #433]: #548
-#546 := (or #570 #596)
-#547 := [def-axiom]: #546
-#436 := [unit-resolution #547 #428]: #596
-#589 := (or #252 #255 #593)
-#248 := [def-axiom]: #589
-#437 := [unit-resolution #248 #436 #531]: #593
-#583 := (not #579)
-#586 := (or #580 #583)
-#572 := [def-axiom]: #586
-#438 := [unit-resolution #572 #417]: #583
-#541 := (or #570 #284)
-#542 := [def-axiom]: #541
-#439 := [unit-resolution #542 #428]: #284
-#561 := (or #564 #218 #579)
-#565 := [def-axiom]: #561
-#440 := [unit-resolution #565 #439 #438]: #564
-#556 := (or #543 #598 #571)
-#551 := [def-axiom]: #556
-#533 := [unit-resolution #551 #440 #437 #537]: false
-#530 := [lemma #533]: #54
-#271 := (or #82 #269)
-#270 := (or #82 #269 #184)
-#185 := [def-axiom]: #270
-#262 := [unit-resolution #185 #88]: #271
-#549 := [unit-resolution #262 #530]: #82
-#550 := (or #49 #252)
-#232 := (or #590 #49 #252)
-#574 := [def-axiom]: #232
-#523 := [unit-resolution #574 #423]: #550
-#515 := [unit-resolution #523 #549]: #252
-#588 := (or #249 #598)
-#247 := [def-axiom]: #588
-#512 := [unit-resolution #247 #515]: #598
-#554 := (or #543 #593 #564)
-#555 := [def-axiom]: #554
-#514 := [unit-resolution #555 #512 #537]: #564
-#562 := (or #571 #284)
-#563 := [def-axiom]: #562
-#524 := [unit-resolution #563 #514]: #284
-#597 := (or #249 #596)
-#592 := [def-axiom]: #597
-#525 := [unit-resolution #592 #515]: #596
-#535 := (or #548 #255 #218)
-#536 := [def-axiom]: #535
-#526 := [unit-resolution #536 #525 #524]: #548
-#522 := (or #269 #580)
-#191 := (or #296 #269 #580)
-#568 := [def-axiom]: #191
-#527 := [unit-resolution #568 #528]: #522
-#516 := [unit-resolution #527 #530]: #580
-#277 := (or #571 #583)
-#560 := [def-axiom]: #277
-#517 := [unit-resolution #560 #514]: #583
-#280 := (or #573 #260 #579)
-#295 := [def-axiom]: #280
-#518 := [unit-resolution #295 #517 #516]: #260
-#538 := (or #379 #223 #570)
-#539 := [def-axiom]: #538
-#519 := [unit-resolution #539 #518 #526]: #379
-[unit-resolution #545 #619 #519]: false
-unsat
-471f8aa77fc4964daee60a13a5a92f756ac79683 116 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#43 := f12
-decl f10 :: S2
-#40 := f10
-#49 := (f3 f10 f12)
-#50 := (= #49 f1)
-#119 := (not #50)
-decl f11 :: S3
-#41 := f11
-#47 := (f3 f10 f11)
-#48 := (= #47 f1)
-#118 := (not #48)
-#120 := (or #118 #119)
-#121 := (not #120)
-#599 := [hypothesis]: #121
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#32 := f9
-#42 := (f7 f9 f11)
-#44 := (f6 #42 f12)
-#45 := (f3 f10 #44)
-#46 := (= #45 f1)
-#79 := (not #46)
-#605 := (or #79 #120)
-#127 := (iff #46 #120)
-#51 := (and #48 #50)
-#80 := (iff #79 #51)
-#130 := (iff #80 #127)
-#124 := (iff #79 #121)
-#128 := (iff #124 #127)
-#129 := [rewrite]: #128
-#125 := (iff #80 #124)
-#122 := (iff #51 #121)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123]: #125
-#131 := [trans #126 #129]: #130
-#52 := (iff #46 #51)
-#53 := (not #52)
-#81 := (iff #53 #80)
-#82 := [rewrite]: #81
-#78 := [asserted]: #53
-#85 := [mp #78 #82]: #80
-#132 := [mp #85 #131]: #127
-#285 := (not #127)
-#267 := (or #79 #120 #285)
