updated certificates

--- a/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra	Wed Dec 23 17:37:42 2009 +0100
@@ -38,6 +38,6 @@
 :assumption (< 0 uf_9)
 :assumption (forall (?x20 T2) (?x21 T2) (implies (= ?x20 ?x21) (= (uf_10 (uf_1 ?x20 ?x21)) 0)))
 :assumption (forall (?x22 T2) (?x23 T2) (implies (not (= ?x22 ?x23)) (< 0 (uf_10 (uf_1 ?x22 ?x23)))))
-:assumption (not (implies (and true (and (forall (?x24 T2) (implies (= ?x24 uf_11) (= (uf_12 ?x24) 0))) (and (forall (?x25 T2) (implies (not (= ?x25 uf_11)) (= (uf_12 ?x25) uf_9))) (forall (?x26 T2) (not (up_13 ?x26)))))) (and (= (uf_12 uf_11) 0) (implies (= (uf_12 uf_11) 0) (and (forall (?x27 T2) (<= 0 (uf_12 ?x27))) (implies (forall (?x28 T2) (<= 0 (uf_12 ?x28))) (and (forall (?x29 T2) (?x30 T2) (implies (and (not (up_13 ?x30)) (up_13 ?x29)) (<= (uf_12 ?x29) (uf_12 ?x30)))) (implies (forall (?x31 T2) (?x32 T2) (implies (and (not (up_13 ?x32)) (up_13 ?x31)) (<= (uf_12 ?x31) (uf_12 ?x32)))) (and (forall (?x33 T2) (?x34 T2) (implies (and (up_13 ?x34) (< (uf_10 (uf_1 ?x34 ?x33)) uf_9)) (<= (uf_12 ?x33) (+ (uf_12 ?x34) (uf_10 (uf_1 ?x34 ?x33)))))) (implies (forall (?x35 T2) (?x36 T2) (implies (and (up_13 ?x36) (< (uf_10 (uf_1 ?x36 ?x35)) uf_9)) (<= (uf_12 ?x35) (+ (uf_12 ?x36) (uf_10 (uf_1 ?x36 ?x35)))))) (and (forall (?x37 T2) (implies (and (not (= ?x37 uf_11)) (< (uf_12 ?x37) uf_9)) (exists (?x38 T2) (and (< (uf_12 ?x38) (uf_12 ?x37)) (and (up_13 ?x38) (= (uf_12 ?x37) (+ (uf_12 ?x38) (uf_10 (uf_1 ?x38 ?x37))))))))) (implies (and (forall (?x39 T2) (implies (and (not (= ?x39 uf_11)) (< (uf_12 ?x39) uf_9)) (exists (?x40 T2) (and (< (uf_12 ?x40) (uf_12 ?x39)) (and (up_13 ?x40) (= (uf_12 ?x39) (+ (uf_12 ?x40) (uf_10 (uf_1 ?x40 ?x39))))))))) (and true (and (= (uf_4 uf_14 uf_11) 0) (and (forall (?x41 T2) (<= 0 (uf_4 uf_14 ?x41))) (and (forall (?x42 T2) (?x43 T2) (implies (and (not (up_6 uf_15 ?x43)) (up_6 uf_15 ?x42)) (<= (uf_4 uf_14 ?x42) (uf_4 uf_14 ?x43)))) (and (forall (?x44 T2) (?x45 T2) (implies (and (up_6 uf_15 ?x45) (< (uf_10 (uf_1 ?x45 ?x44)) uf_9)) (<= (uf_4 uf_14 ?x44) (+ (uf_4 uf_14 ?x45) (uf_10 (uf_1 ?x45 ?x44)))))) (forall (?x46 T2) (implies (and (not (= ?x46 uf_11)) (< (uf_4 uf_14 ?x46) uf_9)) (exists (?x47 T2) (and (< (uf_4 uf_14 ?x47) (uf_4 uf_14 ?x46)) (and (up_6 uf_15 ?x47) (= (uf_4 uf_14 ?x46) (+ (uf_4 uf_14 ?x47) (uf_10 (uf_1 ?x47 ?x46))))))))))))))) (and (implies (and true (and (not (exists (?x48 T2) (and (not (up_6 uf_15 ?x48)) (< (uf_4 uf_14 ?x48) uf_9)))) (and (= uf_16 uf_15) (and (= uf_17 uf_18) (and (= uf_19 uf_14) (= uf_20 uf_21)))))) (and (forall (?x49 T2) (implies (and (not (= ?x49 uf_11)) (< (uf_4 uf_19 ?x49) uf_9)) (exists (?x50 T2) (and (< (uf_4 uf_19 ?x50) (uf_4 uf_19 ?x49)) (= (uf_4 uf_19 ?x49) (+ (uf_4 uf_19 ?x50) (uf_10 (uf_1 ?x50 ?x49)))))))) (implies (forall (?x51 T2) (implies (and (not (= ?x51 uf_11)) (< (uf_4 uf_19 ?x51) uf_9)) (exists (?x52 T2) (and (< (uf_4 uf_19 ?x52) (uf_4 uf_19 ?x51)) (= (uf_4 uf_19 ?x51) (+ (uf_4 uf_19 ?x52) (uf_10 (uf_1 ?x52 ?x51)))))))) (and (forall (?x53 T2) (?x54 T2) (implies (and (< (uf_4 uf_19 ?x54) uf_9) (< (uf_10 (uf_1 ?x54 ?x53)) uf_9)) (<= (uf_4 uf_19 ?x53) (+ (uf_4 uf_19 ?x54) (uf_10 (uf_1 ?x54 ?x53)))))) (implies (forall (?x55 T2) (?x56 T2) (implies (and (< (uf_4 uf_19 ?x56) uf_9) (< (uf_10 (uf_1 ?x56 ?x55)) uf_9)) (<= (uf_4 uf_19 ?x55) (+ (uf_4 uf_19 ?x56) (uf_10 (uf_1 ?x56 ?x55)))))) (= (uf_4 uf_19 uf_11) 0)))))) (implies (and true (and (exists (?x57 T2) (and (not (up_6 uf_15 ?x57)) (< (uf_4 uf_14 ?x57) uf_9))) (and (not (up_6 uf_15 uf_22)) (and (< (uf_4 uf_14 uf_22) uf_9) (and (forall (?x58 T2) (implies (not (up_6 uf_15 ?x58)) (<= (uf_4 uf_14 uf_22) (uf_4 uf_14 ?x58)))) (and (= uf_23 (uf_7 uf_15 uf_22 uf_8)) (and (forall (?x59 T2) (implies (and (< (uf_10 (uf_1 uf_22 ?x59)) uf_9) (< (+ (uf_4 uf_14 uf_22) (uf_10 (uf_1 uf_22 ?x59))) (uf_4 uf_14 ?x59))) (= (uf_24 ?x59) (+ (uf_4 uf_14 uf_22) (uf_10 (uf_1 uf_22 ?x59)))))) (forall (?x60 T2) (implies (not (and (< (uf_10 (uf_1 uf_22 ?x60)) uf_9) (< (+ (uf_4 uf_14 uf_22) (uf_10 (uf_1 uf_22 ?x60))) (uf_4 uf_14 ?x60)))) (= (uf_24 ?x60) (uf_4 uf_14 ?x60))))))))))) (and (forall (?x61 T2) (<= (uf_24 ?x61) (uf_4 uf_14 ?x61))) (implies (forall (?x62 T2) (<= (uf_24 ?x62) (uf_4 uf_14 ?x62))) (and (forall (?x63 T2) (implies (up_6 uf_23 ?x63) (= (uf_24 ?x63) (uf_4 uf_14 ?x63)))) (implies (forall (?x64 T2) (implies (up_6 uf_23 ?x64) (= (uf_24 ?x64) (uf_4 uf_14 ?x64)))) (and (= (uf_24 uf_11) 0) (implies (= (uf_24 uf_11) 0) (and (forall (?x65 T2) (<= 0 (uf_24 ?x65))) (implies (forall (?x66 T2) (<= 0 (uf_24 ?x66))) (and (forall (?x67 T2) (?x68 T2) (implies (and (not (up_6 uf_23 ?x68)) (up_6 uf_23 ?x67)) (<= (uf_24 ?x67) (uf_24 ?x68)))) (implies (forall (?x69 T2) (?x70 T2) (implies (and (not (up_6 uf_23 ?x70)) (up_6 uf_23 ?x69)) (<= (uf_24 ?x69) (uf_24 ?x70)))) (and (forall (?x71 T2) (?x72 T2) (implies (and (up_6 uf_23 ?x72) (< (uf_10 (uf_1 ?x72 ?x71)) uf_9)) (<= (uf_24 ?x71) (+ (uf_24 ?x72) (uf_10 (uf_1 ?x72 ?x71)))))) (implies (forall (?x73 T2) (?x74 T2) (implies (and (up_6 uf_23 ?x74) (< (uf_10 (uf_1 ?x74 ?x73)) uf_9)) (<= (uf_24 ?x73) (+ (uf_24 ?x74) (uf_10 (uf_1 ?x74 ?x73)))))) (forall (?x75 T2) (implies (and (not (= ?x75 uf_11)) (< (uf_24 ?x75) uf_9)) (exists (?x76 T2) (and (< (uf_24 ?x76) (uf_24 ?x75)) (and (up_6 uf_23 ?x76) (= (uf_24 ?x75) (+ (uf_24 ?x76) (uf_10 (uf_1 ?x76 ?x75)))))))))))))))))))))))))))))))))))
+:assumption (not (implies true (implies (forall (?x24 T2) (implies (= ?x24 uf_11) (= (uf_12 ?x24) 0))) (implies (forall (?x25 T2) (implies (not (= ?x25 uf_11)) (= (uf_12 ?x25) uf_9))) (implies (forall (?x26 T2) (not (up_13 ?x26))) (and (= (uf_12 uf_11) 0) (implies (= (uf_12 uf_11) 0) (and (forall (?x27 T2) (<= 0 (uf_12 ?x27))) (implies (forall (?x28 T2) (<= 0 (uf_12 ?x28))) (and (forall (?x29 T2) (?x30 T2) (implies (and (not (up_13 ?x30)) (up_13 ?x29)) (<= (uf_12 ?x29) (uf_12 ?x30)))) (implies (forall (?x31 T2) (?x32 T2) (implies (and (not (up_13 ?x32)) (up_13 ?x31)) (<= (uf_12 ?x31) (uf_12 ?x32)))) (and (forall (?x33 T2) (?x34 T2) (implies (and (up_13 ?x34) (< (uf_10 (uf_1 ?x34 ?x33)) uf_9)) (<= (uf_12 ?x33) (+ (uf_12 ?x34) (uf_10 (uf_1 ?x34 ?x33)))))) (implies (forall (?x35 T2) (?x36 T2) (implies (and (up_13 ?x36) (< (uf_10 (uf_1 ?x36 ?x35)) uf_9)) (<= (uf_12 ?x35) (+ (uf_12 ?x36) (uf_10 (uf_1 ?x36 ?x35)))))) (and (forall (?x37 T2) (implies (and (not (= ?x37 uf_11)) (< (uf_12 ?x37) uf_9)) (exists (?x38 T2) (and (< (uf_12 ?x38) (uf_12 ?x37)) (and (up_13 ?x38) (= (uf_12 ?x37) (+ (uf_12 ?x38) (uf_10 (uf_1 ?x38 ?x37))))))))) (implies (forall (?x39 T2) (implies (and (not (= ?x39 uf_11)) (< (uf_12 ?x39) uf_9)) (exists (?x40 T2) (and (< (uf_12 ?x40) (uf_12 ?x39)) (and (up_13 ?x40) (= (uf_12 ?x39) (+ (uf_12 ?x40) (uf_10 (uf_1 ?x40 ?x39))))))))) (implies true (implies (= (uf_4 uf_14 uf_11) 0) (implies (forall (?x41 T2) (<= 0 (uf_4 uf_14 ?x41))) (implies (forall (?x42 T2) (?x43 T2) (implies (and (not (up_6 uf_15 ?x43)) (up_6 uf_15 ?x42)) (<= (uf_4 uf_14 ?x42) (uf_4 uf_14 ?x43)))) (implies (forall (?x44 T2) (?x45 T2) (implies (and (up_6 uf_15 ?x45) (< (uf_10 (uf_1 ?x45 ?x44)) uf_9)) (<= (uf_4 uf_14 ?x44) (+ (uf_4 uf_14 ?x45) (uf_10 (uf_1 ?x45 ?x44)))))) (implies (forall (?x46 T2) (implies (and (not (= ?x46 uf_11)) (< (uf_4 uf_14 ?x46) uf_9)) (exists (?x47 T2) (and (< (uf_4 uf_14 ?x47) (uf_4 uf_14 ?x46)) (and (up_6 uf_15 ?x47) (= (uf_4 uf_14 ?x46) (+ (uf_4 uf_14 ?x47) (uf_10 (uf_1 ?x47 ?x46))))))))) (and (implies true (implies (not (exists (?x48 T2) (and (not (up_6 uf_15 ?x48)) (< (uf_4 uf_14 ?x48) uf_9)))) (implies (= uf_16 uf_15) (implies (= uf_17 uf_18) (implies (= uf_19 uf_14) (implies (= uf_20 uf_21) (and (forall (?x49 T2) (implies (and (not (= ?x49 uf_11)) (< (uf_4 uf_19 ?x49) uf_9)) (exists (?x50 T2) (and (< (uf_4 uf_19 ?x50) (uf_4 uf_19 ?x49)) (= (uf_4 uf_19 ?x49) (+ (uf_4 uf_19 ?x50) (uf_10 (uf_1 ?x50 ?x49)))))))) (implies (forall (?x51 T2) (implies (and (not (= ?x51 uf_11)) (< (uf_4 uf_19 ?x51) uf_9)) (exists (?x52 T2) (and (< (uf_4 uf_19 ?x52) (uf_4 uf_19 ?x51)) (= (uf_4 uf_19 ?x51) (+ (uf_4 uf_19 ?x52) (uf_10 (uf_1 ?x52 ?x51)))))))) (and (forall (?x53 T2) (?x54 T2) (implies (and (< (uf_4 uf_19 ?x54) uf_9) (< (uf_10 (uf_1 ?x54 ?x53)) uf_9)) (<= (uf_4 uf_19 ?x53) (+ (uf_4 uf_19 ?x54) (uf_10 (uf_1 ?x54 ?x53)))))) (implies (forall (?x55 T2) (?x56 T2) (implies (and (< (uf_4 uf_19 ?x56) uf_9) (< (uf_10 (uf_1 ?x56 ?x55)) uf_9)) (<= (uf_4 uf_19 ?x55) (+ (uf_4 uf_19 ?x56) (uf_10 (uf_1 ?x56 ?x55)))))) (and (= (uf_4 uf_19 uf_11) 0) true))))))))))) (implies true (implies (exists (?x57 T2) (and (not (up_6 uf_15 ?x57)) (< (uf_4 uf_14 ?x57) uf_9))) (implies (not (up_6 uf_15 uf_22)) (implies (< (uf_4 uf_14 uf_22) uf_9) (implies (forall (?x58 T2) (implies (not (up_6 uf_15 ?x58)) (<= (uf_4 uf_14 uf_22) (uf_4 uf_14 ?x58)))) (implies (= uf_23 (uf_7 uf_15 uf_22 uf_8)) (implies (forall (?x59 T2) (implies (and (< (uf_10 (uf_1 uf_22 ?x59)) uf_9) (< (+ (uf_4 uf_14 uf_22) (uf_10 (uf_1 uf_22 ?x59))) (uf_4 uf_14 ?x59))) (= (uf_24 ?x59) (+ (uf_4 uf_14 uf_22) (uf_10 (uf_1 uf_22 ?x59)))))) (implies (forall (?x60 T2) (implies (not (and (< (uf_10 (uf_1 uf_22 ?x60)) uf_9) (< (+ (uf_4 uf_14 uf_22) (uf_10 (uf_1 uf_22 ?x60))) (uf_4 uf_14 ?x60)))) (= (uf_24 ?x60) (uf_4 uf_14 ?x60)))) (and (forall (?x61 T2) (<= (uf_24 ?x61) (uf_4 uf_14 ?x61))) (implies (forall (?x62 T2) (<= (uf_24 ?x62) (uf_4 uf_14 ?x62))) (and (forall (?x63 T2) (implies (up_6 uf_23 ?x63) (= (uf_24 ?x63) (uf_4 uf_14 ?x63)))) (implies (forall (?x64 T2) (implies (up_6 uf_23 ?x64) (= (uf_24 ?x64) (uf_4 uf_14 ?x64)))) (and (= (uf_24 uf_11) 0) (implies (= (uf_24 uf_11) 0) (and (forall (?x65 T2) (<= 0 (uf_24 ?x65))) (implies (forall (?x66 T2) (<= 0 (uf_24 ?x66))) (and (forall (?x67 T2) (?x68 T2) (implies (and (not (up_6 uf_23 ?x68)) (up_6 uf_23 ?x67)) (<= (uf_24 ?x67) (uf_24 ?x68)))) (implies (forall (?x69 T2) (?x70 T2) (implies (and (not (up_6 uf_23 ?x70)) (up_6 uf_23 ?x69)) (<= (uf_24 ?x69) (uf_24 ?x70)))) (and (forall (?x71 T2) (?x72 T2) (implies (and (up_6 uf_23 ?x72) (< (uf_10 (uf_1 ?x72 ?x71)) uf_9)) (<= (uf_24 ?x71) (+ (uf_24 ?x72) (uf_10 (uf_1 ?x72 ?x71)))))) (implies (forall (?x73 T2) (?x74 T2) (implies (and (up_6 uf_23 ?x74) (< (uf_10 (uf_1 ?x74 ?x73)) uf_9)) (<= (uf_24 ?x73) (+ (uf_24 ?x74) (uf_10 (uf_1 ?x74 ?x73)))))) (and (forall (?x75 T2) (implies (and (not (= ?x75 uf_11)) (< (uf_24 ?x75) uf_9)) (exists (?x76 T2) (and (< (uf_24 ?x76) (uf_24 ?x75)) (and (up_6 uf_23 ?x76) (= (uf_24 ?x75) (+ (uf_24 ?x76) (uf_10 (uf_1 ?x76 ?x75))))))))) true)))))))))))))))))))))))))))))))))))))))))))
 :formula true
 )

--- a/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Wed Dec 23 17:37:42 2009 +0100
@@ -1,6631 +1,6542 @@
 #2 := false
-#52 := 0::int
-decl uf_10 :: (-> T1 int)
+decl up_6 :: (-> T4 T2 bool)
+decl ?x47!7 :: (-> T2 T2)
+decl ?x75!20 :: T2
+#2146 := ?x75!20
+#5823 := (?x47!7 ?x75!20)
+decl uf_23 :: T4
+#182 := uf_23
+#16800 := (up_6 uf_23 #5823)
+decl uf_2 :: (-> T1 T2)
 decl uf_1 :: (-> T2 T2 T1)
 decl uf_3 :: (-> T1 T2)
-decl ?x71!19 :: T2
-#2002 := ?x71!19
-decl ?x72!18 :: T2
-#2001 := ?x72!18
-#2007 := (uf_1 ?x72!18 ?x71!19)
-#11538 := (uf_3 #2007)
 decl uf_22 :: T2
-#182 := uf_22
-#18065 := (uf_1 uf_22 #11538)
-#18066 := (uf_10 #18065)
-decl uf_24 :: (-> T2 int)
-#18030 := (uf_24 #11538)
-#952 := -1::int
-#18049 := (* -1::int #18030)
-#18091 := (+ #18049 #18066)
-decl uf_4 :: (-> T3 T2 int)
-decl uf_14 :: T3
-#107 := uf_14
-#185 := (uf_4 uf_14 uf_22)
-#18092 := (+ #185 #18091)
-#18113 := (>= #18092 0::int)
-#18070 := (* -1::int #18066)
-decl uf_9 :: int
-#53 := uf_9
-#18074 := (+ uf_9 #18070)
-#18075 := (<= #18074 0::int)
-#17499 := (not #18075)
-#2008 := (uf_10 #2007)
-#2011 := (* -1::int #2008)
-#2012 := (+ uf_9 #2011)
-#2013 := (<= #2012 0::int)
-#2014 := (not #2013)
-#2005 := (uf_24 ?x72!18)
-#2543 := (* -1::int #2005)
-#2544 := (+ #2543 #2011)
-#2003 := (uf_24 ?x71!19)
-#2545 := (+ #2003 #2544)
-#2546 := (<= #2545 0::int)
-decl up_6 :: (-> T4 T2 bool)
-decl uf_23 :: T4
-#190 := uf_23
-#2015 := (up_6 uf_23 ?x72!18)
-#3106 := (not #2015)
-#3121 := (or #2013 #3106 #2546)
-#3126 := (not #3121)
-decl ?x75!20 :: T2
-#2031 := ?x75!20
-#11 := (:var 0 T2)
-#2035 := (uf_1 #11 ?x75!20)
-#4121 := (pattern #2035)
-#199 := (uf_24 #11)
-#4062 := (pattern #199)
-#216 := (up_6 uf_23 #11)
-#4087 := (pattern #216)
-#2036 := (uf_10 #2035)
-#2032 := (uf_24 ?x75!20)
-#2033 := (* -1::int #2032)
-#2581 := (+ #2033 #2036)
-#2582 := (+ #199 #2581)
-#2585 := (= #2582 0::int)
-#3151 := (not #2585)
-#2034 := (+ #199 #2033)
-#2039 := (>= #2034 0::int)
-#223 := (not #216)
-#3152 := (or #223 #2039 #3151)
-#4122 := (forall (vars (?x76 T2)) (:pat #4087 #4062 #4121) #3152)
-#4127 := (not #4122)
-#10 := (:var 1 T2)
-#90 := (uf_1 #11 #10)
-#3916 := (pattern #90)
-#226 := (uf_24 #10)
-#1337 := (* -1::int #226)
-#1338 := (+ #199 #1337)
-#91 := (uf_10 #90)
-#1363 := (+ #91 #1338)
-#1361 := (>= #1363 0::int)
-#967 := (* -1::int #91)
-#968 := (+ uf_9 #967)
-#969 := (<= #968 0::int)
-#3143 := (or #223 #969 #1361)
-#4113 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #3916) #3143)
-#4118 := (not #4113)
-decl uf_11 :: T2
-#64 := uf_11
-#2557 := (= uf_11 ?x75!20)
-#2043 := (+ uf_9 #2033)
-#2044 := (<= #2043 0::int)
-#4130 := (or #2044 #2557 #4118 #4127)
-decl ?x47!7 :: (-> T2 T2)
-#11097 := (?x47!7 ?x75!20)
-decl uf_15 :: T4
-#113 := uf_15
-#11136 := (up_6 uf_15 #11097)
-#11143 := (uf_4 uf_14 #11097)
-#11144 := (* -1::int #11143)
-#10301 := (uf_4 uf_14 ?x75!20)
-#11145 := (+ #10301 #11144)
-#11146 := (<= #11145 0::int)
-#11137 := (not #11136)
-#11147 := (uf_1 #11097 ?x75!20)
-#11148 := (uf_10 #11147)
-#11149 := (* -1::int #11148)
-#11150 := (+ #11144 #11149)
-#11133 := (+ #10301 #11150)
-#11134 := (= #11133 0::int)
-#11135 := (not #11134)
-#11142 := (or #11135 #11137 #11146)
-#11168 := (not #11142)
-#10403 := (* -1::int #10301)
-#11139 := (+ uf_9 #10403)
-#11140 := (<= #11139 0::int)
-#33430 := (not #11140)
-#2045 := (not #2044)
-#4133 := (not #4130)
-#25286 := [hypothesis]: #4133
-#3757 := (or #4130 #2045)
-#3755 := [def-axiom]: #3757
-#25348 := [unit-resolution #3755 #25286]: #2045
-#10404 := (+ #2032 #10403)
-#7777 := (>= #10404 0::int)
-#10311 := (= #2032 #10301)
-#3601 := (or #4130 #4122)
-#3749 := [def-axiom]: #3601
-#25346 := [unit-resolution #3749 #25286]: #4122
-#30592 := (or #10311 #4127)
-#5832 := (uf_1 uf_22 uf_22)
-#6904 := (uf_3 #5832)
-#8027 := (uf_24 #6904)
-#7883 := (* -1::int #8027)
-#10078 := (+ #2032 #7883)
-#10697 := (<= #10078 0::int)
-#30559 := (not #10697)
-#10700 := (uf_1 #6904 ?x75!20)
-#10701 := (uf_10 #10700)
-#30273 := (<= #10701 0::int)
-#30274 := (not #30273)
-#13994 := (= ?x75!20 #6904)
-#30199 := (not #13994)
-#11031 := (up_6 uf_15 ?x75!20)
-#14001 := (or #11031 #13994)
-#30202 := (not #14001)
+#174 := uf_22
+#4514 := (uf_1 uf_22 uf_22)
+#10482 := (uf_3 #4514)
+#15059 := (uf_1 #10482 ?x75!20)
+#15842 := (uf_3 #15059)
+#16792 := (uf_1 #5823 #15842)
+#19843 := (uf_2 #16792)
 decl uf_7 :: (-> T4 T2 T5 T4)
 decl uf_8 :: T5
 #33 := uf_8
-#8048 := (uf_7 uf_15 #6904 uf_8)
-#13996 := (up_6 #8048 ?x75!20)
-#14006 := (iff #13996 #14001)
+decl uf_15 :: T4
+#110 := uf_15
+#11444 := (uf_7 uf_15 #10482 uf_8)
+#27073 := (up_6 #11444 #19843)
+#27109 := (not #27073)
+#16801 := (not #16800)
+#27231 := (iff #16801 #27109)
+#27229 := (iff #16800 #27073)
+#27227 := (iff #27073 #16800)
+#27215 := (= #19843 #5823)
+#20888 := (= #5823 #19843)
+#11 := (:var 0 T2)
+#10 := (:var 1 T2)
+#12 := (uf_1 #10 #11)
+#3981 := (pattern #12)
+#16 := (uf_2 #12)
+#303 := (= #10 #16)
+#3988 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #3981) #303)
+#307 := (forall (vars (?x4 T2) (?x5 T2)) #303)
+#3991 := (iff #307 #3988)
+#3989 := (iff #303 #303)
+#3990 := [refl]: #3989
+#3992 := [quant-intro #3990]: #3991
+#1642 := (~ #307 #307)
+#1676 := (~ #303 #303)
+#1677 := [refl]: #1676
+#1643 := [nnf-pos #1677]: #1642
+#17 := (= #16 #10)
+#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
+#308 := (iff #18 #307)
+#305 := (iff #17 #303)
+#306 := [rewrite]: #305
+#309 := [quant-intro #306]: #308
+#302 := [asserted]: #18
+#312 := [mp #302 #309]: #307
+#1678 := [mp~ #312 #1643]: #307
+#3993 := [mp #1678 #3992]: #3988
+#8415 := (not #3988)
+#20865 := (or #8415 #20888)
+#20879 := [quant-inst]: #20865
+#27214 := [unit-resolution #20879 #3993]: #20888
+#27216 := [symm #27214]: #27215
+#13523 := (= #11444 uf_23)
+#183 := (uf_7 uf_15 uf_22 uf_8)
+#7113 := (= #183 uf_23)
+#184 := (= uf_23 #183)
+#2150 := (uf_1 #11 ?x75!20)
+#4271 := (pattern #2150)
+decl uf_24 :: (-> T2 int)
+#191 := (uf_24 #11)
+#4211 := (pattern #191)
+#201 := (up_6 uf_23 #11)
+#4237 := (pattern #201)
+#52 := 0::int
+decl uf_10 :: (-> T1 int)
+#2151 := (uf_10 #2150)
+#2147 := (uf_24 ?x75!20)
+#1038 := -1::int
+#2148 := (* -1::int #2147)
+#2745 := (+ #2148 #2151)
+#2746 := (+ #191 #2745)
+#2749 := (= #2746 0::int)
+#3311 := (not #2749)
+#2149 := (+ #191 #2148)
+#2154 := (>= #2149 0::int)
+#208 := (not #201)
+#3312 := (or #208 #2154 #3311)
+#4272 := (forall (vars (?x76 T2)) (:pat #4237 #4211 #4271) #3312)
+#4277 := (not #4272)
+#87 := (uf_1 #11 #10)
+#4066 := (pattern #87)
+#211 := (uf_24 #10)
+#1318 := (* -1::int #211)
+#1319 := (+ #191 #1318)
+#88 := (uf_10 #87)
+#1344 := (+ #88 #1319)
+#1342 := (>= #1344 0::int)
+#1053 := (* -1::int #88)
+decl uf_9 :: int
+#53 := uf_9
+#1054 := (+ uf_9 #1053)
+#1055 := (<= #1054 0::int)
+#3303 := (or #208 #1055 #1342)
+#4263 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #4066) #3303)
+#4268 := (not #4263)
+decl uf_11 :: T2
+#64 := uf_11
+#2721 := (= uf_11 ?x75!20)
+#2158 := (+ uf_9 #2148)
+#2159 := (<= #2158 0::int)
+#4280 := (or #2159 #2721 #4268 #4277)
+#4283 := (not #4280)
+decl ?x71!19 :: T2
+#2117 := ?x71!19
+decl ?x72!18 :: T2
+#2116 := ?x72!18
+#2122 := (uf_1 ?x72!18 ?x71!19)
+#2123 := (uf_10 #2122)
+#2126 := (* -1::int #2123)
+#2120 := (uf_24 ?x72!18)
+#2707 := (* -1::int #2120)
+#2708 := (+ #2707 #2126)
+#2118 := (uf_24 ?x71!19)
+#2709 := (+ #2118 #2708)
+#2710 := (<= #2709 0::int)
+#2130 := (up_6 uf_23 ?x72!18)
+#3266 := (not #2130)
+#2127 := (+ uf_9 #2126)
+#2128 := (<= #2127 0::int)
+#3281 := (or #2128 #3266 #2710)
+#3286 := (not #3281)
+#4286 := (or #3286 #4283)
+#4289 := (not #4286)
+#4254 := (pattern #191 #211)
+#1317 := (>= #1319 0::int)
+#209 := (up_6 uf_23 #10)
+#3243 := (not #209)
+#3258 := (or #201 #3243 #1317)
+#4255 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4254) #3258)
+#4260 := (not #4255)
+#4292 := (or #4260 #4289)
+#4295 := (not #4292)
+decl ?x68!16 :: T2
+#2091 := ?x68!16
+#2095 := (uf_24 ?x68!16)
+#2681 := (* -1::int #2095)
+decl ?x67!17 :: T2
+#2092 := ?x67!17
+#2093 := (uf_24 ?x67!17)
+#2682 := (+ #2093 #2681)
+#2683 := (<= #2682 0::int)
+#2099 := (up_6 uf_23 ?x68!16)
+#2098 := (up_6 uf_23 ?x67!17)
+#3220 := (not #2098)
+#3235 := (or #3220 #2099 #2683)
+#3240 := (not #3235)
+#4298 := (or #3240 #4295)
+#4301 := (not #4298)
+#1308 := (>= #191 0::int)
+#4246 := (forall (vars (?x65 T2)) (:pat #4211) #1308)
+#4251 := (not #4246)
+#4304 := (or #4251 #4301)
+#4307 := (not #4304)
+decl ?x65!15 :: T2
+#2076 := ?x65!15
+#2077 := (uf_24 ?x65!15)
+#2078 := (>= #2077 0::int)
+#2079 := (not #2078)
+#4310 := (or #2079 #4307)
+#4313 := (not #4310)
+#204 := (uf_24 uf_11)
+#205 := (= #204 0::int)
+#1305 := (not #205)
+#4316 := (or #1305 #4313)
+#4319 := (not #4316)
+#4322 := (or #1305 #4319)
+#4325 := (not #4322)
+decl uf_4 :: (-> T3 T2 int)
+decl uf_14 :: T3
+#104 := uf_14
+#107 := (uf_4 uf_14 #11)
+#4090 := (pattern #107)
+#645 := (= #107 #191)
+#662 := (or #208 #645)
+#4238 := (forall (vars (?x63 T2)) (:pat #4237 #4090 #4211) #662)
+#4243 := (not #4238)
+#4328 := (or #4243 #4325)
+#4331 := (not #4328)
+decl ?x63!14 :: T2
+#2052 := ?x63!14
+#2054 := (uf_4 uf_14 ?x63!14)
+#2053 := (uf_24 ?x63!14)
+#2658 := (= #2053 #2054)
+#2056 := (up_6 uf_23 ?x63!14)
+#2057 := (not #2056)
+#2661 := (or #2057 #2658)
+#2664 := (not #2661)
+#4334 := (or #2664 #4331)
+#4337 := (not #4334)
+#1293 := (* -1::int #191)
+#1294 := (+ #107 #1293)
+#1292 := (>= #1294 0::int)
+#4229 := (forall (vars (?x61 T2)) (:pat #4090 #4211) #1292)
+#4234 := (not #4229)
+#4340 := (or #4234 #4337)
+#4343 := (not #4340)
+decl ?x61!13 :: T2
+#2034 := ?x61!13
+#2037 := (uf_4 uf_14 ?x61!13)
+#2648 := (* -1::int #2037)
+#2035 := (uf_24 ?x61!13)
+#2649 := (+ #2035 #2648)
+#2650 := (<= #2649 0::int)
+#2655 := (not #2650)
+#4346 := (or #2655 #4343)
+#4349 := (not #4346)
+#185 := (uf_1 uf_22 #11)
+#4212 := (pattern #185)
+#186 := (uf_10 #185)
+#1431 := (+ #186 #1293)
+#177 := (uf_4 uf_14 uf_22)
+#1432 := (+ #177 #1431)
+#1433 := (= #1432 0::int)
+#1262 := (* -1::int #186)
+#1268 := (* -1::int #177)
+#1269 := (+ #1268 #1262)
+#1270 := (+ #107 #1269)
+#1271 := (<= #1270 0::int)
+#1263 := (+ uf_9 #1262)
+#1264 := (<= #1263 0::int)
+#3212 := (or #1264 #1271 #1433)
+#4221 := (forall (vars (?x59 T2)) (:pat #4212 #4090 #4211) #3212)
+#4226 := (not #4221)
+#3192 := (or #1264 #1271)
+#3193 := (not #3192)
+#3196 := (or #645 #3193)
+#4213 := (forall (vars (?x60 T2)) (:pat #4090 #4211 #4212) #3196)
+#4218 := (not #4213)
+decl ?x48!12 :: T2
+#2011 := ?x48!12
+#2017 := (up_6 uf_15 ?x48!12)
+#2012 := (uf_4 uf_14 ?x48!12)
+#2013 := (* -1::int #2012)
+#2014 := (+ uf_9 #2013)
+#2015 := (<= #2014 0::int)
+#1458 := (+ uf_9 #1268)
+#1459 := (<= #1458 0::int)
+#111 := (up_6 uf_15 #11)
+#4132 := (pattern #111)
+#1446 := (+ #107 #1268)
+#1445 := (>= #1446 0::int)
+#1449 := (or #111 #1445)
+#4203 := (forall (vars (?x58 T2)) (:pat #4132 #4090) #1449)
+#4208 := (not #4203)
+#825 := (not #184)
+#175 := (up_6 uf_15 uf_22)
+#4352 := (or #175 #825 #4208 #1459 #2015 #2017 #4218 #4226 #4349)
+#4355 := (not #4352)
+decl ?x53!11 :: T2
+#1945 := ?x53!11
+decl ?x54!10 :: T2
+#1944 := ?x54!10
+#1950 := (uf_1 ?x54!10 ?x53!11)
+#1951 := (uf_10 #1950)
+#1958 := (* -1::int #1951)
+decl uf_19 :: T3
+#141 := uf_19
+#1948 := (uf_4 uf_19 ?x54!10)
+#1954 := (* -1::int #1948)
+#2605 := (+ #1954 #1958)
+#1946 := (uf_4 uf_19 ?x53!11)
+#2606 := (+ #1946 #2605)
+#2607 := (<= #2606 0::int)
+#1959 := (+ uf_9 #1958)
+#1960 := (<= #1959 0::int)
+#1955 := (+ uf_9 #1954)
+#1956 := (<= #1955 0::int)
+#3156 := (or #1956 #1960 #2607)
+#3161 := (not #3156)
+#149 := (uf_4 uf_19 #10)
+#1175 := (* -1::int #149)
+#146 := (uf_4 uf_19 #11)
+#1176 := (+ #146 #1175)
+#1182 := (+ #88 #1176)
+#1205 := (>= #1182 0::int)
+#1162 := (* -1::int #146)
+#1163 := (+ uf_9 #1162)
+#1164 := (<= #1163 0::int)
+#3124 := (or #1055 #1164 #1205)
+#4165 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #4066) #3124)
+#4170 := (not #4165)
+#161 := (uf_4 uf_19 uf_11)
+#162 := (= #161 0::int)
+#4173 := (or #162 #4170)
+#4176 := (not #4173)
+#4179 := (or #4176 #3161)
+#4182 := (not #4179)
+#4141 := (pattern #146)
+decl ?x50!9 :: (-> T2 T2)
+#1921 := (?x50!9 #11)
+#1924 := (uf_1 #1921 #11)
+#1925 := (uf_10 #1924)
+#2575 := (* -1::int #1925)
+#1922 := (uf_4 uf_19 #1921)
+#2558 := (* -1::int #1922)
+#2576 := (+ #2558 #2575)
+#2577 := (+ #146 #2576)
+#2578 := (= #2577 0::int)
+#3094 := (not #2578)
+#2559 := (+ #146 #2558)
+#2560 := (<= #2559 0::int)
+#3095 := (or #2560 #3094)
+#3096 := (not #3095)
+#65 := (= #11 uf_11)
+#3102 := (or #65 #1164 #3096)
+#4157 := (forall (vars (?x49 T2)) (:pat #4141) #3102)
+#4162 := (not #4157)
+#4185 := (or #4162 #4182)
+#4188 := (not #4185)
+decl ?x49!8 :: T2
+#1881 := ?x49!8
+#1885 := (uf_1 #11 ?x49!8)
+#4142 := (pattern #1885)
+#1886 := (uf_10 #1885)
+#1882 := (uf_4 uf_19 ?x49!8)
+#1883 := (* -1::int #1882)
+#2528 := (+ #1883 #1886)
+#2529 := (+ #146 #2528)
+#2532 := (= #2529 0::int)
+#3058 := (not #2532)
+#1884 := (+ #146 #1883)
+#1889 := (>= #1884 0::int)
+#3059 := (or #1889 #3058)
+#4143 := (forall (vars (?x50 T2)) (:pat #4141 #4142) #3059)
+#4148 := (not #4143)
+#2504 := (= uf_11 ?x49!8)
+#1893 := (+ uf_9 #1883)
+#1894 := (<= #1893 0::int)
+#4151 := (or #1894 #2504 #4148)
+#4154 := (not #4151)
+#4191 := (or #4154 #4188)
+#4194 := (not #4191)
+#1117 := (* -1::int #107)
+#1118 := (+ uf_9 #1117)
+#1119 := (<= #1118 0::int)
+#3044 := (or #111 #1119)
+#4133 := (forall (vars (?x48 T2)) (:pat #4132 #4090) #3044)
+#4138 := (not #4133)
+#495 := (= uf_14 uf_19)
+#586 := (not #495)
+decl uf_16 :: T4
+#136 := uf_16
+#492 := (= uf_15 uf_16)
+#604 := (not #492)
+decl uf_21 :: T3
+#144 := uf_21
+decl uf_20 :: T3
+#143 := uf_20
+#145 := (= uf_20 uf_21)
+#577 := (not #145)
+decl uf_18 :: T2
+#139 := uf_18
+decl uf_17 :: T2
+#138 := uf_17
+#140 := (= uf_17 uf_18)
+#595 := (not #140)
+#4197 := (or #595 #577 #604 #586 #4138 #4194)
+#4200 := (not #4197)
+#4358 := (or #4200 #4355)
+#4361 := (not #4358)
+#1845 := (?x47!7 #11)
+#1846 := (uf_4 uf_14 #1845)
+#2463 := (* -1::int #1846)
+#2478 := (+ #107 #2463)
+#2479 := (<= #2478 0::int)
+#1850 := (uf_1 #1845 #11)
+#1851 := (uf_10 #1850)
+#2464 := (* -1::int #1851)
+#2465 := (+ #2463 #2464)
+#2466 := (+ #107 #2465)
+#2467 := (= #2466 0::int)
+#3028 := (not #2467)
+#1854 := (up_6 uf_15 #1845)
+#3027 := (not #1854)
+#3029 := (or #3027 #3028 #2479)
+#3030 := (not #3029)
+#3036 := (or #65 #1119 #3030)
+#4124 := (forall (vars (?x46 T2)) (:pat #4090) #3036)
+#4129 := (not #4124)
+decl uf_12 :: (-> T2 int)
+#66 := (uf_12 #11)
+#4042 := (pattern #66)
+decl ?x38!6 :: (-> T2 T2)
+#1818 := (?x38!6 #11)
+#1822 := (uf_12 #1818)
+#2422 := (* -1::int #1822)
+#1819 := (uf_1 #1818 #11)
+#1820 := (uf_10 #1819)
+#2439 := (* -1::int #1820)
+#2440 := (+ #2439 #2422)
+#2441 := (+ #66 #2440)
+#2442 := (= #2441 0::int)
+#3000 := (not #2442)
+#2423 := (+ #66 #2422)
+#2424 := (<= #2423 0::int)
+decl up_13 :: (-> T2 bool)
+#1828 := (up_13 #1818)
+#2999 := (not #1828)
+#3001 := (or #2999 #2424 #3000)
+#3002 := (not #3001)
+#1079 := (* -1::int #66)
+#1080 := (+ uf_9 #1079)
+#1081 := (<= #1080 0::int)
+#3008 := (or #65 #1081 #3002)
+#4116 := (forall (vars (?x37 T2)) (:pat #4042) #3008)
+#4121 := (not #4116)
+#113 := (up_6 uf_15 #10)
+#4107 := (pattern #111 #113)
+#115 := (uf_4 uf_14 #10)
+#1131 := (* -1::int #115)
+#1132 := (+ #107 #1131)
+#1135 := (>= #1132 0::int)
+#2965 := (not #113)
+#2980 := (or #111 #2965 #1135)
+#4108 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #4107) #2980)
+#4113 := (not #4108)
+#1133 := (+ #88 #1132)
+#1513 := (>= #1133 0::int)
+#112 := (not #111)
+#2957 := (or #112 #1055 #1513)
+#4099 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #4066) #2957)
+#4104 := (not #4099)
+#1536 := (>= #107 0::int)
+#4091 := (forall (vars (?x41 T2)) (:pat #4090) #1536)
+#4096 := (not #4091)
+#105 := (uf_4 uf_14 uf_11)
+#106 := (= #105 0::int)
+#1547 := (not #106)
+#4364 := (or #1547 #4096 #4104 #4113 #4121 #4129 #4361)
+#4367 := (not #4364)
+decl ?x37!5 :: T2
+#1774 := ?x37!5
+#1775 := (uf_1 #11 ?x37!5)
+#4075 := (pattern #1775)
+#74 := (up_13 #11)
+#4035 := (pattern #74)
+#1777 := (uf_12 ?x37!5)
+#1778 := (* -1::int #1777)
+#1776 := (uf_10 #1775)
+#2390 := (+ #1776 #1778)
+#2391 := (+ #66 #2390)
+#2394 := (= #2391 0::int)
+#2918 := (not #2394)
+#1782 := (+ #66 #1778)
+#1783 := (>= #1782 0::int)
+#75 := (not #74)
+#2919 := (or #75 #1783 #2918)
+#4076 := (forall (vars (?x38 T2)) (:pat #4035 #4042 #4075) #2919)
+#4081 := (not #4076)
+#2366 := (= uf_11 ?x37!5)
+#1787 := (+ uf_9 #1778)
+#1788 := (<= #1787 0::int)
+#4084 := (or #1788 #2366 #4081)
+#4087 := (not #4084)
+#4370 := (or #4087 #4367)
+#4373 := (not #4370)
+#83 := (uf_12 #10)
+#1041 := (* -1::int #83)
+#1068 := (+ #1041 #88)
+#1069 := (+ #66 #1068)
+#1066 := (>= #1069 0::int)
+#2910 := (or #75 #1055 #1066)
+#4067 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #4066) #2910)
+#4072 := (not #4067)
+#4376 := (or #4072 #4373)
+#4379 := (not #4376)
+decl ?x34!3 :: T2
+#1744 := ?x34!3
+#1751 := (uf_12 ?x34!3)
+decl ?x33!4 :: T2
+#1745 := ?x33!4
+#1748 := (uf_12 ?x33!4)
+#1749 := (* -1::int #1748)
+#2353 := (+ #1749 #1751)
+#1746 := (uf_1 ?x34!3 ?x33!4)
+#1747 := (uf_10 #1746)
+#2354 := (+ #1747 #2353)
+#2357 := (>= #2354 0::int)
+#1758 := (up_13 ?x34!3)
+#2873 := (not #1758)
+#1754 := (* -1::int #1747)
+#1755 := (+ uf_9 #1754)
+#1756 := (<= #1755 0::int)
+#2888 := (or #1756 #2873 #2357)
+#8152 := [hypothesis]: #1758
+#4036 := (forall (vars (?x26 T2)) (:pat #4035) #75)
+#76 := (forall (vars (?x26 T2)) #75)
+#4039 := (iff #76 #4036)
+#4037 := (iff #75 #75)
+#4038 := [refl]: #4037
+#4040 := [quant-intro #4038]: #4039
+#1658 := (~ #76 #76)
+#1695 := (~ #75 #75)
+#1696 := [refl]: #1695
+#1659 := [nnf-pos #1696]: #1658
+#67 := (= #66 0::int)
+#70 := (not #65)
+#1605 := (or #70 #67)
+#1608 := (forall (vars (?x24 T2)) #1605)
+#1611 := (not #1608)
+#1539 := (forall (vars (?x41 T2)) #1536)
+#1542 := (not #1539)
+#114 := (and #112 #113)
+#440 := (not #114)
+#1527 := (or #440 #1135)
+#1530 := (forall (vars (?x42 T2) (?x43 T2)) #1527)
+#1533 := (not #1530)
+#1056 := (not #1055)
+#1505 := (and #111 #1056)
+#1510 := (not #1505)
+#1516 := (or #1510 #1513)
+#1519 := (forall (vars (?x44 T2) (?x45 T2)) #1516)
+#1522 := (not #1519)
+#1452 := (forall (vars (?x58 T2)) #1449)
+#1455 := (not #1452)
+#1272 := (not #1271)
+#1265 := (not #1264)
+#1275 := (and #1265 #1272)
+#1428 := (not #1275)
+#1436 := (or #1428 #1433)
+#1439 := (forall (vars (?x59 T2)) #1436)
+#1442 := (not #1439)
+#1366 := (= #1344 0::int)
+#1369 := (not #1317)
+#1378 := (and #201 #1369 #1366)
+#1383 := (exists (vars (?x76 T2)) #1378)
+#1355 := (+ uf_9 #1293)
+#1356 := (<= #1355 0::int)
+#1357 := (not #1356)
+#1360 := (and #70 #1357)
+#1363 := (not #1360)
+#1386 := (or #1363 #1383)
+#1389 := (forall (vars (?x75 T2)) #1386)
+#1334 := (and #201 #1056)
+#1339 := (not #1334)
+#1346 := (or #1339 #1342)
+#1349 := (forall (vars (?x71 T2) (?x72 T2)) #1346)
+#1352 := (not #1349)
+#1392 := (or #1352 #1389)
+#1395 := (and #1349 #1392)
+#210 := (and #208 #209)
+#673 := (not #210)
+#1322 := (or #673 #1317)
+#1325 := (forall (vars (?x67 T2) (?x68 T2)) #1322)
+#1328 := (not #1325)
+#1398 := (or #1328 #1395)
+#1401 := (and #1325 #1398)
+#1311 := (forall (vars (?x65 T2)) #1308)
+#1314 := (not #1311)
+#1404 := (or #1314 #1401)
+#1407 := (and #1311 #1404)
+#1410 := (or #1305 #1407)
+#1413 := (and #205 #1410)
+#667 := (forall (vars (?x63 T2)) #662)
+#783 := (not #667)
+#1416 := (or #783 #1413)
+#1419 := (and #667 #1416)
+#1297 := (forall (vars (?x61 T2)) #1292)
+#1300 := (not #1297)
+#1422 := (or #1300 #1419)
+#1425 := (and #1297 #1422)
+#1281 := (or #645 #1275)
+#1286 := (forall (vars (?x60 T2)) #1281)
+#1289 := (not #1286)
+#1120 := (not #1119)
+#1236 := (and #112 #1120)
+#1239 := (exists (vars (?x48 T2)) #1236)
+#1470 := (not #1239)
+#1494 := (or #175 #825 #1470 #1289 #1425 #1442 #1455 #1459)
+#1165 := (not #1164)
+#1199 := (and #1056 #1165)
+#1202 := (not #1199)
+#1208 := (or #1202 #1205)
+#1211 := (forall (vars (?x53 T2) (?x54 T2)) #1208)
+#1214 := (not #1211)
+#1222 := (or #162 #1214)
+#1227 := (and #1211 #1222)
+#1180 := (= #1182 0::int)
+#1174 := (>= #1176 0::int)
+#1177 := (not #1174)
+#1184 := (and #1177 #1180)
+#1187 := (exists (vars (?x50 T2)) #1184)
+#1168 := (and #70 #1165)
+#1171 := (not #1168)
+#1190 := (or #1171 #1187)
+#1193 := (forall (vars (?x49 T2)) #1190)
+#1196 := (not #1193)
+#1230 := (or #1196 #1227)
+#1233 := (and #1193 #1230)
+#1257 := (or #595 #577 #604 #586 #1233 #1239)
+#1499 := (and #1257 #1494)
+#1136 := (not #1135)
+#1129 := (= #1133 0::int)
+#1145 := (and #111 #1129 #1136)
+#1150 := (exists (vars (?x47 T2)) #1145)
+#1123 := (and #70 #1120)
+#1126 := (not #1123)
+#1153 := (or #1126 #1150)
+#1156 := (forall (vars (?x46 T2)) #1153)
+#1159 := (not #1156)
+#1091 := (= #1069 0::int)
+#1042 := (+ #66 #1041)
+#1040 := (>= #1042 0::int)
+#1094 := (not #1040)
+#1103 := (and #74 #1094 #1091)
+#1108 := (exists (vars (?x38 T2)) #1103)
+#1082 := (not #1081)
+#1085 := (and #70 #1082)
+#1088 := (not #1085)
+#1111 := (or #1088 #1108)
+#1114 := (forall (vars (?x37 T2)) #1111)
+#1550 := (not #1114)
+#1571 := (or #1547 #1550 #1159 #1499 #1522 #1533 #1542)
+#1576 := (and #1114 #1571)
+#1059 := (and #74 #1056)
+#1062 := (not #1059)
+#1070 := (or #1062 #1066)
+#1073 := (forall (vars (?x33 T2) (?x34 T2)) #1070)
+#1076 := (not #1073)
+#1579 := (or #1076 #1576)
+#1582 := (and #1073 #1579)
+#81 := (up_13 #10)
+#82 := (and #75 #81)
+#416 := (not #82)
+#1044 := (or #416 #1040)
+#1047 := (forall (vars (?x29 T2) (?x30 T2)) #1044)
+#1050 := (not #1047)
+#1585 := (or #1050 #1582)
+#1588 := (and #1047 #1585)
+#1031 := (>= #66 0::int)
+#1032 := (forall (vars (?x27 T2)) #1031)
+#1035 := (not #1032)
+#1591 := (or #1035 #1588)
+#1594 := (and #1032 #1591)
+#77 := (uf_12 uf_11)
+#78 := (= #77 0::int)
+#1026 := (not #78)
+#1597 := (or #1026 #1594)
+#1600 := (and #78 #1597)
+#399 := (= uf_9 #66)
+#405 := (or #65 #399)
+#410 := (forall (vars (?x25 T2)) #405)
+#999 := (not #410)
+#990 := (not #76)
+#1623 := (or #990 #999 #1600 #1611)
+#1628 := (not #1623)
+#1 := true
+#216 := (+ #191 #88)
+#223 := (= #211 #216)
+#224 := (and #201 #223)
+#222 := (< #191 #211)
+#225 := (and #222 #224)
+#226 := (exists (vars (?x76 T2)) #225)
+#220 := (< #191 uf_9)
+#221 := (and #70 #220)
+#227 := (implies #221 #226)
+#228 := (forall (vars (?x75 T2)) #227)
+#229 := (and #228 true)
+#217 := (<= #211 #216)
+#89 := (< #88 uf_9)
+#215 := (and #201 #89)
+#218 := (implies #215 #217)
+#219 := (forall (vars (?x71 T2) (?x72 T2)) #218)
+#230 := (implies #219 #229)
+#231 := (and #219 #230)
+#212 := (<= #211 #191)
+#213 := (implies #210 #212)
+#214 := (forall (vars (?x67 T2) (?x68 T2)) #213)
+#232 := (implies #214 #231)
+#233 := (and #214 #232)
+#206 := (<= 0::int #191)
+#207 := (forall (vars (?x65 T2)) #206)
+#234 := (implies #207 #233)
+#235 := (and #207 #234)
+#236 := (implies #205 #235)
+#237 := (and #205 #236)
+#196 := (= #191 #107)
+#202 := (implies #201 #196)
+#203 := (forall (vars (?x63 T2)) #202)
+#238 := (implies #203 #237)
+#239 := (and #203 #238)
+#199 := (<= #191 #107)
+#200 := (forall (vars (?x61 T2)) #199)
+#240 := (implies #200 #239)
+#241 := (and #200 #240)
+#188 := (+ #177 #186)
+#189 := (< #188 #107)
+#187 := (< #186 uf_9)
+#190 := (and #187 #189)
+#195 := (not #190)
+#197 := (implies #195 #196)
+#198 := (forall (vars (?x60 T2)) #197)
+#242 := (implies #198 #241)
+#192 := (= #191 #188)
+#193 := (implies #190 #192)
+#194 := (forall (vars (?x59 T2)) #193)
+#243 := (implies #194 #242)
+#244 := (implies #184 #243)
+#179 := (<= #177 #107)
+#180 := (implies #112 #179)
+#181 := (forall (vars (?x58 T2)) #180)
+#245 := (implies #181 #244)
+#178 := (< #177 uf_9)
+#246 := (implies #178 #245)
+#176 := (not #175)
+#247 := (implies #176 #246)
+#124 := (< #107 uf_9)
+#133 := (and #112 #124)
+#134 := (exists (vars (?x48 T2)) #133)
+#248 := (implies #134 #247)
+#249 := (implies true #248)
+#163 := (and #162 true)
+#151 := (+ #146 #88)
+#158 := (<= #149 #151)
+#147 := (< #146 uf_9)
+#157 := (and #147 #89)
+#159 := (implies #157 #158)
+#160 := (forall (vars (?x53 T2) (?x54 T2)) #159)
+#164 := (implies #160 #163)
+#165 := (and #160 #164)
+#152 := (= #149 #151)
+#150 := (< #146 #149)
+#153 := (and #150 #152)
+#154 := (exists (vars (?x50 T2)) #153)
+#148 := (and #70 #147)
+#155 := (implies #148 #154)
+#156 := (forall (vars (?x49 T2)) #155)
+#166 := (implies #156 #165)
+#167 := (and #156 #166)
+#168 := (implies #145 #167)
+#142 := (= uf_19 uf_14)
+#169 := (implies #142 #168)
+#170 := (implies #140 #169)
+#137 := (= uf_16 uf_15)
+#171 := (implies #137 #170)
+#135 := (not #134)
+#172 := (implies #135 #171)
+#173 := (implies true #172)
+#250 := (and #173 #249)
+#120 := (+ #107 #88)
+#127 := (= #115 #120)
+#128 := (and #111 #127)
+#126 := (< #107 #115)
+#129 := (and #126 #128)
+#130 := (exists (vars (?x47 T2)) #129)
+#125 := (and #70 #124)
+#131 := (implies #125 #130)
+#132 := (forall (vars (?x46 T2)) #131)
+#251 := (implies #132 #250)
+#121 := (<= #115 #120)
+#119 := (and #111 #89)
+#122 := (implies #119 #121)
+#123 := (forall (vars (?x44 T2) (?x45 T2)) #122)
+#252 := (implies #123 #251)
+#116 := (<= #115 #107)
+#117 := (implies #114 #116)
+#118 := (forall (vars (?x42 T2) (?x43 T2)) #117)
+#253 := (implies #118 #252)
+#108 := (<= 0::int #107)
+#109 := (forall (vars (?x41 T2)) #108)
+#254 := (implies #109 #253)
+#255 := (implies #106 #254)
+#256 := (implies true #255)
+#91 := (+ #66 #88)
+#98 := (= #83 #91)
+#99 := (and #74 #98)
+#97 := (< #66 #83)
+#100 := (and #97 #99)
+#101 := (exists (vars (?x38 T2)) #100)
+#95 := (< #66 uf_9)
+#96 := (and #70 #95)
+#102 := (implies #96 #101)
+#103 := (forall (vars (?x37 T2)) #102)
+#257 := (implies #103 #256)
+#258 := (and #103 #257)
+#92 := (<= #83 #91)
+#90 := (and #74 #89)
+#93 := (implies #90 #92)
+#94 := (forall (vars (?x33 T2) (?x34 T2)) #93)
+#259 := (implies #94 #258)
+#260 := (and #94 #259)
+#84 := (<= #83 #66)
+#85 := (implies #82 #84)
+#86 := (forall (vars (?x29 T2) (?x30 T2)) #85)
+#261 := (implies #86 #260)
+#262 := (and #86 #261)
+#79 := (<= 0::int #66)
+#80 := (forall (vars (?x27 T2)) #79)
+#263 := (implies #80 #262)
+#264 := (and #80 #263)
+#265 := (implies #78 #264)
+#266 := (and #78 #265)
+#267 := (implies #76 #266)
+#71 := (= #66 uf_9)
+#72 := (implies #70 #71)
+#73 := (forall (vars (?x25 T2)) #72)
+#268 := (implies #73 #267)
+#68 := (implies #65 #67)
+#69 := (forall (vars (?x24 T2)) #68)
+#269 := (implies #69 #268)
+#270 := (implies true #269)
+#271 := (not #270)
+#1631 := (iff #271 #1628)
+#683 := (+ #88 #191)
+#701 := (= #211 #683)
+#704 := (and #201 #701)
+#707 := (and #222 #704)
+#710 := (exists (vars (?x76 T2)) #707)
+#716 := (not #221)
+#717 := (or #716 #710)
+#722 := (forall (vars (?x75 T2)) #717)
+#686 := (<= #211 #683)
+#680 := (and #89 #201)
+#692 := (not #680)
+#693 := (or #692 #686)
+#698 := (forall (vars (?x71 T2) (?x72 T2)) #693)
+#735 := (not #698)
+#736 := (or #735 #722)
+#741 := (and #698 #736)
+#674 := (or #673 #212)
+#677 := (forall (vars (?x67 T2) (?x68 T2)) #674)
+#747 := (not #677)
+#748 := (or #747 #741)
+#753 := (and #677 #748)
+#759 := (not #207)
+#760 := (or #759 #753)
+#765 := (and #207 #760)
+#670 := (= 0::int #204)
+#771 := (not #670)
+#772 := (or #771 #765)
+#777 := (and #670 #772)
+#784 := (or #783 #777)
+#789 := (and #667 #784)
+#795 := (not #200)
+#796 := (or #795 #789)
+#801 := (and #200 #796)
+#651 := (or #190 #645)
+#656 := (forall (vars (?x60 T2)) #651)
+#807 := (not #656)
+#808 := (or #807 #801)
+#631 := (= #188 #191)
+#637 := (or #195 #631)
+#642 := (forall (vars (?x59 T2)) #637)
+#816 := (not #642)
+#817 := (or #816 #808)
+#826 := (or #825 #817)
+#625 := (or #111 #179)
+#628 := (forall (vars (?x58 T2)) #625)
+#834 := (not #628)
+#835 := (or #834 #826)
+#843 := (not #178)
+#844 := (or #843 #835)
+#852 := (or #175 #844)
+#860 := (or #135 #852)
+#540 := (= 0::int #161)
+#498 := (+ #88 #146)
+#525 := (<= #149 #498)
+#522 := (and #89 #147)
+#531 := (not #522)
+#532 := (or #531 #525)
+#537 := (forall (vars (?x53 T2) (?x54 T2)) #532)
+#553 := (not #537)
+#554 := (or #553 #540)
+#559 := (and #537 #554)
+#501 := (= #149 #498)
+#504 := (and #150 #501)
+#507 := (exists (vars (?x50 T2)) #504)
+#513 := (not #148)
+#514 := (or #513 #507)
+#519 := (forall (vars (?x49 T2)) #514)
+#565 := (not #519)
+#566 := (or #565 #559)
+#571 := (and #519 #566)
+#578 := (or #577 #571)
+#587 := (or #586 #578)
+#596 := (or #595 #587)
+#605 := (or #604 #596)
+#613 := (or #134 #605)
+#872 := (and #613 #860)
+#450 := (+ #88 #107)
+#468 := (= #115 #450)
+#471 := (and #111 #468)
+#474 := (and #126 #471)
+#477 := (exists (vars (?x47 T2)) #474)
+#483 := (not #125)
+#484 := (or #483 #477)
+#489 := (forall (vars (?x46 T2)) #484)
+#878 := (not #489)
+#879 := (or #878 #872)
+#453 := (<= #115 #450)
+#447 := (and #89 #111)
+#459 := (not #447)
+#460 := (or #459 #453)
+#465 := (forall (vars (?x44 T2) (?x45 T2)) #460)
+#887 := (not #465)
+#888 := (or #887 #879)
+#441 := (or #440 #116)
+#444 := (forall (vars (?x42 T2) (?x43 T2)) #441)
+#896 := (not #444)
+#897 := (or #896 #888)
+#905 := (not #109)
+#906 := (or #905 #897)
+#437 := (= 0::int #105)
+#914 := (not #437)
+#915 := (or #914 #906)
+#430 := (not #96)
+#431 := (or #430 #101)
+#434 := (forall (vars (?x37 T2)) #431)
+#930 := (not #434)
+#931 := (or #930 #915)
+#936 := (and #434 #931)
+#423 := (not #90)
+#424 := (or #423 #92)
+#427 := (forall (vars (?x33 T2) (?x34 T2)) #424)
+#942 := (not #427)
+#943 := (or #942 #936)
+#948 := (and #427 #943)
+#417 := (or #416 #84)
+#420 := (forall (vars (?x29 T2) (?x30 T2)) #417)
+#954 := (not #420)
+#955 := (or #954 #948)
+#960 := (and #420 #955)
+#966 := (not #80)
+#967 := (or #966 #960)
+#972 := (and #80 #967)
+#413 := (= 0::int #77)
+#978 := (not #413)
+#979 := (or #978 #972)
+#984 := (and #413 #979)
+#991 := (or #990 #984)
+#1000 := (or #999 #991)
+#385 := (= 0::int #66)
+#391 := (or #70 #385)
+#396 := (forall (vars (?x24 T2)) #391)
+#1008 := (not #396)
+#1009 := (or #1008 #1000)
+#1021 := (not #1009)
+#1629 := (iff #1021 #1628)
+#1626 := (iff #1009 #1623)
+#1614 := (or #990 #1600)
+#1617 := (or #999 #1614)
+#1620 := (or #1611 #1617)
+#1624 := (iff #1620 #1623)
+#1625 := [rewrite]: #1624
+#1621 := (iff #1009 #1620)
+#1618 := (iff #1000 #1617)
+#1615 := (iff #991 #1614)
+#1601 := (iff #984 #1600)
+#1598 := (iff #979 #1597)
+#1595 := (iff #972 #1594)
+#1592 := (iff #967 #1591)
+#1589 := (iff #960 #1588)
+#1586 := (iff #955 #1585)
+#1583 := (iff #948 #1582)
+#1580 := (iff #943 #1579)
+#1577 := (iff #936 #1576)
+#1574 := (iff #931 #1571)
+#1553 := (or #1159 #1499)
+#1556 := (or #1522 #1553)
+#1559 := (or #1533 #1556)
+#1562 := (or #1542 #1559)
+#1565 := (or #1547 #1562)
+#1568 := (or #1550 #1565)
+#1572 := (iff #1568 #1571)
+#1573 := [rewrite]: #1572
+#1569 := (iff #931 #1568)
+#1566 := (iff #915 #1565)
+#1563 := (iff #906 #1562)
+#1560 := (iff #897 #1559)
+#1557 := (iff #888 #1556)
+#1554 := (iff #879 #1553)
+#1500 := (iff #872 #1499)
+#1497 := (iff #860 #1494)
+#1473 := (or #1289 #1425)
+#1476 := (or #1442 #1473)
+#1479 := (or #825 #1476)
+#1482 := (or #1455 #1479)
+#1485 := (or #1459 #1482)
+#1488 := (or #175 #1485)
+#1491 := (or #1470 #1488)
+#1495 := (iff #1491 #1494)
+#1496 := [rewrite]: #1495
+#1492 := (iff #860 #1491)
+#1489 := (iff #852 #1488)
+#1486 := (iff #844 #1485)
+#1483 := (iff #835 #1482)
+#1480 := (iff #826 #1479)
+#1477 := (iff #817 #1476)
+#1474 := (iff #808 #1473)
+#1426 := (iff #801 #1425)
+#1423 := (iff #796 #1422)
+#1420 := (iff #789 #1419)
+#1417 := (iff #784 #1416)
+#1414 := (iff #777 #1413)
+#1411 := (iff #772 #1410)
+#1408 := (iff #765 #1407)
+#1405 := (iff #760 #1404)
+#1402 := (iff #753 #1401)
+#1399 := (iff #748 #1398)
+#1396 := (iff #741 #1395)
+#1393 := (iff #736 #1392)
+#1390 := (iff #722 #1389)
+#1387 := (iff #717 #1386)
+#1384 := (iff #710 #1383)
+#1381 := (iff #707 #1378)
+#1372 := (and #201 #1366)
+#1375 := (and #1369 #1372)
+#1379 := (iff #1375 #1378)
+#1380 := [rewrite]: #1379
+#1376 := (iff #707 #1375)
+#1373 := (iff #704 #1372)
+#1367 := (iff #701 #1366)
+#1368 := [rewrite]: #1367
+#1374 := [monotonicity #1368]: #1373
+#1370 := (iff #222 #1369)
+#1371 := [rewrite]: #1370
+#1377 := [monotonicity #1371 #1374]: #1376
+#1382 := [trans #1377 #1380]: #1381
+#1385 := [quant-intro #1382]: #1384
+#1364 := (iff #716 #1363)
+#1361 := (iff #221 #1360)
+#1358 := (iff #220 #1357)
+#1359 := [rewrite]: #1358
+#1362 := [monotonicity #1359]: #1361
+#1365 := [monotonicity #1362]: #1364
+#1388 := [monotonicity #1365 #1385]: #1387
+#1391 := [quant-intro #1388]: #1390
+#1353 := (iff #735 #1352)
+#1350 := (iff #698 #1349)
+#1347 := (iff #693 #1346)
+#1343 := (iff #686 #1342)
+#1345 := [rewrite]: #1343
+#1340 := (iff #692 #1339)
+#1337 := (iff #680 #1334)
+#1331 := (and #1056 #201)
+#1335 := (iff #1331 #1334)
+#1336 := [rewrite]: #1335
+#1332 := (iff #680 #1331)
+#1057 := (iff #89 #1056)
+#1058 := [rewrite]: #1057
+#1333 := [monotonicity #1058]: #1332
+#1338 := [trans #1333 #1336]: #1337
+#1341 := [monotonicity #1338]: #1340
+#1348 := [monotonicity #1341 #1345]: #1347
+#1351 := [quant-intro #1348]: #1350
+#1354 := [monotonicity #1351]: #1353
+#1394 := [monotonicity #1354 #1391]: #1393
+#1397 := [monotonicity #1351 #1394]: #1396
+#1329 := (iff #747 #1328)
+#1326 := (iff #677 #1325)
+#1323 := (iff #674 #1322)
+#1320 := (iff #212 #1317)
+#1321 := [rewrite]: #1320
+#1324 := [monotonicity #1321]: #1323
+#1327 := [quant-intro #1324]: #1326
+#1330 := [monotonicity #1327]: #1329
+#1400 := [monotonicity #1330 #1397]: #1399
+#1403 := [monotonicity #1327 #1400]: #1402
+#1315 := (iff #759 #1314)
+#1312 := (iff #207 #1311)
+#1309 := (iff #206 #1308)
+#1310 := [rewrite]: #1309
+#1313 := [quant-intro #1310]: #1312
+#1316 := [monotonicity #1313]: #1315
+#1406 := [monotonicity #1316 #1403]: #1405
+#1409 := [monotonicity #1313 #1406]: #1408
+#1306 := (iff #771 #1305)
+#1303 := (iff #670 #205)
+#1304 := [rewrite]: #1303
+#1307 := [monotonicity #1304]: #1306
+#1412 := [monotonicity #1307 #1409]: #1411
+#1415 := [monotonicity #1304 #1412]: #1414
+#1418 := [monotonicity #1415]: #1417
+#1421 := [monotonicity #1418]: #1420
+#1301 := (iff #795 #1300)
+#1298 := (iff #200 #1297)
+#1295 := (iff #199 #1292)
+#1296 := [rewrite]: #1295
+#1299 := [quant-intro #1296]: #1298
+#1302 := [monotonicity #1299]: #1301
+#1424 := [monotonicity #1302 #1421]: #1423
+#1427 := [monotonicity #1299 #1424]: #1426
+#1290 := (iff #807 #1289)
+#1287 := (iff #656 #1286)
+#1284 := (iff #651 #1281)
+#1278 := (or #1275 #645)
+#1282 := (iff #1278 #1281)
+#1283 := [rewrite]: #1282
+#1279 := (iff #651 #1278)
+#1276 := (iff #190 #1275)
+#1273 := (iff #189 #1272)
+#1274 := [rewrite]: #1273
+#1266 := (iff #187 #1265)
+#1267 := [rewrite]: #1266
+#1277 := [monotonicity #1267 #1274]: #1276
+#1280 := [monotonicity #1277]: #1279
+#1285 := [trans #1280 #1283]: #1284
+#1288 := [quant-intro #1285]: #1287
+#1291 := [monotonicity #1288]: #1290
+#1475 := [monotonicity #1291 #1427]: #1474
+#1443 := (iff #816 #1442)
+#1440 := (iff #642 #1439)
+#1437 := (iff #637 #1436)
+#1434 := (iff #631 #1433)
+#1435 := [rewrite]: #1434
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+#1430 := [monotonicity #1277]: #1429
+#1438 := [monotonicity #1430 #1435]: #1437
+#1441 := [quant-intro #1438]: #1440
+#1444 := [monotonicity #1441]: #1443
+#1478 := [monotonicity #1444 #1475]: #1477
+#1481 := [monotonicity #1478]: #1480
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+#1453 := (iff #628 #1452)
+#1450 := (iff #625 #1449)
+#1447 := (iff #179 #1445)
+#1448 := [rewrite]: #1447
+#1451 := [monotonicity #1448]: #1450
+#1454 := [quant-intro #1451]: #1453
+#1457 := [monotonicity #1454]: #1456
+#1484 := [monotonicity #1457 #1481]: #1483
+#1468 := (iff #843 #1459)
+#1460 := (not #1459)
+#1463 := (not #1460)
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+#1465 := [monotonicity #1462]: #1464
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+#1490 := [monotonicity #1487]: #1489
+#1471 := (iff #135 #1470)
+#1240 := (iff #134 #1239)
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+#1121 := (iff #124 #1120)
+#1122 := [rewrite]: #1121
+#1238 := [monotonicity #1122]: #1237
+#1241 := [quant-intro #1238]: #1240
+#1472 := [monotonicity #1241]: #1471
+#1493 := [monotonicity #1472 #1490]: #1492
+#1498 := [trans #1493 #1496]: #1497
+#1260 := (iff #613 #1257)
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+#1245 := (or #586 #1242)
+#1248 := (or #595 #1245)
+#1251 := (or #604 #1248)
+#1254 := (or #1239 #1251)
+#1258 := (iff #1254 #1257)
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+#1255 := (iff #613 #1254)
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+#1246 := (iff #587 #1245)
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+#1231 := (iff #566 #1230)
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+#1224 := [rewrite]: #1223
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+#1217 := (iff #540 #162)
+#1218 := [rewrite]: #1217
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+#1207 := [rewrite]: #1206
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+#1166 := (iff #147 #1165)
+#1167 := [rewrite]: #1166
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+#1204 := [monotonicity #1201]: #1203
+#1210 := [monotonicity #1204 #1207]: #1209
+#1213 := [quant-intro #1210]: #1212
+#1216 := [monotonicity #1213]: #1215
+#1221 := [monotonicity #1216 #1218]: #1220
+#1226 := [trans #1221 #1224]: #1225
+#1229 := [monotonicity #1213 #1226]: #1228
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+#1194 := (iff #519 #1193)
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+#1188 := (iff #507 #1187)
+#1185 := (iff #504 #1184)
+#1181 := (iff #501 #1180)
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+#1178 := (iff #150 #1177)
+#1179 := [rewrite]: #1178
+#1186 := [monotonicity #1179 #1183]: #1185
+#1189 := [quant-intro #1186]: #1188
+#1172 := (iff #513 #1171)
+#1169 := (iff #148 #1168)
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+#1173 := [monotonicity #1170]: #1172
+#1192 := [monotonicity #1173 #1189]: #1191
+#1195 := [quant-intro #1192]: #1194
+#1198 := [monotonicity #1195]: #1197
+#1232 := [monotonicity #1198 #1229]: #1231
+#1235 := [monotonicity #1195 #1232]: #1234
+#1244 := [monotonicity #1235]: #1243
+#1247 := [monotonicity #1244]: #1246
+#1250 := [monotonicity #1247]: #1249
+#1253 := [monotonicity #1250]: #1252
+#1256 := [monotonicity #1241 #1253]: #1255
+#1261 := [trans #1256 #1259]: #1260
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+#1151 := (iff #477 #1150)
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+#1140 := (iff #471 #1139)
+#1130 := (iff #468 #1129)
+#1134 := [rewrite]: #1130
+#1141 := [monotonicity #1134]: #1140
+#1137 := (iff #126 #1136)
+#1138 := [rewrite]: #1137
+#1144 := [monotonicity #1138 #1141]: #1143
+#1149 := [trans #1144 #1147]: #1148
+#1152 := [quant-intro #1149]: #1151
+#1127 := (iff #483 #1126)
+#1124 := (iff #125 #1123)
+#1125 := [monotonicity #1122]: #1124
+#1128 := [monotonicity #1125]: #1127
+#1155 := [monotonicity #1128 #1152]: #1154
+#1158 := [quant-intro #1155]: #1157
+#1161 := [monotonicity #1158]: #1160
+#1555 := [monotonicity #1161 #1501]: #1554
+#1523 := (iff #887 #1522)
+#1520 := (iff #465 #1519)
+#1517 := (iff #460 #1516)
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+#1502 := (and #1056 #111)
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+#1507 := [rewrite]: #1506
+#1503 := (iff #447 #1502)
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+#1509 := [trans #1504 #1507]: #1508
+#1512 := [monotonicity #1509]: #1511
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+#1521 := [quant-intro #1518]: #1520
+#1524 := [monotonicity #1521]: #1523
+#1558 := [monotonicity #1524 #1555]: #1557
+#1534 := (iff #896 #1533)
+#1531 := (iff #444 #1530)
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+#1525 := (iff #116 #1135)
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+#1532 := [quant-intro #1529]: #1531
+#1535 := [monotonicity #1532]: #1534
+#1561 := [monotonicity #1535 #1558]: #1560
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+#1537 := (iff #108 #1536)
+#1538 := [rewrite]: #1537
+#1541 := [quant-intro #1538]: #1540
+#1544 := [monotonicity #1541]: #1543
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+#1548 := (iff #914 #1547)
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+#1093 := [rewrite]: #1092
+#1099 := [monotonicity #1093]: #1098
+#1095 := (iff #97 #1094)
+#1096 := [rewrite]: #1095
+#1102 := [monotonicity #1096 #1099]: #1101
+#1107 := [trans #1102 #1105]: #1106
+#1110 := [quant-intro #1107]: #1109
+#1089 := (iff #430 #1088)
+#1086 := (iff #96 #1085)
+#1083 := (iff #95 #1082)
+#1084 := [rewrite]: #1083
+#1087 := [monotonicity #1084]: #1086
+#1090 := [monotonicity #1087]: #1089
+#1113 := [monotonicity #1090 #1110]: #1112
+#1116 := [quant-intro #1113]: #1115
+#1552 := [monotonicity #1116]: #1551
+#1570 := [monotonicity #1552 #1567]: #1569
+#1575 := [trans #1570 #1573]: #1574
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+#1075 := [quant-intro #1072]: #1074
+#1078 := [monotonicity #1075]: #1077
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+#1584 := [monotonicity #1075 #1581]: #1583
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+#1049 := [quant-intro #1046]: #1048
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+#1596 := [monotonicity #1034 #1593]: #1595
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+#1610 := [quant-intro #1607]: #1609
+#1613 := [monotonicity #1610]: #1612
+#1622 := [monotonicity #1613 #1619]: #1621
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+#725 := (and #722 true)
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+#705 := (iff #224 #704)
+#702 := (iff #223 #701)
+#684 := (= #216 #683)
+#685 := [rewrite]: #684
+#703 := [monotonicity #685]: #702
+#706 := [monotonicity #703]: #705
+#709 := [monotonicity #706]: #708
+#712 := [quant-intro #709]: #711
+#715 := [monotonicity #712]: #714
+#721 := [trans #715 #719]: #720
+#724 := [quant-intro #721]: #723
+#727 := [monotonicity #724]: #726
+#731 := [trans #727 #729]: #730
+#699 := (iff #219 #698)
+#696 := (iff #218 #693)
+#689 := (implies #680 #686)
+#694 := (iff #689 #693)
+#695 := [rewrite]: #694
+#690 := (iff #218 #689)
+#687 := (iff #217 #686)
+#688 := [monotonicity #685]: #687
+#681 := (iff #215 #680)
+#682 := [rewrite]: #681
+#691 := [monotonicity #682 #688]: #690
+#697 := [trans #691 #695]: #696
+#700 := [quant-intro #697]: #699
+#734 := [monotonicity #700 #731]: #733
+#740 := [trans #734 #738]: #739
+#743 := [monotonicity #700 #740]: #742
+#678 := (iff #214 #677)
+#675 := (iff #213 #674)
+#676 := [rewrite]: #675
+#679 := [quant-intro #676]: #678
+#746 := [monotonicity #679 #743]: #745
+#752 := [trans #746 #750]: #751
+#755 := [monotonicity #679 #752]: #754
+#758 := [monotonicity #755]: #757
+#764 := [trans #758 #762]: #763
+#767 := [monotonicity #764]: #766
+#671 := (iff #205 #670)
+#672 := [rewrite]: #671
+#770 := [monotonicity #672 #767]: #769
+#776 := [trans #770 #774]: #775
+#779 := [monotonicity #672 #776]: #778
+#668 := (iff #203 #667)
+#665 := (iff #202 #662)
+#659 := (implies #201 #645)
+#663 := (iff #659 #662)
+#664 := [rewrite]: #663
+#660 := (iff #202 #659)
+#646 := (iff #196 #645)
+#647 := [rewrite]: #646
+#661 := [monotonicity #647]: #660
+#666 := [trans #661 #664]: #665
+#669 := [quant-intro #666]: #668
+#782 := [monotonicity #669 #779]: #781
+#788 := [trans #782 #786]: #787
+#791 := [monotonicity #669 #788]: #790
+#794 := [monotonicity #791]: #793
+#800 := [trans #794 #798]: #799
+#803 := [monotonicity #800]: #802
+#657 := (iff #198 #656)
+#654 := (iff #197 #651)
+#648 := (implies #195 #645)
+#652 := (iff #648 #651)
+#653 := [rewrite]: #652
+#649 := (iff #197 #648)
+#650 := [monotonicity #647]: #649
+#655 := [trans #650 #653]: #654
+#658 := [quant-intro #655]: #657
+#806 := [monotonicity #658 #803]: #805
+#812 := [trans #806 #810]: #811
+#643 := (iff #194 #642)
+#640 := (iff #193 #637)
+#634 := (implies #190 #631)
+#638 := (iff #634 #637)
+#639 := [rewrite]: #638
+#635 := (iff #193 #634)
+#632 := (iff #192 #631)
+#633 := [rewrite]: #632
+#636 := [monotonicity #633]: #635
+#641 := [trans #636 #639]: #640
+#644 := [quant-intro #641]: #643
+#815 := [monotonicity #644 #812]: #814
+#821 := [trans #815 #819]: #820
+#824 := [monotonicity #821]: #823
+#830 := [trans #824 #828]: #829
+#629 := (iff #181 #628)
+#626 := (iff #180 #625)
+#627 := [rewrite]: #626
+#630 := [quant-intro #627]: #629
+#833 := [monotonicity #630 #830]: #832
+#839 := [trans #833 #837]: #838
+#842 := [monotonicity #839]: #841
+#848 := [trans #842 #846]: #847
+#851 := [monotonicity #848]: #850
+#856 := [trans #851 #854]: #855
+#859 := [monotonicity #856]: #858
+#864 := [trans #859 #862]: #863
+#867 := [monotonicity #864]: #866
+#871 := [trans #867 #869]: #870
+#623 := (iff #173 #613)
+#618 := (implies true #613)
+#621 := (iff #618 #613)
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+#619 := (iff #173 #618)
+#616 := (iff #172 #613)
+#610 := (implies #135 #605)
+#614 := (iff #610 #613)
+#615 := [rewrite]: #614
+#611 := (iff #172 #610)
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+#601 := (implies #492 #596)
+#606 := (iff #601 #605)
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+#599 := (iff #170 #596)
+#592 := (implies #140 #587)
+#597 := (iff #592 #596)
+#598 := [rewrite]: #597
+#593 := (iff #170 #592)
+#590 := (iff #169 #587)
+#583 := (implies #495 #578)
+#588 := (iff #583 #587)
+#589 := [rewrite]: #588
+#584 := (iff #169 #583)
+#581 := (iff #168 #578)
+#574 := (implies #145 #571)
+#579 := (iff #574 #578)
+#580 := [rewrite]: #579
+#575 := (iff #168 #574)
+#572 := (iff #167 #571)
+#569 := (iff #166 #566)
+#562 := (implies #519 #559)
+#567 := (iff #562 #566)
+#568 := [rewrite]: #567
+#563 := (iff #166 #562)
+#560 := (iff #165 #559)
+#557 := (iff #164 #554)
+#550 := (implies #537 #540)
+#555 := (iff #550 #554)
+#556 := [rewrite]: #555
+#551 := (iff #164 #550)
+#548 := (iff #163 #540)
+#543 := (and #540 true)
+#546 := (iff #543 #540)
+#547 := [rewrite]: #546
+#544 := (iff #163 #543)
+#541 := (iff #162 #540)
+#542 := [rewrite]: #541
+#545 := [monotonicity #542]: #544
+#549 := [trans #545 #547]: #548
+#538 := (iff #160 #537)
+#535 := (iff #159 #532)
+#528 := (implies #522 #525)
+#533 := (iff #528 #532)
+#534 := [rewrite]: #533
+#529 := (iff #159 #528)
+#526 := (iff #158 #525)
+#499 := (= #151 #498)
+#500 := [rewrite]: #499
+#527 := [monotonicity #500]: #526
+#523 := (iff #157 #522)
+#524 := [rewrite]: #523
+#530 := [monotonicity #524 #527]: #529
+#536 := [trans #530 #534]: #535
+#539 := [quant-intro #536]: #538
+#552 := [monotonicity #539 #549]: #551
+#558 := [trans #552 #556]: #557
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+#520 := (iff #156 #519)
+#517 := (iff #155 #514)
+#510 := (implies #148 #507)
+#515 := (iff #510 #514)
+#516 := [rewrite]: #515
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+#508 := (iff #154 #507)
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+#506 := [monotonicity #503]: #505
+#509 := [quant-intro #506]: #508
+#512 := [monotonicity #509]: #511
+#518 := [trans #512 #516]: #517
+#521 := [quant-intro #518]: #520
+#564 := [monotonicity #521 #561]: #563
+#570 := [trans #564 #568]: #569
+#573 := [monotonicity #521 #570]: #572
+#576 := [monotonicity #573]: #575
+#582 := [trans #576 #580]: #581
+#496 := (iff #142 #495)
+#497 := [rewrite]: #496
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+#591 := [trans #585 #589]: #590
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+#493 := (iff #137 #492)
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+#603 := [monotonicity #494 #600]: #602
+#609 := [trans #603 #607]: #608
+#612 := [monotonicity #609]: #611
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+#490 := (iff #132 #489)
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+#475 := (iff #129 #474)
+#472 := (iff #128 #471)
+#469 := (iff #127 #468)
+#451 := (= #120 #450)
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+#479 := [quant-intro #476]: #478
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+#488 := [trans #482 #486]: #487
+#491 := [quant-intro #488]: #490
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+#883 := [trans #877 #881]: #882
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+#448 := (iff #119 #447)
+#449 := [rewrite]: #448
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+#464 := [trans #458 #462]: #463
+#467 := [quant-intro #464]: #466
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+#892 := [trans #886 #890]: #891
+#445 := (iff #118 #444)
+#442 := (iff #117 #441)
+#443 := [rewrite]: #442
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+#935 := [trans #929 #933]: #934
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+#959 := [trans #953 #957]: #958
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+#983 := [trans #977 #981]: #982
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+#409 := [trans #404 #407]: #408
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+#393 := [rewrite]: #392
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+#387 := [rewrite]: #386
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+#395 := [trans #390 #393]: #394
+#398 := [quant-intro #395]: #397
+#1007 := [monotonicity #398 #1004]: #1006
+#1013 := [trans #1007 #1011]: #1012
+#1016 := [monotonicity #1013]: #1015
+#1020 := [trans #1016 #1018]: #1019
+#1023 := [monotonicity #1020]: #1022
+#1632 := [trans #1023 #1630]: #1631
+#384 := [asserted]: #271
+#1633 := [mp #384 #1632]: #1628
+#1634 := [not-or-elim #1633]: #76
+#1697 := [mp~ #1634 #1659]: #76
+#4041 := [mp #1697 #4040]: #4036
+#5203 := (not #4036)
+#5204 := (or #5203 #2873)
+#5205 := [quant-inst]: #5204
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+#8156 := [lemma #8153]: #2873
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+#2893 := (not #2888)
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+#4063 := (not #4058)
+#4388 := (or #4063 #4385)
+#4391 := (not #4388)
+decl ?x30!1 :: T2
+#1719 := ?x30!1
+#1723 := (uf_12 ?x30!1)
+#2334 := (* -1::int #1723)
+decl ?x29!2 :: T2
+#1720 := ?x29!2
+#1721 := (uf_12 ?x29!2)
+#2335 := (+ #1721 #2334)
+#2336 := (<= #2335 0::int)
+#1727 := (up_13 ?x30!1)
+#1726 := (up_13 ?x29!2)
+#1766 := (not #1726)
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+#8727 := [hypothesis]: #1726
+#5149 := (or #5203 #1766)
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+#8729 := [lemma #8728]: #1766
+#3559 := (or #1968 #1726)
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+#10021 := [unit-resolution #3644 #8729]: #1968
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+#4397 := (not #4394)
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+#4054 := (not #4049)
+#4400 := (or #4054 #4397)
+#4403 := (not #4400)
+decl ?x27!0 :: T2
+#1704 := ?x27!0
+#1705 := (uf_12 ?x27!0)
+#1706 := (>= #1705 0::int)
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+#4426 := [quant-intro #4424]: #4425
+#1933 := (~ #1608 #1608)
+#2022 := (~ #1605 #1605)
+#2023 := [refl]: #2022
+#1934 := [nnf-pos #2023]: #1933
+#1638 := [not-or-elim #1633]: #1608
+#1765 := [mp~ #1638 #1934]: #1608
+#4427 := [mp #1765 #4426]: #4422
+#4964 := [hypothesis]: #1026
+#3570 := (not #4422)
+#4986 := (or #3570 #78)
+#4909 := (= uf_11 uf_11)
+#4907 := (not #4909)
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+#4921 := (iff #4907 #8612)
+#4919 := (iff #4909 true)
+#4920 := [rewrite]: #4919
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+#4963 := [monotonicity #4972]: #4973
+#4982 := [trans #4963 #4975]: #4981
+#4990 := [monotonicity #4982]: #4989
+#5015 := [trans #4990 #5014]: #4989
+#4988 := [quant-inst]: #4987
+#5016 := [mp #4988 #5015]: #4986
+#4971 := [unit-resolution #5016 #4964 #4427]: false
+#5020 := [lemma #4971]: #78
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+#3323 := (forall (vars (?x76 T2)) #3312)
+#3330 := (not #3323)
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+#3199 := (forall (vars (?x60 T2)) #3196)
+#3409 := (not #3199)
+#3412 := (or #175 #825 #1455 #1459 #2015 #2017 #3409 #3410 #3411)
+#3413 := (not #3412)
+#3129 := (forall (vars (?x53 T2) (?x54 T2)) #3124)
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+#3429 := (or #1547 #1542 #3424 #3425 #3426 #3427 #3428)
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+#2930 := (forall (vars (?x38 T2)) #2919)
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+#4374 := (iff #3442 #4373)
+#4371 := (iff #3435 #4370)
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+#4350 := (iff #3411 #4349)
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+#4332 := (iff #3385 #4331)
+#4329 := (iff #3384 #4328)
+#4326 := (iff #3383 #4325)
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+#4305 := (iff #3358 #4304)
+#4302 := (iff #3357 #4301)
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+#4281 := (iff #3331 #4280)
+#4278 := (iff #3330 #4277)
+#4275 := (iff #3323 #4272)
+#4273 := (iff #3312 #3312)
+#4274 := [refl]: #4273
+#4276 := [quant-intro #4274]: #4275
+#4279 := [monotonicity #4276]: #4278
+#4269 := (iff #3329 #4268)
+#4266 := (iff #3308 #4263)
+#4264 := (iff #3303 #3303)
+#4265 := [refl]: #4264
+#4267 := [quant-intro #4265]: #4266
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+#3432 := [rewrite]: #3431
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+#3406 := (and #176 #184 #3199 #3217 #1452 #1460 #2016 #2018 #3403)
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+#3325 := [quant-intro #3322]: #3324
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+#3299 := [trans #3295 #3297]: #3298
+#3302 := [monotonicity #3299]: #3301
+#3307 := [trans #3302 #3305]: #3306
+#3310 := [quant-intro #3307]: #3309
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+#3336 := [trans #3328 #3334]: #3335
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+#3277 := [trans #3273 #3275]: #3276
+#3280 := [monotonicity #3277]: #3279
+#3285 := [trans #3280 #3283]: #3284
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+#3264 := (iff #1325 #3263)
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+#3250 := [monotonicity #3247]: #3249
+#3254 := [trans #3250 #3252]: #3253
+#3257 := [monotonicity #3254]: #3256
+#3262 := [trans #3257 #3260]: #3261
+#3265 := [quant-intro #3262]: #3264
+#3342 := [monotonicity #3265 #3339]: #3341
+#3350 := [trans #3342 #3348]: #3349
+#3241 := (iff #2691 #3240)
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+#3230 := (iff #2672 #3221)
+#3222 := (not #3221)
+#3225 := (not #3222)
+#3228 := (iff #3225 #3221)
+#3229 := [rewrite]: #3228
+#3226 := (iff #2672 #3225)
+#3223 := (iff #2669 #3222)
+#3224 := [rewrite]: #3223
+#3227 := [monotonicity #3224]: #3226
+#3231 := [trans #3227 #3229]: #3230
+#3234 := [monotonicity #3231]: #3233
+#3239 := [trans #3234 #3237]: #3238
+#3242 := [monotonicity #3239]: #3241
+#3353 := [monotonicity #3242 #3350]: #3352
+#3356 := [monotonicity #3353]: #3355
+#3363 := [trans #3356 #3361]: #3362
+#3366 := [monotonicity #3363]: #3365
+#3369 := [monotonicity #3366]: #3368
+#3376 := [trans #3369 #3374]: #3375
+#3379 := [monotonicity #3376]: #3378
+#3382 := [monotonicity #3379]: #3381
+#3389 := [trans #3382 #3387]: #3388
+#3392 := [monotonicity #3389]: #3391
+#3395 := [monotonicity #3392]: #3394
+#3402 := [trans #3395 #3400]: #3401
+#3405 := [monotonicity #3402]: #3404
+#3218 := (iff #1439 #3217)
+#3215 := (iff #1436 #3212)
+#3209 := (or #3192 #1433)
+#3213 := (iff #3209 #3212)
+#3214 := [rewrite]: #3213
+#3210 := (iff #1436 #3209)
+#3207 := (iff #1428 #3192)
+#3202 := (not #3193)
+#3205 := (iff #3202 #3192)
+#3206 := [rewrite]: #3205
+#3203 := (iff #1428 #3202)
+#3194 := (iff #1275 #3193)
+#3195 := [rewrite]: #3194
+#3204 := [monotonicity #3195]: #3203
+#3208 := [trans #3204 #3206]: #3207
+#3211 := [monotonicity #3208]: #3210
+#3216 := [trans #3211 #3214]: #3215
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+#3072 := [quant-intro #3069]: #3071
+#3075 := [monotonicity #3072]: #3074
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+#3057 := [quant-intro #3054]: #3056
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+#2765 := (iff #2185 #2764)
+#2762 := (iff #2180 #2761)
+#2759 := (iff #2176 #2758)
+#2756 := (iff #2173 #2755)
+#2753 := (iff #2156 #2752)
+#2750 := (iff #2153 #2749)
+#2747 := (= #2152 #2746)
+#2748 := [rewrite]: #2747
+#2751 := [monotonicity #2748]: #2750
+#2754 := [monotonicity #2751]: #2753
+#2757 := [monotonicity #2754]: #2756
+#2760 := [quant-intro #2757]: #2759
+#2743 := (iff #2170 #2730)
+#2735 := (not #2730)
+#2738 := (not #2735)
+#2741 := (iff #2738 #2730)
+#2742 := [rewrite]: #2741
+#2739 := (iff #2170 #2738)
+#2736 := (iff #2164 #2735)
+#2733 := (iff #2163 #2730)
+#2727 := (and #2724 #2160)
+#2731 := (iff #2727 #2730)
+#2732 := [rewrite]: #2731
+#2728 := (iff #2163 #2727)
+#2725 := (iff #2162 #2724)
+#2722 := (iff #2161 #2721)
+#2723 := [rewrite]: #2722
+#2726 := [monotonicity #2723]: #2725
+#2729 := [monotonicity #2726]: #2728
+#2734 := [trans #2729 #2732]: #2733
+#2737 := [monotonicity #2734]: #2736
+#2740 := [monotonicity #2737]: #2739
+#2744 := [trans #2740 #2742]: #2743
+#2763 := [monotonicity #2744 #2760]: #2762
+#2766 := [monotonicity #2763]: #2765
+#2771 := [trans #2766 #2769]: #2770
+#2719 := (iff #2134 #2718)
+#2716 := (iff #2133 #2715)
+#2713 := (iff #2125 #2710)
+#2700 := (+ #2120 #2123)
+#2701 := (+ #2119 #2700)
+#2704 := (>= #2701 0::int)
+#2711 := (iff #2704 #2710)
+#2712 := [rewrite]: #2711
+#2705 := (iff #2125 #2704)
+#2702 := (= #2124 #2701)
+#2703 := [rewrite]: #2702
+#2706 := [monotonicity #2703]: #2705
+#2714 := [trans #2706 #2712]: #2713
+#2698 := (iff #2132 #2697)
+#2695 := (iff #2131 #2694)
+#2696 := [rewrite]: #2695
+#2699 := [monotonicity #2696]: #2698
+#2717 := [monotonicity #2699 #2714]: #2716
+#2720 := [monotonicity #2717]: #2719
+#2774 := [monotonicity #2720 #2771]: #2773
+#2777 := [monotonicity #2774]: #2776
+#2692 := (iff #2104 #2691)
+#2689 := (iff #2103 #2688)
+#2686 := (iff #2097 #2683)
+#2675 := (+ #2094 #2095)
+#2678 := (>= #2675 0::int)
+#2684 := (iff #2678 #2683)
+#2685 := [rewrite]: #2684
+#2679 := (iff #2097 #2678)
+#2676 := (= #2096 #2675)
+#2677 := [rewrite]: #2676
+#2680 := [monotonicity #2677]: #2679
+#2687 := [trans #2680 #2685]: #2686
+#2673 := (iff #2102 #2672)
+#2670 := (iff #2101 #2669)
+#2671 := [rewrite]: #2670
+#2674 := [monotonicity #2671]: #2673
+#2690 := [monotonicity #2674 #2687]: #2689
+#2693 := [monotonicity #2690]: #2692
+#2780 := [monotonicity #2693 #2777]: #2779
+#2783 := [monotonicity #2780]: #2782
+#2786 := [monotonicity #2783]: #2785
+#2667 := (iff #2073 #205)
+#2668 := [rewrite]: #2667
+#2789 := [monotonicity #2668 #2786]: #2788
+#2792 := [monotonicity #2789]: #2791
+#2795 := [monotonicity #2792]: #2794
+#2665 := (iff #2059 #2664)
+#2662 := (iff #2058 #2661)
+#2659 := (iff #2055 #2658)
+#2660 := [rewrite]: #2659
+#2663 := [monotonicity #2660]: #2662
+#2666 := [monotonicity #2663]: #2665
+#2798 := [monotonicity #2666 #2795]: #2797
+#2801 := [monotonicity #2798]: #2800
+#2656 := (iff #2040 #2655)
+#2653 := (iff #2039 #2650)
+#2642 := (+ #2036 #2037)
+#2645 := (>= #2642 0::int)
+#2651 := (iff #2645 #2650)
+#2652 := [rewrite]: #2651
+#2646 := (iff #2039 #2645)
+#2643 := (= #2038 #2642)
+#2644 := [rewrite]: #2643
+#2647 := [monotonicity #2644]: #2646
+#2654 := [trans #2647 #2652]: #2653
+#2657 := [monotonicity #2654]: #2656
+#2804 := [monotonicity #2657 #2801]: #2803
+#2640 := (iff #2008 #184)
+#2641 := [rewrite]: #2640
+#2807 := [monotonicity #2641 #2804]: #2806
+#2812 := [trans #2807 #2810]: #2811
+#2638 := (iff #2002 #2635)
+#2632 := (and #140 #145 #492 #495 #2629 #1999)
+#2636 := (iff #2632 #2635)
+#2637 := [rewrite]: #2636
+#2633 := (iff #2002 #2632)
+#2630 := (iff #1992 #2629)
+#2627 := (iff #1988 #2626)
+#2624 := (iff #1984 #2621)
+#2618 := (or #2615 #1980)
+#2622 := (iff #2618 #2621)
+#2623 := [rewrite]: #2622
+#2619 := (iff #1984 #2618)
+#2616 := (iff #1965 #2615)
+#2613 := (iff #1964 #2612)
+#2610 := (iff #1953 #2607)
+#2598 := (+ #1948 #1951)
+#2599 := (+ #1947 #2598)
+#2602 := (>= #2599 0::int)
+#2608 := (iff #2602 #2607)
+#2609 := [rewrite]: #2608
+#2603 := (iff #1953 #2602)
+#2600 := (= #1952 #2599)
+#2601 := [rewrite]: #2600
+#2604 := [monotonicity #2601]: #2603
+#2611 := [trans #2604 #2609]: #2610
+#2596 := (iff #1963 #2595)
+#2593 := (iff #1962 #2592)
+#2594 := [rewrite]: #2593
+#2597 := [monotonicity #2594]: #2596
+#2614 := [monotonicity #2597 #2611]: #2613
+#2617 := [monotonicity #2614]: #2616
+#2620 := [monotonicity #2617]: #2619
+#2625 := [trans #2620 #2623]: #2624
+#2590 := (iff #1938 #2589)
+#2587 := (iff #1935 #2586)
+#2584 := (iff #1930 #2583)
+#2581 := (iff #1927 #2578)
+#2568 := (+ #1922 #1925)
+#2569 := (+ #1162 #2568)
+#2572 := (= #2569 0::int)
+#2579 := (iff #2572 #2578)
+#2580 := [rewrite]: #2579
+#2573 := (iff #1927 #2572)
+#2570 := (= #1926 #2569)
+#2571 := [rewrite]: #2570
+#2574 := [monotonicity #2571]: #2573
+#2582 := [trans #2574 #2580]: #2581
+#2566 := (iff #1929 #2565)
+#2563 := (iff #1928 #2560)
+#2552 := (+ #1162 #1922)
+#2555 := (>= #2552 0::int)
+#2561 := (iff #2555 #2560)
+#2562 := [rewrite]: #2561
+#2556 := (iff #1928 #2555)
+#2553 := (= #1923 #2552)
+#2554 := [rewrite]: #2553
+#2557 := [monotonicity #2554]: #2556
+#2564 := [trans #2557 #2562]: #2563
+#2567 := [monotonicity #2564]: #2566
+#2585 := [monotonicity #2567 #2582]: #2584
+#2588 := [monotonicity #2585]: #2587
+#2591 := [quant-intro #2588]: #2590
+#2628 := [monotonicity #2591 #2625]: #2627
+#2550 := (iff #1914 #2547)
+#2513 := (and #1895 #2507)
+#2544 := (and #2513 #2541)
+#2548 := (iff #2544 #2547)
+#2549 := [rewrite]: #2548
+#2545 := (iff #1914 #2544)
+#2542 := (iff #1910 #2541)
+#2539 := (iff #1907 #2538)
+#2536 := (iff #1891 #2535)
+#2533 := (iff #1888 #2532)
+#2530 := (= #1887 #2529)
+#2531 := [rewrite]: #2530
+#2534 := [monotonicity #2531]: #2533
+#2537 := [monotonicity #2534]: #2536
+#2540 := [monotonicity #2537]: #2539
+#2543 := [quant-intro #2540]: #2542
+#2526 := (iff #1904 #2513)
+#2518 := (not #2513)
+#2521 := (not #2518)
+#2524 := (iff #2521 #2513)
+#2525 := [rewrite]: #2524
+#2522 := (iff #1904 #2521)
+#2519 := (iff #1899 #2518)
+#2516 := (iff #1898 #2513)
+#2510 := (and #2507 #1895)
+#2514 := (iff #2510 #2513)
+#2515 := [rewrite]: #2514
+#2511 := (iff #1898 #2510)
+#2508 := (iff #1897 #2507)
+#2505 := (iff #1896 #2504)
+#2506 := [rewrite]: #2505
+#2509 := [monotonicity #2506]: #2508
+#2512 := [monotonicity #2509]: #2511
+#2517 := [trans #2512 #2515]: #2516
+#2520 := [monotonicity #2517]: #2519
+#2523 := [monotonicity #2520]: #2522
+#2527 := [trans #2523 #2525]: #2526
+#2546 := [monotonicity #2527 #2543]: #2545
+#2551 := [trans #2546 #2549]: #2550
+#2631 := [monotonicity #2551 #2628]: #2630
+#2502 := (iff #1878 #495)
+#2503 := [rewrite]: #2502
+#2500 := (iff #1875 #492)
+#2501 := [rewrite]: #2500
+#2498 := (iff #1872 #145)
+#2499 := [rewrite]: #2498
+#2496 := (iff #1869 #140)
+#2497 := [rewrite]: #2496
+#2634 := [monotonicity #2497 #2499 #2501 #2503 #2631]: #2633
+#2639 := [trans #2634 #2637]: #2638
+#2815 := [monotonicity #2639 #2812]: #2814
+#2494 := (iff #1863 #2493)
+#2491 := (iff #1860 #2490)
+#2488 := (iff #1855 #2487)
+#2485 := (iff #1849 #2484)
+#2482 := (iff #1848 #2479)
+#2472 := (+ #1117 #1846)
+#2475 := (>= #2472 0::int)
+#2480 := (iff #2475 #2479)
+#2481 := [rewrite]: #2480
+#2476 := (iff #1848 #2475)
+#2473 := (= #1847 #2472)
+#2474 := [rewrite]: #2473
+#2477 := [monotonicity #2474]: #2476
+#2483 := [trans #2477 #2481]: #2482
+#2486 := [monotonicity #2483]: #2485
+#2470 := (iff #1853 #2467)
+#2456 := (+ #1846 #1851)
+#2457 := (+ #1117 #2456)
+#2460 := (= #2457 0::int)
+#2468 := (iff #2460 #2467)
+#2469 := [rewrite]: #2468
+#2461 := (iff #1853 #2460)
+#2458 := (= #1852 #2457)
+#2459 := [rewrite]: #2458
+#2462 := [monotonicity #2459]: #2461
+#2471 := [trans #2462 #2469]: #2470
+#2489 := [monotonicity #2471 #2486]: #2488
+#2492 := [monotonicity #2489]: #2491
+#2495 := [quant-intro #2492]: #2494
+#2454 := (iff #1837 #2453)
+#2451 := (iff #1834 #2450)
+#2448 := (iff #1829 #2447)
+#2445 := (iff #1824 #2442)
+#2432 := (+ #1820 #1822)
+#2433 := (+ #1079 #2432)
+#2436 := (= #2433 0::int)
+#2443 := (iff #2436 #2442)
+#2444 := [rewrite]: #2443
+#2437 := (iff #1824 #2436)
+#2434 := (= #1823 #2433)
+#2435 := [rewrite]: #2434
+#2438 := [monotonicity #2435]: #2437
+#2446 := [trans #2438 #2444]: #2445
+#2430 := (iff #1827 #2429)
+#2427 := (iff #1826 #2424)
+#2416 := (+ #1079 #1822)
+#2419 := (>= #2416 0::int)
+#2425 := (iff #2419 #2424)
+#2426 := [rewrite]: #2425
+#2420 := (iff #1826 #2419)
+#2417 := (= #1825 #2416)
+#2418 := [rewrite]: #2417
+#2421 := [monotonicity #2418]: #2420
+#2428 := [trans #2421 #2426]: #2427
+#2431 := [monotonicity #2428]: #2430
+#2449 := [monotonicity #2431 #2446]: #2448
+#2452 := [monotonicity #2449]: #2451
+#2455 := [quant-intro #2452]: #2454
+#2414 := (iff #1813 #106)
+#2415 := [rewrite]: #2414
+#2818 := [monotonicity #2415 #2455 #2495 #2815]: #2817
+#2823 := [trans #2818 #2821]: #2822
+#2412 := (iff #1808 #2409)
+#2375 := (and #1789 #2369)
+#2406 := (and #2375 #2403)
+#2410 := (iff #2406 #2409)
+#2411 := [rewrite]: #2410
+#2407 := (iff #1808 #2406)
+#2404 := (iff #1804 #2403)
+#2401 := (iff #1801 #2400)
+#2398 := (iff #1785 #2397)
+#2395 := (iff #1781 #2394)
+#2392 := (= #1780 #2391)
+#2393 := [rewrite]: #2392
+#2396 := [monotonicity #2393]: #2395
+#2399 := [monotonicity #2396]: #2398
+#2402 := [monotonicity #2399]: #2401
+#2405 := [quant-intro #2402]: #2404
+#2388 := (iff #1798 #2375)
+#2380 := (not #2375)
+#2383 := (not #2380)
+#2386 := (iff #2383 #2375)
+#2387 := [rewrite]: #2386
+#2384 := (iff #1798 #2383)
+#2381 := (iff #1793 #2380)
+#2378 := (iff #1792 #2375)
+#2372 := (and #2369 #1789)
+#2376 := (iff #2372 #2375)
+#2377 := [rewrite]: #2376
+#2373 := (iff #1792 #2372)
+#2370 := (iff #1791 #2369)
+#2367 := (iff #1790 #2366)
+#2368 := [rewrite]: #2367
+#2371 := [monotonicity #2368]: #2370
+#2374 := [monotonicity #2371]: #2373
+#2379 := [trans #2374 #2377]: #2378
+#2382 := [monotonicity #2379]: #2381
+#2385 := [monotonicity #2382]: #2384
+#2389 := [trans #2385 #2387]: #2388
+#2408 := [monotonicity #2389 #2405]: #2407
+#2413 := [trans #2408 #2411]: #2412
+#2826 := [monotonicity #2413 #2823]: #2825
+#2829 := [monotonicity #2826]: #2828
+#2364 := (iff #1762 #2363)
+#2361 := (iff #1761 #2360)
+#2358 := (iff #1753 #2357)
+#2355 := (= #1752 #2354)
+#2356 := [rewrite]: #2355
+#2359 := [monotonicity #2356]: #2358
+#2351 := (iff #1760 #2350)
+#2348 := (iff #1759 #2347)
+#2349 := [rewrite]: #2348
+#2352 := [monotonicity #2349]: #2351
+#2362 := [monotonicity #2352 #2359]: #2361
+#2365 := [monotonicity #2362]: #2364
+#2832 := [monotonicity #2365 #2829]: #2831
+#2835 := [monotonicity #2832]: #2834
+#2345 := (iff #1732 #2344)
+#2342 := (iff #1731 #2341)
+#2339 := (iff #1725 #2336)
+#2328 := (+ #1722 #1723)
+#2331 := (>= #2328 0::int)
+#2337 := (iff #2331 #2336)
+#2338 := [rewrite]: #2337
+#2332 := (iff #1725 #2331)
+#2329 := (= #1724 #2328)
+#2330 := [rewrite]: #2329
+#2333 := [monotonicity #2330]: #2332
+#2340 := [trans #2333 #2338]: #2339
+#2326 := (iff #1730 #2325)
+#2323 := (iff #1729 #2322)
+#2324 := [rewrite]: #2323
+#2327 := [monotonicity #2324]: #2326
+#2343 := [monotonicity #2327 #2340]: #2342
+#2346 := [monotonicity #2343]: #2345
+#2838 := [monotonicity #2346 #2835]: #2837
+#2841 := [monotonicity #2838]: #2840
+#2844 := [monotonicity #2841]: #2843
+#2320 := (iff #1662 #78)
+#2321 := [rewrite]: #2320
+#2847 := [monotonicity #2321 #2844]: #2846
+#2850 := [monotonicity #2847]: #2849
+#1636 := (not #1600)
+#2315 := (~ #1636 #2314)
+#2311 := (not #1597)
+#2312 := (~ #2311 #2310)
+#2307 := (not #1594)
+#2308 := (~ #2307 #2306)
+#2303 := (not #1591)
+#2304 := (~ #2303 #2302)
+#2299 := (not #1588)
+#2300 := (~ #2299 #2298)
+#2295 := (not #1585)
+#2296 := (~ #2295 #2294)
+#2291 := (not #1582)
+#2292 := (~ #2291 #2290)
+#2287 := (not #1579)
+#2288 := (~ #2287 #2286)
+#2283 := (not #1576)
+#2284 := (~ #2283 #2282)
+#2279 := (not #1571)
+#2280 := (~ #2279 #2278)
+#2275 := (not #1542)
+#2276 := (~ #2275 #1539)
+#2273 := (~ #1539 #1539)
+#2271 := (~ #1536 #1536)
+#2272 := [refl]: #2271
+#2274 := [nnf-pos #2272]: #2273
+#2277 := [nnf-neg #2274]: #2276
+#2268 := (not #1533)
+#2269 := (~ #2268 #1530)
+#2266 := (~ #1530 #1530)
+#2264 := (~ #1527 #1527)
+#2265 := [refl]: #2264
+#2267 := [nnf-pos #2265]: #2266
+#2270 := [nnf-neg #2267]: #2269
+#2261 := (not #1522)
+#2262 := (~ #2261 #1519)
+#2259 := (~ #1519 #1519)
+#2257 := (~ #1516 #1516)
+#2258 := [refl]: #2257
+#2260 := [nnf-pos #2258]: #2259
+#2263 := [nnf-neg #2260]: #2262
+#2254 := (not #1499)
+#2255 := (~ #2254 #2253)
+#2250 := (not #1494)
+#2251 := (~ #2250 #2249)
+#2247 := (~ #1460 #1460)
+#2248 := [refl]: #2247
+#2244 := (not #1455)
+#2245 := (~ #2244 #1452)
+#2242 := (~ #1452 #1452)
+#2240 := (~ #1449 #1449)
+#2241 := [refl]: #2240
+#2243 := [nnf-pos #2241]: #2242
+#2246 := [nnf-neg #2243]: #2245
+#2237 := (not #1442)
+#2238 := (~ #2237 #1439)
+#2235 := (~ #1439 #1439)
+#2233 := (~ #1436 #1436)
+#2234 := [refl]: #2233
+#2236 := [nnf-pos #2234]: #2235
+#2239 := [nnf-neg #2236]: #2238
+#2230 := (not #1425)
+#2231 := (~ #2230 #2229)
+#2226 := (not #1422)
+#2227 := (~ #2226 #2225)
+#2222 := (not #1419)
+#2223 := (~ #2222 #2221)
+#2218 := (not #1416)
+#2219 := (~ #2218 #2217)
+#2214 := (not #1413)
+#2215 := (~ #2214 #2213)
+#2210 := (not #1410)
+#2211 := (~ #2210 #2209)
+#2206 := (not #1407)
+#2207 := (~ #2206 #2205)
+#2202 := (not #1404)
+#2203 := (~ #2202 #2201)
+#2198 := (not #1401)
+#2199 := (~ #2198 #2197)
+#2194 := (not #1398)
+#2195 := (~ #2194 #2193)
+#2190 := (not #1395)
+#2191 := (~ #2190 #2189)
+#2186 := (not #1392)
+#2187 := (~ #2186 #2185)
+#2167 := (not #1389)
+#2183 := (~ #2167 #2180)
+#2157 := (exists (vars (?x76 T2)) #2156)
+#2165 := (or #2164 #2157)
+#2166 := (not #2165)
+#2181 := (~ #2166 #2180)
+#2177 := (not #2157)
+#2178 := (~ #2177 #2176)
+#2174 := (~ #2173 #2173)
+#2175 := [refl]: #2174
+#2179 := [nnf-neg #2175]: #2178
+#2171 := (~ #2170 #2170)
+#2172 := [refl]: #2171
+#2182 := [nnf-neg #2172 #2179]: #2181
+#2168 := (~ #2167 #2166)
+#2169 := [sk]: #2168
+#2184 := [trans #2169 #2182]: #2183
+#2143 := (not #1352)
+#2144 := (~ #2143 #1349)
+#2141 := (~ #1349 #1349)
+#2139 := (~ #1346 #1346)
+#2140 := [refl]: #2139
+#2142 := [nnf-pos #2140]: #2141
+#2145 := [nnf-neg #2142]: #2144
+#2188 := [nnf-neg #2145 #2184]: #2187
+#2135 := (~ #1352 #2134)
+#2136 := [sk]: #2135
+#2192 := [nnf-neg #2136 #2188]: #2191
+#2113 := (not #1328)
+#2114 := (~ #2113 #1325)
+#2111 := (~ #1325 #1325)
+#2109 := (~ #1322 #1322)
+#2110 := [refl]: #2109
+#2112 := [nnf-pos #2110]: #2111
+#2115 := [nnf-neg #2112]: #2114
+#2196 := [nnf-neg #2115 #2192]: #2195
+#2105 := (~ #1328 #2104)
+#2106 := [sk]: #2105
+#2200 := [nnf-neg #2106 #2196]: #2199
+#2088 := (not #1314)
+#2089 := (~ #2088 #1311)
+#2086 := (~ #1311 #1311)
+#2084 := (~ #1308 #1308)
+#2085 := [refl]: #2084
+#2087 := [nnf-pos #2085]: #2086
+#2090 := [nnf-neg #2087]: #2089
+#2204 := [nnf-neg #2090 #2200]: #2203
+#2080 := (~ #1314 #2079)
+#2081 := [sk]: #2080
+#2208 := [nnf-neg #2081 #2204]: #2207
+#2074 := (~ #2073 #2073)
+#2075 := [refl]: #2074
+#2212 := [nnf-neg #2075 #2208]: #2211
+#2071 := (~ #1305 #1305)
+#2072 := [refl]: #2071
+#2216 := [nnf-neg #2072 #2212]: #2215
+#2068 := (not #783)
+#2069 := (~ #2068 #667)
+#2066 := (~ #667 #667)
+#2064 := (~ #662 #662)
+#2065 := [refl]: #2064
+#2067 := [nnf-pos #2065]: #2066
+#2070 := [nnf-neg #2067]: #2069
+#2220 := [nnf-neg #2070 #2216]: #2219
+#2060 := (~ #783 #2059)
+#2061 := [sk]: #2060
+#2224 := [nnf-neg #2061 #2220]: #2223
+#2049 := (not #1300)
+#2050 := (~ #2049 #1297)
+#2047 := (~ #1297 #1297)
+#2045 := (~ #1292 #1292)
+#2046 := [refl]: #2045
+#2048 := [nnf-pos #2046]: #2047
+#2051 := [nnf-neg #2048]: #2050
+#2228 := [nnf-neg #2051 #2224]: #2227
+#2041 := (~ #1300 #2040)
+#2042 := [sk]: #2041
+#2232 := [nnf-neg #2042 #2228]: #2231
+#2031 := (not #1289)
+#2032 := (~ #2031 #1286)
+#2029 := (~ #1286 #1286)
+#2027 := (~ #1281 #1281)
+#2028 := [refl]: #2027
+#2030 := [nnf-pos #2028]: #2029
+#2033 := [nnf-neg #2030]: #2032
+#2024 := (not #1470)
+#2025 := (~ #2024 #2019)
+#2020 := (~ #1239 #2019)
+#2021 := [sk]: #2020
+#2026 := [nnf-neg #2021]: #2025
+#2009 := (~ #2008 #2008)
+#2010 := [refl]: #2009
+#2006 := (~ #176 #176)
+#2007 := [refl]: #2006
+#2252 := [nnf-neg #2007 #2010 #2026 #2033 #2232 #2239 #2246 #2248]: #2251
+#2003 := (not #1257)
+#2004 := (~ #2003 #2002)
+#2000 := (~ #1470 #1999)
+#1997 := (~ #1996 #1996)
+#1998 := [refl]: #1997
+#2001 := [nnf-neg #1998]: #2000
+#1993 := (not #1233)
+#1994 := (~ #1993 #1992)
+#1989 := (not #1230)
+#1990 := (~ #1989 #1988)
+#1985 := (not #1227)
+#1986 := (~ #1985 #1984)
+#1981 := (not #1222)
+#1982 := (~ #1981 #1980)
+#1977 := (not #1214)
+#1978 := (~ #1977 #1211)
+#1975 := (~ #1211 #1211)
+#1973 := (~ #1208 #1208)
+#1974 := [refl]: #1973
+#1976 := [nnf-pos #1974]: #1975
+#1979 := [nnf-neg #1976]: #1978
+#1971 := (~ #1970 #1970)
+#1972 := [refl]: #1971
+#1983 := [nnf-neg #1972 #1979]: #1982
+#1966 := (~ #1214 #1965)
+#1967 := [sk]: #1966
+#1987 := [nnf-neg #1967 #1983]: #1986
+#1941 := (not #1196)
+#1942 := (~ #1941 #1938)
+#1939 := (~ #1193 #1938)
+#1936 := (~ #1190 #1935)
+#1931 := (~ #1187 #1930)
+#1932 := [sk]: #1931
+#1919 := (~ #1171 #1171)
+#1920 := [refl]: #1919
+#1937 := [monotonicity #1920 #1932]: #1936
+#1940 := [nnf-pos #1937]: #1939
+#1943 := [nnf-neg #1940]: #1942
+#1991 := [nnf-neg #1943 #1987]: #1990
+#1917 := (~ #1196 #1914)
+#1892 := (exists (vars (?x50 T2)) #1891)
+#1900 := (or #1899 #1892)
+#1901 := (not #1900)
+#1915 := (~ #1901 #1914)
+#1911 := (not #1892)
+#1912 := (~ #1911 #1910)
+#1908 := (~ #1907 #1907)
+#1909 := [refl]: #1908
+#1913 := [nnf-neg #1909]: #1912
+#1905 := (~ #1904 #1904)
+#1906 := [refl]: #1905
+#1916 := [nnf-neg #1906 #1913]: #1915
+#1902 := (~ #1196 #1901)
+#1903 := [sk]: #1902
+#1918 := [trans #1903 #1916]: #1917
+#1995 := [nnf-neg #1918 #1991]: #1994
+#1879 := (~ #1878 #1878)
+#1880 := [refl]: #1879
+#1876 := (~ #1875 #1875)
+#1877 := [refl]: #1876
+#1873 := (~ #1872 #1872)
+#1874 := [refl]: #1873
+#1870 := (~ #1869 #1869)
+#1871 := [refl]: #1870
+#2005 := [nnf-neg #1871 #1874 #1877 #1880 #1995 #2001]: #2004
+#2256 := [nnf-neg #2005 #2252]: #2255
+#1866 := (not #1159)
+#1867 := (~ #1866 #1863)
+#1864 := (~ #1156 #1863)
+#1861 := (~ #1153 #1860)
+#1856 := (~ #1150 #1855)
+#1857 := [sk]: #1856
+#1843 := (~ #1126 #1126)
+#1844 := [refl]: #1843
+#1862 := [monotonicity #1844 #1857]: #1861
+#1865 := [nnf-pos #1862]: #1864
+#1868 := [nnf-neg #1865]: #1867
+#1840 := (not #1550)
+#1841 := (~ #1840 #1837)
+#1838 := (~ #1114 #1837)
+#1835 := (~ #1111 #1834)
+#1830 := (~ #1108 #1829)
+#1831 := [sk]: #1830
+#1816 := (~ #1088 #1088)
+#1817 := [refl]: #1816
+#1836 := [monotonicity #1817 #1831]: #1835
+#1839 := [nnf-pos #1836]: #1838
+#1842 := [nnf-neg #1839]: #1841
+#1814 := (~ #1813 #1813)
+#1815 := [refl]: #1814
+#2281 := [nnf-neg #1815 #1842 #1868 #2256 #2263 #2270 #2277]: #2280
+#1811 := (~ #1550 #1808)
+#1786 := (exists (vars (?x38 T2)) #1785)
+#1794 := (or #1793 #1786)
+#1795 := (not #1794)
+#1809 := (~ #1795 #1808)
+#1805 := (not #1786)
+#1806 := (~ #1805 #1804)
+#1802 := (~ #1801 #1801)
+#1803 := [refl]: #1802
+#1807 := [nnf-neg #1803]: #1806
+#1799 := (~ #1798 #1798)
+#1800 := [refl]: #1799
+#1810 := [nnf-neg #1800 #1807]: #1809
+#1796 := (~ #1550 #1795)
+#1797 := [sk]: #1796
+#1812 := [trans #1797 #1810]: #1811
+#2285 := [nnf-neg #1812 #2281]: #2284
+#1771 := (not #1076)
+#1772 := (~ #1771 #1073)
+#1769 := (~ #1073 #1073)
+#1767 := (~ #1070 #1070)
+#1768 := [refl]: #1767
+#1770 := [nnf-pos #1768]: #1769
+#1773 := [nnf-neg #1770]: #1772
+#2289 := [nnf-neg #1773 #2285]: #2288
+#1763 := (~ #1076 #1762)
+#1764 := [sk]: #1763
+#2293 := [nnf-neg #1764 #2289]: #2292
+#1741 := (not #1050)
+#1742 := (~ #1741 #1047)
+#1739 := (~ #1047 #1047)
+#1737 := (~ #1044 #1044)
+#1738 := [refl]: #1737
+#1740 := [nnf-pos #1738]: #1739
+#1743 := [nnf-neg #1740]: #1742
+#2297 := [nnf-neg #1743 #2293]: #2296
+#1733 := (~ #1050 #1732)
+#1734 := [sk]: #1733
+#2301 := [nnf-neg #1734 #2297]: #2300
+#1716 := (not #1035)
+#1717 := (~ #1716 #1032)
+#1714 := (~ #1032 #1032)
+#1712 := (~ #1031 #1031)
+#1713 := [refl]: #1712
+#1715 := [nnf-pos #1713]: #1714
+#1718 := [nnf-neg #1715]: #1717
+#2305 := [nnf-neg #1718 #2301]: #2304
+#1708 := (~ #1035 #1707)
+#1709 := [sk]: #1708
+#2309 := [nnf-neg #1709 #2305]: #2308
+#1663 := (~ #1662 #1662)
+#1703 := [refl]: #1663
+#2313 := [nnf-neg #1703 #2309]: #2312
+#1701 := (~ #1026 #1026)
+#1702 := [refl]: #1701
+#2316 := [nnf-neg #1702 #2313]: #2315
+#1637 := [not-or-elim #1633]: #1636
+#2317 := [mp~ #1637 #2316]: #2314
+#2318 := [mp #2317 #2850]: #2848
+#3492 := [mp #2318 #3491]: #3489
+#4421 := [mp #3492 #4420]: #4418
+#10019 := [unit-resolution #4421 #5020]: #4415
+#3747 := (or #4412 #4406)
+#3590 := [def-axiom]: #3747
+#10022 := [unit-resolution #3590 #10019]: #4406
+#10023 := (or #4409 #4403)
+#3664 := (* -1::int #1705)
+#3631 := (+ uf_9 #3664)
+#3633 := (<= #3631 0::int)
+#3738 := (= uf_9 #1705)
+#3712 := (= uf_11 ?x27!0)
+#3561 := (not #3712)
+#3560 := (= #1705 0::int)
+#4453 := (not #3560)
+#4452 := [hypothesis]: #1707
+#4504 := (or #4453 #1706)
+#4505 := [th-lemma]: #4504
+#4506 := [unit-resolution #4505 #4452]: #4453
+#3571 := (or #3570 #3560 #3561)
+#3727 := (= ?x27!0 uf_11)
+#3562 := (not #3727)
+#3563 := (or #3562 #3560)
+#3572 := (or #3570 #3563)
+#4443 := (iff #3572 #3571)
+#3585 := (or #3560 #3561)
+#4444 := (or #3570 #3585)
+#4447 := (iff #4444 #3571)
+#4448 := [rewrite]: #4447
+#4445 := (iff #3572 #4444)
+#3583 := (iff #3563 #3585)
+#4429 := (or #3561 #3560)
+#3569 := (iff #4429 #3585)
+#3566 := [rewrite]: #3569
+#3584 := (iff #3563 #4429)
+#3564 := (iff #3562 #3561)
+#3710 := (iff #3727 #3712)
+#3713 := [rewrite]: #3710
+#4428 := [monotonicity #3713]: #3564
+#3576 := [monotonicity #4428]: #3584
+#3567 := [trans #3576 #3566]: #3583
+#4446 := [monotonicity #3567]: #4445
+#4449 := [trans #4446 #4448]: #4443
+#3568 := [quant-inst]: #3572
+#4450 := [mp #3568 #4449]: #3571
+#4507 := [unit-resolution #4450 #4427 #4506]: #3561
+#3695 := (or #3712 #3738)
+#4043 := (forall (vars (?x25 T2)) (:pat #4042) #405)
+#4046 := (iff #410 #4043)
+#4044 := (iff #405 #405)
+#4045 := [refl]: #4044
+#4047 := [quant-intro #4045]: #4046
+#1660 := (~ #410 #410)
+#1698 := (~ #405 #405)
+#1699 := [refl]: #1698
+#1661 := [nnf-pos #1699]: #1660
+#1635 := [not-or-elim #1633]: #410
+#1700 := [mp~ #1635 #1661]: #410
+#4048 := [mp #1700 #4047]: #4043
+#3698 := (not #4043)
+#3699 := (or #3698 #3712 #3738)
+#3730 := (or #3727 #3738)
+#3700 := (or #3698 #3730)
+#3662 := (iff #3700 #3699)
+#3702 := (or #3698 #3695)
+#3653 := (iff #3702 #3699)
+#3660 := [rewrite]: #3653
+#3659 := (iff #3700 #3702)
+#3697 := (iff #3730 #3695)
+#3711 := [monotonicity #3713]: #3697
+#3661 := [monotonicity #3711]: #3659
+#3663 := [trans #3661 #3660]: #3662
+#3701 := [quant-inst]: #3700
+#3654 := [mp #3701 #3663]: #3699
+#4508 := [unit-resolution #3654 #4048]: #3695
+#4509 := [unit-resolution #4508 #4507]: #3738
+#4510 := (not #3738)
+#4511 := (or #4510 #3633)
+#4512 := [th-lemma]: #4511
+#4492 := [unit-resolution #4512 #4509]: #3633
+#4451 := (<= #1705 0::int)
+#4493 := (or #4451 #1706)
+#4494 := [th-lemma]: #4493
+#4495 := [unit-resolution #4494 #4452]: #4451
+#335 := (<= uf_9 0::int)
+#336 := (not #335)
+#54 := (< 0::int uf_9)
+#337 := (iff #54 #336)
+#338 := [rewrite]: #337
+#331 := [asserted]: #54
+#339 := [mp #331 #338]: #336
+#4496 := [th-lemma #339 #4495 #4492]: false
+#4491 := [lemma #4496]: #1706
+#3742 := (or #4409 #1707 #4403)
+#3743 := [def-axiom]: #3742
+#10024 := [unit-resolution #3743 #4491]: #10023
+#10025 := [unit-resolution #10024 #10022]: #4403
+#3766 := (or #4400 #4394)
+#3767 := [def-axiom]: #3766
+#10018 := [unit-resolution #3767 #10025]: #4394
+#3761 := (or #4397 #2108 #4391)
+#3762 := [def-axiom]: #3761
+#10026 := [unit-resolution #3762 #10018]: #4394
+#10027 := [unit-resolution #10026 #10021]: #4391
+#3787 := (or #4388 #4382)
+#3788 := [def-axiom]: #3787
+#10028 := [unit-resolution #3788 #10027]: #4382
+#3783 := (or #4385 #2893 #4379)
+#3784 := [def-axiom]: #3783
+#10029 := [unit-resolution #3784 #10028 #10020]: #4379
+#3771 := (or #4376 #4370)
+#3772 := [def-axiom]: #3771
+#10030 := [unit-resolution #3772 #10029]: #4370
+#10032 := (or #4373 #4367)
+#4499 := [hypothesis]: #4087
+#3969 := (or #4084 #2369)
+#3970 := [def-axiom]: #3969
+#4636 := [unit-resolution #3970 #4499]: #2369
+#4584 := (= uf_9 #1777)
+#4727 := (not #4584)
+#3636 := (or #4084 #1789)
+#3968 := [def-axiom]: #3636
+#4637 := [unit-resolution #3968 #4499]: #1789
+#4737 := (or #4727 #1788)
+#4738 := [th-lemma]: #4737
+#4739 := [unit-resolution #4738 #4637]: #4727
+#4758 := (or #4584 #2366)
+#4728 := [hypothesis]: #4727
+#4729 := [hypothesis]: #2369
+#4641 := (or #3698 #2366 #4584)
+#4585 := (or #1790 #4584)
+#4642 := (or #3698 #4585)
+#4628 := (iff #4642 #4641)
+#4638 := (or #2366 #4584)
+#4644 := (or #3698 #4638)
+#4626 := (iff #4644 #4641)
+#4627 := [rewrite]: #4626
+#4624 := (iff #4642 #4644)
+#4639 := (iff #4585 #4638)
+#4640 := [monotonicity #2368]: #4639
+#4625 := [monotonicity #4640]: #4624
+#4623 := [trans #4625 #4627]: #4628
+#4643 := [quant-inst]: #4642
+#4629 := [mp #4643 #4623]: #4641
+#4730 := [unit-resolution #4629 #4048 #4729 #4728]: false
+#4760 := [lemma #4730]: #4758
+#4740 := [unit-resolution #4760 #4739 #4636]: false
+#4741 := [lemma #4740]: #4084
+#3805 := (or #4373 #4087 #4367)
+#3815 := [def-axiom]: #3805
+#10033 := [unit-resolution #3815 #4741]: #10032
+#10034 := [unit-resolution #10033 #10030]: #4367
+#3800 := (or #4364 #4358)
+#3759 := [def-axiom]: #3800
+#10246 := [unit-resolution #3759 #10034]: #4358
+#3593 := (not #2607)
+#3836 := (or #4364 #106)
+#3832 := [def-axiom]: #3836
+#10035 := [unit-resolution #3832 #10034]: #106
+#8124 := (= #161 #105)
+#4885 := [hypothesis]: #4200
+#3652 := (or #4197 #495)
+#3934 := [def-axiom]: #3652
+#4886 := [unit-resolution #3934 #4885]: #495
+#8139 := [symm #4886]: #142
+#7937 := [monotonicity #8139]: #8124
+#4736 := [trans #7937 #10035]: #162
+#3612 := (or #4173 #1970)
+#3613 := [def-axiom]: #3612
+#7107 := [unit-resolution #3613 #4736]: #4173
+#3939 := (or #4197 #4191)
+#3928 := [def-axiom]: #3939
+#8726 := [unit-resolution #3928 #4885]: #4191
+#10469 := (or #4151 #586)
+#8744 := (?x47!7 ?x49!8)
+#8817 := (uf_4 uf_19 #8744)
+#8836 := (* -1::int #8817)
+#8739 := (uf_4 uf_14 #8744)
+#9868 := (+ #8739 #8836)
+#9874 := (>= #9868 0::int)
+#9867 := (= #8739 #8817)
+#10418 := (= #8817 #8739)
+#6250 := [hypothesis]: #495
+#10417 := [symm #6250]: #142
+#10419 := [monotonicity #10417]: #10418
+#10420 := [symm #10419]: #9867
+#10421 := (not #9867)
+#10416 := (or #10421 #9874)
+#10422 := [th-lemma]: #10416
+#10423 := [unit-resolution #10422 #10420]: #9874
+#8745 := (* -1::int #8739)
+#8586 := (uf_4 uf_14 ?x49!8)
+#8746 := (+ #8586 #8745)
+#8747 := (<= #8746 0::int)
+#8789 := (not #8747)
+#8770 := (up_6 uf_15 #8744)
+#8771 := (not #8770)
+#8748 := (uf_1 #8744 ?x49!8)
+#8749 := (uf_10 #8748)
+#8765 := (* -1::int #8749)
+#8766 := (+ #8745 #8765)
+#8767 := (+ #8586 #8766)
+#8768 := (= #8767 0::int)
+#8769 := (not #8768)
+#8754 := (or #8747 #8769 #8771)
+#8757 := (not #8754)
+#8721 := (* -1::int #8586)
+#8734 := (+ uf_9 #8721)
+#8722 := (<= #8734 0::int)
+#8939 := (not #8722)
+#10424 := [hypothesis]: #4154
+#3622 := (or #4151 #1895)
+#3627 := [def-axiom]: #3622
+#10425 := [unit-resolution #3627 #10424]: #1895
+#8935 := (+ #1882 #8721)
+#8932 := (>= #8935 0::int)
+#8934 := (= #1882 #8586)
+#10426 := (= #8586 #1882)
+#10427 := [monotonicity #6250]: #10426
+#10428 := [symm #10427]: #8934
+#10429 := (not #8934)
+#10430 := (or #10429 #8932)
+#10431 := [th-lemma]: #10430
+#10432 := [unit-resolution #10431 #10428]: #8932
+#8931 := (not #8932)
+#8940 := (or #8939 #8931 #1894)
+#8936 := [hypothesis]: #1895
+#8933 := [hypothesis]: #8722
+#8937 := [hypothesis]: #8932
+#8938 := [th-lemma #8937 #8933 #8936]: false
+#8738 := [lemma #8938]: #8940
+#10433 := [unit-resolution #8738 #10432 #10425]: #8939
+#10443 := (or #8722 #8757)
+#3963 := (or #4151 #2507)
+#3623 := [def-axiom]: #3963
+#10434 := [unit-resolution #3623 #10424]: #2507
+#3825 := (or #4364 #4124)
+#3793 := [def-axiom]: #3825
+#10442 := [unit-resolution #3793 #10034]: #4124
+#8762 := (or #4129 #2504 #8722 #8757)
+#8772 := (or #8771 #8769 #8747)
+#8773 := (not #8772)
+#8753 := (or #1896 #8722 #8773)
+#8775 := (or #4129 #8753)
+#8781 := (iff #8775 #8762)
+#8759 := (or #2504 #8722 #8757)
+#8777 := (or #4129 #8759)
+#8774 := (iff #8777 #8762)
+#8780 := [rewrite]: #8774
+#8778 := (iff #8775 #8777)
+#8760 := (iff #8753 #8759)
+#8752 := (iff #8773 #8757)
+#8755 := (iff #8772 #8754)
+#8756 := [rewrite]: #8755
+#8758 := [monotonicity #8756]: #8752
+#8761 := [monotonicity #2506 #8758]: #8760
+#8779 := [monotonicity #8761]: #8778
+#8782 := [trans #8779 #8780]: #8781
+#8776 := [quant-inst]: #8775
+#8783 := [mp #8776 #8782]: #8762
+#10444 := [unit-resolution #8783 #10442 #10434]: #10443
+#10445 := [unit-resolution #10444 #10433]: #8757
+#8787 := (or #8754 #8789)
+#8790 := [def-axiom]: #8787
+#10446 := [unit-resolution #8790 #10445]: #8789
+#8831 := (+ #1882 #8836)
+#8848 := (<= #8831 0::int)
+#8893 := (+ #8765 #8836)
+#8894 := (+ #1882 #8893)
+#8912 := (= #8894 0::int)
+#9084 := (<= #8894 0::int)
+#9871 := (<= #9868 0::int)
+#10447 := (or #10421 #9871)
+#10448 := [th-lemma]: #10447
+#10449 := [unit-resolution #10448 #10420]: #9871
+#8784 := (<= #8767 0::int)
+#8791 := (or #8754 #8768)
+#8792 := [def-axiom]: #8791
+#10450 := [unit-resolution #8792 #10445]: #8768
+#10451 := (or #8769 #8784)
+#10452 := [th-lemma]: #10451
+#10453 := [unit-resolution #10452 #10450]: #8784
+#8930 := (<= #8935 0::int)
+#10454 := (or #10429 #8930)
+#10455 := [th-lemma]: #10454
+#10456 := [unit-resolution #10455 #10428]: #8930
+#10096 := (not #9871)
+#10098 := (not #8784)
+#10097 := (not #8930)
+#10099 := (or #9084 #10097 #10098 #10096)
+#10059 := [hypothesis]: #9871
+#10060 := [hypothesis]: #8784
+#10062 := [hypothesis]: #8930
+#10063 := (not #9084)
+#10064 := [hypothesis]: #10063
+#10065 := [th-lemma #10064 #10062 #10060 #10059]: false
+#10100 := [lemma #10065]: #10099
+#10457 := [unit-resolution #10100 #10456 #10453 #10449]: #9084
+#9068 := (>= #8894 0::int)
+#8788 := (>= #8767 0::int)
+#10458 := (or #8769 #8788)
+#10459 := [th-lemma]: #10458
+#10460 := [unit-resolution #10459 #10450]: #8788
+#10439 := (not #9874)
+#10007 := (not #8788)
+#10440 := (or #9068 #8931 #10007 #10439)
+#10435 := [hypothesis]: #9874
+#9938 := [hypothesis]: #8788
+#10436 := (not #9068)
+#10437 := [hypothesis]: #10436
+#10438 := [th-lemma #10437 #8937 #9938 #10435]: false
+#10441 := [lemma #10438]: #10440
+#10461 := [unit-resolution #10441 #10432 #10460 #10423]: #9068
+#10462 := (or #8912 #10063 #10436)
+#10463 := [th-lemma]: #10462
+#10464 := [unit-resolution #10463 #10461 #10457]: #8912
+#8911 := (not #8912)
+#8918 := (or #8848 #8911)
+#3964 := (or #4151 #4143)
+#3607 := [def-axiom]: #3964
+#10465 := [unit-resolution #3607 #10424]: #4143
+#9022 := (or #4148 #8848 #8911)
+#8815 := (+ #1883 #8749)
+#8818 := (+ #8817 #8815)
+#8819 := (= #8818 0::int)
+#8820 := (not #8819)
+#8821 := (+ #8817 #1883)
+#8825 := (>= #8821 0::int)
+#8826 := (or #8825 #8820)
+#9031 := (or #4148 #8826)
+#9081 := (iff #9031 #9022)
+#9078 := (or #4148 #8918)
+#9024 := (iff #9078 #9022)
+#9080 := [rewrite]: #9024
+#9079 := (iff #9031 #9078)
+#8919 := (iff #8826 #8918)
+#8916 := (iff #8820 #8911)
+#8915 := (iff #8819 #8912)
+#8886 := (+ #8749 #8817)
+#8887 := (+ #1883 #8886)
+#8890 := (= #8887 0::int)
+#8913 := (iff #8890 #8912)
+#8914 := [rewrite]: #8913
+#8891 := (iff #8819 #8890)
+#8888 := (= #8818 #8887)
+#8889 := [rewrite]: #8888
+#8892 := [monotonicity #8889]: #8891
+#8910 := [trans #8892 #8914]: #8915
+#8917 := [monotonicity #8910]: #8916
+#8857 := (iff #8825 #8848)
+#8827 := (+ #1883 #8817)
+#8833 := (>= #8827 0::int)
+#8849 := (iff #8833 #8848)
+#8856 := [rewrite]: #8849
+#8834 := (iff #8825 #8833)
+#8829 := (= #8821 #8827)
+#8832 := [rewrite]: #8829
+#8835 := [monotonicity #8832]: #8834
+#8858 := [trans #8835 #8856]: #8857
+#8920 := [monotonicity #8858 #8917]: #8919
+#9023 := [monotonicity #8920]: #9079
+#9082 := [trans #9023 #9080]: #9081
+#9032 := [quant-inst]: #9031
+#9083 := [mp #9032 #9082]: #9022
+#10466 := [unit-resolution #9083 #10465]: #8918
+#10467 := [unit-resolution #10466 #10464]: #8848
+#10468 := [th-lemma #10432 #10467 #10446 #10423]: false
+#10470 := [lemma #10468]: #10469
+#8740 := [unit-resolution #10470 #4886]: #4151
+#3941 := (or #4194 #4154 #4188)
+#3945 := [def-axiom]: #3941
+#8741 := [unit-resolution #3945 #8740 #8726]: #4188
+#3672 := (or #4185 #4179)
+#3565 := [def-axiom]: #3672
+#8742 := [unit-resolution #3565 #8741]: #4179
+#3947 := (or #4182 #4176 #3161)
+#3669 := [def-axiom]: #3947
+#8743 := [unit-resolution #3669 #8742 #7107]: #3161
+#3956 := (or #3156 #3593)
+#3958 := [def-axiom]: #3956
+#8786 := [unit-resolution #3958 #8743]: #3593
+#3763 := (or #4364 #4099)
+#3818 := [def-axiom]: #3763
+#10042 := [unit-resolution #3818 #10034]: #4099
+#3953 := (or #3156 #1957)
+#3954 := [def-axiom]: #3953
+#8793 := [unit-resolution #3954 #8743]: #1957
+#3949 := (or #3156 #1961)
+#3955 := [def-axiom]: #3949
+#8794 := [unit-resolution #3955 #8743]: #1961
+#4870 := (or #4197 #1956 #4104 #1960 #2607)
+#4889 := (uf_4 uf_14 ?x53!11)
+#4883 := (= #1946 #4889)
+#4887 := (= #4889 #1946)
+#4882 := [monotonicity #4886]: #4887
+#4888 := [symm #4882]: #4883
+#4890 := (* -1::int #4889)
+#6163 := (+ #1946 #4890)
+#6178 := (<= #6163 0::int)
+#6288 := (not #6178)
+#6191 := [hypothesis]: #3593
+#6244 := [hypothesis]: #1961
+#6247 := [hypothesis]: #4099
+#6249 := [hypothesis]: #1957
+#3938 := (or #4197 #4133)
+#3935 := [def-axiom]: #3938
+#4841 := [unit-resolution #3935 #4885]: #4133
+#6294 := (or #6288 #1956 #4138 #4104 #1960 #2607 #586)
+#5206 := (uf_4 uf_14 ?x54!10)
+#5207 := (* -1::int #5206)
+#5202 := (+ uf_9 #5207)
+#5208 := (<= #5202 0::int)
+#5209 := (up_6 uf_15 ?x54!10)
+#5647 := (not #5209)
+#5579 := (+ #4890 #5206)
+#5580 := (+ #1951 #5579)
+#5572 := (>= #5580 0::int)
+#6194 := (not #5572)
+#6196 := (+ #1948 #5207)
+#6208 := (>= #6196 0::int)
+#6195 := (= #1948 #5206)
+#6209 := (= #5206 #1948)
+#6207 := [monotonicity #6250]: #6209
+#6210 := [symm #6207]: #6195
