%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU776^2 : 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 : n016.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 08:53:08 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU776^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.15 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.36 % Computer : n016.cluster.edu % 0.17/0.36 % Model : x86_64 x86_64 % 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.36 % Memory : 8042.1875MB % 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Tue Jun 2 17:51:54 EDT 2026 % 0.17/0.36 % CPUTime : % 0.32/0.51 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.dpsetconstr (-> $$unsorted $$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted)) % 0.37/0.61 (declare-const tptp.dpsetconstrI Bool) % 0.37/0.61 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.37/0.61 (define tptp.breln1 () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.breln _let_2) _let_2) _let_1))))) % 0.37/0.61 (define tptp.breln1invset () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xy" $$unsorted))) (let ((_let_4 (@var "A" $$unsorted))) (lambda (@list _let_4 _let_1) (_ (_ (_ tptp.dpsetconstr _let_4) _let_4) (lambda (@list _let_2 _let_3) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))) % 0.37/0.61 (define @t1 () (@var "Xu" $$unsorted)) % 0.37/0.61 (define @t2 () (@var "Xz" $$unsorted)) % 0.37/0.61 (define @t3 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.37/0.61 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.37/0.61 (define @t5 () (@list @t2 @t1)) % 0.37/0.61 (define @t6 () (lambda @t5 @t4)) % 0.37/0.61 (define @t7 () (@var "B" $$unsorted)) % 0.37/0.61 (define @t8 () (@var "A" $$unsorted)) % 0.37/0.61 (define @t9 () (_ tptp.dpsetconstr @t8)) % 0.37/0.61 (define @t10 () (_ @t9 @t7)) % 0.37/0.61 (define @t11 () (_ @t10 @t6)) % 0.37/0.61 (define @t12 () (@var "Xy" $$unsorted)) % 0.37/0.61 (define @t13 () (@var "Xx" $$unsorted)) % 0.37/0.61 (define @t14 () (_ (_ tptp.kpair @t13) @t12)) % 0.37/0.61 (define @t15 () (_ tptp.in @t14)) % 0.37/0.61 (define @t16 () (_ @t15 @t11)) % 0.37/0.61 (define @t17 () (_ (_ @t3 @t13) @t12)) % 0.37/0.61 (define @t18 () (=> @t17 @t16)) % 0.37/0.61 (define @t19 () (_ tptp.in @t12)) % 0.37/0.61 (define @t20 () (_ @t19 @t7)) % 0.37/0.61 (define @t21 () (@list @t12)) % 0.37/0.61 (define @t22 () (forall @t21 (=> @t20 @t18))) % 0.37/0.61 (define @t23 () (_ (_ tptp.in @t13) @t8)) % 0.37/0.61 (define @t24 () (=> @t23 @t22)) % 0.37/0.61 (define @t25 () (@list @t8 @t7 @t3 @t13)) % 0.37/0.61 (define @t26 () (forall @t25 @t24)) % 0.37/0.61 (define @t27 () (= tptp.dpsetconstrI @t26)) % 0.37/0.61 (define @t28 () (@var "R" $$unsorted)) % 0.37/0.61 (define @t29 () (_ (_ tptp.kpair @t12) @t13)) % 0.37/0.61 (define @t30 () (_ tptp.in @t29)) % 0.37/0.61 (define @t31 () (_ @t15 @t28)) % 0.37/0.61 (define @t32 () (=> @t31 (_ @t30 (_ (_ tptp.breln1invset @t8) @t28)))) % 0.37/0.61 (define @t33 () (_ @t19 @t8)) % 0.37/0.61 (define @t34 () (=> @t33 @t32)) % 0.37/0.61 (define @t35 () (forall @t21 @t34)) % 0.37/0.61 (define @t36 () (=> @t23 @t35)) % 0.37/0.61 (define @t37 () (@list @t13)) % 0.37/0.61 (define @t38 () (forall @t37 @t36)) % 0.37/0.61 (define @t39 () (=> (_ (_ tptp.breln1 @t8) @t28) @t38)) % 0.37/0.61 (define @t40 () (@list @t8 @t28)) % 0.37/0.61 (define @t41 () (forall @t40 @t39)) % 0.37/0.61 (define @t42 () (=> tptp.dpsetconstrI @t41)) % 0.37/0.61 (define @t43 () (not @t42)) % 0.37/0.61 (define @t44 () (_ tptp.cartprod @t8)) % 0.37/0.61 (define @t45 () (@var "C" $$unsorted)) % 0.37/0.61 (define @t46 () (_ tptp.subset @t45)) % 0.37/0.61 (define @t47 () (_ @t46 (_ @t44 @t7))) % 0.37/0.61 (define @t48 () (lambda (@list @t8 @t7 @t45) @t47)) % 0.37/0.61 (define @t49 () (lambda @t40 (_ (_ (_ tptp.breln @t8) @t8) @t28))) % 0.37/0.61 (define @t50 () (lambda (@list @t13 @t12) (_ @t30 @t28))) % 0.37/0.61 (define @t51 () (_ @t9 @t8)) % 0.37/0.61 (define @t52 () (_ @t51 @t50)) % 0.37/0.61 (define @t53 () (lambda @t40 @t52)) % 0.37/0.61 (define @t54 () (@var "BOUND_VARIABLE_7645" $$unsorted)) % 0.37/0.61 (define @t55 () (@var "BOUND_VARIABLE_7604" $$unsorted)) % 0.37/0.61 (define @t56 () (tptp.kpair @t55 @t54)) % 0.37/0.61 (define @t57 () (@list @t54 @t55)) % 0.37/0.61 (define @t58 () (tptp.dpsetconstr @t8 @t8 (lambda @t57 (tptp.in @t56 @t28)))) % 0.37/0.61 (define @t59 () (@var "BOUND_VARIABLE_7688" $$unsorted)) % 0.37/0.61 (define @t60 () (@var "BOUND_VARIABLE_7690" $$unsorted)) % 0.37/0.61 (define @t61 () (tptp.in (tptp.kpair @t60 @t59) @t58)) % 0.37/0.61 (define @t62 () (not (tptp.in (tptp.kpair @t59 @t60) @t28))) % 0.37/0.61 (define @t63 () (not (tptp.in @t60 @t8))) % 0.37/0.61 (define @t64 () (not (tptp.in @t59 @t8))) % 0.37/0.61 (define @t65 () (tptp.cartprod @t8 @t8)) % 