-#603 := [def-axiom]: #267
-#261 := [unit-resolution #603 #132]: #605
-#272 := [unit-resolution #261 #599]: #79
-#244 := (or #46 #120)
-#392 := (iff #46 #121)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#33 := (f7 f9 #19)
-#34 := (f6 #33 #21)
-#17 := (:var 2 S2)
-#35 := (f3 #17 #34)
-#632 := (pattern #35)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#110 := (not #28)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#109 := (not #26)
-#93 := (or #109 #110)
-#94 := (not #93)
-#36 := (= #35 f1)
-#111 := (iff #36 #94)
-#633 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #632) #111)
-#114 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #111)
-#636 := (iff #114 #633)
-#634 := (iff #111 #111)
-#635 := [refl]: #634
-#637 := [quant-intro #635]: #636
-#37 := (and #26 #28)
-#38 := (iff #36 #37)
-#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
-#115 := (iff #39 #114)
-#112 := (iff #38 #111)
-#95 := (iff #37 #94)
-#96 := [rewrite]: #95
-#113 := [monotonicity #96]: #112
-#116 := [quant-intro #113]: #115
-#91 := (~ #39 #39)
-#106 := (~ #38 #38)
-#107 := [refl]: #106
-#92 := [nnf-pos #107]: #91
-#77 := [asserted]: #39
-#108 := [mp~ #77 #92]: #39
-#117 := [mp #108 #116]: #114
-#638 := [mp #117 #637]: #633
-#273 := (not #633)
-#606 := (or #273 #392)
-#607 := [quant-inst #40 #41 #43]: #606
-#602 := [unit-resolution #607 #638]: #392
-#608 := (not #392)
-#609 := (or #608 #46 #120)
-#604 := [def-axiom]: #609
-#586 := [unit-resolution #604 #602]: #244
-#248 := [unit-resolution #586 #272 #599]: false
-#249 := [lemma #248]: #120
-#284 := (or #46 #121)
-#286 := (or #46 #121 #285)
-#287 := [def-axiom]: #286
-#288 := [unit-resolution #287 #132]: #284
-#250 := [unit-resolution #288 #249]: #46
-#251 := (or #79 #121)
-#610 := (or #608 #79 #121)
-#600 := [def-axiom]: #610
-#588 := [unit-resolution #600 #602]: #251
-[unit-resolution #588 #250 #249]: false
-unsat
-b2bab79e348dd40ef98e9c16bd8f27d0e66abe96 109 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#8 := f4
-decl f10 :: S2
-#40 := f10
-#174 := (f3 f10 f4)
-#260 := (= #174 f1)
-#251 := (not #260)
-decl f11 :: S3
-#41 := f11
-#258 := (f3 f10 f11)
-#173 := (= #258 f1)
-#259 := (not #173)
-#262 := (or #259 #251)
-#263 := (not #262)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#32 := f9
-#42 := (f7 f9 f11)
-#43 := (f6 #42 f4)
-#44 := (f3 f10 #43)
-#45 := (= #44 f1)
-#264 := (iff #45 #263)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#33 := (f7 f9 #19)
-#34 := (f6 #33 #21)
-#17 := (:var 2 S2)
-#35 := (f3 #17 #34)
-#609 := (pattern #35)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#102 := (not #28)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#101 := (not #26)
-#85 := (or #101 #102)
-#86 := (not #85)
-#36 := (= #35 f1)
-#103 := (iff #36 #86)
-#610 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #609) #103)
-#106 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #103)
-#613 := (iff #106 #610)
-#611 := (iff #103 #103)
-#612 := [refl]: #611
-#614 := [quant-intro #612]: #613
-#37 := (and #26 #28)
-#38 := (iff #36 #37)