+#6211 := (not #6195)
+#6212 := (or #6211 #6208)
+#6241 := [th-lemma]: #6212
+#6242 := [unit-resolution #6241 #6210]: #6208
+#6192 := [hypothesis]: #6178
+#6289 := (not #6208)
+#6290 := (or #6194 #6288 #2607 #6289)
+#6190 := [hypothesis]: #6208
+#6187 := [hypothesis]: #5572
+#6193 := [th-lemma #6187 #6192 #6191 #6190]: false
+#6291 := [lemma #6193]: #6290
+#6243 := [unit-resolution #6291 #6192 #6191 #6242]: #6194
+#6248 := (or #5647 #5572)
+#5669 := (or #4104 #1960 #5647 #5572)
+#5605 := (+ #5206 #4890)
+#5606 := (+ #1951 #5605)
+#5646 := (>= #5606 0::int)
+#5578 := (or #5647 #1960 #5646)
+#5674 := (or #4104 #5578)
+#5939 := (iff #5674 #5669)
+#5670 := (or #1960 #5647 #5572)
+#5676 := (or #4104 #5670)
+#5909 := (iff #5676 #5669)
+#5910 := [rewrite]: #5909
+#5677 := (iff #5674 #5676)
+#5673 := (iff #5578 #5670)
+#5598 := (or #5647 #1960 #5572)
+#5671 := (iff #5598 #5670)
+#5672 := [rewrite]: #5671
+#5601 := (iff #5578 #5598)
+#5599 := (iff #5646 #5572)
+#5581 := (= #5606 #5580)
+#5582 := [rewrite]: #5581
+#5600 := [monotonicity #5582]: #5599
+#5602 := [monotonicity #5600]: #5601
+#5668 := [trans #5602 #5672]: #5673
+#5678 := [monotonicity #5668]: #5677
+#5940 := [trans #5678 #5910]: #5939
+#5675 := [quant-inst]: #5674
+#5941 := [mp #5675 #5940]: #5669
+#6177 := [unit-resolution #5941 #6247 #6244]: #6248
+#6189 := [unit-resolution #6177 #6243]: #5647
+#5211 := (or #5208 #5209)
+#6168 := [hypothesis]: #4133
+#5237 := (or #4138 #5208 #5209)
+#5210 := (or #5209 #5208)
+#5238 := (or #4138 #5210)
+#5244 := (iff #5238 #5237)
+#5240 := (or #4138 #5211)
+#5242 := (iff #5240 #5237)
+#5243 := [rewrite]: #5242
+#5235 := (iff #5238 #5240)
+#5212 := (iff #5210 #5211)
+#5236 := [rewrite]: #5212
+#5241 := [monotonicity #5236]: #5235
+#5245 := [trans #5241 #5243]: #5244
+#5239 := [quant-inst]: #5238
+#5293 := [mp #5239 #5245]: #5237
+#6292 := [unit-resolution #5293 #6168]: #5211
+#6287 := [unit-resolution #6292 #6189]: #5208
+#6293 := [th-lemma #6242 #6287 #6249]: false
+#6295 := [lemma #6293]: #6294
+#4866 := [unit-resolution #6295 #4841 #6249 #6247 #6244 #6191 #4886]: #6288
+#4867 := (not #4883)
+#4868 := (or #4867 #6178)
+#4869 := [th-lemma]: #4868
+#4840 := [unit-resolution #4869 #4866 #4888]: false
+#4865 := [lemma #4840]: #4870
+#8795 := [unit-resolution #4865 #8794 #8793 #10042 #4885 #8786]: false
+#8798 := [lemma #8795]: #4197
+#3834 := (or #4361 #4200 #4355)
+#3835 := [def-axiom]: #3834
+#10367 := [unit-resolution #3835 #8798 #10246]: #4355
+#3856 := (or #4352 #184)
+#3842 := [def-axiom]: #3856
+#10380 := [unit-resolution #3842 #10367]: #184
+#10381 := [symm #10380]: #7113
+#13521 := (= #11444 #183)
+#13346 := (= #10482 uf_22)
+#10483 := (= uf_22 #10482)
+#13 := (uf_3 #12)
+#295 := (= #11 #13)
+#3982 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #3981) #295)
+#299 := (forall (vars (?x2 T2) (?x3 T2)) #295)
+#3985 := (iff #299 #3982)
+#3983 := (iff #295 #295)
+#3984 := [refl]: #3983
+#3986 := [quant-intro #3984]: #3985
+#1641 := (~ #299 #299)
+#1673 := (~ #295 #295)
+#1674 := [refl]: #1673
+#1639 := [nnf-pos #1674]: #1641
+#14 := (= #13 #11)
+#15 := (forall (vars (?x2 T2) (?x3 T2)) #14)
+#300 := (iff #15 #299)
+#297 := (iff #14 #295)
+#298 := [rewrite]: #297
+#301 := [quant-intro #298]: #300
+#294 := [asserted]: #15
+#304 := [mp #294 #301]: #299
+#1675 := [mp~ #304 #1639]: #299
+#3987 := [mp #1675 #3986]: #3982
+#7756 := (not #3982)
+#10489 := (or #7756 #10483)
+#10490 := [quant-inst]: #10489
+#13345 := [unit-resolution #10490 #3987]: #10483
+#13347 := [symm #13345]: #13346
+#13522 := [monotonicity #13347]: #13521
+#13524 := [trans #13522 #10381]: #13523
+#27228 := [monotonicity #13524 #27216]: #27227
+#27230 := [symm #27228]: #27229
+#27232 := [monotonicity #27230]: #27231
+#27226 := [hypothesis]: #16801
+#27233 := [mp #27226 #27232]: #27109
+#27075 := (= #10482 #19843)
+#25893 := (up_6 uf_15 #19843)
+#27081 := (or #25893 #27075)
+#27086 := (iff #27073 #27081)
 #30 := (:var 1 T5)
 #20 := (:var 2 T2)
 #29 := (:var 3 T4)
 #31 := (uf_7 #29 #20 #30)
 #32 := (up_6 #31 #11)
-#3845 := (pattern #32)
+#4001 := (pattern #32)
 #35 := (up_6 #29 #11)
 #34 := (= #30 uf_8)
 #24 := (= #11 #20)
 #36 := (ite #24 #34 #35)
 #37 := (iff #32 #36)
-#3846 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #3845) #37)
+#4002 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #4001) #37)
 #38 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #37)
-#3849 := (iff #38 #3846)
-#3847 := (iff #37 #37)
-#3848 := [refl]: #3847
-#3850 := [quant-intro #3848]: #3849
-#1505 := (~ #38 #38)
-#1541 := (~ #37 #37)
-#1542 := [refl]: #1541
-#1506 := [nnf-pos #1542]: #1505
-#309 := [asserted]: #38
-#1543 := [mp~ #309 #1506]: #38
-#3851 := [mp #1543 #3850]: #3846
-#6010 := (not #3846)
-#30184 := (or #6010 #14006)
-#5970 := (= uf_8 uf_8)
-#13995 := (ite #13994 #5970 #11031)
-#13997 := (iff #13996 #13995)
-#30185 := (or #6010 #13997)
-#30191 := (iff #30185 #30184)
-#30193 := (iff #30184 #30184)
-#30194 := [rewrite]: #30193
-#14007 := (iff #13997 #14006)
-#14004 := (iff #13995 #14001)
-#1 := true
-#13998 := (ite #13994 true #11031)
-#14002 := (iff #13998 #14001)
-#14003 := [rewrite]: #14002
-#13999 := (iff #13995 #13998)
-#5975 := (iff #5970 true)
-#5976 := [rewrite]: #5975
-#14000 := [monotonicity #5976]: #13999
-#14005 := [trans #14000 #14003]: #14004
-#14008 := [monotonicity #14005]: #14007
-#30192 := [monotonicity #14008]: #30191
-#30195 := [trans #30192 #30194]: #30191
-#30190 := [quant-inst]: #30185
-#30196 := [mp #30190 #30195]: #30184
-#30517 := [unit-resolution #30196 #3851]: #14006
-#30208 := (not #13996)
-#9424 := (up_6 uf_23 ?x75!20)
-#9640 := (not #9424)
-#30526 := (iff #9640 #30208)
-#30524 := (iff #9424 #13996)
-#30522 := (iff #13996 #9424)
-#8591 := (= #8048 uf_23)
-#191 := (uf_7 uf_15 uf_22 uf_8)
-#7418 := (= #191 uf_23)
-#192 := (= uf_23 #191)
-#4136 := (or #3126 #4133)
-#4139 := (not #4136)
-#4104 := (pattern #199 #226)
-#1336 := (>= #1338 0::int)
-#224 := (up_6 uf_23 #10)
-#3083 := (not #224)
-#3098 := (or #216 #3083 #1336)
-#4105 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4104) #3098)
-#4110 := (not #4105)
-#4142 := (or #4110 #4139)
-#4145 := (not #4142)
-decl ?x68!16 :: T2
-#1976 := ?x68!16
-#1980 := (uf_24 ?x68!16)
-#2517 := (* -1::int #1980)
-decl ?x67!17 :: T2
-#1977 := ?x67!17
-#1978 := (uf_24 ?x67!17)
-#2518 := (+ #1978 #2517)
-#2519 := (<= #2518 0::int)
-#1984 := (up_6 uf_23 ?x68!16)
-#1983 := (up_6 uf_23 ?x67!17)
-#3060 := (not #1983)
-#3075 := (or #3060 #1984 #2519)
-#3080 := (not #3075)
-#4148 := (or #3080 #4145)
-#4151 := (not #4148)
-#1327 := (>= #199 0::int)
-#4096 := (forall (vars (?x65 T2)) (:pat #4062) #1327)
-#4101 := (not #4096)
-#4154 := (or #4101 #4151)
-#4157 := (not #4154)
-decl ?x65!15 :: T2
-#1961 := ?x65!15
-#1962 := (uf_24 ?x65!15)
-#1963 := (>= #1962 0::int)
-#1964 := (not #1963)
-#4160 := (or #1964 #4157)
-#4163 := (not #4160)
-#219 := (uf_24 uf_11)
-#220 := (= #219 0::int)
-#1324 := (not #220)
-#4166 := (or #1324 #4163)
-#4169 := (not #4166)
-#4172 := (or #1324 #4169)
-#4175 := (not #4172)
-#110 := (uf_4 uf_14 #11)
-#3940 := (pattern #110)
-#658 := (= #110 #199)
-#700 := (or #223 #658)
-#4088 := (forall (vars (?x63 T2)) (:pat #4087 #3940 #4062) #700)
-#4093 := (not #4088)
-#4178 := (or #4093 #4175)
-#4181 := (not #4178)
-decl ?x63!14 :: T2
-#1937 := ?x63!14
-#1939 := (uf_4 uf_14 ?x63!14)
-#1938 := (uf_24 ?x63!14)
-#2494 := (= #1938 #1939)
-#1941 := (up_6 uf_23 ?x63!14)
-#1942 := (not #1941)
-#2497 := (or #1942 #2494)
-#2500 := (not #2497)
-#4184 := (or #2500 #4181)
-#4187 := (not #4184)
-#1248 := (* -1::int #199)
-#1313 := (+ #110 #1248)
-#1312 := (>= #1313 0::int)
-#4079 := (forall (vars (?x61 T2)) (:pat #3940 #4062) #1312)
-#4084 := (not #4079)
-#4190 := (or #4084 #4187)
-#4193 := (not #4190)
-decl ?x61!13 :: T2
-#1919 := ?x61!13
-#1922 := (uf_4 uf_14 ?x61!13)
-#2484 := (* -1::int #1922)
-#1920 := (uf_24 ?x61!13)
-#2485 := (+ #1920 #2484)
-#2486 := (<= #2485 0::int)
-#2491 := (not #2486)
-#4196 := (or #2491 #4193)
-#4199 := (not #4196)
-#193 := (uf_1 uf_22 #11)
-#4061 := (pattern #193)
-#194 := (uf_10 #193)
-#1229 := (* -1::int #194)
-#1235 := (* -1::int #185)
-#1236 := (+ #1235 #1229)
-#1237 := (+ #110 #1236)
-#1238 := (<= #1237 0::int)
-#1230 := (+ uf_9 #1229)
-#1231 := (<= #1230 0::int)
-#3032 := (or #1231 #1238)
-#3033 := (not #3032)
-#3054 := (or #658 #3033)
-#4071 := (forall (vars (?x60 T2)) (:pat #3940 #4062 #4061) #3054)
-#4076 := (not #4071)
-#1249 := (+ #194 #1248)
-#1250 := (+ #185 #1249)
-#1251 := (= #1250 0::int)
-#3046 := (or #1231 #1238 #1251)
-#4063 := (forall (vars (?x59 T2)) (:pat #4061 #3940 #4062) #3046)
-#4068 := (not #4063)
-decl ?x48!12 :: T2
-#1886 := ?x48!12
-#1892 := (up_6 uf_15 ?x48!12)
-#1887 := (uf_4 uf_14 ?x48!12)
-#1888 := (* -1::int #1887)
-#1889 := (+ uf_9 #1888)
-#1890 := (<= #1889 0::int)
-#1281 := (+ uf_9 #1235)
-#1282 := (<= #1281 0::int)
-#114 := (up_6 uf_15 #11)
-#3982 := (pattern #114)
-#1272 := (+ #110 #1235)
-#1271 := (>= #1272 0::int)
-#1275 := (or #114 #1271)
-#4053 := (forall (vars (?x58 T2)) (:pat #3982 #3940) #1275)
-#4058 := (not #4053)
-#3249 := (not #192)
-#183 := (up_6 uf_15 uf_22)
-#4202 := (or #183 #3249 #4058 #1282 #1890 #1892 #4068 #4076 #4199)
-#4205 := (not #4202)
-decl ?x53!11 :: T2
-#1827 := ?x53!11
-decl ?x54!10 :: T2
-#1826 := ?x54!10
-#1832 := (uf_1 ?x54!10 ?x53!11)
-#1833 := (uf_10 #1832)
-#1840 := (* -1::int #1833)
-decl uf_19 :: T3
-#150 := uf_19
-#1830 := (uf_4 uf_19 ?x54!10)
-#1836 := (* -1::int #1830)
-#2443 := (+ #1836 #1840)
-#1828 := (uf_4 uf_19 ?x53!11)
-#2444 := (+ #1828 #2443)
-#2445 := (<= #2444 0::int)
-#1841 := (+ uf_9 #1840)
-#1842 := (<= #1841 0::int)
-#1837 := (+ uf_9 #1836)
-#1838 := (<= #1837 0::int)
-#2992 := (or #1838 #1842 #2445)
-#2997 := (not #2992)
-#163 := (uf_4 uf_19 #10)
-#1165 := (* -1::int #163)
-#160 := (uf_4 uf_19 #11)
-#1166 := (+ #160 #1165)
-#1172 := (+ #91 #1166)
-#1195 := (>= #1172 0::int)
-#1152 := (* -1::int #160)
-#1153 := (+ uf_9 #1152)
-#1154 := (<= #1153 0::int)
-#2960 := (or #969 #1154 #1195)
-#4015 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #3916) #2960)
-#4020 := (not #4015)
-#175 := (uf_4 uf_19 uf_11)
-#176 := (= #175 0::int)
-#4023 := (or #176 #4020)
-#4026 := (not #4023)
-#4029 := (or #4026 #2997)
-#4032 := (not #4029)
-#3991 := (pattern #160)
-decl ?x50!9 :: (-> T2 T2)
-#1803 := (?x50!9 #11)
-#1806 := (uf_1 #1803 #11)
-#1807 := (uf_10 #1806)
-#2413 := (* -1::int #1807)
-#1804 := (uf_4 uf_19 #1803)
-#2396 := (* -1::int #1804)
-#2414 := (+ #2396 #2413)
-#2415 := (+ #160 #2414)
-#2416 := (= #2415 0::int)
-#2930 := (not #2416)
-#2397 := (+ #160 #2396)
-#2398 := (<= #2397 0::int)
-#2931 := (or #2398 #2930)
-#2932 := (not #2931)
-#65 := (= #11 uf_11)
-#2938 := (or #65 #1154 #2932)
-#4007 := (forall (vars (?x49 T2)) (:pat #3991) #2938)
-#4012 := (not #4007)
-#4035 := (or #4012 #4032)
-#4038 := (not #4035)
-decl ?x49!8 :: T2
-#1763 := ?x49!8
-#1767 := (uf_1 #11 ?x49!8)
-#3992 := (pattern #1767)
-#1768 := (uf_10 #1767)
-#1764 := (uf_4 uf_19 ?x49!8)
-#1765 := (* -1::int #1764)
-#2366 := (+ #1765 #1768)
-#2367 := (+ #160 #2366)
-#2370 := (= #2367 0::int)
-#2894 := (not #2370)
-#1766 := (+ #160 #1765)
-#1771 := (>= #1766 0::int)
-#2895 := (or #1771 #2894)
-#3993 := (forall (vars (?x50 T2)) (:pat #3991 #3992) #2895)
-#3998 := (not #3993)
-#2342 := (= uf_11 ?x49!8)
-#1775 := (+ uf_9 #1765)
-#1776 := (<= #1775 0::int)
-#4001 := (or #1776 #2342 #3998)
-#4004 := (not #4001)
-#4041 := (or #4004 #4038)
-#4044 := (not #4041)
-#1054 := (* -1::int #110)
-#1055 := (+ uf_9 #1054)
-#1056 := (<= #1055 0::int)
-#2880 := (or #114 #1056)
-#3983 := (forall (vars (?x48 T2)) (:pat #3982 #3940) #2880)
-#3988 := (not #3983)
-#533 := (= uf_14 uf_19)
-#3023 := (not #533)
-decl uf_16 :: T4
-#145 := uf_16
-#530 := (= uf_15 uf_16)
-#3022 := (not #530)
-decl uf_21 :: T3
-#153 := uf_21
-decl uf_20 :: T3
-#152 := uf_20
-#154 := (= uf_20 uf_21)
-#3021 := (not #154)
-decl uf_18 :: T2
-#148 := uf_18
-decl uf_17 :: T2
-#147 := uf_17
-#149 := (= uf_17 uf_18)
-#3020 := (not #149)
-#4047 := (or #3020 #3021 #3022 #3023 #3988 #4044)
-#4050 := (not #4047)
-#4208 := (or #4050 #4205)
-#4211 := (not #4208)
-#1708 := (?x47!7 #11)
-#1709 := (uf_4 uf_14 #1708)
-#2309 := (* -1::int #1709)
-#2324 := (+ #110 #2309)
-#2325 := (<= #2324 0::int)
-#1713 := (uf_1 #1708 #11)
-#1714 := (uf_10 #1713)
-#2310 := (* -1::int #1714)
-#2311 := (+ #2309 #2310)
-#2312 := (+ #110 #2311)
-#2313 := (= #2312 0::int)
-#2864 := (not #2313)
-#1717 := (up_6 uf_15 #1708)
-#2863 := (not #1717)
-#2865 := (or #2863 #2864 #2325)
-#2866 := (not #2865)
-#2872 := (or #65 #1056 #2866)
-#3974 := (forall (vars (?x46 T2)) (:pat #3940) #2872)
-#3979 := (not #3974)
-decl uf_12 :: (-> T2 int)
-#66 := (uf_12 #11)
-#3886 := (pattern #66)
-decl ?x38!6 :: (-> T2 T2)
-#1680 := (?x38!6 #11)
-#1684 := (uf_12 #1680)
-#2268 := (* -1::int #1684)
-#1681 := (uf_1 #1680 #11)
-#1682 := (uf_10 #1681)
-#2285 := (* -1::int #1682)
-#2286 := (+ #2285 #2268)
-#2287 := (+ #66 #2286)
-#2288 := (= #2287 0::int)
-#2836 := (not #2288)
-#2269 := (+ #66 #2268)
-#2270 := (<= #2269 0::int)
-decl up_13 :: (-> T2 bool)
-#1690 := (up_13 #1680)
-#2835 := (not #1690)
-#2837 := (or #2835 #2270 #2836)
-#2838 := (not #2837)
-#993 := (* -1::int #66)
-#994 := (+ uf_9 #993)
-#995 := (<= #994 0::int)
-#2844 := (or #65 #995 #2838)
-#3966 := (forall (vars (?x37 T2)) (:pat #3886) #2844)
-#3971 := (not #3966)
-#116 := (up_6 uf_15 #10)
-#3957 := (pattern #114 #116)
-#118 := (uf_4 uf_14 #10)
-#1045 := (* -1::int #118)
-#1046 := (+ #110 #1045)
-#1069 := (>= #1046 0::int)
-#2801 := (not #116)
-#2816 := (or #114 #2801 #1069)
-#3958 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #3957) #2816)
-#3963 := (not #3958)
-#1047 := (+ #91 #1046)
-#1043 := (>= #1047 0::int)
-#115 := (not #114)
-#2793 := (or #115 #969 #1043)
-#3949 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #3916) #2793)
-#3954 := (not #3949)
-#1101 := (>= #110 0::int)
-#3941 := (forall (vars (?x41 T2)) (:pat #3940) #1101)
-#3946 := (not #3941)
-#108 := (uf_4 uf_14 uf_11)
-#109 := (= #108 0::int)
-#3266 := (not #109)
-#4214 := (or #3266 #3946 #3954 #3963 #3971 #3979 #4211)
-#4217 := (not #4214)
-decl ?x37!5 :: T2
-#1636 := ?x37!5
-#1637 := (uf_1 #11 ?x37!5)
-#3925 := (pattern #1637)
-#74 := (up_13 #11)
-#3879 := (pattern #74)
-#1639 := (uf_12 ?x37!5)
-#1640 := (* -1::int #1639)
-#1638 := (uf_10 #1637)
-#2238 := (+ #1638 #1640)
-#2239 := (+ #66 #2238)
-#2242 := (= #2239 0::int)
-#2754 := (not #2242)
-#1644 := (+ #66 #1640)
-#1645 := (>= #1644 0::int)
-#75 := (not #74)
-#2755 := (or #75 #1645 #2754)
-#3926 := (forall (vars (?x38 T2)) (:pat #3879 #3886 #3925) #2755)
-#3931 := (not #3926)
-#2214 := (= uf_11 ?x37!5)
-#1649 := (+ uf_9 #1640)
-#1650 := (<= #1649 0::int)
-#3934 := (or #1650 #2214 #3931)
-#3937 := (not #3934)
-#4220 := (or #3937 #4217)
-#4223 := (not #4220)
-#86 := (uf_12 #10)
-#955 := (* -1::int #86)
-#982 := (+ #955 #91)
-#983 := (+ #66 #982)
-#980 := (>= #983 0::int)
-#2746 := (or #75 #969 #980)
-#3917 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #3916) #2746)
-#3922 := (not #3917)
-#4226 := (or #3922 #4223)
-#4229 := (not #4226)
-decl ?x34!3 :: T2
-#1606 := ?x34!3
-#1613 := (uf_12 ?x34!3)
-decl ?x33!4 :: T2
-#1607 := ?x33!4
-#1610 := (uf_12 ?x33!4)
-#1611 := (* -1::int #1610)
-#2201 := (+ #1611 #1613)
-#1608 := (uf_1 ?x34!3 ?x33!4)
-#1609 := (uf_10 #1608)
-#2202 := (+ #1609 #2201)
-#2205 := (>= #2202 0::int)
-#1620 := (up_13 ?x34!3)
-#2709 := (not #1620)
-#1616 := (* -1::int #1609)
-#1617 := (+ uf_9 #1616)
-#1618 := (<= #1617 0::int)
-#2724 := (or #1618 #2709 #2205)
-#2729 := (not #2724)
-#4232 := (or #2729 #4229)
-#4235 := (not #4232)
-#84 := (up_13 #10)
-#3907 := (pattern #74 #84)
-#956 := (+ #66 #955)
-#954 := (>= #956 0::int)
-#1898 := (not #84)
-#2701 := (or #74 #1898 #954)
-#3908 := (forall (vars (?x29 T2) (?x30 T2)) (:pat #3907) #2701)
-#3913 := (not #3908)
-#4238 := (or #3913 #4235)
-#4241 := (not #4238)
-decl ?x30!1 :: T2
-#1581 := ?x30!1
-#1585 := (uf_12 ?x30!1)
-#2182 := (* -1::int #1585)
-decl ?x29!2 :: T2
-#1582 := ?x29!2
-#1583 := (uf_12 ?x29!2)
-#2183 := (+ #1583 #2182)
-#2184 := (<= #2183 0::int)
-#1589 := (up_13 ?x30!1)
-#1588 := (up_13 ?x29!2)
-#1597 := (not #1588)
-#1948 := (or #1597 #1589 #2184)
-#2022 := (not #1948)
-#4244 := (or #2022 #4241)
-#4247 := (not #4244)
-#945 := (>= #66 0::int)
-#3899 := (forall (vars (?x27 T2)) (:pat #3886) #945)
-#3904 := (not #3899)
-#4250 := (or #3904 #4247)
-#4253 := (not #4250)
-decl ?x27!0 :: T2
-#1566 := ?x27!0
-#1567 := (uf_12 ?x27!0)
-#1568 := (>= #1567 0::int)
-#1569 := (not #1568)
-#4256 := (or #1569 #4253)
-#4259 := (not #4256)
-#80 := (uf_12 uf_11)
-#81 := (= #80 0::int)
-#940 := (not #81)
-#4262 := (or #940 #4259)
-#4265 := (not #4262)
-#4992 := [hypothesis]: #940
-#67 := (= #66 0::int)
-#70 := (not #65)
-#921 := (or #70 #67)
-#3893 := (forall (vars (?x24 T2)) (:pat #3886) #921)
-#924 := (forall (vars (?x24 T2)) #921)
-#3896 := (iff #924 #3893)
-#3894 := (iff #921 #921)
-#3895 := [refl]: #3894
-#3897 := [quant-intro #3895]: #3896
-#1521 := (~ #924 #924)
-#1560 := (~ #921 #921)
-#1561 := [refl]: #1560
-#1522 := [nnf-pos #1561]: #1521
-#397 := (= uf_9 #66)
-#403 := (or #65 #397)
-#408 := (forall (vars (?x25 T2)) #403)
-#76 := (forall (vars (?x26 T2)) #75)
-#930 := (and #76 #408 #924)
-#1385 := (= #1363 0::int)
-#1388 := (not #1336)
-#1397 := (and #216 #1388 #1385)
-#1402 := (exists (vars (?x76 T2)) #1397)
-#1374 := (+ uf_9 #1248)
-#1375 := (<= #1374 0::int)
-#1376 := (not #1375)
-#1379 := (and #70 #1376)
-#1382 := (not #1379)
-#1405 := (or #1382 #1402)
-#1408 := (forall (vars (?x75 T2)) #1405)
-#970 := (not #969)
-#1353 := (and #216 #970)
-#1358 := (not #1353)
-#1365 := (or #1358 #1361)
-#1368 := (forall (vars (?x71 T2) (?x72 T2)) #1365)
-#1371 := (not #1368)
-#1411 := (or #1371 #1408)
-#1414 := (and #1368 #1411)
-#225 := (and #223 #224)
-#711 := (not #225)
-#1341 := (or #711 #1336)
-#1344 := (forall (vars (?x67 T2) (?x68 T2)) #1341)
-#1347 := (not #1344)
-#1417 := (or #1347 #1414)
-#1420 := (and #1344 #1417)
-#1330 := (forall (vars (?x65 T2)) #1327)
-#1333 := (not #1330)
-#1423 := (or #1333 #1420)
-#1426 := (and #1330 #1423)
-#1429 := (or #1324 #1426)
-#1432 := (and #220 #1429)
-#705 := (forall (vars (?x63 T2)) #700)
-#814 := (not #705)
-#1435 := (or #814 #1432)
-#1438 := (and #705 #1435)
-#1316 := (forall (vars (?x61 T2)) #1312)
-#1319 := (not #1316)
-#1441 := (or #1319 #1438)
-#1444 := (and #1316 #1441)
-#1283 := (not #1282)
-#1278 := (forall (vars (?x58 T2)) #1275)
-#1239 := (not #1238)
-#1232 := (not #1231)
-#1242 := (and #1232 #1239)
-#1263 := (or #658 #1242)
-#1268 := (forall (vars (?x60 T2)) #1263)
-#1245 := (not #1242)
-#1254 := (or #1245 #1251)
-#1257 := (forall (vars (?x59 T2)) #1254)
-#1057 := (not #1056)
-#1132 := (and #115 #1057)
-#1135 := (exists (vars (?x48 T2)) #1132)
-#184 := (not #183)
-#1304 := (and #184 #192 #1135 #1257 #1268 #1278 #1283)
-#1309 := (not #1304)
-#1447 := (or #1309 #1444)
-#1155 := (not #1154)
-#1189 := (and #970 #1155)
-#1192 := (not #1189)
-#1198 := (or #1192 #1195)
-#1201 := (forall (vars (?x53 T2) (?x54 T2)) #1198)
-#1204 := (not #1201)
-#1212 := (or #176 #1204)
-#1217 := (and #1201 #1212)
-#1170 := (= #1172 0::int)
-#1164 := (>= #1166 0::int)
-#1167 := (not #1164)
-#1174 := (and #1167 #1170)
-#1177 := (exists (vars (?x50 T2)) #1174)
-#1158 := (and #70 #1155)
-#1161 := (not #1158)
-#1180 := (or #1161 #1177)
-#1183 := (forall (vars (?x49 T2)) #1180)
-#1186 := (not #1183)
-#1220 := (or #1186 #1217)
-#1223 := (and #1183 #1220)
-#1138 := (not #1135)
-#1144 := (and #149 #154 #530 #533 #1138)
-#1149 := (not #1144)
-#1226 := (or #1149 #1223)
-#1450 := (and #1226 #1447)
-#1104 := (forall (vars (?x41 T2)) #1101)
-#117 := (and #115 #116)
-#456 := (not #117)
-#1095 := (or #456 #1069)
-#1098 := (forall (vars (?x42 T2) (?x43 T2)) #1095)
-#1070 := (not #1069)
-#1066 := (= #1047 0::int)
-#1079 := (and #114 #1066 #1070)
-#1084 := (exists (vars (?x47 T2)) #1079)
-#1060 := (and #70 #1057)
-#1063 := (not #1060)
-#1087 := (or #1063 #1084)
-#1090 := (forall (vars (?x46 T2)) #1087)
-#1034 := (and #114 #970)
-#1039 := (not #1034)
-#1048 := (or #1039 #1043)
-#1051 := (forall (vars (?x44 T2) (?x45 T2)) #1048)
-#1005 := (= #983 0::int)
-#1008 := (not #954)
-#1017 := (and #74 #1008 #1005)
-#1022 := (exists (vars (?x38 T2)) #1017)
-#996 := (not #995)
-#999 := (and #70 #996)
-#1002 := (not #999)
-#1025 := (or #1002 #1022)
-#1028 := (forall (vars (?x37 T2)) #1025)
-#1124 := (and #109 #1028 #1051 #1090 #1098 #1104)
-#1129 := (not #1124)
-#1453 := (or #1129 #1450)
-#1456 := (and #1028 #1453)
-#973 := (and #74 #970)
-#976 := (not #973)
-#984 := (or #976 #980)
-#987 := (forall (vars (?x33 T2) (?x34 T2)) #984)
-#990 := (not #987)
-#1459 := (or #990 #1456)
-#1462 := (and #987 #1459)
-#85 := (and #75 #84)
-#432 := (not #85)
-#958 := (or #432 #954)
-#961 := (forall (vars (?x29 T2) (?x30 T2)) #958)
-#964 := (not #961)
-#1465 := (or #964 #1462)
-#1468 := (and #961 #1465)
-#946 := (forall (vars (?x27 T2)) #945)
-#949 := (not #946)
-#1471 := (or #949 #1468)
-#1474 := (and #946 #1471)
-#1477 := (or #940 #1474)
-#1480 := (and #81 #1477)
-#935 := (not #930)
-#1483 := (or #935 #1480)
-#1486 := (not #1483)
-#231 := (+ #199 #91)
-#238 := (= #226 #231)
-#239 := (and #216 #238)
-#237 := (< #199 #226)
-#240 := (and #237 #239)
-#241 := (exists (vars (?x76 T2)) #240)
-#235 := (< #199 uf_9)
-#236 := (and #70 #235)
-#242 := (implies #236 #241)
-#243 := (forall (vars (?x75 T2)) #242)
-#232 := (<= #226 #231)
-#92 := (< #91 uf_9)
-#230 := (and #216 #92)
-#233 := (implies #230 #232)
-#234 := (forall (vars (?x71 T2) (?x72 T2)) #233)
-#244 := (implies #234 #243)
-#245 := (and #234 #244)
-#227 := (<= #226 #199)
-#228 := (implies #225 #227)
-#229 := (forall (vars (?x67 T2) (?x68 T2)) #228)
-#246 := (implies #229 #245)
-#247 := (and #229 #246)
-#221 := (<= 0::int #199)
-#222 := (forall (vars (?x65 T2)) #221)
-#248 := (implies #222 #247)
-#249 := (and #222 #248)
-#250 := (implies #220 #249)
-#251 := (and #220 #250)
-#204 := (= #199 #110)
-#217 := (implies #216 #204)
-#218 := (forall (vars (?x63 T2)) #217)
-#252 := (implies #218 #251)
-#253 := (and #218 #252)
-#214 := (<= #199 #110)
-#215 := (forall (vars (?x61 T2)) #214)
-#254 := (implies #215 #253)
-#255 := (and #215 #254)
-#196 := (+ #185 #194)
-#197 := (< #196 #110)
-#195 := (< #194 uf_9)
-#198 := (and #195 #197)
-#203 := (not #198)
-#205 := (implies #203 #204)
-#206 := (forall (vars (?x60 T2)) #205)
-#200 := (= #199 #196)
-#201 := (implies #198 #200)
-#202 := (forall (vars (?x59 T2)) #201)
-#207 := (and #202 #206)
-#208 := (and #192 #207)
-#187 := (<= #185 #110)
-#188 := (implies #115 #187)
-#189 := (forall (vars (?x58 T2)) #188)
-#209 := (and #189 #208)
-#186 := (< #185 uf_9)
-#210 := (and #186 #209)
-#211 := (and #184 #210)
-#127 := (< #110 uf_9)
-#142 := (and #115 #127)
-#143 := (exists (vars (?x48 T2)) #142)
-#212 := (and #143 #211)
-#213 := (and true #212)
-#256 := (implies #213 #255)
-#165 := (+ #160 #91)
-#172 := (<= #163 #165)
-#161 := (< #160 uf_9)
-#171 := (and #161 #92)
-#173 := (implies #171 #172)
-#174 := (forall (vars (?x53 T2) (?x54 T2)) #173)
-#177 := (implies #174 #176)
-#178 := (and #174 #177)
-#166 := (= #163 #165)
-#164 := (< #160 #163)
-#167 := (and #164 #166)
-#168 := (exists (vars (?x50 T2)) #167)
-#162 := (and #70 #161)
-#169 := (implies #162 #168)
-#170 := (forall (vars (?x49 T2)) #169)
-#179 := (implies #170 #178)
-#180 := (and #170 #179)
-#151 := (= uf_19 uf_14)
-#155 := (and #151 #154)
-#156 := (and #149 #155)
-#146 := (= uf_16 uf_15)
-#157 := (and #146 #156)
-#144 := (not #143)
-#158 := (and #144 #157)
-#159 := (and true #158)
-#181 := (implies #159 #180)
-#257 := (and #181 #256)
-#123 := (+ #110 #91)
-#130 := (= #118 #123)
-#131 := (and #114 #130)
-#129 := (< #110 #118)
-#132 := (and #129 #131)
-#133 := (exists (vars (?x47 T2)) #132)
-#128 := (and #70 #127)
-#134 := (implies #128 #133)
-#135 := (forall (vars (?x46 T2)) #134)
-#124 := (<= #118 #123)
-#122 := (and #114 #92)
-#125 := (implies #122 #124)
-#126 := (forall (vars (?x44 T2) (?x45 T2)) #125)
-#136 := (and #126 #135)
-#119 := (<= #118 #110)
-#120 := (implies #117 #119)
-#121 := (forall (vars (?x42 T2) (?x43 T2)) #120)
-#137 := (and #121 #136)
-#111 := (<= 0::int #110)
-#112 := (forall (vars (?x41 T2)) #111)
-#138 := (and #112 #137)
-#139 := (and #109 #138)
-#140 := (and true #139)
-#94 := (+ #66 #91)
-#101 := (= #86 #94)
-#102 := (and #74 #101)
-#100 := (< #66 #86)
-#103 := (and #100 #102)
-#104 := (exists (vars (?x38 T2)) #103)
-#98 := (< #66 uf_9)
-#99 := (and #70 #98)
-#105 := (implies #99 #104)
-#106 := (forall (vars (?x37 T2)) #105)
-#141 := (and #106 #140)
-#258 := (implies #141 #257)
-#259 := (and #106 #258)
-#95 := (<= #86 #94)
-#93 := (and #74 #92)
-#96 := (implies #93 #95)
-#97 := (forall (vars (?x33 T2) (?x34 T2)) #96)
-#260 := (implies #97 #259)
-#261 := (and #97 #260)
-#87 := (<= #86 #66)
-#88 := (implies #85 #87)
-#89 := (forall (vars (?x29 T2) (?x30 T2)) #88)
-#262 := (implies #89 #261)
-#263 := (and #89 #262)
-#82 := (<= 0::int #66)
-#83 := (forall (vars (?x27 T2)) #82)
-#264 := (implies #83 #263)
-#265 := (and #83 #264)
-#266 := (implies #81 #265)
-#267 := (and #81 #266)
-#71 := (= #66 uf_9)
-#72 := (implies #70 #71)
-#73 := (forall (vars (?x25 T2)) #72)
-#77 := (and #73 #76)
-#68 := (implies #65 #67)
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-#839 := (or #838 #832)
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-#560 := (+ #91 #160)
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-#934 := [trans #929 #932]: #933
-#937 := [monotonicity #934]: #936
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-#691 := (iff #213 #690)
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-#3273 := (or #3266 #3269 #3267 #3268 #3270 #3271 #3272)
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-#2162 := (or #940 #2158)
-#2688 := (iff #2162 #2687)
-#2685 := (iff #2158 #2684)
-#2682 := (iff #2154 #2681)
-#2679 := (iff #2150 #2678)
-#2676 := (iff #2146 #2675)
-#2673 := (iff #2142 #2672)
-#2670 := (iff #2138 #2669)
-#2667 := (iff #2134 #2666)
-#2664 := (iff #2130 #2663)
-#2661 := (iff #2126 #2658)
-#2652 := (and #109 #2299 #1051 #2339 #1098 #1104)
-#2655 := (and #2652 #2649)
-#2659 := (iff #2655 #2658)
-#2660 := [rewrite]: #2659
-#2656 := (iff #2126 #2655)
-#2650 := (iff #2122 #2649)
-#2647 := (iff #2118 #2644)
-#2641 := (and #1913 #2638)
-#2645 := (iff #2641 #2644)
-#2646 := [rewrite]: #2645
-#2642 := (iff #2118 #2641)
-#2639 := (iff #2114 #2638)
-#2636 := (iff #2110 #2635)
-#2633 := (iff #2106 #2632)
-#2630 := (iff #2102 #2629)
-#2627 := (iff #2098 #2626)
-#2624 := (iff #2094 #2623)
-#2621 := (iff #2090 #2620)
-#2618 := (iff #2086 #2617)
-#2615 := (iff #2082 #2614)
-#2612 := (iff #2078 #2611)
-#2609 := (iff #2074 #2608)
-#2606 := (iff #2070 #2603)
-#2566 := (and #2045 #2560)
-#2597 := (and #2566 #2594)
-#2600 := (and #1368 #2597)
-#2604 := (iff #2600 #2603)
-#2605 := [rewrite]: #2604
-#2601 := (iff #2070 #2600)
-#2598 := (iff #2065 #2597)
-#2595 := (iff #2061 #2594)
-#2592 := (iff #2058 #2591)
-#2589 := (iff #2041 #2588)
-#2586 := (iff #2038 #2585)
-#2583 := (= #2037 #2582)
-#2584 := [rewrite]: #2583
-#2587 := [monotonicity #2584]: #2586
-#2590 := [monotonicity #2587]: #2589
-#2593 := [monotonicity #2590]: #2592
-#2596 := [quant-intro #2593]: #2595
-#2579 := (iff #2055 #2566)
-#2571 := (not #2566)
-#2574 := (not #2571)
-#2577 := (iff #2574 #2566)
-#2578 := [rewrite]: #2577
-#2575 := (iff #2055 #2574)
-#2572 := (iff #2049 #2571)
-#2569 := (iff #2048 #2566)
-#2563 := (and #2560 #2045)
-#2567 := (iff #2563 #2566)
-#2568 := [rewrite]: #2567
-#2564 := (iff #2048 #2563)
-#2561 := (iff #2047 #2560)
-#2558 := (iff #2046 #2557)
-#2559 := [rewrite]: #2558
-#2562 := [monotonicity #2559]: #2561
-#2565 := [monotonicity #2562]: #2564
-#2570 := [trans #2565 #2568]: #2569
-#2573 := [monotonicity #2570]: #2572
-#2576 := [monotonicity #2573]: #2575
-#2580 := [trans #2576 #2578]: #2579
-#2599 := [monotonicity #2580 #2596]: #2598
-#2602 := [monotonicity #2599]: #2601
-#2607 := [trans #2602 #2605]: #2606
-#2555 := (iff #2019 #2554)
-#2552 := (iff #2018 #2551)
-#2549 := (iff #2010 #2546)
-#2536 := (+ #2005 #2008)
-#2537 := (+ #2004 #2536)
-#2540 := (>= #2537 0::int)
-#2547 := (iff #2540 #2546)
-#2548 := [rewrite]: #2547
-#2541 := (iff #2010 #2540)
-#2538 := (= #2009 #2537)
-#2539 := [rewrite]: #2538
-#2542 := [monotonicity #2539]: #2541
-#2550 := [trans #2542 #2548]: #2549
-#2534 := (iff #2017 #2533)
-#2531 := (iff #2016 #2530)
-#2532 := [rewrite]: #2531
-#2535 := [monotonicity #2532]: #2534
-#2553 := [monotonicity #2535 #2550]: #2552
-#2556 := [monotonicity #2553]: #2555
-#2610 := [monotonicity #2556 #2607]: #2609
-#2613 := [monotonicity #2610]: #2612
-#2528 := (iff #1989 #2527)
-#2525 := (iff #1988 #2524)
-#2522 := (iff #1982 #2519)
-#2511 := (+ #1979 #1980)
-#2514 := (>= #2511 0::int)
-#2520 := (iff #2514 #2519)
-#2521 := [rewrite]: #2520
-#2515 := (iff #1982 #2514)
-#2512 := (= #1981 #2511)
-#2513 := [rewrite]: #2512
-#2516 := [monotonicity #2513]: #2515
-#2523 := [trans #2516 #2521]: #2522
-#2509 := (iff #1987 #2508)
-#2506 := (iff #1986 #2505)
-#2507 := [rewrite]: #2506
-#2510 := [monotonicity #2507]: #2509
-#2526 := [monotonicity #2510 #2523]: #2525
-#2529 := [monotonicity #2526]: #2528
-#2616 := [monotonicity #2529 #2613]: #2615
-#2619 := [monotonicity #2616]: #2618
-#2622 := [monotonicity #2619]: #2621
-#2503 := (iff #1958 #220)
-#2504 := [rewrite]: #2503
-#2625 := [monotonicity #2504 #2622]: #2624
-#2628 := [monotonicity #2625]: #2627
-#2631 := [monotonicity #2628]: #2630
-#2501 := (iff #1944 #2500)
-#2498 := (iff #1943 #2497)
-#2495 := (iff #1940 #2494)
-#2496 := [rewrite]: #2495
-#2499 := [monotonicity #2496]: #2498
-#2502 := [monotonicity #2499]: #2501
-#2634 := [monotonicity #2502 #2631]: #2633
-#2637 := [monotonicity #2634]: #2636
-#2492 := (iff #1925 #2491)
-#2489 := (iff #1924 #2486)
-#2478 := (+ #1921 #1922)
-#2481 := (>= #2478 0::int)
-#2487 := (iff #2481 #2486)
-#2488 := [rewrite]: #2487
-#2482 := (iff #1924 #2481)
-#2479 := (= #1923 #2478)
-#2480 := [rewrite]: #2479
-#2483 := [monotonicity #2480]: #2482
-#2490 := [trans #2483 #2488]: #2489
-#2493 := [monotonicity #2490]: #2492
-#2640 := [monotonicity #2493 #2637]: #2639
-#2643 := [monotonicity #2640]: #2642
-#2648 := [trans #2643 #2646]: #2647
-#2476 := (iff #1878 #2473)
-#2470 := (and #1757 #2467)
-#2474 := (iff #2470 #2473)
-#2475 := [rewrite]: #2474
-#2471 := (iff #1878 #2470)
-#2468 := (iff #1874 #2467)
-#2465 := (iff #1870 #2464)
-#2462 := (iff #1866 #2459)
-#2456 := (or #2453 #1862)
-#2460 := (iff #2456 #2459)
-#2461 := [rewrite]: #2460
-#2457 := (iff #1866 #2456)
-#2454 := (iff #1847 #2453)
-#2451 := (iff #1846 #2450)
-#2448 := (iff #1835 #2445)
-#2436 := (+ #1830 #1833)
-#2437 := (+ #1829 #2436)
-#2440 := (>= #2437 0::int)
-#2446 := (iff #2440 #2445)
-#2447 := [rewrite]: #2446
-#2441 := (iff #1835 #2440)
-#2438 := (= #1834 #2437)
-#2439 := [rewrite]: #2438
-#2442 := [monotonicity #2439]: #2441
-#2449 := [trans #2442 #2447]: #2448
-#2434 := (iff #1845 #2433)
-#2431 := (iff #1844 #2430)
-#2432 := [rewrite]: #2431
-#2435 := [monotonicity #2432]: #2434
-#2452 := [monotonicity #2435 #2449]: #2451
-#2455 := [monotonicity #2452]: #2454
-#2458 := [monotonicity #2455]: #2457
-#2463 := [trans #2458 #2461]: #2462
-#2428 := (iff #1820 #2427)
-#2425 := (iff #1817 #2424)
-#2422 := (iff #1812 #2421)
-#2419 := (iff #1809 #2416)
-#2406 := (+ #1804 #1807)
-#2407 := (+ #1152 #2406)
-#2410 := (= #2407 0::int)
-#2417 := (iff #2410 #2416)
-#2418 := [rewrite]: #2417
-#2411 := (iff #1809 #2410)
-#2408 := (= #1808 #2407)
-#2409 := [rewrite]: #2408
-#2412 := [monotonicity #2409]: #2411
-#2420 := [trans #2412 #2418]: #2419
-#2404 := (iff #1811 #2403)
-#2401 := (iff #1810 #2398)
-#2390 := (+ #1152 #1804)
-#2393 := (>= #2390 0::int)
-#2399 := (iff #2393 #2398)
-#2400 := [rewrite]: #2399
-#2394 := (iff #1810 #2393)
-#2391 := (= #1805 #2390)
-#2392 := [rewrite]: #2391
-#2395 := [monotonicity #2392]: #2394
-#2402 := [trans #2395 #2400]: #2401
-#2405 := [monotonicity #2402]: #2404
-#2423 := [monotonicity #2405 #2420]: #2422
-#2426 := [monotonicity #2423]: #2425
-#2429 := [quant-intro #2426]: #2428
-#2466 := [monotonicity #2429 #2463]: #2465
-#2388 := (iff #1796 #2385)
-#2351 := (and #1777 #2345)
-#2382 := (and #2351 #2379)
-#2386 := (iff #2382 #2385)
-#2387 := [rewrite]: #2386
-#2383 := (iff #1796 #2382)
-#2380 := (iff #1792 #2379)
-#2377 := (iff #1789 #2376)
-#2374 := (iff #1773 #2373)
-#2371 := (iff #1770 #2370)
-#2368 := (= #1769 #2367)
-#2369 := [rewrite]: #2368
-#2372 := [monotonicity #2369]: #2371
-#2375 := [monotonicity #2372]: #2374
-#2378 := [monotonicity #2375]: #2377
-#2381 := [quant-intro #2378]: #2380
-#2364 := (iff #1786 #2351)
-#2356 := (not #2351)
-#2359 := (not #2356)
-#2362 := (iff #2359 #2351)
-#2363 := [rewrite]: #2362
-#2360 := (iff #1786 #2359)
-#2357 := (iff #1781 #2356)
-#2354 := (iff #1780 #2351)
-#2348 := (and #2345 #1777)
-#2352 := (iff #2348 #2351)
-#2353 := [rewrite]: #2352
-#2349 := (iff #1780 #2348)
-#2346 := (iff #1779 #2345)
-#2343 := (iff #1778 #2342)
-#2344 := [rewrite]: #2343
-#2347 := [monotonicity #2344]: #2346
-#2350 := [monotonicity #2347]: #2349
-#2355 := [trans #2350 #2353]: #2354
-#2358 := [monotonicity #2355]: #2357
-#2361 := [monotonicity #2358]: #2360
-#2365 := [trans #2361 #2363]: #2364
-#2384 := [monotonicity #2365 #2381]: #2383
-#2389 := [trans #2384 #2387]: #2388
-#2469 := [monotonicity #2389 #2466]: #2468
-#2472 := [monotonicity #2469]: #2471
-#2477 := [trans #2472 #2475]: #2476
-#2651 := [monotonicity #2477 #2648]: #2650
-#2653 := (iff #1737 #2652)
-#2340 := (iff #1726 #2339)
-#2337 := (iff #1723 #2336)
-#2334 := (iff #1718 #2333)
-#2331 := (iff #1712 #2330)
-#2328 := (iff #1711 #2325)
-#2318 := (+ #1054 #1709)
-#2321 := (>= #2318 0::int)
-#2326 := (iff #2321 #2325)
-#2327 := [rewrite]: #2326
-#2322 := (iff #1711 #2321)
-#2319 := (= #1710 #2318)
-#2320 := [rewrite]: #2319
-#2323 := [monotonicity #2320]: #2322
-#2329 := [trans #2323 #2327]: #2328
-#2332 := [monotonicity #2329]: #2331
-#2316 := (iff #1716 #2313)
-#2302 := (+ #1709 #1714)
-#2303 := (+ #1054 #2302)
-#2306 := (= #2303 0::int)
-#2314 := (iff #2306 #2313)
-#2315 := [rewrite]: #2314
-#2307 := (iff #1716 #2306)
-#2304 := (= #1715 #2303)
-#2305 := [rewrite]: #2304
-#2308 := [monotonicity #2305]: #2307
-#2317 := [trans #2308 #2315]: #2316
-#2335 := [monotonicity #2317 #2332]: #2334
-#2338 := [monotonicity #2335]: #2337
-#2341 := [quant-intro #2338]: #2340
-#2300 := (iff #1699 #2299)
-#2297 := (iff #1696 #2296)
-#2294 := (iff #1691 #2293)
-#2291 := (iff #1686 #2288)
-#2278 := (+ #1682 #1684)
-#2279 := (+ #993 #2278)
-#2282 := (= #2279 0::int)
-#2289 := (iff #2282 #2288)
-#2290 := [rewrite]: #2289
-#2283 := (iff #1686 #2282)
-#2280 := (= #1685 #2279)
-#2281 := [rewrite]: #2280
-#2284 := [monotonicity #2281]: #2283
-#2292 := [trans #2284 #2290]: #2291
-#2276 := (iff #1689 #2275)
-#2273 := (iff #1688 #2270)
-#2262 := (+ #993 #1684)
-#2265 := (>= #2262 0::int)
-#2271 := (iff #2265 #2270)
-#2272 := [rewrite]: #2271
-#2266 := (iff #1688 #2265)
-#2263 := (= #1687 #2262)
-#2264 := [rewrite]: #2263
-#2267 := [monotonicity #2264]: #2266
-#2274 := [trans #2267 #2272]: #2273
-#2277 := [monotonicity #2274]: #2276
-#2295 := [monotonicity #2277 #2292]: #2294
-#2298 := [monotonicity #2295]: #2297
-#2301 := [quant-intro #2298]: #2300
-#2654 := [monotonicity #2301 #2341]: #2653
-#2657 := [monotonicity #2654 #2651]: #2656
-#2662 := [trans #2657 #2660]: #2661
-#2260 := (iff #1671 #2257)
-#2223 := (and #1651 #2217)
-#2254 := (and #2223 #2251)
-#2258 := (iff #2254 #2257)
-#2259 := [rewrite]: #2258
-#2255 := (iff #1671 #2254)
-#2252 := (iff #1667 #2251)
-#2249 := (iff #1664 #2248)
-#2246 := (iff #1647 #2245)
-#2243 := (iff #1643 #2242)
-#2240 := (= #1642 #2239)
-#2241 := [rewrite]: #2240
-#2244 := [monotonicity #2241]: #2243
-#2247 := [monotonicity #2244]: #2246
-#2250 := [monotonicity #2247]: #2249
-#2253 := [quant-intro #2250]: #2252
-#2236 := (iff #1661 #2223)
-#2228 := (not #2223)
-#2231 := (not #2228)
-#2234 := (iff #2231 #2223)
-#2235 := [rewrite]: #2234
-#2232 := (iff #1661 #2231)
-#2229 := (iff #1655 #2228)
-#2226 := (iff #1654 #2223)
-#2220 := (and #2217 #1651)
-#2224 := (iff #2220 #2223)
-#2225 := [rewrite]: #2224
-#2221 := (iff #1654 #2220)
-#2218 := (iff #1653 #2217)
-#2215 := (iff #1652 #2214)
-#2216 := [rewrite]: #2215
-#2219 := [monotonicity #2216]: #2218
-#2222 := [monotonicity #2219]: #2221
-#2227 := [trans #2222 #2225]: #2226
-#2230 := [monotonicity #2227]: #2229
-#2233 := [monotonicity #2230]: #2232
-#2237 := [trans #2233 #2235]: #2236
-#2256 := [monotonicity #2237 #2253]: #2255
-#2261 := [trans #2256 #2259]: #2260
-#2665 := [monotonicity #2261 #2662]: #2664
-#2668 := [monotonicity #2665]: #2667
-#2212 := (iff #1624 #2211)
-#2209 := (iff #1623 #2208)
-#2206 := (iff #1615 #2205)
-#2203 := (= #1614 #2202)
-#2204 := [rewrite]: #2203
-#2207 := [monotonicity #2204]: #2206
-#2199 := (iff #1622 #2198)
-#2196 := (iff #1621 #2195)
-#2197 := [rewrite]: #2196
-#2200 := [monotonicity #2197]: #2199
-#2210 := [monotonicity #2200 #2207]: #2209
-#2213 := [monotonicity #2210]: #2212
-#2671 := [monotonicity #2213 #2668]: #2670
-#2674 := [monotonicity #2671]: #2673
-#2193 := (iff #1594 #2192)
-#2190 := (iff #1593 #2189)
-#2187 := (iff #1587 #2184)
-#2176 := (+ #1584 #1585)
-#2179 := (>= #2176 0::int)
-#2185 := (iff #2179 #2184)
-#2186 := [rewrite]: #2185
-#2180 := (iff #1587 #2179)
-#2177 := (= #1586 #2176)
-#2178 := [rewrite]: #2177
-#2181 := [monotonicity #2178]: #2180
-#2188 := [trans #2181 #2186]: #2187
-#2174 := (iff #1592 #2173)
-#2171 := (iff #1591 #2170)
-#2172 := [rewrite]: #2171
-#2175 := [monotonicity #2172]: #2174
-#2191 := [monotonicity #2175 #2188]: #2190
-#2194 := [monotonicity #2191]: #2193
-#2677 := [monotonicity #2194 #2674]: #2676
-#2680 := [monotonicity #2677]: #2679
-#2683 := [monotonicity #2680]: #2682
-#2168 := (iff #1523 #81)
-#2169 := [rewrite]: #2168
-#2686 := [monotonicity #2169 #2683]: #2685
-#2689 := [monotonicity #2686]: #2688
-#1496 := (not #1480)
-#2163 := (~ #1496 #2162)
-#2159 := (not #1477)
-#2160 := (~ #2159 #2158)
-#2155 := (not #1474)
-#2156 := (~ #2155 #2154)
-#2151 := (not #1471)
-#2152 := (~ #2151 #2150)
-#2147 := (not #1468)
-#2148 := (~ #2147 #2146)
-#2143 := (not #1465)
-#2144 := (~ #2143 #2142)
-#2139 := (not #1462)
-#2140 := (~ #2139 #2138)
-#2135 := (not #1459)
-#2136 := (~ #2135 #2134)
-#2131 := (not #1456)
-#2132 := (~ #2131 #2130)
-#2127 := (not #1453)
-#2128 := (~ #2127 #2126)
-#2123 := (not #1450)
-#2124 := (~ #2123 #2122)
-#2119 := (not #1447)
-#2120 := (~ #2119 #2118)
-#2115 := (not #1444)
-#2116 := (~ #2115 #2114)
-#2111 := (not #1441)
-#2112 := (~ #2111 #2110)
-#2107 := (not #1438)
-#2108 := (~ #2107 #2106)
-#2103 := (not #1435)
-#2104 := (~ #2103 #2102)
-#2099 := (not #1432)
-#2100 := (~ #2099 #2098)
-#2095 := (not #1429)
-#2096 := (~ #2095 #2094)
-#2091 := (not #1426)
-#2092 := (~ #2091 #2090)
-#2087 := (not #1423)
-#2088 := (~ #2087 #2086)
-#2083 := (not #1420)
-#2084 := (~ #2083 #2082)
-#2079 := (not #1417)
-#2080 := (~ #2079 #2078)
-#2075 := (not #1414)
-#2076 := (~ #2075 #2074)
-#2071 := (not #1411)
-#2072 := (~ #2071 #2070)
-#2052 := (not #1408)
-#2068 := (~ #2052 #2065)
-#2042 := (exists (vars (?x76 T2)) #2041)
-#2050 := (or #2049 #2042)
-#2051 := (not #2050)
-#2066 := (~ #2051 #2065)
-#2062 := (not #2042)
-#2063 := (~ #2062 #2061)
-#2059 := (~ #2058 #2058)
-#2060 := [refl]: #2059
-#2064 := [nnf-neg #2060]: #2063
-#2056 := (~ #2055 #2055)
-#2057 := [refl]: #2056
-#2067 := [nnf-neg #2057 #2064]: #2066
-#2053 := (~ #2052 #2051)
-#2054 := [sk]: #2053
-#2069 := [trans #2054 #2067]: #2068
-#2028 := (not #1371)
-#2029 := (~ #2028 #1368)
-#2026 := (~ #1368 #1368)
-#2024 := (~ #1365 #1365)
-#2025 := [refl]: #2024
-#2027 := [nnf-pos #2025]: #2026
-#2030 := [nnf-neg #2027]: #2029
-#2073 := [nnf-neg #2030 #2069]: #2072
-#2020 := (~ #1371 #2019)
-#2021 := [sk]: #2020
-#2077 := [nnf-neg #2021 #2073]: #2076
-#1998 := (not #1347)
-#1999 := (~ #1998 #1344)
-#1996 := (~ #1344 #1344)
-#1994 := (~ #1341 #1341)
-#1995 := [refl]: #1994
-#1997 := [nnf-pos #1995]: #1996
-#2000 := [nnf-neg #1997]: #1999
-#2081 := [nnf-neg #2000 #2077]: #2080
-#1990 := (~ #1347 #1989)
-#1991 := [sk]: #1990
-#2085 := [nnf-neg #1991 #2081]: #2084
-#1973 := (not #1333)
-#1974 := (~ #1973 #1330)
-#1971 := (~ #1330 #1330)
-#1969 := (~ #1327 #1327)
-#1970 := [refl]: #1969
-#1972 := [nnf-pos #1970]: #1971
-#1975 := [nnf-neg #1972]: #1974
-#2089 := [nnf-neg #1975 #2085]: #2088
-#1965 := (~ #1333 #1964)
-#1966 := [sk]: #1965
-#2093 := [nnf-neg #1966 #2089]: #2092
-#1959 := (~ #1958 #1958)
-#1960 := [refl]: #1959
-#2097 := [nnf-neg #1960 #2093]: #2096
-#1956 := (~ #1324 #1324)
-#1957 := [refl]: #1956
-#2101 := [nnf-neg #1957 #2097]: #2100
-#1953 := (not #814)
-#1954 := (~ #1953 #705)
-#1951 := (~ #705 #705)
-#1949 := (~ #700 #700)
-#1950 := [refl]: #1949
-#1952 := [nnf-pos #1950]: #1951
-#1955 := [nnf-neg #1952]: #1954
-#2105 := [nnf-neg #1955 #2101]: #2104
-#1945 := (~ #814 #1944)
-#1946 := [sk]: #1945
-#2109 := [nnf-neg #1946 #2105]: #2108
-#1934 := (not #1319)
-#1935 := (~ #1934 #1316)
-#1932 := (~ #1316 #1316)
-#1930 := (~ #1312 #1312)
-#1931 := [refl]: #1930
-#1933 := [nnf-pos #1931]: #1932
-#1936 := [nnf-neg #1933]: #1935
-#2113 := [nnf-neg #1936 #2109]: #2112
-#1926 := (~ #1319 #1925)
-#1927 := [sk]: #1926
-#2117 := [nnf-neg #1927 #2113]: #2116
-#1916 := (not #1309)
-#1917 := (~ #1916 #1913)
-#1914 := (~ #1304 #1913)
-#1911 := (~ #1283 #1283)
-#1912 := [refl]: #1911
-#1909 := (~ #1278 #1278)
-#1907 := (~ #1275 #1275)
-#1908 := [refl]: #1907
-#1910 := [nnf-pos #1908]: #1909
-#1905 := (~ #1268 #1268)
-#1903 := (~ #1263 #1263)
-#1904 := [refl]: #1903
-#1906 := [nnf-pos #1904]: #1905
-#1901 := (~ #1257 #1257)
-#1899 := (~ #1254 #1254)
-#1900 := [refl]: #1899
-#1902 := [nnf-pos #1900]: #1901
-#1895 := (~ #1135 #1894)
-#1896 := [sk]: #1895
-#1884 := (~ #192 #192)
-#1885 := [refl]: #1884
-#1882 := (~ #184 #184)
-#1883 := [refl]: #1882
-#1915 := [monotonicity #1883 #1885 #1896 #1902 #1906 #1910 #1912]: #1914
-#1918 := [nnf-neg #1915]: #1917
-#2121 := [nnf-neg #1918 #2117]: #2120
-#1879 := (not #1226)
-#1880 := (~ #1879 #1878)
-#1875 := (not #1223)
-#1876 := (~ #1875 #1874)
-#1871 := (not #1220)
-#1872 := (~ #1871 #1870)
-#1867 := (not #1217)
-#1868 := (~ #1867 #1866)
-#1863 := (not #1212)
-#1864 := (~ #1863 #1862)
-#1859 := (not #1204)
-#1860 := (~ #1859 #1201)
-#1857 := (~ #1201 #1201)
-#1855 := (~ #1198 #1198)
-#1856 := [refl]: #1855
-#1858 := [nnf-pos #1856]: #1857
-#1861 := [nnf-neg #1858]: #1860
-#1853 := (~ #1852 #1852)
-#1854 := [refl]: #1853
-#1865 := [nnf-neg #1854 #1861]: #1864
-#1848 := (~ #1204 #1847)
-#1849 := [sk]: #1848
-#1869 := [nnf-neg #1849 #1865]: #1868
-#1823 := (not #1186)
-#1824 := (~ #1823 #1820)
-#1821 := (~ #1183 #1820)
-#1818 := (~ #1180 #1817)
-#1813 := (~ #1177 #1812)
-#1814 := [sk]: #1813
-#1801 := (~ #1161 #1161)
-#1802 := [refl]: #1801
-#1819 := [monotonicity #1802 #1814]: #1818
-#1822 := [nnf-pos #1819]: #1821
-#1825 := [nnf-neg #1822]: #1824
-#1873 := [nnf-neg #1825 #1869]: #1872
-#1799 := (~ #1186 #1796)
-#1774 := (exists (vars (?x50 T2)) #1773)
-#1782 := (or #1781 #1774)
-#1783 := (not #1782)
-#1797 := (~ #1783 #1796)
-#1793 := (not #1774)
-#1794 := (~ #1793 #1792)
-#1790 := (~ #1789 #1789)
-#1791 := [refl]: #1790
-#1795 := [nnf-neg #1791]: #1794
-#1787 := (~ #1786 #1786)
-#1788 := [refl]: #1787
-#1798 := [nnf-neg #1788 #1795]: #1797
-#1784 := (~ #1186 #1783)
-#1785 := [sk]: #1784
-#1800 := [trans #1785 #1798]: #1799
-#1877 := [nnf-neg #1800 #1873]: #1876
-#1760 := (not #1149)
-#1761 := (~ #1760 #1757)
-#1758 := (~ #1144 #1757)
-#1755 := (~ #1138 #1754)
-#1752 := (~ #1751 #1751)
-#1753 := [refl]: #1752
-#1756 := [nnf-neg #1753]: #1755
-#1749 := (~ #533 #533)
-#1750 := [refl]: #1749
-#1747 := (~ #530 #530)
-#1748 := [refl]: #1747
-#1745 := (~ #154 #154)
-#1746 := [refl]: #1745
-#1743 := (~ #149 #149)
-#1744 := [refl]: #1743
-#1759 := [monotonicity #1744 #1746 #1748 #1750 #1756]: #1758
-#1762 := [nnf-neg #1759]: #1761
-#1881 := [nnf-neg #1762 #1877]: #1880
-#2125 := [nnf-neg #1881 #2121]: #2124
-#1740 := (not #1129)
-#1741 := (~ #1740 #1737)
-#1738 := (~ #1124 #1737)
-#1735 := (~ #1104 #1104)
-#1733 := (~ #1101 #1101)
-#1734 := [refl]: #1733
-#1736 := [nnf-pos #1734]: #1735
-#1731 := (~ #1098 #1098)
-#1729 := (~ #1095 #1095)
-#1730 := [refl]: #1729
-#1732 := [nnf-pos #1730]: #1731
-#1727 := (~ #1090 #1726)
-#1724 := (~ #1087 #1723)
-#1719 := (~ #1084 #1718)
-#1720 := [sk]: #1719
-#1706 := (~ #1063 #1063)
-#1707 := [refl]: #1706
-#1725 := [monotonicity #1707 #1720]: #1724
-#1728 := [nnf-pos #1725]: #1727
-#1704 := (~ #1051 #1051)
-#1702 := (~ #1048 #1048)
-#1703 := [refl]: #1702
-#1705 := [nnf-pos #1703]: #1704
-#1700 := (~ #1028 #1699)
-#1697 := (~ #1025 #1696)
-#1692 := (~ #1022 #1691)
-#1693 := [sk]: #1692
-#1678 := (~ #1002 #1002)
-#1679 := [refl]: #1678
-#1698 := [monotonicity #1679 #1693]: #1697
-#1701 := [nnf-pos #1698]: #1700
-#1676 := (~ #109 #109)
-#1677 := [refl]: #1676
-#1739 := [monotonicity #1677 #1701 #1705 #1728 #1732 #1736]: #1738
-#1742 := [nnf-neg #1739]: #1741
-#2129 := [nnf-neg #1742 #2125]: #2128
-#1658 := (not #1028)
-#1674 := (~ #1658 #1671)
-#1648 := (exists (vars (?x38 T2)) #1647)
-#1656 := (or #1655 #1648)
-#1657 := (not #1656)
-#1672 := (~ #1657 #1671)
-#1668 := (not #1648)
-#1669 := (~ #1668 #1667)
-#1665 := (~ #1664 #1664)
-#1666 := [refl]: #1665
-#1670 := [nnf-neg #1666]: #1669
-#1662 := (~ #1661 #1661)
-#1663 := [refl]: #1662
-#1673 := [nnf-neg #1663 #1670]: #1672
-#1659 := (~ #1658 #1657)
-#1660 := [sk]: #1659
-#1675 := [trans #1660 #1673]: #1674
-#2133 := [nnf-neg #1675 #2129]: #2132
-#1633 := (not #990)
-#1634 := (~ #1633 #987)
-#1631 := (~ #987 #987)
-#1629 := (~ #984 #984)
-#1630 := [refl]: #1629
-#1632 := [nnf-pos #1630]: #1631
-#1635 := [nnf-neg #1632]: #1634
-#2137 := [nnf-neg #1635 #2133]: #2136
-#1625 := (~ #990 #1624)
-#1626 := [sk]: #1625
-#2141 := [nnf-neg #1626 #2137]: #2140
-#1603 := (not #964)
-#1604 := (~ #1603 #961)
-#1601 := (~ #961 #961)
-#1599 := (~ #958 #958)
-#1600 := [refl]: #1599
-#1602 := [nnf-pos #1600]: #1601
-#1605 := [nnf-neg #1602]: #1604
-#2145 := [nnf-neg #1605 #2141]: #2144
-#1595 := (~ #964 #1594)
-#1596 := [sk]: #1595
-#2149 := [nnf-neg #1596 #2145]: #2148
-#1578 := (not #949)
-#1579 := (~ #1578 #946)
-#1576 := (~ #946 #946)
-#1574 := (~ #945 #945)
-#1575 := [refl]: #1574
-#1577 := [nnf-pos #1575]: #1576
-#1580 := [nnf-neg #1577]: #1579
-#2153 := [nnf-neg #1580 #2149]: #2152
-#1570 := (~ #949 #1569)
-#1571 := [sk]: #1570
-#2157 := [nnf-neg #1571 #2153]: #2156
-#1524 := (~ #1523 #1523)
-#1565 := [refl]: #1524
-#2161 := [nnf-neg #1565 #2157]: #2160
-#1563 := (~ #940 #940)
-#1564 := [refl]: #1563
-#2164 := [nnf-neg #1564 #2161]: #2163
-#1497 := [not-or-elim #1491]: #1496
-#2165 := [mp~ #1497 #2164]: #2162
-#2166 := [mp #2165 #2689]: #2687
-#3336 := [mp #2166 #3335]: #3333
-#4271 := [mp #3336 #4270]: #4268
-#6202 := [unit-resolution #4271 #4994]: #4265
-#3591 := (or #4262 #4256)
-#3434 := [def-axiom]: #3591
-#6203 := [unit-resolution #3434 #6202]: #4256
-#6204 := (or #4259 #4253)
-#333 := (<= uf_9 0::int)
-#334 := (not #333)
-#54 := (< 0::int uf_9)
-#335 := (iff #54 #334)
-#336 := [rewrite]: #335
-#329 := [asserted]: #54
-#337 := [mp #329 #336]: #334
-#4524 := (* -1::int #1567)
-#4525 := (+ uf_9 #4524)
-#4534 := (<= #4525 0::int)
-#3581 := (= uf_9 #1567)
-#3568 := (= uf_11 ?x27!0)
-#4428 := (not #3568)
-#4541 := (= #1567 0::int)
-#4864 := (not #4541)
-#4858 := [hypothesis]: #1569
-#4865 := (or #4864 #1568)
-#4866 := [th-lemma]: #4865
-#4867 := [unit-resolution #4866 #4858]: #4864
-#4873 := (or #4872 #4428 #4541)
-#3582 := (= ?x27!0 uf_11)
-#4542 := (not #3582)
-#4427 := (or #4542 #4541)
-#4874 := (or #4872 #4427)
-#4860 := (iff #4874 #4873)
-#4550 := (or #4428 #4541)
-#4876 := (or #4872 #4550)
-#4879 := (iff #4876 #4873)
-#4859 := [rewrite]: #4879
-#4877 := (iff #4874 #4876)
-#4553 := (iff #4427 #4550)
-#4362 := (iff #4542 #4428)
-#3573 := (iff #3582 #3568)
-#3558 := [rewrite]: #3573
-#4538 := [monotonicity #3558]: #4362
-#4871 := [monotonicity #4538]: #4553
-#4878 := [monotonicity #4871]: #4877
-#4861 := [trans #4878 #4859]: #4860
-#4875 := [quant-inst]: #4874
-#4862 := [mp #4875 #4861]: #4873
-#4868 := [unit-resolution #4862 #3898 #4867]: #4428
-#3560 := (or #3568 #3581)
-#3887 := (forall (vars (?x25 T2)) (:pat #3886) #403)
-#3890 := (iff #408 #3887)
-#3888 := (iff #403 #403)
-#3889 := [refl]: #3888
-#3891 := [quant-intro #3889]: #3890
-#1519 := (~ #408 #408)
-#1557 := (~ #403 #403)
-#1558 := [refl]: #1557
-#1520 := [nnf-pos #1558]: #1519
-#1494 := [and-elim #1492]: #408
-#1559 := [mp~ #1494 #1520]: #408
-#3892 := [mp #1559 #3891]: #3887
-#3569 := (not #3887)
-#4289 := (or #3569 #3568 #3581)
-#3578 := (or #3582 #3581)
-#4290 := (or #3569 #3578)
-#4364 := (iff #4290 #4289)
-#4292 := (or #3569 #3560)
-#4308 := (iff #4292 #4289)
-#4363 := [rewrite]: #4308
-#4307 := (iff #4290 #4292)
-#3561 := (iff #3578 #3560)
-#3565 := [monotonicity #3558]: #3561
-#4288 := [monotonicity #3565]: #4307
-#4365 := [trans #4288 #4363]: #4364
-#4291 := [quant-inst]: #4290
-#4366 := [mp #4291 #4365]: #4289
-#4883 := [unit-resolution #4366 #3892]: #3560
-#4884 := [unit-resolution #4883 #4868]: #3581
-#4909 := (not #3581)
-#4910 := (or #4909 #4534)
-#4911 := [th-lemma]: #4910
-#4912 := [unit-resolution #4911 #4884]: #4534
-#4863 := (<= #1567 0::int)
-#4913 := (or #4863 #1568)
-#4908 := [th-lemma]: #4913
-#4914 := [unit-resolution #4908 #4858]: #4863
-#4915 := [th-lemma #4914 #4912 #337]: false
-#4916 := [lemma #4915]: #1568
-#3586 := (or #4259 #1569 #4253)
-#3587 := [def-axiom]: #3586
-#6205 := [unit-resolution #3587 #4916]: #6204
-#6206 := [unit-resolution #6205 #6203]: #4253
-#3610 := (or #4250 #4244)
-#3611 := [def-axiom]: #3610
-#6207 := [unit-resolution #3611 #6206]: #4244
-#5458 := [hypothesis]: #1588
-#3880 := (forall (vars (?x26 T2)) (:pat #3879) #75)
-#3883 := (iff #76 #3880)
-#3881 := (iff #75 #75)
-#3882 := [refl]: #3881
-#3884 := [quant-intro #3882]: #3883
-#1517 := (~ #76 #76)
-#1554 := (~ #75 #75)
-#1555 := [refl]: #1554
-#1518 := [nnf-pos #1555]: #1517
-#1493 := [and-elim #1492]: #76
-#1556 := [mp~ #1493 #1518]: #76
-#3885 := [mp #1556 #3884]: #3880
-#4999 := (not #3880)
-#5000 := (or #4999 #1597)
-#5001 := [quant-inst]: #5000
-#5459 := [unit-resolution #5001 #3885 #5458]: false
-#5460 := [lemma #5459]: #1597
-#3403 := (or #1948 #1588)
-#3488 := [def-axiom]: #3403
-#6208 := [unit-resolution #3488 #5460]: #1948
-#3605 := (or #4247 #2022 #4241)
-#3606 := [def-axiom]: #3605
-#6209 := [unit-resolution #3606 #6208 #6207]: #4241
-#3631 := (or #4238 #4232)
-#3632 := [def-axiom]: #3631
-#6210 := [unit-resolution #3632 #6209]: #4232
-#5548 := [hypothesis]: #1620
-#5094 := (or #4999 #2709)
-#5095 := [quant-inst]: #5094
-#5549 := [unit-resolution #5095 #3885 #5548]: false
-#5553 := [lemma #5549]: #2709
-#3474 := (or #2724 #1620)
-#3809 := [def-axiom]: #3474
-#6211 := [unit-resolution #3809 #5553]: #2724
-#3627 := (or #4235 #2729 #4229)
-#3628 := [def-axiom]: #3627
-#6212 := [unit-resolution #3628 #6211 #6210]: #4229
-#3615 := (or #4226 #4220)
-#3616 := [def-axiom]: #3615
-#6213 := [unit-resolution #3616 #6212]: #4220
-#5484 := (= uf_9 #1639)
-#5561 := (not #5484)
-#5559 := [hypothesis]: #3937
-#3480 := (or #3934 #1651)
-#3812 := [def-axiom]: #3480
-#5560 := [unit-resolution #3812 #5559]: #1651
-#5562 := (or #5561 #1650)
-#5563 := [th-lemma]: #5562
-#5564 := [unit-resolution #5563 #5560]: #5561
-#3813 := (or #3934 #2217)
-#3814 := [def-axiom]: #3813
-#5565 := [unit-resolution #3814 #5559]: #2217
-#5504 := (or #3569 #2214 #5484)
-#5485 := (or #1652 #5484)
-#5505 := (or #3569 #5485)
-#5519 := (iff #5505 #5504)
-#5501 := (or #2214 #5484)
-#5506 := (or #3569 #5501)
-#5509 := (iff #5506 #5504)
-#5510 := [rewrite]: #5509
-#5507 := (iff #5505 #5506)
-#5502 := (iff #5485 #5501)
-#5503 := [monotonicity #2216]: #5502
-#5508 := [monotonicity #5503]: #5507
-#5521 := [trans #5508 #5510]: #5519
-#5500 := [quant-inst]: #5505
-#5522 := [mp #5500 #5521]: #5504
-#5566 := [unit-resolution #5522 #3892 #5565 #5564]: false
-#5567 := [lemma #5566]: #3934
-#3649 := (or #4223 #3937 #4217)
-#3659 := [def-axiom]: #3649
-#6214 := [unit-resolution #3659 #5567 #6213]: #4217
-#5359 := (or #4214 #4205)
-#4367 := (?x47!7 ?x49!8)
-#4714 := (uf_4 uf_19 #4367)
-#4751 := (* -1::int #4714)
-#4368 := (uf_4 uf_14 #4367)
-#5011 := (+ #4368 #4751)
-#5015 := (<= #5011 0::int)
-#5010 := (= #4368 #4714)
-#5211 := (= #4714 #4368)
-#5206 := [hypothesis]: #4202
-#5207 := [hypothesis]: #4217
-#3644 := (or #4214 #4208)
-#3603 := [def-axiom]: #3644
-#5208 := [unit-resolution #3603 #5207]: #4208
-#3678 := (or #4211 #4050 #4205)
-#3679 := [def-axiom]: #3678
-#5209 := [unit-resolution #3679 #5208 #5206]: #4050
-#3496 := (or #4047 #533)
-#3778 := [def-axiom]: #3496
-#5210 := [unit-resolution #3778 #5209]: #533
-#5205 := [symm #5210]: #151
-#5212 := [monotonicity #5205]: #5211
-#5213 := [symm #5212]: #5010
-#5214 := (not #5010)
-#5215 := (or #5214 #5015)
-#5268 := [th-lemma]: #5215
-#5269 := [unit-resolution #5268 #5213]: #5015
-#4369 := (* -1::int #4368)
-#4353 := (uf_1 #4367 ?x49!8)
-#4354 := (uf_10 #4353)
-#4355 := (* -1::int #4354)
-#4432 := (+ #4355 #4369)
-#4301 := (uf_4 uf_14 ?x49!8)
-#4433 := (+ #4301 #4432)
-#4520 := (<= #4433 0::int)
-#4436 := (= #4433 0::int)
-#4418 := (not #4436)
-#4359 := (up_6 uf_15 #4367)
-#4360 := (not #4359)
-#4351 := (+ #4301 #4369)
-#4352 := (<= #4351 0::int)
-#4423 := (or #4352 #4360 #4418)
-#4442 := (not #4423)
-#4302 := (* -1::int #4301)
-#4303 := (+ uf_9 #4302)
-#4283 := (<= #4303 0::int)
-#4675 := (not #4283)
-#3783 := (or #4047 #4041)
-#3772 := [def-axiom]: #3783
-#5270 := [unit-resolution #3772 #5209]: #4041
-#3680 := (or #4214 #109)
-#3676 := [def-axiom]: #3680
-#5271 := [unit-resolution #3676 #5207]: #109
-#5272 := (= #175 #108)
-#5273 := [monotonicity #5205]: #5272
-#5274 := [trans #5273 #5271]: #176
-#3456 := (or #4023 #1852)
-#3457 := [def-axiom]: #3456
-#5275 := [unit-resolution #3457 #5274]: #4023
-#3782 := (or #4047 #3983)
-#3779 := [def-axiom]: #3782
-#5276 := [unit-resolution #3779 #5209]: #3983
-#3607 := (or #4214 #3949)
-#3662 := [def-axiom]: #3607
-#5256 := [unit-resolution #3662 #5207]: #3949
-#4685 := (or #2992 #3954 #3988 #3023)
-#4370 := (uf_4 uf_14 ?x54!10)
-#4371 := (* -1::int #4370)
-#4552 := (+ #1830 #4371)
-#4554 := (>= #4552 0::int)
-#4551 := (= #1830 #4370)
-#4633 := (= #4370 #1830)
-#4632 := [hypothesis]: #533
-#4634 := [monotonicity #4632]: #4633
-#4635 := [symm #4634]: #4551
-#4636 := (not #4551)
-#4637 := (or #4636 #4554)
-#4638 := [th-lemma]: #4637
-#4620 := [unit-resolution #4638 #4635]: #4554
-#3503 := (uf_4 uf_14 ?x53!11)
-#3504 := (* -1::int #3503)
-#4545 := (+ #1828 #3504)
-#4549 := (<= #4545 0::int)
-#4544 := (= #1828 #3503)
-#4621 := (= #3503 #1828)
-#4622 := [monotonicity #4632]: #4621
-#4623 := [symm #4622]: #4544
-#4624 := (not #4544)
-#4619 := (or #4624 #4549)
-#4625 := [th-lemma]: #4619
-#4626 := [unit-resolution #4625 #4623]: #4549
-#3437 := (not #2445)
-#4627 := [hypothesis]: #2997
-#3800 := (or #2992 #3437)
-#3802 := [def-axiom]: #3800
-#4628 := [unit-resolution #3802 #4627]: #3437
-#4822 := [hypothesis]: #3983
-#4826 := [hypothesis]: #3949
-#3793 := (or #2992 #1843)
-#3799 := [def-axiom]: #3793
-#4629 := [unit-resolution #3799 #4627]: #1843
-#4372 := (+ uf_9 #4371)
-#4373 := (<= #4372 0::int)
-#4820 := (not #4373)
-#3797 := (or #2992 #1839)
-#3798 := [def-axiom]: #3797
-#4680 := [unit-resolution #3798 #4627]: #1839
-#4816 := (not #4554)
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-#4450 := (>= #4447 0::int)
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-#4383 := (iff #4380 #4382)
-#4377 := (iff #4375 #4376)
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-#4384 := [monotonicity #4378]: #4383
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-#4461 := (or #3954 #1842 #4444 #4450)
-#4439 := (+ #4370 #3504)
-#4440 := (+ #1833 #4439)
-#4443 := (>= #4440 0::int)
-#4445 := (or #4444 #1842 #4443)
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-#4467 := (iff #4464 #4461)
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-#4471 := [mp #4463 #4470]: #4461
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-#4669 := (+ #1764 #4302)
-#4671 := (>= #4669 0::int)
-#4668 := (= #1764 #4301)
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-#5262 := [monotonicity #5210]: #5261
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-#4356 := (+ #4301 #4350)
-#4357 := (= #4356 0::int)
-#4358 := (not #4357)
-#4429 := (or #4360 #4358 #4352)
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-#4416 := (iff #4429 #4421)
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-#4434 := (= #4356 #4433)
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-#9709 := (up_6 uf_15 #8339)
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+#4005 := (iff #38 #4002)
+#4003 := (iff #37 #37)
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+#4006 := [quant-intro #4004]: #4005
+#1646 := (~ #38 #38)
+#1682 := (~ #37 #37)
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+#1647 := [nnf-pos #1683]: #1646
+#311 := [asserted]: #38
+#1684 := [mp~ #311 #1647]: #38
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+#6538 := (not #4002)
+#27089 := (or #6538 #27086)
+#3681 := (= uf_8 uf_8)
+#27069 := (= #19843 #10482)
+#27070 := (ite #27069 #3681 #25893)
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+#27090 := (or #6538 #27074)
+#27092 := (iff #27090 #27089)
+#27094 := (iff #27089 #27089)
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+#27087 := (iff #27074 #27086)
+#27084 := (iff #27070 #27081)
+#27078 := (ite #27075 true #25893)
+#27082 := (iff #27078 #27081)
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+#27079 := (iff #27070 #27078)
+#3684 := (iff #3681 true)
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+#27085 := [trans #27080 #27083]: #27084
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+#27097 := [mp #27091 #27096]: #27089
+#27196 := [unit-resolution #27097 #4007]: #27086
+#27106 := (not #27086)
+#27223 := (or #27106 #27073)
+#5835 := (up_6 uf_15 #5823)
+#27219 := (iff #5835 #25893)
+#27217 := (iff #25893 #5835)
+#27218 := [monotonicity #27216]: #27217
+#27220 := [symm #27218]: #27219
+#5836 := (not #5835)
+#5828 := (uf_1 #5823 ?x75!20)
+#5829 := (uf_10 #5828)
+#5830 := (* -1::int #5829)
+#5824 := (uf_4 uf_14 #5823)
+#5825 := (* -1::int #5824)
+#5831 := (+ #5825 #5830)
+#5561 := (uf_4 uf_14 ?x75!20)
+#5832 := (+ #5561 #5831)
+#5833 := (= #5832 0::int)
+#5834 := (not #5833)
+#5826 := (+ #5561 #5825)
+#5827 := (<= #5826 0::int)
+#5842 := (or #5827 #5834 #5836)
+#5845 := (not #5842)
+#5591 := (* -1::int #5561)
+#5839 := (+ uf_9 #5591)
+#5840 := (<= #5839 0::int)
+#22585 := (not #5840)
+#6522 := [hypothesis]: #3240
+#3920 := (not #2683)
+#3921 := (or #3235 #3920)
+#3915 := [def-axiom]: #3921
+#6523 := [unit-resolution #3915 #6522]: #3920
+#13600 := (or #3235 #2683)
+#6436 := (uf_1 uf_22 ?x68!16)
+#6437 := (uf_10 #6436)
+#6462 := (+ #2681 #6437)
+#6463 := (+ #177 #6462)
+#13033 := (<= #6463 0::int)
+#6466 := (= #6463 0::int)
+#6403 := (uf_4 uf_14 ?x68!16)
+#6420 := (* -1::int #6403)
+#6455 := (+ #6420 #6437)
+#6456 := (+ #177 #6455)
+#6457 := (>= #6456 0::int)
+#6441 := (* -1::int #6437)
+#6445 := (+ uf_9 #6441)
+#6446 := (<= #6445 0::int)
+#6492 := (or #6446 #6457)
+#6495 := (not #6492)
+#6489 := (= #2095 #6403)
+#9335 := (not #6489)
+#6421 := (+ #2095 #6420)
+#13056 := (>= #6421 0::int)
+#13361 := (not #13056)
+#12929 := (= ?x67!17 #10482)
+#6205 := (up_6 uf_15 ?x67!17)
+#12936 := (or #6205 #12929)
+#12931 := (up_6 #11444 ?x67!17)
+#12941 := (iff #12931 #12936)
+#12895 := (or #6538 #12941)
+#12930 := (ite #12929 #3681 #6205)
+#12932 := (iff #12931 #12930)
+#12896 := (or #6538 #12932)
+#12898 := (iff #12896 #12895)
+#12894 := (iff #12895 #12895)
+#12900 := [rewrite]: #12894
+#12942 := (iff #12932 #12941)
+#12939 := (iff #12930 #12936)
+#12933 := (ite #12929 true #6205)
+#12937 := (iff #12933 #12936)
+#12938 := [rewrite]: #12937
+#12934 := (iff #12930 #12933)
+#12935 := [monotonicity #3673]: #12934
+#12940 := [trans #12935 #12938]: #12939
+#12943 := [monotonicity #12940]: #12942
+#12899 := [monotonicity #12943]: #12898
+#12901 := [trans #12899 #12900]: #12898
+#12897 := [quant-inst]: #12896
+#12902 := [mp #12897 #12901]: #12895
+#13389 := [unit-resolution #12902 #4007]: #12941
+#11402 := (iff #2098 #12931)
+#13390 := (iff #12931 #2098)
+#11401 := [monotonicity #13524]: #13390
+#13535 := [symm #11401]: #11402
+#3775 := (or #3235 #2098)
+#3776 := [def-axiom]: #3775
+#6525 := [unit-resolution #3776 #6522]: #2098
+#13536 := [mp #6525 #13535]: #12931
+#12962 := (not #12931)
+#12959 := (not #12941)
+#12963 := (or #12959 #12962 #12936)
+#12964 := [def-axiom]: #12963
+#13537 := [unit-resolution #12964 #13536 #13389]: #12936
+#10975 := [hypothesis]: #3920
+#6233 := (+ #177 #6420)
+#6234 := (<= #6233 0::int)
+#3749 := (up_6 uf_15 ?x68!16)
+#12831 := (not #3749)
+#12761 := (= ?x68!16 #10482)
+#12767 := (or #3749 #12761)
+#12836 := (not #12767)
+#12763 := (up_6 #11444 ?x68!16)
+#12796 := (iff #12763 #12767)
+#12793 := (or #6538 #12796)
+#12762 := (ite #12761 #3681 #3749)
+#12764 := (iff #12763 #12762)
+#12799 := (or #6538 #12764)
+#12801 := (iff #12799 #12793)
+#12803 := (iff #12793 #12793)
+#12828 := [rewrite]: #12803
+#12797 := (iff #12764 #12796)
+#12794 := (iff #12762 #12767)
+#12759 := (ite #12761 true #3749)
+#12768 := (iff #12759 #12767)
+#12769 := [rewrite]: #12768
+#12765 := (iff #12762 #12759)
+#12766 := [monotonicity #3673]: #12765
+#12795 := [trans #12766 #12769]: #12794
+#12798 := [monotonicity #12795]: #12797
+#12802 := [monotonicity #12798]: #12801
+#12829 := [trans #12802 #12828]: #12801
+#12800 := [quant-inst]: #12799
+#12830 := [mp #12800 #12829]: #12793
+#13565 := [unit-resolution #12830 #4007]: #12796
+#12866 := (not #12763)
+#13564 := (iff #2100 #12866)
+#13568 := (iff #2099 #12763)
+#13566 := (iff #12763 #2099)
+#13567 := [monotonicity #13524]: #13566
+#13569 := [symm #13567]: #13568
+#13570 := [monotonicity #13569]: #13564
+#3918 := (or #3235 #2100)
+#3919 := [def-axiom]: #3918
+#6524 := [unit-resolution #3919 #6522]: #2100
+#13571 := [mp #6524 #13570]: #12866
+#12863 := (not #12796)
+#12864 := (or #12863 #12763 #12836)
+#12865 := [def-axiom]: #12864
+#13572 := [unit-resolution #12865 #13571 #13565]: #12836
+#12832 := (or #12767 #12831)
+#12827 := [def-axiom]: #12832
+#13573 := [unit-resolution #12827 #13572]: #12831
+#6238 := (or #3749 #6234)
+#3838 := (or #4352 #4203)
+#3839 := [def-axiom]: #3838
+#10794 := [unit-resolution #3839 #10367]: #4203
+#13087 := (or #4208 #3749 #6234)
+#6251 := (+ #6403 #1268)
+#6252 := (>= #6251 0::int)
+#6253 := (or #3749 #6252)
+#13085 := (or #4208 #6253)
+#13095 := (iff #13085 #13087)
+#13091 := (or #4208 #6238)
+#13093 := (iff #13091 #13087)
+#13094 := [rewrite]: #13093
+#13084 := (iff #13085 #13091)
+#6239 := (iff #6253 #6238)
+#6236 := (iff #6252 #6234)
+#6254 := (+ #1268 #6403)
+#6257 := (>= #6254 0::int)
+#6232 := (iff #6257 #6234)
+#6235 := [rewrite]: #6232
+#6258 := (iff #6252 #6257)
+#6255 := (= #6251 #6254)
+#6256 := [rewrite]: #6255
+#6259 := [monotonicity #6256]: #6258
+#6237 := [trans #6259 #6235]: #6236
+#6240 := [monotonicity #6237]: #6239
+#13092 := [monotonicity #6240]: #13084
+#13096 := [trans #13092 #13094]: #13095
+#13090 := [quant-inst]: #13085
+#13098 := [mp #13090 #13096]: #13087
+#13574 := [unit-resolution #13098 #10794]: #6238
+#10559 := [unit-resolution #13574 #13573]: #6234
+#12956 := (not #12936)
+#13360 := (not #6234)
+#13379 := (or #13361 #2683 #13360 #12956)
+#4526 := (uf_24 uf_22)
+#4567 := (* -1::int #4526)
+#6154 := (+ #2093 #4567)
+#13335 := (<= #6154 0::int)
+#13334 := (= #2093 #4526)
+#6206 := (= ?x67!17 uf_22)
+#13343 := [hypothesis]: #12936
+#10290 := (not #6205)
+#10815 := (uf_4 uf_14 #10482)
+#10842 := (* -1::int #10815)
+#6176 := (uf_4 uf_14 ?x67!17)
+#13287 := (+ #6176 #10842)
+#13288 := (<= #13287 0::int)
+#13464 := (not #13288)
+#13357 := [hypothesis]: #6234
+#5358 := (* -1::int #6176)
+#5458 := (+ #2093 #5358)
+#5459 := (<= #5458 0::int)
+#3715 := (or #4352 #4346)
+#3826 := [def-axiom]: #3715
+#10824 := [unit-resolution #3826 #10367]: #4346
+#3847 := (or #4352 #4213)
+#3820 := [def-axiom]: #3847
+#10373 := [unit-resolution #3820 #10367]: #4213
+#3821 := (or #4352 #4221)
+#3822 := [def-axiom]: #3821
+#10825 := [unit-resolution #3822 #10367]: #4221
+#6791 := (or #2650 #4226 #4218)
+#6483 := (uf_1 uf_22 ?x61!13)
+#6484 := (uf_10 #6483)
+#6567 := (+ #2036 #6484)
+#6568 := (+ #177 #6567)
+#6588 := (>= #6568 0::int)
+#6570 := (= #6568 0::int)
+#6544 := (* -1::int #6484)
+#6540 := (+ uf_9 #6544)
+#6548 := (<= #6540 0::int)
+#6625 := (not #6548)
+#6558 := (+ #2648 #6484)
+#6553 := (+ #177 #6558)
+#6559 := (>= #6553 0::int)
+#6596 := (or #6548 #6559)
+#6598 := (not #6596)
+#6593 := (= #2035 #2037)
+#6749 := (not #6593)
+#6733 := [hypothesis]: #2655
+#6752 := (or #6749 #2650)
+#6753 := [th-lemma]: #6752
+#6748 := [unit-resolution #6753 #6733]: #6749
+#6754 := [hypothesis]: #4213
+#6603 := (or #4218 #6593 #6598)
+#6545 := (+ #1268 #6544)
+#6546 := (+ #2037 #6545)
+#6547 := (<= #6546 0::int)
+#6589 := (or #6548 #6547)
+#6591 := (not #6589)
+#6592 := (= #2037 #2035)
+#6590 := (or #6592 #6591)
+#6604 := (or #4218 #6590)
+#6621 := (iff #6604 #6603)
+#6601 := (or #6593 #6598)
+#6606 := (or #4218 #6601)
+#6619 := (iff #6606 #6603)
+#6620 := [rewrite]: #6619
+#6617 := (iff #6604 #6606)
+#6564 := (iff #6590 #6601)
+#6599 := (iff #6591 #6598)
+#6597 := (iff #6589 #6596)
+#6562 := (iff #6547 #6559)
+#6550 := (+ #2037 #6544)
+#6551 := (+ #1268 #6550)
+#6555 := (<= #6551 0::int)
+#6560 := (iff #6555 #6559)
+#6561 := [rewrite]: #6560
+#6556 := (iff #6547 #6555)
+#6552 := (= #6546 #6551)
+#6554 := [rewrite]: #6552
+#6557 := [monotonicity #6554]: #6556
+#6563 := [trans #6557 #6561]: #6562
+#6565 := [monotonicity #6563]: #6597
+#6600 := [monotonicity #6565]: #6599
+#6594 := (iff #6592 #6593)
+#6595 := [rewrite]: #6594
+#6602 := [monotonicity #6595 #6600]: #6564
+#6618 := [monotonicity #6602]: #6617
+#6622 := [trans #6618 #6620]: #6621
+#6605 := [quant-inst]: #6604
+#6623 := [mp #6605 #6622]: #6603
+#6755 := [unit-resolution #6623 #6754 #6748]: #6598
+#6626 := (or #6596 #6625)
+#6627 := [def-axiom]: #6626
+#6756 := [unit-resolution #6627 #6755]: #6625
+#6628 := (not #6559)
+#6629 := (or #6596 #6628)
+#6630 := [def-axiom]: #6629
+#6757 := [unit-resolution #6630 #6755]: #6628
+#6574 := (or #6548 #6559 #6570)
+#6758 := [hypothesis]: #4221
+#6576 := (or #4226 #6548 #6559 #6570)
+#6542 := (+ #6484 #2036)
+#6543 := (+ #177 #6542)
+#6541 := (= #6543 0::int)
+#6549 := (or #6548 #6547 #6541)
+#6577 := (or #4226 #6549)
+#6585 := (iff #6577 #6576)
+#6580 := (or #4226 #6574)
+#6582 := (iff #6580 #6576)
+#6583 := [rewrite]: #6582
+#6578 := (iff #6577 #6580)
+#6572 := (iff #6549 #6574)
+#6571 := (iff #6541 #6570)
+#6566 := (= #6543 #6568)
+#6569 := [rewrite]: #6566
+#6573 := [monotonicity #6569]: #6571
+#6575 := [monotonicity #6563 #6573]: #6572
+#6581 := [monotonicity #6575]: #6578
+#6586 := [trans #6581 #6583]: #6585
+#6579 := [quant-inst]: #6577
+#6584 := [mp #6579 #6586]: #6576
+#6782 := [unit-resolution #6584 #6758]: #6574
+#6783 := [unit-resolution #6782 #6757 #6756]: #6570
+#6784 := (not #6570)
+#6785 := (or #6784 #6588)
+#6786 := [th-lemma]: #6785
+#6781 := [unit-resolution #6786 #6783]: #6588
+#6624 := (>= #2649 0::int)
+#6787 := (or #6624 #2650)
+#6788 := [th-lemma]: #6787
+#6789 := [unit-resolution #6788 #6733]: #6624
+#6790 := [th-lemma #6789 #6757 #6781]: false
+#6815 := [lemma #6790]: #6791
+#10826 := [unit-resolution #6815 #10825 #10373]: #2650
+#3853 := (or #4349 #2655 #4343)
+#3854 := [def-axiom]: #3853
+#10827 := [unit-resolution #3854 #10826 #10824]: #4343
+#3866 := (or #4340 #4229)
+#3867 := [def-axiom]: #3866
+#10835 := [unit-resolution #3867 #10827]: #4229
+#10497 := (or #4234 #5459)
+#5451 := (+ #6176 #2094)
+#5452 := (>= #5451 0::int)
+#10498 := (or #4234 #5452)
+#10502 := (iff #10498 #10497)
+#10504 := (iff #10497 #10497)
+#10505 := [rewrite]: #10504
+#5485 := (iff #5452 #5459)
+#5453 := (+ #2094 #6176)
+#5450 := (>= #5453 0::int)
+#5460 := (iff #5450 #5459)
+#5484 := [rewrite]: #5460
+#5456 := (iff #5452 #5450)
+#5454 := (= #5451 #5453)
+#5455 := [rewrite]: #5454
+#5457 := [monotonicity #5455]: #5456
+#5486 := [trans #5457 #5484]: #5485
+#10503 := [monotonicity #5486]: #10502
+#10506 := [trans #10503 #10505]: #10502
+#10501 := [quant-inst]: #10498
+#10507 := [mp #10501 #10506]: #10497
+#11063 := [unit-resolution #10507 #10835]: #5459
+#10550 := (+ #177 #10842)
+#10551 := (>= #10550 0::int)
+#10851 := (= #177 #10815)
+#13455 := (= #10815 #177)
+#13456 := [monotonicity #13347]: #13455
+#13457 := [symm #13456]: #10851
+#13458 := (not #10851)
+#13459 := (or #13458 #10551)
+#13460 := [th-lemma]: #13459
+#13461 := [unit-resolution #13460 #13457]: #10551
+#13358 := [hypothesis]: #13056
+#13331 := (not #10551)
+#11754 := (not #5459)
+#13362 := (or #13464 #11754 #2683 #13360 #13331 #13361)
+#13363 := [th-lemma]: #13362
+#13364 := [unit-resolution #13363 #13358 #13461 #11063 #13357 #10975]: #13464
+#13586 := (or #10290 #13288)
+#13575 := [hypothesis]: #13464
+#10840 := (up_6 uf_15 #10482)
+#13580 := (not #10840)
+#13581 := (iff #176 #13580)
+#13578 := (iff #175 #10840)
+#13576 := (iff #10840 #175)
+#13577 := [monotonicity #13347]: #13576
+#13579 := [symm #13577]: #13578
+#13582 := [monotonicity #13579]: #13581
+#3855 := (or #4352 #176)
+#3850 := [def-axiom]: #3855
+#10368 := [unit-resolution #3850 #10367]: #176
+#13583 := [mp #10368 #13582]: #13580
+#13584 := [hypothesis]: #6205
+#3799 := (or #4364 #4108)
+#3823 := [def-axiom]: #3799
+#10473 := [unit-resolution #3823 #10034]: #4108
+#13489 := (or #4113 #10290 #10840 #13288)
+#13250 := (+ #10815 #5358)
+#13251 := (>= #13250 0::int)
+#13282 := (or #10840 #10290 #13251)
+#13491 := (or #4113 #13282)
+#13502 := (iff #13491 #13489)
+#13306 := (or #10290 #10840 #13288)
+#13497 := (or #4113 #13306)
+#13500 := (iff #13497 #13489)
+#13501 := [rewrite]: #13500
+#13498 := (iff #13491 #13497)
+#13319 := (iff #13282 #13306)
+#13311 := (or #10840 #10290 #13288)
+#13315 := (iff #13311 #13306)
+#13318 := [rewrite]: #13315
+#13316 := (iff #13282 #13311)
+#13309 := (iff #13251 #13288)
+#13283 := (+ #5358 #10815)
+#13286 := (>= #13283 0::int)
+#13289 := (iff #13286 #13288)
+#13290 := [rewrite]: #13289
+#13280 := (iff #13251 #13286)
+#13284 := (= #13250 #13283)
+#13285 := [rewrite]: #13284
+#13281 := [monotonicity #13285]: #13280
+#13310 := [trans #13281 #13290]: #13309
+#13317 := [monotonicity #13310]: #13316
+#13320 := [trans #13317 #13318]: #13319
+#13499 := [monotonicity #13320]: #13498
+#13369 := [trans #13499 #13501]: #13502
+#13492 := [quant-inst]: #13491
+#13383 := [mp #13492 #13369]: #13489
+#13585 := [unit-resolution #13383 #10473 #13584 #13583 #13575]: false
+#13587 := [lemma #13585]: #13586
+#13359 := [unit-resolution #13587 #13364]: #10290
+#12957 := (or #12956 #6205 #12929)
+#12958 := [def-axiom]: #12957
+#13336 := [unit-resolution #12958 #13359 #13343]: #12929
+#13380 := [trans #13336 #13347]: #6206
+#13381 := [monotonicity #13380]: #13334
+#13374 := (not #13334)
+#13382 := (or #13374 #13335)
+#13438 := [th-lemma]: #13382
+#13375 := [unit-resolution #13438 #13381]: #13335
+#4768 := (+ #177 #4567)
+#4769 := (>= #4768 0::int)
+#9856 := (or #4234 #4769)
+#9857 := [quant-inst]: #9856
+#10836 := [unit-resolution #9857 #10835]: #4769
+#13378 := [th-lemma #10975 #13357 #13358 #10836 #13375]: false
+#13372 := [lemma #13378]: #13379
+#10577 := [unit-resolution #13372 #10559 #10975 #13537]: #13361
+#11369 := (or #9335 #13056)
+#13408 := [th-lemma]: #11369
+#13409 := [unit-resolution #13408 #10577]: #9335
+#6498 := (or #6489 #6495)
+#13035 := (or #4218 #6489 #6495)
+#6442 := (+ #1268 #6441)
+#6443 := (+ #6403 #6442)
+#6444 := (<= #6443 0::int)
+#6485 := (or #6446 #6444)
+#6486 := (not #6485)
+#6487 := (= #6403 #2095)
+#6488 := (or #6487 #6486)
+#13036 := (or #4218 #6488)
+#13053 := (iff #13036 #13035)
+#13049 := (or #4218 #6498)
+#13052 := (iff #13049 #13035)
+#13047 := [rewrite]: #13052
+#13050 := (iff #13036 #13049)
+#6499 := (iff #6488 #6498)
+#6496 := (iff #6486 #6495)
+#6493 := (iff #6485 #6492)
+#6460 := (iff #6444 #6457)
+#6448 := (+ #6403 #6441)
+#6449 := (+ #1268 #6448)
+#6452 := (<= #6449 0::int)
+#6458 := (iff #6452 #6457)
+#6459 := [rewrite]: #6458
+#6453 := (iff #6444 #6452)
+#6450 := (= #6443 #6449)
+#6451 := [rewrite]: #6450
+#6454 := [monotonicity #6451]: #6453
+#6461 := [trans #6454 #6459]: #6460
+#6494 := [monotonicity #6461]: #6493
+#6497 := [monotonicity #6494]: #6496
+#6490 := (iff #6487 #6489)
+#6491 := [rewrite]: #6490
+#6500 := [monotonicity #6491 #6497]: #6499
+#13051 := [monotonicity #6500]: #13050
+#13054 := [trans #13051 #13047]: #13053
+#13048 := [quant-inst]: #13036
+#13055 := [mp #13048 #13054]: #13035
+#13387 := [unit-resolution #13055 #10373]: #6498
+#13388 := [unit-resolution #13387 #13409]: #6495
+#13385 := (or #6492 #6466)
+#13434 := (not #6466)
+#13435 := [hypothesis]: #13434
+#13057 := (not #6446)
+#13439 := [hypothesis]: #6495
+#13077 := (or #6492 #13057)
+#13078 := [def-axiom]: #13077
+#13365 := [unit-resolution #13078 #13439]: #13057
+#13079 := (not #6457)
+#13080 := (or #6492 #13079)
+#13081 := [def-axiom]: #13080
+#13366 := [unit-resolution #13081 #13439]: #13079
+#6469 := (or #6446 #6457 #6466)
+#13012 := (or #4226 #6446 #6457 #6466)
+#6438 := (+ #6437 #2681)
+#6439 := (+ #177 #6438)
+#6440 := (= #6439 0::int)
+#6447 := (or #6446 #6444 #6440)
+#13013 := (or #4226 #6447)
+#13031 := (iff #13013 #13012)
+#13015 := (or #4226 #6469)
+#13029 := (iff #13015 #13012)
+#13030 := [rewrite]: #13029
+#13027 := (iff #13013 #13015)
+#6470 := (iff #6447 #6469)
+#6467 := (iff #6440 #6466)
+#6464 := (= #6439 #6463)
+#6465 := [rewrite]: #6464
+#6468 := [monotonicity #6465]: #6467
+#6471 := [monotonicity #6461 #6468]: #6470
+#13028 := [monotonicity #6471]: #13027
+#13026 := [trans #13028 #13030]: #13031
+#13014 := [quant-inst]: #13013
+#13032 := [mp #13014 #13026]: #13012
+#13367 := [unit-resolution #13032 #10825]: #6469
+#13368 := [unit-resolution #13367 #13366 #13365 #13435]: false
+#13386 := [lemma #13368]: #13385
+#13488 := [unit-resolution #13386 #13388]: #6466
+#13588 := (or #13434 #13033)
+#13589 := [th-lemma]: #13588
+#13590 := [unit-resolution #13589 #13488]: #13033
+#12924 := (uf_1 #10482 ?x68!16)
+#12925 := (uf_10 #12924)
+#13060 := (* -1::int #12925)
+#13437 := (+ #6437 #13060)
+#13441 := (>= #13437 0::int)
+#13436 := (= #6437 #12925)
+#13445 := (= #12925 #6437)
+#13443 := (= #12924 #6436)
+#13444 := [monotonicity #13347]: #13443
+#13446 := [monotonicity #13444]: #13445
+#13447 := [symm #13446]: #13436
+#13448 := (not #13436)
+#13449 := (or #13448 #13441)
+#13450 := [th-lemma]: #13449
+#13451 := [unit-resolution #13450 #13447]: #13441
+#13410 := (<= #12925 0::int)
+#13411 := (not #13410)
+#12833 := (not #12761)
+#12834 := (or #12767 #12833)
+#12835 := [def-axiom]: #12834
+#13591 := [unit-resolution #12835 #13572]: #12833
 #56 := (uf_10 #12)
-#57 := (= #56 0::int)
+#371 := (<= #56 0::int)
+#372 := (not #371)
 #55 := (= #10 #11)
+#375 := (or #55 #372)
+#4029 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #3981) #375)
+#378 := (forall (vars (?x22 T2) (?x23 T2)) #375)
+#4032 := (iff #378 #4029)
+#4030 := (iff #375 #375)
+#4031 := [refl]: #4030
+#4033 := [quant-intro #4031]: #4032
+#1656 := (~ #378 #378)
+#1655 := (~ #375 #375)
+#1693 := [refl]: #1655
+#1657 := [nnf-pos #1693]: #1656
+#61 := (< 0::int #56)
 #60 := (not #55)
-#353 := (or #60 #57)
-#3867 := (forall (vars (?x20 T2) (?x21 T2)) (:pat #3825) #353)
-#356 := (forall (vars (?x20 T2) (?x21 T2)) #353)
-#3870 := (iff #356 #3867)
-#3868 := (iff #353 #353)
-#3869 := [refl]: #3868
-#3871 := [quant-intro #3869]: #3870
-#1511 := (~ #356 #356)
-#1550 := (~ #353 #353)
-#1551 := [refl]: #1550
-#1512 := [nnf-pos #1551]: #1511
+#62 := (implies #60 #61)
+#63 := (forall (vars (?x22 T2) (?x23 T2)) #62)
+#381 := (iff #63 #378)
+#365 := (or #55 #61)
+#368 := (forall (vars (?x22 T2) (?x23 T2)) #365)
+#379 := (iff #368 #378)
+#376 := (iff #365 #375)
+#373 := (iff #61 #372)
+#374 := [rewrite]: #373
+#377 := [monotonicity #374]: #376
+#380 := [quant-intro #377]: #379
+#369 := (iff #63 #368)
+#366 := (iff #62 #365)
+#367 := [rewrite]: #366
+#370 := [quant-intro #367]: #369
+#382 := [trans #370 #380]: #381
+#364 := [asserted]: #63
+#383 := [mp #364 #382]: #378
+#1694 := [mp~ #383 #1657]: #378
+#4034 := [mp #1694 #4033]: #4029
+#7051 := (not #4029)
+#13419 := (or #7051 #12761 #13411)
+#13412 := (= #10482 ?x68!16)
+#13413 := (or #13412 #13411)
+#13420 := (or #7051 #13413)
+#13427 := (iff #13420 #13419)
+#13416 := (or #12761 #13411)
+#13422 := (or #7051 #13416)
+#13425 := (iff #13422 #13419)
+#13426 := [rewrite]: #13425
+#13423 := (iff #13420 #13422)
+#13417 := (iff #13413 #13416)
+#13414 := (iff #13412 #12761)
+#13415 := [rewrite]: #13414
+#13418 := [monotonicity #13415]: #13417
+#13424 := [monotonicity #13418]: #13423
+#13428 := [trans #13424 #13426]: #13427
+#13421 := [quant-inst]: #13420
+#13429 := [mp #13421 #13428]: #13419
+#13592 := [unit-resolution #13429 #4034 #13591]: #13411
+#13463 := (not #13033)
+#13465 := (or #13463 #2683 #13464 #12761)
+#13442 := [hypothesis]: #13288
+#13452 := [hypothesis]: #12833
+#13453 := [unit-resolution #13429 #4034 #13452]: #13411
+#13454 := [hypothesis]: #13033
+#13462 := [th-lemma #13461 #11063 #10975 #13454 #13453 #13451 #13442]: false
+#13466 := [lemma #13462]: #13465
+#13593 := [unit-resolution #13466 #13590 #10975 #13591]: #13464
+#13594 := [unit-resolution #13587 #13593]: #10290
+#13595 := [unit-resolution #12958 #13594 #13537]: #12929
+#13596 := [trans #13595 #13347]: #6206
+#13597 := [monotonicity #13596]: #13334
+#13598 := [unit-resolution #13438 #13597]: #13335
+#13599 := [th-lemma #13598 #10975 #10836 #13592 #13451 #13590]: false
+#13601 := [lemma #13599]: #13600
+#13863 := [unit-resolution #13601 #6523 #6522]: false
+#13851 := [lemma #13863]: #3235
+#7476 := (uf_1 uf_22 ?x63!14)
+#8409 := (uf_2 #7476)
+#8528 := (up_6 uf_15 #8409)
+#8582 := (iff #8528 #175)
+#8563 := (iff #175 #8528)
+#8410 := (= uf_22 #8409)
+#8416 := (or #8415 #8410)
+#8417 := [quant-inst]: #8416
+#8694 := [unit-resolution #8417 #3993]: #8410
+#10477 := [monotonicity #8694]: #8563
+#10478 := [symm #10477]: #8582
+#7477 := (uf_10 #7476)
+#6712 := (* -1::int #2054)
+#7563 := (+ #6712 #7477)
+#7564 := (+ #177 #7563)
+#7637 := (>= #7564 0::int)
+#7832 := (not #7637)
+#7478 := (* -1::int #7477)
+#7480 := (+ uf_9 #7478)
+#7481 := (<= #7480 0::int)
+#7636 := (or #7481 #7637)
+#7631 := (not #7636)
+#3931 := (not #2658)
+#10371 := [hypothesis]: #2664
+#3932 := (or #2661 #3931)
+#3927 := [def-axiom]: #3932
+#10372 := [unit-resolution #3927 #10371]: #3931
+#7698 := (or #4218 #2658 #7631)
+#7472 := (+ #1268 #7478)
+#7479 := (+ #2054 #7472)
+#7474 := (<= #7479 0::int)
+#7482 := (or #7481 #7474)
+#7280 := (not #7482)
+#7373 := (or #2055 #7280)
+#7694 := (or #4218 #7373)
+#6817 := (iff #7694 #7698)
+#7696 := (or #2658 #7631)
+#7699 := (or #4218 #7696)
+#7724 := (iff #7699 #7698)
+#7720 := [rewrite]: #7724
+#7704 := (iff #7694 #7699)
+#7697 := (iff #7373 #7696)
+#7626 := (iff #7280 #7631)
+#7629 := (iff #7482 #7636)
+#7627 := (iff #7474 #7637)
+#7374 := (+ #2054 #7478)
+#7380 := (+ #1268 #7374)
+#7281 := (<= #7380 0::int)
+#7662 := (iff #7281 #7637)
+#7663 := [rewrite]: #7662
+#7369 := (iff #7474 #7281)
+#7381 := (= #7479 #7380)
+#7498 := [rewrite]: #7381
+#7370 := [monotonicity #7498]: #7369
+#7628 := [trans #7370 #7663]: #7627
+#7630 := [monotonicity #7628]: #7629
+#7632 := [monotonicity #7630]: #7626
+#7695 := [monotonicity #2660 #7632]: #7697
+#7723 := [monotonicity #7695]: #7704
+#7303 := [trans #7723 #7720]: #6817
+#7700 := [quant-inst]: #7694
+#7483 := [mp #7700 #7303]: #7698
+#10375 := [unit-resolution #7483 #10373 #10372]: #7631
+#7871 := (or #7636 #7832)
+#7872 := [def-axiom]: #7871
+#10377 := [unit-resolution #7872 #10375]: #7832
+#8188 := (= uf_22 ?x63!14)
+#8259 := (not #8188)
+#9020 := (or #8259 #7637)
+#7408 := (+ #177 #6712)
+#8885 := (>= #7408 0::int)
+#8884 := (= #177 #2054)
+#8950 := (= #2054 #177)
+#8129 := (= ?x63!14 uf_22)
+#8946 := [hypothesis]: #8188
+#8947 := [symm #8946]: #8129
+#8951 := [monotonicity #8947]: #8950
+#8983 := [symm #8951]: #8884
+#8984 := (not #8884)
+#8985 := (or #8984 #8885)
+#8981 := [th-lemma]: #8985
+#8977 := [unit-resolution #8981 #8983]: #8885
+#10121 := [hypothesis]: #7832
+#8408 := (>= #7477 0::int)
+#8398 := (= #7477 0::int)
+#8399 := (or #8259 #8398)
+#57 := (= #56 0::int)
+#355 := (or #60 #57)
+#4023 := (forall (vars (?x20 T2) (?x21 T2)) (:pat #3981) #355)
+#358 := (forall (vars (?x20 T2) (?x21 T2)) #355)
+#4026 := (iff #358 #4023)
+#4024 := (iff #355 #355)
+#4025 := [refl]: #4024
+#4027 := [quant-intro #4025]: #4026
+#1652 := (~ #358 #358)
+#1691 := (~ #355 #355)
+#1692 := [refl]: #1691
+#1653 := [nnf-pos #1692]: #1652
 #58 := (implies #55 #57)
 #59 := (forall (vars (?x20 T2) (?x21 T2)) #58)
-#359 := (iff #59 #356)
-#332 := (= 0::int #56)
-#343 := (or #60 #332)
-#348 := (forall (vars (?x20 T2) (?x21 T2)) #343)
-#357 := (iff #348 #356)
-#354 := (iff #343 #353)
-#351 := (iff #332 #57)
-#352 := [rewrite]: #351
-#355 := [monotonicity #352]: #354
-#358 := [quant-intro #355]: #357
-#349 := (iff #59 #348)
-#346 := (iff #58 #343)
-#340 := (implies #55 #332)
-#344 := (iff #340 #343)
-#345 := [rewrite]: #344
-#341 := (iff #58 #340)
-#338 := (iff #57 #332)
-#339 := [rewrite]: #338
-#342 := [monotonicity #339]: #341
-#347 := [trans #342 #345]: #346
-#350 := [quant-intro #347]: #349
-#360 := [trans #350 #358]: #359
-#330 := [asserted]: #59
-#361 := [mp #330 #360]: #356
-#1513 := [mp~ #361 #1512]: #356
-#3872 := [mp #1513 #3871]: #3867
-#8154 := (not #3867)
-#8319 := (or #8154 #8159 #8299)
-#8250 := (= #6904 ?x63!14)
-#8305 := (not #8250)
-#8306 := (or #8305 #8299)
-#8324 := (or #8154 #8306)
-#8351 := (iff #8324 #8319)
-#8326 := (or #8154 #8309)
-#8342 := (iff #8326 #8319)
-#8343 := [rewrite]: #8342
-#8336 := (iff #8324 #8326)
-#8317 := (iff #8306 #8309)
-#8307 := (iff #8305 #8159)
-#8252 := (iff #8250 #8074)
-#8253 := [rewrite]: #8252
-#8308 := [monotonicity #8253]: #8307
-#8318 := [monotonicity #8308]: #8317
-#8337 := [monotonicity #8318]: #8336
-#8352 := [trans #8337 #8343]: #8351
-#8325 := [quant-inst]: #8324
-#8384 := [mp #8325 #8352]: #8319
-#9745 := [unit-resolution #8384 #3872]: #8309
-#9746 := [unit-resolution #9745 #9744]: #8159
-#6665 := (or #6768 #7863 #8074)
-#6767 := [def-axiom]: #6665
-#9747 := [unit-resolution #6767 #9746 #9739]: #7863
-#9755 := [mp #9747 #9754]: #9709
-#9710 := (not #9709)
-#9767 := (or #9708 #9710)
-#8353 := (up_6 uf_15 #6904)
-#9763 := (not #8353)
-#9764 := (iff #184 #9763)
-#9761 := (iff #183 #8353)
-#9759 := (iff #8353 #183)
-#9760 := [monotonicity #9758]: #9759
-#9762 := [symm #9760]: #9761
-#9765 := [monotonicity #9762]: #9764
-#3699 := (or #4202 #184)
-#3694 := [def-axiom]: #3699
-#7018 := [unit-resolution #3694 #6215]: #184
-#9766 := [mp #7018 #9765]: #9763
-#3643 := (or #4214 #3958)
-#3667 := [def-axiom]: #3643
-#7019 := [unit-resolution #3667 #6214]: #3958
-#9715 := (or #3963 #8353 #9708 #9710)
-#9711 := (or #8353 #9710 #9708)
-#9716 := (or #3963 #9711)
-#9723 := (iff #9716 #9715)
-#9712 := (or #8353 #9708 #9710)
-#9718 := (or #3963 #9712)
-#9721 := (iff #9718 #9715)
-#9722 := [rewrite]: #9721
-#9719 := (iff #9716 #9718)
-#9713 := (iff #9711 #9712)
-#9714 := [rewrite]: #9713
-#9720 := [monotonicity #9714]: #9719
-#9724 := [trans #9720 #9722]: #9723
-#9717 := [quant-inst]: #9716
-#9725 := [mp #9717 #9724]: #9715
-#9768 := [unit-resolution #9725 #7019 #9766]: #9767
-#9769 := [unit-resolution #9768 #9755]: #9708
-#9770 := [hypothesis]: #7886
-#8219 := (* -1::int #8213)
-#8387 := (+ #7892 #8219)
-#8393 := (>= #8387 0::int)
-#8386 := (= #7892 #8213)
-#9773 := (= #8213 #7892)
-#9771 := (= #8212 #7891)
-#9772 := [monotonicity #9758]: #9771
-#9774 := [monotonicity #9772]: #9773
-#9775 := [symm #9774]: #8386
-#9776 := (not #8386)
-#9777 := (or #9776 #8393)
-#9778 := [th-lemma]: #9777
-#9779 := [unit-resolution #9778 #9775]: #8393
-#8385 := (>= #8213 0::int)
-#9780 := (or #8385 #8269)
-#9781 := [th-lemma]: #9780
-#9782 := [unit-resolution #9781 #9740]: #8385
-#9730 := (+ #1939 #9706)
-#9737 := (<= #9730 0::int)
-#9729 := (= #1939 #9705)
-#9783 := (= #9705 #1939)
-#9784 := [monotonicity #9750]: #9783
-#9785 := [symm #9784]: #9729
-#9786 := (not #9729)
-#9787 := (or #9786 #9737)
-#9788 := [th-lemma]: #9787
-#9789 := [unit-resolution #9788 #9785]: #9737
-#8369 := (* -1::int #8358)
-#9504 := (+ #185 #8369)
-#9300 := (>= #9504 0::int)
-#9503 := (= #185 #8358)
-#9790 := (= #8358 #185)
-#9791 := [monotonicity #9758]: #9790
-#9792 := [symm #9791]: #9503
-#9793 := (not #9503)
-#9794 := (or #9793 #9300)
-#9795 := [th-lemma]: #9794
-#9796 := [unit-resolution #9795 #9792]: #9300
-#9797 := [th-lemma #9796 #9789 #9782 #9779 #9770 #9769]: false
-#9799 := [lemma #9797]: #9798
-#9021 := [unit-resolution #9799 #9017 #9019]: #8269
-#8254 := (or #8074 #8270)
-#369 := (<= #56 0::int)
-#370 := (not #369)
-#373 := (or #55 #370)
-#3873 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #3825) #373)
-#376 := (forall (vars (?x22 T2) (?x23 T2)) #373)
-#3876 := (iff #376 #3873)
-#3874 := (iff #373 #373)
-#3875 := [refl]: #3874
-#3877 := [quant-intro #3875]: #3876
-#1515 := (~ #376 #376)
-#1514 := (~ #373 #373)
-#1552 := [refl]: #1514
-#1516 := [nnf-pos #1552]: #1515
-#61 := (< 0::int #56)
-#62 := (implies #60 #61)
-#63 := (forall (vars (?x22 T2) (?x23 T2)) #62)
-#379 := (iff #63 #376)
-#363 := (or #55 #61)
-#366 := (forall (vars (?x22 T2) (?x23 T2)) #363)
-#377 := (iff #366 #376)
-#374 := (iff #363 #373)
-#371 := (iff #61 #370)
-#372 := [rewrite]: #371
-#375 := [monotonicity #372]: #374
-#378 := [quant-intro #375]: #377
-#367 := (iff #63 #366)
-#364 := (iff #62 #363)
-#365 := [rewrite]: #364
-#368 := [quant-intro #365]: #367
-#380 := [trans #368 #378]: #379
-#362 := [asserted]: #63
-#381 := [mp #362 #380]: #376
-#1553 := [mp~ #381 #1516]: #376
-#3878 := [mp #1553 #3877]: #3873
-#7324 := (not #3873)
-#8256 := (or #7324 #8074 #8270)
-#8251 := (or #8250 #8270)
-#8300 := (or #7324 #8251)
-#8316 := (iff #8300 #8256)
-#8302 := (or #7324 #8254)
-#8320 := (iff #8302 #8256)
-#8321 := [rewrite]: #8320
-#8303 := (iff #8300 #8302)
-#8249 := (iff #8251 #8254)
-#8255 := [monotonicity #8253]: #8249
-#8304 := [monotonicity #8255]: #8303
-#8322 := [trans #8304 #8321]: #8316
-#8301 := [quant-inst]: #8300
-#8323 := [mp #8301 #8322]: #8256
-#9022 := [unit-resolution #8323 #3878]: #8254
-#9013 := [unit-resolution #9022 #9021]: #8074
-#8832 := [trans #9013 #9758]: #8831
-#9155 := [monotonicity #8832]: #9114
-#9158 := [symm #9155]: #9157
-#9154 := (= #1938 #185)
-#5830 := (uf_24 uf_22)
-#9156 := (= #5830 #185)
-#5879 := (= #185 #5830)
-#5833 := (uf_10 #5832)
-#5849 := (>= #5833 0::int)
-#5837 := (* -1::int #5833)
-#5841 := (+ uf_9 #5837)
-#5842 := (<= #5841 0::int)
-#5881 := (or #5842 #5849)
-#6879 := (= #5833 0::int)
-decl uf_2 :: (-> T1 T2)
-#5488 := (uf_1 uf_22 uf_11)
-#8349 := (uf_2 #5488)
-#8700 := (uf_1 #8349 #8349)
-#8701 := (uf_10 #8700)
-#9648 := (= #8701 0::int)
-#9665 := (or #8154 #9648)
-#9649 := (= #8349 #8349)
-#9650 := (not #9649)
-#9651 := (or #9650 #9648)
-#9666 := (or #8154 #9651)
-#9668 := (iff #9666 #9665)
-#9670 := (iff #9665 #9665)
-#9671 := [rewrite]: #9670
-#9663 := (iff #9651 #9648)
-#9658 := (or false #9648)
-#9661 := (iff #9658 #9648)
-#9662 := [rewrite]: #9661
-#9659 := (iff #9651 #9658)
-#9656 := (iff #9650 false)
-#9654 := (iff #9650 #4945)
-#9652 := (iff #9649 true)
-#9653 := [rewrite]: #9652
-#9655 := [monotonicity #9653]: #9654
-#9657 := [trans #9655 #4943]: #9656
-#9660 := [monotonicity #9657]: #9659
-#9664 := [trans #9660 #9662]: #9663
-#9669 := [monotonicity #9664]: #9668
-#9672 := [trans #9669 #9671]: #9668
-#9667 := [quant-inst]: #9666
-#9673 := [mp #9667 #9672]: #9665
-#9675 := [unit-resolution #9673 #3872]: #9648
-#9684 := (= #5833 #8701)
-#9682 := (= #5832 #8700)
-#9680 := (= #8700 #5832)
-#9048 := (= #8349 uf_22)
-#8350 := (= uf_22 #8349)
-#16 := (uf_2 #12)
-#301 := (= #10 #16)
-#3832 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #3825) #301)
-#305 := (forall (vars (?x4 T2) (?x5 T2)) #301)
-#3835 := (iff #305 #3832)
-#3833 := (iff #301 #301)
-#3834 := [refl]: #3833
-#3836 := [quant-intro #3834]: #3835
-#1501 := (~ #305 #305)
-#1535 := (~ #301 #301)
-#1536 := [refl]: #1535
-#1502 := [nnf-pos #1536]: #1501
-#17 := (= #16 #10)
-#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
-#306 := (iff #18 #305)
-#303 := (iff #17 #301)
-#304 := [rewrite]: #303
-#307 := [quant-intro #304]: #306
-#300 := [asserted]: #18
-#310 := [mp #300 #307]: #305
-#1537 := [mp~ #310 #1502]: #305
-#3837 := [mp #1537 #3836]: #3832
-#8156 := (not #3832)
-#8355 := (or #8156 #8350)
-#8356 := [quant-inst]: #8355
-#9047 := [unit-resolution #8356 #3837]: #8350
-#9049 := [symm #9047]: #9048
-#9681 := [monotonicity #9049 #9049]: #9680
-#9683 := [symm #9681]: #9682
-#9685 := [monotonicity #9683]: #9684
-#9686 := [trans #9685 #9675]: #6879
-#5907 := (not #5849)
-#9687 := [hypothesis]: #5907
-#9688 := (not #6879)
-#9689 := (or #9688 #5849)
-#9690 := [th-lemma]: #9689
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-#5887 := (or #5879 #5884)
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-#5896 := (iff #5893 #5890)
-#5897 := [rewrite]: #5896
-#5894 := (iff #5891 #5893)
-#5888 := (iff #5880 #5887)
-#5885 := (iff #5878 #5884)
-#5882 := (iff #5877 #5881)
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-#5846 := (<= #5837 0::int)
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-#5851 := [rewrite]: #5850
-#5847 := (iff #5840 #5846)
-#5844 := (= #5839 #5837)
-#5845 := [rewrite]: #5844
-#5848 := [monotonicity #5845]: #5847
-#5853 := [trans #5848 #5851]: #5852
-#5883 := [monotonicity #5853]: #5882
-#5886 := [monotonicity #5883]: #5885
-#5889 := [monotonicity #5886]: #5888
-#5895 := [monotonicity #5889]: #5894
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-#5892 := [quant-inst]: #5891
-#5900 := [mp #5892 #5899]: #5890
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-#6044 := (>= #6043 0::int)
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+#8400 := (uf_3 #7476)
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+#10112 := (iff #7164 #10074)
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+#6973 := [quant-inst]: #6990
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+#6854 := (or #4243 #4860 #6838)
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+#6855 := (or #4243 #6832)
+#6953 := (iff #6855 #6854)
+#6950 := (or #4243 #6844)
+#6947 := (iff #6950 #6854)
+#6948 := [rewrite]: #6947
+#6951 := (iff #6855 #6950)
+#6845 := (iff #6832 #6844)
+#6846 := [monotonicity #6843]: #6845
+#6952 := [monotonicity #6846]: #6951
+#6954 := [trans #6952 #6948]: #6953
+#6949 := [quant-inst]: #6855
+#6955 := [mp #6949 #6954]: #6854
+#7611 := [unit-resolution #6955 #7743]: #6844
+#7791 := [unit-resolution #7611 #7790]: #4860
+#7824 := [mp #7791 #7818]: #7486
+#7382 := (not #7522)
+#7485 := (or #7382 #7495 #4454)
+#3736 := [def-axiom]: #7485
+#7825 := [unit-resolution #3736 #7824 #7616]: #4454
+#7376 := (or #7539 #7375)
+#7377 := [def-axiom]: #7376
+#7826 := [unit-resolution #7377 #7825]: #7375
+#7614 := (or #7514 #7613)
+#7661 := (or #7051 #7514 #7613)
+#7665 := (or #7051 #7614)
+#7668 := (iff #7665 #7661)
+#7669 := [rewrite]: #7668
+#7667 := [quant-inst]: #7665
+#7670 := [mp #7667 #7669]: #7661
+#7827 := [unit-resolution #7670 #4034]: #7614
+#7828 := [unit-resolution #7827 #7826]: #7613
+#7572 := (or #7701 #7612)
+#7573 := [th-lemma]: #7572
+#7622 := [unit-resolution #7573 #7828]: #7701
+#7623 := [th-lemma #7622 #7762 #7625 #7722]: false
+#7829 := [lemma #7623]: #7751
+#10977 := [unit-resolution #7829 #10825 #10373 #8978 #10380 #10035]: #10976
+#10978 := [unit-resolution #10977 #10830]: #4307
+#3898 := (or #4304 #4298)
+#3899 := [def-axiom]: #3898
+#27197 := [unit-resolution #3899 #10978]: #4298
+#3897 := (or #4301 #3240 #4295)
+#3889 := [def-axiom]: #3897
+#27200 := [unit-resolution #3889 #27197]: #4298
+#27201 := [unit-resolution #27200 #13851]: #4295
+#3811 := (or #4292 #4286)
+#3812 := [def-axiom]: #3811
+#27202 := [unit-resolution #3812 #27201]: #4286
+#27203 := (or #4289 #4283)
+#6911 := (uf_1 uf_22 ?x71!19)
+#6912 := (uf_10 #6911)
+#6865 := (uf_4 uf_14 ?x71!19)
+#6895 := (* -1::int #6865)
+#6930 := (+ #6895 #6912)
+#6931 := (+ #177 #6930)
+#6932 := (>= #6931 0::int)
+#18852 := (not #6932)
+#6916 := (* -1::int #6912)
+#19137 := (+ #2123 #6916)
+#19141 := (>= #19137 0::int)
+#19136 := (= #2123 #6912)
+#19003 := (= #2122 #6911)
+#5904 := (= ?x72!18 uf_22)
+#15400 := (= ?x72!18 #10482)
+#5903 := (up_6 uf_15 ?x72!18)
+#6616 := (not #5903)
+#5874 := (uf_4 uf_14 ?x72!18)
+#6991 := (+ #5874 #6895)
+#6992 := (+ #2123 #6991)
+#6993 := (>= #6992 0::int)
+#19560 := (not #6993)
+#6896 := (+ #2118 #6895)
+#6897 := (<= #6896 0::int)
+#18663 := (or #4234 #6897)
+#6887 := (+ #6865 #2119)
+#6888 := (>= #6887 0::int)
+#18661 := (or #4234 #6888)
+#18693 := (iff #18661 #18663)
+#18718 := (iff #18663 #18663)
+#18749 := [rewrite]: #18718
+#6900 := (iff #6888 #6897)
+#6889 := (+ #2119 #6865)
+#6892 := (>= #6889 0::int)
+#6898 := (iff #6892 #6897)
+#6899 := [rewrite]: #6898
+#6893 := (iff #6888 #6892)
+#6890 := (= #6887 #6889)
+#6891 := [rewrite]: #6890
+#6894 := [monotonicity #6891]: #6893
+#6901 := [trans #6894 #6899]: #6900
+#18748 := [monotonicity #6901]: #18693
+#18750 := [trans #18748 #18749]: #18693
+#18692 := [quant-inst]: #18661
+#18745 := [mp #18692 #18750]: #18663
+#19541 := [unit-resolution #18745 #10835]: #6897
+#3755 := (not #2710)
+#19547 := [hypothesis]: #3286
+#3756 := (or #3281 #3755)
+#3909 := [def-axiom]: #3756
+#19548 := [unit-resolution #3909 #19547]: #3755
+#5966 := (* -1::int #5874)
+#5967 := (+ #2120 #5966)
+#17815 := (>= #5967 0::int)
+#5879 := (= #2120 #5874)
+#3924 := (or #3281 #2130)
+#3753 := [def-axiom]: #3924
+#19549 := [unit-resolution #3753 #19547]: #2130
+#10831 := [unit-resolution #3876 #10830]: #4238
+#16861 := (or #4243 #3266 #5879)
+#5875 := (= #5874 #2120)
+#5878 := (or #3266 #5875)
+#16856 := (or #4243 #5878)
+#17034 := (iff #16856 #16861)
+#5882 := (or #3266 #5879)
+#16863 := (or #4243 #5882)
+#16865 := (iff #16863 #16861)
+#16726 := [rewrite]: #16865
+#16864 := (iff #16856 #16863)
+#5883 := (iff #5878 #5882)
+#5880 := (iff #5875 #5879)
+#5881 := [rewrite]: #5880
+#5884 := [monotonicity #5881]: #5883
+#16860 := [monotonicity #5884]: #16864
+#17035 := [trans #16860 #16726]: #17034
+#16862 := [quant-inst]: #16856
+#17042 := [mp #16862 #17035]: #16861
+#19515 := [unit-resolution #17042 #10831 #19549]: #5879
+#19551 := (not #5879)
+#19558 := (or #19551 #17815)
+#19559 := [th-lemma]: #19558
+#19557 := [unit-resolution #19559 #19515]: #17815
+#19579 := (not #6897)
+#19578 := (not #17815)
+#19580 := (or #19560 #19578 #19579 #2710)
+#19585 := [th-lemma]: #19580
+#19586 := [unit-resolution #19585 #19557 #19548 #19541]: #19560
+#19584 := (or #6616 #6993)
+#3923 := (or #3281 #2129)
+#3917 := [def-axiom]: #3923
+#19575 := [unit-resolution #3917 #19547]: #2129
+#18880 := (or #4104 #2128 #6616 #6993)
+#6994 := (or #6616 #2128 #6993)
+#18885 := (or #4104 #6994)
+#18786 := (iff #18885 #18880)
+#6995 := (or #2128 #6616 #6993)
+#18887 := (or #4104 #6995)
+#18855 := (iff #18887 #18880)
+#18785 := [rewrite]: #18855
+#18888 := (iff #18885 #18887)
+#6996 := (iff #6994 #6995)
+#6997 := [rewrite]: #6996
+#18854 := [monotonicity #6997]: #18888
+#18784 := [trans #18854 #18785]: #18786
+#18886 := [quant-inst]: #18885
+#18853 := [mp #18886 #18784]: #18880
+#18782 := [unit-resolution #18853 #10042 #19575]: #19584
+#19562 := [unit-resolution #18782 #19586]: #6616
+#15415 := (or #5903 #15400)
+#15410 := (up_6 #11444 ?x72!18)
+#15420 := (iff #15410 #15415)
+#17068 := (or #6538 #15420)
+#15401 := (ite #15400 #3681 #5903)
+#15411 := (iff #15410 #15401)
+#17041 := (or #6538 #15411)
+#17071 := (iff #17041 #17068)
+#17075 := (iff #17068 #17068)
+#17033 := [rewrite]: #17075
+#15421 := (iff #15411 #15420)
+#15418 := (iff #15401 #15415)
+#15412 := (ite #15400 true #5903)
+#15416 := (iff #15412 #15415)
+#15417 := [rewrite]: #15416
+#15413 := (iff #15401 #15412)
+#15414 := [monotonicity #3673]: #15413
+#15419 := [trans #15414 #15417]: #15418
+#15422 := [monotonicity #15419]: #15421
+#17069 := [monotonicity #15422]: #17071
+#17076 := [trans #17069 #17033]: #17071
+#17070 := [quant-inst]: #17041
+#17077 := [mp #17070 #17076]: #17068
+#19567 := [unit-resolution #17077 #4007]: #15420
+#19566 := (iff #2130 #15410)
+#19561 := (iff #15410 #2130)
+#19568 := [monotonicity #13524]: #19561
+#19576 := [symm #19568]: #19566
+#19577 := [mp #19549 #19576]: #15410
+#17132 := (not #15410)
+#17134 := (not #15420)
+#17137 := (or #17134 #17132 #15415)
+#17138 := [def-axiom]: #17137
+#19571 := [unit-resolution #17138 #19577 #19567]: #15415
+#17112 := (not #15415)
+#17133 := (or #17112 #5903 #15400)
+#17128 := [def-axiom]: #17133
+#19546 := [unit-resolution #17128 #19571 #19562]: #15400
+#18949 := [trans #19546 #13347]: #5904
+#19152 := [monotonicity #18949]: #19003
+#19266 := [monotonicity #19152]: #19136
+#19321 := (not #19136)
+#18783 := (or #19321 #19141)
+#19327 := [th-lemma]: #18783
+#19424 := [unit-resolution #19327 #19266]: #19141
+#7076 := (uf_2 #2122)
+#7082 := (uf_4 uf_14 #7076)
+#7096 := (* -1::int #7082)
+#7097 := (+ #177 #7096)
+#7098 := (<= #7097 0::int)
+#19129 := (= #177 #7082)
+#19009 := (= #7082 #177)
+#19025 := (= #7076 uf_22)
+#19026 := (= #7076 #10482)
+#19488 := (= #7076 ?x72!18)
+#7077 := (= ?x72!18 #7076)
+#18938 := (or #8415 #7077)
+#18939 := [quant-inst]: #18938
+#19425 := [unit-resolution #18939 #3993]: #7077
+#19489 := [symm #19425]: #19488
+#19027 := [trans #19489 #19546]: #19026
+#19116 := [trans #19027 #13347]: #19025
+#19117 := [monotonicity #19116]: #19009
+#19124 := [symm #19117]: #19129
+#19125 := (not #19129)
+#19118 := (or #19125 #7098)
+#19126 := [th-lemma]: #19118
+#19494 := [unit-resolution #19126 #19124]: #7098
+#18959 := (+ #5874 #7096)
+#18942 := (>= #18959 0::int)
+#18958 := (= #5874 #7082)
+#19503 := [monotonicity #19425]: #18958
+#19714 := (not #18958)
+#19715 := (or #19714 #18942)
+#19716 := [th-lemma]: #19715
+#19717 := [unit-resolution #19716 #19503]: #18942
+#19840 := (not #19141)
+#19719 := (not #18942)
+#19718 := (not #7098)
+#19720 := (or #18852 #19579 #2710 #19718 #19719 #19578 #19840)
+#19721 := [th-lemma]: #19720
+#19722 := [unit-resolution #19721 #19541 #19557 #19548 #19717 #19494 #19424]: #18852
+#6920 := (+ uf_9 #6916)
+#6921 := (<= #6920 0::int)
+#18850 := (not #6921)
+#19841 := (or #18850 #19840 #2128)
+#19836 := [hypothesis]: #2129
+#19837 := [hypothesis]: #6921
+#19838 := [hypothesis]: #19141
+#19839 := [th-lemma #19838 #19837 #19836]: false
+#19842 := [lemma #19839]: #19841
+#19748 := [unit-resolution #19842 #19424 #19575]: #18850
+#6937 := (+ #2119 #6912)
+#6938 := (+ #177 #6937)
+#6941 := (= #6938 0::int)
+#19752 := (not #6941)
+#18700 := (>= #6938 0::int)
+#19749 := (not #18700)
+#19750 := (or #19749 #2710 #19718 #19719 #19578 #19840)
+#19746 := [th-lemma]: #19750
+#19747 := [unit-resolution #19746 #19557 #19548 #19717 #19494 #19424]: #19749
+#19753 := (or #19752 #18700)
+#19754 := [th-lemma]: #19753
+#19751 := [unit-resolution #19754 #19747]: #19752
+#6944 := (or #6921 #6932 #6941)
+#18751 := (or #4226 #6921 #6932 #6941)
+#6913 := (+ #6912 #2119)
+#6914 := (+ #177 #6913)
+#6915 := (= #6914 0::int)
+#6917 := (+ #1268 #6916)
+#6918 := (+ #6865 #6917)
+#6919 := (<= #6918 0::int)
+#6922 := (or #6921 #6919 #6915)
+#18752 := (or #4226 #6922)
+#18697 := (iff #18752 #18751)
+#18811 := (or #4226 #6944)
+#18691 := (iff #18811 #18751)
+#18696 := [rewrite]: #18691
+#18695 := (iff #18752 #18811)
+#6945 := (iff #6922 #6944)
+#6942 := (iff #6915 #6941)
+#6939 := (= #6914 #6938)
+#6940 := [rewrite]: #6939
+#6943 := [monotonicity #6940]: #6942
+#6935 := (iff #6919 #6932)
+#6923 := (+ #6865 #6916)
+#6924 := (+ #1268 #6923)
+#6927 := (<= #6924 0::int)
+#6933 := (iff #6927 #6932)
+#6934 := [rewrite]: #6933
+#6928 := (iff #6919 #6927)
+#6925 := (= #6918 #6924)
+#6926 := [rewrite]: #6925
+#6929 := [monotonicity #6926]: #6928
+#6936 := [trans #6929 #6934]: #6935
+#6946 := [monotonicity #6936 #6943]: #6945
+#18690 := [monotonicity #6946]: #18695
+#18694 := [trans #18690 #18696]: #18697
+#18816 := [quant-inst]: #18752
+#18698 := [mp #18816 #18694]: #18751
+#19755 := [unit-resolution #18698 #10825]: #6944
+#19756 := [unit-resolution #19755 #19751 #19748 #19722]: false
+#19782 := [lemma #19756]: #3281
+#3808 := (or #4289 #3286 #4283)
+#3809 := [def-axiom]: #3808
+#27204 := [unit-resolution #3809 #19782]: #27203
+#27205 := [unit-resolution #27204 #27202]: #4283