0.37/0.61 (define @t66 () (tptp.subset @t28 @t65)) % 0.37/0.61 (define @t67 () (not @t66)) % 0.37/0.61 (define @t68 () (or @t67 @t64 @t63 @t62 @t61)) % 0.37/0.61 (define @t69 () (@list @t8 @t28 @t59 @t60)) % 0.37/0.61 (define @t70 () (forall @t69 @t68)) % 0.37/0.61 (define @t71 () (tptp.dpsetconstr @t8 @t7 @t3)) % 0.37/0.61 (define @t72 () (@var "BOUND_VARIABLE_7559" $$unsorted)) % 0.37/0.61 (define @t73 () (tptp.in (tptp.kpair @t13 @t72) @t71)) % 0.37/0.61 (define @t74 () (not (_ @t3 @t13 @t72))) % 0.37/0.61 (define @t75 () (not (tptp.in @t72 @t7))) % 0.37/0.61 (define @t76 () (tptp.in @t13 @t8)) % 0.37/0.61 (define @t77 () (not @t76)) % 0.37/0.61 (define @t78 () (or @t75 @t74 @t73)) % 0.37/0.61 (define @t79 () (or @t77 @t78)) % 0.37/0.61 (define @t80 () (forall (@list @t8 @t7 @t3 @t13 @t72) @t79)) % 0.37/0.61 (define @t81 () (@list @t72)) % 0.37/0.61 (define @t82 () (forall @t81 @t79)) % 0.37/0.61 (define @t83 () (forall @t81 @t78)) % 0.37/0.61 (define @t84 () (@list @t12)) % 0.37/0.61 (define @t85 () (or @t77 @t83)) % 0.37/0.61 (define @t86 () (tptp.kpair @t13 @t12)) % 0.37/0.61 (define @t87 () (_ @t3 @t13 @t12)) % 0.37/0.61 (define @t88 () (not @t87)) % 0.37/0.61 (define @t89 () (tptp.in @t12 @t7)) % 0.37/0.61 (define @t90 () (not @t89)) % 0.37/0.61 (define @t91 () (forall @t21 (or @t90 @t88 (tptp.in @t86 @t71)))) % 0.37/0.61 (define @t92 () (not @t23)) % 0.37/0.61 (define @t93 () (or @t92 @t91)) % 0.37/0.61 (define @t94 () (_ @t3 @t2 @t1)) % 0.37/0.61 (define @t95 () (lambda @t5 @t94)) % 0.37/0.61 (define @t96 () (tptp.dpsetconstr @t8 @t7 @t95)) % 0.37/0.61 (define @t97 () (tptp.in @t86 @t96)) % 0.37/0.61 (define @t98 () (or @t90 @t88 @t97)) % 0.37/0.61 (define @t99 () (_ tptp.in @t86)) % 0.37/0.61 (define @t100 () (not @t17)) % 0.37/0.61 (define @t101 () (not @t20)) % 0.37/0.61 (define @t102 () (or @t101 @t100 @t16)) % 0.37/0.61 (define @t103 () (=> tptp.dpsetconstrI @t70)) % 0.37/0.61 (define @t104 () (or @t64 @t63 @t62 @t61)) % 0.37/0.61 (define @t105 () (or @t67 @t104)) % 0.37/0.61 (define @t106 () (forall @t69 @t105)) % 0.37/0.61 (define @t107 () (@list @t59 @t60)) % 0.37/0.61 (define @t108 () (forall @t107 @t105)) % 0.37/0.61 (define @t109 () (forall @t107 @t104)) % 0.37/0.61 (define @t110 () (@var "BOUND_VARIABLE_7662" $$unsorted)) % 0.37/0.61 (define @t111 () (or @t67 @t109)) % 0.37/0.61 (define @t112 () (tptp.in (tptp.kpair @t110 @t13) @t58)) % 0.37/0.61 (define @t113 () (not (tptp.in (tptp.kpair @t13 @t110) @t28))) % 0.37/0.61 (define @t114 () (not (tptp.in @t110 @t8))) % 0.37/0.61 (define @t115 () (or @t77 @t114 @t113 @t112)) % 0.37/0.61 (define @t116 () (@list @t13 @t110)) % 0.37/0.61 (define @t117 () (forall @t116 @t115)) % 0.37/0.61 (define @t118 () (_ @t44 @t8)) % 0.37/0.62 (define @t119 () (_ tptp.subset @t28)) % 0.37/0.62 (define @t120 () (_ @t119 @t118)) % 0.37/0.62 (define @t121 () (not @t120)) % 0.37/0.62 (define @t122 () (or @t121 @t117)) % 0.37/0.62 (define @t123 () (or @t114 @t113 @t112)) % 0.37/0.62 (define @t124 () (or @t77 @t123)) % 0.37/0.62 (define @t125 () (forall @t116 @t124)) % 0.37/0.62 (define @t126 () (@list @t110)) % 0.37/0.62 (define @t127 () (forall @t126 @t124)) % 0.37/0.62 (define @t128 () (forall @t126 @t123)) % 0.37/0.62 (define @t129 () (or @t77 @t128)) % 0.37/0.62 (define @t130 () (tptp.kpair @t12 @t13)) % 0.37/0.62 (define @t131 () (tptp.in @t86 @t28)) % 0.37/0.62 (define @t132 () (not @t131)) % 0.37/0.62 (define @t133 () (tptp.in @t12 @t8)) % 0.37/0.62 (define @t134 () (not @t133)) % 0.37/0.62 (define @t135 () (forall @t21 (or @t134 @t132 (tptp.in @t130 @t58)))) % 0.37/0.62 (define @t136 () (or @t92 @t135)) % 0.37/0.62 (define @t137 () (tptp.kpair @t55 @t13)) % 0.37/0.62 (define @t138 () (tptp.in @t137 @t28)) % 0.37/0.62 (define @t139 () (@list @t13 @t55)) % 0.37/0.62 (define @t140 () (lambda @t139 @t138)) % 0.37/0.62 (define @t141 () (tptp.dpsetconstr @t8 @t8 @t140)) % 0.37/0.62 (define @t142 () (tptp.in @t130 @t141)) % 0.37/0.62 (define @t143 () (or @t134 @t132 @t142)) % 0.37/0.62 (define @t144 () (forall @t21 @t143)) % 0.37/0.62 (define @t145 () (=> @t23 @t144)) % 0.37/0.62 (define @t146 () (_ (_ tptp.kpair @t55) @t13)) % 0.37/0.62 (define @t147 () (_ (_ tptp.in @t146) @t28)) % 0.37/0.62 (define @t148 () (lambda @t139 @t147)) % 0.37/0.62 (define @t149 () (_ @t51 @t148)) % 0.37/0.62 (define @t150 () (_ @t30 @t149)) % 0.37/0.62 (define @t151 () (not @t31)) % 0.37/0.62 (define @t152 () (not @t33)) % 0.37/0.62 (define @t153 () (or @t152 @t151 @t150)) % 0.37/0.62 (define @t154 () (=> @t31 @t150)) % 0.37/0.62 (define @t155 () (=> @t31 (_ @t30 @t52))) % 0.37/0.62 (define @t156 () (=> @t33 @t155)) % 0.37/0.62 (define @t157 () (@list @t28)) % 0.37/0.62 (define @t158 () (lambda @t157 @t52)) % 0.37/0.62 (define @t159 () (_ @t53 @t8)) % 0.37/0.62 (define @t160 () (=> @t31 (_ @t30 (_ @t159 @t28)))) % 0.37/0.62 (define @t161 () (=> @t33 @t160)) % 0.37/0.62 (define @t162 () (forall @t21 @t161)) % 0.37/0.62 (define @t163 () (=> @t23 @t162)) % 0.37/0.62 (define @t164 () (forall @t37 @t163)) % 0.37/0.62 (define @t165 () (lambda @t157 @t120)) % 0.37/0.62 (define @t166 () (_ (lambda @t40 @t120) @t8)) % 0.37/0.62 (define @t167 () (=> (_ @t166 @t28) @t164)) % 0.37/0.62 (define @t168 () (forall @t40 @t167)) % 0.37/0.62 (define @t169 () (=> tptp.dpsetconstrI @t168)) % 0.37/0.62 (define @t170 () (lambda (@list @t45) (_ @t46 @t118))) % 0.37/0.62 (define @t171 () (lambda (@list @t7 @t45) @t47)) % 0.37/0.62 (define @t172 () (@quantifiers_skolemize @t70 1)) % 0.37/0.62 (define @t173 () (tptp.in @t56 @t172)) % 0.37/0.62 (define @t174 () (lambda @t57 @t173)) % 0.37/0.62 (define @t175 () (@purify @t174)) % 0.37/0.62 (define @t176 () (@quantifiers_skolemize @t70 0)) % 0.37/0.62 (define @t177 () (@quantifiers_skolemize @t70 2)) % 0.37/0.62 (define @t178 () (@quantifiers_skolemize @t70 3)) % 0.37/0.62 (define @t179 () (tptp.kpair @t178 @t177)) % 0.37/0.62 (define @t180 () (tptp.in @t179 (tptp.dpsetconstr @t176 @t176 @t175))) % 0.37/0.62 (define @t181 () (tptp.in (tptp.kpair @t177 @t178) @t172)) % 0.37/0.62 (define @t182 () (not @t181)) % 0.37/0.62 (define @t183 () (tptp.in @t178 @t176)) % 0.37/0.62 (define @t184 () (not @t183)) % 0.37/0.62 (define @t185 () (tptp.in @t177 @t176)) % 0.37/0.62 (define @t186 () (not @t185)) % 0.37/0.62 (define @t187 () (not (tptp.subset @t172 (tptp.cartprod @t176 @t176)))) % 0.37/0.62 (define @t188 () (or @t187 @t186 @t184 @t182 @t180)) % 0.37/0.62 (define @t189 () (not @t188)) % 0.37/0.62 (define @t190 () (not @t70)) % 0.37/0.62 (define @t191 () (tptp.dpsetconstr @t176 @t176 @t174)) % 0.37/0.62 (define @t192 () (tptp.in @t179 @t191)) % 0.37/0.62 (define @t193 () (or @t187 @t186 @t184 @t182 @t192)) % 0.37/0.62 (define @t194 () (not @t193)) % 0.37/0.62 (define @t195 () (@list true)) % 0.37/0.62 (define @t196 () (@list @t188)) % 0.37/0.62 (define @t197 () (_ @t175 @t54 @t55)) % 0.37/0.62 (define @t198 () (_ @t174 @t54 @t55)) % 0.37/0.62 (define @t199 () (= @t197 @t198)) % 0.37/0.62 (define @t200 () (forall @t57 @t199)) % 0.37/0.62 (define @t201 () (_ @t175 @t178 @t177)) % 0.37/0.62 (define @t202 () (not @t201)) % 0.37/0.62 (define @t203 () (or @t184 @t186 @t202 @t180)) % 0.37/0.62 (define @t204 () (= @t181 @t201)) % 0.37/0.62 (assume @p1 @t27) % 0.37/0.62 (assume @p2 @t43) % 0.37/0.62 (assume @p3 true) % 0.37/0.62 (step @p4 (= tptp.breln @t48) :rule refl :args (@t48)) % 0.37/0.62 (step @p5 (= tptp.breln1 @t49) :rule refl :args (@t49)) % 0.37/0.62 (step @p6 (= tptp.breln1invset @t53) :rule refl :args (@t53)) % 0.37/0.62 (step @p7 :rule refl :args (@t70)) % 0.37/0.62 (step @p8 :rule aci_norm :args ((= @t79 (or @t77 @t75 @t74 @t73)))) % 0.37/0.62 (step @p9 :rule cong :premises (@p8) :args (@t80)) % 0.37/0.62 (step @p10 :rule quant-merge-prenex :args ((= (forall @t25 @t82) @t80))) % 0.37/0.62 (step @p11 :rule alpha_equiv :args (@t83 (@list @t72) @t84)) % 0.37/0.62 (step @p12 :rule refl :args (@t77)) % 0.37/0.62 (step @p13 :rule nary_cong :premises (@p12 @p11) :args (@t85)) % 0.37/0.62 (step @p14 :rule quant-miniscope-or :args ((= @t82 @t85))) % 0.37/0.62 (step @p15 :rule trans :premises (@p14 @p13)) % 0.37/0.62 (step @p16 :rule symm :premises (@p15)) % 0.37/0.62 (step @p17 :rule cong :premises (@p16) :args ((forall @t25 (or @t77 @t91)))) % 0.37/0.62 (step @p18 :rule trans :premises (@p17 @p10)) % 0.37/0.62 (step @p19 :rule trans :premises (@p18 @p9)) % 0.37/0.62 (step @p20 :rule refl :args (@t91)) % 0.37/0.62 (step @p21 :rule refl :args (@t76)) % 0.37/0.62 (step @p22 :rule refl :args (@t23)) % 0.37/0.62 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t23 @t76))) % 0.37/0.62 (step @p24 :rule symm :premises (@p23)) % 0.37/0.62 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.37/0.62 (step @p26 :rule cong :premises (@p25) :args (@t92)) % 0.37/0.62 (step @p27 :rule nary_cong :premises (@p26 @p20) :args (@t93)) % 0.37/0.62 (step @p28 :rule cong :premises (@p27) :args ((forall @t25 @t93))) % 0.37/0.62 (step @p29 :rule trans :premises (@p28 @p19)) % 0.37/0.62 (step @p30 :rule bool-impl-elim :args (@t23 @t91)) % 0.37/0.62 (step @p31 :rule cong :premises (@p30) :args ((forall @t25 (=> @t23 @t91)))) % 0.37/0.62 (step @p32 :rule trans :premises (@p31 @p29)) % 0.37/0.62 (step @p33 :rule lambda-elim :args ((= @t95 @t3))) % 0.37/0.62 (step @p34 :rule refl :args (@t7)) % 0.37/0.62 (step @p35 :rule refl :args (@t8)) % 0.37/0.62 (step @p36 :rule cong :premises (@p35 @p34 @p33) :args (@t96)) % 0.37/0.62 (step @p37 :rule refl :args (@t86)) % 0.37/0.62 (step @p38 :rule cong :premises (@p37 @p36) :args (@t97)) % 0.37/0.62 (step @p39 :rule refl :args (@t88)) % 