-#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
-#107 := (iff #39 #106)
-#104 := (iff #38 #103)
-#87 := (iff #37 #86)
-#88 := [rewrite]: #87
-#105 := [monotonicity #88]: #104
-#108 := [quant-intro #105]: #107
-#83 := (~ #39 #39)
-#98 := (~ #38 #38)
-#99 := [refl]: #98
-#84 := [nnf-pos #99]: #83
-#71 := [asserted]: #39
-#100 := [mp~ #71 #84]: #39
-#109 := [mp #100 #108]: #106
-#615 := [mp #109 #614]: #610
-#244 := (not #610)
-#580 := (or #244 #264)
-#582 := [quant-inst #40 #41 #8]: #580
-#261 := [unit-resolution #582 #615]: #264
-#584 := (not #264)
-#265 := (or #584 #263)
-#46 := (not #45)
-#47 := (not #46)
-#73 := (iff #47 #45)
-#74 := [rewrite]: #73
-#72 := [asserted]: #47
-#77 := [mp #72 #74]: #45
-#581 := (or #584 #46 #263)
-#587 := [def-axiom]: #581
-#563 := [unit-resolution #587 #77]: #265
-#225 := [unit-resolution #563 #261]: #263
-#576 := (or #262 #260)
-#249 := [def-axiom]: #576
-#226 := [unit-resolution #249 #225]: #260
-#7 := (:var 0 S2)
-#9 := (f3 #7 f4)
-#588 := (pattern #9)
-#10 := (= #9 f1)
-#11 := (not #10)
-#589 := (forall (vars (?v0 S2)) (:pat #588) #11)
-#12 := (forall (vars (?v0 S2)) #11)
-#592 := (iff #12 #589)
-#590 := (iff #11 #11)
-#591 := [refl]: #590
-#593 := [quant-intro #591]: #592
-#91 := (~ #12 #12)
-#89 := (~ #11 #11)
-#90 := [refl]: #89
-#92 := [nnf-pos #90]: #91
-#68 := [asserted]: #12
-#76 := [mp~ #68 #92]: #12
-#594 := [mp #76 #593]: #589
-#237 := (not #589)
-#579 := (or #237 #251)
-#221 := [quant-inst #40]: #579
-[unit-resolution #221 #594 #226]: false
-unsat
-dbeac9b623875d59b5f7c86d653da3da9cd2d29b 131 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#13 := f5
-decl f10 :: S2
-#40 := f10
-#269 := (f3 f10 f5)
-#248 := (= #269 f1)
-#584 := (not #248)
-decl f11 :: S3
-#41 := f11
-#46 := (f3 f10 f11)
-#47 := (= #46 f1)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#32 := f9
-#42 := (f7 f9 f11)
-#43 := (f6 #42 f5)
-#44 := (f3 f10 #43)
-#45 := (= #44 f1)
-#262 := (not #47)
-#580 := [hypothesis]: #262
-#268 := (or #45 #47)
-#75 := (not #45)
-#76 := (iff #75 #47)
-#48 := (iff #45 #47)
-#49 := (not #48)
-#77 := (iff #49 #76)
-#78 := [rewrite]: #77
-#74 := [asserted]: #49
-#81 := [mp #74 #78]: #76
-#177 := (not #76)
-#266 := (or #45 #47 #177)
-#267 := [def-axiom]: #266
-#265 := [unit-resolution #267 #81]: #268
-#253 := [unit-resolution #265 #580]: #45
-#586 := (or #262 #584)
-#589 := (or #586 #47)
-#590 := [def-axiom]: #589
-#232 := [unit-resolution #590 #580]: #586
-#242 := (not #586)
-#570 := (or #75 #242)
-#373 := (iff #45 #242)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#33 := (f7 f9 #19)
-#34 := (f6 #33 #21)
-#17 := (:var 2 S2)
-#35 := (f3 #17 #34)
-#613 := (pattern #35)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#106 := (not #28)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#105 := (not #26)
-#89 := (or #105 #106)
-#90 := (not #89)
-#36 := (= #35 f1)
-#107 := (iff #36 #90)
-#614 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #613) #107)
-#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #107)
-#617 := (iff #110 #614)