+#3913 := (or #4280 #2160)
+#3911 := [def-axiom]: #3913
+#27206 := [unit-resolution #3911 #27205]: #2160
+#5592 := (+ #2147 #5591)
+#18461 := (>= #5592 0::int)
+#5566 := (= #2147 #5561)
+#3757 := (or #4280 #4272)
+#3905 := [def-axiom]: #3757
+#27207 := [unit-resolution #3905 #27205]: #4272
+#18570 := (or #5566 #4277)
+#15060 := (uf_10 #15059)
+#15086 := (* -1::int #15060)
+#11725 := (uf_24 #10482)
+#11723 := (* -1::int #11725)
+#15087 := (+ #11723 #15086)
+#15088 := (+ #2147 #15087)
+#15741 := (>= #15088 0::int)
+#5607 := (uf_1 uf_22 ?x75!20)
+#5608 := (uf_10 #5607)
+#15832 := (+ #5608 #15086)
+#15834 := (>= #15832 0::int)
+#15831 := (= #5608 #15060)
+#18427 := (= #15060 #5608)
+#18425 := (= #15059 #5607)
+#18426 := [monotonicity #13347]: #18425
+#18428 := [monotonicity #18426]: #18427
+#18429 := [symm #18428]: #15831
+#18424 := (not #15831)
+#18430 := (or #18424 #15834)
+#18431 := [th-lemma]: #18430
+#18432 := [unit-resolution #18431 #18429]: #15834
+#11677 := (+ #4526 #11723)
+#8662 := (>= #11677 0::int)
+#8604 := (= #4526 #11725)
+#18433 := (= #11725 #4526)
+#18434 := [monotonicity #13347]: #18433
+#18441 := [symm #18434]: #8604
+#18442 := (not #8604)
+#18440 := (or #18442 #8662)
+#18443 := [th-lemma]: #18440
+#18444 := [unit-resolution #18443 #18441]: #8662
+#5633 := (+ #2148 #5608)
+#5634 := (+ #177 #5633)
+#15560 := (<= #5634 0::int)
+#5637 := (= #5634 0::int)
+#5612 := (* -1::int #5608)
+#5616 := (+ uf_9 #5612)
+#5617 := (<= #5616 0::int)
+#15577 := (not #5617)
+#5626 := (+ #5591 #5608)
+#5627 := (+ #177 #5626)
+#5628 := (>= #5627 0::int)
+#5659 := (or #5617 #5628)
+#5662 := (not #5659)
+#18518 := (not #5566)
+#18445 := [hypothesis]: #18518
+#5665 := (or #5566 #5662)
+#15564 := (or #4218 #5566 #5662)
+#5613 := (+ #1268 #5612)
+#5614 := (+ #5561 #5613)
+#5615 := (<= #5614 0::int)
+#5656 := (or #5617 #5615)
+#5657 := (not #5656)
+#5562 := (= #5561 #2147)
+#5658 := (or #5562 #5657)
+#15565 := (or #4218 #5658)
+#15574 := (iff #15565 #15564)
+#15567 := (or #4218 #5665)
+#15570 := (iff #15567 #15564)
+#15571 := [rewrite]: #15570
+#15568 := (iff #15565 #15567)
+#5666 := (iff #5658 #5665)
+#5663 := (iff #5657 #5662)
+#5660 := (iff #5656 #5659)
+#5631 := (iff #5615 #5628)
+#5619 := (+ #5561 #5612)
+#5620 := (+ #1268 #5619)
+#5623 := (<= #5620 0::int)
+#5629 := (iff #5623 #5628)
+#5630 := [rewrite]: #5629
+#5624 := (iff #5615 #5623)
+#5621 := (= #5614 #5620)
+#5622 := [rewrite]: #5621
+#5625 := [monotonicity #5622]: #5624
+#5632 := [trans #5625 #5630]: #5631
+#5661 := [monotonicity #5632]: #5660
+#5664 := [monotonicity #5661]: #5663
+#5567 := (iff #5562 #5566)
+#5568 := [rewrite]: #5567
+#5667 := [monotonicity #5568 #5664]: #5666
+#15569 := [monotonicity #5667]: #15568
+#15575 := [trans #15569 #15571]: #15574
+#15566 := [quant-inst]: #15565
+#15576 := [mp #15566 #15575]: #15564
+#18449 := [unit-resolution #15576 #10373]: #5665
+#18450 := [unit-resolution #18449 #18445]: #5662
+#15578 := (or #5659 #15577)
+#15608 := [def-axiom]: #15578
+#18453 := [unit-resolution #15608 #18450]: #15577
+#15724 := (not #5628)
+#15725 := (or #5659 #15724)
+#15726 := [def-axiom]: #15725
+#18454 := [unit-resolution #15726 #18450]: #15724
+#5640 := (or #5617 #5628 #5637)
+#15352 := (or #4226 #5617 #5628 #5637)
+#5609 := (+ #5608 #2148)
+#5610 := (+ #177 #5609)
+#5611 := (= #5610 0::int)
+#5618 := (or #5617 #5615 #5611)
+#15353 := (or #4226 #5618)
+#15526 := (iff #15353 #15352)
+#15377 := (or #4226 #5640)
+#15505 := (iff #15377 #15352)
+#15506 := [rewrite]: #15505
+#15408 := (iff #15353 #15377)
+#5641 := (iff #5618 #5640)
+#5638 := (iff #5611 #5637)
+#5635 := (= #5610 #5634)
+#5636 := [rewrite]: #5635
+#5639 := [monotonicity #5636]: #5638
+#5642 := [monotonicity #5632 #5639]: #5641
+#15409 := [monotonicity #5642]: #15408
+#15549 := [trans #15409 #15506]: #15526
+#15376 := [quant-inst]: #15353
+#15550 := [mp #15376 #15549]: #15352
+#18490 := [unit-resolution #15550 #10825]: #5640
+#18491 := [unit-resolution #18490 #18454 #18453]: #5637
+#18492 := (not #5637)
+#18493 := (or #18492 #15560)
+#18494 := [th-lemma]: #18493
+#18495 := [unit-resolution #18494 #18491]: #15560
+#18499 := (not #15834)
+#18498 := (not #4769)
+#18497 := (not #8662)
+#18496 := (not #15560)
+#18500 := (or #15741 #18496 #18497 #18498 #18499)
+#18501 := [th-lemma]: #18500
+#18502 := [unit-resolution #18501 #18495 #18444 #10836 #18432]: #15741
+#15740 := (<= #15088 0::int)
+#15833 := (<= #15832 0::int)
+#18503 := (or #18424 #15833)
+#18504 := [th-lemma]: #18503
+#18505 := [unit-resolution #18504 #18429]: #15833
+#9287 := (<= #4768 0::int)
+#4527 := (= #177 #4526)
+#4776 := (up_6 uf_23 uf_22)
+#3683 := (up_6 #183 uf_22)
+#10821 := (iff #3683 #4776)
+#10819 := (iff #4776 #3683)
+#10820 := [monotonicity #10380]: #10819
+#10822 := [symm #10820]: #10821
 #46 := (:var 0 T5)
 #45 := (:var 2 T4)
 #47 := (uf_7 #45 #10 #46)
-#3860 := (pattern #47)
-#319 := (= uf_8 #46)
+#4016 := (pattern #47)
+#321 := (= uf_8 #46)
 #48 := (up_6 #47 #10)
-#323 := (iff #48 #319)
-#3861 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #3860) #323)
-#326 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #323)
-#3864 := (iff #326 #3861)
-#3862 := (iff #323 #323)
-#3863 := [refl]: #3862
-#3865 := [quant-intro #3863]: #3864
-#1509 := (~ #326 #326)
-#1547 := (~ #323 #323)
-#1548 := [refl]: #1547
-#1510 := [nnf-pos #1548]: #1509
+#325 := (iff #48 #321)
+#4017 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #4016) #325)
+#328 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #325)
+#4020 := (iff #328 #4017)
+#4018 := (iff #325 #325)
+#4019 := [refl]: #4018
+#4021 := [quant-intro #4019]: #4020
+#1650 := (~ #328 #328)
+#1688 := (~ #325 #325)
+#1689 := [refl]: #1688
+#1651 := [nnf-pos #1689]: #1650
 #49 := (= #46 uf_8)
 #50 := (iff #48 #49)
 #51 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #50)
-#327 := (iff #51 #326)
-#324 := (iff #50 #323)
-#321 := (iff #49 #319)
-#322 := [rewrite]: #321
-#325 := [monotonicity #322]: #324
-#328 := [quant-intro #325]: #327
-#318 := [asserted]: #51
-#331 := [mp #318 #328]: #326
-#1549 := [mp~ #331 #1510]: #326
-#3866 := [mp #1549 #3865]: #3861
-#5984 := (not #3861)
-#5985 := (or #5984 #5971)
-#5974 := (iff #5971 #5970)
-#5986 := (or #5984 #5974)
-#5988 := (iff #5986 #5985)
-#5990 := (iff #5985 #5985)
-#5991 := [rewrite]: #5990
-#5982 := (iff #5974 #5971)
-#5977 := (iff #5971 true)
-#5980 := (iff #5977 #5971)
-#5981 := [rewrite]: #5980
-#5978 := (iff #5974 #5977)
-#5979 := [monotonicity #5976]: #5978
-#5983 := [trans #5979 #5981]: #5982
-#5989 := [monotonicity #5983]: #5988
-#5992 := [trans #5989 #5991]: #5988
-#5987 := [quant-inst]: #5986
-#5993 := [mp #5987 #5992]: #5985
-#29383 := [unit-resolution #5993 #3866]: #5971
-#29388 := [mp #29383 #29387]: #8020
-#30588 := [hypothesis]: #4122
-#8023 := (not #8020)
-#23013 := (or #4127 #8023 #10697 #10725)
-#10702 := (+ #2033 #10701)
-#10703 := (+ #8027 #10702)
-#10704 := (= #10703 0::int)
-#10717 := (not #10704)
-#10718 := (+ #8027 #2033)
-#10716 := (>= #10718 0::int)
-#10711 := (or #8023 #10716 #10717)
-#22922 := (or #4127 #10711)
-#22994 := (iff #22922 #23013)
-#10742 := (or #8023 #10697 #10725)
-#22980 := (or #4127 #10742)
-#22955 := (iff #22980 #23013)
-#22999 := [rewrite]: #22955
-#22906 := (iff #22922 #22980)
-#10798 := (iff #10711 #10742)
-#10726 := (iff #10717 #10725)
-#10719 := (iff #10704 #10722)
-#10746 := (+ #8027 #10701)
-#10747 := (+ #2033 #10746)
-#10750 := (= #10747 0::int)
-#10715 := (iff #10750 #10722)
-#10723 := [rewrite]: #10715
-#10730 := (iff #10704 #10750)
-#10748 := (= #10703 #10747)
-#10749 := [rewrite]: #10748
-#10731 := [monotonicity #10749]: #10730
-#10724 := [trans #10731 #10723]: #10719
-#10727 := [monotonicity #10724]: #10726
-#10694 := (iff #10716 #10697)
-#10712 := (+ #2033 #8027)
-#10695 := (>= #10712 0::int)
-#10698 := (iff #10695 #10697)
-#10699 := [rewrite]: #10698
-#10710 := (iff #10716 #10695)
-#10713 := (= #10718 #10712)
-#10714 := [rewrite]: #10713
-#10696 := [monotonicity #10714]: #10710
-#10745 := [trans #10696 #10699]: #10694
-#10796 := [monotonicity #10745 #10727]: #10798
-#21369 := [monotonicity #10796]: #22906
-#17898 := [trans #21369 #22999]: #22994
-#22936 := [quant-inst]: #22922
-#17881 := [mp #22936 #17898]: #23013
-#30590 := [unit-resolution #17881 #30588 #29388]: #30589
-#30591 := [unit-resolution #30590 #30587 #30566]: false
-#30593 := [lemma #30591]: #30592
-#25195 := [unit-resolution #30593 #25346]: #10311
-#35020 := (or #30518 #7777)
-#35021 := [th-lemma]: #35020
-#25253 := [unit-resolution #35021 #25195]: #7777
-#33354 := (not #7777)
-#33351 := (or #33430 #33354 #2044)
-#33352 := [hypothesis]: #11140
-#38137 := [hypothesis]: #2045
-#33346 := [hypothesis]: #7777
-#33353 := [th-lemma #33346 #38137 #33352]: false
-#33355 := [lemma #33353]: #33351
-#25263 := [unit-resolution #33355 #25253 #25348]: #33430
-#25380 := (or #11140 #11168)
-#3758 := (or #4130 #2560)
-#3640 := [def-axiom]: #3758
-#25347 := [unit-resolution #3640 #25286]: #2560
-#10947 := [unit-resolution #3637 #6214]: #3974
-#19098 := (or #3979 #2557 #11140 #11168)
-#11132 := (or #11137 #11135 #11146)
-#11138 := (not #11132)
-#11141 := (or #2046 #11140 #11138)
-#24415 := (or #3979 #11141)
-#24431 := (iff #24415 #19098)
-#11165 := (or #2557 #11140 #11168)
-#24132 := (or #3979 #11165)
-#24604 := (iff #24132 #19098)
-#24448 := [rewrite]: #24604
-#24350 := (iff #24415 #24132)
-#11171 := (iff #11141 #11165)
-#11169 := (iff #11138 #11168)
-#11166 := (iff #11132 #11142)
-#11167 := [rewrite]: #11166
-#11170 := [monotonicity #11167]: #11169
-#11172 := [monotonicity #2559 #11170]: #11171
-#24430 := [monotonicity #11172]: #24350
-#24397 := [trans #24430 #24448]: #24431
-#24390 := [quant-inst]: #24415
-#24306 := [mp #24390 #24397]: #19098
-#25352 := [unit-resolution #24306 #10947 #25347]: #25380
-#25354 := [unit-resolution #25352 #25263]: #11168
-#24534 := (or #11142 #11136)
-#24551 := [def-axiom]: #24534
-#25381 := [unit-resolution #24551 #25354]: #11136
-#31877 := (up_6 uf_23 #11097)
-#31878 := (not #31877)
-#35062 := (or #11142 #31878 #4127)
-#24524 := (not #11146)
-#38825 := [hypothesis]: #11168
-#24595 := (or #11142 #24524)
-#24514 := [def-axiom]: #24595
-#38826 := [unit-resolution #24514 #38825]: #24524
-#31875 := (uf_24 #11097)
-#31894 := (* -1::int #31875)
-#32091 := (+ #2032 #31894)
-#32092 := (<= #32091 0::int)
-#33436 := [hypothesis]: #31877
-#32104 := (+ #11149 #31894)
-#32105 := (+ #2032 #32104)
-#32106 := (= #32105 0::int)
-#35038 := (iff #11134 #32106)
-#35034 := (iff #32106 #11134)
-#35015 := (= #32105 #11133)
-#35029 := (= #11133 #32105)
-#31895 := (+ #11143 #31894)
-#33428 := (<= #31895 0::int)
-#31876 := (= #11143 #31875)
-#31880 := (or #31876 #31878)
-#31423 := (or #4093 #31876 #31878)
-#31879 := (or #31878 #31876)
-#31434 := (or #4093 #31879)
-#31443 := (iff #31434 #31423)
-#31441 := (or #4093 #31880)
-#31431 := (iff #31441 #31423)
-#31440 := [rewrite]: #31431
-#31433 := (iff #31434 #31441)
-#31881 := (iff #31879 #31880)
-#31882 := [rewrite]: #31881
-#31442 := [monotonicity #31882]: #31433
-#31436 := [trans #31442 #31440]: #31443
-#31435 := [quant-inst]: #31434
-#31444 := [mp #31435 #31436]: #31423
-#33899 := [unit-resolution #31444 #13487]: #31880
-#33904 := [unit-resolution #33899 #33436]: #31876
-#23171 := (not #31876)
-#16263 := (or #23171 #33428)
-#31645 := [th-lemma]: #16263
-#31947 := [unit-resolution #31645 #33904]: #33428
-#31896 := (>= #31895 0::int)
-#31469 := (or #4084 #31896)
-#31470 := [quant-inst]: #31469
-#29796 := [unit-resolution #31470 #7037]: #31896
-#10405 := (<= #10404 0::int)
-#25597 := [unit-resolution #30593 #30588]: #10311
-#34536 := (or #30518 #10405)
-#34894 := [th-lemma]: #34536
-#34869 := [unit-resolution #34894 #25597]: #10405
-#35016 := [unit-resolution #35021 #25597]: #7777
-#35035 := [th-lemma #35016 #34869 #29796 #31947]: #35029
-#35036 := [symm #35035]: #35015
-#35037 := [monotonicity #35036]: #35034
-#35039 := [symm #35037]: #35038
-#24631 := (or #11142 #11134)
-#18952 := [def-axiom]: #24631
-#33451 := [unit-resolution #18952 #38825]: #11134
-#35064 := [mp #33451 #35039]: #32106
-#32111 := (not #32106)
-#32114 := (or #31878 #32092 #32111)
-#31607 := (or #4127 #31878 #32092 #32111)
-#32078 := (+ #2033 #11148)
-#32079 := (+ #31875 #32078)
-#32080 := (= #32079 0::int)
-#32081 := (not #32080)
-#32082 := (+ #31875 #2033)
-#32083 := (>= #32082 0::int)
-#32084 := (or #31878 #32083 #32081)
-#31608 := (or #4127 #32084)
-#31636 := (iff #31608 #31607)
-#31565 := (or #4127 #32114)
-#31606 := (iff #31565 #31607)
-#31635 := [rewrite]: #31606
-#31633 := (iff #31608 #31565)
-#32115 := (iff #32084 #32114)
-#32112 := (iff #32081 #32111)
-#32109 := (iff #32080 #32106)
-#32097 := (+ #11148 #31875)
-#32098 := (+ #2033 #32097)
-#32101 := (= #32098 0::int)
-#32107 := (iff #32101 #32106)
-#32108 := [rewrite]: #32107
-#32102 := (iff #32080 #32101)
-#32099 := (= #32079 #32098)
-#32100 := [rewrite]: #32099
-#32103 := [monotonicity #32100]: #32102
-#32110 := [trans #32103 #32108]: #32109
-#32113 := [monotonicity #32110]: #32112
-#32095 := (iff #32083 #32092)
-#32085 := (+ #2033 #31875)
-#32088 := (>= #32085 0::int)
-#32093 := (iff #32088 #32092)
-#32094 := [rewrite]: #32093
-#32089 := (iff #32083 #32088)
-#32086 := (= #32082 #32085)
-#32087 := [rewrite]: #32086
-#32090 := [monotonicity #32087]: #32089
-#32096 := [trans #32090 #32094]: #32095
-#32116 := [monotonicity #32096 #32113]: #32115
-#31634 := [monotonicity #32116]: #31633
-#17991 := [trans #31634 #31635]: #31636
-#31598 := [quant-inst]: #31608
-#23660 := [mp #31598 #17991]: #31607
-#35065 := [unit-resolution #23660 #30588]: #32114
-#35066 := [unit-resolution #35065 #35064 #33436]: #32092
-#35067 := [th-lemma #35016 #29796 #35066 #38826]: false
-#35063 := [lemma #35067]: #35062
-#25287 := [unit-resolution #35063 #25354 #25346]: #31878
-#38842 := (or #31877 #11137)
-#36185 := (up_6 #8048 #11097)
-#38820 := (not #36185)
-#38838 := (iff #31878 #38820)
-#38836 := (iff #31877 #36185)
-#38834 := (iff #36185 #31877)
-#38835 := [monotonicity #8592]: #38834
-#38837 := [symm #38835]: #38836
-#38839 := [monotonicity #38837]: #38838
-#38833 := [hypothesis]: #31878
-#38840 := [mp #38833 #38839]: #38820
-#36187 := (= #6904 #11097)
-#36206 := (or #11136 #36187)
-#36190 := (iff #36185 #36206)
-#38800 := (or #6010 #36190)
-#36182 := (= #11097 #6904)
-#36183 := (ite #36182 #5970 #11136)
-#36186 := (iff #36185 #36183)
-#38801 := (or #6010 #36186)
-#38803 := (iff #38801 #38800)
-#38805 := (iff #38800 #38800)
-#38806 := [rewrite]: #38805
-#36191 := (iff #36186 #36190)
-#36209 := (iff #36183 #36206)
-#36203 := (ite #36187 true #11136)
-#36207 := (iff #36203 #36206)
-#36208 := [rewrite]: #36207
-#36204 := (iff #36183 #36203)
-#36188 := (iff #36182 #36187)
-#36202 := [rewrite]: #36188
-#36205 := [monotonicity #36202 #5976]: #36204
-#36210 := [trans #36205 #36208]: #36209
-#36192 := [monotonicity #36210]: #36191
-#38804 := [monotonicity #36192]: #38803
-#38807 := [trans #38804 #38806]: #38803
-#38802 := [quant-inst]: #38801
-#38808 := [mp #38802 #38807]: #38800
-#38827 := [unit-resolution #38808 #3851]: #36190
-#38817 := (not #36190)
-#38830 := (or #38817 #36185)
-#38828 := [hypothesis]: #11136
-#38809 := (or #36206 #11137)
-#38810 := [def-axiom]: #38809
-#38829 := [unit-resolution #38810 #38828]: #36206
-#38814 := (not #36206)
-#38818 := (or #38817 #36185 #38814)
-#38819 := [def-axiom]: #38818
-#38831 := [unit-resolution #38819 #38829]: #38830
-#38832 := [unit-resolution #38831 #38827]: #36185
-#38841 := [unit-resolution #38832 #38840]: false
-#38843 := [lemma #38841]: #38842
-#25282 := [unit-resolution #38843 #25287 #25381]: false
-#25366 := [lemma #25282]: #4130
-#5604 := (= #108 #219)
-#25448 := (iff #5604 #220)
-#25447 := [commutativity]: #1322
-#25445 := (iff #5604 #708)
-#6918 := [unit-resolution #3676 #6214]: #109
-#25446 := [monotonicity #6918]: #25445
-#25449 := [trans #25446 #25447]: #25448
-#5555 := (uf_10 #5488)
-#5558 := (* -1::int #5555)
-#5571 := (+ uf_9 #5558)
-#5572 := (<= #5571 0::int)
-#5568 := (+ #1235 #5558)
-#5569 := (+ #108 #5568)
-#5570 := (<= #5569 0::int)
-#5606 := (or #5570 #5572)
-#5486 := (+ #108 #1235)
-#7088 := (<= #5486 0::int)
-#3577 := (<= #108 0::int)
-#6919 := (or #3266 #3577)
-#6920 := [th-lemma]: #6919
-#6921 := [unit-resolution #6920 #6918]: #3577
-#5969 := (>= #185 0::int)
-#3681 := (or #4214 #3941)
-#3661 := [def-axiom]: #3681
-#7734 := [unit-resolution #3661 #6214]: #3941
-#5972 := (or #3946 #5969)
-#5973 := [quant-inst]: #5972
-#7735 := [unit-resolution #5973 #7734]: #5969
-#5140 := (not #3577)
-#25432 := (not #5969)
-#25433 := (or #7088 #25432 #5140)
-#25434 := [th-lemma]: #25433
-#25435 := [unit-resolution #25434 #7735 #6921]: #7088
-#8448 := (+ #5555 #5837)
-#8450 := (>= #8448 0::int)
-#8695 := (uf_1 #6904 uf_11)
-#8696 := (uf_10 #8695)
-#9032 := (= #8696 0::int)
-#22996 := (not #9032)
-#15055 := (>= #8696 0::int)
-#22691 := (not #15055)
-#10009 := (not #8450)
-#23412 := [hypothesis]: #10009
-#22699 := (or #8450 #22691)
-#8632 := (* -1::int #8696)
-#15323 := (+ #5555 #8632)
-#15325 := (>= #15323 0::int)
-#9629 := (= #5555 #8696)
-#23372 := (= #8696 #5555)
-#23413 := (= #8695 #5488)
-#23441 := [monotonicity #9758]: #23413
-#23440 := [monotonicity #23441]: #23372
-#23446 := [symm #23440]: #9629
-#23447 := (not #9629)
-#23449 := (or #23447 #15325)
-#23379 := [th-lemma]: #23449
-#22669 := [unit-resolution #23379 #23446]: #15325
-#22695 := (not #15325)
-#23448 := (or #8450 #23491 #22691 #22695)
-#22698 := [th-lemma]: #23448
-#22700 := [unit-resolution #22698 #22669 #22632]: #22699
-#22883 := [unit-resolution #22700 #23412]: #22691
-#23043 := (or #22996 #15055)
-#23450 := [th-lemma]: #23043
-#23034 := [unit-resolution #23450 #22883]: #22996
-#8929 := (= uf_11 #6904)
-#8788 := (<= #8696 0::int)
-#8449 := (<= #8448 0::int)
-#10435 := (or #8450 #8449)
-#10434 := [th-lemma]: #10435
-#23407 := [unit-resolution #10434 #23412]: #8449
-#10438 := (not #8449)
-#23443 := (or #10438 #8788)
-#22944 := (or #10438 #23491 #8788 #22695)
-#23411 := [th-lemma]: #22944
-#23409 := [unit-resolution #23411 #22669 #22632]: #23443
-#23442 := [unit-resolution #23409 #23407]: #8788
-#8794 := (not #8788)
-#8933 := (or #8794 #8929)
-#12371 := (or #7324 #8794 #8929)
-#8795 := (= #6904 uf_11)
-#8796 := (or #8795 #8794)
-#12524 := (or #7324 #8796)
-#13058 := (iff #12524 #12371)
-#12579 := (or #7324 #8933)
-#13029 := (iff #12579 #12371)
-#13057 := [rewrite]: #13029
-#12620 := (iff #12524 #12579)
-#8965 := (iff #8796 #8933)
-#8931 := (or #8929 #8794)
-#8934 := (iff #8931 #8933)
-#8964 := [rewrite]: #8934
-#8932 := (iff #8796 #8931)
-#8924 := (iff #8795 #8929)
-#8930 := [rewrite]: #8924
-#8928 := [monotonicity #8930]: #8932
-#8966 := [trans #8928 #8964]: #8965
-#12543 := [monotonicity #8966]: #12620
-#13028 := [trans #12543 #13057]: #13058
-#12621 := [quant-inst]: #12524
-#13055 := [mp #12621 #13028]: #12371
-#23444 := [unit-resolution #13055 #3878]: #8933
-#20374 := [unit-resolution #23444 #23442]: #8929
-#9008 := (not #8929)
-#9009 := (or #9008 #9032)
-#12859 := (or #8154 #9008 #9032)
-#9033 := (not #8795)
-#9007 := (or #9033 #9032)
-#13122 := (or #8154 #9007)
-#13134 := (iff #13122 #12859)
-#12878 := (or #8154 #9009)
-#13147 := (iff #12878 #12859)
-#13150 := [rewrite]: #13147
-#13131 := (iff #13122 #12878)
-#9010 := (iff #9007 #9009)
-#9006 := (iff #9033 #9008)
-#9031 := [monotonicity #8930]: #9006
-#9011 := [monotonicity #9031]: #9010
-#13120 := [monotonicity #9011]: #13131
-#13149 := [trans #13120 #13150]: #13134
-#13056 := [quant-inst]: #13122
-#13151 := [mp #13056 #13149]: #12859
-#23445 := [unit-resolution #13151 #3872]: #9009
-#11092 := [unit-resolution #23445 #20374 #23034]: false
-#17852 := [lemma #11092]: #8450
-#25436 := (not #7088)
-#25439 := (or #5570 #10009 #25436)
-#25437 := (or #5570 #5907 #10009 #25436)
-#25438 := [th-lemma]: #25437
-#25440 := [unit-resolution #25438 #9692]: #25439
-#25441 := [unit-resolution #25440 #17852 #25435]: #5570
-#5629 := (not #5570)
-#5630 := (or #5606 #5629)
-#5631 := [def-axiom]: #5630
-#25442 := [unit-resolution #5631 #25441]: #5606
-#5609 := (not #5606)
-#5612 := (or #5604 #5609)
-#5615 := (or #4076 #5604 #5609)
-#5602 := (or #5572 #5570)
-#5603 := (not #5602)
-#5605 := (or #5604 #5603)
-#5616 := (or #4076 #5605)
-#5623 := (iff #5616 #5615)
-#5618 := (or #4076 #5612)
-#5621 := (iff #5618 #5615)
-#5622 := [rewrite]: #5621
-#5619 := (iff #5616 #5618)
-#5613 := (iff #5605 #5612)
-#5610 := (iff #5603 #5609)
-#5607 := (iff #5602 #5606)
-#5608 := [rewrite]: #5607
-#5611 := [monotonicity #5608]: #5610
-#5614 := [monotonicity #5611]: #5613
-#5620 := [monotonicity #5614]: #5619
-#5624 := [trans #5620 #5622]: #5623
-#5617 := [quant-inst]: #5616
-#5625 := [mp #5617 #5624]: #5615
-#25443 := [unit-resolution #5625 #6216]: #5612
-#25444 := [unit-resolution #25443 #25442]: #5604
-#25450 := [mp #25444 #25449]: #220
-#3717 := (or #4178 #4172)
-#3721 := [def-axiom]: #3717
-#13489 := [unit-resolution #3721 #13486]: #4172
-#3716 := (or #4175 #1324 #4169)
-#3718 := [def-axiom]: #3716
-#25451 := [unit-resolution #3718 #13489]: #4172
-#25452 := [unit-resolution #25451 #25450]: #4169
-#3723 := (or #4166 #4160)
-#3725 := [def-axiom]: #3723
-#25453 := [unit-resolution #3725 #25452]: #4160
-#25454 := (or #4163 #4157)
-#8769 := (or #4093 #1963)
-#8407 := (uf_4 uf_14 ?x65!15)
-#8699 := (>= #8407 0::int)
-#8702 := (or #3946 #8699)
-#8703 := [quant-inst]: #8702
-#8764 := [unit-resolution #8703 #7734]: #8699
-#9046 := [hypothesis]: #1964
-#8438 := (* -1::int #8407)
-#8439 := (+ #1962 #8438)
-#8763 := (>= #8439 0::int)
-#8412 := (= #1962 #8407)
-#9060 := [hypothesis]: #4088
-#9082 := (or #8412 #1963 #4093)
-#8454 := (uf_1 uf_22 ?x65!15)
-#8455 := (uf_10 #8454)
-#8429 := (* -1::int #1962)
-#8511 := (+ #8429 #8455)
-#8512 := (+ #185 #8511)
-#8532 := (<= #8512 0::int)
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-#18093 := (= #18068 #18092)
-#18094 := [rewrite]: #18093
-#18097 := [monotonicity #18094]: #18096
-#18089 := (iff #18073 #18086)
-#18077 := (+ #11646 #18070)
-#18078 := (+ #1235 #18077)
-#18081 := (<= #18078 0::int)
-#18087 := (iff #18081 #18086)
-#18088 := [rewrite]: #18087
-#18082 := (iff #18073 #18081)
-#18079 := (= #18072 #18078)
-#18080 := [rewrite]: #18079
-#18083 := [monotonicity #18080]: #18082
-#18090 := [trans #18083 #18088]: #18089
-#18100 := [monotonicity #18090 #18097]: #18099
-#17346 := [monotonicity #18100]: #17363
-#17364 := [trans #17346 #17359]: #17345
-#17381 := [quant-inst]: #17396
-#17317 := [mp #17381 #17364]: #17115
-#26504 := [unit-resolution #17317 #6220 #26503 #26498 #26497]: false
-#26506 := [lemma #26504]: #26505
-#25751 := [unit-resolution #26506 #25750 #26498 #26503]: false
-#25739 := [lemma #25751]: #25738
-#30267 := [unit-resolution #25739 #30266 #30169]: #18113
-#25874 := (uf_2 #25777)
-#25875 := (= #23089 #25874)
-#28275 := (not #25875)
-#28360 := [hypothesis]: #28275
-#28362 := (or #8156 #25875)
-#28363 := [quant-inst]: #28362
-#28361 := [unit-resolution #28363 #3837 #28360]: false
-#28364 := [lemma #28361]: #25875
-#28276 := (or #28275 #17229)
-#28264 := (= #11552 #10897)
-#28260 := (= #11547 #23089)
-#28258 := (= #25874 #23089)
-#28251 := [hypothesis]: #25875
-#28259 := [symm #28251]: #28258
-#28256 := (= #11547 #25874)
-#28257 := [monotonicity #27568]: #28256
-#28261 := [trans #28257 #28259]: #28260
-#28263 := [trans #28261 #26801]: #28262
-#28265 := [monotonicity #28263]: #28264
-#28273 := [symm #28265]: #17229
-#28210 := [hypothesis]: #22790
-#28274 := [unit-resolution #28210 #28273]: false
-#28277 := [lemma #28274]: #28276
-#26555 := [unit-resolution #28277 #28364]: #17229
-#30245 := [unit-resolution #22771 #26555]: #17121
-#18258 := (+ #2003 #18049)
-#18261 := (<= #18258 0::int)
-#17226 := (= #2003 #18030)
-#27788 := [monotonicity #27574]: #17226
-#21452 := (not #17226)
-#27567 := [hypothesis]: #21452
-#27789 := [unit-resolution #27567 #27788]: false
-#27872 := [lemma #27789]: #17226
-#22901 := (or #21452 #18261)
-#22182 := [th-lemma]: #22901
-#30269 := [unit-resolution #22182 #27872]: #18261
-[th-lemma #30269 #30245 #30138 #30133 #30156 #30210 #30267]: false
+#329 := (iff #51 #328)
+#326 := (iff #50 #325)
+#323 := (iff #49 #321)
+#324 := [rewrite]: #323
+#327 := [monotonicity #324]: #326
+#330 := [quant-intro #327]: #329
+#320 := [asserted]: #51
+#333 := [mp #320 #330]: #328
+#1690 := [mp~ #333 #1651]: #328
+#4022 := [mp #1690 #4021]: #4017
+#8841 := (not #4017)
+#8843 := (or #8841 #3683)
+#3682 := (iff #3683 #3681)
+#8837 := (or #8841 #3682)
+#8844 := (iff #8837 #8843)
+#8846 := (iff #8843 #8843)
+#8847 := [rewrite]: #8846
+#3668 := (iff #3682 #3683)
+#3674 := (iff #3683 true)
+#3676 := (iff #3674 #3683)
+#3677 := [rewrite]: #3676
+#3675 := (iff #3682 #3674)
+#3667 := [monotonicity #3673]: #3675
+#3678 := [trans #3667 #3677]: #3668
+#8845 := [monotonicity #3678]: #8844
+#8842 := [trans #8845 #8847]: #8844
+#8838 := [quant-inst]: #8837
+#9410 := [mp #8838 #8842]: #8843
+#10818 := [unit-resolution #9410 #4022]: #3683
+#10823 := [mp #10818 #10822]: #4776
+#4777 := (not #4776)
+#4781 := (or #4527 #4777)
+#10191 := (or #4243 #4527 #4777)
+#4780 := (or #4777 #4527)
+#10192 := (or #4243 #4780)
+#10250 := (iff #10192 #10191)
+#10193 := (or #4243 #4781)
+#10248 := (iff #10193 #10191)
+#10249 := [rewrite]: #10248
+#10194 := (iff #10192 #10193)
+#4782 := (iff #4780 #4781)
+#4783 := [rewrite]: #4782
+#10247 := [monotonicity #4783]: #10194
+#10252 := [trans #10247 #10249]: #10250
+#10190 := [quant-inst]: #10192
+#10253 := [mp #10190 #10252]: #10191
+#10832 := [unit-resolution #10253 #10831]: #4781
+#10833 := [unit-resolution #10832 #10823]: #4527
+#9343 := (not #4527)
+#9344 := (or #9343 #9287)
+#9345 := [th-lemma]: #9344
+#10834 := [unit-resolution #9345 #10833]: #9287
+#11672 := (<= #11677 0::int)
+#18506 := (or #18442 #11672)
+#18507 := [th-lemma]: #18506
+#18508 := [unit-resolution #18507 #18441]: #11672
+#15561 := (>= #5634 0::int)
+#18482 := (or #18492 #15561)
+#18483 := [th-lemma]: #18482
+#18481 := [unit-resolution #18483 #18491]: #15561
+#18487 := (not #15833)
+#18486 := (not #9287)
+#18485 := (not #11672)
+#18484 := (not #15561)
+#18488 := (or #15740 #18484 #18485 #18486 #18487)
+#18489 := [th-lemma]: #18488
+#17776 := [unit-resolution #18489 #18481 #18508 #10834 #18505]: #15740
+#15089 := (= #15088 0::int)
+#15094 := (not #15089)
+#14996 := (+ #2147 #11723)
+#15074 := (<= #14996 0::int)
+#18551 := (not #15074)
+#17160 := (uf_3 #5828)
+#17947 := (uf_1 #10482 #17160)
+#17948 := (uf_10 #17947)
+#17950 := (* -1::int #17948)
+#18119 := (+ #5608 #17950)
+#18161 := (>= #18119 0::int)
+#18116 := (= #5608 #17948)
+#17971 := (= #17948 #5608)
+#17965 := (= #17947 #5607)
+#17826 := (= #17160 ?x75!20)
+#17161 := (= ?x75!20 #17160)
+#17164 := (or #7756 #17161)
+#17165 := [quant-inst]: #17164
+#17777 := [unit-resolution #17165 #3987]: #17161
+#17827 := [symm #17777]: #17826
+#17970 := [monotonicity #13347 #17827]: #17965
+#17974 := [monotonicity #17970]: #17971
+#17975 := [symm #17974]: #18116
+#17976 := (not #18116)
+#17979 := (or #17976 #18161)
+#18037 := [th-lemma]: #17979
+#18038 := [unit-resolution #18037 #17975]: #18161
+#18048 := (<= #17948 0::int)
+#18049 := (not #18048)
+#18467 := (= #10482 #17160)
+#17898 := (not #18467)
+#18462 := (up_6 uf_15 #17160)
+#18473 := (or #18462 #18467)
+#17926 := (not #18473)
+#18465 := (up_6 #11444 #17160)
+#18478 := (iff #18465 #18473)
+#17873 := (or #6538 #18478)
+#18463 := (= #17160 #10482)
+#18464 := (ite #18463 #3681 #18462)
+#18466 := (iff #18465 #18464)
+#17874 := (or #6538 #18466)
+#17876 := (iff #17874 #17873)
+#17892 := (iff #17873 #17873)
+#17893 := [rewrite]: #17892
+#18479 := (iff #18466 #18478)
+#18476 := (iff #18464 #18473)
+#18470 := (ite #18467 true #18462)
+#18474 := (iff #18470 #18473)
+#18475 := [rewrite]: #18474
+#18471 := (iff #18464 #18470)
+#18468 := (iff #18463 #18467)
+#18469 := [rewrite]: #18468
+#18472 := [monotonicity #18469 #3673]: #18471
+#18477 := [trans #18472 #18475]: #18476
+#18480 := [monotonicity #18477]: #18479
+#17891 := [monotonicity #18480]: #17876
+#17894 := [trans #17891 #17893]: #17876
+#17875 := [quant-inst]: #17874
+#17895 := [mp #17875 #17894]: #17873
+#18337 := [unit-resolution #17895 #4007]: #18478
+#17931 := (not #18465)
+#4948 := (up_6 uf_23 ?x75!20)
+#4949 := (not #4948)
+#18452 := (iff #4949 #17931)
+#18352 := (iff #4948 #18465)
+#18341 := (iff #18465 #4948)
+#18342 := [monotonicity #13524 #17827]: #18341
+#18451 := [symm #18342]: #18352
+#18455 := [monotonicity #18451]: #18452
+#5569 := (or #4949 #5566)
+#14917 := (or #4243 #4949 #5566)
+#5565 := (or #4949 #5562)
+#14918 := (or #4243 #5565)
+#15338 := (iff #14918 #14917)
+#15153 := (or #4243 #5569)
+#15201 := (iff #15153 #14917)
+#15202 := [rewrite]: #15201
+#15162 := (iff #14918 #15153)
+#5570 := (iff #5565 #5569)
+#5571 := [monotonicity #5568]: #5570
+#15163 := [monotonicity #5571]: #15162
+#15339 := [trans #15163 #15202]: #15338
+#15152 := [quant-inst]: #14918
+#15340 := [mp #15152 #15339]: #14917
+#18516 := [unit-resolution #15340 #10831]: #5569
+#18338 := [unit-resolution #18516 #18445]: #4949
+#18456 := [mp #18338 #18455]: #17931
+#17929 := (not #18478)
+#17930 := (or #17929 #18465 #17926)
+#17925 := [def-axiom]: #17930
+#18457 := [unit-resolution #17925 #18456 #18337]: #17926
+#17899 := (or #18473 #17898)
+#17900 := [def-axiom]: #17899
+#18460 := [unit-resolution #17900 #18457]: #17898
+#18064 := (or #18049 #18467)
+#18066 := (or #7051 #18049 #18467)
+#18063 := (or #18467 #18049)
+#18067 := (or #7051 #18063)
+#18081 := (iff #18067 #18066)
+#18073 := (or #7051 #18064)
+#18075 := (iff #18073 #18066)
+#18076 := [rewrite]: #18075
+#18071 := (iff #18067 #18073)
+#18062 := (iff #18063 #18064)
+#18065 := [rewrite]: #18062
+#18074 := [monotonicity #18065]: #18071
+#18082 := [trans #18074 #18076]: #18081
+#18072 := [quant-inst]: #18067
+#18080 := [mp #18072 #18082]: #18066
+#18549 := [unit-resolution #18080 #4034]: #18064
+#18550 := [unit-resolution #18549 #18460]: #18049
+#18552 := (not #18161)
+#18553 := (or #18551 #18496 #18497 #18498 #18048 #18552)
+#18554 := [th-lemma]: #18553
+#18555 := [unit-resolution #18554 #18495 #18444 #10836 #18550 #18038]: #18551
+#18562 := (or #15074 #15094)
+#11728 := (up_6 uf_23 #10482)
+#18558 := (iff #3683 #11728)
+#18556 := (iff #11728 #3683)
+#18557 := [monotonicity #10380 #13347]: #18556
+#18559 := [symm #18557]: #18558
+#18560 := [mp #10818 #18559]: #11728
+#18561 := [hypothesis]: #4272
+#11732 := (not #11728)
+#15729 := (or #4277 #11732 #15074 #15094)
+#15061 := (+ #2148 #15060)
+#15062 := (+ #11725 #15061)
+#15063 := (= #15062 0::int)
+#15064 := (not #15063)
+#15065 := (+ #11725 #2148)
+#15066 := (>= #15065 0::int)
+#15067 := (or #11732 #15066 #15064)
+#15730 := (or #4277 #15067)
+#15737 := (iff #15730 #15729)
+#15097 := (or #11732 #15074 #15094)
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+#15735 := (iff #15732 #15729)
+#15736 := [rewrite]: #15735
+#15733 := (iff #15730 #15732)
+#15098 := (iff #15067 #15097)
+#15095 := (iff #15064 #15094)
+#15092 := (iff #15063 #15089)
+#15079 := (+ #11725 #15060)
+#15080 := (+ #2148 #15079)
+#15083 := (= #15080 0::int)
+#15090 := (iff #15083 #15089)
+#15091 := [rewrite]: #15090
+#15084 := (iff #15063 #15083)
+#15081 := (= #15062 #15080)
+#15082 := [rewrite]: #15081
+#15085 := [monotonicity #15082]: #15084
+#15093 := [trans #15085 #15091]: #15092
+#15096 := [monotonicity #15093]: #15095
+#15077 := (iff #15066 #15074)
+#15068 := (+ #2148 #11725)
+#15071 := (>= #15068 0::int)
+#15075 := (iff #15071 #15074)
+#15076 := [rewrite]: #15075
+#15072 := (iff #15066 #15071)
+#15069 := (= #15065 #15068)
+#15070 := [rewrite]: #15069
+#15073 := [monotonicity #15070]: #15072
+#15078 := [trans #15073 #15076]: #15077
+#15099 := [monotonicity #15078 #15096]: #15098
+#15734 := [monotonicity #15099]: #15733
+#15738 := [trans #15734 #15736]: #15737
+#15731 := [quant-inst]: #15730
+#15739 := [mp #15731 #15738]: #15729
+#18563 := [unit-resolution #15739 #18561 #18560]: #18562
+#18564 := [unit-resolution #18563 #18555]: #15094
+#18566 := (not #15741)
+#18565 := (not #15740)
+#18567 := (or #15089 #18565 #18566)
+#18568 := [th-lemma]: #18567
+#18569 := [unit-resolution #18568 #18564 #17776 #18502]: false
+#18571 := [lemma #18569]: #18570
+#27208 := [unit-resolution #18571 #27207]: #5566
+#18519 := (or #18518 #18461)
+#18520 := [th-lemma]: #18519
+#27209 := [unit-resolution #18520 #27208]: #18461
+#22580 := (not #18461)
+#22586 := (or #22585 #22580 #2159)
+#22581 := [hypothesis]: #2160
+#22582 := [hypothesis]: #18461
+#22583 := [hypothesis]: #5840
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+#22587 := [lemma #22584]: #22586
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+#3914 := (or #4280 #2724)
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+#27211 := [unit-resolution #3796 #27205]: #2724
+#16286 := (or #4129 #2721 #5840 #5845)
+#5837 := (or #5836 #5834 #5827)
+#5838 := (not #5837)
+#5841 := (or #2161 #5840 #5838)
+#16309 := (or #4129 #5841)
+#16464 := (iff #16309 #16286)
+#5848 := (or #2721 #5840 #5845)
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+#16414 := (iff #16025 #16286)
+#16302 := [rewrite]: #16414
+#16445 := (iff #16309 #16025)
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+#5846 := (iff #5838 #5845)
+#5843 := (iff #5837 #5842)
+#5844 := [rewrite]: #5843
+#5847 := [monotonicity #5844]: #5846
+#5850 := [monotonicity #2723 #5847]: #5849
+#16461 := [monotonicity #5850]: #16445
+#16413 := [trans #16461 #16302]: #16464
+#16307 := [quant-inst]: #16309
+#16444 := [mp #16307 #16413]: #16286
+#27212 := [unit-resolution #16444 #10442 #27211 #27210]: #5845
+#16693 := (or #5842 #5835)
+#16554 := [def-axiom]: #16693
+#27213 := [unit-resolution #16554 #27212]: #5835
+#27221 := [mp #27213 #27220]: #25893
+#25894 := (not #25893)
+#27098 := (or #27081 #25894)
+#27099 := [def-axiom]: #27098
+#27222 := [unit-resolution #27099 #27221]: #27081
+#27103 := (not #27081)
+#27107 := (or #27106 #27073 #27103)
+#27108 := [def-axiom]: #27107
+#27224 := [unit-resolution #27108 #27222]: #27223
+#27225 := [unit-resolution #27224 #27196]: #27073
+#27234 := [unit-resolution #27225 #27233]: false
+#27235 := [lemma #27234]: #16800
+#16798 := (uf_24 #5823)
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+#22559 := (not #17011)
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+#16589 := (or #5842 #15902)
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+#22552 := [unit-resolution #16412 #27212]: #15902
+#16818 := (+ #5824 #16817)
+#16819 := (>= #16818 0::int)
+#16900 := (or #4234 #16819)
+#15938 := [quant-inst]: #16900
+#22558 := [unit-resolution #15938 #10835]: #16819
+#22544 := (not #16819)
+#23021 := (or #22559 #5827 #22580 #22544)
+#22554 := [th-lemma]: #23021
+#18055 := [unit-resolution #22554 #27209 #22558 #22552]: #22559
+#16977 := (+ #5830 #16817)
+#16978 := (+ #2147 #16977)
+#17021 := (= #16978 0::int)
+#19944 := (>= #16978 0::int)
+#9360 := (>= #5832 0::int)
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+#16042 := [unit-resolution #16618 #27212]: #5833
+#21361 := (or #5834 #9360)
+#21365 := [th-lemma]: #21361
+#22952 := [unit-resolution #21365 #16042]: #9360
+#22974 := (not #9360)
+#23033 := (or #19944 #22974 #22580 #22544)
+#22976 := [th-lemma]: #23033
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+#16799 := (= #5824 #16798)
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+#17444 := [monotonicity #16805]: #19064
+#19082 := [trans #17444 #19070]: #15937
+#19040 := [quant-inst]: #18032
+#17767 := [mp #19040 #19082]: #17738
+#18817 := [unit-resolution #17767 #10831]: #16803
+#23050 := [unit-resolution #18817 #27235]: #16799
+#23024 := (not #16799)
+#23019 := (or #23024 #22549)
+#23047 := [th-lemma]: #23019
+#23015 := [unit-resolution #23047 #23050]: #22549
+#5593 := (<= #5592 0::int)
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+#20442 := [hypothesis]: #20441
+#20353 := (or #4234 #5593)
+#5583 := (+ #5561 #2148)
+#5584 := (>= #5583 0::int)
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+#20377 := (iff #20370 #20353)
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+#5596 := (iff #5584 #5593)
+#5585 := (+ #2148 #5561)
+#5588 := (>= #5585 0::int)
+#5594 := (iff #5588 #5593)
+#5595 := [rewrite]: #5594
+#5589 := (iff #5584 #5588)
+#5586 := (= #5583 #5585)
+#5587 := [rewrite]: #5586
+#5590 := [monotonicity #5587]: #5589
+#5597 := [trans #5590 #5595]: #5596
+#20383 := [monotonicity #5597]: #20377
+#20388 := [trans #20383 #20387]: #20377
+#20376 := [quant-inst]: #20370
+#20438 := [mp #20376 #20388]: #20353
+#20437 := [unit-resolution #20438 #10835 #20442]: false
+#20443 := [lemma #20437]: #5593
+#15900 := (<= #5832 0::int)
+#23077 := (or #5834 #15900)
+#23040 := [th-lemma]: #23077
+#23022 := [unit-resolution #23040 #16042]: #15900
+#23053 := (not #22549)
+#22936 := (not #15900)
+#23179 := (or #16979 #22936 #20441 #23053)
+#23061 := [th-lemma]: #23179
+#23075 := [unit-resolution #23061 #23022 #20443 #23015]: #16979
+#23181 := (not #19944)
+#23180 := (not #16979)
+#23059 := (or #17021 #23180 #23181)
+#23057 := [th-lemma]: #23059
+#23182 := [unit-resolution #23057 #23075 #22955]: #17021
+#17026 := (not #17021)
+#17029 := (or #16801 #17011 #17026)
+#19879 := (or #4277 #16801 #17011 #17026)
+#16998 := (+ #2148 #5829)
+#16999 := (+ #16798 #16998)
+#17000 := (= #16999 0::int)
+#17001 := (not #17000)
+#16962 := (+ #16798 #2148)
+#17002 := (>= #16962 0::int)
+#17003 := (or #16801 #17002 #17001)
+#19880 := (or #4277 #17003)
+#19850 := (iff #19880 #19879)
+#19873 := (or #4277 #17029)
+#19915 := (iff #19873 #19879)
+#19874 := [rewrite]: #19915
+#20138 := (iff #19880 #19873)
+#17030 := (iff #17003 #17029)
+#17027 := (iff #17001 #17026)
+#17024 := (iff #17000 #17021)
+#16970 := (+ #5829 #16798)
+#16971 := (+ #2148 #16970)
+#17018 := (= #16971 0::int)
+#17022 := (iff #17018 #17021)
+#17023 := [rewrite]: #17022
+#17019 := (iff #17000 #17018)
+#17016 := (= #16999 #16971)
+#17017 := [rewrite]: #17016
+#17020 := [monotonicity #17017]: #17019
+#17025 := [trans #17020 #17023]: #17024
+#17028 := [monotonicity #17025]: #17027
+#17014 := (iff #17002 #17011)
+#17004 := (+ #2148 #16798)
+#17007 := (>= #17004 0::int)
+#17012 := (iff #17007 #17011)
+#17013 := [rewrite]: #17012
+#17008 := (iff #17002 #17007)
+#17005 := (= #16962 #17004)
+#17006 := [rewrite]: #17005
+#17009 := [monotonicity #17006]: #17008
+#17015 := [trans #17009 #17013]: #17014
+#17031 := [monotonicity #17015 #17028]: #17030
+#20025 := [monotonicity #17031]: #20138
+#20123 := [trans #20025 #19874]: #19850
+#19878 := [quant-inst]: #19880
+#19916 := [mp #19878 #20123]: #19879
+#23081 := [unit-resolution #19916 #27207]: #17029
+[unit-resolution #23081 #23182 #18055 #27235]: false
 unsat

--- a/src/HOL/Boogie/Examples/cert/Boogie_max	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/Boogie_max	Wed Dec 23 17:37:42 2009 +0100
@@ -14,6 +14,6 @@
   (uf_3 Int Int)
   (uf_1 Int)
  )
-:assumption (not (implies (and true (and (< 0 uf_1) (and (= uf_2 (uf_3 0)) (and (<= 0 0) (and (<= 0 0) (and (<= 1 1) (<= 1 1))))))) (and (forall (?x1 Int) (implies (and (<= 0 ?x1) (< ?x1 1)) (<= (uf_3 ?x1) uf_2))) (implies (forall (?x2 Int) (implies (and (<= 0 ?x2) (< ?x2 1)) (<= (uf_3 ?x2) uf_2))) (and (= (uf_3 0) uf_2) (implies (and (= (uf_3 0) uf_2) (and true (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (forall (?x3 Int) (implies (and (<= 0 ?x3) (< ?x3 uf_5)) (<= (uf_3 ?x3) uf_6))) (and (= (uf_3 uf_4) uf_6) (and (<= 0 uf_4) (<= 1 uf_5))))))) (and (implies (and true (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (<= uf_1 uf_5) (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (= uf_7 uf_4) (and (= uf_8 uf_6) (= uf_9 uf_5))))))) (and (exists (?x4 Int) (implies (and (<= 0 ?x4) (< ?x4 uf_1)) (= (uf_3 ?x4) uf_8))) (implies (exists (?x5 Int) (implies (and (<= 0 ?x5) (< ?x5 uf_1)) (= (uf_3 ?x5) uf_8))) (forall (?x6 Int) (implies (and (<= 0 ?x6) (< ?x6 uf_1)) (<= (uf_3 ?x6) uf_8)))))) (implies (and true (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (< uf_5 uf_1) (and (<= 0 uf_4) (<= 1 uf_5))))) (and (implies (and true (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (< uf_6 (uf_3 uf_5)) (and (= uf_10 (uf_3 uf_5)) (and (and (<= 1 uf_5) (<= 1 uf_5)) (and (= uf_11 uf_5) (and (= uf_12 uf_10) (and true (and (and (<= 0 uf_11) (<= 1 uf_5)) (and (= uf_13 (+ uf_5 1)) (and (<= 0 uf_11) (<= 2 uf_13)))))))))))) (and (forall (?x7 Int) (implies (and (<= 0 ?x7) (< ?x7 uf_13)) (<= (uf_3 ?x7) uf_12))) (implies (forall (?x8 Int) (implies (and (<= 0 ?x8) (< ?x8 uf_13)) (<= (uf_3 ?x8) uf_12))) (= (uf_3 uf_11) uf_12)))) (implies (and true (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (<= (uf_3 uf_5) uf_6) (and (and (<= 0 uf_4) (<= 1 uf_5)) (and (= uf_11 uf_4) (and (= uf_12 uf_6) (and true (and (and (<= 0 uf_11) (<= 1 uf_5)) (and (= uf_13 (+ uf_5 1)) (and (<= 0 uf_11) (<= 2 uf_13))))))))))) (and (forall (?x9 Int) (implies (and (<= 0 ?x9) (< ?x9 uf_13)) (<= (uf_3 ?x9) uf_12))) (implies (forall (?x10 Int) (implies (and (<= 0 ?x10) (< ?x10 uf_13)) (<= (uf_3 ?x10) uf_12))) (= (uf_3 uf_11) uf_12)))))))))))))
+:assumption (not (implies true (implies (< 0 uf_1) (implies (= uf_2 (uf_3 0)) (implies (and (<= 0 0) (and (<= 0 0) (and (<= 1 1) (<= 1 1)))) (and (forall (?x1 Int) (implies (and (<= 0 ?x1) (< ?x1 1)) (<= (uf_3 ?x1) uf_2))) (implies (forall (?x2 Int) (implies (and (<= 0 ?x2) (< ?x2 1)) (<= (uf_3 ?x2) uf_2))) (and (= (uf_3 0) uf_2) (implies (= (uf_3 0) uf_2) (implies true (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (forall (?x3 Int) (implies (and (<= 0 ?x3) (< ?x3 uf_5)) (<= (uf_3 ?x3) uf_6))) (implies (= (uf_3 uf_4) uf_6) (implies (and (<= 0 uf_4) (<= 1 uf_5)) (and (implies true (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (<= uf_1 uf_5) (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (= uf_7 uf_4) (implies (= uf_8 uf_6) (implies (= uf_9 uf_5) (and (exists (?x4 Int) (implies (and (<= 0 ?x4) (< ?x4 uf_1)) (= (uf_3 ?x4) uf_8))) (implies (exists (?x5 Int) (implies (and (<= 0 ?x5) (< ?x5 uf_1)) (= (uf_3 ?x5) uf_8))) (and (forall (?x6 Int) (implies (and (<= 0 ?x6) (< ?x6 uf_1)) (<= (uf_3 ?x6) uf_8))) true)))))))))) (implies true (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (< uf_5 uf_1) (implies (and (<= 0 uf_4) (<= 1 uf_5)) (and (implies true (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (< uf_6 (uf_3 uf_5)) (implies (= uf_10 (uf_3 uf_5)) (implies (and (<= 1 uf_5) (<= 1 uf_5)) (implies (= uf_11 uf_5) (implies (= uf_12 uf_10) (implies true (implies (and (<= 0 uf_11) (<= 1 uf_5)) (implies (= uf_13 (+ uf_5 1)) (implies (and (<= 0 uf_11) (<= 2 uf_13)) (and (forall (?x7 Int) (implies (and (<= 0 ?x7) (< ?x7 uf_13)) (<= (uf_3 ?x7) uf_12))) (implies (forall (?x8 Int) (implies (and (<= 0 ?x8) (< ?x8 uf_13)) (<= (uf_3 ?x8) uf_12))) (and (= (uf_3 uf_11) uf_12) true)))))))))))))) (implies true (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (<= (uf_3 uf_5) uf_6) (implies (and (<= 0 uf_4) (<= 1 uf_5)) (implies (= uf_11 uf_4) (implies (= uf_12 uf_6) (implies true (implies (and (<= 0 uf_11) (<= 1 uf_5)) (implies (= uf_13 (+ uf_5 1)) (implies (and (<= 0 uf_11) (<= 2 uf_13)) (and (forall (?x9 Int) (implies (and (<= 0 ?x9) (< ?x9 uf_13)) (<= (uf_3 ?x9) uf_12))) (implies (forall (?x10 Int) (implies (and (<= 0 ?x10) (< ?x10 uf_13)) (<= (uf_3 ?x10) uf_12))) (and (= (uf_3 uf_11) uf_12) true)))))))))))))))))))))))))))))))))
 :formula true
 )

--- a/src/HOL/Boogie/Examples/cert/Boogie_max.proof	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/Boogie_max.proof	Wed Dec 23 17:37:42 2009 +0100
@@ -1,1995 +1,2224 @@
 #2 := false
+#4 := 0::int
 decl uf_3 :: (-> int int)
-decl ?x1!0 :: int
-#870 := ?x1!0
-#871 := (uf_3 ?x1!0)
+#8 := (uf_3 0::int)
+#647 := -1::int
+#2054 := (* -1::int #8)
 decl uf_2 :: int
 #7 := uf_2
-#1833 := (= uf_2 #871)
-#4 := 0::int
-#8 := (uf_3 0::int)
-#1842 := (= #8 #871)
-#1841 := (= #871 #8)
-#1860 := (= ?x1!0 0::int)
-#11 := 1::int
-#873 := (>= ?x1!0 1::int)
-#874 := (not #873)
-#875 := (>= ?x1!0 0::int)
-#913 := (not #875)
-#516 := -1::int
-#827 := (* -1::int #871)
-#828 := (+ uf_2 #827)
-#872 := (>= #828 0::int)
-#1208 := (or #872 #873 #913)
-#1213 := (not #1208)
-decl ?x4!1 :: int
-#900 := ?x4!1
-#908 := (uf_3 ?x4!1)
-decl uf_8 :: int
-#49 := uf_8
-#1055 := (= uf_8 #908)
-#905 := (>= ?x4!1 0::int)
-#1286 := (not #905)
-#901 := (* -1::int ?x4!1)
+#2050 := (+ uf_2 #2054)
+#2051 := (>= #2050 0::int)
+#9 := (= uf_2 #8)
 decl uf_1 :: int
 #5 := uf_1
-#902 := (+ uf_1 #901)
-#903 := (<= #902 0::int)
-#1301 := (or #903 #1286 #1055)
-#1332 := (not #1301)
-decl ?x6!2 :: int
-#918 := ?x6!2
-#919 := (uf_3 ?x6!2)
-#1079 := (* -1::int #919)
-#1080 := (+ uf_8 #1079)
-#1081 := (>= #1080 0::int)
-#926 := (>= ?x6!2 0::int)
-#1306 := (not #926)
-#922 := (* -1::int ?x6!2)
-#923 := (+ uf_1 #922)
-#924 := (<= #923 0::int)
-#1474 := (or #924 #1306 #1081 #1332)
-#1477 := (not #1474)
-#19 := (:var 0 int)
-#23 := (uf_3 #19)
-#1986 := (pattern #23)
-#604 := (* -1::int #19)
-#605 := (+ uf_1 #604)
-#606 := (<= #605 0::int)
-#505 := (>= #19 0::int)
-#1216 := (not #505)
-#61 := (= #23 uf_8)
-#1275 := (or #61 #1216 #606)
-#1280 := (not #1275)
-#2047 := (forall (vars (?x4 int)) (:pat #1986) #1280)
-#2052 := (or #2047 #1477)
-#2055 := (not #2052)
-decl uf_5 :: int
-#30 := uf_5
-#533 := (* -1::int uf_5)
-#583 := (+ uf_1 #533)
-#584 := (<= #583 0::int)
-#650 := (not #584)
-#557 := (>= uf_5 1::int)
-#1349 := (not #557)
-decl uf_4 :: int
-#28 := uf_4
-#555 := (>= uf_4 0::int)
-#1348 := (not #555)
-decl uf_9 :: int
-#51 := uf_9
-#216 := (= uf_5 uf_9)
-#1347 := (not #216)
+#965 := (<= uf_1 0::int)
 decl uf_6 :: int
-#35 := uf_6
-#213 := (= uf_6 uf_8)
-#1346 := (not #213)
-decl uf_7 :: int
-#47 := uf_7
-#210 := (= uf_4 uf_7)
-#1345 := (not #210)
-#2058 := (or #1345 #1346 #1347 #1348 #1349 #650 #2055)
-#2061 := (not #2058)
-decl ?x7!3 :: int
-#954 := ?x7!3
-#955 := (uf_3 ?x7!3)
-#1138 := (* -1::int #955)
-decl uf_12 :: int
-#81 := uf_12
-#1139 := (+ uf_12 #1138)
-#1140 := (>= #1139 0::int)
-#1116 := (* -1::int ?x7!3)
+#32 := uf_6
+#922 := (* -1::int uf_6)
+#16 := (:var 0 int)
+#20 := (uf_3 #16)
+#923 := (+ #20 #922)
+#924 := (<= #923 0::int)
+decl uf_5 :: int
+#27 := uf_5
+#717 := (* -1::int uf_5)
+#912 := (+ #16 #717)
+#911 := (>= #912 0::int)
+#913 := (not #911)
+#636 := (>= #16 0::int)
+#916 := (and #636 #913)
+#919 := (not #916)
+#927 := (or #919 #924)
+#930 := (forall (vars (?x3 int)) #927)
+#933 := (not #930)
+#64 := (uf_3 uf_5)
+#815 := (* -1::int #64)
+#816 := (+ uf_6 #815)
+#814 := (>= #816 0::int)
+#813 := (not #814)
+decl uf_11 :: int
+#69 := uf_11
+#749 := (>= uf_11 0::int)
+#11 := 1::int
+#666 := (>= uf_5 1::int)
+#804 := (and #666 #749)
+#807 := (not #804)
 decl uf_13 :: int
-#85 := uf_13
-#1117 := (+ uf_13 #1116)
-#1118 := (<= #1117 0::int)
-#961 := (>= ?x7!3 0::int)
-#1389 := (not #961)
-#1404 := (or #1389 #1118 #1140)
-#1409 := (not #1404)
-#733 := (* -1::int uf_12)
-#734 := (+ #23 #733)
-#735 := (<= #734 0::int)
-#674 := (* -1::int uf_13)
-#723 := (+ #19 #674)
-#722 := (>= #723 0::int)
-#1371 := (or #1216 #722 #735)
-#2003 := (forall (vars (?x7 int)) (:pat #1986) #1371)
-#2008 := (not #2003)
-decl uf_11 :: int
-#79 := uf_11
-#106 := (uf_3 uf_11)
-#358 := (= uf_12 #106)
-#2011 := (or #358 #2008)
-#2014 := (not #2011)
-#2017 := (or #2014 #1409)
-#2020 := (not #2017)
-#74 := (uf_3 uf_5)
-#679 := (* -1::int #74)
-#680 := (+ uf_6 #679)
-#678 := (>= #680 0::int)
-#681 := (not #678)
-#675 := (+ uf_5 #674)
-#673 := (= #675 -1::int)
-#1423 := (not #673)
-#88 := 2::int
-#671 := (>= uf_13 2::int)
-#1422 := (not #671)
-#668 := (>= uf_11 0::int)
-#1421 := (not #668)
-#385 := (= uf_6 uf_12)
-#1435 := (not #385)
-#382 := (= uf_4 uf_11)
-#1434 := (not #382)
-#2029 := (or #1434 #1435 #1348 #1349 #1421 #1422 #1423 #681 #2020)
-#2032 := (not #2029)
+#75 := uf_13
+#761 := (* -1::int uf_13)
+#798 := (+ uf_5 #761)
+#797 := (= #798 -1::int)
+#801 := (not #797)
+decl uf_12 :: int
+#71 := uf_12
+#772 := (* -1::int uf_12)
+#773 := (+ #20 #772)
+#774 := (<= #773 0::int)
+#762 := (+ #16 #761)
+#760 := (>= #762 0::int)
+#763 := (not #760)
+#766 := (and #636 #763)
+#769 := (not #766)
+#777 := (or #769 #774)
+#780 := (forall (vars (?x7 int)) #777)
+#783 := (not #780)
+#86 := (uf_3 uf_11)
+#302 := (= uf_12 #86)
+#789 := (or #302 #783)
+#794 := (and #780 #789)
+#78 := 2::int
+#752 := (>= uf_13 2::int)
+#754 := (and #749 #752)
+#757 := (not #754)
+decl uf_4 :: int
+#25 := uf_4
+#663 := (>= uf_4 0::int)
+#668 := (and #663 #666)
+#671 := (not #668)
+#421 := (= uf_6 uf_12)
+#427 := (not #421)
+#418 := (= uf_4 uf_11)
+#436 := (not #418)
+#877 := (or #436 #427 #671 #757 #794 #801 #807 #813)
+#810 := (not #666)
 decl uf_10 :: int
-#76 := uf_10
-#296 := (= uf_10 uf_12)
-#1420 := (not #296)
-#293 := (= uf_5 uf_11)
-#1419 := (not #293)
-#288 := (= #74 uf_10)
-#1418 := (not #288)
-#2023 := (or #1418 #1419 #1420 #1348 #1349 #1421 #1422 #1423 #678 #2020)
-#2026 := (not #2023)
-#2035 := (or #2026 #2032)
-#2038 := (not #2035)
-#2041 := (or #1348 #1349 #584 #2038)
-#2044 := (not #2041)
-#2064 := (or #2044 #2061)
-#2067 := (not #2064)
-#543 := (* -1::int uf_6)
-#544 := (+ #23 #543)
-#545 := (<= #544 0::int)
-#534 := (+ #19 #533)
-#532 := (>= #534 0::int)
-#1253 := (or #1216 #532 #545)
-#1995 := (forall (vars (?x3 int)) (:pat #1986) #1253)
-#2000 := (not #1995)
-#519 := (* -1::int #23)
-#520 := (+ uf_2 #519)
-#518 := (>= #520 0::int)
-#508 := (>= #19 1::int)
-#1231 := (or #1216 #508 #518)
-#1987 := (forall (vars (?x1 int)) (:pat #1986) #1231)
-#1992 := (not #1987)
-#39 := (uf_3 uf_4)
-#183 := (= uf_6 #39)
-#1461 := (not #183)
-#2070 := (or #1461 #1348 #1349 #1992 #2000 #2067)
-#1123 := (not #1118)
-#2073 := (not #2070)
-#2289 := [hypothesis]: #2073
-#1885 := (or #2070 #2064)
-#1887 := [def-axiom]: #1885
-#2290 := [unit-resolution #1887 #2289]: #2064
-#1898 := (or #2070 #1995)
-#1884 := [def-axiom]: #1898
-#2227 := [unit-resolution #1884 #2289]: #1995
-#1907 := (or #2070 #183)
-#1891 := [def-axiom]: #1907
-#2228 := [unit-resolution #1891 #2289]: #183
-#2142 := (or #2058 #1461 #2000)
-#2082 := (uf_3 uf_7)
-#2086 := (= uf_8 #2082)
-#2136 := (= #39 #2082)
-#2134 := (= #2082 #39)
-#48 := (= uf_7 uf_4)
-#2119 := [hypothesis]: #2061
-#1824 := (or #2058 #210)
-#1825 := [def-axiom]: #1824
-#2130 := [unit-resolution #1825 #2119]: #210
-#2131 := [symm #2130]: #48
-#2135 := [monotonicity #2131]: #2134
-#2137 := [symm #2135]: #2136
-#2138 := (= uf_8 #39)
-#2132 := [hypothesis]: #183
-#50 := (= uf_8 uf_6)
-#1826 := (or #2058 #213)
-#1827 := [def-axiom]: #1826
-#2121 := [unit-resolution #1827 #2119]: #213
-#2133 := [symm #2121]: #50
-#2139 := [trans #2133 #2132]: #2138
-#2140 := [trans #2139 #2137]: #2086
-#2114 := (not #2086)
-#2080 := (>= uf_7 0::int)
-#2081 := (not #2080)
-#1577 := (* -1::int uf_7)
-#1575 := (+ uf_1 #1577)
-#1578 := (<= #1575 0::int)
-#2092 := (or #1578 #2081 #2086)
-#2097 := (not #2092)
-#1911 := (or #2058 #2052)
-#1912 := [def-axiom]: #1911
-#2120 := [unit-resolution #1912 #2119]: #2052
-#630 := (* -1::int uf_8)
-#1747 := (+ uf_6 #630)
-#1737 := (<= #1747 0::int)
-#2122 := (or #1346 #1737)
-#2123 := [th-lemma]: #2122
-#2124 := [unit-resolution #2123 #2121]: #1737
-#1630 := [hypothesis]: #1995
-#1899 := (or #2058 #584)
-#1901 := [def-axiom]: #1899
-#2125 := [unit-resolution #1901 #2119]: #584
-#1656 := (not #1737)
-#1615 := (or #1474 #650 #2000 #1656)
-#1642 := [hypothesis]: #584
-#1724 := (+ uf_5 #922)
-#1725 := (<= #1724 0::int)
-#1717 := (+ uf_6 #1079)
-#1718 := (>= #1717 0::int)
-#1645 := (not #1718)
-#1652 := [hypothesis]: #1737
-#1810 := (not #1081)
-#1621 := [hypothesis]: #1477
-#1811 := (or #1474 #1810)
-#1770 := [def-axiom]: #1811
-#1623 := [unit-resolution #1770 #1621]: #1810
-#1639 := (or #1645 #1081 #1656)
-#1653 := [hypothesis]: #1810
-#1654 := [hypothesis]: #1718
-#1655 := [th-lemma #1654 #1653 #1652]: false
-#1641 := [lemma #1655]: #1639
-#1628 := [unit-resolution #1641 #1623 #1652]: #1645
-#1631 := (or #1718 #1725)
-#1927 := (or #1474 #926)
-#1809 := [def-axiom]: #1927
-#1629 := [unit-resolution #1809 #1621]: #926
-#1699 := (or #2000 #1306 #1718 #1725)
-#1729 := (+ #919 #543)
-#1730 := (<= #1729 0::int)
-#1733 := (+ ?x6!2 #533)
-#1734 := (>= #1733 0::int)
-#1738 := (or #1306 #1734 #1730)
-#1707 := (or #2000 #1738)
-#1686 := (iff #1707 #1699)
-#1702 := (or #1306 #1718 #1725)
-#1693 := (or #2000 #1702)
-#1695 := (iff #1693 #1699)
-#1697 := [rewrite]: #1695
-#1694 := (iff #1707 #1693)
-#1705 := (iff #1738 #1702)
-#1698 := (or #1306 #1725 #1718)
-#1703 := (iff #1698 #1702)
-#1704 := [rewrite]: #1703
-#1700 := (iff #1738 #1698)
-#1709 := (iff #1730 #1718)
-#1711 := (+ #543 #919)
-#1714 := (<= #1711 0::int)
-#1719 := (iff #1714 #1718)
-#1720 := [rewrite]: #1719
-#1715 := (iff #1730 #1714)
-#1712 := (= #1729 #1711)
-#1713 := [rewrite]: #1712
-#1716 := [monotonicity #1713]: #1715
-#1721 := [trans #1716 #1720]: #1709
-#1708 := (iff #1734 #1725)
-#1731 := (+ #533 ?x6!2)
-#1735 := (>= #1731 0::int)
-#1723 := (iff #1735 #1725)
-#1726 := [rewrite]: #1723
-#1736 := (iff #1734 #1735)
-#1739 := (= #1733 #1731)
-#1732 := [rewrite]: #1739
-#1722 := [monotonicity #1732]: #1736
-#1710 := [trans #1722 #1726]: #1708
-#1701 := [monotonicity #1710 #1721]: #1700
-#1706 := [trans #1701 #1704]: #1705
-#1696 := [monotonicity #1706]: #1694
-#1687 := [trans #1696 #1697]: #1686
-#1692 := [quant-inst]: #1707
-#1688 := [mp #1692 #1687]: #1699
-#1632 := [unit-resolution #1688 #1630 #1629]: #1631
-#1633 := [unit-resolution #1632 #1628]: #1725
-#925 := (not #924)
-#1926 := (or #1474 #925)
-#1924 := [def-axiom]: #1926
-#1622 := [unit-resolution #1924 #1621]: #925
-#1634 := [th-lemma #1622 #1633 #1642]: false
-#1617 := [lemma #1634]: #1615
-#2126 := [unit-resolution #1617 #2125 #1630 #2124]: #1474
-#1815 := (or #2055 #2047 #1477)
-#1823 := [def-axiom]: #1815
-#2127 := [unit-resolution #1823 #2126 #2120]: #2047
-#1919 := (not #2047)
-#2100 := (or #1919 #2097)
-#2083 := (= #2082 uf_8)
-#2084 := (or #2083 #2081 #1578)
-#2085 := (not #2084)
-#2101 := (or #1919 #2085)
-#2103 := (iff #2101 #2100)
-#2105 := (iff #2100 #2100)
-#2106 := [rewrite]: #2105
-#2098 := (iff #2085 #2097)
-#2095 := (iff #2084 #2092)
-#2089 := (or #2086 #2081 #1578)
-#2093 := (iff #2089 #2092)
-#2094 := [rewrite]: #2093
-#2090 := (iff #2084 #2089)
-#2087 := (iff #2083 #2086)
-#2088 := [rewrite]: #2087
-#2091 := [monotonicity #2088]: #2090
-#2096 := [trans #2091 #2094]: #2095
-#2099 := [monotonicity #2096]: #2098
-#2104 := [monotonicity #2099]: #2103
-#2107 := [trans #2104 #2106]: #2103
-#2102 := [quant-inst]: #2101
-#2108 := [mp #2102 #2107]: #2100
-#2128 := [unit-resolution #2108 #2127]: #2097
-#2115 := (or #2092 #2114)
-#2116 := [def-axiom]: #2115
-#2129 := [unit-resolution #2116 #2128]: #2114
-#2141 := [unit-resolution #2129 #2140]: false
-#2143 := [lemma #2141]: #2142
-#2229 := [unit-resolution #2143 #2228 #2227]: #2058
-#1906 := (or #2067 #2044 #2061)
-#1900 := [def-axiom]: #1906
-#2299 := [unit-resolution #1900 #2229 #2290]: #2044
-#1934 := (or #2041 #2035)
-#1928 := [def-axiom]: #1934
-#2376 := [unit-resolution #1928 #2299]: #2035
-#2374 := (or #2029 #2000 #1461)
-#2334 := [hypothesis]: #2032
-#1952 := (or #2029 #2017)
-#1941 := [def-axiom]: #1952
-#2335 := [unit-resolution #1941 #2334]: #2017
-#2226 := (= #39 #106)
-#2340 := (= #106 #39)
-#112 := (= uf_11 uf_4)
-#1678 := (or #2029 #382)
-#1679 := [def-axiom]: #1678
-#2336 := [unit-resolution #1679 #2334]: #382
-#2337 := [symm #2336]: #112
-#2341 := [monotonicity #2337]: #2340
-#2342 := [symm #2341]: #2226
-#2343 := (= uf_12 #39)
-#113 := (= uf_12 uf_6)
-#1953 := (or #2029 #385)
-#1957 := [def-axiom]: #1953
-#2338 := [unit-resolution #1957 #2334]: #385
-#2339 := [symm #2338]: #113
-#2344 := [trans #2339 #2132]: #2343
-#2345 := [trans #2344 #2342]: #358
-#970 := (not #358)
-#1643 := (or #2011 #970)
-#1978 := [def-axiom]: #1643
-#2346 := [unit-resolution #1978 #2345]: #2011
-#1977 := (or #2020 #2014 #1409)
-#1620 := [def-axiom]: #1977
-#2347 := [unit-resolution #1620 #2346 #2335]: #1409
-#1981 := (or #1404 #1123)
-#1982 := [def-axiom]: #1981
-#2348 := [unit-resolution #1982 #2347]: #1123
-#1664 := (>= #675 -1::int)
-#1665 := (or #2029 #673)
-#1947 := [def-axiom]: #1665
-#2349 := [unit-resolution #1947 #2334]: #673
-#2350 := (or #1423 #1664)
-#2351 := [th-lemma]: #2350
-#2352 := [unit-resolution #2351 #2349]: #1664
-#2241 := (+ uf_5 #1116)
-#2311 := (>= #2241 0::int)
-#2367 := (not #2311)
-#2300 := (= uf_5 ?x7!3)
-#2331 := (not #2300)
-#2310 := (= #74 #955)
-#2315 := (not #2310)
-#2314 := (+ #74 #1138)
-#2316 := (>= #2314 0::int)
-#2320 := (not #2316)
-#1951 := (or #2029 #678)
-#1948 := [def-axiom]: #1951
-#2353 := [unit-resolution #1948 #2334]: #678
-#1983 := (not #1140)
-#1984 := (or #1404 #1983)
-#1979 := [def-axiom]: #1984
-#2354 := [unit-resolution #1979 #2347]: #1983
-#1579 := (+ uf_6 #733)
-#1955 := (<= #1579 0::int)
-#2355 := (or #1435 #1955)
-#2356 := [th-lemma]: #2355
-#2357 := [unit-resolution #2356 #2338]: #1955
-#2296 := (not #1955)
-#2321 := (or #2320 #2296 #1140 #681)
-#2317 := [hypothesis]: #678
-#2292 := [hypothesis]: #1983
-#2291 := [hypothesis]: #1955
-#2318 := [hypothesis]: #2316
-#2319 := [th-lemma #2318 #2291 #2292 #2317]: false
-#2322 := [lemma #2319]: #2321
-#2358 := [unit-resolution #2322 #2357 #2354 #2353]: #2320
-#2323 := (or #2315 #2316)
-#2324 := [th-lemma]: #2323
-#2359 := [unit-resolution #2324 #2358]: #2315
-#2332 := (or #2331 #2310)
-#2328 := [hypothesis]: #2300
-#2329 := [monotonicity #2328]: #2310
-#2327 := [hypothesis]: #2315
-#2330 := [unit-resolution #2327 #2329]: false
-#2333 := [lemma #2330]: #2332
-#2360 := [unit-resolution #2333 #2359]: #2331
-#2370 := (or #2300 #2367)
-#2242 := (<= #2241 0::int)
-#2253 := (+ uf_6 #1138)
-#2254 := (>= #2253 0::int)
-#2295 := (not #2254)
-#2297 := (or #2295 #1140 #2296)
-#2293 := [hypothesis]: #2254
-#2294 := [th-lemma #2293 #2292 #2291]: false
-#2298 := [lemma #2294]: #2297
-#2361 := [unit-resolution #2298 #2354 #2357]: #2295
-#2363 := (or #2242 #2254)
-#1648 := (or #1404 #961)
-#1649 := [def-axiom]: #1648
-#2362 := [unit-resolution #1649 #2347]: #961
-#2262 := (or #2000 #1389 #2242 #2254)
-#2230 := (+ #955 #543)
-#2231 := (<= #2230 0::int)
-#2232 := (+ ?x7!3 #533)
-#2233 := (>= #2232 0::int)
-#2234 := (or #1389 #2233 #2231)
-#2263 := (or #2000 #2234)
-#2270 := (iff #2263 #2262)
-#2259 := (or #1389 #2242 #2254)
-#2265 := (or #2000 #2259)
-#2268 := (iff #2265 #2262)
-#2269 := [rewrite]: #2268
-#2266 := (iff #2263 #2265)
-#2260 := (iff #2234 #2259)
-#2257 := (iff #2231 #2254)
-#2247 := (+ #543 #955)
-#2250 := (<= #2247 0::int)
-#2255 := (iff #2250 #2254)
-#2256 := [rewrite]: #2255
-#2251 := (iff #2231 #2250)
-#2248 := (= #2230 #2247)
-#2249 := [rewrite]: #2248
-#2252 := [monotonicity #2249]: #2251
-#2258 := [trans #2252 #2256]: #2257
-#2245 := (iff #2233 #2242)
-#2235 := (+ #533 ?x7!3)
-#2238 := (>= #2235 0::int)
-#2243 := (iff #2238 #2242)
-#2244 := [rewrite]: #2243
-#2239 := (iff #2233 #2238)
-#2236 := (= #2232 #2235)
-#2237 := [rewrite]: #2236
-#2240 := [monotonicity #2237]: #2239
-#2246 := [trans #2240 #2244]: #2245
-#2261 := [monotonicity #2246 #2258]: #2260
-#2267 := [monotonicity #2261]: #2266
-#2271 := [trans #2267 #2269]: #2270
-#2264 := [quant-inst]: #2263
-#2272 := [mp #2264 #2271]: #2262
-#2364 := [unit-resolution #2272 #1630 #2362]: #2363
-#2365 := [unit-resolution #2364 #2361]: #2242
-#2366 := (not #2242)
-#2368 := (or #2300 #2366 #2367)
-#2369 := [th-lemma]: #2368
-#2371 := [unit-resolution #2369 #2365]: #2370
-#2372 := [unit-resolution #2371 #2360]: #2367
-#2373 := [th-lemma #2372 #2352 #2348]: false
-#2375 := [lemma #2373]: #2374
-#2377 := [unit-resolution #2375 #2227 #2228]: #2029
-#1940 := (or #2038 #2026 #2032)
-#1946 := [def-axiom]: #1940
-#2378 := [unit-resolution #1946 #2377 #2376]: #2026
-#1970 := (or #2023 #2017)
-#1973 := [def-axiom]: #1970
-#2379 := [unit-resolution #1973 #2378]: #2017
-#2388 := (= #74 #106)
-#2384 := (= #106 #74)
-#80 := (= uf_11 uf_5)
-#1625 := (or #2023 #293)
-#1626 := [def-axiom]: #1625
-#2382 := [unit-resolution #1626 #2378]: #293
-#2383 := [symm #2382]: #80
-#2385 := [monotonicity #2383]: #2384
-#2389 := [symm #2385]: #2388
-#2390 := (= uf_12 #74)
-#77 := (= uf_10 #74)
-#1961 := (or #2023 #288)
-#1624 := [def-axiom]: #1961
-#2381 := [unit-resolution #1624 #2378]: #288
-#2387 := [symm #2381]: #77
-#82 := (= uf_12 uf_10)
-#1627 := (or #2023 #296)
-#1963 := [def-axiom]: #1627
-#2380 := [unit-resolution #1963 #2378]: #296
-#2386 := [symm #2380]: #82
-#2391 := [trans #2386 #2387]: #2390
-#2392 := [trans #2391 #2389]: #358
-#2393 := [unit-resolution #1978 #2392]: #2011
-#2394 := [unit-resolution #1620 #2393 #2379]: #1409
-#2395 := [unit-resolution #1982 #2394]: #1123
-#2157 := (+ #74 #733)
-#2158 := (<= #2157 0::int)
-#2156 := (= #74 uf_12)
-#2396 := [trans #2381 #2380]: #2156
-#2397 := (not #2156)
-#2398 := (or #2397 #2158)
-#2399 := [th-lemma]: #2398
-#2400 := [unit-resolution #2399 #2396]: #2158
-#1612 := (or #2023 #681)
-#1972 := [def-axiom]: #1612
-#2401 := [unit-resolution #1972 #2378]: #681
-#2402 := [unit-resolution #1979 #2394]: #1983
-#2403 := (not #2158)
-#2404 := (or #2295 #1140 #2403 #678)
-#2405 := [th-lemma]: #2404
-#2406 := [unit-resolution #2405 #2402 #2401 #2400]: #2295
-#2407 := [unit-resolution #1649 #2394]: #961
-#2408 := [unit-resolution #2272 #2227 #2407 #2406]: #2242
-#2409 := (or #2320 #1140 #2403)
-#2410 := [th-lemma]: #2409
-#2411 := [unit-resolution #2410 #2402 #2400]: #2320
-#2412 := [unit-resolution #2324 #2411]: #2315
-#2413 := [unit-resolution #2333 #2412]: #2331
-#2414 := [unit-resolution #2369 #2413 #2408]: #2367
-#1971 := (or #2023 #673)
-#1611 := [def-axiom]: #1971
-#2415 := [unit-resolution #1611 #2378]: #673
-#2416 := [unit-resolution #2351 #2415]: #1664
-#2417 := [th-lemma #2416 #2414 #2395]: false
-#2418 := [lemma #2417]: #2070
-#2076 := (or #1213 #2073)
-#1283 := (forall (vars (?x4 int)) #1280)
-#1480 := (or #1283 #1477)
-#1483 := (not #1480)
-#1486 := (or #1345 #1346 #1347 #1348 #1349 #650 #1483)
-#1489 := (not #1486)
-#1376 := (forall (vars (?x7 int)) #1371)
-#1382 := (not #1376)
-#1383 := (or #358 #1382)
-#1384 := (not #1383)
-#1412 := (or #1384 #1409)
-#1424 := (not #1412)
-#1436 := (or #1434 #1435 #1348 #1349 #1421 #1422 #1423 #681 #1424)
-#1437 := (not #1436)
-#1425 := (or #1418 #1419 #1420 #1348 #1349 #1421 #1422 #1423 #678 #1424)
-#1426 := (not #1425)
-#1442 := (or #1426 #1437)
-#1448 := (not #1442)
-#1449 := (or #1348 #1349 #584 #1448)
-#1450 := (not #1449)
-#1495 := (or #1450 #1489)
-#1500 := (not #1495)
-#1258 := (forall (vars (?x3 int)) #1253)
-#1463 := (not #1258)
-#1236 := (forall (vars (?x1 int)) #1231)
-#1462 := (not #1236)
-#1503 := (or #1461 #1348 #1349 #1462 #1463 #1500)
-#1506 := (not #1503)
-#1509 := (or #1213 #1506)
-#2077 := (iff #1509 #2076)
-#2074 := (iff #1506 #2073)
-#2071 := (iff #1503 #2070)
-#2068 := (iff #1500 #2067)
-#2065 := (iff #1495 #2064)
-#2062 := (iff #1489 #2061)
-#2059 := (iff #1486 #2058)
-#2056 := (iff #1483 #2055)
-#2053 := (iff #1480 #2052)
-#2050 := (iff #1283 #2047)
-#2048 := (iff #1280 #1280)
-#2049 := [refl]: #2048
-#2051 := [quant-intro #2049]: #2050
-#2054 := [monotonicity #2051]: #2053
-#2057 := [monotonicity #2054]: #2056
-#2060 := [monotonicity #2057]: #2059
-#2063 := [monotonicity #2060]: #2062
-#2045 := (iff #1450 #2044)
-#2042 := (iff #1449 #2041)
-#2039 := (iff #1448 #2038)
-#2036 := (iff #1442 #2035)
-#2033 := (iff #1437 #2032)
-#2030 := (iff #1436 #2029)
-#2021 := (iff #1424 #2020)
-#2018 := (iff #1412 #2017)
-#2015 := (iff #1384 #2014)
-#2012 := (iff #1383 #2011)
-#2009 := (iff #1382 #2008)
-#2006 := (iff #1376 #2003)
-#2004 := (iff #1371 #1371)
-#2005 := [refl]: #2004
-#2007 := [quant-intro #2005]: #2006
-#2010 := [monotonicity #2007]: #2009
-#2013 := [monotonicity #2010]: #2012
-#2016 := [monotonicity #2013]: #2015
-#2019 := [monotonicity #2016]: #2018
-#2022 := [monotonicity #2019]: #2021
-#2031 := [monotonicity #2022]: #2030
-#2034 := [monotonicity #2031]: #2033
-#2027 := (iff #1426 #2026)
-#2024 := (iff #1425 #2023)
-#2025 := [monotonicity #2022]: #2024
-#2028 := [monotonicity #2025]: #2027
-#2037 := [monotonicity #2028 #2034]: #2036
-#2040 := [monotonicity #2037]: #2039
-#2043 := [monotonicity #2040]: #2042
-#2046 := [monotonicity #2043]: #2045
-#2066 := [monotonicity #2046 #2063]: #2065
-#2069 := [monotonicity #2066]: #2068
-#2001 := (iff #1463 #2000)
-#1998 := (iff #1258 #1995)
-#1996 := (iff #1253 #1253)
-#1997 := [refl]: #1996
-#1999 := [quant-intro #1997]: #1998
-#2002 := [monotonicity #1999]: #2001
-#1993 := (iff #1462 #1992)
-#1990 := (iff #1236 #1987)
-#1988 := (iff #1231 #1231)
-#1989 := [refl]: #1988
-#1991 := [quant-intro #1989]: #1990
-#1994 := [monotonicity #1991]: #1993
-#2072 := [monotonicity #1994 #2002 #2069]: #2071
-#2075 := [monotonicity #2072]: #2074
-#2078 := [monotonicity #2075]: #2077
-#1126 := (and #961 #1123)
-#1129 := (not #1126)
-#1145 := (or #1129 #1140)
-#1148 := (not #1145)
-#724 := (not #722)
-#727 := (and #505 #724)
-#730 := (not #727)
-#738 := (or #730 #735)
-#741 := (forall (vars (?x7 int)) #738)
-#980 := (and #970 #741)
-#1154 := (or #980 #1148)
-#1172 := (and #382 #385 #555 #557 #668 #671 #673 #678 #1154)
-#1162 := (and #288 #293 #296 #555 #557 #668 #671 #673 #681 #1154)
-#1177 := (or #1162 #1172)
-#1183 := (and #555 #557 #650 #1177)
-#1067 := (and #925 #926)
-#1070 := (not #1067)
-#1086 := (or #1070 #1081)
-#1089 := (not #1086)
-#904 := (not #903)
-#1058 := (and #904 #905)
-#1061 := (not #1058)
-#1064 := (or #1055 #1061)
-#1092 := (and #1064 #1089)
-#607 := (not #606)
-#610 := (and #505 #607)
-#613 := (not #610)
-#619 := (or #61 #613)
-#894 := (not #619)
-#897 := (forall (vars (?x4 int)) #894)
-#1095 := (or #897 #1092)
-#1101 := (and #210 #213 #216 #555 #557 #584 #1095)
-#1188 := (or #1101 #1183)
-#531 := (not #532)
-#537 := (and #505 #531)
-#540 := (not #537)
-#548 := (or #540 #545)
-#551 := (forall (vars (?x3 int)) #548)
-#506 := (not #508)
-#510 := (and #505 #506)
-#513 := (not #510)
-#522 := (or #513 #518)
-#525 := (forall (vars (?x1 int)) #522)
-#1194 := (and #183 #525 #551 #555 #557 #1188)
-#1036 := (and #874 #875)
-#1039 := (not #1036)
-#1045 := (or #872 #1039)
-#1050 := (not #1045)
-#1199 := (or #1050 #1194)
-#1512 := (iff #1199 #1509)
-#1321 := (or #924 #1306 #1081)
-#1333 := (or #1332 #1321)
-#1334 := (not #1333)
-#1339 := (or #1283 #1334)
-#1350 := (not #1339)
-#1351 := (or #1345 #1346 #1347 #1348 #1349 #650 #1350)
-#1352 := (not #1351)
-#1455 := (or #1352 #1450)
-#1464 := (not #1455)
-#1465 := (or #1461 #1348 #1349 #1462 #1463 #1464)
-#1466 := (not #1465)
-#1471 := (or #1213 #1466)
-#1510 := (iff #1471 #1509)
-#1507 := (iff #1466 #1506)
-#1504 := (iff #1465 #1503)
-#1501 := (iff #1464 #1500)
-#1498 := (iff #1455 #1495)
-#1492 := (or #1489 #1450)
-#1496 := (iff #1492 #1495)
-#1497 := [rewrite]: #1496
-#1493 := (iff #1455 #1492)
-#1490 := (iff #1352 #1489)
-#1487 := (iff #1351 #1486)
-#1484 := (iff #1350 #1483)
-#1481 := (iff #1339 #1480)
-#1478 := (iff #1334 #1477)
-#1475 := (iff #1333 #1474)
-#1476 := [rewrite]: #1475
-#1479 := [monotonicity #1476]: #1478
-#1482 := [monotonicity #1479]: #1481
-#1485 := [monotonicity #1482]: #1484
-#1488 := [monotonicity #1485]: #1487
-#1491 := [monotonicity #1488]: #1490
-#1494 := [monotonicity #1491]: #1493
-#1499 := [trans #1494 #1497]: #1498
-#1502 := [monotonicity #1499]: #1501
-#1505 := [monotonicity #1502]: #1504
-#1508 := [monotonicity #1505]: #1507
-#1511 := [monotonicity #1508]: #1510
-#1472 := (iff #1199 #1471)
-#1469 := (iff #1194 #1466)
-#1458 := (and #183 #1236 #1258 #555 #557 #1455)
-#1467 := (iff #1458 #1466)
-#1468 := [rewrite]: #1467
-#1459 := (iff #1194 #1458)
-#1456 := (iff #1188 #1455)
-#1453 := (iff #1183 #1450)
-#1445 := (and #555 #557 #650 #1442)
-#1451 := (iff #1445 #1450)
-#1452 := [rewrite]: #1451
-#1446 := (iff #1183 #1445)
-#1443 := (iff #1177 #1442)
-#1440 := (iff #1172 #1437)
-#1431 := (and #382 #385 #555 #557 #668 #671 #673 #678 #1412)
-#1438 := (iff #1431 #1437)
-#1439 := [rewrite]: #1438
-#1432 := (iff #1172 #1431)
-#1413 := (iff #1154 #1412)
-#1410 := (iff #1148 #1409)
-#1407 := (iff #1145 #1404)
-#1390 := (or #1389 #1118)
-#1401 := (or #1390 #1140)
-#1405 := (iff #1401 #1404)
-#1406 := [rewrite]: #1405
-#1402 := (iff #1145 #1401)
-#1399 := (iff #1129 #1390)
-#1391 := (not #1390)
-#1394 := (not #1391)
-#1397 := (iff #1394 #1390)
-#1398 := [rewrite]: #1397
-#1395 := (iff #1129 #1394)
-#1392 := (iff #1126 #1391)
-#1393 := [rewrite]: #1392
-#1396 := [monotonicity #1393]: #1395
-#1400 := [trans #1396 #1398]: #1399
-#1403 := [monotonicity #1400]: #1402
-#1408 := [trans #1403 #1406]: #1407
-#1411 := [monotonicity #1408]: #1410
-#1387 := (iff #980 #1384)
-#1379 := (and #970 #1376)
-#1385 := (iff #1379 #1384)
-#1386 := [rewrite]: #1385
-#1380 := (iff #980 #1379)
-#1377 := (iff #741 #1376)
-#1374 := (iff #738 #1371)
-#1357 := (or #1216 #722)
-#1368 := (or #1357 #735)
-#1372 := (iff #1368 #1371)
-#1373 := [rewrite]: #1372
-#1369 := (iff #738 #1368)
-#1366 := (iff #730 #1357)
-#1358 := (not #1357)
-#1361 := (not #1358)
-#1364 := (iff #1361 #1357)
-#1365 := [rewrite]: #1364
-#1362 := (iff #730 #1361)
-#1359 := (iff #727 #1358)
-#1360 := [rewrite]: #1359
-#1363 := [monotonicity #1360]: #1362
-#1367 := [trans #1363 #1365]: #1366
-#1370 := [monotonicity #1367]: #1369
-#1375 := [trans #1370 #1373]: #1374
-#1378 := [quant-intro #1375]: #1377
-#1381 := [monotonicity #1378]: #1380
-#1388 := [trans #1381 #1386]: #1387
-#1414 := [monotonicity #1388 #1411]: #1413
-#1433 := [monotonicity #1414]: #1432
-#1441 := [trans #1433 #1439]: #1440
-#1429 := (iff #1162 #1426)
-#1415 := (and #288 #293 #296 #555 #557 #668 #671 #673 #681 #1412)
-#1427 := (iff #1415 #1426)
-#1428 := [rewrite]: #1427
-#1416 := (iff #1162 #1415)
-#1417 := [monotonicity #1414]: #1416
-#1430 := [trans #1417 #1428]: #1429
-#1444 := [monotonicity #1430 #1441]: #1443
-#1447 := [monotonicity #1444]: #1446
-#1454 := [trans #1447 #1452]: #1453
-#1355 := (iff #1101 #1352)
-#1342 := (and #210 #213 #216 #555 #557 #584 #1339)
-#1353 := (iff #1342 #1352)
-#1354 := [rewrite]: #1353
-#1343 := (iff #1101 #1342)
-#1340 := (iff #1095 #1339)
-#1337 := (iff #1092 #1334)
-#1326 := (not #1321)
-#1329 := (and #1301 #1326)
-#1335 := (iff #1329 #1334)
-#1336 := [rewrite]: #1335
-#1330 := (iff #1092 #1329)
-#1327 := (iff #1089 #1326)
-#1324 := (iff #1086 #1321)
-#1307 := (or #924 #1306)
-#1318 := (or #1307 #1081)
-#1322 := (iff #1318 #1321)
-#1323 := [rewrite]: #1322
-#1319 := (iff #1086 #1318)
-#1316 := (iff #1070 #1307)
-#1308 := (not #1307)
-#1311 := (not #1308)
-#1314 := (iff #1311 #1307)
-#1315 := [rewrite]: #1314
-#1312 := (iff #1070 #1311)
-#1309 := (iff #1067 #1308)
-#1310 := [rewrite]: #1309
-#1313 := [monotonicity #1310]: #1312
-#1317 := [trans #1313 #1315]: #1316
-#1320 := [monotonicity #1317]: #1319
-#1325 := [trans #1320 #1323]: #1324
-#1328 := [monotonicity #1325]: #1327
-#1304 := (iff #1064 #1301)
-#1287 := (or #903 #1286)
-#1298 := (or #1055 #1287)
-#1302 := (iff #1298 #1301)
-#1303 := [rewrite]: #1302
-#1299 := (iff #1064 #1298)
-#1296 := (iff #1061 #1287)
-#1288 := (not #1287)
-#1291 := (not #1288)
-#1294 := (iff #1291 #1287)
-#1295 := [rewrite]: #1294
-#1292 := (iff #1061 #1291)
-#1289 := (iff #1058 #1288)
-#1290 := [rewrite]: #1289
-#1293 := [monotonicity #1290]: #1292
-#1297 := [trans #1293 #1295]: #1296
-#1300 := [monotonicity #1297]: #1299
-#1305 := [trans #1300 #1303]: #1304
-#1331 := [monotonicity #1305 #1328]: #1330
-#1338 := [trans #1331 #1336]: #1337
-#1284 := (iff #897 #1283)
-#1281 := (iff #894 #1280)
-#1278 := (iff #619 #1275)
-#1261 := (or #1216 #606)
-#1272 := (or #61 #1261)
-#1276 := (iff #1272 #1275)
-#1277 := [rewrite]: #1276
-#1273 := (iff #619 #1272)
-#1270 := (iff #613 #1261)
-#1262 := (not #1261)
-#1265 := (not #1262)
-#1268 := (iff #1265 #1261)
-#1269 := [rewrite]: #1268
-#1266 := (iff #613 #1265)
-#1263 := (iff #610 #1262)
-#1264 := [rewrite]: #1263
-#1267 := [monotonicity #1264]: #1266
-#1271 := [trans #1267 #1269]: #1270
-#1274 := [monotonicity #1271]: #1273
-#1279 := [trans #1274 #1277]: #1278
-#1282 := [monotonicity #1279]: #1281
-#1285 := [quant-intro #1282]: #1284
-#1341 := [monotonicity #1285 #1338]: #1340
-#1344 := [monotonicity #1341]: #1343
-#1356 := [trans #1344 #1354]: #1355
-#1457 := [monotonicity #1356 #1454]: #1456
-#1259 := (iff #551 #1258)
-#1256 := (iff #548 #1253)
-#1239 := (or #1216 #532)
-#1250 := (or #1239 #545)
-#1254 := (iff #1250 #1253)
-#1255 := [rewrite]: #1254
-#1251 := (iff #548 #1250)
-#1248 := (iff #540 #1239)
-#1240 := (not #1239)
-#1243 := (not #1240)
-#1246 := (iff #1243 #1239)
-#1247 := [rewrite]: #1246
-#1244 := (iff #540 #1243)
-#1241 := (iff #537 #1240)
-#1242 := [rewrite]: #1241
-#1245 := [monotonicity #1242]: #1244
-#1249 := [trans #1245 #1247]: #1248
-#1252 := [monotonicity #1249]: #1251
-#1257 := [trans #1252 #1255]: #1256
-#1260 := [quant-intro #1257]: #1259
-#1237 := (iff #525 #1236)
-#1234 := (iff #522 #1231)
-#1217 := (or #1216 #508)
-#1228 := (or #1217 #518)
-#1232 := (iff #1228 #1231)
-#1233 := [rewrite]: #1232
-#1229 := (iff #522 #1228)
-#1226 := (iff #513 #1217)
-#1218 := (not #1217)
-#1221 := (not #1218)
-#1224 := (iff #1221 #1217)
-#1225 := [rewrite]: #1224
-#1222 := (iff #513 #1221)
-#1219 := (iff #510 #1218)
-#1220 := [rewrite]: #1219
-#1223 := [monotonicity #1220]: #1222
-#1227 := [trans #1223 #1225]: #1226
-#1230 := [monotonicity #1227]: #1229
-#1235 := [trans #1230 #1233]: #1234
-#1238 := [quant-intro #1235]: #1237
-#1460 := [monotonicity #1238 #1260 #1457]: #1459
-#1470 := [trans #1460 #1468]: #1469
-#1214 := (iff #1050 #1213)
-#1211 := (iff #1045 #1208)
-#914 := (or #873 #913)
-#1205 := (or #872 #914)
-#1209 := (iff #1205 #1208)
-#1210 := [rewrite]: #1209
-#1206 := (iff #1045 #1205)
-#1203 := (iff #1039 #914)
-#882 := (not #914)
-#935 := (not #882)
-#1035 := (iff #935 #914)
-#1202 := [rewrite]: #1035
-#968 := (iff #1039 #935)
-#883 := (iff #1036 #882)
-#934 := [rewrite]: #883
-#969 := [monotonicity #934]: #968
-#1204 := [trans #969 #1202]: #1203
-#1207 := [monotonicity #1204]: #1206
-#1212 := [trans #1207 #1210]: #1211
-#1215 := [monotonicity #1212]: #1214
-#1473 := [monotonicity #1215 #1470]: #1472
-#1513 := [trans #1473 #1511]: #1512
-#832 := (and #183 #551 #555 #557)
-#778 := (and #382 #385 #555 #557 #668 #671 #673 #678)
-#783 := (not #778)
-#992 := (not #783)
-#956 := (+ #955 #733)
-#957 := (<= #956 0::int)
-#958 := (+ ?x7!3 #674)
-#959 := (>= #958 0::int)
-#960 := (not #959)
-#962 := (and #961 #960)
-#963 := (not #962)
-#964 := (or #963 #957)
-#965 := (not #964)
-#984 := (or #965 #980)
-#995 := (and #984 #992)
-#714 := (and #288 #293 #296 #555 #557 #668 #671 #673 #681)
-#719 := (not #714)
-#951 := (not #719)
-#988 := (and #951 #984)
-#999 := (or #988 #995)
-#659 := (and #555 #557 #650)
-#664 := (not #659)
-#948 := (not #664)
-#1003 := (and #948 #999)
-#920 := (+ #919 #630)
-#921 := (<= #920 0::int)
-#927 := (and #926 #925)
-#928 := (not #927)
-#929 := (or #928 #921)
-#930 := (not #929)
-#906 := (and #905 #904)
-#907 := (not #906)
-#909 := (= #908 uf_8)
-#910 := (or #909 #907)
-#936 := (and #910 #930)
-#940 := (or #897 #936)
-#596 := (and #210 #213 #216 #555 #557 #584)
-#601 := (not #596)
-#891 := (not #601)
-#944 := (and #891 #940)
-#1007 := (or #944 #1003)
-#1026 := (and #525 #1007 #832)
-#876 := (and #875 #874)
-#877 := (not #876)
-#878 := (or #877 #872)
-#879 := (not #878)
-#1030 := (or #879 #1026)
-#1200 := (iff #1030 #1199)
-#1197 := (iff #1026 #1194)
-#1191 := (and #525 #1188 #832)
-#1195 := (iff #1191 #1194)
-#1196 := [rewrite]: #1195
-#1192 := (iff #1026 #1191)
-#1189 := (iff #1007 #1188)
-#1186 := (iff #1003 #1183)
-#1180 := (and #659 #1177)
-#1184 := (iff #1180 #1183)
-#1185 := [rewrite]: #1184
-#1181 := (iff #1003 #1180)
-#1178 := (iff #999 #1177)
-#1175 := (iff #995 #1172)
-#1169 := (and #1154 #778)
-#1173 := (iff #1169 #1172)
-#1174 := [rewrite]: #1173
-#1170 := (iff #995 #1169)
-#1167 := (iff #992 #778)
-#1168 := [rewrite]: #1167
-#1157 := (iff #984 #1154)
-#1151 := (or #1148 #980)
-#1155 := (iff #1151 #1154)
-#1156 := [rewrite]: #1155
-#1152 := (iff #984 #1151)
-#1149 := (iff #965 #1148)
-#1146 := (iff #964 #1145)
-#1143 := (iff #957 #1140)
-#1132 := (+ #733 #955)
-#1135 := (<= #1132 0::int)
-#1141 := (iff #1135 #1140)
-#1142 := [rewrite]: #1141
-#1136 := (iff #957 #1135)
-#1133 := (= #956 #1132)
-#1134 := [rewrite]: #1133
-#1137 := [monotonicity #1134]: #1136
-#1144 := [trans #1137 #1142]: #1143
-#1130 := (iff #963 #1129)
-#1127 := (iff #962 #1126)
-#1124 := (iff #960 #1123)
-#1121 := (iff #959 #1118)
-#1110 := (+ #674 ?x7!3)
-#1113 := (>= #1110 0::int)
-#1119 := (iff #1113 #1118)
-#1120 := [rewrite]: #1119
-#1114 := (iff #959 #1113)
-#1111 := (= #958 #1110)
-#1112 := [rewrite]: #1111
-#1115 := [monotonicity #1112]: #1114
-#1122 := [trans #1115 #1120]: #1121
-#1125 := [monotonicity #1122]: #1124
-#1128 := [monotonicity #1125]: #1127
-#1131 := [monotonicity #1128]: #1130
-#1147 := [monotonicity #1131 #1144]: #1146
-#1150 := [monotonicity #1147]: #1149
-#1153 := [monotonicity #1150]: #1152
-#1158 := [trans #1153 #1156]: #1157
-#1171 := [monotonicity #1158 #1168]: #1170
-#1176 := [trans #1171 #1174]: #1175
-#1165 := (iff #988 #1162)
-#1159 := (and #714 #1154)
-#1163 := (iff #1159 #1162)
-#1164 := [rewrite]: #1163
-#1160 := (iff #988 #1159)
-#1108 := (iff #951 #714)
-#1109 := [rewrite]: #1108
-#1161 := [monotonicity #1109 #1158]: #1160
-#1166 := [trans #1161 #1164]: #1165
-#1179 := [monotonicity #1166 #1176]: #1178
-#1106 := (iff #948 #659)
-#1107 := [rewrite]: #1106
-#1182 := [monotonicity #1107 #1179]: #1181
-#1187 := [trans #1182 #1185]: #1186
-#1104 := (iff #944 #1101)
-#1098 := (and #596 #1095)
-#1102 := (iff #1098 #1101)
-#1103 := [rewrite]: #1102
-#1099 := (iff #944 #1098)
-#1096 := (iff #940 #1095)
-#1093 := (iff #936 #1092)
-#1090 := (iff #930 #1089)
-#1087 := (iff #929 #1086)
-#1084 := (iff #921 #1081)
-#1073 := (+ #630 #919)
-#1076 := (<= #1073 0::int)
-#1082 := (iff #1076 #1081)
-#1083 := [rewrite]: #1082
-#1077 := (iff #921 #1076)
-#1074 := (= #920 #1073)
-#1075 := [rewrite]: #1074
-#1078 := [monotonicity #1075]: #1077
-#1085 := [trans #1078 #1083]: #1084
-#1071 := (iff #928 #1070)
-#1068 := (iff #927 #1067)
-#1069 := [rewrite]: #1068
-#1072 := [monotonicity #1069]: #1071
-#1088 := [monotonicity #1072 #1085]: #1087
-#1091 := [monotonicity #1088]: #1090
-#1065 := (iff #910 #1064)
-#1062 := (iff #907 #1061)
-#1059 := (iff #906 #1058)
-#1060 := [rewrite]: #1059
-#1063 := [monotonicity #1060]: #1062
-#1056 := (iff #909 #1055)
-#1057 := [rewrite]: #1056
-#1066 := [monotonicity #1057 #1063]: #1065
-#1094 := [monotonicity #1066 #1091]: #1093
-#1097 := [monotonicity #1094]: #1096
-#1053 := (iff #891 #596)
-#1054 := [rewrite]: #1053
-#1100 := [monotonicity #1054 #1097]: #1099
-#1105 := [trans #1100 #1103]: #1104
-#1190 := [monotonicity #1105 #1187]: #1189
-#1193 := [monotonicity #1190]: #1192
-#1198 := [trans #1193 #1196]: #1197
-#1051 := (iff #879 #1050)
-#1048 := (iff #878 #1045)
-#1042 := (or #1039 #872)
-#1046 := (iff #1042 #1045)
-#1047 := [rewrite]: #1046
-#1043 := (iff #878 #1042)
-#1040 := (iff #877 #1039)
-#1037 := (iff #876 #1036)
-#1038 := [rewrite]: #1037
-#1041 := [monotonicity #1038]: #1040
-#1044 := [monotonicity #1041]: #1043
-#1049 := [trans #1044 #1047]: #1048
-#1052 := [monotonicity #1049]: #1051
-#1201 := [monotonicity #1052 #1198]: #1200
-#837 := (not #832)
-#744 := (not #741)
-#750 := (or #358 #744)
-#755 := (and #741 #750)
-#786 := (or #755 #783)
-#758 := (or #719 #755)
-#789 := (and #758 #786)
-#792 := (or #664 #789)
-#631 := (+ #23 #630)
-#632 := (<= #631 0::int)
-#635 := (or #613 #632)
-#638 := (forall (vars (?x6 int)) #635)
-#624 := (exists (vars (?x4 int)) #619)
-#627 := (not #624)
-#641 := (or #627 #638)
-#644 := (and #624 #641)
-#647 := (or #601 #644)
-#795 := (and #647 #792)
-#528 := (not #525)
-#858 := (or #528 #795 #837)
-#863 := (and #525 #858)
-#866 := (not #863)
-#1031 := (~ #866 #1030)
-#1027 := (not #858)
-#1028 := (~ #1027 #1026)
-#1023 := (not #837)
-#1024 := (~ #1023 #832)
-#1021 := (~ #832 #832)
-#1019 := (~ #557 #557)
-#1020 := [refl]: #1019
-#1017 := (~ #555 #555)
-#1018 := [refl]: #1017
-#1015 := (~ #551 #551)
-#1013 := (~ #548 #548)
-#1014 := [refl]: #1013
-#1016 := [nnf-pos #1014]: #1015
-#1011 := (~ #183 #183)
-#1012 := [refl]: #1011
-#1022 := [monotonicity #1012 #1016 #1018 #1020]: #1021
-#1025 := [nnf-neg #1022]: #1024
-#1008 := (not #795)
-#1009 := (~ #1008 #1007)
-#1004 := (not #792)
-#1005 := (~ #1004 #1003)
-#1000 := (not #789)
-#1001 := (~ #1000 #999)
-#996 := (not #786)
-#997 := (~ #996 #995)
-#993 := (~ #992 #992)
-#994 := [refl]: #993
-#985 := (not #755)
-#986 := (~ #985 #984)
-#981 := (not #750)
-#982 := (~ #981 #980)
-#977 := (not #744)
-#978 := (~ #977 #741)
-#975 := (~ #741 #741)
-#973 := (~ #738 #738)
-#974 := [refl]: #973
-#976 := [nnf-pos #974]: #975
-#979 := [nnf-neg #976]: #978
-#971 := (~ #970 #970)
-#972 := [refl]: #971
-#983 := [nnf-neg #972 #979]: #982
-#966 := (~ #744 #965)
-#967 := [sk]: #966
-#987 := [nnf-neg #967 #983]: #986
-#998 := [nnf-neg #987 #994]: #997
-#989 := (not #758)
-#990 := (~ #989 #988)
-#952 := (~ #951 #951)
-#953 := [refl]: #952
-#991 := [nnf-neg #953 #987]: #990
-#1002 := [nnf-neg #991 #998]: #1001
-#949 := (~ #948 #948)
-#950 := [refl]: #949
-#1006 := [nnf-neg #950 #1002]: #1005
-#945 := (not #647)
-#946 := (~ #945 #944)
-#941 := (not #644)
-#942 := (~ #941 #940)
-#937 := (not #641)
-#938 := (~ #937 #936)
-#931 := (not #638)
-#932 := (~ #931 #930)
-#933 := [sk]: #932
-#915 := (not #627)
-#916 := (~ #915 #910)
-#911 := (~ #624 #910)
-#912 := [sk]: #911
-#917 := [nnf-neg #912]: #916
-#939 := [nnf-neg #917 #933]: #938
-#898 := (~ #627 #897)
-#895 := (~ #894 #894)
-#896 := [refl]: #895
-#899 := [nnf-neg #896]: #898
-#943 := [nnf-neg #899 #939]: #942
-#892 := (~ #891 #891)
-#893 := [refl]: #892
-#947 := [nnf-neg #893 #943]: #946
-#1010 := [nnf-neg #947 #1006]: #1009
-#888 := (not #528)
-#889 := (~ #888 #525)
-#886 := (~ #525 #525)
-#884 := (~ #522 #522)
-#885 := [refl]: #884
-#887 := [nnf-pos #885]: #886
-#890 := [nnf-neg #887]: #889
-#1029 := [nnf-neg #890 #1010 #1025]: #1028
-#880 := (~ #528 #879)
-#881 := [sk]: #880
-#1032 := [nnf-neg #881 #1029]: #1031
-#9 := (= uf_2 #8)
-#575 := (and #9 #183 #551 #555 #557)
-#580 := (not #575)
-#798 := (or #580 #795)
-#801 := (and #9 #798)
-#804 := (or #528 #801)
-#807 := (and #525 #804)
-#822 := (not #807)
-#867 := (iff #822 #866)
-#864 := (iff #807 #863)
-#861 := (iff #804 #858)
-#843 := (or #795 #837)
-#855 := (or #528 #843)
-#859 := (iff #855 #858)
-#860 := [rewrite]: #859
-#856 := (iff #804 #855)
-#853 := (iff #801 #843)
+#66 := uf_10
+#283 := (= uf_10 uf_12)
+#361 := (not #283)
+#280 := (= uf_5 uf_11)
+#370 := (not #280)
+#275 := (= #64 uf_10)
+#388 := (not #275)
+#853 := (or #388 #370 #361 #810 #671 #757 #794 #801 #807 #814)
+#882 := (and #853 #877)
+#718 := (+ uf_1 #717)
+#719 := (<= #718 0::int)
+#903 := (or #671 #719 #882)
+#722 := (not #719)
+decl uf_8 :: int
+#41 := uf_8
+#700 := (* -1::int uf_8)
+#701 := (+ #20 #700)
+#702 := (<= #701 0::int)
+#674 := (* -1::int #16)
+#675 := (+ uf_1 #674)
+#676 := (<= #675 0::int)
+#677 := (not #676)
+#680 := (and #636 #677)
+#683 := (not #680)
+#705 := (or #683 #702)
+#708 := (forall (vars (?x6 int)) #705)
+#47 := (= #20 uf_8)
+#689 := (or #47 #683)
+#694 := (exists (vars (?x4 int)) #689)
+#697 := (not #694)
+#711 := (or #697 #708)
+#714 := (and #694 #711)
+decl uf_9 :: int
+#43 := uf_9
+#180 := (= uf_5 uf_9)
+#218 := (not #180)
+#177 := (= uf_6 uf_8)
+#227 := (not #177)
+decl uf_7 :: int
+#39 := uf_7
+#174 := (= uf_4 uf_7)
+#236 := (not #174)
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+#523 := (not #171)
+#556 := (not #9)
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+#956 := (and #9 #951)
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+#649 := (>= #651 0::int)
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 #1 := true
-#848 := (and true #843)
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-#810 := (or #500 #807)
-#813 := (not #810)
-#107 := (= #106 uf_12)
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-#20 := (<= 0::int #19)
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-#104 := (implies #102 #103)
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-#109 := (and #105 #108)
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-#83 := (<= 0::int uf_11)
-#90 := (and #83 #89)
-#86 := (+ uf_5 1::int)
-#87 := (= uf_13 #86)
-#91 := (and #87 #90)
-#31 := (<= 1::int uf_5)
-#84 := (and #83 #31)
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-#93 := (and true #92)
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-#115 := (and #112 #114)
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-#111 := (<= #74 uf_6)
-#117 := (and #111 #116)
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-#119 := (and true #118)
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-#71 := (and #70 #32)
-#72 := (and #32 #71)
-#73 := (and true #72)
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-#59 := (< #19 uf_1)
-#60 := (and #20 #59)
-#65 := (implies #60 #64)
-#66 := (forall (vars (?x6 int)) #65)
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-#67 := (implies #63 #66)
-#68 := (and #63 #67)
-#52 := (= uf_9 uf_5)
-#53 := (and #50 #52)
-#54 := (and #48 #53)
-#55 := (and #32 #54)
-#46 := (<= uf_1 uf_5)
-#56 := (and #46 #55)
-#57 := (and #32 #56)
-#58 := (and true #57)
-#69 := (implies #58 #68)
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-#40 := (= #39 uf_6)
-#41 := (and #40 #32)
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-#33 := (< #19 uf_5)
-#34 := (and #20 #33)
-#37 := (implies #34 #36)
-#38 := (forall (vars (?x3 int)) #37)
-#42 := (and #38 #41)
-#43 := (and #32 #42)
-#44 := (and true #43)
-#27 := (= #8 uf_2)
-#45 := (and #27 #44)
-#124 := (implies #45 #123)
-#125 := (and #27 #124)
-#24 := (<= #23 uf_2)
-#21 := (< #19 1::int)
-#22 := (and #20 #21)
-#25 := (implies #22 #24)
-#26 := (forall (vars (?x1 int)) #25)
-#126 := (implies #26 #125)
-#127 := (and #26 #126)
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+#88 := (and #87 true)
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+#125 := (and #23 #124)
 #12 := (<= 1::int 1::int)
 #13 := (and #12 #12)
 #10 := (<= 0::int 0::int)
 #14 := (and #10 #13)
 #15 := (and #10 #14)
-#16 := (and #9 #15)
+#126 := (implies #15 #125)
+#127 := (implies #9 #126)
 #6 := (< 0::int uf_1)
-#17 := (and #6 #16)
-#18 := (and true #17)
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-#816 := (iff #129 #813)
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-#467 := (or #466 #460)
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-#814 := (iff #472 #813)
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-#780 := [rewrite]: #779
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-#559 := [rewrite]: #558
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-#768 := [monotonicity #765]: #767
-#561 := (iff #32 #560)
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-#771 := [monotonicity #562 #768]: #770
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-#762 := [rewrite]: #761
-#774 := [monotonicity #762 #771]: #773
-#777 := [monotonicity #562 #774]: #776
-#782 := [trans #777 #780]: #781
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+#782 := [quant-intro #779]: #781
 #785 := [monotonicity #782]: #784
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-#658 := [monotonicity #562 #655]: #657
-#663 := [trans #658 #661]: #662
-#666 := [monotonicity #663]: #665
-#794 := [monotonicity #666 #791]: #793
-#648 := (iff #270 #647)
-#645 := (iff #263 #644)
-#642 := (iff #258 #641)
-#639 := (iff #251 #638)
-#636 := (iff #248 #635)
-#633 := (iff #64 #632)
-#634 := [rewrite]: #633
-#614 := (iff #241 #613)
-#611 := (iff #60 #610)
-#608 := (iff #59 #607)
-#609 := [rewrite]: #608
-#612 := [monotonicity #504 #609]: #611
-#615 := [monotonicity #612]: #614
-#637 := [monotonicity #615 #634]: #636
-#640 := [quant-intro #637]: #639
-#628 := (iff #257 #627)
-#625 := (iff #245 #624)
-#622 := (iff #242 #619)
-#616 := (or #613 #61)
-#620 := (iff #616 #619)
-#621 := [rewrite]: #620
-#617 := (iff #242 #616)
-#618 := [monotonicity #615]: #617
-#623 := [trans #618 #621]: #622
-#626 := [quant-intro #623]: #625
+#788 := [monotonicity #785]: #787
+#793 := [trans #788 #791]: #792
+#796 := [monotonicity #782 #793]: #795
+#758 := (iff #327 #757)
+#755 := (iff #80 #754)
+#751 := (iff #79 #752)
+#753 := [rewrite]: #751
+#748 := (iff #73 #749)
+#750 := [rewrite]: #748
+#756 := [monotonicity #750 #753]: #755
+#759 := [monotonicity #756]: #758
+#828 := [monotonicity #759 #796]: #827
+#802 := (iff #336 #801)
+#799 := (iff #292 #797)
+#800 := [rewrite]: #799
+#803 := [monotonicity #800]: #802
+#831 := [monotonicity #803 #828]: #830
+#808 := (iff #345 #807)
+#805 := (iff #286 #804)
+#665 := (iff #28 #666)
+#667 := [rewrite]: #665
+#806 := [monotonicity #667 #750]: #805
+#809 := [monotonicity #806]: #808
+#834 := [monotonicity #809 #831]: #833
+#864 := [monotonicity #834]: #863
+#867 := [monotonicity #864]: #866
+#672 := (iff #245 #671)
+#669 := (iff #29 #668)
+#662 := (iff #26 #663)
+#664 := [rewrite]: #662
+#670 := [monotonicity #664 #667]: #669
+#673 := [monotonicity #670]: #672
+#870 := [monotonicity #673 #867]: #869
+#860 := (iff #453 #813)
+#858 := (iff #102 #814)
+#859 := [rewrite]: #858
+#861 := [monotonicity #859]: #860
+#873 := [monotonicity #861 #870]: #872
+#876 := [monotonicity #673 #873]: #875
+#881 := [trans #876 #879]: #880
+#856 := (iff #406 #853)
+#835 := (or #361 #832)
+#838 := (or #370 #835)
+#841 := (or #810 #838)
+#844 := (or #388 #841)
+#847 := (or #814 #844)
+#850 := (or #671 #847)
+#854 := (iff #850 #853)
+#855 := [rewrite]: #854
+#851 := (iff #406 #850)
+#848 := (iff #398 #847)
+#845 := (iff #389 #844)
+#842 := (iff #380 #841)
+#839 := (iff #371 #838)
+#836 := (iff #362 #835)
+#837 := [monotonicity #834]: #836
+#840 := [monotonicity #837]: #839
+#811 := (iff #379 #810)
+#812 := [monotonicity #667]: #811
+#843 := [monotonicity #812 #840]: #842
+#846 := [monotonicity #843]: #845
+#824 := (iff #397 #814)
+#819 := (not #813)
+#822 := (iff #819 #814)
+#823 := [rewrite]: #822
+#820 := (iff #397 #819)
+#817 := (iff #65 #813)
+#818 := [rewrite]: #817
+#821 := [monotonicity #818]: #820
+#825 := [trans #821 #823]: #824
+#849 := [monotonicity #825 #846]: #848
+#852 := [monotonicity #673 #849]: #851
+#857 := [trans #852 #855]: #856
+#884 := [monotonicity #857 #881]: #883
+#896 := [monotonicity #673 #884]: #895
+#892 := (iff #488 #719)
+#887 := (not #722)
+#890 := (iff #887 #719)
+#891 := [rewrite]: #890
+#888 := (iff #488 #887)
+#885 := (iff #63 #722)
+#886 := [rewrite]: #885
+#889 := [monotonicity #886]: #888
+#893 := [trans #889 #891]: #892
+#899 := [monotonicity #893 #896]: #898
+#902 := [monotonicity #673 #899]: #901
+#907 := [trans #902 #905]: #906
+#746 := (iff #263 #743)
+#725 := (or #218 #714)
+#728 := (or #227 #725)
+#731 := (or #236 #728)
+#734 := (or #671 #731)
+#737 := (or #722 #734)
+#740 := (or #671 #737)
+#744 := (iff #740 #743)
+#745 := [rewrite]: #744
+#741 := (iff #263 #740)
+#738 := (iff #255 #737)
+#735 := (iff #246 #734)
+#732 := (iff #237 #731)
+#729 := (iff #228 #728)
+#726 := (iff #219 #725)
+#715 := (iff #212 #714)
+#712 := (iff #207 #711)
+#709 := (iff #193 #708)
+#706 := (iff #190 #705)
+#703 := (iff #50 #702)
+#704 := [rewrite]: #703
+#684 := (iff #183 #683)
+#681 := (iff #46 #680)
+#678 := (iff #45 #677)
+#679 := [rewrite]: #678
+#682 := [monotonicity #635 #679]: #681
+#685 := [monotonicity #682]: #684
+#707 := [monotonicity #685 #704]: #706
+#710 := [quant-intro #707]: #709
+#698 := (iff #206 #697)
+#695 := (iff #187 #694)
+#692 := (iff #184 #689)
+#686 := (or #683 #47)
+#690 := (iff #686 #689)
+#691 := [rewrite]: #690
+#687 := (iff #184 #686)
+#688 := [monotonicity #685]: #687
+#693 := [trans #688 #691]: #692
+#696 := [quant-intro #693]: #695
+#699 := [monotonicity #696]: #698
+#713 := [monotonicity #699 #710]: #712
+#716 := [monotonicity #696 #713]: #715
+#727 := [monotonicity #716]: #726
+#730 := [monotonicity #727]: #729
+#733 := [monotonicity #730]: #732
+#736 := [monotonicity #673 #733]: #735
+#723 := (iff #254 #722)
+#720 := (iff #38 #719)
+#721 := [rewrite]: #720
+#724 := [monotonicity #721]: #723
+#739 := [monotonicity #724 #736]: #738
+#742 := [monotonicity #673 #739]: #741
+#747 := [trans #742 #745]: #746
+#910 := [monotonicity #747 #907]: #909
+#938 := [monotonicity #673 #910]: #937
+#941 := [monotonicity #938]: #940
+#934 := (iff #532 #933)
+#931 := (iff #168 #930)
+#928 := (iff #165 #927)
+#925 := (iff #33 #924)
+#926 := [rewrite]: #925
+#920 := (iff #164 #919)
+#917 := (iff #31 #916)
+#914 := (iff #30 #913)
+#915 := [rewrite]: #914
+#918 := [monotonicity #635 #915]: #917
+#921 := [monotonicity #918]: #920
+#929 := [monotonicity #921 #926]: #928
+#932 := [quant-intro #929]: #931
+#935 := [monotonicity #932]: #934
+#944 := [monotonicity #935 #941]: #943
+#947 := [monotonicity #673 #944]: #946
+#950 := [monotonicity #947]: #949
+#955 := [trans #950 #953]: #954
+#958 := [monotonicity #955]: #957
+#660 := (iff #568 #659)
+#657 := (iff #159 #656)
+#654 := (iff #156 #653)
+#648 := (iff #21 #649)
+#652 := [rewrite]: #648
+#645 := (iff #155 #644)
+#642 := (iff #19 #641)
+#638 := (iff #18 #637)
+#640 := [rewrite]: #638
+#643 := [monotonicity #635 #640]: #642
+#646 := [monotonicity #643]: #645
+#655 := [monotonicity #646 #652]: #654
+#658 := [quant-intro #655]: #657
+#661 := [monotonicity #658]: #660
+#961 := [monotonicity #661 #958]: #960
+#964 := [monotonicity #658 #961]: #963
+#632 := (iff #580 false)
+#627 := (not true)
+#630 := (iff #627 false)
+#631 := [rewrite]: #630
+#628 := (iff #580 #627)
+#625 := (iff #152 true)
+#617 := (and true true)
+#620 := (and true #617)
+#623 := (iff #620 true)
+#624 := [rewrite]: #623
+#621 := (iff #152 #620)
+#618 := (iff #149 #617)
+#615 := (iff #12 true)
+#616 := [rewrite]: #615
+#613 := (iff #10 true)
+#614 := [rewrite]: #613
+#619 := [monotonicity #614 #616]: #618
+#622 := [monotonicity #614 #619]: #621
+#626 := [trans #622 #624]: #625
 #629 := [monotonicity #626]: #628
-#643 := [monotonicity #629 #640]: #642
-#646 := [monotonicity #626 #643]: #645
-#602 := (iff #269 #601)
-#599 := (iff #231 #596)
-#587 := (and #560 #222)
-#590 := (and #584 #587)
-#593 := (and #560 #590)
-#597 := (iff #593 #596)
-#598 := [rewrite]: #597
-#594 := (iff #231 #593)
-#591 := (iff #228 #590)
-#588 := (iff #225 #587)
-#589 := [monotonicity #562]: #588
-#585 := (iff #46 #584)
-#586 := [rewrite]: #585
-#592 := [monotonicity #586 #589]: #591
-#595 := [monotonicity #562 #592]: #594
-#600 := [trans #595 #598]: #599
-#603 := [monotonicity #600]: #602
-#649 := [monotonicity #603 #646]: #648
-#797 := [monotonicity #649 #794]: #796
-#581 := (iff #442 #580)
-#578 := (iff #207 #575)
-#563 := (and #560 #183)
-#566 := (and #551 #563)
-#569 := (and #560 #566)
-#572 := (and #9 #569)
-#576 := (iff #572 #575)
-#577 := [rewrite]: #576
-#573 := (iff #207 #572)
-#570 := (iff #197 #569)
-#567 := (iff #194 #566)
-#564 := (iff #189 #563)
-#565 := [monotonicity #562]: #564
-#552 := (iff #180 #551)
-#549 := (iff #177 #548)
-#546 := (iff #36 #545)
-#547 := [rewrite]: #546
-#541 := (iff #176 #540)
-#538 := (iff #34 #537)
-#535 := (iff #33 #531)
-#536 := [rewrite]: #535
-#539 := [monotonicity #504 #536]: #538
-#542 := [monotonicity #539]: #541
-#550 := [monotonicity #542 #547]: #549
-#553 := [quant-intro #550]: #552
-#568 := [monotonicity #553 #565]: #567
-#571 := [monotonicity #562 #568]: #570
-#574 := [monotonicity #571]: #573
-#579 := [trans #574 #577]: #578
-#582 := [monotonicity #579]: #581
-#800 := [monotonicity #582 #797]: #799
-#803 := [monotonicity #800]: #802
-#529 := (iff #454 #528)
-#526 := (iff #171 #525)
-#523 := (iff #168 #522)
-#517 := (iff #24 #518)
-#521 := [rewrite]: #517
-#514 := (iff #167 #513)
-#511 := (iff #22 #510)
-#507 := (iff #21 #506)
-#509 := [rewrite]: #507
-#512 := [monotonicity #504 #509]: #511
-#515 := [monotonicity #512]: #514
-#524 := [monotonicity #515 #521]: #523
-#527 := [quant-intro #524]: #526
-#530 := [monotonicity #527]: #529
-#806 := [monotonicity #530 #803]: #805
-#809 := [monotonicity #527 #806]: #808
-#501 := (iff #466 #500)
-#498 := (iff #157 #495)
-#483 := (and true true)
-#486 := (and true #483)
-#489 := (and #9 #486)
-#492 := (and #480 #489)
-#496 := (iff #492 #495)
-#497 := [rewrite]: #496
-#493 := (iff #157 #492)
-#490 := (iff #154 #489)
-#487 := (iff #151 #486)
-#484 := (iff #148 #483)
-#477 := (iff #12 true)
-#478 := [rewrite]: #477
-#475 := (iff #10 true)
-#476 := [rewrite]: #475
-#485 := [monotonicity #476 #478]: #484
-#488 := [monotonicity #476 #485]: #487
-#491 := [monotonicity #488]: #490
-#481 := (iff #6 #480)
+#633 := [trans #629 #631]: #632
+#978 := [monotonicity #633 #964]: #977
+#981 := [monotonicity #978]: #980
+#974 := (iff #597 #965)
+#966 := (not #965)
+#969 := (not #966)
+#972 := (iff #969 #965)
+#973 := [rewrite]: #972
+#970 := (iff #597 #969)
+#967 := (iff #6 #966)
+#968 := [rewrite]: #967
+#971 := [monotonicity #968]: #970
+#975 := [trans #971 #973]: #974
+#984 := [monotonicity #975 #981]: #983
+#989 := [trans #984 #987]: #988
+#992 := [monotonicity #989]: #991
+#611 := (iff #130 #610)
+#608 := (iff #129 #598)
+#603 := (implies true #598)
+#606 := (iff #603 #598)
+#607 := [rewrite]: #606
+#604 := (iff #129 #603)
+#601 := (iff #128 #598)
+#594 := (implies #6 #589)
+#599 := (iff #594 #598)
+#600 := [rewrite]: #599
+#595 := (iff #128 #594)
+#592 := (iff #127 #589)
+#586 := (implies #9 #581)
+#590 := (iff #586 #589)
+#591 := [rewrite]: #590
+#587 := (iff #127 #586)
+#584 := (iff #126 #581)
+#577 := (implies #152 #574)
+#582 := (iff #577 #581)
+#583 := [rewrite]: #582
+#578 := (iff #126 #577)
+#575 := (iff #125 #574)
+#572 := (iff #124 #569)
+#565 := (implies #159 #562)
+#570 := (iff #565 #569)
+#571 := [rewrite]: #570
+#566 := (iff #124 #565)
+#563 := (iff #123 #562)
+#560 := (iff #122 #557)
+#553 := (implies #9 #541)
+#558 := (iff #553 #557)
+#559 := [rewrite]: #558
+#554 := (iff #122 #553)
+#551 := (iff #121 #541)
+#546 := (implies true #541)
+#549 := (iff #546 #541)
+#550 := [rewrite]: #549
+#547 := (iff #121 #546)
+#544 := (iff #120 #541)
+#538 := (implies #29 #533)
+#542 := (iff #538 #541)
+#543 := [rewrite]: #542
+#539 := (iff #120 #538)
+#536 := (iff #119 #533)
+#529 := (implies #168 #524)
+#534 := (iff #529 #533)
+#535 := [rewrite]: #534
+#530 := (iff #119 #529)
+#527 := (iff #118 #524)
+#520 := (implies #171 #515)
+#525 := (iff #520 #524)
+#526 := [rewrite]: #525
+#521 := (iff #118 #520)
+#518 := (iff #117 #515)
+#512 := (implies #29 #509)
+#516 := (iff #512 #515)
+#517 := [rewrite]: #516
+#513 := (iff #117 #512)
+#510 := (iff #116 #509)
+#507 := (iff #115 #497)
+#502 := (implies true #497)
+#505 := (iff #502 #497)
+#506 := [rewrite]: #505
+#503 := (iff #115 #502)
+#500 := (iff #114 #497)
+#494 := (implies #29 #489)
+#498 := (iff #494 #497)
+#499 := [rewrite]: #498
+#495 := (iff #114 #494)
+#492 := (iff #113 #489)
+#485 := (implies #63 #480)
+#490 := (iff #485 #489)
+#491 := [rewrite]: #490
+#486 := (iff #113 #485)
+#483 := (iff #112 #480)
+#477 := (implies #29 #474)
+#481 := (iff #477 #480)
 #482 := [rewrite]: #481
-#494 := [monotonicity #482 #491]: #493
-#499 := [trans #494 #497]: #498
-#502 := [monotonicity #499]: #501
-#812 := [monotonicity #502 #809]: #811
-#815 := [monotonicity #812]: #814
-#473 := (iff #129 #472)
-#470 := (iff #128 #467)
-#463 := (implies #157 #460)
-#468 := (iff #463 #467)
-#469 := [rewrite]: #468
-#464 := (iff #128 #463)
-#461 := (iff #127 #460)
-#458 := (iff #126 #455)
-#451 := (implies #171 #448)
-#456 := (iff #451 #455)
-#457 := [rewrite]: #456
-#452 := (iff #126 #451)
-#449 := (iff #125 #448)
-#446 := (iff #124 #443)
-#439 := (implies #207 #436)
-#444 := (iff #439 #443)
-#445 := [rewrite]: #444
-#440 := (iff #124 #439)
-#437 := (iff #123 #436)
-#434 := (iff #122 #431)
-#427 := (implies #278 #424)
-#432 := (iff #427 #431)
-#433 := [rewrite]: #432
-#428 := (iff #122 #427)
-#425 := (iff #121 #424)
-#422 := (iff #120 #419)
-#415 := (implies #405 #370)
-#420 := (iff #415 #419)
-#421 := [rewrite]: #420
-#416 := (iff #120 #415)
-#371 := (iff #109 #370)
-#368 := (iff #108 #365)
-#361 := (implies #355 #358)
-#366 := (iff #361 #365)
-#367 := [rewrite]: #366
-#362 := (iff #108 #361)
-#359 := (iff #107 #358)
-#360 := [rewrite]: #359
-#356 := (iff #105 #355)
-#353 := (iff #104 #352)
-#354 := [rewrite]: #353
-#357 := [quant-intro #354]: #356
-#363 := [monotonicity #357 #360]: #362
-#369 := [trans #363 #367]: #368
-#372 := [monotonicity #357 #369]: #371
-#413 := (iff #119 #405)
-#408 := (and true #405)
-#411 := (iff #408 #405)
-#412 := [rewrite]: #411
-#409 := (iff #119 #408)
-#406 := (iff #118 #405)
-#403 := (iff #117 #402)
-#400 := (iff #116 #399)
-#397 := (iff #115 #396)
-#394 := (iff #114 #391)
-#388 := (and #385 #316)
-#392 := (iff #388 #391)
-#393 := [rewrite]: #392
-#389 := (iff #114 #388)
-#324 := (iff #93 #316)
-#319 := (and true #316)
-#322 := (iff #319 #316)
