%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : DAT027_1 : TPTP v9.2.1. Released v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:14:22 AM UTC 2026 % Result : Theorem 45.37s 45.60s % Output : Proof 45.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : DAT027_1 : TPTP v9.2.1. Released v5.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.06/0.25 % Computer : n012.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Mon Jun 1 22:26:03 EDT 2026 % 0.06/0.25 % CPUTime : % 0.06/0.32 %----Proving TF0_ARI % 45.37/45.60 --- Run --finite-model-find --decision=internal at 45... % 45.37/45.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 45.37/45.60 % SZS status Theorem % 45.37/45.60 % SZS output start Proof % 45.37/45.60 ( % 45.37/45.60 (declare-sort tptp.collection 0) % 45.37/45.60 (declare-const tptp.remove (-> Int tptp.collection tptp.collection)) % 45.37/45.60 (declare-const tptp.add (-> Int tptp.collection tptp.collection)) % 45.37/45.60 (declare-const tptp.in (-> Int tptp.collection Bool)) % 45.37/45.60 (declare-const tptp.empty tptp.collection) % 45.37/45.60 (define @t1 () (@var "U" Int)) % 45.37/45.60 (define @t2 () (@var "W" tptp.collection)) % 45.37/45.60 (define @t3 () (@var "V" Int)) % 45.37/45.60 (define @t4 () (@var "Y" tptp.collection)) % 45.37/45.60 (define @t5 () (@var "X" Int)) % 45.37/45.60 (define @t6 () (@var "X1" tptp.collection)) % 45.37/45.60 (define @t7 () (@var "X2" Int)) % 45.37/45.60 (define @t8 () (@var "Z" Int)) % 45.37/45.60 (define @t9 () (forall (@list @t8 @t6 @t7) (= (or (tptp.in @t8 @t6) (= @t8 @t7)) (tptp.in @t8 (tptp.add @t7 @t6))))) % 45.37/45.60 (define @t10 () (@var "X4" tptp.collection)) % 45.37/45.60 (define @t11 () (@var "X5" Int)) % 45.37/45.60 (define @t12 () (@var "X3" Int)) % 45.37/45.60 (define @t13 () (forall (@list @t12 @t10 @t11) (= (and (tptp.in @t12 @t10) (not (= @t12 @t11))) (tptp.in @t12 (tptp.remove @t11 @t10))))) % 45.37/45.60 (define @t14 () (@var "U" tptp.collection)) % 45.37/45.60 (define @t15 () (tptp.in @t8 @t14)) % 45.37/45.60 (define @t16 () (=> @t15 (> @t8 0))) % 45.37/45.60 (define @t17 () (@list @t8)) % 45.37/45.60 (define @t18 () (forall @t17 @t16)) % 45.37/45.60 (define @t19 () (@var "V" tptp.collection)) % 45.37/45.60 (define @t20 () (@var "W" Int)) % 45.37/45.60 (define @t21 () (tptp.remove @t20 @t19)) % 45.37/45.60 (define @t22 () (+ @t20 @t5)) % 45.37/45.60 (define @t23 () (tptp.add @t22 @t21)) % 45.37/45.60 (define @t24 () (= @t14 @t23)) % 45.37/45.60 (define @t25 () (>= @t5 0)) % 45.37/45.60 (define @t26 () (tptp.in @t20 @t19)) % 45.37/45.60 (define @t27 () (@var "Y" Int)) % 45.37/45.60 (define @t28 () (tptp.in @t27 @t19)) % 45.37/45.60 (define @t29 () (=> @t28 (> @t27 0))) % 45.37/45.60 (define @t30 () (@list @t27)) % 45.37/45.60 (define @t31 () (forall @t30 @t29)) % 45.37/45.60 (define @t32 () (and @t31 @t26 @t25 @t24)) % 45.37/45.60 (define @t33 () (=> @t32 @t18)) % 45.37/45.60 (define @t34 () (@list @t14 @t19 @t20 @t5)) % 45.37/45.60 (define @t35 () (forall @t34 @t33)) % 45.37/45.60 (define @t36 () (not @t35)) % 45.37/45.60 (define @t37 () (@var "BOUND_VARIABLE_7514" Int)) % 45.37/45.60 (define @t38 () (>= @t37 1)) % 45.37/45.60 (define @t39 () (+ @t5 @t20)) % 45.37/45.60 (define @t40 () (tptp.add @t39 @t21)) % 45.37/45.60 (define @t41 () (not (tptp.in @t37 @t40))) % 45.37/45.60 (define @t42 () (not @t25)) % 45.37/45.60 (define @t43 () (not @t26)) % 45.37/45.60 (define @t44 () (>= @t27 1)) % 45.37/45.60 (define @t45 () (forall @t30 (or (not @t28) @t44))) % 45.37/45.60 (define @t46 () (not @t45)) % 45.37/45.60 (define @t47 () (or @t46 @t43 @t42 @t41 @t38)) % 45.37/45.60 (define @t48 () (not (= @t40 @t40))) % 45.37/45.60 (define @t49 () (or @t46 @t43 @t42 @t48 @t41 @t38)) % 45.37/45.60 (define @t50 () (@list @t19 @t20 @t5 @t37)) % 45.37/45.60 (define @t51 () (not (tptp.in @t37 @t14))) % 45.37/45.60 (define @t52 () (= @t14 @t40)) % 45.37/45.60 (define @t53 () (not @t52)) % 45.37/45.60 (define @t54 () (or @t53 @t46 @t43 @t42 @t53 @t51 @t38)) % 45.37/45.60 (define @t55 () (@list @t14)) % 45.37/45.60 (define @t56 () (or @t46 @t43 @t42 @t53 @t51 @t38)) % 45.37/45.60 (define @t57 () (forall @t55 @t56)) % 45.37/45.60 (define @t58 () (forall @t50 @t57)) % 45.37/45.60 (define @t59 () (forall (@list @t19 @t20 @t5 @t37 @t14) @t56)) % 45.37/45.60 (define @t60 () (@list @t14 @t19 @t20 @t5 @t37)) % 45.37/45.60 (define @t61 () (or @t51 @t38)) % 45.37/45.60 (define @t62 () (or @t46 @t43 @t42 @t53 @t61)) % 45.37/45.60 (define @t63 () (forall @t60 @t62)) % 45.37/45.60 (define @t64 () (@list @t37)) % 45.37/45.60 (define @t65 () (forall @t64 @t62)) % 45.37/45.60 (define @t66 () (forall @t64 @t61)) % 45.37/45.60 (define @t67 () (or @t46 @t43 @t42 @t53 @t66)) % 45.37/45.60 (define @t68 () (>= @t8 1)) % 45.37/45.60 (define @t69 () (forall @t17 (or (not @t15) @t68))) % 45.37/45.60 (define @t70 () (or @t46 @t43 @t42 @t53 @t69)) % 45.37/45.60 (define @t71 () (or @t46 @t43 @t42 @t53)) % 45.37/45.60 (define @t72 () (and @t45 @t26 @t25 @t52)) % 45.37/45.60 (define @t73 () (+ 0 1)) % 45.37/45.60 (define @t74 () (>= @t8 @t73)) % 45.37/45.60 (define @t75 () (>= @t27 @t73)) % 45.37/45.60 (define @t76 () (forall @t50 @t47)) % 45.37/45.60 (define @t77 () (@quantifiers_skolemize @t76 3)) % 45.37/45.60 (define @t78 () (>= @t77 1)) % 45.37/45.60 (define @t79 () (@quantifiers_skolemize @t76 0)) % 45.37/45.60 (define @t80 () (@quantifiers_skolemize @t76 1)) % 45.37/45.60 (define @t81 () (tptp.remove @t80 @t79)) % 45.37/45.60 (define @t82 () (@quantifiers_skolemize @t76 2)) % 45.37/45.60 (define @t83 () (+ @t80 @t82)) % 45.37/45.60 (define @t84 () (tptp.in @t77 (tptp.add @t83 @t81))) % 45.37/45.60 (define @t85 () (not @t84)) % 45.37/45.60 (define @t86 () (>= @t82 0)) % 45.37/45.60 (define @t87 () (not @t86)) % 45.37/45.60 (define @t88 () (tptp.in @t80 @t79)) % 45.37/45.60 (define @t89 () (not @t88)) % 45.37/45.60 (define @t90 () (forall @t30 (or (not (tptp.in @t27 @t79)) @t44))) % 45.37/45.60 (define @t91 () (not @t90)) % 45.37/45.60 (define @t92 () (or @t91 @t89 @t87 @t85 @t78)) % 45.37/45.60 (define @t93 () (not @t92)) % 45.37/45.60 (define @t94 () (not @t76)) % 45.37/45.60 (define @t95 () (+ @t82 @t80)) % 45.37/45.60 (define @t96 () (tptp.add @t95 @t81)) % 45.37/45.60 (define @t97 () (tptp.in @t77 @t96)) % 45.37/45.60 (define @t98 () (not @t97)) % 45.37/45.60 (define @t99 () (or @t91 @t89 @t87 @t98 @t78)) % 45.37/45.60 (define @t100 () (not @t99)) % 45.37/45.60 (define @t101 () (@list true)) % 45.37/45.60 (define @t102 () (@list @t92)) % 45.37/45.60 (define @t103 () (= @t80 @t77)) % 45.37/45.60 (define @t104 () (= @t77 @t80)) % 45.37/45.60 (define @t105 () (not @t104)) % 45.37/45.60 (define @t106 () (tptp.in @t77 @t79)) % 45.37/45.60 (define @t107 () (and @t106 @t105)) % 45.37/45.60 (define @t108 () (tptp.in @t77 @t81)) % 45.37/45.60 (define @t109 () (= @t107 @t108)) % 45.37/45.60 (define @t110 () (and @t106 (not @t103))) % 45.37/45.60 (define @t111 () (= @t108 @t110)) % 45.37/45.60 (define @t112 () (@list false)) % 45.37/45.60 (define @t113 () (* -1 @t82)) % 45.37/45.60 (define @t114 () (+ @t113 @t77)) % 45.37/45.60 (define @t115 () (- @t80 @t114)) % 45.37/45.60 (define @t116 () (= @t80 @t114)) % 45.37/45.60 (define @t117 () (= @t77 @t83)) % 45.37/45.60 (define @t118 () (or @t108 @t117)) % 45.37/45.60 (define @t119 () (= @t118 @t84)) % 45.37/45.60 (define @t120 () (or @t108 @t116)) % 45.37/45.60 (define @t121 () (= @t84 @t120)) % 45.37/45.60 (define @t122 () (@list false false)) % 45.37/45.60 (define @t123 () (>= @t80 1)) % 45.37/45.60 (define @t124 () (or @t89 @t123)) % 45.37/45.60 (define @t125 () (not @t78)) % 45.37/45.60 (define @t126 () (not @t123)) % 45.37/45.60 (define @t127 () (not @t116)) % 45.37/45.60 (define @t128 () (* -1 @t77)) % 45.37/45.60 (define @t129 () (+ @t80 @t82 @t128)) % 45.37/45.60 (define @t130 () (= @t129 0)) % 45.37/45.60 (define @t131 () (* -1 1)) % 45.37/45.60 (define @t132 () (* -1 0)) % 45.37/45.60 (define @t133 () (+ 0 1 @t132 @t131)) % 45.37/45.60 (define @t134 () (* -1 @t80)) % 45.37/45.60 (define @t135 () (+ @t134 @t113 @t128 @t77 @t82 @t80)) % 45.37/45.60 (define @t136 () (+ @t129 @t77 @t113 @t134)) % 45.37/45.60 (define @t137 () (>= @t136 @t133)) % 45.37/45.60 (define @t138 () (and @t123 @t86 @t125 @t116)) % 45.37/45.60 (define @t139 () (@list true false)) % 45.37/45.60 (define @t140 () (not @t106)) % 45.37/45.60 (define @t141 () (or @t140 @t78)) % 45.37/45.60 (define @t142 () (not @t141)) % 45.37/45.60 (assume @p1 (forall (@list @t1) (not (tptp.in @t1 tptp.empty)))) % 45.37/45.60 (assume @p2 (forall (@list @t3 @t2) (tptp.in @t3 (tptp.add @t3 @t2)))) % 45.37/45.60 (assume @p3 (forall (@list @t5 @t4) (not (tptp.in @t5 (tptp.remove @t5 @t4))))) % 45.37/45.60 (assume @p4 @t9) % 45.37/45.60 (assume @p5 @t13) % 45.37/45.60 (assume @p6 @t36) % 45.37/45.60 (assume @p7 true) % 45.37/45.60 (step @p8 :rule aci_norm :args ((= (or @t46 @t43 @t42 false @t41 @t38) @t47))) % 45.37/45.60 (step @p9 :rule refl :args (@t38)) % 45.37/45.60 (step @p10 :rule refl :args (@t41)) % 45.37/45.60 (step @p11 :rule evaluate :args ((not true))) % 45.37/45.60 (step @p12 :rule eq-refl :args (@t40)) % 45.37/45.60 (step @p13 :rule cong :premises (@p12) :args (@t48)) % 45.37/45.60 (step @p14 :rule trans :premises (@p13 @p11)) % 45.37/45.60 (step @p15 :rule refl :args (@t42)) % 45.37/45.60 (step @p16 :rule refl :args (@t43)) % 45.37/45.60 (step @p17 :rule refl :args (@t46)) % 45.37/45.60 (step @p18 :rule nary_cong :premises (@p17 @p16 @p15 @p14 @p10 @p9) :args (@t49)) % 45.37/45.60 (step @p19 :rule trans :premises (@p18 @p8)) % 45.37/45.60 (step @p20 :rule cong :premises (@p19) :args ((forall @t50 @t49))) % 45.37/45.60 (step @p21 :rule quant-var-elim-eq :args ((= (forall @t55 @t54) @t49))) % 45.37/45.60 (step @p22 :rule aci_norm :args ((= @t56 @t54))) % 45.37/45.60 (step @p23 :rule cong :premises (@p22) :args (@t57)) % 45.37/45.60 (step @p24 :rule trans :premises (@p23 @p21)) % 45.37/45.60 (step @p25 :rule cong :premises (@p24) :args (@t58)) % 45.37/45.60 (step @p26 :rule quant-merge-prenex :args ((= @t58 @t59))) % 45.37/45.60 (step @p27 :rule symm :premises (@p26)) % 45.37/45.60 (step @p28 :rule quant_var_reordering :args ((= (forall @t60 @t56) @t59))) % 45.37/45.60 (step @p29 :rule trans :premises (@p28 @p27 @p25)) % 45.37/45.60 (step @p30 :rule trans :premises (@p29 @p20)) % 45.37/45.60 (step @p31 :rule aci_norm :args ((= @t62 @t56))) % 45.37/45.60 (step @p32 :rule cong :premises (@p31) :args (@t63)) % 45.37/45.60 (step @p33 :rule trans :premises (@p32 @p30)) % 45.37/45.60 (step @p34 :rule quant-merge-prenex :args ((= (forall @t34 @t65) @t63))) % 45.37/45.60 (step @p35 :rule alpha_equiv :args (@t66 (@list @t37) (@list @t8))) % 45.37/45.60 (step @p36 :rule refl :args (@t53)) % 45.37/45.60 (step @p37 :rule refl :args (@t42)) % 45.37/45.60 (step @p38 :rule refl :args (@t43)) % 45.37/45.60 (step @p39 :rule refl :args (@t46)) % 