-#615 := (iff #107 #107)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#37 := (and #26 #28)
-#38 := (iff #36 #37)
-#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
-#111 := (iff #39 #110)
-#108 := (iff #38 #107)
-#91 := (iff #37 #90)
-#92 := [rewrite]: #91
-#109 := [monotonicity #92]: #108
-#112 := [quant-intro #109]: #111
-#87 := (~ #39 #39)
-#102 := (~ #38 #38)
-#103 := [refl]: #102
-#88 := [nnf-pos #103]: #87
-#73 := [asserted]: #39
-#104 := [mp~ #73 #88]: #39
-#113 := [mp #104 #112]: #110
-#619 := [mp #113 #618]: #614
-#254 := (not #614)
-#587 := (or #254 #373)
-#588 := [quant-inst #40 #41 #13]: #587
-#569 := [unit-resolution #588 #619]: #373
-#245 := (not #373)
-#583 := (or #245 #75 #242)
-#225 := [def-axiom]: #583
-#571 := [unit-resolution #225 #569]: #570
-#572 := [unit-resolution #571 #232 #253]: false
-#573 := [lemma #572]: #47
-#264 := (or #75 #262)
-#263 := (or #75 #262 #177)
-#178 := [def-axiom]: #263
-#255 := [unit-resolution #178 #81]: #264
-#568 := [unit-resolution #255 #573]: #75
-#574 := (or #45 #586)
-#582 := (or #245 #45 #586)
-#241 := [def-axiom]: #582
-#216 := [unit-resolution #241 #569]: #574
-#217 := [unit-resolution #216 #568]: #586
-#581 := (or #242 #262 #584)
-#240 := [def-axiom]: #581
-#578 := [unit-resolution #240 #217 #573]: #584
-#7 := (:var 0 S2)
-#14 := (f3 #7 f5)
-#599 := (pattern #14)
-#15 := (= #14 f1)
-#600 := (forall (vars (?v0 S2)) (:pat #599) #15)
-#16 := (forall (vars (?v0 S2)) #15)
-#603 := (iff #16 #600)
-#601 := (iff #15 #15)
-#602 := [refl]: #601
-#604 := [quant-intro #602]: #603
-#83 := (~ #16 #16)
-#82 := (~ #15 #15)
-#97 := [refl]: #82
-#84 := [nnf-pos #97]: #83
-#71 := [asserted]: #16
-#98 := [mp~ #71 #84]: #16
-#605 := [mp #98 #604]: #600
-#211 := (not #600)
-#575 := (or #211 #248)
-#577 := [quant-inst #40]: #575
-[unit-resolution #577 #605 #578]: false
-unsat
-51ce95475567a2e196bafe1aa52fd86168910e25 144 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#41 := f11
-decl f10 :: S2
-#40 := f10
-#272 := (f3 f10 f11)
-#251 := (= #272 f1)
-#587 := (not #251)
-decl f12 :: S3
-#43 := f12
-#589 := (f3 f10 f12)
-#245 := (= #589 f1)
-#376 := (not #245)
-#590 := (or #376 #587)
-#591 := (not #590)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#32 := f9
-#47 := (f7 f9 f12)
-#48 := (f6 #47 f11)
-#49 := (f3 f10 #48)
-#50 := (= #49 f1)
-#265 := (not #50)
-#575 := [hypothesis]: #265
-#187 := (or #50 #590)
-#574 := (iff #50 #591)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#33 := (f7 f9 #19)
-#34 := (f6 #33 #21)
-#17 := (:var 2 S2)
-#35 := (f3 #17 #34)
-#616 := (pattern #35)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#109 := (not #28)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#108 := (not #26)
-#92 := (or #108 #109)
-#93 := (not #92)
-#36 := (= #35 f1)
-#110 := (iff #36 #93)
-#617 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #616) #110)
-#113 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #110)
-#620 := (iff #113 #617)
-#618 := (iff #110 #110)
-#619 := [refl]: #618
-#621 := [quant-intro #619]: #620
-#37 := (and #26 #28)