0.37/0.62 (step @p40 :rule refl :args (@t90)) % 0.37/0.62 (step @p41 :rule nary_cong :premises (@p40 @p39 @p38) :args (@t98)) % 0.37/0.62 (step @p42 :rule cong :premises (@p41) :args ((forall @t21 @t98))) % 0.37/0.62 (step @p43 :rule refl :args ((tptp.in @t14 @t11))) % 0.37/0.62 (step @p44 :rule refl :args ((tptp.dpsetconstr @t8 @t7 @t6))) % 0.37/0.62 (step @p45 :rule refl :args (@t94)) % 0.37/0.62 (step @p46 :rule cong :premises (@p45) :args (@t95)) % 0.37/0.62 (step @p47 :rule refl :args (@t7)) % 0.37/0.62 (step @p48 :rule refl :args (@t8)) % 0.37/0.62 (step @p49 :rule cong :premises (@p48 @p47 @p46) :args (@t96)) % 0.37/0.62 (step @p50 :rule trans :premises (@p49 @p44)) % 0.37/0.62 (step @p51 :rule refl :args (@t86)) % 0.37/0.62 (step @p52 :rule cong :premises (@p51 @p50) :args (@t97)) % 0.37/0.62 (step @p53 :rule trans :premises (@p52 @p43)) % 0.37/0.62 (step @p54 :rule refl :args (tptp.in)) % 0.37/0.62 (step @p55 :rule ho_cong :premises (@p54 @p51)) % 0.37/0.62 (step @p56 :rule ho_cong :premises (@p55 @p50)) % 0.37/0.62 (step @p57 :rule cong :premises (@p56 @p53) :args ((= (_ @t99 @t96) @t97))) % 0.37/0.62 (step @p58 :rule symm :premises (@p57)) % 0.37/0.62 (step @p59 :rule refl :args (@t16)) % 0.37/0.62 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 0.37/0.62 (step @p61 :rule refl :args (@t10)) % 0.37/0.62 (step @p62 :rule ho_cong :premises (@p61 @p46)) % 0.37/0.62 (step @p63 :rule cong :premises (@p62 @p50) :args ((= (_ @t10 @t95) @t96))) % 0.37/0.62 (step @p64 :rule symm :premises (@p63)) % 0.37/0.62 (step @p65 :rule refl :args (@t11)) % 0.37/0.62 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.37/0.62 (step @p67 :rule refl :args (@t4)) % 0.37/0.62 (step @p68 :rule cong :premises (@p67 @p45) :args ((= @t4 @t94))) % 0.37/0.62 (step @p69 :rule symm :premises (@p68)) % 0.37/0.62 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.37/0.62 (step @p71 :rule cong :premises (@p70) :args (@t6)) % 0.37/0.62 (step @p72 :rule ho_cong :premises (@p61 @p71)) % 0.37/0.62 (step @p73 :rule trans :premises (@p72 @p66)) % 0.37/0.62 (step @p74 :rule refl :args (@t14)) % 0.37/0.62 (step @p75 :rule cong :premises (@p74 @p51) :args ((= @t14 @t86))) % 0.37/0.62 (step @p76 :rule symm :premises (@p75)) % 0.37/0.62 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 0.37/0.62 (step @p78 :rule ho_cong :premises (@p54 @p77)) % 0.37/0.62 (step @p79 :rule ho_cong :premises (@p78 @p73)) % 0.37/0.62 (step @p80 :rule trans :premises (@p79 @p60)) % 0.37/0.62 (step @p81 :rule refl :args (@t87)) % 0.37/0.62 (step @p82 :rule refl :args (@t17)) % 0.37/0.62 (step @p83 :rule cong :premises (@p82 @p81) :args ((= @t17 @t87))) % 0.37/0.62 (step @p84 :rule symm :premises (@p83)) % 0.37/0.62 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.37/0.62 (step @p86 :rule cong :premises (@p85) :args (@t100)) % 0.37/0.62 (step @p87 :rule refl :args (@t89)) % 0.37/0.62 (step @p88 :rule refl :args (@t20)) % 0.37/0.62 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t20 @t89))) % 0.37/0.62 (step @p90 :rule symm :premises (@p89)) % 0.37/0.62 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.37/0.62 (step @p92 :rule cong :premises (@p91) :args (@t101)) % 0.37/0.62 (step @p93 :rule nary_cong :premises (@p92 @p86 @p80) :args (@t102)) % 0.37/0.62 (step @p94 :rule cong :premises (@p93) :args ((forall @t21 @t102))) % 0.37/0.62 (step @p95 :rule trans :premises (@p94 @p42)) % 0.37/0.62 (step @p96 :rule aci_norm :args ((= (or @t101 (or @t100 @t16)) @t102))) % 0.37/0.62 (step @p97 :rule bool-impl-elim :args (@t17 @t16)) % 0.37/0.62 (step @p98 :rule refl :args (@t101)) % 0.37/0.62 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or @t101 @t18))) % 0.37/0.62 (step @p100 :rule trans :premises (@p99 @p96)) % 0.37/0.62 (step @p101 :rule bool-impl-elim :args (@t20 @t18)) % 0.37/0.62 (step @p102 :rule trans :premises (@p101 @p100)) % 0.37/0.62 (step @p103 :rule cong :premises (@p102) :args (@t22)) % 0.37/0.62 (step @p104 :rule trans :premises (@p103 @p95)) % 0.37/0.62 (step @p105 :rule refl :args (@t23)) % 0.37/0.62 (step @p106 :rule cong :premises (@p105 @p104) :args (@t24)) % 0.37/0.62 (step @p107 :rule cong :premises (@p106) :args (@t26)) % 0.37/0.62 (step @p108 :rule trans :premises (@p107 @p32)) % 0.37/0.62 (step @p109 :rule refl :args (tptp.dpsetconstrI)) % 0.37/0.62 (step @p110 :rule cong :premises (@p109 @p108) :args (@t27)) % 0.37/0.62 (step @p111 :rule eq_resolve :premises (@p1 @p110)) % 0.37/0.62 (step @p112 :rule cong :premises (@p111 @p7) :args (@t103)) % 0.37/0.62 (step @p113 :rule cong :premises (@p112) :args ((not @t103))) % 0.37/0.62 (step @p114 :rule aci_norm :args ((= @t105 @t68))) % 0.37/0.62 (step @p115 :rule cong :premises (@p114) :args (@t106)) % 0.37/0.62 (step @p116 :rule quant-merge-prenex :args ((= (forall @t40 @t108) @t106))) % 0.37/0.62 (step @p117 :rule alpha_equiv :args (@t109 (@list @t59 @t60) (@list @t13 @t110))) % 0.37/0.62 (step @p118 :rule refl :args (@t67)) % 0.37/0.62 (step @p119 :rule nary_cong :premises (@p118 @p117) :args (@t111)) % 0.37/0.62 (step @p120 :rule quant-miniscope-or :args ((= @t108 @t111))) % 0.37/0.62 (step @p121 :rule trans :premises (@p120 @p119)) % 0.37/0.62 (step @p122 :rule symm :premises (@p121)) % 0.37/0.62 (step @p123 :rule cong :premises (@p122) :args ((forall @t40 (or @t67 @t117)))) % 0.37/0.62 (step @p124 :rule trans :premises (@p123 @p116)) % 0.37/0.62 (step @p125 :rule trans :premises (@p124 @p115)) % 0.37/0.62 (step @p126 :rule refl :args (@t117)) % 0.37/0.62 (step @p127 :rule refl :args ((tptp.subset @t28 @t118))) % 0.37/0.62 (step @p128 :rule refl :args (@t65)) % 0.37/0.62 (step @p129 :rule refl :args (@t28)) % 0.37/0.62 (step @p130 :rule cong :premises (@p129 @p128) :args (@t66)) % 0.37/0.62 (step @p131 :rule trans :premises (@p130 @p127)) % 0.37/0.62 (step @p132 :rule refl :args (@t119)) % 0.37/0.62 (step @p133 :rule ho_cong :premises (@p132 @p128)) % 0.37/0.62 (step @p134 :rule cong :premises (@p133 @p131) :args ((= (_ @t119 @t65) @t66))) % 0.37/0.62 (step @p135 :rule symm :premises (@p134)) % 0.37/0.62 (step @p136 :rule refl :args (@t120)) % 0.37/0.62 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.37/0.62 (step @p138 :rule refl :args (@t118)) % 0.37/0.62 (step @p139 :rule cong :premises (@p138 @p128) :args ((= @t118 @t65))) % 0.37/0.62 (step @p140 :rule symm :premises (@p139)) % 0.37/0.62 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.37/0.62 (step @p142 :rule ho_cong :premises (@p132 @p141)) % 0.37/0.62 (step @p143 :rule trans :premises (@p142 @p137)) % 0.37/0.62 (step @p144 :rule cong :premises (@p143) :args (@t121)) % 0.37/0.62 (step @p145 :rule nary_cong :premises (@p144 @p126) :args (@t122)) % 0.37/0.62 (step @p146 :rule cong :premises (@p145) :args ((forall @t40 @t122))) % 0.37/0.62 (step @p147 :rule trans :premises (@p146 @p125)) % 0.37/0.62 (step @p148 :rule bool-impl-elim :args (@t120 @t117)) % 0.37/0.62 (step @p149 :rule cong :premises (@p148) :args ((forall @t40 (=> @t120 @t117)))) % 0.37/0.62 (step @p150 :rule trans :premises (@p149 @p147)) % 0.37/0.62 (step @p151 :rule aci_norm :args ((= @t124 @t115))) % 0.37/0.62 (step @p152 :rule cong :premises (@p151) :args (@t125)) % 0.37/0.62 (step @p153 :rule quant-merge-prenex :args ((= (forall @t37 @t127) @t125))) % 0.37/0.62 (step @p154 :rule alpha_equiv :args (@t128 (@list @t110) @t84)) % 0.37/0.62 (step @p155 :rule nary_cong :premises (@p12 @p154) :args (@t129)) % 0.37/0.62 (step @p156 :rule quant-miniscope-or :args ((= @t127 @t129))) % 0.37/0.62 (step @p157 :rule trans :premises (@p156 @p155)) % 0.37/0.62 (step @p158 :rule symm :premises (@p157)) % 0.37/0.62 (step @p159 :rule cong :premises (@p158) :args ((forall @t37 (or @t77 @t135)))) % 0.37/0.62 (step @p160 :rule trans :premises (@p159 @p153)) % 0.37/0.62 (step @p161 :rule trans :premises (@p160 @p152)) % 0.37/0.62 (step @p162 :rule refl :args (@t135)) % 0.37/0.62 (step @p163 :rule nary_cong :premises (@p26 @p162) :args (@t136)) % 0.37/0.62 (step @p164 :rule cong :premises (@p163) :args ((forall @t37 @t136))) % 0.37/0.62 (step @p165 :rule trans :premises (@p164 @p161)) % 0.37/0.62 (step @p166 :rule bool-impl-elim :args (@t23 @t135)) % 0.37/0.62 (step @p167 :rule cong :premises (@p166) :args ((forall @t37 (=> @t23 @t135)))) % 0.37/0.62 (step @p168 :rule trans :premises (@p167 @p165)) % 0.37/0.62 (step @p169 :rule alpha_equiv :args (@t140 (@list @t13) (@list @t54))) % 0.37/0.62 (step @p170 :rule cong :premises (@p48 @p48 @p169) :args (@t141)) % 0.37/0.62 (step @p171 :rule refl :args (@t130)) % 0.37/0.62 (step @p172 :rule cong :premises (@p171 @p170) :args (@t142)) % 0.37/0.62 (step @p173 :rule refl :args (@t132)) % 0.37/0.62 (step @p174 :rule refl :args (@t134)) % 0.37/0.62 (step @p175 :rule nary_cong :premises (@p174 @p173 @p172) :args (@t143)) % 0.37/0.62 (step @p176 :rule cong :premises (@p175) :args (@t144)) % 0.37/0.62 (step @p177 :rule cong :premises (@p22 @p176) :args (@t145)) % 0.37/0.62 (step @p178 :rule cong :premises (@p177) :args ((forall @t37 @t145))) % 0.37/0.62 (step @p179 :rule trans :premises (@p178 @p168)) % 0.37/0.62 (step @p180 :rule refl :args ((tptp.in @t29 @t149))) % 0.37/0.62 (step @p181 :rule refl :args ((tptp.dpsetconstr @t8 @t8 @t148))) % 0.37/0.62 (step @p182 :rule refl :args ((tptp.in @t146 @t28))) % 0.37/0.62 (step @p183 :rule refl :args (@t137)) % 0.37/0.62 (step @p184 :rule cong :premises (@p183 @p129) :args (@t138)) % 0.37/0.62 (step @p185 :rule trans :premises (@p184 @p182)) % 0.37/0.62 (step @p186 :rule cong :premises (@p185) :args (@t140)) % 0.37/0.62 (step @p187 :rule cong :premises (@p48 @p48 @p186) :args (@t141)) % 0.37/0.62 (step @p188 :rule trans :premises (@p187 @p181)) % 0.37/0.62 (step @p189 :rule refl :args (@t130)) % 0.37/0.62 (step @p190 :rule cong :premises (@p189 @p188) :args (@t142)) % 0.37/0.62 (step @p191 :rule trans :premises (@p190 @p180)) % 0.37/0.62 (step @p192 :rule ho_cong :premises (@p54 @p189)) % 0.37/0.62 (step @p193 :rule ho_cong :premises (@p192 @p188)) % 0.37/0.62 (step @p194 :rule cong :premises (@p193 @p191) :args ((= (_ (_ tptp.in @t130) @t141) @t142))) % 0.37/0.62 (step @p195 :rule symm :premises (@p194)) % 0.37/0.62 (step @p196 :rule refl :args (@t150)) % 0.37/0.62 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.37/0.62 (step @p198 :rule refl :args (@t51)) % 0.37/0.62 (step @p199 :rule ho_cong :premises (@p198 @p186)) % 0.37/0.62 (step @p200 :rule cong :premises (@p199 @p188) :args ((= (_ @t51 @t140) @t141))) % 0.37/0.62 (step @p201 :rule symm :premises (@p200)) % 0.37/0.62 (step @p202 :rule refl :args (@t149)) % 0.37/0.62 (step @p203 :rule eq_resolve :premises (@p202 @p201)) % 0.37/0.62 (step @p204 :rule ho_cong :premises (@p54 @p183)) % 0.37/0.62 (step @p205 :rule ho_cong :premises (@p204 @p129)) % 0.37/0.62 (step @p206 :rule cong :premises (@p205 @p185) :args ((= (_ (_ tptp.in @t137) @t28) @t138))) % 0.37/0.62 (step @p207 :rule symm :premises (@p206)) % 0.37/0.62 (step @p208 :rule refl :args (@t147)) % 0.37/0.62 (step @p209 :rule eq_resolve :premises (@p208 @p207)) % 0.37/0.62 (step @p210 :rule refl :args (@t146)) % 0.37/0.62 (step @p211 :rule cong :premises (@p210 @p183) :args ((= @t146 @t137))) % 0.37/0.62 (step @p212 :rule symm :premises (@p211)) % 0.37/0.62 (step @p213 :rule eq_resolve :premises (@p210 @p212)) % 0.37/0.62 (step @p214 :rule ho_cong :premises (@p54 @p213)) % 0.37/0.62 (step @p215 :rule ho_cong :premises (@p214 @p129)) % 0.37/0.62 (step @p216 :rule trans :premises (@p215 @p209)) % 0.37/0.62 (step @p217 :rule cong :premises (@p216) :args (@t148)) % 0.37/0.62 (step @p218 :rule ho_cong :premises (@p198 @p217)) % 0.37/0.62 (step @p219 :rule trans :premises (@p218 @p203)) % 0.37/0.62 (step @p220 :rule refl :args (@t29)) % 0.37/0.62 (step @p221 :rule cong :premises (@p220 @p189) :args ((= @t29 @t130))) % 0.37/0.62 (step @p222 :rule symm :premises (@p221)) % 0.37/0.62 (step @p223 :rule eq_resolve :premises (@p220 @p222)) % 0.37/0.62 (step @p224 :rule ho_cong :premises (@p54 @p223)) % 0.37/0.62 (step @p225 :rule ho_cong :premises (@p224 @p219)) % 0.37/0.62 (step @p226 :rule trans :premises (@p225 @p197)) % 0.37/0.62 (step @p227 :rule refl :args ((tptp.in @t14 @t28))) % 0.37/0.62 (step @p228 :rule cong :premises (@p51 @p129) :args (@t131)) % 0.37/0.62 (step @p229 :rule trans :premises (@p228 @p227)) % 0.37/0.62 (step @p230 :rule ho_cong :premises (@p55 @p129)) % 0.37/0.62 (step @p231 :rule cong :premises (@p230 @p229) :args ((= (_ @t99 @t28) @t131))) % 0.37/0.62 (step @p232 :rule symm :premises (@p231)) % 0.37/0.62 (step @p233 :rule refl :args (@t31)) % 0.37/0.62 (step @p234 :rule eq_resolve :premises (@p233 @p232)) % 0.37/0.62 (step @p235 :rule ho_cong :premises (@p78 @p129)) % 0.37/0.62 (step @p236 :rule trans :premises (@p235 @p234)) % 0.37/0.62 (step @p237 :rule cong :premises (@p236) :args (@t151)) % 0.37/0.62 (step @p238 :rule refl :args (@t133)) % 0.37/0.62 (step @p239 :rule refl :args (@t33)) % 0.37/0.62 (step @p240 :rule cong :premises (@p239 @p238) :args ((= @t33 @t133))) % 0.37/0.62 (step @p241 :rule symm :premises (@p240)) % 0.37/0.62 (step @p242 :rule eq_resolve :premises (@p239 @p241)) % 0.37/0.62 (step @p243 :rule cong :premises (@p242) :args (@t152)) % 0.37/0.62 (step @p244 :rule nary_cong :premises (@p243 @p237 @p226) :args (@t153)) % 0.37/0.62 (step @p245 :rule cong :premises (@p244) :args ((forall @t21 @t153))) % 0.37/0.62 (step @p246 :rule aci_norm :args ((= (or @t152 (or @t151 @t150)) @t153))) % 0.37/0.62 (step @p247 :rule bool-impl-elim :args (@t31 @t150)) % 0.37/0.62 (step @p248 :rule refl :args (@t152)) % 0.37/0.62 (step @p249 :rule nary_cong :premises (@p248 @p247) :args ((or @t152 @t154))) % 0.37/0.62 (step @p250 :rule trans :premises (@p249 @p246)) % 0.37/0.62 (step @p251 :rule bool-impl-elim :args (@t33 @t154)) % 0.37/0.62 (step @p252 :rule trans :premises (@p251 @p250)) % 0.37/0.62 (step @p253 :rule cong :premises (@p252) :args ((forall @t21 (=> @t33 @t154)))) % 0.37/0.62 (step @p254 :rule trans :premises (@p253 @p245)) % 0.37/0.62 (step @p255 :rule alpha_equiv :args (@t50 @t84 (@list @t55))) % 0.37/0.62 (step @p256 :rule ho_cong :premises (@p198 @p255)) % 0.37/0.62 (step @p257 :rule refl :args (@t30)) % 0.37/0.62 (step @p258 :rule ho_cong :premises (@p257 @p256)) % 0.37/0.62 (step @p259 :rule cong :premises (@p233 @p258) :args (@t155)) % 0.37/0.62 (step @p260 :rule cong :premises (@p239 @p259) :args (@t156)) % 