actually run Z3 for "SMT_Tests" when "ISABELLE_FULL_TEST" is enabled
authorblanchet
Wed, 02 Jan 2013 09:31:25 +0100
changeset 50666 6f48853f08d5
parent 50665 c9daeff9516e
child 50667 e0cba8893691
actually run Z3 for "SMT_Tests" when "ISABELLE_FULL_TEST" is enabled
src/HOL/ROOT
src/HOL/SMT_Examples/SMT_Examples.thy
src/HOL/SMT_Examples/SMT_Tests.certs
src/HOL/SMT_Examples/SMT_Tests.thy
--- 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 :=