-#38 := (iff #36 #37)
-#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
-#114 := (iff #39 #113)
-#111 := (iff #38 #110)
-#94 := (iff #37 #93)
-#95 := [rewrite]: #94
-#112 := [monotonicity #95]: #111
-#115 := [quant-intro #112]: #114
-#90 := (~ #39 #39)
-#105 := (~ #38 #38)
-#106 := [refl]: #105
-#91 := [nnf-pos #106]: #90
-#76 := [asserted]: #39
-#107 := [mp~ #76 #91]: #39
-#116 := [mp #107 #115]: #113
-#622 := [mp #116 #621]: #617
-#592 := (not #617)
-#571 := (or #592 #574)
-#577 := [quant-inst #40 #43 #41]: #571
-#576 := [unit-resolution #577 #622]: #574
-#579 := (not #574)
-#582 := (or #579 #50 #590)
-#568 := [def-axiom]: #582
-#564 := [unit-resolution #568 #576]: #187
-#565 := [unit-resolution #564 #575]: #590
-#583 := (or #587 #376)
-#256 := (not #583)
-#42 := (f7 f9 f11)
-#44 := (f6 #42 f12)
-#45 := (f3 f10 #44)
-#46 := (= #45 f1)
-#271 := (or #46 #50)
-#78 := (not #46)
-#79 := (iff #78 #50)
-#51 := (iff #46 #50)
-#52 := (not #51)
-#80 := (iff #52 #79)
-#81 := [rewrite]: #80
-#77 := [asserted]: #52
-#84 := [mp #77 #81]: #79
-#180 := (not #79)
-#269 := (or #46 #50 #180)
-#270 := [def-axiom]: #269
-#268 := [unit-resolution #270 #84]: #271
-#287 := [unit-resolution #268 #575]: #46
-#562 := (or #78 #256)
-#257 := (iff #46 #256)
-#593 := (or #592 #257)
-#588 := [quant-inst #40 #41 #43]: #593
-#288 := [unit-resolution #588 #622]: #257
-#586 := (not #257)
-#232 := (or #586 #78 #256)
-#233 := [def-axiom]: #232
-#566 := [unit-resolution #233 #288]: #562
-#563 := [unit-resolution #566 #287]: #256
-#594 := (or #583 #251)
-#584 := [def-axiom]: #594
-#567 := [unit-resolution #584 #563]: #251
-#243 := (or #583 #245)
-#248 := [def-axiom]: #243
-#277 := [unit-resolution #248 #563]: #245
-#220 := (or #591 #376 #587)
-#581 := [def-axiom]: #220
-#278 := [unit-resolution #581 #277 #567 #565]: false
-#279 := [lemma #278]: #50
-#280 := (or #265 #591)
-#569 := (or #579 #265 #591)
-#276 := [def-axiom]: #569
-#558 := [unit-resolution #276 #576]: #280
-#559 := [unit-resolution #558 #279]: #591
-#580 := (or #590 #251)
-#219 := [def-axiom]: #580
-#273 := [unit-resolution #219 #559]: #251
-#267 := (or #78 #265)
-#266 := (or #78 #265 #180)
-#181 := [def-axiom]: #266
-#258 := [unit-resolution #181 #84]: #267
-#556 := [unit-resolution #258 #279]: #78
-#560 := (or #46 #583)
-#228 := (or #586 #46 #583)
-#570 := [def-axiom]: #228
-#557 := [unit-resolution #570 #288]: #560
-#561 := [unit-resolution #557 #556]: #583
-#214 := (or #590 #245)
-#578 := [def-axiom]: #214
-#550 := [unit-resolution #578 #559]: #245
-#585 := (or #256 #587 #376)
-#244 := [def-axiom]: #585
-[unit-resolution #244 #550 #561 #273]: false
-unsat
-4830d9673cbce4109d7a294d06cddebfbef2b503 116 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#41 := f11
-decl f10 :: S2
-#40 := f10
-#46 := (f3 f10 f11)
-#47 := (= #46 f1)
-#262 := (not #47)
-#568 := [hypothesis]: #262
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#32 := f9
-#42 := (f7 f9 f11)
-#43 := (f6 #42 f11)
-#44 := (f3 f10 #43)
-#45 := (= #44 f1)
-#268 := (or #45 #47)
-#75 := (not #45)
-#76 := (iff #75 #47)