-#323 := [rewrite]: #322
-#320 := (iff #93 #319)
-#317 := (iff #92 #316)
-#314 := (iff #91 #311)
-#308 := (and #305 #90)
-#312 := (iff #308 #311)
-#313 := [rewrite]: #312
-#309 := (iff #91 #308)
-#306 := (iff #87 #305)
-#303 := (= #86 #302)
+#478 := (iff #112 #477)
+#475 := (iff #111 #474)
+#472 := (iff #110 #462)
+#467 := (implies true #462)
+#470 := (iff #467 #462)
+#471 := [rewrite]: #470
+#468 := (iff #110 #467)
+#465 := (iff #109 #462)
+#459 := (implies #29 #454)
+#463 := (iff #459 #462)
+#464 := [rewrite]: #463
+#460 := (iff #109 #459)
+#457 := (iff #108 #454)
+#450 := (implies #102 #445)
+#455 := (iff #450 #454)
+#456 := [rewrite]: #455
+#451 := (iff #108 #450)
+#448 := (iff #107 #445)
+#442 := (implies #29 #437)
+#446 := (iff #442 #445)
+#447 := [rewrite]: #446
+#443 := (iff #107 #442)
+#440 := (iff #106 #437)
+#433 := (implies #418 #428)
+#438 := (iff #433 #437)
+#439 := [rewrite]: #438
+#434 := (iff #106 #433)
+#431 := (iff #105 #428)
+#424 := (implies #421 #346)
+#429 := (iff #424 #428)
+#430 := [rewrite]: #429
+#425 := (iff #105 #424)
+#356 := (iff #94 #346)
+#351 := (implies true #346)
+#354 := (iff #351 #346)
+#355 := [rewrite]: #354
+#352 := (iff #94 #351)
+#349 := (iff #93 #346)
+#342 := (implies #286 #337)
+#347 := (iff #342 #346)
+#348 := [rewrite]: #347
+#343 := (iff #93 #342)
+#340 := (iff #92 #337)
+#333 := (implies #292 #328)
+#338 := (iff #333 #337)
+#339 := [rewrite]: #338
+#334 := (iff #92 #333)
+#331 := (iff #91 #328)
+#324 := (implies #80 #321)
+#329 := (iff #324 #328)
+#330 := [rewrite]: #329
+#325 := (iff #91 #324)
+#322 := (iff #90 #321)
+#319 := (iff #89 #316)
+#312 := (implies #299 #302)
+#317 := (iff #312 #316)
+#318 := [rewrite]: #317
+#313 := (iff #89 #312)
+#310 := (iff #88 #302)
+#305 := (and #302 true)
+#308 := (iff #305 #302)
+#309 := [rewrite]: #308
+#306 := (iff #88 #305)
+#303 := (iff #87 #302)
 #304 := [rewrite]: #303
 #307 := [monotonicity #304]: #306
-#310 := [monotonicity #307]: #309
-#315 := [trans #310 #313]: #314
-#300 := (iff #84 #299)
-#301 := [rewrite]: #300
-#318 := [monotonicity #301 #315]: #317
-#321 := [monotonicity #318]: #320
-#325 := [trans #321 #323]: #324
-#386 := (iff #113 #385)
-#387 := [rewrite]: #386
-#390 := [monotonicity #387 #325]: #389
-#395 := [trans #390 #393]: #394
-#383 := (iff #112 #382)
-#384 := [rewrite]: #383
-#398 := [monotonicity #384 #395]: #397
-#401 := [monotonicity #398]: #400
-#404 := [monotonicity #401]: #403
-#407 := [monotonicity #404]: #406
-#410 := [monotonicity #407]: #409
-#414 := [trans #410 #412]: #413
-#417 := [monotonicity #414 #372]: #416
-#423 := [trans #417 #421]: #422
-#380 := (iff #110 #377)
-#373 := (implies #341 #370)
-#378 := (iff #373 #377)
-#379 := [rewrite]: #378
-#374 := (iff #110 #373)
-#349 := (iff #100 #341)
-#344 := (and true #341)
-#347 := (iff #344 #341)
-#348 := [rewrite]: #347
-#345 := (iff #100 #344)
-#342 := (iff #99 #341)
-#339 := (iff #98 #338)
-#336 := (iff #97 #335)
-#333 := (iff #96 #332)
-#330 := (iff #95 #329)
-#327 := (iff #94 #326)
-#297 := (iff #82 #296)
+#311 := [trans #307 #309]: #310
+#300 := (iff #85 #299)
+#297 := (iff #84 #296)
 #298 := [rewrite]: #297
-#328 := [monotonicity #298 #325]: #327
-#294 := (iff #80 #293)
-#295 := [rewrite]: #294
-#331 := [monotonicity #295 #328]: #330
-#291 := (iff #78 #31)
-#292 := [rewrite]: #291
-#334 := [monotonicity #292 #331]: #333
-#289 := (iff #77 #288)
-#290 := [rewrite]: #289
-#337 := [monotonicity #290 #334]: #336
-#340 := [monotonicity #337]: #339
-#343 := [monotonicity #340]: #342
-#346 := [monotonicity #343]: #345
-#350 := [trans #346 #348]: #349
-#375 := [monotonicity #350 #372]: #374
-#381 := [trans #375 #379]: #380
-#426 := [monotonicity #381 #423]: #425
-#286 := (iff #73 #278)
-#281 := (and true #278)
-#284 := (iff #281 #278)
+#301 := [quant-intro #298]: #300
+#314 := [monotonicity #301 #311]: #313
+#320 := [trans #314 #318]: #319
+#323 := [monotonicity #301 #320]: #322
+#326 := [monotonicity #323]: #325
+#332 := [trans #326 #330]: #331
+#293 := (iff #77 #292)
+#290 := (= #76 #289)
+#291 := [rewrite]: #290
+#294 := [monotonicity #291]: #293
+#335 := [monotonicity #294 #332]: #334
+#341 := [trans #335 #339]: #340
+#287 := (iff #74 #286)
+#288 := [rewrite]: #287
+#344 := [monotonicity #288 #341]: #343
+#350 := [trans #344 #348]: #349
+#353 := [monotonicity #350]: #352
+#357 := [trans #353 #355]: #356
+#422 := (iff #104 #421)
+#423 := [rewrite]: #422
+#426 := [monotonicity #423 #357]: #425
+#432 := [trans #426 #430]: #431
+#419 := (iff #103 #418)
+#420 := [rewrite]: #419
+#435 := [monotonicity #420 #432]: #434
+#441 := [trans #435 #439]: #440
+#444 := [monotonicity #441]: #443
+#449 := [trans #444 #447]: #448
+#452 := [monotonicity #449]: #451
+#458 := [trans #452 #456]: #457
+#461 := [monotonicity #458]: #460
+#466 := [trans #461 #464]: #465
+#469 := [monotonicity #466]: #468
+#473 := [trans #469 #471]: #472
+#416 := (iff #101 #406)
+#411 := (implies true #406)
+#414 := (iff #411 #406)
+#415 := [rewrite]: #414
+#412 := (iff #101 #411)
+#409 := (iff #100 #406)
+#403 := (implies #29 #398)
+#407 := (iff #403 #406)
+#408 := [rewrite]: #407
+#404 := (iff #100 #403)
+#401 := (iff #99 #398)
+#394 := (implies #65 #389)
+#399 := (iff #394 #398)
+#400 := [rewrite]: #399
+#395 := (iff #99 #394)
+#392 := (iff #98 #389)
+#385 := (implies #275 #380)
+#390 := (iff #385 #389)
+#391 := [rewrite]: #390
+#386 := (iff #98 #385)
+#383 := (iff #97 #380)
+#376 := (implies #28 #371)
+#381 := (iff #376 #380)
+#382 := [rewrite]: #381
+#377 := (iff #97 #376)
+#374 := (iff #96 #371)
+#367 := (implies #280 #362)
+#372 := (iff #367 #371)
+#373 := [rewrite]: #372
+#368 := (iff #96 #367)
+#365 := (iff #95 #362)
+#358 := (implies #283 #346)
+#363 := (iff #358 #362)
+#364 := [rewrite]: #363
+#359 := (iff #95 #358)
+#284 := (iff #72 #283)
 #285 := [rewrite]: #284
-#282 := (iff #73 #281)
-#279 := (iff #72 #278)
-#276 := (iff #71 #275)
+#360 := [monotonicity #285 #357]: #359
+#366 := [trans #360 #364]: #365
+#281 := (iff #70 #280)
+#282 := [rewrite]: #281
+#369 := [monotonicity #282 #366]: #368
+#375 := [trans #369 #373]: #374
+#278 := (iff #68 #28)
+#279 := [rewrite]: #278
+#378 := [monotonicity #279 #375]: #377
+#384 := [trans #378 #382]: #383
+#276 := (iff #67 #275)
 #277 := [rewrite]: #276
-#280 := [monotonicity #277]: #279
-#283 := [monotonicity #280]: #282
-#287 := [trans #283 #285]: #286
-#429 := [monotonicity #287 #426]: #428
-#435 := [trans #429 #433]: #434
-#273 := (iff #69 #270)
-#266 := (implies #231 #263)
-#271 := (iff #266 #270)
+#387 := [monotonicity #277 #384]: #386
+#393 := [trans #387 #391]: #392
+#396 := [monotonicity #393]: #395
+#402 := [trans #396 #400]: #401
+#405 := [monotonicity #402]: #404
+#410 := [trans #405 #408]: #409
+#413 := [monotonicity #410]: #412
+#417 := [trans #413 #415]: #416
+#476 := [monotonicity #417 #473]: #475
+#479 := [monotonicity #476]: #478
+#484 := [trans #479 #482]: #483
+#487 := [monotonicity #484]: #486
+#493 := [trans #487 #491]: #492
+#496 := [monotonicity #493]: #495
+#501 := [trans #496 #499]: #500
+#504 := [monotonicity #501]: #503
+#508 := [trans #504 #506]: #507
+#273 := (iff #62 #263)
+#268 := (implies true #263)
+#271 := (iff #268 #263)
 #272 := [rewrite]: #271
-#267 := (iff #69 #266)
-#264 := (iff #68 #263)
-#261 := (iff #67 #258)
-#254 := (implies #245 #251)
-#259 := (iff #254 #258)
-#260 := [rewrite]: #259
-#255 := (iff #67 #254)
-#252 := (iff #66 #251)
-#249 := (iff #65 #248)
-#250 := [rewrite]: #249
-#253 := [quant-intro #250]: #252
-#246 := (iff #63 #245)
-#243 := (iff #62 #242)
-#244 := [rewrite]: #243
-#247 := [quant-intro #244]: #246
-#256 := [monotonicity #247 #253]: #255
-#262 := [trans #256 #260]: #261
-#265 := [monotonicity #247 #262]: #264
-#239 := (iff #58 #231)
-#234 := (and true #231)
-#237 := (iff #234 #231)
-#238 := [rewrite]: #237
-#235 := (iff #58 #234)
-#232 := (iff #57 #231)
-#229 := (iff #56 #228)
-#226 := (iff #55 #225)
-#223 := (iff #54 #222)
-#220 := (iff #53 #219)
-#217 := (iff #52 #216)
-#218 := [rewrite]: #217
-#214 := (iff #50 #213)
-#215 := [rewrite]: #214
-#221 := [monotonicity #215 #218]: #220
-#211 := (iff #48 #210)
-#212 := [rewrite]: #211
-#224 := [monotonicity #212 #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#240 := [trans #236 #238]: #239
-#268 := [monotonicity #240 #265]: #267
-#274 := [trans #268 #272]: #273
-#438 := [monotonicity #274 #435]: #437
-#208 := (iff #45 #207)
-#205 := (iff #44 #197)
-#200 := (and true #197)
-#203 := (iff #200 #197)
-#204 := [rewrite]: #203
-#201 := (iff #44 #200)
-#198 := (iff #43 #197)
-#195 := (iff #42 #194)
-#192 := (iff #41 #189)
-#186 := (and #183 #32)
-#190 := (iff #186 #189)
-#191 := [rewrite]: #190
-#187 := (iff #41 #186)
-#184 := (iff #40 #183)
-#185 := [rewrite]: #184
-#188 := [monotonicity #185]: #187
-#193 := [trans #188 #191]: #192
-#181 := (iff #38 #180)
-#178 := (iff #37 #177)
+#269 := (iff #62 #268)
+#266 := (iff #61 #263)
+#260 := (implies #29 #255)
+#264 := (iff #260 #263)
+#265 := [rewrite]: #264
+#261 := (iff #61 #260)
+#258 := (iff #60 #255)
+#251 := (implies #38 #246)
+#256 := (iff #251 #255)
+#257 := [rewrite]: #256
+#252 := (iff #60 #251)
+#249 := (iff #59 #246)
+#242 := (implies #29 #237)
+#247 := (iff #242 #246)
+#248 := [rewrite]: #247
+#243 := (iff #59 #242)
+#240 := (iff #58 #237)
+#233 := (implies #174 #228)
+#238 := (iff #233 #237)
+#239 := [rewrite]: #238
+#234 := (iff #58 #233)
+#231 := (iff #57 #228)
+#224 := (implies #177 #219)
+#229 := (iff #224 #228)
+#230 := [rewrite]: #229
+#225 := (iff #57 #224)
+#222 := (iff #56 #219)
+#215 := (implies #180 #212)
+#220 := (iff #215 #219)
+#221 := [rewrite]: #220
+#216 := (iff #56 #215)
+#213 := (iff #55 #212)
+#210 := (iff #54 #207)
+#203 := (implies #187 #193)
+#208 := (iff #203 #207)
+#209 := [rewrite]: #208
+#204 := (iff #54 #203)
+#201 := (iff #53 #193)
+#196 := (and #193 true)
+#199 := (iff #196 #193)
+#200 := [rewrite]: #199
+#197 := (iff #53 #196)
+#194 := (iff #52 #193)
+#191 := (iff #51 #190)
+#192 := [rewrite]: #191
+#195 := [quant-intro #192]: #194
+#198 := [monotonicity #195]: #197
+#202 := [trans #198 #200]: #201
+#188 := (iff #49 #187)
+#185 := (iff #48 #184)
+#186 := [rewrite]: #185
+#189 := [quant-intro #186]: #188
+#205 := [monotonicity #189 #202]: #204
+#211 := [trans #205 #209]: #210
+#214 := [monotonicity #189 #211]: #213
+#181 := (iff #44 #180)
+#182 := [rewrite]: #181
+#217 := [monotonicity #182 #214]: #216
+#223 := [trans #217 #221]: #222
+#178 := (iff #42 #177)
 #179 := [rewrite]: #178
-#182 := [quant-intro #179]: #181
-#196 := [monotonicity #182 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [monotonicity #199]: #201
-#206 := [trans #202 #204]: #205
-#174 := (iff #27 #9)
-#175 := [rewrite]: #174
-#209 := [monotonicity #175 #206]: #208
-#441 := [monotonicity #209 #438]: #440
-#447 := [trans #441 #445]: #446
-#450 := [monotonicity #175 #447]: #449
-#172 := (iff #26 #171)
-#169 := (iff #25 #168)
-#170 := [rewrite]: #169
-#173 := [quant-intro #170]: #172
-#453 := [monotonicity #173 #450]: #452
-#459 := [trans #453 #457]: #458
-#462 := [monotonicity #173 #459]: #461
-#165 := (iff #18 #157)
-#160 := (and true #157)
-#163 := (iff #160 #157)
-#164 := [rewrite]: #163
-#161 := (iff #18 #160)
-#158 := (iff #17 #157)
-#155 := (iff #16 #154)
-#152 := (iff #15 #151)
-#149 := (iff #14 #148)
-#146 := (iff #13 #12)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#166 := [trans #162 #164]: #165
-#465 := [monotonicity #166 #462]: #464
-#471 := [trans #465 #469]: #470
-#474 := [monotonicity #471]: #473
-#817 := [trans #474 #815]: #816
-#145 := [asserted]: #129
-#818 := [mp #145 #817]: #813
-#819 := [not-or-elim #818]: #495
-#820 := [and-elim #819]: #9
-#824 := [iff-true #820]: #826
-#831 := [monotonicity #824]: #830
-#836 := [trans #831 #834]: #835
-#839 := [monotonicity #836]: #838
-#842 := [monotonicity #839]: #841
-#847 := [trans #842 #845]: #846
-#850 := [monotonicity #824 #847]: #849
-#854 := [trans #850 #852]: #853
-#857 := [monotonicity #854]: #856
-#862 := [trans #857 #860]: #861
-#865 := [monotonicity #862]: #864
-#868 := [monotonicity #865]: #867
-#823 := [not-or-elim #818]: #822
-#869 := [mp #823 #868]: #866
-#1033 := [mp~ #869 #1032]: #1030
-#1034 := [mp #1033 #1201]: #1199
-#1514 := [mp #1034 #1513]: #1509
-#2079 := [mp #1514 #2078]: #2076
-#1835 := [unit-resolution #2079 #2418]: #1213
-#1658 := (or #1208 #874)
-#1659 := [def-axiom]: #1658
-#1728 := [unit-resolution #1659 #1835]: #874
-#1650 := (or #1208 #875)
-#1661 := [def-axiom]: #1650
-#1839 := [unit-resolution #1661 #1835]: #875
-#1840 := [th-lemma #1839 #1728]: #1860
-#1846 := [monotonicity #1840]: #1841
-#1843 := [symm #1846]: #1842
-#1813 := [trans #820 #1843]: #1833
-#1572 := (not #872)
-#1657 := (or #1208 #1572)
-#1573 := [def-axiom]: #1657
-#1772 := [unit-resolution #1573 #1835]: #1572
-#1806 := (not #1833)
-#1803 := (or #1806 #872)
-#1805 := [th-lemma]: #1803
-[unit-resolution #1805 #1772 #1813]: false
+#226 := [monotonicity #179 #223]: #225
+#232 := [trans #226 #230]: #231
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#235 := [monotonicity #176 #232]: #234
+#241 := [trans #235 #239]: #240
+#244 := [monotonicity #241]: #243
+#250 := [trans #244 #248]: #249
+#253 := [monotonicity #250]: #252
+#259 := [trans #253 #257]: #258
+#262 := [monotonicity #259]: #261
+#267 := [trans #262 #265]: #266
+#270 := [monotonicity #267]: #269
+#274 := [trans #270 #272]: #273
+#511 := [monotonicity #274 #508]: #510
+#514 := [monotonicity #511]: #513
+#519 := [trans #514 #517]: #518
+#172 := (iff #37 #171)
+#173 := [rewrite]: #172
+#522 := [monotonicity #173 #519]: #521
+#528 := [trans #522 #526]: #527
+#169 := (iff #35 #168)
+#166 := (iff #34 #165)
+#167 := [rewrite]: #166
+#170 := [quant-intro #167]: #169
+#531 := [monotonicity #170 #528]: #530
+#537 := [trans #531 #535]: #536
+#540 := [monotonicity #537]: #539
+#545 := [trans #540 #543]: #544
+#548 := [monotonicity #545]: #547
+#552 := [trans #548 #550]: #551
+#162 := (iff #24 #9)
+#163 := [rewrite]: #162
+#555 := [monotonicity #163 #552]: #554
+#561 := [trans #555 #559]: #560
+#564 := [monotonicity #163 #561]: #563
+#160 := (iff #23 #159)
+#157 := (iff #22 #156)
+#158 := [rewrite]: #157
+#161 := [quant-intro #158]: #160
+#567 := [monotonicity #161 #564]: #566
+#573 := [trans #567 #571]: #572
+#576 := [monotonicity #161 #573]: #575
+#153 := (iff #15 #152)
+#150 := (iff #14 #149)
+#147 := (iff #13 #12)
+#148 := [rewrite]: #147
+#151 := [monotonicity #148]: #150
+#154 := [monotonicity #151]: #153
+#579 := [monotonicity #154 #576]: #578
+#585 := [trans #579 #583]: #584
+#588 := [monotonicity #585]: #587
+#593 := [trans #588 #591]: #592
+#596 := [monotonicity #593]: #595
+#602 := [trans #596 #600]: #601
+#605 := [monotonicity #602]: #604
+#609 := [trans #605 #607]: #608
+#612 := [monotonicity #609]: #611
+#994 := [trans #612 #992]: #993
+#146 := [asserted]: #130
+#995 := [mp #146 #994]: #990
+#996 := [not-or-elim #995]: #9
+#2042 := (or #556 #2051)
+#2066 := [th-lemma]: #2042
+#2043 := [unit-resolution #2066 #996]: #2051
+decl ?x1!0 :: int
+#1039 := ?x1!0
+#1040 := (uf_3 ?x1!0)
+#1037 := (* -1::int #1040)
+#1038 := (+ uf_2 #1037)
+#1041 := (>= #1038 0::int)
+#1780 := (not #1041)
+#1044 := (>= ?x1!0 0::int)
+#1094 := (not #1044)
+#1042 := (>= ?x1!0 1::int)
+#1427 := (or #1041 #1042 #1094)
+#1432 := (not #1427)
+decl ?x4!1 :: int
+#1081 := ?x4!1
+#1089 := (uf_3 ?x4!1)
+#1262 := (= uf_8 #1089)
+#1086 := (>= ?x4!1 0::int)
+#1505 := (not #1086)
+#1082 := (* -1::int ?x4!1)
+#1083 := (+ uf_1 #1082)
+#1084 := (<= #1083 0::int)
+#1520 := (or #1084 #1505 #1262)
+#1551 := (not #1520)
+decl ?x6!2 :: int
+#1099 := ?x6!2
+#1100 := (uf_3 ?x6!2)
+#1286 := (* -1::int #1100)
+#1287 := (+ uf_8 #1286)
+#1288 := (>= #1287 0::int)
+#1107 := (>= ?x6!2 0::int)
+#1525 := (not #1107)
+#1103 := (* -1::int ?x6!2)
+#1104 := (+ uf_1 #1103)
+#1105 := (<= #1104 0::int)
+#1682 := (or #1105 #1525 #1288 #1551)
+#1685 := (not #1682)
+#2194 := (pattern #20)
+#1435 := (not #636)
+#1494 := (or #47 #1435 #676)
+#1499 := (not #1494)
+#2255 := (forall (vars (?x4 int)) (:pat #2194) #1499)
+#2260 := (or #2255 #1685)
+#2263 := (not #2260)
+#1564 := (not #663)
+#2266 := (or #236 #227 #218 #1564 #810 #722 #2263)
+#2269 := (not #2266)
+decl ?x7!3 :: int
+#1148 := ?x7!3
+#1149 := (uf_3 ?x7!3)
+#1351 := (* -1::int #1149)
+#1352 := (+ uf_12 #1351)
+#1353 := (>= #1352 0::int)
+#1329 := (* -1::int ?x7!3)
+#1330 := (+ uf_13 #1329)
+#1331 := (<= #1330 0::int)
+#1155 := (>= ?x7!3 0::int)
+#1604 := (not #1155)
+#1619 := (or #1604 #1331 #1353)
+#1624 := (not #1619)
+#1586 := (or #1435 #760 #774)
+#2211 := (forall (vars (?x7 int)) (:pat #2194) #1586)
+#2216 := (not #2211)
+#2219 := (or #302 #2216)
+#2222 := (not #2219)
+#2225 := (or #2222 #1624)
+#2228 := (not #2225)
+#1634 := (not #752)
+#1633 := (not #749)
+#2237 := (or #436 #427 #1564 #810 #1633 #1634 #801 #813 #2228)
+#2240 := (not #2237)
+#2231 := (or #388 #370 #361 #1564 #810 #1633 #1634 #801 #814 #2228)
+#2234 := (not #2231)
+#2243 := (or #2234 #2240)
+#2246 := (not #2243)
+#2249 := (or #1564 #810 #719 #2246)
+#2252 := (not #2249)
+#2272 := (or #2252 #2269)
+#2275 := (not #2272)
+#1472 := (or #1435 #911 #924)
+#2203 := (forall (vars (?x3 int)) (:pat #2194) #1472)
+#2208 := (not #2203)
+#1450 := (or #1435 #639 #649)
+#2195 := (forall (vars (?x1 int)) (:pat #2194) #1450)
+#2200 := (not #2195)
+#2278 := (or #523 #1564 #810 #2200 #2208 #2275)
+#1336 := (not #1331)
+#2281 := (not #2278)
+#2525 := [hypothesis]: #2281
+#2115 := (or #2278 #171)
+#2099 := [def-axiom]: #2115
+#2526 := [unit-resolution #2099 #2525]: #171
+#2093 := (or #2278 #2272)
+#2095 := [def-axiom]: #2093
+#2527 := [unit-resolution #2095 #2525]: #2272
+#2106 := (or #2278 #2203)
+#2092 := [def-axiom]: #2106
+#2528 := [unit-resolution #2092 #2525]: #2203
+#2347 := (or #2266 #523 #2208)
+#1786 := (uf_3 uf_7)
+#2291 := (= uf_8 #1786)
+#2341 := (= #36 #1786)
+#2339 := (= #1786 #36)
+#2324 := [hypothesis]: #2269
+#2032 := (or #2266 #174)
+#2033 := [def-axiom]: #2032
+#2335 := [unit-resolution #2033 #2324]: #174
+#2336 := [symm #2335]: #40
+#2340 := [monotonicity #2336]: #2339
+#2342 := [symm #2340]: #2341
+#2343 := (= uf_8 #36)
+#2337 := [hypothesis]: #171
+#2034 := (or #2266 #177)
+#2035 := [def-axiom]: #2034
+#2326 := [unit-resolution #2035 #2324]: #177
+#2338 := [symm #2326]: #42
+#2344 := [trans #2338 #2337]: #2343
+#2345 := [trans #2344 #2342]: #2291
+#2319 := (not #2291)
+#1785 := (>= uf_7 0::int)
+#1783 := (not #1785)
+#1795 := (* -1::int uf_7)
+#1782 := (+ uf_1 #1795)
+#1784 := (<= #1782 0::int)
+#2297 := (or #1784 #1783 #2291)
+#2302 := (not #2297)
+#2119 := (or #2266 #2260)
+#2120 := [def-axiom]: #2119
+#2325 := [unit-resolution #2120 #2324]: #2260
+#1953 := (+ uf_6 #700)
+#1954 := (<= #1953 0::int)
+#2327 := (or #227 #1954)
+#2328 := [th-lemma]: #2327
+#2329 := [unit-resolution #2328 #2326]: #1954
+#1831 := [hypothesis]: #2203
+#2107 := (or #2266 #719)
+#2109 := [def-axiom]: #2107
+#2330 := [unit-resolution #2109 #2324]: #719
+#1862 := (not #1954)
+#1841 := (or #1682 #722 #2208 #1862)
+#1864 := [hypothesis]: #719
+#1943 := (+ uf_5 #1103)
+#1944 := (<= #1943 0::int)
+#1922 := (+ uf_6 #1286)
+#1923 := (>= #1922 0::int)
+#1861 := (not #1923)
+#1855 := [hypothesis]: #1954
+#2018 := (not #1288)
+#1847 := [hypothesis]: #1685
+#2019 := (or #1682 #2018)
+#1978 := [def-axiom]: #2019
+#1849 := [unit-resolution #1978 #1847]: #2018
+#1863 := (or #1861 #1288 #1862)
+#1846 := [hypothesis]: #2018
+#1859 := [hypothesis]: #1923
+#1860 := [th-lemma #1859 #1846 #1855]: false
+#1853 := [lemma #1860]: #1863
+#1850 := [unit-resolution #1853 #1849 #1855]: #1861
+#1836 := (or #1923 #1944)
+#2135 := (or #1682 #1107)
+#2017 := [def-axiom]: #2135
+#1829 := [unit-resolution #2017 #1847]: #1107
+#1912 := (or #2208 #1525 #1923 #1944)
+#1955 := (+ #1100 #922)
+#1945 := (<= #1955 0::int)
+#1935 := (+ ?x6!2 #717)
+#1937 := (>= #1935 0::int)
+#1938 := (or #1525 #1937 #1945)
+#1913 := (or #2208 #1938)
+#1904 := (iff #1913 #1912)
+#1906 := (or #1525 #1923 #1944)
+#1907 := (or #2208 #1906)
+#1901 := (iff #1907 #1912)
+#1902 := [rewrite]: #1901
+#1915 := (iff #1913 #1907)
+#1910 := (iff #1938 #1906)
+#1928 := (or #1525 #1944 #1923)
+#1908 := (iff #1928 #1906)
+#1909 := [rewrite]: #1908
+#1917 := (iff #1938 #1928)
+#1926 := (iff #1945 #1923)
+#1934 := (+ #922 #1100)
+#1919 := (<= #1934 0::int)
+#1924 := (iff #1919 #1923)
+#1925 := [rewrite]: #1924
+#1920 := (iff #1945 #1919)
+#1916 := (= #1955 #1934)
+#1918 := [rewrite]: #1916
+#1921 := [monotonicity #1918]: #1920
+#1927 := [trans #1921 #1925]: #1926
+#1933 := (iff #1937 #1944)
+#1941 := (+ #717 ?x6!2)
+#1939 := (>= #1941 0::int)
+#1930 := (iff #1939 #1944)
+#1932 := [rewrite]: #1930
+#1947 := (iff #1937 #1939)
+#1942 := (= #1935 #1941)
+#1946 := [rewrite]: #1942
+#1940 := [monotonicity #1946]: #1947
+#1931 := [trans #1940 #1932]: #1933
+#1929 := [monotonicity #1931 #1927]: #1917
+#1911 := [trans #1929 #1909]: #1910
+#1900 := [monotonicity #1911]: #1915
+#1903 := [trans #1900 #1902]: #1904
+#1914 := [quant-inst]: #1913
+#1905 := [mp #1914 #1903]: #1912
+#1837 := [unit-resolution #1905 #1831 #1829]: #1836
+#1838 := [unit-resolution #1837 #1850]: #1944
+#1106 := (not #1105)
+#2134 := (or #1682 #1106)
+#2132 := [def-axiom]: #2134
+#1839 := [unit-resolution #2132 #1847]: #1106
+#1840 := [th-lemma #1839 #1838 #1864]: false
+#1830 := [lemma #1840]: #1841
+#2331 := [unit-resolution #1830 #2330 #1831 #2329]: #1682
+#2023 := (or #2263 #2255 #1685)
+#2031 := [def-axiom]: #2023
+#2332 := [unit-resolution #2031 #2331 #2325]: #2255
+#2127 := (not #2255)
+#2305 := (or #2127 #2302)
+#2288 := (= #1786 uf_8)
+#2289 := (or #2288 #1783 #1784)
+#2290 := (not #2289)
+#2306 := (or #2127 #2290)
+#2308 := (iff #2306 #2305)
+#2310 := (iff #2305 #2305)
+#2311 := [rewrite]: #2310
+#2303 := (iff #2290 #2302)
+#2300 := (iff #2289 #2297)
+#2294 := (or #2291 #1783 #1784)
+#2298 := (iff #2294 #2297)
+#2299 := [rewrite]: #2298
+#2295 := (iff #2289 #2294)
+#2292 := (iff #2288 #2291)
+#2293 := [rewrite]: #2292
+#2296 := [monotonicity #2293]: #2295
+#2301 := [trans #2296 #2299]: #2300
+#2304 := [monotonicity #2301]: #2303
+#2309 := [monotonicity #2304]: #2308
+#2312 := [trans #2309 #2311]: #2308
+#2307 := [quant-inst]: #2306
+#2313 := [mp #2307 #2312]: #2305
+#2333 := [unit-resolution #2313 #2332]: #2302
+#2320 := (or #2297 #2319)
+#2321 := [def-axiom]: #2320
+#2334 := [unit-resolution #2321 #2333]: #2319
+#2346 := [unit-resolution #2334 #2345]: false
+#2348 := [lemma #2346]: #2347
+#2529 := [unit-resolution #2348 #2526 #2528]: #2266
+#2114 := (or #2275 #2252 #2269)
+#2108 := [def-axiom]: #2114
+#2548 := [unit-resolution #2108 #2529 #2527]: #2252
+#2142 := (or #2249 #2243)
+#2136 := [def-axiom]: #2142
+#2614 := [unit-resolution #2136 #2548]: #2243
+#2355 := (or #302 #2246 #523)
+#2349 := (= #64 #86)
+#1950 := (= #86 #64)
+#2314 := [hypothesis]: #2243
+#1164 := (not #302)
+#1791 := [hypothesis]: #1164
+#1803 := (or #2237 #302 #523)
+#1808 := (= #36 #86)
+#1790 := (= #86 #36)
+#1788 := [hypothesis]: #2240
+#1886 := (or #2237 #418)
+#1887 := [def-axiom]: #1886
+#1789 := [unit-resolution #1887 #1788]: #418
+#1792 := [symm #1789]: #103
+#1812 := [monotonicity #1792]: #1790
+#1810 := [symm #1812]: #1808
+#1813 := (= uf_12 #36)
+#2161 := (or #2237 #421)
+#2165 := [def-axiom]: #2161
+#1793 := [unit-resolution #2165 #1788]: #421
+#1794 := [symm #1793]: #104
+#1796 := [trans #1794 #2337]: #1813
+#1799 := [trans #1796 #1810]: #302
+#1800 := [unit-resolution #1791 #1799]: false
+#1804 := [lemma #1800]: #1803
+#2315 := [unit-resolution #1804 #1791 #2337]: #2237
+#2148 := (or #2246 #2234 #2240)
+#2154 := [def-axiom]: #2148
+#2316 := [unit-resolution #2154 #2315 #2314]: #2234
+#1833 := (or #2231 #280)
+#1834 := [def-axiom]: #1833
+#2322 := [unit-resolution #1834 #2316]: #280
+#2323 := [symm #2322]: #70
+#1805 := [monotonicity #2323]: #1950
+#2350 := [symm #1805]: #2349
+#2351 := (= uf_12 #64)
+#2169 := (or #2231 #275)
+#1832 := [def-axiom]: #2169
+#2318 := [unit-resolution #1832 #2316]: #275
+#1806 := [symm #2318]: #67
+#1835 := (or #2231 #283)
+#2171 := [def-axiom]: #1835
+#2317 := [unit-resolution #2171 #2316]: #283
+#1798 := [symm #2317]: #72
+#2352 := [trans #1798 #1806]: #2351
+#2353 := [trans #2352 #2350]: #302
+#2354 := [unit-resolution #1791 #2353]: false
+#2356 := [lemma #2354]: #2355
+#2615 := [unit-resolution #2356 #2614 #2526]: #302
+#1851 := (or #2219 #1164)
+#2186 := [def-axiom]: #1851
+#2616 := [unit-resolution #2186 #2615]: #2219
+#2612 := (or #2237 #2208 #2222)
+#2583 := [hypothesis]: #2219
+#2160 := (or #2237 #2225)
+#2149 := [def-axiom]: #2160
+#2584 := [unit-resolution #2149 #1788]: #2225
+#2185 := (or #2228 #2222 #1624)
+#1828 := [def-axiom]: #2185
+#2585 := [unit-resolution #1828 #2584 #2583]: #1624
+#2189 := (or #1619 #1336)
+#2190 := [def-axiom]: #2189
+#2586 := [unit-resolution #2190 #2585]: #1336
+#2415 := (+ uf_5 #1329)
+#2560 := (>= #2415 0::int)
+#2601 := (not #2560)
+#2549 := (= uf_5 ?x7!3)
+#2580 := (not #2549)
+#2559 := (= #64 #1149)
+#2564 := (not #2559)
+#2563 := (+ #64 #1351)
+#2565 := (>= #2563 0::int)
+#2569 := (not #2565)
+#2159 := (or #2237 #814)
+#2156 := [def-axiom]: #2159
+#2587 := [unit-resolution #2156 #1788]: #814
+#2191 := (not #1353)
+#2192 := (or #1619 #2191)
+#2187 := [def-axiom]: #2192
+#2588 := [unit-resolution #2187 #2585]: #2191
+#1787 := (+ uf_6 #772)
+#2163 := (<= #1787 0::int)
+#2589 := (or #427 #2163)
+#2590 := [th-lemma]: #2589
+#2591 := [unit-resolution #2590 #1793]: #2163
+#2539 := (not #2163)
+#2570 := (or #2569 #2539 #1353 #813)
+#2566 := [hypothesis]: #814
+#2531 := [hypothesis]: #2191
+#2533 := [hypothesis]: #2163
+#2567 := [hypothesis]: #2565
+#2568 := [th-lemma #2567 #2533 #2531 #2566]: false
+#2571 := [lemma #2568]: #2570
+#2592 := [unit-resolution #2571 #2591 #2588 #2587]: #2569
+#2572 := (or #2564 #2565)
+#2573 := [th-lemma]: #2572
+#2593 := [unit-resolution #2573 #2592]: #2564
+#2581 := (or #2580 #2559)
+#2577 := [hypothesis]: #2549
+#2578 := [monotonicity #2577]: #2559
+#2576 := [hypothesis]: #2564
+#2579 := [unit-resolution #2576 #2578]: false
+#2582 := [lemma #2579]: #2581
+#2594 := [unit-resolution #2582 #2593]: #2580
+#2604 := (or #2549 #2601)
+#2416 := (<= #2415 0::int)
+#2427 := (+ uf_6 #1351)
+#2428 := (>= #2427 0::int)
+#2545 := (not #2428)
+#2546 := (or #2545 #2539 #1353)
+#2543 := [hypothesis]: #2428
+#2544 := [th-lemma #2533 #2531 #2543]: false
+#2547 := [lemma #2544]: #2546
+#2595 := [unit-resolution #2547 #2591 #2588]: #2545
+#2597 := (or #2416 #2428)
+#1856 := (or #1619 #1155)
+#1857 := [def-axiom]: #1856
+#2596 := [unit-resolution #1857 #2585]: #1155
+#2436 := (or #2208 #1604 #2416 #2428)
+#2404 := (+ #1149 #922)
+#2405 := (<= #2404 0::int)
+#2406 := (+ ?x7!3 #717)
+#2407 := (>= #2406 0::int)
+#2408 := (or #1604 #2407 #2405)
+#2437 := (or #2208 #2408)
+#2444 := (iff #2437 #2436)
+#2433 := (or #1604 #2416 #2428)
+#2439 := (or #2208 #2433)
+#2442 := (iff #2439 #2436)
+#2443 := [rewrite]: #2442
+#2440 := (iff #2437 #2439)
+#2434 := (iff #2408 #2433)
+#2431 := (iff #2405 #2428)
+#2421 := (+ #922 #1149)
+#2424 := (<= #2421 0::int)
+#2429 := (iff #2424 #2428)
+#2430 := [rewrite]: #2429
+#2425 := (iff #2405 #2424)
+#2422 := (= #2404 #2421)
+#2423 := [rewrite]: #2422
+#2426 := [monotonicity #2423]: #2425
+#2432 := [trans #2426 #2430]: #2431
+#2419 := (iff #2407 #2416)
+#2409 := (+ #717 ?x7!3)
+#2412 := (>= #2409 0::int)
+#2417 := (iff #2412 #2416)
+#2418 := [rewrite]: #2417
+#2413 := (iff #2407 #2412)
+#2410 := (= #2406 #2409)
+#2411 := [rewrite]: #2410
+#2414 := [monotonicity #2411]: #2413
+#2420 := [trans #2414 #2418]: #2419
+#2435 := [monotonicity #2420 #2432]: #2434
+#2441 := [monotonicity #2435]: #2440
+#2445 := [trans #2441 #2443]: #2444
+#2438 := [quant-inst]: #2437
+#2446 := [mp #2438 #2445]: #2436
+#2598 := [unit-resolution #2446 #1831 #2596]: #2597
+#2599 := [unit-resolution #2598 #2595]: #2416
+#2600 := (not #2416)
+#2602 := (or #2549 #2600 #2601)
+#2603 := [th-lemma]: #2602
+#2605 := [unit-resolution #2603 #2599]: #2604
+#2606 := [unit-resolution #2605 #2594]: #2601
+#1872 := (>= #798 -1::int)
+#1873 := (or #2237 #797)
+#2155 := [def-axiom]: #1873
+#2607 := [unit-resolution #2155 #1788]: #797
+#2608 := (or #801 #1872)
+#2609 := [th-lemma]: #2608
+#2610 := [unit-resolution #2609 #2607]: #1872
+#2611 := [th-lemma #2610 #2606 #2586]: false
+#2613 := [lemma #2611]: #2612
+#2617 := [unit-resolution #2613 #2528 #2616]: #2237
+#2618 := [unit-resolution #2154 #2617 #2614]: #2234
+#2178 := (or #2231 #2225)
+#2181 := [def-axiom]: #2178
+#2619 := [unit-resolution #2181 #2618]: #2225
+#2620 := [unit-resolution #1828 #2619 #2616]: #1624
+#2621 := [unit-resolution #2190 #2620]: #1336
+#2397 := (+ #64 #772)
+#2398 := (<= #2397 0::int)
+#2396 := (= #64 uf_12)
+#2622 := [unit-resolution #2171 #2618]: #283
+#2623 := [unit-resolution #1832 #2618]: #275
+#2624 := [trans #2623 #2622]: #2396
+#2625 := (not #2396)
+#2626 := (or #2625 #2398)
+#2627 := [th-lemma]: #2626
+#2628 := [unit-resolution #2627 #2624]: #2398
+#1820 := (or #2231 #813)
+#2180 := [def-axiom]: #1820
+#2629 := [unit-resolution #2180 #2618]: #813
+#2630 := [unit-resolution #2187 #2620]: #2191
+#2631 := (not #2398)
+#2632 := (or #2545 #1353 #2631 #814)
+#2633 := [th-lemma]: #2632
+#2634 := [unit-resolution #2633 #2630 #2629 #2628]: #2545
+#2635 := [unit-resolution #1857 #2620]: #1155
+#2636 := [unit-resolution #2446 #2528 #2635]: #2597
+#2637 := [unit-resolution #2636 #2634]: #2416
+#2638 := (or #2569 #1353 #2631)
+#2639 := [th-lemma]: #2638
+#2640 := [unit-resolution #2639 #2630 #2628]: #2569
+#2641 := [unit-resolution #2573 #2640]: #2564
+#2642 := [unit-resolution #2582 #2641]: #2580
+#2643 := [unit-resolution #2603 #2642 #2637]: #2601
+#2179 := (or #2231 #797)
+#1819 := [def-axiom]: #2179
+#2644 := [unit-resolution #1819 #2618]: #797
+#2645 := [unit-resolution #2609 #2644]: #1872
+#2646 := [th-lemma #2645 #2643 #2621]: false
+#2647 := [lemma #2646]: #2278
+#2284 := (or #1432 #2281)
+#1502 := (forall (vars (?x4 int)) #1499)
+#1688 := (or #1502 #1685)
+#1691 := (not #1688)
+#1694 := (or #236 #227 #218 #1564 #810 #722 #1691)
+#1697 := (not #1694)
+#1591 := (forall (vars (?x7 int)) #1586)
+#1597 := (not #1591)
+#1598 := (or #302 #1597)
+#1599 := (not #1598)
+#1627 := (or #1599 #1624)
+#1635 := (not #1627)
+#1645 := (or #436 #427 #1564 #810 #1633 #1634 #801 #813 #1635)
+#1646 := (not #1645)
+#1636 := (or #388 #370 #361 #1564 #810 #1633 #1634 #801 #814 #1635)
+#1637 := (not #1636)
+#1651 := (or #1637 #1646)
+#1657 := (not #1651)
+#1658 := (or #1564 #810 #719 #1657)
+#1659 := (not #1658)
+#1703 := (or #1659 #1697)
+#1708 := (not #1703)
+#1477 := (forall (vars (?x3 int)) #1472)
+#1671 := (not #1477)
+#1455 := (forall (vars (?x1 int)) #1450)
+#1670 := (not #1455)
+#1711 := (or #523 #1564 #810 #1670 #1671 #1708)
+#1714 := (not #1711)
+#1717 := (or #1432 #1714)
+#2285 := (iff #1717 #2284)
+#2282 := (iff #1714 #2281)
+#2279 := (iff #1711 #2278)
+#2276 := (iff #1708 #2275)
+#2273 := (iff #1703 #2272)
+#2270 := (iff #1697 #2269)
+#2267 := (iff #1694 #2266)
+#2264 := (iff #1691 #2263)
+#2261 := (iff #1688 #2260)
+#2258 := (iff #1502 #2255)
+#2256 := (iff #1499 #1499)
+#2257 := [refl]: #2256
+#2259 := [quant-intro #2257]: #2258
+#2262 := [monotonicity #2259]: #2261
+#2265 := [monotonicity #2262]: #2264
+#2268 := [monotonicity #2265]: #2267
+#2271 := [monotonicity #2268]: #2270
+#2253 := (iff #1659 #2252)
+#2250 := (iff #1658 #2249)
+#2247 := (iff #1657 #2246)
+#2244 := (iff #1651 #2243)
+#2241 := (iff #1646 #2240)
+#2238 := (iff #1645 #2237)
+#2229 := (iff #1635 #2228)
+#2226 := (iff #1627 #2225)
+#2223 := (iff #1599 #2222)
+#2220 := (iff #1598 #2219)
+#2217 := (iff #1597 #2216)
+#2214 := (iff #1591 #2211)
+#2212 := (iff #1586 #1586)
+#2213 := [refl]: #2212
+#2215 := [quant-intro #2213]: #2214
+#2218 := [monotonicity #2215]: #2217
+#2221 := [monotonicity #2218]: #2220
+#2224 := [monotonicity #2221]: #2223
+#2227 := [monotonicity #2224]: #2226
+#2230 := [monotonicity #2227]: #2229
+#2239 := [monotonicity #2230]: #2238
+#2242 := [monotonicity #2239]: #2241
+#2235 := (iff #1637 #2234)
+#2232 := (iff #1636 #2231)
+#2233 := [monotonicity #2230]: #2232
+#2236 := [monotonicity #2233]: #2235
+#2245 := [monotonicity #2236 #2242]: #2244
+#2248 := [monotonicity #2245]: #2247
+#2251 := [monotonicity #2248]: #2250
+#2254 := [monotonicity #2251]: #2253
+#2274 := [monotonicity #2254 #2271]: #2273
+#2277 := [monotonicity #2274]: #2276
+#2209 := (iff #1671 #2208)
+#2206 := (iff #1477 #2203)
+#2204 := (iff #1472 #1472)
+#2205 := [refl]: #2204
+#2207 := [quant-intro #2205]: #2206
+#2210 := [monotonicity #2207]: #2209
+#2201 := (iff #1670 #2200)
+#2198 := (iff #1455 #2195)
+#2196 := (iff #1450 #1450)
+#2197 := [refl]: #2196
+#2199 := [quant-intro #2197]: #2198
+#2202 := [monotonicity #2199]: #2201
+#2280 := [monotonicity #2202 #2210 #2277]: #2279
+#2283 := [monotonicity #2280]: #2282
+#2286 := [monotonicity #2283]: #2285
+#1339 := (and #1155 #1336)
+#1342 := (not #1339)
+#1358 := (or #1342 #1353)
+#1361 := (not #1358)
+#1174 := (and #1164 #780)
+#1367 := (or #1174 #1361)
+#1391 := (and #418 #421 #663 #666 #749 #752 #797 #814 #1367)
+#1379 := (and #275 #280 #283 #663 #666 #749 #752 #797 #813 #1367)
+#1396 := (or #1379 #1391)
+#1402 := (and #663 #666 #722 #1396)
+#1274 := (and #1106 #1107)
+#1277 := (not #1274)
+#1293 := (or #1277 #1288)
+#1296 := (not #1293)
+#1085 := (not #1084)
+#1265 := (and #1085 #1086)
+#1268 := (not #1265)
+#1271 := (or #1262 #1268)
+#1299 := (and #1271 #1296)
+#1075 := (not #689)
+#1078 := (forall (vars (?x4 int)) #1075)
+#1302 := (or #1078 #1299)
+#1308 := (and #174 #177 #180 #663 #666 #719 #1302)
+#1407 := (or #1308 #1402)
+#1413 := (and #171 #656 #663 #666 #930 #1407)
+#1043 := (not #1042)
+#1235 := (and #1043 #1044)
+#1238 := (not #1235)
+#1244 := (or #1041 #1238)
+#1249 := (not #1244)
+#1418 := (or #1249 #1413)
+#1720 := (iff #1418 #1717)
+#1540 := (or #1105 #1525 #1288)
+#1552 := (or #1551 #1540)
+#1553 := (not #1552)
+#1558 := (or #1502 #1553)
+#1565 := (not #1558)
+#1566 := (or #236 #227 #218 #1564 #810 #722 #1565)
+#1567 := (not #1566)
+#1664 := (or #1567 #1659)
+#1672 := (not #1664)
+#1673 := (or #523 #1564 #810 #1670 #1671 #1672)
+#1674 := (not #1673)
+#1679 := (or #1432 #1674)
+#1718 := (iff #1679 #1717)
+#1715 := (iff #1674 #1714)
+#1712 := (iff #1673 #1711)
+#1709 := (iff #1672 #1708)
+#1706 := (iff #1664 #1703)
+#1700 := (or #1697 #1659)
+#1704 := (iff #1700 #1703)
+#1705 := [rewrite]: #1704
+#1701 := (iff #1664 #1700)
+#1698 := (iff #1567 #1697)
+#1695 := (iff #1566 #1694)
+#1692 := (iff #1565 #1691)
+#1689 := (iff #1558 #1688)
+#1686 := (iff #1553 #1685)
+#1683 := (iff #1552 #1682)
+#1684 := [rewrite]: #1683
+#1687 := [monotonicity #1684]: #1686
+#1690 := [monotonicity #1687]: #1689
+#1693 := [monotonicity #1690]: #1692
+#1696 := [monotonicity #1693]: #1695
+#1699 := [monotonicity #1696]: #1698
+#1702 := [monotonicity #1699]: #1701
+#1707 := [trans #1702 #1705]: #1706
+#1710 := [monotonicity #1707]: #1709
+#1713 := [monotonicity #1710]: #1712
+#1716 := [monotonicity #1713]: #1715
+#1719 := [monotonicity #1716]: #1718
+#1680 := (iff #1418 #1679)
+#1677 := (iff #1413 #1674)
+#1667 := (and #171 #1455 #663 #666 #1477 #1664)
+#1675 := (iff #1667 #1674)
+#1676 := [rewrite]: #1675
+#1668 := (iff #1413 #1667)
+#1665 := (iff #1407 #1664)
+#1662 := (iff #1402 #1659)
+#1654 := (and #663 #666 #722 #1651)
+#1660 := (iff #1654 #1659)
+#1661 := [rewrite]: #1660
+#1655 := (iff #1402 #1654)
+#1652 := (iff #1396 #1651)
+#1649 := (iff #1391 #1646)
+#1642 := (and #418 #421 #663 #666 #749 #752 #797 #814 #1627)
+#1647 := (iff #1642 #1646)
+#1648 := [rewrite]: #1647
+#1643 := (iff #1391 #1642)
+#1628 := (iff #1367 #1627)
+#1625 := (iff #1361 #1624)
+#1622 := (iff #1358 #1619)
+#1605 := (or #1604 #1331)
+#1616 := (or #1605 #1353)
+#1620 := (iff #1616 #1619)
+#1621 := [rewrite]: #1620
+#1617 := (iff #1358 #1616)
+#1614 := (iff #1342 #1605)
+#1606 := (not #1605)
+#1609 := (not #1606)
+#1612 := (iff #1609 #1605)
+#1613 := [rewrite]: #1612
+#1610 := (iff #1342 #1609)
+#1607 := (iff #1339 #1606)
+#1608 := [rewrite]: #1607
+#1611 := [monotonicity #1608]: #1610
+#1615 := [trans #1611 #1613]: #1614
+#1618 := [monotonicity #1615]: #1617
+#1623 := [trans #1618 #1621]: #1622
+#1626 := [monotonicity #1623]: #1625
+#1602 := (iff #1174 #1599)
+#1594 := (and #1164 #1591)
+#1600 := (iff #1594 #1599)
+#1601 := [rewrite]: #1600
+#1595 := (iff #1174 #1594)
+#1592 := (iff #780 #1591)
+#1589 := (iff #777 #1586)
+#1572 := (or #1435 #760)
+#1583 := (or #1572 #774)
+#1587 := (iff #1583 #1586)
+#1588 := [rewrite]: #1587
+#1584 := (iff #777 #1583)
+#1581 := (iff #769 #1572)
+#1573 := (not #1572)
+#1576 := (not #1573)
+#1579 := (iff #1576 #1572)
+#1580 := [rewrite]: #1579
+#1577 := (iff #769 #1576)
+#1574 := (iff #766 #1573)
+#1575 := [rewrite]: #1574
+#1578 := [monotonicity #1575]: #1577
+#1582 := [trans #1578 #1580]: #1581
+#1585 := [monotonicity #1582]: #1584
+#1590 := [trans #1585 #1588]: #1589
+#1593 := [quant-intro #1590]: #1592
+#1596 := [monotonicity #1593]: #1595
+#1603 := [trans #1596 #1601]: #1602
+#1629 := [monotonicity #1603 #1626]: #1628
+#1644 := [monotonicity #1629]: #1643
+#1650 := [trans #1644 #1648]: #1649
+#1640 := (iff #1379 #1637)
+#1630 := (and #275 #280 #283 #663 #666 #749 #752 #797 #813 #1627)
+#1638 := (iff #1630 #1637)
+#1639 := [rewrite]: #1638
+#1631 := (iff #1379 #1630)
+#1632 := [monotonicity #1629]: #1631
+#1641 := [trans #1632 #1639]: #1640
+#1653 := [monotonicity #1641 #1650]: #1652
+#1656 := [monotonicity #1653]: #1655
+#1663 := [trans #1656 #1661]: #1662
+#1570 := (iff #1308 #1567)
+#1561 := (and #174 #177 #180 #663 #666 #719 #1558)
+#1568 := (iff #1561 #1567)
+#1569 := [rewrite]: #1568
+#1562 := (iff #1308 #1561)
+#1559 := (iff #1302 #1558)
+#1556 := (iff #1299 #1553)
+#1545 := (not #1540)
+#1548 := (and #1520 #1545)
+#1554 := (iff #1548 #1553)
+#1555 := [rewrite]: #1554
+#1549 := (iff #1299 #1548)
+#1546 := (iff #1296 #1545)
+#1543 := (iff #1293 #1540)
+#1526 := (or #1105 #1525)
+#1537 := (or #1526 #1288)
+#1541 := (iff #1537 #1540)
+#1542 := [rewrite]: #1541
+#1538 := (iff #1293 #1537)
+#1535 := (iff #1277 #1526)
+#1527 := (not #1526)
+#1530 := (not #1527)
+#1533 := (iff #1530 #1526)
+#1534 := [rewrite]: #1533
+#1531 := (iff #1277 #1530)
+#1528 := (iff #1274 #1527)
+#1529 := [rewrite]: #1528
+#1532 := [monotonicity #1529]: #1531
+#1536 := [trans #1532 #1534]: #1535
+#1539 := [monotonicity #1536]: #1538
+#1544 := [trans #1539 #1542]: #1543
+#1547 := [monotonicity #1544]: #1546
+#1523 := (iff #1271 #1520)
+#1506 := (or #1084 #1505)
+#1517 := (or #1262 #1506)
+#1521 := (iff #1517 #1520)
+#1522 := [rewrite]: #1521
+#1518 := (iff #1271 #1517)
+#1515 := (iff #1268 #1506)
+#1507 := (not #1506)
+#1510 := (not #1507)
+#1513 := (iff #1510 #1506)
+#1514 := [rewrite]: #1513
+#1511 := (iff #1268 #1510)
+#1508 := (iff #1265 #1507)
+#1509 := [rewrite]: #1508
+#1512 := [monotonicity #1509]: #1511
+#1516 := [trans #1512 #1514]: #1515
+#1519 := [monotonicity #1516]: #1518
+#1524 := [trans #1519 #1522]: #1523
+#1550 := [monotonicity #1524 #1547]: #1549
+#1557 := [trans #1550 #1555]: #1556
+#1503 := (iff #1078 #1502)
+#1500 := (iff #1075 #1499)
+#1497 := (iff #689 #1494)
+#1480 := (or #1435 #676)
+#1491 := (or #47 #1480)
+#1495 := (iff #1491 #1494)
+#1496 := [rewrite]: #1495
+#1492 := (iff #689 #1491)
+#1489 := (iff #683 #1480)
+#1481 := (not #1480)
+#1484 := (not #1481)
+#1487 := (iff #1484 #1480)
+#1488 := [rewrite]: #1487
+#1485 := (iff #683 #1484)
+#1482 := (iff #680 #1481)
+#1483 := [rewrite]: #1482
+#1486 := [monotonicity #1483]: #1485
+#1490 := [trans #1486 #1488]: #1489
+#1493 := [monotonicity #1490]: #1492
+#1498 := [trans #1493 #1496]: #1497
+#1501 := [monotonicity #1498]: #1500
+#1504 := [quant-intro #1501]: #1503
+#1560 := [monotonicity #1504 #1557]: #1559
+#1563 := [monotonicity #1560]: #1562
+#1571 := [trans #1563 #1569]: #1570
+#1666 := [monotonicity #1571 #1663]: #1665
+#1478 := (iff #930 #1477)
+#1475 := (iff #927 #1472)
+#1458 := (or #1435 #911)
+#1469 := (or #1458 #924)
+#1473 := (iff #1469 #1472)
+#1474 := [rewrite]: #1473
+#1470 := (iff #927 #1469)
+#1467 := (iff #919 #1458)
+#1459 := (not #1458)
+#1462 := (not #1459)
+#1465 := (iff #1462 #1458)
+#1466 := [rewrite]: #1465
+#1463 := (iff #919 #1462)
+#1460 := (iff #916 #1459)
+#1461 := [rewrite]: #1460
+#1464 := [monotonicity #1461]: #1463
+#1468 := [trans #1464 #1466]: #1467
+#1471 := [monotonicity #1468]: #1470
+#1476 := [trans #1471 #1474]: #1475
+#1479 := [quant-intro #1476]: #1478
+#1456 := (iff #656 #1455)
+#1453 := (iff #653 #1450)
+#1436 := (or #1435 #639)
+#1447 := (or #1436 #649)
+#1451 := (iff #1447 #1450)
+#1452 := [rewrite]: #1451
+#1448 := (iff #653 #1447)
+#1445 := (iff #644 #1436)
+#1437 := (not #1436)
+#1440 := (not #1437)
+#1443 := (iff #1440 #1436)
+#1444 := [rewrite]: #1443
+#1441 := (iff #644 #1440)
+#1438 := (iff #641 #1437)
+#1439 := [rewrite]: #1438
+#1442 := [monotonicity #1439]: #1441
+#1446 := [trans #1442 #1444]: #1445
+#1449 := [monotonicity #1446]: #1448
+#1454 := [trans #1449 #1452]: #1453
+#1457 := [quant-intro #1454]: #1456
+#1669 := [monotonicity #1457 #1479 #1666]: #1668
+#1678 := [trans #1669 #1676]: #1677
+#1433 := (iff #1249 #1432)
+#1430 := (iff #1244 #1427)
+#1095 := (or #1042 #1094)
+#1424 := (or #1041 #1095)
+#1428 := (iff #1424 #1427)
+#1429 := [rewrite]: #1428
+#1425 := (iff #1244 #1424)
+#1422 := (iff #1238 #1095)
+#1162 := (not #1095)
+#1052 := (not #1162)
+#1234 := (iff #1052 #1095)
+#1421 := [rewrite]: #1234
+#1115 := (iff #1238 #1052)
+#1163 := (iff #1235 #1162)
+#1051 := [rewrite]: #1163
+#1116 := [monotonicity #1051]: #1115
+#1423 := [trans #1116 #1421]: #1422
+#1426 := [monotonicity #1423]: #1425
+#1431 := [trans #1426 #1429]: #1430
+#1434 := [monotonicity #1431]: #1433
+#1681 := [monotonicity #1434 #1678]: #1680
+#1721 := [trans #1681 #1719]: #1720
+#1185 := (not #807)
+#1182 := (not #801)
+#1150 := (+ #1149 #772)
+#1151 := (<= #1150 0::int)
+#1152 := (+ ?x7!3 #761)
+#1153 := (>= #1152 0::int)
+#1154 := (not #1153)
+#1156 := (and #1155 #1154)
+#1157 := (not #1156)
+#1158 := (or #1157 #1151)
+#1159 := (not #1158)
+#1178 := (or #1159 #1174)
+#1145 := (not #757)
+#1063 := (not #671)
+#1197 := (not #427)
+#1194 := (not #436)
+#1202 := (and #1194 #1197 #1063 #1145 #1178 #1182 #1185 #819)
+#1142 := (not #810)
+#1139 := (not #361)
+#1136 := (not #370)
+#1133 := (not #388)
+#1190 := (and #1133 #1136 #1139 #1142 #1063 #1145 #1178 #1182 #1185 #813)
+#1206 := (or #1190 #1202)
+#1210 := (and #1063 #722 #1206)
+#1101 := (+ #1100 #700)
+#1102 := (<= #1101 0::int)
+#1108 := (and #1107 #1106)
+#1109 := (not #1108)
+#1110 := (or #1109 #1102)
+#1111 := (not #1110)
+#1087 := (and #1086 #1085)
+#1088 := (not #1087)
+#1090 := (= #1089 uf_8)
+#1091 := (or #1090 #1088)
+#1117 := (and #1091 #1111)
+#1121 := (or #1078 #1117)
+#1072 := (not #218)
+#1069 := (not #227)
+#1066 := (not #236)
+#1127 := (and #1066 #1069 #1072 #1063 #1121 #887)
+#1214 := (or #1127 #1210)
+#1053 := (not #523)
+#1225 := (and #1053 #656 #1063 #1214 #930)
+#1045 := (and #1044 #1043)
+#1046 := (not #1045)
+#1047 := (or #1046 #1041)
+#1048 := (not #1047)
+#1229 := (or #1048 #1225)
+#1419 := (iff #1229 #1418)
+#1416 := (iff #1225 #1413)
+#1410 := (and #171 #656 #668 #1407 #930)
+#1414 := (iff #1410 #1413)
+#1415 := [rewrite]: #1414
+#1411 := (iff #1225 #1410)
+#1408 := (iff #1214 #1407)
+#1405 := (iff #1210 #1402)
+#1399 := (and #668 #722 #1396)
+#1403 := (iff #1399 #1402)
+#1404 := [rewrite]: #1403
+#1400 := (iff #1210 #1399)
+#1397 := (iff #1206 #1396)
+#1394 := (iff #1202 #1391)
+#1388 := (and #418 #421 #668 #754 #1367 #797 #804 #814)
+#1392 := (iff #1388 #1391)
+#1393 := [rewrite]: #1392
+#1389 := (iff #1202 #1388)
+#1374 := (iff #1185 #804)
+#1375 := [rewrite]: #1374
+#1372 := (iff #1182 #797)
+#1373 := [rewrite]: #1372
+#1370 := (iff #1178 #1367)
+#1364 := (or #1361 #1174)
+#1368 := (iff #1364 #1367)
+#1369 := [rewrite]: #1368
+#1365 := (iff #1178 #1364)
+#1362 := (iff #1159 #1361)
+#1359 := (iff #1158 #1358)
+#1356 := (iff #1151 #1353)
+#1345 := (+ #772 #1149)
+#1348 := (<= #1345 0::int)
+#1354 := (iff #1348 #1353)
+#1355 := [rewrite]: #1354
+#1349 := (iff #1151 #1348)
+#1346 := (= #1150 #1345)
+#1347 := [rewrite]: #1346
+#1350 := [monotonicity #1347]: #1349
+#1357 := [trans #1350 #1355]: #1356
+#1343 := (iff #1157 #1342)
+#1340 := (iff #1156 #1339)
+#1337 := (iff #1154 #1336)
+#1334 := (iff #1153 #1331)
+#1323 := (+ #761 ?x7!3)
+#1326 := (>= #1323 0::int)
+#1332 := (iff #1326 #1331)
+#1333 := [rewrite]: #1332
+#1327 := (iff #1153 #1326)
+#1324 := (= #1152 #1323)
+#1325 := [rewrite]: #1324
+#1328 := [monotonicity #1325]: #1327
+#1335 := [trans #1328 #1333]: #1334
+#1338 := [monotonicity #1335]: #1337
+#1341 := [monotonicity #1338]: #1340
+#1344 := [monotonicity #1341]: #1343
+#1360 := [monotonicity #1344 #1357]: #1359
+#1363 := [monotonicity #1360]: #1362
+#1366 := [monotonicity #1363]: #1365
+#1371 := [trans #1366 #1369]: #1370
+#1321 := (iff #1145 #754)
+#1322 := [rewrite]: #1321
+#1254 := (iff #1063 #668)
+#1255 := [rewrite]: #1254
+#1386 := (iff #1197 #421)
+#1387 := [rewrite]: #1386
+#1384 := (iff #1194 #418)
+#1385 := [rewrite]: #1384
+#1390 := [monotonicity #1385 #1387 #1255 #1322 #1371 #1373 #1375 #823]: #1389
+#1395 := [trans #1390 #1393]: #1394
+#1382 := (iff #1190 #1379)
+#1376 := (and #275 #280 #283 #666 #668 #754 #1367 #797 #804 #813)
+#1380 := (iff #1376 #1379)
+#1381 := [rewrite]: #1380
+#1377 := (iff #1190 #1376)
+#1319 := (iff #1142 #666)
+#1320 := [rewrite]: #1319
+#1317 := (iff #1139 #283)
+#1318 := [rewrite]: #1317
+#1315 := (iff #1136 #280)
+#1316 := [rewrite]: #1315
+#1313 := (iff #1133 #275)
+#1314 := [rewrite]: #1313
+#1378 := [monotonicity #1314 #1316 #1318 #1320 #1255 #1322 #1371 #1373 #1375]: #1377
+#1383 := [trans #1378 #1381]: #1382
+#1398 := [monotonicity #1383 #1395]: #1397
+#1401 := [monotonicity #1255 #1398]: #1400
+#1406 := [trans #1401 #1404]: #1405
+#1311 := (iff #1127 #1308)
+#1305 := (and #174 #177 #180 #668 #1302 #719)
+#1309 := (iff #1305 #1308)
+#1310 := [rewrite]: #1309
+#1306 := (iff #1127 #1305)
+#1303 := (iff #1121 #1302)
+#1300 := (iff #1117 #1299)
+#1297 := (iff #1111 #1296)
+#1294 := (iff #1110 #1293)
+#1291 := (iff #1102 #1288)
+#1280 := (+ #700 #1100)
+#1283 := (<= #1280 0::int)
+#1289 := (iff #1283 #1288)
+#1290 := [rewrite]: #1289
+#1284 := (iff #1102 #1283)
+#1281 := (= #1101 #1280)
+#1282 := [rewrite]: #1281
+#1285 := [monotonicity #1282]: #1284
+#1292 := [trans #1285 #1290]: #1291
+#1278 := (iff #1109 #1277)
+#1275 := (iff #1108 #1274)
+#1276 := [rewrite]: #1275
+#1279 := [monotonicity #1276]: #1278
+#1295 := [monotonicity #1279 #1292]: #1294
+#1298 := [monotonicity #1295]: #1297
+#1272 := (iff #1091 #1271)
+#1269 := (iff #1088 #1268)
+#1266 := (iff #1087 #1265)
+#1267 := [rewrite]: #1266
+#1270 := [monotonicity #1267]: #1269
+#1263 := (iff #1090 #1262)
+#1264 := [rewrite]: #1263
+#1273 := [monotonicity #1264 #1270]: #1272
+#1301 := [monotonicity #1273 #1298]: #1300
+#1304 := [monotonicity #1301]: #1303
+#1260 := (iff #1072 #180)
+#1261 := [rewrite]: #1260
+#1258 := (iff #1069 #177)
+#1259 := [rewrite]: #1258
+#1256 := (iff #1066 #174)
+#1257 := [rewrite]: #1256
+#1307 := [monotonicity #1257 #1259 #1261 #1255 #1304 #891]: #1306
+#1312 := [trans #1307 #1310]: #1311
+#1409 := [monotonicity #1312 #1406]: #1408
+#1252 := (iff #1053 #171)
+#1253 := [rewrite]: #1252
+#1412 := [monotonicity #1253 #1255 #1409]: #1411
+#1417 := [trans #1412 #1415]: #1416
+#1250 := (iff #1048 #1249)
+#1247 := (iff #1047 #1244)
+#1241 := (or #1238 #1041)
+#1245 := (iff #1241 #1244)
+#1246 := [rewrite]: #1245
+#1242 := (iff #1047 #1241)
+#1239 := (iff #1046 #1238)
+#1236 := (iff #1045 #1235)
+#1237 := [rewrite]: #1236
+#1240 := [monotonicity #1237]: #1239
+#1243 := [monotonicity #1240]: #1242
+#1248 := [trans #1243 #1246]: #1247
+#1251 := [monotonicity #1248]: #1250
+#1420 := [monotonicity #1251 #1417]: #1419
+#1025 := (or #523 #659 #671 #908 #933)
+#1030 := (and #656 #1025)
+#1033 := (not #1030)
+#1230 := (~ #1033 #1229)
+#1226 := (not #1025)
+#1227 := (~ #1226 #1225)
+#1222 := (not #933)
+#1223 := (~ #1222 #930)
+#1220 := (~ #930 #930)
+#1218 := (~ #927 #927)
+#1219 := [refl]: #1218
+#1221 := [nnf-pos #1219]: #1220
+#1224 := [nnf-neg #1221]: #1223
+#1215 := (not #908)
+#1216 := (~ #1215 #1214)
+#1211 := (not #903)
+#1212 := (~ #1211 #1210)
+#1207 := (not #882)
+#1208 := (~ #1207 #1206)
+#1203 := (not #877)
+#1204 := (~ #1203 #1202)
+#1200 := (~ #819 #819)
+#1201 := [refl]: #1200
+#1186 := (~ #1185 #1185)
+#1187 := [refl]: #1186
+#1183 := (~ #1182 #1182)
+#1184 := [refl]: #1183
+#1179 := (not #794)
+#1180 := (~ #1179 #1178)
+#1175 := (not #789)
+#1176 := (~ #1175 #1174)
+#1171 := (not #783)
+#1172 := (~ #1171 #780)
+#1169 := (~ #780 #780)
+#1167 := (~ #777 #777)
+#1168 := [refl]: #1167
+#1170 := [nnf-pos #1168]: #1169
+#1173 := [nnf-neg #1170]: #1172
+#1165 := (~ #1164 #1164)
+#1166 := [refl]: #1165
+#1177 := [nnf-neg #1166 #1173]: #1176
+#1160 := (~ #783 #1159)
+#1161 := [sk]: #1160
+#1181 := [nnf-neg #1161 #1177]: #1180
+#1146 := (~ #1145 #1145)
+#1147 := [refl]: #1146
+#1064 := (~ #1063 #1063)
+#1065 := [refl]: #1064
+#1198 := (~ #1197 #1197)
+#1199 := [refl]: #1198
+#1195 := (~ #1194 #1194)
+#1196 := [refl]: #1195
+#1205 := [nnf-neg #1196 #1199 #1065 #1147 #1181 #1184 #1187 #1201]: #1204
+#1191 := (not #853)
+#1192 := (~ #1191 #1190)
+#1188 := (~ #813 #813)
+#1189 := [refl]: #1188
+#1143 := (~ #1142 #1142)
+#1144 := [refl]: #1143
+#1140 := (~ #1139 #1139)
+#1141 := [refl]: #1140
+#1137 := (~ #1136 #1136)
+#1138 := [refl]: #1137
+#1134 := (~ #1133 #1133)
+#1135 := [refl]: #1134
+#1193 := [nnf-neg #1135 #1138 #1141 #1144 #1065 #1147 #1181 #1184 #1187 #1189]: #1192
+#1209 := [nnf-neg #1193 #1205]: #1208
+#1131 := (~ #722 #722)
+#1132 := [refl]: #1131
+#1213 := [nnf-neg #1065 #1132 #1209]: #1212
+#1128 := (not #743)
+#1129 := (~ #1128 #1127)
+#1125 := (~ #887 #887)
+#1126 := [refl]: #1125
+#1122 := (not #714)
+#1123 := (~ #1122 #1121)
+#1118 := (not #711)
+#1119 := (~ #1118 #1117)
+#1112 := (not #708)
+#1113 := (~ #1112 #1111)
+#1114 := [sk]: #1113
+#1096 := (not #697)
+#1097 := (~ #1096 #1091)
+#1092 := (~ #694 #1091)
+#1093 := [sk]: #1092
+#1098 := [nnf-neg #1093]: #1097
+#1120 := [nnf-neg #1098 #1114]: #1119
+#1079 := (~ #697 #1078)
+#1076 := (~ #1075 #1075)
+#1077 := [refl]: #1076
+#1080 := [nnf-neg #1077]: #1079
+#1124 := [nnf-neg #1080 #1120]: #1123
+#1073 := (~ #1072 #1072)
+#1074 := [refl]: #1073
+#1070 := (~ #1069 #1069)
+#1071 := [refl]: #1070
+#1067 := (~ #1066 #1066)
+#1068 := [refl]: #1067
+#1130 := [nnf-neg #1068 #1071 #1074 #1065 #1124 #1126]: #1129
+#1217 := [nnf-neg #1130 #1213]: #1216
+#1060 := (not #659)
+#1061 := (~ #1060 #656)
+#1058 := (~ #656 #656)
+#1056 := (~ #653 #653)
+#1057 := [refl]: #1056
+#1059 := [nnf-pos #1057]: #1058
+#1062 := [nnf-neg #1059]: #1061
+#1054 := (~ #1053 #1053)
+#1055 := [refl]: #1054
+#1228 := [nnf-neg #1055 #1062 #1065 #1217 #1224]: #1227
+#1049 := (~ #659 #1048)
+#1050 := [sk]: #1049
+#1231 := [nnf-neg #1050 #1228]: #1230
+#997 := (not #962)
+#1034 := (iff #997 #1033)
+#1031 := (iff #962 #1030)
+#1028 := (iff #959 #1025)
+#1010 := (or #523 #671 #908 #933)
+#1022 := (or #659 #1010)
+#1026 := (iff #1022 #1025)
+#1027 := [rewrite]: #1026
+#1023 := (iff #959 #1022)
+#1020 := (iff #956 #1010)
+#1015 := (and true #1010)
+#1018 := (iff #1015 #1010)
+#1019 := [rewrite]: #1018
+#1016 := (iff #956 #1015)
+#1013 := (iff #951 #1010)
+#1007 := (or false #523 #671 #908 #933)
+#1011 := (iff #1007 #1010)
+#1012 := [rewrite]: #1011
+#1008 := (iff #951 #1007)
+#1005 := (iff #556 false)
+#1003 := (iff #556 #627)
+#1002 := (iff #9 true)
+#1000 := [iff-true #996]: #1002
+#1004 := [monotonicity #1000]: #1003
+#1006 := [trans #1004 #631]: #1005
+#1009 := [monotonicity #1006]: #1008
+#1014 := [trans #1009 #1012]: #1013
+#1017 := [monotonicity #1000 #1014]: #1016
+#1021 := [trans #1017 #1019]: #1020
+#1024 := [monotonicity #1021]: #1023
+#1029 := [trans #1024 #1027]: #1028
+#1032 := [monotonicity #1029]: #1031
+#1035 := [monotonicity #1032]: #1034
+#998 := [not-or-elim #995]: #997
+#1036 := [mp #998 #1035]: #1033
+#1232 := [mp~ #1036 #1231]: #1229
+#1233 := [mp #1232 #1420]: #1418
+#1722 := [mp #1233 #1721]: #1717
+#2287 := [mp #1722 #2286]: #2284
+#1936 := [unit-resolution #2287 #2647]: #1432
+#1865 := (or #1427 #1780)
+#1781 := [def-axiom]: #1865
+#2047 := [unit-resolution #1781 #1936]: #1780
+#2062 := (+ #8 #1037)
+#2041 := (>= #2062 0::int)
+#2067 := (= #8 #1040)
+#2045 := (= #1040 #8)
+#2040 := (= ?x1!0 0::int)
+#1866 := (or #1427 #1043)
+#1867 := [def-axiom]: #1866
+#2048 := [unit-resolution #1867 #1936]: #1043
+#1858 := (or #1427 #1044)
+#1869 := [def-axiom]: #1858
+#2049 := [unit-resolution #1869 #1936]: #1044
+#2046 := [th-lemma #2049 #2048]: #2040
+#2014 := [monotonicity #2046]: #2045
+#2021 := [symm #2014]: #2067
+#1980 := (not #2067)
+#2011 := (or #1980 #2041)
+#2013 := [th-lemma]: #2011
+#2015 := [unit-resolution #2013 #2021]: #2041
+[th-lemma #2015 #2047 #2043]: false
 unsat

--- a/src/HOL/Boogie/Examples/cert/VCC_maximum	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/VCC_maximum	Wed Dec 23 17:37:42 2009 +0100
@@ -687,6 +687,6 @@
 :assumption (distinct uf_282)
 :assumption (distinct uf_42)
 :assumption (distinct uf_263 uf_14 uf_262 uf_261)
-:assumption (not (implies (and (and (<= 0 uf_283) (<= uf_283 uf_78)) (and (and (<= 0 uf_284) (<= uf_284 uf_76)) (and (and (<= 0 uf_285) (<= uf_285 uf_76)) (and (< uf_286 1099511627776) (and (< 0 uf_286) (and (and (= (uf_27 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288)))) uf_9) (and (= (uf_25 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288)))) uf_26) (and (= (uf_48 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) (uf_124 uf_7 uf_286)) uf_9) (and (= (uf_24 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288)))) uf_9) (and (not (= (uf_12 (uf_124 uf_7 uf_286)) uf_14)) (= (uf_23 (uf_124 uf_7 uf_286)) uf_9)))))) (and (= (uf_203 uf_287) uf_9) (and (and (= (uf_202 uf_281 uf_287) uf_9) (= (uf_55 uf_287) uf_9)) (and (forall (?x771 T19) (< (uf_289 ?x771) uf_290) :pat { (uf_289 ?x771) }) (and (and (up_291 uf_287 uf_281 uf_280 (uf_29 (uf_43 uf_7 uf_288)) (uf_6 uf_7)) (up_292 uf_287 uf_281 uf_280 (uf_43 uf_7 uf_288) (uf_6 uf_7))) (and (up_291 uf_287 uf_281 uf_279 uf_286 uf_4) (and (= uf_293 (uf_173 uf_287)) (and (forall (?x772 T5) (iff (= (uf_294 uf_293 ?x772) uf_9) false) :pat { (uf_294 uf_293 ?x772) }) (and (<= 0 uf_286) (<= uf_286 uf_76))))))))))))))) (and (= (uf_200 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) uf_282) uf_9) (implies (= (uf_200 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) uf_282) uf_9) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (implies (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (and (= uf_295 (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7))) (and (up_291 uf_287 uf_278 uf_277 uf_295 uf_7) (and (up_291 uf_287 uf_276 uf_275 0 uf_4) (and (up_291 uf_287 uf_274 uf_273 1 uf_4) (and (<= 1 1) (and (<= 1 1) (and (<= 0 0) (<= 0 0))))))))) (and (<= 1 uf_286) (implies (<= 1 uf_286) (and (forall (?x773 Int) (implies (and (and (<= 0 ?x773) (<= ?x773 uf_76)) (< ?x773 1)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x773 uf_7)) uf_295))) (implies (forall (?x774 Int) (implies (and (and (<= 0 ?x774) (<= ?x774 uf_76)) (< ?x774 1)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x774 uf_7)) uf_295))) (and (and (< 0 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_295)) (implies (and (and (< 0 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_295)) (and (and (<= 0 uf_296) (<= uf_296 uf_78)) (and (and (<= 0 uf_297) (<= uf_297 uf_76)) (and (and (<= 0 uf_298) (<= uf_298 uf_76)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= uf_298 uf_286) (and (forall (?x775 Int) (implies (and (and (<= 0 ?x775) (<= ?x775 uf_76)) (< ?x775 uf_298)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x775 uf_7)) uf_296))) (and (and (< uf_297 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_297 uf_7)) uf_296)) (and (<= 1 uf_298) (<= 0 uf_297)))))))))) (and (implies (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (not true) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (= (uf_202 uf_272 uf_287) uf_9) (= (uf_55 uf_287) uf_9)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= 1 uf_298) (<= 0 uf_297)))))))) (and up_216 (implies (and up_216 (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (= uf_299 uf_296) (and (= uf_300 uf_298) (and (= uf_301 uf_297) (= uf_302 uf_296)))))))) (and (forall (?x776 Int) (implies (and (and (<= 0 ?x776) (<= ?x776 uf_76)) (< ?x776 uf_286)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x776 uf_7)) uf_302))) (implies (forall (?x777 Int) (implies (and (and (<= 0 ?x777) (<= ?x777 uf_76)) (< ?x777 uf_286)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x777 uf_7)) uf_302))) (exists (?x778 Int) (and (<= 0 ?x778) (and (<= ?x778 uf_76) (and (< ?x778 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x778 uf_7)) uf_302)))))))))) (implies (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (forall (?x779 T5) (implies (not (= (uf_12 (uf_13 (uf_25 uf_287 ?x779))) uf_261)) (not (= (uf_12 (uf_13 (uf_25 uf_287 ?x779))) uf_261))) :pat { (uf_40 (uf_41 uf_287) ?x779) }) (and (forall (?x780 T5) (implies (= (uf_68 uf_287 ?x780) uf_9) (and (= (uf_19 (uf_20 uf_287) ?x780) (uf_19 (uf_20 uf_287) ?x780)) (= (uf_68 uf_287 ?x780) uf_9))) :pat { (uf_19 (uf_20 uf_287) ?x780) }) (and (forall (?x781 T5) (implies (= (uf_68 uf_287 ?x781) uf_9) (and (= (uf_40 (uf_41 uf_287) ?x781) (uf_40 (uf_41 uf_287) ?x781)) (= (uf_68 uf_287 ?x781) uf_9))) :pat { (uf_40 (uf_41 uf_287) ?x781) }) (and (forall (?x782 T5) (implies (= (uf_68 uf_287 ?x782) uf_9) (and (= (uf_58 (uf_59 uf_287) ?x782) (uf_58 (uf_59 uf_287) ?x782)) (= (uf_68 uf_287 ?x782) uf_9))) :pat { (uf_58 (uf_59 uf_287) ?x782) }) (and (<= (uf_173 uf_287) (uf_173 uf_287)) (and (forall (?x783 T5) (<= (uf_172 uf_287 ?x783) (uf_172 uf_287 ?x783)) :pat { (uf_172 uf_287 ?x783) }) (= (uf_178 uf_287 uf_287) uf_9))))))) (and (and (<= (uf_173 uf_287) (uf_173 uf_287)) (and (forall (?x784 T5) (<= (uf_172 uf_287 ?x784) (uf_172 uf_287 ?x784)) :pat { (uf_172 uf_287 ?x784) }) (= (uf_178 uf_287 uf_287) uf_9))) (and (and (= (uf_202 uf_272 uf_287) uf_9) (= (uf_55 uf_287) uf_9)) (and (up_291 uf_287 uf_272 uf_273 uf_298 uf_4) (and (up_291 uf_287 uf_272 uf_275 uf_297 uf_4) (and (up_291 uf_287 uf_272 uf_277 uf_296 uf_7) (and (up_291 uf_287 uf_272 uf_279 uf_286 uf_4) (and (and (up_291 uf_287 uf_272 uf_280 (uf_29 (uf_43 uf_7 uf_288)) (uf_6 uf_7)) (up_292 uf_287 uf_272 uf_280 (uf_43 uf_7 uf_288) (uf_6 uf_7))) (and (and (= (uf_59 uf_287) (uf_59 uf_287)) (= (uf_41 uf_287) (uf_41 uf_287))) (and (<= 1 uf_298) (<= 0 uf_297)))))))))))))) (and (implies (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (< uf_298 uf_286) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= 1 uf_298) (<= 0 uf_297))))) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (and (<= 1 uf_298) (<= 0 uf_297))) (and (implies (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (< uf_296 (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7))) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= 1 uf_298) (<= 0 uf_297))))) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (and (= uf_303 (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7))) (and (up_291 uf_287 uf_271 uf_277 uf_303 uf_7) (and (up_291 uf_287 uf_270 uf_275 uf_298 uf_4) (and (and (<= 1 uf_298) (<= 1 uf_298)) (and (= uf_304 uf_303) (and (= uf_305 uf_298) (and (<= 1 uf_298) (<= 0 uf_305))))))))) (and (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (implies (and (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (and (= uf_306 (+ uf_298 1)) (and (up_291 uf_287 uf_269 uf_273 uf_306 uf_4) (and (<= 2 uf_306) (<= 0 uf_305))))) (and (<= uf_306 uf_286) (implies (<= uf_306 uf_286) (and (forall (?x785 Int) (implies (and (and (<= 0 ?x785) (<= ?x785 uf_76)) (< ?x785 uf_306)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x785 uf_7)) uf_304))) (implies (forall (?x786 Int) (implies (and (and (<= 0 ?x786) (<= ?x786 uf_76)) (< ?x786 uf_306)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x786 uf_7)) uf_304))) (and (< uf_305 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_305 uf_7)) uf_304))))))))))))) (implies (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_296) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (= uf_304 uf_296) (and (= uf_305 uf_297) (and (<= 1 uf_298) (<= 0 uf_305))))))))) (and (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (implies (and (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (and (= uf_306 (+ uf_298 1)) (and (up_291 uf_287 uf_269 uf_273 uf_306 uf_4) (and (<= 2 uf_306) (<= 0 uf_305))))) (and (<= uf_306 uf_286) (implies (<= uf_306 uf_286) (and (forall (?x787 Int) (implies (and (and (<= 0 ?x787) (<= ?x787 uf_76)) (< ?x787 uf_306)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x787 uf_7)) uf_304))) (implies (forall (?x788 Int) (implies (and (and (<= 0 ?x788) (<= ?x788 uf_76)) (< ?x788 uf_306)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x788 uf_7)) uf_304))) (and (< uf_305 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_305 uf_7)) uf_304))))))))))))))) (implies (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= uf_286 uf_298) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (<= 1 uf_298) (<= 0 uf_297))))))) (and up_216 (implies (and up_216 (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (<= 1 uf_298) (<= 0 uf_297)) (and (= uf_299 uf_296) (and (= uf_300 uf_298) (and (= uf_301 uf_297) (= uf_302 uf_296)))))))) (and (forall (?x789 Int) (implies (and (and (<= 0 ?x789) (<= ?x789 uf_76)) (< ?x789 uf_286)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x789 uf_7)) uf_302))) (implies (forall (?x790 Int) (implies (and (and (<= 0 ?x790) (<= ?x790 uf_76)) (< ?x790 uf_286)) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x790 uf_7)) uf_302))) (exists (?x791 Int) (and (<= 0 ?x791) (and (<= ?x791 uf_76) (and (< ?x791 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x791 uf_7)) uf_302)))))))))))))))))))))))))))
+:assumption (not (implies (and (<= 0 uf_283) (<= uf_283 uf_78)) (implies (and (<= 0 uf_284) (<= uf_284 uf_76)) (implies (and (<= 0 uf_285) (<= uf_285 uf_76)) (implies (< uf_286 1099511627776) (implies (< 0 uf_286) (implies (and (= (uf_27 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288)))) uf_9) (and (= (uf_25 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288)))) uf_26) (and (= (uf_48 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) (uf_124 uf_7 uf_286)) uf_9) (and (= (uf_24 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288)))) uf_9) (and (not (= (uf_12 (uf_124 uf_7 uf_286)) uf_14)) (= (uf_23 (uf_124 uf_7 uf_286)) uf_9)))))) (implies (= (uf_203 uf_287) uf_9) (implies (and (= (uf_202 uf_281 uf_287) uf_9) (= (uf_55 uf_287) uf_9)) (implies (forall (?x771 T19) (< (uf_289 ?x771) uf_290) :pat { (uf_289 ?x771) }) (implies (and (up_291 uf_287 uf_281 uf_280 (uf_29 (uf_43 uf_7 uf_288)) (uf_6 uf_7)) (up_292 uf_287 uf_281 uf_280 (uf_43 uf_7 uf_288) (uf_6 uf_7))) (implies (up_291 uf_287 uf_281 uf_279 uf_286 uf_4) (implies (= uf_293 (uf_173 uf_287)) (implies (forall (?x772 T5) (iff (= (uf_294 uf_293 ?x772) uf_9) false) :pat { (uf_294 uf_293 ?x772) }) (implies (and (<= 0 uf_286) (<= uf_286 uf_76)) (and (= (uf_200 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) uf_282) uf_9) (implies (= (uf_200 uf_287 (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) (uf_43 (uf_124 uf_7 uf_286) (uf_116 (uf_43 uf_7 uf_288))) uf_282) uf_9) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_9)) (implies (= uf_295 (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7))) (implies (up_291 uf_287 uf_278 uf_277 uf_295 uf_7) (implies (up_291 uf_287 uf_276 uf_275 0 uf_4) (implies (up_291 uf_287 uf_274 uf_273 1 uf_4) (implies (and (<= 1 1) (and (<= 1 1) (and (<= 0 0) (<= 0 0)))) (and (<= 1 uf_286) (implies (<= 1 uf_286) (and (forall (?x773 Int) (implies (and (<= 0 ?x773) (<= ?x773 uf_76)) (implies (< ?x773 1) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x773 uf_7)) uf_295)))) (implies (forall (?x774 Int) (implies (and (<= 0 ?x774) (<= ?x774 uf_76)) (implies (< ?x774 1) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x774 uf_7)) uf_295)))) (and (and (< 0 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_295)) (implies (and (< 0 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) 0 uf_7)) uf_295)) (implies (and (<= 0 uf_296) (<= uf_296 uf_78)) (implies (and (<= 0 uf_297) (<= uf_297 uf_76)) (implies (and (<= 0 uf_298) (<= uf_298 uf_76)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (<= uf_298 uf_286) (implies (forall (?x775 Int) (implies (and (<= 0 ?x775) (<= ?x775 uf_76)) (implies (< ?x775 uf_298) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x775 uf_7)) uf_296)))) (implies (and (< uf_297 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_297 uf_7)) uf_296)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (not true) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (= (uf_202 uf_272 uf_287) uf_9) (= (uf_55 uf_287) uf_9)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and up_216 (implies up_216 (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (= uf_299 uf_296) (implies (= uf_300 uf_298) (implies (= uf_301 uf_297) (implies (= uf_302 uf_296) (and (forall (?x776 Int) (implies (and (<= 0 ?x776) (<= ?x776 uf_76)) (implies (< ?x776 uf_286) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x776 uf_7)) uf_302)))) (implies (forall (?x777 Int) (implies (and (<= 0 ?x777) (<= ?x777 uf_76)) (implies (< ?x777 uf_286) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x777 uf_7)) uf_302)))) (and (exists (?x778 Int) (and (<= 0 ?x778) (and (<= ?x778 uf_76) (and (< ?x778 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x778 uf_7)) uf_302))))) true))))))))))))))))))) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (forall (?x779 T5) (implies (not (= (uf_12 (uf_13 (uf_25 uf_287 ?x779))) uf_261)) (not (= (uf_12 (uf_13 (uf_25 uf_287 ?x779))) uf_261))) :pat { (uf_40 (uf_41 uf_287) ?x779) }) (and (forall (?x780 T5) (implies (= (uf_68 uf_287 ?x780) uf_9) (and (= (uf_19 (uf_20 uf_287) ?x780) (uf_19 (uf_20 uf_287) ?x780)) (= (uf_68 uf_287 ?x780) uf_9))) :pat { (uf_19 (uf_20 uf_287) ?x780) }) (and (forall (?x781 T5) (implies (= (uf_68 uf_287 ?x781) uf_9) (and (= (uf_40 (uf_41 uf_287) ?x781) (uf_40 (uf_41 uf_287) ?x781)) (= (uf_68 uf_287 ?x781) uf_9))) :pat { (uf_40 (uf_41 uf_287) ?x781) }) (and (forall (?x782 T5) (implies (= (uf_68 uf_287 ?x782) uf_9) (and (= (uf_58 (uf_59 uf_287) ?x782) (uf_58 (uf_59 uf_287) ?x782)) (= (uf_68 uf_287 ?x782) uf_9))) :pat { (uf_58 (uf_59 uf_287) ?x782) }) (and (<= (uf_173 uf_287) (uf_173 uf_287)) (and (forall (?x783 T5) (<= (uf_172 uf_287 ?x783) (uf_172 uf_287 ?x783)) :pat { (uf_172 uf_287 ?x783) }) (= (uf_178 uf_287 uf_287) uf_9))))))) (implies (and (<= (uf_173 uf_287) (uf_173 uf_287)) (and (forall (?x784 T5) (<= (uf_172 uf_287 ?x784) (uf_172 uf_287 ?x784)) :pat { (uf_172 uf_287 ?x784) }) (= (uf_178 uf_287 uf_287) uf_9))) (implies (and (= (uf_202 uf_272 uf_287) uf_9) (= (uf_55 uf_287) uf_9)) (implies (up_291 uf_287 uf_272 uf_273 uf_298 uf_4) (implies (up_291 uf_287 uf_272 uf_275 uf_297 uf_4) (implies (up_291 uf_287 uf_272 uf_277 uf_296 uf_7) (implies (up_291 uf_287 uf_272 uf_279 uf_286 uf_4) (implies (and (up_291 uf_287 uf_272 uf_280 (uf_29 (uf_43 uf_7 uf_288)) (uf_6 uf_7)) (up_292 uf_287 uf_272 uf_280 (uf_43 uf_7 uf_288) (uf_6 uf_7))) (implies (and (= (uf_59 uf_287) (uf_59 uf_287)) (= (uf_41 uf_287) (uf_41 uf_287))) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (< uf_298 uf_286) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (< uf_296 (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7))) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_24 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (and (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (and (= (uf_48 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7) uf_7) uf_9) (= (uf_68 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_9)) (implies (= uf_303 (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7))) (implies (up_291 uf_287 uf_271 uf_277 uf_303 uf_7) (implies (up_291 uf_287 uf_270 uf_275 uf_298 uf_4) (implies (and (<= 1 uf_298) (<= 1 uf_298)) (implies (= uf_304 uf_303) (implies (= uf_305 uf_298) (implies (and (<= 1 uf_298) (<= 0 uf_305)) (and (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (implies (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (implies (= uf_306 (+ uf_298 1)) (implies (up_291 uf_287 uf_269 uf_273 uf_306 uf_4) (implies (and (<= 2 uf_306) (<= 0 uf_305)) (and (<= uf_306 uf_286) (implies (<= uf_306 uf_286) (and (forall (?x785 Int) (implies (and (<= 0 ?x785) (<= ?x785 uf_76)) (implies (< ?x785 uf_306) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x785 uf_7)) uf_304)))) (implies (forall (?x786 Int) (implies (and (<= 0 ?x786) (<= ?x786 uf_76)) (implies (< ?x786 uf_306) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x786 uf_7)) uf_304)))) (and (and (< uf_305 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_305 uf_7)) uf_304)) true))))))))))))))))))))))))) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_298 uf_7)) uf_296) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (= uf_304 uf_296) (implies (= uf_305 uf_297) (implies (and (<= 1 uf_298) (<= 0 uf_305)) (and (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (implies (and (<= 0 (+ uf_298 1)) (<= (+ uf_298 1) uf_76)) (implies (= uf_306 (+ uf_298 1)) (implies (up_291 uf_287 uf_269 uf_273 uf_306 uf_4) (implies (and (<= 2 uf_306) (<= 0 uf_305)) (and (<= uf_306 uf_286) (implies (<= uf_306 uf_286) (and (forall (?x787 Int) (implies (and (<= 0 ?x787) (<= ?x787 uf_76)) (implies (< ?x787 uf_306) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x787 uf_7)) uf_304)))) (implies (forall (?x788 Int) (implies (and (<= 0 ?x788) (<= ?x788 uf_76)) (implies (< ?x788 uf_306) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x788 uf_7)) uf_304)))) (and (and (< uf_305 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) uf_305 uf_7)) uf_304)) true)))))))))))))))))))))))))))) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (<= uf_286 uf_298) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (and up_216 (implies up_216 (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (and (<= 1 uf_298) (<= 0 uf_297)) (implies (= uf_299 uf_296) (implies (= uf_300 uf_298) (implies (= uf_301 uf_297) (implies (= uf_302 uf_296) (and (forall (?x789 Int) (implies (and (<= 0 ?x789) (<= ?x789 uf_76)) (implies (< ?x789 uf_286) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x789 uf_7)) uf_302)))) (implies (forall (?x790 Int) (implies (and (<= 0 ?x790) (<= ?x790 uf_76)) (implies (< ?x790 uf_286) (<= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x790 uf_7)) uf_302)))) (and (exists (?x791 Int) (and (<= 0 ?x791) (and (<= ?x791 uf_76) (and (< ?x791 uf_286) (= (uf_110 uf_287 (uf_66 (uf_43 uf_7 uf_288) ?x791 uf_7)) uf_302))))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 :formula true
 )

--- a/src/HOL/Boogie/Examples/cert/VCC_maximum.proof	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/VCC_maximum.proof	Wed Dec 23 17:37:42 2009 +0100
@@ -1,309 +1,106 @@
 #2 := false
-decl ?x785!14 :: int
-#17756 := ?x785!14
-decl uf_298 :: int
-#3087 := uf_298
-#30181 := (= uf_298 ?x785!14)
-#121 := 0::int
-#4042 := -1::int
-#18020 := (* -1::int ?x785!14)
-decl uf_306 :: int
-#3256 := uf_306
-#18021 := (+ uf_306 #18020)
-#18022 := (<= #18021 0::int)
 decl uf_110 :: (-> T4 T5 int)
 decl uf_66 :: (-> T5 int T3 T5)
 decl uf_7 :: T3
 #10 := uf_7
+decl ?x785!14 :: int
+#18296 := ?x785!14
 decl uf_43 :: (-> T3 int T5)
 decl uf_288 :: int
 #2978 := uf_288
 #2979 := (uf_43 uf_7 uf_288)
-#17764 := (uf_66 #2979 ?x785!14 uf_7)
+#18301 := (uf_66 #2979 ?x785!14 uf_7)
 decl uf_287 :: T4
 #2976 := uf_287
-#17765 := (uf_110 uf_287 #17764)
-#18007 := (* -1::int #17765)
+#18302 := (uf_110 uf_287 #18301)
+decl uf_298 :: int
+#3069 := uf_298
+#3181 := (uf_66 #2979 uf_298 uf_7)
+#3190 := (uf_110 uf_287 #3181)
+#30497 := (= #3190 #18302)
+#30502 := (not #30497)
+#121 := 0::int
+#4044 := -1::int
+#18623 := (* -1::int #18302)
+#30501 := (+ #3190 #18623)
+#30503 := (>= #30501 0::int)
+#30513 := (not #30503)
 decl uf_304 :: int
-#3239 := uf_304
-#18008 := (+ uf_304 #18007)
-#18009 := (>= #18008 0::int)
-#17761 := (>= ?x785!14 0::int)
-#21511 := (not #17761)
-#7471 := 4294967295::int
-#17757 := (<= ?x785!14 4294967295::int)
-#21510 := (not #17757)
-#21526 := (or #21510 #21511 #18009 #18022)
-#21531 := (not #21526)
+#3197 := uf_304
+#13279 := (* -1::int uf_304)
+#30155 := (+ #3190 #13279)
+#30108 := (<= #30155 0::int)
+#30154 := (= #3190 uf_304)
+decl uf_303 :: int
+#3192 := uf_303
+#12313 := (= uf_303 uf_304)
+#18624 := (+ uf_304 #18623)
+#18625 := (>= #18624 0::int)
+#18610 := (* -1::int ?x785!14)
+decl uf_306 :: int
+#3207 := uf_306
+#18611 := (+ uf_306 #18610)
+#18612 := (<= #18611 0::int)
+#18298 := (>= ?x785!14 0::int)
+#22078 := (not #18298)
+#7473 := 4294967295::int
+#18297 := (<= ?x785!14 4294967295::int)
+#22077 := (not #18297)
+#22093 := (or #22077 #22078 #18612 #18625)
+#22098 := (not #22093)
 #161 := (:var 0 int)
-#3072 := (uf_66 #2979 #161 uf_7)
-#22468 := (pattern #3072)
-#14378 := (<= #161 4294967295::int)
-#18695 := (not #14378)
-#13112 := (* -1::int uf_304)
-#3073 := (uf_110 uf_287 #3072)
-#13113 := (+ #3073 #13112)
-#13114 := (<= #13113 0::int)
-#13062 := (* -1::int uf_306)
-#13097 := (+ #161 #13062)
-#13096 := (>= #13097 0::int)
-#4041 := (>= #161 0::int)
-#4963 := (not #4041)
-#21492 := (or #4963 #13096 #13114 #18695)
-#22485 := (forall (vars (?x785 int)) (:pat #22468) #21492)
-#22490 := (not #22485)
+#3053 := (uf_66 #2979 #161 uf_7)
+#23000 := (pattern #3053)
+#14916 := (<= #161 4294967295::int)
+#19295 := (not #14916)
+#3054 := (uf_110 uf_287 #3053)
+#13280 := (+ #3054 #13279)
+#13281 := (<= #13280 0::int)
+#13260 := (* -1::int uf_306)
+#13268 := (+ #161 #13260)
+#13267 := (>= #13268 0::int)
+#4043 := (>= #161 0::int)
+#4965 := (not #4043)
+#22059 := (or #4965 #13267 #13281 #19295)
+#23017 := (forall (vars (?x785 int)) (:pat #23000) #22059)
+#23022 := (not #23017)
 decl uf_305 :: int
-#3241 := uf_305
-#13126 := (* -1::int uf_305)
+#3199 := uf_305
+#13301 := (* -1::int uf_305)
 decl uf_286 :: int
 #2973 := uf_286
-#13127 := (+ uf_286 #13126)
-#13128 := (<= #13127 0::int)
-#3271 := (uf_66 #2979 uf_305 uf_7)
-#3272 := (uf_110 uf_287 #3271)
-#12446 := (= uf_304 #3272)
-#21466 := (not #12446)
-#21467 := (or #21466 #13128)
-#21468 := (not #21467)
-#22493 := (or #21468 #22490)
-#3220 := (uf_66 #2979 uf_298 uf_7)
-#3230 := (uf_110 uf_287 #3220)
-#28730 := (= #3230 #3272)
-#28979 := (= #3272 #3230)
-#29112 := (= #3271 #3220)
-decl uf_144 :: (-> T3 T3)
-decl uf_124 :: (-> T3 int T3)
-#2977 := (uf_124 uf_7 uf_286)
-#24108 := (uf_144 #2977)
-decl uf_125 :: (-> T5 T5 int)
-decl uf_116 :: (-> T5 int)
-decl uf_28 :: (-> int T5)
-decl uf_29 :: (-> T5 int)
-#3013 := (uf_29 #2979)
-#23935 := (uf_28 #3013)
-#26317 := (uf_116 #23935)
-#26333 := (uf_43 #24108 #26317)
-decl uf_13 :: (-> T5 T3)
-#26868 := (uf_13 #26333)
-#27481 := (uf_66 #26333 uf_298 #26868)
-#27482 := (uf_125 #27481 #26333)
-#2980 := (uf_116 #2979)
-#26469 := (uf_43 #24108 #2980)
-#27555 := (uf_66 #26469 #27482 #24108)
-#27664 := (= #27555 #3220)
-#27655 := (= #24108 uf_7)
-#24109 := (= uf_7 #24108)
-#326 := (:var 1 T3)
-#1358 := (uf_124 #326 #161)
-#1592 := (pattern #1358)
-#1605 := (uf_144 #1358)
-#8271 := (= #326 #1605)
-#8275 := (forall (vars (?x388 T3) (?x389 int)) (:pat #1592) #8271)
-#16576 := (~ #8275 #8275)
-#16574 := (~ #8271 #8271)
-#16575 := [refl]: #16574
-#16577 := [nnf-pos #16575]: #16576
-#1606 := (= #1605 #326)
-#1607 := (forall (vars (?x388 T3) (?x389 int)) (:pat #1592) #1606)
-#8276 := (iff #1607 #8275)
-#8273 := (iff #1606 #8271)
-#8274 := [rewrite]: #8273
-#8277 := [quant-intro #8274]: #8276
-#8270 := [asserted]: #1607
-#8280 := [mp #8270 #8277]: #8275
-#16578 := [mp~ #8280 #16577]: #8275
-#24112 := (not #8275)
-#24113 := (or #24112 #24109)
-#24114 := [quant-inst]: #24113
-#27654 := [unit-resolution #24114 #16578]: #24109
-#27656 := [symm #27654]: #27655
-#27657 := (= #27482 uf_298)
-#26369 := (uf_13 #23935)
-#28212 := (uf_66 #23935 uf_298 #26369)
-#28213 := (uf_125 #28212 #23935)
-#29709 := (= #28213 uf_298)
-#28214 := (= uf_298 #28213)
-#15 := (:var 1 T5)
-#1390 := (uf_13 #15)
-#1391 := (uf_66 #15 #161 #1390)
-#1392 := (pattern #1391)
-#1393 := (uf_125 #1391 #15)
-#7663 := (= #161 #1393)
-#7667 := (forall (vars (?x319 T5) (?x320 int)) (:pat #1392) #7663)
-#16288 := (~ #7667 #7667)
-#16286 := (~ #7663 #7663)
-#16287 := [refl]: #16286
-#16289 := [nnf-pos #16287]: #16288
-#1394 := (= #1393 #161)
-#1395 := (forall (vars (?x319 T5) (?x320 int)) (:pat #1392) #1394)
-#7668 := (iff #1395 #7667)
-#7665 := (iff #1394 #7663)
-#7666 := [rewrite]: #7665
-#7669 := [quant-intro #7666]: #7668
-#7662 := [asserted]: #1395
-#7672 := [mp #7662 #7669]: #7667
-#16290 := [mp~ #7672 #16289]: #7667
-#26376 := (not #7667)
-#28217 := (or #26376 #28214)
-#28218 := [quant-inst]: #28217
-#28873 := [unit-resolution #28218 #16290]: #28214
-#29710 := [symm #28873]: #29709
-#28080 := (= #27482 #28213)
-#29457 := (= #28213 #27482)
-#27795 := (= #23935 #26333)
-#27716 := (= #2979 #26333)
-#27718 := (= #26333 #2979)
-#27783 := (= #26317 uf_288)
-#27660 := (= #2980 uf_288)
-#24227 := (= uf_288 #2980)
-#2697 := (uf_43 #326 #161)
-#22405 := (pattern #2697)
-#2698 := (uf_116 #2697)
-#11208 := (= #161 #2698)
-#22406 := (forall (vars (?x718 T3) (?x719 int)) (:pat #22405) #11208)
-#11212 := (forall (vars (?x718 T3) (?x719 int)) #11208)
-#22409 := (iff #11212 #22406)
-#22407 := (iff #11208 #11208)
-#22408 := [refl]: #22407
-#22410 := [quant-intro #22408]: #22409
-#17483 := (~ #11212 #11212)
-#17481 := (~ #11208 #11208)
-#17482 := [refl]: #17481
-#17484 := [nnf-pos #17482]: #17483
-#2699 := (= #2698 #161)
-#2700 := (forall (vars (?x718 T3) (?x719 int)) #2699)
-#11213 := (iff #2700 #11212)
-#11210 := (iff #2699 #11208)
-#11211 := [rewrite]: #11210
-#11214 := [quant-intro #11211]: #11213
-#11207 := [asserted]: #2700
-#11217 := [mp #11207 #11214]: #11212
-#17485 := [mp~ #11217 #17484]: #11212
-#22411 := [mp #17485 #22410]: #22406
-#24181 := (not #22406)
-#24232 := (or #24181 #24227)
-#24233 := [quant-inst]: #24232
-#27659 := [unit-resolution #24233 #22411]: #24227
-#27661 := [symm #27659]: #27660
-#27710 := (= #26317 #2980)
-#27708 := (= #23935 #2979)
-#23936 := (= #2979 #23935)
-#23 := (:var 0 T5)
-#93 := (uf_29 #23)
-#22316 := (pattern #93)
-#94 := (uf_28 #93)
-#3540 := (= #23 #94)
-#22317 := (forall (vars (?x14 T5)) (:pat #22316) #3540)
-#3543 := (forall (vars (?x14 T5)) #3540)
-#22318 := (iff #3543 #22317)
-#22320 := (iff #22317 #22317)
-#22321 := [rewrite]: #22320
-#22319 := [rewrite]: #22318
-#22322 := [trans #22319 #22321]: #22318
-#15525 := (~ #3543 #3543)
-#15515 := (~ #3540 #3540)
-#15516 := [refl]: #15515
-#15581 := [nnf-pos #15516]: #15525
-#95 := (= #94 #23)
-#96 := (forall (vars (?x14 T5)) #95)
-#3544 := (iff #96 #3543)
-#3541 := (iff #95 #3540)
-#3542 := [rewrite]: #3541
-#3545 := [quant-intro #3542]: #3544
-#3539 := [asserted]: #96
-#3548 := [mp #3539 #3545]: #3543
-#15582 := [mp~ #3548 #15581]: #3543
-#22323 := [mp #15582 #22322]: #22317
-#23939 := (not #22317)
-#23940 := (or #23939 #23936)
-#23941 := [quant-inst]: #23940
-#27707 := [unit-resolution #23941 #22323]: #23936
-#27709 := [symm #27707]: #27708
-#27711 := [monotonicity #27709]: #27710
-#27784 := [trans #27711 #27661]: #27783
-#27789 := [monotonicity #27656 #27784]: #27718
-#27790 := [symm #27789]: #27716
-#27796 := [trans #27709 #27790]: #27795
-#29455 := (= #28212 #27481)
-#29453 := (= #3220 #27481)
-#29451 := (= #27481 #3220)
-#29423 := (= #26868 uf_7)
-#24223 := (uf_13 #2979)
-#27846 := (= #24223 uf_7)
-#24224 := (= uf_7 #24223)
-#2701 := (uf_13 #2697)
-#11216 := (= #326 #2701)
-#22412 := (forall (vars (?x720 T3) (?x721 int)) (:pat #22405) #11216)
-#11220 := (forall (vars (?x720 T3) (?x721 int)) #11216)
-#22415 := (iff #11220 #22412)
-#22413 := (iff #11216 #11216)
-#22414 := [refl]: #22413
-#22416 := [quant-intro #22414]: #22415
-#17488 := (~ #11220 #11220)
-#17486 := (~ #11216 #11216)
-#17487 := [refl]: #17486
-#17489 := [nnf-pos #17487]: #17488
-#2702 := (= #2701 #326)
-#2703 := (forall (vars (?x720 T3) (?x721 int)) #2702)
-#11221 := (iff #2703 #11220)
-#11218 := (iff #2702 #11216)
-#11219 := [rewrite]: #11218
-#11222 := [quant-intro #11219]: #11221
-#11215 := [asserted]: #2703
-#11225 := [mp #11215 #11222]: #11220
-#17490 := [mp~ #11225 #17489]: #11220
-#22417 := [mp #17490 #22416]: #22412
-#24175 := (not #22412)
-#24229 := (or #24175 #24224)
-#24230 := [quant-inst]: #24229
-#27843 := [unit-resolution #24230 #22417]: #24224
-#27847 := [symm #27843]: #27846
-#29421 := (= #26868 #24223)
-#29422 := [monotonicity #27789]: #29421
-#29424 := [trans #29422 #27847]: #29423
-#29452 := [monotonicity #27789 #29424]: #29451
-#29454 := [symm #29452]: #29453
-#29449 := (= #28212 #3220)
-#27848 := (= #26369 uf_7)
-#27844 := (= #26369 #24223)
-#27845 := [monotonicity #27709]: #27844
-#27849 := [trans #27845 #27847]: #27848
-#29450 := [monotonicity #27709 #27849]: #29449
-#29456 := [trans #29450 #29454]: #29455
-#29458 := [monotonicity #29456 #27796]: #29457
-#29441 := [symm #29458]: #28080
-#29711 := [trans #29441 #29710]: #27657
-#27662 := (= #26469 #2979)
-#27663 := [monotonicity #27656 #27661]: #27662
-#29712 := [monotonicity #27663 #29711 #27656]: #27664
-#29208 := (= #3271 #27555)
-#29074 := (= uf_305 #27482)
-#28951 := (= uf_305 #28213)
-#3242 := (= uf_305 uf_298)
-#12383 := (= uf_298 uf_305)
-#22496 := (not #22493)
-#22499 := (or #22496 #21531)
-#22502 := (not #22499)
-#13090 := (+ uf_286 #13062)
-#13089 := (>= #13090 0::int)
-#13093 := (not #13089)
-#22505 := (or #13093 #22502)
-#22508 := (not #22505)
-#22511 := (or #13093 #22508)
-#22514 := (not #22511)
-#15126 := 4294967294::int
-#15127 := (<= uf_298 4294967294::int)
-#17745 := (not #15127)
-#13063 := (+ uf_298 #13062)
-#13061 := (= #13063 -1::int)
-#21556 := (not #13061)
+#13302 := (+ uf_286 #13301)
+#13303 := (<= #13302 0::int)
+#3219 := (uf_66 #2979 uf_305 uf_7)
+#3220 := (uf_110 uf_287 #3219)
+#12352 := (= uf_304 #3220)
+#22044 := (not #12352)
+#22045 := (or #22044 #13303)
+#22046 := (not #22045)
+#23025 := (or #22046 #23022)
+#23028 := (not #23025)
+#23031 := (or #23028 #22098)
+#23034 := (not #23031)
+#13261 := (+ uf_286 #13260)
+#13259 := (>= #13261 0::int)
+#13264 := (not #13259)
+#23037 := (or #13264 #23034)
+#23040 := (not #23037)
+#23043 := (or #13264 #23040)
+#23046 := (not #23043)
+#15608 := 4294967294::int
+#15609 := (<= uf_298 4294967294::int)
+#18279 := (not #15609)
+#13328 := (+ uf_298 #13260)
+#13327 := (= #13328 -1::int)
+#13331 := (not #13327)
 #892 := 2::int
-#13059 := (>= uf_306 2::int)
-#21555 := (not #13059)
-#13051 := (>= uf_298 -1::int)
-#17742 := (not #13051)
-#13017 := (>= uf_305 0::int)
-#21554 := (not #13017)
+#13251 := (>= uf_306 2::int)
+#22121 := (not #13251)
+#13243 := (>= uf_298 -1::int)
+#18276 := (not #13243)
+#13234 := (>= uf_305 0::int)
+#22120 := (not #13234)
 decl up_291 :: (-> T4 T1 T1 int T3 bool)
 decl uf_4 :: T3
 #7 := uf_4
@@ -311,1019 +108,1174 @@
 #2946 := uf_273
 decl uf_269 :: T1
 #2942 := uf_269
-#3258 := (up_291 uf_287 uf_269 uf_273 uf_306 uf_4)
-#21553 := (not #3258)
-#22517 := (or #21553 #21554 #17742 #21555 #21556 #17745 #22514)
-#22520 := (not #22517)
-#22523 := (or #17742 #17745 #22520)
-#22526 := (not #22523)
+#3209 := (up_291 uf_287 uf_269 uf_273 uf_306 uf_4)
+#12401 := (not #3209)
+#23049 := (or #12401 #22120 #18276 #22121 #13331 #18279 #23046)
+#23052 := (not #23049)
+#23055 := (or #18276 #18279 #23052)
+#23058 := (not #23055)
 #4 := 1::int
-#12913 := (>= uf_298 1::int)
-#21575 := (not #12913)
-#21574 := (not #12383)
-decl uf_303 :: int
-#3234 := uf_303
-#12380 := (= uf_303 uf_304)
-#21573 := (not #12380)
-#12375 := (= #3230 uf_303)
-#21572 := (not #12375)
+#13225 := (>= uf_298 1::int)
+#13365 := (not #13225)
+#12316 := (= uf_298 uf_305)
+#12440 := (not #12316)
+#12449 := (not #12313)
+#12308 := (= #3190 uf_303)
+#12485 := (not #12308)
 decl uf_68 :: (-> T4 T5 T2)
-#3226 := (uf_68 uf_287 #3220)
+#3187 := (uf_68 uf_287 #3181)
 decl uf_9 :: T2
 #19 := uf_9
-#12355 := (= uf_9 #3226)
-#17730 := (not #12355)
+#12302 := (= uf_9 #3187)
+#18247 := (not #12302)
 decl uf_48 :: (-> T5 T3 T2)
-#3221 := (uf_48 #3220 uf_7)
-#12346 := (= uf_9 #3221)
-#17721 := (not #12346)
+#3182 := (uf_48 #3181 uf_7)
+#12293 := (= uf_9 #3182)
+#18238 := (not #12293)
 decl uf_275 :: T1
 #2948 := uf_275
 decl uf_270 :: T1
 #2943 := uf_270
-#3237 := (up_291 uf_287 uf_270 uf_275 uf_298 uf_4)
-#21571 := (not #3237)
+#3195 := (up_291 uf_287 uf_270 uf_275 uf_298 uf_4)
+#12467 := (not #3195)
 decl uf_277 :: T1
 #2950 := uf_277
 decl uf_271 :: T1
 #2944 := uf_271
-#3236 := (up_291 uf_287 uf_271 uf_277 uf_303 uf_7)
-#21570 := (not #3236)
-#22529 := (or #21570 #21571 #17721 #17730 #21572 #21573 #21574 #21575 #21554 #22526)
-#22532 := (not #22529)
-#12998 := (* -1::int #3230)
+#3194 := (up_291 uf_287 uf_271 uf_277 uf_303 uf_7)
+#12476 := (not #3194)
+#23061 := (or #12476 #12467 #18238 #18247 #12485 #12449 #12440 #13365 #22120 #23058)
+#23064 := (not #23061)
+#13418 := (* -1::int #3190)
 decl uf_296 :: int
-#3079 := uf_296
-#12999 := (+ uf_296 #12998)
-#12997 := (>= #12999 0::int)
-#12996 := (not #12997)
+#3061 := uf_296
+#13419 := (+ uf_296 #13418)
+#13417 := (>= #13419 0::int)
+#13416 := (not #13417)
 decl uf_297 :: int
-#3083 := uf_297
-#12910 := (>= uf_297 0::int)
-#21602 := (not #12910)
-#12524 := (= uf_297 uf_305)
-#21614 := (not #12524)
-#12521 := (= uf_296 uf_304)
-#21613 := (not #12521)
-#22559 := (or #21613 #21614 #21602 #21575 #12996 #21554 #22526)
-#22562 := (not #22559)
-#22535 := (or #17721 #17730 #22532)
-#22538 := (not #22535)
+#3065 := uf_297
+#13222 := (>= uf_297 0::int)
+#22161 := (not #13222)
+#12551 := (= uf_297 uf_305)
+#12557 := (not #12551)
+#12548 := (= uf_296 uf_304)
+#12566 := (not #12548)
+#23091 := (or #12566 #12557 #22161 #13365 #22120 #13416 #23058)
+#23094 := (not #23091)
+#23067 := (or #18238 #18247 #23064)
+#23070 := (not #23067)
 decl uf_24 :: (-> T4 T5 T2)
-#3223 := (uf_24 uf_287 #3220)
-#12349 := (= uf_9 #3223)
-#17724 := (not #12349)
-#22541 := (or #17721 #17724 #22538)
-#22544 := (not #22541)
-#22547 := (or #17721 #17724 #22544)
-#22550 := (not #22547)
-#22553 := (or #21602 #21575 #12997 #22550)
-#22556 := (not #22553)
-#22565 := (or #22556 #22562)
-#22568 := (not #22565)
-#22571 := (or #17721 #17730 #21602 #21575 #22568)
-#22574 := (not #22571)
+#3184 := (uf_24 uf_287 #3181)
+#12296 := (= uf_9 #3184)
+#18241 := (not #12296)
+#23073 := (or #18238 #18241 #23070)
+#23076 := (not #23073)
+#23079 := (or #18238 #18241 #23076)
+#23082 := (not #23079)
+#23085 := (or #22161 #13365 #13417 #23082)
+#23088 := (not #23085)
+#23097 := (or #23088 #23094)
+#23100 := (not #23097)
+#23103 := (or #18238 #18247 #22161 #13365 #23100)
+#23106 := (not #23103)
 decl uf_25 :: (-> T4 T5 T5)
 decl uf_135 :: (-> T14 T5)
 decl uf_58 :: (-> T13 T5 T14)
 decl uf_59 :: (-> T4 T13)
-#3175 := (uf_59 uf_287)
-#27095 := (uf_58 #3175 #3220)
-#28578 := (uf_135 #27095)
-#28581 := (uf_25 uf_287 #28578)
+#3150 := (uf_59 uf_287)
+#27629 := (uf_58 #3150 #3181)
+#29089 := (uf_135 #27629)
+#29092 := (uf_25 uf_287 #29089)
 decl uf_26 :: T5
 #77 := uf_26
-#28582 := (= uf_26 #28581)
+#29093 := (= uf_26 #29092)
 decl uf_210 :: (-> T4 T5 T2)
-#28579 := (uf_210 uf_287 #28578)
-#28580 := (= uf_9 #28579)
-#28638 := (or #28580 #28582)
-#28641 := (not #28638)
+#29090 := (uf_210 uf_287 #29089)
+#29091 := (= uf_9 #29090)
+#29149 := (or #29091 #29093)
+#29152 := (not #29149)
 decl uf_136 :: (-> T14 T2)
-#28591 := (uf_136 #27095)
-#28592 := (= uf_9 #28591)
-#28593 := (not #28592)
+#29102 := (uf_136 #27629)
+#29103 := (= uf_9 #29102)
+#29104 := (not #29103)
 decl uf_27 :: (-> T4 T5 T2)
-#28588 := (uf_27 uf_287 #28578)
-#28589 := (= uf_9 #28588)
-#28590 := (not #28589)
-#28632 := (or #28590 #28593)
-#28635 := (not #28632)
+#29099 := (uf_27 uf_287 #29089)
+#29100 := (= uf_9 #29099)
+#29101 := (not #29100)
+#29143 := (or #29101 #29104)
+#29146 := (not #29143)
 decl uf_12 :: (-> T3 T8)
-#27351 := (uf_13 #3220)
-#28596 := (uf_12 #27351)
+decl uf_13 :: (-> T5 T3)
+#27885 := (uf_13 #3181)
+#29107 := (uf_12 #27885)
 decl uf_14 :: T8
 #28 := uf_14
-#28614 := (= uf_14 #28596)
-#28629 := (not #28614)
-#28585 := (uf_13 #28578)
-#28586 := (uf_12 #28585)
-#28587 := (= uf_14 #28586)
-#28647 := (or #28587 #28629 #28635 #28641)
-#28652 := (not #28647)
-#28603 := (uf_25 uf_287 #3220)
-#28604 := (= uf_26 #28603)
-#28601 := (uf_210 uf_287 #3220)
-#28602 := (= uf_9 #28601)
-#28617 := (or #28602 #28604)
-#28620 := (not #28617)
-#28623 := (or #28614 #28620)
-#28626 := (not #28623)
-#28655 := (or #28626 #28652)
-#28658 := (not #28655)
-#28661 := (or #17724 #28658)
-#28664 := (not #28661)
-decl up_67 :: (-> T14 bool)
+#29125 := (= uf_14 #29107)
+#29140 := (not #29125)
+#29096 := (uf_13 #29089)
+#29097 := (uf_12 #29096)
+#29098 := (= uf_14 #29097)
+#29158 := (or #29098 #29140 #29146 #29152)
+#29163 := (not #29158)
+#29114 := (uf_25 uf_287 #3181)
+#29115 := (= uf_26 #29114)
+#29112 := (uf_210 uf_287 #3181)
+#29113 := (= uf_9 #29112)
+#29128 := (or #29113 #29115)
+#29131 := (not #29128)
+#29134 := (or #29125 #29131)
+#29137 := (not #29134)
+#29166 := (or #29137 #29163)
+#29169 := (not #29166)
+#29172 := (or #18241 #29169)
+#29175 := (not #29172)
+#29178 := (iff #12302 #29175)
+#29750 := (not #29178)
+#29945 := [hypothesis]: #29750
+#23 := (:var 0 T5)
+#47 := (:var 1 T4)
+#2381 := (uf_68 #47 #23)
+#2382 := (pattern #2381)
+#282 := (uf_59 #47)
+#2384 := (uf_58 #282 #23)
+#2388 := (uf_135 #2384)
+#2399 := (uf_210 #47 #2388)
+#10480 := (= uf_9 #2399)
+#2397 := (uf_25 #47 #2388)
+#10477 := (= uf_26 #2397)
+#10483 := (or #10477 #10480)
+#21752 := (not #10483)
+#2393 := (uf_13 #2388)
+#2394 := (uf_12 #2393)
+#10471 := (= uf_14 #2394)
+#2389 := (uf_27 #47 #2388)
+#10462 := (= uf_9 #2389)
+#10465 := (not #10462)
+#2385 := (uf_136 #2384)
+#10456 := (= uf_9 #2385)
+#10459 := (not #10456)
+#10468 := (or #10459 #10465)
+#21751 := (not #10468)
+#26 := (uf_13 #23)
+#27 := (uf_12 #26)
+#29 := (= #27 uf_14)
+#52 := (not #29)
+#21753 := (or #52 #21751 #10471 #21752)
+#21754 := (not #21753)
+#2405 := (uf_210 #47 #23)
+#10495 := (= uf_9 #2405)
+#142 := (uf_25 #47 #23)
+#3617 := (= uf_26 #142)
+#10498 := (or #3617 #10495)
+#21746 := (not #10498)
+#21747 := (or #29 #21746)
+#21748 := (not #21747)
+#21757 := (or #21748 #21754)
+#21763 := (not #21757)
+#146 := (uf_24 #47 #23)
+#3623 := (= uf_9 #146)
+#11068 := (not #3623)
+#21764 := (or #11068 #21763)
+#21765 := (not #21764)
+#10452 := (= uf_9 #2381)
+#21770 := (iff #10452 #21765)
+#21773 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #21770)
+#10474 := (not #10471)
+#10516 := (and #29 #10468 #10474 #10483)
+#10501 := (and #52 #10498)
+#10522 := (or #10501 #10516)
+#10527 := (and #3623 #10522)
+#10530 := (iff #10452 #10527)
+#10533 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #10530)
+#21774 := (iff #10533 #21773)
+#21771 := (iff #10530 #21770)
+#21768 := (iff #10527 #21765)
+#21760 := (and #3623 #21757)
+#21766 := (iff #21760 #21765)
+#21767 := [rewrite]: #21766
+#21761 := (iff #10527 #21760)
+#21758 := (iff #10522 #21757)
+#21755 := (iff #10516 #21754)
+#21756 := [rewrite]: #21755
+#21749 := (iff #10501 #21748)
+#21750 := [rewrite]: #21749
+#21759 := [monotonicity #21750 #21756]: #21758
+#21762 := [monotonicity #21759]: #21761
+#21769 := [trans #21762 #21767]: #21768
+#21772 := [monotonicity #21769]: #21771
+#21775 := [quant-intro #21772]: #21774
+#17696 := (~ #10533 #10533)
+#17694 := (~ #10530 #10530)
+#17695 := [refl]: #17694
+#17697 := [nnf-pos #17695]: #17696
+#2406 := (= #2405 uf_9)
+#143 := (= #142 uf_26)
+#2407 := (or #143 #2406)
+#2408 := (and #52 #2407)
+#2400 := (= #2399 uf_9)
+#2398 := (= #2397 uf_26)
+#2401 := (or #2398 #2400)
+#2395 := (= #2394 uf_14)
+#2396 := (not #2395)
+#2402 := (and #2396 #2401)
+#2390 := (= #2389 uf_9)
+#2391 := (not #2390)
+#2386 := (= #2385 uf_9)
+#2387 := (not #2386)
+#2392 := (or #2387 #2391)
+#2403 := (and #2392 #2402)
+#2404 := (and #29 #2403)
+#2409 := (or #2404 #2408)
+#147 := (= #146 uf_9)
+#2410 := (and #147 #2409)
+#2383 := (= #2381 uf_9)
+#2411 := (iff #2383 #2410)
+#2412 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #2411)
+#10536 := (iff #2412 #10533)
+#10486 := (and #10474 #10483)
+#10489 := (and #10468 #10486)
+#10492 := (and #29 #10489)
+#10504 := (or #10492 #10501)
+#10507 := (and #3623 #10504)
+#10510 := (iff #10452 #10507)
+#10513 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #10510)
+#10534 := (iff #10513 #10533)
+#10531 := (iff #10510 #10530)
+#10528 := (iff #10507 #10527)
+#10525 := (iff #10504 #10522)
+#10519 := (or #10516 #10501)
+#10523 := (iff #10519 #10522)
+#10524 := [rewrite]: #10523
+#10520 := (iff #10504 #10519)
+#10517 := (iff #10492 #10516)
+#10518 := [rewrite]: #10517
+#10521 := [monotonicity #10518]: #10520
+#10526 := [trans #10521 #10524]: #10525
+#10529 := [monotonicity #10526]: #10528
+#10532 := [monotonicity #10529]: #10531
+#10535 := [quant-intro #10532]: #10534
+#10514 := (iff #2412 #10513)
+#10511 := (iff #2411 #10510)
+#10508 := (iff #2410 #10507)
+#10505 := (iff #2409 #10504)
+#10502 := (iff #2408 #10501)
+#10499 := (iff #2407 #10498)
+#10496 := (iff #2406 #10495)
+#10497 := [rewrite]: #10496
+#3618 := (iff #143 #3617)
+#3619 := [rewrite]: #3618
+#10500 := [monotonicity #3619 #10497]: #10499
+#10503 := [monotonicity #10500]: #10502
+#10493 := (iff #2404 #10492)
+#10490 := (iff #2403 #10489)
+#10487 := (iff #2402 #10486)
+#10484 := (iff #2401 #10483)
+#10481 := (iff #2400 #10480)
+#10482 := [rewrite]: #10481
+#10478 := (iff #2398 #10477)
+#10479 := [rewrite]: #10478
+#10485 := [monotonicity #10479 #10482]: #10484
+#10475 := (iff #2396 #10474)
+#10472 := (iff #2395 #10471)
+#10473 := [rewrite]: #10472
+#10476 := [monotonicity #10473]: #10475
+#10488 := [monotonicity #10476 #10485]: #10487
+#10469 := (iff #2392 #10468)
+#10466 := (iff #2391 #10465)
+#10463 := (iff #2390 #10462)
+#10464 := [rewrite]: #10463
+#10467 := [monotonicity #10464]: #10466
+#10460 := (iff #2387 #10459)
+#10457 := (iff #2386 #10456)
+#10458 := [rewrite]: #10457
+#10461 := [monotonicity #10458]: #10460
+#10470 := [monotonicity #10461 #10467]: #10469
+#10491 := [monotonicity #10470 #10488]: #10490
+#10494 := [monotonicity #10491]: #10493
+#10506 := [monotonicity #10494 #10503]: #10505
+#3624 := (iff #147 #3623)
+#3625 := [rewrite]: #3624
+#10509 := [monotonicity #3625 #10506]: #10508
+#10454 := (iff #2383 #10452)
+#10455 := [rewrite]: #10454
+#10512 := [monotonicity #10455 #10509]: #10511
+#10515 := [quant-intro #10512]: #10514
+#10537 := [trans #10515 #10535]: #10536
+#10451 := [asserted]: #2412
+#10538 := [mp #10451 #10537]: #10533
+#17698 := [mp~ #10538 #17697]: #10533
+#21776 := [mp #17698 #21775]: #21773
+#27259 := (not #21773)
+#29859 := (or #27259 #29178)
+#29094 := (or #29093 #29091)
+#29095 := (not #29094)
+#29105 := (or #29104 #29101)
+#29106 := (not #29105)
+#29108 := (= #29107 uf_14)
+#29109 := (not #29108)
+#29110 := (or #29109 #29106 #29098 #29095)
+#29111 := (not #29110)
+#29116 := (or #29115 #29113)
+#29117 := (not #29116)
+#29118 := (or #29108 #29117)
+#29119 := (not #29118)
+#29120 := (or #29119 #29111)
+#29121 := (not #29120)
+#29122 := (or #18241 #29121)
+#29123 := (not #29122)
+#29124 := (iff #12302 #29123)
+#29860 := (or #27259 #29124)
+#29862 := (iff #29860 #29859)
+#29690 := (iff #29859 #29859)
+#29691 := [rewrite]: #29690
+#29179 := (iff #29124 #29178)
+#29176 := (iff #29123 #29175)
+#29173 := (iff #29122 #29172)
+#29170 := (iff #29121 #29169)
+#29167 := (iff #29120 #29166)
+#29164 := (iff #29111 #29163)
+#29161 := (iff #29110 #29158)
+#29155 := (or #29140 #29146 #29098 #29152)
+#29159 := (iff #29155 #29158)
+#29160 := [rewrite]: #29159
+#29156 := (iff #29110 #29155)
+#29153 := (iff #29095 #29152)
+#29150 := (iff #29094 #29149)
+#29151 := [rewrite]: #29150
+#29154 := [monotonicity #29151]: #29153
+#29147 := (iff #29106 #29146)
+#29144 := (iff #29105 #29143)
+#29145 := [rewrite]: #29144
+#29148 := [monotonicity #29145]: #29147
+#29141 := (iff #29109 #29140)
+#29126 := (iff #29108 #29125)
+#29127 := [rewrite]: #29126
+#29142 := [monotonicity #29127]: #29141
+#29157 := [monotonicity #29142 #29148 #29154]: #29156
+#29162 := [trans #29157 #29160]: #29161
+#29165 := [monotonicity #29162]: #29164
+#29138 := (iff #29119 #29137)
+#29135 := (iff #29118 #29134)
+#29132 := (iff #29117 #29131)
+#29129 := (iff #29116 #29128)
+#29130 := [rewrite]: #29129
+#29133 := [monotonicity #29130]: #29132
+#29136 := [monotonicity #29127 #29133]: #29135
+#29139 := [monotonicity #29136]: #29138
+#29168 := [monotonicity #29139 #29165]: #29167
+#29171 := [monotonicity #29168]: #29170
+#29174 := [monotonicity #29171]: #29173
+#29177 := [monotonicity #29174]: #29176
+#29180 := [monotonicity #29177]: #29179
+#29689 := [monotonicity #29180]: #29862
+#29674 := [trans #29689 #29691]: #29862
+#29861 := [quant-inst]: #29860
+#29675 := [mp #29861 #29674]: #29859
+#29979 := [unit-resolution #29675 #21776 #29945]: false
+#29980 := [lemma #29979]: #29178
+#30580 := (or #29750 #12302)
+#29847 := [hypothesis]: #29158
+decl uf_116 :: (-> T5 int)
+#2980 := (uf_116 #2979)
+decl uf_124 :: (-> T3 int T3)
+#2977 := (uf_124 uf_7 uf_286)
+#2981 := (uf_43 #2977 #2980)
+#2984 := (uf_25 uf_287 #2981)
+#29898 := (= #2984 #29092)
+#29899 := (= #29092 #2984)
+#30393 := (= #29089 #2981)
 decl uf_143 :: (-> T3 int)
-#24110 := (uf_143 #2977)
-#26391 := (uf_124 #24108 #24110)
-#26392 := (uf_43 #26391 #2980)
-#27485 := (uf_66 #26392 #27482 #24108)
-#27491 := (uf_58 #3175 #27485)
-#27497 := (up_67 #27491)
-#27498 := (not #27497)
-#27494 := (uf_135 #27491)
-#27495 := (= #26392 #27494)
-#27496 := (not #27495)
-#27492 := (uf_136 #27491)
-#27493 := (= uf_9 #27492)
-#27488 := (uf_24 uf_287 #27485)
-#27489 := (= uf_9 #27488)
-#27490 := (not #27489)
-#27519 := (or #27490 #27493 #27496 #27498)
-#27522 := (not #27519)
-#30005 := [hypothesis]: #27519
-#27503 := (>= #27482 0::int)
-#28457 := (* -1::int #28213)
-#28081 := (+ #27482 #28457)
-#28082 := (>= #28081 0::int)
-#29442 := (not #28080)
-#29440 := (or #29442 #28082)
-#29443 := [th-lemma]: #29440
-#29444 := [unit-resolution #29443 #29441]: #28082
-#13392 := (>= uf_298 0::int)
+#24645 := (uf_143 #2977)
+decl uf_144 :: (-> T3 T3)
+#24643 := (uf_144 #2977)
+#26925 := (uf_124 #24643 #24645)
+#26926 := (uf_43 #26925 #2980)
+#28291 := (= #26926 #2981)
+#28289 := (= #26925 #2977)
+#28287 := (= #24645 uf_286)
+#24646 := (= uf_286 #24645)
+#326 := (:var 1 T3)
+#1358 := (uf_124 #326 #161)
+#1592 := (pattern #1358)
+#1602 := (uf_143 #1358)
+#8266 := (= #161 #1602)
+#8269 := (forall (vars (?x386 T3) (?x387 int)) (:pat #1592) #8266)
+#17072 := (~ #8269 #8269)
+#17070 := (~ #8266 #8266)
+#17071 := [refl]: #17070
+#17073 := [nnf-pos #17071]: #17072
+#1603 := (= #1602 #161)
+#1604 := (forall (vars (?x386 T3) (?x387 int)) (:pat #1592) #1603)
+#8270 := (iff #1604 #8269)
+#8267 := (iff #1603 #8266)
+#8268 := [rewrite]: #8267
+#8271 := [quant-intro #8268]: #8270
+#8265 := [asserted]: #1604
+#8274 := [mp #8265 #8271]: #8269
+#17074 := [mp~ #8274 #17073]: #8269
+#24652 := (not #8269)
+#24653 := (or #24652 #24646)
+#24654 := [quant-inst]: #24653
+#28210 := [unit-resolution #24654 #17074]: #24646
+#28288 := [symm #28210]: #28287
+#28189 := (= #24643 uf_7)
+#24644 := (= uf_7 #24643)
+#1605 := (uf_144 #1358)
+#8273 := (= #326 #1605)
+#8277 := (forall (vars (?x388 T3) (?x389 int)) (:pat #1592) #8273)
+#17077 := (~ #8277 #8277)
+#17075 := (~ #8273 #8273)
+#17076 := [refl]: #17075
+#17078 := [nnf-pos #17076]: #17077
+#1606 := (= #1605 #326)
+#1607 := (forall (vars (?x388 T3) (?x389 int)) (:pat #1592) #1606)
+#8278 := (iff #1607 #8277)
+#8275 := (iff #1606 #8273)
+#8276 := [rewrite]: #8275
+#8279 := [quant-intro #8276]: #8278
+#8272 := [asserted]: #1607
+#8282 := [mp #8272 #8279]: #8277
+#17079 := [mp~ #8282 #17078]: #8277
+#24647 := (not #8277)
+#24648 := (or #24647 #24644)
+#24649 := [quant-inst]: #24648
+#28188 := [unit-resolution #24649 #17079]: #24644
+#28190 := [symm #28188]: #28189
+#28290 := [monotonicity #28190 #28288]: #28289
+#28292 := [monotonicity #28290]: #28291
+#30391 := (= #29089 #26926)
+decl uf_125 :: (-> T5 T5 int)
+decl uf_28 :: (-> int T5)
+decl uf_29 :: (-> T5 int)
+#3013 := (uf_29 #2979)
+#24470 := (uf_28 #3013)
+#26903 := (uf_13 #24470)
+#28922 := (uf_66 #24470 uf_298 #26903)
+#28923 := (uf_125 #28922 #24470)
+#28947 := (uf_66 #26926 #28923 #24643)
+#28951 := (uf_58 #3150 #28947)
+#28954 := (uf_135 #28951)
+#30390 := (= #28954 #26926)
+#28955 := (= #26926 #28954)
+decl up_67 :: (-> T14 bool)
+#28957 := (up_67 #28951)
+#28958 := (not #28957)
+#28956 := (not #28955)