0.37/0.62 (step @p261 :rule cong :premises (@p260) :args ((forall @t21 @t156))) % 0.37/0.62 (step @p262 :rule trans :premises (@p261 @p254)) % 0.37/0.62 (step @p263 :rule beta-reduce :args ((= (_ @t158 @t28) @t52))) % 0.37/0.62 (step @p264 :rule refl :args (@t28)) % 0.37/0.62 (step @p265 :rule beta-reduce :args ((= @t159 @t158))) % 0.37/0.62 (step @p266 :rule ho_cong :premises (@p265 @p264)) % 0.37/0.62 (step @p267 :rule trans :premises (@p266 @p263)) % 0.37/0.62 (step @p268 :rule refl :args (@t30)) % 0.37/0.62 (step @p269 :rule ho_cong :premises (@p268 @p267)) % 0.37/0.62 (step @p270 :rule refl :args (@t31)) % 0.37/0.62 (step @p271 :rule cong :premises (@p270 @p269) :args (@t160)) % 0.37/0.62 (step @p272 :rule refl :args (@t33)) % 0.37/0.62 (step @p273 :rule cong :premises (@p272 @p271) :args (@t161)) % 0.37/0.62 (step @p274 :rule cong :premises (@p273) :args (@t162)) % 0.37/0.62 (step @p275 :rule trans :premises (@p274 @p262)) % 0.37/0.62 (step @p276 :rule cong :premises (@p105 @p275) :args (@t163)) % 0.37/0.62 (step @p277 :rule cong :premises (@p276) :args (@t164)) % 0.37/0.62 (step @p278 :rule trans :premises (@p277 @p179)) % 0.37/0.62 (step @p279 :rule beta-reduce :args ((= (_ @t165 @t28) @t120))) % 0.37/0.62 (step @p280 :rule beta-reduce :args ((= @t166 @t165))) % 0.37/0.62 (step @p281 :rule ho_cong :premises (@p280 @p264)) % 0.37/0.62 (step @p282 :rule trans :premises (@p281 @p279)) % 0.37/0.62 (step @p283 :rule cong :premises (@p282 @p278) :args (@t167)) % 0.37/0.62 (step @p284 :rule cong :premises (@p283) :args (@t168)) % 0.37/0.62 (step @p285 :rule trans :premises (@p284 @p150)) % 0.37/0.62 (step @p286 :rule cong :premises (@p109 @p285) :args (@t169)) % 0.37/0.62 (step @p287 :rule cong :premises (@p286) :args ((not @t169))) % 0.37/0.62 (step @p288 :rule ho_cong :premises (@p6 @p35)) % 0.37/0.62 (step @p289 :rule ho_cong :premises (@p288 @p264)) % 0.37/0.62 (step @p290 :rule ho_cong :premises (@p268 @p289)) % 0.37/0.62 (step @p291 :rule cong :premises (@p270 @p290) :args (@t32)) % 0.37/0.62 (step @p292 :rule cong :premises (@p272 @p291) :args (@t34)) % 0.37/0.62 (step @p293 :rule cong :premises (@p292) :args (@t35)) % 0.37/0.62 (step @p294 :rule cong :premises (@p105 @p293) :args (@t36)) % 0.37/0.62 (step @p295 :rule cong :premises (@p294) :args (@t38)) % 0.37/0.62 (step @p296 :rule beta-reduce :args ((= (_ @t170 @t28) @t120))) % 0.37/0.62 (step @p297 :rule beta-reduce :args ((= (_ @t171 @t8) @t170))) % 0.37/0.62 (step @p298 :rule beta-reduce :args ((= (_ @t48 @t8) @t171))) % 0.37/0.62 (step @p299 :rule ho_cong :premises (@p298 @p35)) % 0.37/0.62 (step @p300 :rule trans :premises (@p299 @p297)) % 0.37/0.62 (step @p301 :rule ho_cong :premises (@p300 @p264)) % 0.37/0.62 (step @p302 :rule trans :premises (@p301 @p296)) % 0.37/0.62 (step @p303 :rule ho_cong :premises (@p4 @p35)) % 0.37/0.62 (step @p304 :rule ho_cong :premises (@p303 @p35)) % 0.37/0.62 (step @p305 :rule ho_cong :premises (@p304 @p264)) % 0.37/0.62 (step @p306 :rule trans :premises (@p305 @p302)) % 0.37/0.62 (step @p307 :rule cong :premises (@p306) :args (@t49)) % 0.37/0.62 (step @p308 :rule trans :premises (@p5 @p307)) % 0.37/0.62 (step @p309 :rule ho_cong :premises (@p308 @p35)) % 0.37/0.62 (step @p310 :rule ho_cong :premises (@p309 @p264)) % 0.37/0.62 (step @p311 :rule cong :premises (@p310 @p295) :args (@t39)) % 0.37/0.62 (step @p312 :rule cong :premises (@p311) :args (@t41)) % 0.37/0.62 (step @p313 :rule cong :premises (@p109 @p312) :args (@t42)) % 0.37/0.62 (step @p314 :rule cong :premises (@p313) :args (@t43)) % 0.37/0.62 (step @p315 :rule trans :premises (@p314 @p287)) % 0.37/0.62 (step @p316 :rule trans :premises (@p315 @p113)) % 0.37/0.62 (step @p317 :rule eq_resolve :premises (@p2 @p316)) % 0.37/0.62 (step @p318 :rule not_implies_elim2 :premises (@p317)) % 0.37/0.62 (step @p319 :rule refl :args (@t189)) % 0.37/0.62 (step @p320 :rule bool-double-not-elim :args (@t70)) % 0.37/0.62 (step @p321 :rule nary_cong :premises (@p320 @p319) :args ((or (not @t190) @t189))) % 0.37/0.62 (step @p322 :rule eq-refl :args (@t174)) % 0.37/0.62 (step @p323 :rule skolem_intro :args (@t175)) % 0.37/0.62 (step @p324 :rule refl :args (@t174)) % 0.37/0.62 (step @p325 :rule cong :premises (@p324 @p323) :args ((= @t174 @t175))) % 0.37/0.62 (step @p326 :rule trans :premises (@p325 @p322)) % 0.37/0.62 (step @p327 :rule true_elim :premises (@p326)) % 0.37/0.62 (step @p328 :rule refl :args (@t176)) % 0.37/0.62 (step @p329 :rule cong :premises (@p328 @p328 @p327) :args (@t191)) % 0.37/0.62 (step @p330 :rule refl :args (@t179)) % 0.37/0.62 (step @p331 :rule cong :premises (@p330 @p329) :args (@t192)) % 0.37/0.62 (step @p332 :rule refl :args (@t182)) % 0.37/0.62 (step @p333 :rule refl :args (@t184)) % 0.37/0.62 (step @p334 :rule refl :args (@t186)) % 