-#48 := (iff #45 #47)
-#49 := (not #48)
-#77 := (iff #49 #76)
-#78 := [rewrite]: #77
-#74 := [asserted]: #49
-#81 := [mp #74 #78]: #76
-#177 := (not #76)
-#266 := (or #45 #47 #177)
-#267 := [def-axiom]: #266
-#265 := [unit-resolution #267 #81]: #268
-#574 := [unit-resolution #265 #568]: #45
-#575 := (or #75 #47)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#33 := (f7 f9 #19)
-#34 := (f6 #33 #21)
-#17 := (:var 2 S2)
-#35 := (f3 #17 #34)
-#613 := (pattern #35)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#106 := (not #28)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#105 := (not #26)
-#89 := (or #105 #106)
-#90 := (not #89)
-#36 := (= #35 f1)
-#107 := (iff #36 #90)
-#614 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #613) #107)
-#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #107)
-#617 := (iff #110 #614)
-#615 := (iff #107 #107)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#37 := (and #26 #28)
-#38 := (iff #36 #37)
-#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
-#111 := (iff #39 #110)
-#108 := (iff #38 #107)
-#91 := (iff #37 #90)
-#92 := [rewrite]: #91
-#109 := [monotonicity #92]: #108
-#112 := [quant-intro #109]: #111
-#87 := (~ #39 #39)
-#102 := (~ #38 #38)
-#103 := [refl]: #102
-#88 := [nnf-pos #103]: #87
-#73 := [asserted]: #39
-#104 := [mp~ #73 #88]: #39
-#113 := [mp #104 #112]: #110
-#619 := [mp #113 #618]: #614
-#591 := (not #614)
-#581 := (or #591 #48)
-#269 := (or #262 #262)
-#248 := (not #269)
-#584 := (iff #45 #248)
-#240 := (or #591 #584)
-#582 := (iff #240 #581)
-#583 := (iff #581 #581)
-#225 := [rewrite]: #583
-#590 := (iff #584 #48)
-#588 := (iff #248 #47)
-#373 := (not #262)
-#254 := (iff #373 #47)
-#587 := [rewrite]: #254
-#580 := (iff #248 #373)
-#586 := (iff #269 #262)
-#242 := [rewrite]: #586
-#253 := [monotonicity #242]: #580
-#589 := [trans #253 #587]: #588
-#585 := [monotonicity #589]: #590
-#241 := [monotonicity #585]: #582
-#567 := [trans #241 #225]: #582
-#245 := [quant-inst #40 #41 #41]: #240
-#229 := [mp #245 #567]: #581
-#211 := [unit-resolution #229 #619]: #48
-#232 := (or #49 #75 #47)
-#569 := [def-axiom]: #232
-#577 := [unit-resolution #569 #211]: #575
-#216 := [unit-resolution #577 #574 #568]: false
-#217 := [lemma #216]: #47
-#264 := (or #75 #262)
-#263 := (or #75 #262 #177)
-#178 := [def-axiom]: #263
-#255 := [unit-resolution #178 #81]: #264
-#578 := [unit-resolution #255 #217]: #75
-#576 := (or #45 #262)
-#230 := (or #49 #45 #262)
-#231 := [def-axiom]: #230
-#579 := [unit-resolution #231 #211]: #576
-[unit-resolution #579 #578 #217]: false
-unsat
-204f9f43d50dba080fa0264b17e4ee9000821fb0 207 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f13 :: S3
-#45 := f13
-decl f10 :: S2
-#40 := f10
-#579 := (f3 f10 f13)
-#580 := (= #579 f1)
-#575 := (not #580)
-decl f12 :: S3
-#43 := f12
-#584 := (f3 f10 f12)
-#223 := (= #584 f1)
-#570 := (not #223)
-#567 := (or #570 #575)
-#571 := (not #567)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#32 := f9
-#44 := (f7 f9 f12)
-#46 := (f6 #44 f13)
-#593 := (f3 f10 #46)
