%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU745^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:53:00 AM UTC 2026 % Result : Theorem 0.40s 0.62s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU745^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n001.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:51:05 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.52 %----Proving TH0 % 0.40/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.62 % SZS status Theorem % 0.40/0.62 % SZS output start Proof % 0.40/0.62 ( % 0.40/0.62 (declare-sort $$unsorted 0) % 0.40/0.62 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.62 (declare-const tptp.inComplementUnionImpNotIn1 Bool) % 0.40/0.62 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.62 (declare-const tptp.setminusI Bool) % 0.40/0.62 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.62 (declare-const tptp.setminus (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.62 (define @t1 () (@var "B" $$unsorted)) % 0.40/0.62 (define @t2 () (@var "A" $$unsorted)) % 0.40/0.62 (define @t3 () (_ tptp.setminus @t2)) % 0.40/0.62 (define @t4 () (_ @t3 @t1)) % 0.40/0.62 (define @t5 () (@var "Xx" $$unsorted)) % 0.40/0.62 (define @t6 () (_ tptp.in @t5)) % 0.40/0.62 (define @t7 () (_ @t6 @t4)) % 0.40/0.62 (define @t8 () (_ @t6 @t1)) % 0.40/0.62 (define @t9 () (not @t8)) % 0.40/0.62 (define @t10 () (=> @t9 @t7)) % 0.40/0.62 (define @t11 () (_ @t6 @t2)) % 0.40/0.62 (define @t12 () (@list @t2 @t1 @t5)) % 0.40/0.62 (define @t13 () (forall @t12 (=> @t11 @t10))) % 0.40/0.62 (define @t14 () (= tptp.setminusI @t13)) % 0.40/0.62 (define @t15 () (@var "X" $$unsorted)) % 0.40/0.62 (define @t16 () (_ @t6 @t15)) % 0.40/0.62 (define @t17 () (not @t16)) % 0.40/0.62 (define @t18 () (@var "Y" $$unsorted)) % 0.40/0.62 (define @t19 () (_ (_ tptp.binunion @t15) @t18)) % 0.40/0.62 (define @t20 () (_ @t3 @t19)) % 0.40/0.62 (define @t21 () (_ @t6 @t20)) % 0.40/0.62 (define @t22 () (=> @t21 @t17)) % 0.40/0.62 (define @t23 () (@list @t5)) % 0.40/0.62 (define @t24 () (forall @t23 (=> @t11 @t22))) % 0.40/0.62 (define @t25 () (_ tptp.powerset @t2)) % 0.40/0.62 (define @t26 () (_ tptp.in @t18)) % 0.40/0.62 (define @t27 () (_ @t26 @t25)) % 0.40/0.62 (define @t28 () (=> @t27 @t24)) % 0.40/0.62 (define @t29 () (@list @t18)) % 0.40/0.62 (define @t30 () (forall @t29 @t28)) % 0.40/0.62 (define @t31 () (_ tptp.in @t15)) % 0.40/0.62 (define @t32 () (_ @t31 @t25)) % 0.40/0.62 (define @t33 () (=> @t32 @t30)) % 0.40/0.62 (define @t34 () (@list @t2 @t15)) % 0.40/0.62 (define @t35 () (forall @t34 @t33)) % 0.40/0.62 (define @t36 () (= tptp.inComplementUnionImpNotIn1 @t35)) % 0.40/0.62 (define @t37 () (_ @t3 @t15)) % 0.40/0.62 (define @t38 () (_ @t6 @t37)) % 0.40/0.62 (define @t39 () (=> @t21 @t38)) % 0.40/0.62 (define @t40 () (forall @t23 (=> @t11 @t39))) % 0.40/0.62 (define @t41 () (=> @t27 @t40)) % 0.40/0.62 (define @t42 () (forall @t29 @t41)) % 0.40/0.62 (define @t43 () (=> @t32 @t42)) % 0.40/0.62 (define @t44 () (forall @t34 @t43)) % 0.40/0.62 (define @t45 () (=> tptp.inComplementUnionImpNotIn1 @t44)) % 0.40/0.62 (define @t46 () (=> tptp.setminusI @t45)) % 0.40/0.62 (define @t47 () (not @t46)) % 0.40/0.62 (define @t48 () (tptp.setminus @t2 @t15)) % 0.40/0.62 (define @t49 () (@var "BOUND_VARIABLE_7587" $$unsorted)) % 0.40/0.62 (define @t50 () (tptp.in @t49 @t48)) % 0.40/0.62 (define @t51 () (@var "BOUND_VARIABLE_7585" $$unsorted)) % 0.40/0.62 (define @t52 () (not (tptp.in @t49 (tptp.setminus @t2 (tptp.binunion @t15 @t51))))) % 0.40/0.62 (define @t53 () (not (tptp.in @t49 @t2))) % 