%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU874^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:53:27 AM UTC 2026 % Result : Theorem 202.38s 202.66s % Output : Proof 202.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU874^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n003.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:55:59 EDT 2026 % 0.17/0.34 % CPUTime : % 0.26/0.49 %----Proving TH0 % 202.38/202.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 202.38/202.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 202.38/202.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 202.38/202.66 --- Run --ho-elim --full-saturate-quant at 18s... % 202.38/202.66 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 202.38/202.66 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 202.38/202.66 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 202.38/202.66 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 202.38/202.66 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 202.38/202.66 % SZS status Theorem % 202.38/202.66 % SZS output start Proof % 202.38/202.66 ( % 202.38/202.66 (declare-sort tptp.a 0) % 202.38/202.66 (declare-const tptp.cX (-> tptp.a Bool)) % 202.38/202.66 (define @t1 () (@var "Xx" tptp.a)) % 202.38/202.66 (define @t2 () (@var "S" (-> tptp.a Bool))) % 202.38/202.66 (define @t3 () (_ @t2 @t1)) % 202.38/202.66 (define @t4 () (@var "Xx0" tptp.a)) % 202.38/202.66 (define @t5 () (_ tptp.cX @t4)) % 202.38/202.66 (define @t6 () (_ @t2 @t4)) % 202.38/202.66 (define @t7 () (@list @t4)) % 202.38/202.66 (define @t8 () (forall @t7 (=> @t6 @t5))) % 202.38/202.66 (define @t9 () (@var "X0" (-> (-> tptp.a Bool) Bool))) % 202.38/202.66 (define @t10 () (_ @t9 @t2)) % 202.38/202.66 (define @t11 () (@var "Xz" tptp.a)) % 202.38/202.66 (define @t12 () (@var "Xt" tptp.a)) % 202.38/202.66 (define @t13 () (= @t12 @t11)) % 202.38/202.66 (define @t14 () (@var "Xx0" (-> tptp.a Bool))) % 202.38/202.66 (define @t15 () (_ @t14 @t11)) % 202.38/202.66 (define @t16 () (or @t15 @t13)) % 202.38/202.66 (define @t17 () (@list @t11)) % 202.38/202.66 (define @t18 () (lambda @t17 @t16)) % 202.38/202.66 (define @t19 () (_ @t9 @t18)) % 202.38/202.66 (define @t20 () (_ @t2 @t12)) % 202.38/202.66 (define @t21 () (@list @t12)) % 202.38/202.66 (define @t22 () (forall @t21 (=> @t20 @t19))) % 202.38/202.66 (define @t23 () (_ @t9 @t14)) % 202.38/202.66 (define @t24 () (=> @t23 @t22)) % 202.38/202.66 (define @t25 () (@list @t14)) % 202.38/202.66 (define @t26 () (forall @t25 @t24)) % 202.38/202.66 (define @t27 () (@var "Xy" tptp.a)) % 202.38/202.66 (define @t28 () (lambda (@list @t27) false)) % 202.38/202.66 (define @t29 () (and (_ @t9 @t28) @t26)) % 202.38/202.66 (define @t30 () (=> @t29 @t10)) % 202.38/202.66 (define @t31 () (@list @t9)) % 202.38/202.66 (define @t32 () (forall @t31 @t30)) % 202.38/202.66 (define @t33 () (and @t32 @t8 @t3)) % 202.38/202.66 (define @t34 () (@list @t2)) % 202.38/202.66 (define @t35 () (exists @t34 @t33)) % 202.38/202.66 (define @t36 () (@list @t1)) % 202.38/202.66 (define @t37 () (lambda @t36 @t35)) % 