+#28952 := (uf_136 #28951)
+#28953 := (= uf_9 #28952)
+#28948 := (uf_24 uf_287 #28947)
+#28949 := (= uf_9 #28948)
+#28950 := (not #28949)
+#28979 := (or #28950 #28953 #28956 #28958)
+#28982 := (not #28979)
+#28972 := (* -1::int #28923)
+#28973 := (+ #24645 #28972)
+#28974 := (<= #28973 0::int)
+#30321 := (not #28974)
+#29082 := (+ uf_298 #28972)
+#29084 := (>= #29082 0::int)
+#28924 := (= uf_298 #28923)
+#15 := (:var 1 T5)
+#1390 := (uf_13 #15)
+#1391 := (uf_66 #15 #161 #1390)
+#1392 := (pattern #1391)
+#1393 := (uf_125 #1391 #15)
+#7665 := (= #161 #1393)
+#7669 := (forall (vars (?x319 T5) (?x320 int)) (:pat #1392) #7665)
+#16789 := (~ #7669 #7669)
+#16787 := (~ #7665 #7665)
+#16788 := [refl]: #16787
+#16790 := [nnf-pos #16788]: #16789
+#1394 := (= #1393 #161)
+#1395 := (forall (vars (?x319 T5) (?x320 int)) (:pat #1392) #1394)
+#7670 := (iff #1395 #7669)
+#7667 := (iff #1394 #7665)
+#7668 := [rewrite]: #7667
+#7671 := [quant-intro #7668]: #7670
+#7664 := [asserted]: #1395
+#7674 := [mp #7664 #7671]: #7669
+#16791 := [mp~ #7674 #16790]: #7669
+#26910 := (not #7669)
+#28927 := (or #26910 #28924)
+#28928 := [quant-inst]: #28927
+#29280 := [unit-resolution #28928 #16791]: #28924
+#29281 := (not #28924)
+#30320 := (or #29281 #29084)
+#30315 := [th-lemma]: #30320
+#30316 := [unit-resolution #30315 #29280]: #29084
+#13246 := (* -1::int uf_298)
+#13509 := (+ uf_286 #13246)
+#13510 := (<= #13509 0::int)
+#13511 := (not #13510)
+#23109 := (or #18238 #18247 #23106)
+#23112 := (not #23109)
+#23115 := (or #18238 #18241 #23112)
+#23118 := (not #23115)
+#23121 := (or #18238 #18241 #23118)
+#23124 := (not #23121)
+#23127 := (or #22161 #13365 #13510 #23124)
+#23130 := (not #23127)
 decl ?x776!15 :: int
-#17865 := ?x776!15
-#18168 := (* -1::int ?x776!15)
-#18169 := (+ uf_286 #18168)
-#18170 := (<= #18169 0::int)
-#17873 := (uf_66 #2979 ?x776!15 uf_7)
-#17874 := (uf_110 uf_287 #17873)
-#18155 := (* -1::int #17874)
+#18420 := ?x776!15
+#18425 := (uf_66 #2979 ?x776!15 uf_7)
+#18426 := (uf_110 uf_287 #18425)
+#18771 := (* -1::int #18426)
 decl uf_302 :: int
-#3128 := uf_302
-#18156 := (+ uf_302 #18155)
-#18157 := (>= #18156 0::int)
-#17870 := (>= ?x776!15 0::int)
-#21709 := (not #17870)
-#17866 := (<= ?x776!15 4294967295::int)
-#21708 := (not #17866)
-#21724 := (or #21708 #21709 #18157 #18170)
-#21729 := (not #21724)
-#12727 := (* -1::int uf_286)
-#13271 := (+ #161 #12727)
-#13270 := (>= #13271 0::int)
-#3142 := (= #3073 uf_302)
-#21682 := (not #3142)
-#21683 := (or #21682 #4963 #13270 #18695)
-#22609 := (forall (vars (?x778 int)) (:pat #22468) #21683)
-#22614 := (not #22609)
-#13286 := (* -1::int uf_302)
-#13287 := (+ #3073 #13286)
-#13288 := (<= #13287 0::int)
-#21674 := (or #4963 #13270 #13288 #18695)
-#22601 := (forall (vars (?x776 int)) (:pat #22468) #21674)
-#22606 := (not #22601)
-#22617 := (or #22606 #22614)
-#22620 := (not #22617)
-#22623 := (or #22620 #21729)
-#22626 := (not #22623)
-#12965 := (* -1::int uf_298)
-#12966 := (+ uf_286 #12965)
-#12967 := (<= #12966 0::int)
-#12968 := (not #12967)
-#12122 := (= uf_296 uf_302)
-#21741 := (not #12122)
+#3096 := uf_302
+#18772 := (+ uf_302 #18771)
+#18773 := (>= #18772 0::int)
+#18758 := (* -1::int ?x776!15)
+#18759 := (+ uf_286 #18758)
+#18760 := (<= #18759 0::int)
+#18422 := (>= ?x776!15 0::int)
+#22255 := (not #18422)
+#18421 := (<= ?x776!15 4294967295::int)
+#22254 := (not #18421)
+#22270 := (or #22254 #22255 #18760 #18773)
+#22275 := (not #22270)
+#13151 := (* -1::int uf_286)
+#13539 := (+ #161 #13151)
+#13538 := (>= #13539 0::int)
+#3103 := (= #3054 uf_302)
+#22228 := (not #3103)
+#22229 := (or #22228 #4965 #13538 #19295)
+#23141 := (forall (vars (?x778 int)) (:pat #23000) #22229)
+#23146 := (not #23141)
+#13550 := (* -1::int uf_302)
+#13551 := (+ #3054 #13550)
+#13552 := (<= #13551 0::int)
+#22220 := (or #4965 #13538 #13552 #19295)
+#23133 := (forall (vars (?x776 int)) (:pat #23000) #22220)
+#23138 := (not #23133)
+#23149 := (or #23138 #23146)
+#23152 := (not #23149)
+#23155 := (or #23152 #22275)
+#23158 := (not #23155)
+#12017 := (= uf_296 uf_302)
+#12052 := (not #12017)
 decl uf_301 :: int
-#3126 := uf_301
-#12119 := (= uf_297 uf_301)
-#21740 := (not #12119)
+#3094 := uf_301
+#12014 := (= uf_297 uf_301)
+#12061 := (not #12014)
 decl uf_300 :: int
-#3124 := uf_300
-#12116 := (= uf_298 uf_300)
-#21739 := (not #12116)
+#3092 := uf_300
+#12011 := (= uf_298 uf_300)
+#12070 := (not #12011)
 decl uf_299 :: int
-#3122 := uf_299
-#12113 := (= uf_296 uf_299)
-#21738 := (not #12113)
-#22629 := (or #21738 #21739 #21740 #21741 #21602 #21575 #12968 #22626)
-#22632 := (not #22629)
-#22577 := (or #17721 #17730 #22574)
-#22580 := (not #22577)
-#22583 := (or #17721 #17724 #22580)
-#22586 := (not #22583)
-#22589 := (or #17721 #17724 #22586)
-#22592 := (not #22589)
-#22595 := (or #21602 #21575 #12967 #22592)
-#22598 := (not #22595)
-#22635 := (or #22598 #22632)
-#22638 := (not #22635)
-#13378 := (* -1::int uf_296)
-#13379 := (+ #3073 #13378)
-#13380 := (<= #13379 0::int)
-#13363 := (+ #161 #12965)
-#13362 := (>= #13363 0::int)
-#21458 := (or #4963 #13362 #13380 #18695)
-#22477 := (forall (vars (?x775 int)) (:pat #22468) #21458)
-#22482 := (not #22477)
+#3090 := uf_299
+#12008 := (= uf_296 uf_299)
+#12079 := (not #12008)
+#23161 := (or #12079 #12070 #12061 #12052 #22161 #13365 #13511 #23158)
+#23164 := (not #23161)
+#23167 := (or #23130 #23164)
+#23170 := (not #23167)
+#13715 := (* -1::int uf_296)
+#13716 := (+ #3054 #13715)
+#13717 := (<= #13716 0::int)
+#13704 := (+ #161 #13246)
+#13703 := (>= #13704 0::int)
+#22036 := (or #4965 #13703 #13717 #19295)
+#23009 := (forall (vars (?x775 int)) (:pat #23000) #22036)
+#23014 := (not #23009)
 #1331 := 255::int
-#15107 := (<= uf_296 255::int)
-#21770 := (not #15107)
-#15096 := (<= uf_297 4294967295::int)
-#21769 := (not #15096)
-#15085 := (<= uf_298 4294967295::int)
-#21768 := (not #15085)
-#13402 := (>= uf_296 0::int)
-#21766 := (not #13402)
-#21765 := (not #13392)
-#13389 := (>= #12966 0::int)
-#21764 := (not #13389)
-#13356 := (* -1::int uf_297)
-#13357 := (+ uf_286 #13356)
-#13358 := (<= #13357 0::int)
-#12740 := (<= uf_286 0::int)
+#15594 := (<= uf_296 255::int)
+#22305 := (not #15594)
+#15577 := (<= uf_297 4294967295::int)
+#22304 := (not #15577)
+#15560 := (<= uf_298 4294967295::int)
+#22303 := (not #15560)
+#13765 := (>= uf_296 0::int)
+#22301 := (not #13765)
+#13743 := (>= uf_298 0::int)
+#22300 := (not #13743)
+#13737 := (>= #13509 0::int)
+#13740 := (not #13737)
+#13686 := (* -1::int uf_297)
+#13687 := (+ uf_286 #13686)
+#13688 := (<= #13687 0::int)
+#13217 := (<= uf_286 0::int)
 decl uf_178 :: (-> T4 T4 T2)
-#3187 := (uf_178 uf_287 uf_287)
-#12261 := (= uf_9 #3187)
-#21763 := (not #12261)
+#3162 := (uf_178 uf_287 uf_287)
+#12254 := (= uf_9 #3162)
+#13683 := (not #12254)
 decl uf_202 :: (-> T1 T4 T2)
 decl uf_272 :: T1
 #2945 := uf_272
-#3113 := (uf_202 uf_272 uf_287)
-#12067 := (= uf_9 #3113)
-#21762 := (not #12067)
-#3100 := (uf_66 #2979 uf_297 uf_7)
-#3101 := (uf_110 uf_287 #3100)
-#12030 := (= uf_296 #3101)
-#21761 := (not #12030)
+#3087 := (uf_202 uf_272 uf_287)
+#11997 := (= uf_9 #3087)
+#14996 := (not #11997)
+#3082 := (uf_66 #2979 uf_297 uf_7)
+#3083 := (uf_110 uf_287 #3082)
+#11989 := (= uf_296 #3083)
+#22299 := (not #11989)
 decl up_292 :: (-> T4 T1 T1 T5 T3 bool)
 decl uf_6 :: (-> T3 T3)
 #11 := (uf_6 uf_7)
 decl uf_280 :: T1
 #2953 := uf_280
-#3200 := (up_292 uf_287 uf_272 uf_280 #2979 #11)
-#21760 := (not #3200)
-#3199 := (up_291 uf_287 uf_272 uf_280 #3013 #11)
-#21759 := (not #3199)
+#3175 := (up_292 uf_287 uf_272 uf_280 #2979 #11)
+#22298 := (not #3175)
+#3174 := (up_291 uf_287 uf_272 uf_280 #3013 #11)
+#22297 := (not #3174)
 decl uf_279 :: T1
 #2952 := uf_279
-#3198 := (up_291 uf_287 uf_272 uf_279 uf_286 uf_4)
-#21758 := (not #3198)
-#3197 := (up_291 uf_287 uf_272 uf_277 uf_296 uf_7)
-#21757 := (not #3197)
-#3196 := (up_291 uf_287 uf_272 uf_275 uf_297 uf_4)
-#21756 := (not #3196)
-#3195 := (up_291 uf_287 uf_272 uf_273 uf_298 uf_4)
-#21755 := (not #3195)
-#3044 := (uf_66 #2979 0::int uf_7)
-#3054 := (uf_110 uf_287 #3044)
+#3173 := (up_291 uf_287 uf_272 uf_279 uf_286 uf_4)
+#12742 := (not #3173)
+#3172 := (up_291 uf_287 uf_272 uf_277 uf_296 uf_7)
+#12751 := (not #3172)
+#3171 := (up_291 uf_287 uf_272 uf_275 uf_297 uf_4)
+#12760 := (not #3171)
+#3170 := (up_291 uf_287 uf_272 uf_273 uf_298 uf_4)
+#12769 := (not #3170)
+#3031 := (uf_66 #2979 0::int uf_7)
+#3041 := (uf_110 uf_287 #3031)
 decl uf_295 :: int
-#3053 := uf_295
-#3055 := (= uf_295 #3054)
-#17676 := (not #3055)
-#22641 := (or #17676 #21755 #21756 #21757 #21758 #21759 #21760 #21761 #21762 #21763 #12740 #21602 #21575 #13358 #21764 #21765 #21766 #21768 #21769 #21770 #22482 #22638)
-#22644 := (not #22641)
-#22647 := (or #17676 #12740 #22644)
-#22650 := (not #22647)
-#12886 := (* -1::int #3073)
-#12887 := (+ uf_295 #12886)
-#12885 := (>= #12887 0::int)
-#12869 := (>= #161 1::int)
-#21436 := (or #4963 #12869 #12885 #18695)
-#22469 := (forall (vars (?x773 int)) (:pat #22468) #21436)
-#22474 := (not #22469)
-#22653 := (or #22474 #22650)
-#22656 := (not #22653)
+#3040 := uf_295
+#3042 := (= uf_295 #3041)
+#12976 := (not #3042)
+#23173 := (or #12976 #12769 #12760 #12751 #12742 #22297 #22298 #22299 #14996 #13683 #13217 #22161 #13365 #13688 #13740 #22300 #22301 #22303 #22304 #22305 #23014 #23170)
+#23176 := (not #23173)
+#23179 := (or #12976 #13217 #23176)
+#23182 := (not #23179)
+#13197 := (* -1::int #3054)
+#13198 := (+ uf_295 #13197)
+#13196 := (>= #13198 0::int)
+#13184 := (>= #161 1::int)
+#22025 := (or #4965 #13184 #13196 #19295)
+#23001 := (forall (vars (?x773 int)) (:pat #23000) #22025)
+#23006 := (not #23001)
+#23185 := (or #23006 #23182)
+#23188 := (not #23185)
 decl ?x773!13 :: int
-#17651 := ?x773!13
-#17658 := (uf_66 #2979 ?x773!13 uf_7)
-#17659 := (uf_110 uf_287 #17658)
-#17660 := (* -1::int #17659)
-#17661 := (+ uf_295 #17660)
-#17662 := (>= #17661 0::int)
-#17655 := (>= ?x773!13 0::int)
-#21399 := (not #17655)
-#17653 := (>= ?x773!13 1::int)
-#17652 := (<= ?x773!13 4294967295::int)
-#21398 := (not #17652)
-#21414 := (or #21398 #17653 #21399 #17662)
-#21419 := (not #21414)
-#22659 := (or #21419 #22656)
-#22662 := (not #22659)
-#12863 := (>= uf_286 1::int)
-#12866 := (not #12863)
-#22665 := (or #12866 #22662)
-#22668 := (not #22665)
-#22671 := (or #12866 #22668)
-#22674 := (not #22671)
-#3050 := (uf_68 uf_287 #3044)
-#11979 := (= uf_9 #3050)
-#17640 := (not #11979)
-#3045 := (uf_48 #3044 uf_7)
-#11970 := (= uf_9 #3045)
-#17631 := (not #11970)
+#18159 := ?x773!13
+#18169 := (>= ?x773!13 1::int)
+#18164 := (uf_66 #2979 ?x773!13 uf_7)
+#18165 := (uf_110 uf_287 #18164)
+#18166 := (* -1::int #18165)
+#18167 := (+ uf_295 #18166)
+#18168 := (>= #18167 0::int)
+#18161 := (>= ?x773!13 0::int)
+#21999 := (not #18161)
+#18160 := (<= ?x773!13 4294967295::int)
+#21998 := (not #18160)
+#22014 := (or #21998 #21999 #18168 #18169)
+#22019 := (not #22014)
+#23191 := (or #22019 #23188)
+#23194 := (not #23191)
+#13178 := (>= uf_286 1::int)
+#13181 := (not #13178)
+#23197 := (or #13181 #23194)
+#23200 := (not #23197)
+#23203 := (or #13181 #23200)
+#23206 := (not #23203)
+#3037 := (uf_68 uf_287 #3031)
+#11937 := (= uf_9 #3037)
+#18136 := (not #11937)
+#3032 := (uf_48 #3031 uf_7)
+#11928 := (= uf_9 #3032)
+#18127 := (not #11928)
 decl uf_274 :: T1
 #2947 := uf_274
-#3058 := (up_291 uf_287 uf_274 uf_273 1::int uf_4)
-#21813 := (not #3058)
+#3045 := (up_291 uf_287 uf_274 uf_273 1::int uf_4)
+#12949 := (not #3045)
 decl uf_276 :: T1
 #2949 := uf_276
-#3057 := (up_291 uf_287 uf_276 uf_275 0::int uf_4)
-#21812 := (not #3057)
+#3044 := (up_291 uf_287 uf_276 uf_275 0::int uf_4)
+#12958 := (not #3044)
 decl uf_278 :: T1
 #2951 := uf_278
-#3056 := (up_291 uf_287 uf_278 uf_277 uf_295 uf_7)
-#21811 := (not #3056)
-#22677 := (or #17676 #21811 #21812 #21813 #17631 #17640 #22674)
-#22680 := (not #22677)
-#22683 := (or #17631 #17640 #22680)
-#22686 := (not #22683)
-#3047 := (uf_24 uf_287 #3044)
-#11973 := (= uf_9 #3047)
-#17634 := (not #11973)
-#22689 := (or #17631 #17634 #22686)
-#22692 := (not #22689)
-#26286 := (uf_13 #3044)
-#26287 := (= #24108 #26286)
-#26260 := (uf_48 #3044 #24108)
-#26261 := (= uf_9 #26260)
-#26289 := (iff #26261 #26287)
-#233 := (:var 0 T3)
-#2666 := (uf_48 #15 #233)
-#2667 := (pattern #2666)
-#11138 := (= uf_9 #2666)
-#9039 := (= #233 #1390)
-#11159 := (iff #9039 #11138)
-#22399 := (forall (vars (?x712 T5) (?x713 T3)) (:pat #2667) #11159)
-#11164 := (forall (vars (?x712 T5) (?x713 T3)) #11159)
-#22402 := (iff #11164 #22399)
-#22400 := (iff #11159 #11159)
-#22401 := [refl]: #22400
-#22403 := [quant-intro #22401]: #22402
-#17468 := (~ #11164 #11164)
-#17466 := (~ #11159 #11159)
-#17467 := [refl]: #17466
-#17469 := [nnf-pos #17467]: #17468
-#1890 := (= #1390 #233)
-#2668 := (= #2666 uf_9)
-#2673 := (iff #2668 #1890)
-#2674 := (forall (vars (?x712 T5) (?x713 T3)) #2673)
-#11165 := (iff #2674 #11164)
-#11162 := (iff #2673 #11159)
-#11155 := (iff #11138 #9039)
-#11160 := (iff #11155 #11159)
-#11161 := [rewrite]: #11160
-#11157 := (iff #2673 #11155)
-#9040 := (iff #1890 #9039)
-#9041 := [rewrite]: #9040
-#11140 := (iff #2668 #11138)
-#11141 := [rewrite]: #11140
-#11158 := [monotonicity #11141 #9041]: #11157
-#11163 := [trans #11158 #11161]: #11162
-#11166 := [quant-intro #11163]: #11165
-#11154 := [asserted]: #2674
-#11169 := [mp #11154 #11166]: #11164
-#17470 := [mp~ #11169 #17469]: #11164
-#22404 := [mp #17470 #22403]: #22399
-#25427 := (not #22399)
-#26306 := (or #25427 #26289)
-#26288 := (iff #26287 #26261)
-#26307 := (or #25427 #26288)
-#26363 := (iff #26307 #26306)
-#26462 := (iff #26306 #26306)
-#26453 := [rewrite]: #26462
-#26290 := (iff #26288 #26289)
-#26291 := [rewrite]: #26290
-#26459 := [monotonicity #26291]: #26363
-#26518 := [trans #26459 #26453]: #26363
-#26300 := [quant-inst]: #26307
-#26463 := [mp #26300 #26518]: #26306
-#26613 := [unit-resolution #26463 #22404]: #26289
-#26268 := (not #26261)
-#26569 := (iff #17631 #26268)
-#26567 := (iff #11970 #26261)
-#26657 := (iff #26261 #11970)
-#26615 := (= #26260 #3045)
-#26616 := [monotonicity #27656]: #26615
-#26658 := [monotonicity #26616]: #26657
-#26568 := [symm #26658]: #26567
-#26617 := [monotonicity #26568]: #26569
-#26614 := [hypothesis]: #17631
-#26618 := [mp #26614 #26617]: #26268
-#26660 := (= #24223 #26286)
-#26622 := (= #26286 #24223)
-#26620 := (= #3044 #2979)
-#26566 := (= #3044 #26333)
-#26311 := (uf_66 #23935 0::int #24108)
-#26336 := (= #26311 #26333)
-#26339 := (not #26336)
-decl uf_138 :: (-> T5 T5 T2)
-#26312 := (uf_138 #26311 #23935)
-#26313 := (= uf_9 #26312)
-#26314 := (not #26313)
-#26345 := (or #26314 #26339)
-#26350 := (not #26345)
-#247 := (:var 1 int)
-#21 := (:var 2 T5)
-#1576 := (uf_66 #21 #247 #233)
-#1577 := (pattern #1576)
-#1578 := (uf_138 #1576 #21)
-#8220 := (= uf_9 #1578)
-#20314 := (not #8220)
-decl uf_139 :: (-> T3 int)
-#1581 := (uf_139 #233)
-#1582 := (* #247 #1581)
-#1580 := (uf_116 #21)
-#1583 := (+ #1580 #1582)
-#1584 := (uf_43 #233 #1583)
-#1585 := (= #1576 #1584)
-#20313 := (not #1585)
-#20315 := (or #20313 #20314)
-#20316 := (not #20315)
-#20319 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #20316)
-#8226 := (and #1585 #8220)
-#8231 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #8226)
-#20320 := (iff #8231 #20319)
-#20317 := (iff #8226 #20316)
-#20318 := [rewrite]: #20317
-#20321 := [quant-intro #20318]: #20320
-#16546 := (~ #8231 #8231)
-#16544 := (~ #8226 #8226)
-#16545 := [refl]: #16544
-#16547 := [nnf-pos #16545]: #16546
-#1579 := (= #1578 uf_9)
-#1586 := (and #1579 #1585)
-#1587 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #1586)
-#8232 := (iff #1587 #8231)
-#8229 := (iff #1586 #8226)
-#8223 := (and #8220 #1585)
-#8227 := (iff #8223 #8226)
-#8228 := [rewrite]: #8227
-#8224 := (iff #1586 #8223)
-#8221 := (iff #1579 #8220)
-#8222 := [rewrite]: #8221
-#8225 := [monotonicity #8222]: #8224
-#8230 := [trans #8225 #8228]: #8229
-#8233 := [quant-intro #8230]: #8232
-#8219 := [asserted]: #1587
-#8236 := [mp #8219 #8233]: #8231
-#16548 := [mp~ #8236 #16547]: #8231
-#20322 := [mp #16548 #20321]: #20319
-#26353 := (not #20319)
-#26293 := (or #26353 #26350)
-#26315 := (uf_139 #24108)
-#26316 := (* 0::int #26315)
-#26318 := (+ #26317 #26316)
-#26319 := (uf_43 #24108 #26318)
-#26320 := (= #26311 #26319)
-#26321 := (not #26320)
-#26322 := (or #26321 #26314)
-#26323 := (not #26322)
-#26294 := (or #26353 #26323)
-#26295 := (iff #26294 #26293)
-#26310 := (iff #26293 #26293)
-#26297 := [rewrite]: #26310
-#26351 := (iff #26323 #26350)
-#26348 := (iff #26322 #26345)
-#26342 := (or #26339 #26314)
-#26346 := (iff #26342 #26345)
-#26347 := [rewrite]: #26346
-#26343 := (iff #26322 #26342)
-#26340 := (iff #26321 #26339)
-#26337 := (iff #26320 #26336)
-#26334 := (= #26319 #26333)
-#26331 := (= #26318 #26317)
-#26326 := (+ #26317 0::int)
-#26329 := (= #26326 #26317)
-#26330 := [rewrite]: #26329
-#26327 := (= #26318 #26326)
-#26324 := (= #26316 0::int)
-#26325 := [rewrite]: #26324
-#26328 := [monotonicity #26325]: #26327
-#26332 := [trans #26328 #26330]: #26331
-#26335 := [monotonicity #26332]: #26334
-#26338 := [monotonicity #26335]: #26337
-#26341 := [monotonicity #26338]: #26340
-#26344 := [monotonicity #26341]: #26343
-#26349 := [trans #26344 #26347]: #26348
-#26352 := [monotonicity #26349]: #26351
-#26296 := [monotonicity #26352]: #26295
-#26298 := [trans #26296 #26297]: #26295
-#26292 := [quant-inst]: #26294
-#26299 := [mp #26292 #26298]: #26293
-#27785 := [unit-resolution #26299 #20322]: #26350
-#26385 := (or #26345 #26336)
-#26458 := [def-axiom]: #26385
-#27786 := [unit-resolution #26458 #27785]: #26336
-#27787 := (= #3044 #26311)
-#27788 := [monotonicity #27707 #27654]: #27787
-#26619 := [trans #27788 #27786]: #26566
-#26621 := [trans #26619 #27789]: #26620
-#26609 := [monotonicity #26621]: #26622
-#26661 := [symm #26609]: #26660
-#26662 := (= #24108 #24223)
-#26645 := [trans #27656 #27843]: #26662
-#26647 := [trans #26645 #26661]: #26287
-#26503 := (not #26287)
-#26502 := (not #26289)
-#26504 := (or #26502 #26261 #26503)
-#26505 := [def-axiom]: #26504
-#26659 := [unit-resolution #26505 #26647 #26618 #26613]: false
-#26648 := [lemma #26659]: #11970
-#28096 := (or #17631 #22692)
-#22695 := (or #17631 #17634 #22692)
-#22698 := (not #22695)
+#3043 := (up_291 uf_287 uf_278 uf_277 uf_295 uf_7)
+#12967 := (not #3043)
+#23209 := (or #12976 #12967 #12958 #12949 #18127 #18136 #23206)
+#23212 := (not #23209)
+#23215 := (or #18127 #18136 #23212)
+#23218 := (not #23215)
+#3034 := (uf_24 uf_287 #3031)
+#11931 := (= uf_9 #3034)
+#18130 := (not #11931)
+#23221 := (or #18127 #18130 #23218)
+#23224 := (not #23221)
+#23227 := (or #18127 #18130 #23224)
+#23230 := (not #23227)
 decl uf_200 :: (-> T4 T5 T5 T16 T2)
 decl uf_282 :: T16
 #2957 := uf_282
-#2981 := (uf_43 #2977 #2980)
-#3042 := (uf_200 uf_287 #2981 #2981 uf_282)
-#11967 := (= uf_9 #3042)
-#12702 := (not #11967)
-#22701 := (or #12702 #22698)
-#22704 := (not #22701)
-#24010 := (uf_116 #2981)
-#25399 := (uf_43 #2977 #24010)
-#25810 := (uf_13 #25399)
-#26056 := (uf_12 #25810)
-#26059 := (= uf_14 #26056)
-#26178 := (not #26059)
+#3029 := (uf_200 uf_287 #2981 #2981 uf_282)
+#11925 := (= uf_9 #3029)
+#13009 := (not #11925)
+#23233 := (or #13009 #23230)
+#23236 := (not #23233)
+#24545 := (uf_116 #2981)
+#25933 := (uf_43 #2977 #24545)
+#26480 := (uf_200 uf_287 #25933 #25933 uf_282)
+#26725 := (= #26480 #3029)
+#26728 := (= #3029 #26480)
+#25940 := (= #2981 #25933)
+#2986 := (uf_48 #2981 #2977)
+#11869 := (= uf_9 #2986)
+decl uf_23 :: (-> T3 T2)
+#2993 := (uf_23 #2977)
+#11881 := (= uf_9 #2993)
 #2990 := (uf_12 #2977)
-#11873 := (= uf_14 #2990)
-#11876 := (not #11873)
-#26179 := (iff #11876 #26178)
-#26176 := (iff #11873 #26059)
-#26195 := (iff #26059 #11873)
-#26171 := (= #26056 #2990)
-#26169 := (= #25810 #2977)
-#24228 := (uf_13 #2981)
-#27920 := (= #24228 #2977)
-#24231 := (= #2977 #24228)
-#24236 := (or #24175 #24231)
-#24237 := [quant-inst]: #24236
-#27857 := [unit-resolution #24237 #22417]: #24231
-#27921 := [symm #27857]: #27920
-#26162 := (= #25810 #24228)
-#27876 := (= #25399 #2981)
-#25406 := (= #2981 #25399)
-#2986 := (uf_48 #2981 #2977)
-#11867 := (= uf_9 #2986)
+#11875 := (= uf_14 #2990)
+#11878 := (not #11875)
+#2988 := (uf_24 uf_287 #2981)
+#11872 := (= uf_9 #2988)
+#11866 := (= uf_26 #2984)
+#2982 := (uf_27 uf_287 #2981)
+#11862 := (= uf_9 #2982)
+#13937 := (and #11862 #11866 #11869 #11872 #11878 #11881)
 decl uf_283 :: int
 #2961 := uf_283
-#12768 := (* -1::int uf_283)
+#13993 := (* -1::int uf_283)
 decl uf_78 :: int
 #429 := uf_78
-#12769 := (+ uf_78 #12768)
-#12767 := (>= #12769 0::int)
-#12765 := (>= uf_283 0::int)
+#13994 := (+ uf_78 #13993)
+#13992 := (>= #13994 0::int)
+#13990 := (>= uf_283 0::int)
+#13997 := (and #13990 #13992)
+#14000 := (not #13997)
 decl uf_284 :: int
 #2965 := uf_284
-#12760 := (* -1::int uf_284)
+#13979 := (* -1::int uf_284)
 decl uf_76 :: int
 #409 := uf_76
-#12761 := (+ uf_76 #12760)
-#12759 := (>= #12761 0::int)
-#12757 := (>= uf_284 0::int)
+#13980 := (+ uf_76 #13979)
+#13978 := (>= #13980 0::int)
+#13976 := (>= uf_284 0::int)
+#13983 := (and #13976 #13978)
+#13986 := (not #13983)
 decl uf_285 :: int
 #2969 := uf_285
-#12752 := (* -1::int uf_285)
-#12753 := (+ uf_76 #12752)
-#12751 := (>= #12753 0::int)
-#12749 := (>= uf_285 0::int)
+#13965 := (* -1::int uf_285)
+#13966 := (+ uf_76 #13965)
+#13964 := (>= #13966 0::int)
+#13962 := (>= uf_285 0::int)
+#13969 := (and #13962 #13964)
+#13972 := (not #13969)
 #1042 := 1099511627776::int
-#12744 := (>= uf_286 1099511627776::int)
-#12745 := (not #12744)
-#12741 := (not #12740)
+#13950 := (>= uf_286 1099511627776::int)
+#13940 := (not #13937)
 decl uf_289 :: (-> T19 int)
 #3007 := (:var 0 T19)
 #3008 := (uf_289 #3007)
 #3009 := (pattern #3008)
 decl uf_290 :: int
 #3010 := uf_290
-#12733 := (* -1::int uf_290)
-#12734 := (+ #3008 #12733)
-#12732 := (>= #12734 0::int)
-#12731 := (not #12732)
-#12737 := (forall (vars (?x771 T19)) (:pat #3009) #12731)
-#12728 := (+ uf_76 #12727)
-#12726 := (>= #12728 0::int)
-#12724 := (>= uf_286 0::int)
+#13927 := (* -1::int uf_290)
+#13928 := (+ #3008 #13927)
+#13926 := (>= #13928 0::int)
+#13925 := (not #13926)
+#13931 := (forall (vars (?x771 T19)) (:pat #3009) #13925)
+#13934 := (not #13931)
+#13218 := (not #13217)
+#13781 := (and #3042 #13218)
+#13786 := (not #13781)
+#13769 := (+ uf_78 #13715)
+#13768 := (>= #13769 0::int)
+#13772 := (and #13765 #13768)
+#13775 := (not #13772)
+#13756 := (+ uf_76 #13686)
+#13755 := (>= #13756 0::int)
+#13759 := (and #13222 #13755)
+#13762 := (not #13759)
+#13247 := (+ uf_76 #13246)
+#13746 := (>= #13247 0::int)
+#13749 := (and #13743 #13746)
+#13752 := (not #13749)
+#4355 := (* -1::int uf_76)
+#4356 := (+ #161 #4355)
+#4357 := (<= #4356 0::int)
+#4364 := (and #4043 #4357)
+#5579 := (not #4364)
+#13726 := (or #5579 #13703 #13717)
+#13731 := (forall (vars (?x775 int)) #13726)
+#13734 := (not #13731)
+#13689 := (not #13688)
+#13695 := (and #11989 #13689)
+#13700 := (not #13695)
+#13540 := (not #13538)
+#13578 := (and #3103 #4043 #4357 #13540)
+#13583 := (exists (vars (?x778 int)) #13578)
+#13561 := (or #5579 #13538 #13552)
+#13566 := (forall (vars (?x776 int)) #13561)
+#13586 := (not #13566)
+#13592 := (or #13586 #13583)
+#13597 := (and #13566 #13592)
+#13227 := (and #13222 #13225)
+#13230 := (not #13227)
+decl up_216 :: bool
+#2482 := up_216
+#12113 := (not up_216)
+#13624 := (or #12113 #12079 #12070 #12061 #12052 #13230 #13597)
+#13629 := (and up_216 #13624)
+#13654 := (or #13230 #13511 #13629)
+#13245 := (>= #13247 1::int)
+#13334 := (and #13243 #13245)
+#13337 := (not #13334)
+#13304 := (not #13303)
+#13310 := (and #12352 #13304)
+#13290 := (or #5579 #13267 #13281)
+#13295 := (forall (vars (?x785 int)) #13290)
+#13298 := (not #13295)
+#13315 := (or #13298 #13310)
+#13318 := (and #13295 #13315)
+#13321 := (or #13264 #13318)
+#13324 := (and #13259 #13321)
+#13253 := (and #13234 #13251)
+#13256 := (not #13253)
+#13352 := (or #12401 #13256 #13324 #13331 #13337)
+#13360 := (and #13243 #13245 #13352)
+#13236 := (and #13225 #13234)
+#13239 := (not #13236)
+#13471 := (or #12566 #12557 #13230 #13239 #13360 #13416)
+#12305 := (and #12293 #12302)
+#12494 := (not #12305)
+#13392 := (or #12476 #12467 #12494 #12485 #12449 #12440 #13365 #13239 #13360)
+#13400 := (and #12293 #12302 #13392)
+#12299 := (and #12293 #12296)
+#12506 := (not #12299)
+#13405 := (or #12506 #13400)
+#13411 := (and #12293 #12296 #13405)
+#13441 := (or #13230 #13411 #13417)
+#13476 := (and #13441 #13471)
+#13485 := (or #12494 #13230 #13476)
+#13493 := (and #12293 #12302 #13485)
+#13498 := (or #12506 #13493)
+#13504 := (and #12293 #12296 #13498)
+#13533 := (or #13230 #13504 #13510)
+#13659 := (and #13533 #13654)
+decl uf_55 :: (-> T4 T2)
+#3004 := (uf_55 uf_287)
+#11905 := (= uf_9 #3004)
+#12003 := (and #11905 #11997)
+#12141 := (not #12003)
+#3176 := (and #3174 #3175)
+#12733 := (not #3176)
+#13852 := (or #12769 #12760 #12751 #12742 #12733 #12141 #13683 #13230 #13659 #13700 #13734 #13740 #13752 #13762 #13775 #13786)
+#13860 := (and #3042 #13218 #13852)
+#13206 := (or #5579 #13184 #13196)
+#13211 := (forall (vars (?x773 int)) #13206)
+#13214 := (not #13211)
+#13865 := (or #13214 #13860)
+#13868 := (and #13211 #13865)
+#13871 := (or #13181 #13868)
+#13874 := (and #13178 #13871)
+#11940 := (and #11928 #11937)
+#12985 := (not #11940)
+#13895 := (or #12976 #12967 #12958 #12949 #12985 #13874)
+#13903 := (and #11928 #11937 #13895)
+#11934 := (and #11928 #11931)
+#12997 := (not #11934)
+#13908 := (or #12997 #13903)
+#13914 := (and #11928 #11931 #13908)
+#13919 := (or #13009 #13914)
+#13922 := (and #11925 #13919)
+#13152 := (+ uf_76 #13151)
+#13150 := (>= #13152 0::int)
+#13148 := (>= uf_286 0::int)
+#13155 := (and #13148 #13150)
+#13158 := (not #13155)
 decl uf_294 :: (-> int T5 T2)
 decl uf_293 :: int
 #3018 := uf_293
 #3021 := (uf_294 uf_293 #23)
 #3022 := (pattern #3021)
-#11909 := (= uf_9 #3021)
-#11915 := (not #11909)
-#11920 := (forall (vars (?x772 T5)) (:pat #3022) #11915)
-decl uf_55 :: (-> T4 T2)
-#3004 := (uf_55 uf_287)
-#11903 := (= uf_9 #3004)
+#11911 := (= uf_9 #3021)
+#11917 := (not #11911)
+#11922 := (forall (vars (?x772 T5)) (:pat #3022) #11917)
+#13030 := (not #11922)
 decl uf_281 :: T1
 #2954 := uf_281
 #3002 := (uf_202 uf_281 uf_287)
-#11900 := (= uf_9 #3002)
+#11902 := (= uf_9 #3002)
+#11908 := (and #11902 #11905)
+#13075 := (not #11908)
 decl uf_203 :: (-> T4 T2)
 #3000 := (uf_203 uf_287)
-#11897 := (= uf_9 #3000)
-decl uf_23 :: (-> T3 T2)
-#2993 := (uf_23 #2977)
-#11879 := (= uf_9 #2993)
-#2988 := (uf_24 uf_287 #2981)
-#11870 := (= uf_9 #2988)
-#2984 := (uf_25 uf_287 #2981)
-#11864 := (= uf_26 #2984)
-#2982 := (uf_27 uf_287 #2981)
-#11860 := (= uf_9 #2982)
+#11899 := (= uf_9 #3000)
+#13084 := (not #11899)
 decl uf_173 :: (-> T4 int)
 #3019 := (uf_173 uf_287)
 #3020 := (= uf_293 #3019)
+#13039 := (not #3020)
 #3017 := (up_291 uf_287 uf_281 uf_279 uf_286 uf_4)
+#13048 := (not #3017)
 #3015 := (up_292 uf_287 uf_281 uf_280 #2979 #11)
 #3014 := (up_291 uf_287 uf_281 uf_280 #3013 #11)
-#12823 := (and #3014 #3015 #3017 #3020 #11860 #11864 #11867 #11870 #11876 #11879 #11897 #11900 #11903 #11920 #12724 #12726 #12737 #12741 #12745 #12749 #12751 #12757 #12759 #12765 #12767)
-#13406 := (+ uf_78 #13378)
-#13405 := (>= #13406 0::int)
-#13399 := (+ uf_76 #13356)
-#13398 := (>= #13399 0::int)
-#13055 := (+ uf_76 #12965)
-#13395 := (>= #13055 0::int)
-#13364 := (not #13362)
-#4353 := (* -1::int uf_76)
-#4354 := (+ #161 #4353)
-#4355 := (<= #4354 0::int)
-#13370 := (and #4041 #4355 #13364)
-#13375 := (not #13370)
-#13383 := (or #13375 #13380)
-#13386 := (forall (vars (?x775 int)) #13383)
-#13359 := (not #13358)
-#13448 := (and #3055 #12030 #12741 #12910 #12913 #13359 #13386 #13389 #13392 #13395 #13398 #13402 #13405)
-#13453 := (not #13448)
-#13342 := (and #12910 #12913 #12967)
-#13347 := (not #13342)
-#13272 := (not #13270)
-#13306 := (and #3142 #4041 #4355 #13272)
-#13311 := (exists (vars (?x778 int)) #13306)
-#13278 := (and #4041 #4355 #13272)
-#13283 := (not #13278)
-#13291 := (or #13283 #13288)
-#13294 := (forall (vars (?x776 int)) #13291)
-#13314 := (not #13294)
-#13320 := (or #13314 #13311)
-#13325 := (and #13294 #13320)
-decl up_216 :: bool
-#2482 := up_216
-#13262 := (and up_216 #12113 #12116 #12119 #12122 #12910 #12913)
-#13267 := (not #13262)
-#13328 := (or #13267 #13325)
-#13331 := (and up_216 #13328)
-#13350 := (or #13331 #13347)
-#13211 := (and #12521 #12524 #12910 #12913 #12997 #13017)
-#13216 := (not #13211)
-#13129 := (not #13128)
-#13135 := (and #12446 #13129)
-#13098 := (not #13096)
-#13104 := (and #4041 #4355 #13098)
-#13109 := (not #13104)
-#13117 := (or #13109 #13114)
-#13120 := (forall (vars (?x785 int)) #13117)
-#13123 := (not #13120)
-#13140 := (or #13123 #13135)
-#13143 := (and #13120 #13140)
-#13146 := (or #13093 #13143)
-#13149 := (and #13089 #13146)
-#13054 := (>= #13055 1::int)
-#13081 := (and #3258 #13017 #13051 #13054 #13059 #13061)
-#13086 := (not #13081)
-#13152 := (or #13086 #13149)
-#13158 := (and #13051 #13054 #13152)
-#13219 := (or #13158 #13216)
-#13043 := (and #3236 #3237 #12346 #12355 #12375 #12380 #12383 #12913 #13017)
-#13048 := (not #13043)
-#13163 := (or #13048 #13158)
-#13169 := (and #12346 #12355 #13163)
-#12352 := (and #12346 #12349)
-#12503 := (not #12352)
-#13174 := (or #12503 #13169)
-#13180 := (and #12346 #12349 #13174)
-#13008 := (and #12910 #12913 #12996)
-#13013 := (not #13008)
-#13185 := (or #13013 #13180)
-#13222 := (and #13185 #13219)
-#12988 := (and #12346 #12355 #12910 #12913)
-#12993 := (not #12988)
-#13225 := (or #12993 #13222)
-#13231 := (and #12346 #12355 #13225)
-#13236 := (or #12503 #13231)
-#13242 := (and #12346 #12349 #13236)
-#12977 := (and #12910 #12913 #12968)
-#12982 := (not #12977)
-#13247 := (or #12982 #13242)
-#13353 := (and #13247 #13350)
-#12957 := (and #3195 #3196 #3197 #3198 #3199 #3200 #11903 #12067 #12261 #12910 #12913)
-#12962 := (not #12957)
-#13462 := (or #12962 #13353 #13453)
-#13470 := (and #3055 #12741 #13462)
-#12870 := (not #12869)
-#12876 := (and #4041 #4355 #12870)
-#12881 := (not #12876)
-#12889 := (or #12881 #12885)
-#12892 := (forall (vars (?x773 int)) #12889)
-#12895 := (not #12892)
-#13475 := (or #12895 #13470)
-#13478 := (and #12892 #13475)
-#13481 := (or #12866 #13478)
-#13484 := (and #12863 #13481)
-#12855 := (and #3055 #3056 #3057 #3058 #11970 #11979)
-#12860 := (not #12855)
-#13487 := (or #12860 #13484)
-#13493 := (and #11970 #11979 #13487)
-#11976 := (and #11970 #11973)
-#12690 := (not #11976)
-#13498 := (or #12690 #13493)
-#13504 := (and #11970 #11973 #13498)
-#13509 := (or #12702 #13504)
-#13512 := (and #11967 #13509)
-#12828 := (not #12823)
-#13515 := (or #12828 #13512)
-#13518 := (not #13515)
-#3137 := (< #161 uf_286)
-#3143 := (and #3137 #3142)
+#3016 := (and #3014 #3015)
+#13057 := (not #3016)
+#14045 := (or #13057 #13048 #13039 #13084 #13075 #13030 #13158 #13217 #13922 #13934 #13940 #13950 #13972 #13986 #14000)
+#14050 := (not #14045)
+#1 := true
+#3098 := (< #161 uf_286)
+#3104 := (and #3098 #3103)
 #411 := (<= #161 uf_76)
-#3144 := (and #411 #3143)
+#3105 := (and #411 #3104)
 #285 := (<= 0::int #161)
-#3145 := (and #285 #3144)
-#3146 := (exists (vars (?x778 int)) #3145)
-#3139 := (<= #3073 uf_302)
+#3106 := (and #285 #3105)
+#3107 := (exists (vars (?x778 int)) #3106)
+#3108 := (and #3107 true)
+#3099 := (<= #3054 uf_302)
+#3100 := (implies #3098 #3099)
 #412 := (and #285 #411)
-#3138 := (and #412 #3137)
-#3140 := (implies #3138 #3139)
-#3141 := (forall (vars (?x776 int)) #3140)
-#3147 := (implies #3141 #3146)
-#3148 := (and #3141 #3147)
-#3129 := (= uf_302 uf_296)
-#3127 := (= uf_301 uf_297)
-#3130 := (and #3127 #3129)
-#3125 := (= uf_300 uf_298)
-#3131 := (and #3125 #3130)
-#3123 := (= uf_299 uf_296)
-#3132 := (and #3123 #3131)
-#3084 := (<= 0::int uf_297)
-#3091 := (<= 1::int uf_298)
-#3092 := (and #3091 #3084)
-#3133 := (and #3092 #3132)
-#3134 := (and #3092 #3133)
-#3135 := (and #3092 #3134)
-#3136 := (and up_216 #3135)
-#3149 := (implies #3136 #3148)
-#3150 := (and up_216 #3149)
-#3116 := (and #3092 #3092)
-#3304 := (and #3092 #3116)
-#3305 := (and #3092 #3304)
-#3303 := (<= uf_286 uf_298)
-#3306 := (and #3303 #3305)
-#3307 := (and #3092 #3306)
-#3308 := (implies #3307 #3150)
-#3273 := (= #3272 uf_304)
-#3270 := (< uf_305 uf_286)
-#3274 := (and #3270 #3273)
-#3267 := (<= #3073 uf_304)
-#3265 := (< #161 uf_306)
-#3266 := (and #412 #3265)
-#3268 := (implies #3266 #3267)
-#3269 := (forall (vars (?x785 int)) #3268)
-#3275 := (implies #3269 #3274)
-#3276 := (and #3269 #3275)
-#3264 := (<= uf_306 uf_286)
-#3277 := (implies #3264 #3276)
-#3278 := (and #3264 #3277)
-#3243 := (<= 0::int uf_305)
-#3259 := (<= 2::int uf_306)
-#3260 := (and #3259 #3243)
-#3261 := (and #3258 #3260)
-#3252 := (+ uf_298 1::int)
-#3257 := (= uf_306 #3252)
-#3262 := (and #3257 #3261)
-#3254 := (<= #3252 uf_76)
-#3253 := (<= 0::int #3252)
-#3255 := (and #3253 #3254)
-#3263 := (and #3255 #3262)
-#3279 := (implies #3263 #3278)
-#3280 := (and #3255 #3279)
-#3244 := (and #3091 #3243)
-#3288 := (= uf_305 uf_297)
-#3289 := (and #3288 #3244)
-#3287 := (= uf_304 uf_296)
-#3290 := (and #3287 #3289)
-#3291 := (and #3092 #3290)
-#3292 := (and #3092 #3291)
-#3293 := (and #3092 #3292)
-#3286 := (<= #3230 uf_296)
-#3294 := (and #3286 #3293)
-#3295 := (and #3092 #3294)
-#3296 := (implies #3295 #3280)
-#3245 := (and #3242 #3244)
-#3240 := (= uf_304 uf_303)
-#3246 := (and #3240 #3245)
-#3238 := (and #3091 #3091)
-#3247 := (and #3238 #3246)
-#3248 := (and #3237 #3247)
-#3249 := (and #3236 #3248)
-#3235 := (= uf_303 #3230)
-#3250 := (and #3235 #3249)
-#3227 := (= #3226 uf_9)
-#3222 := (= #3221 uf_9)
-#3228 := (and #3222 #3227)
-#3251 := (and #3228 #3250)
-#3281 := (implies #3251 #3280)
-#3282 := (and #3228 #3281)
-#3224 := (= #3223 uf_9)
-#3225 := (and #3222 #3224)
-#3283 := (implies #3225 #3282)
-#3284 := (and #3225 #3283)
-#3231 := (< uf_296 #3230)
-#3232 := (and #3231 #3116)
-#3233 := (and #3092 #3232)
-#3285 := (implies #3233 #3284)
-#3297 := (and #3285 #3296)
-#3229 := (and #3228 #3092)
-#3298 := (implies #3229 #3297)
-#3299 := (and #3228 #3298)
-#3300 := (implies #3225 #3299)
-#3301 := (and #3225 #3300)
-#3217 := (< uf_298 uf_286)
-#3218 := (and #3217 #3116)
-#3219 := (and #3092 #3218)
-#3302 := (implies #3219 #3301)
-#3309 := (and #3302 #3308)
+#3101 := (implies #412 #3100)
+#3102 := (forall (vars (?x776 int)) #3101)
+#3109 := (implies #3102 #3108)
+#3110 := (and #3102 #3109)
+#3097 := (= uf_302 uf_296)
+#3111 := (implies #3097 #3110)
+#3095 := (= uf_301 uf_297)
+#3112 := (implies #3095 #3111)
+#3093 := (= uf_300 uf_298)
+#3113 := (implies #3093 #3112)
+#3091 := (= uf_299 uf_296)
+#3114 := (implies #3091 #3113)
+#3066 := (<= 0::int uf_297)
+#3073 := (<= 1::int uf_298)
+#3074 := (and #3073 #3066)
+#3115 := (implies #3074 #3114)
+#3116 := (implies #3074 #3115)
+#3117 := (implies #3074 #3116)
+#3118 := (implies up_216 #3117)
+#3119 := (and up_216 #3118)
+#3120 := (implies #3074 #3119)
+#3121 := (implies #3074 #3120)
+#3269 := (implies #3074 #3121)
+#3270 := (implies #3074 #3269)
+#3268 := (<= uf_286 uf_298)
+#3271 := (implies #3268 #3270)
+#3272 := (implies #3074 #3271)
+#3221 := (= #3220 uf_304)
+#3218 := (< uf_305 uf_286)
+#3222 := (and #3218 #3221)
+#3223 := (and #3222 true)
+#3214 := (<= #3054 uf_304)
+#3213 := (< #161 uf_306)
+#3215 := (implies #3213 #3214)
+#3216 := (implies #412 #3215)
+#3217 := (forall (vars (?x785 int)) #3216)
+#3224 := (implies #3217 #3223)
+#3225 := (and #3217 #3224)
+#3212 := (<= uf_306 uf_286)
+#3226 := (implies #3212 #3225)
+#3227 := (and #3212 #3226)
+#3201 := (<= 0::int uf_305)
+#3210 := (<= 2::int uf_306)
+#3211 := (and #3210 #3201)
+#3228 := (implies #3211 #3227)
+#3229 := (implies #3209 #3228)
+#3203 := (+ uf_298 1::int)
+#3208 := (= uf_306 #3203)
+#3230 := (implies #3208 #3229)
+#3205 := (<= #3203 uf_76)
+#3204 := (<= 0::int #3203)
+#3206 := (and #3204 #3205)
+#3231 := (implies #3206 #3230)
+#3232 := (and #3206 #3231)
+#3202 := (and #3073 #3201)
+#3233 := (implies #3202 #3232)
+#3250 := (= uf_305 uf_297)
+#3251 := (implies #3250 #3233)
+#3249 := (= uf_304 uf_296)
+#3252 := (implies #3249 #3251)
+#3253 := (implies #3074 #3252)
+#3254 := (implies #3074 #3253)
+#3255 := (implies #3074 #3254)
+#3248 := (<= #3190 uf_296)
+#3256 := (implies #3248 #3255)
+#3257 := (implies #3074 #3256)
+#3200 := (= uf_305 uf_298)
+#3234 := (implies #3200 #3233)
+#3198 := (= uf_304 uf_303)
+#3235 := (implies #3198 #3234)
+#3196 := (and #3073 #3073)
+#3236 := (implies #3196 #3235)
+#3237 := (implies #3195 #3236)
+#3238 := (implies #3194 #3237)
+#3193 := (= uf_303 #3190)
+#3239 := (implies #3193 #3238)
+#3188 := (= #3187 uf_9)
+#3183 := (= #3182 uf_9)
+#3189 := (and #3183 #3188)
+#3240 := (implies #3189 #3239)
+#3241 := (and #3189 #3240)
+#3185 := (= #3184 uf_9)
+#3186 := (and #3183 #3185)
+#3242 := (implies #3186 #3241)
+#3243 := (and #3186 #3242)
+#3244 := (implies #3074 #3243)
+#3245 := (implies #3074 #3244)
+#3191 := (< uf_296 #3190)
+#3246 := (implies #3191 #3245)
+#3247 := (implies #3074 #3246)
+#3258 := (and #3247 #3257)
+#3259 := (implies #3074 #3258)
+#3260 := (implies #3189 #3259)
+#3261 := (and #3189 #3260)
+#3262 := (implies #3186 #3261)
+#3263 := (and #3186 #3262)
+#3264 := (implies #3074 #3263)
+#3265 := (implies #3074 #3264)
+#3180 := (< uf_298 uf_286)
+#3266 := (implies #3180 #3265)
+#3267 := (implies #3074 #3266)
+#3273 := (and #3267 #3272)
+#3274 := (implies #3074 #3273)
 decl uf_41 :: (-> T4 T12)
-#3152 := (uf_41 uf_287)
-#3203 := (= #3152 #3152)
-#3202 := (= #3175 #3175)
-#3204 := (and #3202 #3203)
-#3205 := (and #3204 #3092)
-#3201 := (and #3199 #3200)
-#3206 := (and #3201 #3205)
-#3207 := (and #3198 #3206)
-#3208 := (and #3197 #3207)
-#3209 := (and #3196 #3208)
-#3210 := (and #3195 #3209)
+#3127 := (uf_41 uf_287)
+#3178 := (= #3127 #3127)
+#3177 := (= #3150 #3150)
+#3179 := (and #3177 #3178)
+#3275 := (implies #3179 #3274)
+#3276 := (implies #3176 #3275)
+#3277 := (implies #3173 #3276)
+#3278 := (implies #3172 #3277)
+#3279 := (implies #3171 #3278)
+#3280 := (implies #3170 #3279)
 #3005 := (= #3004 uf_9)
-#3114 := (= #3113 uf_9)
-#3115 := (and #3114 #3005)
-#3211 := (and #3115 #3210)
-#3188 := (= #3187 uf_9)
+#3088 := (= #3087 uf_9)
+#3089 := (and #3088 #3005)
+#3281 := (implies #3089 #3280)
+#3163 := (= #3162 uf_9)
 decl uf_172 :: (-> T4 T5 int)
-#3183 := (uf_172 uf_287 #23)
-#3184 := (pattern #3183)
-#3185 := (<= #3183 #3183)
-#3186 := (forall (vars (?x783 T5)) (:pat #3184) #3185)
-#3189 := (and #3186 #3188)
-#3182 := (<= #3019 #3019)
-#3190 := (and #3182 #3189)
-#3212 := (and #3190 #3211)
-#3176 := (uf_58 #3175 #23)
-#3177 := (pattern #3176)
-#3165 := (uf_68 uf_287 #23)
-#3166 := (= #3165 uf_9)
-#3178 := (= #3176 #3176)
-#3179 := (and #3178 #3166)
-#3180 := (implies #3166 #3179)
-#3181 := (forall (vars (?x782 T5)) (:pat #3177) #3180)
-#3191 := (and #3181 #3190)
+#3158 := (uf_172 uf_287 #23)
+#3159 := (pattern #3158)
+#3160 := (<= #3158 #3158)
+#3161 := (forall (vars (?x783 T5)) (:pat #3159) #3160)
+#3164 := (and #3161 #3163)
+#3157 := (<= #3019 #3019)
+#3165 := (and #3157 #3164)
+#3282 := (implies #3165 #3281)
+#3151 := (uf_58 #3150 #23)
+#3152 := (pattern #3151)
+#3140 := (uf_68 uf_287 #23)
+#3141 := (= #3140 uf_9)
+#3153 := (= #3151 #3151)
+#3154 := (and #3153 #3141)
+#3155 := (implies #3141 #3154)
+#3156 := (forall (vars (?x782 T5)) (:pat #3152) #3155)
+#3166 := (and #3156 #3165)
 decl uf_40 :: (-> T12 T5 T11)
-#3153 := (uf_40 #3152 #23)
-#3154 := (pattern #3153)
-#3171 := (= #3153 #3153)
-#3172 := (and #3171 #3166)
-#3173 := (implies #3166 #3172)
-#3174 := (forall (vars (?x781 T5)) (:pat #3154) #3173)
-#3192 := (and #3174 #3191)
+#3128 := (uf_40 #3127 #23)
+#3129 := (pattern #3128)
+#3146 := (= #3128 #3128)
+#3147 := (and #3146 #3141)
+#3148 := (implies #3141 #3147)
+#3149 := (forall (vars (?x781 T5)) (:pat #3129) #3148)
+#3167 := (and #3149 #3166)
 decl uf_19 :: (-> T9 T5 int)
 decl uf_20 :: (-> T4 T9)
-#3162 := (uf_20 uf_287)
-#3163 := (uf_19 #3162 #23)
-#3164 := (pattern #3163)
-#3167 := (= #3163 #3163)
-#3168 := (and #3167 #3166)
-#3169 := (implies #3166 #3168)
-#3170 := (forall (vars (?x780 T5)) (:pat #3164) #3169)
-#3193 := (and #3170 #3192)
+#3137 := (uf_20 uf_287)
+#3138 := (uf_19 #3137 #23)
+#3139 := (pattern #3138)
+#3142 := (= #3138 #3138)
+#3143 := (and #3142 #3141)
+#3144 := (implies #3141 #3143)
+#3145 := (forall (vars (?x780 T5)) (:pat #3139) #3144)
+#3168 := (and #3145 #3167)
 decl uf_261 :: T8
 #2837 := uf_261
-#3155 := (uf_25 uf_287 #23)
-#3156 := (uf_13 #3155)
-#3157 := (uf_12 #3156)
-#3158 := (= #3157 uf_261)
-#3159 := (not #3158)
-#3160 := (implies #3159 #3159)
-#3161 := (forall (vars (?x779 T5)) (:pat #3154) #3160)
-#3194 := (and #3161 #3193)
-#3213 := (and #3194 #3212)
-#3214 := (and #3092 #3213)
-#3215 := (and #3092 #3214)
-#3216 := (and #3092 #3215)
-#3310 := (implies #3216 #3309)
-#3117 := (and #3115 #3116)
-#3118 := (and #3092 #3117)
-#3119 := (and #3092 #3118)
-#1 := true
-#3112 := (not true)
-#3120 := (and #3112 #3119)
-#3121 := (and #3092 #3120)
-#3151 := (implies #3121 #3150)
-#3311 := (and #3151 #3310)
-#3102 := (= #3101 uf_296)
-#3099 := (< uf_297 uf_286)
-#3103 := (and #3099 #3102)
-#3104 := (and #3103 #3092)
-#3096 := (<= #3073 uf_296)
-#3094 := (< #161 uf_298)
-#3095 := (and #412 #3094)
-#3097 := (implies #3095 #3096)
-#3098 := (forall (vars (?x775 int)) #3097)
-#3105 := (and #3098 #3104)
-#3093 := (<= uf_298 uf_286)
-#3106 := (and #3093 #3105)
-#3107 := (and #3092 #3106)
-#3089 := (<= uf_298 uf_76)
-#3088 := (<= 0::int uf_298)
-#3090 := (and #3088 #3089)
-#3108 := (and #3090 #3107)
-#3085 := (<= uf_297 uf_76)
-#3086 := (and #3084 #3085)
-#3109 := (and #3086 #3108)
-#3081 := (<= uf_296 uf_78)
-#3080 := (<= 0::int uf_296)
-#3082 := (and #3080 #3081)
-#3110 := (and #3082 #3109)
-#3077 := (= #3054 uf_295)
+#3130 := (uf_25 uf_287 #23)
+#3131 := (uf_13 #3130)
+#3132 := (uf_12 #3131)
+#3133 := (= #3132 uf_261)
+#3134 := (not #3133)
+#3135 := (implies #3134 #3134)
+#3136 := (forall (vars (?x779 T5)) (:pat #3129) #3135)
+#3169 := (and #3136 #3168)
+#3283 := (implies #3169 #3282)
+#3284 := (implies #3074 #3283)
+#3285 := (implies #3074 #3284)
+#3286 := (implies #3074 #3285)
+#3122 := (implies #3089 #3121)
+#3123 := (implies #3074 #3122)
+#3124 := (implies #3074 #3123)
+#3086 := (not true)
+#3125 := (implies #3086 #3124)
+#3126 := (implies #3074 #3125)
+#3287 := (and #3126 #3286)
+#3288 := (implies #3074 #3287)
+#3084 := (= #3083 uf_296)
+#3081 := (< uf_297 uf_286)
+#3085 := (and #3081 #3084)
+#3289 := (implies #3085 #3288)
+#3077 := (<= #3054 uf_296)
+#3076 := (< #161 uf_298)
+#3078 := (implies #3076 #3077)
+#3079 := (implies #412 #3078)
+#3080 := (forall (vars (?x775 int)) #3079)
+#3290 := (implies #3080 #3289)
+#3075 := (<= uf_298 uf_286)
+#3291 := (implies #3075 #3290)
+#3292 := (implies #3074 #3291)
+#3071 := (<= uf_298 uf_76)
+#3070 := (<= 0::int uf_298)
+#3072 := (and #3070 #3071)
+#3293 := (implies #3072 #3292)
+#3067 := (<= uf_297 uf_76)
+#3068 := (and #3066 #3067)
+#3294 := (implies #3068 #3293)
+#3063 := (<= uf_296 uf_78)
+#3062 := (<= 0::int uf_296)
+#3064 := (and #3062 #3063)
+#3295 := (implies #3064 #3294)
+#3059 := (= #3041 uf_295)
 #2975 := (< 0::int uf_286)
-#3078 := (and #2975 #3077)
-#3111 := (and #3078 #3110)
-#3312 := (implies #3111 #3311)
-#3313 := (and #3078 #3312)
-#3074 := (<= #3073 uf_295)
-#3070 := (< #161 1::int)
-#3071 := (and #412 #3070)
-#3075 := (implies #3071 #3074)
-#3076 := (forall (vars (?x773 int)) #3075)
-#3314 := (implies #3076 #3313)
-#3315 := (and #3076 #3314)
-#3069 := (<= 1::int uf_286)
-#3316 := (implies #3069 #3315)
-#3317 := (and #3069 #3316)
-#3060 := (<= 0::int 0::int)
-#3061 := (and #3060 #3060)
-#3059 := (<= 1::int 1::int)
-#3062 := (and #3059 #3061)
-#3063 := (and #3059 #3062)
-#3064 := (and #3058 #3063)
-#3065 := (and #3057 #3064)
-#3066 := (and #3056 #3065)
-#3067 := (and #3055 #3066)
-#3051 := (= #3050 uf_9)
-#3046 := (= #3045 uf_9)
-#3052 := (and #3046 #3051)
-#3068 := (and #3052 #3067)
-#3318 := (implies #3068 #3317)
-#3319 := (and #3052 #3318)
-#3048 := (= #3047 uf_9)
+#3060 := (and #2975 #3059)
+#3296 := (implies #3060 #3295)
+#3297 := (and #3060 #3296)
+#3055 := (<= #3054 uf_295)
+#3052 := (< #161 1::int)
+#3056 := (implies #3052 #3055)
+#3057 := (implies #412 #3056)
+#3058 := (forall (vars (?x773 int)) #3057)
+#3298 := (implies #3058 #3297)
+#3299 := (and #3058 #3298)
+#3051 := (<= 1::int uf_286)
+#3300 := (implies #3051 #3299)
+#3301 := (and #3051 #3300)
+#3047 := (<= 0::int 0::int)
+#3048 := (and #3047 #3047)
+#3046 := (<= 1::int 1::int)
 #3049 := (and #3046 #3048)
-#3320 := (implies #3049 #3319)
-#3321 := (and #3049 #3320)
-#3043 := (= #3042 uf_9)
-#3322 := (implies #3043 #3321)
-#3323 := (and #3043 #3322)
+#3050 := (and #3046 #3049)
+#3302 := (implies #3050 #3301)
+#3303 := (implies #3045 #3302)
+#3304 := (implies #3044 #3303)
+#3305 := (implies #3043 #3304)
+#3306 := (implies #3042 #3305)
+#3038 := (= #3037 uf_9)
+#3033 := (= #3032 uf_9)
+#3039 := (and #3033 #3038)
+#3307 := (implies #3039 #3306)
+#3308 := (and #3039 #3307)
+#3035 := (= #3034 uf_9)
+#3036 := (and #3033 #3035)
+#3309 := (implies #3036 #3308)
+#3310 := (and #3036 #3309)
+#3030 := (= #3029 uf_9)
+#3311 := (implies #3030 #3310)
+#3312 := (and #3030 #3311)
 #3027 := (<= uf_286 uf_76)
 #3026 := (<= 0::int uf_286)
 #3028 := (and #3026 #3027)
+#3313 := (implies #3028 #3312)
 #3023 := (= #3021 uf_9)
 #3024 := (iff #3023 false)
 #3025 := (forall (vars (?x772 T5)) (:pat #3022) #3024)
-#3029 := (and #3025 #3028)
-#3030 := (and #3020 #3029)
-#3031 := (and #3017 #3030)
-#3016 := (and #3014 #3015)
-#3032 := (and #3016 #3031)
+#3314 := (implies #3025 #3313)
+#3315 := (implies #3020 #3314)
+#3316 := (implies #3017 #3315)
+#3317 := (implies #3016 #3316)
 #3011 := (< #3008 uf_290)
 #3012 := (forall (vars (?x771 T19)) (:pat #3009) #3011)
-#3033 := (and #3012 #3032)
+#3318 := (implies #3012 #3317)
 #3003 := (= #3002 uf_9)
 #3006 := (and #3003 #3005)
-#3034 := (and #3006 #3033)
+#3319 := (implies #3006 #3318)
 #3001 := (= #3000 uf_9)
-#3035 := (and #3001 #3034)
+#3320 := (implies #3001 #3319)
 #2994 := (= #2993 uf_9)
 #2991 := (= #2990 uf_14)
 #2992 := (not #2991)
@@ -1336,1710 +1288,2237 @@
 #2998 := (and #2985 #2997)
 #2983 := (= #2982 uf_9)
 #2999 := (and #2983 #2998)
-#3036 := (and #2999 #3035)
-#3037 := (and #2975 #3036)
+#3321 := (implies #2999 #3320)
+#3322 := (implies #2975 #3321)
 #2974 := (< uf_286 1099511627776::int)
-#3038 := (and #2974 #3037)
+#3323 := (implies #2974 #3322)
 #2971 := (<= uf_285 uf_76)
 #2970 := (<= 0::int uf_285)
 #2972 := (and #2970 #2971)
-#3039 := (and #2972 #3038)
+#3324 := (implies #2972 #3323)
 #2967 := (<= uf_284 uf_76)
 #2966 := (<= 0::int uf_284)
 #2968 := (and #2966 #2967)
-#3040 := (and #2968 #3039)
+#3325 := (implies #2968 #3324)
 #2963 := (<= uf_283 uf_78)
 #2962 := (<= 0::int uf_283)
 #2964 := (and #2962 #2963)
-#3041 := (and #2964 #3040)
-#3324 := (implies #3041 #3323)
-#3325 := (not #3324)
-#13521 := (iff #3325 #13518)
-#12020 := (and #3084 #3091)
-#12605 := (and #3303 #12020)
-#12608 := (and #12020 #12605)
-#12614 := (not #12608)
-#12146 := (not #3138)
-#12147 := (or #12146 #3139)
-#12150 := (forall (vars (?x776 int)) #12147)
-#12156 := (not #12150)
-#12157 := (or #3146 #12156)
-#12162 := (and #12150 #12157)
-#12125 := (and #12119 #12122)
-#12128 := (and #12116 #12125)
-#12131 := (and #12113 #12128)
-#12134 := (and #12020 #12131)
-#12137 := (and #12020 #12134)
-#12140 := (and #12020 #12137)
-#12143 := (and up_216 #12140)
-#12168 := (not #12143)
-#12169 := (or #12168 #12162)
-#12174 := (and up_216 #12169)
-#12615 := (or #12174 #12614)
-#12530 := (and #3244 #12524)
-#12535 := (and #12521 #12530)
-#12538 := (and #12020 #12535)
-#12541 := (and #12020 #12538)
-#12544 := (and #12020 #12541)
-#12547 := (and #3286 #12544)
-#12550 := (and #12020 #12547)
-#12556 := (not #12550)
-#12449 := (and #3270 #12446)
-#12439 := (not #3266)
-#12440 := (or #12439 #3267)
-#12443 := (forall (vars (?x785 int)) #12440)
-#12455 := (not #12443)
-#12456 := (or #12455 #12449)
-#12461 := (and #12443 #12456)
-#12467 := (not #3264)
-#12468 := (or #12467 #12461)
-#12473 := (and #3264 #12468)
-#12427 := (and #3243 #3259)
-#12430 := (and #3258 #12427)
-#12412 := (+ 1::int uf_298)
-#12424 := (= uf_306 #12412)
-#12433 := (and #12424 #12430)
-#12418 := (<= #12412 uf_76)
-#12415 := (<= 0::int #12412)
-#12421 := (and #12415 #12418)
-#12436 := (and #12421 #12433)
-#12479 := (not #12436)
-#12480 := (or #12479 #12473)
-#12485 := (and #12421 #12480)
-#12557 := (or #12485 #12556)
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+#13223 := [rewrite]: #13221
+#13229 := [monotonicity #13223 #13226]: #13228
+#13232 := [monotonicity #13229]: #13231
+#13614 := [monotonicity #13232 #13611]: #13613
+#13617 := [monotonicity #13232 #13614]: #13616
+#13620 := [monotonicity #13232 #13617]: #13619
+#13623 := [monotonicity #13620]: #13622
+#13628 := [trans #13623 #13626]: #13627
+#13631 := [monotonicity #13628]: #13630
+#13638 := [monotonicity #13232 #13631]: #13637
+#13641 := [monotonicity #13232 #13638]: #13640
+#13644 := [monotonicity #13232 #13641]: #13643
+#13647 := [monotonicity #13232 #13644]: #13646
+#13634 := (iff #12698 #13511)
+#13632 := (iff #3268 #13510)
+#13633 := [rewrite]: #13632
+#13635 := [monotonicity #13633]: #13634
+#13650 := [monotonicity #13635 #13647]: #13649
+#13653 := [monotonicity #13232 #13650]: #13652
+#13658 := [trans #13653 #13656]: #13657
+#13536 := (iff #12674 #13533)
+#13521 := (or #13230 #13504)
+#13524 := (or #13230 #13521)
+#13527 := (or #13510 #13524)
+#13530 := (or #13230 #13527)
+#13534 := (iff #13530 #13533)
+#13535 := [rewrite]: #13534
+#13531 := (iff #12674 #13530)
+#13528 := (iff #12666 #13527)
+#13525 := (iff #12657 #13524)
+#13522 := (iff #12649 #13521)
+#13507 := (iff #12643 #13504)
+#13501 := (and #12299 #13498)
 #13505 := (iff #13501 #13504)
 #13506 := [rewrite]: #13505
-#13502 := (iff #12696 #13501)
-#13499 := (iff #12691 #13498)
-#13496 := (iff #12684 #13493)
-#13490 := (and #11982 #13487)
+#13502 := (iff #12643 #13501)
+#13499 := (iff #12638 #13498)
+#13496 := (iff #12632 #13493)
+#13490 := (and #12305 #13485)
 #13494 := (iff #13490 #13493)
 #13495 := [rewrite]: #13494
-#13491 := (iff #12684 #13490)
-#13488 := (iff #12679 #13487)
-#13485 := (iff #12672 #13484)
-#13482 := (iff #12667 #13481)
-#13479 := (iff #12660 #13478)
-#13476 := (iff #12655 #13475)
-#13473 := (iff #12648 #13470)
-#13442 := (and #12741 #3055)
-#13467 := (and #13442 #13462)
-#13471 := (iff #13467 #13470)
-#13472 := [rewrite]: #13471
-#13468 := (iff #12648 #13467)
-#13465 := (iff #12643 #13462)
-#13456 := (or #12962 #13353)
-#13459 := (or #13453 #13456)
-#13463 := (iff #13459 #13462)
-#13464 := [rewrite]: #13463
-#13460 := (iff #12643 #13459)
-#13457 := (iff #12627 #13456)
-#13354 := (iff #12620 #13353)
-#13351 := (iff #12615 #13350)
-#13348 := (iff #12614 #13347)
-#13345 := (iff #12608 #13342)
-#12915 := (and #12910 #12913)
-#13336 := (and #12967 #12915)
-#13339 := (and #12915 #13336)
-#13343 := (iff #13339 #13342)
-#13344 := [rewrite]: #13343
-#13340 := (iff #12608 #13339)
-#13337 := (iff #12605 #13336)
-#12916 := (iff #12020 #12915)
-#12912 := (iff #3091 #12913)
-#12914 := [rewrite]: #12912
-#12909 := (iff #3084 #12910)
-#12911 := [rewrite]: #12909
-#12917 := [monotonicity #12911 #12914]: #12916
-#13334 := (iff #3303 #12967)
-#13335 := [rewrite]: #13334
-#13338 := [monotonicity #13335 #12917]: #13337
-#13341 := [monotonicity #12917 #13338]: #13340
-#13346 := [trans #13341 #13344]: #13345
-#13349 := [monotonicity #13346]: #13348
-#13332 := (iff #12174 #13331)
-#13329 := (iff #12169 #13328)
-#13326 := (iff #12162 #13325)
-#13323 := (iff #12157 #13320)
-#13317 := (or #13311 #13314)
-#13321 := (iff #13317 #13320)
-#13322 := [rewrite]: #13321
-#13318 := (iff #12157 #13317)
-#13315 := (iff #12156 #13314)
-#13295 := (iff #12150 #13294)
-#13292 := (iff #12147 #13291)
-#13289 := (iff #3139 #13288)
-#13290 := [rewrite]: #13289
-#13284 := (iff #12146 #13283)
-#13281 := (iff #3138 #13278)
-#4362 := (and #4041 #4355)
-#13275 := (and #4362 #13272)
-#13279 := (iff #13275 #13278)
-#13280 := [rewrite]: #13279
-#13276 := (iff #3138 #13275)
-#13273 := (iff #3137 #13272)
-#13274 := [rewrite]: #13273
-#4363 := (iff #412 #4362)
-#4356 := (iff #411 #4355)
-#4357 := [rewrite]: #4356
-#4039 := (iff #285 #4041)
-#4040 := [rewrite]: #4039
-#4364 := [monotonicity #4040 #4357]: #4363
-#13277 := [monotonicity #4364 #13274]: #13276
-#13282 := [trans #13277 #13280]: #13281
-#13285 := [monotonicity #13282]: #13284
-#13293 := [monotonicity #13285 #13290]: #13292
-#13296 := [quant-intro #13293]: #13295
-#13316 := [monotonicity #13296]: #13315
-#13312 := (iff #3146 #13311)
-#13309 := (iff #3145 #13306)
-#13297 := (and #13272 #3142)
-#13300 := (and #4355 #13297)
-#13303 := (and #4041 #13300)
-#13307 := (iff #13303 #13306)
-#13308 := [rewrite]: #13307
-#13304 := (iff #3145 #13303)
-#13301 := (iff #3144 #13300)
-#13298 := (iff #3143 #13297)
-#13299 := [monotonicity #13274]: #13298
-#13302 := [monotonicity #4357 #13299]: #13301
-#13305 := [monotonicity #4040 #13302]: #13304
-#13310 := [trans #13305 #13308]: #13309
-#13313 := [quant-intro #13310]: #13312
-#13319 := [monotonicity #13313 #13316]: #13318
-#13324 := [trans #13319 #13322]: #13323
-#13327 := [monotonicity #13296 #13324]: #13326
-#13268 := (iff #12168 #13267)
-#13265 := (iff #12143 #13262)
-#13250 := (and #12915 #12131)
-#13253 := (and #12915 #13250)
-#13256 := (and #12915 #13253)
-#13259 := (and up_216 #13256)
-#13263 := (iff #13259 #13262)
-#13264 := [rewrite]: #13263
-#13260 := (iff #12143 #13259)
-#13257 := (iff #12140 #13256)
-#13254 := (iff #12137 #13253)
-#13251 := (iff #12134 #13250)
-#13252 := [monotonicity #12917]: #13251
-#13255 := [monotonicity #12917 #13252]: #13254
-#13258 := [monotonicity #12917 #13255]: #13257
-#13261 := [monotonicity #13258]: #13260
-#13266 := [trans #13261 #13264]: #13265
-#13269 := [monotonicity #13266]: #13268
-#13330 := [monotonicity #13269 #13327]: #13329
+#13491 := (iff #12632 #13490)
+#13488 := (iff #12627 #13485)
+#13479 := (or #13230 #13476)
+#13482 := (or #12494 #13479)
+#13486 := (iff #13482 #13485)
+#13487 := [rewrite]: #13486
+#13483 := (iff #12627 #13482)
+#13480 := (iff #12619 #13479)
+#13477 := (iff #12613 #13476)
+#13474 := (iff #12608 #13471)
+#13368 := (or #13239 #13360)
+#13450 := (or #13368 #12557)
+#13453 := (or #12566 #13450)
+#13456 := (or #13230 #13453)
+#13459 := (or #13230 #13456)
+#13462 := (or #13230 #13459)
+#13465 := (or #13416 #13462)
+#13468 := (or #13230 #13465)
+#13472 := (iff #13468 #13471)
+#13473 := [rewrite]: #13472
+#13469 := (iff #12608 #13468)
+#13466 := (iff #12600 #13465)
+#13463 := (iff #12591 #13462)
+#13460 := (iff #12583 #13459)
+#13457 := (iff #12575 #13456)
+#13454 := (iff #12567 #13453)
+#13451 := (iff #12558 #13450)
+#13369 := (iff #12432 #13368)
+#13363 := (iff #12425 #13360)
+#13357 := (and #13334 #13352)
+#13361 := (iff #13357 #13360)
+#13362 := [rewrite]: #13361
+#13358 := (iff #12425 #13357)
+#13355 := (iff #12420 #13352)
+#13340 := (or #13256 #13324)
+#13343 := (or #12401 #13340)
+#13346 := (or #13331 #13343)
+#13349 := (or #13337 #13346)
+#13353 := (iff #13349 #13352)
+#13354 := [rewrite]: #13353
+#13350 := (iff #12420 #13349)
+#13347 := (iff #12411 #13346)
+#13344 := (iff #12402 #13343)
+#13341 := (iff #12393 #13340)
+#13325 := (iff #12386 #13324)
+#13322 := (iff #12381 #13321)
+#13319 := (iff #12374 #13318)
+#13316 := (iff #12369 #13315)
+#13313 := (iff #12355 #13310)
+#13307 := (and #13304 #12352)
+#13311 := (iff #13307 #13310)
+#13312 := [rewrite]: #13311
+#13308 := (iff #12355 #13307)
+#13305 := (iff #3218 #13304)
+#13306 := [rewrite]: #13305
+#13309 := [monotonicity #13306]: #13308
+#13314 := [trans #13309 #13312]: #13313
+#13299 := (iff #12368 #13298)
+#13296 := (iff #12349 #13295)
+#13293 := (iff #12344 #13290)
+#13284 := (or #13267 #13281)
+#13287 := (or #5579 #13284)
+#13291 := (iff #13287 #13290)
+#13292 := [rewrite]: #13291
+#13288 := (iff #12344 #13287)
+#13285 := (iff #12338 #13284)
+#13282 := (iff #3214 #13281)
+#13283 := [rewrite]: #13282
+#13277 := (iff #12337 #13267)
+#13269 := (not #13267)
+#13272 := (not #13269)
+#13275 := (iff #13272 #13267)
+#13276 := [rewrite]: #13275
+#13273 := (iff #12337 #13272)
+#13270 := (iff #3213 #13269)
+#13271 := [rewrite]: #13270
+#13274 := [monotonicity #13271]: #13273
+#13278 := [trans #13274 #13276]: #13277
+#13286 := [monotonicity #13278 #13283]: #13285
+#13289 := [monotonicity #5581 #13286]: #13288
+#13294 := [trans #13289 #13292]: #13293
+#13297 := [quant-intro #13294]: #13296
+#13300 := [monotonicity #13297]: #13299
+#13317 := [monotonicity #13300 #13314]: #13316
+#13320 := [monotonicity #13297 #13317]: #13319
+#13265 := (iff #12380 #13264)
+#13262 := (iff #3212 #13259)
+#13263 := [rewrite]: #13262
+#13266 := [monotonicity #13263]: #13265
+#13323 := [monotonicity #13266 #13320]: #13322
+#13326 := [monotonicity #13263 #13323]: #13325
+#13257 := (iff #12392 #13256)
+#13254 := (iff #12334 #13253)
+#13250 := (iff #3210 #13251)
+#13252 := [rewrite]: #13250
+#13233 := (iff #3201 #13234)
+#13235 := [rewrite]: #13233
+#13255 := [monotonicity #13235 #13252]: #13254
+#13258 := [monotonicity #13255]: #13257
+#13342 := [monotonicity #13258 #13326]: #13341
+#13345 := [monotonicity #13342]: #13344
+#13332 := (iff #12410 #13331)
+#13329 := (iff #12331 #13327)
+#13330 := [rewrite]: #13329
 #13333 := [monotonicity #13330]: #13332
-#13352 := [monotonicity #13333 #13349]: #13351
-#13248 := (iff #12592 #13247)
-#13245 := (iff #12585 #13242)
-#13239 := (and #12352 #13236)
-#13243 := (iff #13239 #13242)
-#13244 := [rewrite]: #13243
-#13240 := (iff #12585 #13239)
-#13237 := (iff #12580 #13236)
-#13234 := (iff #12574 #13231)
-#13228 := (and #12358 #13225)
-#13232 := (iff #13228 #13231)
-#13233 := [rewrite]: #13232
-#13229 := (iff #12574 #13228)
-#13226 := (iff #12569 #13225)
-#13223 := (iff #12562 #13222)
-#13220 := (iff #12557 #13219)
-#13217 := (iff #12556 #13216)
-#13214 := (iff #12550 #13211)
-#13019 := (and #12913 #13017)
-#13190 := (and #13019 #12524)
-#13193 := (and #12521 #13190)
-#13196 := (and #12915 #13193)
-#13199 := (and #12915 #13196)
-#13202 := (and #12915 #13199)
-#13205 := (and #12997 #13202)
-#13208 := (and #12915 #13205)
-#13212 := (iff #13208 #13211)
-#13213 := [rewrite]: #13212
-#13209 := (iff #12550 #13208)
-#13206 := (iff #12547 #13205)
-#13203 := (iff #12544 #13202)
-#13200 := (iff #12541 #13199)
-#13197 := (iff #12538 #13196)
-#13194 := (iff #12535 #13193)
-#13191 := (iff #12530 #13190)
-#13020 := (iff #3244 #13019)
-#13016 := (iff #3243 #13017)
-#13018 := [rewrite]: #13016
-#13021 := [monotonicity #12914 #13018]: #13020
-#13192 := [monotonicity #13021]: #13191
-#13195 := [monotonicity #13192]: #13194
-#13198 := [monotonicity #12917 #13195]: #13197
-#13201 := [monotonicity #12917 #13198]: #13200
-#13204 := [monotonicity #12917 #13201]: #13203
-#13188 := (iff #3286 #12997)
-#13189 := [rewrite]: #13188
-#13207 := [monotonicity #13189 #13204]: #13206
-#13210 := [monotonicity #12917 #13207]: #13209
-#13215 := [trans #13210 #13213]: #13214
-#13218 := [monotonicity #13215]: #13217
-#13161 := (iff #12485 #13158)
-#13075 := (and #13051 #13054)
-#13155 := (and #13075 #13152)
-#13159 := (iff #13155 #13158)
-#13160 := [rewrite]: #13159
-#13156 := (iff #12485 #13155)
-#13153 := (iff #12480 #13152)
-#13150 := (iff #12473 #13149)
-#13147 := (iff #12468 #13146)
-#13144 := (iff #12461 #13143)
-#13141 := (iff #12456 #13140)
-#13138 := (iff #12449 #13135)
-#13132 := (and #13129 #12446)
-#13136 := (iff #13132 #13135)
-#13137 := [rewrite]: #13136
-#13133 := (iff #12449 #13132)
-#13130 := (iff #3270 #13129)
-#13131 := [rewrite]: #13130
-#13134 := [monotonicity #13131]: #13133
-#13139 := [trans #13134 #13137]: #13138
-#13124 := (iff #12455 #13123)
-#13121 := (iff #12443 #13120)
-#13118 := (iff #12440 #13117)
-#13115 := (iff #3267 #13114)
-#13116 := [rewrite]: #13115
-#13110 := (iff #12439 #13109)
-#13107 := (iff #3266 #13104)
-#13101 := (and #4362 #13098)
-#13105 := (iff #13101 #13104)
-#13106 := [rewrite]: #13105
-#13102 := (iff #3266 #13101)
-#13099 := (iff #3265 #13098)
-#13100 := [rewrite]: #13099
-#13103 := [monotonicity #4364 #13100]: #13102
-#13108 := [trans #13103 #13106]: #13107
-#13111 := [monotonicity #13108]: #13110
-#13119 := [monotonicity #13111 #13116]: #13118
-#13122 := [quant-intro #13119]: #13121
-#13125 := [monotonicity #13122]: #13124
-#13142 := [monotonicity #13125 #13139]: #13141
-#13145 := [monotonicity #13122 #13142]: #13144
-#13094 := (iff #12467 #13093)
-#13091 := (iff #3264 #13089)
-#13092 := [rewrite]: #13091
-#13095 := [monotonicity #13092]: #13094
-#13148 := [monotonicity #13095 #13145]: #13147
-#13151 := [monotonicity #13092 #13148]: #13150
-#13087 := (iff #12479 #13086)
-#13084 := (iff #12436 #13081)
-#13066 := (and #13017 #13059)
-#13069 := (and #3258 #13066)
-#13072 := (and #13061 #13069)
-#13078 := (and #13075 #13072)
-#13082 := (iff #13078 #13081)
-#13083 := [rewrite]: #13082
-#13079 := (iff #12436 #13078)
-#13073 := (iff #12433 #13072)
-#13070 := (iff #12430 #13069)
-#13067 := (iff #12427 #13066)
-#13058 := (iff #3259 #13059)
-#13060 := [rewrite]: #13058
-#13068 := [monotonicity #13018 #13060]: #13067
-#13071 := [monotonicity #13068]: #13070
-#13064 := (iff #12424 #13061)
-#13065 := [rewrite]: #13064
-#13074 := [monotonicity #13065 #13071]: #13073
-#13076 := (iff #12421 #13075)
-#13056 := (iff #12418 #13054)
-#13057 := [rewrite]: #13056
-#13052 := (iff #12415 #13051)
-#13053 := [rewrite]: #13052
-#13077 := [monotonicity #13053 #13057]: #13076
-#13080 := [monotonicity #13077 #13074]: #13079
-#13085 := [trans #13080 #13083]: #13084
-#13088 := [monotonicity #13085]: #13087
-#13154 := [monotonicity #13088 #13151]: #13153
-#13157 := [monotonicity #13077 #13154]: #13156
-#13162 := [trans #13157 #13160]: #13161
-#13221 := [monotonicity #13162 #13218]: #13220
-#13186 := (iff #12516 #13185)
-#13183 := (iff #12509 #13180)
-#13177 := (and #12352 #13174)
-#13181 := (iff #13177 #13180)
-#13182 := [rewrite]: #13181
-#13178 := (iff #12509 #13177)
-#13175 := (iff #12504 #13174)
-#13172 := (iff #12497 #13169)
-#13166 := (and #12358 #13163)
-#13170 := (iff #13166 #13169)
-#13171 := [rewrite]: #13170
-#13167 := (iff #12497 #13166)
-#13164 := (iff #12492 #13163)
-#13049 := (iff #12491 #13048)
-#13046 := (iff #12409 #13043)
-#13022 := (and #13019 #12383)
-#13025 := (and #12380 #13022)
-#13028 := (and #12913 #13025)
-#13031 := (and #3237 #13028)
-#13034 := (and #3236 #13031)
-#13037 := (and #12375 #13034)
-#13040 := (and #12358 #13037)
-#13044 := (iff #13040 #13043)
-#13045 := [rewrite]: #13044
-#13041 := (iff #12409 #13040)
-#13038 := (iff #12406 #13037)
-#13035 := (iff #12403 #13034)
-#13032 := (iff #12400 #13031)
-#13029 := (iff #12397 #13028)
-#13026 := (iff #12394 #13025)
-#13023 := (iff #12389 #13022)
-#13024 := [monotonicity #13021]: #13023
-#13027 := [monotonicity #13024]: #13026
-#13030 := [monotonicity #12914 #13027]: #13029
-#13033 := [monotonicity #13030]: #13032
-#13036 := [monotonicity #13033]: #13035
-#13039 := [monotonicity #13036]: #13038
-#13042 := [monotonicity #13039]: #13041
-#13047 := [trans #13042 #13045]: #13046
-#13050 := [monotonicity #13047]: #13049
-#13165 := [monotonicity #13050 #13162]: #13164
-#13168 := [monotonicity #13165]: #13167
-#13173 := [trans #13168 #13171]: #13172
-#13176 := [monotonicity #13173]: #13175
-#13179 := [monotonicity #13176]: #13178
-#13184 := [trans #13179 #13182]: #13183
-#13014 := (iff #12515 #13013)
-#13011 := (iff #12372 #13008)
-#13002 := (and #12996 #12915)
-#13005 := (and #12915 #13002)
-#13009 := (iff #13005 #13008)
-#13010 := [rewrite]: #13009
-#13006 := (iff #12372 #13005)
-#13003 := (iff #12369 #13002)
-#13000 := (iff #3231 #12996)
-#13001 := [rewrite]: #13000
-#13004 := [monotonicity #13001 #12917]: #13003
-#13007 := [monotonicity #12917 #13004]: #13006
-#13012 := [trans #13007 #13010]: #13011
-#13015 := [monotonicity #13012]: #13014
-#13187 := [monotonicity #13015 #13184]: #13186
-#13224 := [monotonicity #13187 #13221]: #13223
-#12994 := (iff #12568 #12993)
-#12991 := (iff #12364 #12988)
-#12985 := (and #12915 #12358)
-#12989 := (iff #12985 #12988)
-#12990 := [rewrite]: #12989
-#12986 := (iff #12364 #12985)
-#12987 := [monotonicity #12917]: #12986
-#12992 := [trans #12987 #12990]: #12991
-#12995 := [monotonicity #12992]: #12994
-#13227 := [monotonicity #12995 #13224]: #13226
-#13230 := [monotonicity #13227]: #13229
-#13235 := [trans #13230 #13233]: #13234
-#13238 := [monotonicity #13235]: #13237
+#13348 := [monotonicity #13333 #13345]: #13347
+#13338 := (iff #12419 #13337)
+#13335 := (iff #12328 #13334)
+#13248 := (iff #12325 #13245)
+#13249 := [rewrite]: #13248
+#13242 := (iff #12322 #13243)
+#13244 := [rewrite]: #13242
+#13336 := [monotonicity #13244 #13249]: #13335
+#13339 := [monotonicity #13336]: #13338
+#13351 := [monotonicity #13339 #13348]: #13350
+#13356 := [trans #13351 #13354]: #13355
+#13359 := [monotonicity #13336 #13356]: #13358
+#13364 := [trans #13359 #13362]: #13363
+#13240 := (iff #12431 #13239)
+#13237 := (iff #3202 #13236)
+#13238 := [monotonicity #13226 #13235]: #13237
 #13241 := [monotonicity #13238]: #13240
-#13246 := [trans #13241 #13244]: #13245
-#12983 := (iff #12591 #12982)
-#12980 := (iff #12343 #12977)
-#12971 := (and #12968 #12915)
-#12974 := (and #12915 #12971)
-#12978 := (iff #12974 #12977)
-#12979 := [rewrite]: #12978
-#12975 := (iff #12343 #12974)
-#12972 := (iff #12340 #12971)
-#12969 := (iff #3217 #12968)
-#12970 := [rewrite]: #12969
-#12973 := [monotonicity #12970 #12917]: #12972
-#12976 := [monotonicity #12917 #12973]: #12975
-#12981 := [trans #12976 #12979]: #12980
-#12984 := [monotonicity #12981]: #12983
-#13249 := [monotonicity #12984 #13246]: #13248
-#13355 := [monotonicity #13249 #13352]: #13354
-#12963 := (iff #12626 #12962)
-#12960 := (iff #12337 #12957)
-#12918 := (and #3201 #12915)
-#12921 := (and #3198 #12918)
-#12924 := (and #3197 #12921)
-#12927 := (and #3196 #12924)
-#12930 := (and #3195 #12927)
-#12933 := (and #12073 #12930)
-#12936 := (and true #12261)
-#12939 := (and true #12936)
-#12942 := (and #12939 #12933)
-#12945 := (and #12939 #12942)
-#12948 := (and #12915 #12945)
-#12951 := (and #12915 #12948)
-#12954 := (and #12915 #12951)
-#12958 := (iff #12954 #12957)
-#12959 := [rewrite]: #12958
-#12955 := (iff #12337 #12954)
-#12952 := (iff #12334 #12951)
-#12949 := (iff #12331 #12948)
-#12946 := (iff #12328 #12945)
-#12943 := (iff #12325 #12942)
-#12934 := (iff #12322 #12933)
-#12931 := (iff #12319 #12930)
-#12928 := (iff #12316 #12927)
-#12925 := (iff #12313 #12924)
-#12922 := (iff #12310 #12921)
-#12919 := (iff #12307 #12918)
-#12920 := [monotonicity #12917]: #12919
-#12923 := [monotonicity #12920]: #12922
-#12926 := [monotonicity #12923]: #12925
-#12929 := [monotonicity #12926]: #12928
-#12932 := [monotonicity #12929]: #12931
-#12935 := [monotonicity #12932]: #12934
-#12940 := (iff #12267 #12939)
-#12937 := (iff #12264 #12936)
-#12905 := (iff #3186 true)
-#12900 := (forall (vars (?x783 T5)) (:pat #3184) true)
-#12903 := (iff #12900 true)
-#12904 := [elim-unused]: #12903
-#12901 := (iff #3186 #12900)
-#12898 := (iff #3185 true)
-#12899 := [rewrite]: #12898
-#12902 := [quant-intro #12899]: #12901
-#12906 := [trans #12902 #12904]: #12905
-#12938 := [monotonicity #12906]: #12937
-#12907 := (iff #3182 true)
-#12908 := [rewrite]: #12907
-#12941 := [monotonicity #12908 #12938]: #12940
-#12944 := [monotonicity #12941 #12935]: #12943
-#12947 := [monotonicity #12941 #12944]: #12946
-#12950 := [monotonicity #12917 #12947]: #12949
-#12953 := [monotonicity #12917 #12950]: #12952
-#12956 := [monotonicity #12917 #12953]: #12955
-#12961 := [trans #12956 #12959]: #12960
-#12964 := [monotonicity #12961]: #12963
-#13458 := [monotonicity #12964 #13355]: #13457
-#13454 := (iff #12642 #13453)
-#13451 := (iff #12062 #13448)
-#13409 := (and #13359 #12030)
-#13412 := (and #12915 #13409)
-#13415 := (and #13386 #13412)
-#13418 := (and #13389 #13415)
-#13421 := (and #12915 #13418)
-#13424 := (and #13392 #13395)
-#13427 := (and #13424 #13421)
-#13430 := (and #12910 #13398)
-#13433 := (and #13430 #13427)
-#13436 := (and #13402 #13405)
-#13439 := (and #13436 #13433)
-#13445 := (and #13442 #13439)
-#13449 := (iff #13445 #13448)
-#13450 := [rewrite]: #13449
-#13446 := (iff #12062 #13445)
-#13440 := (iff #12059 #13439)
-#13434 := (iff #12056 #13433)
-#13428 := (iff #12053 #13427)
-#13422 := (iff #12050 #13421)
-#13419 := (iff #12047 #13418)
-#13416 := (iff #12044 #13415)
-#13413 := (iff #12039 #13412)
-#13410 := (iff #12033 #13409)
-#13360 := (iff #3099 #13359)
-#13361 := [rewrite]: #13360
-#13411 := [monotonicity #13361]: #13410
-#13414 := [monotonicity #12917 #13411]: #13413
-#13387 := (iff #12027 #13386)
-#13384 := (iff #12024 #13383)
-#13381 := (iff #3096 #13380)
-#13382 := [rewrite]: #13381
-#13376 := (iff #12023 #13375)
-#13373 := (iff #3095 #13370)
-#13367 := (and #4362 #13364)
-#13371 := (iff #13367 #13370)
-#13372 := [rewrite]: #13371
-#13368 := (iff #3095 #13367)
-#13365 := (iff #3094 #13364)
-#13366 := [rewrite]: #13365
-#13369 := [monotonicity #4364 #13366]: #13368
-#13374 := [trans #13369 #13372]: #13373
-#13377 := [monotonicity #13374]: #13376
-#13385 := [monotonicity #13377 #13382]: #13384
-#13388 := [quant-intro #13385]: #13387
-#13417 := [monotonicity #13388 #13414]: #13416
-#13390 := (iff #3093 #13389)
-#13391 := [rewrite]: #13390
-#13420 := [monotonicity #13391 #13417]: #13419
-#13423 := [monotonicity #12917 #13420]: #13422
-#13425 := (iff #3090 #13424)
-#13396 := (iff #3089 #13395)
-#13397 := [rewrite]: #13396
-#13393 := (iff #3088 #13392)
+#13370 := [monotonicity #13241 #13364]: #13369
+#13452 := [monotonicity #13370]: #13451
+#13455 := [monotonicity #13452]: #13454
+#13458 := [monotonicity #13232 #13455]: #13457
+#13461 := [monotonicity #13232 #13458]: #13460
+#13464 := [monotonicity #13232 #13461]: #13463
+#13448 := (iff #12599 #13416)
+#13446 := (iff #3248 #13417)
+#13447 := [rewrite]: #13446
+#13449 := [monotonicity #13447]: #13448
+#13467 := [monotonicity #13449 #13464]: #13466
+#13470 := [monotonicity #13232 #13467]: #13469
+#13475 := [trans #13470 #13473]: #13474
+#13444 := (iff #12543 #13441)
+#13429 := (or #13230 #13411)
+#13432 := (or #13230 #13429)
+#13435 := (or #13417 #13432)
+#13438 := (or #13230 #13435)
+#13442 := (iff #13438 #13441)
+#13443 := [rewrite]: #13442
+#13439 := (iff #12543 #13438)
+#13436 := (iff #12535 #13435)
+#13433 := (iff #12526 #13432)
+#13430 := (iff #12518 #13429)
+#13414 := (iff #12512 #13411)
+#13408 := (and #12299 #13405)
+#13412 := (iff #13408 #13411)
+#13413 := [rewrite]: #13412
+#13409 := (iff #12512 #13408)
+#13406 := (iff #12507 #13405)
+#13403 := (iff #12500 #13400)
+#13397 := (and #12305 #13392)
+#13401 := (iff #13397 #13400)
+#13402 := [rewrite]: #13401
+#13398 := (iff #12500 #13397)
+#13395 := (iff #12495 #13392)
+#13371 := (or #12440 #13368)
+#13374 := (or #12449 #13371)
+#13377 := (or #13365 #13374)
+#13380 := (or #12467 #13377)
+#13383 := (or #12476 #13380)
+#13386 := (or #12485 #13383)
+#13389 := (or #12494 #13386)
+#13393 := (iff #13389 #13392)
 #13394 := [rewrite]: #13393
-#13426 := [monotonicity #13394 #13397]: #13425
-#13429 := [monotonicity #13426 #13423]: #13428
-#13431 := (iff #3086 #13430)
-#13400 := (iff #3085 #13398)
-#13401 := [rewrite]: #13400
-#13432 := [monotonicity #12911 #13401]: #13431
-#13435 := [monotonicity #13432 #13429]: #13434
-#13437 := (iff #3082 #13436)
-#13407 := (iff #3081 #13405)
-#13408 := [rewrite]: #13407
-#13403 := (iff #3080 #13402)
-#13404 := [rewrite]: #13403
-#13438 := [monotonicity #13404 #13408]: #13437
-#13441 := [monotonicity #13438 #13435]: #13440
-#13443 := (iff #12017 #13442)
-#12742 := (iff #2975 #12741)
-#12743 := [rewrite]: #12742
-#13444 := [monotonicity #12743]: #13443
-#13447 := [monotonicity #13444 #13441]: #13446
-#13452 := [trans #13447 #13450]: #13451
-#13455 := [monotonicity #13452]: #13454
-#13461 := [monotonicity #13455 #13458]: #13460
-#13466 := [trans #13461 #13464]: #13465
-#13469 := [monotonicity #13444 #13466]: #13468
-#13474 := [trans #13469 #13472]: #13473
-#12896 := (iff #12654 #12895)
-#12893 := (iff #12012 #12892)
-#12890 := (iff #12009 #12889)
-#12884 := (iff #3074 #12885)
-#12888 := [rewrite]: #12884
-#12882 := (iff #12008 #12881)
-#12879 := (iff #3071 #12876)
-#12873 := (and #4362 #12870)
-#12877 := (iff #12873 #12876)
-#12878 := [rewrite]: #12877
-#12874 := (iff #3071 #12873)
-#12871 := (iff #3070 #12870)
-#12872 := [rewrite]: #12871
-#12875 := [monotonicity #4364 #12872]: #12874
-#12880 := [trans #12875 #12878]: #12879
-#12883 := [monotonicity #12880]: #12882
-#12891 := [monotonicity #12883 #12888]: #12890
-#12894 := [quant-intro #12891]: #12893
-#12897 := [monotonicity #12894]: #12896
-#13477 := [monotonicity #12897 #13474]: #13476
-#13480 := [monotonicity #12894 #13477]: #13479
-#12867 := (iff #12666 #12866)
-#12864 := (iff #3069 #12863)
-#12865 := [rewrite]: #12864
-#12868 := [monotonicity #12865]: #12867
-#13483 := [monotonicity #12868 #13480]: #13482
-#13486 := [monotonicity #12865 #13483]: #13485
-#12861 := (iff #12678 #12860)
-#12858 := (iff #12005 #12855)
-#12293 := (and true true)
-#12837 := (and true #12293)
-#12840 := (and #3058 #12837)
-#12843 := (and #3057 #12840)
-#12846 := (and #3056 #12843)
-#12849 := (and #3055 #12846)
-#12852 := (and #11982 #12849)
-#12856 := (iff #12852 #12855)
-#12857 := [rewrite]: #12856
-#12853 := (iff #12005 #12852)
-#12850 := (iff #12002 #12849)
-#12847 := (iff #11999 #12846)
-#12844 := (iff #11996 #12843)
-#12841 := (iff #11993 #12840)
-#12838 := (iff #11990 #12837)
-#12835 := (iff #11987 #12293)
-#12833 := (iff #3060 true)
-#12834 := [rewrite]: #12833
-#12831 := (iff #3059 true)
-#12832 := [rewrite]: #12831
-#12836 := [monotonicity #12832 #12834]: #12835
-#12839 := [monotonicity #12832 #12836]: #12838
-#12842 := [monotonicity #12839]: #12841
-#12845 := [monotonicity #12842]: #12844
-#12848 := [monotonicity #12845]: #12847
-#12851 := [monotonicity #12848]: #12850
-#12854 := [monotonicity #12851]: #12853
-#12859 := [trans #12854 #12857]: #12858
-#12862 := [monotonicity #12859]: #12861
-#13489 := [monotonicity #12862 #13486]: #13488
+#13390 := (iff #12495 #13389)
+#13387 := (iff #12486 #13386)
+#13384 := (iff #12477 #13383)
+#13381 := (iff #12468 #13380)
+#13378 := (iff #12459 #13377)
+#13375 := (iff #12450 #13374)
+#13372 := (iff #12441 #13371)
+#13373 := [monotonicity #13370]: #13372
+#13376 := [monotonicity #13373]: #13375
+#13366 := (iff #12458 #13365)
+#13367 := [monotonicity #13226]: #13366
+#13379 := [monotonicity #13367 #13376]: #13378
+#13382 := [monotonicity #13379]: #13381
+#13385 := [monotonicity #13382]: #13384
+#13388 := [monotonicity #13385]: #13387
+#13391 := [monotonicity #13388]: #13390
+#13396 := [trans #13391 #13394]: #13395
+#13399 := [monotonicity #13396]: #13398
+#13404 := [trans #13399 #13402]: #13403
+#13407 := [monotonicity #13404]: #13406
+#13410 := [monotonicity #13407]: #13409
+#13415 := [trans #13410 #13413]: #13414
+#13431 := [monotonicity #13232 #13415]: #13430
+#13434 := [monotonicity #13232 #13431]: #13433
+#13427 := (iff #12534 #13417)
+#13422 := (not #13416)
+#13425 := (iff #13422 #13417)
+#13426 := [rewrite]: #13425
+#13423 := (iff #12534 #13422)
+#13420 := (iff #3191 #13416)
+#13421 := [rewrite]: #13420
+#13424 := [monotonicity #13421]: #13423
+#13428 := [trans #13424 #13426]: #13427
+#13437 := [monotonicity #13428 #13434]: #13436
+#13440 := [monotonicity #13232 #13437]: #13439
+#13445 := [trans #13440 #13443]: #13444
+#13478 := [monotonicity #13445 #13475]: #13477
+#13481 := [monotonicity #13232 #13478]: #13480
+#13484 := [monotonicity #13481]: #13483
+#13489 := [trans #13484 #13487]: #13488
 #13492 := [monotonicity #13489]: #13491
 #13497 := [trans #13492 #13495]: #13496
 #13500 := [monotonicity #13497]: #13499
 #13503 := [monotonicity #13500]: #13502
 #13508 := [trans #13503 #13506]: #13507
-#13511 := [monotonicity #13508]: #13510
-#13514 := [monotonicity #13511]: #13513
-#12829 := (iff #12714 #12828)
-#12826 := (iff #11964 #12823)
-#12772 := (and #12724 #12726)
-#12775 := (and #12772 #11920)
-#12778 := (and #3020 #12775)
-#12781 := (and #3017 #12778)
-#12784 := (and #3016 #12781)
-#12787 := (and #12737 #12784)
-#12790 := (and #11906 #12787)
-#12793 := (and #11897 #12790)
-#12796 := (and #11894 #12793)
-#12799 := (and #12741 #12796)
-#12802 := (and #12745 #12799)
-#12805 := (and #12749 #12751)
-#12808 := (and #12805 #12802)
-#12811 := (and #12757 #12759)
-#12814 := (and #12811 #12808)
-#12817 := (and #12765 #12767)
-#12820 := (and #12817 #12814)
-#12824 := (iff #12820 #12823)
-#12825 := [rewrite]: #12824
-#12821 := (iff #11964 #12820)
-#12815 := (iff #11961 #12814)
-#12809 := (iff #11958 #12808)
-#12803 := (iff #11955 #12802)
-#12800 := (iff #11952 #12799)
-#12797 := (iff #11949 #12796)
-#12794 := (iff #11946 #12793)
-#12791 := (iff #11943 #12790)
-#12788 := (iff #11940 #12787)
-#12785 := (iff #11937 #12784)
-#12782 := (iff #11934 #12781)
-#12779 := (iff #11931 #12778)
-#12776 := (iff #11926 #12775)
-#12773 := (iff #3028 #12772)
-#12729 := (iff #3027 #12726)
-#12730 := [rewrite]: #12729
-#12723 := (iff #3026 #12724)
-#12725 := [rewrite]: #12723
-#12774 := [monotonicity #12725 #12730]: #12773
-#12777 := [monotonicity #12774]: #12776
-#12780 := [monotonicity #12777]: #12779
-#12783 := [monotonicity #12780]: #12782
-#12786 := [monotonicity #12783]: #12785
-#12738 := (iff #3012 #12737)
-#12735 := (iff #3011 #12731)
-#12736 := [rewrite]: #12735
-#12739 := [quant-intro #12736]: #12738
-#12789 := [monotonicity #12739 #12786]: #12788
-#12792 := [monotonicity #12789]: #12791
-#12795 := [monotonicity #12792]: #12794
-#12798 := [monotonicity #12795]: #12797
-#12801 := [monotonicity #12743 #12798]: #12800
-#12746 := (iff #2974 #12745)
-#12747 := [rewrite]: #12746
-#12804 := [monotonicity #12747 #12801]: #12803
-#12806 := (iff #2972 #12805)
-#12754 := (iff #2971 #12751)
-#12755 := [rewrite]: #12754
-#12748 := (iff #2970 #12749)
-#12750 := [rewrite]: #12748
-#12807 := [monotonicity #12750 #12755]: #12806
-#12810 := [monotonicity #12807 #12804]: #12809
-#12812 := (iff #2968 #12811)
-#12762 := (iff #2967 #12759)
+#13523 := [monotonicity #13232 #13508]: #13522
+#13526 := [monotonicity #13232 #13523]: #13525
+#13519 := (iff #12665 #13510)
+#13514 := (not #13511)
+#13517 := (iff #13514 #13510)
+#13518 := [rewrite]: #13517
+#13515 := (iff #12665 #13514)
+#13512 := (iff #3180 #13511)
+#13513 := [rewrite]: #13512
+#13516 := [monotonicity #13513]: #13515
+#13520 := [trans #13516 #13518]: #13519
+#13529 := [monotonicity #13520 #13526]: #13528
+#13532 := [monotonicity #13232 #13529]: #13531
+#13537 := [trans #13532 #13535]: #13536
+#13661 := [monotonicity #13537 #13658]: #13660
+#13791 := [monotonicity #13232 #13661]: #13790
+#13794 := [monotonicity #13791]: #13793
+#13797 := [monotonicity #13794]: #13796
+#13800 := [monotonicity #13797]: #13799
+#13803 := [monotonicity #13800]: #13802
+#13806 := [monotonicity #13803]: #13805
+#13809 := [monotonicity #13806]: #13808
+#13684 := (iff #12786 #13683)
+#13681 := (iff #12260 #12254)
+#13673 := (and true #12254)
+#13676 := (and true #13673)
+#13679 := (iff #13676 #12254)
+#13680 := [rewrite]: #13679
+#13677 := (iff #12260 #13676)
+#13674 := (iff #12257 #13673)
+#13669 := (iff #3161 true)
+#13664 := (forall (vars (?x783 T5)) (:pat #3159) true)
+#13667 := (iff #13664 true)
+#13668 := [elim-unused]: #13667
+#13665 := (iff #3161 #13664)
+#13662 := (iff #3160 true)
+#13663 := [rewrite]: #13662
+#13666 := [quant-intro #13663]: #13665
+#13670 := [trans #13666 #13668]: #13669
+#13675 := [monotonicity #13670]: #13674
+#13671 := (iff #3157 true)
+#13672 := [rewrite]: #13671
+#13678 := [monotonicity #13672 #13675]: #13677
+#13682 := [trans #13678 #13680]: #13681
+#13685 := [monotonicity #13682]: #13684
+#13812 := [monotonicity #13685 #13809]: #13811
+#13815 := [monotonicity #13685 #13812]: #13814
+#13818 := [monotonicity #13232 #13815]: #13817
+#13821 := [monotonicity #13232 #13818]: #13820
+#13824 := [monotonicity #13232 #13821]: #13823
+#13827 := [monotonicity #13232 #13824]: #13826
+#13701 := (iff #12842 #13700)
+#13698 := (iff #11992 #13695)
+#13692 := (and #13689 #11989)
+#13696 := (iff #13692 #13695)
+#13697 := [rewrite]: #13696
+#13693 := (iff #11992 #13692)
+#13690 := (iff #3081 #13689)
+#13691 := [rewrite]: #13690
+#13694 := [monotonicity #13691]: #13693
+#13699 := [trans #13694 #13697]: #13698
+#13702 := [monotonicity #13699]: #13701
+#13830 := [monotonicity #13702 #13827]: #13829
+#13735 := (iff #12851 #13734)
+#13732 := (iff #11986 #13731)
+#13729 := (iff #11981 #13726)
+#13720 := (or #13703 #13717)
+#13723 := (or #5579 #13720)
+#13727 := (iff #13723 #13726)
+#13728 := [rewrite]: #13727
+#13724 := (iff #11981 #13723)
+#13721 := (iff #11975 #13720)
+#13718 := (iff #3077 #13717)
+#13719 := [rewrite]: #13718
+#13713 := (iff #11974 #13703)
+#13705 := (not #13703)
+#13708 := (not #13705)
+#13711 := (iff #13708 #13703)
+#13712 := [rewrite]: #13711
+#13709 := (iff #11974 #13708)
+#13706 := (iff #3076 #13705)
+#13707 := [rewrite]: #13706
+#13710 := [monotonicity #13707]: #13709
+#13714 := [trans #13710 #13712]: #13713
+#13722 := [monotonicity #13714 #13719]: #13721
+#13725 := [monotonicity #5581 #13722]: #13724
+#13730 := [trans #13725 #13728]: #13729
+#13733 := [quant-intro #13730]: #13732
+#13736 := [monotonicity #13733]: #13735
+#13833 := [monotonicity #13736 #13830]: #13832
+#13741 := (iff #12860 #13740)
+#13738 := (iff #3075 #13737)
+#13739 := [rewrite]: #13738
+#13742 := [monotonicity #13739]: #13741
+#13836 := [monotonicity #13742 #13833]: #13835
+#13839 := [monotonicity #13232 #13836]: #13838
+#13753 := (iff #12877 #13752)
+#13750 := (iff #3072 #13749)
+#13747 := (iff #3071 #13746)
+#13748 := [rewrite]: #13747
+#13744 := (iff #3070 #13743)
+#13745 := [rewrite]: #13744
+#13751 := [monotonicity #13745 #13748]: #13750
+#13754 := [monotonicity #13751]: #13753
+#13842 := [monotonicity #13754 #13839]: #13841
+#13763 := (iff #12886 #13762)
+#13760 := (iff #3068 #13759)
+#13757 := (iff #3067 #13755)
+#13758 := [rewrite]: #13757
+#13761 := [monotonicity #13223 #13758]: #13760
+#13764 := [monotonicity #13761]: #13763
+#13845 := [monotonicity #13764 #13842]: #13844
+#13776 := (iff #12895 #13775)
+#13773 := (iff #3064 #13772)
+#13770 := (iff #3063 #13768)
+#13771 := [rewrite]: #13770
+#13766 := (iff #3062 #13765)
+#13767 := [rewrite]: #13766
+#13774 := [monotonicity #13767 #13771]: #13773
+#13777 := [monotonicity #13774]: #13776
+#13848 := [monotonicity #13777 #13845]: #13847
+#13787 := (iff #12904 #13786)
+#13784 := (iff #11968 #13781)
+#13782 := (iff #13778 #13781)
+#13783 := [rewrite]: #13782
+#13779 := (iff #11968 #13778)
+#13219 := (iff #2975 #13218)
+#13220 := [rewrite]: #13219
+#13780 := [monotonicity #13220]: #13779
+#13785 := [trans #13780 #13783]: #13784
+#13788 := [monotonicity #13785]: #13787
+#13851 := [monotonicity #13788 #13848]: #13850
+#13856 := [trans #13851 #13854]: #13855
+#13859 := [monotonicity #13780 #13856]: #13858
+#13864 := [trans #13859 #13862]: #13863
+#13215 := (iff #12916 #13214)
+#13212 := (iff #11963 #13211)
+#13209 := (iff #11958 #13206)
+#13200 := (or #13184 #13196)
+#13203 := (or #5579 #13200)
+#13207 := (iff #13203 #13206)
+#13208 := [rewrite]: #13207
+#13204 := (iff #11958 #13203)
+#13201 := (iff #11952 #13200)
+#13195 := (iff #3055 #13196)
+#13199 := [rewrite]: #13195
+#13193 := (iff #11951 #13184)
+#13185 := (not #13184)
+#13188 := (not #13185)
+#13191 := (iff #13188 #13184)
+#13192 := [rewrite]: #13191
+#13189 := (iff #11951 #13188)
+#13186 := (iff #3052 #13185)
+#13187 := [rewrite]: #13186
+#13190 := [monotonicity #13187]: #13189
+#13194 := [trans #13190 #13192]: #13193
+#13202 := [monotonicity #13194 #13199]: #13201
+#13205 := [monotonicity #5581 #13202]: #13204
+#13210 := [trans #13205 #13208]: #13209
+#13213 := [quant-intro #13210]: #13212
+#13216 := [monotonicity #13213]: #13215
+#13867 := [monotonicity #13216 #13864]: #13866
+#13870 := [monotonicity #13213 #13867]: #13869
+#13182 := (iff #12928 #13181)
+#13179 := (iff #3051 #13178)
+#13180 := [rewrite]: #13179
+#13183 := [monotonicity #13180]: #13182
+#13873 := [monotonicity #13183 #13870]: #13872
+#13876 := [monotonicity #13180 #13873]: #13875
+#13176 := (iff #12940 false)
+#11995 := (iff #3086 false)
+#11996 := [rewrite]: #11995
+#13174 := (iff #12940 #3086)
+#13172 := (iff #11948 true)
+#12286 := (and true true)
+#13167 := (and true #12286)
+#13170 := (iff #13167 true)
+#13171 := [rewrite]: #13170
+#13168 := (iff #11948 #13167)
+#13165 := (iff #11945 #12286)
+#13163 := (iff #3047 true)
+#13164 := [rewrite]: #13163
+#13161 := (iff #3046 true)
+#13162 := [rewrite]: #13161
+#13166 := [monotonicity #13162 #13164]: #13165
+#13169 := [monotonicity #13162 #13166]: #13168
+#13173 := [trans #13169 #13171]: #13172
+#13175 := [monotonicity #13173]: #13174
+#13177 := [trans #13175 #11996]: #13176
+#13879 := [monotonicity #13177 #13876]: #13878
+#13882 := [monotonicity #13879]: #13881
+#13885 := [monotonicity #13882]: #13884
+#13888 := [monotonicity #13885]: #13887
+#13891 := [monotonicity #13888]: #13890
+#13894 := [monotonicity #13891]: #13893
+#13899 := [trans #13894 #13897]: #13898
+#13902 := [monotonicity #13899]: #13901
+#13907 := [trans #13902 #13905]: #13906
+#13910 := [monotonicity #13907]: #13909
+#13913 := [monotonicity #13910]: #13912
+#13918 := [trans #13913 #13916]: #13917
+#13921 := [monotonicity #13918]: #13920
+#13924 := [monotonicity #13921]: #13923
+#13159 := (iff #13021 #13158)
+#13156 := (iff #3028 #13155)
+#13153 := (iff #3027 #13150)
+#13154 := [rewrite]: #13153
+#13147 := (iff #3026 #13148)
+#13149 := [rewrite]: #13147
+#13157 := [monotonicity #13149 #13154]: #13156
+#13160 := [monotonicity #13157]: #13159
+#14005 := [monotonicity #13160 #13924]: #14004
+#14008 := [monotonicity #14005]: #14007
+#14011 := [monotonicity #14008]: #14010
+#14014 := [monotonicity #14011]: #14013
+#14017 := [monotonicity #14014]: #14016
+#13935 := (iff #13066 #13934)
+#13932 := (iff #3012 #13931)
+#13929 := (iff #3011 #13925)
+#13930 := [rewrite]: #13929
+#13933 := [quant-intro #13930]: #13932
+#13936 := [monotonicity #13933]: #13935
+#14020 := [monotonicity #13936 #14017]: #14019
+#14023 := [monotonicity #14020]: #14022
+#14026 := [monotonicity #14023]: #14025
+#13941 := (iff #13093 #13940)
+#13938 := (iff #11896 #13937)
+#13939 := [rewrite]: #13938
+#13942 := [monotonicity #13939]: #13941
+#14029 := [monotonicity #13942 #14026]: #14028
+#13948 := (iff #13102 #13217)
+#13943 := (not #13218)
+#13946 := (iff #13943 #13217)
+#13947 := [rewrite]: #13946
+#13944 := (iff #13102 #13943)
+#13945 := [monotonicity #13220]: #13944
+#13949 := [trans #13945 #13947]: #13948
+#14032 := [monotonicity #13949 #14029]: #14031
+#13959 := (iff #13111 #13950)
+#13951 := (not #13950)
+#13954 := (not #13951)
+#13957 := (iff #13954 #13950)
+#13958 := [rewrite]: #13957
+#13955 := (iff #13111 #13954)
+#13952 := (iff #2974 #13951)
+#13953 := [rewrite]: #13952
+#13956 := [monotonicity #13953]: #13955
+#13960 := [trans #13956 #13958]: #13959
+#14035 := [monotonicity #13960 #14032]: #14034
+#13973 := (iff #13120 #13972)
+#13970 := (iff #2972 #13969)
+#13967 := (iff #2971 #13964)
+#13968 := [rewrite]: #13967
+#13961 := (iff #2970 #13962)
+#13963 := [rewrite]: #13961
+#13971 := [monotonicity #13963 #13968]: #13970
+#13974 := [monotonicity #13971]: #13973
+#14038 := [monotonicity #13974 #14035]: #14037
+#13987 := (iff #13129 #13986)
+#13984 := (iff #2968 #13983)
+#13981 := (iff #2967 #13978)
+#13982 := [rewrite]: #13981
+#13975 := (iff #2966 #13976)
+#13977 := [rewrite]: #13975
+#13985 := [monotonicity #13977 #13982]: #13984
+#13988 := [monotonicity #13985]: #13987
+#14041 := [monotonicity #13988 #14038]: #14040
+#14001 := (iff #13138 #14000)
+#13998 := (iff #2964 #13997)
+#13995 := (iff #2963 #13992)
+#13996 := [rewrite]: #13995
+#13989 := (iff #2962 #13990)
+#13991 := [rewrite]: #13989
+#13999 := [monotonicity #13991 #13996]: #13998
+#14002 := [monotonicity #13999]: #14001
+#14044 := [monotonicity #14002 #14041]: #14043
+#14049 := [trans #14044 #14047]: #14048
+#14052 := [monotonicity #14049]: #14051
+#13145 := (iff #3327 #13144)
+#13142 := (iff #3326 #13139)
+#13135 := (implies #2964 #13130)
+#13140 := (iff #13135 #13139)
+#13141 := [rewrite]: #13140
+#13136 := (iff #3326 #13135)
+#13133 := (iff #3325 #13130)
+#13126 := (implies #2968 #13121)
+#13131 := (iff #13126 #13130)
+#13132 := [rewrite]: #13131
+#13127 := (iff #3325 #13126)
+#13124 := (iff #3324 #13121)
+#13117 := (implies #2972 #13112)
+#13122 := (iff #13117 #13121)
+#13123 := [rewrite]: #13122
+#13118 := (iff #3324 #13117)
+#13115 := (iff #3323 #13112)
+#13108 := (implies #2974 #13103)
+#13113 := (iff #13108 #13112)
+#13114 := [rewrite]: #13113
+#13109 := (iff #3323 #13108)
+#13106 := (iff #3322 #13103)
+#13099 := (implies #2975 #13094)
+#13104 := (iff #13099 #13103)
+#13105 := [rewrite]: #13104
+#13100 := (iff #3322 #13099)
+#13097 := (iff #3321 #13094)
+#13090 := (implies #11896 #13085)
+#13095 := (iff #13090 #13094)
+#13096 := [rewrite]: #13095
+#13091 := (iff #3321 #13090)
+#13088 := (iff #3320 #13085)
+#13081 := (implies #11899 #13076)
+#13086 := (iff #13081 #13085)
+#13087 := [rewrite]: #13086
+#13082 := (iff #3320 #13081)
+#13079 := (iff #3319 #13076)
+#13072 := (implies #11908 #13067)
+#13077 := (iff #13072 #13076)
+#13078 := [rewrite]: #13077
+#13073 := (iff #3319 #13072)
+#13070 := (iff #3318 #13067)
+#13063 := (implies #3012 #13058)
+#13068 := (iff #13063 #13067)
+#13069 := [rewrite]: #13068
+#13064 := (iff #3318 #13063)
+#13061 := (iff #3317 #13058)
+#13054 := (implies #3016 #13049)
+#13059 := (iff #13054 #13058)
+#13060 := [rewrite]: #13059
+#13055 := (iff #3317 #13054)
+#13052 := (iff #3316 #13049)
+#13045 := (implies #3017 #13040)
+#13050 := (iff #13045 #13049)
+#13051 := [rewrite]: #13050
+#13046 := (iff #3316 #13045)
+#13043 := (iff #3315 #13040)
+#13036 := (implies #3020 #13031)
+#13041 := (iff #13036 #13040)
+#13042 := [rewrite]: #13041
+#13037 := (iff #3315 #13036)
+#13034 := (iff #3314 #13031)
+#13027 := (implies #11922 #13022)
+#13032 := (iff #13027 #13031)
+#13033 := [rewrite]: #13032
+#13028 := (iff #3314 #13027)
+#13025 := (iff #3313 #13022)
+#13018 := (implies #3028 #13015)
+#13023 := (iff #13018 #13022)
+#13024 := [rewrite]: #13023
+#13019 := (iff #3313 #13018)
+#13016 := (iff #3312 #13015)
+#13013 := (iff #3311 #13010)
+#13006 := (implies #11925 #13003)
+#13011 := (iff #13006 #13010)
+#13012 := [rewrite]: #13011
+#13007 := (iff #3311 #13006)
+#13004 := (iff #3310 #13003)
+#13001 := (iff #3309 #12998)
+#12994 := (implies #11934 #12991)
+#12999 := (iff #12994 #12998)
+#13000 := [rewrite]: #12999
+#12995 := (iff #3309 #12994)
+#12992 := (iff #3308 #12991)
+#12989 := (iff #3307 #12986)
+#12982 := (implies #11940 #12977)
+#12987 := (iff #12982 #12986)
+#12988 := [rewrite]: #12987
+#12983 := (iff #3307 #12982)
+#12980 := (iff #3306 #12977)
+#12973 := (implies #3042 #12968)
+#12978 := (iff #12973 #12977)
+#12979 := [rewrite]: #12978
+#12974 := (iff #3306 #12973)
+#12971 := (iff #3305 #12968)
+#12964 := (implies #3043 #12959)
+#12969 := (iff #12964 #12968)
+#12970 := [rewrite]: #12969
+#12965 := (iff #3305 #12964)
+#12962 := (iff #3304 #12959)
+#12955 := (implies #3044 #12950)
+#12960 := (iff #12955 #12959)
+#12961 := [rewrite]: #12960
+#12956 := (iff #3304 #12955)
+#12953 := (iff #3303 #12950)
+#12946 := (implies #3045 #12941)
+#12951 := (iff #12946 #12950)
+#12952 := [rewrite]: #12951
+#12947 := (iff #3303 #12946)
+#12944 := (iff #3302 #12941)
+#12937 := (implies #11948 #12934)
+#12942 := (iff #12937 #12941)
+#12943 := [rewrite]: #12942
+#12938 := (iff #3302 #12937)
+#12935 := (iff #3301 #12934)
+#12932 := (iff #3300 #12929)
+#12925 := (implies #3051 #12922)
+#12930 := (iff #12925 #12929)
+#12931 := [rewrite]: #12930
+#12926 := (iff #3300 #12925)
+#12923 := (iff #3299 #12922)
+#12920 := (iff #3298 #12917)
+#12913 := (implies #11963 #12910)
+#12918 := (iff #12913 #12917)
+#12919 := [rewrite]: #12918
+#12914 := (iff #3298 #12913)
+#12911 := (iff #3297 #12910)
+#12908 := (iff #3296 #12905)
+#12901 := (implies #11968 #12896)
+#12906 := (iff #12901 #12905)
+#12907 := [rewrite]: #12906
+#12902 := (iff #3296 #12901)
+#12899 := (iff #3295 #12896)
+#12892 := (implies #3064 #12887)
+#12897 := (iff #12892 #12896)
+#12898 := [rewrite]: #12897
+#12893 := (iff #3295 #12892)
+#12890 := (iff #3294 #12887)
+#12883 := (implies #3068 #12878)
+#12888 := (iff #12883 #12887)
+#12889 := [rewrite]: #12888
+#12884 := (iff #3294 #12883)
+#12881 := (iff #3293 #12878)
+#12874 := (implies #3072 #12869)
+#12879 := (iff #12874 #12878)
+#12880 := [rewrite]: #12879
+#12875 := (iff #3293 #12874)
+#12872 := (iff #3292 #12869)
+#12866 := (implies #11971 #12861)
+#12870 := (iff #12866 #12869)
+#12871 := [rewrite]: #12870
+#12867 := (iff #3292 #12866)
+#12864 := (iff #3291 #12861)
+#12857 := (implies #3075 #12852)
+#12862 := (iff #12857 #12861)
+#12863 := [rewrite]: #12862
+#12858 := (iff #3291 #12857)
+#12855 := (iff #3290 #12852)
+#12848 := (implies #11986 #12843)
+#12853 := (iff #12848 #12852)
+#12854 := [rewrite]: #12853
+#12849 := (iff #3290 #12848)
+#12846 := (iff #3289 #12843)
+#12839 := (implies #11992 #12834)
+#12844 := (iff #12839 #12843)
+#12845 := [rewrite]: #12844
+#12840 := (iff #3289 #12839)
+#12837 := (iff #3288 #12834)
+#12831 := (implies #11971 #12819)
+#12835 := (iff #12831 #12834)
+#12836 := [rewrite]: #12835
+#12832 := (iff #3288 #12831)
+#12829 := (iff #3287 #12819)
+#12824 := (and true #12819)
+#12827 := (iff #12824 #12819)
+#12828 := [rewrite]: #12827
+#12825 := (iff #3287 #12824)
+#12822 := (iff #3286 #12819)
+#12816 := (implies #11971 #12811)
+#12820 := (iff #12816 #12819)
+#12821 := [rewrite]: #12820
+#12817 := (iff #3286 #12816)
+#12814 := (iff #3285 #12811)
+#12808 := (implies #11971 #12803)
+#12812 := (iff #12808 #12811)
+#12813 := [rewrite]: #12812
+#12809 := (iff #3285 #12808)
+#12806 := (iff #3284 #12803)
+#12800 := (implies #11971 #12795)
+#12804 := (iff #12800 #12803)
+#12805 := [rewrite]: #12804
+#12801 := (iff #3284 #12800)
+#12798 := (iff #3283 #12795)
+#12792 := (implies #12260 #12787)
+#12796 := (iff #12792 #12795)
+#12797 := [rewrite]: #12796
+#12793 := (iff #3283 #12792)
+#12790 := (iff #3282 #12787)
+#12783 := (implies #12260 #12778)
+#12788 := (iff #12783 #12787)
+#12789 := [rewrite]: #12788
+#12784 := (iff #3282 #12783)
+#12781 := (iff #3281 #12778)
+#12775 := (implies #12003 #12770)
+#12779 := (iff #12775 #12778)
+#12780 := [rewrite]: #12779
+#12776 := (iff #3281 #12775)
+#12773 := (iff #3280 #12770)
+#12766 := (implies #3170 #12761)
+#12771 := (iff #12766 #12770)
+#12772 := [rewrite]: #12771
+#12767 := (iff #3280 #12766)
+#12764 := (iff #3279 #12761)
+#12757 := (implies #3171 #12752)
+#12762 := (iff #12757 #12761)
 #12763 := [rewrite]: #12762
-#12756 := (iff #2966 #12757)
-#12758 := [rewrite]: #12756
-#12813 := [monotonicity #12758 #12763]: #12812
-#12816 := [monotonicity #12813 #12810]: #12815
-#12818 := (iff #2964 #12817)
-#12770 := (iff #2963 #12767)
-#12771 := [rewrite]: #12770
-#12764 := (iff #2962 #12765)
-#12766 := [rewrite]: #12764
-#12819 := [monotonicity #12766 #12771]: #12818
-#12822 := [monotonicity #12819 #12816]: #12821
-#12827 := [trans #12822 #12825]: #12826
-#12830 := [monotonicity #12827]: #12829
-#13517 := [monotonicity #12830 #13514]: #13516
-#13520 := [monotonicity #13517]: #13519
-#12721 := (iff #3325 #12720)
-#12718 := (iff #3324 #12715)
-#12711 := (implies #11964 #12708)
-#12716 := (iff #12711 #12715)
-#12717 := [rewrite]: #12716
-#12712 := (iff #3324 #12711)
-#12709 := (iff #3323 #12708)
-#12706 := (iff #3322 #12703)
-#12699 := (implies #11967 #12696)
-#12704 := (iff #12699 #12703)
-#12705 := [rewrite]: #12704
-#12700 := (iff #3322 #12699)
-#12697 := (iff #3321 #12696)
-#12694 := (iff #3320 #12691)
-#12687 := (implies #11976 #12684)
-#12692 := (iff #12687 #12691)
-#12693 := [rewrite]: #12692
-#12688 := (iff #3320 #12687)
-#12685 := (iff #3319 #12684)
-#12682 := (iff #3318 #12679)
-#12675 := (implies #12005 #12672)
-#12680 := (iff #12675 #12679)
-#12681 := [rewrite]: #12680
-#12676 := (iff #3318 #12675)
-#12673 := (iff #3317 #12672)
-#12670 := (iff #3316 #12667)
-#12663 := (implies #3069 #12660)
-#12668 := (iff #12663 #12667)
-#12669 := [rewrite]: #12668
-#12664 := (iff #3316 #12663)
-#12661 := (iff #3315 #12660)
-#12658 := (iff #3314 #12655)
-#12651 := (implies #12012 #12648)
-#12656 := (iff #12651 #12655)
-#12657 := [rewrite]: #12656
-#12652 := (iff #3314 #12651)
-#12649 := (iff #3313 #12648)
-#12646 := (iff #3312 #12643)
-#12639 := (implies #12062 #12627)
-#12644 := (iff #12639 #12643)
-#12645 := [rewrite]: #12644
-#12640 := (iff #3312 #12639)
-#12637 := (iff #3311 #12627)
-#12632 := (and true #12627)
-#12635 := (iff #12632 #12627)
-#12636 := [rewrite]: #12635
-#12633 := (iff #3311 #12632)
-#12630 := (iff #3310 #12627)
-#12623 := (implies #12337 #12620)
-#12628 := (iff #12623 #12627)
+#12758 := (iff #3279 #12757)
+#12755 := (iff #3278 #12752)
+#12748 := (implies #3172 #12743)
+#12753 := (iff #12748 #12752)
+#12754 := [rewrite]: #12753
+#12749 := (iff #3278 #12748)
+#12746 := (iff #3277 #12743)
+#12739 := (implies #3173 #12734)
+#12744 := (iff #12739 #12743)
+#12745 := [rewrite]: #12744
+#12740 := (iff #3277 #12739)
+#12737 := (iff #3276 #12734)
+#12730 := (implies #3176 #12718)
+#12735 := (iff #12730 #12734)
+#12736 := [rewrite]: #12735
+#12731 := (iff #3276 #12730)
+#12728 := (iff #3275 #12718)
+#12723 := (implies true #12718)
+#12726 := (iff #12723 #12718)
+#12727 := [rewrite]: #12726
+#12724 := (iff #3275 #12723)
+#12721 := (iff #3274 #12718)
+#12715 := (implies #11971 #12712)
+#12719 := (iff #12715 #12718)
+#12720 := [rewrite]: #12719
+#12716 := (iff #3274 #12715)
+#12713 := (iff #3273 #12712)
+#12710 := (iff #3272 #12707)
+#12704 := (implies #11971 #12699)
+#12708 := (iff #12704 #12707)
+#12709 := [rewrite]: #12708
+#12705 := (iff #3272 #12704)
+#12702 := (iff #3271 #12699)
+#12695 := (implies #3268 #12690)
+#12700 := (iff #12695 #12699)
+#12701 := [rewrite]: #12700
+#12696 := (iff #3271 #12695)
+#12693 := (iff #3270 #12690)
+#12687 := (implies #11971 #12682)
+#12691 := (iff #12687 #12690)
+#12692 := [rewrite]: #12691
+#12688 := (iff #3270 #12687)
+#12685 := (iff #3269 #12682)
+#12679 := (implies #11971 #12133)
+#12683 := (iff #12679 #12682)
+#12684 := [rewrite]: #12683
+#12680 := (iff #3269 #12679)
+#12136 := (iff #3121 #12133)
+#12130 := (implies #11971 #12125)
+#12134 := (iff #12130 #12133)
+#12135 := [rewrite]: #12134
+#12131 := (iff #3121 #12130)
+#12128 := (iff #3120 #12125)
+#12122 := (implies #11971 #12119)
+#12126 := (iff #12122 #12125)
+#12127 := [rewrite]: #12126
+#12123 := (iff #3120 #12122)
+#12120 := (iff #3119 #12119)
+#12117 := (iff #3118 #12114)
+#12110 := (implies up_216 #12105)
+#12115 := (iff #12110 #12114)
+#12116 := [rewrite]: #12115
+#12111 := (iff #3118 #12110)
+#12108 := (iff #3117 #12105)
+#12102 := (implies #11971 #12097)
+#12106 := (iff #12102 #12105)
+#12107 := [rewrite]: #12106
+#12103 := (iff #3117 #12102)
+#12100 := (iff #3116 #12097)
+#12094 := (implies #11971 #12089)
+#12098 := (iff #12094 #12097)
+#12099 := [rewrite]: #12098
+#12095 := (iff #3116 #12094)
+#12092 := (iff #3115 #12089)
+#12085 := (implies #11971 #12080)
+#12090 := (iff #12085 #12089)
+#12091 := [rewrite]: #12090
+#12086 := (iff #3115 #12085)
+#12083 := (iff #3114 #12080)
+#12076 := (implies #12008 #12071)
+#12081 := (iff #12076 #12080)
+#12082 := [rewrite]: #12081
+#12077 := (iff #3114 #12076)
+#12074 := (iff #3113 #12071)
+#12067 := (implies #12011 #12062)
+#12072 := (iff #12067 #12071)
+#12073 := [rewrite]: #12072
+#12068 := (iff #3113 #12067)
+#12065 := (iff #3112 #12062)
+#12058 := (implies #12014 #12053)
+#12063 := (iff #12058 #12062)
+#12064 := [rewrite]: #12063
+#12059 := (iff #3112 #12058)
+#12056 := (iff #3111 #12053)
+#12049 := (implies #12017 #12046)
+#12054 := (iff #12049 #12053)
+#12055 := [rewrite]: #12054
+#12050 := (iff #3111 #12049)
+#12047 := (iff #3110 #12046)
+#12044 := (iff #3109 #12041)
+#12037 := (implies #12032 #3107)
+#12042 := (iff #12037 #12041)
+#12043 := [rewrite]: #12042
+#12038 := (iff #3109 #12037)
+#12035 := (iff #3108 #3107)
+#12036 := [rewrite]: #12035
+#12033 := (iff #3102 #12032)
+#12030 := (iff #3101 #12027)
+#12024 := (implies #412 #12021)
+#12028 := (iff #12024 #12027)
+#12029 := [rewrite]: #12028
+#12025 := (iff #3101 #12024)
+#12022 := (iff #3100 #12021)
+#12023 := [rewrite]: #12022
+#12026 := [monotonicity #12023]: #12025
+#12031 := [trans #12026 #12029]: #12030
+#12034 := [quant-intro #12031]: #12033
+#12039 := [monotonicity #12034 #12036]: #12038
+#12045 := [trans #12039 #12043]: #12044
+#12048 := [monotonicity #12034 #12045]: #12047
+#12018 := (iff #3097 #12017)
+#12019 := [rewrite]: #12018
+#12051 := [monotonicity #12019 #12048]: #12050
+#12057 := [trans #12051 #12055]: #12056
+#12015 := (iff #3095 #12014)
+#12016 := [rewrite]: #12015
+#12060 := [monotonicity #12016 #12057]: #12059