0.40/0.62 (define @t54 () (tptp.powerset @t2)) % 0.40/0.62 (define @t55 () (not (tptp.in @t51 @t54))) % 0.40/0.62 (define @t56 () (tptp.in @t15 @t54)) % 0.40/0.62 (define @t57 () (not @t56)) % 0.40/0.62 (define @t58 () (or @t57 @t55 @t53 @t52 @t50)) % 0.40/0.62 (define @t59 () (@list @t2 @t15 @t51 @t49)) % 0.40/0.62 (define @t60 () (forall @t59 @t58)) % 0.40/0.62 (define @t61 () (@var "BOUND_VARIABLE_7532" $$unsorted)) % 0.40/0.62 (define @t62 () (not (tptp.in @t61 @t15))) % 0.40/0.62 (define @t63 () (@var "BOUND_VARIABLE_7530" $$unsorted)) % 0.40/0.62 (define @t64 () (not (tptp.in @t61 (tptp.setminus @t2 (tptp.binunion @t15 @t63))))) % 0.40/0.62 (define @t65 () (not (tptp.in @t61 @t2))) % 0.40/0.62 (define @t66 () (not (tptp.in @t63 @t54))) % 0.40/0.62 (define @t67 () (or @t66 @t65 @t64 @t62)) % 0.40/0.62 (define @t68 () (or @t57 @t67)) % 0.40/0.62 (define @t69 () (forall (@list @t2 @t15 @t63 @t61) @t68)) % 0.40/0.62 (define @t70 () (@list @t63 @t61)) % 0.40/0.62 (define @t71 () (forall @t70 @t68)) % 0.40/0.62 (define @t72 () (forall @t70 @t67)) % 0.40/0.62 (define @t73 () (@var "BOUND_VARIABLE_7506" $$unsorted)) % 0.40/0.62 (define @t74 () (or @t57 @t72)) % 0.40/0.62 (define @t75 () (not (tptp.in @t73 @t15))) % 0.40/0.62 (define @t76 () (tptp.binunion @t15 @t18)) % 0.40/0.62 (define @t77 () (tptp.setminus @t2 @t76)) % 0.40/0.62 (define @t78 () (not (tptp.in @t73 @t77))) % 0.40/0.62 (define @t79 () (not (tptp.in @t73 @t2))) % 0.40/0.62 (define @t80 () (tptp.in @t18 @t54)) % 0.40/0.62 (define @t81 () (not @t80)) % 0.40/0.62 (define @t82 () (or @t81 @t79 @t78 @t75)) % 0.40/0.62 (define @t83 () (@list @t18 @t73)) % 0.40/0.62 (define @t84 () (forall @t83 @t82)) % 0.40/0.62 (define @t85 () (not @t32)) % 0.40/0.62 (define @t86 () (or @t85 @t84)) % 0.40/0.62 (define @t87 () (or @t79 @t78 @t75)) % 0.40/0.62 (define @t88 () (or @t81 @t87)) % 0.40/0.62 (define @t89 () (forall @t83 @t88)) % 0.40/0.62 (define @t90 () (@list @t73)) % 0.40/0.62 (define @t91 () (forall @t90 @t88)) % 0.40/0.62 (define @t92 () (forall @t90 @t87)) % 0.40/0.62 (define @t93 () (@list @t5)) % 0.40/0.62 (define @t94 () (or @t81 @t92)) % 0.40/0.62 (define @t95 () (tptp.in @t5 @t15)) % 0.40/0.62 (define @t96 () (tptp.in @t5 @t77)) % 0.40/0.62 (define @t97 () (not @t96)) % 0.40/0.62 (define @t98 () (tptp.in @t5 @t2)) % 0.40/0.62 (define @t99 () (not @t98)) % 0.40/0.62 (define @t100 () (forall @t23 (or @t99 @t97 (not @t95)))) % 0.40/0.62 (define @t101 () (not @t27)) % 0.40/0.62 (define @t102 () (or @t101 @t100)) % 0.40/0.62 (define @t103 () (not @t21)) % 0.40/0.62 (define @t104 () (not @t11)) % 0.40/0.62 (define @t105 () (or @t104 @t103 @t17)) % 0.40/0.62 (define @t106 () (=> tptp.inComplementUnionImpNotIn1 @t60)) % 0.40/0.62 (define @t107 () (tptp.setminus @t2 @t1)) % 0.40/0.62 (define @t108 () (tptp.in @t5 @t107)) % 0.40/0.62 (define @t109 () (tptp.in @t5 @t1)) % 0.40/0.62 (define @t110 () (or @t104 @t8 @t7)) % 0.40/0.62 (define @t111 () (=> tptp.setminusI @t106)) % 0.40/0.62 (define @t112 () (or @t55 @t53 @t52 @t50)) % 0.40/0.62 (define @t113 () (or @t57 @t112)) % 0.40/0.62 (define @t114 () (forall @t59 @t113)) % 0.40/0.62 (define @t115 () (@list @t51 @t49)) % 0.40/0.62 (define @t116 () (forall @t115 @t113)) % 0.40/0.62 (define @t117 () (forall @t115 @t112)) % 0.40/0.62 (define @t118 () (@var "BOUND_VARIABLE_7566" $$unsorted)) % 0.40/0.62 (define @t119 () (or @t57 @t117)) % 0.40/0.62 (define @t120 () (tptp.in @t118 @t48)) % 0.40/0.62 (define @t121 () (not (tptp.in @t118 @t77))) % 0.40/0.62 (define @t122 () (not (tptp.in @t118 @t2))) % 0.40/0.62 (define @t123 () (or @t81 @t122 @t121 @t120)) % 0.40/0.62 (define @t124 () (@list @t18 @t118)) % 0.40/0.62 (define @t125 () (forall @t124 @t123)) % 0.40/0.62 (define @t126 () (or @t85 @t125)) % 0.40/0.62 (define @t127 () (or @t122 @t121 @t120)) % 0.40/0.62 (define @t128 () (or @t81 @t127)) % 0.40/0.62 (define @t129 () (forall @t124 @t128)) % 0.40/0.62 (define @t130 () (@list @t118)) % 0.40/0.62 (define @t131 () (forall @t130 @t128)) % 0.40/0.62 (define @t132 () (forall @t130 @t127)) % 0.40/0.62 (define @t133 () (or @t81 @t132)) % 0.40/0.62 (define @t134 () (tptp.in @t5 @t48)) % 0.40/0.62 (define @t135 () (forall @t23 (or @t99 @t97 @t134))) % 0.40/0.62 (define @t136 () (or @t101 @t135)) % 0.40/0.62 (define @t137 () (or @t104 @t103 @t38)) % 0.40/0.62 (define @t138 () (@quantifiers_skolemize @t60 0)) % 0.40/0.62 (define @t139 () (tptp.powerset @t138)) % 0.40/0.62 (define @t140 () (@quantifiers_skolemize @t60 1)) % 0.40/0.62 (define @t141 () (tptp.in @t140 @t139)) % 0.40/0.62 (define @t142 () (@quantifiers_skolemize @t60 3)) % 0.40/0.62 (define @t143 () (tptp.in @t142 (tptp.setminus @t138 @t140))) % 0.40/0.62 (define @t144 () (@quantifiers_skolemize @t60 2)) % 0.40/0.62 (define @t145 () (tptp.in @t142 (tptp.setminus @t138 (tptp.binunion @t140 @t144)))) % 0.40/0.62 (define @t146 () (not @t145)) % 0.40/0.62 (define @t147 () (tptp.in @t142 @t138)) % 0.40/0.62 (define @t148 () (not @t147)) % 0.40/0.62 (define @t149 () (tptp.in @t144 @t139)) % 0.40/0.62 (define @t150 () (not @t149)) % 0.40/0.62 (define @t151 () (not @t141)) % 0.40/0.62 (define @t152 () (or @t151 @t150 @t148 @t146 @t143)) % 0.40/0.62 (define @t153 () (@list true)) % 0.40/0.62 (define @t154 () (@list @t152)) % 0.40/0.62 (define @t155 () (tptp.in @t142 @t140)) % 0.40/0.62 (define @t156 () (or @t148 @t155 @t143)) % 0.40/0.62 (define @t157 () (not @t155)) % 0.40/0.62 (define @t158 () (or @t151 @t150 @t148 @t146 @t157)) % 0.40/0.62 (assume @p1 @t14) % 0.40/0.62 (assume @p2 @t36) % 0.40/0.62 (assume @p3 @t47) % 0.40/0.62 (assume @p4 true) % 0.40/0.62 (step @p5 :rule refl :args (@t60)) % 0.40/0.62 (step @p6 :rule aci_norm :args ((= @t68 (or @t57 @t66 @t65 @t64 @t62)))) % 0.40/0.62 (step @p7 :rule cong :premises (@p6) :args (@t69)) % 0.40/0.62 (step @p8 :rule quant-merge-prenex :args ((= (forall @t34 @t71) @t69))) % 0.40/0.62 (step @p9 :rule alpha_equiv :args (@t72 (@list @t63 @t61) (@list @t18 @t73))) % 0.40/0.62 (step @p10 :rule refl :args (@t57)) % 0.40/0.62 (step @p11 :rule nary_cong :premises (@p10 @p9) :args (@t74)) % 0.40/0.62 (step @p12 :rule quant-miniscope-or :args ((= @t71 @t74))) % 0.40/0.62 (step @p13 :rule trans :premises (@p12 @p11)) % 0.40/0.62 (step @p14 :rule symm :premises (@p13)) % 0.40/0.62 (step @p15 :rule cong :premises (@p14) :args ((forall @t34 (or @t57 @t84)))) % 0.40/0.62 (step @p16 :rule trans :premises (@p15 @p8)) % 0.40/0.62 (step @p17 :rule trans :premises (@p16 @p7)) % 0.40/0.62 (step @p18 :rule refl :args (@t84)) % 0.40/0.62 (step @p19 :rule refl :args ((tptp.in @t15 @t25))) % 0.40/0.62 (step @p20 :rule refl :args (@t54)) % 0.40/0.62 (step @p21 :rule refl :args (@t15)) % 0.40/0.62 (step @p22 :rule cong :premises (@p21 @p20) :args (@t56)) % 0.40/0.62 (step @p23 :rule trans :premises (@p22 @p19)) % 0.40/0.62 (step @p24 :rule refl :args (@t31)) % 0.40/0.62 (step @p25 :rule ho_cong :premises (@p24 @p20)) % 0.40/0.62 (step @p26 :rule cong :premises (@p25 @p23) :args ((= (_ @t31 @t54) @t56))) % 0.40/0.62 (step @p27 :rule symm :premises (@p26)) % 0.40/0.62 (step @p28 :rule refl :args (@t32)) % 0.40/0.62 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 