-#249 := (= #593 f1)
-#281 := (iff #249 #571)
-#379 := (not #281)
-decl f11 :: S3
-#41 := f11
-#276 := (f3 f10 f11)
-#255 := (= #276 f1)
-#591 := (not #255)
-#282 := (or #591 #570)
-#283 := (not #282)
-#42 := (f7 f9 f11)
-#50 := (f6 #42 f12)
-#594 := (f3 f10 #50)
-#595 := (= #594 f1)
-#400 := (iff #595 #283)
-#543 := (not #400)
-#401 := [hypothesis]: #543
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#33 := (f7 f9 #19)
-#34 := (f6 #33 #21)
-#17 := (:var 2 S2)
-#35 := (f3 #17 #34)
-#620 := (pattern #35)
-#27 := (f3 #17 #21)
-#28 := (= #27 f1)
-#113 := (not #28)
-#25 := (f3 #17 #19)
-#26 := (= #25 f1)
-#112 := (not #26)
-#96 := (or #112 #113)
-#97 := (not #96)
-#36 := (= #35 f1)
-#114 := (iff #36 #97)
-#621 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #620) #114)
-#117 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #114)
-#624 := (iff #117 #621)
-#622 := (iff #114 #114)
-#623 := [refl]: #622
-#625 := [quant-intro #623]: #624
-#37 := (and #26 #28)
-#38 := (iff #36 #37)
-#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
-#118 := (iff #39 #117)
-#115 := (iff #38 #114)
-#98 := (iff #37 #97)
-#99 := [rewrite]: #98
-#116 := [monotonicity #99]: #115
-#119 := [quant-intro #116]: #118
-#94 := (~ #39 #39)
-#109 := (~ #38 #38)
-#110 := [refl]: #109
-#95 := [nnf-pos #110]: #94
-#80 := [asserted]: #39
-#111 := [mp~ #80 #95]: #39
-#120 := [mp #111 #119]: #117
-#626 := [mp #120 #625]: #621
-#596 := (not #621)
-#544 := (or #596 #400)
-#545 := [quant-inst #40 #41 #43]: #544
-#402 := [unit-resolution #545 #626 #401]: false
-#537 := [lemma #402]: #400
-#578 := (not #595)
-#581 := (or #578 #575)
-#218 := (not #581)
-#51 := (f7 f9 #50)
-#52 := (f6 #51 f13)
-#53 := (f3 f10 #52)
-#54 := (= #53 f1)
-#380 := (not #249)
-#587 := (or #591 #380)
-#260 := (not #587)
-#47 := (f6 #42 #46)
-#48 := (f3 f10 #47)
-#49 := (= #48 f1)
-#269 := (not #54)
-#559 := [hypothesis]: #269
-#275 := (or #49 #54)
-#82 := (not #49)
-#83 := (iff #82 #54)
-#55 := (iff #49 #54)
-#56 := (not #55)
-#84 := (iff #56 #83)
-#85 := [rewrite]: #84
-#81 := [asserted]: #56
-#88 := [mp #81 #85]: #83
-#184 := (not #83)
-#273 := (or #49 #54 #184)
-#274 := [def-axiom]: #273
-#272 := [unit-resolution #274 #88]: #275
-#284 := [unit-resolution #272 #559]: #49
-#424 := (or #82 #260)
-#261 := (iff #49 #260)
-#597 := (or #596 #261)
-#592 := [quant-inst #40 #41 #46]: #597
-#423 := [unit-resolution #592 #626]: #261
-#590 := (not #261)
-#236 := (or #590 #82 #260)
-#237 := [def-axiom]: #236
-#383 := [unit-resolution #237 #423]: #424
-#531 := [unit-resolution #383 #284]: #260
-#598 := (or #587 #255)
-#588 := [def-axiom]: #598
-#433 := [unit-resolution #588 #531]: #255
-#562 := (or #596 #281)
-#546 := [quant-inst #40 #43 #45]: #562
-#528 := [unit-resolution #546 #626]: #281
-#532 := (or #379 #571)
-#247 := (or #587 #249)
-#252 := [def-axiom]: #247
-#529 := [unit-resolution #252 #531]: #249
-#535 := (or #379 #380 #571)
-#536 := [def-axiom]: #535
-#417 := [unit-resolution #536 #529]: #532
-#432 := [unit-resolution #417 #528]: #571
-#547 := (or #567 #223)
