%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU657^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n007.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 08:52:36 AM UTC 2026 % Result : Theorem 0.34s 0.60s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU657^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n007.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 17:43:56 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.51 %----Proving TH0 % 0.34/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.60 % SZS status Theorem % 0.34/0.60 % SZS output start Proof % 0.34/0.60 ( % 0.34/0.60 (declare-sort $$unsorted 0) % 0.34/0.60 (declare-const tptp.emptyset $$unsorted) % 0.34/0.60 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.60 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.34/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.34/0.60 (declare-const tptp.ksndpairEq Bool) % 0.34/0.60 (declare-const tptp.kfstpairEq Bool) % 0.34/0.60 (declare-const tptp.kfst (-> $$unsorted $$unsorted)) % 0.34/0.60 (declare-const tptp.ksnd (-> $$unsorted $$unsorted)) % 0.34/0.60 (define tptp.iskpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (let ((_let_4 (@var "A" $$unsorted))) (let ((_let_5 (_ tptp.setunion _let_4))) (lambda (@list _let_4) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_5) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_5) (= _let_4 (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset)))))))))))))) % 0.34/0.60 (define tptp.kpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (lambda (@list _let_2 _let_1) (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset))))))) % 0.34/0.60 (define @t1 () (@var "Xx" $$unsorted)) % 0.34/0.60 (define @t2 () (@var "Xy" $$unsorted)) % 0.34/0.60 (define @t3 () (_ (_ tptp.kpair @t1) @t2)) % 0.34/0.60 (define @t4 () (= (_ tptp.kfst @t3) @t1)) % 0.34/0.60 (define @t5 () (@list @t1 @t2)) % 0.34/0.60 (define @t6 () (forall @t5 @t4)) % 0.34/0.60 (define @t7 () (= tptp.kfstpairEq @t6)) % 0.34/0.60 (define @t8 () (= (_ tptp.ksnd @t3) @t2)) % 0.34/0.60 (define @t9 () (forall @t5 @t8)) % 0.34/0.60 (define @t10 () (= tptp.ksndpairEq @t9)) % 0.34/0.60 (define @t11 () (@var "Xu" $$unsorted)) % 0.34/0.60 (define @t12 () (_ tptp.ksnd @t11)) % 0.34/0.60 (define @t13 () (_ tptp.kfst @t11)) % 0.34/0.60 (define @t14 () (= (_ (_ tptp.kpair @t13) @t12) @t11)) % 0.34/0.60 (define @t15 () (=> (_ tptp.iskpair @t11) @t14)) % 0.34/0.60 (define @t16 () (@list @t11)) % 0.34/0.60 (define @t17 () (forall @t16 @t15)) % 0.34/0.60 (define @t18 () (=> tptp.ksndpairEq @t17)) % 0.34/0.60 (define @t19 () (=> tptp.kfstpairEq @t18)) % 0.34/0.60 (define @t20 () (not @t19)) % 0.34/0.60 (define @t21 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 0.34/0.60 (define @t22 () (_ tptp.setadjoin @t1)) % 0.34/0.60 (define @t23 () (_ @t22 @t21)) % 0.34/0.60 (define @t24 () (_ (_ tptp.setadjoin @t23) tptp.emptyset)) % 0.34/0.60 (define @t25 () (_ @t22 tptp.emptyset)) % 0.34/0.60 (define @t26 () (_ (_ tptp.setadjoin @t25) @t24)) % 0.34/0.60 (define @t27 () (@var "A" $$unsorted)) % 0.34/0.60 (define @t28 () (= @t27 @t26)) % 0.34/0.60 (define @t29 () (_ tptp.setunion @t27)) % 0.34/0.60 (define @t30 () (_ tptp.in @t2)) % 0.34/0.60 (define @t31 () (_ @t30 @t29)) % 0.34/0.60 (define @t32 () (and @t31 @t28)) % 0.34/0.60 (define @t33 () (@list @t2)) % 0.34/0.60 (define @t34 () (exists @t33 @t32)) % 0.34/0.60 (define @t35 () (_ tptp.in @t1)) % 0.34/0.60 (define @t36 () (_ @t35 @t29)) % 0.34/0.60 (define @t37 () (and @t36 @t34)) % 0.34/0.60 (define @t38 () (@list @t1)) % 0.34/0.60 (define @t39 () (exists @t38 @t37)) % 0.34/0.60 (define @t40 () (@list @t27)) % 0.34/0.60 (define @t41 () (lambda @t40 @t39)) % 0.34/0.60 (define @t42 () (lambda @t5 @t26)) % 0.34/0.60 (define @t43 () (@var "BOUND_VARIABLE_7640" $$unsorted)) % 0.34/0.60 (define @t44 () (@var "BOUND_VARIABLE_7638" $$unsorted)) % 0.34/0.60 (define @t45 () (tptp.setadjoin (tptp.setadjoin @t44 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t44 (tptp.setadjoin @t43 tptp.emptyset)) tptp.emptyset))) % 0.34/0.60 (define @t46 () (tptp.setunion @t45)) % 0.34/0.60 (define @t47 () (not (tptp.in @t43 @t46))) % 0.34/0.60 (define @t48 () (not (tptp.in @t44 @t46))) % 0.34/0.60 (define @t49 () (tptp.kfst @t45)) % 0.34/0.60 (define @t50 () (= @t45 (tptp.setadjoin (tptp.setadjoin @t49 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t49 (tptp.setadjoin (tptp.ksnd @t45) tptp.emptyset)) tptp.emptyset)))) % 0.34/0.60 (define @t51 () (or @t50 @t48 @t47)) % 0.34/0.60 (define @t52 () (@list @t44 @t43)) % 0.34/0.60 (define @t53 () (forall @t52 @t51)) % 0.34/0.60 (define @t54 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.34/0.60 (define @t55 () (tptp.setadjoin @t1 @t54)) % 0.34/0.60 (define @t56 () (tptp.setadjoin @t55 tptp.emptyset)) % 0.34/0.60 (define @t57 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.34/0.60 (define @t58 () (tptp.setadjoin @t57 @t56)) % 0.34/0.60 (define @t59 () (tptp.ksnd @t58)) % 0.34/0.60 (define @t60 () (_ tptp.ksnd @t26)) % 0.34/0.60 (define @t61 () (= @t2 @t60)) % 0.34/0.60 (define @t62 () (lambda @t33 @t26)) % 0.34/0.60 (define @t63 () (_ @t42 @t1)) % 0.34/0.60 (define @t64 () (_ @t63 @t2)) % 0.34/0.60 (define @t65 () (= (_ tptp.ksnd @t64) @t2)) % 0.34/0.60 (define @t66 () (forall @t5 @t65)) % 0.34/0.60 (define @t67 () (=> tptp.ksndpairEq @t53)) % 0.34/0.60 (define @t68 () (tptp.kfst @t58)) % 0.34/0.60 (define @t69 () (_ tptp.kfst @t26)) % 0.34/0.60 (define @t70 () (= @t1 @t69)) % 0.34/0.60 (define @t71 () (= (_ tptp.kfst @t64) @t1)) % 0.34/0.60 (define @t72 () (forall @t5 @t71)) % 0.34/0.60 (define @t73 () (=> tptp.kfstpairEq @t67)) % 0.34/0.60 (define @t74 () (not (= @t45 @t45))) % 0.34/0.60 (define @t75 () (or @t50 @t48 @t47 @t74)) % 0.34/0.60 (define @t76 () (not (= @t11 @t45))) % 0.34/0.60 (define @t77 () (tptp.setunion @t11)) % 0.34/0.60 (define @t78 () (not (tptp.in @t43 @t77))) % 0.34/0.60 (define @t79 () (not (tptp.in @t44 @t77))) % 0.34/0.60 (define @t80 () (tptp.ksnd @t11)) % 0.34/0.60 (define @t81 () (tptp.setadjoin @t80 tptp.emptyset)) % 0.34/0.60 (define @t82 () (tptp.kfst @t11)) % 0.34/0.60 (define @t83 () (tptp.setadjoin @t82 @t81)) % 0.34/0.60 (define @t84 () (tptp.setadjoin @t83 tptp.emptyset)) % 0.34/0.60 (define @t85 () (tptp.setadjoin @t82 tptp.emptyset)) % 0.34/0.60 (define @t86 () (tptp.setadjoin @t85 @t84)) % 0.34/0.60 (define @t87 () (= @t11 @t86)) % 0.34/0.60 (define @t88 () (or @t76 @t87 @t79 @t78 @t76)) % 0.34/0.60 (define @t89 () (or @t87 @t79 @t78 @t76)) % 0.34/0.60 (define @t90 () (forall @t16 @t89)) % 0.34/0.60 (define @t91 () (forall @t52 @t90)) % 0.34/0.60 (define @t92 () (forall (@list @t44 @t43 @t11) @t89)) % 0.34/0.60 (define @t93 () (@list @t11 @t44 @t43)) % 0.34/0.60 (define @t94 () (not (= @t45 @t11))) % 0.34/0.60 (define @t95 () (or @t87 @t79 @t78 @t94)) % 0.34/0.60 (define @t96 () (or @t79 @t78 @t94)) % 0.34/0.60 (define @t97 () (or @t96 @t87)) % 0.34/0.60 (define @t98 () (forall @t93 @t97)) % 0.34/0.60 (define @t99 () (forall @t52 @t97)) % 0.34/0.60 (define @t100 () (forall @t52 @t96)) % 0.34/0.60 (define @t101 () (@var "BOUND_VARIABLE_7480" $$unsorted)) % 0.34/0.60 (define @t102 () (or @t100 @t87)) % 0.34/0.60 (define @t103 () (tptp.setadjoin @t57 (tptp.setadjoin (tptp.setadjoin @t1 (tptp.setadjoin @t101 tptp.emptyset)) tptp.emptyset))) % 0.34/0.60 (define @t104 () (not (tptp.in @t101 @t77))) % 0.34/0.60 (define @t105 () (not (tptp.in @t1 @t77))) % 0.34/0.60 (define @t106 () (@list @t1 @t101)) % 0.34/0.60 (define @t107 () (forall @t106 (or @t105 @t104 (not (= @t103 @t11))))) % 0.34/0.60 (define @t108 () (_ (_ tptp.setadjoin @t12) tptp.emptyset)) % 0.34/0.60 (define @t109 () (_ tptp.setadjoin @t13)) % 0.34/0.60 (define @t110 () (_ @t109 @t108)) % 0.34/0.60 (define @t111 () (_ (_ tptp.setadjoin @t110) tptp.emptyset)) % 0.34/0.60 (define @t112 () (_ @t109 tptp.emptyset)) % 0.34/0.60 (define @t113 () (_ tptp.setadjoin @t112)) % 0.34/0.60 (define @t114 () (_ @t113 @t111)) % 0.34/0.60 (define @t115 () (_ tptp.setadjoin @t82)) % 0.34/0.60 (define @t116 () (= @t11 @t114)) % 0.34/0.60 (define @t117 () (or @t107 @t116)) % 0.34/0.60 (define @t118 () (not @t107)) % 0.34/0.60 (define @t119 () (lambda @t33 (_ @t113 (_ (_ tptp.setadjoin (_ @t109 @t21)) tptp.emptyset)))) % 0.34/0.60 (define @t120 () (_ @t42 @t13)) % 0.34/0.60 (define @t121 () (= (_ @t120 @t12) @t11)) % 0.34/0.60 (define @t122 () (not (= @t11 @t103))) % 0.34/0.60 (define @t123 () (or @t105 @t104 @t122)) % 0.34/0.60 (define @t124 () (forall @t106 @t123)) % 0.34/0.60 (define @t125 () (not @t124)) % 0.34/0.60 (define @t126 () (not (= @t27 @t103))) % 0.34/0.60 (define @t127 () (tptp.setunion @t27)) % 0.34/0.60 (define @t128 () (not (tptp.in @t101 @t127))) % 0.34/0.60 (define @t129 () (tptp.in @t1 @t127)) % 0.34/0.60 (define @t130 () (not @t129)) % 0.34/0.60 (define @t131 () (or @t130 @t128 @t126)) % 0.34/0.60 (define @t132 () (_ (lambda @t40 (not (forall @t106 @t131))) @t11)) % 0.34/0.60 (define @t133 () (=> @t132 @t121)) % 0.34/0.60 (define @t134 () (forall @t16 @t133)) % 0.34/0.60 (define @t135 () (=> tptp.ksndpairEq @t134)) % 0.34/0.60 (define @t136 () (=> tptp.kfstpairEq @t135)) % 0.34/0.60 (define @t137 () (or @t128 @t126)) % 0.34/0.60 (define @t138 () (or @t130 @t137)) % 0.34/0.60 (define @t139 () (forall @t106 @t138)) % 0.34/0.60 (define @t140 () (@list @t101)) % 0.34/0.60 (define @t141 () (forall @t140 @t138)) % 0.34/0.60 (define @t142 () (forall @t140 @t137)) % 0.34/0.60 (define @t143 () (or @t130 @t142)) % 0.34/0.60 (define @t144 () (tptp.in @t2 @t127)) % 0.34/0.60 (define @t145 () (forall @t33 (or (not @t144) (not (= @t27 @t58))))) % 0.34/0.60 (define @t146 () (not @t36)) % 0.34/0.60 (define @t147 () (or @t146 @t145)) % 0.34/0.60 (define @t148 () (not @t145)) % 0.34/0.60 (define @t149 () (and @t36 @t148)) % 0.34/0.60 (define @t150 () (forall @t38 (not @t149))) % 0.34/0.60 (define @t151 () (not @t150)) % 0.34/0.60 (define @t152 () (not @t28)) % 0.34/0.60 (define @t153 () (not @t31)) % 0.34/0.60 (define @t154 () (or @t153 @t152)) % 0.34/0.60 (define @t155 () (forall @t33 (not @t32))) % 0.34/0.60 (define @t156 () (not @t155)) % 0.34/0.60 (define @t157 () (@quantifiers_skolemize @t53 1)) % 0.34/0.60 (define @t158 () (tptp.setadjoin @t157 tptp.emptyset)) % 0.34/0.60 (define @t159 () (@quantifiers_skolemize @t53 0)) % 0.34/0.60 (define @t160 () (tptp.setadjoin @t159 @t158)) % 0.34/0.60 (define @t161 () (tptp.setadjoin @t160 tptp.emptyset)) % 0.34/0.60 (define @t162 () (tptp.setadjoin @t159 tptp.emptyset)) % 0.34/0.60 (define @t163 () (tptp.setadjoin @t162 @t161)) % 0.34/0.60 (define @t164 () (tptp.setunion @t163)) % 0.34/0.60 (define @t165 () (tptp.ksnd @t163)) % 0.34/0.60 (define @t166 () (tptp.kfst @t163)) % 0.34/0.60 (define @t167 () (= @t163 (tptp.setadjoin (tptp.setadjoin @t166 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t166 (tptp.setadjoin @t165 tptp.emptyset)) tptp.emptyset)))) % 0.34/0.60 (define @t168 () (or @t167 (not (tptp.in @t159 @t164)) (not (tptp.in @t157 @t164)))) % 0.34/0.60 (define @t169 () (@list @t159 @t157)) % 0.34/0.60 (define @t170 () (= @t159 @t166)) % 0.34/0.60 (define @t171 () (= @t157 @t165)) % 0.34/0.60 (define @t172 () (and @t170 @t171)) % 0.34/0.60 (assume @p1 @t7) % 0.34/0.60 (assume @p2 @t10) % 0.34/0.60 (assume @p3 @t20) % 0.34/0.60 (assume @p4 true) % 0.34/0.60 (step @p5 (= tptp.iskpair @t41) :rule refl :args (@t41)) % 0.34/0.60 (step @p6 (= tptp.kpair @t42) :rule refl :args (@t42)) % 