0.40/0.62 (step @p30 :rule refl :args (@t25)) % 0.40/0.62 (step @p31 :rule cong :premises (@p30 @p20) :args ((= @t25 @t54))) % 0.40/0.62 (step @p32 :rule symm :premises (@p31)) % 0.40/0.62 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.40/0.62 (step @p34 :rule ho_cong :premises (@p24 @p33)) % 0.40/0.62 (step @p35 :rule trans :premises (@p34 @p29)) % 0.40/0.62 (step @p36 :rule cong :premises (@p35) :args (@t85)) % 0.40/0.62 (step @p37 :rule nary_cong :premises (@p36 @p18) :args (@t86)) % 0.40/0.62 (step @p38 :rule cong :premises (@p37) :args ((forall @t34 @t86))) % 0.40/0.62 (step @p39 :rule trans :premises (@p38 @p17)) % 0.40/0.62 (step @p40 :rule bool-impl-elim :args (@t32 @t84)) % 0.40/0.62 (step @p41 :rule cong :premises (@p40) :args ((forall @t34 (=> @t32 @t84)))) % 0.40/0.62 (step @p42 :rule trans :premises (@p41 @p39)) % 0.40/0.62 (step @p43 :rule aci_norm :args ((= @t88 @t82))) % 0.40/0.62 (step @p44 :rule cong :premises (@p43) :args (@t89)) % 0.40/0.62 (step @p45 :rule quant-merge-prenex :args ((= (forall @t29 @t91) @t89))) % 0.40/0.62 (step @p46 :rule alpha_equiv :args (@t92 (@list @t73) @t93)) % 0.40/0.62 (step @p47 :rule refl :args (@t81)) % 0.40/0.62 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t94)) % 0.40/0.62 (step @p49 :rule quant-miniscope-or :args ((= @t91 @t94))) % 0.40/0.62 (step @p50 :rule trans :premises (@p49 @p48)) % 0.40/0.62 (step @p51 :rule symm :premises (@p50)) % 0.40/0.62 (step @p52 :rule cong :premises (@p51) :args ((forall @t29 (or @t81 @t100)))) % 0.40/0.62 (step @p53 :rule trans :premises (@p52 @p45)) % 0.40/0.62 (step @p54 :rule trans :premises (@p53 @p44)) % 0.40/0.62 (step @p55 :rule refl :args (@t100)) % 0.40/0.62 (step @p56 :rule refl :args ((tptp.in @t18 @t25))) % 0.40/0.62 (step @p57 :rule refl :args (@t18)) % 0.40/0.62 (step @p58 :rule cong :premises (@p57 @p20) :args (@t80)) % 0.40/0.62 (step @p59 :rule trans :premises (@p58 @p56)) % 0.40/0.62 (step @p60 :rule refl :args (@t26)) % 0.40/0.62 (step @p61 :rule ho_cong :premises (@p60 @p20)) % 0.40/0.62 (step @p62 :rule cong :premises (@p61 @p59) :args ((= (_ @t26 @t54) @t80))) % 0.40/0.62 (step @p63 :rule symm :premises (@p62)) % 0.40/0.62 (step @p64 :rule refl :args (@t27)) % 0.40/0.62 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 0.40/0.62 (step @p66 :rule ho_cong :premises (@p60 @p33)) % 0.40/0.62 (step @p67 :rule trans :premises (@p66 @p65)) % 0.40/0.62 (step @p68 :rule cong :premises (@p67) :args (@t101)) % 0.40/0.62 (step @p69 :rule nary_cong :premises (@p68 @p55) :args (@t102)) % 0.40/0.62 (step @p70 :rule cong :premises (@p69) :args ((forall @t29 @t102))) % 0.40/0.62 (step @p71 :rule trans :premises (@p70 @p54)) % 0.40/0.62 (step @p72 :rule bool-impl-elim :args (@t27 @t100)) % 0.40/0.62 (step @p73 :rule cong :premises (@p72) :args ((forall @t29 (=> @t27 @t100)))) % 0.40/0.62 (step @p74 :rule trans :premises (@p73 @p71)) % 0.40/0.62 (step @p75 :rule refl :args (@t95)) % 0.40/0.62 (step @p76 :rule refl :args (@t16)) % 0.40/0.62 (step @p77 :rule cong :premises (@p76 @p75) :args ((= @t16 @t95))) % 0.40/0.62 (step @p78 :rule symm :premises (@p77)) % 0.40/0.62 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.40/0.62 (step @p80 :rule cong :premises (@p79) :args (@t17)) % 0.40/0.62 (step @p81 :rule refl :args ((tptp.in @t5 @t20))) % 0.40/0.62 (step @p82 :rule refl :args ((tptp.setminus @t2 @t19))) % 0.40/0.62 (step @p83 :rule refl :args (@t76)) % 0.40/0.62 (step @p84 :rule refl :args (@t2)) % 0.40/0.62 (step @p85 :rule cong :premises (@p84 @p83) :args (@t77)) % 0.40/0.62 (step @p86 :rule trans :premises (@p85 @p82)) % 0.40/0.62 (step @p87 :rule refl :args (@t5)) % 0.40/0.62 (step @p88 :rule cong :premises (@p87 @p86) :args (@t96)) % 0.40/0.62 (step @p89 :rule trans :premises (@p88 @p81)) % 0.40/0.62 (step @p90 :rule refl :args (@t6)) % 0.40/0.62 (step @p91 :rule ho_cong :premises (@p90 @p86)) % 0.40/0.62 (step @p92 :rule cong :premises (@p91 @p89) :args ((= (_ @t6 @t77) @t96))) % 0.40/0.62 (step @p93 :rule symm :premises (@p92)) % 0.40/0.62 (step @p94 :rule refl :args (@t21)) % 0.40/0.62 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.40/0.62 (step @p96 :rule refl :args (@t3)) % 0.40/0.62 (step @p97 :rule ho_cong :premises (@p96 @p83)) % 0.40/0.62 (step @p98 :rule cong :premises (@p97 @p86) :args ((= (_ @t3 @t76) @t77))) % 0.40/0.62 (step @p99 :rule symm :premises (@p98)) % 0.40/0.62 (step @p100 :rule refl :args (@t20)) % 0.40/0.62 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.40/0.62 (step @p102 :rule refl :args (@t19)) % 0.40/0.62 (step @p103 :rule cong :premises (@p102 @p83) :args ((= @t19 @t76))) % 0.40/0.62 (step @p104 :rule symm :premises (@p103)) % 0.40/0.62 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 0.40/0.62 (step @p106 :rule ho_cong :premises (@p96 @p105)) % 0.40/0.62 (step @p107 :rule trans :premises (@p106 @p101)) % 0.40/0.62 (step @p108 :rule ho_cong :premises (@p90 @p107)) % 0.40/0.62 (step @p109 :rule trans :premises (@p108 @p95)) % 0.40/0.62 (step @p110 :rule cong :premises (@p109) :args (@t103)) % 0.40/0.62 (step @p111 :rule refl :args (@t98)) % 0.40/0.62 (step @p112 :rule refl :args (@t11)) % 0.40/0.62 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t11 @t98))) % 0.40/0.62 (step @p114 :rule symm :premises (@p113)) % 0.40/0.62 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.40/0.62 (step @p116 :rule cong :premises (@p115) :args (@t104)) % 0.40/0.62 (step @p117 :rule nary_cong :premises (@p116 @p110 @p80) :args (@t105)) % 0.40/0.62 (step @p118 :rule cong :premises (@p117) :args ((forall @t23 @t105))) % 0.40/0.62 (step @p119 :rule aci_norm :args ((= (or @t104 (or @t103 @t17)) @t105))) % 0.40/0.62 (step @p120 :rule bool-impl-elim :args (@t21 @t17)) % 0.40/0.62 (step @p121 :rule refl :args (@t104)) % 0.40/0.62 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or @t104 @t22))) % 0.40/0.62 (step @p123 :rule trans :premises (@p122 @p119)) % 0.40/0.62 (step @p124 :rule bool-impl-elim :args (@t11 @t22)) % 0.40/0.62 (step @p125 :rule trans :premises (@p124 @p123)) % 0.40/0.62 (step @p126 :rule cong :premises (@p125) :args (@t24)) % 0.40/0.62 (step @p127 :rule trans :premises (@p126 @p118)) % 0.40/0.62 (step @p128 :rule refl :args (@t27)) % 0.40/0.62 (step @p129 :rule cong :premises (@p128 @p127) :args (@t28)) % 0.40/0.62 (step @p130 :rule cong :premises (@p129) :args (@t30)) % 0.40/0.62 (step @p131 :rule trans :premises (@p130 @p74)) % 0.40/0.62 (step @p132 :rule refl :args (@t32)) % 0.40/0.62 (step @p133 :rule cong :premises (@p132 @p131) :args (@t33)) % 0.40/0.62 (step @p134 :rule cong :premises (@p133) :args (@t35)) % 0.40/0.62 (step @p135 :rule trans :premises (@p134 @p42)) % 0.40/0.62 (step @p136 :rule refl :args (tptp.inComplementUnionImpNotIn1)) % 0.40/0.62 (step @p137 :rule cong :premises (@p136 @p135) :args (@t36)) % 0.40/0.62 (step @p138 :rule eq_resolve :premises (@p2 @p137)) % 0.40/0.62 (step @p139 :rule cong :premises (@p138 @p5) :args (@t106)) % 0.40/0.62 (step @p140 :rule refl :args ((tptp.in @t5 @t4))) % 0.40/0.62 (step @p141 :rule refl :args (@t107)) % 0.40/0.62 (step @p142 :rule cong :premises (@p87 @p141) :args (@t108)) % 