0.37/0.62 (step @p335 :rule refl :args (@t187)) % 0.37/0.62 (step @p336 :rule nary_cong :premises (@p335 @p334 @p333 @p332 @p331) :args (@t193)) % 0.37/0.62 (step @p337 :rule cong :premises (@p336) :args (@t194)) % 0.37/0.62 (step @p338 :rule refl :args (@t190)) % 0.37/0.62 (step @p339 :rule cong :premises (@p338 @p337) :args ((=> @t190 @t194))) % 0.37/0.62 (assume-push @p397 @t190) % 0.37/0.62 (step @p341 :rule skolemize :premises (@p318)) % 0.37/0.62 (step-pop @p398 :rule scope :premises (@p341)) % 0.37/0.62 (step @p342 :rule process_scope :premises (@p398) :args (@t194)) % 0.37/0.62 (step @p344 :rule eq_resolve :premises (@p342 @p339)) % 0.37/0.62 (step @p345 :rule implies_elim :premises (@p344)) % 0.37/0.62 (step @p346 :rule eq_resolve :premises (@p345 @p321)) % 0.37/0.62 (step @p347 :rule chain_m_resolution :premises (@p346 @p318) :args (@t189 @t195 (@list @t70))) % 0.37/0.62 (step @p348 :rule bool-double-not-elim :args (@t181)) % 0.37/0.62 (step @p349 :rule refl :args (@t188)) % 0.37/0.62 (step @p350 :rule nary_cong :premises (@p349 @p348) :args ((or @t188 (not @t182)))) % 0.37/0.62 (step @p351 :rule cnf_or_neg :args (@t188 3)) % 0.37/0.62 (step @p352 :rule eq_resolve :premises (@p351 @p350)) % 0.37/0.62 (step @p353 :rule reordering :premises (@p352) :args ((or @t181 @t188))) % 0.37/0.62 (step @p354 :rule chain_m_resolution :premises (@p353 @p347) :args (@t181 @t195 @t196)) % 0.37/0.62 (step @p355 :rule eq-symm :args (@t197 @t173)) % 0.37/0.62 (step @p356 :rule beta-reduce :args ((= @t198 @t173))) % 0.37/0.62 (step @p357 :rule refl :args (@t197)) % 0.37/0.62 (step @p358 :rule cong :premises (@p357 @p356) :args (@t199)) % 0.37/0.62 (step @p359 :rule trans :premises (@p358 @p355)) % 0.37/0.62 (step @p360 :rule cong :premises (@p359) :args (@t200)) % 0.37/0.62 (step @p361 :rule quant-unused-vars :args ((= (forall @t57 true) true))) % 0.37/0.62 (step @p362 :rule eq-refl :args (@t198)) % 0.37/0.62 (step @p363 :rule cong :premises (@p362) :args ((forall @t57 (= @t198 @t198)))) % 0.37/0.62 (step @p364 :rule trans :premises (@p363 @p361)) % 0.37/0.62 (step @p365 :rule refl :args (@t198)) % 0.37/0.62 (step @p366 :rule refl :args (@t55)) % 0.37/0.62 (step @p367 :rule refl :args (@t54)) % 0.37/0.62 (step @p368 :rule ho_cong :premises (@p323 @p367 @p366)) % 0.37/0.62 (step @p369 :rule cong :premises (@p368 @p365) :args (@t199)) % 0.37/0.62 (step @p370 :rule cong :premises (@p369) :args (@t200)) % 0.37/0.62 (step @p371 :rule trans :premises (@p370 @p364)) % 0.37/0.62 (step @p372 :rule true_elim :premises (@p371)) % 0.37/0.62 (step @p373 :rule eq_resolve :premises (@p372 @p360)) % 0.37/0.62 (step @p374 :rule instantiate :premises (@p373) :args ((@list @t178 @t177))) % 0.37/0.62 (step @p375 :rule not_implies_elim1 :premises (@p317)) % 0.37/0.62 (step @p376 :rule instantiate :premises (@p375) :args ((@list @t176 @t176 @t175 @t178 @t177))) % 0.37/0.62 (step @p377 :rule cnf_or_neg :args (@t188 4)) % 0.37/0.62 (step @p378 :rule chain_m_resolution :premises (@p377 @p347) :args ((not @t180) @t195 @t196)) % 0.37/0.62 (step @p379 :rule bool-double-not-elim :args (@t183)) % 0.37/0.62 (step @p380 :rule nary_cong :premises (@p349 @p379) :args ((or @t188 (not @t184)))) % 0.37/0.62 (step @p381 :rule cnf_or_neg :args (@t188 2)) % 0.37/0.62 (step @p382 :rule eq_resolve :premises (@p381 @p380)) % 0.37/0.62 (step @p383 :rule reordering :premises (@p382) :args ((or @t183 @t188))) % 0.37/0.62 (step @p384 :rule chain_m_resolution :premises (@p383 @p347) :args (@t183 @t195 @t196)) % 0.37/0.62 (step @p385 :rule bool-double-not-elim :args (@t185)) % 0.37/0.62 (step @p386 :rule nary_cong :premises (@p349 @p385) :args ((or @t188 (not @t186)))) % 0.37/0.62 (step @p387 :rule cnf_or_neg :args (@t188 1)) % 0.37/0.62 (step @p388 :rule eq_resolve :premises (@p387 @p386)) % 0.37/0.62 (step @p389 :rule reordering :premises (@p388) :args ((or @t185 @t188))) % 0.37/0.62 (step @p390 :rule chain_m_resolution :premises (@p389 @p347) :args (@t185 @t195 @t196)) % 0.37/0.62 (step @p391 :rule cnf_or_pos :args (@t203)) % 0.37/0.62 (step @p392 :rule reordering :premises (@p391) :args ((or @t186 @t184 @t180 @t202 (not @t203)))) % 0.37/0.62 (step @p393 :rule chain_m_resolution :premises (@p392 @p390 @p384 @p378 @p376) :args (@t202 (@list false false true false) (@list @t185 @t183 @t180 @t203))) % 0.37/0.62 (step @p394 :rule cnf_equiv_pos1 :args (@t204)) % 0.37/0.62 (step @p395 :rule reordering :premises (@p394) :args ((or @t182 @t201 (not @t204)))) % 0.37/0.62 (step @p396 false :rule chain_m_resolution :premises (@p395 @p393 @p374 @p354) :args (false (@list true false false) (@list @t201 @t204 @t181))) % 0.37/0.62 ) % 0.37/0.62 % SZS output end Proof % 0.37/0.62 % cvc5 exiting %------------------------------------------------------------------------------