0.34/0.60 (step @p7 :rule refl :args (@t53)) % 0.34/0.60 (step @p8 :rule refl :args ((tptp.ksnd @t26))) % 0.34/0.60 (step @p9 :rule refl :args ((tptp.setadjoin @t25 @t24))) % 0.34/0.60 (step @p10 :rule refl :args ((tptp.setadjoin @t23 tptp.emptyset))) % 0.34/0.60 (step @p11 :rule refl :args (tptp.emptyset)) % 0.34/0.60 (step @p12 :rule refl :args ((tptp.setadjoin @t1 @t21))) % 0.34/0.60 (step @p13 :rule refl :args (@t54)) % 0.34/0.60 (step @p14 :rule refl :args (@t1)) % 0.34/0.60 (step @p15 :rule cong :premises (@p14 @p13) :args (@t55)) % 0.34/0.60 (step @p16 :rule trans :premises (@p15 @p12)) % 0.34/0.60 (step @p17 :rule cong :premises (@p16 @p11) :args (@t56)) % 0.34/0.60 (step @p18 :rule trans :premises (@p17 @p10)) % 0.34/0.60 (step @p19 :rule refl :args (@t57)) % 0.34/0.60 (step @p20 :rule cong :premises (@p19 @p18) :args (@t58)) % 0.34/0.60 (step @p21 :rule trans :premises (@p20 @p9)) % 0.34/0.60 (step @p22 :rule cong :premises (@p21) :args (@t59)) % 0.34/0.60 (step @p23 :rule trans :premises (@p22 @p8)) % 0.34/0.60 (step @p24 :rule refl :args (tptp.ksnd)) % 0.34/0.60 (step @p25 :rule ho_cong :premises (@p24 @p21)) % 0.34/0.60 (step @p26 :rule cong :premises (@p25 @p23) :args ((= (_ tptp.ksnd @t58) @t59))) % 0.34/0.60 (step @p27 :rule symm :premises (@p26)) % 0.34/0.60 (step @p28 :rule refl :args (@t60)) % 0.34/0.60 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 0.34/0.60 (step @p30 :rule refl :args (tptp.setadjoin)) % 0.34/0.60 (step @p31 :rule ho_cong :premises (@p30 @p19)) % 0.34/0.60 (step @p32 :rule ho_cong :premises (@p31 @p18)) % 0.34/0.60 (step @p33 :rule cong :premises (@p32 @p21) :args ((= (_ (_ tptp.setadjoin @t57) @t56) @t58))) % 0.34/0.60 (step @p34 :rule symm :premises (@p33)) % 0.34/0.60 (step @p35 :rule refl :args (@t26)) % 0.34/0.60 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 0.34/0.60 (step @p37 :rule ho_cong :premises (@p30 @p16)) % 0.34/0.60 (step @p38 :rule ho_cong :premises (@p37 @p11)) % 0.34/0.60 (step @p39 :rule cong :premises (@p38 @p18) :args ((= (_ (_ tptp.setadjoin @t55) tptp.emptyset) @t56))) % 0.34/0.60 (step @p40 :rule symm :premises (@p39)) % 0.34/0.60 (step @p41 :rule refl :args (@t24)) % 0.34/0.60 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.34/0.60 (step @p43 :rule refl :args (@t22)) % 0.34/0.60 (step @p44 :rule ho_cong :premises (@p43 @p13)) % 0.34/0.60 (step @p45 :rule cong :premises (@p44 @p16) :args ((= (_ @t22 @t54) @t55))) % 0.34/0.60 (step @p46 :rule symm :premises (@p45)) % 0.34/0.60 (step @p47 :rule refl :args (@t23)) % 0.34/0.60 (step @p48 :rule eq_resolve :premises (@p47 @p46)) % 0.34/0.60 (step @p49 :rule refl :args (@t21)) % 0.34/0.60 (step @p50 :rule cong :premises (@p49 @p13) :args ((= @t21 @t54))) % 0.34/0.60 (step @p51 :rule symm :premises (@p50)) % 0.34/0.60 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.34/0.60 (step @p53 :rule ho_cong :premises (@p43 @p52)) % 0.34/0.60 (step @p54 :rule trans :premises (@p53 @p48)) % 0.34/0.60 (step @p55 :rule ho_cong :premises (@p30 @p54)) % 0.34/0.60 (step @p56 :rule ho_cong :premises (@p55 @p11)) % 0.34/0.60 (step @p57 :rule trans :premises (@p56 @p42)) % 0.34/0.60 (step @p58 :rule refl :args (@t25)) % 0.34/0.60 (step @p59 :rule cong :premises (@p58 @p19) :args ((= @t25 @t57))) % 0.34/0.60 (step @p60 :rule symm :premises (@p59)) % 0.34/0.60 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.34/0.60 (step @p62 :rule ho_cong :premises (@p30 @p61)) % 0.34/0.60 (step @p63 :rule ho_cong :premises (@p62 @p57)) % 0.34/0.60 (step @p64 :rule trans :premises (@p63 @p36)) % 0.34/0.60 (step @p65 :rule ho_cong :premises (@p24 @p64)) % 0.34/0.60 (step @p66 :rule trans :premises (@p65 @p29)) % 0.34/0.60 (step @p67 :rule refl :args (@t2)) % 0.34/0.60 (step @p68 :rule cong :premises (@p67 @p66) :args (@t61)) % 0.34/0.60 (step @p69 :rule cong :premises (@p68) :args ((forall @t5 @t61))) % 0.34/0.60 (step @p70 :rule eq-symm :args (@t60 @t2)) % 0.34/0.60 (step @p71 :rule refl :args (@t2)) % 0.34/0.60 (step @p72 :rule beta-reduce :args 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% 0.34/0.60 (step @p316 :rule trans :premises (@p315 @p314)) % 0.34/0.60 (step @p317 :rule refl :args (@t27)) % 0.34/0.60 (step @p318 :rule cong :premises (@p317 @p64) :args (@t28)) % 0.34/0.60 (step @p319 :rule cong :premises (@p318) :args (@t152)) % 0.34/0.60 (step @p320 :rule refl :args ((tptp.in @t2 @t29))) % 0.34/0.61 (step @p321 :rule cong :premises (@p67 @p288) :args (@t144)) % 0.34/0.61 (step @p322 :rule trans :premises (@p321 @p320)) % 0.34/0.61 (step @p323 :rule refl :args (@t30)) % 0.34/0.61 (step @p324 :rule ho_cong :premises (@p323 @p288)) % 0.34/0.61 (step @p325 :rule cong :premises (@p324 @p322) :args ((= (_ @t30 @t127) @t144))) % 0.34/0.61 (step @p326 :rule symm :premises (@p325)) % 0.34/0.61 (step @p327 :rule refl :args (@t31)) % 0.34/0.61 (step @p328 :rule eq_resolve :premises (@p327 @p326)) % 0.34/0.61 (step @p329 :rule ho_cong :premises (@p323 @p300)) % 0.34/0.61 (step @p330 :rule trans :premises (@p329 @p328)) % 0.34/0.61 (step @p331 :rule cong :premises (@p330) :args (@t153)) % 0.34/0.61 (step @p332 :rule nary_cong :premises (@p331 @p319) :args (@t154)) % 0.34/0.61 (step @p333 :rule cong :premises (@p332) :args ((forall @t33 @t154))) % 0.34/0.61 (step @p334 :rule bool-and-de-morgan :args (@t31 @t28 true)) % 0.34/0.61 (step @p335 :rule cong :premises (@p334) :args (@t155)) % 0.34/0.61 (step @p336 :rule trans :premises (@p335 @p333)) % 0.34/0.61 (step @p337 :rule cong :premises (@p336) :args (@t156)) % 0.34/0.61 (step @p338 :rule exists-elim :args ((= @t34 @t156))) % 0.34/0.61 (step @p339 :rule trans :premises (@p338 @p337)) % 0.34/0.61 (step @p340 :rule refl :args (@t36)) % 0.34/0.61 (step @p341 :rule nary_cong :premises (@p340 @p339) :args (@t37)) % 0.34/0.61 (step @p342 :rule cong :premises (@p341) :args (@t39)) % 0.34/0.61 (step @p343 :rule trans :premises (@p342 @p316)) % 0.34/0.61 (step @p344 :rule cong :premises (@p343) :args (@t41)) % 0.34/0.61 (step @p345 :rule trans :premises (@p5 @p344)) % 0.34/0.61 (step @p346 :rule ho_cong :premises (@p345 @p247)) % 0.34/0.61 (step @p347 :rule cong :premises (@p346 @p273) :args (@t15)) % 0.34/0.61 (step @p348 :rule cong :premises (@p347) :args (@t17)) % 0.34/0.61 (step @p349 :rule cong :premises (@p82 @p348) :args (@t18)) % 0.34/0.61 (step @p350 :rule cong :premises (@p114 @p349) :args (@t19)) % 0.34/0.61 (step @p351 :rule cong :premises (@p350) :args (@t20)) % 0.34/0.61 (step @p352 :rule trans :premises (@p351 @p269)) % 0.34/0.61 (step @p353 :rule trans :premises (@p352 @p123)) % 0.34/0.61 (step @p354 :rule eq_resolve :premises (@p3 @p353)) % 0.34/0.61 (step @p355 :rule not_implies_elim2 :premises (@p354)) % 0.34/0.61 (step @p356 :rule not_implies_elim2 :premises (@p355)) % 0.34/0.61 (step @p357 :rule skolemize :premises (@p356)) % 0.34/0.61 (step @p358 :rule cnf_or_neg :args (@t168 0)) % 0.34/0.61 (step @p359 :rule chain_m_resolution :premises (@p358 @p357) :args ((not @t167) (@list true) (@list @t168))) % 0.34/0.61 (step @p360 :rule not_implies_elim1 :premises (@p354)) % 0.34/0.61 (step @p361 :rule instantiate :premises (@p360) :args (@t169)) % 0.34/0.61 (step @p362 :rule not_implies_elim1 :premises (@p355)) % 0.34/0.61 (step @p363 :rule instantiate :premises (@p362) :args (@t169)) % 0.34/0.61 (assume-push @p380 @t170) % 0.34/0.61 (assume-push @p381 @t171) % 0.34/0.61 (step @p366 :rule refl :args (tptp.emptyset)) % 0.34/0.61 (step @p367 :rule cong :premises (@p363 @p366) :args (@t158)) % 0.34/0.61 (step @p368 :rule cong :premises (@p361 @p367) :args (@t160)) % 0.34/0.61 (step @p369 :rule cong :premises (@p368 @p366) :args (@t161)) % 0.34/0.61 (step @p370 :rule cong :premises (@p361 @p366) :args (@t162)) % 0.34/0.61 (step @p371 :rule cong :premises (@p370 @p369) :args (@t163)) % 0.34/0.61 (step-pop @p382 :rule scope :premises (@p371)) % 0.34/0.61 (step-pop @p383 :rule scope :premises (@p382)) % 0.34/0.61 (step @p372 :rule process_scope :premises (@p383) :args (@t167)) % 0.34/0.61 (step @p375 :rule implies_elim :premises (@p372)) % 0.34/0.61 (step @p376 :rule cnf_and_neg :args (@t172)) % 0.34/0.61 (step @p377 :rule resolution :premises (@p376 @p375) :args (true @t172)) % 0.34/0.61 (step @p378 :rule reordering :premises (@p377) :args ((or @t167 (not @t170) (not @t171)))) % 0.34/0.61 (step @p379 false :rule chain_m_resolution :premises (@p378 @p363 @p361 @p359) :args (false (@list false false true) (@list @t171 @t170 @t167))) % 0.34/0.61 ) % 0.34/0.61 % SZS output end Proof % 0.34/0.61 % cvc5 exiting %------------------------------------------------------------------------------