+#12066 := [trans #12060 #12064]: #12065
+#12012 := (iff #3093 #12011)
+#12013 := [rewrite]: #12012
+#12069 := [monotonicity #12013 #12066]: #12068
+#12075 := [trans #12069 #12073]: #12074
+#12009 := (iff #3091 #12008)
+#12010 := [rewrite]: #12009
+#12078 := [monotonicity #12010 #12075]: #12077
+#12084 := [trans #12078 #12082]: #12083
+#11972 := (iff #3074 #11971)
+#11973 := [rewrite]: #11972
+#12087 := [monotonicity #11973 #12084]: #12086
+#12093 := [trans #12087 #12091]: #12092
+#12096 := [monotonicity #11973 #12093]: #12095
+#12101 := [trans #12096 #12099]: #12100
+#12104 := [monotonicity #11973 #12101]: #12103
+#12109 := [trans #12104 #12107]: #12108
+#12112 := [monotonicity #12109]: #12111
+#12118 := [trans #12112 #12116]: #12117
+#12121 := [monotonicity #12118]: #12120
+#12124 := [monotonicity #11973 #12121]: #12123
+#12129 := [trans #12124 #12127]: #12128
+#12132 := [monotonicity #11973 #12129]: #12131
+#12137 := [trans #12132 #12135]: #12136
+#12681 := [monotonicity #11973 #12137]: #12680
+#12686 := [trans #12681 #12684]: #12685
+#12689 := [monotonicity #11973 #12686]: #12688
+#12694 := [trans #12689 #12692]: #12693
+#12697 := [monotonicity #12694]: #12696
+#12703 := [trans #12697 #12701]: #12702
+#12706 := [monotonicity #11973 #12703]: #12705
+#12711 := [trans #12706 #12709]: #12710
+#12677 := (iff #3267 #12674)
+#12671 := (implies #11971 #12666)
+#12675 := (iff #12671 #12674)
+#12676 := [rewrite]: #12675
+#12672 := (iff #3267 #12671)
+#12669 := (iff #3266 #12666)
+#12662 := (implies #3180 #12657)
+#12667 := (iff #12662 #12666)
+#12668 := [rewrite]: #12667
+#12663 := (iff #3266 #12662)
+#12660 := (iff #3265 #12657)
+#12654 := (implies #11971 #12649)
+#12658 := (iff #12654 #12657)
+#12659 := [rewrite]: #12658
+#12655 := (iff #3265 #12654)
+#12652 := (iff #3264 #12649)
+#12646 := (implies #11971 #12643)
+#12650 := (iff #12646 #12649)
+#12651 := [rewrite]: #12650
+#12647 := (iff #3264 #12646)
+#12644 := (iff #3263 #12643)
+#12641 := (iff #3262 #12638)
+#12635 := (implies #12299 #12632)
+#12639 := (iff #12635 #12638)
+#12640 := [rewrite]: #12639
+#12636 := (iff #3262 #12635)
+#12633 := (iff #3261 #12632)
+#12630 := (iff #3260 #12627)
+#12624 := (implies #12305 #12619)
+#12628 := (iff #12624 #12627)
 #12629 := [rewrite]: #12628
-#12624 := (iff #3310 #12623)
-#12621 := (iff #3309 #12620)
-#12618 := (iff #3308 #12615)
-#12611 := (implies #12608 #12174)
-#12616 := (iff #12611 #12615)
-#12617 := [rewrite]: #12616
-#12612 := (iff #3308 #12611)
-#12175 := (iff #3150 #12174)
-#12172 := (iff #3149 #12169)
-#12165 := (implies #12143 #12162)
-#12170 := (iff #12165 #12169)
-#12171 := [rewrite]: #12170
-#12166 := (iff #3149 #12165)
-#12163 := (iff #3148 #12162)
-#12160 := (iff #3147 #12157)
-#12153 := (implies #12150 #3146)
-#12158 := (iff #12153 #12157)
-#12159 := [rewrite]: #12158
-#12154 := (iff #3147 #12153)
-#12151 := (iff #3141 #12150)
-#12148 := (iff #3140 #12147)
-#12149 := [rewrite]: #12148
-#12152 := [quant-intro #12149]: #12151
-#12155 := [monotonicity #12152]: #12154
-#12161 := [trans #12155 #12159]: #12160
-#12164 := [monotonicity #12152 #12161]: #12163
-#12144 := (iff #3136 #12143)
-#12141 := (iff #3135 #12140)
-#12138 := (iff #3134 #12137)
-#12135 := (iff #3133 #12134)
-#12132 := (iff #3132 #12131)
-#12129 := (iff #3131 #12128)
-#12126 := (iff #3130 #12125)
-#12123 := (iff #3129 #12122)
-#12124 := [rewrite]: #12123
-#12120 := (iff #3127 #12119)
-#12121 := [rewrite]: #12120
-#12127 := [monotonicity #12121 #12124]: #12126
-#12117 := (iff #3125 #12116)
-#12118 := [rewrite]: #12117
-#12130 := [monotonicity #12118 #12127]: #12129
-#12114 := (iff #3123 #12113)
-#12115 := [rewrite]: #12114
-#12133 := [monotonicity #12115 #12130]: #12132
-#12021 := (iff #3092 #12020)
-#12022 := [rewrite]: #12021
-#12136 := [monotonicity #12022 #12133]: #12135
-#12139 := [monotonicity #12022 #12136]: #12138
-#12142 := [monotonicity #12022 #12139]: #12141
-#12145 := [monotonicity #12142]: #12144
-#12167 := [monotonicity #12145 #12164]: #12166
-#12173 := [trans #12167 #12171]: #12172
-#12176 := [monotonicity #12173]: #12175
-#12609 := (iff #3307 #12608)
-#12606 := (iff #3306 #12605)
-#12603 := (iff #3305 #12020)
-#12078 := (and #12020 #12020)
-#12081 := (iff #12078 #12020)
-#12082 := [rewrite]: #12081
-#12601 := (iff #3305 #12078)
-#12599 := (iff #3304 #12020)
-#12597 := (iff #3304 #12078)
-#12083 := (iff #3116 #12020)
-#12079 := (iff #3116 #12078)
-#12080 := [monotonicity #12022 #12022]: #12079
-#12084 := [trans #12080 #12082]: #12083
-#12598 := [monotonicity #12022 #12084]: #12597
-#12600 := [trans #12598 #12082]: #12599
-#12602 := [monotonicity #12022 #12600]: #12601
-#12604 := [trans #12602 #12082]: #12603
-#12607 := [monotonicity #12604]: #12606
-#12610 := [monotonicity #12022 #12607]: #12609
-#12613 := [monotonicity #12610 #12176]: #12612
-#12619 := [trans #12613 #12617]: #12618
-#12595 := (iff #3302 #12592)
-#12588 := (implies #12343 #12585)
-#12593 := (iff #12588 #12592)
-#12594 := [rewrite]: #12593
-#12589 := (iff #3302 #12588)
-#12586 := (iff #3301 #12585)
-#12583 := (iff #3300 #12580)
-#12577 := (implies #12352 #12574)
-#12581 := (iff #12577 #12580)
-#12582 := [rewrite]: #12581
-#12578 := (iff #3300 #12577)
-#12575 := (iff #3299 #12574)
-#12572 := (iff #3298 #12569)
-#12565 := (implies #12364 #12562)
-#12570 := (iff #12565 #12569)
-#12571 := [rewrite]: #12570
-#12566 := (iff #3298 #12565)
-#12563 := (iff #3297 #12562)
-#12560 := (iff #3296 #12557)
-#12553 := (implies #12550 #12485)
-#12558 := (iff #12553 #12557)
-#12559 := [rewrite]: #12558
-#12554 := (iff #3296 #12553)
-#12486 := (iff #3280 #12485)
-#12483 := (iff #3279 #12480)
-#12476 := (implies #12436 #12473)
-#12481 := (iff #12476 #12480)
-#12482 := [rewrite]: #12481
-#12477 := (iff #3279 #12476)
-#12474 := (iff #3278 #12473)
-#12471 := (iff #3277 #12468)
-#12464 := (implies #3264 #12461)
+#12625 := (iff #3260 #12624)
+#12622 := (iff #3259 #12619)
+#12616 := (implies #11971 #12613)
+#12620 := (iff #12616 #12619)
+#12621 := [rewrite]: #12620
+#12617 := (iff #3259 #12616)
+#12614 := (iff #3258 #12613)
+#12611 := (iff #3257 #12608)
+#12605 := (implies #11971 #12600)
+#12609 := (iff #12605 #12608)
+#12610 := [rewrite]: #12609
+#12606 := (iff #3257 #12605)
+#12603 := (iff #3256 #12600)
+#12596 := (implies #3248 #12591)
+#12601 := (iff #12596 #12600)
+#12602 := [rewrite]: #12601
+#12597 := (iff #3256 #12596)
+#12594 := (iff #3255 #12591)
+#12588 := (implies #11971 #12583)
+#12592 := (iff #12588 #12591)
+#12593 := [rewrite]: #12592
+#12589 := (iff #3255 #12588)
+#12586 := (iff #3254 #12583)
+#12580 := (implies #11971 #12575)
+#12584 := (iff #12580 #12583)
+#12585 := [rewrite]: #12584
+#12581 := (iff #3254 #12580)
+#12578 := (iff #3253 #12575)
+#12572 := (implies #11971 #12567)
+#12576 := (iff #12572 #12575)
+#12577 := [rewrite]: #12576
+#12573 := (iff #3253 #12572)
+#12570 := (iff #3252 #12567)
+#12563 := (implies #12548 #12558)
+#12568 := (iff #12563 #12567)
+#12569 := [rewrite]: #12568
+#12564 := (iff #3252 #12563)
+#12561 := (iff #3251 #12558)
+#12554 := (implies #12551 #12432)
+#12559 := (iff #12554 #12558)
+#12560 := [rewrite]: #12559
+#12555 := (iff #3251 #12554)
+#12435 := (iff #3233 #12432)
+#12428 := (implies #3202 #12425)
+#12433 := (iff #12428 #12432)
+#12434 := [rewrite]: #12433
+#12429 := (iff #3233 #12428)
+#12426 := (iff #3232 #12425)
+#12423 := (iff #3231 #12420)
+#12416 := (implies #12328 #12411)
+#12421 := (iff #12416 #12420)
+#12422 := [rewrite]: #12421
+#12417 := (iff #3231 #12416)
+#12414 := (iff #3230 #12411)
+#12407 := (implies #12331 #12402)
+#12412 := (iff #12407 #12411)
+#12413 := [rewrite]: #12412
+#12408 := (iff #3230 #12407)
+#12405 := (iff #3229 #12402)
+#12398 := (implies #3209 #12393)
+#12403 := (iff #12398 #12402)
+#12404 := [rewrite]: #12403
+#12399 := (iff #3229 #12398)
+#12396 := (iff #3228 #12393)
+#12389 := (implies #12334 #12386)
+#12394 := (iff #12389 #12393)
+#12395 := [rewrite]: #12394
+#12390 := (iff #3228 #12389)
+#12387 := (iff #3227 #12386)
+#12384 := (iff #3226 #12381)
+#12377 := (implies #3212 #12374)
+#12382 := (iff #12377 #12381)
+#12383 := [rewrite]: #12382
+#12378 := (iff #3226 #12377)
+#12375 := (iff #3225 #12374)
+#12372 := (iff #3224 #12369)
+#12365 := (implies #12349 #12355)
+#12370 := (iff #12365 #12369)
+#12371 := [rewrite]: #12370
+#12366 := (iff #3224 #12365)
+#12363 := (iff #3223 #12355)
+#12358 := (and #12355 true)
+#12361 := (iff #12358 #12355)
+#12362 := [rewrite]: #12361
+#12359 := (iff #3223 #12358)
+#12356 := (iff #3222 #12355)
+#12353 := (iff #3221 #12352)
+#12354 := [rewrite]: #12353
+#12357 := [monotonicity #12354]: #12356
+#12360 := [monotonicity #12357]: #12359
+#12364 := [trans #12360 #12362]: #12363
+#12350 := (iff #3217 #12349)
+#12347 := (iff #3216 #12344)
+#12341 := (implies #412 #12338)
+#12345 := (iff #12341 #12344)
+#12346 := [rewrite]: #12345
+#12342 := (iff #3216 #12341)
+#12339 := (iff #3215 #12338)
+#12340 := [rewrite]: #12339
+#12343 := [monotonicity #12340]: #12342
+#12348 := [trans #12343 #12346]: #12347
+#12351 := [quant-intro #12348]: #12350
+#12367 := [monotonicity #12351 #12364]: #12366
+#12373 := [trans #12367 #12371]: #12372
+#12376 := [monotonicity #12351 #12373]: #12375
+#12379 := [monotonicity #12376]: #12378
+#12385 := [trans #12379 #12383]: #12384
+#12388 := [monotonicity #12385]: #12387
+#12335 := (iff #3211 #12334)
+#12336 := [rewrite]: #12335
+#12391 := [monotonicity #12336 #12388]: #12390
+#12397 := [trans #12391 #12395]: #12396
+#12400 := [monotonicity #12397]: #12399
+#12406 := [trans #12400 #12404]: #12405
+#12332 := (iff #3208 #12331)
+#12320 := (= #3203 #12319)
+#12321 := [rewrite]: #12320
+#12333 := [monotonicity #12321]: #12332
+#12409 := [monotonicity #12333 #12406]: #12408
+#12415 := [trans #12409 #12413]: #12414
+#12329 := (iff #3206 #12328)
+#12326 := (iff #3205 #12325)
+#12327 := [monotonicity #12321]: #12326
+#12323 := (iff #3204 #12322)
+#12324 := [monotonicity #12321]: #12323
+#12330 := [monotonicity #12324 #12327]: #12329
+#12418 := [monotonicity #12330 #12415]: #12417
+#12424 := [trans #12418 #12422]: #12423
+#12427 := [monotonicity #12330 #12424]: #12426
+#12430 := [monotonicity #12427]: #12429
+#12436 := [trans #12430 #12434]: #12435
+#12552 := (iff #3250 #12551)
+#12553 := [rewrite]: #12552
+#12556 := [monotonicity #12553 #12436]: #12555
+#12562 := [trans #12556 #12560]: #12561
+#12549 := (iff #3249 #12548)
+#12550 := [rewrite]: #12549
+#12565 := [monotonicity #12550 #12562]: #12564
+#12571 := [trans #12565 #12569]: #12570
+#12574 := [monotonicity #11973 #12571]: #12573
+#12579 := [trans #12574 #12577]: #12578
+#12582 := [monotonicity #11973 #12579]: #12581
+#12587 := [trans #12582 #12585]: #12586
+#12590 := [monotonicity #11973 #12587]: #12589
+#12595 := [trans #12590 #12593]: #12594
+#12598 := [monotonicity #12595]: #12597
+#12604 := [trans #12598 #12602]: #12603
+#12607 := [monotonicity #11973 #12604]: #12606
+#12612 := [trans #12607 #12610]: #12611
+#12546 := (iff #3247 #12543)
+#12540 := (implies #11971 #12535)
+#12544 := (iff #12540 #12543)
+#12545 := [rewrite]: #12544
+#12541 := (iff #3247 #12540)
+#12538 := (iff #3246 #12535)
+#12531 := (implies #3191 #12526)
+#12536 := (iff #12531 #12535)
+#12537 := [rewrite]: #12536
+#12532 := (iff #3246 #12531)
+#12529 := (iff #3245 #12526)
+#12523 := (implies #11971 #12518)
+#12527 := (iff #12523 #12526)
+#12528 := [rewrite]: #12527
+#12524 := (iff #3245 #12523)
+#12521 := (iff #3244 #12518)
+#12515 := (implies #11971 #12512)
+#12519 := (iff #12515 #12518)
+#12520 := [rewrite]: #12519
+#12516 := (iff #3244 #12515)
+#12513 := (iff #3243 #12512)
+#12510 := (iff #3242 #12507)
+#12503 := (implies #12299 #12500)
+#12508 := (iff #12503 #12507)
+#12509 := [rewrite]: #12508
+#12504 := (iff #3242 #12503)
+#12501 := (iff #3241 #12500)
+#12498 := (iff #3240 #12495)
+#12491 := (implies #12305 #12486)
+#12496 := (iff #12491 #12495)
+#12497 := [rewrite]: #12496
+#12492 := (iff #3240 #12491)
+#12489 := (iff #3239 #12486)
+#12482 := (implies #12308 #12477)
+#12487 := (iff #12482 #12486)
+#12488 := [rewrite]: #12487
+#12483 := (iff #3239 #12482)
+#12480 := (iff #3238 #12477)
+#12473 := (implies #3194 #12468)
+#12478 := (iff #12473 #12477)
+#12479 := [rewrite]: #12478
+#12474 := (iff #3238 #12473)
+#12471 := (iff #3237 #12468)
+#12464 := (implies #3195 #12459)
 #12469 := (iff #12464 #12468)
 #12470 := [rewrite]: #12469
-#12465 := (iff #3277 #12464)
-#12462 := (iff #3276 #12461)
-#12459 := (iff #3275 #12456)
-#12452 := (implies #12443 #12449)
-#12457 := (iff #12452 #12456)
-#12458 := [rewrite]: #12457
-#12453 := (iff #3275 #12452)
-#12450 := (iff #3274 #12449)
-#12447 := (iff #3273 #12446)
-#12448 := [rewrite]: #12447
-#12451 := [monotonicity #12448]: #12450
-#12444 := (iff #3269 #12443)
-#12441 := (iff #3268 #12440)
-#12442 := [rewrite]: #12441
-#12445 := [quant-intro #12442]: #12444
-#12454 := [monotonicity #12445 #12451]: #12453
-#12460 := [trans #12454 #12458]: #12459
-#12463 := [monotonicity #12445 #12460]: #12462
+#12465 := (iff #3237 #12464)
+#12462 := (iff #3236 #12459)
+#12455 := (implies #3073 #12450)
+#12460 := (iff #12455 #12459)
+#12461 := [rewrite]: #12460
+#12456 := (iff #3236 #12455)
+#12453 := (iff #3235 #12450)
+#12446 := (implies #12313 #12441)
+#12451 := (iff #12446 #12450)
+#12452 := [rewrite]: #12451
+#12447 := (iff #3235 #12446)
+#12444 := (iff #3234 #12441)
+#12437 := (implies #12316 #12432)
+#12442 := (iff #12437 #12441)
+#12443 := [rewrite]: #12442
+#12438 := (iff #3234 #12437)
+#12317 := (iff #3200 #12316)
+#12318 := [rewrite]: #12317
+#12439 := [monotonicity #12318 #12436]: #12438
+#12445 := [trans #12439 #12443]: #12444
+#12314 := (iff #3198 #12313)
+#12315 := [rewrite]: #12314
+#12448 := [monotonicity #12315 #12445]: #12447
+#12454 := [trans #12448 #12452]: #12453
+#12311 := (iff #3196 #3073)
+#12312 := [rewrite]: #12311
+#12457 := [monotonicity #12312 #12454]: #12456
+#12463 := [trans #12457 #12461]: #12462
 #12466 := [monotonicity #12463]: #12465
 #12472 := [trans #12466 #12470]: #12471
 #12475 := [monotonicity #12472]: #12474
-#12437 := (iff #3263 #12436)
-#12434 := (iff #3262 #12433)
-#12431 := (iff #3261 #12430)
-#12428 := (iff #3260 #12427)
-#12429 := [rewrite]: #12428
-#12432 := [monotonicity #12429]: #12431
-#12425 := (iff #3257 #12424)
-#12413 := (= #3252 #12412)
-#12414 := [rewrite]: #12413
-#12426 := [monotonicity #12414]: #12425
-#12435 := [monotonicity #12426 #12432]: #12434
-#12422 := (iff #3255 #12421)
-#12419 := (iff #3254 #12418)
-#12420 := [monotonicity #12414]: #12419
-#12416 := (iff #3253 #12415)
-#12417 := [monotonicity #12414]: #12416
-#12423 := [monotonicity #12417 #12420]: #12422
-#12438 := [monotonicity #12423 #12435]: #12437
-#12478 := [monotonicity #12438 #12475]: #12477
-#12484 := [trans #12478 #12482]: #12483
-#12487 := [monotonicity #12423 #12484]: #12486
-#12551 := (iff #3295 #12550)
-#12548 := (iff #3294 #12547)
-#12545 := (iff #3293 #12544)
-#12542 := (iff #3292 #12541)
-#12539 := (iff #3291 #12538)
-#12536 := (iff #3290 #12535)
-#12533 := (iff #3289 #12530)
-#12527 := (and #12524 #3244)
-#12531 := (iff #12527 #12530)
-#12532 := [rewrite]: #12531
-#12528 := (iff #3289 #12527)
-#12525 := (iff #3288 #12524)
-#12526 := [rewrite]: #12525
-#12529 := [monotonicity #12526]: #12528
-#12534 := [trans #12529 #12532]: #12533
-#12522 := (iff #3287 #12521)
-#12523 := [rewrite]: #12522
-#12537 := [monotonicity #12523 #12534]: #12536
-#12540 := [monotonicity #12022 #12537]: #12539
-#12543 := [monotonicity #12022 #12540]: #12542
-#12546 := [monotonicity #12022 #12543]: #12545
-#12549 := [monotonicity #12546]: #12548
-#12552 := [monotonicity #12022 #12549]: #12551
-#12555 := [monotonicity #12552 #12487]: #12554
-#12561 := [trans #12555 #12559]: #12560
-#12519 := (iff #3285 #12516)
-#12512 := (implies #12372 #12509)
-#12517 := (iff #12512 #12516)
-#12518 := [rewrite]: #12517
-#12513 := (iff #3285 #12512)
-#12510 := (iff #3284 #12509)
-#12507 := (iff #3283 #12504)
-#12500 := (implies #12352 #12497)
-#12505 := (iff #12500 #12504)
-#12506 := [rewrite]: #12505
-#12501 := (iff #3283 #12500)
-#12498 := (iff #3282 #12497)
-#12495 := (iff #3281 #12492)
-#12488 := (implies #12409 #12485)
-#12493 := (iff #12488 #12492)
-#12494 := [rewrite]: #12493
-#12489 := (iff #3281 #12488)
-#12410 := (iff #3251 #12409)
-#12407 := (iff #3250 #12406)
-#12404 := (iff #3249 #12403)
-#12401 := (iff #3248 #12400)
-#12398 := (iff #3247 #12397)
-#12395 := (iff #3246 #12394)
-#12392 := (iff #3245 #12389)
-#12386 := (and #12383 #3244)
-#12390 := (iff #12386 #12389)
-#12391 := [rewrite]: #12390
-#12387 := (iff #3245 #12386)
-#12384 := (iff #3242 #12383)
-#12385 := [rewrite]: #12384
-#12388 := [monotonicity #12385]: #12387
-#12393 := [trans #12388 #12391]: #12392
-#12381 := (iff #3240 #12380)
-#12382 := [rewrite]: #12381
-#12396 := [monotonicity #12382 #12393]: #12395
-#12378 := (iff #3238 #3091)
-#12379 := [rewrite]: #12378
-#12399 := [monotonicity #12379 #12396]: #12398
-#12402 := [monotonicity #12399]: #12401
-#12405 := [monotonicity #12402]: #12404
-#12376 := (iff #3235 #12375)
-#12377 := [rewrite]: #12376
-#12408 := [monotonicity #12377 #12405]: #12407
-#12359 := (iff #3228 #12358)
-#12356 := (iff #3227 #12355)
-#12357 := [rewrite]: #12356
-#12347 := (iff #3222 #12346)
-#12348 := [rewrite]: #12347
-#12360 := [monotonicity #12348 #12357]: #12359
-#12411 := [monotonicity #12360 #12408]: #12410
-#12490 := [monotonicity #12411 #12487]: #12489
-#12496 := [trans #12490 #12494]: #12495
-#12499 := [monotonicity #12360 #12496]: #12498
-#12353 := (iff #3225 #12352)
-#12350 := (iff #3224 #12349)
-#12351 := [rewrite]: #12350
-#12354 := [monotonicity #12348 #12351]: #12353
-#12502 := [monotonicity #12354 #12499]: #12501
-#12508 := [trans #12502 #12506]: #12507
-#12511 := [monotonicity #12354 #12508]: #12510
-#12373 := (iff #3233 #12372)
-#12370 := (iff #3232 #12369)
-#12371 := [monotonicity #12084]: #12370
-#12374 := [monotonicity #12022 #12371]: #12373
-#12514 := [monotonicity #12374 #12511]: #12513
-#12520 := [trans #12514 #12518]: #12519
-#12564 := [monotonicity #12520 #12561]: #12563
-#12367 := (iff #3229 #12364)
-#12361 := (and #12358 #12020)
-#12365 := (iff #12361 #12364)
-#12366 := [rewrite]: #12365
-#12362 := (iff #3229 #12361)
-#12363 := [monotonicity #12360 #12022]: #12362
-#12368 := [trans #12363 #12366]: #12367
-#12567 := [monotonicity #12368 #12564]: #12566
-#12573 := [trans #12567 #12571]: #12572
-#12576 := [monotonicity #12360 #12573]: #12575
-#12579 := [monotonicity #12354 #12576]: #12578
-#12584 := [trans #12579 #12582]: #12583
-#12587 := [monotonicity #12354 #12584]: #12586
-#12344 := (iff #3219 #12343)
-#12341 := (iff #3218 #12340)
-#12342 := [monotonicity #12084]: #12341
-#12345 := [monotonicity #12022 #12342]: #12344
-#12590 := [monotonicity #12345 #12587]: #12589
-#12596 := [trans #12590 #12594]: #12595
-#12622 := [monotonicity #12596 #12619]: #12621
-#12338 := (iff #3216 #12337)
-#12335 := (iff #3215 #12334)
-#12332 := (iff #3214 #12331)
-#12329 := (iff #3213 #12328)
-#12326 := (iff #3212 #12325)
-#12323 := (iff #3211 #12322)
-#12320 := (iff #3210 #12319)
-#12317 := (iff #3209 #12316)
-#12314 := (iff #3208 #12313)
-#12311 := (iff #3207 #12310)
-#12308 := (iff #3206 #12307)
-#12305 := (iff #3205 #12020)
-#12300 := (and true #12020)
-#12303 := (iff #12300 #12020)
+#12481 := [trans #12475 #12479]: #12480
+#12309 := (iff #3193 #12308)
+#12310 := [rewrite]: #12309
+#12484 := [monotonicity #12310 #12481]: #12483
+#12490 := [trans #12484 #12488]: #12489
+#12306 := (iff #3189 #12305)
+#12303 := (iff #3188 #12302)
 #12304 := [rewrite]: #12303
-#12301 := (iff #3205 #12300)
-#12298 := (iff #3204 true)
-#12296 := (iff #12293 true)
-#12297 := [rewrite]: #12296
-#12294 := (iff #3204 #12293)
-#12291 := (iff #3203 true)
-#12292 := [rewrite]: #12291
-#12289 := (iff #3202 true)
+#12294 := (iff #3183 #12293)
+#12295 := [rewrite]: #12294
+#12307 := [monotonicity #12295 #12304]: #12306
+#12493 := [monotonicity #12307 #12490]: #12492
+#12499 := [trans #12493 #12497]: #12498
+#12502 := [monotonicity #12307 #12499]: #12501
+#12300 := (iff #3186 #12299)
+#12297 := (iff #3185 #12296)
+#12298 := [rewrite]: #12297
+#12301 := [monotonicity #12295 #12298]: #12300
+#12505 := [monotonicity #12301 #12502]: #12504
+#12511 := [trans #12505 #12509]: #12510
+#12514 := [monotonicity #12301 #12511]: #12513
+#12517 := [monotonicity #11973 #12514]: #12516
+#12522 := [trans #12517 #12520]: #12521
+#12525 := [monotonicity #11973 #12522]: #12524
+#12530 := [trans #12525 #12528]: #12529
+#12533 := [monotonicity #12530]: #12532
+#12539 := [trans #12533 #12537]: #12538
+#12542 := [monotonicity #11973 #12539]: #12541
+#12547 := [trans #12542 #12545]: #12546
+#12615 := [monotonicity #12547 #12612]: #12614
+#12618 := [monotonicity #11973 #12615]: #12617
+#12623 := [trans #12618 #12621]: #12622
+#12626 := [monotonicity #12307 #12623]: #12625
+#12631 := [trans #12626 #12629]: #12630
+#12634 := [monotonicity #12307 #12631]: #12633
+#12637 := [monotonicity #12301 #12634]: #12636
+#12642 := [trans #12637 #12640]: #12641
+#12645 := [monotonicity #12301 #12642]: #12644
+#12648 := [monotonicity #11973 #12645]: #12647
+#12653 := [trans #12648 #12651]: #12652
+#12656 := [monotonicity #11973 #12653]: #12655
+#12661 := [trans #12656 #12659]: #12660
+#12664 := [monotonicity #12661]: #12663
+#12670 := [trans #12664 #12668]: #12669
+#12673 := [monotonicity #11973 #12670]: #12672
+#12678 := [trans #12673 #12676]: #12677
+#12714 := [monotonicity #12678 #12711]: #12713
+#12717 := [monotonicity #11973 #12714]: #12716
+#12722 := [trans #12717 #12720]: #12721
+#12291 := (iff #3179 true)
+#12289 := (iff #12286 true)
 #12290 := [rewrite]: #12289
-#12295 := [monotonicity #12290 #12292]: #12294
-#12299 := [trans #12295 #12297]: #12298
-#12302 := [monotonicity #12299 #12022]: #12301
-#12306 := [trans #12302 #12304]: #12305
-#12309 := [monotonicity #12306]: #12308
-#12312 := [monotonicity #12309]: #12311
-#12315 := [monotonicity #12312]: #12314
-#12318 := [monotonicity #12315]: #12317
-#12321 := [monotonicity #12318]: #12320
-#12076 := (iff #3115 #12073)
-#12070 := (and #12067 #11903)
-#12074 := (iff #12070 #12073)
-#12075 := [rewrite]: #12074
-#12071 := (iff #3115 #12070)
-#11904 := (iff #3005 #11903)
-#11905 := [rewrite]: #11904
-#12068 := (iff #3114 #12067)
-#12069 := [rewrite]: #12068
-#12072 := [monotonicity #12069 #11905]: #12071
-#12077 := [trans #12072 #12075]: #12076
-#12324 := [monotonicity #12077 #12321]: #12323
-#12268 := (iff #3190 #12267)
-#12265 := (iff #3189 #12264)
-#12262 := (iff #3188 #12261)
-#12263 := [rewrite]: #12262
-#12266 := [monotonicity #12263]: #12265
-#12269 := [monotonicity #12266]: #12268
-#12327 := [monotonicity #12269 #12324]: #12326
-#12287 := (iff #3194 #12267)
-#12270 := (and true #12267)
-#12273 := (iff #12270 #12267)
-#12274 := [rewrite]: #12273
-#12285 := (iff #3194 #12270)
-#12283 := (iff #3193 #12267)
-#12281 := (iff #3193 #12270)
-#12279 := (iff #3192 #12267)
-#12277 := (iff #3192 #12270)
-#12275 := (iff #3191 #12267)
-#12271 := (iff #3191 #12270)
-#12259 := (iff #3181 true)
-#12254 := (forall (vars (?x782 T5)) (:pat #3177) true)
-#12257 := (iff #12254 true)
-#12258 := [elim-unused]: #12257
-#12255 := (iff #3181 #12254)
-#12252 := (iff #3180 true)
-#12204 := (= uf_9 #3165)
-#12216 := (implies #12204 #12204)
-#12219 := (iff #12216 true)
-#12220 := [rewrite]: #12219
-#12250 := (iff #3180 #12216)
-#12248 := (iff #3179 #12204)
-#12209 := (and true #12204)
-#12212 := (iff #12209 #12204)
+#12287 := (iff #3179 #12286)
+#12284 := (iff #3178 true)
+#12285 := [rewrite]: #12284
+#12282 := (iff #3177 true)
+#12283 := [rewrite]: #12282
+#12288 := [monotonicity #12283 #12285]: #12287
+#12292 := [trans #12288 #12290]: #12291
+#12725 := [monotonicity #12292 #12722]: #12724
+#12729 := [trans #12725 #12727]: #12728
+#12732 := [monotonicity #12729]: #12731
+#12738 := [trans #12732 #12736]: #12737
+#12741 := [monotonicity #12738]: #12740
+#12747 := [trans #12741 #12745]: #12746
+#12750 := [monotonicity #12747]: #12749
+#12756 := [trans #12750 #12754]: #12755
+#12759 := [monotonicity #12756]: #12758
+#12765 := [trans #12759 #12763]: #12764
+#12768 := [monotonicity #12765]: #12767
+#12774 := [trans #12768 #12772]: #12773
+#12006 := (iff #3089 #12003)
+#12000 := (and #11997 #11905)
+#12004 := (iff #12000 #12003)
+#12005 := [rewrite]: #12004
+#12001 := (iff #3089 #12000)
+#11906 := (iff #3005 #11905)
+#11907 := [rewrite]: #11906
+#11998 := (iff #3088 #11997)
+#11999 := [rewrite]: #11998
+#12002 := [monotonicity #11999 #11907]: #12001
+#12007 := [trans #12002 #12005]: #12006
+#12777 := [monotonicity #12007 #12774]: #12776
+#12782 := [trans #12777 #12780]: #12781
+#12261 := (iff #3165 #12260)
+#12258 := (iff #3164 #12257)
+#12255 := (iff #3163 #12254)
+#12256 := [rewrite]: #12255
+#12259 := [monotonicity #12256]: #12258
+#12262 := [monotonicity #12259]: #12261
+#12785 := [monotonicity #12262 #12782]: #12784
+#12791 := [trans #12785 #12789]: #12790
+#12280 := (iff #3169 #12260)
+#12263 := (and true #12260)
+#12266 := (iff #12263 #12260)
+#12267 := [rewrite]: #12266
+#12278 := (iff #3169 #12263)
+#12276 := (iff #3168 #12260)
+#12274 := (iff #3168 #12263)
+#12272 := (iff #3167 #12260)
+#12270 := (iff #3167 #12263)
+#12268 := (iff #3166 #12260)
+#12264 := (iff #3166 #12263)
+#12252 := (iff #3156 true)
+#12247 := (forall (vars (?x782 T5)) (:pat #3152) true)
+#12250 := (iff #12247 true)
+#12251 := [elim-unused]: #12250
+#12248 := (iff #3156 #12247)
+#12245 := (iff #3155 true)
+#12197 := (= uf_9 #3140)
+#12209 := (implies #12197 #12197)
+#12212 := (iff #12209 true)
 #12213 := [rewrite]: #12212
-#12246 := (iff #3179 #12209)
-#12205 := (iff #3166 #12204)
+#12243 := (iff #3155 #12209)
+#12241 := (iff #3154 #12197)
+#12202 := (and true #12197)
+#12205 := (iff #12202 #12197)
 #12206 := [rewrite]: #12205
-#12244 := (iff #3178 true)
-#12245 := [rewrite]: #12244
-#12247 := [monotonicity #12245 #12206]: #12246
-#12249 := [trans #12247 #12213]: #12248
-#12251 := [monotonicity #12206 #12249]: #12250
-#12253 := [trans #12251 #12220]: #12252
-#12256 := [quant-intro #12253]: #12255
-#12260 := [trans #12256 #12258]: #12259
-#12272 := [monotonicity #12260 #12269]: #12271
-#12276 := [trans #12272 #12274]: #12275
-#12242 := (iff #3174 true)
-#12197 := (forall (vars (?x779 T5)) (:pat #3154) true)
-#12200 := (iff #12197 true)
-#12201 := [elim-unused]: #12200
-#12240 := (iff #3174 #12197)
-#12238 := (iff #3173 true)
-#12236 := (iff #3173 #12216)
-#12234 := (iff #3172 #12204)
-#12232 := (iff #3172 #12209)
-#12230 := (iff #3171 true)
-#12231 := [rewrite]: #12230
-#12233 := [monotonicity #12231 #12206]: #12232
-#12235 := [trans #12233 #12213]: #12234
-#12237 := [monotonicity #12206 #12235]: #12236
-#12239 := [trans #12237 #12220]: #12238
-#12241 := [quant-intro #12239]: #12240
-#12243 := [trans #12241 #12201]: #12242
-#12278 := [monotonicity #12243 #12276]: #12277
-#12280 := [trans #12278 #12274]: #12279
-#12228 := (iff #3170 true)
-#12223 := (forall (vars (?x780 T5)) (:pat #3164) true)
-#12226 := (iff #12223 true)
-#12227 := [elim-unused]: #12226
-#12224 := (iff #3170 #12223)
-#12221 := (iff #3169 true)
-#12217 := (iff #3169 #12216)
-#12214 := (iff #3168 #12204)
-#12210 := (iff #3168 #12209)
-#12207 := (iff #3167 true)
-#12208 := [rewrite]: #12207
-#12211 := [monotonicity #12208 #12206]: #12210
+#12239 := (iff #3154 #12202)
+#12198 := (iff #3141 #12197)
+#12199 := [rewrite]: #12198
+#12237 := (iff #3153 true)
+#12238 := [rewrite]: #12237
+#12240 := [monotonicity #12238 #12199]: #12239
+#12242 := [trans #12240 #12206]: #12241
+#12244 := [monotonicity #12199 #12242]: #12243
+#12246 := [trans #12244 #12213]: #12245
+#12249 := [quant-intro #12246]: #12248
+#12253 := [trans #12249 #12251]: #12252
+#12265 := [monotonicity #12253 #12262]: #12264
+#12269 := [trans #12265 #12267]: #12268
+#12235 := (iff #3149 true)
+#12190 := (forall (vars (?x779 T5)) (:pat #3129) true)
+#12193 := (iff #12190 true)
+#12194 := [elim-unused]: #12193
+#12233 := (iff #3149 #12190)
+#12231 := (iff #3148 true)
+#12229 := (iff #3148 #12209)
+#12227 := (iff #3147 #12197)
+#12225 := (iff #3147 #12202)
+#12223 := (iff #3146 true)
+#12224 := [rewrite]: #12223
+#12226 := [monotonicity #12224 #12199]: #12225
+#12228 := [trans #12226 #12206]: #12227
+#12230 := [monotonicity #12199 #12228]: #12229
+#12232 := [trans #12230 #12213]: #12231
+#12234 := [quant-intro #12232]: #12233
+#12236 := [trans #12234 #12194]: #12235
+#12271 := [monotonicity #12236 #12269]: #12270
+#12273 := [trans #12271 #12267]: #12272
+#12221 := (iff #3145 true)
+#12216 := (forall (vars (?x780 T5)) (:pat #3139) true)
+#12219 := (iff #12216 true)
+#12220 := [elim-unused]: #12219
+#12217 := (iff #3145 #12216)
+#12214 := (iff #3144 true)
+#12210 := (iff #3144 #12209)
+#12207 := (iff #3143 #12197)
+#12203 := (iff #3143 #12202)
+#12200 := (iff #3142 true)
+#12201 := [rewrite]: #12200
+#12204 := [monotonicity #12201 #12199]: #12203
+#12208 := [trans #12204 #12206]: #12207
+#12211 := [monotonicity #12199 #12208]: #12210
 #12215 := [trans #12211 #12213]: #12214
-#12218 := [monotonicity #12206 #12215]: #12217
+#12218 := [quant-intro #12215]: #12217
 #12222 := [trans #12218 #12220]: #12221
-#12225 := [quant-intro #12222]: #12224
-#12229 := [trans #12225 #12227]: #12228
-#12282 := [monotonicity #12229 #12280]: #12281
-#12284 := [trans #12282 #12274]: #12283
-#12202 := (iff #3161 true)
-#12198 := (iff #3161 #12197)
-#12195 := (iff #3160 true)
-#12184 := (= uf_261 #3157)
-#12187 := (not #12184)
-#12190 := (implies #12187 #12187)
-#12193 := (iff #12190 true)
-#12194 := [rewrite]: #12193
-#12191 := (iff #3160 #12190)
-#12188 := (iff #3159 #12187)
-#12185 := (iff #3158 #12184)
-#12186 := [rewrite]: #12185
-#12189 := [monotonicity #12186]: #12188
-#12192 := [monotonicity #12189 #12189]: #12191
+#12275 := [monotonicity #12222 #12273]: #12274
+#12277 := [trans #12275 #12267]: #12276
+#12195 := (iff #3136 true)
+#12191 := (iff #3136 #12190)
+#12188 := (iff #3135 true)
+#12177 := (= uf_261 #3132)
+#12180 := (not #12177)
+#12183 := (implies #12180 #12180)
+#12186 := (iff #12183 true)
+#12187 := [rewrite]: #12186
+#12184 := (iff #3135 #12183)
+#12181 := (iff #3134 #12180)
+#12178 := (iff #3133 #12177)
+#12179 := [rewrite]: #12178
+#12182 := [monotonicity #12179]: #12181
+#12185 := [monotonicity #12182 #12182]: #12184
+#12189 := [trans #12185 #12187]: #12188
+#12192 := [quant-intro #12189]: #12191
 #12196 := [trans #12192 #12194]: #12195
-#12199 := [quant-intro #12196]: #12198
-#12203 := [trans #12199 #12201]: #12202
-#12286 := [monotonicity #12203 #12284]: #12285
-#12288 := [trans #12286 #12274]: #12287
-#12330 := [monotonicity #12288 #12327]: #12329
-#12333 := [monotonicity #12022 #12330]: #12332
-#12336 := [monotonicity #12022 #12333]: #12335
-#12339 := [monotonicity #12022 #12336]: #12338
-#12625 := [monotonicity #12339 #12622]: #12624
-#12631 := [trans #12625 #12629]: #12630
-#12182 := (iff #3151 true)
-#12177 := (implies false #12174)
-#12180 := (iff #12177 true)
-#12181 := [rewrite]: #12180
-#12178 := (iff #3151 #12177)
-#12111 := (iff #3121 false)
-#12106 := (and #12020 false)
-#12109 := (iff #12106 false)
-#12110 := [rewrite]: #12109
-#12107 := (iff #3121 #12106)
-#12104 := (iff #3120 false)
-#12088 := (and #12020 #12073)
-#12093 := (and #12020 #12088)
-#12096 := (and #12020 #12093)
-#12099 := (and false #12096)
-#12102 := (iff #12099 false)
-#12103 := [rewrite]: #12102
-#12100 := (iff #3120 #12099)
-#12097 := (iff #3119 #12096)
-#12094 := (iff #3118 #12093)
-#12091 := (iff #3117 #12088)
-#12085 := (and #12073 #12020)
-#12089 := (iff #12085 #12088)
-#12090 := [rewrite]: #12089
-#12086 := (iff #3117 #12085)
-#12087 := [monotonicity #12077 #12084]: #12086
-#12092 := [trans #12087 #12090]: #12091
-#12095 := [monotonicity #12022 #12092]: #12094
-#12098 := [monotonicity #12022 #12095]: #12097
-#12065 := (iff #3112 false)
-#12066 := [rewrite]: #12065
-#12101 := [monotonicity #12066 #12098]: #12100
-#12105 := [trans #12101 #12103]: #12104
-#12108 := [monotonicity #12022 #12105]: #12107
-#12112 := [trans #12108 #12110]: #12111
-#12179 := [monotonicity #12112 #12176]: #12178
-#12183 := [trans #12179 #12181]: #12182
-#12634 := [monotonicity #12183 #12631]: #12633
-#12638 := [trans #12634 #12636]: #12637
-#12063 := (iff #3111 #12062)
-#12060 := (iff #3110 #12059)
-#12057 := (iff #3109 #12056)
-#12054 := (iff #3108 #12053)
-#12051 := (iff #3107 #12050)
-#12048 := (iff #3106 #12047)
-#12045 := (iff #3105 #12044)
-#12042 := (iff #3104 #12039)
-#12036 := (and #12033 #12020)
-#12040 := (iff #12036 #12039)
-#12041 := [rewrite]: #12040
-#12037 := (iff #3104 #12036)
-#12034 := (iff #3103 #12033)
-#12031 := (iff #3102 #12030)
-#12032 := [rewrite]: #12031
-#12035 := [monotonicity #12032]: #12034
-#12038 := [monotonicity #12035 #12022]: #12037
-#12043 := [trans #12038 #12041]: #12042
-#12028 := (iff #3098 #12027)
-#12025 := (iff #3097 #12024)
-#12026 := [rewrite]: #12025
-#12029 := [quant-intro #12026]: #12028
-#12046 := [monotonicity #12029 #12043]: #12045
-#12049 := [monotonicity #12046]: #12048
-#12052 := [monotonicity #12022 #12049]: #12051
-#12055 := [monotonicity #12052]: #12054
-#12058 := [monotonicity #12055]: #12057
-#12061 := [monotonicity #12058]: #12060
-#12018 := (iff #3078 #12017)
-#12015 := (iff #3077 #3055)
-#12016 := [rewrite]: #12015
-#12019 := [monotonicity #12016]: #12018
-#12064 := [monotonicity #12019 #12061]: #12063
-#12641 := [monotonicity #12064 #12638]: #12640
-#12647 := [trans #12641 #12645]: #12646
-#12650 := [monotonicity #12019 #12647]: #12649
-#12013 := (iff #3076 #12012)
-#12010 := (iff #3075 #12009)
-#12011 := [rewrite]: #12010
-#12014 := [quant-intro #12011]: #12013
-#12653 := [monotonicity #12014 #12650]: #12652
-#12659 := [trans #12653 #12657]: #12658
-#12662 := [monotonicity #12014 #12659]: #12661
-#12665 := [monotonicity #12662]: #12664
-#12671 := [trans #12665 #12669]: #12670
-#12674 := [monotonicity #12671]: #12673
-#12006 := (iff #3068 #12005)
-#12003 := (iff #3067 #12002)
-#12000 := (iff #3066 #11999)
-#11997 := (iff #3065 #11996)
-#11994 := (iff #3064 #11993)
-#11991 := (iff #3063 #11990)
-#11988 := (iff #3062 #11987)
-#11985 := (iff #3061 #3060)
-#11986 := [rewrite]: #11985
-#11989 := [monotonicity #11986]: #11988
-#11992 := [monotonicity #11989]: #11991
-#11995 := [monotonicity #11992]: #11994
-#11998 := [monotonicity #11995]: #11997
-#12001 := [monotonicity #11998]: #12000
-#12004 := [monotonicity #12001]: #12003
-#11983 := (iff #3052 #11982)
-#11980 := (iff #3051 #11979)
-#11981 := [rewrite]: #11980
-#11971 := (iff #3046 #11970)
-#11972 := [rewrite]: #11971
-#11984 := [monotonicity #11972 #11981]: #11983
-#12007 := [monotonicity #11984 #12004]: #12006
-#12677 := [monotonicity #12007 #12674]: #12676
-#12683 := [trans #12677 #12681]: #12682
-#12686 := [monotonicity #11984 #12683]: #12685
-#11977 := (iff #3049 #11976)
-#11974 := (iff #3048 #11973)
-#11975 := [rewrite]: #11974
-#11978 := [monotonicity #11972 #11975]: #11977
-#12689 := [monotonicity #11978 #12686]: #12688
-#12695 := [trans #12689 #12693]: #12694
-#12698 := [monotonicity #11978 #12695]: #12697
-#11968 := (iff #3043 #11967)
-#11969 := [rewrite]: #11968
-#12701 := [monotonicity #11969 #12698]: #12700
-#12707 := [trans #12701 #12705]: #12706
-#12710 := [monotonicity #11969 #12707]: #12709
-#11965 := (iff #3041 #11964)
-#11962 := (iff #3040 #11961)
-#11959 := (iff #3039 #11958)
-#11956 := (iff #3038 #11955)
-#11953 := (iff #3037 #11952)
-#11950 := (iff #3036 #11949)
-#11947 := (iff #3035 #11946)
-#11944 := (iff #3034 #11943)
-#11941 := (iff #3033 #11940)
-#11938 := (iff #3032 #11937)
-#11935 := (iff #3031 #11934)
-#11932 := (iff #3030 #11931)
-#11929 := (iff #3029 #11926)
-#11923 := (and #11920 #3028)
-#11927 := (iff #11923 #11926)
-#11928 := [rewrite]: #11927
-#11924 := (iff #3029 #11923)
-#11921 := (iff #3025 #11920)
-#11918 := (iff #3024 #11915)
-#11912 := (iff #11909 false)
-#11916 := (iff #11912 #11915)
-#11917 := [rewrite]: #11916
-#11913 := (iff #3024 #11912)
-#11910 := (iff #3023 #11909)
-#11911 := [rewrite]: #11910
-#11914 := [monotonicity #11911]: #11913
-#11919 := [trans #11914 #11917]: #11918
-#11922 := [quant-intro #11919]: #11921
-#11925 := [monotonicity #11922]: #11924
-#11930 := [trans #11925 #11928]: #11929
-#11933 := [monotonicity #11930]: #11932
-#11936 := [monotonicity #11933]: #11935
-#11939 := [monotonicity #11936]: #11938
-#11942 := [monotonicity #11939]: #11941
-#11907 := (iff #3006 #11906)
-#11901 := (iff #3003 #11900)
-#11902 := [rewrite]: #11901
-#11908 := [monotonicity #11902 #11905]: #11907
-#11945 := [monotonicity #11908 #11942]: #11944
-#11898 := (iff #3001 #11897)
-#11899 := [rewrite]: #11898
-#11948 := [monotonicity #11899 #11945]: #11947
-#11895 := (iff #2999 #11894)
-#11892 := (iff #2998 #11891)
-#11889 := (iff #2997 #11888)
-#11886 := (iff #2996 #11885)
-#11883 := (iff #2995 #11882)
-#11880 := (iff #2994 #11879)
-#11881 := [rewrite]: #11880
-#11877 := (iff #2992 #11876)
-#11874 := (iff #2991 #11873)
-#11875 := [rewrite]: #11874
-#11878 := [monotonicity #11875]: #11877
-#11884 := [monotonicity #11878 #11881]: #11883
-#11871 := (iff #2989 #11870)
-#11872 := [rewrite]: #11871
-#11887 := [monotonicity #11872 #11884]: #11886
-#11868 := (iff #2987 #11867)
-#11869 := [rewrite]: #11868
-#11890 := [monotonicity #11869 #11887]: #11889
-#11865 := (iff #2985 #11864)
-#11866 := [rewrite]: #11865
-#11893 := [monotonicity #11866 #11890]: #11892
-#11862 := (iff #2983 #11860)
-#11863 := [rewrite]: #11862
-#11896 := [monotonicity #11863 #11893]: #11895
-#11951 := [monotonicity #11896 #11948]: #11950
-#11954 := [monotonicity #11951]: #11953
+#12279 := [monotonicity #12196 #12277]: #12278
+#12281 := [trans #12279 #12267]: #12280
+#12794 := [monotonicity #12281 #12791]: #12793
+#12799 := [trans #12794 #12797]: #12798
+#12802 := [monotonicity #11973 #12799]: #12801
+#12807 := [trans #12802 #12805]: #12806
+#12810 := [monotonicity #11973 #12807]: #12809
+#12815 := [trans #12810 #12813]: #12814
+#12818 := [monotonicity #11973 #12815]: #12817
+#12823 := [trans #12818 #12821]: #12822
+#12175 := (iff #3126 true)
+#12170 := (implies #11971 true)
+#12173 := (iff #12170 true)
+#12174 := [rewrite]: #12173
+#12171 := (iff #3126 #12170)
+#12168 := (iff #3125 true)
+#12142 := (or #12141 #12133)
+#12150 := (or #12088 #12142)
+#12158 := (or #12088 #12150)
+#12163 := (implies false #12158)
+#12166 := (iff #12163 true)
+#12167 := [rewrite]: #12166
+#12164 := (iff #3125 #12163)
+#12161 := (iff #3124 #12158)
+#12155 := (implies #11971 #12150)
+#12159 := (iff #12155 #12158)
+#12160 := [rewrite]: #12159
+#12156 := (iff #3124 #12155)
+#12153 := (iff #3123 #12150)
+#12147 := (implies #11971 #12142)
+#12151 := (iff #12147 #12150)
+#12152 := [rewrite]: #12151
+#12148 := (iff #3123 #12147)
+#12145 := (iff #3122 #12142)
+#12138 := (implies #12003 #12133)
+#12143 := (iff #12138 #12142)
+#12144 := [rewrite]: #12143
+#12139 := (iff #3122 #12138)
+#12140 := [monotonicity #12007 #12137]: #12139
+#12146 := [trans #12140 #12144]: #12145
+#12149 := [monotonicity #11973 #12146]: #12148
+#12154 := [trans #12149 #12152]: #12153
+#12157 := [monotonicity #11973 #12154]: #12156
+#12162 := [trans #12157 #12160]: #12161
+#12165 := [monotonicity #11996 #12162]: #12164
+#12169 := [trans #12165 #12167]: #12168
+#12172 := [monotonicity #11973 #12169]: #12171
+#12176 := [trans #12172 #12174]: #12175
+#12826 := [monotonicity #12176 #12823]: #12825
+#12830 := [trans #12826 #12828]: #12829
+#12833 := [monotonicity #11973 #12830]: #12832
+#12838 := [trans #12833 #12836]: #12837
+#11993 := (iff #3085 #11992)
+#11990 := (iff #3084 #11989)
+#11991 := [rewrite]: #11990
+#11994 := [monotonicity #11991]: #11993
+#12841 := [monotonicity #11994 #12838]: #12840
+#12847 := [trans #12841 #12845]: #12846
+#11987 := (iff #3080 #11986)
+#11984 := (iff #3079 #11981)
+#11978 := (implies #412 #11975)
+#11982 := (iff #11978 #11981)
+#11983 := [rewrite]: #11982
+#11979 := (iff #3079 #11978)
+#11976 := (iff #3078 #11975)
+#11977 := [rewrite]: #11976
+#11980 := [monotonicity #11977]: #11979
+#11985 := [trans #11980 #11983]: #11984
+#11988 := [quant-intro #11985]: #11987
+#12850 := [monotonicity #11988 #12847]: #12849
+#12856 := [trans #12850 #12854]: #12855
+#12859 := [monotonicity #12856]: #12858
+#12865 := [trans #12859 #12863]: #12864
+#12868 := [monotonicity #11973 #12865]: #12867
+#12873 := [trans #12868 #12871]: #12872
+#12876 := [monotonicity #12873]: #12875
+#12882 := [trans #12876 #12880]: #12881
+#12885 := [monotonicity #12882]: #12884
+#12891 := [trans #12885 #12889]: #12890
+#12894 := [monotonicity #12891]: #12893
+#12900 := [trans #12894 #12898]: #12899
+#11969 := (iff #3060 #11968)
+#11966 := (iff #3059 #3042)
+#11967 := [rewrite]: #11966
+#11970 := [monotonicity #11967]: #11969
+#12903 := [monotonicity #11970 #12900]: #12902
+#12909 := [trans #12903 #12907]: #12908
+#12912 := [monotonicity #11970 #12909]: #12911
+#11964 := (iff #3058 #11963)
+#11961 := (iff #3057 #11958)
+#11955 := (implies #412 #11952)
+#11959 := (iff #11955 #11958)
+#11960 := [rewrite]: #11959
+#11956 := (iff #3057 #11955)
+#11953 := (iff #3056 #11952)
+#11954 := [rewrite]: #11953
 #11957 := [monotonicity #11954]: #11956
-#11960 := [monotonicity #11957]: #11959
-#11963 := [monotonicity #11960]: #11962
-#11966 := [monotonicity #11963]: #11965
-#12713 := [monotonicity #11966 #12710]: #12712
-#12719 := [trans #12713 #12717]: #12718
-#12722 := [monotonicity #12719]: #12721
-#13522 := [trans #12722 #13520]: #13521
-#11859 := [asserted]: #3325
-#13523 := [mp #11859 #13522]: #13518
-#13524 := [not-or-elim #13523]: #12823
-#13531 := [and-elim #13524]: #11867
-#11145 := (not #11138)
+#11962 := [trans #11957 #11960]: #11961
+#11965 := [quant-intro #11962]: #11964
+#12915 := [monotonicity #11965 #12912]: #12914
+#12921 := [trans #12915 #12919]: #12920
+#12924 := [monotonicity #11965 #12921]: #12923
+#12927 := [monotonicity #12924]: #12926
+#12933 := [trans #12927 #12931]: #12932
+#12936 := [monotonicity #12933]: #12935
+#11949 := (iff #3050 #11948)
+#11946 := (iff #3049 #11945)
+#11943 := (iff #3048 #3047)
+#11944 := [rewrite]: #11943
+#11947 := [monotonicity #11944]: #11946
+#11950 := [monotonicity #11947]: #11949
+#12939 := [monotonicity #11950 #12936]: #12938
+#12945 := [trans #12939 #12943]: #12944
+#12948 := [monotonicity #12945]: #12947
+#12954 := [trans #12948 #12952]: #12953
+#12957 := [monotonicity #12954]: #12956
+#12963 := [trans #12957 #12961]: #12962
+#12966 := [monotonicity #12963]: #12965
+#12972 := [trans #12966 #12970]: #12971
+#12975 := [monotonicity #12972]: #12974
+#12981 := [trans #12975 #12979]: #12980
+#11941 := (iff #3039 #11940)
+#11938 := (iff #3038 #11937)
+#11939 := [rewrite]: #11938
+#11929 := (iff #3033 #11928)
+#11930 := [rewrite]: #11929
+#11942 := [monotonicity #11930 #11939]: #11941
+#12984 := [monotonicity #11942 #12981]: #12983
+#12990 := [trans #12984 #12988]: #12989
+#12993 := [monotonicity #11942 #12990]: #12992
+#11935 := (iff #3036 #11934)
+#11932 := (iff #3035 #11931)
+#11933 := [rewrite]: #11932
+#11936 := [monotonicity #11930 #11933]: #11935
+#12996 := [monotonicity #11936 #12993]: #12995
+#13002 := [trans #12996 #13000]: #13001
+#13005 := [monotonicity #11936 #13002]: #13004
+#11926 := (iff #3030 #11925)
+#11927 := [rewrite]: #11926
+#13008 := [monotonicity #11927 #13005]: #13007
+#13014 := [trans #13008 #13012]: #13013
+#13017 := [monotonicity #11927 #13014]: #13016
+#13020 := [monotonicity #13017]: #13019
+#13026 := [trans #13020 #13024]: #13025
+#11923 := (iff #3025 #11922)
+#11920 := (iff #3024 #11917)
+#11914 := (iff #11911 false)
+#11918 := (iff #11914 #11917)
+#11919 := [rewrite]: #11918
+#11915 := (iff #3024 #11914)
+#11912 := (iff #3023 #11911)
+#11913 := [rewrite]: #11912
+#11916 := [monotonicity #11913]: #11915
+#11921 := [trans #11916 #11919]: #11920
+#11924 := [quant-intro #11921]: #11923
+#13029 := [monotonicity #11924 #13026]: #13028
+#13035 := [trans #13029 #13033]: #13034
+#13038 := [monotonicity #13035]: #13037
+#13044 := [trans #13038 #13042]: #13043
+#13047 := [monotonicity #13044]: #13046
+#13053 := [trans #13047 #13051]: #13052
+#13056 := [monotonicity #13053]: #13055
+#13062 := [trans #13056 #13060]: #13061
+#13065 := [monotonicity #13062]: #13064
+#13071 := [trans #13065 #13069]: #13070
+#11909 := (iff #3006 #11908)
+#11903 := (iff #3003 #11902)
+#11904 := [rewrite]: #11903
+#11910 := [monotonicity #11904 #11907]: #11909
+#13074 := [monotonicity #11910 #13071]: #13073
+#13080 := [trans #13074 #13078]: #13079
+#11900 := (iff #3001 #11899)
+#11901 := [rewrite]: #11900
+#13083 := [monotonicity #11901 #13080]: #13082
+#13089 := [trans #13083 #13087]: #13088
+#11897 := (iff #2999 #11896)
+#11894 := (iff #2998 #11893)
+#11891 := (iff #2997 #11890)
+#11888 := (iff #2996 #11887)
+#11885 := (iff #2995 #11884)
+#11882 := (iff #2994 #11881)
+#11883 := [rewrite]: #11882
+#11879 := (iff #2992 #11878)
+#11876 := (iff #2991 #11875)
+#11877 := [rewrite]: #11876
+#11880 := [monotonicity #11877]: #11879
+#11886 := [monotonicity #11880 #11883]: #11885
+#11873 := (iff #2989 #11872)
+#11874 := [rewrite]: #11873
+#11889 := [monotonicity #11874 #11886]: #11888
+#11870 := (iff #2987 #11869)
+#11871 := [rewrite]: #11870
+#11892 := [monotonicity #11871 #11889]: #11891
+#11867 := (iff #2985 #11866)
+#11868 := [rewrite]: #11867
+#11895 := [monotonicity #11868 #11892]: #11894
+#11864 := (iff #2983 #11862)
+#11865 := [rewrite]: #11864
+#11898 := [monotonicity #11865 #11895]: #11897
+#13092 := [monotonicity #11898 #13089]: #13091
+#13098 := [trans #13092 #13096]: #13097
+#13101 := [monotonicity #13098]: #13100
+#13107 := [trans #13101 #13105]: #13106
+#13110 := [monotonicity #13107]: #13109
+#13116 := [trans #13110 #13114]: #13115
+#13119 := [monotonicity #13116]: #13118
+#13125 := [trans #13119 #13123]: #13124
+#13128 := [monotonicity #13125]: #13127
+#13134 := [trans #13128 #13132]: #13133
+#13137 := [monotonicity #13134]: #13136
+#13143 := [trans #13137 #13141]: #13142
+#13146 := [monotonicity #13143]: #13145
+#14054 := [trans #13146 #14052]: #14053
+#11861 := [asserted]: #3327
+#14055 := [mp #11861 #14054]: #14050
+#14073 := [not-or-elim #14055]: #13937
+#14076 := [and-elim #14073]: #11869
+#233 := (:var 0 T3)
+#2666 := (uf_48 #15 #233)
+#2667 := (pattern #2666)
+#11140 := (= uf_9 #2666)
+#11147 := (not #11140)
 #1259 := (uf_116 #15)
 #2669 := (uf_43 #233 #1259)
 #2670 := (= #15 #2669)
-#11146 := (or #2670 #11145)
-#11151 := (forall (vars (?x710 T5) (?x711 T3)) (:pat #2667) #11146)
-#17463 := (~ #11151 #11151)
-#17461 := (~ #11146 #11146)
-#17462 := [refl]: #17461
-#17464 := [nnf-pos #17462]: #17463
+#11148 := (or #2670 #11147)
+#11153 := (forall (vars (?x710 T5) (?x711 T3)) (:pat #2667) #11148)
+#17964 := (~ #11153 #11153)
+#17962 := (~ #11148 #11148)
+#17963 := [refl]: #17962
+#17965 := [nnf-pos #17963]: #17964
+#2668 := (= #2666 uf_9)
 #2671 := (implies #2668 #2670)
 #2672 := (forall (vars (?x710 T5) (?x711 T3)) (:pat #2667) #2671)
-#11152 := (iff #2672 #11151)
-#11149 := (iff #2671 #11146)
-#11142 := (implies #11138 #2670)
-#11147 := (iff #11142 #11146)
-#11148 := [rewrite]: #11147
-#11143 := (iff #2671 #11142)
-#11144 := [monotonicity #11141]: #11143
-#11150 := [trans #11144 #11148]: #11149
-#11153 := [quant-intro #11150]: #11152
-#11137 := [asserted]: #2672
-#11156 := [mp #11137 #11153]: #11151
-#17465 := [mp~ #11156 #17464]: #11151
-#25398 := (not #11867)
-#25411 := (not #11151)
-#25412 := (or #25411 #25398 #25406)
-#25407 := (or #25406 #25398)
-#25413 := (or #25411 #25407)
-#25420 := (iff #25413 #25412)
-#25408 := (or #25398 #25406)
-#25415 := (or #25411 #25408)
-#25418 := (iff #25415 #25412)
-#25419 := [rewrite]: #25418
-#25416 := (iff #25413 #25415)
-#25409 := (iff #25407 #25408)
-#25410 := [rewrite]: #25409
-#25417 := [monotonicity #25410]: #25416
-#25421 := [trans #25417 #25419]: #25420
-#25414 := [quant-inst]: #25413
-#25422 := [mp #25414 #25421]: #25412
-#27875 := [unit-resolution #25422 #17465 #13531]: #25406
-#27877 := [symm #27875]: #27876
-#26168 := [monotonicity #27877]: #26162
-#26170 := [trans #26168 #27921]: #26169
-#26172 := [monotonicity #26170]: #26171
-#26174 := [monotonicity #26172]: #26195
-#26177 := [symm #26174]: #26176
-#26161 := [monotonicity #26177]: #26179
-#13533 := [and-elim #13524]: #11876
-#26175 := [mp #13533 #26161]: #26178
+#11154 := (iff #2672 #11153)
+#11151 := (iff #2671 #11148)
+#11144 := (implies #11140 #2670)
+#11149 := (iff #11144 #11148)
+#11150 := [rewrite]: #11149
+#11145 := (iff #2671 #11144)
+#11142 := (iff #2668 #11140)
+#11143 := [rewrite]: #11142
+#11146 := [monotonicity #11143]: #11145
+#11152 := [trans #11146 #11150]: #11151
+#11155 := [quant-intro #11152]: #11154
+#11139 := [asserted]: #2672
+#11158 := [mp #11139 #11155]: #11153
+#17966 := [mp~ #11158 #17965]: #11153
+#25932 := (not #11869)
+#25945 := (not #11153)
+#25946 := (or #25945 #25932 #25940)
+#25941 := (or #25940 #25932)
+#25947 := (or #25945 #25941)
+#25954 := (iff #25947 #25946)
+#25942 := (or #25932 #25940)
+#25949 := (or #25945 #25942)
+#25952 := (iff #25949 #25946)
+#25953 := [rewrite]: #25952
+#25950 := (iff #25947 #25949)
+#25943 := (iff #25941 #25942)
+#25944 := [rewrite]: #25943
+#25951 := [monotonicity #25944]: #25950
+#25955 := [trans #25951 #25953]: #25954
+#25948 := [quant-inst]: #25947
+#25956 := [mp #25948 #25955]: #25946
+#28304 := [unit-resolution #25956 #17966 #14076]: #25940
+#26515 := [monotonicity #28304 #28304]: #26728
+#26577 := [symm #26515]: #26725
+#26481 := (= uf_9 #26480)
 decl uf_196 :: (-> T4 T5 T5 T2)
-#25944 := (uf_196 uf_287 #25399 #25399)
-#25945 := (= uf_9 #25944)
-#25966 := (not #25945)
-#25946 := (uf_200 uf_287 #25399 #25399 uf_282)
-#25947 := (= uf_9 #25946)
-#25949 := (iff #25945 #25947)
+#26478 := (uf_196 uf_287 #25933 #25933)
+#26479 := (= uf_9 #26478)
+#26483 := (iff #26479 #26481)
 #2245 := (:var 0 T16)
+#21 := (:var 2 T5)
 #13 := (:var 3 T4)
 #2256 := (uf_200 #13 #21 #15 #2245)
 #2257 := (pattern #2256)
 #2259 := (uf_196 #13 #21 #15)
-#10101 := (= uf_9 #2259)
-#10097 := (= uf_9 #2256)
-#10104 := (iff #10097 #10101)
-#10107 := (forall (vars (?x586 T4) (?x587 T5) (?x588 T5) (?x589 T16)) (:pat #2257) #10104)
-#17105 := (~ #10107 #10107)
-#17103 := (~ #10104 #10104)
-#17104 := [refl]: #17103
-#17106 := [nnf-pos #17104]: #17105
+#10103 := (= uf_9 #2259)
+#10099 := (= uf_9 #2256)
+#10106 := (iff #10099 #10103)
+#10109 := (forall (vars (?x586 T4) (?x587 T5) (?x588 T5) (?x589 T16)) (:pat #2257) #10106)
+#17606 := (~ #10109 #10109)
+#17604 := (~ #10106 #10106)
+#17605 := [refl]: #17604
+#17607 := [nnf-pos #17605]: #17606
 #2260 := (= #2259 uf_9)
 #2258 := (= #2256 uf_9)
 #2261 := (iff #2258 #2260)
 #2262 := (forall (vars (?x586 T4) (?x587 T5) (?x588 T5) (?x589 T16)) (:pat #2257) #2261)
-#10108 := (iff #2262 #10107)
-#10105 := (iff #2261 #10104)
-#10102 := (iff #2260 #10101)
-#10103 := [rewrite]: #10102
-#10099 := (iff #2258 #10097)
-#10100 := [rewrite]: #10099
-#10106 := [monotonicity #10100 #10103]: #10105
-#10109 := [quant-intro #10106]: #10108
-#10096 := [asserted]: #2262
-#10112 := [mp #10096 #10109]: #10107
-#17107 := [mp~ #10112 #17106]: #10107
-#25955 := (not #10107)
-#25953 := (or #25955 #25949)
-#25948 := (iff #25947 #25945)
-#25956 := (or #25955 #25948)
-#25958 := (iff #25956 #25953)
-#25960 := (iff #25953 #25953)
-#25961 := [rewrite]: #25960
-#25950 := (iff #25948 #25949)
-#25951 := [rewrite]: #25950
-#25959 := [monotonicity #25951]: #25958
-#25978 := [trans #25959 #25961]: #25958
-#25957 := [quant-inst]: #25956
-#25964 := [mp #25957 #25978]: #25953
-#26163 := [unit-resolution #25964 #17107]: #25949
-#25963 := (not #25947)
-#26189 := (iff #12702 #25963)
-#26188 := (iff #11967 #25947)
-#26167 := (iff #25947 #11967)
-#26165 := (= #25946 #3042)
-#26166 := [monotonicity #27877 #27877]: #26165
-#26187 := [monotonicity #26166]: #26167
-#26186 := [symm #26187]: #26188
-#26190 := [monotonicity #26186]: #26189
-#26164 := [hypothesis]: #12702
-#26191 := [mp #26164 #26190]: #25963
-#25967 := (not #25949)
-#25969 := (or #25967 #25966 #25947)
-#25970 := [def-axiom]: #25969
-#26192 := [unit-resolution #25970 #26191 #26163]: #25966
-#26048 := (uf_24 uf_287 #25399)
-#26049 := (= uf_9 #26048)
-#26196 := (= #2988 #26048)
-#26193 := (= #26048 #2988)
-#26194 := [monotonicity #27877]: #26193
-#26198 := [symm #26194]: #26196
-#13532 := [and-elim #13524]: #11870
-#26199 := [trans #13532 #26198]: #26049
-#26051 := (uf_48 #25399 #25810)
-#26052 := (= uf_9 #26051)
-#26202 := (= #2986 #26051)
-#26197 := (= #26051 #2986)
-#26200 := [monotonicity #27877 #26170]: #26197
-#26203 := [symm #26200]: #26202
-#26204 := [trans #13531 #26203]: #26052
-#26053 := (not #26052)
-#26050 := (not #26049)
-#26225 := (or #25945 #26050 #26053 #26059)
-#25822 := (uf_25 uf_287 #25399)
-#26054 := (= uf_26 #25822)
-#26213 := (= #2984 #25822)
-#26185 := (= #25822 #2984)
-#26211 := [monotonicity #27877]: #26185
-#26212 := [symm #26211]: #26213
-#13530 := [and-elim #13524]: #11864
-#26214 := [trans #13530 #26212]: #26054
-#25848 := (uf_27 uf_287 #25399)
-#25849 := (= uf_9 #25848)
-#26218 := (= #2982 #25848)
-#26215 := (= #25848 #2982)
-#26216 := [monotonicity #27877]: #26215
-#26224 := [symm #26216]: #26218
-#13529 := [and-elim #13524]: #11860
-#26246 := [trans #13529 #26224]: #25849
-#25811 := (uf_23 #25810)
-#25818 := (= uf_9 #25811)
-#26250 := (= #2993 #25811)
-#26247 := (= #25811 #2993)
-#26248 := [monotonicity #26170]: #26247
-#26251 := [symm #26248]: #26250
-#13534 := [and-elim #13524]: #11879
-#26252 := [trans #13534 #26251]: #25818
-#13537 := [and-elim #13524]: #11903
-#47 := (:var 1 T4)
+#10110 := (iff #2262 #10109)
+#10107 := (iff #2261 #10106)
+#10104 := (iff #2260 #10103)
+#10105 := [rewrite]: #10104
+#10101 := (iff #2258 #10099)
+#10102 := [rewrite]: #10101
+#10108 := [monotonicity #10102 #10105]: #10107
+#10111 := [quant-intro #10108]: #10110
+#10098 := [asserted]: #2262
+#10114 := [mp #10098 #10111]: #10109
+#17608 := [mp~ #10114 #17607]: #10109
+#26501 := (not #10109)
+#26502 := (or #26501 #26483)
+#26482 := (iff #26481 #26479)
+#26499 := (or #26501 #26482)
+#26504 := (iff #26499 #26502)
+#26506 := (iff #26502 #26502)
+#26486 := [rewrite]: #26506
+#26484 := (iff #26482 #26483)
+#26485 := [rewrite]: #26484
+#26505 := [monotonicity #26485]: #26504
+#26488 := [trans #26505 #26486]: #26504
+#26503 := [quant-inst]: #26499
+#26489 := [mp #26503 #26488]: #26502
+#26699 := [unit-resolution #26489 #17608]: #26483
+#26490 := (not #26483)
+#26518 := (or #26490 #26481)
+#26344 := (uf_13 #25933)
+#26590 := (uf_12 #26344)
+#26593 := (= uf_14 #26590)
+#26712 := (not #26593)
+#26713 := (iff #11878 #26712)
+#26710 := (iff #11875 #26593)
+#26729 := (iff #26593 #11875)
+#26705 := (= #26590 #2990)
+#26703 := (= #26344 #2977)
+#24763 := (uf_13 #2981)
+#28352 := (= #24763 #2977)
+#24766 := (= #2977 #24763)
+#2697 := (uf_43 #326 #161)
+#22937 := (pattern #2697)
+#2701 := (uf_13 #2697)
+#11218 := (= #326 #2701)
+#22944 := (forall (vars (?x720 T3) (?x721 int)) (:pat #22937) #11218)
+#11222 := (forall (vars (?x720 T3) (?x721 int)) #11218)
+#22947 := (iff #11222 #22944)
+#22945 := (iff #11218 #11218)
+#22946 := [refl]: #22945
+#22948 := [quant-intro #22946]: #22947
+#17989 := (~ #11222 #11222)
+#17987 := (~ #11218 #11218)
+#17988 := [refl]: #17987
+#17990 := [nnf-pos #17988]: #17989
+#2702 := (= #2701 #326)
+#2703 := (forall (vars (?x720 T3) (?x721 int)) #2702)
+#11223 := (iff #2703 #11222)
+#11220 := (iff #2702 #11218)
+#11221 := [rewrite]: #11220
+#11224 := [quant-intro #11221]: #11223
+#11217 := [asserted]: #2703
+#11227 := [mp #11217 #11224]: #11222
+#17991 := [mp~ #11227 #17990]: #11222
+#22949 := [mp #17991 #22948]: #22944
+#24710 := (not #22944)
+#24771 := (or #24710 #24766)
+#24772 := [quant-inst]: #24771
+#28286 := [unit-resolution #24772 #22949]: #24766
+#28353 := [symm #28286]: #28352
+#26696 := (= #26344 #24763)
+#28305 := (= #25933 #2981)
+#28306 := [symm #28304]: #28305
+#26702 := [monotonicity #28306]: #26696
+#26704 := [trans #26702 #28353]: #26703
+#26706 := [monotonicity #26704]: #26705
+#26708 := [monotonicity #26706]: #26729
+#26711 := [symm #26708]: #26710
+#26727 := [monotonicity #26711]: #26713
+#14078 := [and-elim #14073]: #11878
+#26737 := [mp #14078 #26727]: #26712
+#26582 := (uf_24 uf_287 #25933)
+#26583 := (= uf_9 #26582)
+#26744 := (= #2988 #26582)
+#26738 := (= #26582 #2988)
+#26719 := [monotonicity #28306]: #26738
+#26747 := [symm #26719]: #26744
+#14077 := [and-elim #14073]: #11872
+#26746 := [trans #14077 #26747]: #26583
+#26585 := (uf_48 #25933 #26344)
+#26586 := (= uf_9 #26585)
+#26751 := (= #2986 #26585)
+#26748 := (= #26585 #2986)
+#26749 := [monotonicity #28306 #26704]: #26748
+#26752 := [symm #26749]: #26751
+#26758 := [trans #14076 #26752]: #26586
+#26587 := (not #26586)
+#26584 := (not #26583)
+#26819 := (or #26584 #26587 #26593)
+#26356 := (uf_25 uf_287 #25933)
+#26588 := (= uf_26 #26356)
+#26784 := (= #2984 #26356)
+#26780 := (= #26356 #2984)
+#26781 := [monotonicity #28306]: #26780
+#26785 := [symm #26781]: #26784
+#14075 := [and-elim #14073]: #11866
+#26779 := [trans #14075 #26785]: #26588
+#26500 := (not #26479)
+#26786 := [hypothesis]: #26500
+#26382 := (uf_27 uf_287 #25933)
+#26383 := (= uf_9 #26382)
+#26789 := (= #2982 #26382)
+#26759 := (= #26382 #2982)
+#26787 := [monotonicity #28306]: #26759
+#26810 := [symm #26787]: #26789
+#14074 := [and-elim #14073]: #11862
+#26811 := [trans #14074 #26810]: #26383
+#26345 := (uf_23 #26344)
+#26352 := (= uf_9 #26345)
+#26835 := (= #2993 #26345)
+#26812 := (= #26345 #2993)
+#26813 := [monotonicity #26704]: #26812
+#26800 := [symm #26813]: #26835
+#14079 := [and-elim #14073]: #11881
+#26836 := [trans #14079 #26800]: #26352
+#14062 := [not-or-elim #14055]: #11908
+#14064 := [and-elim #14062]: #11905
 #2217 := (uf_196 #47 #23 #23)
 #2218 := (pattern #2217)
-#9982 := (= uf_9 #2217)
+#9984 := (= uf_9 #2217)
 #227 := (uf_55 #47)
-#3897 := (= uf_9 #227)
-#18563 := (not #3897)
-#146 := (uf_24 #47 #23)
-#3621 := (= uf_9 #146)
-#11066 := (not #3621)
-#26 := (uf_13 #23)
+#3899 := (= uf_9 #227)
+#19163 := (not #3899)
 #144 := (uf_48 #23 #26)
-#3618 := (= uf_9 #144)
-#18438 := (not #3618)
-#142 := (uf_25 #47 #23)
-#3615 := (= uf_26 #142)
-#18437 := (not #3615)
+#3620 := (= uf_9 #144)
+#19038 := (not #3620)
+#19037 := (not #3617)
 #135 := (uf_27 #47 #23)
-#3600 := (= uf_9 #135)
-#10691 := (not #3600)
+#3602 := (= uf_9 #135)
+#10693 := (not #3602)
 #71 := (uf_23 #26)
-#3453 := (= uf_9 #71)
-#10746 := (not #3453)
-#27 := (uf_12 #26)
-#29 := (= #27 uf_14)
-#20996 := (or #29 #10746 #10691 #18437 #18438 #11066 #18563 #9982)
-#21001 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #20996)
-#52 := (not #29)
-#9997 := (and #52 #3453 #3600 #3615 #3618 #3621 #3897)
-#10000 := (not #9997)
-#10006 := (or #9982 #10000)
-#10011 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #10006)
-#21002 := (iff #10011 #21001)
-#20999 := (iff #10006 #20996)
-#20982 := (or #29 #10746 #10691 #18437 #18438 #11066 #18563)
-#20993 := (or #9982 #20982)
-#20997 := (iff #20993 #20996)
-#20998 := [rewrite]: #20997
-#20994 := (iff #10006 #20993)
-#20991 := (iff #10000 #20982)
-#20983 := (not #20982)
-#20986 := (not #20983)
-#20989 := (iff #20986 #20982)
-#20990 := [rewrite]: #20989
-#20987 := (iff #10000 #20986)
-#20984 := (iff #9997 #20983)
-#20985 := [rewrite]: #20984
-#20988 := [monotonicity #20985]: #20987
-#20992 := [trans #20988 #20990]: #20991
-#20995 := [monotonicity #20992]: #20994
-#21000 := [trans #20995 #20998]: #20999
-#21003 := [quant-intro #21000]: #21002
-#17073 := (~ #10011 #10011)
-#17071 := (~ #10006 #10006)
-#17072 := [refl]: #17071
-#17074 := [nnf-pos #17072]: #17073
+#3455 := (= uf_9 #71)
+#10748 := (not #3455)
+#21596 := (or #29 #10748 #10693 #19037 #19038 #11068 #19163 #9984)
+#21601 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #21596)
+#9999 := (and #52 #3455 #3602 #3617 #3620 #3623 #3899)
+#10002 := (not #9999)
+#10008 := (or #9984 #10002)
+#10013 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #10008)
+#21602 := (iff #10013 #21601)
+#21599 := (iff #10008 #21596)
+#21582 := (or #29 #10748 #10693 #19037 #19038 #11068 #19163)
+#21593 := (or #9984 #21582)
+#21597 := (iff #21593 #21596)
+#21598 := [rewrite]: #21597
+#21594 := (iff #10008 #21593)
+#21591 := (iff #10002 #21582)
+#21583 := (not #21582)
+#21586 := (not #21583)
+#21589 := (iff #21586 #21582)
+#21590 := [rewrite]: #21589
+#21587 := (iff #10002 #21586)
+#21584 := (iff #9999 #21583)
+#21585 := [rewrite]: #21584
+#21588 := [monotonicity #21585]: #21587
+#21592 := [trans #21588 #21590]: #21591
+#21595 := [monotonicity #21592]: #21594
+#21600 := [trans #21595 #21598]: #21599
+#21603 := [quant-intro #21600]: #21602
+#17574 := (~ #10013 #10013)
+#17572 := (~ #10008 #10008)
+#17573 := [refl]: #17572
+#17575 := [nnf-pos #17573]: #17574
 #2225 := (= #2217 uf_9)
 #72 := (= #71 uf_9)
 #2219 := (and #52 #72)
-#147 := (= #146 uf_9)
 #2220 := (and #147 #2219)
 #145 := (= #144 uf_9)
 #2221 := (and #145 #2220)
-#143 := (= #142 uf_26)
 #2222 := (and #143 #2221)
 #136 := (= #135 uf_9)
 #2223 := (and #136 #2222)
@@ -3047,1764 +3526,1771 @@
 #2224 := (and #229 #2223)
 #2226 := (implies #2224 #2225)
 #2227 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #2226)
-#10014 := (iff #2227 #10011)
-#9963 := (and #52 #3453)
-#9967 := (and #3621 #9963)
-#9970 := (and #3618 #9967)
-#9973 := (and #3615 #9970)
-#9976 := (and #3600 #9973)
-#9979 := (and #3897 #9976)
-#9988 := (not #9979)
-#9989 := (or #9988 #9982)
-#9994 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #9989)
-#10012 := (iff #9994 #10011)
-#10009 := (iff #9989 #10006)
-#10003 := (or #10000 #9982)
-#10007 := (iff #10003 #10006)
-#10008 := [rewrite]: #10007
-#10004 := (iff #9989 #10003)
-#10001 := (iff #9988 #10000)
-#9998 := (iff #9979 #9997)
-#9999 := [rewrite]: #9998
-#10002 := [monotonicity #9999]: #10001
-#10005 := [monotonicity #10002]: #10004
-#10010 := [trans #10005 #10008]: #10009
-#10013 := [quant-intro #10010]: #10012
-#9995 := (iff #2227 #9994)
-#9992 := (iff #2226 #9989)
-#9985 := (implies #9979 #9982)
-#9990 := (iff #9985 #9989)
-#9991 := [rewrite]: #9990
-#9986 := (iff #2226 #9985)
-#9983 := (iff #2225 #9982)
-#9984 := [rewrite]: #9983
-#9980 := (iff #2224 #9979)
-#9977 := (iff #2223 #9976)
-#9974 := (iff #2222 #9973)
-#9971 := (iff #2221 #9970)
-#9968 := (iff #2220 #9967)
-#9965 := (iff #2219 #9963)
-#3454 := (iff #72 #3453)
-#3455 := [rewrite]: #3454
-#9966 := [monotonicity #3455]: #9965
-#3622 := (iff #147 #3621)
-#3623 := [rewrite]: #3622
-#9969 := [monotonicity #3623 #9966]: #9968
-#3619 := (iff #145 #3618)
-#3620 := [rewrite]: #3619
-#9972 := [monotonicity #3620 #9969]: #9971
-#3616 := (iff #143 #3615)
-#3617 := [rewrite]: #3616
-#9975 := [monotonicity #3617 #9972]: #9974
-#3602 := (iff #136 #3600)
-#3603 := [rewrite]: #3602
-#9978 := [monotonicity #3603 #9975]: #9977
-#3899 := (iff #229 #3897)
-#3900 := [rewrite]: #3899
-#9981 := [monotonicity #3900 #9978]: #9980
-#9987 := [monotonicity #9981 #9984]: #9986
-#9993 := [trans #9987 #9991]: #9992
-#9996 := [quant-intro #9993]: #9995
-#10015 := [trans #9996 #10013]: #10014
-#9962 := [asserted]: #2227
-#10016 := [mp #9962 #10015]: #10011
-#17075 := [mp~ #10016 #17074]: #10011
-#21004 := [mp #17075 #21003]: #21001
-#26055 := (not #26054)
-#25875 := (not #25849)
-#25819 := (not #25818)
-#23948 := (not #11903)
-#26041 := (not #21001)
-#26043 := (or #26041 #23948 #25819 #25875 #25945 #26050 #26053 #26055 #26059)
-#26057 := (= #26056 uf_14)
-#26058 := (or #26057 #25819 #25875 #26055 #26053 #26050 #23948 #25945)
-#26044 := (or #26041 #26058)
-#26031 := (iff #26044 #26043)
-#26065 := (or #23948 #25819 #25875 #25945 #26050 #26053 #26055 #26059)
-#26046 := (or #26041 #26065)
-#26028 := (iff #26046 #26043)
-#26030 := [rewrite]: #26028
-#26047 := (iff #26044 #26046)
-#26068 := (iff #26058 #26065)
-#26062 := (or #26059 #25819 #25875 #26055 #26053 #26050 #23948 #25945)
-#26066 := (iff #26062 #26065)
-#26067 := [rewrite]: #26066
-#26063 := (iff #26058 #26062)
-#26060 := (iff #26057 #26059)
-#26061 := [rewrite]: #26060
-#26064 := [monotonicity #26061]: #26063
-#26069 := [trans #26064 #26067]: #26068
-#26042 := [monotonicity #26069]: #26047
-#26032 := [trans #26042 #26030]: #26031
-#26045 := [quant-inst]: #26044
-#26033 := [mp #26045 #26032]: #26043
-#26253 := [unit-resolution #26033 #21004 #13537 #26252 #26246 #26214]: #26225
-#26254 := [unit-resolution #26253 #26204 #26199 #26192 #26175]: false
-#26255 := [lemma #26254]: #11967
-#22707 := (or #12702 #22704)
-#21694 := (forall (vars (?x778 int)) #21683)
-#21701 := (not #21694)
-#21679 := (forall (vars (?x776 int)) #21674)
-#21700 := (not #21679)
-#21702 := (or #21700 #21701)
-#21703 := (not #21702)
-#21732 := (or #21703 #21729)
-#21742 := (not #21732)
-#21743 := (or #21738 #21739 #21740 #21741 #21602 #21575 #12968 #21742)
-#21744 := (not #21743)
-#21497 := (forall (vars (?x785 int)) #21492)
-#21503 := (not #21497)
-#21504 := (or #21468 #21503)
-#21505 := (not #21504)
-#21534 := (or #21505 #21531)
-#21540 := (not #21534)
-#21541 := (or #13093 #21540)
-#21542 := (not #21541)
-#21547 := (or #13093 #21542)
-#21557 := (not #21547)
-#21558 := (or #21553 #21554 #17742 #21555 #21556 #17745 #21557)
-#21559 := (not #21558)
-#21564 := (or #17742 #17745 #21559)
-#21576 := (not #21564)
-#21615 := (or #21613 #21614 #21602 #21575 #12996 #21554 #21576)
-#21616 := (not #21615)
-#21577 := (or #21570 #21571 #17721 #17730 #21572 #21573 #21574 #21575 #21554 #21576)
-#21578 := (not #21577)
-#21583 := (or #17721 #17730 #21578)
-#21589 := (not #21583)
-#21590 := (or #17721 #17724 #21589)
-#21591 := (not #21590)
-#21596 := (or #17721 #17724 #21591)
-#21603 := (not #21596)
-#21604 := (or #21602 #21575 #12997 #21603)
-#21605 := (not #21604)
-#21621 := (or #21605 #21616)
-#21627 := (not #21621)
-#21628 := (or #17721 #17730 #21602 #21575 #21627)
-#21629 := (not #21628)
-#21634 := (or #17721 #17730 #21629)
-#21640 := (not #21634)
-#21641 := (or #17721 #17724 #21640)
-#21642 := (not #21641)
-#21647 := (or #17721 #17724 #21642)
-#21653 := (not #21647)
-#21654 := (or #21602 #21575 #12967 #21653)
-#21655 := (not #21654)
-#21749 := (or #21655 #21744)
-#21771 := (not #21749)
-#21463 := (forall (vars (?x775 int)) #21458)
-#21767 := (not #21463)
-#21772 := (or #17676 #21755 #21756 #21757 #21758 #21759 #21760 #21761 #21762 #21763 #12740 #21602 #21575 #13358 #21764 #21765 #21766 #21768 #21769 #21770 #21767 #21771)
-#21773 := (not #21772)
-#21778 := (or #17676 #12740 #21773)
-#21785 := (not #21778)
-#21441 := (forall (vars (?x773 int)) #21436)
-#21784 := (not #21441)
-#21786 := (or #21784 #21785)
-#21787 := (not #21786)
-#21792 := (or #21419 #21787)
-#21798 := (not #21792)
-#21799 := (or #12866 #21798)
-#21800 := (not #21799)
-#21805 := (or #12866 #21800)
-#21814 := (not #21805)
-#21815 := (or #17676 #21811 #21812 #21813 #17631 #17640 #21814)
-#21816 := (not #21815)
-#21821 := (or #17631 #17640 #21816)
-#21827 := (not #21821)
-#21828 := (or #17631 #17634 #21827)
-#21829 := (not #21828)
-#21834 := (or #17631 #17634 #21829)
-#21840 := (not #21834)
-#21841 := (or #12702 #21840)
-#21842 := (not #21841)
-#21847 := (or #12702 #21842)
-#22708 := (iff #21847 #22707)
-#22705 := (iff #21842 #22704)
-#22702 := (iff #21841 #22701)
-#22699 := (iff #21840 #22698)
-#22696 := (iff #21834 #22695)
-#22693 := (iff #21829 #22692)
-#22690 := (iff #21828 #22689)
-#22687 := (iff #21827 #22686)
-#22684 := (iff #21821 #22683)
-#22681 := (iff #21816 #22680)
-#22678 := (iff #21815 #22677)
-#22675 := (iff #21814 #22674)
-#22672 := (iff #21805 #22671)
-#22669 := (iff #21800 #22668)
-#22666 := (iff #21799 #22665)
-#22663 := (iff #21798 #22662)
-#22660 := (iff #21792 #22659)
-#22657 := (iff #21787 #22656)
-#22654 := (iff #21786 #22653)
-#22651 := (iff #21785 #22650)
-#22648 := (iff #21778 #22647)
-#22645 := (iff #21773 #22644)
-#22642 := (iff #21772 #22641)
-#22639 := (iff #21771 #22638)
-#22636 := (iff #21749 #22635)
-#22633 := (iff #21744 #22632)
-#22630 := (iff #21743 #22629)
-#22627 := (iff #21742 #22626)
-#22624 := (iff #21732 #22623)
-#22621 := (iff #21703 #22620)
-#22618 := (iff #21702 #22617)
-#22615 := (iff #21701 #22614)
-#22612 := (iff #21694 #22609)
-#22610 := (iff #21683 #21683)
-#22611 := [refl]: #22610
-#22613 := [quant-intro #22611]: #22612
-#22616 := [monotonicity #22613]: #22615
-#22607 := (iff #21700 #22606)
-#22604 := (iff #21679 #22601)
-#22602 := (iff #21674 #21674)
-#22603 := [refl]: #22602
-#22605 := [quant-intro #22603]: #22604
-#22608 := [monotonicity #22605]: #22607
-#22619 := [monotonicity #22608 #22616]: #22618
-#22622 := [monotonicity #22619]: #22621
-#22625 := [monotonicity #22622]: #22624
-#22628 := [monotonicity #22625]: #22627
-#22631 := [monotonicity #22628]: #22630
-#22634 := [monotonicity #22631]: #22633
-#22599 := (iff #21655 #22598)
-#22596 := (iff #21654 #22595)
-#22593 := (iff #21653 #22592)
-#22590 := (iff #21647 #22589)
-#22587 := (iff #21642 #22586)
-#22584 := (iff #21641 #22583)
-#22581 := (iff #21640 #22580)
-#22578 := (iff #21634 #22577)
-#22575 := (iff #21629 #22574)
-#22572 := (iff #21628 #22571)
-#22569 := (iff #21627 #22568)
-#22566 := (iff #21621 #22565)
-#22563 := (iff #21616 #22562)
-#22560 := (iff #21615 #22559)
-#22527 := (iff #21576 #22526)
-#22524 := (iff #21564 #22523)
-#22521 := (iff #21559 #22520)
-#22518 := (iff #21558 #22517)
-#22515 := (iff #21557 #22514)
-#22512 := (iff #21547 #22511)
-#22509 := (iff #21542 #22508)
-#22506 := (iff #21541 #22505)
-#22503 := (iff #21540 #22502)
-#22500 := (iff #21534 #22499)
-#22497 := (iff #21505 #22496)
-#22494 := (iff #21504 #22493)
-#22491 := (iff #21503 #22490)
-#22488 := (iff #21497 #22485)
-#22486 := (iff #21492 #21492)
-#22487 := [refl]: #22486
-#22489 := [quant-intro #22487]: #22488
-#22492 := [monotonicity #22489]: #22491
-#22495 := [monotonicity #22492]: #22494
-#22498 := [monotonicity #22495]: #22497
-#22501 := [monotonicity #22498]: #22500
-#22504 := [monotonicity #22501]: #22503
-#22507 := [monotonicity #22504]: #22506
-#22510 := [monotonicity #22507]: #22509
-#22513 := [monotonicity #22510]: #22512
-#22516 := [monotonicity #22513]: #22515
-#22519 := [monotonicity #22516]: #22518
-#22522 := [monotonicity #22519]: #22521
-#22525 := [monotonicity #22522]: #22524
-#22528 := [monotonicity #22525]: #22527
-#22561 := [monotonicity #22528]: #22560
-#22564 := [monotonicity #22561]: #22563
-#22557 := (iff #21605 #22556)
-#22554 := (iff #21604 #22553)
-#22551 := (iff #21603 #22550)
-#22548 := (iff #21596 #22547)
-#22545 := (iff #21591 #22544)
-#22542 := (iff #21590 #22541)
-#22539 := (iff #21589 #22538)
-#22536 := (iff #21583 #22535)
-#22533 := (iff #21578 #22532)
-#22530 := (iff #21577 #22529)
-#22531 := [monotonicity #22528]: #22530
-#22534 := [monotonicity #22531]: #22533
-#22537 := [monotonicity #22534]: #22536
-#22540 := [monotonicity #22537]: #22539
-#22543 := [monotonicity #22540]: #22542
-#22546 := [monotonicity #22543]: #22545
-#22549 := [monotonicity #22546]: #22548
-#22552 := [monotonicity #22549]: #22551
-#22555 := [monotonicity #22552]: #22554
-#22558 := [monotonicity #22555]: #22557
-#22567 := [monotonicity #22558 #22564]: #22566
-#22570 := [monotonicity #22567]: #22569
-#22573 := [monotonicity #22570]: #22572
-#22576 := [monotonicity #22573]: #22575
-#22579 := [monotonicity #22576]: #22578
-#22582 := [monotonicity #22579]: #22581
-#22585 := [monotonicity #22582]: #22584
-#22588 := [monotonicity #22585]: #22587
-#22591 := [monotonicity #22588]: #22590
-#22594 := [monotonicity #22591]: #22593
-#22597 := [monotonicity #22594]: #22596
-#22600 := [monotonicity #22597]: #22599
-#22637 := [monotonicity #22600 #22634]: #22636
-#22640 := [monotonicity #22637]: #22639
-#22483 := (iff #21767 #22482)
-#22480 := (iff #21463 #22477)
-#22478 := (iff #21458 #21458)
-#22479 := [refl]: #22478
-#22481 := [quant-intro #22479]: #22480
-#22484 := [monotonicity #22481]: #22483
-#22643 := [monotonicity #22484 #22640]: #22642
-#22646 := [monotonicity #22643]: #22645
-#22649 := [monotonicity #22646]: #22648
-#22652 := [monotonicity #22649]: #22651
-#22475 := (iff #21784 #22474)
-#22472 := (iff #21441 #22469)
-#22470 := (iff #21436 #21436)
-#22471 := [refl]: #22470
-#22473 := [quant-intro #22471]: #22472
-#22476 := [monotonicity #22473]: #22475
-#22655 := [monotonicity #22476 #22652]: #22654
-#22658 := [monotonicity #22655]: #22657
-#22661 := [monotonicity #22658]: #22660
-#22664 := [monotonicity #22661]: #22663
-#22667 := [monotonicity #22664]: #22666
-#22670 := [monotonicity #22667]: #22669
-#22673 := [monotonicity #22670]: #22672
-#22676 := [monotonicity #22673]: #22675
-#22679 := [monotonicity #22676]: #22678
-#22682 := [monotonicity #22679]: #22681
-#22685 := [monotonicity #22682]: #22684
-#22688 := [monotonicity #22685]: #22687
-#22691 := [monotonicity #22688]: #22690
-#22694 := [monotonicity #22691]: #22693
-#22697 := [monotonicity #22694]: #22696
-#22700 := [monotonicity #22697]: #22699
-#22703 := [monotonicity #22700]: #22702
-#22706 := [monotonicity #22703]: #22705
-#22709 := [monotonicity #22706]: #22708
-#18175 := (not #18170)
-#18181 := (and #17866 #17870 #18175)
-#18186 := (not #18181)
-#18189 := (or #18157 #18186)
-#18192 := (not #18189)
-#15260 := (and #3142 #4041 #13272 #14378)
-#17890 := (not #15260)
-#17893 := (forall (vars (?x778 int)) #17890)
-#15235 := (and #4041 #13272 #14378)
-#15240 := (not #15235)
-#15246 := (or #13288 #15240)
-#15251 := (forall (vars (?x776 int)) #15246)
-#17897 := (and #15251 #17893)
-#18198 := (or #17897 #18192)
-#18206 := (and #12113 #12116 #12119 #12122 #12910 #12913 #12967 #18198)
-#18027 := (not #18022)
-#18033 := (and #17757 #17761 #18027)
-#18038 := (not #18033)
-#18041 := (or #18009 #18038)
-#18044 := (not #18041)
-#15146 := (and #4041 #13098 #14378)
-#15151 := (not #15146)
-#15157 := (or #13114 #15151)
-#15162 := (forall (vars (?x785 int)) #15157)
-#17774 := (not #13135)
-#17784 := (and #17774 #15162)
-#18050 := (or #17784 #18044)
-#18055 := (and #13089 #18050)
-#18058 := (or #13093 #18055)
-#18064 := (and #3258 #13017 #13051 #13059 #13061 #15127 #18058)
-#18069 := (or #17742 #17745 #18064)
-#18107 := (and #12521 #12524 #12910 #12913 #12997 #13017 #18069)
-#18075 := (and #3236 #3237 #12346 #12355 #12375 #12380 #12383 #12913 #13017 #18069)
-#18080 := (or #17721 #17730 #18075)
-#18086 := (and #12346 #12349 #18080)
-#18091 := (or #17721 #17724 #18086)
-#18097 := (and #12910 #12913 #12996 #18091)
-#18112 := (or #18097 #18107)
-#18118 := (and #12346 #12355 #12910 #12913 #18112)
-#18123 := (or #17721 #17730 #18118)
-#18129 := (and #12346 #12349 #18123)
-#18134 := (or #17721 #17724 #18129)
-#18140 := (and #12910 #12913 #12968 #18134)
-#18211 := (or #18140 #18206)
-#15060 := (and #4041 #13364 #14378)
-#15065 := (not #15060)
-#15071 := (or #13380 #15065)
-#15076 := (forall (vars (?x775 int)) #15071)
-#18217 := (and #3055 #3195 #3196 #3197 #3198 #3199 #3200 #12030 #12067 #12261 #12741 #12910 #12913 #13359 #13389 #13392 #13402 #15076 #15085 #15096 #15107 #18211)
-#18222 := (or #17676 #12740 #18217)
-#15035 := (and #4041 #12870 #14378)
-#15040 := (not #15035)
-#15046 := (or #12885 #15040)
-#15051 := (forall (vars (?x773 int)) #15046)
-#18225 := (and #15051 #18222)
-#17654 := (not #17653)
-#17971 := (and #17652 #17654 #17655)
-#17974 := (not #17971)
-#17977 := (or #17662 #17974)
-#17980 := (not #17977)
-#18228 := (or #17980 #18225)
-#18231 := (and #12863 #18228)
-#18234 := (or #12866 #18231)
-#18240 := (and #3055 #3056 #3057 #3058 #11970 #11979 #18234)
-#18245 := (or #17631 #17640 #18240)
-#18251 := (and #11970 #11973 #18245)
-#18256 := (or #17631 #17634 #18251)
-#18259 := (and #11967 #18256)
-#18262 := (or #12702 #18259)
-#21848 := (iff #18262 #21847)
-#21845 := (iff #18259 #21842)
-#21837 := (and #11967 #21834)
-#21843 := (iff #21837 #21842)
-#21844 := [rewrite]: #21843
-#21838 := (iff #18259 #21837)
-#21835 := (iff #18256 #21834)
-#21832 := (iff #18251 #21829)
-#21824 := (and #11970 #11973 #21821)
-#21830 := (iff #21824 #21829)
-#21831 := [rewrite]: #21830
-#21825 := (iff #18251 #21824)
-#21822 := (iff #18245 #21821)
-#21819 := (iff #18240 #21816)
-#21808 := (and #3055 #3056 #3057 #3058 #11970 #11979 #21805)
-#21817 := (iff #21808 #21816)
-#21818 := [rewrite]: #21817
-#21809 := (iff #18240 #21808)
-#21806 := (iff #18234 #21805)
-#21803 := (iff #18231 #21800)
-#21795 := (and #12863 #21792)
-#21801 := (iff #21795 #21800)
-#21802 := [rewrite]: #21801
-#21796 := (iff #18231 #21795)
-#21793 := (iff #18228 #21792)
-#21790 := (iff #18225 #21787)
-#21781 := (and #21441 #21778)
-#21788 := (iff #21781 #21787)
-#21789 := [rewrite]: #21788
-#21782 := (iff #18225 #21781)
-#21779 := (iff #18222 #21778)
-#21776 := (iff #18217 #21773)
-#21752 := (and #3055 #3195 #3196 #3197 #3198 #3199 #3200 #12030 #12067 #12261 #12741 #12910 #12913 #13359 #13389 #13392 #13402 #21463 #15085 #15096 #15107 #21749)
-#21774 := (iff #21752 #21773)
-#21775 := [rewrite]: #21774
-#21753 := (iff #18217 #21752)
-#21750 := (iff #18211 #21749)
-#21747 := (iff #18206 #21744)
-#21735 := (and #12113 #12116 #12119 #12122 #12910 #12913 #12967 #21732)
-#21745 := (iff #21735 #21744)
-#21746 := [rewrite]: #21745
-#21736 := (iff #18206 #21735)
-#21733 := (iff #18198 #21732)
-#21730 := (iff #18192 #21729)
-#21727 := (iff #18189 #21724)
-#21710 := (or #21708 #21709 #18170)
-#21721 := (or #18157 #21710)
-#21725 := (iff #21721 #21724)
-#21726 := [rewrite]: #21725
-#21722 := (iff #18189 #21721)
-#21719 := (iff #18186 #21710)
-#21711 := (not #21710)
-#21714 := (not #21711)
-#21717 := (iff #21714 #21710)
-#21718 := [rewrite]: #21717
-#21715 := (iff #18186 #21714)
-#21712 := (iff #18181 #21711)
-#21713 := [rewrite]: #21712
-#21716 := [monotonicity #21713]: #21715
-#21720 := [trans #21716 #21718]: #21719
-#21723 := [monotonicity #21720]: #21722
-#21728 := [trans #21723 #21726]: #21727
-#21731 := [monotonicity #21728]: #21730
-#21706 := (iff #17897 #21703)
-#21697 := (and #21679 #21694)
-#21704 := (iff #21697 #21703)
-#21705 := [rewrite]: #21704
-#21698 := (iff #17897 #21697)
-#21695 := (iff #17893 #21694)
-#21692 := (iff #17890 #21683)
-#21684 := (not #21683)
-#21687 := (not #21684)
-#21690 := (iff #21687 #21683)
-#21691 := [rewrite]: #21690
-#21688 := (iff #17890 #21687)
-#21685 := (iff #15260 #21684)
-#21686 := [rewrite]: #21685
-#21689 := [monotonicity #21686]: #21688
-#21693 := [trans #21689 #21691]: #21692
-#21696 := [quant-intro #21693]: #21695
-#21680 := (iff #15251 #21679)
-#21677 := (iff #15246 #21674)
-#21660 := (or #4963 #13270 #18695)
-#21671 := (or #13288 #21660)
-#21675 := (iff #21671 #21674)
-#21676 := [rewrite]: #21675
-#21672 := (iff #15246 #21671)
-#21669 := (iff #15240 #21660)
-#21661 := (not #21660)
-#21664 := (not #21661)
-#21667 := (iff #21664 #21660)
-#21668 := [rewrite]: #21667
-#21665 := (iff #15240 #21664)
-#21662 := (iff #15235 #21661)
-#21663 := [rewrite]: #21662
-#21666 := [monotonicity #21663]: #21665
-#21670 := [trans #21666 #21668]: #21669
-#21673 := [monotonicity #21670]: #21672
-#21678 := [trans #21673 #21676]: #21677
-#21681 := [quant-intro #21678]: #21680
-#21699 := [monotonicity #21681 #21696]: #21698
-#21707 := [trans #21699 #21705]: #21706
-#21734 := [monotonicity #21707 #21731]: #21733
-#21737 := [monotonicity #21734]: #21736
-#21748 := [trans #21737 #21746]: #21747
-#21658 := (iff #18140 #21655)
-#21650 := (and #12910 #12913 #12968 #21647)
-#21656 := (iff #21650 #21655)
-#21657 := [rewrite]: #21656
-#21651 := (iff #18140 #21650)
-#21648 := (iff #18134 #21647)
-#21645 := (iff #18129 #21642)
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-#21549 := [monotonicity #21546]: #21548
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-#21566 := [monotonicity #21563]: #21565
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-#21585 := [monotonicity #21582]: #21584
-#21588 := [monotonicity #21585]: #21587
-#21595 := [trans #21588 #21593]: #21594
-#21598 := [monotonicity #21595]: #21597
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-#21626 := [monotonicity #21623]: #21625
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-#21464 := (iff #15076 #21463)
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-#18006 := [monotonicity #18003]: #18005
-#18013 := [trans #18006 #18011]: #18012
-#18043 := [monotonicity #18013 #18040]: #18042
-#18046 := [monotonicity #18043]: #18045
-#18049 := [monotonicity #18046]: #18048
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-#18057 := [monotonicity #18000 #18054]: #18056
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-#17998 := [rewrite]: #17997
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-#18074 := [monotonicity #17996 #18071]: #18073
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-#18090 := [trans #18085 #18088]: #18089
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-#18096 := [monotonicity #17994 #18093]: #18095
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-#18114 := [monotonicity #18101 #18111]: #18113
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-#18117 := [monotonicity #17992 #18114]: #18116
-#18122 := [trans #18117 #18120]: #18121
-#18125 := [monotonicity #18122]: #18124
-#18128 := [monotonicity #17990 #18125]: #18127
-#18133 := [trans #18128 #18131]: #18132
-#18136 := [monotonicity #18133]: #18135
-#17987 := (iff #17718 #12977)
-#17988 := [rewrite]: #17987
-#18139 := [monotonicity #17988 #18136]: #18138
-#18144 := [trans #18139 #18142]: #18143
-#18213 := [monotonicity #18144 #18210]: #18212
-#17985 := (iff #17682 #14482)
-#17986 := [rewrite]: #17985
-#18216 := [monotonicity #17986 #18213]: #18215
-#18221 := [trans #18216 #18219]: #18220
-#17983 := (iff #17679 #12740)
-#17984 := [rewrite]: #17983
-#18224 := [monotonicity #17984 #18221]: #18223
-#18227 := [monotonicity #18224]: #18226
-#17981 := (iff #17664 #17980)
-#17978 := (iff #17663 #17977)
-#17975 := (iff #17657 #17974)
-#17972 := (iff #17656 #17971)
-#17973 := [rewrite]: #17972
-#17976 := [monotonicity #17973]: #17975
-#17979 := [monotonicity #17976]: #17978
-#17982 := [monotonicity #17979]: #17981
-#18230 := [monotonicity #17982 #18227]: #18229
-#17969 := (iff #17648 #12863)
-#17970 := [rewrite]: #17969
-#18233 := [monotonicity #17970 #18230]: #18232
-#18236 := [monotonicity #18233]: #18235
-#17967 := (iff #17643 #12855)
-#17968 := [rewrite]: #17967
-#18239 := [monotonicity #17968 #18236]: #18238
-#18244 := [trans #18239 #18242]: #18243
-#18247 := [monotonicity #18244]: #18246
-#17965 := (iff #17637 #11976)
-#17966 := [rewrite]: #17965
-#18250 := [monotonicity #17966 #18247]: #18249
-#18255 := [trans #18250 #18253]: #18254
-#18258 := [monotonicity #18255]: #18257
-#17963 := (iff #17628 #11967)
-#17964 := [rewrite]: #17963
-#18261 := [monotonicity #17964 #18258]: #18260
-#18264 := [monotonicity #18261]: #18263
-#15265 := (exists (vars (?x778 int)) #15260)
-#15254 := (not #15251)
-#15268 := (or #15254 #15265)
-#15271 := (and #15251 #15268)
-#15277 := (or #13347 #14498 #15271)
-#15165 := (not #15162)
-#15171 := (or #13135 #15165)
-#15176 := (and #15162 #15171)
-#15179 := (or #13093 #15176)
-#15182 := (and #13089 #15179)
-#15185 := (or #15140 #15182)
-#15188 := (and #13051 #15127 #15185)
-#15209 := (or #13216 #15188)
-#15191 := (or #13048 #15188)
-#15194 := (and #12346 #12355 #15191)
-#15197 := (or #12503 #15194)
-#15200 := (and #12346 #12349 #15197)
-#15203 := (or #13013 #15200)
-#15214 := (and #15203 #15209)
-#15217 := (or #12993 #15214)
-#15220 := (and #12346 #12355 #15217)
-#15223 := (or #12503 #15220)
-#15226 := (and #12346 #12349 #15223)
-#15229 := (or #12982 #15226)
-#15282 := (and #15229 #15277)
-#15120 := (not #15115)
-#15288 := (or #14487 #15120 #15282)
-#15293 := (and #3055 #12741 #15288)
-#15054 := (not #15051)
-#15296 := (or #15054 #15293)
-#15299 := (and #15051 #15296)
-#15302 := (or #12866 #15299)
-#15305 := (and #12863 #15302)
-#15308 := (or #12860 #15305)
-#15311 := (and #11970 #11979 #15308)
-#15314 := (or #12690 #15311)
-#15317 := (and #11970 #11973 #15314)
-#15320 := (or #12702 #15317)
-#15323 := (and #11967 #15320)
-#15326 := (not #15323)
-#17958 := (~ #15326 #17957)
-#17954 := (not #15320)
-#17955 := (~ #17954 #17953)
-#17950 := (not #15317)
-#17951 := (~ #17950 #17949)
-#17946 := (not #15314)
-#17947 := (~ #17946 #17945)
-#17942 := (not #15311)
-#17943 := (~ #17942 #17941)
-#17938 := (not #15308)
-#17939 := (~ #17938 #17937)
-#17934 := (not #15305)
-#17935 := (~ #17934 #17933)
-#17930 := (not #15302)
-#17931 := (~ #17930 #17929)
-#17926 := (not #15299)
-#17927 := (~ #17926 #17925)
-#17922 := (not #15296)
-#17923 := (~ #17922 #17921)
-#17918 := (not #15293)
-#17919 := (~ #17918 #17917)
-#17914 := (not #15288)
-#17915 := (~ #17914 #17913)
-#17910 := (not #15282)
-#17911 := (~ #17910 #17909)
-#17906 := (not #15277)
-#17907 := (~ #17906 #17905)
-#17902 := (not #15271)
-#17903 := (~ #17902 #17901)
-#17898 := (not #15268)
-#17899 := (~ #17898 #17897)
-#17894 := (not #15265)
-#17895 := (~ #17894 #17893)
-#17891 := (~ #17890 #17890)
-#17892 := [refl]: #17891
-#17896 := [nnf-neg #17892]: #17895
-#17887 := (not #15254)
-#17888 := (~ #17887 #15251)
-#17885 := (~ #15251 #15251)
-#17883 := (~ #15246 #15246)
-#17884 := [refl]: #17883
-#17886 := [nnf-pos #17884]: #17885
-#17889 := [nnf-neg #17886]: #17888
-#17900 := [nnf-neg #17889 #17896]: #17899
-#17879 := (~ #15254 #17878)
-#17880 := [sk]: #17879
-#17904 := [nnf-neg #17880 #17900]: #17903
-#17863 := (~ #17862 #17862)
-#17864 := [refl]: #17863
-#17860 := (~ #17859 #17859)
-#17861 := [refl]: #17860
-#17908 := [nnf-neg #17861 #17864 #17904]: #17907
-#17856 := (not #15229)
-#17857 := (~ #17856 #17855)
-#17852 := (not #15226)
-#17853 := (~ #17852 #17851)
-#17848 := (not #15223)
-#17849 := (~ #17848 #17847)
-#17844 := (not #15220)
-#17845 := (~ #17844 #17843)
-#17840 := (not #15217)
-#17841 := (~ #17840 #17839)
-#17836 := (not #15214)
-#17837 := (~ #17836 #17835)
-#17832 := (not #15209)
-#17833 := (~ #17832 #17831)
-#17805 := (not #15188)
-#17806 := (~ #17805 #17804)
-#17801 := (not #15185)
-#17802 := (~ #17801 #17800)
-#17797 := (not #15182)
-#17798 := (~ #17797 #17796)
-#17793 := (not #15179)
-#17794 := (~ #17793 #17792)
-#17789 := (not #15176)
-#17790 := (~ #17789 #17788)
-#17785 := (not #15171)
-#17786 := (~ #17785 #17784)
-#17781 := (not #15165)
-#17782 := (~ #17781 #15162)
-#17779 := (~ #15162 #15162)
-#17777 := (~ #15157 #15157)
-#17778 := [refl]: #17777
-#17780 := [nnf-pos #17778]: #17779
-#17783 := [nnf-neg #17780]: #17782
-#17775 := (~ #17774 #17774)
-#17776 := [refl]: #17775
-#17787 := [nnf-neg #17776 #17783]: #17786
-#17770 := (~ #15165 #17769)
-#17771 := [sk]: #17770
-#17791 := [nnf-neg #17771 #17787]: #17790
-#17754 := (~ #17753 #17753)
-#17755 := [refl]: #17754
-#17795 := [nnf-neg #17755 #17791]: #17794
-#17751 := (~ #13093 #13093)
-#17752 := [refl]: #17751
-#17799 := [nnf-neg #17752 #17795]: #17798
-#17749 := (~ #17748 #17748)
-#17750 := [refl]: #17749
-#17803 := [nnf-neg #17750 #17799]: #17802
-#17746 := (~ #17745 #17745)
-#17747 := [refl]: #17746
-#17743 := (~ #17742 #17742)
-#17744 := [refl]: #17743
-#17807 := [nnf-neg #17744 #17747 #17803]: #17806
-#17829 := (~ #17828 #17828)
-#17830 := [refl]: #17829
-#17834 := [nnf-neg #17830 #17807]: #17833
-#17825 := (not #15203)
-#17826 := (~ #17825 #17824)
-#17821 := (not #15200)
-#17822 := (~ #17821 #17820)
-#17817 := (not #15197)
-#17818 := (~ #17817 #17816)
-#17813 := (not #15194)
-#17814 := (~ #17813 #17812)
-#17809 := (not #15191)
-#17810 := (~ #17809 #17808)
-#17740 := (~ #17739 #17739)
-#17741 := [refl]: #17740
-#17811 := [nnf-neg #17741 #17807]: #17810
-#17731 := (~ #17730 #17730)
-#17732 := [refl]: #17731
-#17722 := (~ #17721 #17721)
-#17723 := [refl]: #17722
-#17815 := [nnf-neg #17723 #17732 #17811]: #17814
-#17728 := (~ #17727 #17727)
-#17729 := [refl]: #17728
-#17819 := [nnf-neg #17729 #17815]: #17818
-#17725 := (~ #17724 #17724)
-#17726 := [refl]: #17725
-#17823 := [nnf-neg #17723 #17726 #17819]: #17822
-#17737 := (~ #17736 #17736)
-#17738 := [refl]: #17737
-#17827 := [nnf-neg #17738 #17823]: #17826
-#17838 := [nnf-neg #17827 #17834]: #17837
-#17734 := (~ #17733 #17733)
-#17735 := [refl]: #17734
-#17842 := [nnf-neg #17735 #17838]: #17841
-#17846 := [nnf-neg #17723 #17732 #17842]: #17845
-#17850 := [nnf-neg #17729 #17846]: #17849
-#17854 := [nnf-neg #17723 #17726 #17850]: #17853
-#17719 := (~ #17718 #17718)
-#17720 := [refl]: #17719
-#17858 := [nnf-neg #17720 #17854]: #17857
-#17912 := [nnf-neg #17858 #17908]: #17911
-#17715 := (not #15120)
-#17716 := (~ #17715 #15115)
-#17713 := (~ #15115 #15115)
-#17711 := (~ #15107 #15107)
-#17712 := [refl]: #17711
-#17709 := (~ #15096 #15096)
-#17710 := [refl]: #17709
-#17707 := (~ #15085 #15085)
-#17708 := [refl]: #17707
-#17705 := (~ #15076 #15076)
-#17703 := (~ #15071 #15071)
-#17704 := [refl]: #17703
-#17706 := [nnf-pos #17704]: #17705
-#17701 := (~ #13402 #13402)
-#17702 := [refl]: #17701
-#17699 := (~ #13392 #13392)
-#17700 := [refl]: #17699
-#17697 := (~ #13389 #13389)
-#17698 := [refl]: #17697
-#17695 := (~ #13359 #13359)
-#17696 := [refl]: #17695
-#17693 := (~ #12913 #12913)
-#17694 := [refl]: #17693
-#17691 := (~ #12910 #12910)
-#17692 := [refl]: #17691
-#17689 := (~ #12741 #12741)
-#17690 := [refl]: #17689
-#17687 := (~ #12030 #12030)
-#17688 := [refl]: #17687
-#17685 := (~ #3055 #3055)
-#17686 := [refl]: #17685
-#17714 := [monotonicity #17686 #17688 #17690 #17692 #17694 #17696 #17698 #17700 #17702 #17706 #17708 #17710 #17712]: #17713
-#17717 := [nnf-neg #17714]: #17716
-#17683 := (~ #17682 #17682)
-#17684 := [refl]: #17683
-#17916 := [nnf-neg #17684 #17717 #17912]: #17915
-#17680 := (~ #17679 #17679)
-#17681 := [refl]: #17680
-#17677 := (~ #17676 #17676)
-#17678 := [refl]: #17677
-#17920 := [nnf-neg #17678 #17681 #17916]: #17919
-#17673 := (not #15054)
-#17674 := (~ #17673 #15051)
-#17671 := (~ #15051 #15051)
-#17669 := (~ #15046 #15046)
-#17670 := [refl]: #17669
-#17672 := [nnf-pos #17670]: #17671
-#17675 := [nnf-neg #17672]: #17674
-#17924 := [nnf-neg #17675 #17920]: #17923
-#17665 := (~ #15054 #17664)
-#17666 := [sk]: #17665
-#17928 := [nnf-neg #17666 #17924]: #17927
-#17649 := (~ #17648 #17648)
-#17650 := [refl]: #17649
-#17932 := [nnf-neg #17650 #17928]: #17931
-#17646 := (~ #12866 #12866)
-#17647 := [refl]: #17646
-#17936 := [nnf-neg #17647 #17932]: #17935
-#17644 := (~ #17643 #17643)
-#17645 := [refl]: #17644
-#17940 := [nnf-neg #17645 #17936]: #17939
-#17641 := (~ #17640 #17640)
-#17642 := [refl]: #17641
-#17632 := (~ #17631 #17631)
-#17633 := [refl]: #17632
-#17944 := [nnf-neg #17633 #17642 #17940]: #17943
-#17638 := (~ #17637 #17637)
-#17639 := [refl]: #17638
-#17948 := [nnf-neg #17639 #17944]: #17947
-#17635 := (~ #17634 #17634)
-#17636 := [refl]: #17635
-#17952 := [nnf-neg #17633 #17636 #17948]: #17951
-#17629 := (~ #17628 #17628)
-#17630 := [refl]: #17629
-#17956 := [nnf-neg #17630 #17952]: #17955
-#17626 := (~ #12702 #12702)
-#17627 := [refl]: #17626
-#17959 := [nnf-neg #17627 #17956]: #17958
-#14519 := (or #13325 #13347 #14498)
-#14524 := (and #13247 #14519)
-#14530 := (or #13453 #14487 #14524)
-#14535 := (and #3055 #12741 #14530)
-#14538 := (or #12895 #14535)
-#14541 := (and #12892 #14538)
-#14544 := (or #12866 #14541)
-#14547 := (and #12863 #14544)
-#14550 := (or #12860 #14547)
-#14553 := (and #11970 #11979 #14550)
-#14556 := (or #12690 #14553)
-#14559 := (and #11970 #11973 #14556)
-#14562 := (or #12702 #14559)
-#14565 := (and #11967 #14562)
-#14568 := (not #14565)
-#15327 := (iff #14568 #15326)
-#15324 := (iff #14565 #15323)
-#15321 := (iff #14562 #15320)
-#15318 := (iff #14559 #15317)
-#15315 := (iff #14556 #15314)
-#15312 := (iff #14553 #15311)
-#15309 := (iff #14550 #15308)
-#15306 := (iff #14547 #15305)
-#15303 := (iff #14544 #15302)
-#15300 := (iff #14541 #15299)
-#15297 := (iff #14538 #15296)
-#15294 := (iff #14535 #15293)
-#15291 := (iff #14530 #15288)
-#15285 := (or #15120 #14487 #15282)
-#15289 := (iff #15285 #15288)
-#15290 := [rewrite]: #15289
-#15286 := (iff #14530 #15285)
-#15283 := (iff #14524 #15282)
-#15280 := (iff #14519 #15277)
-#15274 := (or #15271 #13347 #14498)
-#15278 := (iff #15274 #15277)
-#15279 := [rewrite]: #15278
-#15275 := (iff #14519 #15274)
-#15272 := (iff #13325 #15271)
-#15269 := (iff #13320 #15268)
-#15266 := (iff #13311 #15265)
-#15263 := (iff #13306 #15260)
-#15257 := (and #3142 #4041 #14378 #13272)
-#15261 := (iff #15257 #15260)
-#15262 := [rewrite]: #15261
-#15258 := (iff #13306 #15257)
-#14373 := (iff #4355 #14378)
-#14394 := -4294967295::int
-#14386 := (+ -4294967295::int #161)
-#14379 := (<= #14386 0::int)
-#14375 := (iff #14379 #14378)
-#14376 := [rewrite]: #14375
-#14380 := (iff #4355 #14379)
-#14381 := (= #4354 #14386)
-#14387 := (+ #161 -4294967295::int)
-#14383 := (= #14387 #14386)
-#14384 := [rewrite]: #14383
-#14388 := (= #4354 #14387)
-#14389 := (= #4353 -4294967295::int)
-#14395 := (* -1::int 4294967295::int)
-#14391 := (= #14395 -4294967295::int)
-#14392 := [rewrite]: #14391
-#14396 := (= #4353 #14395)
-#7476 := (= uf_76 4294967295::int)
+#10016 := (iff #2227 #10013)
+#9965 := (and #52 #3455)
+#9969 := (and #3623 #9965)
+#9972 := (and #3620 #9969)
+#9975 := (and #3617 #9972)
+#9978 := (and #3602 #9975)
+#9981 := (and #3899 #9978)
+#9990 := (not #9981)
+#9991 := (or #9990 #9984)
+#9996 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #9991)
+#10014 := (iff #9996 #10013)
+#10011 := (iff #9991 #10008)
+#10005 := (or #10002 #9984)
+#10009 := (iff #10005 #10008)
+#10010 := [rewrite]: #10009
+#10006 := (iff #9991 #10005)
+#10003 := (iff #9990 #10002)
+#10000 := (iff #9981 #9999)
+#10001 := [rewrite]: #10000
+#10004 := [monotonicity #10001]: #10003
+#10007 := [monotonicity #10004]: #10006
+#10012 := [trans #10007 #10010]: #10011
+#10015 := [quant-intro #10012]: #10014
+#9997 := (iff #2227 #9996)
+#9994 := (iff #2226 #9991)
+#9987 := (implies #9981 #9984)
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+#9973 := (iff #2221 #9972)
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+#9967 := (iff #2219 #9965)
+#3456 := (iff #72 #3455)
+#3457 := [rewrite]: #3456
+#9968 := [monotonicity #3457]: #9967
+#9971 := [monotonicity #3625 #9968]: #9970
+#3621 := (iff #145 #3620)
+#3622 := [rewrite]: #3621
+#9974 := [monotonicity #3622 #9971]: #9973
+#9977 := [monotonicity #3619 #9974]: #9976
+#3604 := (iff #136 #3602)
+#3605 := [rewrite]: #3604
+#9980 := [monotonicity #3605 #9977]: #9979
+#3901 := (iff #229 #3899)
+#3902 := [rewrite]: #3901
+#9983 := [monotonicity #3902 #9980]: #9982
+#9989 := [monotonicity #9983 #9986]: #9988
+#9995 := [trans #9989 #9993]: #9994
+#9998 := [quant-intro #9995]: #9997
+#10017 := [trans #9998 #10015]: #10016
+#9964 := [asserted]: #2227
+#10018 := [mp #9964 #10017]: #10013
+#17576 := [mp~ #10018 #17575]: #10013
+#21604 := [mp #17576 #21603]: #21601
+#26589 := (not #26588)
+#26409 := (not #26383)
+#26353 := (not #26352)
+#24483 := (not #11905)
+#26517 := (not #21601)
+#26520 := (or #26517 #24483 #26353 #26409 #26479 #26584 #26587 #26589 #26593)
+#26591 := (= #26590 uf_14)
+#26592 := (or #26591 #26353 #26409 #26589 #26587 #26584 #24483 #26479)
+#26521 := (or #26517 #26592)
+#26572 := (iff #26521 #26520)
+#26599 := (or #24483 #26353 #26409 #26479 #26584 #26587 #26589 #26593)
+#26523 := (or #26517 #26599)
+#26570 := (iff #26523 #26520)
+#26571 := [rewrite]: #26570
+#26574 := (iff #26521 #26523)
+#26602 := (iff #26592 #26599)
+#26596 := (or #26593 #26353 #26409 #26589 #26587 #26584 #24483 #26479)
+#26600 := (iff #26596 #26599)
+#26601 := [rewrite]: #26600
+#26597 := (iff #26592 #26596)
+#26594 := (iff #26591 #26593)
+#26595 := [rewrite]: #26594
+#26598 := [monotonicity #26595]: #26597
+#26603 := [trans #26598 #26601]: #26602
+#26569 := [monotonicity #26603]: #26574
+#26568 := [trans #26569 #26571]: #26572
+#26522 := [quant-inst]: #26521
+#26573 := [mp #26522 #26568]: #26520
+#26837 := [unit-resolution #26573 #21604 #14064 #26836 #26811 #26786 #26779]: #26819
+#26838 := [unit-resolution #26837 #26758 #26746 #26737]: false
+#26899 := [lemma #26838]: #26479
+#26492 := (or #26490 #26500 #26481)
+#26493 := [def-axiom]: #26492
+#26513 := [unit-resolution #26493 #26899]: #26518
+#26519 := [unit-resolution #26513 #26699]: #26481
+#26578 := [trans #26519 #26577]: #11925
+#26514 := [hypothesis]: #13009
+#26580 := [unit-resolution #26514 #26578]: false
+#26581 := [lemma #26580]: #11925
+#23239 := (or #13009 #23236)
+#22240 := (forall (vars (?x778 int)) #22229)
+#22247 := (not #22240)
+#22225 := (forall (vars (?x776 int)) #22220)
+#22246 := (not #22225)
+#22248 := (or #22246 #22247)
+#22249 := (not #22248)
+#22278 := (or #22249 #22275)
+#22284 := (not #22278)
+#22285 := (or #12079 #12070 #12061 #12052 #22161 #13365 #13511 #22284)
+#22286 := (not #22285)
+#22064 := (forall (vars (?x785 int)) #22059)
+#22070 := (not #22064)
+#22071 := (or #22046 #22070)
+#22072 := (not #22071)
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+#22066 := [quant-intro #22063]: #22065
+#22054 := (iff #18313 #22045)
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+#18831 := [monotonicity #18828]: #18830
+#18529 := (iff #18151 #11940)
+#18530 := [rewrite]: #18529
+#18527 := (iff #18148 #3045)
+#18528 := [rewrite]: #18527
+#18525 := (iff #18145 #3044)
+#18526 := [rewrite]: #18525
+#18523 := (iff #18142 #3043)
+#18524 := [rewrite]: #18523
+#18521 := (iff #18139 #3042)
+#18522 := [rewrite]: #18521
+#18834 := [monotonicity #18522 #18524 #18526 #18528 #18530 #18831]: #18833
+#18839 := [trans #18834 #18837]: #18838
+#18842 := [monotonicity #18839]: #18841
+#18519 := (iff #18133 #11934)
+#18520 := [rewrite]: #18519
+#18845 := [monotonicity #18520 #18842]: #18844
+#18850 := [trans #18845 #18848]: #18849
+#18853 := [monotonicity #18850]: #18852
+#18517 := (iff #18124 #11925)
+#18518 := [rewrite]: #18517
+#18856 := [monotonicity #18518 #18853]: #18855
+#18859 := [monotonicity #18856]: #18858
+#15735 := (exists (vars (?x778 int)) #15730)
+#15724 := (not #15721)
+#15738 := (or #15724 #15735)
+#15741 := (and #15721 #15738)
+#15744 := (or #12079 #12070 #12061 #12052 #13230 #13511 #15741)
+#15625 := (not #15622)
+#15631 := (or #13310 #15625)
+#15636 := (and #15622 #15631)
+#15639 := (or #13264 #15636)
+#15642 := (and #13259 #15639)
+#15654 := (or #12401 #13256 #13331 #15642 #15648)
+#15659 := (and #13243 #15609 #15654)
+#15685 := (or #12566 #12557 #13230 #13239 #13416 #15659)
+#15662 := (or #12476 #12467 #12494 #12485 #12449 #12440 #13365 #13239 #15659)
+#15665 := (and #12293 #12302 #15662)
+#15668 := (or #12506 #15665)
+#15671 := (and #12293 #12296 #15668)
+#15677 := (or #13230 #13417 #15671)
+#15690 := (and #15677 #15685)
+#15693 := (or #12494 #13230 #15690)
+#15696 := (and #12293 #12302 #15693)
+#15699 := (or #12506 #15696)
+#15702 := (and #12293 #12296 #15699)
+#15708 := (or #13230 #13510 #15702)
+#15747 := (and #15708 #15744)
+#15551 := (not #15548)
+#15753 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #13700 #13740 #13786 #15551 #15568 #15585 #15602 #15747)
+#15758 := (and #3042 #13218 #15753)
+#15537 := (not #15534)
+#15761 := (or #15537 #15758)
+#15764 := (and #15534 #15761)
+#15767 := (or #13181 #15764)
+#15770 := (and #13178 #15767)
+#15773 := (or #12976 #12967 #12958 #12949 #12985 #15770)
+#15776 := (and #11928 #11937 #15773)
+#15779 := (or #12997 #15776)
+#15782 := (and #11928 #11931 #15779)
+#15785 := (or #13009 #15782)
+#15788 := (and #11925 #15785)
+#15791 := (not #15788)
+#18512 := (~ #15791 #18511)
+#18508 := (not #15785)
+#18509 := (~ #18508 #18507)
+#18504 := (not #15782)
+#18505 := (~ #18504 #18503)
+#18500 := (not #15779)
+#18501 := (~ #18500 #18499)
+#18496 := (not #15776)
+#18497 := (~ #18496 #18495)
+#18492 := (not #15773)
+#18493 := (~ #18492 #18491)
+#18488 := (not #15770)
+#18489 := (~ #18488 #18487)
+#18484 := (not #15767)
+#18485 := (~ #18484 #18483)
+#18480 := (not #15764)
+#18481 := (~ #18480 #18479)
+#18476 := (not #15761)
+#18477 := (~ #18476 #18475)
+#18472 := (not #15758)
+#18473 := (~ #18472 #18471)
+#18468 := (not #15753)
+#18469 := (~ #18468 #18467)
+#18464 := (not #15747)
+#18465 := (~ #18464 #18463)
+#18460 := (not #15744)
+#18461 := (~ #18460 #18459)
+#18456 := (not #15741)
+#18457 := (~ #18456 #18455)
+#18452 := (not #15738)
+#18453 := (~ #18452 #18451)
+#18448 := (not #15735)
+#18449 := (~ #18448 #18447)
+#18445 := (~ #18444 #18444)
+#18446 := [refl]: #18445
+#18450 := [nnf-neg #18446]: #18449
+#18441 := (not #15724)
+#18442 := (~ #18441 #15721)
+#18439 := (~ #15721 #15721)
+#18437 := (~ #15716 #15716)
+#18438 := [refl]: #18437
+#18440 := [nnf-pos #18438]: #18439
+#18443 := [nnf-neg #18440]: #18442
+#18454 := [nnf-neg #18443 #18450]: #18453
+#18433 := (~ #15724 #18432)
+#18434 := [sk]: #18433
+#18458 := [nnf-neg #18434 #18454]: #18457
+#18418 := (~ #13514 #13514)
+#18419 := [refl]: #18418
+#18209 := (~ #18208 #18208)
+#18210 := [refl]: #18209
+#18416 := (~ #18415 #18415)
+#18417 := [refl]: #18416
+#18413 := (~ #18412 #18412)
+#18414 := [refl]: #18413
+#18410 := (~ #18409 #18409)
+#18411 := [refl]: #18410
+#18407 := (~ #18406 #18406)
+#18408 := [refl]: #18407
+#18462 := [nnf-neg #18408 #18411 #18414 #18417 #18210 #18419 #18458]: #18461
+#18403 := (not #15708)
+#18404 := (~ #18403 #18402)
+#18399 := (not #15702)