45.37/45.60 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37 @p36 @p35) :args (@t67)) % 45.37/45.60 (step @p41 :rule quant-miniscope-or :args ((= @t65 @t67))) % 45.37/45.60 (step @p42 :rule trans :premises (@p41 @p40)) % 45.37/45.60 (step @p43 :rule symm :premises (@p42)) % 45.37/45.60 (step @p44 :rule cong :premises (@p43) :args ((forall @t34 @t70))) % 45.37/45.60 (step @p45 :rule trans :premises (@p44 @p34)) % 45.37/45.60 (step @p46 :rule trans :premises (@p45 @p33)) % 45.37/45.60 (step @p47 :rule aci_norm :args ((= (or @t71 @t69) @t70))) % 45.37/45.60 (step @p48 :rule refl :args (@t69)) % 45.37/45.60 (step @p49 :rule aci_norm :args ((= (or @t46 (or @t43 (or @t42 @t53))) @t71))) % 45.37/45.60 (step @p50 :rule bool-and-de-morgan :args (@t25 @t52 true)) % 45.37/45.60 (step @p51 :rule nary_cong :premises (@p38 @p50) :args ((or @t43 (not (and @t25 @t52))))) % 45.37/45.60 (step @p52 :rule bool-and-de-morgan :args (@t26 @t25 (and @t52))) % 45.37/45.60 (step @p53 :rule trans :premises (@p52 @p51)) % 45.37/45.60 (step @p54 :rule nary_cong :premises (@p39 @p53) :args ((or @t46 (not (and @t26 @t25 @t52))))) % 45.37/45.60 (step @p55 :rule bool-and-de-morgan :args (@t45 @t26 (and @t25 @t52))) % 45.37/45.60 (step @p56 :rule trans :premises (@p55 @p54)) % 45.37/45.60 (step @p57 :rule trans :premises (@p56 @p49)) % 45.37/45.60 (step @p58 :rule nary_cong :premises (@p57 @p48) :args ((or (not @t72) @t69))) % 45.37/45.60 (step @p59 :rule trans :premises (@p58 @p47)) % 45.37/45.60 (step @p60 :rule bool-impl-elim :args (@t72 @t69)) % 45.37/45.60 (step @p61 :rule trans :premises (@p60 @p59)) % 45.37/45.60 (step @p62 :rule cong :premises (@p61) :args ((forall @t34 (=> @t72 @t69)))) % 45.37/45.60 (step @p63 :rule trans :premises (@p62 @p46)) % 45.37/45.60 (step @p64 :rule bool-impl-elim :args (@t15 @t68)) % 45.37/45.60 (step @p65 :rule cong :premises (@p64) :args ((forall @t17 (=> @t15 @t68)))) % 45.37/45.60 (step @p66 :rule bool-double-not-elim :args (@t68)) % 45.37/45.60 (step @p67 :rule evaluate :args (@t73)) % 45.37/45.60 (step @p68 :rule refl :args (@t8)) % 45.37/45.60 (step @p69 :rule cong :premises (@p68 @p67) :args (@t74)) % 45.37/45.60 (step @p70 :rule cong :premises (@p69) :args ((not @t74))) % 45.37/45.60 (step @p71 :rule arith-leq-norm :args (@t8 0)) % 45.37/45.60 (step @p72 :rule trans :premises (@p71 @p70)) % 45.37/45.60 (step @p73 :rule cong :premises (@p72) :args ((not (<= @t8 0)))) % 45.37/45.60 (step @p74 :rule trans :premises (@p73 @p66)) % 45.37/45.60 (step @p75 :rule arith-elim-leq :args (@t8 0)) % 45.37/45.60 (step @p76 :rule symm :premises (@p75)) % 45.37/45.60 (step @p77 :rule cong :premises (@p76) :args ((not (>= 0 @t8)))) % 45.37/45.60 (step @p78 :rule arith-elim-gt :args (@t8 0)) % 45.37/45.60 (step @p79 :rule trans :premises (@p78 @p77)) % 45.37/45.60 (step @p80 :rule trans :premises (@p79 @p74)) % 45.37/45.60 (step @p81 :rule refl :args (@t15)) % 45.37/45.60 (step @p82 :rule cong :premises (@p81 @p80) :args (@t16)) % 45.37/45.60 (step @p83 :rule cong :premises (@p82) :args (@t18)) % 45.37/45.60 (step @p84 :rule trans :premises (@p83 @p65)) % 45.37/45.60 (step @p85 :rule refl :args (@t21)) % 45.37/45.60 (step @p86 :rule arith_poly_norm :args ((= @t22 @t39))) % 45.37/45.60 (step @p87 :rule cong :premises (@p86 @p85) :args (@t23)) % 45.37/45.60 (step @p88 :rule refl :args (@t14)) % 45.37/45.60 (step @p89 :rule cong :premises (@p88 @p87) :args (@t24)) % 45.37/45.60 (step @p90 :rule refl :args (@t25)) % 45.37/45.60 (step @p91 :rule refl :args (@t26)) % 45.37/45.60 (step @p92 :rule bool-impl-elim :args (@t28 @t44)) % 45.37/45.60 (step @p93 :rule cong :premises (@p92) :args ((forall @t30 (=> @t28 @t44)))) % 45.37/45.60 (step @p94 :rule bool-double-not-elim :args (@t44)) % 45.37/45.60 (step @p95 :rule refl :args (@t27)) % 45.37/45.60 (step @p96 :rule cong :premises (@p95 @p67) :args (@t75)) % 45.37/45.60 (step @p97 :rule cong :premises (@p96) :args ((not @t75))) % 45.37/45.60 (step @p98 :rule arith-leq-norm :args (@t27 0)) % 45.37/45.60 (step @p99 :rule trans :premises (@p98 @p97)) % 45.37/45.60 (step @p100 :rule cong :premises (@p99) :args ((not (<= @t27 0)))) % 45.37/45.60 (step @p101 :rule trans :premises (@p100 @p94)) % 45.37/45.60 (step @p102 :rule arith-elim-leq :args (@t27 0)) % 45.37/45.60 (step @p103 :rule symm :premises (@p102)) % 45.37/45.60 (step @p104 :rule cong :premises (@p103) :args ((not (>= 0 @t27)))) % 45.37/45.60 (step @p105 :rule arith-elim-gt :args (@t27 0)) % 45.37/45.60 (step @p106 :rule trans :premises (@p105 @p104)) % 45.37/45.60 (step @p107 :rule trans :premises (@p106 @p101)) % 45.37/45.60 (step @p108 :rule refl :args (@t28)) % 45.37/45.60 (step @p109 :rule cong :premises (@p108 @p107) :args (@t29)) % 45.37/45.60 (step @p110 :rule cong :premises (@p109) :args (@t31)) % 45.37/45.60 (step @p111 :rule trans :premises (@p110 @p93)) % 45.37/45.60 (step @p112 :rule nary_cong :premises (@p111 @p91 @p90 @p89) :args (@t32)) % 45.37/45.60 (step @p113 :rule cong :premises (@p112 @p84) :args (@t33)) % 45.37/45.60 (step @p114 :rule cong :premises (@p113) :args (@t35)) % 45.37/45.60 (step @p115 :rule trans :premises (@p114 @p63)) % 45.37/45.60 (step @p116 :rule cong :premises (@p115) :args (@t36)) % 45.37/45.60 (step @p117 :rule eq_resolve :premises (@p6 @p116)) % 45.37/45.60 (step @p118 :rule refl :args (@t93)) % 45.37/45.60 (step @p119 :rule bool-double-not-elim :args (@t76)) % 45.37/45.60 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t94) @t93))) % 45.37/45.60 (step @p121 :rule refl :args (@t78)) % 45.37/45.60 (step @p122 :rule refl :args (@t81)) % 45.37/45.60 (step @p123 :rule arith_poly_norm :args ((= @t95 @t83))) % 45.37/45.60 (step @p124 :rule cong :premises (@p123 @p122) :args (@t96)) % 45.37/45.60 (step @p125 :rule refl :args (@t77)) % 45.37/45.60 (step @p126 :rule cong :premises (@p125 @p124) :args (@t97)) % 45.37/45.60 (step @p127 :rule cong :premises (@p126) :args (@t98)) % 45.37/45.60 (step @p128 :rule refl :args (@t87)) % 45.37/45.60 (step @p129 :rule refl :args (@t89)) % 45.37/45.60 (step @p130 :rule refl :args (@t91)) % 45.37/45.60 (step @p131 :rule nary_cong :premises (@p130 @p129 @p128 @p127 @p121) :args (@t99)) % 45.37/45.60 (step @p132 :rule cong :premises (@p131) :args (@t100)) % 45.37/45.60 (step @p133 :rule refl :args (@t94)) % 45.37/45.60 (step @p134 :rule cong :premises (@p133 @p132) :args ((=> @t94 @t100))) % 45.37/45.60 (assume-push @p295 @t94) % 45.37/45.60 (step @p136 :rule skolemize :premises (@p117)) % 45.37/45.60 (step-pop @p296 :rule scope :premises (@p136)) % 45.37/45.60 (step @p137 :rule process_scope :premises (@p296) :args (@t100)) % 45.37/45.60 (step @p139 :rule eq_resolve :premises (@p137 @p134)) % 45.37/45.60 (step @p140 :rule implies_elim :premises (@p139)) % 45.37/45.60 (step @p141 :rule eq_resolve :premises (@p140 @p120)) % 45.37/45.60 (step @p142 :rule chain_m_resolution :premises (@p141 @p117) :args (@t93 @t101 (@list @t76))) % 45.37/45.60 (step @p143 :rule bool-double-not-elim :args (@t90)) % 45.37/45.60 (step @p144 :rule refl :args (@t92)) % 45.37/45.60 (step @p145 :rule nary_cong :premises (@p144 @p143) :args ((or @t92 (not @t91)))) % 45.37/45.60 (step @p146 :rule cnf_or_neg :args (@t92 0)) % 45.37/45.60 (step @p147 :rule eq_resolve :premises (@p146 @p145)) % 45.37/45.60 (step @p148 :rule reordering :premises (@p147) :args ((or @t90 @t92))) % 45.37/45.60 (step @p149 :rule chain_m_resolution :premises (@p148 @p142) :args (@t90 @t101 @t102)) % 45.37/45.60 (step @p150 :rule arith_poly_norm :args ((= (* 1 (- @t77 @t80)) (* -1 (- @t80 @t77))))) % 45.37/45.60 (step @p151 :rule arith_poly_norm_rel :premises (@p150) :args ((= @t104 @t103))) % 45.37/45.60 (step @p152 :rule cong :premises (@p151) :args (@t105)) % 45.37/45.60 (step @p153 :rule refl :args (@t106)) % 45.37/45.60 (step @p154 :rule nary_cong :premises (@p153 @p152) :args (@t107)) % 45.37/45.60 (step @p155 :rule refl :args (@t108)) % 45.37/45.60 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t108 @t107))) % 45.37/45.60 (step @p157 :rule eq-symm :args (@t107 @t108)) % 45.37/45.60 (step @p158 :rule trans :premises (@p157 @p156)) % 45.37/45.60 (step @p159 :rule refl :args (@t13)) % 45.37/45.60 (step @p160 :rule cong :premises (@p159 @p158) :args ((=> @t13 @t109))) % 45.37/45.60 (assume-push @p297 @t13) % 45.37/45.60 (step @p162 :rule instantiate :premises (@p5) :args ((@list @t77 @t79 @t80))) % 45.37/45.60 (step-pop @p298 :rule scope :premises (@p162)) % 45.37/45.60 (step @p163 :rule process_scope :premises (@p298) :args (@t109)) % 45.37/45.60 (step @p165 :rule eq_resolve :premises (@p163 @p160)) % 45.37/45.60 (step @p166 :rule implies_elim :premises (@p165)) % 45.37/45.60 (step @p167 :rule chain_m_resolution :premises (@p166 @p5) :args (@t111 @t112 (@list @t13))) % 45.37/45.60 (step @p168 :rule arith_poly_norm :args ((= (* 1 (- @t77 @t83)) (* -1 @t115)))) % 45.37/45.60 (step @p169 :rule arith_poly_norm_rel :premises (@p168) :args ((= @t117 @t116))) % 45.37/45.60 (step @p170 :rule nary_cong :premises (@p155 @p169) :args (@t118)) % 45.37/45.60 (step @p171 :rule refl :args (@t84)) % 45.37/45.60 (step @p172 :rule cong :premises (@p171 @p170) :args ((= @t84 @t118))) % 45.37/45.60 (step @p173 :rule eq-symm :args (@t118 @t84)) % 45.37/45.60 (step @p174 :rule trans :premises (@p173 @p172)) % 45.37/45.60 (step @p175 :rule refl :args (@t9)) % 45.37/45.60 (step @p176 :rule cong :premises (@p175 @p174) :args ((=> @t9 @t119))) % 45.37/45.60 (assume-push @p299 @t9) % 45.37/45.60 (step @p178 :rule instantiate :premises (@p4) :args ((@list @t77 @t81 @t83))) % 45.37/45.60 (step-pop @p300 :rule scope :premises (@p178)) % 45.37/45.60 (step @p179 :rule process_scope :premises (@p300) :args (@t119)) % 45.37/45.60 (step @p181 :rule eq_resolve :premises (@p179 @p176)) % 45.37/45.60 (step @p182 :rule implies_elim :premises (@p181)) % 45.37/45.60 (step @p183 :rule chain_m_resolution :premises (@p182 @p4) :args (@t121 @t112 (@list @t9))) % 45.37/45.60 (step @p184 :rule bool-double-not-elim :args (@t84)) % 45.37/45.60 (step @p185 :rule nary_cong :premises (@p144 @p184) :args ((or @t92 (not @t85)))) % 45.37/45.60 (step @p186 :rule cnf_or_neg :args (@t92 3)) % 45.37/45.60 (step @p187 :rule eq_resolve :premises (@p186 @p185)) % 45.37/45.60 (step @p188 :rule reordering :premises (@p187) :args ((or @t84 @t92))) % 45.37/45.60 (step @p189 :rule chain_m_resolution :premises (@p188 @p142) :args (@t84 @t101 @t102)) % 45.37/45.60 (step @p190 :rule cnf_equiv_pos1 :args (@t121)) % 45.37/45.60 (step @p191 :rule reordering :premises (@p190) :args ((or @t85 @t120 (not @t121)))) % 45.37/45.60 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p183) :args (@t120 @t122 (@list @t84 @t121))) % 45.37/45.60 (step @p193 :rule instantiate :premises (@p149) :args ((@list @t80))) % 45.37/45.60 (step @p194 :rule bool-double-not-elim :args (@t88)) % 45.37/45.60 (step @p195 :rule nary_cong :premises (@p144 @p194) :args ((or @t92 (not @t89)))) % 45.37/45.60 (step @p196 :rule cnf_or_neg :args (@t92 1)) % 45.37/45.60 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 45.37/45.60 (step @p198 :rule reordering :premises (@p197) :args ((or @t88 @t92))) % 45.37/45.60 (step @p199 :rule chain_m_resolution :premises (@p198 @p142) :args (@t88 @t101 @t102)) % 45.37/45.60 (step @p200 :rule cnf_or_pos :args (@t124)) % 45.37/45.60 (step @p201 :rule reordering :premises (@p200) :args ((or @t89 @t123 (not @t124)))) % 45.37/45.60 (step @p202 :rule chain_m_resolution :premises (@p201 @p199 @p193) :args (@t123 @t122 (@list @t88 @t124))) % 45.37/45.60 (step @p203 :rule cnf_or_neg :args (@t92 4)) % 45.37/45.60 (step @p204 :rule chain_m_resolution :premises (@p203 @p142) :args (@t125 @t101 @t102)) % 45.37/45.60 (step @p205 :rule bool-double-not-elim :args (@t86)) % 45.37/45.60 (step @p206 :rule nary_cong :premises (@p144 @p205) :args ((or @t92 (not @t87)))) % 45.37/45.60 (step @p207 :rule cnf_or_neg :args (@t92 2)) % 45.37/45.60 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 45.37/45.60 (step @p209 :rule reordering :premises (@p208) :args ((or @t86 @t92))) % 45.37/45.60 (step @p210 :rule chain_m_resolution :premises (@p209 @p142) :args (@t86 @t101 @t102)) % 45.37/45.60 (step @p211 :rule refl :args (@t126)) % 45.37/45.60 (step @p212 :rule refl :args (@t127)) % 45.37/45.60 (step @p213 :rule bool-double-not-elim :args (@t78)) % 45.37/45.60 (step @p214 :rule nary_cong :premises (@p128 @p213 @p212 @p211) :args ((or @t87 (not @t125) @t127 @t126))) % 45.37/45.60 (assume-push @p301 @t123) % 45.37/45.60 (assume-push @p302 @t86) % 45.37/45.60 (assume-push @p303 @t125) % 45.37/45.60 (assume-push @p304 @t116) % 45.37/45.60 (assume-push @p305 @t130) % 45.37/45.60 (step @p220 :rule evaluate :args ((>= 0 0))) % 45.37/45.60 (step @p221 :rule evaluate :args ((+ 0 1 0 -1))) % 45.37/45.60 (step @p222 :rule evaluate :args (@t131)) % 45.37/45.60 (step @p223 :rule evaluate :args (@t132)) % 45.37/45.60 (step @p224 :rule refl :args (1)) % 45.37/45.60 (step @p225 :rule refl :args (0)) % 45.37/45.60 (step @p226 :rule nary_cong :premises (@p225 @p224 @p223 @p222) :args (@t133)) % 45.37/45.60 (step @p227 :rule trans :premises (@p226 @p221)) % 45.37/45.60 (step @p228 :rule arith_poly_norm :args ((= @t135 0))) % 45.37/45.60 (step @p229 :rule arith_poly_norm :args ((= @t136 @t135))) % 45.37/45.60 (step @p230 :rule trans :premises (@p229 @p228)) % 45.37/45.60 (step @p231 :rule cong :premises (@p230 @p227) :args (@t137)) % 45.37/45.60 (step @p232 :rule trans :premises (@p231 @p220)) % 45.37/45.60 (step @p233 :rule cong :premises (@p232) :args ((not @t137))) % 45.37/45.60 (step @p234 :rule trans :premises (@p233 @p11)) % 45.37/45.60 (step @p235 :rule arith-elim-lt :args (@t136 @t133)) % 45.37/45.60 (step @p236 :rule trans :premises (@p235 @p234)) % 45.37/45.60 (step @p237 :rule arith_mult_neg :args (-1 @t123)) % 45.37/45.60 (step @p238 :rule evaluate :args ((< -1 0))) % 45.37/45.60 (step @p239 :rule true_elim :premises (@p238)) % 45.37/45.60 (step @p240 :rule and_intro :premises (@p239 @p202)) % 45.37/45.60 (step @p241 :rule modus_ponens :premises (@p240 @p237)) % 45.37/45.60 (step @p242 :rule arith_mult_neg :args (-1 @t86)) % 45.37/45.60 (step @p243 :rule and_intro :premises (@p239 @p210)) % 45.37/45.60 (step @p244 :rule modus_ponens :premises (@p243 @p242)) % 45.37/45.60 (step @p245 :rule arith-elim-lt :args (@t77 1)) % 45.37/45.60 (step @p246 :rule symm :premises (@p245)) % 45.37/45.60 (step @p247 :rule eq_resolve :premises (@p204 @p246)) % 45.37/45.60 (step @p248 :rule arith_sum_ub :premises (@p305 @p247 @p244 @p241)) % 45.37/45.60 (step @p249 false :rule eq_resolve :premises (@p248 @p236)) % 45.37/45.60 (step-pop @p306 :rule scope :premises (@p249)) % 45.37/45.60 (step @p250 :rule process_scope :premises (@p306) :args (false)) % 45.37/45.60 (step @p252 :rule arith_poly_norm :args ((= (* 1 (- @t129 0)) (* 1 @t115)))) % 45.37/45.60 (step @p253 :rule arith_poly_norm_rel :premises (@p252) :args ((= @t130 @t116))) % 45.37/45.60 (step @p254 :rule symm :premises (@p253)) % 45.37/45.60 (step @p255 :rule eq_resolve :premises (@p304 @p254)) % 45.37/45.60 (step @p256 false :rule contra :premises (@p255 @p250)) % 45.37/45.60 (step-pop @p307 :rule scope :premises (@p256)) % 45.37/45.60 (step-pop @p308 :rule scope :premises (@p307)) % 45.37/45.60 (step-pop @p309 :rule scope :premises (@p308)) % 45.37/45.60 (step-pop @p310 :rule scope :premises (@p309)) % 45.37/45.60 (step @p257 :rule process_scope :premises (@p310) :args (false)) % 45.37/45.60 (assume-push @p311 @t86) % 45.37/45.60 (assume-push @p312 @t125) % 45.37/45.60 (assume-push @p313 @t116) % 45.37/45.60 (assume-push @p314 @t123) % 45.37/45.60 (step @p266 :rule and_intro :premises (@p202 @p210 @p204 @p313)) % 45.37/45.60 (step-pop @p315 :rule scope :premises (@p266)) % 45.37/45.60 (step-pop @p316 :rule scope :premises (@p315)) % 45.37/45.60 (step-pop @p317 :rule scope :premises (@p316)) % 45.37/45.60 (step-pop @p318 :rule scope :premises (@p317)) % 45.37/45.60 (step @p267 :rule process_scope :premises (@p318) :args (@t138)) % 45.37/45.60 (step @p272 :rule implies_elim :premises (@p267)) % 45.37/45.60 (step @p273 :rule resolution :premises (@p272 @p257) :args (true @t138)) % 45.37/45.60 (step @p274 :rule not_and :premises (@p273)) % 45.37/45.60 (step @p275 :rule eq_resolve :premises (@p274 @p214)) % 45.37/45.60 (step @p276 :rule chain_m_resolution :premises (@p275 @p210 @p204 @p202) :args (@t127 (@list false true false) (@list @t86 @t78 @t123))) % 45.37/45.60 (step @p277 :rule cnf_or_pos :args (@t120)) % 45.37/45.60 (step @p278 :rule reordering :premises (@p277) :args ((or @t108 @t116 (not @t120)))) % 45.37/45.60 (step @p279 :rule chain_m_resolution :premises (@p278 @p276 @p192) :args (@t108 @t139 (@list @t116 @t120))) % 45.37/45.60 (step @p280 :rule cnf_equiv_pos1 :args (@t111)) % 45.37/45.60 (step @p281 :rule reordering :premises (@p280) :args ((or (not @t108) @t110 (not @t111)))) % 45.37/45.60 (step @p282 :rule chain_m_resolution :premises (@p281 @p279 @p167) :args (@t110 @t122 (@list @t108 @t111))) % 45.37/45.60 (step @p283 :rule cnf_and_pos :args (@t110 0)) % 45.37/45.60 (step @p284 :rule reordering :premises (@p283) :args ((or @t106 (not @t110)))) % 45.37/45.60 (step @p285 :rule chain_m_resolution :premises (@p284 @p282) :args (@t106 @t112 (@list @t110))) % 45.37/45.60 (step @p286 :rule cnf_or_pos :args (@t141)) % 45.37/45.60 (step @p287 :rule reordering :premises (@p286) :args ((or @t78 @t140 @t142))) % 45.37/45.60 (step @p288 :rule chain_m_resolution :premises (@p287 @p204 @p285) :args (@t142 @t139 (@list @t78 @t106))) % 45.37/45.60 (assume-push @p319 @t90) % 45.37/45.60 (step @p290 :rule instantiate :premises (@p149) :args ((@list @t77))) % 45.37/45.60 (step-pop @p320 :rule scope :premises (@p290)) % 45.37/45.60 (step @p291 :rule process_scope :premises (@p320) :args (@t141)) % 45.37/45.60 (step @p293 :rule implies_elim :premises (@p291)) % 45.37/45.60 (step @p294 false :rule chain_m_resolution :premises (@p293 @p288 @p149) :args (false @t139 (@list @t141 @t90))) % 45.37/45.60 ) % 45.37/45.60 % SZS output end Proof % 45.37/45.60 % cvc5 exiting %------------------------------------------------------------------------------