202.38/202.66 (define @t38 () (= tptp.cX @t37)) % 202.38/202.66 (define @t39 () (not @t38)) % 202.38/202.66 (define @t40 () (_ @t2 @t1)) % 202.38/202.66 (define @t41 () (tptp.cX @t4)) % 202.38/202.66 (define @t42 () (_ @t2 @t4)) % 202.38/202.66 (define @t43 () (forall @t7 (or (not @t42) @t41))) % 202.38/202.66 (define @t44 () (not @t43)) % 202.38/202.66 (define @t45 () (_ @t9 @t2)) % 202.38/202.66 (define @t46 () (@var "BOUND_VARIABLE_7479" tptp.a)) % 202.38/202.66 (define @t47 () (_ @t14 @t11)) % 202.38/202.66 (define @t48 () (lambda @t17 (or @t47 (= @t11 @t46)))) % 202.38/202.66 (define @t49 () (_ @t9 @t48)) % 202.38/202.66 (define @t50 () (not (_ @t2 @t46))) % 202.38/202.66 (define @t51 () (_ @t9 @t14)) % 202.38/202.66 (define @t52 () (not @t51)) % 202.38/202.66 (define @t53 () (@list @t14 @t46)) % 202.38/202.66 (define @t54 () (forall @t53 (or @t52 @t50 @t49))) % 202.38/202.66 (define @t55 () (not @t54)) % 202.38/202.66 (define @t56 () (@var "BOUND_VARIABLE_7854" tptp.a)) % 202.38/202.66 (define @t57 () (lambda (@list @t56) false)) % 202.38/202.66 (define @t58 () (_ @t9 @t57)) % 202.38/202.66 (define @t59 () (not @t58)) % 202.38/202.66 (define @t60 () (forall @t31 (or @t59 @t55 @t45))) % 202.38/202.66 (define @t61 () (not @t60)) % 202.38/202.66 (define @t62 () (lambda @t36 (not (forall @t34 (or @t61 @t44 (not @t40)))))) % 202.38/202.66 (define @t63 () (@purify @t62)) % 202.38/202.66 (define @t64 () (= tptp.cX @t62)) % 202.38/202.66 (define @t65 () (not @t3)) % 202.38/202.66 (define @t66 () (or @t61 @t44 @t65)) % 202.38/202.66 (define @t67 () (and @t60 @t43 @t3)) % 202.38/202.66 (define @t68 () (forall @t34 (not @t67))) % 202.38/202.66 (define @t69 () (not @t68)) % 202.38/202.66 (define @t70 () (not @t6)) % 202.38/202.66 (define @t71 () (or @t70 @t5)) % 202.38/202.66 (define @t72 () (_ @t9 @t57)) % 202.38/202.66 (define @t73 () (not @t72)) % 202.38/202.66 (define @t74 () (or @t73 @t55 @t10)) % 202.38/202.66 (define @t75 () (and @t72 @t54)) % 202.38/202.66 (define @t76 () (or @t47 (= @t46 @t11))) % 202.38/202.66 (define @t77 () (lambda @t17 @t76)) % 202.38/202.66 (define @t78 () (_ @t9 @t77)) % 202.38/202.66 (define @t79 () (or @t52 @t50 @t78)) % 202.38/202.66 (define @t80 () (or @t50 @t78)) % 202.38/202.66 (define @t81 () (or @t52 @t80)) % 202.38/202.66 (define @t82 () (forall @t53 @t81)) % 202.38/202.66 (define @t83 () (@list @t46)) % 202.38/202.66 (define @t84 () (forall @t83 @t81)) % 202.38/202.66 (define @t85 () (forall @t83 @t80)) % 202.38/202.66 (define @t86 () (or @t52 @t85)) % 202.38/202.66 (define @t87 () (or @t47 @t13)) % 202.38/202.66 (define @t88 () (lambda @t17 @t87)) % 202.38/202.66 (define @t89 () (_ @t9 @t88)) % 202.38/202.66 (define @t90 () (_ @t2 @t12)) % 202.38/202.66 (define @t91 () (forall @t21 (or (not @t90) @t89))) % 202.38/202.66 (define @t92 () (not @t23)) % 202.38/202.66 (define @t93 () (or @t92 @t91)) % 202.38/202.66 (define @t94 () (not @t20)) % 202.38/202.66 (define @t95 () (or @t94 @t19)) % 202.38/202.66 (define @t96 () (@const 0 tptp.a)) % 202.38/202.66 (define @t97 () (forall @t34 (or @t61 @t44 (not (_ @t2 @t96))))) % 202.38/202.66 (define @t98 () (not @t97)) % 202.38/202.66 (define @t99 () (= (_ @t62 @t96) @t98)) % 202.38/202.66 (define @t100 () (_ @t63 @t96)) % 202.38/202.66 (define @t101 () (tptp.cX @t96)) % 202.38/202.66 (define @t102 () (= @t101 @t100)) % 202.38/202.66 (define @t103 () (not @t102)) % 202.38/202.66 (define @t104 () (= tptp.cX @t63)) % 202.38/202.66 (define @t105 () (or @t104 @t103)) % 202.38/202.66 (define @t106 () (= @t101 @t98)) % 202.38/202.66 (define @t107 () (@list true)) % 202.38/202.66 (define @t108 () (not @t101)) % 202.38/202.66 (define @t109 () (not @t98)) % 202.38/202.66 (define @t110 () (= @t11 @t96)) % 202.38/202.66 (define @t111 () (@purify @t57)) % 202.38/202.66 (define @t112 () (or (_ @t111 @t11) @t110)) % 202.38/202.66 (define @t113 () (lambda @t17 @t112)) % 202.38/202.66 (define @t114 () (@purify @t113)) % 202.38/202.66 (define @t115 () (_ @t114 @t96)) % 202.38/202.66 (define @t116 () (not @t115)) % 202.38/202.66 (define @t117 () (forall @t7 (or (not (_ @t114 @t4)) @t41))) % 202.38/202.66 (define @t118 () (not @t117)) % 202.38/202.66 (define @t119 () (not (_ @t114 @t46))) % 202.38/202.66 (define @t120 () (forall @t31 (or @t59 (not (forall @t53 (or @t52 @t119 @t49))) (_ @t9 @t114)))) % 202.38/202.66 (define @t121 () (not @t120)) % 202.38/202.66 (define @t122 () (or @t121 @t118 @t116)) % 202.38/202.66 (define @t123 () (_ @t114 @t11)) % 202.38/202.66 (define @t124 () (_ @t113 @t11)) % 202.38/202.66 (define @t125 () (= @t123 @t124)) % 202.38/202.66 (define @t126 () (forall @t17 @t125)) % 202.38/202.66 (define @t127 () (_ @t111 @t96)) % 202.38/202.66 (define @t128 () (or @t127 (= @t96 @t96))) % 202.38/202.66 (define @t129 () (= @t128 @t115)) % 202.38/202.66 (define @t130 () (forall @t17 (= @t112 @t123))) % 202.38/202.66 (define @t131 () (@list @t96)) % 202.38/202.66 (define @t132 () (@list false)) % 202.38/202.66 (define @t133 () (@list @t130)) % 202.38/202.66 (define @t134 () (@quantifiers_skolemize @t120 0)) % 202.38/202.66 (define @t135 () (_ @t134 @t111)) % 202.38/202.66 (define @t136 () (_ @t134 @t114)) % 202.38/202.66 (define @t137 () (forall @t53 (or (not (_ @t134 @t14)) @t119 (_ @t134 @t48)))) % 202.38/202.66 (define @t138 () (not @t137)) % 202.38/202.66 (define @t139 () (not @t135)) % 202.38/202.66 (define @t140 () (or @t139 @t138 @t136)) % 202.38/202.66 (define @t141 () (_ @t134 @t113)) % 202.38/202.66 (define @t142 () (or @t139 @t116 @t141)) % 202.38/202.66 (define @t143 () (or @t139 @t116 @t136)) % 202.38/202.66 (define @t144 () (not @t140)) % 202.38/202.66 (define @t145 () (_ @t134 @t57)) % 202.38/202.66 (define @t146 () (not @t145)) % 202.38/202.66 (define @t147 () (or @t146 @t138 @t136)) % 202.38/202.66 (define @t148 () (not @t147)) % 202.38/202.66 (define @t149 () (@quantifiers_skolemize @t117 0)) % 202.38/202.66 (define @t150 () (tptp.cX @t149)) % 202.38/202.66 (define @t151 () (_ @t114 @t149)) % 202.38/202.66 (define @t152 () (not @t151)) % 202.38/202.66 (define @t153 () (or @t152 @t150)) % 202.38/202.66 (define @t154 () (not @t153)) % 202.38/202.66 (define @t155 () (= @t96 @t149)) % 202.38/202.66 (define @t156 () (_ @t57 @t149)) % 202.38/202.66 (define @t157 () (_ @t111 @t149)) % 202.38/202.66 (define @t158 () (or @t157 @t155)) % 202.38/202.66 (define @t159 () (= @t151 @t158)) % 202.38/202.66 (define @t160 () (or @t157 (= @t149 @t96))) % 202.38/202.66 (define @t161 () (= @t160 @t151)) % 202.38/202.66 (define @t162 () (= @t151 @t155)) % 202.38/202.66 (define @t163 () (not @t155)) % 202.38/202.66 (define @t164 () (not @t150)) % 202.38/202.66 (define @t165 () (and @t101 @t155 @t164)) % 202.38/202.66 (define @t166 () (@quantifiers_skolemize @t97 0)) % 202.38/202.66 (define @t167 () (_ @t166 @t96)) % 202.38/202.66 (define @t168 () (not @t167)) % 202.38/202.66 (define @t169 () (forall @t7 (or (not (_ @t166 @t4)) @t41))) % 202.38/202.66 (define @t170 () (not @t169)) % 202.38/202.66 (define @t171 () (or (not (forall @t31 (or @t59 (not (forall @t53 (or @t52 (not (_ @t166 @t46)) @t49))) (_ @t9 @t166)))) @t170 @t168)) % 202.38/202.66 (define @t172 () (not @t171)) % 202.38/202.66 (define @t173 () (@list @t171)) % 202.38/202.66 (define @t174 () (or @t168 @t101)) % 202.38/202.66 (define @t175 () (not @t174)) % 202.38/202.66 (define @t176 () (@list true false)) % 202.38/202.66 (assume @p1 @t39) % 202.38/202.66 (assume @p2 true) % 202.38/202.66 (step @p3 :rule eq-refl :args (@t62)) % 202.38/202.66 (step @p4 :rule skolem_intro :args (@t63)) % 202.38/202.66 (step @p5 :rule refl :args (@t62)) % 202.38/202.66 (step @p6 :rule cong :premises (@p5 @p4) :args ((= @t62 @t63))) % 202.38/202.66 (step @p7 :rule trans :premises (@p6 @p3)) % 202.38/202.66 (step @p8 :rule true_elim :premises (@p7)) % 202.38/202.66 (step @p9 :rule refl :args (tptp.cX)) % 202.38/202.66 (step @p10 :rule cong :premises (@p9 @p8) :args (@t64)) % 202.38/202.66 (step @p11 :rule cong :premises (@p10) :args ((not @t64))) % 202.38/202.66 (step @p12 :rule refl :args (@t40)) % 202.38/202.66 (step @p13 :rule refl :args (@t3)) % 202.38/202.66 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t3 @t40))) % 202.38/202.66 (step @p15 :rule symm :premises (@p14)) % 202.38/202.66 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 202.38/202.66 (step @p17 :rule cong :premises (@p16) :args (@t65)) % 202.38/202.66 (step @p18 :rule refl :args (@t44)) % 202.38/202.66 (step @p19 :rule refl :args (@t61)) % 202.38/202.66 (step @p20 :rule nary_cong :premises (@p19 @p18 @p17) :args (@t66)) % 202.38/202.66 (step @p21 :rule cong :premises (@p20) :args ((forall @t34 @t66))) % 202.38/202.66 (step @p22 :rule aci_norm :args ((= (or @t61 (or @t44 @t65)) @t66))) % 202.38/202.66 (step @p23 :rule bool-and-de-morgan :args (@t43 @t3 true)) % 202.38/202.66 (step @p24 :rule nary_cong :premises (@p19 @p23) :args ((or @t61 (not (and @t43 @t3))))) % 202.38/202.66 (step @p25 :rule bool-and-de-morgan :args (@t60 @t43 (and @t3))) % 202.38/202.66 (step @p26 :rule trans :premises (@p25 @p24)) % 202.38/202.66 (step @p27 :rule trans :premises (@p26 @p22)) % 202.38/202.66 (step @p28 :rule cong :premises (@p27) :args (@t68)) % 202.38/202.66 (step @p29 :rule trans :premises (@p28 @p21)) % 202.38/202.66 (step @p30 :rule cong :premises (@p29) :args (@t69)) % 202.38/202.66 (step @p31 :rule exists-elim :args ((= (exists @t34 @t67) @t69))) % 202.38/202.66 (step @p32 :rule trans :premises (@p31 @p30)) % 202.38/202.66 (step @p33 :rule refl :args (@t3)) % 202.38/202.66 (step @p34 :rule refl :args (@t41)) % 202.38/202.66 (step @p35 :rule refl :args (@t5)) % 202.38/202.66 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t5 @t41))) % 202.38/202.66 (step @p37 :rule symm :premises (@p36)) % 202.38/202.66 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 202.38/202.66 (step @p39 :rule refl :args (@t42)) % 202.38/202.66 (step @p40 :rule refl :args (@t6)) % 202.38/202.66 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t6 @t42))) % 202.38/202.66 (step @p42 :rule symm :premises (@p41)) % 202.38/202.66 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 202.38/202.66 (step @p44 :rule cong :premises (@p43) :args (@t70)) % 202.38/202.66 (step @p45 :rule nary_cong :premises (@p44 @p38) :args (@t71)) % 202.38/202.66 (step @p46 :rule cong :premises (@p45) :args ((forall @t7 @t71))) % 202.38/202.66 (step @p47 :rule bool-impl-elim :args (@t6 @t5)) % 202.38/202.66 (step @p48 :rule cong :premises (@p47) :args (@t8)) % 202.38/202.66 (step @p49 :rule trans :premises (@p48 @p46)) % 202.38/202.66 (step @p50 :rule refl :args (@t45)) % 202.38/202.66 (step @p51 :rule refl :args (@t10)) % 202.38/202.66 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t10 @t45))) % 202.38/202.66 (step @p53 :rule symm :premises (@p52)) % 202.38/202.66 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 202.38/202.66 (step @p55 :rule refl :args (@t55)) % 202.38/202.66 (step @p56 :rule refl :args ((_ @t9 @t57))) % 202.38/202.66 (step @p57 :rule refl :args (@t57)) % 202.38/202.66 (step @p58 :rule cong :premises (@p57) :args (@t58)) % 202.38/202.66 (step @p59 :rule trans :premises (@p58 @p56)) % 202.38/202.66 (step @p60 :rule refl :args (@t9)) % 202.38/202.66 (step @p61 :rule ho_cong :premises (@p60 @p57)) % 202.38/202.66 (step @p62 :rule cong :premises (@p61 @p59) :args ((= @t72 @t58))) % 202.38/202.66 (step @p63 :rule symm :premises (@p62)) % 202.38/202.66 (step @p64 :rule refl :args ((_ @t9 @t57))) % 202.38/202.66 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 202.38/202.66 (step @p66 :rule cong :premises (@p65) :args (@t73)) % 202.38/202.66 (step @p67 :rule nary_cong :premises (@p66 @p55 @p54) :args (@t74)) % 202.38/202.66 (step @p68 :rule cong :premises (@p67) :args ((forall @t31 @t74))) % 202.38/202.66 (step @p69 :rule aci_norm :args ((= (or (or @t73 @t55) @t10) @t74))) % 202.38/202.66 (step @p70 :rule bool-and-de-morgan :args (@t72 @t54 true)) % 202.38/202.66 (step @p71 :rule nary_cong :premises (@p70 @p51) :args ((or (not @t75) @t10))) % 202.38/202.66 (step @p72 :rule trans :premises (@p71 @p69)) % 202.38/202.66 (step @p73 :rule bool-impl-elim :args (@t75 @t10)) % 202.38/202.66 (step @p74 :rule trans :premises (@p73 @p72)) % 202.38/202.66 (step @p75 :rule cong :premises (@p74) :args ((forall @t31 (=> @t75 @t10)))) % 202.38/202.66 (step @p76 :rule trans :premises (@p75 @p68)) % 202.38/202.66 (step @p77 :rule refl :args (@t10)) % 202.38/202.66 (step @p78 :rule eq-symm :args (@t46 @t11)) % 202.38/202.66 (step @p79 :rule refl :args (@t47)) % 202.38/202.66 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t76)) % 202.38/202.66 (step @p81 :rule cong :premises (@p80) :args (@t77)) % 202.38/202.66 (step @p82 :rule cong :premises (@p81) :args (@t78)) % 202.38/202.66 (step @p83 :rule refl :args (@t50)) % 202.38/202.66 (step @p84 :rule refl :args (@t52)) % 202.38/202.66 (step @p85 :rule nary_cong :premises (@p84 @p83 @p82) :args (@t79)) % 202.38/202.66 (step @p86 :rule aci_norm :args ((= @t81 @t79))) % 202.38/202.66 (step @p87 :rule trans :premises (@p86 @p85)) % 202.38/202.66 (step @p88 :rule cong :premises (@p87) :args (@t82)) % 202.38/202.66 (step @p89 :rule quant-merge-prenex :args ((= (forall @t25 @t84) @t82))) % 202.38/202.66 (step @p90 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202.38/202.66 (step @p302 :rule skolemize :premises (@p421)) % 202.38/202.66 (step-pop @p422 :rule scope :premises (@p302)) % 202.38/202.66 (step @p303 :rule process_scope :premises (@p422) :args (@t154)) % 202.38/202.66 (step @p305 :rule implies_elim :premises (@p303)) % 202.38/202.66 (step @p306 :rule eq_resolve :premises (@p305 @p300)) % 202.38/202.66 (step @p307 :rule bool-double-not-elim :args (@t151)) % 202.38/202.66 (step @p308 :rule refl :args (@t153)) % 202.38/202.66 (step @p309 :rule nary_cong :premises (@p308 @p307) :args ((or @t153 (not @t152)))) % 202.38/202.66 (step @p310 :rule cnf_or_neg :args (@t153 0)) % 202.38/202.66 (step @p311 :rule eq_resolve :premises (@p310 @p309)) % 202.38/202.66 (step @p312 :rule reordering :premises (@p311) :args ((or @t151 @t153))) % 202.38/202.66 (step @p313 :rule cnf_or_neg :args (@t153 1)) % 202.38/202.66 (step @p314 :rule aci_norm :args ((= (or false @t155) @t155))) % 202.38/202.66 (step @p315 :rule refl :args (@t155)) % 202.38/202.66 (step @p316 :rule evaluate :args ((not false))) % 202.38/202.66 (step @p317 :rule beta-reduce :args ((= @t156 false))) % 202.38/202.66 (step @p318 :rule cong :premises (@p317) :args ((not @t156))) % 202.38/202.66 (step @p319 :rule trans :premises (@p318 @p316)) % 202.38/202.66 (step @p320 :rule refl :args (@t149)) % 202.38/202.66 (step @p321 :rule ho_cong :premises (@p247 @p320)) % 202.38/202.66 (step @p322 :rule cong :premises (@p321) :args ((not @t157))) % 202.38/202.66 (step @p323 :rule bool-eq-false :args (@t157)) % 202.38/202.66 (step @p324 :rule trans :premises (@p323 @p322 @p319)) % 202.38/202.66 (step @p325 :rule true_elim :premises (@p324)) % 202.38/202.66 (step @p326 :rule nary_cong :premises (@p325 @p315) :args (@t158)) % 202.38/202.66 (step @p327 :rule trans :premises (@p326 @p314)) % 202.38/202.66 (step @p328 :rule refl :args (@t151)) % 202.38/202.66 (step @p329 :rule cong :premises (@p328 @p327) :args (@t159)) % 202.38/202.66 (step @p330 :rule cong :premises (@p224 @p329) :args ((=> @t130 @t159))) % 202.38/202.66 (step @p331 :rule eq-symm :args (@t149 @t96)) % 202.38/202.66 (step @p332 :rule refl :args (@t157)) % 202.38/202.66 (step @p333 :rule nary_cong :premises (@p332 @p331) :args (@t160)) % 202.38/202.66 (step @p334 :rule cong :premises (@p328 @p333) :args ((= @t151 @t160))) % 202.38/202.66 (step @p335 :rule eq-symm :args (@t160 @t151)) % 202.38/202.66 (step @p336 :rule trans :premises (@p335 @p334)) % 202.38/202.66 (step @p337 :rule cong :premises (@p224 @p336) :args ((=> @t130 @t161))) % 202.38/202.66 (assume-push @p423 @t130) % 202.38/202.66 (step @p339 :rule instantiate :premises (@p212) :args ((@list @t149))) % 202.38/202.66 (step-pop @p424 :rule scope :premises (@p339)) % 202.38/202.66 (step @p340 :rule process_scope :premises (@p424) :args (@t161)) % 202.38/202.66 (step @p342 :rule eq_resolve :premises (@p340 @p337)) % 202.38/202.66 (step @p343 :rule eq_resolve :premises (@p342 @p330)) % 202.38/202.66 (step @p344 :rule implies_elim :premises (@p343)) % 202.38/202.66 (step @p345 :rule chain_m_resolution :premises (@p344 @p212) :args (@t162 @t132 @t133)) % 202.38/202.66 (step @p346 :rule cnf_equiv_pos1 :args (@t162)) % 202.38/202.66 (step @p347 :rule reordering :premises (@p346) :args ((or @t152 @t155 (not @t162)))) % 202.38/202.66 (step @p348 :rule refl :args (@t163)) % 202.38/202.66 (step @p349 :rule bool-double-not-elim :args (@t150)) % 202.38/202.66 (step @p350 :rule nary_cong :premises (@p183 @p349 @p348) :args ((or @t108 (not @t164) @t163))) % 202.38/202.66 (assume-push @p425 @t101) % 202.38/202.66 (assume-push @p426 @t155) % 202.38/202.66 (assume-push @p427 @t164) % 202.38/202.66 (step @p354 :rule evaluate :args ((= false true))) % 202.38/202.66 (step @p355 :rule true_intro :premises (@p425)) % 202.38/202.66 (step @p356 :rule symm :premises (@p426)) % 202.38/202.66 (step @p357 :rule cong :premises (@p356) :args (@t150)) % 202.38/202.66 (step @p358 :rule false_intro :premises (@p427)) % 202.38/202.66 (step @p359 :rule symm :premises (@p358)) % 202.38/202.66 (step @p360 :rule trans :premises (@p359 @p357 @p355)) % 202.38/202.66 (step @p361 false :rule eq_resolve :premises (@p360 @p354)) % 202.38/202.66 (step-pop @p428 :rule scope :premises (@p361)) % 202.38/202.66 (step-pop @p429 :rule scope :premises (@p428)) % 202.38/202.66 (step-pop @p430 :rule scope :premises (@p429)) % 202.38/202.66 (step @p362 :rule process_scope :premises (@p430) :args (false)) % 202.38/202.66 (assume-push @p431 @t101) % 202.38/202.66 (assume-push @p432 @t164) % 202.38/202.66 (assume-push @p433 @t155) % 202.38/202.66 (step @p369 :rule and_intro :premises (@p431 @p433 @p432)) % 202.38/202.66 (step-pop @p434 :rule scope :premises (@p369)) % 202.38/202.66 (step-pop @p435 :rule scope :premises (@p434)) % 202.38/202.66 (step-pop @p436 :rule scope :premises (@p435)) % 202.38/202.66 (step @p370 :rule process_scope :premises (@p436) :args (@t165)) % 202.38/202.66 (step @p374 :rule implies_elim :premises (@p370)) % 202.38/202.66 (step @p375 :rule resolution :premises (@p374 @p362) :args (true @t165)) % 202.38/202.66 (step @p376 :rule not_and :premises (@p375)) % 202.38/202.66 (step @p377 :rule eq_resolve :premises (@p376 @p350)) % 202.38/202.66 (step @p378 :rule chain_m_resolution :premises (@p377 @p347 @p345 @p313 @p312 @p306 @p297 @p295 @p232 @p193 @p188 @p181) :args (@t108 (@list false false true false true true false false false false true) (@list @t155 @t162 @t150 @t151 @t153 @t117 @t120 @t115 @t122 @t97 @t106))) % 202.38/202.66 (step @p379 :rule cnf_equiv_neg1 :args (@t106)) % 202.38/202.66 (step @p380 :rule reordering :premises (@p379) :args ((or @t101 @t98 @t106))) % 202.38/202.66 (step @p381 :rule chain_m_resolution :premises (@p380 @p378 @p181) :args (@t98 (@list true true) (@list @t101 @t106))) % 202.38/202.66 (step @p382 :rule refl :args (@t172)) % 202.38/202.66 (step @p383 :rule nary_cong :premises (@p182 @p382) :args ((or @t109 @t172))) % 202.38/202.66 (assume-push @p437 @t98) % 202.38/202.66 (step @p385 :rule skolemize :premises (@p437)) % 202.38/202.66 (step-pop @p438 :rule scope :premises (@p385)) % 202.38/202.66 (step @p386 :rule process_scope :premises (@p438) :args (@t172)) % 202.38/202.66 (step @p388 :rule implies_elim :premises (@p386)) % 202.38/202.66 (step @p389 :rule eq_resolve :premises (@p388 @p383)) % 202.38/202.66 (step @p390 :rule chain_m_resolution :premises (@p389 @p381) :args (@t172 @t107 (@list @t97))) % 202.38/202.66 (step @p391 :rule bool-double-not-elim :args (@t169)) % 202.38/202.66 (step @p392 :rule refl :args (@t171)) % 202.38/202.66 (step @p393 :rule nary_cong :premises (@p392 @p391) :args ((or @t171 (not @t170)))) % 202.38/202.66 (step @p394 :rule cnf_or_neg :args (@t171 1)) % 202.38/202.66 (step @p395 :rule eq_resolve :premises (@p394 @p393)) % 202.38/202.66 (step @p396 :rule reordering :premises (@p395) :args ((or @t169 @t171))) % 202.38/202.66 (step @p397 :rule chain_m_resolution :premises (@p396 @p390) :args (@t169 @t107 @t173)) % 202.38/202.66 (step @p398 :rule bool-double-not-elim :args (@t167)) % 202.38/202.66 (step @p399 :rule nary_cong :premises (@p392 @p398) :args ((or @t171 (not @t168)))) % 202.38/202.66 (step @p400 :rule cnf_or_neg :args (@t171 2)) % 202.38/202.66 (step @p401 :rule eq_resolve :premises (@p400 @p399)) % 202.38/202.66 (step @p402 :rule reordering :premises (@p401) :args ((or @t167 @t171))) % 202.38/202.66 (step @p403 :rule chain_m_resolution :premises (@p402 @p390) :args (@t167 @t107 @t173)) % 202.38/202.66 (step @p404 :rule cnf_or_pos :args (@t174)) % 202.38/202.66 (step @p405 :rule reordering :premises (@p404) :args ((or @t101 @t168 @t175))) % 202.38/202.66 (step @p406 :rule chain_m_resolution :premises (@p405 @p378 @p403) :args (@t175 @t176 (@list @t101 @t167))) % 202.38/202.66 (assume-push @p439 @t169) % 202.38/202.66 (step @p408 :rule instantiate :premises (@p439) :args (@t131)) % 202.38/202.66 (step-pop @p440 :rule scope :premises (@p408)) % 202.38/202.66 (step @p409 :rule process_scope :premises (@p440) :args (@t174)) % 202.38/202.66 (step @p411 :rule implies_elim :premises (@p409)) % 202.38/202.66 (step @p412 false :rule chain_m_resolution :premises (@p411 @p406 @p397) :args (false @t176 (@list @t174 @t169))) % 202.38/202.66 ) % 202.38/202.66 % SZS output end Proof % 202.38/202.66 % cvc5 exiting %------------------------------------------------------------------------------