0.40/0.62 (step @p143 :rule trans :premises (@p142 @p140)) % 0.40/0.62 (step @p144 :rule ho_cong :premises (@p90 @p141)) % 0.40/0.62 (step @p145 :rule cong :premises (@p144 @p143) :args ((= (_ @t6 @t107) @t108))) % 0.40/0.62 (step @p146 :rule symm :premises (@p145)) % 0.40/0.62 (step @p147 :rule refl :args (@t7)) % 0.40/0.62 (step @p148 :rule eq_resolve :premises (@p147 @p146)) % 0.40/0.62 (step @p149 :rule refl :args (@t4)) % 0.40/0.62 (step @p150 :rule cong :premises (@p149 @p141) :args ((= @t4 @t107))) % 0.40/0.62 (step @p151 :rule symm :premises (@p150)) % 0.40/0.62 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 0.40/0.62 (step @p153 :rule ho_cong :premises (@p90 @p152)) % 0.40/0.62 (step @p154 :rule trans :premises (@p153 @p148)) % 0.40/0.62 (step @p155 :rule refl :args (@t109)) % 0.40/0.62 (step @p156 :rule refl :args (@t8)) % 0.40/0.62 (step @p157 :rule cong :premises (@p156 @p155) :args ((= @t8 @t109))) % 0.40/0.62 (step @p158 :rule symm :premises (@p157)) % 0.40/0.62 (step @p159 :rule eq_resolve :premises (@p156 @p158)) % 0.40/0.62 (step @p160 :rule nary_cong :premises (@p116 @p159 @p154) :args (@t110)) % 0.40/0.62 (step @p161 :rule cong :premises (@p160) :args ((forall @t12 @t110))) % 0.40/0.62 (step @p162 :rule aci_norm :args ((= (or @t104 (or @t8 @t7)) @t110))) % 0.40/0.62 (step @p163 :rule bool-double-not-elim :args (@t8)) % 0.40/0.62 (step @p164 :rule nary_cong :premises (@p163 @p147) :args ((or (not @t9) @t7))) % 0.40/0.62 (step @p165 :rule bool-impl-elim :args (@t9 @t7)) % 0.40/0.62 (step @p166 :rule trans :premises (@p165 @p164)) % 0.40/0.62 (step @p167 :rule nary_cong :premises (@p121 @p166) :args ((or @t104 @t10))) % 0.40/0.62 (step @p168 :rule trans :premises (@p167 @p162)) % 0.40/0.62 (step @p169 :rule bool-impl-elim :args (@t11 @t10)) % 0.40/0.62 (step @p170 :rule trans :premises (@p169 @p168)) % 0.40/0.62 (step @p171 :rule cong :premises (@p170) :args (@t13)) % 0.40/0.62 (step @p172 :rule trans :premises (@p171 @p161)) % 0.40/0.62 (step @p173 :rule refl :args (tptp.setminusI)) % 0.40/0.62 (step @p174 :rule cong :premises (@p173 @p172) :args (@t14)) % 0.40/0.62 (step @p175 :rule eq_resolve :premises (@p1 @p174)) % 0.40/0.62 (step @p176 :rule cong :premises (@p175 @p139) :args (@t111)) % 0.40/0.62 (step @p177 :rule cong :premises (@p176) :args ((not @t111))) % 0.40/0.62 (step @p178 :rule aci_norm :args ((= @t113 @t58))) % 0.40/0.62 (step @p179 :rule cong :premises (@p178) :args (@t114)) % 0.40/0.62 (step @p180 :rule quant-merge-prenex :args ((= (forall @t34 @t116) @t114))) % 0.40/0.62 (step @p181 :rule alpha_equiv :args (@t117 (@list @t51 @t49) (@list @t18 @t118))) % 0.40/0.62 (step @p182 :rule nary_cong :premises (@p10 @p181) :args (@t119)) % 0.40/0.62 (step @p183 :rule quant-miniscope-or :args ((= @t116 @t119))) % 0.40/0.62 (step @p184 :rule trans :premises (@p183 @p182)) % 0.40/0.62 (step @p185 :rule symm :premises (@p184)) % 0.40/0.62 (step @p186 :rule cong :premises (@p185) :args ((forall @t34 (or @t57 @t125)))) % 0.40/0.62 (step @p187 :rule trans :premises (@p186 @p180)) % 0.40/0.62 (step @p188 :rule trans :premises (@p187 @p179)) % 0.40/0.62 (step @p189 :rule refl :args (@t125)) % 0.40/0.62 (step @p190 :rule nary_cong :premises (@p36 @p189) :args (@t126)) % 0.40/0.62 (step @p191 :rule cong :premises (@p190) :args ((forall @t34 @t126))) % 0.40/0.62 (step @p192 :rule trans :premises (@p191 @p188)) % 0.40/0.62 (step @p193 :rule bool-impl-elim :args (@t32 @t125)) % 0.40/0.62 (step @p194 :rule cong :premises (@p193) :args ((forall @t34 (=> @t32 @t125)))) % 0.40/0.62 (step @p195 :rule