-#541 := [def-axiom]: #547
-#434 := [unit-resolution #541 #432]: #223
-#561 := (or #283 #591 #570)
-#565 := [def-axiom]: #561
-#435 := [unit-resolution #565 #434 #433]: #283
-#436 := (or #54 #581)
-#582 := (iff #54 #218)
-#224 := (or #596 #582)
-#585 := [quant-inst #40 #50 #45]: #224
-#428 := [unit-resolution #585 #626]: #582
-#296 := (not #582)
-#297 := (or #296 #54 #581)
-#298 := [def-axiom]: #297
-#437 := [unit-resolution #298 #428]: #436
-#438 := [unit-resolution #437 #559]: #581
-#542 := (or #567 #580)
-#548 := [def-axiom]: #542
-#439 := [unit-resolution #548 #432]: #580
-#280 := (or #218 #578 #575)
-#295 := [def-axiom]: #280
-#440 := [unit-resolution #295 #439 #438]: #578
-#554 := (or #543 #595 #282)
-#555 := [def-axiom]: #554
-#533 := [unit-resolution #555 #440 #435 #537]: false
-#530 := [lemma #533]: #54
-#549 := (or #269 #218)
-#191 := (or #296 #269 #218)
-#568 := [def-axiom]: #191
-#550 := [unit-resolution #568 #428]: #549
-#523 := [unit-resolution #550 #530]: #218
-#583 := (or #581 #595)
-#586 := [def-axiom]: #583
-#515 := [unit-resolution #586 #523]: #595
-#556 := (or #543 #578 #283)
-#551 := [def-axiom]: #556
-#512 := [unit-resolution #551 #515 #537]: #283
-#560 := (or #282 #223)
-#564 := [def-axiom]: #560
-#514 := [unit-resolution #564 #512]: #223
-#572 := (or #581 #580)
-#573 := [def-axiom]: #572
-#524 := [unit-resolution #573 #523]: #580
-#381 := (or #571 #570 #575)
-#382 := [def-axiom]: #381
-#525 := [unit-resolution #382 #524 #514]: #571
-#271 := (or #82 #269)
-#270 := (or #82 #269 #184)
-#185 := [def-axiom]: #270
-#262 := [unit-resolution #185 #88]: #271
-#526 := [unit-resolution #262 #530]: #82
-#522 := (or #49 #587)
-#232 := (or #590 #49 #587)
-#574 := [def-axiom]: #232
-#527 := [unit-resolution #574 #423]: #522
-#516 := [unit-resolution #527 #526]: #587
-#563 := (or #282 #255)
-#277 := [def-axiom]: #563
-#517 := [unit-resolution #277 #512]: #255
-#589 := (or #260 #591 #380)
-#248 := [def-axiom]: #589
-#518 := [unit-resolution #248 #517 #516]: #380
-#538 := (or #379 #249 #567)
-#539 := [def-axiom]: #538
-#519 := [unit-resolution #539 #518 #525]: #379
-[unit-resolution #546 #626 #519]: false
-unsat
-1dccf1446c06f99d08b664c523373d60beeb86a5 22 0
-#2 := false
-decl f13 :: (-> S7 S3 S4)
-decl f4 :: S3
-#7 := f4
-decl f14 :: S7
-#49 := f14
-#50 := (f13 f14 f4)
-#51 := (= #50 #50)
-#52 := (not #51)
-#86 := (iff #52 false)
-#1 := true
-#81 := (not true)
-#84 := (iff #81 false)
-#85 := [rewrite]: #84
-#82 := (iff #52 #81)
-#79 := (iff #51 true)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#87 := [trans #83 #85]: #86
-#78 := [asserted]: #52
-[mp #78 #87]: false
-unsat

--- a/src/HOL/SMT_Examples/SMT_Tests.thy	Wed Jan 02 09:13:50 2013 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.thy	Wed Jan 02 09:31:25 2013 +0100
@@ -8,16 +8,8 @@
 imports Complex_Main
 begin
 
-declare [[smt_oracle = false]]
-declare [[smt_certificates = "SMT_Tests.certs"]]
-declare [[smt_read_only_certificates = true]]
-
-
-
 smt_status
 
-
-
 text {* Most examples are taken from various Isabelle theories and from HOL4. *}