+#18400 := (~ #18399 #18398)
+#18395 := (not #15699)
+#18396 := (~ #18395 #18394)
+#18391 := (not #15696)
+#18392 := (~ #18391 #18390)
+#18387 := (not #15693)
+#18388 := (~ #18387 #18386)
+#18383 := (not #15690)
+#18384 := (~ #18383 #18382)
+#18379 := (not #15685)
+#18380 := (~ #18379 #18378)
+#18347 := (not #15659)
+#18348 := (~ #18347 #18346)
+#18343 := (not #15654)
+#18344 := (~ #18343 #18342)
+#18340 := (~ #18339 #18339)
+#18341 := [refl]: #18340
+#18336 := (not #15642)
+#18337 := (~ #18336 #18335)
+#18332 := (not #15639)
+#18333 := (~ #18332 #18331)
+#18328 := (not #15636)
+#18329 := (~ #18328 #18327)
+#18324 := (not #15631)
+#18325 := (~ #18324 #18323)
+#18320 := (not #15625)
+#18321 := (~ #18320 #15622)
+#18318 := (~ #15622 #15622)
+#18316 := (~ #15617 #15617)
+#18317 := [refl]: #18316
+#18319 := [nnf-pos #18317]: #18318
+#18322 := [nnf-neg #18319]: #18321
+#18314 := (~ #18313 #18313)
+#18315 := [refl]: #18314
+#18326 := [nnf-neg #18315 #18322]: #18325
+#18309 := (~ #15625 #18308)
+#18310 := [sk]: #18309
+#18330 := [nnf-neg #18310 #18326]: #18329
+#18294 := (~ #18293 #18293)
+#18295 := [refl]: #18294
+#18334 := [nnf-neg #18295 #18330]: #18333
+#18291 := (~ #13264 #13264)
+#18292 := [refl]: #18291
+#18338 := [nnf-neg #18292 #18334]: #18337
+#18289 := (~ #18288 #18288)
+#18290 := [refl]: #18289
+#18286 := (~ #18285 #18285)
+#18287 := [refl]: #18286
+#18283 := (~ #18282 #18282)
+#18284 := [refl]: #18283
+#18345 := [nnf-neg #18284 #18287 #18290 #18338 #18341]: #18344
+#18280 := (~ #18279 #18279)
+#18281 := [refl]: #18280
+#18277 := (~ #18276 #18276)
+#18278 := [refl]: #18277
+#18349 := [nnf-neg #18278 #18281 #18345]: #18348
+#18376 := (~ #13422 #13422)
+#18377 := [refl]: #18376
+#18274 := (~ #18273 #18273)
+#18275 := [refl]: #18274
+#18374 := (~ #18373 #18373)
+#18375 := [refl]: #18374
+#18371 := (~ #18370 #18370)
+#18372 := [refl]: #18371
+#18381 := [nnf-neg #18372 #18375 #18210 #18275 #18377 #18349]: #18380
+#18367 := (not #15677)
+#18368 := (~ #18367 #18366)
+#18363 := (not #15671)
+#18364 := (~ #18363 #18362)
+#18359 := (not #15668)
+#18360 := (~ #18359 #18358)
+#18355 := (not #15665)
+#18356 := (~ #18355 #18354)
+#18351 := (not #15662)
+#18352 := (~ #18351 #18350)
+#18271 := (~ #18270 #18270)
+#18272 := [refl]: #18271
+#18268 := (~ #18267 #18267)
+#18269 := [refl]: #18268
+#18265 := (~ #18264 #18264)
+#18266 := [refl]: #18265
+#18262 := (~ #18261 #18261)
+#18263 := [refl]: #18262
+#18251 := (~ #18250 #18250)
+#18252 := [refl]: #18251
+#18259 := (~ #18258 #18258)
+#18260 := [refl]: #18259
+#18256 := (~ #18255 #18255)
+#18257 := [refl]: #18256
+#18353 := [nnf-neg #18257 #18260 #18252 #18263 #18266 #18269 #18272 #18275 #18349]: #18352
+#18248 := (~ #18247 #18247)
+#18249 := [refl]: #18248
+#18239 := (~ #18238 #18238)
+#18240 := [refl]: #18239
+#18357 := [nnf-neg #18240 #18249 #18353]: #18356
+#18245 := (~ #18244 #18244)
+#18246 := [refl]: #18245
+#18361 := [nnf-neg #18246 #18357]: #18360
+#18242 := (~ #18241 #18241)
+#18243 := [refl]: #18242
+#18365 := [nnf-neg #18240 #18243 #18361]: #18364
+#18253 := (~ #13416 #13416)
+#18254 := [refl]: #18253
+#18369 := [nnf-neg #18210 #18254 #18365]: #18368
+#18385 := [nnf-neg #18369 #18381]: #18384
+#18389 := [nnf-neg #18252 #18210 #18385]: #18388
+#18393 := [nnf-neg #18240 #18249 #18389]: #18392
+#18397 := [nnf-neg #18246 #18393]: #18396
+#18401 := [nnf-neg #18240 #18243 #18397]: #18400
+#18236 := (~ #13511 #13511)
+#18237 := [refl]: #18236
+#18405 := [nnf-neg #18210 #18237 #18401]: #18404
+#18466 := [nnf-neg #18405 #18462]: #18465
+#18234 := (~ #18233 #18233)
+#18235 := [refl]: #18234
+#18231 := (~ #18230 #18230)
+#18232 := [refl]: #18231
+#18228 := (~ #18227 #18227)
+#18229 := [refl]: #18228
+#18224 := (not #15551)
+#18225 := (~ #18224 #15548)
+#18222 := (~ #15548 #15548)
+#18220 := (~ #15543 #15543)
+#18221 := [refl]: #18220
+#18223 := [nnf-pos #18221]: #18222
+#18226 := [nnf-neg #18223]: #18225
+#18218 := (~ #18217 #18217)
+#18219 := [refl]: #18218
+#18215 := (~ #18214 #18214)
+#18216 := [refl]: #18215
+#18212 := (~ #18211 #18211)
+#18213 := [refl]: #18212
+#18206 := (~ #18205 #18205)
+#18207 := [refl]: #18206
+#18203 := (~ #18202 #18202)
+#18204 := [refl]: #18203
+#18200 := (~ #18199 #18199)
+#18201 := [refl]: #18200
+#18197 := (~ #18196 #18196)
+#18198 := [refl]: #18197
+#18194 := (~ #18193 #18193)
+#18195 := [refl]: #18194
+#18191 := (~ #18190 #18190)
+#18192 := [refl]: #18191
+#18188 := (~ #18187 #18187)
+#18189 := [refl]: #18188
+#18470 := [nnf-neg #18189 #18192 #18195 #18198 #18201 #18204 #18207 #18210 #18213 #18216 #18219 #18226 #18229 #18232 #18235 #18466]: #18469
+#18185 := (~ #13943 #13943)
+#18186 := [refl]: #18185
+#18183 := (~ #12976 #12976)
+#18184 := [refl]: #18183
+#18474 := [nnf-neg #18184 #18186 #18470]: #18473
+#18180 := (not #15537)
+#18181 := (~ #18180 #15534)
+#18178 := (~ #15534 #15534)
+#18176 := (~ #15529 #15529)
+#18177 := [refl]: #18176
+#18179 := [nnf-pos #18177]: #18178
+#18182 := [nnf-neg #18179]: #18181
+#18478 := [nnf-neg #18182 #18474]: #18477
+#18172 := (~ #15537 #18171)
+#18173 := [sk]: #18172
+#18482 := [nnf-neg #18173 #18478]: #18481
+#18157 := (~ #18156 #18156)
+#18158 := [refl]: #18157
+#18486 := [nnf-neg #18158 #18482]: #18485
+#18154 := (~ #13181 #13181)
+#18155 := [refl]: #18154
+#18490 := [nnf-neg #18155 #18486]: #18489
+#18152 := (~ #18151 #18151)
+#18153 := [refl]: #18152
+#18149 := (~ #18148 #18148)
+#18150 := [refl]: #18149
+#18146 := (~ #18145 #18145)
+#18147 := [refl]: #18146
+#18143 := (~ #18142 #18142)
+#18144 := [refl]: #18143
+#18140 := (~ #18139 #18139)
+#18141 := [refl]: #18140
+#18494 := [nnf-neg #18141 #18144 #18147 #18150 #18153 #18490]: #18493
+#18137 := (~ #18136 #18136)
+#18138 := [refl]: #18137
+#18128 := (~ #18127 #18127)
+#18129 := [refl]: #18128
+#18498 := [nnf-neg #18129 #18138 #18494]: #18497
+#18134 := (~ #18133 #18133)
+#18135 := [refl]: #18134
+#18502 := [nnf-neg #18135 #18498]: #18501
+#18131 := (~ #18130 #18130)
+#18132 := [refl]: #18131
+#18506 := [nnf-neg #18129 #18132 #18502]: #18505
+#18125 := (~ #18124 #18124)
+#18126 := [refl]: #18125
+#18510 := [nnf-neg #18126 #18506]: #18509
+#18122 := (~ #13009 #13009)
+#18123 := [refl]: #18122
+#18513 := [nnf-neg #18123 #18510]: #18512
+#15021 := (or #12079 #12070 #12061 #12052 #13230 #13511 #13597)
+#15026 := (and #13533 #15021)
+#15032 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #13700 #13734 #13740 #13752 #13762 #13775 #13786 #15026)
+#15037 := (and #3042 #13218 #15032)
+#15040 := (or #13214 #15037)
+#15043 := (and #13211 #15040)
+#15046 := (or #13181 #15043)
+#15049 := (and #13178 #15046)
+#15052 := (or #12976 #12967 #12958 #12949 #12985 #15049)
+#15055 := (and #11928 #11937 #15052)
+#15058 := (or #12997 #15055)
+#15061 := (and #11928 #11931 #15058)
+#15064 := (or #13009 #15061)
+#15067 := (and #11925 #15064)
+#15070 := (not #15067)
+#15792 := (iff #15070 #15791)
+#15789 := (iff #15067 #15788)
+#15786 := (iff #15064 #15785)
+#15783 := (iff #15061 #15782)
+#15780 := (iff #15058 #15779)
+#15777 := (iff #15055 #15776)
+#15774 := (iff #15052 #15773)
+#15771 := (iff #15049 #15770)
+#15768 := (iff #15046 #15767)
+#15765 := (iff #15043 #15764)
+#15762 := (iff #15040 #15761)
+#15759 := (iff #15037 #15758)
+#15756 := (iff #15032 #15753)
+#15750 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #13700 #15551 #13740 #15568 #15585 #15602 #13786 #15747)
+#15754 := (iff #15750 #15753)
+#15755 := [rewrite]: #15754
+#15751 := (iff #15032 #15750)
+#15748 := (iff #15026 #15747)
+#15745 := (iff #15021 #15744)
+#15742 := (iff #13597 #15741)
+#15739 := (iff #13592 #15738)
+#15736 := (iff #13583 #15735)
+#15733 := (iff #13578 #15730)
+#15727 := (and #3103 #4043 #14916 #13540)
+#15731 := (iff #15727 #15730)
+#15732 := [rewrite]: #15731
+#15728 := (iff #13578 #15727)
+#14911 := (iff #4357 #14916)
+#14932 := -4294967295::int
+#14924 := (+ -4294967295::int #161)
+#14917 := (<= #14924 0::int)
+#14913 := (iff #14917 #14916)
+#14914 := [rewrite]: #14913
+#14918 := (iff #4357 #14917)
+#14919 := (= #4356 #14924)
+#14925 := (+ #161 -4294967295::int)
+#14921 := (= #14925 #14924)
+#14922 := [rewrite]: #14921
+#14926 := (= #4356 #14925)
+#14927 := (= #4355 -4294967295::int)
+#14933 := (* -1::int 4294967295::int)
+#14929 := (= #14933 -4294967295::int)
+#14930 := [rewrite]: #14929
+#14934 := (= #4355 #14933)
+#7478 := (= uf_76 4294967295::int)
 #947 := 65536::int
 #1322 := (* 65536::int 65536::int)
 #1327 := (- #1322 1::int)
 #1328 := (= uf_76 #1327)
-#7477 := (iff #1328 #7476)
-#7474 := (= #1327 4294967295::int)
+#7479 := (iff #1328 #7478)
+#7476 := (= #1327 4294967295::int)
 #1010 := 4294967296::int
-#7467 := (- 4294967296::int 1::int)
-#7472 := (= #7467 4294967295::int)
-#7473 := [rewrite]: #7472
-#7469 := (= #1327 #7467)
-#7438 := (= #1322 4294967296::int)
-#7439 := [rewrite]: #7438
-#7470 := [monotonicity #7439]: #7469
-#7475 := [trans #7470 #7473]: #7474
-#7478 := [monotonicity #7475]: #7477
-#7466 := [asserted]: #1328
-#7481 := [mp #7466 #7478]: #7476
-#14393 := [monotonicity #7481]: #14396
-#14390 := [trans #14393 #14392]: #14389
-#14385 := [monotonicity #14390]: #14388
-#14382 := [trans #14385 #14384]: #14381
-#14377 := [monotonicity #14382]: #14380
-#14374 := [trans #14377 #14376]: #14373
-#15259 := [monotonicity #14374]: #15258
-#15264 := [trans #15259 #15262]: #15263
-#15267 := [quant-intro #15264]: #15266
-#15255 := (iff #13314 #15254)
-#15252 := (iff #13294 #15251)
-#15249 := (iff #13291 #15246)
-#15243 := (or #15240 #13288)
-#15247 := (iff #15243 #15246)
-#15248 := [rewrite]: #15247
-#15244 := (iff #13291 #15243)
-#15241 := (iff #13283 #15240)
-#15238 := (iff #13278 #15235)
-#15232 := (and #4041 #14378 #13272)
-#15236 := (iff #15232 #15235)
-#15237 := [rewrite]: #15236
-#15233 := (iff #13278 #15232)
-#15234 := [monotonicity #14374]: #15233
-#15239 := [trans #15234 #15237]: #15238
-#15242 := [monotonicity #15239]: #15241
-#15245 := [monotonicity #15242]: #15244
-#15250 := [trans #15245 #15248]: #15249
-#15253 := [quant-intro #15250]: #15252
-#15256 := [monotonicity #15253]: #15255
-#15270 := [monotonicity #15256 #15267]: #15269
-#15273 := [monotonicity #15253 #15270]: #15272
-#15276 := [monotonicity #15273]: #15275
-#15281 := [trans #15276 #15279]: #15280
-#15230 := (iff #13247 #15229)
-#15227 := (iff #13242 #15226)
-#15224 := (iff #13236 #15223)
-#15221 := (iff #13231 #15220)
-#15218 := (iff #13225 #15217)
-#15215 := (iff #13222 #15214)
-#15212 := (iff #13219 #15209)
-#15206 := (or #15188 #13216)
-#15210 := (iff #15206 #15209)
-#15211 := [rewrite]: #15210
-#15207 := (iff #13219 #15206)
-#15189 := (iff #13158 #15188)
-#15186 := (iff #13152 #15185)
-#15183 := (iff #13149 #15182)
-#15180 := (iff #13146 #15179)
-#15177 := (iff #13143 #15176)
-#15174 := (iff #13140 #15171)
-#15168 := (or #15165 #13135)
-#15172 := (iff #15168 #15171)
-#15173 := [rewrite]: #15172
-#15169 := (iff #13140 #15168)
-#15166 := (iff #13123 #15165)
-#15163 := (iff #13120 #15162)
-#15160 := (iff #13117 #15157)
-#15154 := (or #15151 #13114)
-#15158 := (iff #15154 #15157)
-#15159 := [rewrite]: #15158
-#15155 := (iff #13117 #15154)
-#15152 := (iff #13109 #15151)
-#15149 := (iff #13104 #15146)
-#15143 := (and #4041 #14378 #13098)
-#15147 := (iff #15143 #15146)
-#15148 := [rewrite]: #15147
-#15144 := (iff #13104 #15143)
-#15145 := [monotonicity #14374]: #15144
-#15150 := [trans #15145 #15148]: #15149
-#15153 := [monotonicity #15150]: #15152
-#15156 := [monotonicity #15153]: #15155
-#15161 := [trans #15156 #15159]: #15160
-#15164 := [quant-intro #15161]: #15163
-#15167 := [monotonicity #15164]: #15166
-#15170 := [monotonicity #15167]: #15169
-#15175 := [trans #15170 #15173]: #15174
-#15178 := [monotonicity #15164 #15175]: #15177
-#15181 := [monotonicity #15178]: #15180
-#15184 := [monotonicity #15181]: #15183
-#15141 := (iff #13086 #15140)
-#15138 := (iff #13081 #15135)
-#15132 := (and #3258 #13017 #13051 #15127 #13059 #13061)
-#15136 := (iff #15132 #15135)
-#15137 := [rewrite]: #15136
-#15133 := (iff #13081 #15132)
-#15130 := (iff #13054 #15127)
-#15079 := (+ 4294967295::int #12965)
-#15123 := (>= #15079 1::int)
-#15128 := (iff #15123 #15127)
-#15129 := [rewrite]: #15128
-#15124 := (iff #13054 #15123)
-#15080 := (= #13055 #15079)
-#15081 := [monotonicity #7481]: #15080
-#15125 := [monotonicity #15081]: #15124
-#15131 := [trans #15125 #15129]: #15130
-#15134 := [monotonicity #15131]: #15133
-#15139 := [trans #15134 #15137]: #15138
-#15142 := [monotonicity #15139]: #15141
-#15187 := [monotonicity #15142 #15184]: #15186
-#15190 := [monotonicity #15131 #15187]: #15189
-#15208 := [monotonicity #15190]: #15207
-#15213 := [trans #15208 #15211]: #15212
-#15204 := (iff #13185 #15203)
-#15201 := (iff #13180 #15200)
-#15198 := (iff #13174 #15197)
-#15195 := (iff #13169 #15194)
-#15192 := (iff #13163 #15191)
-#15193 := [monotonicity #15190]: #15192
-#15196 := [monotonicity #15193]: #15195
-#15199 := [monotonicity #15196]: #15198
-#15202 := [monotonicity #15199]: #15201
-#15205 := [monotonicity #15202]: #15204
-#15216 := [monotonicity #15205 #15213]: #15215
-#15219 := [monotonicity #15216]: #15218
-#15222 := [monotonicity #15219]: #15221
-#15225 := [monotonicity #15222]: #15224
-#15228 := [monotonicity #15225]: #15227
-#15231 := [monotonicity #15228]: #15230
-#15284 := [monotonicity #15231 #15281]: #15283
-#15121 := (iff #13453 #15120)
-#15118 := (iff #13448 #15115)
-#15112 := (and #3055 #12030 #12741 #12910 #12913 #13359 #15076 #13389 #13392 #15085 #15096 #13402 #15107)
-#15116 := (iff #15112 #15115)
-#15117 := [rewrite]: #15116
-#15113 := (iff #13448 #15112)
-#15110 := (iff #13405 #15107)
-#15101 := (+ 255::int #13378)
-#15104 := (>= #15101 0::int)
-#15108 := (iff #15104 #15107)
-#15109 := [rewrite]: #15108
-#15105 := (iff #13405 #15104)
-#15102 := (= #13406 #15101)
+#7469 := (- 4294967296::int 1::int)
+#7474 := (= #7469 4294967295::int)
+#7475 := [rewrite]: #7474
+#7471 := (= #1327 #7469)
+#7440 := (= #1322 4294967296::int)
+#7441 := [rewrite]: #7440
+#7472 := [monotonicity #7441]: #7471
+#7477 := [trans #7472 #7475]: #7476
+#7480 := [monotonicity #7477]: #7479
+#7468 := [asserted]: #1328
+#7483 := [mp #7468 #7480]: #7478
+#14931 := [monotonicity #7483]: #14934
+#14928 := [trans #14931 #14930]: #14927
+#14923 := [monotonicity #14928]: #14926
+#14920 := [trans #14923 #14922]: #14919
+#14915 := [monotonicity #14920]: #14918
+#14912 := [trans #14915 #14914]: #14911
+#15729 := [monotonicity #14912]: #15728
+#15734 := [trans #15729 #15732]: #15733
+#15737 := [quant-intro #15734]: #15736
+#15725 := (iff #13586 #15724)
+#15722 := (iff #13566 #15721)
+#15719 := (iff #13561 #15716)
+#15713 := (or #14158 #13538 #13552)
+#15717 := (iff #15713 #15716)
+#15718 := [rewrite]: #15717
+#15714 := (iff #13561 #15713)
+#14155 := (iff #5579 #14158)
+#14160 := (iff #4364 #14159)
+#14157 := [monotonicity #14912]: #14160
+#14156 := [monotonicity #14157]: #14155
+#15715 := [monotonicity #14156]: #15714
+#15720 := [trans #15715 #15718]: #15719
+#15723 := [quant-intro #15720]: #15722
+#15726 := [monotonicity #15723]: #15725
+#15740 := [monotonicity #15726 #15737]: #15739
+#15743 := [monotonicity #15723 #15740]: #15742
+#15746 := [monotonicity #15743]: #15745
+#15711 := (iff #13533 #15708)
+#15705 := (or #13230 #15702 #13510)
+#15709 := (iff #15705 #15708)
+#15710 := [rewrite]: #15709
+#15706 := (iff #13533 #15705)
+#15703 := (iff #13504 #15702)
+#15700 := (iff #13498 #15699)
+#15697 := (iff #13493 #15696)
+#15694 := (iff #13485 #15693)
+#15691 := (iff #13476 #15690)
+#15688 := (iff #13471 #15685)
+#15682 := (or #12566 #12557 #13230 #13239 #15659 #13416)
+#15686 := (iff #15682 #15685)
+#15687 := [rewrite]: #15686
+#15683 := (iff #13471 #15682)
+#15660 := (iff #13360 #15659)
+#15657 := (iff #13352 #15654)
+#15651 := (or #12401 #13256 #15642 #13331 #15648)
+#15655 := (iff #15651 #15654)
+#15656 := [rewrite]: #15655
+#15652 := (iff #13352 #15651)
+#15649 := (iff #13337 #15648)
+#15646 := (iff #13334 #15645)
+#15612 := (iff #13245 #15609)
+#15554 := (+ 4294967295::int #13246)
+#15605 := (>= #15554 1::int)
+#15610 := (iff #15605 #15609)
+#15611 := [rewrite]: #15610
+#15606 := (iff #13245 #15605)
+#15555 := (= #13247 #15554)
+#15556 := [monotonicity #7483]: #15555
+#15607 := [monotonicity #15556]: #15606
+#15613 := [trans #15607 #15611]: #15612
+#15647 := [monotonicity #15613]: #15646
+#15650 := [monotonicity #15647]: #15649
+#15643 := (iff #13324 #15642)
+#15640 := (iff #13321 #15639)
+#15637 := (iff #13318 #15636)
+#15634 := (iff #13315 #15631)
+#15628 := (or #15625 #13310)
+#15632 := (iff #15628 #15631)
+#15633 := [rewrite]: #15632
+#15629 := (iff #13315 #15628)
+#15626 := (iff #13298 #15625)
+#15623 := (iff #13295 #15622)
+#15620 := (iff #13290 #15617)
+#15614 := (or #14158 #13267 #13281)
+#15618 := (iff #15614 #15617)
+#15619 := [rewrite]: #15618
+#15615 := (iff #13290 #15614)
+#15616 := [monotonicity #14156]: #15615
+#15621 := [trans #15616 #15619]: #15620
+#15624 := [quant-intro #15621]: #15623
+#15627 := [monotonicity #15624]: #15626
+#15630 := [monotonicity #15627]: #15629
+#15635 := [trans #15630 #15633]: #15634
+#15638 := [monotonicity #15624 #15635]: #15637
+#15641 := [monotonicity #15638]: #15640
+#15644 := [monotonicity #15641]: #15643
+#15653 := [monotonicity #15644 #15650]: #15652
+#15658 := [trans #15653 #15656]: #15657
+#15661 := [monotonicity #15613 #15658]: #15660
+#15684 := [monotonicity #15661]: #15683
+#15689 := [trans #15684 #15687]: #15688
+#15680 := (iff #13441 #15677)
+#15674 := (or #13230 #15671 #13417)
+#15678 := (iff #15674 #15677)
+#15679 := [rewrite]: #15678
+#15675 := (iff #13441 #15674)
+#15672 := (iff #13411 #15671)
+#15669 := (iff #13405 #15668)
+#15666 := (iff #13400 #15665)
+#15663 := (iff #13392 #15662)
+#15664 := [monotonicity #15661]: #15663
+#15667 := [monotonicity #15664]: #15666
+#15670 := [monotonicity #15667]: #15669
+#15673 := [monotonicity #15670]: #15672
+#15676 := [monotonicity #15673]: #15675
+#15681 := [trans #15676 #15679]: #15680
+#15692 := [monotonicity #15681 #15689]: #15691
+#15695 := [monotonicity #15692]: #15694
+#15698 := [monotonicity #15695]: #15697
+#15701 := [monotonicity #15698]: #15700
+#15704 := [monotonicity #15701]: #15703
+#15707 := [monotonicity #15704]: #15706
+#15712 := [trans #15707 #15710]: #15711
+#15749 := [monotonicity #15712 #15746]: #15748
+#15603 := (iff #13775 #15602)
+#15600 := (iff #13772 #15599)
+#15597 := (iff #13768 #15594)
+#15588 := (+ 255::int #13715)
+#15591 := (>= #15588 0::int)
+#15595 := (iff #15591 #15594)
+#15596 := [rewrite]: #15595
+#15592 := (iff #13768 #15591)
+#15589 := (= #13769 #15588)
 #1332 := (= uf_78 255::int)
-#7480 := [asserted]: #1332
-#15103 := [monotonicity #7480]: #15102
-#15106 := [monotonicity #15103]: #15105
-#15111 := [trans #15106 #15109]: #15110
-#15099 := (iff #13398 #15096)
-#15090 := (+ 4294967295::int #13356)
-#15093 := (>= #15090 0::int)
-#15097 := (iff #15093 #15096)
-#15098 := [rewrite]: #15097
-#15094 := (iff #13398 #15093)
-#15091 := (= #13399 #15090)
-#15092 := [monotonicity #7481]: #15091
-#15095 := [monotonicity #15092]: #15094
-#15100 := [trans #15095 #15098]: #15099
-#15088 := (iff #13395 #15085)
-#15082 := (>= #15079 0::int)
-#15086 := (iff #15082 #15085)
-#15087 := [rewrite]: #15086
-#15083 := (iff #13395 #15082)
-#15084 := [monotonicity #15081]: #15083
-#15089 := [trans #15084 #15087]: #15088
-#15077 := (iff #13386 #15076)
-#15074 := (iff #13383 #15071)
-#15068 := (or #15065 #13380)
-#15072 := (iff #15068 #15071)
-#15073 := [rewrite]: #15072
-#15069 := (iff #13383 #15068)
-#15066 := (iff #13375 #15065)
-#15063 := (iff #13370 #15060)
-#15057 := (and #4041 #14378 #13364)
-#15061 := (iff #15057 #15060)
-#15062 := [rewrite]: #15061
-#15058 := (iff #13370 #15057)
-#15059 := [monotonicity #14374]: #15058
-#15064 := [trans #15059 #15062]: #15063
-#15067 := [monotonicity #15064]: #15066
-#15070 := [monotonicity #15067]: #15069
-#15075 := [trans #15070 #15073]: #15074
-#15078 := [quant-intro #15075]: #15077
-#15114 := [monotonicity #15078 #15089 #15100 #15111]: #15113
-#15119 := [trans #15114 #15117]: #15118
-#15122 := [monotonicity #15119]: #15121
-#15287 := [monotonicity #15122 #15284]: #15286
-#15292 := [trans #15287 #15290]: #15291
-#15295 := [monotonicity #15292]: #15294
-#15055 := (iff #12895 #15054)
-#15052 := (iff #12892 #15051)
-#15049 := (iff #12889 #15046)
-#15043 := (or #15040 #12885)
-#15047 := (iff #15043 #15046)
-#15048 := [rewrite]: #15047
-#15044 := (iff #12889 #15043)
-#15041 := (iff #12881 #15040)
-#15038 := (iff #12876 #15035)
-#15032 := (and #4041 #14378 #12870)
-#15036 := (iff #15032 #15035)
-#15037 := [rewrite]: #15036
-#15033 := (iff #12876 #15032)
-#15034 := [monotonicity #14374]: #15033
-#15039 := [trans #15034 #15037]: #15038
+#7482 := [asserted]: #1332
+#15590 := [monotonicity #7482]: #15589
+#15593 := [monotonicity #15590]: #15592
+#15598 := [trans #15593 #15596]: #15597
+#15601 := [monotonicity #15598]: #15600
+#15604 := [monotonicity #15601]: #15603
+#15586 := (iff #13762 #15585)
+#15583 := (iff #13759 #15582)
+#15580 := (iff #13755 #15577)
+#15571 := (+ 4294967295::int #13686)
+#15574 := (>= #15571 0::int)
+#15578 := (iff #15574 #15577)
+#15579 := [rewrite]: #15578
+#15575 := (iff #13755 #15574)
+#15572 := (= #13756 #15571)
+#15573 := [monotonicity #7483]: #15572
+#15576 := [monotonicity #15573]: #15575
+#15581 := [trans #15576 #15579]: #15580
+#15584 := [monotonicity #15581]: #15583
+#15587 := [monotonicity #15584]: #15586
+#15569 := (iff #13752 #15568)
+#15566 := (iff #13749 #15565)
+#15563 := (iff #13746 #15560)
+#15557 := (>= #15554 0::int)
+#15561 := (iff #15557 #15560)
+#15562 := [rewrite]: #15561
+#15558 := (iff #13746 #15557)
+#15559 := [monotonicity #15556]: #15558
+#15564 := [trans #15559 #15562]: #15563
+#15567 := [monotonicity #15564]: #15566
+#15570 := [monotonicity #15567]: #15569
+#15552 := (iff #13734 #15551)
+#15549 := (iff #13731 #15548)
+#15546 := (iff #13726 #15543)
+#15540 := (or #14158 #13703 #13717)
+#15544 := (iff #15540 #15543)
+#15545 := [rewrite]: #15544
+#15541 := (iff #13726 #15540)
+#15542 := [monotonicity #14156]: #15541
+#15547 := [trans #15542 #15545]: #15546
+#15550 := [quant-intro #15547]: #15549
+#15553 := [monotonicity #15550]: #15552
+#15752 := [monotonicity #15553 #15570 #15587 #15604 #15749]: #15751
+#15757 := [trans #15752 #15755]: #15756
+#15760 := [monotonicity #15757]: #15759
+#15538 := (iff #13214 #15537)
+#15535 := (iff #13211 #15534)
+#15532 := (iff #13206 #15529)
+#15526 := (or #14158 #13184 #13196)
+#15530 := (iff #15526 #15529)
+#15531 := [rewrite]: #15530
+#15527 := (iff #13206 #15526)
+#15528 := [monotonicity #14156]: #15527
+#15533 := [trans #15528 #15531]: #15532
+#15536 := [quant-intro #15533]: #15535
+#15539 := [monotonicity #15536]: #15538
+#15763 := [monotonicity #15539 #15760]: #15762
+#15766 := [monotonicity #15536 #15763]: #15765
+#15769 := [monotonicity #15766]: #15768
+#15772 := [monotonicity #15769]: #15771
+#15775 := [monotonicity #15772]: #15774
+#15778 := [monotonicity #15775]: #15777
+#15781 := [monotonicity #15778]: #15780
+#15784 := [monotonicity #15781]: #15783
+#15787 := [monotonicity #15784]: #15786
+#15790 := [monotonicity #15787]: #15789
+#15793 := [monotonicity #15790]: #15792
+#14070 := (not #13922)
+#15071 := (iff #14070 #15070)
+#15068 := (iff #13922 #15067)
+#15065 := (iff #13919 #15064)
+#15062 := (iff #13914 #15061)
+#15059 := (iff #13908 #15058)
+#15056 := (iff #13903 #15055)
+#15053 := (iff #13895 #15052)
+#15050 := (iff #13874 #15049)
+#15047 := (iff #13871 #15046)
+#15044 := (iff #13868 #15043)
+#15041 := (iff #13865 #15040)
+#15038 := (iff #13860 #15037)
+#15035 := (iff #13852 #15032)
+#15029 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #15026 #13700 #13734 #13740 #13752 #13762 #13775 #13786)
+#15033 := (iff #15029 #15032)
+#15034 := [rewrite]: #15033
+#15030 := (iff #13852 #15029)
+#15027 := (iff #13659 #15026)
+#15024 := (iff #13654 #15021)
+#15006 := (or #12079 #12070 #12061 #12052 #13230 #13597)
+#15018 := (or #13230 #13511 #15006)
+#15022 := (iff #15018 #15021)
+#15023 := [rewrite]: #15022
+#15019 := (iff #13654 #15018)
+#15016 := (iff #13629 #15006)
+#15011 := (and true #15006)
+#15014 := (iff #15011 #15006)
+#15015 := [rewrite]: #15014
+#15012 := (iff #13629 #15011)
+#15009 := (iff #13624 #15006)
+#15003 := (or false #12079 #12070 #12061 #12052 #13230 #13597)
+#15007 := (iff #15003 #15006)
+#15008 := [rewrite]: #15007
+#15004 := (iff #13624 #15003)
+#15001 := (iff #12113 false)
+#14999 := (iff #12113 #3086)
+#14737 := (iff up_216 true)
+#10742 := [asserted]: up_216
+#14738 := [iff-true #10742]: #14737
+#15000 := [monotonicity #14738]: #14999
+#15002 := [trans #15000 #11996]: #15001
+#15005 := [monotonicity #15002]: #15004
+#15010 := [trans #15005 #15008]: #15009
+#15013 := [monotonicity #14738 #15010]: #15012
+#15017 := [trans #15013 #15015]: #15016
+#15020 := [monotonicity #15017]: #15019
+#15025 := [trans #15020 #15023]: #15024
+#15028 := [monotonicity #15025]: #15027
+#14997 := (iff #12141 #14996)
+#14994 := (iff #12003 #11997)
+#14989 := (and true #11997)
+#14992 := (iff #14989 #11997)
+#14993 := [rewrite]: #14992
+#14990 := (iff #12003 #14989)
+#14979 := (iff #11905 true)
+#14980 := [iff-true #14064]: #14979
+#14991 := [monotonicity #14980]: #14990
+#14995 := [trans #14991 #14993]: #14994
+#14998 := [monotonicity #14995]: #14997
+#15031 := [monotonicity #14998 #15028]: #15030
+#15036 := [trans #15031 #15034]: #15035
+#15039 := [monotonicity #15036]: #15038
 #15042 := [monotonicity #15039]: #15041
 #15045 := [monotonicity #15042]: #15044
-#15050 := [trans #15045 #15048]: #15049
-#15053 := [quant-intro #15050]: #15052
-#15056 := [monotonicity #15053]: #15055
-#15298 := [monotonicity #15056 #15295]: #15297
-#15301 := [monotonicity #15053 #15298]: #15300
-#15304 := [monotonicity #15301]: #15303
-#15307 := [monotonicity #15304]: #15306
-#15310 := [monotonicity #15307]: #15309
-#15313 := [monotonicity #15310]: #15312
-#15316 := [monotonicity #15313]: #15315
-#15319 := [monotonicity #15316]: #15318
-#15322 := [monotonicity #15319]: #15321
-#15325 := [monotonicity #15322]: #15324
-#15328 := [monotonicity #15325]: #15327
-#13550 := (not #13512)
-#14569 := (iff #13550 #14568)
-#14566 := (iff #13512 #14565)
-#14563 := (iff #13509 #14562)
-#14560 := (iff #13504 #14559)
-#14557 := (iff #13498 #14556)
-#14554 := (iff #13493 #14553)
-#14551 := (iff #13487 #14550)
-#14548 := (iff #13484 #14547)
-#14545 := (iff #13481 #14544)
-#14542 := (iff #13478 #14541)
-#14539 := (iff #13475 #14538)
-#14536 := (iff #13470 #14535)
-#14533 := (iff #13462 #14530)
-#14527 := (or #14487 #14524 #13453)
-#14531 := (iff #14527 #14530)
-#14532 := [rewrite]: #14531
-#14528 := (iff #13462 #14527)
-#14525 := (iff #13353 #14524)
-#14522 := (iff #13350 #14519)
-#14504 := (or #13325 #14498)
-#14516 := (or #14504 #13347)
-#14520 := (iff #14516 #14519)
-#14521 := [rewrite]: #14520
-#14517 := (iff #13350 #14516)
-#14514 := (iff #13331 #14504)
-#14509 := (and true #14504)
-#14512 := (iff #14509 #14504)
-#14513 := [rewrite]: #14512
-#14510 := (iff #13331 #14509)
-#14507 := (iff #13328 #14504)
-#14501 := (or #14498 #13325)
-#14505 := (iff #14501 #14504)
-#14506 := [rewrite]: #14505
-#14502 := (iff #13328 #14501)
-#14499 := (iff #13267 #14498)
-#14496 := (iff #13262 #14493)
-#14490 := (and true #12113 #12116 #12119 #12122 #12910 #12913)
-#14494 := (iff #14490 #14493)
-#14495 := [rewrite]: #14494
-#14491 := (iff #13262 #14490)
-#14199 := (iff up_216 true)
-#10740 := [asserted]: up_216
-#14200 := [iff-true #10740]: #14199
-#14492 := [monotonicity #14200]: #14491
-#14497 := [trans #14492 #14495]: #14496
-#14500 := [monotonicity #14497]: #14499
-#14503 := [monotonicity #14500]: #14502
-#14508 := [trans #14503 #14506]: #14507
-#14511 := [monotonicity #14200 #14508]: #14510
-#14515 := [trans #14511 #14513]: #14514
-#14518 := [monotonicity #14515]: #14517
-#14523 := [trans #14518 #14521]: #14522
-#14526 := [monotonicity #14523]: #14525
-#14488 := (iff #12962 #14487)
-#14485 := (iff #12957 #14482)
-#14479 := (and #3195 #3196 #3197 #3198 #3199 #3200 true #12067 #12261 #12910 #12913)
-#14483 := (iff #14479 #14482)
-#14484 := [rewrite]: #14483
-#14480 := (iff #12957 #14479)
-#14453 := (iff #11903 true)
-#14454 := [iff-true #13537]: #14453
-#14481 := [monotonicity #14454]: #14480
-#14486 := [trans #14481 #14484]: #14485
-#14489 := [monotonicity #14486]: #14488
-#14529 := [monotonicity #14489 #14526]: #14528
-#14534 := [trans #14529 #14532]: #14533
-#14537 := [monotonicity #14534]: #14536
-#14540 := [monotonicity #14537]: #14539
-#14543 := [monotonicity #14540]: #14542
-#14546 := [monotonicity #14543]: #14545
-#14549 := [monotonicity #14546]: #14548
-#14552 := [monotonicity #14549]: #14551
-#14555 := [monotonicity #14552]: #14554
-#14558 := [monotonicity #14555]: #14557
-#14561 := [monotonicity #14558]: #14560
-#14564 := [monotonicity #14561]: #14563
-#14567 := [monotonicity #14564]: #14566
-#14570 := [monotonicity #14567]: #14569
-#13551 := [not-or-elim #13523]: #13550
-#14571 := [mp #13551 #14570]: #14568
-#15329 := [mp #14571 #15328]: #15326
-#17960 := [mp~ #15329 #17959]: #17957
-#17961 := [mp #17960 #18264]: #18262
-#21850 := [mp #17961 #21849]: #21847
-#22710 := [mp #21850 #22709]: #22707
-#28083 := [unit-resolution #22710 #26255]: #22704
-#23931 := (or #22701 #22695)
-#23932 := [def-axiom]: #23931
-#28084 := [unit-resolution #23932 #28083]: #22695
+#15048 := [monotonicity #15045]: #15047
+#15051 := [monotonicity #15048]: #15050
+#15054 := [monotonicity #15051]: #15053
+#15057 := [monotonicity #15054]: #15056
+#15060 := [monotonicity #15057]: #15059
+#15063 := [monotonicity #15060]: #15062
+#15066 := [monotonicity #15063]: #15065
+#15069 := [monotonicity #15066]: #15068
+#15072 := [monotonicity #15069]: #15071
+#14071 := [not-or-elim #14055]: #14070
+#15073 := [mp #14071 #15072]: #15070
+#15794 := [mp #15073 #15793]: #15791
+#18514 := [mp~ #15794 #18513]: #18511
+#18515 := [mp #18514 #18859]: #18857
+#22382 := [mp #18515 #22381]: #22379
+#23242 := [mp #22382 #23241]: #23239
+#28633 := [unit-resolution #23242 #26581]: #23236
+#24466 := (or #23233 #23227)
+#24467 := [def-axiom]: #24466
+#28634 := [unit-resolution #24467 #28633]: #23227
 decl uf_15 :: (-> T5 T6 T2)
 decl uf_16 :: (-> T4 T5 T6)
-#26003 := (uf_16 uf_287 #25399)
-#26479 := (uf_15 #26392 #26003)
-#26480 := (= uf_9 #26479)
-#26004 := (uf_15 #25399 #26003)
-#28108 := (= #26004 #26479)
-#28104 := (= #26479 #26004)
-#27888 := (= #26392 #25399)
-#27862 := (= #26392 #2981)
-#27860 := (= #26391 #2977)
-#27858 := (= #24110 uf_286)
-#24111 := (= uf_286 #24110)
-#1602 := (uf_143 #1358)
-#8264 := (= #161 #1602)
-#8267 := (forall (vars (?x386 T3) (?x387 int)) (:pat #1592) #8264)
-#16571 := (~ #8267 #8267)
-#16569 := (~ #8264 #8264)
-#16570 := [refl]: #16569
-#16572 := [nnf-pos #16570]: #16571
-#1603 := (= #1602 #161)
-#1604 := (forall (vars (?x386 T3) (?x387 int)) (:pat #1592) #1603)
-#8268 := (iff #1604 #8267)
-#8265 := (iff #1603 #8264)
-#8266 := [rewrite]: #8265
-#8269 := [quant-intro #8266]: #8268
-#8263 := [asserted]: #1604
-#8272 := [mp #8263 #8269]: #8267
-#16573 := [mp~ #8272 #16572]: #8267
-#24117 := (not #8267)
-#24118 := (or #24117 #24111)
-#24119 := [quant-inst]: #24118
-#27676 := [unit-resolution #24119 #16573]: #24111
-#27859 := [symm #27676]: #27858
-#27861 := [monotonicity #27656 #27859]: #27860
-#27863 := [monotonicity #27861]: #27862
-#27889 := [trans #27863 #27875]: #27888
-#28105 := [monotonicity #27889]: #28104
-#28109 := [symm #28105]: #28108
-#26005 := (= uf_9 #26004)
+#26537 := (uf_16 uf_287 #25933)
+#27013 := (uf_15 #26926 #26537)
+#27014 := (= uf_9 #27013)
+#26538 := (uf_15 #25933 #26537)
+#26539 := (= uf_9 #26538)
+#26735 := (or #13009 #26539)
+#26726 := [monotonicity #28306 #28306]: #26725
+#26743 := [symm #26726]: #26728
+#26700 := [hypothesis]: #11925
+#26730 := [trans #26700 #26743]: #26481
 decl uf_53 :: (-> T4 T5 T6)
-#25994 := (uf_53 uf_287 #25399)
-#25995 := (uf_15 #23 #25994)
-#26000 := (pattern #25995)
+#26528 := (uf_53 uf_287 #25933)
+#26529 := (uf_15 #23 #26528)
+#26534 := (pattern #26529)
 decl up_197 :: (-> T3 bool)
-#25998 := (up_197 #25810)
-#25996 := (= uf_9 #25995)
-#25997 := (not #25996)
+#26532 := (up_197 #26344)
+#26530 := (= uf_9 #26529)
+#26531 := (not #26530)
 decl uf_147 :: (-> T5 T6 T2)
 decl uf_192 :: (-> T7 T6)
 decl uf_11 :: (-> T4 T5 T7)
-#25990 := (uf_11 uf_287 #25399)
-#25991 := (uf_192 #25990)
-#25992 := (uf_147 #23 #25991)
-#25993 := (= uf_9 #25992)
-#26010 := (or #25993 #25997 #25998)
-#26013 := (forall (vars (?x577 T5)) (:pat #26000) #26010)
-#26016 := (not #26013)
-#26006 := (not #26005)
-#26019 := (or #25875 #26006 #26016)
-#26022 := (not #26019)
-#28086 := (= #3042 #25946)
-#28089 := [symm #26166]: #28086
-#28090 := [trans #26255 #28089]: #25947
-#25968 := (or #25967 #25945 #25963)
-#25965 := [def-axiom]: #25968
-#28091 := [unit-resolution #25965 #28090 #26163]: #25945
-#26025 := (or #25966 #26022)
+#26524 := (uf_11 uf_287 #25933)
+#26525 := (uf_192 #26524)
+#26526 := (uf_147 #23 #26525)
+#26527 := (= uf_9 #26526)
+#26544 := (or #26527 #26531 #26532)
+#26547 := (forall (vars (?x577 T5)) (:pat #26534) #26544)
+#26550 := (not #26547)
+#26540 := (not #26539)
+#26553 := (or #26409 #26540 #26550)
+#26732 := [hypothesis]: #26540
+#26626 := (or #26553 #26539)
+#26630 := [def-axiom]: #26626
+#26733 := [unit-resolution #26630 #26732]: #26553
 #14 := (:var 2 T4)
 #2166 := (uf_196 #14 #15 #23)
 #2228 := (pattern #2166)
@@ -4814,82 +5300,82 @@
 #2158 := (uf_11 #13 #15)
 #2236 := (uf_192 #2158)
 #2237 := (uf_147 #23 #2236)
-#10024 := (= uf_9 #2237)
-#10018 := (= uf_9 #2230)
-#21005 := (not #10018)
+#10026 := (= uf_9 #2237)
+#10020 := (= uf_9 #2230)
+#21605 := (not #10020)
 #1382 := (uf_13 #21)
 #2232 := (up_197 #1382)
-#21020 := (or #2232 #21005 #10024)
-#21025 := (forall (vars (?x577 T5)) (:pat #2231) #21020)
-#21031 := (not #21025)
+#21620 := (or #2232 #21605 #10026)
+#21625 := (forall (vars (?x577 T5)) (:pat #2231) #21620)
+#21631 := (not #21625)
 #2145 := (uf_16 #14 #23)
 #2146 := (uf_15 #15 #2145)
-#9724 := (= uf_9 #2146)
-#20840 := (not #9724)
+#9726 := (= uf_9 #2146)
+#21440 := (not #9726)
 #180 := (uf_27 #14 #15)
-#3718 := (= uf_9 #180)
-#10361 := (not #3718)
-#21032 := (or #10361 #20840 #21031)
-#21033 := (not #21032)
-#9772 := (= uf_9 #2166)
-#10048 := (not #9772)
-#21038 := (or #10048 #21033)
-#21041 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #21038)
+#3720 := (= uf_9 #180)
+#10363 := (not #3720)
+#21632 := (or #10363 #21440 #21631)
+#21633 := (not #21632)
+#9774 := (= uf_9 #2166)
+#10050 := (not #9774)
+#21638 := (or #10050 #21633)
+#21641 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #21638)
 #2233 := (not #2232)
-#10021 := (and #2233 #10018)
-#10030 := (not #10021)
-#10031 := (or #10030 #10024)
-#10036 := (forall (vars (?x577 T5)) (:pat #2231) #10031)
-#10057 := (and #3718 #9724 #10036)
-#10060 := (or #10048 #10057)
-#10063 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #10060)
-#21042 := (iff #10063 #21041)
-#21039 := (iff #10060 #21038)
-#21036 := (iff #10057 #21033)
-#21028 := (and #3718 #9724 #21025)
-#21034 := (iff #21028 #21033)
-#21035 := [rewrite]: #21034
-#21029 := (iff #10057 #21028)
-#21026 := (iff #10036 #21025)
-#21023 := (iff #10031 #21020)
-#21006 := (or #2232 #21005)
-#21017 := (or #21006 #10024)
-#21021 := (iff #21017 #21020)
-#21022 := [rewrite]: #21021
-#21018 := (iff #10031 #21017)
-#21015 := (iff #10030 #21006)
-#21007 := (not #21006)
-#21010 := (not #21007)
-#21013 := (iff #21010 #21006)
-#21014 := [rewrite]: #21013
-#21011 := (iff #10030 #21010)
-#21008 := (iff #10021 #21007)
-#21009 := [rewrite]: #21008
-#21012 := [monotonicity #21009]: #21011
-#21016 := [trans #21012 #21014]: #21015
-#21019 := [monotonicity #21016]: #21018
-#21024 := [trans #21019 #21022]: #21023
-#21027 := [quant-intro #21024]: #21026
-#21030 := [monotonicity #21027]: #21029
-#21037 := [trans #21030 #21035]: #21036
-#21040 := [monotonicity #21037]: #21039
-#21043 := [quant-intro #21040]: #21042
-#17090 := (~ #10063 #10063)
-#17088 := (~ #10060 #10060)
-#17086 := (~ #10057 #10057)
-#17084 := (~ #10036 #10036)
-#17082 := (~ #10031 #10031)
-#17083 := [refl]: #17082
-#17085 := [nnf-pos #17083]: #17084
-#17080 := (~ #9724 #9724)
-#17081 := [refl]: #17080
-#17078 := (~ #3718 #3718)
-#17079 := [refl]: #17078
-#17087 := [monotonicity #17079 #17081 #17085]: #17086
-#17076 := (~ #10048 #10048)
-#17077 := [refl]: #17076
-#17089 := [monotonicity #17077 #17087]: #17088
-#17091 := [nnf-pos #17089]: #17090
+#10023 := (and #2233 #10020)
+#10032 := (not #10023)
+#10033 := (or #10032 #10026)
+#10038 := (forall (vars (?x577 T5)) (:pat #2231) #10033)
+#10059 := (and #3720 #9726 #10038)
+#10062 := (or #10050 #10059)
+#10065 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #10062)
+#21642 := (iff #10065 #21641)
+#21639 := (iff #10062 #21638)
+#21636 := (iff #10059 #21633)
+#21628 := (and #3720 #9726 #21625)
+#21634 := (iff #21628 #21633)
+#21635 := [rewrite]: #21634
+#21629 := (iff #10059 #21628)
+#21626 := (iff #10038 #21625)
+#21623 := (iff #10033 #21620)
+#21606 := (or #2232 #21605)
+#21617 := (or #21606 #10026)
+#21621 := (iff #21617 #21620)
+#21622 := [rewrite]: #21621
+#21618 := (iff #10033 #21617)
+#21615 := (iff #10032 #21606)
+#21607 := (not #21606)
+#21610 := (not #21607)
+#21613 := (iff #21610 #21606)
+#21614 := [rewrite]: #21613
+#21611 := (iff #10032 #21610)
+#21608 := (iff #10023 #21607)
+#21609 := [rewrite]: #21608
+#21612 := [monotonicity #21609]: #21611
+#21616 := [trans #21612 #21614]: #21615
+#21619 := [monotonicity #21616]: #21618
+#21624 := [trans #21619 #21622]: #21623
+#21627 := [quant-intro #21624]: #21626
+#21630 := [monotonicity #21627]: #21629
+#21637 := [trans #21630 #21635]: #21636
+#21640 := [monotonicity #21637]: #21639
+#21643 := [quant-intro #21640]: #21642
+#17591 := (~ #10065 #10065)
+#17589 := (~ #10062 #10062)
+#17587 := (~ #10059 #10059)
+#17585 := (~ #10038 #10038)
+#17583 := (~ #10033 #10033)
+#17584 := [refl]: #17583
+#17586 := [nnf-pos #17584]: #17585
+#17581 := (~ #9726 #9726)
+#17582 := [refl]: #17581
+#17579 := (~ #3720 #3720)
+#17580 := [refl]: #17579
+#17588 := [monotonicity #17580 #17582 #17586]: #17587
+#17577 := (~ #10050 #10050)
+#17578 := [refl]: #17577
+#17590 := [monotonicity #17578 #17588]: #17589
+#17592 := [nnf-pos #17590]: #17591
 #2238 := (= #2237 uf_9)
 #2234 := (= #2230 uf_9)
 #2235 := (and #2233 #2234)
@@ -4902,148 +5388,197 @@
 #2167 := (= #2166 uf_9)
 #2243 := (implies #2167 #2242)
 #2244 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #2243)
-#10066 := (iff #2244 #10063)
-#10039 := (and #3718 #10036)
-#10042 := (and #9724 #10039)
-#10049 := (or #10048 #10042)
-#10054 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #10049)
-#10064 := (iff #10054 #10063)
-#10061 := (iff #10049 #10060)
-#10058 := (iff #10042 #10057)
-#10059 := [rewrite]: #10058
-#10062 := [monotonicity #10059]: #10061
-#10065 := [quant-intro #10062]: #10064
-#10055 := (iff #2244 #10054)
-#10052 := (iff #2243 #10049)
-#10045 := (implies #9772 #10042)
-#10050 := (iff #10045 #10049)
-#10051 := [rewrite]: #10050
-#10046 := (iff #2243 #10045)
-#10043 := (iff #2242 #10042)
-#10040 := (iff #2241 #10039)
-#10037 := (iff #2240 #10036)
-#10034 := (iff #2239 #10031)
-#10027 := (implies #10021 #10024)
-#10032 := (iff #10027 #10031)
-#10033 := [rewrite]: #10032
-#10028 := (iff #2239 #10027)
-#10025 := (iff #2238 #10024)
-#10026 := [rewrite]: #10025
-#10022 := (iff #2235 #10021)
-#10019 := (iff #2234 #10018)
-#10020 := [rewrite]: #10019
-#10023 := [monotonicity #10020]: #10022
-#10029 := [monotonicity #10023 #10026]: #10028
-#10035 := [trans #10029 #10033]: #10034
-#10038 := [quant-intro #10035]: #10037
-#3719 := (iff #184 #3718)
-#3720 := [rewrite]: #3719
-#10041 := [monotonicity #3720 #10038]: #10040
-#9725 := (iff #2151 #9724)
-#9726 := [rewrite]: #9725
-#10044 := [monotonicity #9726 #10041]: #10043
-#9773 := (iff #2167 #9772)
-#9774 := [rewrite]: #9773
-#10047 := [monotonicity #9774 #10044]: #10046
-#10053 := [trans #10047 #10051]: #10052
-#10056 := [quant-intro #10053]: #10055
-#10067 := [trans #10056 #10065]: #10066
-#10017 := [asserted]: #2244
-#10068 := [mp #10017 #10067]: #10063
-#17092 := [mp~ #10068 #17091]: #10063
-#21044 := [mp #17092 #21043]: #21041
-#25985 := (not #21041)
-#25981 := (or #25985 #25966 #26022)
-#25999 := (or #25998 #25997 #25993)
-#26001 := (forall (vars (?x577 T5)) (:pat #26000) #25999)
-#26002 := (not #26001)
-#26007 := (or #25875 #26006 #26002)
-#26008 := (not #26007)
-#26009 := (or #25966 #26008)
-#25982 := (or #25985 #26009)
-#26075 := (iff #25982 #25981)
-#25987 := (or #25985 #26025)
-#26040 := (iff #25987 #25981)
-#26072 := [rewrite]: #26040
-#25988 := (iff #25982 #25987)
-#26026 := (iff #26009 #26025)
-#26023 := (iff #26008 #26022)
-#26020 := (iff #26007 #26019)
-#26017 := (iff #26002 #26016)
-#26014 := (iff #26001 #26013)
-#26011 := (iff #25999 #26010)
-#26012 := [rewrite]: #26011
-#26015 := [quant-intro #26012]: #26014
-#26018 := [monotonicity #26015]: #26017
-#26021 := [monotonicity #26018]: #26020
-#26024 := [monotonicity #26021]: #26023
-#26027 := [monotonicity #26024]: #26026
-#25989 := [monotonicity #26027]: #25988
-#26076 := [trans #25989 #26072]: #26075
-#25986 := [quant-inst]: #25982
-#26071 := [mp #25986 #26076]: #25981
-#28092 := [unit-resolution #26071 #21044]: #26025
-#28093 := [unit-resolution #28092 #28091]: #26022
-#26074 := (or #26019 #26005)
-#26078 := [def-axiom]: #26074
-#28094 := [unit-resolution #26078 #28093]: #26005
-#28088 := [trans #28094 #28109]: #26480
-#26481 := (not #26480)
-#26516 := (or #11973 #26481)
-#26470 := (uf_66 #26469 0::int #24108)
-#26474 := (uf_24 uf_287 #26470)
-#26475 := (= uf_9 #26474)
-#26476 := (not #26475)
-#26451 := (iff #17634 #26476)
-#26449 := (iff #11973 #26475)
-#26446 := (iff #26475 #11973)
-#26467 := (= #26474 #3047)
-#26465 := (= #26470 #3044)
-#26466 := [monotonicity #27663 #27656]: #26465
-#26468 := [monotonicity #26466]: #26467
-#26448 := [monotonicity #26468]: #26446
-#26450 := [symm #26448]: #26449
-#26452 := [monotonicity #26450]: #26451
-#26464 := [hypothesis]: #17634
-#26447 := [mp #26464 #26452]: #26476
-#26471 := (uf_58 #3175 #26470)
-#26472 := (uf_136 #26471)
-#26473 := (= uf_9 #26472)
-#26486 := (or #26473 #26476)
-#26489 := (not #26486)
+#10068 := (iff #2244 #10065)
+#10041 := (and #3720 #10038)
+#10044 := (and #9726 #10041)
+#10051 := (or #10050 #10044)
+#10056 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #10051)
+#10066 := (iff #10056 #10065)
+#10063 := (iff #10051 #10062)
+#10060 := (iff #10044 #10059)
+#10061 := [rewrite]: #10060
+#10064 := [monotonicity #10061]: #10063
+#10067 := [quant-intro #10064]: #10066
+#10057 := (iff #2244 #10056)
+#10054 := (iff #2243 #10051)
+#10047 := (implies #9774 #10044)
+#10052 := (iff #10047 #10051)
+#10053 := [rewrite]: #10052
+#10048 := (iff #2243 #10047)
+#10045 := (iff #2242 #10044)
+#10042 := (iff #2241 #10041)
+#10039 := (iff #2240 #10038)
+#10036 := (iff #2239 #10033)
+#10029 := (implies #10023 #10026)
+#10034 := (iff #10029 #10033)
+#10035 := [rewrite]: #10034
+#10030 := (iff #2239 #10029)
+#10027 := (iff #2238 #10026)
+#10028 := [rewrite]: #10027
+#10024 := (iff #2235 #10023)
+#10021 := (iff #2234 #10020)
+#10022 := [rewrite]: #10021
+#10025 := [monotonicity #10022]: #10024
+#10031 := [monotonicity #10025 #10028]: #10030
+#10037 := [trans #10031 #10035]: #10036
+#10040 := [quant-intro #10037]: #10039
+#3721 := (iff #184 #3720)
+#3722 := [rewrite]: #3721
+#10043 := [monotonicity #3722 #10040]: #10042
+#9727 := (iff #2151 #9726)
+#9728 := [rewrite]: #9727
+#10046 := [monotonicity #9728 #10043]: #10045
+#9775 := (iff #2167 #9774)
+#9776 := [rewrite]: #9775
+#10049 := [monotonicity #9776 #10046]: #10048
+#10055 := [trans #10049 #10053]: #10054
+#10058 := [quant-intro #10055]: #10057
+#10069 := [trans #10058 #10067]: #10068
+#10019 := [asserted]: #2244
+#10070 := [mp #10019 #10069]: #10065
+#17593 := [mp~ #10070 #17592]: #10065
+#21644 := [mp #17593 #21643]: #21641
+#26556 := (not #26553)
+#26648 := (not #21641)
+#26649 := (or #26648 #26500 #26556)
+#26533 := (or #26532 #26531 #26527)
+#26535 := (forall (vars (?x577 T5)) (:pat #26534) #26533)
+#26536 := (not #26535)
+#26541 := (or #26409 #26540 #26536)
+#26542 := (not #26541)
+#26543 := (or #26500 #26542)
+#26637 := (or #26648 #26543)
+#26621 := (iff #26637 #26649)
+#26559 := (or #26500 #26556)
+#26639 := (or #26648 #26559)
+#26677 := (iff #26639 #26649)
+#26625 := [rewrite]: #26677
+#26675 := (iff #26637 #26639)
+#26560 := (iff #26543 #26559)
+#26557 := (iff #26542 #26556)
+#26554 := (iff #26541 #26553)
+#26551 := (iff #26536 #26550)
+#26548 := (iff #26535 #26547)
+#26545 := (iff #26533 #26544)
+#26546 := [rewrite]: #26545
+#26549 := [quant-intro #26546]: #26548
+#26552 := [monotonicity #26549]: #26551
+#26555 := [monotonicity #26552]: #26554
+#26558 := [monotonicity #26555]: #26557
+#26561 := [monotonicity #26558]: #26560
+#26676 := [monotonicity #26561]: #26675
+#26627 := [trans #26676 #26625]: #26621
+#26638 := [quant-inst]: #26637
+#26623 := [mp #26638 #26627]: #26649
+#26731 := [unit-resolution #26623 #21644 #26733]: #26500
+#26497 := (not #26481)
+#26491 := (or #26490 #26479 #26497)
+#26487 := [def-axiom]: #26491
+#26734 := [unit-resolution #26487 #26731 #26730 #26699]: false
+#26736 := [lemma #26734]: #26735
+#28635 := [unit-resolution #26736 #26581]: #26539
+#26723 := (or #26540 #27014)
+#26701 := (= #26538 #27013)
+#26697 := (= #27013 #26538)
+#28317 := (= #26926 #25933)
+#28318 := [trans #28292 #28304]: #28317
+#26698 := [monotonicity #28318]: #26697
+#26721 := [symm #26698]: #26701
+#26709 := [hypothesis]: #26539
+#26722 := [trans #26709 #26721]: #27014
+#27015 := (not #27014)
+#26695 := [hypothesis]: #27015
+#26720 := [unit-resolution #26695 #26722]: false
+#26724 := [lemma #26720]: #26723
+#28636 := [unit-resolution #26724 #28635]: #27014
+#27050 := (or #11931 #27015)
+#27003 := (uf_43 #24643 #2980)
+#27004 := (uf_66 #27003 0::int #24643)
+#27008 := (uf_24 uf_287 #27004)
+#27009 := (= uf_9 #27008)
+#27010 := (not #27009)
+#26985 := (iff #18130 #27010)
+#26983 := (iff #11931 #27009)
+#26980 := (iff #27009 #11931)
+#27001 := (= #27008 #3034)
+#26999 := (= #27004 #3031)
+#28196 := (= #27003 #2979)
+#28194 := (= #2980 uf_288)
+#24762 := (= uf_288 #2980)
+#2698 := (uf_116 #2697)
+#11210 := (= #161 #2698)
+#22938 := (forall (vars (?x718 T3) (?x719 int)) (:pat #22937) #11210)
+#11214 := (forall (vars (?x718 T3) (?x719 int)) #11210)
+#22941 := (iff #11214 #22938)
+#22939 := (iff #11210 #11210)
+#22940 := [refl]: #22939
+#22942 := [quant-intro #22940]: #22941
+#17984 := (~ #11214 #11214)
+#17982 := (~ #11210 #11210)
+#17983 := [refl]: #17982
+#17985 := [nnf-pos #17983]: #17984
+#2699 := (= #2698 #161)
+#2700 := (forall (vars (?x718 T3) (?x719 int)) #2699)
+#11215 := (iff #2700 #11214)
+#11212 := (iff #2699 #11210)
+#11213 := [rewrite]: #11212
+#11216 := [quant-intro #11213]: #11215
+#11209 := [asserted]: #2700
+#11219 := [mp #11209 #11216]: #11214
+#17986 := [mp~ #11219 #17985]: #11214
+#22943 := [mp #17986 #22942]: #22938
+#24716 := (not #22938)
+#24767 := (or #24716 #24762)
+#24768 := [quant-inst]: #24767
+#28193 := [unit-resolution #24768 #22943]: #24762
+#28195 := [symm #28193]: #28194
+#28197 := [monotonicity #28190 #28195]: #28196
+#27000 := [monotonicity #28197 #28190]: #26999
+#27002 := [monotonicity #27000]: #27001
+#26982 := [monotonicity #27002]: #26980
+#26984 := [symm #26982]: #26983
+#26986 := [monotonicity #26984]: #26985
+#26998 := [hypothesis]: #18130
+#26981 := [mp #26998 #26986]: #27010
+#27005 := (uf_58 #3150 #27004)
+#27006 := (uf_136 #27005)
+#27007 := (= uf_9 #27006)
+#27020 := (or #27007 #27010)
+#27023 := (not #27020)
 decl uf_22 :: (-> T3 T2)
-#26482 := (uf_22 #24108)
-#26483 := (= uf_9 #26482)
+#27016 := (uf_22 #24643)
+#27017 := (= uf_9 #27016)
 #2783 := (uf_22 uf_7)
-#27694 := (= #2783 #26482)
-#27691 := (= #26482 #2783)
-#27692 := [monotonicity #27656]: #27691
-#27695 := [symm #27692]: #27694
-#11384 := (= uf_9 #2783)
+#28228 := (= #2783 #27016)
+#28225 := (= #27016 #2783)
+#28226 := [monotonicity #28190]: #28225
+#28229 := [symm #28226]: #28228
+#11386 := (= uf_9 #2783)
 #2784 := (= #2783 uf_9)
-#11386 := (iff #2784 #11384)
-#11387 := [rewrite]: #11386
-#11383 := [asserted]: #2784
-#11390 := [mp #11383 #11387]: #11384
-#27696 := [trans #11390 #27695]: #26483
-#26484 := (not #26483)
-#26512 := (or #26484 #26489)
-#27697 := [hypothesis]: #26480
-#26427 := (<= #24110 0::int)
-#26454 := (not #26427)
-#13542 := [and-elim #13524]: #12741
-#26410 := (* -1::int #24110)
-#26519 := (+ uf_286 #26410)
-#26520 := (<= #26519 0::int)
-#27677 := (not #24111)
-#27678 := (or #27677 #26520)
-#27679 := [th-lemma]: #27678
-#27680 := [unit-resolution #27679 #27676]: #26520
-#27686 := (not #26520)
-#26455 := (or #26454 #12740 #27686)
-#26456 := [th-lemma]: #26455
-#26457 := [unit-resolution #26456 #27680 #13542]: #26454
+#11388 := (iff #2784 #11386)
+#11389 := [rewrite]: #11388
+#11385 := [asserted]: #2784
+#11392 := [mp #11385 #11389]: #11386
+#28230 := [trans #11392 #28229]: #27017
+#27018 := (not #27017)
+#27046 := (or #27018 #27023)
+#28231 := [hypothesis]: #27014
+#26961 := (<= #24645 0::int)
+#26988 := (not #26961)
+#14069 := [not-or-elim #14055]: #13218
+#26944 := (* -1::int #24645)
+#27053 := (+ uf_286 #26944)
+#27054 := (<= #27053 0::int)
+#28211 := (not #24646)
+#28212 := (or #28211 #27054)
+#28213 := [th-lemma]: #28212
+#28214 := [unit-resolution #28213 #28210]: #27054
+#28220 := (not #27054)
+#26989 := (or #26988 #13217 #28220)
+#26990 := [th-lemma]: #26989
+#26991 := [unit-resolution #26990 #28214 #14069]: #26988
 #237 := (uf_22 #233)
+#247 := (:var 1 int)
 #762 := (:var 4 int)
 #2069 := (uf_43 #233 #762)
 #2070 := (uf_66 #2069 #247 #233)
@@ -5060,59 +5595,59 @@
 #2084 := (uf_58 #1545 #2070)
 #2085 := (pattern #2068 #2084 #237)
 #2090 := (uf_136 #2084)
-#9532 := (= uf_9 #2090)
+#9534 := (= uf_9 #2090)
 #2088 := (uf_24 #1373 #2070)
-#9529 := (= uf_9 #2088)
-#20750 := (not #9529)
-#20751 := (or #20750 #9532)
-#20752 := (not #20751)
-#9473 := (= uf_9 #2068)
-#20726 := (not #9473)
+#9531 := (= uf_9 #2088)
+#21350 := (not #9531)
+#21351 := (or #21350 #9534)
+#21352 := (not #21351)
+#9475 := (= uf_9 #2068)
+#21326 := (not #9475)
 #2073 := (uf_55 #1373)
-#9470 := (= uf_9 #2073)
-#20725 := (not #9470)
-#4045 := (* -1::int #268)
-#6109 := (+ #247 #4045)
-#6706 := (>= #6109 0::int)
-#4307 := (>= #247 0::int)
-#18663 := (not #4307)
-#3926 := (= uf_9 #237)
-#10244 := (not #3926)
-#20758 := (or #10244 #18663 #6706 #20725 #20726 #20752)
-#20763 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #20758)
-#9535 := (not #9532)
-#9538 := (and #9529 #9535)
-#7773 := (not #6706)
-#9511 := (and #3926 #4307 #7773 #9470 #9473)
-#9516 := (not #9511)
-#9552 := (or #9516 #9538)
-#9555 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #9552)
-#20764 := (iff #9555 #20763)
-#20761 := (iff #9552 #20758)
-#20727 := (or #10244 #18663 #6706 #20725 #20726)
-#20755 := (or #20727 #20752)
-#20759 := (iff #20755 #20758)
-#20760 := [rewrite]: #20759
-#20756 := (iff #9552 #20755)
-#20753 := (iff #9538 #20752)
-#20754 := [rewrite]: #20753
-#20736 := (iff #9516 #20727)
-#20728 := (not #20727)
-#20731 := (not #20728)
-#20734 := (iff #20731 #20727)
-#20735 := [rewrite]: #20734
-#20732 := (iff #9516 #20731)
-#20729 := (iff #9511 #20728)
-#20730 := [rewrite]: #20729
-#20733 := [monotonicity #20730]: #20732
-#20737 := [trans #20733 #20735]: #20736
-#20757 := [monotonicity #20737 #20754]: #20756
-#20762 := [trans #20757 #20760]: #20761
-#20765 := [quant-intro #20762]: #20764
-#16956 := (~ #9555 #9555)
-#16954 := (~ #9552 #9552)
-#16955 := [refl]: #16954
-#16957 := [nnf-pos #16955]: #16956
+#9472 := (= uf_9 #2073)
+#21325 := (not #9472)
+#4047 := (* -1::int #268)
+#6111 := (+ #247 #4047)
+#6708 := (>= #6111 0::int)
+#4309 := (>= #247 0::int)
+#19263 := (not #4309)
+#3928 := (= uf_9 #237)
+#10246 := (not #3928)
+#21358 := (or #10246 #19263 #6708 #21325 #21326 #21352)
+#21363 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #21358)
+#9537 := (not #9534)
+#9540 := (and #9531 #9537)
+#7775 := (not #6708)
+#9513 := (and #3928 #4309 #7775 #9472 #9475)
+#9518 := (not #9513)
+#9554 := (or #9518 #9540)
+#9557 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #9554)
+#21364 := (iff #9557 #21363)
+#21361 := (iff #9554 #21358)
+#21327 := (or #10246 #19263 #6708 #21325 #21326)
+#21355 := (or #21327 #21352)
+#21359 := (iff #21355 #21358)
+#21360 := [rewrite]: #21359
+#21356 := (iff #9554 #21355)
+#21353 := (iff #9540 #21352)
+#21354 := [rewrite]: #21353
+#21336 := (iff #9518 #21327)
+#21328 := (not #21327)
+#21331 := (not #21328)
+#21334 := (iff #21331 #21327)
+#21335 := [rewrite]: #21334
+#21332 := (iff #9518 #21331)
+#21329 := (iff #9513 #21328)
+#21330 := [rewrite]: #21329
+#21333 := [monotonicity #21330]: #21332
+#21337 := [trans #21333 #21335]: #21336
+#21357 := [monotonicity #21337 #21354]: #21356
+#21362 := [trans #21357 #21360]: #21361
+#21365 := [quant-intro #21362]: #21364
+#17457 := (~ #9557 #9557)
+#17455 := (~ #9554 #9554)
+#17456 := [refl]: #17455
+#17458 := [nnf-pos #17456]: #17457
 #2091 := (= #2090 uf_9)
 #2092 := (not #2091)
 #2089 := (= #2088 uf_9)
@@ -5128,531 +5663,512 @@
 #2078 := (and #2074 #2077)
 #2094 := (implies #2078 #2093)
 #2095 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #2094)
-#9558 := (iff #2095 #9555)
-#9479 := (and #1435 #9473)
-#9484 := (and #3926 #9479)
-#9487 := (and #9470 #9484)
-#9493 := (not #9487)
-#9544 := (or #9493 #9538)
-#9549 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #9544)
-#9556 := (iff #9549 #9555)
-#9553 := (iff #9544 #9552)
-#9517 := (iff #9493 #9516)
-#9514 := (iff #9487 #9511)
-#7776 := (and #4307 #7773)
-#9502 := (and #7776 #9473)
-#9505 := (and #3926 #9502)
-#9508 := (and #9470 #9505)
-#9512 := (iff #9508 #9511)
-#9513 := [rewrite]: #9512
-#9509 := (iff #9487 #9508)
-#9506 := (iff #9484 #9505)
-#9503 := (iff #9479 #9502)
-#7777 := (iff #1435 #7776)
-#7774 := (iff #1434 #7773)
-#7775 := [rewrite]: #7774
-#4306 := (iff #397 #4307)
-#4308 := [rewrite]: #4306
-#7778 := [monotonicity #4308 #7775]: #7777
-#9504 := [monotonicity #7778]: #9503
-#9507 := [monotonicity #9504]: #9506
-#9510 := [monotonicity #9507]: #9509
-#9515 := [trans #9510 #9513]: #9514
-#9518 := [monotonicity #9515]: #9517
-#9554 := [monotonicity #9518]: #9553
-#9557 := [quant-intro #9554]: #9556
-#9550 := (iff #2095 #9549)
-#9547 := (iff #2094 #9544)
-#9541 := (implies #9487 #9538)
-#9545 := (iff #9541 #9544)
-#9546 := [rewrite]: #9545
-#9542 := (iff #2094 #9541)
-#9539 := (iff #2093 #9538)
-#9536 := (iff #2092 #9535)
-#9533 := (iff #2091 #9532)
-#9534 := [rewrite]: #9533
-#9537 := [monotonicity #9534]: #9536
-#9530 := (iff #2089 #9529)
-#9531 := [rewrite]: #9530
-#9540 := [monotonicity #9531 #9537]: #9539
-#9488 := (iff #2078 #9487)
-#9485 := (iff #2077 #9484)
-#9482 := (iff #2076 #9479)
-#9476 := (and #9473 #1435)
-#9480 := (iff #9476 #9479)
-#9481 := [rewrite]: #9480
-#9477 := (iff #2076 #9476)
-#9474 := (iff #2075 #9473)
-#9475 := [rewrite]: #9474
-#9478 := [monotonicity #9475]: #9477
-#9483 := [trans #9478 #9481]: #9482
-#3927 := (iff #238 #3926)
-#3928 := [rewrite]: #3927
-#9486 := [monotonicity #3928 #9483]: #9485
-#9471 := (iff #2074 #9470)
-#9472 := [rewrite]: #9471
-#9489 := [monotonicity #9472 #9486]: #9488
-#9543 := [monotonicity #9489 #9540]: #9542
-#9548 := [trans #9543 #9546]: #9547
-#9551 := [quant-intro #9548]: #9550
-#9559 := [trans #9551 #9557]: #9558
-#9528 := [asserted]: #2095
-#9560 := [mp #9528 #9559]: #9555
-#16958 := [mp~ #9560 #16957]: #9555
-#20766 := [mp #16958 #20765]: #20763
-#26500 := (not #20763)
-#26360 := (or #26500 #23948 #26427 #26481 #26484 #26489)
-#26477 := (or #26476 #26473)
-#26478 := (not #26477)
-#26411 := (+ 0::int #26410)
-#26412 := (>= #26411 0::int)
-#26413 := (>= 0::int 0::int)
-#26414 := (not #26413)
-#26485 := (or #26484 #26414 #26412 #23948 #26481 #26478)
-#26361 := (or #26500 #26485)
-#26382 := (iff #26361 #26360)
-#26495 := (or #23948 #26427 #26481 #26484 #26489)
-#26378 := (or #26500 #26495)
-#26380 := (iff #26378 #26360)
-#26381 := [rewrite]: #26380
-#26379 := (iff #26361 #26378)
-#26498 := (iff #26485 #26495)
-#26492 := (or #26484 false #26427 #23948 #26481 #26489)
-#26496 := (iff #26492 #26495)
-#26497 := [rewrite]: #26496
-#26493 := (iff #26485 #26492)
-#26490 := (iff #26478 #26489)
-#26487 := (iff #26477 #26486)
-#26488 := [rewrite]: #26487
-#26491 := [monotonicity #26488]: #26490
-#26430 := (iff #26412 #26427)
-#26424 := (>= #26410 0::int)
-#26428 := (iff #26424 #26427)
-#26429 := [rewrite]: #26428
-#26425 := (iff #26412 #26424)
-#26422 := (= #26411 #26410)
-#26423 := [rewrite]: #26422
-#26426 := [monotonicity #26423]: #26425
-#26431 := [trans #26426 #26429]: #26430
-#26420 := (iff #26414 false)
-#26418 := (iff #26414 #3112)
-#26416 := (iff #26413 true)
-#26417 := [rewrite]: #26416
-#26419 := [monotonicity #26417]: #26418
-#26421 := [trans #26419 #12066]: #26420
-#26494 := [monotonicity #26421 #26431 #26491]: #26493
-#26499 := [trans #26494 #26497]: #26498
-#26377 := [monotonicity #26499]: #26379
-#26383 := [trans #26377 #26381]: #26382
-#26362 := [quant-inst]: #26361
-#26384 := [mp #26362 #26383]: #26360
-#26513 := [unit-resolution #26384 #20766 #13537 #26457 #27697]: #26512
-#26514 := [unit-resolution #26513 #27696]: #26489
-#26460 := (or #26486 #26475)
-#26461 := [def-axiom]: #26460
-#26515 := [unit-resolution #26461 #26514 #26447]: false
-#26517 := [lemma #26515]: #26516
-#28095 := [unit-resolution #26517 #28088]: #11973
-#23927 := (or #22698 #17631 #17634 #22692)
-#23928 := [def-axiom]: #23927
-#28097 := [unit-resolution #23928 #28095 #28084]: #28096
-#28098 := [unit-resolution #28097 #26648]: #22692
-#23917 := (or #22689 #22683)
-#23918 := [def-axiom]: #23917
-#28087 := [unit-resolution #23918 #28098]: #22683
-#26562 := (not #26473)
-#28100 := [unit-resolution #26384 #20766 #13537 #26457 #28088]: #26512
-#28101 := [unit-resolution #28100 #27696]: #26489
-#27944 := (or #26486 #26562)
-#27945 := [def-axiom]: #27944
-#28102 := [unit-resolution #27945 #28101]: #26562
-#28103 := (or #11979 #26473)
-#27942 := (or #11979 #26473 #17634)
-#26742 := (uf_58 #3175 #23935)
-#26748 := (uf_135 #26742)
-#26751 := (uf_25 uf_287 #26748)
-#26752 := (= uf_26 #26751)
-#26749 := (uf_210 uf_287 #26748)
-#26750 := (= uf_9 #26749)
-#27416 := (or #26750 #26752)
-#27420 := (not #27416)
-#26775 := (uf_12 #26369)
-#26938 := (= uf_14 #26775)
-#27415 := (not #26938)
-#26755 := (uf_13 #26748)
-#26756 := (uf_12 #26755)
-#26757 := (= uf_14 #26756)
-#26758 := (uf_27 uf_287 #26748)
-#26753 := (= uf_9 #26758)
-#26743 := (not #26753)
-#26744 := (uf_136 #26742)
-#26745 := (= uf_9 #26744)
-#26746 := (not #26745)
-#26747 := (or #26746 #26743)
-#26774 := (not #26747)
-#27536 := (or #26774 #26757 #27415 #27420)
-#27005 := (not #27536)
-#26817 := (uf_210 uf_287 #23935)
-#26862 := (= uf_9 #26817)
-#26863 := (uf_25 uf_287 #23935)
-#26810 := (= uf_26 #26863)
-#26811 := (or #26810 #26862)
-#26809 := (not #26811)
-#26987 := (or #26809 #26938)
-#27412 := (not #26987)
-#27012 := (or #27412 #27005)
-#27030 := (not #27012)
-#26867 := (uf_24 uf_287 #23935)
-#26988 := (= uf_9 #26867)
-#27804 := (= #3047 #26867)
-#27801 := (= #26867 #3047)
-#27799 := (= #23935 #3044)
-#27793 := (= #26311 #3044)
-#27794 := [symm #27788]: #27793
-#27797 := (= #23935 #26311)
-#27791 := (= #26333 #26311)
-#27792 := [symm #27786]: #27791
-#27798 := [trans #27796 #27792]: #27797
-#27800 := [trans #27798 #27794]: #27799
-#27802 := [monotonicity #27800]: #27801
-#27805 := [symm #27802]: #27804
-#27782 := [hypothesis]: #11973
-#27806 := [trans #27782 #27805]: #26988
-#26989 := (not #26988)
-#27033 := (or #26989 #27030)
-#27035 := (not #27033)
-#26992 := (uf_68 uf_287 #23935)
-#26997 := (= uf_9 #26992)
-#27541 := (iff #26997 #27035)
-#2381 := (uf_68 #47 #23)
-#2382 := (pattern #2381)
-#282 := (uf_59 #47)
-#2384 := (uf_58 #282 #23)
-#2388 := (uf_135 #2384)
-#2399 := (uf_210 #47 #2388)
-#10478 := (= uf_9 #2399)
-#2397 := (uf_25 #47 #2388)
-#10475 := (= uf_26 #2397)
-#10481 := (or #10475 #10478)
-#21152 := (not #10481)
-#2393 := (uf_13 #2388)
-#2394 := (uf_12 #2393)
-#10469 := (= uf_14 #2394)
-#2389 := (uf_27 #47 #2388)
-#10460 := (= uf_9 #2389)
-#10463 := (not #10460)
-#2385 := (uf_136 #2384)
-#10454 := (= uf_9 #2385)
-#10457 := (not #10454)
-#10466 := (or #10457 #10463)
-#21151 := (not #10466)
-#21153 := (or #52 #21151 #10469 #21152)
-#21154 := (not #21153)
-#2405 := (uf_210 #47 #23)
-#10493 := (= uf_9 #2405)
-#10496 := (or #3615 #10493)
-#21146 := (not #10496)
-#21147 := (or #29 #21146)
-#21148 := (not #21147)
-#21157 := (or #21148 #21154)
-#21163 := (not #21157)
-#21164 := (or #11066 #21163)
-#21165 := (not #21164)
-#10450 := (= uf_9 #2381)
-#21170 := (iff #10450 #21165)
-#21173 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #21170)
-#10472 := (not #10469)
-#10514 := (and #29 #10466 #10472 #10481)
-#10499 := (and #52 #10496)
-#10520 := (or #10499 #10514)
-#10525 := (and #3621 #10520)
-#10528 := (iff #10450 #10525)
-#10531 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #10528)
-#21174 := (iff #10531 #21173)
-#21171 := (iff #10528 #21170)
-#21168 := (iff #10525 #21165)
-#21160 := (and #3621 #21157)
-#21166 := (iff #21160 #21165)
-#21167 := [rewrite]: #21166
-#21161 := (iff #10525 #21160)
-#21158 := (iff #10520 #21157)
-#21155 := (iff #10514 #21154)
-#21156 := [rewrite]: #21155
-#21149 := (iff #10499 #21148)
-#21150 := [rewrite]: #21149
-#21159 := [monotonicity #21150 #21156]: #21158
-#21162 := [monotonicity #21159]: #21161
-#21169 := [trans #21162 #21167]: #21168
-#21172 := [monotonicity #21169]: #21171
-#21175 := [quant-intro #21172]: #21174
-#17195 := (~ #10531 #10531)
-#17193 := (~ #10528 #10528)
-#17194 := [refl]: #17193
-#17196 := [nnf-pos #17194]: #17195
-#2406 := (= #2405 uf_9)
-#2407 := (or #143 #2406)
-#2408 := (and #52 #2407)
-#2400 := (= #2399 uf_9)
-#2398 := (= #2397 uf_26)
-#2401 := (or #2398 #2400)
-#2395 := (= #2394 uf_14)
-#2396 := (not #2395)
-#2402 := (and #2396 #2401)
-#2390 := (= #2389 uf_9)
-#2391 := (not #2390)
-#2386 := (= #2385 uf_9)
-#2387 := (not #2386)
-#2392 := (or #2387 #2391)
-#2403 := (and #2392 #2402)
-#2404 := (and #29 #2403)
-#2409 := (or #2404 #2408)
-#2410 := (and #147 #2409)
-#2383 := (= #2381 uf_9)
-#2411 := (iff #2383 #2410)
-#2412 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #2411)
-#10534 := (iff #2412 #10531)
-#10484 := (and #10472 #10481)
-#10487 := (and #10466 #10484)
-#10490 := (and #29 #10487)
-#10502 := (or #10490 #10499)
-#10505 := (and #3621 #10502)
-#10508 := (iff #10450 #10505)
-#10511 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #10508)
-#10532 := (iff #10511 #10531)
-#10529 := (iff #10508 #10528)
-#10526 := (iff #10505 #10525)
-#10523 := (iff #10502 #10520)
-#10517 := (or #10514 #10499)
-#10521 := (iff #10517 #10520)
-#10522 := [rewrite]: #10521
-#10518 := (iff #10502 #10517)
-#10515 := (iff #10490 #10514)
-#10516 := [rewrite]: #10515
-#10519 := [monotonicity #10516]: #10518
-#10524 := [trans #10519 #10522]: #10523
-#10527 := [monotonicity #10524]: #10526
-#10530 := [monotonicity #10527]: #10529
-#10533 := [quant-intro #10530]: #10532
-#10512 := (iff #2412 #10511)
-#10509 := (iff #2411 #10508)
-#10506 := (iff #2410 #10505)
-#10503 := (iff #2409 #10502)
-#10500 := (iff #2408 #10499)
-#10497 := (iff #2407 #10496)
-#10494 := (iff #2406 #10493)
-#10495 := [rewrite]: #10494
-#10498 := [monotonicity #3617 #10495]: #10497
-#10501 := [monotonicity #10498]: #10500
-#10491 := (iff #2404 #10490)
-#10488 := (iff #2403 #10487)
-#10485 := (iff #2402 #10484)
-#10482 := (iff #2401 #10481)
-#10479 := (iff #2400 #10478)
-#10480 := [rewrite]: #10479
-#10476 := (iff #2398 #10475)
-#10477 := [rewrite]: #10476
-#10483 := [monotonicity #10477 #10480]: #10482
-#10473 := (iff #2396 #10472)
-#10470 := (iff #2395 #10469)
-#10471 := [rewrite]: #10470
-#10474 := [monotonicity #10471]: #10473
-#10486 := [monotonicity #10474 #10483]: #10485
-#10467 := (iff #2392 #10466)
-#10464 := (iff #2391 #10463)
-#10461 := (iff #2390 #10460)
-#10462 := [rewrite]: #10461
-#10465 := [monotonicity #10462]: #10464
-#10458 := (iff #2387 #10457)
-#10455 := (iff #2386 #10454)
-#10456 := [rewrite]: #10455
-#10459 := [monotonicity #10456]: #10458
-#10468 := [monotonicity #10459 #10465]: #10467
-#10489 := [monotonicity #10468 #10486]: #10488
-#10492 := [monotonicity #10489]: #10491
-#10504 := [monotonicity #10492 #10501]: #10503
-#10507 := [monotonicity #3623 #10504]: #10506
-#10452 := (iff #2383 #10450)
-#10453 := [rewrite]: #10452
-#10510 := [monotonicity #10453 #10507]: #10509
-#10513 := [quant-intro #10510]: #10512
-#10535 := [trans #10513 #10533]: #10534
-#10449 := [asserted]: #2412
-#10536 := [mp #10449 #10535]: #10531
-#17197 := [mp~ #10536 #17196]: #10531
-#21176 := [mp #17197 #21175]: #21173
-#27590 := (not #21173)
-#27615 := (or #27590 #27541)
-#26727 := (or #26752 #26750)
-#26754 := (not #26727)
-#26776 := (= #26775 uf_14)
-#26814 := (not #26776)
-#26815 := (or #26814 #26774 #26757 #26754)
-#26816 := (not #26815)
-#26812 := (or #26776 #26809)
-#26807 := (not #26812)
-#26813 := (or #26807 #26816)
-#26866 := (not #26813)
-#26990 := (or #26989 #26866)
-#26991 := (not #26990)
-#26937 := (iff #26997 #26991)
-#26626 := (or #27590 #26937)
-#26665 := (iff #26626 #27615)
-#26670 := (iff #27615 #27615)
-#26671 := [rewrite]: #26670
-#27542 := (iff #26937 #27541)
-#27038 := (iff #26991 #27035)
-#27034 := (iff #26990 #27033)
-#27031 := (iff #26866 #27030)
-#27013 := (iff #26813 #27012)
-#27008 := (iff #26816 #27005)
-#27554 := (iff #26815 #27536)
-#27550 := (or #27415 #26774 #26757 #27420)
-#27534 := (iff #27550 #27536)
-#27533 := [rewrite]: #27534
-#27546 := (iff #26815 #27550)
-#27475 := (iff #26754 #27420)
-#27418 := (iff #26727 #27416)
-#27419 := [rewrite]: #27418
-#27549 := [monotonicity #27419]: #27475
-#27410 := (iff #26814 #27415)
-#26936 := (iff #26776 #26938)
-#26983 := [rewrite]: #26936
-#27048 := [monotonicity #26983]: #27410
-#27535 := [monotonicity #27048 #27549]: #27546
-#27539 := [trans #27535 #27533]: #27554
-#27011 := [monotonicity #27539]: #27008
-#27413 := (iff #26807 #27412)
-#27010 := (iff #26812 #26987)
-#26984 := (or #26938 #26809)
-#26982 := (iff #26984 #26987)
-#27009 := [rewrite]: #26982
-#26985 := (iff #26812 #26984)
-#26986 := [monotonicity #26983]: #26985
-#27047 := [trans #26986 #27009]: #27010
-#27414 := [monotonicity #27047]: #27413
-#27028 := [monotonicity #27414 #27011]: #27013
-#27032 := [monotonicity #27028]: #27031
-#27029 := [monotonicity #27032]: #27034
-#27540 := [monotonicity #27029]: #27038
-#27543 := [monotonicity #27540]: #27542
-#26666 := [monotonicity #27543]: #26665
-#26672 := [trans #26666 #26671]: #26665
-#26627 := [quant-inst]: #26626
-#26941 := [mp #26627 #26672]: #27615
-#27807 := [unit-resolution #26941 #21176]: #27541
-#27775 := (not #26997)
-#27815 := (iff #17640 #27775)
-#27813 := (iff #11979 #26997)
-#27811 := (iff #26997 #11979)
-#27809 := (= #26992 #3050)
-#27810 := [monotonicity #27800]: #27809
-#27812 := [monotonicity #27810]: #27811
-#27814 := [symm #27812]: #27813
-#27816 := [monotonicity #27814]: #27815
-#27808 := [hypothesis]: #17640
-#27817 := [mp #27808 #27816]: #27775
-#27772 := (not #27541)
-#27773 := (or #27772 #26997 #27033)
-#27774 := [def-axiom]: #27773
-#27818 := [unit-resolution #27774 #27817 #27807]: #27033
-#27770 := (or #27035 #26989 #27030)
-#27771 := [def-axiom]: #27770
-#27819 := [unit-resolution #27771 #27818 #27806]: #27030
-#27835 := (iff #26562 #26746)
-#27833 := (iff #26473 #26745)
-#27831 := (iff #26745 #26473)
-#27829 := (= #26744 #26472)
-#27827 := (= #26742 #26471)
-#26222 := (uf_58 #3175 #3044)
-#27825 := (= #26222 #26471)
-#27823 := (= #26471 #26222)
-#27824 := [monotonicity #26466]: #27823
-#27826 := [symm #27824]: #27825
-#27821 := (= #26742 #26222)
-#27822 := [monotonicity #27800]: #27821
-#27828 := [trans #27822 #27826]: #27827
-#27830 := [monotonicity #27828]: #27829
-#27832 := [monotonicity #27830]: #27831
-#27834 := [symm #27832]: #27833
-#27836 := [monotonicity #27834]: #27835
-#27820 := [hypothesis]: #26562
-#27837 := [mp #27820 #27836]: #26746
-#27732 := (or #26747 #26745)
-#27733 := [def-axiom]: #27732
-#27838 := [unit-resolution #27733 #27837]: #26747
-#24648 := (uf_12 uf_7)
-#27854 := (= #24648 #26775)
-#27850 := (= #26775 #24648)
-#27851 := [monotonicity #27849]: #27850
-#27855 := [symm #27851]: #27854
-#24649 := (= uf_14 #24648)
-#24656 := (iff #11384 #24649)
+#9560 := (iff #2095 #9557)
+#9481 := (and #1435 #9475)
+#9486 := (and #3928 #9481)
+#9489 := (and #9472 #9486)
+#9495 := (not #9489)
+#9546 := (or #9495 #9540)
+#9551 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #9546)
+#9558 := (iff #9551 #9557)
+#9555 := (iff #9546 #9554)
+#9519 := (iff #9495 #9518)
+#9516 := (iff #9489 #9513)
+#7778 := (and #4309 #7775)
+#9504 := (and #7778 #9475)
+#9507 := (and #3928 #9504)
+#9510 := (and #9472 #9507)
+#9514 := (iff #9510 #9513)
+#9515 := [rewrite]: #9514
+#9511 := (iff #9489 #9510)
+#9508 := (iff #9486 #9507)
+#9505 := (iff #9481 #9504)
+#7779 := (iff #1435 #7778)
+#7776 := (iff #1434 #7775)
+#7777 := [rewrite]: #7776
+#4308 := (iff #397 #4309)
+#4310 := [rewrite]: #4308
+#7780 := [monotonicity #4310 #7777]: #7779
+#9506 := [monotonicity #7780]: #9505
+#9509 := [monotonicity #9506]: #9508
+#9512 := [monotonicity #9509]: #9511
+#9517 := [trans #9512 #9515]: #9516
+#9520 := [monotonicity #9517]: #9519
+#9556 := [monotonicity #9520]: #9555
+#9559 := [quant-intro #9556]: #9558
+#9552 := (iff #2095 #9551)
+#9549 := (iff #2094 #9546)
+#9543 := (implies #9489 #9540)
+#9547 := (iff #9543 #9546)
+#9548 := [rewrite]: #9547
+#9544 := (iff #2094 #9543)
+#9541 := (iff #2093 #9540)
+#9538 := (iff #2092 #9537)
+#9535 := (iff #2091 #9534)
+#9536 := [rewrite]: #9535
+#9539 := [monotonicity #9536]: #9538
+#9532 := (iff #2089 #9531)
+#9533 := [rewrite]: #9532
+#9542 := [monotonicity #9533 #9539]: #9541
+#9490 := (iff #2078 #9489)
+#9487 := (iff #2077 #9486)
+#9484 := (iff #2076 #9481)
+#9478 := (and #9475 #1435)
+#9482 := (iff #9478 #9481)
+#9483 := [rewrite]: #9482
+#9479 := (iff #2076 #9478)
+#9476 := (iff #2075 #9475)
+#9477 := [rewrite]: #9476
+#9480 := [monotonicity #9477]: #9479
+#9485 := [trans #9480 #9483]: #9484
+#3929 := (iff #238 #3928)
+#3930 := [rewrite]: #3929
+#9488 := [monotonicity #3930 #9485]: #9487
+#9473 := (iff #2074 #9472)
+#9474 := [rewrite]: #9473
+#9491 := [monotonicity #9474 #9488]: #9490
+#9545 := [monotonicity #9491 #9542]: #9544
+#9550 := [trans #9545 #9548]: #9549
+#9553 := [quant-intro #9550]: #9552
+#9561 := [trans #9553 #9559]: #9560
+#9530 := [asserted]: #2095
+#9562 := [mp #9530 #9561]: #9557
+#17459 := [mp~ #9562 #17458]: #9557
+#21366 := [mp #17459 #21365]: #21363
+#27034 := (not #21363)
+#26894 := (or #27034 #24483 #26961 #27015 #27018 #27023)
+#27011 := (or #27010 #27007)
+#27012 := (not #27011)
+#26945 := (+ 0::int #26944)
+#26946 := (>= #26945 0::int)
+#26947 := (>= 0::int 0::int)
+#26948 := (not #26947)
+#27019 := (or #27018 #26948 #26946 #24483 #27015 #27012)
+#26895 := (or #27034 #27019)
+#26916 := (iff #26895 #26894)
+#27029 := (or #24483 #26961 #27015 #27018 #27023)
+#26912 := (or #27034 #27029)
+#26914 := (iff #26912 #26894)
+#26915 := [rewrite]: #26914
+#26913 := (iff #26895 #26912)
+#27032 := (iff #27019 #27029)
+#27026 := (or #27018 false #26961 #24483 #27015 #27023)
+#27030 := (iff #27026 #27029)
+#27031 := [rewrite]: #27030
+#27027 := (iff #27019 #27026)
+#27024 := (iff #27012 #27023)
+#27021 := (iff #27011 #27020)
+#27022 := [rewrite]: #27021
+#27025 := [monotonicity #27022]: #27024
+#26964 := (iff #26946 #26961)
+#26958 := (>= #26944 0::int)
+#26962 := (iff #26958 #26961)
+#26963 := [rewrite]: #26962
+#26959 := (iff #26946 #26958)
+#26956 := (= #26945 #26944)
+#26957 := [rewrite]: #26956
+#26960 := [monotonicity #26957]: #26959
+#26965 := [trans #26960 #26963]: #26964
+#26954 := (iff #26948 false)
+#26952 := (iff #26948 #3086)
+#26950 := (iff #26947 true)
+#26951 := [rewrite]: #26950
+#26953 := [monotonicity #26951]: #26952
+#26955 := [trans #26953 #11996]: #26954
+#27028 := [monotonicity #26955 #26965 #27025]: #27027
+#27033 := [trans #27028 #27031]: #27032
+#26911 := [monotonicity #27033]: #26913
+#26917 := [trans #26911 #26915]: #26916
+#26896 := [quant-inst]: #26895
+#26918 := [mp #26896 #26917]: #26894
+#27047 := [unit-resolution #26918 #21366 #14064 #26991 #28231]: #27046
+#27048 := [unit-resolution #27047 #28230]: #27023
+#26994 := (or #27020 #27009)
+#26995 := [def-axiom]: #26994
+#27049 := [unit-resolution #26995 #27048 #26981]: false
+#27051 := [lemma #27049]: #27050
+#28637 := [unit-resolution #27051 #28636]: #11931
+#26777 := (or #23215 #18130 #23230)
+#26772 := [hypothesis]: #23227
+#26773 := [hypothesis]: #11931
+#26774 := [hypothesis]: #23218
+#24440 := (or #23215 #11928)
+#24441 := [def-axiom]: #24440
+#26769 := [unit-resolution #24441 #26774]: #11928
+#24452 := (or #23221 #23215)
+#24453 := [def-axiom]: #24452
+#26775 := [unit-resolution #24453 #26774]: #23221
+#24462 := (or #23230 #18127 #18130 #23224)
+#24463 := [def-axiom]: #24462
+#26776 := [unit-resolution #24463 #26775 #26769 #26773 #26772]: false
+#26778 := [lemma #26776]: #26777
+#28638 := [unit-resolution #26778 #28637 #28634]: #23215
+#28373 := (or #11937 #27015)
+#26756 := (uf_58 #3150 #3031)
+#27079 := (uf_135 #26756)
+#27082 := (uf_25 uf_287 #27079)
+#27083 := (= uf_26 #27082)
+#27080 := (uf_210 uf_287 #27079)
+#27081 := (= uf_9 #27080)
+#27189 := (or #27081 #27083)
+#27202 := (not #27189)
+#27071 := (uf_136 #26756)
+#27072 := (= uf_9 #27071)
+#27073 := (not #27072)
+#27069 := (uf_27 uf_287 #27079)
+#27070 := (= uf_9 #27069)
+#27065 := (not #27070)
+#27184 := (or #27065 #27073)
+#27186 := (not #27184)
+#26820 := (uf_13 #3031)
+#27094 := (uf_12 #26820)
+#27144 := (= uf_14 #27094)
+#27181 := (not #27144)
+#27066 := (uf_13 #27079)
+#27067 := (uf_12 #27066)
+#27068 := (= uf_14 #27067)
+#27227 := (or #27068 #27181 #27186 #27202)
+#27231 := (not #27227)
+#27100 := (uf_25 uf_287 #3031)
+#27101 := (= uf_26 #27100)
+#27093 := (uf_210 uf_287 #3031)
+#27099 := (= uf_9 #27093)
+#27146 := (or #27099 #27101)
+#27149 := (not #27146)
+#27192 := (or #27144 #27149)
+#27195 := (not #27192)
+#27239 := (or #27195 #27231)
+#27243 := (not #27239)
+#27240 := (or #18130 #27243)
+#27248 := (not #27240)
+#27255 := (iff #11937 #27248)
+#27260 := (or #27259 #27255)
+#27084 := (or #27083 #27081)
+#27085 := (not #27084)
+#27074 := (or #27073 #27065)
+#27075 := (not #27074)
+#27095 := (= #27094 uf_14)
+#27096 := (not #27095)
+#27097 := (or #27096 #27075 #27068 #27085)
+#27098 := (not #27097)
+#27102 := (or #27101 #27099)
+#27103 := (not #27102)
+#27151 := (or #27095 #27103)
+#27152 := (not #27151)
+#27153 := (or #27152 #27098)
+#27154 := (not #27153)
+#27155 := (or #18130 #27154)
+#27156 := (not #27155)
+#27143 := (iff #11937 #27156)
+#27261 := (or #27259 #27143)
+#27288 := (iff #27261 #27260)
+#27290 := (iff #27260 #27260)
+#27291 := [rewrite]: #27290
+#27256 := (iff #27143 #27255)
+#27249 := (iff #27156 #27248)
+#27246 := (iff #27155 #27240)
+#27244 := (iff #27154 #27243)
+#27241 := (iff #27153 #27239)
+#27232 := (iff #27098 #27231)
+#27229 := (iff #27097 #27227)
+#27224 := (or #27181 #27186 #27068 #27202)
+#27228 := (iff #27224 #27227)
+#27223 := [rewrite]: #27228
+#27225 := (iff #27097 #27224)
+#27203 := (iff #27085 #27202)
+#27190 := (iff #27084 #27189)
+#27201 := [rewrite]: #27190
+#27222 := [monotonicity #27201]: #27203
+#27187 := (iff #27075 #27186)
+#27185 := (iff #27074 #27184)
+#27180 := [rewrite]: #27185
+#27188 := [monotonicity #27180]: #27187
+#27182 := (iff #27096 #27181)
+#27142 := (iff #27095 #27144)
+#27145 := [rewrite]: #27142
+#27183 := [monotonicity #27145]: #27182
+#27226 := [monotonicity #27183 #27188 #27222]: #27225
+#27230 := [trans #27226 #27223]: #27229
+#27233 := [monotonicity #27230]: #27232
+#27196 := (iff #27152 #27195)
+#27193 := (iff #27151 #27192)
+#27150 := (iff #27103 #27149)
+#27147 := (iff #27102 #27146)
+#27148 := [rewrite]: #27147
+#27191 := [monotonicity #27148]: #27150
+#27194 := [monotonicity #27145 #27191]: #27193
+#27179 := [monotonicity #27194]: #27196
+#27242 := [monotonicity #27179 #27233]: #27241
+#27245 := [monotonicity #27242]: #27244
+#27247 := [monotonicity #27245]: #27246
+#27250 := [monotonicity #27247]: #27249
+#27257 := [monotonicity #27250]: #27256
+#27289 := [monotonicity #27257]: #27288
+#27292 := [trans #27289 #27291]: #27288
+#27287 := [quant-inst]: #27261
+#27277 := [mp #27287 #27292]: #27260
+#28168 := [unit-resolution #27277 #21776]: #27255
+#27430 := (not #27255)
+#28169 := (or #27430 #27240)
+#28163 := [hypothesis]: #18136
+#27433 := (or #27430 #11937 #27240)
+#27434 := [def-axiom]: #27433
+#26920 := [unit-resolution #27434 #28163]: #28169
+#26921 := [unit-resolution #26920 #28168]: #27240
+#26923 := (or #27248 #27243)
+#26922 := [unit-resolution #27051 #28231]: #11931
+#27431 := (or #27248 #18130 #27243)
+#27432 := [def-axiom]: #27431
+#26924 := [unit-resolution #27432 #26922]: #26923
+#27055 := [unit-resolution #26924 #26921]: #27243
+#27389 := (or #27239 #27227)
+#27387 := [def-axiom]: #27389
+#27157 := [unit-resolution #27387 #27055]: #27227
+#27545 := (not #27007)
+#27206 := (iff #27545 #27073)
+#27204 := (iff #27007 #27072)
+#27199 := (= #27006 #27071)
+#27160 := (= #27005 #26756)
+#27161 := [monotonicity #27000]: #27160
+#27200 := [monotonicity #27161]: #27199
+#27205 := [monotonicity #27200]: #27204
+#27475 := [monotonicity #27205]: #27206
+#27546 := (or #27020 #27545)
+#27547 := [def-axiom]: #27546
+#27159 := [unit-resolution #27547 #27048]: #27545
+#27476 := [mp #27159 #27475]: #27073
+#27310 := (or #27184 #27072)
+#27305 := [def-axiom]: #27310
+#27477 := [unit-resolution #27305 #27476]: #27184
+#25182 := (uf_12 uf_7)
+#28283 := (= #25182 #27094)
+#28279 := (= #27094 #25182)
+#28277 := (= #26820 uf_7)
+#24758 := (uf_13 #2979)
+#28275 := (= #24758 uf_7)
+#24759 := (= uf_7 #24758)
+#24764 := (or #24710 #24759)
+#24765 := [quant-inst]: #24764
+#27482 := [unit-resolution #24765 #22949]: #24759
+#28276 := [symm #27482]: #28275
+#28273 := (= #26820 #24758)
+#28256 := (= #3031 #2979)
+#26851 := (uf_116 #24470)
+#26867 := (uf_43 #24643 #26851)
+#28252 := (= #26867 #2979)
+#27548 := (= #26851 uf_288)
+#28244 := (= #26851 #2980)
+#28242 := (= #24470 #2979)
+#24471 := (= #2979 #24470)
+#93 := (uf_29 #23)
+#22848 := (pattern #93)
+#94 := (uf_28 #93)
+#3542 := (= #23 #94)
+#22849 := (forall (vars (?x14 T5)) (:pat #22848) #3542)
+#3545 := (forall (vars (?x14 T5)) #3542)
+#22850 := (iff #3545 #22849)
+#22852 := (iff #22849 #22849)
+#22853 := [rewrite]: #22852
+#22851 := [rewrite]: #22850
+#22854 := [trans #22851 #22853]: #22850
+#16026 := (~ #3545 #3545)
+#16016 := (~ #3542 #3542)
+#16017 := [refl]: #16016
+#16082 := [nnf-pos #16017]: #16026
+#95 := (= #94 #23)
+#96 := (forall (vars (?x14 T5)) #95)
+#3546 := (iff #96 #3545)
+#3543 := (iff #95 #3542)
+#3544 := [rewrite]: #3543
+#3547 := [quant-intro #3544]: #3546
+#3541 := [asserted]: #96
+#3550 := [mp #3541 #3547]: #3545
+#16083 := [mp~ #3550 #16082]: #3545
+#22855 := [mp #16083 #22854]: #22849
+#24474 := (not #22849)
+#24475 := (or #24474 #24471)
+#24476 := [quant-inst]: #24475
+#28241 := [unit-resolution #24476 #22855]: #24471
+#28243 := [symm #28241]: #28242
+#28245 := [monotonicity #28243]: #28244
+#27549 := [trans #28245 #28195]: #27548
+#28126 := [monotonicity #28190 #27549]: #28252
+#28266 := (= #3031 #26867)
+#26845 := (uf_66 #24470 0::int #24643)
+#26870 := (= #26845 #26867)
+#26873 := (not #26870)
+decl uf_138 :: (-> T5 T5 T2)
+#26846 := (uf_138 #26845 #24470)
+#26847 := (= uf_9 #26846)
+#26848 := (not #26847)
+#26879 := (or #26848 #26873)
+#26884 := (not #26879)
+#1576 := (uf_66 #21 #247 #233)
+#1577 := (pattern #1576)
+#1578 := (uf_138 #1576 #21)
+#8222 := (= uf_9 #1578)
+#20914 := (not #8222)
+decl uf_139 :: (-> T3 int)
+#1581 := (uf_139 #233)
+#1582 := (* #247 #1581)
+#1580 := (uf_116 #21)
+#1583 := (+ #1580 #1582)
+#1584 := (uf_43 #233 #1583)
+#1585 := (= #1576 #1584)
+#20913 := (not #1585)
+#20915 := (or #20913 #20914)
+#20916 := (not #20915)
+#20919 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #20916)
+#8228 := (and #1585 #8222)
+#8233 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #8228)
+#20920 := (iff #8233 #20919)
+#20917 := (iff #8228 #20916)
+#20918 := [rewrite]: #20917
+#20921 := [quant-intro #20918]: #20920
+#17047 := (~ #8233 #8233)
+#17045 := (~ #8228 #8228)
+#17046 := [refl]: #17045
+#17048 := [nnf-pos #17046]: #17047
+#1579 := (= #1578 uf_9)
+#1586 := (and #1579 #1585)
+#1587 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #1586)
+#8234 := (iff #1587 #8233)
+#8231 := (iff #1586 #8228)
+#8225 := (and #8222 #1585)
+#8229 := (iff #8225 #8228)
+#8230 := [rewrite]: #8229
+#8226 := (iff #1586 #8225)
+#8223 := (iff #1579 #8222)
+#8224 := [rewrite]: #8223
+#8227 := [monotonicity #8224]: #8226
+#8232 := [trans #8227 #8230]: #8231
+#8235 := [quant-intro #8232]: #8234
+#8221 := [asserted]: #1587
+#8238 := [mp #8221 #8235]: #8233
+#17049 := [mp~ #8238 #17048]: #8233
+#20922 := [mp #17049 #20921]: #20919
+#26887 := (not #20919)
+#26833 := (or #26887 #26884)
+#26849 := (uf_139 #24643)
+#26850 := (* 0::int #26849)
+#26852 := (+ #26851 #26850)
+#26853 := (uf_43 #24643 #26852)
+#26854 := (= #26845 #26853)
+#26855 := (not #26854)
+#26856 := (or #26855 #26848)
+#26857 := (not #26856)
+#26834 := (or #26887 #26857)
+#26919 := (iff #26834 #26833)
+#26993 := (iff #26833 #26833)
+#26996 := [rewrite]: #26993
+#26885 := (iff #26857 #26884)
+#26882 := (iff #26856 #26879)
+#26876 := (or #26873 #26848)
+#26880 := (iff #26876 #26879)
+#26881 := [rewrite]: #26880
+#26877 := (iff #26856 #26876)
+#26874 := (iff #26855 #26873)
+#26871 := (iff #26854 #26870)
+#26868 := (= #26853 #26867)
+#26865 := (= #26852 #26851)
+#26860 := (+ #26851 0::int)
+#26863 := (= #26860 #26851)
+#26864 := [rewrite]: #26863
+#26861 := (= #26852 #26860)
+#26858 := (= #26850 0::int)
+#26859 := [rewrite]: #26858
+#26862 := [monotonicity #26859]: #26861
+#26866 := [trans #26862 #26864]: #26865
+#26869 := [monotonicity #26866]: #26868
+#26872 := [monotonicity #26869]: #26871
+#26875 := [monotonicity #26872]: #26874
+#26878 := [monotonicity #26875]: #26877
+#26883 := [trans #26878 #26881]: #26882
+#26886 := [monotonicity #26883]: #26885
+#26992 := [monotonicity #26886]: #26919
+#26997 := [trans #26992 #26996]: #26919
+#26897 := [quant-inst]: #26834
+#26987 := [mp #26897 #26997]: #26833
+#27579 := [unit-resolution #26987 #20922]: #26884
+#27037 := (or #26879 #26870)
+#27038 := [def-axiom]: #27037
+#27634 := [unit-resolution #27038 #27579]: #26870
+#28085 := (= #3031 #26845)
+#28125 := [monotonicity #28241 #28188]: #28085
+#28267 := [trans #28125 #27634]: #28266
+#28257 := [trans #28267 #28126]: #28256
+#28274 := [monotonicity #28257]: #28273
+#28278 := [trans #28274 #28276]: #28277
+#28280 := [monotonicity #28278]: #28279
+#28284 := [symm #28280]: #28283
+#25183 := (= uf_14 #25182)
+#25190 := (iff #11386 #25183)
 #2308 := (pattern #237)
 #2836 := (uf_12 #233)
-#11557 := (= uf_14 #2836)
-#11561 := (iff #3926 #11557)
-#11564 := (forall (vars (?x761 T3)) (:pat #2308) #11561)
-#17583 := (~ #11564 #11564)
-#17581 := (~ #11561 #11561)
-#17582 := [refl]: #17581
-#17584 := [nnf-pos #17582]: #17583
+#11559 := (= uf_14 #2836)
+#11563 := (iff #3928 #11559)
+#11566 := (forall (vars (?x761 T3)) (:pat #2308) #11563)
+#18084 := (~ #11566 #11566)
+#18082 := (~ #11563 #11563)
+#18083 := [refl]: #18082
+#18085 := [nnf-pos #18083]: #18084
 #2849 := (= #2836 uf_14)
 #2850 := (iff #238 #2849)
 #2851 := (forall (vars (?x761 T3)) (:pat #2308) #2850)
-#11565 := (iff #2851 #11564)
-#11562 := (iff #2850 #11561)
-#11559 := (iff #2849 #11557)
-#11560 := [rewrite]: #11559
-#11563 := [monotonicity #3928 #11560]: #11562
-#11566 := [quant-intro #11563]: #11565
-#11556 := [asserted]: #2851
-#11569 := [mp #11556 #11566]: #11564
-#17585 := [mp~ #11569 #17584]: #11564
-#24280 := (not #11564)
-#24659 := (or #24280 #24656)
-#24660 := [quant-inst]: #24659
-#27839 := [unit-resolution #24660 #17585]: #24656
-#24661 := (not #24656)
-#27840 := (or #24661 #24649)
-#24665 := (not #11384)
-#24666 := (or #24661 #24665 #24649)
-#24667 := [def-axiom]: #24666
-#27841 := [unit-resolution #24667 #11390]: #27840
-#27842 := [unit-resolution #27841 #27839]: #24649
-#27856 := [trans #27842 #27855]: #26938
-#27751 := (not #26757)
-#27930 := (iff #11876 #27751)
-#27928 := (iff #11873 #26757)
-#27926 := (iff #26757 #11873)
-#27924 := (= #26756 #2990)
-#27922 := (= #26755 #2977)
-#27918 := (= #26755 #24228)
-#27916 := (= #26748 #2981)
-#27914 := (= #26748 #26392)
-#26393 := (uf_66 #26392 0::int #24108)
-#26397 := (uf_58 #3175 #26393)
-#26400 := (uf_135 #26397)
-#27912 := (= #26400 #26392)
-#26401 := (= #26392 #26400)
-#26403 := (up_67 #26397)
-#26404 := (not #26403)
-#26402 := (not #26401)
-#26398 := (uf_136 #26397)
-#26399 := (= uf_9 #26398)
-#26394 := (uf_24 uf_287 #26393)
-#26395 := (= uf_9 #26394)
-#26396 := (not #26395)
-#26432 := (or #26396 #26399 #26402 #26404)
-#26435 := (not #26432)
-#26407 := (uf_24 uf_287 #26392)
-#26408 := (= uf_9 #26407)
-#27867 := (= #2988 #26407)
-#27864 := (= #26407 #2988)
-#27865 := [monotonicity #27863]: #27864
-#27868 := [symm #27865]: #27867
-#27869 := [trans #13532 #27868]: #26408
-#26409 := (not #26408)
-#27870 := (or #26409 #26435)
+#11567 := (iff #2851 #11566)
+#11564 := (iff #2850 #11563)
+#11561 := (iff #2849 #11559)
+#11562 := [rewrite]: #11561
+#11565 := [monotonicity #3930 #11562]: #11564
+#11568 := [quant-intro #11565]: #11567
+#11558 := [asserted]: #2851
+#11571 := [mp #11558 #11568]: #11566
+#18086 := [mp~ #11571 #18085]: #11566
+#24814 := (not #11566)
+#25193 := (or #24814 #25190)
+#25194 := [quant-inst]: #25193
+#27478 := [unit-resolution #25194 #18086]: #25190
+#25195 := (not #25190)
+#27479 := (or #25195 #25183)
+#25199 := (not #11386)
+#25200 := (or #25195 #25199 #25183)
+#25201 := [def-axiom]: #25200
+#27480 := [unit-resolution #25201 #11392]: #27479
+#27481 := [unit-resolution #27480 #27478]: #25183
+#28285 := [trans #27481 #28284]: #27144
+#27341 := (not #27068)
+#28362 := (iff #11878 #27341)
+#28360 := (iff #11875 #27068)
+#28358 := (iff #27068 #11875)
+#28356 := (= #27067 #2990)
+#28354 := (= #27066 #2977)
+#28350 := (= #27066 #24763)
+#28348 := (= #27079 #2981)
+#28346 := (= #27079 #26926)
+#26927 := (uf_66 #26926 0::int #24643)
+#26931 := (uf_58 #3150 #26927)
+#26934 := (uf_135 #26931)
+#28344 := (= #26934 #26926)
+#26935 := (= #26926 #26934)
+#26937 := (up_67 #26931)
+#26938 := (not #26937)
+#26936 := (not #26935)
+#26932 := (uf_136 #26931)
+#26933 := (= uf_9 #26932)
+#26928 := (uf_24 uf_287 #26927)
+#26929 := (= uf_9 #26928)
+#26930 := (not #26929)
+#26966 := (or #26930 #26933 #26936 #26938)
+#26969 := (not #26966)
+#26941 := (uf_24 uf_287 #26926)
+#26942 := (= uf_9 #26941)
+#28296 := (= #2988 #26941)
+#28293 := (= #26941 #2988)
+#28294 := [monotonicity #28292]: #28293
+#28297 := [symm #28294]: #28296
+#28298 := [trans #14077 #28297]: #26942
+#26943 := (not #26942)
+#28299 := (or #26943 #26969)
 #277 := (:var 3 int)
 #310 := (:var 2 T3)
 #1470 := (uf_124 #310 #247)
@@ -5668,59 +6184,59 @@
 #1472 := (pattern #1469 #1471)
 #1478 := (uf_66 #1471 #161 #310)
 #1486 := (uf_24 #35 #1478)
-#7931 := (= uf_9 #1486)
-#20090 := (not #7931)
+#7933 := (= uf_9 #1486)
+#20690 := (not #7933)
 #1479 := (uf_58 #1473 #1478)
 #1482 := (uf_136 #1479)
-#7925 := (= uf_9 #1482)
+#7927 := (= uf_9 #1482)
 #1480 := (uf_135 #1479)
-#7922 := (= #1471 #1480)
-#20089 := (not #7922)
+#7924 := (= #1471 #1480)
+#20689 := (not #7924)
 #1485 := (up_67 #1479)
-#20088 := (not #1485)
-#20091 := (or #20088 #20089 #7925 #20090)
-#20092 := (not #20091)
+#20688 := (not #1485)
+#20691 := (or #20688 #20689 #7927 #20690)
+#20692 := (not #20691)
 #1476 := (uf_24 #35 #1471)
-#7919 := (= uf_9 #1476)
-#7954 := (not #7919)
-#5234 := (* -1::int #247)
-#6114 := (+ #161 #5234)
-#6115 := (>= #6114 0::int)
-#20098 := (or #4963 #6115 #7954 #20092)
-#20103 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #20098)
-#7928 := (not #7925)
-#7963 := (and #1485 #7922 #7928 #7931)
-#7618 := (not #6115)
-#7621 := (and #4041 #7618)
-#7624 := (not #7621)
-#7972 := (or #7624 #7954 #7963)
-#7977 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #7972)
-#20104 := (iff #7977 #20103)
-#20101 := (iff #7972 #20098)
-#19973 := (or #4963 #6115)
-#20095 := (or #19973 #7954 #20092)
-#20099 := (iff #20095 #20098)
-#20100 := [rewrite]: #20099
-#20096 := (iff #7972 #20095)
-#20093 := (iff #7963 #20092)
-#20094 := [rewrite]: #20093
-#19982 := (iff #7624 #19973)
-#19974 := (not #19973)
-#19977 := (not #19974)
-#19980 := (iff #19977 #19973)
-#19981 := [rewrite]: #19980
-#19978 := (iff #7624 #19977)
-#19975 := (iff #7621 #19974)
-#19976 := [rewrite]: #19975
-#19979 := [monotonicity #19976]: #19978
-#19983 := [trans #19979 #19981]: #19982
-#20097 := [monotonicity #19983 #20094]: #20096
-#20102 := [trans #20097 #20100]: #20101
-#20105 := [quant-intro #20102]: #20104
-#16323 := (~ #7977 #7977)
-#16321 := (~ #7972 #7972)
-#16322 := [refl]: #16321
-#16324 := [nnf-pos #16322]: #16323
+#7921 := (= uf_9 #1476)
+#7956 := (not #7921)
+#5236 := (* -1::int #247)
+#6116 := (+ #161 #5236)
+#6117 := (>= #6116 0::int)
+#20698 := (or #4965 #6117 #7956 #20692)
+#20703 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #20698)
+#7930 := (not #7927)
+#7965 := (and #1485 #7924 #7930 #7933)
+#7620 := (not #6117)
+#7623 := (and #4043 #7620)
+#7626 := (not #7623)
+#7974 := (or #7626 #7956 #7965)
+#7979 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #7974)
+#20704 := (iff #7979 #20703)
+#20701 := (iff #7974 #20698)
+#20573 := (or #4965 #6117)
+#20695 := (or #20573 #7956 #20692)
+#20699 := (iff #20695 #20698)
+#20700 := [rewrite]: #20699
+#20696 := (iff #7974 #20695)
+#20693 := (iff #7965 #20692)
+#20694 := [rewrite]: #20693
+#20582 := (iff #7626 #20573)
+#20574 := (not #20573)
+#20577 := (not #20574)
+#20580 := (iff #20577 #20573)
+#20581 := [rewrite]: #20580
+#20578 := (iff #7626 #20577)
+#20575 := (iff #7623 #20574)
+#20576 := [rewrite]: #20575
+#20579 := [monotonicity #20576]: #20578
+#20583 := [trans #20579 #20581]: #20582
+#20697 := [monotonicity #20583 #20694]: #20696
+#20702 := [trans #20697 #20700]: #20701
+#20705 := [quant-intro #20702]: #20704
+#16824 := (~ #7979 #7979)
+#16822 := (~ #7974 #7974)
+#16823 := [refl]: #16822
+#16825 := [nnf-pos #16823]: #16824
 #1487 := (= #1486 uf_9)
 #1488 := (and #1485 #1487)
 #1483 := (= #1482 uf_9)
@@ -5734,1585 +6250,1541 @@
 #1477 := (= #1476 uf_9)
 #1492 := (implies #1477 #1491)
 #1493 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #1492)
-#7980 := (iff #1493 #7977)
-#7934 := (and #1485 #7931)
-#7937 := (and #7928 #7934)
-#7940 := (and #7922 #7937)
-#7588 := (not #1372)
-#7946 := (or #7588 #7940)
-#7955 := (or #7954 #7946)
-#7960 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #7955)
-#7978 := (iff #7960 #7977)
-#7975 := (iff #7955 #7972)
-#7966 := (or #7624 #7963)
-#7969 := (or #7954 #7966)
-#7973 := (iff #7969 #7972)
-#7974 := [rewrite]: #7973
-#7970 := (iff #7955 #7969)
-#7967 := (iff #7946 #7966)
-#7964 := (iff #7940 #7963)
-#7965 := [rewrite]: #7964
-#7625 := (iff #7588 #7624)
-#7622 := (iff #1372 #7621)
-#7619 := (iff #1371 #7618)
-#7620 := [rewrite]: #7619
-#7623 := [monotonicity #4040 #7620]: #7622
-#7626 := [monotonicity #7623]: #7625
-#7968 := [monotonicity #7626 #7965]: #7967
-#7971 := [monotonicity #7968]: #7970
-#7976 := [trans #7971 #7974]: #7975
-#7979 := [quant-intro #7976]: #7978
-#7961 := (iff #1493 #7960)
-#7958 := (iff #1492 #7955)
-#7951 := (implies #7919 #7946)
-#7956 := (iff #7951 #7955)
-#7957 := [rewrite]: #7956
-#7952 := (iff #1492 #7951)
-#7949 := (iff #1491 #7946)
-#7943 := (implies #1372 #7940)
-#7947 := (iff #7943 #7946)
-#7948 := [rewrite]: #7947
-#7944 := (iff #1491 #7943)
-#7941 := (iff #1490 #7940)
-#7938 := (iff #1489 #7937)
-#7935 := (iff #1488 #7934)
-#7932 := (iff #1487 #7931)
-#7933 := [rewrite]: #7932
-#7936 := [monotonicity #7933]: #7935
-#7929 := (iff #1484 #7928)
-#7926 := (iff #1483 #7925)
-#7927 := [rewrite]: #7926
-#7930 := [monotonicity #7927]: #7929
-#7939 := [monotonicity #7930 #7936]: #7938
-#7923 := (iff #1481 #7922)
-#7924 := [rewrite]: #7923
-#7942 := [monotonicity #7924 #7939]: #7941
-#7945 := [monotonicity #7942]: #7944
-#7950 := [trans #7945 #7948]: #7949
-#7920 := (iff #1477 #7919)
-#7921 := [rewrite]: #7920
-#7953 := [monotonicity #7921 #7950]: #7952
-#7959 := [trans #7953 #7957]: #7958
-#7962 := [quant-intro #7959]: #7961
-#7981 := [trans #7962 #7979]: #7980
-#7918 := [asserted]: #1493
-#7982 := [mp #7918 #7981]: #7977
-#16325 := [mp~ #7982 #16324]: #7977
-#20106 := [mp #16325 #20105]: #20103
-#26542 := (not #20103)
-#26543 := (or #26542 #26409 #26427 #26435)
-#26405 := (or #26404 #26402 #26399 #26396)
-#26406 := (not #26405)
-#26415 := (or #26414 #26412 #26409 #26406)
-#26544 := (or #26542 #26415)
-#26551 := (iff #26544 #26543)
-#26441 := (or #26409 #26427 #26435)
-#26546 := (or #26542 #26441)
-#26549 := (iff #26546 #26543)
-#26550 := [rewrite]: #26549
-#26547 := (iff #26544 #26546)
-#26444 := (iff #26415 #26441)
-#26438 := (or false #26427 #26409 #26435)
-#26442 := (iff #26438 #26441)
-#26443 := [rewrite]: #26442
-#26439 := (iff #26415 #26438)
-#26436 := (iff #26406 #26435)
-#26433 := (iff #26405 #26432)
-#26434 := [rewrite]: #26433
-#26437 := [monotonicity #26434]: #26436
-#26440 := [monotonicity #26421 #26431 #26437]: #26439
-#26445 := [trans #26440 #26443]: #26444
-#26548 := [monotonicity #26445]: #26547
-#26532 := [trans #26548 #26550]: #26551
-#26545 := [quant-inst]: #26544
-#26533 := [mp #26545 #26532]: #26543
-#27871 := [unit-resolution #26533 #20106 #26457]: #27870
-#27872 := [unit-resolution #27871 #27869]: #26435
-#26538 := (or #26432 #26401)
-#26539 := [def-axiom]: #26538
-#27873 := [unit-resolution #26539 #27872]: #26401
-#27913 := [symm #27873]: #27912
-#27910 := (= #26748 #26400)
-#27908 := (= #26742 #26397)
-#27906 := (= #26222 #26397)
-#27904 := (= #26397 #26222)
-#27902 := (= #26393 #3044)
-#27900 := (= #26393 #26311)
-#27898 := (= #26393 #26333)
-#27896 := (= #26393 #2979)
-#26574 := (uf_116 #25399)
-#26588 := (uf_43 #24108 #26574)
-#27892 := (= #26588 #2979)
-#27884 := (= #26574 uf_288)
-#27882 := (= #26574 #2980)
-#27880 := (= #24010 #2980)
-#24234 := (= #2980 #24010)
-#24239 := (or #24181 #24234)
-#24240 := [quant-inst]: #24239
-#27874 := [unit-resolution #24240 #22411]: #24234
-#27881 := [symm #27874]: #27880
-#27878 := (= #26574 #24010)
-#27879 := [monotonicity #27877]: #27878
-#27883 := [trans #27879 #27881]: #27882
-#27885 := [trans #27883 #27661]: #27884
-#27893 := [monotonicity #27656 #27885]: #27892
-#27894 := (= #26393 #26588)
-#26570 := (uf_66 #25399 0::int #24108)
-#26591 := (= #26570 #26588)
-#26594 := (not #26591)
-#26571 := (uf_138 #26570 #25399)
-#26572 := (= uf_9 #26571)
-#26573 := (not #26572)
-#26600 := (or #26573 #26594)
-#26605 := (not #26600)
-#26652 := (or #26353 #26605)
-#26575 := (+ #26574 #26316)
-#26576 := (uf_43 #24108 #26575)
-#26577 := (= #26570 #26576)
-#26578 := (not #26577)
-#26579 := (or #26578 #26573)
-#26580 := (not #26579)
-#26653 := (or #26353 #26580)
-#26655 := (iff #26653 #26652)
-#26667 := (iff #26652 #26652)
-#26668 := [rewrite]: #26667
-#26606 := (iff #26580 #26605)
-#26603 := (iff #26579 #26600)
-#26597 := (or #26594 #26573)
-#26601 := (iff #26597 #26600)
-#26602 := [rewrite]: #26601
-#26598 := (iff #26579 #26597)
-#26595 := (iff #26578 #26594)
-#26592 := (iff #26577 #26591)
-#26589 := (= #26576 #26588)
-#26586 := (= #26575 #26574)
-#26581 := (+ #26574 0::int)
-#26584 := (= #26581 #26574)
-#26585 := [rewrite]: #26584
-#26582 := (= #26575 #26581)
-#26583 := [monotonicity #26325]: #26582
-#26587 := [trans #26583 #26585]: #26586
-#26590 := [monotonicity #26587]: #26589
-#26593 := [monotonicity #26590]: #26592
-#26596 := [monotonicity #26593]: #26595
-#26599 := [monotonicity #26596]: #26598
-#26604 := [trans #26599 #26602]: #26603
-#26607 := [monotonicity #26604]: #26606
-#26656 := [monotonicity #26607]: #26655
-#26669 := [trans #26656 #26668]: #26655
-#26654 := [quant-inst]: #26653
-#26688 := [mp #26654 #26669]: #26652
-#27886 := [unit-resolution #26688 #20322]: #26605
-#26692 := (or #26600 #26591)
-#26693 := [def-axiom]: #26692
-#27887 := [unit-resolution #26693 #27886]: #26591
-#27890 := (= #26393 #26570)
-#27891 := [monotonicity #27889]: #27890
-#27895 := [trans #27891 #27887]: #27894
-#27897 := [trans #27895 #27893]: #27896
-#27899 := [trans #27897 #27790]: #27898
-#27901 := [trans #27899 #27792]: #27900
-#27903 := [trans #27901 #27794]: #27902
-#27905 := [monotonicity #27903]: #27904
-#27907 := [symm #27905]: #27906
-#27909 := [trans #27822 #27907]: #27908
-#27911 := [monotonicity #27909]: #27910
-#27915 := [trans #27911 #27913]: #27914
-#27917 := [trans #27915 #27863]: #27916
-#27919 := [monotonicity #27917]: #27918
-#27923 := [trans #27919 #27921]: #27922
-#27925 := [monotonicity #27923]: #27924
-#27927 := [monotonicity #27925]: #27926
-#27929 := [symm #27927]: #27928
-#27931 := [monotonicity #27929]: #27930
-#27932 := [mp #13533 #27931]: #27751
-#27936 := (= #2984 #26751)
-#27933 := (= #26751 #2984)
-#27934 := [monotonicity #27917]: #27933
-#27937 := [symm #27934]: #27936
-#27938 := [trans #13530 #27937]: #26752
-#27744 := (not #26752)
-#27745 := (or #27416 #27744)
-#27746 := [def-axiom]: #27745
-#27939 := [unit-resolution #27746 #27938]: #27416
-#27758 := (or #27005 #26774 #26757 #27415 #27420)
-#27759 := [def-axiom]: #27758
-#27940 := [unit-resolution #27759 #27939 #27932 #27856 #27838]: #27005
-#27762 := (or #27012 #27536)
-#27763 := [def-axiom]: #27762
-#27941 := [unit-resolution #27763 #27940 #27819]: false
-#27943 := [lemma #27941]: #27942
-#28112 := [unit-resolution #27943 #28095]: #28103
-#28113 := [unit-resolution #28112 #28102]: #11979
-#23911 := (or #22686 #17631 #17640 #22680)
-#23912 := [def-axiom]: #23911
-#28111 := [unit-resolution #23912 #28113 #26648 #28087]: #22680
-#23901 := (or #22677 #22671)
-#23902 := [def-axiom]: #23901
-#28114 := [unit-resolution #23902 #28111]: #22671
-#28072 := [hypothesis]: #12866
-#28073 := [th-lemma #13542 #28072]: false
-#28074 := [lemma #28073]: #12863
-#23887 := (or #22674 #12866 #22668)
-#23888 := [def-axiom]: #23887
-#28115 := [unit-resolution #23888 #28074 #28114]: #22668
-#23879 := (or #22665 #22659)
-#23880 := [def-axiom]: #23879
-#28116 := [unit-resolution #23880 #28115]: #22659
-#23889 := (or #22677 #3055)
-#23890 := [def-axiom]: #23889
-#28117 := [unit-resolution #23890 #28111]: #3055
-#26943 := [hypothesis]: #22641
-#26945 := (or #22650 #17676 #22644)
-#23863 := (or #22650 #17676 #12740 #22644)
-#23864 := [def-axiom]: #23863
-#26946 := [unit-resolution #23864 #13542]: #26945
-#28110 := [unit-resolution #26946 #26943 #28117]: #22650
-#23867 := (or #22653 #22647)
-#23868 := [def-axiom]: #23867
-#28118 := [unit-resolution #23868 #28110]: #22653
-#27722 := (or #17676 #17653 #22662 #22644)
-#26876 := (* -1::int #3054)
-#26877 := (+ uf_295 #26876)
-#26878 := (>= #26877 0::int)
-#26623 := (not #26878)
-#27630 := [hypothesis]: #17654
-#23562 := (not #17662)
-#26942 := [hypothesis]: #22659
-#26944 := [hypothesis]: #3055
-#26947 := [unit-resolution #26946 #26944 #26943]: #22650
-#26948 := [unit-resolution #23868 #26947]: #22653
-#23875 := (or #22662 #21419 #22656)
-#23876 := [def-axiom]: #23875
-#27014 := [unit-resolution #23876 #26948 #26942]: #21419
-#23563 := (or #21414 #23562)
-#23564 := [def-axiom]: #23563
-#27015 := [unit-resolution #23564 #27014]: #23562
-#23560 := (or #21414 #17655)
-#23561 := [def-axiom]: #23560
-#27045 := [unit-resolution #23561 #27014]: #17655
-#26624 := (or #26623 #17662 #21399 #17653)
-#27616 := [hypothesis]: #26878
-#27617 := [hypothesis]: #23562
-#27037 := (+ #3054 #17660)
-#27039 := (>= #27037 0::int)
-#27036 := (= #3054 #17659)
-#27629 := (= #17659 #3054)
-#27633 := (= #17658 #3044)
-#27614 := (= ?x773!13 0::int)
-#27631 := [hypothesis]: #17655
-#27632 := [th-lemma #27631 #27630]: #27614
-#27634 := [monotonicity #27632]: #27633
-#27635 := [monotonicity #27634]: #27629
-#26386 := [symm #27635]: #27036
-#26387 := (not #27036)
-#26388 := (or #26387 #27039)
-#26389 := [th-lemma]: #26388
-#26390 := [unit-resolution #26389 #26386]: #27039
-#26521 := [th-lemma #26390 #27617 #27616]: false
-#26625 := [lemma #26521]: #26624
-#27100 := [unit-resolution #26625 #27045 #27015 #27630]: #26623
-#27551 := (or #17676 #26878)
-#27591 := [th-lemma]: #27551
-#27592 := [unit-resolution #27591 #26944 #27100]: false
-#27723 := [lemma #27592]: #27722
-#28119 := [unit-resolution #27723 #26943 #28117 #28116]: #17653
-#23558 := (or #21414 #17654)
-#23559 := [def-axiom]: #23558
-#28120 := [unit-resolution #23559 #28119]: #21414
-#28121 := [unit-resolution #23876 #28120 #28118 #28116]: false
-#28122 := [lemma #28121]: #22644
-#23841 := (or #22641 #13392)
-#23842 := [def-axiom]: #23841
-#29445 := [unit-resolution #23842 #28122]: #13392
-#27504 := (not #27503)