trans :premises (@p194 @p192)) % 0.40/0.62 (step @p196 :rule aci_norm :args ((= @t128 @t123))) % 0.40/0.62 (step @p197 :rule cong :premises (@p196) :args (@t129)) % 0.40/0.62 (step @p198 :rule quant-merge-prenex :args ((= (forall @t29 @t131) @t129))) % 0.40/0.62 (step @p199 :rule alpha_equiv :args (@t132 (@list @t118) @t93)) % 0.40/0.62 (step @p200 :rule nary_cong :premises (@p47 @p199) :args (@t133)) % 0.40/0.62 (step @p201 :rule quant-miniscope-or :args ((= @t131 @t133))) % 0.40/0.62 (step @p202 :rule trans :premises (@p201 @p200)) % 0.40/0.62 (step @p203 :rule symm :premises (@p202)) % 0.40/0.62 (step @p204 :rule cong :premises (@p203) :args ((forall @t29 (or @t81 @t135)))) % 0.40/0.62 (step @p205 :rule trans :premises (@p204 @p198)) % 0.40/0.62 (step @p206 :rule trans :premises (@p205 @p197)) % 0.40/0.62 (step @p207 :rule refl :args (@t135)) % 0.40/0.62 (step @p208 :rule nary_cong :premises (@p68 @p207) :args (@t136)) % 0.40/0.62 (step @p209 :rule cong :premises (@p208) :args ((forall @t29 @t136))) % 0.40/0.62 (step @p210 :rule trans :premises (@p209 @p206)) % 0.40/0.62 (step @p211 :rule bool-impl-elim :args (@t27 @t135)) % 0.40/0.62 (step @p212 :rule cong :premises (@p211) :args ((forall @t29 (=> @t27 @t135)))) % 0.40/0.62 (step @p213 :rule trans :premises (@p212 @p210)) % 0.40/0.62 (step @p214 :rule refl :args ((tptp.in @t5 @t37))) % 0.40/0.62 (step @p215 :rule refl :args (@t48)) % 0.40/0.62 (step @p216 :rule cong :premises (@p87 @p215) :args (@t134)) % 0.40/0.62 (step @p217 :rule trans :premises (@p216 @p214)) % 0.40/0.62 (step @p218 :rule ho_cong :premises (@p90 @p215)) % 0.40/0.62 (step @p219 :rule cong :premises (@p218 @p217) :args ((= (_ @t6 @t48) @t134))) % 0.40/0.62 (step @p220 :rule symm :premises (@p219)) % 0.40/0.62 (step @p221 :rule refl :args (@t38)) % 0.40/0.62 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.40/0.62 (step @p223 :rule refl :args (@t37)) % 0.40/0.62 (step @p224 :rule cong :premises (@p223 @p215) :args ((= @t37 @t48))) % 0.40/0.62 (step @p225 :rule symm :premises (@p224)) % 0.40/0.62 (step @p226 :rule eq_resolve :premises (@p223 @p225)) % 0.40/0.62 (step @p227 :rule ho_cong :premises (@p90 @p226)) % 0.40/0.62 (step @p228 :rule trans :premises (@p227 @p222)) % 0.40/0.62 (step @p229 :rule nary_cong :premises (@p116 @p110 @p228) :args (@t137)) % 0.40/0.62 (step @p230 :rule cong :premises (@p229) :args ((forall @t23 @t137))) % 0.40/0.62 (step @p231 :rule aci_norm :args ((= (or @t104 (or @t103 @t38)) @t137))) % 0.40/0.62 (step @p232 :rule bool-impl-elim :args (@t21 @t38)) % 0.40/0.62 (step @p233 :rule nary_cong :premises (@p121 @p232) :args ((or @t104 @t39))) % 0.40/0.62 (step @p234 :rule trans :premises (@p233 @p231)) % 0.40/0.62 (step @p235 :rule bool-impl-elim :args (@t11 @t39)) % 0.40/0.62 (step @p236 :rule trans :premises (@p235 @p234)) % 0.40/0.62 (step @p237 :rule cong :premises (@p236) :args (@t40)) % 0.40/0.62 (step @p238 :rule trans :premises (@p237 @p230)) % 0.40/0.62 (step @p239 :rule cong :premises (@p128 @p238) :args (@t41)) % 0.40/0.62 (step @p240 :rule cong :premises (@p239) :args (@t42)) % 0.40/0.62 (step @p241 :rule trans :premises (@p240 @p213)) % 0.40/0.62 (step @p242 :rule cong :premises (@p132 @p241) :args (@t43)) % 0.40/0.62 (step @p243 :rule cong :premises (@p242) :args (@t44)) % 0.40/0.62 (step @p244 :rule trans :premises (@p243 @p195)) % 0.40/0.62 (step @p245 :rule cong :premises (@p136 @p244) :args (@t45)) % 0.40/0.62 (step @p246 :rule cong :premises (@p173 @p245) :args (@t46)) % 0.40/0.62 (step @p247 :rule cong :premises (@p246) :args (@t47)) % 0.40/0.62 (step @p248 :rule trans :premises (@p247 @p177)) % 0.40/0.62 (step @p249 :rule eq_resolve :premises (@p3 @p248)) % 0.40/0.62 (step @p250 :rule not_implies_elim2 :premises (@p249)) % 0.40/0.62 (step @p251 :rule not_implies_elim2 :premises (@p250)) % 0.40/0.62 (step @p252 :rule skolemize :premises (@p251)) % 0.40/0.62 (step @p253 :rule bool-double-not-elim :args (@t141)) % 0.40/0.62 (step @p254 :rule refl :args (@t152)) % 0.40/0.62 (step @p255 :rule nary_cong :premises (@p254 @p253) :args ((or @t152 (not @t151)))) % 0.40/0.62 (step @p256 :rule cnf_or_neg :args (@t152 0)) % 0.40/0.62 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 0.40/0.62 (step @p258 :rule reordering :premises (@p257) :args ((or @t141 @t152))) % 0.40/0.62 (step @p259 :rule chain_m_resolution :premises (@p258 @p252) :args (@t141 @t153 @t154)) % 0.40/0.62 (step @p260 :rule bool-double-not-elim :args (@t149)) % 0.40/0.62 (step @p261 :rule nary_cong :premises (@p254 @p260) :args ((or @t152 (not @t150)))) % 0.40/0.62 (step @p262 :rule cnf_or_neg :args (@t152 1)) % 0.40/0.62 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.40/0.62 (step @p264 :rule reordering :premises (@p263) :args ((or @t149 @t152))) % 0.40/0.62 (step @p265 :rule chain_m_resolution :premises (@p264 @p252) :args (@t149 @t153 @t154)) % 0.40/0.62 (step @p266 :rule bool-double-not-elim :args (@t147)) % 0.40/0.62 (step @p267 :rule nary_cong :premises (@p254 @p266) :args ((or @t152 (not @t148)))) % 0.40/0.62 (step @p268 :rule cnf_or_neg :args (@t152 2)) % 0.40/0.62 (step @p269 :rule eq_resolve :premises (@p268 @p267)) % 0.40/0.62 (step @p270 :rule reordering :premises (@p269) :args ((or @t147 @t152))) % 0.40/0.62 (step @p271 :rule chain_m_resolution :premises (@p270 @p252) :args (@t147 @t153 @t154)) % 0.40/0.62 (step @p272 :rule bool-double-not-elim :args (@t145)) % 0.40/0.62 (step @p273 :rule nary_cong :premises (@p254 @p272) :args ((or @t152 (not @t146)))) % 0.40/0.62 (step @p274 :rule cnf_or_neg :args (@t152 3)) % 0.40/0.62 (step @p275 :rule eq_resolve :premises (@p274 @p273)) % 0.40/0.62 (step @p276 :rule reordering :premises (@p275) :args ((or @t145 @t152))) % 0.40/0.62 (step @p277 :rule chain_m_resolution :premises (@p276 @p252) :args (@t145 @t153 @t154)) % 0.40/0.62 (step @p278 :rule not_implies_elim1 :premises (@p250)) % 0.40/0.62 (step @p279 :rule instantiate :premises (@p278) :args ((@list @t138 @t140 @t144 @t142))) % 0.40/0.62 (step @p280 :rule not_implies_elim1 :premises (@p249)) % 0.40/0.62 (step @p281 :rule instantiate :premises (@p280) :args ((@list @t138 @t140 @t142))) % 0.40/0.62 (step @p282 :rule cnf_or_neg :args (@t152 4)) % 0.40/0.62 (step @p283 :rule chain_m_resolution :premises (@p282 @p252) :args ((not @t143) @t153 @t154)) % 0.40/0.62 (step @p284 :rule cnf_or_pos :args (@t156)) % 0.40/0.62 (step @p285 :rule reordering :premises (@p284) :args ((or @t148 @t143 @t155 (not @t156)))) % 0.40/0.62 (step @p286 :rule chain_m_resolution :premises (@p285 @p271 @p283 @p281) :args (@t155 (@list false true false) (@list @t147 @t143 @t156))) % 0.40/0.62 (step @p287 :rule cnf_or_pos :args (@t158)) % 0.40/0.62 (step @p288 :rule reordering :premises (@p287) :args ((or @t151 @t150 @t148 @t146 @t157 (not @t158)))) % 0.40/0.62 (step @p289 false :rule chain_m_resolution :premises (@p288 @p286 @p279 @p277 @p271 @p265 @p259) :args (false (@list false false false false false false) (@list @t155 @t158 @t145 @t147 @t149 @t141))) % 0.40/0.62 ) % 0.40/0.62 % SZS output end Proof % 0.40/0.62 % cvc5 exiting %------------------------------------------------------------------------------