src/HOL/SMT/Examples/cert/z3_arith_quant_08.proof

+#2 := false
+#9 := 1::int
+decl ?x1!1 :: int
+#91 := ?x1!1
+#68 := -2::int
+#129 := (* -2::int ?x1!1)
+decl ?x2!0 :: int
+#90 := ?x2!0
+#7 := 2::int
+#128 := (* 2::int ?x2!0)
+#130 := (+ #128 #129)
+#131 := (<= #130 1::int)
+#136 := (not #131)
+#55 := 0::int
+#53 := -1::int
+#115 := (* -1::int ?x1!1)
+#116 := (+ ?x2!0 #115)
+#117 := (<= #116 0::int)
+#139 := (or #117 #136)
+#142 := (not #139)
+#92 := (* -2::int ?x2!0)
+#93 := (* 2::int ?x1!1)
+#94 := (+ #93 #92)
+#95 := (>= #94 -1::int)
+#96 := (not #95)
+#97 := (* -1::int ?x2!0)
+#98 := (+ ?x1!1 #97)
+#99 := (>= #98 0::int)
+#100 := (or #99 #96)
+#101 := (not #100)
+#143 := (iff #101 #142)
+#140 := (iff #100 #139)
+#137 := (iff #96 #136)
+#134 := (iff #95 #131)
+#122 := (+ #92 #93)
+#125 := (>= #122 -1::int)
+#132 := (iff #125 #131)
+#133 := [rewrite]: #132
+#126 := (iff #95 #125)
+#123 := (= #94 #122)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124]: #126
+#135 := [trans #127 #133]: #134
+#138 := [monotonicity #135]: #137
+#120 := (iff #99 #117)
+#109 := (+ #97 ?x1!1)
+#112 := (>= #109 0::int)
+#118 := (iff #112 #117)
+#119 := [rewrite]: #118
+#113 := (iff #99 #112)
+#110 := (= #98 #109)
+#111 := [rewrite]: #110
+#114 := [monotonicity #111]: #113
+#121 := [trans #114 #119]: #120
+#141 := [monotonicity #121 #138]: #140
+#144 := [monotonicity #141]: #143
+#5 := (:var 0 int)
+#71 := (* -2::int #5)
+#4 := (:var 1 int)
+#8 := (* 2::int #4)
+#72 := (+ #8 #71)
+#70 := (>= #72 -1::int)
+#69 := (not #70)
+#57 := (* -1::int #5)
+#58 := (+ #4 #57)
+#56 := (>= #58 0::int)
+#75 := (or #56 #69)
+#78 := (forall (vars (?x1 int) (?x2 int)) #75)
+#81 := (not #78)
+#102 := (~ #81 #101)
+#103 := [sk]: #102
+#11 := (* 2::int #5)
+#10 := (+ #8 1::int)
+#12 := (< #10 #11)
+#6 := (< #4 #5)
+#13 := (implies #6 #12)
+#14 := (forall (vars (?x1 int) (?x2 int)) #13)
+#15 := (not #14)
+#84 := (iff #15 #81)
+#32 := (+ 1::int #8)
+#35 := (< #32 #11)
+#41 := (not #6)
+#42 := (or #41 #35)
+#47 := (forall (vars (?x1 int) (?x2 int)) #42)
+#50 := (not #47)
+#82 := (iff #50 #81)
+#79 := (iff #47 #78)
+#76 := (iff #42 #75)
+#73 := (iff #35 #69)
+#74 := [rewrite]: #73
+#66 := (iff #41 #56)
+#54 := (not #56)
+#61 := (not #54)
+#64 := (iff #61 #56)
+#65 := [rewrite]: #64
+#62 := (iff #41 #61)
+#59 := (iff #6 #54)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#77 := [monotonicity #67 #74]: #76
+#80 := [quant-intro #77]: #79
+#83 := [monotonicity #80]: #82
+#51 := (iff #15 #50)
+#48 := (iff #14 #47)
+#45 := (iff #13 #42)
+#38 := (implies #6 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #13 #38)
+#36 := (iff #12 #35)
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [quant-intro #46]: #48
+#52 := [monotonicity #49]: #51
+#85 := [trans #52 #83]: #84
+#31 := [asserted]: #15
+#86 := [mp #31 #85]: #81
+#106 := [mp~ #86 #103]: #101
+#107 := [mp #106 #144]: #142
+#146 := [not-or-elim #107]: #131
+#108 := (not #117)
+#145 := [not-or-elim #107]: #108
+[th-lemma #145 #146]: false
+unsat