-#29446 := [hypothesis]: #27504
-#28547 := (+ uf_298 #28457)
-#28548 := (<= #28547 0::int)
-#28874 := (not #28214)
-#28877 := (or #28874 #28548)
-#28878 := [th-lemma]: #28877
-#28879 := [unit-resolution #28878 #28873]: #28548
-#29447 := [th-lemma #28879 #29446 #29445 #29444]: false
-#29448 := [lemma #29447]: #27503
-#27512 := (* -1::int #27482)
-#27513 := (+ #24110 #27512)
-#27514 := (<= #27513 0::int)
-#27685 := (not #27514)
-#27640 := (+ uf_298 #27512)
-#27642 := (>= #27640 0::int)
-#28549 := (>= #28547 0::int)
-#29966 := (or #28874 #28549)
-#29967 := [th-lemma]: #29966
-#29968 := [unit-resolution #29967 #28873]: #28549
-#29981 := (not #28549)
-#29823 := (or #27642 #29981)
-#28076 := (<= #28081 0::int)
-#29972 := (or #29442 #28076)
-#29973 := [th-lemma]: #29972
-#29974 := [unit-resolution #29973 #29441]: #28076
-#29980 := (not #28076)
-#29822 := (or #27642 #29980 #29981)
-#29806 := [th-lemma]: #29822
-#29824 := [unit-resolution #29806 #29974]: #29823
-#29825 := [unit-resolution #29824 #29968]: #27642
-#26869 := (uf_66 #26333 uf_297 #26868)
-#26870 := (uf_125 #26869 #26333)
-#26951 := (>= #26870 0::int)
-#26967 := (* -1::int #26870)
-#27040 := (+ uf_297 #26967)
-#27041 := (<= #27040 0::int)
-#28165 := (uf_66 #23935 uf_297 #26369)
-#28166 := (uf_125 #28165 #23935)
-#28318 := (* -1::int #28166)
-#28542 := (+ uf_297 #28318)
-#28543 := (<= #28542 0::int)
-#28167 := (= uf_297 #28166)
-#28235 := (or #26376 #28167)
-#28236 := [quant-inst]: #28235
-#29826 := [unit-resolution #28236 #16290]: #28167
-#29683 := (not #28167)
-#29774 := (or #29683 #28543)
-#29726 := [th-lemma]: #29774
-#29779 := [unit-resolution #29726 #29826]: #28543
-#28480 := (not #28543)
-#28695 := (or #27041 #28480)
-#28077 := (+ #26870 #28318)
-#28079 := (>= #28077 0::int)
-#28075 := (= #26870 #28166)
-#29841 := (= #28166 #26870)
-#29845 := (= #28165 #26869)
-#29730 := (= #3100 #26869)
-#29728 := (= #26869 #3100)
-#29729 := [monotonicity #27789 #29424]: #29728
-#29731 := [symm #29729]: #29730
-#29679 := (= #28165 #3100)
-#29727 := [monotonicity #27709 #27849]: #29679
-#28496 := [trans #29727 #29731]: #29845
-#28499 := [monotonicity #28496 #27796]: #29841
-#28479 := [symm #28499]: #28075
-#28498 := (not #28075)
-#29842 := (or #28498 #28079)
-#29843 := [th-lemma]: #29842
-#29844 := [unit-resolution #29843 #28479]: #28079
-#29828 := (not #28079)
-#28495 := (or #27041 #29828 #28480)
-#28481 := [th-lemma]: #28495
-#29827 := [unit-resolution #28481 #29844]: #28695
-#28696 := [unit-resolution #29827 #29779]: #27041
-#28864 := (not #27041)
-#28989 := (or #26951 #28864)
-#23833 := (or #22641 #12910)
-#23834 := [def-axiom]: #23833
-#28862 := [unit-resolution #23834 #28122]: #12910
-#28497 := (or #26951 #21602 #28864)
-#28963 := [th-lemma]: #28497
-#28984 := [unit-resolution #28963 #28862]: #28989
-#28691 := [unit-resolution #28984 #28696]: #26951
-#26952 := (not #26951)
-#28840 := (or #22629 #26952)
-#23851 := (or #22641 #22477)
-#23852 := [def-axiom]: #23851
-#28540 := [unit-resolution #23852 #28122]: #22477
-#23825 := (or #22641 #12030)
-#23826 := [def-axiom]: #23825
-#28875 := [unit-resolution #23826 #28122]: #12030
-#23847 := (or #22641 #15096)
-#23848 := [def-axiom]: #23847
-#28849 := [unit-resolution #23848 #28122]: #15096
-#23837 := (or #22641 #13359)
-#23838 := [def-axiom]: #23837
-#28859 := [unit-resolution #23838 #28122]: #13359
-#27404 := (or #22629 #26952 #13358 #21769 #21761 #22482)
-#27249 := (uf_66 #2979 #26870 uf_7)
-#27250 := (uf_110 uf_287 #27249)
-#27253 := (= uf_302 #27250)
-#27359 := (= #3101 #27250)
-#27372 := (= #27250 #3101)
-#27366 := (= #27249 #3100)
-#27364 := (= #26870 uf_297)
-#26871 := (= uf_297 #26870)
-#26874 := (or #26376 #26871)
-#26875 := [quant-inst]: #26874
-#27363 := [unit-resolution #26875 #16290]: #26871
-#27365 := [symm #27363]: #27364
-#27367 := [monotonicity #27365]: #27366
-#27373 := [monotonicity #27367]: #27372
-#27374 := [symm #27373]: #27359
-#27375 := (= uf_302 #3101)
-#27368 := [hypothesis]: #12030
-#27369 := [hypothesis]: #22632
-#23793 := (or #22629 #12122)
-#23794 := [def-axiom]: #23793
-#27370 := [unit-resolution #23794 #27369]: #12122
-#27371 := [symm #27370]: #3129
-#27376 := [trans #27371 #27368]: #27375
-#27377 := [trans #27376 #27374]: #27253
-#27234 := (<= #26870 4294967295::int)
-#27378 := [hypothesis]: #15096
-#27042 := (>= #27040 0::int)
-#27379 := (not #26871)
-#27380 := (or #27379 #27042)
-#27381 := [th-lemma]: #27380
-#27382 := [unit-resolution #27381 #27363]: #27042
-#27383 := (not #27042)
-#27384 := (or #27234 #21769 #27383)
-#27385 := [th-lemma]: #27384
-#27386 := [unit-resolution #27385 #27382 #27378]: #27234
-#27276 := (+ uf_286 #26967)
-#27277 := (<= #27276 0::int)
-#27388 := (not #27277)
-#27387 := [hypothesis]: #13359
-#27389 := (or #27388 #13358 #27383)
-#27390 := [th-lemma]: #27389
-#27391 := [unit-resolution #27390 #27382 #27387]: #27388
-#27256 := (not #27253)
-#27235 := (not #27234)
-#27401 := (or #27235 #27256 #27277)
-#27392 := [hypothesis]: #26951
-#23801 := (or #22629 #22623)
-#23802 := [def-axiom]: #23801
-#27393 := [unit-resolution #23802 #27369]: #22623
-#27046 := (+ uf_296 #13286)
-#27049 := (<= #27046 0::int)
-#27394 := (or #21741 #27049)
-#27395 := [th-lemma]: #27394
-#27396 := [unit-resolution #27395 #27370]: #27049
-#27300 := [hypothesis]: #22477
-#23799 := (or #22629 #12967)
-#23800 := [def-axiom]: #23799
-#27397 := [unit-resolution #23800 #27369]: #12967
-#27291 := (not #27049)
-#27306 := (or #21724 #12968 #22482 #27291)
-#27294 := [hypothesis]: #12967
-#27117 := (+ uf_298 #18168)
-#27118 := (<= #27117 0::int)
-#27129 := (+ uf_296 #18155)
-#27130 := (>= #27129 0::int)
-#27290 := (not #27130)
-#27284 := [hypothesis]: #27049
-#23774 := (not #18157)
-#27295 := [hypothesis]: #21729
-#23775 := (or #21724 #23774)
-#23776 := [def-axiom]: #23775
-#27296 := [unit-resolution #23776 #27295]: #23774
-#27292 := (or #27290 #18157 #27291)
-#27285 := [hypothesis]: #23774
-#27288 := [hypothesis]: #27130
-#27289 := [th-lemma #27288 #27285 #27284]: false
-#27293 := [lemma #27289]: #27292
-#27297 := [unit-resolution #27293 #27296 #27284]: #27290
-#27301 := (or #27118 #27130)
-#23772 := (or #21724 #17870)
-#23773 := [def-axiom]: #23772
-#27298 := [unit-resolution #23773 #27295]: #17870
-#23770 := (or #21724 #17866)
-#23771 := [def-axiom]: #23770
-#27299 := [unit-resolution #23771 #27295]: #17866
-#27143 := (or #22482 #21708 #21709 #27118 #27130)
-#27106 := (+ #17874 #13378)
-#27107 := (<= #27106 0::int)
-#27108 := (+ ?x776!15 #12965)
-#27109 := (>= #27108 0::int)
-#27110 := (or #21709 #27109 #27107 #21708)
-#27144 := (or #22482 #27110)
-#27151 := (iff #27144 #27143)
-#27138 := (or #21708 #21709 #27118 #27130)
-#27146 := (or #22482 #27138)
-#27149 := (iff #27146 #27143)
-#27150 := [rewrite]: #27149
-#27147 := (iff #27144 #27146)
-#27141 := (iff #27110 #27138)
-#27135 := (or #21709 #27118 #27130 #21708)
-#27139 := (iff #27135 #27138)
-#27140 := [rewrite]: #27139
-#27136 := (iff #27110 #27135)
-#27133 := (iff #27107 #27130)
-#27123 := (+ #13378 #17874)
-#27126 := (<= #27123 0::int)
-#27131 := (iff #27126 #27130)
-#27132 := [rewrite]: #27131
-#27127 := (iff #27107 #27126)
-#27124 := (= #27106 #27123)
-#27125 := [rewrite]: #27124
-#27128 := [monotonicity #27125]: #27127
-#27134 := [trans #27128 #27132]: #27133
-#27121 := (iff #27109 #27118)
-#27111 := (+ #12965 ?x776!15)
-#27114 := (>= #27111 0::int)
-#27119 := (iff #27114 #27118)
-#27120 := [rewrite]: #27119
-#27115 := (iff #27109 #27114)
-#27112 := (= #27108 #27111)
-#27113 := [rewrite]: #27112
-#27116 := [monotonicity #27113]: #27115
-#27122 := [trans #27116 #27120]: #27121
-#27137 := [monotonicity #27122 #27134]: #27136
-#27142 := [trans #27137 #27140]: #27141
-#27148 := [monotonicity #27142]: #27147
-#27152 := [trans #27148 #27150]: #27151
-#27145 := [quant-inst]: #27144
-#27153 := [mp #27145 #27152]: #27143
-#27302 := [unit-resolution #27153 #27300 #27299 #27298]: #27301
-#27303 := [unit-resolution #27302 #27297]: #27118
-#23777 := (or #21724 #18175)
-#23778 := [def-axiom]: #23777
-#27304 := [unit-resolution #23778 #27295]: #18175
-#27305 := [th-lemma #27304 #27303 #27294]: false
-#27307 := [lemma #27305]: #27306
-#27398 := [unit-resolution #27307 #27397 #27300 #27396]: #21724
-#23785 := (or #22626 #22620 #21729)
-#23786 := [def-axiom]: #23785
-#27399 := [unit-resolution #23786 #27398 #27393]: #22620
-#23766 := (or #22617 #22609)
-#23767 := [def-axiom]: #23766
-#27400 := [unit-resolution #23767 #27399]: #22609
-#27313 := (or #22614 #26952 #27235 #27256 #27277)
-#27240 := (+ #26870 #12727)
-#27241 := (>= #27240 0::int)
-#27248 := (= #27250 uf_302)
-#27251 := (not #27248)
-#27252 := (or #27251 #26952 #27241 #27235)
-#27314 := (or #22614 #27252)
-#27321 := (iff #27314 #27313)
-#27308 := (or #26952 #27235 #27256 #27277)
-#27316 := (or #22614 #27308)
-#27319 := (iff #27316 #27313)
-#27320 := [rewrite]: #27319
-#27317 := (iff #27314 #27316)
-#27311 := (iff #27252 #27308)
-#27257 := (or #27256 #26952 #27277 #27235)
-#27309 := (iff #27257 #27308)
-#27310 := [rewrite]: #27309
-#27258 := (iff #27252 #27257)
-#27287 := (iff #27241 #27277)
-#27271 := (+ #12727 #26870)
-#27268 := (>= #27271 0::int)
-#27278 := (iff #27268 #27277)
-#27286 := [rewrite]: #27278
-#27274 := (iff #27241 #27268)
-#27272 := (= #27240 #27271)
-#27273 := [rewrite]: #27272
-#27275 := [monotonicity #27273]: #27274
-#27189 := [trans #27275 #27286]: #27287
-#27269 := (iff #27251 #27256)
-#27254 := (iff #27248 #27253)
-#27255 := [rewrite]: #27254
-#27270 := [monotonicity #27255]: #27269
-#27281 := [monotonicity #27270 #27189]: #27258
-#27312 := [trans #27281 #27310]: #27311
-#27318 := [monotonicity #27312]: #27317
-#27322 := [trans #27318 #27320]: #27321
-#27315 := [quant-inst]: #27314
-#27323 := [mp #27315 #27322]: #27313
-#27402 := [unit-resolution #27323 #27400 #27392]: #27401
-#27403 := [unit-resolution #27402 #27391 #27386 #27377]: false
-#27405 := [lemma #27403]: #27404
-#28978 := [unit-resolution #27405 #28859 #28849 #28875 #28540]: #28840
-#28985 := [unit-resolution #28978 #28691]: #22629
-#23853 := (or #22641 #22635)
-#23854 := [def-axiom]: #23853
-#29133 := [unit-resolution #23854 #28122]: #22635
-#23809 := (or #22638 #22598 #22632)
-#23810 := [def-axiom]: #23809
-#29134 := [unit-resolution #23810 #29133]: #22635
-#28988 := [unit-resolution #29134 #28985]: #22598
-#23758 := (or #22595 #12968)
-#23759 := [def-axiom]: #23758
-#28538 := [unit-resolution #23759 #28988]: #12968
-#27687 := (not #27642)
-#28488 := (or #27685 #27687 #12967)
-#27688 := (or #27685 #27686 #27687 #12967)
-#27689 := [th-lemma]: #27688
-#28539 := [unit-resolution #27689 #27680]: #28488
-#28525 := [unit-resolution #28539 #28538 #29825]: #27685
-#29715 := (or #26542 #26409 #27504 #27514 #27522)
-#27499 := (or #27498 #27496 #27493 #27490)
-#27500 := (not #27499)
-#27501 := (+ #27482 #26410)
-#27502 := (>= #27501 0::int)
-#27505 := (or #27504 #27502 #26409 #27500)
-#29716 := (or #26542 #27505)
-#29738 := (iff #29716 #29715)
-#27528 := (or #26409 #27504 #27514 #27522)
-#29718 := (or #26542 #27528)
-#29737 := (iff #29718 #29715)
-#29721 := [rewrite]: #29737
-#29735 := (iff #29716 #29718)
-#27531 := (iff #27505 #27528)
-#27525 := (or #27504 #27514 #26409 #27522)
-#27529 := (iff #27525 #27528)
-#27530 := [rewrite]: #27529
-#27526 := (iff #27505 #27525)
-#27523 := (iff #27500 #27522)
-#27520 := (iff #27499 #27519)
+#7982 := (iff #1493 #7979)
+#7936 := (and #1485 #7933)
+#7939 := (and #7930 #7936)
+#7942 := (and #7924 #7939)
+#7590 := (not #1372)
+#7948 := (or #7590 #7942)
+#7957 := (or #7956 #7948)
+#7962 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #7957)
+#7980 := (iff #7962 #7979)
+#7977 := (iff #7957 #7974)
+#7968 := (or #7626 #7965)
+#7971 := (or #7956 #7968)
+#7975 := (iff #7971 #7974)
+#7976 := [rewrite]: #7975
+#7972 := (iff #7957 #7971)
+#7969 := (iff #7948 #7968)
+#7966 := (iff #7942 #7965)
+#7967 := [rewrite]: #7966
+#7627 := (iff #7590 #7626)
+#7624 := (iff #1372 #7623)
+#7621 := (iff #1371 #7620)
+#7622 := [rewrite]: #7621
+#7625 := [monotonicity #4042 #7622]: #7624
+#7628 := [monotonicity #7625]: #7627
+#7970 := [monotonicity #7628 #7967]: #7969
+#7973 := [monotonicity #7970]: #7972
+#7978 := [trans #7973 #7976]: #7977
+#7981 := [quant-intro #7978]: #7980
+#7963 := (iff #1493 #7962)
+#7960 := (iff #1492 #7957)
+#7953 := (implies #7921 #7948)
+#7958 := (iff #7953 #7957)
+#7959 := [rewrite]: #7958
+#7954 := (iff #1492 #7953)
+#7951 := (iff #1491 #7948)
+#7945 := (implies #1372 #7942)
+#7949 := (iff #7945 #7948)
+#7950 := [rewrite]: #7949
+#7946 := (iff #1491 #7945)
+#7943 := (iff #1490 #7942)
+#7940 := (iff #1489 #7939)
+#7937 := (iff #1488 #7936)
+#7934 := (iff #1487 #7933)
+#7935 := [rewrite]: #7934
+#7938 := [monotonicity #7935]: #7937
+#7931 := (iff #1484 #7930)
+#7928 := (iff #1483 #7927)
+#7929 := [rewrite]: #7928
+#7932 := [monotonicity #7929]: #7931
+#7941 := [monotonicity #7932 #7938]: #7940
+#7925 := (iff #1481 #7924)
+#7926 := [rewrite]: #7925
+#7944 := [monotonicity #7926 #7941]: #7943
+#7947 := [monotonicity #7944]: #7946
+#7952 := [trans #7947 #7950]: #7951
+#7922 := (iff #1477 #7921)
+#7923 := [rewrite]: #7922
+#7955 := [monotonicity #7923 #7952]: #7954
+#7961 := [trans #7955 #7959]: #7960
+#7964 := [quant-intro #7961]: #7963
+#7983 := [trans #7964 #7981]: #7982
+#7920 := [asserted]: #1493
+#7984 := [mp #7920 #7983]: #7979
+#16826 := [mp~ #7984 #16825]: #7979
+#20706 := [mp #16826 #20705]: #20703
+#27469 := (not #20703)
+#27470 := (or #27469 #26943 #26961 #26969)
+#26939 := (or #26938 #26936 #26933 #26930)
+#26940 := (not #26939)
+#26949 := (or #26948 #26946 #26943 #26940)
+#27471 := (or #27469 #26949)
+#27516 := (iff #27471 #27470)
+#26975 := (or #26943 #26961 #26969)
+#27517 := (or #27469 #26975)
+#27520 := (iff #27517 #27470)
 #27521 := [rewrite]: #27520
-#27524 := [monotonicity #27521]: #27523
-#27517 := (iff #27502 #27514)
-#27506 := (+ #26410 #27482)
-#27509 := (>= #27506 0::int)
-#27515 := (iff #27509 #27514)
-#27516 := [rewrite]: #27515
-#27510 := (iff #27502 #27509)
-#27507 := (= #27501 #27506)
-#27508 := [rewrite]: #27507
-#27511 := [monotonicity #27508]: #27510
-#27518 := [trans #27511 #27516]: #27517
-#27527 := [monotonicity #27518 #27524]: #27526
-#27532 := [trans #27527 #27530]: #27531
-#29736 := [monotonicity #27532]: #29735
-#29739 := [trans #29736 #29721]: #29738
-#29717 := [quant-inst]: #29716
-#29740 := [mp #29717 #29739]: #29715
-#29511 := [unit-resolution #29740 #20106 #28525 #27869 #29448 #30005]: false
-#29510 := [lemma #29511]: #27522
-#28981 := (or #27519 #28652)
-#29570 := [hypothesis]: #28647
-#29836 := [hypothesis]: #27522
-#29772 := (or #27519 #27495)
-#29773 := [def-axiom]: #29772
-#29837 := [unit-resolution #29773 #29836]: #27495
-#27556 := (uf_58 #3175 #27555)
-#27557 := (uf_136 #27556)
-#27558 := (= uf_9 #27557)
-#29038 := (not #27558)
-#27559 := (uf_24 uf_287 #27555)
-#27560 := (= uf_9 #27559)
-#27561 := (not #27560)
-#27565 := (or #27558 #27561)
-#27568 := (not #27565)
-#27579 := (or #26500 #23948 #26481 #26484 #27504 #27514 #27568)
-#27562 := (or #27561 #27558)
-#27563 := (not #27562)
-#27564 := (or #26484 #27504 #27502 #23948 #26481 #27563)
-#27580 := (or #26500 #27564)
-#27587 := (iff #27580 #27579)
-#27574 := (or #23948 #26481 #26484 #27504 #27514 #27568)
-#27582 := (or #26500 #27574)
-#27585 := (iff #27582 #27579)
-#27586 := [rewrite]: #27585
-#27583 := (iff #27580 #27582)
-#27577 := (iff #27564 #27574)
-#27571 := (or #26484 #27504 #27514 #23948 #26481 #27568)
-#27575 := (iff #27571 #27574)
-#27576 := [rewrite]: #27575
-#27572 := (iff #27564 #27571)
-#27569 := (iff #27563 #27568)
-#27566 := (iff #27562 #27565)
-#27567 := [rewrite]: #27566
-#27570 := [monotonicity #27567]: #27569
-#27573 := [monotonicity #27518 #27570]: #27572
-#27578 := [trans #27573 #27576]: #27577
-#27584 := [monotonicity #27578]: #27583
-#27588 := [trans #27584 #27586]: #27587
-#27581 := [quant-inst]: #27580
-#27589 := [mp #27581 #27588]: #27579
-#29312 := [unit-resolution #27589 #20766 #13537 #28088 #28525 #27696 #29448]: #27568
-#29777 := (or #27565 #29038)
-#29778 := [def-axiom]: #29777
-#28973 := [unit-resolution #29778 #29312]: #29038
-#29704 := (or #28652 #27496 #27558)
-#29567 := (= #2984 #28581)
-#29558 := (= #28581 #2984)
-#29931 := (= #28578 #2981)
-#29929 := (= #28578 #26392)
-#29927 := (= #27494 #26392)
-#29874 := [hypothesis]: #27495
-#29928 := [symm #29874]: #29927
-#29925 := (= #28578 #27494)
-#29923 := (= #27095 #27491)
-#29921 := (= #27491 #27095)
-#29919 := (= #27485 #3220)
-#28238 := (uf_116 #3220)
-#28242 := (uf_43 #24108 #28238)
-#29913 := (= #28242 #3220)
-#28243 := (= #3220 #28242)
-#27349 := (uf_48 #3220 #24108)
-#27350 := (= uf_9 #27349)
-#29876 := (= #3221 #27349)
-#27638 := (= #27349 #3221)
-#27639 := [monotonicity #27656]: #27638
-#29877 := [symm #27639]: #29876
-#27352 := (= #24108 #27351)
-#27453 := (* uf_298 #26315)
-#26823 := (uf_116 #26333)
-#27454 := (+ #26823 #27453)
-#27455 := (uf_43 #24108 #27454)
-#27597 := (uf_13 #27455)
-#27734 := (= #27597 #27351)
-#27730 := (= #27351 #27597)
-#27728 := (= #3220 #27455)
-#27449 := (uf_66 #26333 uf_298 #24108)
-#27456 := (= #27449 #27455)
-#27457 := (not #27456)
-#27450 := (uf_138 #27449 #26333)
-#27451 := (= uf_9 #27450)
-#27452 := (not #27451)
-#27460 := (or #27452 #27457)
-#27463 := (not #27460)
-#27468 := (or #26353 #27463)
-#27458 := (or #27457 #27452)
-#27459 := (not #27458)
-#27466 := (or #26353 #27459)
-#27470 := (iff #27466 #27468)
-#27472 := (iff #27468 #27468)
-#27473 := [rewrite]: #27472
-#27464 := (iff #27459 #27463)
-#27461 := (iff #27458 #27460)
-#27462 := [rewrite]: #27461
-#27465 := [monotonicity #27462]: #27464
-#27471 := [monotonicity #27465]: #27470
-#27474 := [trans #27471 #27473]: #27470
-#27469 := [quant-inst]: #27466
-#27544 := [mp #27469 #27474]: #27468
-#27720 := [unit-resolution #27544 #20322]: #27463
-#27547 := (or #27460 #27456)
-#27548 := [def-axiom]: #27547
-#27721 := [unit-resolution #27548 #27720]: #27456
-#27726 := (= #3220 #27449)
-#27724 := (= #27449 #3220)
-#27714 := (= uf_288 #26317)
-#27712 := (= #2980 #26317)
-#27713 := [symm #27711]: #27712
-#27715 := [trans #27659 #27713]: #27714
-#27717 := [monotonicity #27654 #27715]: #27716
-#27719 := [symm #27717]: #27718
-#27725 := [monotonicity #27719 #27656]: #27724
-#27727 := [symm #27725]: #27726
-#27729 := [trans #27727 #27721]: #27728
-#27731 := [monotonicity #27729]: #27730
-#27735 := [symm #27731]: #27734
-#27598 := (= #24108 #27597)
-#27537 := (or #24175 #27598)
-#27538 := [quant-inst]: #27537
-#27706 := [unit-resolution #27538 #22417]: #27598
-#27736 := [trans #27706 #27735]: #27352
-#27231 := (not #27352)
-#27348 := (iff #27350 #27352)
-#27356 := (or #25427 #27348)
-#27353 := (iff #27352 #27350)
-#27357 := (or #25427 #27353)
-#27227 := (iff #27357 #27356)
-#27229 := (iff #27356 #27356)
-#27191 := [rewrite]: #27229
-#27354 := (iff #27353 #27348)
-#27355 := [rewrite]: #27354
-#27228 := [monotonicity #27355]: #27227
-#27192 := [trans #27228 #27191]: #27227
-#27226 := [quant-inst]: #27357
-#27230 := [mp #27226 #27192]: #27356
-#27636 := [unit-resolution #27230 #22404]: #27348
-#27411 := (not #27350)
-#27619 := (iff #17721 #27411)
-#27484 := (iff #12346 #27350)
-#27647 := (iff #27350 #12346)
-#27648 := [monotonicity #27639]: #27647
-#27618 := [symm #27648]: #27484
-#27693 := [monotonicity #27618]: #27619
-#27637 := [hypothesis]: #17721
-#27704 := [mp #27637 #27693]: #27411
-#27225 := (not #27348)
-#27232 := (or #27225 #27350 #27231)
-#27233 := [def-axiom]: #27232
-#27705 := [unit-resolution #27233 #27704 #27636]: #27231
-#27737 := [unit-resolution #27705 #27736]: false
-#27738 := [lemma #27737]: #12346
-#29878 := [trans #27738 #29877]: #27350
-#28251 := (or #27411 #28243)
-#28339 := (or #25411 #27411 #28243)
-#28250 := (or #28243 #27411)
-#28357 := (or #25411 #28250)
-#28372 := (iff #28357 #28339)
-#28362 := (or #25411 #28251)
-#28364 := (iff #28362 #28339)
-#28371 := [rewrite]: #28364
-#28363 := (iff #28357 #28362)
-#28252 := (iff #28250 #28251)
-#28253 := [rewrite]: #28252
-#28349 := [monotonicity #28253]: #28363
-#28380 := [trans #28349 #28371]: #28372
-#28361 := [quant-inst]: #28357
-#28381 := [mp #28361 #28380]: #28339
-#29879 := [unit-resolution #28381 #17465]: #28251
-#29880 := [unit-resolution #29879 #29878]: #28243
-#29914 := [symm #29880]: #29913
-#29917 := (= #27485 #28242)
-#29001 := (* #26315 #27482)
-#29004 := (+ #26574 #29001)
-#29007 := (uf_43 #24108 #29004)
-#29911 := (= #29007 #28242)
-#29905 := (= #29004 #28238)
-#28185 := (+ #26317 #27453)
-#28186 := (uf_43 #24108 #28185)
-#28369 := (uf_116 #28186)
-#29901 := (= #28369 #28238)
-#29887 := (= #28186 #3220)
-#28181 := (uf_66 #23935 uf_298 #24108)
-#29885 := (= #28181 #3220)
-#29886 := [monotonicity #27709 #27656]: #29885
-#29883 := (= #28186 #28181)
-#28187 := (= #28181 #28186)
-#28188 := (not #28187)
-#28182 := (uf_138 #28181 #23935)
-#28183 := (= uf_9 #28182)
-#28184 := (not #28183)
-#28191 := (or #28184 #28188)
-#28194 := (not #28191)
-#28286 := (or #26353 #28194)
-#28189 := (or #28188 #28184)
-#28190 := (not #28189)
-#28287 := (or #26353 #28190)
-#28288 := (iff #28287 #28286)
-#28290 := (iff #28286 #28286)
-#28262 := [rewrite]: #28290
-#28195 := (iff #28190 #28194)
-#28192 := (iff #28189 #28191)
-#28193 := [rewrite]: #28192
-#28196 := [monotonicity #28193]: #28195
-#28289 := [monotonicity #28196]: #28288
-#28263 := [trans #28289 #28262]: #28288
-#28283 := [quant-inst]: #28287
-#28254 := [mp #28283 #28263]: #28286
-#29881 := [unit-resolution #28254 #20322]: #28194
-#28267 := (or #28191 #28187)
-#28265 := [def-axiom]: #28267
-#29882 := [unit-resolution #28265 #29881]: #28187
-#29884 := [symm #29882]: #29883
-#29888 := [trans #29884 #29886]: #29887
-#29902 := [monotonicity #29888]: #29901
-#29903 := (= #29004 #28369)
-#28370 := (= #28185 #28369)
-#28373 := (* -1::int #28369)
-#28374 := (+ #27453 #28373)
-#28375 := (+ #26317 #28374)
-#28843 := (<= #28375 0::int)
-#28376 := (= #28375 0::int)
-#28838 := (or #24181 #28376)
-#28842 := (or #24181 #28370)
-#28912 := (iff #28842 #28838)
-#28907 := (iff #28838 #28838)
-#28908 := [rewrite]: #28907
-#28377 := (iff #28370 #28376)
-#28378 := [rewrite]: #28377
-#28841 := [monotonicity #28378]: #28912
-#28865 := [trans #28841 #28908]: #28912
-#28911 := [quant-inst]: #28842
-#28839 := [mp #28911 #28865]: #28838
-#29889 := [unit-resolution #28839 #22411]: #28376
-#29890 := (not #28376)
-#29891 := (or #29890 #28843)
-#29892 := [th-lemma]: #29891
-#29893 := [unit-resolution #29892 #29889]: #28843
-#28765 := (>= #28375 0::int)
-#29894 := (or #29890 #28765)
-#29895 := [th-lemma]: #29894
-#29896 := [unit-resolution #29895 #29889]: #28765
-#29897 := [th-lemma #29896 #29893]: #28370
-#29899 := (= #29004 #28185)
-#29868 := (= #28185 #29004)
-#29869 := (* -1::int #29004)
-#29870 := (+ #28185 #29869)
-#29871 := (<= #29870 0::int)
-#29267 := (* -1::int #26574)
-#29276 := (+ #24010 #29267)
-#29277 := (<= #29276 0::int)
-#29271 := (= #24010 #26574)
-#29860 := [symm #27879]: #29271
-#29861 := (not #29271)
-#29862 := (or #29861 #29277)
-#29863 := [th-lemma]: #29862
-#29935 := [unit-resolution #29863 #29860]: #29277
-#28718 := (>= #26315 1::int)
-#28559 := (= #26315 1::int)
+#27518 := (iff #27471 #27517)
+#26978 := (iff #26949 #26975)
+#26972 := (or false #26961 #26943 #26969)
+#26976 := (iff #26972 #26975)
+#26977 := [rewrite]: #26976
+#26973 := (iff #26949 #26972)
+#26970 := (iff #26940 #26969)
+#26967 := (iff #26939 #26966)
+#26968 := [rewrite]: #26967
+#26971 := [monotonicity #26968]: #26970
+#26974 := [monotonicity #26955 #26965 #26971]: #26973
+#26979 := [trans #26974 #26977]: #26978
+#27519 := [monotonicity #26979]: #27518
+#27522 := [trans #27519 #27521]: #27516
+#27472 := [quant-inst]: #27471
+#27523 := [mp #27472 #27522]: #27470
+#28300 := [unit-resolution #27523 #20706 #26991]: #28299
+#28301 := [unit-resolution #28300 #28298]: #26969
+#27540 := (or #26966 #26935)
+#27541 := [def-axiom]: #27540
+#28302 := [unit-resolution #27541 #28301]: #26935
+#28345 := [symm #28302]: #28344
+#28342 := (= #27079 #26934)
+#28340 := (= #26756 #26931)
+#28338 := (= #26931 #26756)
+#28336 := (= #26927 #3031)
+#28326 := (= #26845 #3031)
+#28327 := [symm #28125]: #28326
+#28334 := (= #26927 #26845)
+#28324 := (= #26867 #26845)
+#28325 := [symm #27634]: #28324
+#28332 := (= #26927 #26867)
+#28250 := (= #2979 #26867)
+#28323 := [symm #28126]: #28250
+#28330 := (= #26927 #2979)
+#27108 := (uf_116 #25933)
+#27122 := (uf_43 #24643 #27108)
+#28321 := (= #27122 #2979)
+#28313 := (= #27108 uf_288)
+#28311 := (= #27108 #2980)
+#28309 := (= #24545 #2980)
+#24769 := (= #2980 #24545)
+#24774 := (or #24716 #24769)
+#24775 := [quant-inst]: #24774
+#28303 := [unit-resolution #24775 #22943]: #24769
+#28310 := [symm #28303]: #28309
+#28307 := (= #27108 #24545)
+#28308 := [monotonicity #28306]: #28307
+#28312 := [trans #28308 #28310]: #28311
+#28314 := [trans #28312 #28195]: #28313
+#28322 := [monotonicity #28190 #28314]: #28321
+#28328 := (= #26927 #27122)
+#27104 := (uf_66 #25933 0::int #24643)
+#27125 := (= #27104 #27122)
+#27128 := (not #27125)
+#27105 := (uf_138 #27104 #25933)
+#27106 := (= uf_9 #27105)
+#27107 := (not #27106)
+#27134 := (or #27107 #27128)
+#27139 := (not #27134)
+#28084 := (or #26887 #27139)
+#27109 := (+ #27108 #26850)
+#27110 := (uf_43 #24643 #27109)
+#27111 := (= #27104 #27110)
+#27112 := (not #27111)
+#27113 := (or #27112 #27107)
+#27114 := (not #27113)
+#28069 := (or #26887 #27114)
+#28068 := (iff #28069 #28084)
+#28088 := (iff #28084 #28084)
+#28073 := [rewrite]: #28088
+#27140 := (iff #27114 #27139)
+#27137 := (iff #27113 #27134)
+#27131 := (or #27128 #27107)
+#27135 := (iff #27131 #27134)
+#27136 := [rewrite]: #27135
+#27132 := (iff #27113 #27131)
+#27129 := (iff #27112 #27128)
+#27126 := (iff #27111 #27125)
+#27123 := (= #27110 #27122)
+#27120 := (= #27109 #27108)
+#27115 := (+ #27108 0::int)
+#27118 := (= #27115 #27108)
+#27119 := [rewrite]: #27118
+#27116 := (= #27109 #27115)
+#27117 := [monotonicity #26859]: #27116
+#27121 := [trans #27117 #27119]: #27120
+#27124 := [monotonicity #27121]: #27123
+#27127 := [monotonicity #27124]: #27126
+#27130 := [monotonicity #27127]: #27129
+#27133 := [monotonicity #27130]: #27132
+#27138 := [trans #27133 #27136]: #27137
+#27141 := [monotonicity #27138]: #27140
+#28067 := [monotonicity #27141]: #28068
+#28074 := [trans #28067 #28073]: #28068
+#28070 := [quant-inst]: #28069
+#28075 := [mp #28070 #28074]: #28084
+#28315 := [unit-resolution #28075 #20922]: #27139
+#28124 := (or #27134 #27125)
+#28149 := [def-axiom]: #28124
+#28316 := [unit-resolution #28149 #28315]: #27125
+#28319 := (= #26927 #27104)
+#28320 := [monotonicity #28318]: #28319
+#28329 := [trans #28320 #28316]: #28328
+#28331 := [trans #28329 #28322]: #28330
+#28333 := [trans #28331 #28323]: #28332
+#28335 := [trans #28333 #28325]: #28334
+#28337 := [trans #28335 #28327]: #28336
+#28339 := [monotonicity #28337]: #28338
+#28341 := [symm #28339]: #28340
+#28343 := [monotonicity #28341]: #28342
+#28347 := [trans #28343 #28345]: #28346
+#28349 := [trans #28347 #28292]: #28348
+#28351 := [monotonicity #28349]: #28350
+#28355 := [trans #28351 #28353]: #28354
+#28357 := [monotonicity #28355]: #28356
+#28359 := [monotonicity #28357]: #28358
+#28361 := [symm #28359]: #28360
+#28363 := [monotonicity #28361]: #28362
+#28364 := [mp #14078 #28363]: #27341
+#28368 := (= #2984 #27082)
+#28365 := (= #27082 #2984)
+#28366 := [monotonicity #28349]: #28365
+#28369 := [symm #28366]: #28368
+#28370 := [trans #14075 #28369]: #27083
+#27342 := (not #27083)
+#27343 := (or #27189 #27342)
+#27344 := [def-axiom]: #27343
+#28371 := [unit-resolution #27344 #28370]: #27189
+#27399 := (or #27231 #27068 #27181 #27186 #27202)
+#27400 := [def-axiom]: #27399
+#28372 := [unit-resolution #27400 #28371 #28364 #28285 #27477 #27157]: false
+#28374 := [lemma #28372]: #28373
+#28639 := [unit-resolution #28374 #28636]: #11937
+#28640 := (or #23218 #18136 #23212)
+#26821 := (= #24643 #26820)
+#26794 := (uf_48 #3031 #24643)
+#26795 := (= uf_9 #26794)
+#26823 := (iff #26795 #26821)
+#9041 := (= #233 #1390)
+#11161 := (iff #9041 #11140)
+#22931 := (forall (vars (?x712 T5) (?x713 T3)) (:pat #2667) #11161)
+#11166 := (forall (vars (?x712 T5) (?x713 T3)) #11161)
+#22934 := (iff #11166 #22931)
+#22932 := (iff #11161 #11161)
+#22933 := [refl]: #22932
+#22935 := [quant-intro #22933]: #22934
+#17969 := (~ #11166 #11166)
+#17967 := (~ #11161 #11161)
+#17968 := [refl]: #17967
+#17970 := [nnf-pos #17968]: #17969
+#1890 := (= #1390 #233)
+#2673 := (iff #2668 #1890)
+#2674 := (forall (vars (?x712 T5) (?x713 T3)) #2673)
+#11167 := (iff #2674 #11166)
+#11164 := (iff #2673 #11161)
+#11157 := (iff #11140 #9041)
+#11162 := (iff #11157 #11161)
+#11163 := [rewrite]: #11162
+#11159 := (iff #2673 #11157)
+#9042 := (iff #1890 #9041)
+#9043 := [rewrite]: #9042
+#11160 := [monotonicity #11143 #9043]: #11159
+#11165 := [trans #11160 #11163]: #11164
+#11168 := [quant-intro #11165]: #11167
+#11156 := [asserted]: #2674
+#11171 := [mp #11156 #11168]: #11166
+#17971 := [mp~ #11171 #17970]: #11166
+#22936 := [mp #17971 #22935]: #22931
+#25961 := (not #22931)
+#26770 := (or #25961 #26823)
+#26822 := (iff #26821 #26795)
+#26771 := (or #25961 #26822)
+#26809 := (iff #26771 #26770)
+#26816 := (iff #26770 #26770)
+#26817 := [rewrite]: #26816
+#26824 := (iff #26822 #26823)
+#26825 := [rewrite]: #26824
+#26815 := [monotonicity #26825]: #26809
+#26818 := [trans #26815 #26817]: #26809
+#26814 := [quant-inst]: #26771
+#26796 := [mp #26814 #26818]: #26770
+#26798 := [unit-resolution #26796 #22936]: #26823
+#26802 := (not #26795)
+#26827 := (iff #18127 #26802)
+#26893 := (iff #11928 #26795)
+#26842 := (iff #26795 #11928)
+#26840 := (= #26794 #3032)
+#26841 := [monotonicity #28190]: #26840
+#26898 := [monotonicity #26841]: #26842
+#26843 := [symm #26898]: #26893
+#26828 := [monotonicity #26843]: #26827
+#26839 := [hypothesis]: #18127
+#26826 := [mp #26839 #26828]: #26802
+#26829 := (= #24758 #26820)
+#26830 := [symm #28274]: #26829
+#26844 := (= #24643 #24758)
+#26831 := [trans #28190 #27482]: #26844
+#26832 := [trans #26831 #26830]: #26821
+#26797 := (not #26821)
+#26799 := (not #26823)
+#26760 := (or #26799 #26795 #26797)
+#26783 := [def-axiom]: #26760
+#26900 := [unit-resolution #26783 #26832 #26826 #26798]: false
+#26901 := [lemma #26900]: #11928
+#24446 := (or #23218 #18127 #18136 #23212)
+#24447 := [def-axiom]: #24446
+#28641 := [unit-resolution #24447 #26901]: #28640
+#28642 := [unit-resolution #28641 #28639 #28638]: #23212
+#24424 := (or #23209 #3042)
+#24425 := [def-axiom]: #24424
+#28643 := [unit-resolution #24425 #28642]: #3042
+#24436 := (or #23209 #23203)
+#24437 := [def-axiom]: #24436
+#29322 := [unit-resolution #24437 #28642]: #23203
+#28521 := [hypothesis]: #13181
+#28522 := [th-lemma #14069 #28521]: false
+#28523 := [lemma #28522]: #13178
+#24422 := (or #23206 #13181 #23200)
+#24423 := [def-axiom]: #24422
+#29323 := [unit-resolution #24423 #28523 #29322]: #23200
+#24414 := (or #23197 #23191)
+#24415 := [def-axiom]: #24414
+#29332 := [unit-resolution #24415 #29323]: #23191
+#27410 := (* -1::int #3041)
+#27411 := (+ uf_295 #27410)
+#27412 := (>= #27411 0::int)
+#28644 := (or #12976 #27412)
+#28645 := [th-lemma]: #28644
+#28646 := [unit-resolution #28645 #28643]: #27412
+#24092 := (not #18168)
+#28647 := [hypothesis]: #22019
+#24093 := (or #22014 #24092)
+#24094 := [def-axiom]: #24093
+#28648 := [unit-resolution #24094 #28647]: #24092
+#28607 := (+ #3041 #18166)
+#28609 := (>= #28607 0::int)
+#28606 := (= #3041 #18165)
+#28655 := (= #18165 #3041)
+#28653 := (= #18164 #3031)
+#28651 := (= ?x773!13 0::int)
+#24095 := (not #18169)
+#24096 := (or #22014 #24095)
+#24097 := [def-axiom]: #24096
+#28649 := [unit-resolution #24097 #28647]: #24095
+#24090 := (or #22014 #18161)
+#24091 := [def-axiom]: #24090
+#28650 := [unit-resolution #24091 #28647]: #18161
+#28652 := [th-lemma #28650 #28649]: #28651
+#28654 := [monotonicity #28652]: #28653
+#28656 := [monotonicity #28654]: #28655
+#28657 := [symm #28656]: #28606
+#28658 := (not #28606)
+#28659 := (or #28658 #28609)
+#28660 := [th-lemma]: #28659
+#28661 := [unit-resolution #28660 #28657]: #28609
+#28662 := [th-lemma #28661 #28648 #28646]: false
+#28663 := [lemma #28662]: #22014
+#24410 := (or #23194 #22019 #23188)
+#24411 := [def-axiom]: #24410
+#29333 := [unit-resolution #24411 #28663 #29332]: #23188
+#24402 := (or #23185 #23179)
+#24403 := [def-axiom]: #24402
+#29334 := [unit-resolution #24403 #29333]: #23179
+#29335 := (or #23182 #12976 #23176)
+#24398 := (or #23182 #12976 #13217 #23176)
+#24399 := [def-axiom]: #24398
+#29336 := [unit-resolution #24399 #14069]: #29335
+#29337 := [unit-resolution #29336 #29334 #28643]: #23176
+#24388 := (or #23173 #23167)
+#24389 := [def-axiom]: #24388
+#29338 := [unit-resolution #24389 #29337]: #23167
+#24386 := (or #23173 #23009)
+#24387 := [def-axiom]: #24386
+#29339 := [unit-resolution #24387 #29337]: #23009
+#24360 := (or #23173 #11989)
+#24361 := [def-axiom]: #24360
+#29340 := [unit-resolution #24361 #29337]: #11989
+#24382 := (or #23173 #15577)
+#24383 := [def-axiom]: #24382
+#29341 := [unit-resolution #24383 #29337]: #15577
+#24372 := (or #23173 #13689)
+#24373 := [def-axiom]: #24372
+#29342 := [unit-resolution #24373 #29337]: #13689
+#27402 := (uf_13 #26867)
+#27403 := (uf_66 #26867 uf_297 #27402)
+#27404 := (uf_125 #27403 #26867)
+#27485 := (>= #27404 0::int)
+#24368 := (or #23173 #13222)
+#24369 := [def-axiom]: #24368
+#29343 := [unit-resolution #24369 #29337]: #13222
+#27501 := (* -1::int #27404)
+#27574 := (+ uf_297 #27501)
+#27575 := (<= #27574 0::int)
+#27405 := (= uf_297 #27404)
+#28694 := (uf_66 #24470 uf_297 #26903)
+#28695 := (uf_125 #28694 #24470)
+#29365 := (= #28695 #27404)
+#29363 := (= #27404 #28695)
+#29344 := (= #26867 #24470)
+#29345 := [trans #28126 #28241]: #29344
+#29360 := (= #27403 #28694)
+#29358 := (= #3082 #28694)
+#29356 := (= #28694 #3082)
+#29348 := (= #26903 uf_7)
+#29346 := (= #26903 #24758)
+#29347 := [monotonicity #28243]: #29346
+#29349 := [trans #29347 #28276]: #29348
+#29357 := [monotonicity #28243 #29349]: #29356
+#29359 := [symm #29357]: #29358
+#29354 := (= #27403 #3082)
+#29352 := (= #27402 uf_7)
+#29350 := (= #27402 #24758)
+#29351 := [monotonicity #28126]: #29350
+#29353 := [trans #29351 #28276]: #29352
+#29355 := [monotonicity #28126 #29353]: #29354
+#29361 := [trans #29355 #29359]: #29360
+#29364 := [monotonicity #29361 #29345]: #29363
+#29366 := [symm #29364]: #29365
+#28696 := (= uf_297 #28695)
+#28699 := (or #26910 #28696)
+#28700 := [quant-inst]: #28699
+#29362 := [unit-resolution #28700 #16791]: #28696
+#29367 := [trans #29362 #29366]: #27405
+#27913 := (not #27405)
+#29368 := (or #27913 #27575)
+#29369 := [th-lemma]: #29368
+#29370 := [unit-resolution #29369 #29367]: #27575
+#29371 := (not #27575)
+#29372 := (or #27485 #22161 #29371)
+#29373 := [th-lemma]: #29372
+#29374 := [unit-resolution #29373 #29370 #29343]: #27485
+#27486 := (not #27485)
+#27938 := (or #23161 #27486 #13688 #22304 #22299 #23014)
+#27783 := (uf_66 #2979 #27404 uf_7)
+#27784 := (uf_110 uf_287 #27783)
+#27787 := (= uf_302 #27784)
+#27893 := (= #3083 #27784)
+#27906 := (= #27784 #3083)
+#27900 := (= #27783 #3082)
+#27898 := (= #27404 uf_297)
+#27408 := (or #26910 #27405)
+#27409 := [quant-inst]: #27408
+#27897 := [unit-resolution #27409 #16791]: #27405
+#27899 := [symm #27897]: #27898
+#27901 := [monotonicity #27899]: #27900
+#27907 := [monotonicity #27901]: #27906
+#27908 := [symm #27907]: #27893
+#27909 := (= uf_302 #3083)
+#27902 := [hypothesis]: #11989
+#27903 := [hypothesis]: #23164
+#24328 := (or #23161 #12017)
+#24329 := [def-axiom]: #24328
+#27904 := [unit-resolution #24329 #27903]: #12017
+#27905 := [symm #27904]: #3097
+#27910 := [trans #27905 #27902]: #27909
+#27911 := [trans #27910 #27908]: #27787
+#27768 := (<= #27404 4294967295::int)
+#27912 := [hypothesis]: #15577
+#27576 := (>= #27574 0::int)
+#27914 := (or #27913 #27576)
+#27915 := [th-lemma]: #27914
+#27916 := [unit-resolution #27915 #27897]: #27576
+#27917 := (not #27576)
+#27918 := (or #27768 #22304 #27917)
+#27919 := [th-lemma]: #27918
+#27920 := [unit-resolution #27919 #27916 #27912]: #27768
+#27810 := (+ uf_286 #27501)
+#27811 := (<= #27810 0::int)
+#27922 := (not #27811)
+#27921 := [hypothesis]: #13689
+#27923 := (or #27922 #13688 #27917)
+#27924 := [th-lemma]: #27923
+#27925 := [unit-resolution #27924 #27916 #27921]: #27922
+#27790 := (not #27787)
+#27769 := (not #27768)
+#27935 := (or #27769 #27790 #27811)
+#27926 := [hypothesis]: #27485
+#24336 := (or #23161 #23155)
+#24337 := [def-axiom]: #24336
+#27927 := [unit-resolution #24337 #27903]: #23155
+#27580 := (+ uf_296 #13550)
+#27583 := (<= #27580 0::int)
+#27928 := (or #12052 #27583)
+#27929 := [th-lemma]: #27928
+#27930 := [unit-resolution #27929 #27904]: #27583
+#27834 := [hypothesis]: #23009
+#24334 := (or #23161 #13510)
+#24335 := [def-axiom]: #24334
+#27931 := [unit-resolution #24335 #27903]: #13510
+#27825 := (not #27583)
+#27840 := (or #22270 #13511 #23014 #27825)
+#27828 := [hypothesis]: #13510
+#27651 := (+ uf_298 #18758)
+#27652 := (<= #27651 0::int)
+#27663 := (+ uf_296 #18771)
+#27664 := (>= #27663 0::int)
+#27824 := (not #27664)
+#27818 := [hypothesis]: #27583
+#24311 := (not #18773)
+#27829 := [hypothesis]: #22275
+#24312 := (or #22270 #24311)
+#24313 := [def-axiom]: #24312
+#27830 := [unit-resolution #24313 #27829]: #24311
+#27826 := (or #27824 #18773 #27825)
+#27819 := [hypothesis]: #24311
+#27822 := [hypothesis]: #27664
+#27823 := [th-lemma #27822 #27819 #27818]: false
+#27827 := [lemma #27823]: #27826
+#27831 := [unit-resolution #27827 #27830 #27818]: #27824
+#27835 := (or #27652 #27664)
+#24306 := (or #22270 #18422)
+#24307 := [def-axiom]: #24306
+#27832 := [unit-resolution #24307 #27829]: #18422
+#24304 := (or #22270 #18421)
+#24305 := [def-axiom]: #24304
+#27833 := [unit-resolution #24305 #27829]: #18421
+#27677 := (or #23014 #22254 #22255 #27652 #27664)
+#27640 := (+ #18426 #13715)
+#27641 := (<= #27640 0::int)
+#27642 := (+ ?x776!15 #13246)
+#27643 := (>= #27642 0::int)
+#27644 := (or #22255 #27643 #27641 #22254)
+#27678 := (or #23014 #27644)
+#27685 := (iff #27678 #27677)
+#27672 := (or #22254 #22255 #27652 #27664)
+#27680 := (or #23014 #27672)
+#27683 := (iff #27680 #27677)
+#27684 := [rewrite]: #27683
+#27681 := (iff #27678 #27680)
+#27675 := (iff #27644 #27672)
+#27669 := (or #22255 #27652 #27664 #22254)
+#27673 := (iff #27669 #27672)
+#27674 := [rewrite]: #27673
+#27670 := (iff #27644 #27669)
+#27667 := (iff #27641 #27664)
+#27657 := (+ #13715 #18426)
+#27660 := (<= #27657 0::int)
+#27665 := (iff #27660 #27664)
+#27666 := [rewrite]: #27665
+#27661 := (iff #27641 #27660)
+#27658 := (= #27640 #27657)
+#27659 := [rewrite]: #27658
+#27662 := [monotonicity #27659]: #27661
+#27668 := [trans #27662 #27666]: #27667
+#27655 := (iff #27643 #27652)
+#27645 := (+ #13246 ?x776!15)
+#27648 := (>= #27645 0::int)
+#27653 := (iff #27648 #27652)
+#27654 := [rewrite]: #27653
+#27649 := (iff #27643 #27648)
+#27646 := (= #27642 #27645)
+#27647 := [rewrite]: #27646
+#27650 := [monotonicity #27647]: #27649
+#27656 := [trans #27650 #27654]: #27655
+#27671 := [monotonicity #27656 #27668]: #27670
+#27676 := [trans #27671 #27674]: #27675
+#27682 := [monotonicity #27676]: #27681
+#27686 := [trans #27682 #27684]: #27685
+#27679 := [quant-inst]: #27678
+#27687 := [mp #27679 #27686]: #27677
+#27836 := [unit-resolution #27687 #27834 #27833 #27832]: #27835
+#27837 := [unit-resolution #27836 #27831]: #27652
+#24308 := (not #18760)
+#24309 := (or #22270 #24308)
+#24310 := [def-axiom]: #24309
+#27838 := [unit-resolution #24310 #27829]: #24308
+#27839 := [th-lemma #27838 #27837 #27828]: false
+#27841 := [lemma #27839]: #27840
+#27932 := [unit-resolution #27841 #27931 #27834 #27930]: #22270
+#24320 := (or #23158 #23152 #22275)
+#24321 := [def-axiom]: #24320
+#27933 := [unit-resolution #24321 #27932 #27927]: #23152
+#24300 := (or #23149 #23141)
+#24301 := [def-axiom]: #24300
+#27934 := [unit-resolution #24301 #27933]: #23141
+#27847 := (or #23146 #27486 #27769 #27790 #27811)
+#27774 := (+ #27404 #13151)
+#27775 := (>= #27774 0::int)
+#27782 := (= #27784 uf_302)
+#27785 := (not #27782)
+#27786 := (or #27785 #27486 #27775 #27769)
+#27848 := (or #23146 #27786)
+#27855 := (iff #27848 #27847)
+#27842 := (or #27486 #27769 #27790 #27811)
+#27850 := (or #23146 #27842)
+#27853 := (iff #27850 #27847)
+#27854 := [rewrite]: #27853
+#27851 := (iff #27848 #27850)
+#27845 := (iff #27786 #27842)
+#27791 := (or #27790 #27486 #27811 #27769)
+#27843 := (iff #27791 #27842)
+#27844 := [rewrite]: #27843
+#27792 := (iff #27786 #27791)
+#27821 := (iff #27775 #27811)
+#27805 := (+ #13151 #27404)
+#27802 := (>= #27805 0::int)
+#27812 := (iff #27802 #27811)
+#27820 := [rewrite]: #27812
+#27808 := (iff #27775 #27802)
+#27806 := (= #27774 #27805)
+#27807 := [rewrite]: #27806
+#27809 := [monotonicity #27807]: #27808
+#27723 := [trans #27809 #27820]: #27821
+#27803 := (iff #27785 #27790)
+#27788 := (iff #27782 #27787)
+#27789 := [rewrite]: #27788
+#27804 := [monotonicity #27789]: #27803
+#27815 := [monotonicity #27804 #27723]: #27792
+#27846 := [trans #27815 #27844]: #27845
+#27852 := [monotonicity #27846]: #27851
+#27856 := [trans #27852 #27854]: #27855
+#27849 := [quant-inst]: #27848
+#27857 := [mp #27849 #27856]: #27847
+#27936 := [unit-resolution #27857 #27934 #27926]: #27935
+#27937 := [unit-resolution #27936 #27925 #27920 #27911]: false
+#27939 := [lemma #27937]: #27938
+#29375 := [unit-resolution #27939 #29374 #29342 #29341 #29340 #29339]: #23161
+#24344 := (or #23170 #23130 #23164)
+#24345 := [def-axiom]: #24344
+#29376 := [unit-resolution #24345 #29375 #29338]: #23130
+#24292 := (or #23127 #13511)
+#24293 := [def-axiom]: #24292
+#29377 := [unit-resolution #24293 #29376]: #13511
+#30318 := (not #29084)
+#30322 := (or #30321 #28220 #30318 #13510)
+#30323 := [th-lemma]: #30322
+#30324 := [unit-resolution #30323 #28214 #29377 #30316]: #30321
+#28963 := (>= #28923 0::int)
+#28964 := (not #28963)
+#29278 := [hypothesis]: #28964
+#24376 := (or #23173 #13743)
+#24377 := [def-axiom]: #24376
+#29279 := [unit-resolution #24377 #29337]: #13743
+#29083 := (<= #29082 0::int)
+#29282 := (or #29281 #29083)
+#29267 := [th-lemma]: #29282
+#29268 := [unit-resolution #29267 #29280]: #29083
+#29269 := [th-lemma #29268 #29279 #29278]: false
+#29270 := [lemma #29269]: #28963
+#30337 := (or #28964 #28974 #28982)
+#28993 := (or #27469 #26943 #28964 #28974 #28982)
+#28959 := (or #28958 #28956 #28953 #28950)
+#28960 := (not #28959)
+#28961 := (+ #28923 #26944)
+#28962 := (>= #28961 0::int)
+#28965 := (or #28964 #28962 #26943 #28960)
+#28994 := (or #27469 #28965)
+#29001 := (iff #28994 #28993)
+#28988 := (or #26943 #28964 #28974 #28982)
+#28996 := (or #27469 #28988)
+#28999 := (iff #28996 #28993)
+#29000 := [rewrite]: #28999
+#28997 := (iff #28994 #28996)
+#28991 := (iff #28965 #28988)
+#28985 := (or #28964 #28974 #26943 #28982)
+#28989 := (iff #28985 #28988)
+#28990 := [rewrite]: #28989
+#28986 := (iff #28965 #28985)
+#28983 := (iff #28960 #28982)
+#28980 := (iff #28959 #28979)
+#28981 := [rewrite]: #28980
+#28984 := [monotonicity #28981]: #28983
+#28977 := (iff #28962 #28974)
+#28966 := (+ #26944 #28923)
+#28969 := (>= #28966 0::int)
+#28975 := (iff #28969 #28974)
+#28976 := [rewrite]: #28975
+#28970 := (iff #28962 #28969)
+#28967 := (= #28961 #28966)
+#28968 := [rewrite]: #28967
+#28971 := [monotonicity #28968]: #28970
+#28978 := [trans #28971 #28976]: #28977
+#28987 := [monotonicity #28978 #28984]: #28986
+#28992 := [trans #28987 #28990]: #28991
+#28998 := [monotonicity #28992]: #28997
+#29002 := [trans #28998 #29000]: #29001
+#28995 := [quant-inst]: #28994
+#29003 := [mp #28995 #29002]: #28993
+#30342 := [unit-resolution #29003 #20706 #28298]: #30337
+#30331 := [unit-resolution #30342 #29270 #30324]: #28982
+#29009 := (or #28979 #28955)
+#29010 := [def-axiom]: #29009
+#30332 := [unit-resolution #29010 #30331]: #28955
+#30385 := [symm #30332]: #30390
+#30388 := (= #29089 #28954)
+#30353 := (= #27629 #28951)
+#30351 := (= #28951 #27629)
+#30349 := (= #28947 #3181)
+#28847 := (uf_116 #3181)
+#28851 := (uf_43 #24643 #28847)
+#30362 := (= #28851 #3181)
+#28852 := (= #3181 #28851)
+#27883 := (uf_48 #3181 #24643)
+#27884 := (= uf_9 #27883)
+#30356 := (= #3182 #27883)
+#28172 := (= #27883 #3182)
+#28173 := [monotonicity #28190]: #28172
+#30335 := [symm #28173]: #30356
+#27886 := (= #24643 #27885)
+#27987 := (* uf_298 #26849)
+#27357 := (uf_116 #26867)
+#27988 := (+ #27357 #27987)
+#27989 := (uf_43 #24643 #27988)
+#28131 := (uf_13 #27989)
+#28268 := (= #28131 #27885)
+#28264 := (= #27885 #28131)
+#28262 := (= #3181 #27989)
+#27983 := (uf_66 #26867 uf_298 #24643)
+#27990 := (= #27983 #27989)
+#27991 := (not #27990)
+#27984 := (uf_138 #27983 #26867)
+#27985 := (= uf_9 #27984)
+#27986 := (not #27985)
+#27994 := (or #27986 #27991)
+#27997 := (not #27994)
+#28002 := (or #26887 #27997)
+#27992 := (or #27991 #27986)
+#27993 := (not #27992)
+#28000 := (or #26887 #27993)
+#28004 := (iff #28000 #28002)
+#28006 := (iff #28002 #28002)
+#28007 := [rewrite]: #28006
+#27998 := (iff #27993 #27997)
+#27995 := (iff #27992 #27994)
+#27996 := [rewrite]: #27995
+#27999 := [monotonicity #27996]: #27998
+#28005 := [monotonicity #27999]: #28004
+#28008 := [trans #28005 #28007]: #28004
+#28003 := [quant-inst]: #28000
+#28078 := [mp #28003 #28008]: #28002
+#28254 := [unit-resolution #28078 #20922]: #27997
+#28081 := (or #27994 #27990)
+#28082 := [def-axiom]: #28081
+#28255 := [unit-resolution #28082 #28254]: #27990
+#28260 := (= #3181 #27983)
+#28258 := (= #27983 #3181)
+#28248 := (= uf_288 #26851)
+#28246 := (= #2980 #26851)
+#28247 := [symm #28245]: #28246
+#28249 := [trans #28193 #28247]: #28248
+#28251 := [monotonicity #28188 #28249]: #28250
+#28253 := [symm #28251]: #28252
+#28259 := [monotonicity #28253 #28190]: #28258
+#28261 := [symm #28259]: #28260
+#28263 := [trans #28261 #28255]: #28262
+#28265 := [monotonicity #28263]: #28264
+#28269 := [symm #28265]: #28268
+#28132 := (= #24643 #28131)
+#28071 := (or #24710 #28132)
+#28072 := [quant-inst]: #28071
+#28240 := [unit-resolution #28072 #22949]: #28132
+#28270 := [trans #28240 #28269]: #27886
+#27765 := (not #27886)
+#27882 := (iff #27884 #27886)
+#27890 := (or #25961 #27882)
+#27887 := (iff #27886 #27884)
+#27891 := (or #25961 #27887)
+#27761 := (iff #27891 #27890)
+#27763 := (iff #27890 #27890)
+#27725 := [rewrite]: #27763
+#27888 := (iff #27887 #27882)
+#27889 := [rewrite]: #27888
+#27762 := [monotonicity #27889]: #27761
+#27726 := [trans #27762 #27725]: #27761
+#27760 := [quant-inst]: #27891
+#27764 := [mp #27760 #27726]: #27890
+#28170 := [unit-resolution #27764 #22936]: #27882
+#27945 := (not #27884)
+#28153 := (iff #18238 #27945)
+#28018 := (iff #12293 #27884)
+#28181 := (iff #27884 #12293)
+#28182 := [monotonicity #28173]: #28181
+#28152 := [symm #28182]: #28018
+#28227 := [monotonicity #28152]: #28153
+#28171 := [hypothesis]: #18238
+#28238 := [mp #28171 #28227]: #27945
+#27759 := (not #27882)
+#27766 := (or #27759 #27884 #27765)
+#27767 := [def-axiom]: #27766
+#28239 := [unit-resolution #27767 #28238 #28170]: #27765
+#28271 := [unit-resolution #28239 #28270]: false
+#28272 := [lemma #28271]: #12293
+#30336 := [trans #28272 #30335]: #27884
+#28860 := (or #27945 #28852)
+#28863 := (or #25945 #27945 #28852)
+#28859 := (or #28852 #27945)
+#28864 := (or #25945 #28859)
+#28871 := (iff #28864 #28863)
+#28866 := (or #25945 #28860)
+#28869 := (iff #28866 #28863)
+#28870 := [rewrite]: #28869
+#28867 := (iff #28864 #28866)
+#28861 := (iff #28859 #28860)
+#28862 := [rewrite]: #28861
+#28868 := [monotonicity #28862]: #28867
+#28872 := [trans #28868 #28870]: #28871
+#28865 := [quant-inst]: #28864
+#28873 := [mp #28865 #28872]: #28863
+#30364 := [unit-resolution #28873 #17966]: #28860
+#30347 := [unit-resolution #30364 #30336]: #28852
+#30363 := [symm #30347]: #30362
+#30346 := (= #28947 #28851)
+#29189 := (* #26849 #28923)
+#29193 := (+ #27108 #29189)
+#29195 := (uf_43 #24643 #29193)
+#30360 := (= #29195 #28851)
+#30340 := (= #29193 #28847)
+#30304 := (= #28847 #29193)
+#30305 := (* -1::int #29193)
+#30306 := (+ #28847 #30305)
+#30307 := (<= #30306 0::int)
+#28720 := (* -1::int #26851)
+#28721 := (+ #24545 #28720)
+#28723 := (>= #28721 0::int)
+#28719 := (= #24545 #26851)
+#30302 := [trans #28310 #28247]: #28719
+#30378 := (not #28719)
+#30355 := (or #30378 #28723)
+#30325 := [th-lemma]: #30355
+#30384 := [unit-resolution #30325 #30302]: #28723
+#29387 := (* -1::int #27108)
+#29388 := (+ #24545 #29387)
+#29389 := (<= #29388 0::int)
+#29386 := (= #24545 #27108)
+#30386 := [symm #28308]: #29386
+#30387 := (not #29386)
+#30405 := (or #30387 #29389)
+#30406 := [th-lemma]: #30405
+#30401 := [unit-resolution #30406 #30386]: #29389
+#28895 := (+ #26851 #27987)
+#28896 := (uf_43 #24643 #28895)
+#29061 := (uf_116 #28896)
+#29065 := (* -1::int #29061)
+#29086 := (+ #28847 #29065)
+#29087 := (<= #29086 0::int)
+#29085 := (= #28847 #29061)
+#30447 := (= #29061 #28847)
+#30411 := (= #28896 #3181)
+#28891 := (uf_66 #24470 uf_298 #24643)
+#30409 := (= #28891 #3181)
+#30410 := [monotonicity #28243 #28190]: #30409
+#30404 := (= #28896 #28891)
+#28897 := (= #28891 #28896)
+#28898 := (not #28897)
+#28892 := (uf_138 #28891 #24470)
+#28893 := (= uf_9 #28892)
+#28894 := (not #28893)
+#28901 := (or #28894 #28898)
+#28904 := (not #28901)
+#28907 := (or #26887 #28904)
+#28899 := (or #28898 #28894)
+#28900 := (not #28899)
+#28908 := (or #26887 #28900)
+#28910 := (iff #28908 #28907)
+#28912 := (iff #28907 #28907)
+#28913 := [rewrite]: #28912
+#28905 := (iff #28900 #28904)
+#28902 := (iff #28899 #28901)
+#28903 := [rewrite]: #28902
+#28906 := [monotonicity #28903]: #28905
+#28911 := [monotonicity #28906]: #28910
+#28914 := [trans #28911 #28913]: #28910
+#28909 := [quant-inst]: #28908
+#28915 := [mp #28909 #28914]: #28907
+#30402 := [unit-resolution #28915 #20922]: #28904
+#28918 := (or #28901 #28897)
+#28919 := [def-axiom]: #28918
+#30407 := [unit-resolution #28919 #30402]: #28897
+#30408 := [symm #30407]: #30404
+#30421 := [trans #30408 #30410]: #30411
+#30448 := [monotonicity #30421]: #30447
+#30449 := [symm #30448]: #29085
+#30450 := (not #29085)
+#30445 := (or #30450 #29087)
+#30451 := [th-lemma]: #30445
+#30417 := [unit-resolution #30451 #30449]: #29087
+#29066 := (+ #27987 #29065)
+#29067 := (+ #26851 #29066)
+#29081 := (>= #29067 0::int)
+#29068 := (= #29067 0::int)
+#29071 := (or #24716 #29068)
+#29062 := (= #28895 #29061)
+#29072 := (or #24716 #29062)
+#29074 := (iff #29072 #29071)
+#29076 := (iff #29071 #29071)
+#29077 := [rewrite]: #29076
+#29069 := (iff #29062 #29068)
+#29070 := [rewrite]: #29069
+#29075 := [monotonicity #29070]: #29074
+#29078 := [trans #29075 #29077]: #29074
+#29073 := [quant-inst]: #29072
+#29079 := [mp #29073 #29078]: #29071
+#30452 := [unit-resolution #29079 #22943]: #29068
+#30453 := (not #29068)
+#30446 := (or #30453 #29081)
+#30454 := [th-lemma]: #30446
+#30455 := [unit-resolution #30454 #30452]: #29081
+#28726 := (>= #26849 1::int)
+#28724 := (= #26849 1::int)
 #2932 := (uf_139 uf_7)
 #2933 := (= #2932 1::int)
-#11811 := [asserted]: #2933
-#29875 := (= #26315 #2932)
-#29943 := [monotonicity #27656]: #29875
-#29944 := [trans #29943 #11811]: #28559
-#29945 := (not #28559)
-#29946 := (or #29945 #28718)
-#29947 := [th-lemma]: #29946
-#29948 := [unit-resolution #29947 #29944]: #28718
-#28736 := (<= #26315 1::int)
-#29949 := (or #29945 #28736)
-#29950 := [th-lemma]: #29949
-#29951 := [unit-resolution #29950 #29944]: #28736
-#28558 := (* -1::int #26317)
-#28545 := (+ #24010 #28558)
-#28694 := (>= #28545 0::int)
-#28692 := (= #24010 #26317)
-#29952 := [trans #27881 #27713]: #28692
-#29953 := (not #28692)
-#29954 := (or #29953 #28694)
-#29955 := [th-lemma]: #29954
-#29956 := [unit-resolution #29955 #29952]: #28694
-#29962 := (not #28548)
-#29961 := (not #28082)
-#29960 := (not #29277)
-#29958 := (not #28736)
-#29957 := (not #28718)
-#29959 := (not #28694)
-#29963 := (or #29871 #29957 #29958 #29959 #29957 #29958 #29960 #29961 #29962)
-#29964 := [th-lemma]: #29963
-#29965 := [unit-resolution #29964 #28879 #29956 #29951 #29948 #29935 #29444]: #29871
-#29872 := (>= #29870 0::int)
-#29285 := (>= #29276 0::int)
-#29969 := (or #29861 #29285)
-#29970 := [th-lemma]: #29969
-#29971 := [unit-resolution #29970 #29860]: #29285
-#28693 := (<= #28545 0::int)
-#29975 := (or #29953 #28693)
-#29976 := [th-lemma]: #29975
-#29977 := [unit-resolution #29976 #29952]: #28693
-#29979 := (not #29285)
-#29978 := (not #28693)
-#29982 := (or #29872 #29957 #29958 #29978 #29957 #29958 #29979 #29980 #29981)
-#29983 := [th-lemma]: #29982
-#29984 := [unit-resolution #29983 #29977 #29974 #29951 #29948 #29971 #29968]: #29872
-#29986 := (not #29872)
-#29985 := (not #29871)
-#29987 := (or #29868 #29985 #29986)
-#29988 := [th-lemma]: #29987
-#29989 := [unit-resolution #29988 #29984 #29965]: #29868
-#29577 := [symm #29989]: #29899
-#29571 := [trans #29577 #29897]: #29903
-#29578 := [trans #29571 #29902]: #29905
-#29562 := [monotonicity #29578]: #29911
-#29915 := (= #27485 #29007)
-#28990 := (uf_66 #25399 #27482 #24108)
-#29010 := (= #28990 #29007)
-#29013 := (not #29010)
-#28991 := (uf_138 #28990 #25399)
-#28992 := (= uf_9 #28991)
-#28993 := (not #28992)
-#29019 := (or #28993 #29013)
-#29024 := (not #29019)
-#29041 := (or #26353 #29024)
-#28994 := (* #27482 #26315)
-#28995 := (+ #26574 #28994)
-#28996 := (uf_43 #24108 #28995)
-#28997 := (= #28990 #28996)
-#28998 := (not #28997)
-#28999 := (or #28998 #28993)
-#29000 := (not #28999)
-#29040 := (or #26353 #29000)
-#29039 := (iff #29040 #29041)
-#29056 := (iff #29041 #29041)
-#29073 := [rewrite]: #29056
-#29025 := (iff #29000 #29024)
-#29022 := (iff #28999 #29019)
-#29016 := (or #29013 #28993)
-#29020 := (iff #29016 #29019)
-#29021 := [rewrite]: #29020
-#29017 := (iff #28999 #29016)
-#29014 := (iff #28998 #29013)
-#29011 := (iff #28997 #29010)
-#29008 := (= #28996 #29007)
-#29005 := (= #28995 #29004)
-#29002 := (= #28994 #29001)
-#29003 := [rewrite]: #29002
-#29006 := [monotonicity #29003]: #29005
-#29009 := [monotonicity #29006]: #29008
-#29012 := [monotonicity #29009]: #29011
-#29015 := [monotonicity #29012]: #29014
-#29018 := [monotonicity #29015]: #29017
-#29023 := [trans #29018 #29021]: #29022
-#29026 := [monotonicity #29023]: #29025
-#29072 := [monotonicity #29026]: #29039
-#29107 := [trans #29072 #29073]: #29039
-#29071 := [quant-inst]: #29040
-#29108 := [mp #29071 #29107]: #29041
-#29907 := [unit-resolution #29108 #20322]: #29024
-#29209 := (or #29019 #29010)
-#29207 := [def-axiom]: #29209
-#29908 := [unit-resolution #29207 #29907]: #29010
-#29909 := (= #27485 #28990)
-#29910 := [monotonicity #27889]: #29909
-#29916 := [trans #29910 #29908]: #29915
-#29561 := [trans #29916 #29562]: #29917
-#29502 := [trans #29561 #29914]: #29919
-#29563 := [monotonicity #29502]: #29921
-#29555 := [symm #29563]: #29923
-#29392 := [monotonicity #29555]: #29925
-#29556 := [trans #29392 #29928]: #29929
-#29557 := [trans #29556 #27863]: #29931
-#29559 := [monotonicity #29557]: #29558
-#29568 := [symm #29559]: #29567
-#29565 := [trans #13530 #29568]: #28582
-#29532 := (not #28582)
-#29533 := (or #28638 #29532)
-#29534 := [def-axiom]: #29533
-#29569 := [unit-resolution #29534 #29565]: #28638
-#29695 := (= #24648 #28596)
-#29691 := (= #28596 #24648)
-#29574 := (= #27351 uf_7)
-#29573 := (= #27351 #24108)
-#28379 := (or #27225 #27411 #27352)
-#28382 := [def-axiom]: #28379
-#29572 := [unit-resolution #28382 #29878 #27636]: #27352
-#29566 := [symm #29572]: #29573
-#29575 := [trans #29566 #27656]: #29574
-#29692 := [monotonicity #29575]: #29691
-#29696 := [symm #29692]: #29695
-#29582 := [trans #27842 #29696]: #28614
-#29507 := (not #28587)
-#29688 := (iff #11876 #29507)
-#29586 := (iff #11873 #28587)
-#28726 := (iff #28587 #11873)
-#29579 := (= #28586 #2990)
-#29592 := (= #28585 #2977)
-#29583 := (= #28585 #24228)
-#29581 := [monotonicity #29557]: #29583
-#29593 := [trans #29581 #27921]: #29592
-#29584 := [monotonicity #29593]: #29579
-#29585 := [monotonicity #29584]: #28726
-#29687 := [symm #29585]: #29586
-#29689 := [monotonicity #29687]: #29688
-#29690 := [mp #13533 #29689]: #29507
-#29698 := (iff #29038 #28593)
-#29699 := (iff #27558 #28592)
-#29686 := (iff #28592 #27558)
-#29677 := (= #28591 #27557)
-#29676 := (= #27095 #27556)
-#29673 := (= #27556 #27095)
-#29675 := [monotonicity #29712]: #29673
-#29674 := [symm #29675]: #29676
-#29684 := [monotonicity #29674]: #29677
-#29697 := [monotonicity #29684]: #29686
-#29700 := [symm #29697]: #29699
-#29685 := [monotonicity #29700]: #29698
-#29706 := [hypothesis]: #29038
-#29701 := [mp #29706 #29685]: #28593
-#29506 := (or #28632 #28592)
-#29471 := [def-axiom]: #29506
-#29702 := [unit-resolution #29471 #29701]: #28632
-#29554 := (or #28652 #28587 #28629 #28635 #28641)
-#29541 := [def-axiom]: #29554
-#29703 := [unit-resolution #29541 #29702 #29690 #29582 #29569 #29570]: false
-#29705 := [lemma #29703]: #29704
-#29110 := [unit-resolution #29705 #28973 #29837 #29570]: false
-#28980 := [lemma #29110]: #28981
-#30221 := [unit-resolution #28980 #29510]: #28652
-#28160 := (or #28655 #28647)
-#28159 := [def-axiom]: #28160
-#30222 := [unit-resolution #28159 #30221]: #28655
-#29319 := (or #28664 #28658)
-#29325 := (or #12349 #12967)
-#23835 := (or #22641 #12913)
-#23836 := [def-axiom]: #23835
-#29317 := [unit-resolution #23836 #28122]: #12913
-#29318 := (or #12349 #21575 #12967)
-#27702 := (or #12349 #21575 #26481 #12967)
-#27645 := [hypothesis]: #12913
-#27641 := (<= #27640 0::int)
-#27483 := (= uf_298 #27482)
-#27486 := (or #26376 #27483)
-#27487 := [quant-inst]: #27486
-#27646 := [unit-resolution #27487 #16290]: #27483
-#27649 := (not #27483)
-#27650 := (or #27649 #27641)
-#27651 := [th-lemma]: #27650
-#27652 := [unit-resolution #27651 #27646]: #27641
-#27672 := (iff #17724 #27561)
-#27670 := (iff #12349 #27560)
-#27668 := (iff #27560 #12349)
-#27666 := (= #27559 #3223)
-#27658 := [symm #27646]: #27657
-#27665 := [monotonicity #27663 #27658 #27656]: #27664
-#27667 := [monotonicity #27665]: #27666
-#27669 := [monotonicity #27667]: #27668
-#27671 := [symm #27669]: #27670
-#27673 := [monotonicity #27671]: #27672
-#27653 := [hypothesis]: #17724
-#27674 := [mp #27653 #27673]: #27561
-#27593 := (or #27565 #27560)
-#27594 := [def-axiom]: #27593
-#27675 := [unit-resolution #27594 #27674]: #27565
-#27681 := [hypothesis]: #12968
-#27682 := (or #27649 #27642)
-#27683 := [th-lemma]: #27682
-#27684 := [unit-resolution #27683 #27646]: #27642
-#27690 := [unit-resolution #27689 #27684 #27681 #27680]: #27685
-#27698 := (or #27504 #27514 #27568)
-#27699 := [unit-resolution #27589 #20766 #13537 #27697 #27696]: #27698
-#27700 := [unit-resolution #27699 #27690 #27675]: #27504
-#27701 := [th-lemma #27700 #27652 #27645]: false
-#27703 := [lemma #27701]: #27702
-#29322 := [unit-resolution #27703 #28088]: #29318
-#29326 := [unit-resolution #29322 #29317]: #29325
-#29327 := [unit-resolution #29326 #28538]: #12349
-#28201 := (or #28664 #17724 #28658)
-#28206 := [def-axiom]: #28201
-#29320 := [unit-resolution #28206 #29327]: #29319
-#30225 := [unit-resolution #29320 #30222]: #28664
-#29321 := (or #12355 #28661)
-#28667 := (iff #12355 #28664)
-#29514 := (not #28667)
-#29693 := [hypothesis]: #29514
-#29473 := (or #27590 #28667)
-#28583 := (or #28582 #28580)
-#28584 := (not #28583)
-#28594 := (or #28593 #28590)
-#28595 := (not #28594)
-#28597 := (= #28596 uf_14)
-#28598 := (not #28597)
-#28599 := (or #28598 #28595 #28587 #28584)
-#28600 := (not #28599)
-#28605 := (or #28604 #28602)
-#28606 := (not #28605)
-#28607 := (or #28597 #28606)
-#28608 := (not #28607)
-#28609 := (or #28608 #28600)
-#28610 := (not #28609)
-#28611 := (or #17724 #28610)
-#28612 := (not #28611)
-#28613 := (iff #12355 #28612)
-#29474 := (or #27590 #28613)
-#29531 := (iff #29474 #29473)
-#29536 := (iff #29473 #29473)
-#29509 := [rewrite]: #29536
-#28668 := (iff #28613 #28667)
-#28665 := (iff #28612 #28664)
-#28662 := (iff #28611 #28661)
-#28659 := (iff #28610 #28658)
-#28656 := (iff #28609 #28655)
-#28653 := (iff #28600 #28652)
-#28650 := (iff #28599 #28647)
-#28644 := (or #28629 #28635 #28587 #28641)
-#28648 := (iff #28644 #28647)
-#28649 := [rewrite]: #28648
-#28645 := (iff #28599 #28644)
-#28642 := (iff #28584 #28641)
-#28639 := (iff #28583 #28638)
-#28640 := [rewrite]: #28639
-#28643 := [monotonicity #28640]: #28642
-#28636 := (iff #28595 #28635)
-#28633 := (iff #28594 #28632)
-#28634 := [rewrite]: #28633
-#28637 := [monotonicity #28634]: #28636
-#28630 := (iff #28598 #28629)
-#28615 := (iff #28597 #28614)
-#28616 := [rewrite]: #28615
-#28631 := [monotonicity #28616]: #28630
-#28646 := [monotonicity #28631 #28637 #28643]: #28645
-#28651 := [trans #28646 #28649]: #28650
-#28654 := [monotonicity #28651]: #28653
-#28627 := (iff #28608 #28626)
-#28624 := (iff #28607 #28623)
-#28621 := (iff #28606 #28620)
-#28618 := (iff #28605 #28617)
-#28619 := [rewrite]: #28618
-#28622 := [monotonicity #28619]: #28621
-#28625 := [monotonicity #28616 #28622]: #28624
-#28628 := [monotonicity #28625]: #28627
-#28657 := [monotonicity #28628 #28654]: #28656
-#28660 := [monotonicity #28657]: #28659
-#28663 := [monotonicity #28660]: #28662
-#28666 := [monotonicity #28663]: #28665
-#28669 := [monotonicity #28666]: #28668
-#29535 := [monotonicity #28669]: #29531
-#29520 := [trans #29535 #29509]: #29531
-#29472 := [quant-inst]: #29474
-#29508 := [mp #29472 #29520]: #29473
-#29694 := [unit-resolution #29508 #21176 #29693]: false
-#29580 := [lemma #29694]: #28667
-#28208 := (or #29514 #12355 #28661)
-#28211 := [def-axiom]: #28208
-#29345 := [unit-resolution #28211 #29580]: #29321
-#30226 := [unit-resolution #29345 #30225]: #12355
-#29853 := (or #17730 #22574)
-#23760 := (or #22595 #22589)
-#23761 := [def-axiom]: #23760
-#29386 := [unit-resolution #23761 #28988]: #22589
-#29389 := (or #22592 #17724 #22586)
-#23752 := (or #22592 #17721 #17724 #22586)
-#23753 := [def-axiom]: #23752
-#29181 := [unit-resolution #23753 #27738]: #29389
-#29213 := [unit-resolution #29181 #29386 #29327]: #22586
-#23742 := (or #22583 #22577)
-#23743 := [def-axiom]: #23742
-#29850 := [unit-resolution #23743 #29213]: #22577
-#29851 := (or #22580 #17730 #22574)
-#23736 := (or #22580 #17721 #17730 #22574)
-#23737 := [def-axiom]: #23736
-#29852 := [unit-resolution #23737 #27738]: #29851
-#29854 := [unit-resolution #29852 #29850]: #29853
-#30229 := [unit-resolution #29854 #30226]: #22574
-#30232 := (or #22571 #22532)
-#28690 := [unit-resolution #29740 #20106 #28525 #27869 #29448]: #27522
-#28541 := [unit-resolution #29773 #28690]: #27495
-#29313 := [unit-resolution #29705 #28973 #28541]: #28652
-#29314 := [unit-resolution #28159 #29313]: #28655
-#29323 := [unit-resolution #29320 #29314]: #28664
-#29346 := [unit-resolution #29345 #29323]: #12355
-#29264 := [unit-resolution #29854 #29346]: #22574
-#29855 := [hypothesis]: #22526
-#23652 := (or #22529 #22523)
-#23653 := [def-axiom]: #23652
-#29856 := [unit-resolution #23653 #29855]: #22529
-#23708 := (or #22559 #22523)
-#23709 := [def-axiom]: #23708
-#29857 := [unit-resolution #23709 #29855]: #22559
-#29858 := (or #22571 #22562 #22532)
-#28575 := (or #22571 #17724 #22562 #22532)
-#28560 := [hypothesis]: #12349
-#28561 := [hypothesis]: #22529
-#28562 := [hypothesis]: #22574
-#23720 := (or #22571 #12355)
-#23721 := [def-axiom]: #23720
-#28563 := [unit-resolution #23721 #28562]: #12355
-#28564 := (or #22538 #17730 #22532)
-#23662 := (or #22538 #17721 #17730 #22532)
-#23663 := [def-axiom]: #23662
-#28565 := [unit-resolution #23663 #27738]: #28564
-#28566 := [unit-resolution #28565 #28563 #28561]: #22538
-#23668 := (or #22541 #22535)
-#23669 := [def-axiom]: #23668
-#28567 := [unit-resolution #23669 #28566]: #22541
-#28568 := [hypothesis]: #22559
-#23726 := (or #22571 #22565)
-#23727 := [def-axiom]: #23726
-#28569 := [unit-resolution #23727 #28562]: #22565
-#23716 := (or #22568 #22556 #22562)
-#23717 := [def-axiom]: #23716
-#28570 := [unit-resolution #23717 #28569 #28568]: #22556
-#23686 := (or #22553 #22547)
-#23687 := [def-axiom]: #23686
-#28571 := [unit-resolution #23687 #28570]: #22547
-#28572 := (or #22550 #17724 #22544)
-#23678 := (or #22550 #17721 #17724 #22544)
-#23679 := [def-axiom]: #23678
-#28573 := [unit-resolution #23679 #27738]: #28572
-#28574 := [unit-resolution #28573 #28571 #28567 #28560]: false
-#28576 := [lemma #28574]: #28575
-#29859 := [unit-resolution #28576 #29327]: #29858
-#29993 := [unit-resolution #29859 #29857 #29856 #29264]: false
-#29994 := [lemma #29993]: #22523
-#30143 := (or #22526 #22520)
-#28967 := (or #15127 #12967)
-#14990 := (<= uf_286 4294967295::int)
-#14993 := (iff #12726 #14990)
-#14984 := (+ 4294967295::int #12727)
-#14987 := (>= #14984 0::int)
-#14991 := (iff #14987 #14990)
-#14992 := [rewrite]: #14991
-#14988 := (iff #12726 #14987)
-#14985 := (= #12728 #14984)
-#14986 := [monotonicity #7481]: #14985
-#14989 := [monotonicity #14986]: #14988
-#14994 := [trans #14989 #14992]: #14993
-#13540 := [and-elim #13524]: #12726
-#14995 := [mp #13540 #14994]: #14990
-#28956 := [hypothesis]: #17745
-#28957 := [th-lemma #27681 #28956 #14995]: false
-#28968 := [lemma #28957]: #28967
-#30138 := [unit-resolution #28968 #28538]: #15127
-#30141 := (or #22526 #17745 #22520)
-#30136 := (or #21575 #13051)
-#30139 := [th-lemma]: #30136
-#30140 := [unit-resolution #30139 #29317]: #13051
-#23632 := (or #22526 #17742 #17745 #22520)
-#23633 := [def-axiom]: #23632
-#30142 := [unit-resolution #23633 #30140]: #30141
-#30144 := [unit-resolution #30142 #30138]: #30143
-#30150 := [unit-resolution #30144 #29994]: #22520
-#23622 := (or #22517 #22511)
-#23623 := [def-axiom]: #23622
-#30127 := [unit-resolution #23623 #30150]: #22511
-#23568 := (>= #13063 -1::int)
-#23618 := (or #22517 #13061)
-#23619 := [def-axiom]: #23618
-#30124 := [unit-resolution #23619 #30150]: #13061
-#30129 := (or #21556 #23568)
-#30128 := [th-lemma]: #30129
-#30130 := [unit-resolution #30128 #30124]: #23568
-#29095 := (not #23568)
-#30131 := (or #13089 #29095)
-#29096 := (or #13089 #12967 #29095)
-#29081 := [hypothesis]: #23568
-#29082 := [hypothesis]: #13093
-#29094 := [th-lemma #29082 #27681 #29081]: false
-#29097 := [lemma #29094]: #29096
-#30132 := [unit-resolution #29097 #28538]: #30131
-#30133 := [unit-resolution #30132 #30130]: #13089
-#23608 := (or #22514 #13093 #22508)
-#23609 := [def-axiom]: #23608
-#30134 := [unit-resolution #23609 #30133 #30127]: #22508
-#23600 := (or #22505 #22499)
-#23601 := [def-axiom]: #23600
-#30135 := [unit-resolution #23601 #30134]: #22499
-#23693 := (+ uf_297 #13126)
-#23695 := (>= #23693 0::int)
-#30148 := [hypothesis]: #22562
-#23698 := (or #22559 #12524)
-#23699 := [def-axiom]: #23698
-#30154 := [unit-resolution #23699 #30148]: #12524
-#30155 := (or #21614 #23695)
-#30153 := [th-lemma]: #30155
-#30156 := [unit-resolution #30153 #30154]: #23695
-#30164 := (not #23695)
-#30174 := (or #13129 #30164)
-#30165 := (or #13129 #13358 #30164)
-#30173 := [th-lemma]: #30165
-#30146 := [unit-resolution #30173 #28859]: #30174
-#30163 := [unit-resolution #30146 #30156]: #13129
-#30161 := (= #3101 #3272)
-#30159 := (= #3272 #3101)
-#30157 := (= #3271 #3100)
-#30149 := (= #28166 uf_297)
-#30166 := [symm #29826]: #30149
-#30147 := [trans #28479 #30166]: #27364
-#30152 := [monotonicity #30147]: #27366
-#30172 := (= #3271 #27249)
-#30170 := (= uf_305 #26870)
-#30168 := (= uf_305 #28166)
-#30167 := [symm #30154]: #3288
-#30169 := [trans #30167 #29826]: #30168
-#30171 := [trans #30169 #28499]: #30170
-#30180 := [monotonicity #30171]: #30172
-#30151 := [trans #30180 #30152]: #30157
-#30160 := [monotonicity #30151]: #30159
-#30162 := [symm #30160]: #30161
-#30194 := (= uf_304 #3101)
-#23696 := (or #22559 #12521)
-#23697 := [def-axiom]: #23696
-#30145 := [unit-resolution #23697 #30148]: #12521
-#30158 := [symm #30145]: #3287
-#30195 := [trans #30158 #28875]: #30194
-#30190 := [trans #30195 #30162]: #12446
-#23573 := (or #21468 #21466 #13128)
-#23574 := [def-axiom]: #23573
-#30196 := [unit-resolution #23574 #30190 #30163]: #21468
-#23575 := (or #22493 #21467)
-#23576 := [def-axiom]: #23575
-#30197 := [unit-resolution #23576 #30196]: #22493
-#23596 := (or #22502 #22496 #21531)
-#23597 := [def-axiom]: #23596
-#30176 := [unit-resolution #23597 #30197 #30135]: #21531
-#23588 := (or #21526 #18027)
-#23589 := [def-axiom]: #23588
-#30178 := [unit-resolution #23589 #30176]: #18027
-#29153 := (+ uf_298 #18020)
-#30137 := (>= #29153 0::int)
-#30208 := (not #30137)
-#30288 := (not #30181)
-#30175 := (= #3230 #17765)
-#30256 := (not #30175)
-#30251 := (+ #3230 #18007)
-#30253 := (>= #30251 0::int)
-#30263 := (not #30253)
-#23704 := (or #22559 #12997)
-#23705 := [def-axiom]: #23704
-#30179 := [unit-resolution #23705 #30148]: #12997
-#23690 := (+ uf_296 #13112)
-#23691 := (<= #23690 0::int)
-#30199 := (or #21613 #23691)
-#30200 := [th-lemma]: #30199
-#30182 := [unit-resolution #30200 #30145]: #23691
-#23585 := (not #18009)
-#23586 := (or #21526 #23585)
-#23587 := [def-axiom]: #23586
-#30183 := [unit-resolution #23587 #30176]: #23585
-#30264 := (not #23691)
-#30265 := (or #30263 #18009 #30264 #12996)
-#30258 := [hypothesis]: #12997
-#30259 := [hypothesis]: #23691
-#30260 := [hypothesis]: #23585
-#30261 := [hypothesis]: #30253
-#30262 := [th-lemma #30261 #30260 #30259 #30258]: false
-#30266 := [lemma #30262]: #30265
-#30184 := [unit-resolution #30266 #30183 #30182 #30179]: #30263
-#30257 := (or #30256 #30253)
-#30267 := [th-lemma]: #30257
-#30185 := [unit-resolution #30267 #30184]: #30256
-#30289 := (or #30288 #30175)
-#30284 := (= #17765 #3230)
-#30282 := (= #17764 #3220)
-#30280 := (= #17764 #27555)
-#30276 := (= ?x785!14 #27482)
-#30274 := (= ?x785!14 #28213)
-#30272 := (= ?x785!14 uf_298)
-#30271 := [hypothesis]: #30181
-#30273 := [symm #30271]: #30272
-#30275 := [trans #30273 #28873]: #30274
-#30277 := [trans #30275 #29458]: #30276
-#30278 := (= #2979 #26469)
-#30279 := [symm #27663]: #30278
-#30281 := [monotonicity #30279 #30277 #27654]: #30280
-#30283 := [trans #30281 #29712]: #30282
-#30285 := [monotonicity #30283]: #30284
-#30286 := [symm #30285]: #30175
-#30250 := [hypothesis]: #30256
-#30287 := [unit-resolution #30250 #30286]: false
-#30290 := [lemma #30287]: #30289
-#30186 := [unit-resolution #30290 #30185]: #30288
-#30213 := (or #30181 #30208)
-#29154 := (<= #29153 0::int)
-#29165 := (+ uf_296 #18007)
-#29166 := (>= #29165 0::int)
-#30187 := (not #29166)
-#30177 := (or #30187 #18009 #30264)
-#30207 := [th-lemma]: #30177
-#30189 := [unit-resolution #30207 #30183 #30182]: #30187
-#23583 := (or #21526 #17761)
-#23584 := [def-axiom]: #23583
-#30191 := [unit-resolution #23584 #30176]: #17761
-#23581 := (or #21526 #17757)
-#23582 := [def-axiom]: #23581
-#30192 := [unit-resolution #23582 #30176]: #17757
-#30050 := (or #22482 #21510 #21511 #29154 #29166)
-#29142 := (+ #17765 #13378)
-#29143 := (<= #29142 0::int)
-#29144 := (+ ?x785!14 #12965)
-#29145 := (>= #29144 0::int)
-#29146 := (or #21511 #29145 #29143 #21510)
-#30051 := (or #22482 #29146)
-#30058 := (iff #30051 #30050)
-#29174 := (or #21510 #21511 #29154 #29166)
-#30053 := (or #22482 #29174)
-#30056 := (iff #30053 #30050)
+#11813 := [asserted]: #2933
+#30462 := (= #26849 #2932)
+#30463 := [monotonicity #28190]: #30462
+#30464 := [trans #30463 #11813]: #28724
+#30465 := (not #28724)
+#30466 := (or #30465 #28726)
+#30461 := [th-lemma]: #30466
+#30416 := [unit-resolution #30461 #30464]: #28726
+#28725 := (<= #26849 1::int)
+#30467 := (or #30465 #28725)
+#30422 := [th-lemma]: #30467
+#30468 := [unit-resolution #30422 #30464]: #28725
+#30482 := (not #29389)
+#30487 := (not #29083)
+#30486 := (not #28725)
+#30484 := (not #28726)
+#30471 := (not #28723)
+#30470 := (not #29081)
+#30469 := (not #29087)
+#30483 := (or #30307 #30469 #30470 #30471 #30484 #30486 #30484 #30486 #30487 #30482)
+#30488 := [th-lemma]: #30483
+#30485 := [unit-resolution #30488 #30468 #30416 #30455 #29268 #30417 #30401 #30384]: #30307
+#30317 := (>= #30306 0::int)
+#28722 := (<= #28721 0::int)
+#30489 := (or #30378 #28722)
+#30490 := [th-lemma]: #30489
+#30491 := [unit-resolution #30490 #30302]: #28722
+#29390 := (>= #29388 0::int)
+#30492 := (or #30387 #29390)
+#30493 := [th-lemma]: #30492
+#30494 := [unit-resolution #30493 #30386]: #29390
+#29088 := (>= #29086 0::int)
+#30495 := (or #30450 #29088)
+#30498 := [th-lemma]: #30495
+#30530 := [unit-resolution #30498 #30449]: #29088
+#29080 := (<= #29067 0::int)
+#30531 := (or #30453 #29080)
+#30532 := [th-lemma]: #30531
+#30533 := [unit-resolution #30532 #30452]: #29080
+#30537 := (not #29390)
+#30536 := (not #28722)
+#30535 := (not #29080)
+#30534 := (not #29088)
+#30538 := (or #30317 #30534 #30535 #30536 #30484 #30486 #30484 #30486 #30318 #30537)
+#30539 := [th-lemma]: #30538
+#30540 := [unit-resolution #30539 #30468 #30416 #30533 #30316 #30530 #30494 #30491]: #30317
+#30542 := (not #30317)
+#30541 := (not #30307)
+#30543 := (or #30304 #30541 #30542)
+#30544 := [th-lemma]: #30543
+#30545 := [unit-resolution #30544 #30540 #30485]: #30304
+#29850 := [symm #30545]: #30340
+#29848 := [monotonicity #29850]: #30360
+#30376 := (= #28947 #29195)
+#29247 := (uf_66 #25933 #28923 #24643)
+#29198 := (= #29247 #29195)
+#29266 := (= #29195 #29247)
+#29276 := (not #29266)
+#29248 := (uf_138 #29247 #25933)
+#29249 := (= uf_9 #29248)
+#29182 := (not #29249)
+#29306 := (or #29182 #29276)
+#29310 := (not #29306)
+#29317 := (or #26887 #29310)
+#29183 := (* #28923 #26849)
+#29181 := (+ #27108 #29183)
+#29184 := (uf_43 #24643 #29181)
+#29185 := (= #29247 #29184)
+#29186 := (not #29185)
+#29187 := (or #29186 #29182)
+#29188 := (not #29187)
+#29318 := (or #26887 #29188)
+#29327 := (iff #29318 #29317)
+#29329 := (iff #29317 #29317)
+#29330 := [rewrite]: #29329
+#29311 := (iff #29188 #29310)
+#29308 := (iff #29187 #29306)
+#29303 := (or #29276 #29182)
+#29307 := (iff #29303 #29306)
+#29302 := [rewrite]: #29307
+#29304 := (iff #29187 #29303)
+#29287 := (iff #29186 #29276)
+#29274 := (iff #29185 #29266)
+#29272 := (iff #29198 #29266)
+#29273 := [rewrite]: #29272
+#29199 := (iff #29185 #29198)
+#29196 := (= #29184 #29195)
+#29191 := (= #29181 #29193)
+#29277 := (= #29183 #29189)
+#29192 := [rewrite]: #29277
+#29194 := [monotonicity #29192]: #29191
+#29197 := [monotonicity #29194]: #29196
+#29271 := [monotonicity #29197]: #29199
+#29275 := [trans #29271 #29273]: #29274
+#29288 := [monotonicity #29275]: #29287
+#29305 := [monotonicity #29288]: #29304
+#29309 := [trans #29305 #29302]: #29308
+#29312 := [monotonicity #29309]: #29311
+#29328 := [monotonicity #29312]: #29327
+#29331 := [trans #29328 #29330]: #29327
+#29326 := [quant-inst]: #29318
+#29324 := [mp #29326 #29331]: #29317
+#30334 := [unit-resolution #29324 #20922]: #29310
+#29382 := (or #29306 #29266)
+#29383 := [def-axiom]: #29382
+#30357 := [unit-resolution #29383 #30334]: #29266
+#30359 := [symm #30357]: #29198
+#30333 := (= #28947 #29247)
+#30358 := [monotonicity #28318]: #30333
+#30339 := [trans #30358 #30359]: #30376
+#29851 := [trans #30339 #29848]: #30346
+#29852 := [trans #29851 #30363]: #30349
+#29893 := [monotonicity #29852]: #30351
+#29853 := [symm #29893]: #30353
+#29854 := [monotonicity #29853]: #30388
+#29855 := [trans #29854 #30385]: #30391
+#29856 := [trans #29855 #28292]: #30393
+#29902 := [monotonicity #29856]: #29899
+#29910 := [symm #29902]: #29898
+#29866 := [trans #14075 #29910]: #29093
+#29863 := (not #29093)
+#29864 := (or #29149 #29863)
+#29865 := [def-axiom]: #29864
+#29868 := [unit-resolution #29865 #29866]: #29149
+#29981 := (= #25182 #29107)
+#29939 := (= #29107 #25182)
+#29897 := (= #27885 uf_7)
+#29867 := (= #27885 #24643)
+#28874 := (or #27759 #27945 #27886)
+#28875 := [def-axiom]: #28874
+#29869 := [unit-resolution #28875 #30336 #28170]: #27886
+#29904 := [symm #29869]: #29867
+#29938 := [trans #29904 #28190]: #29897
+#29978 := [monotonicity #29938]: #29939
+#29947 := [symm #29978]: #29981
+#29948 := [trans #27481 #29947]: #29125
+#29688 := (not #29098)
+#29881 := (iff #11878 #29688)
+#29879 := (iff #11875 #29098)
+#29877 := (iff #29098 #11875)
+#29892 := (= #29097 #2990)
+#29889 := (= #29096 #2977)
+#29687 := (= #29096 #24763)
+#29949 := [monotonicity #29856]: #29687
+#29891 := [trans #29949 #28353]: #29889
+#29890 := [monotonicity #29891]: #29892
+#29878 := [monotonicity #29890]: #29877
+#29880 := [symm #29878]: #29879
+#29876 := [monotonicity #29880]: #29881
+#29944 := [mp #14078 #29876]: #29688
+#29015 := (uf_66 #27003 #28923 #24643)
+#29016 := (uf_58 #3150 #29015)
+#29017 := (uf_136 #29016)
+#29018 := (= uf_9 #29017)
+#29050 := (not #29018)
+#30097 := (iff #29050 #29104)
+#30107 := (iff #29018 #29103)
+#30105 := (iff #29103 #29018)
+#29984 := (= #29102 #29017)
+#29995 := (= #27629 #29016)
+#29993 := (= #29016 #27629)
+#29950 := (= #29015 #3181)
+#29983 := (= #28923 uf_298)
+#29952 := [symm #29280]: #29983
+#29951 := [monotonicity #28197 #29952 #28190]: #29950
+#29994 := [monotonicity #29951]: #29993
+#29707 := [symm #29994]: #29995
+#29996 := [monotonicity #29707]: #29984
+#30106 := [monotonicity #29996]: #30105
+#30110 := [symm #30106]: #30107
+#30116 := [monotonicity #30110]: #30097
+#29019 := (uf_24 uf_287 #29015)
+#29020 := (= uf_9 #29019)
+#29021 := (not #29020)
+#29025 := (or #29018 #29021)
+#29028 := (not #29025)
+#29977 := (or #28964 #28974 #29028)
+#29039 := (or #27034 #24483 #27015 #27018 #28964 #28974 #29028)
+#29022 := (or #29021 #29018)
+#29023 := (not #29022)
+#29024 := (or #27018 #28964 #28962 #24483 #27015 #29023)
+#29040 := (or #27034 #29024)
+#29047 := (iff #29040 #29039)
+#29034 := (or #24483 #27015 #27018 #28964 #28974 #29028)
+#29042 := (or #27034 #29034)
+#29045 := (iff #29042 #29039)
+#29046 := [rewrite]: #29045
+#29043 := (iff #29040 #29042)
+#29037 := (iff #29024 #29034)
+#29031 := (or #27018 #28964 #28974 #24483 #27015 #29028)
+#29035 := (iff #29031 #29034)
+#29036 := [rewrite]: #29035
+#29032 := (iff #29024 #29031)
+#29029 := (iff #29023 #29028)
+#29026 := (iff #29022 #29025)
+#29027 := [rewrite]: #29026
+#29030 := [monotonicity #29027]: #29029
+#29033 := [monotonicity #28978 #29030]: #29032
+#29038 := [trans #29033 #29036]: #29037
+#29044 := [monotonicity #29038]: #29043
+#29048 := [trans #29044 #29046]: #29047
+#29041 := [quant-inst]: #29040
+#29049 := [mp #29041 #29048]: #29039
+#29985 := [unit-resolution #29049 #21366 #14064 #28636 #28230]: #29977
+#29986 := [unit-resolution #29985 #29270 #30324]: #29028
+#29051 := (or #29025 #29050)
+#29052 := [def-axiom]: #29051
+#29943 := [unit-resolution #29052 #29986]: #29050
+#30117 := [mp #29943 #30116]: #29104
+#29857 := (or #29143 #29103)
+#29858 := [def-axiom]: #29857
+#30151 := [unit-resolution #29858 #30117]: #29143
+#29678 := (or #29163 #29098 #29140 #29146 #29152)
+#29700 := [def-axiom]: #29678
+#30152 := [unit-resolution #29700 #30151 #29944 #29948 #29868 #29847]: false
+#30153 := [lemma #30152]: #29163
+#29736 := (or #29166 #29158)
+#29737 := [def-axiom]: #29736
+#30575 := [unit-resolution #29737 #30153]: #29166
+#24370 := (or #23173 #13225)
+#24371 := [def-axiom]: #24370
+#29434 := [unit-resolution #24371 #29337]: #13225
+#28236 := (or #12296 #13365 #27015 #13510)
+#28179 := [hypothesis]: #13225
+#28015 := (uf_66 #26867 uf_298 #27402)
+#28016 := (uf_125 #28015 #26867)
+#28046 := (* -1::int #28016)
+#28174 := (+ uf_298 #28046)
+#28175 := (<= #28174 0::int)
+#28017 := (= uf_298 #28016)
+#28020 := (or #26910 #28017)
+#28021 := [quant-inst]: #28020
+#28180 := [unit-resolution #28021 #16791]: #28017
+#28183 := (not #28017)
+#28184 := (or #28183 #28175)
+#28185 := [th-lemma]: #28184
+#28186 := [unit-resolution #28185 #28180]: #28175
+#28037 := (>= #28016 0::int)
+#28038 := (not #28037)
+#28089 := (uf_66 #27003 #28016 #24643)
+#28093 := (uf_24 uf_287 #28089)
+#28094 := (= uf_9 #28093)
+#28095 := (not #28094)
+#28090 := (uf_58 #3150 #28089)
+#28091 := (uf_136 #28090)
+#28092 := (= uf_9 #28091)
+#28099 := (or #28092 #28095)
+#28206 := (iff #18241 #28095)
+#28204 := (iff #12296 #28094)
+#28202 := (iff #28094 #12296)
+#28200 := (= #28093 #3184)
+#28198 := (= #28089 #3181)
+#28191 := (= #28016 uf_298)
+#28192 := [symm #28180]: #28191
+#28199 := [monotonicity #28197 #28192 #28190]: #28198
+#28201 := [monotonicity #28199]: #28200
+#28203 := [monotonicity #28201]: #28202
+#28205 := [symm #28203]: #28204
+#28207 := [monotonicity #28205]: #28206
+#28187 := [hypothesis]: #18241
+#28208 := [mp #28187 #28207]: #28095
+#28127 := (or #28099 #28094)
+#28128 := [def-axiom]: #28127
+#28209 := [unit-resolution #28128 #28208]: #28099
+#28047 := (+ #24645 #28046)
+#28048 := (<= #28047 0::int)
+#28219 := (not #28048)
+#28215 := [hypothesis]: #13511
+#28176 := (>= #28174 0::int)
+#28216 := (or #28183 #28176)
+#28217 := [th-lemma]: #28216
+#28218 := [unit-resolution #28217 #28180]: #28176
+#28221 := (not #28176)
+#28222 := (or #28219 #28220 #28221 #13510)
+#28223 := [th-lemma]: #28222
+#28224 := [unit-resolution #28223 #28218 #28215 #28214]: #28219
+#28102 := (not #28099)
+#28232 := (or #28038 #28048 #28102)
+#28113 := (or #27034 #24483 #27015 #27018 #28038 #28048 #28102)
+#28096 := (or #28095 #28092)
+#28097 := (not #28096)
+#28035 := (+ #28016 #26944)
+#28036 := (>= #28035 0::int)
+#28098 := (or #27018 #28038 #28036 #24483 #27015 #28097)
+#28114 := (or #27034 #28098)
+#28121 := (iff #28114 #28113)
+#28108 := (or #24483 #27015 #27018 #28038 #28048 #28102)
+#28116 := (or #27034 #28108)
+#28119 := (iff #28116 #28113)
+#28120 := [rewrite]: #28119
+#28117 := (iff #28114 #28116)
+#28111 := (iff #28098 #28108)
+#28105 := (or #27018 #28038 #28048 #24483 #27015 #28102)
+#28109 := (iff #28105 #28108)
+#28110 := [rewrite]: #28109
+#28106 := (iff #28098 #28105)
+#28103 := (iff #28097 #28102)
+#28100 := (iff #28096 #28099)
+#28101 := [rewrite]: #28100
+#28104 := [monotonicity #28101]: #28103
+#28051 := (iff #28036 #28048)
+#28040 := (+ #26944 #28016)
+#28043 := (>= #28040 0::int)
+#28049 := (iff #28043 #28048)
+#28050 := [rewrite]: #28049
+#28044 := (iff #28036 #28043)
+#28041 := (= #28035 #28040)
+#28042 := [rewrite]: #28041
+#28045 := [monotonicity #28042]: #28044
+#28052 := [trans #28045 #28050]: #28051
+#28107 := [monotonicity #28052 #28104]: #28106
+#28112 := [trans #28107 #28110]: #28111
+#28118 := [monotonicity #28112]: #28117
+#28122 := [trans #28118 #28120]: #28121
+#28115 := [quant-inst]: #28114
+#28123 := [mp #28115 #28122]: #28113
+#28233 := [unit-resolution #28123 #21366 #14064 #28231 #28230]: #28232
+#28234 := [unit-resolution #28233 #28224 #28209]: #28038
+#28235 := [th-lemma #28234 #28186 #28179]: false
+#28237 := [lemma #28235]: #28236
+#29435 := [unit-resolution #28237 #29377 #28636 #29434]: #12296
+#29885 := (or #29175 #18241 #29169)
+#29886 := [def-axiom]: #29885
+#30576 := [unit-resolution #29886 #29435 #30575]: #29175
+#29751 := (or #29750 #12302 #29172)
+#29749 := [def-axiom]: #29751
+#30581 := [unit-resolution #29749 #30576]: #30580
+#30582 := [unit-resolution #30581 #29980]: #12302
+#30590 := (or #18247 #23106)
+#24294 := (or #23127 #23121)
+#24295 := [def-axiom]: #24294
+#30583 := [unit-resolution #24295 #29376]: #23121
+#30584 := (or #23124 #18241 #23118)
+#24286 := (or #23124 #18238 #18241 #23118)
+#24287 := [def-axiom]: #24286
+#30585 := [unit-resolution #24287 #28272]: #30584
+#30586 := [unit-resolution #30585 #29435 #30583]: #23118
+#24276 := (or #23115 #23109)
+#24277 := [def-axiom]: #24276
+#30587 := [unit-resolution #24277 #30586]: #23109
+#30588 := (or #23112 #18247 #23106)
+#24270 := (or #23112 #18238 #18247 #23106)
+#24271 := [def-axiom]: #24270
+#30589 := [unit-resolution #24271 #28272]: #30588
+#30591 := [unit-resolution #30589 #30587]: #30590
+#30592 := [unit-resolution #30591 #30582]: #23106
+#30593 := (or #23103 #23064)
+#24118 := (not #18612)
+#30252 := (= #3083 #3220)
+#30250 := (= #3220 #3083)
+#30246 := (= #3219 #3082)
+#30243 := [hypothesis]: #23094
+#24232 := (or #23091 #12551)
+#24233 := [def-axiom]: #24232
+#30244 := [unit-resolution #24233 #30243]: #12551
+#30245 := [symm #30244]: #3250
+#30247 := [monotonicity #30245]: #30246
+#30251 := [monotonicity #30247]: #30250
+#30253 := [symm #30251]: #30252
+#30254 := (= uf_304 #3083)
+#24230 := (or #23091 #12548)
+#24231 := [def-axiom]: #24230
+#30248 := [unit-resolution #24231 #30243]: #12548
+#30249 := [symm #30248]: #3249
+#30255 := [trans #30249 #29340]: #30254
+#30256 := [trans #30255 #30253]: #12352
+#24227 := (+ uf_297 #13301)
+#24229 := (>= #24227 0::int)
+#30257 := (or #12557 #24229)
+#30258 := [th-lemma]: #30257
+#30209 := [unit-resolution #30258 #30244]: #24229
+#29871 := (not #24229)
+#29872 := (or #13304 #29871)
+#29900 := [hypothesis]: #24229
+#29901 := [hypothesis]: #13303
+#29870 := [th-lemma #29901 #29900 #29342]: false
+#29873 := [lemma #29870]: #29872
+#30213 := [unit-resolution #29873 #30209]: #13304
+#24106 := (or #22046 #22044 #13303)
+#24107 := [def-axiom]: #24106
+#30214 := [unit-resolution #24107 #30213 #30256]: #22046
+#24108 := (or #23025 #22045)
+#24109 := [def-axiom]: #24108
+#30210 := [unit-resolution #24109 #30214]: #23025
+#24242 := (or #23091 #23055)
+#24243 := [def-axiom]: #24242
+#30215 := [unit-resolution #24243 #30243]: #23055
+#30219 := (or #23058 #23052)
+#15520 := (<= uf_286 4294967295::int)
+#15523 := (iff #13150 #15520)
+#15514 := (+ 4294967295::int #13151)
+#15517 := (>= #15514 0::int)
+#15521 := (iff #15517 #15520)
+#15522 := [rewrite]: #15521
+#15518 := (iff #13150 #15517)
+#15515 := (= #13152 #15514)
+#15516 := [monotonicity #7483]: #15515
+#15519 := [monotonicity #15516]: #15518
+#15524 := [trans #15519 #15522]: #15523
+#14066 := [not-or-elim #14055]: #13155
+#14068 := [and-elim #14066]: #13150
+#15525 := [mp #14068 #15524]: #15520
+#29378 := [hypothesis]: #18279
+#29379 := [th-lemma #29378 #29377 #15525]: false
+#29380 := [lemma #29379]: #15609
+#30216 := (or #13365 #13243)
+#30217 := [th-lemma]: #30216
+#30218 := [unit-resolution #30217 #29434]: #13243
+#24166 := (or #23058 #18276 #18279 #23052)
+#24167 := [def-axiom]: #24166
+#30220 := [unit-resolution #24167 #30218 #29380]: #30219
+#30221 := [unit-resolution #30220 #30215]: #23052
+#24156 := (or #23049 #23043)
+#24157 := [def-axiom]: #24156
+#30223 := [unit-resolution #24157 #30221]: #23043
+#24101 := (>= #13328 -1::int)
+#24152 := (or #23049 #13327)
+#24153 := [def-axiom]: #24152
+#30224 := [unit-resolution #24153 #30221]: #13327
+#30222 := (or #13331 #24101)
+#30225 := [th-lemma]: #30222
+#30226 := [unit-resolution #30225 #30224]: #24101
+#29915 := (not #24101)
+#29916 := (or #13259 #29915)
+#29874 := [hypothesis]: #24101
+#29875 := [hypothesis]: #13264
+#29909 := [th-lemma #29875 #29377 #29874]: false
+#29917 := [lemma #29909]: #29916
+#30227 := [unit-resolution #29917 #30226]: #13259
+#24142 := (or #23046 #13264 #23040)
+#24143 := [def-axiom]: #24142
+#30228 := [unit-resolution #24143 #30227 #30223]: #23040
+#24134 := (or #23037 #23031)
+#24135 := [def-axiom]: #24134
+#30229 := [unit-resolution #24135 #30228]: #23031
+#24130 := (or #23034 #23028 #22098)
+#24131 := [def-axiom]: #24130
+#30230 := [unit-resolution #24131 #30229 #30210]: #22098
+#24119 := (or #22093 #24118)
+#24120 := [def-axiom]: #24119
+#30271 := [unit-resolution #24120 #30230]: #24118
+#30015 := (+ uf_298 #18610)
+#30242 := (>= #30015 0::int)
+#30270 := (not #30242)
+#30496 := (= uf_298 ?x785!14)
+#30527 := (not #30496)
+#24240 := (or #23091 #13417)
+#24241 := [def-axiom]: #24240
+#30232 := [unit-resolution #24241 #30243]: #13417
+#24224 := (+ uf_296 #13279)
+#24225 := (<= #24224 0::int)
+#30234 := (or #12566 #24225)
+#30235 := [th-lemma]: #30234
+#30233 := [unit-resolution #30235 #30248]: #24225
+#24121 := (not #18625)
+#24122 := (or #22093 #24121)
+#24123 := [def-axiom]: #24122
+#30236 := [unit-resolution #24123 #30230]: #24121
+#30514 := (not #24225)
+#30515 := (or #30513 #18625 #30514 #13416)
+#30508 := [hypothesis]: #13417
+#30509 := [hypothesis]: #24225
+#30510 := [hypothesis]: #24121
+#30511 := [hypothesis]: #30503
+#30512 := [th-lemma #30511 #30510 #30509 #30508]: false
+#30516 := [lemma #30512]: #30515
+#30237 := [unit-resolution #30516 #30236 #30233 #30232]: #30513
+#30504 := (or #30502 #30503)
+#30505 := [th-lemma]: #30504
+#30238 := [unit-resolution #30505 #30237]: #30502
+#30528 := (or #30527 #30497)
+#30523 := (= #18302 #3190)
+#30521 := (= #18301 #3181)
+#30519 := (= ?x785!14 uf_298)
+#30518 := [hypothesis]: #30496
+#30520 := [symm #30518]: #30519
+#30522 := [monotonicity #30520]: #30521
+#30524 := [monotonicity #30522]: #30523
+#30525 := [symm #30524]: #30497
+#30517 := [hypothesis]: #30502
+#30526 := [unit-resolution #30517 #30525]: false
+#30529 := [lemma #30526]: #30528
+#30239 := [unit-resolution #30529 #30238]: #30527
+#30274 := (or #30496 #30270)
+#30013 := (<= #30015 0::int)
+#30051 := (+ uf_296 #18623)
+#30052 := (>= #30051 0::int)
+#30240 := (not #30052)
+#30241 := (or #30240 #18625 #30514)
+#30283 := [th-lemma]: #30241
+#30284 := [unit-resolution #30283 #30233 #30236]: #30240
+#30286 := (or #30013 #30052)
+#24116 := (or #22093 #18298)
+#24117 := [def-axiom]: #24116
+#30285 := [unit-resolution #24117 #30230]: #18298
+#24114 := (or #22093 #18297)
+#24115 := [def-axiom]: #24114
+#30280 := [unit-resolution #24115 #30230]: #18297
+#30068 := (or #23014 #22077 #22078 #30013 #30052)
+#29997 := (+ #18302 #13715)
+#29992 := (<= #29997 0::int)
+#29998 := (+ ?x785!14 #13246)
+#29999 := (>= #29998 0::int)
+#30001 := (or #22078 #29999 #29992 #22077)
+#30069 := (or #23014 #30001)
+#30076 := (iff #30069 #30068)
+#30063 := (or #22077 #22078 #30013 #30052)
+#30071 := (or #23014 #30063)
+#30074 := (iff #30071 #30068)
+#30075 := [rewrite]: #30074
+#30072 := (iff #30069 #30071)
+#30066 := (iff #30001 #30063)
+#30060 := (or #22078 #30013 #30052 #22077)
+#30064 := (iff #30060 #30063)
+#30065 := [rewrite]: #30064
+#30061 := (iff #30001 #30060)
+#30058 := (iff #29992 #30052)
+#30046 := (+ #13715 #18302)
+#30048 := (<= #30046 0::int)
+#30056 := (iff #30048 #30052)
 #30057 := [rewrite]: #30056
-#30054 := (iff #30051 #30053)
-#29177 := (iff #29146 #29174)
-#29171 := (or #21511 #29154 #29166 #21510)
-#29175 := (iff #29171 #29174)
-#29176 := [rewrite]: #29175
-#29172 := (iff #29146 #29171)
-#29169 := (iff #29143 #29166)
-#29159 := (+ #13378 #17765)
-#29162 := (<= #29159 0::int)
-#29167 := (iff #29162 #29166)
-#29168 := [rewrite]: #29167
-#29163 := (iff #29143 #29162)
-#29160 := (= #29142 #29159)
-#29161 := [rewrite]: #29160
-#29164 := [monotonicity #29161]: #29163
-#29170 := [trans #29164 #29168]: #29169
-#29157 := (iff #29145 #29154)
-#29147 := (+ #12965 ?x785!14)
-#29150 := (>= #29147 0::int)
-#29155 := (iff #29150 #29154)
-#29156 := [rewrite]: #29155
-#29151 := (iff #29145 #29150)
-#29148 := (= #29144 #29147)
-#29149 := [rewrite]: #29148
-#29152 := [monotonicity #29149]: #29151
-#29158 := [trans #29152 #29156]: #29157
-#29173 := [monotonicity #29158 #29170]: #29172
-#29178 := [trans #29173 #29176]: #29177
-#30055 := [monotonicity #29178]: #30054
-#30059 := [trans #30055 #30057]: #30058
-#30052 := [quant-inst]: #30051
-#30060 := [mp #30052 #30059]: #30050
-#30193 := [unit-resolution #30060 #28540 #30192 #30191 #30189]: #29154
-#30210 := (not #29154)
-#30211 := (or #30181 #30210 #30208)
-#30212 := [th-lemma]: #30211
-#30214 := [unit-resolution #30212 #30193]: #30213
-#30215 := [unit-resolution #30214 #30186]: #30208
-#30216 := [th-lemma #30130 #30215 #30178]: false
-#30219 := [lemma #30216]: #22559
-#30241 := [unit-resolution #29859 #30219]: #30232
-#30236 := [unit-resolution #30241 #30229]: #22532
-#23646 := (or #22529 #12383)
-#23647 := [def-axiom]: #23646
-#30293 := [unit-resolution #23647 #30236]: #12383
-#28986 := [symm #30293]: #3242
-#29080 := [trans #28986 #28873]: #28951
-#29269 := [trans #29080 #29458]: #29074
-#29334 := [monotonicity #30279 #29269 #27654]: #29208
-#29357 := [trans #29334 #29712]: #29112
-#29125 := [monotonicity #29357]: #28979
-#28987 := [symm #29125]: #28730
-#29079 := (= uf_304 #3230)
-#23642 := (or #22529 #12375)
-#23643 := [def-axiom]: #23642
-#28983 := [unit-resolution #23643 #30236]: #12375
-#29211 := [symm #28983]: #3235
-#23644 := (or #22529 #12380)
-#23645 := [def-axiom]: #23644
-#29034 := [unit-resolution #23645 #30236]: #12380
-#28946 := [symm #29034]: #3240
-#28982 := [trans #28946 #29211]: #29079
-#29212 := [trans #28982 #28987]: #12446
-#28731 := [hypothesis]: #21466
-#29304 := [unit-resolution #28731 #29212]: false
-#28976 := [lemma #29304]: #12446
-#30304 := (or #21466 #21468)
-#28528 := (+ uf_298 #13126)
-#28529 := (>= #28528 0::int)
-#30294 := (or #21574 #28529)
-#30295 := [th-lemma]: #30294
-#30296 := [unit-resolution #30295 #30293]: #28529
-#30297 := [hypothesis]: #21467
-#30298 := [hypothesis]: #12446
-#30299 := [unit-resolution #23574 #30298 #30297]: #13128
-#30300 := (not #28529)
-#30301 := (or #13129 #12967 #30300)
-#30302 := [th-lemma]: #30301
-#30303 := [unit-resolution #30302 #30299 #30296 #28538]: false
-#30305 := [lemma #30303]: #30304
-#29076 := [unit-resolution #30305 #28976]: #21468
-#29124 := [unit-resolution #23576 #29076]: #22493
-#28962 := [unit-resolution #23597 #30135]: #22499
-#29358 := [unit-resolution #28962 #29124]: #21531
-#23692 := (>= #23690 0::int)
-#30027 := (not #23692)
-#29111 := [unit-resolution #23727 #30229]: #22565
-#29289 := (or #22568 #22556)
-#29333 := [unit-resolution #23717 #30219]: #29289
-#29311 := [unit-resolution #29333 #29111]: #22556
-#23684 := (or #22553 #12996)
-#23685 := [def-axiom]: #23684
-#29113 := [unit-resolution #23685 #29311]: #12996
-#29780 := (+ #3230 #13112)
-#29809 := (<= #29780 0::int)
-#29719 := (= #3230 uf_304)
-#29564 := (or #22529 #29719)
-#29576 := [hypothesis]: #22532
-#29720 := [unit-resolution #23645 #29576]: #12380
-#29761 := [unit-resolution #23643 #29576]: #12375
-#29723 := [trans #29761 #29720]: #29719
-#30001 := (not #29719)
-#29829 := [hypothesis]: #30001
-#29786 := [unit-resolution #29829 #29723]: false
-#29787 := [lemma #29786]: #29564
-#30237 := [unit-resolution #29787 #30236]: #29719
-#30002 := (or #30001 #29809)
-#30003 := [th-lemma]: #30002
-#30238 := [unit-resolution #30003 #30237]: #29809
-#30026 := (not #29809)
-#30028 := (or #30026 #30027 #12997)
-#30023 := [hypothesis]: #29809
-#30024 := [hypothesis]: #12996
-#30025 := [hypothesis]: #23692
-#30020 := [th-lemma #30025 #30024 #30023]: false
-#30029 := [lemma #30020]: #30028
-#29339 := [unit-resolution #30029 #30238 #29113]: #30027
-#29268 := (or #23692 #23691)
-#29308 := [th-lemma]: #29268
-#29306 := [unit-resolution #29308 #29339]: #23691
-#29309 := [unit-resolution #23587 #29358]: #23585
-#29290 := [unit-resolution #30207 #29309 #29306]: #30187
-#30126 := (or #21526 #29166 #30181)
-#30089 := [hypothesis]: #30288
-#30114 := [hypothesis]: #21531
-#30115 := [unit-resolution #23589 #30114]: #18027
-#30110 := (or #30137 #18022 #29095)
-#30116 := [th-lemma]: #30110
-#30117 := [unit-resolution #30116 #30115 #30130]: #30137
-#30113 := [unit-resolution #30212 #30117 #30089]: #30210
-#30118 := [hypothesis]: #30187
-#30119 := [unit-resolution #23584 #30114]: #17761
-#30120 := [unit-resolution #23582 #30114]: #17757
-#30125 := [unit-resolution #30060 #28540 #30120 #30119 #30118 #30113]: false
-#30076 := [lemma #30125]: #30126
-#29305 := [unit-resolution #30076 #29290 #29358]: #30181
-#30233 := (or #30263 #18009)
-#30239 := [th-lemma #30261 #30260 #30238]: false
-#30234 := [lemma #30239]: #30233
-#28425 := [unit-resolution #30234 #29309]: #30263
-#29077 := [unit-resolution #30267 #28425]: #30256
-[unit-resolution #30290 #29077 #29305]: false
+#30049 := (iff #29992 #30048)
+#30047 := (= #29997 #30046)
+#30042 := [rewrite]: #30047
+#30050 := [monotonicity #30042]: #30049
+#30059 := [trans #30050 #30057]: #30058
+#30030 := (iff #29999 #30013)
+#30002 := (+ #13246 ?x785!14)
+#30012 := (>= #30002 0::int)
+#30016 := (iff #30012 #30013)
+#30017 := [rewrite]: #30016
+#30000 := (iff #29999 #30012)
+#30007 := (= #29998 #30002)
+#30008 := [rewrite]: #30007
+#30014 := [monotonicity #30008]: #30000
+#30031 := [trans #30014 #30017]: #30030
+#30062 := [monotonicity #30031 #30059]: #30061
+#30067 := [trans #30062 #30065]: #30066
+#30073 := [monotonicity #30067]: #30072
+#30077 := [trans #30073 #30075]: #30076
+#30070 := [quant-inst]: #30069
+#30078 := [mp #30070 #30077]: #30068
+#30287 := [unit-resolution #30078 #29339 #30280 #30285]: #30286
+#30288 := [unit-resolution #30287 #30284]: #30013
+#30289 := (not #30013)
+#30299 := (or #30496 #30289 #30270)
+#30273 := [th-lemma]: #30299
+#30269 := [unit-resolution #30273 #30288]: #30274
+#30275 := [unit-resolution #30269 #30239]: #30270
+#30276 := [th-lemma #30275 #30226 #30271]: false
+#30272 := [lemma #30276]: #23091
+#29441 := (or #23103 #23094 #23064)
+#29421 := [hypothesis]: #23061
+#29422 := [hypothesis]: #23106
+#24254 := (or #23103 #12302)
+#24255 := [def-axiom]: #24254
+#29425 := [unit-resolution #24255 #29422]: #12302
+#29426 := (or #23070 #18247 #23064)
+#24196 := (or #23070 #18238 #18247 #23064)
+#24197 := [def-axiom]: #24196
+#29427 := [unit-resolution #24197 #28272]: #29426
+#29428 := [unit-resolution #29427 #29425 #29421]: #23070
+#24202 := (or #23073 #23067)
+#24203 := [def-axiom]: #24202
+#29429 := [unit-resolution #24203 #29428]: #23073
+#29430 := [hypothesis]: #23091
+#24260 := (or #23103 #23097)
+#24261 := [def-axiom]: #24260
+#29431 := [unit-resolution #24261 #29422]: #23097
+#24250 := (or #23100 #23088 #23094)
+#24251 := [def-axiom]: #24250
+#29432 := [unit-resolution #24251 #29431 #29430]: #23088
+#24220 := (or #23085 #23079)
+#24221 := [def-axiom]: #24220
+#29433 := [unit-resolution #24221 #29432]: #23079
+#29438 := (or #23082 #23076)
+#29436 := (or #23082 #18241 #23076)
+#24212 := (or #23082 #18238 #18241 #23076)
+#24213 := [def-axiom]: #24212
+#29437 := [unit-resolution #24213 #28272]: #29436
+#29439 := [unit-resolution #29437 #29435]: #29438
+#29440 := [unit-resolution #29439 #29433 #29429]: false
+#29442 := [lemma #29440]: #29441
+#30594 := [unit-resolution #29442 #30272]: #30593
+#30595 := [unit-resolution #30594 #30592]: #23064
+#24178 := (or #23061 #12313)
+#24179 := [def-axiom]: #24178
+#30596 := [unit-resolution #24179 #30595]: #12313
+#24176 := (or #23061 #12308)
+#24177 := [def-axiom]: #24176
+#30597 := [unit-resolution #24177 #30595]: #12308
+#30598 := [trans #30597 #30596]: #30154
+#30599 := (not #30154)
+#30600 := (or #30599 #30108)
+#30601 := [th-lemma]: #30600
+#30602 := [unit-resolution #30601 #30598]: #30108
+#24186 := (or #23061 #23055)
+#24187 := [def-axiom]: #24186
+#30603 := [unit-resolution #24187 #30595]: #23055
+#30604 := [unit-resolution #30220 #30603]: #23052
+#30605 := [unit-resolution #24157 #30604]: #23043
+#30606 := [unit-resolution #24153 #30604]: #13327
+#30607 := [unit-resolution #30225 #30606]: #24101
+#30608 := [unit-resolution #29917 #30607]: #13259
+#30609 := [unit-resolution #24143 #30608 #30605]: #23040
+#30610 := [unit-resolution #24135 #30609]: #23031
+#30619 := (= #3190 #3220)
+#30615 := (= #3220 #3190)
+#30613 := (= #3219 #3181)
+#24180 := (or #23061 #12316)
+#24181 := [def-axiom]: #24180
+#30611 := [unit-resolution #24181 #30595]: #12316
+#30612 := [symm #30611]: #3200
+#30614 := [monotonicity #30612]: #30613
+#30616 := [monotonicity #30614]: #30615
+#30620 := [symm #30616]: #30619
+#30621 := (= uf_304 #3190)
+#30618 := [symm #30597]: #3193
+#30617 := [symm #30596]: #3198
+#30622 := [trans #30617 #30618]: #30621
+#30623 := [trans #30622 #30620]: #12352
+#29903 := (+ uf_298 #13301)
+#29849 := (>= #29903 0::int)
+#30624 := (or #12440 #29849)
+#30625 := [th-lemma]: #30624
+#30626 := [unit-resolution #30625 #30611]: #29849
+#30627 := (not #29849)
+#30628 := (or #13304 #30627 #13510)
+#30629 := [th-lemma]: #30628
+#30630 := [unit-resolution #30629 #29377 #30626]: #13304
+#30631 := [unit-resolution #24107 #30630 #30623]: #22046
+#30632 := [unit-resolution #24109 #30631]: #23025
+#30633 := [unit-resolution #24131 #30632 #30610]: #22098
+#30634 := [unit-resolution #24123 #30633]: #24121
+#30635 := (not #30108)
+#30636 := (or #30513 #18625 #30635)
+#30637 := [th-lemma]: #30636
+#30638 := [unit-resolution #30637 #30634 #30602]: #30513
+#30639 := [unit-resolution #30505 #30638]: #30502
+#30640 := [unit-resolution #24120 #30633]: #24118
+#30641 := (or #30242 #18612 #29915)
+#30642 := [th-lemma]: #30641
+#30643 := [unit-resolution #30642 #30640 #30607]: #30242
+#30644 := [unit-resolution #24261 #30592]: #23097
+#30645 := (or #23100 #23088)
+#30646 := [unit-resolution #24251 #30272]: #30645
+#30647 := [unit-resolution #30646 #30644]: #23088
+#24218 := (or #23085 #13416)
+#24219 := [def-axiom]: #24218
+#30648 := [unit-resolution #24219 #30647]: #13416
+#30649 := (or #24225 #30635 #13417)
+#30650 := [th-lemma]: #30649
+#30651 := [unit-resolution #30650 #30648 #30602]: #24225
+#30652 := [unit-resolution #30283 #30634 #30651]: #30240
+#30653 := [unit-resolution #24117 #30633]: #18298
+#30654 := [unit-resolution #24115 #30633]: #18297
+#30655 := [unit-resolution #30078 #29339 #30654 #30653 #30652]: #30013
+#30656 := [unit-resolution #30273 #30655 #30643]: #30496
+[unit-resolution #30529 #30656 #30639]: false
 unsat