%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU632^2 : 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 : n005.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 08:52:30 AM UTC 2026 % Result : Theorem 245.63s 245.87s % Output : Proof 245.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU632^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n005.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 17:43:33 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 245.63/245.87 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 245.63/245.87 --- 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... % 245.63/245.87 --- 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... % 245.63/245.87 --- Run --ho-elim --full-saturate-quant at 18s... % 245.63/245.87 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 245.63/245.87 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 245.63/245.87 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 245.63/245.87 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 245.63/245.87 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 245.63/245.87 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 18s... % 245.63/245.87 % SZS status Theorem % 245.63/245.87 % SZS output start Proof % 245.63/245.87 ( % 245.63/245.87 (declare-sort $$unsorted 0) % 245.63/245.87 (declare-const tptp.emptyset $$unsorted) % 245.63/245.87 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 245.63/245.87 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 245.63/245.87 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 245.63/245.87 (declare-const tptp.cartprodmempair1 Bool) % 245.63/245.87 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 245.63/245.87 (declare-const tptp.kpairp Bool) % 245.63/245.87 (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" $$unsorted))) (let ((_let_5 (_ tptp.setunion _let_4))) (lambda (@list _let_4) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_5) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_5) (= _let_4 (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset)))))))))))))) % 245.63/245.87 (define tptp.kpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (lambda (@list _let_2 _let_1) (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset))))))) % 245.63/245.87 (define @t1 () (@var "Xy" $$unsorted)) % 245.63/245.87 (define @t2 () (@var "Xx" $$unsorted)) % 245.63/245.87 (define @t3 () (_ (_ tptp.kpair @t2) @t1)) % 245.63/245.87 (define @t4 () (@list @t2 @t1)) % 245.63/245.87 (define @t5 () (forall @t4 (_ tptp.iskpair @t3))) % 245.63/245.87 (define @t6 () (= tptp.kpairp @t5)) % 245.63/245.87 (define @t7 () (@var "Xu" $$unsorted)) % 245.63/245.87 (define @t8 () (= @t7 @t3)) % 245.63/245.87 (define @t9 () (@var "B" $$unsorted)) % 245.63/245.87 (define @t10 () (_ tptp.in @t1)) % 245.63/245.87 (define @t11 () (_ @t10 @t9)) % 245.63/245.87 (define @t12 () (and @t11 @t8)) % 245.63/245.87 (define @t13 () (@list @t1)) % 245.63/245.87 (define @t14 () (exists @t13 @t12)) % 245.63/245.87 (define @t15 () (@var "A" $$unsorted)) % 245.63/245.87 (define @t16 () (_ tptp.in @t2)) % 245.63/245.87 (define @t17 () (_ @t16 @t15)) % 245.63/245.87 (define @t18 () (and @t17 @t14)) % 245.63/245.87 (define @t19 () (@list @t2)) % 245.63/245.87 (define @t20 () (exists @t19 @t18)) % 245.63/245.87 (define @t21 () (_ (_ tptp.cartprod @t15) @t9)) % 245.63/245.87 (define @t22 () (_ tptp.in @t7)) % 245.63/245.87 (define @t23 () (_ @t22 @t21)) % 245.63/245.87 (define @t24 () (=> @t23 @t20)) % 245.63/245.87 (define @t25 () (@list @t15 @t9 @t7)) % 245.63/245.87 (define @t26 () (forall @t25 @t24)) % 245.63/245.87 (define @t27 () (= tptp.cartprodmempair1 @t26)) % 245.63/245.87 (define @t28 () (=> @t23 (_ tptp.iskpair @t7))) % 245.63/245.87 (define @t29 () (forall @t25 @t28)) % 245.63/245.87 (define @t30 () (=> tptp.cartprodmempair1 @t29)) % 245.63/245.87 (define @t31 () (=> tptp.kpairp @t30)) % 245.63/245.87 (define @t32 () (not @t31)) % 245.63/245.87 (define @t33 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 245.63/245.87 (define @t34 () (_ tptp.setadjoin @t2)) % 245.63/245.87 (define @t35 () (_ @t34 @t33)) % 245.63/245.87 (define @t36 () (_ (_ tptp.setadjoin @t35) tptp.emptyset)) % 245.63/245.87 (define @t37 () (_ @t34 tptp.emptyset)) % 245.63/245.87 (define @t38 () (_ (_ tptp.setadjoin @t37) @t36)) % 245.63/245.87 (define @t39 () (= @t15 @t38)) % 245.63/245.87 (define @t40 () (_ tptp.setunion @t15)) % 245.63/245.87 (define @t41 () (_ @t10 @t40)) % 245.63/245.87 (define @t42 () (and @t41 @t39)) % 245.63/245.87 (define @t43 () (exists @t13 @t42)) % 245.63/245.87 (define @t44 () (_ @t16 @t40)) % 245.63/245.87 (define @t45 () (and @t44 @t43)) % 245.63/245.87 (define @t46 () (exists @t19 @t45)) % 245.63/245.87 (define @t47 () (@list @t15)) % 245.63/245.87 (define @t48 () (lambda @t47 @t46)) % 245.63/245.87 (define @t49 () (lambda @t4 @t38)) % 245.63/245.87 (define @t50 () (@var "BOUND_VARIABLE_7481" $$unsorted)) % 245.63/245.87 (define @t51 () (tptp.setadjoin @t50 tptp.emptyset)) % 245.63/245.87 (define @t52 () (tptp.setadjoin @t2 tptp.emptyset)) % 245.63/245.87 (define @t53 () (tptp.setadjoin @t52 (tptp.setadjoin (tptp.setadjoin @t2 @t51) tptp.emptyset))) % 245.63/245.87 (define @t54 () (tptp.setunion @t7)) % 245.63/245.87 (define @t55 () (not (tptp.in @t50 @t54))) % 245.63/245.87 (define @t56 () (not (tptp.in @t2 @t54))) % 245.63/245.87 (define @t57 () (@list @t2 @t50)) % 245.63/245.87 (define @t58 () (not (forall @t57 (or @t56 @t55 (not (= @t53 @t7)))))) % 245.63/245.87 (define @t59 () (tptp.cartprod @t15 @t9)) % 245.63/245.87 (define @t60 () (tptp.in @t7 @t59)) % 245.63/245.87 (define @t61 () (not @t60)) % 245.63/245.87 (define @t62 () (forall @t25 (or @t61 @t58))) % 245.63/245.87 (define @t63 () (@var "BOUND_VARIABLE_7632" $$unsorted)) % 245.63/245.87 (define @t64 () (tptp.setadjoin @t52 (tptp.setadjoin (tptp.setadjoin @t2 (tptp.setadjoin @t63 tptp.emptyset)) tptp.emptyset))) % 245.63/245.87 (define @t65 () (not (tptp.in @t63 @t9))) % 245.63/245.87 (define @t66 () (tptp.in @t2 @t15)) % 245.63/245.87 (define @t67 () (not @t66)) % 245.63/245.87 (define @t68 () (@list @t2 @t63)) % 245.63/245.87 (define @t69 () (not (forall @t68 (or @t67 @t65 (not (= @t7 @t64)))))) % 245.63/245.87 (define @t70 () (not @t23)) % 245.63/245.87 (define @t71 () (or @t70 @t69)) % 245.63/245.87 (define @t72 () (not (= @t64 @t7))) % 245.63/245.87 (define @t73 () (or @t67 @t65 @t72)) % 245.63/245.87 (define @t74 () (or @t65 @t72)) % 245.63/245.87 (define @t75 () (or @t67 @t74)) % 245.63/245.87 (define @t76 () (forall @t68 @t75)) % 245.63/245.87 (define @t77 () (@list @t63)) % 245.63/245.87 (define @t78 () (forall @t77 @t75)) % 245.63/245.87 (define @t79 () (forall @t77 @t74)) % 245.63/245.87 (define @t80 () (@list @t1)) % 245.63/245.87 (define @t81 () (or @t67 @t79)) % 245.63/245.87 (define @t82 () (tptp.setadjoin @t1 tptp.emptyset)) % 245.63/245.87 (define @t83 () (tptp.setadjoin @t2 @t82)) % 245.63/245.87 (define @t84 () (tptp.setadjoin @t83 tptp.emptyset)) % 245.63/245.87 (define @t85 () (tptp.setadjoin @t52 @t84)) % 245.63/245.87 (define @t86 () (tptp.in @t1 @t9)) % 245.63/245.87 (define @t87 () (forall @t13 (or (not @t86) (not (= @t85 @t7))))) % 245.63/245.87 (define @t88 () (not @t17)) % 245.63/245.87 (define @t89 () (or @t88 @t87)) % 245.63/245.87 (define @t90 () (not @t87)) % 245.63/245.87 (define @t91 () (and @t17 @t90)) % 245.63/245.87 (define @t92 () (forall @t19 (not @t91))) % 245.63/245.87 (define @t93 () (not @t92)) % 245.63/245.87 (define @t94 () (= @t38 @t7)) % 245.63/245.87 (define @t95 () (not @t94)) % 245.63/245.87 (define @t96 () (not @t11)) % 245.63/245.87 (define @t97 () (or @t96 @t95)) % 245.63/245.87 (define @t98 () (and @t11 @t94)) % 245.63/245.87 (define @t99 () (forall @t13 (not @t98))) % 245.63/245.87 (define @t100 () (not @t99)) % 245.63/245.87 (define @t101 () (lambda @t13 @t38)) % 245.63/245.87 (define @t102 () (_ @t49 @t2)) % 245.63/245.87 (define @t103 () (_ @t102 @t1)) % 245.63/245.87 (define @t104 () (= @t7 @t103)) % 245.63/245.87 (define @t105 () (and @t11 @t104)) % 245.63/245.87 (define @t106 () (exists @t13 @t105)) % 245.63/245.87 (define @t107 () (and @t17 @t106)) % 245.63/245.87 (define @t108 () (exists @t19 @t107)) % 245.63/245.87 (define @t109 () (=> @t23 @t108)) % 245.63/245.87 (define @t110 () (forall @t25 @t109)) % 245.63/245.87 (define @t111 () (=> tptp.cartprodmempair1 @t62)) % 245.63/245.87 (define @t112 () (@var "BOUND_VARIABLE_7555" $$unsorted)) % 245.63/245.87 (define @t113 () (tptp.setadjoin (tptp.setadjoin @t112 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t112 @t51) tptp.emptyset))) % 245.63/245.87 (define @t114 () (= @t38 @t113)) % 245.63/245.87 (define @t115 () (not @t114)) % 245.63/245.87 (define @t116 () (tptp.setunion @t38)) % 245.63/245.87 (define @t117 () (tptp.in @t50 @t116)) % 245.63/245.87 (define @t118 () (not @t117)) % 245.63/245.87 (define @t119 () (tptp.in @t112 @t116)) % 245.63/245.87 (define @t120 () (not @t119)) % 245.63/245.87 (define @t121 () (or @t120 @t118 @t115)) % 245.63/245.87 (define @t122 () (@list @t112 @t50)) % 245.63/245.87 (define @t123 () (forall @t122 @t121)) % 245.63/245.87 (define @t124 () (not @t123)) % 245.63/245.87 (define @t125 () (tptp.setunion @t15)) % 245.63/245.87 (define @t126 () (not (tptp.in @t50 @t125))) % 245.63/245.87 (define @t127 () (not (= @t15 @t53))) % 245.63/245.87 (define @t128 () (tptp.in @t2 @t125)) % 245.63/245.87 (define @t129 () (not @t128)) % 245.63/245.87 (define @t130 () (or @t129 @t126 @t127)) % 245.63/245.87 (define @t131 () (forall @t57 @t130)) % 245.63/245.87 (define @t132 () (not @t131)) % 245.63/245.87 (define @t133 () (lambda @t47 @t132)) % 245.63/245.87 (define @t134 () (forall @t4 (_ @t133 @t103))) % 245.63/245.87 (define @t135 () (or @t126 @t127)) % 245.63/245.87 (define @t136 () (or @t129 @t135)) % 245.63/245.87 (define @t137 () (forall @t57 @t136)) % 245.63/245.87 (define @t138 () (@list @t50)) % 245.63/245.87 (define @t139 () (forall @t138 @t136)) % 245.63/245.87 (define @t140 () (forall @t138 @t135)) % 245.63/245.87 (define @t141 () (or @t129 @t140)) % 245.63/245.87 (define @t142 () (tptp.in @t1 @t125)) % 245.63/245.87 (define @t143 () (forall @t13 (or (not @t142) (not (= @t15 @t85))))) % 245.63/245.87 (define @t144 () (not @t44)) % 245.63/245.87 (define @t145 () (or @t144 @t143)) % 245.63/245.87 (define @t146 () (not @t143)) % 245.63/245.87 (define @t147 () (and @t44 @t146)) % 245.63/245.87 (define @t148 () (forall @t19 (not @t147))) % 245.63/245.87 (define @t149 () (not @t148)) % 245.63/245.87 (define @t150 () (not @t39)) % 245.63/245.87 (define @t151 () (not @t41)) % 245.63/245.87 (define @t152 () (or @t151 @t150)) % 245.63/245.87 (define @t153 () (forall @t13 (not @t42))) % 245.63/245.87 (define @t154 () (not @t153)) % 245.63/245.87 (define @t155 () (=> tptp.kpairp @t111)) % 245.63/245.87 (define @t156 () (or @t70 @t58)) % 245.63/245.87 (define @t157 () (not (= @t7 @t53))) % 245.63/245.87 (define @t158 () (or @t56 @t55 @t157)) % 245.63/245.87 (define @t159 () (forall @t57 @t158)) % 245.63/245.87 (define @t160 () (not @t159)) % 245.63/245.87 (define @t161 () (_ @t133 @t7)) % 245.63/245.87 (define @t162 () (=> @t23 @t161)) % 245.63/245.87 (define @t163 () (forall @t25 @t162)) % 245.63/245.87 (define @t164 () (=> tptp.cartprodmempair1 @t163)) % 245.63/245.87 (define @t165 () (=> tptp.kpairp @t164)) % 245.63/245.87 (define @t166 () (@quantifiers_skolemize @t62 2)) % 245.63/245.87 (define @t167 () (@quantifiers_skolemize @t62 1)) % 245.63/245.87 (define @t168 () (not (tptp.in @t63 @t167))) % 245.63/245.87 (define @t169 () (@quantifiers_skolemize @t62 0)) % 245.63/245.87 (define @t170 () (not (tptp.in @t2 @t169))) % 245.63/245.87 (define @t171 () (forall @t68 (or @t170 @t168 (not (= @t64 @t166))))) % 245.63/245.87 (define @t172 () (@quantifiers_skolemize @t171 1)) % 245.63/245.87 (define @t173 () (@quantifiers_skolemize @t171 0)) % 245.63/245.87 (define @t174 () (tptp.setadjoin (tptp.setadjoin @t173 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t173 (tptp.setadjoin @t172 tptp.emptyset)) tptp.emptyset))) % 245.63/245.87 (define @t175 () (not (= @t174 @t113))) % 245.63/245.87 (define @t176 () (tptp.setunion @t174)) % 245.63/245.87 (define @t177 () (not (tptp.in @t50 @t176))) % 245.63/245.87 (define @t178 () (not (tptp.in @t112 @t176))) % 245.63/245.87 (define @t179 () (or @t178 @t177 @t175)) % 245.63/245.87 (define @t180 () (forall @t122 @t179)) % 245.63/245.87 (define @t181 () (not @t180)) % 245.63/245.87 (define @t182 () (tptp.setunion @t85)) % 245.63/245.87 (define @t183 () (forall @t4 (not (forall @t122 (or (not (tptp.in @t112 @t182)) (not (tptp.in @t50 @t182)) (not (= @t85 @t113))))))) % 245.63/245.87 (define @t184 () (forall @t122 (or @t178 @t177 (not (= @t113 @t174))))) % 245.63/245.87 (define @t185 () (not @t184)) % 245.63/245.87 (define @t186 () (@list false)) % 245.63/245.87 (define @t187 () (@quantifiers_skolemize @t184 1)) % 245.63/245.87 (define @t188 () (@quantifiers_skolemize @t184 0)) % 245.63/245.87 (define @t189 () (tptp.setadjoin (tptp.setadjoin @t188 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t188 (tptp.setadjoin @t187 tptp.emptyset)) tptp.emptyset))) % 245.63/245.87 (define @t190 () (= @t174 @t189)) % 245.63/245.87 (define @t191 () (not @t190)) % 245.63/245.87 (define @t192 () (tptp.in @t187 @t176)) % 245.63/245.87 (define @t193 () (not @t192)) % 245.63/245.87 (define @t194 () (tptp.in @t188 @t176)) % 245.63/245.87 (define @t195 () (not @t194)) % 245.63/245.87 (define @t196 () (or @t195 @t193 @t191)) % 245.63/245.87 (define @t197 () (not @t196)) % 245.63/245.87 (define @t198 () (not (= @t189 @t174))) % 245.63/245.87 (define @t199 () (or @t195 @t193 @t198)) % 245.63/245.87 (define @t200 () (not @t199)) % 245.63/245.87 (define @t201 () (@list true)) % 245.63/245.87 (define @t202 () (@list @t196)) % 245.63/245.87 (define @t203 () (not (= @t166 @t64))) % 245.63/245.87 (define @t204 () (or @t170 @t168 @t203)) % 245.63/245.87 (define @t205 () (forall @t68 @t204)) % 245.63/245.87 (define @t206 () (not @t205)) % 245.63/245.87 (define @t207 () (tptp.in @t166 (tptp.cartprod @t169 @t167))) % 245.63/245.87 (define @t208 () (not @t207)) % 245.63/245.87 (define @t209 () (or @t208 @t206)) % 245.63/245.87 (define @t210 () (forall @t25 (or @t61 @t69))) % 245.63/245.87 (define @t211 () (not @t171)) % 245.63/245.87 (define @t212 () (or @t208 @t211)) % 245.63/245.87 (define @t213 () (tptp.setunion @t166)) % 245.63/245.87 (define @t214 () (forall @t57 (or (not (tptp.in @t2 @t213)) (not (tptp.in @t50 @t213)) (not (= @t53 @t166))))) % 245.63/245.87 (define @t215 () (not @t214)) % 245.63/245.87 (define @t216 () (or @t208 @t215)) % 245.63/245.87 (define @t217 () (@list @t216)) % 245.63/245.87 (define @t218 () (= @t166 @t174)) % 245.63/245.87 (define @t219 () (not @t218)) % 245.63/245.87 (define @t220 () (not (tptp.in @t172 @t167))) % 245.63/245.87 (define @t221 () (not (tptp.in @t173 @t169))) % 245.63/245.87 (define @t222 () (or @t221 @t220 @t219)) % 245.63/245.87 (define @t223 () (not @t222)) % 245.63/245.87 (define @t224 () (not (= @t174 @t166))) % 245.63/245.87 (define @t225 () (or @t221 @t220 @t224)) % 245.63/245.87 (define @t226 () (not @t225)) % 245.63/245.87 (define @t227 () (tptp.in @t188 @t213)) % 245.63/245.87 (define @t228 () (not (= @t189 @t166))) % 245.63/245.87 (define @t229 () (tptp.in @t187 @t213)) % 245.63/245.87 (define @t230 () (not @t229)) % 245.63/245.87 (define @t231 () (not @t227)) % 245.63/245.87 (define @t232 () (or @t231 @t230 @t228)) % 245.63/245.87 (define @t233 () (= @t166 @t189)) % 245.63/245.87 (define @t234 () (not @t233)) % 245.63/245.87 (define @t235 () (or @t231 @t230 @t234)) % 245.63/245.87 (assume @p1 @t6) % 245.63/245.87 (assume @p2 @t27) % 245.63/245.87 (assume @p3 @t32) % 245.63/245.87 (assume @p4 true) % 245.63/245.87 (step @p5 (= tptp.iskpair @t48) :rule refl :args (@t48)) % 245.63/245.87 (step @p6 (= tptp.kpair @t49) :rule refl :args (@t49)) % 245.63/245.87 (step @p7 :rule refl :args (@t62)) % 245.63/245.87 (step @p8 :rule refl :args (@t69)) % 245.63/245.87 (step @p9 :rule refl :args ((tptp.in @t7 @t21))) % 245.63/245.87 (step @p10 :rule refl :args (@t59)) % 245.63/245.87 (step @p11 :rule refl :args (@t7)) % 245.63/245.87 (step @p12 :rule cong :premises (@p11 @p10) :args (@t60)) % 245.63/245.87 (step @p13 :rule trans :premises (@p12 @p9)) % 245.63/245.87 (step @p14 :rule refl :args (@t22)) % 245.63/245.87 (step @p15 :rule ho_cong :premises (@p14 @p10)) % 245.63/245.87 (step @p16 :rule cong :premises (@p15 @p13) :args ((= (_ @t22 @t59) @t60))) % 245.63/245.87 (step @p17 :rule symm :premises (@p16)) % 245.63/245.87 (step @p18 :rule refl :args (@t23)) % 245.63/245.87 (step @p19 :rule eq_resolve :premises (@p18 @p17)) % 245.63/245.87 (step @p20 :rule refl :args (@t21)) % 245.63/245.87 (step @p21 :rule cong :premises (@p20 @p10) :args ((= @t21 @t59))) % 245.63/245.87 (step @p22 :rule symm :premises (@p21)) % 245.63/245.87 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 245.63/245.87 (step @p24 :rule ho_cong :premises (@p14 @p23)) % 245.63/245.87 (step @p25 :rule trans :premises (@p24 @p19)) % 245.63/245.87 (step @p26 :rule cong :premises (@p25) :args (@t70)) % 245.63/245.87 (step @p27 :rule nary_cong :premises (@p26 @p8) :args (@t71)) % 245.63/245.87 (step @p28 :rule cong :premises (@p27) :args ((forall @t25 @t71))) % 245.63/245.87 (step @p29 :rule bool-impl-elim :args (@t23 @t69)) % 245.63/245.87 (step @p30 :rule cong :premises (@p29) :args ((forall @t25 (=> @t23 @t69)))) % 245.63/245.87 (step @p31 :rule trans :premises (@p30 @p28)) % 245.63/245.87 (step @p32 :rule eq-symm :args (@t64 @t7)) % 245.63/245.87 (step @p33 :rule cong :premises (@p32) :args (@t72)) % 245.63/245.87 (step @p34 :rule refl :args (@t65)) % 245.63/245.87 (step @p35 :rule refl :args (@t67)) % 245.63/245.87 (step @p36 :rule nary_cong :premises (@p35 @p34 @p33) :args (@t73)) % 245.63/245.87 (step @p37 :rule aci_norm :args ((= @t75 @t73))) % 245.63/245.87 (step @p38 :rule trans :premises (@p37 @p36)) % 245.63/245.87 (step @p39 :rule cong :premises (@p38) :args (@t76)) % 245.63/245.87 (step @p40 :rule quant-merge-prenex :args ((= (forall @t19 @t78) @t76))) % 245.63/245.87 (step @p41 :rule alpha_equiv :args (@t79 (@list @t63) @t80)) % 245.63/245.87 (step @p42 :rule refl :args (@t67)) % 245.63/245.87 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t81)) % 245.63/245.87 (step @p44 :rule quant-miniscope-or :args ((= @t78 @t81))) % 245.63/245.87 (step @p45 :rule trans :premises (@p44 @p43)) % 245.63/245.87 (step @p46 :rule symm :premises (@p45)) % 245.63/245.87 (step @p47 :rule cong :premises (@p46) :args ((forall @t19 (or @t67 @t87)))) % 245.63/245.87 (step @p48 :rule trans :premises (@p47 @p40)) % 245.63/245.87 (step @p49 :rule trans :premises (@p48 @p39)) % 245.63/245.87 (step @p50 :rule refl :args (@t87)) % 245.63/245.87 (step @p51 :rule refl :args (@t66)) % 245.63/245.87 (step @p52 :rule refl :args (@t17)) % 245.63/245.87 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t17 @t66))) % 245.63/245.87 (step @p54 :rule symm :premises (@p53)) % 245.63/245.87 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 245.63/245.87 (step @p56 :rule cong :premises (@p55) :args (@t88)) % 245.63/245.87 (step @p57 :rule nary_cong :premises (@p56 @p50) :args (@t89)) % 245.63/245.87 (step @p58 :rule cong :premises (@p57) :args ((forall @t19 @t89))) % 245.63/245.87 (step @p59 :rule trans :premises (@p58 @p49)) % 245.63/245.87 (step @p60 :rule bool-double-not-elim :args (@t87)) % 245.63/245.87 (step @p61 :rule refl :args (@t88)) % 245.63/245.87 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((or @t88 (not @t90)))) % 245.63/245.87 (step @p63 :rule bool-and-de-morgan :args (@t17 @t90 true)) % 245.63/245.87 (step @p64 :rule trans :premises (@p63 @p62)) % 245.63/245.87 (step @p65 :rule cong :premises (@p64) :args (@t92)) % 245.63/245.87 (step @p66 :rule trans :premises (@p65 @p59)) % 245.63/245.87 (step @p67 :rule cong :premises (@p66) :args (@t93)) % 245.63/245.87 (step @p68 :rule exists-elim :args ((= (exists @t19 @t91) @t93))) % 245.63/245.87 (step @p69 :rule trans :premises (@p68 @p67)) % 245.63/245.87 (step @p70 :rule refl :args ((tptp.setadjoin @t37 @t36))) % 245.63/245.87 (step @p71 :rule refl :args ((tptp.setadjoin @t35 tptp.emptyset))) % 245.63/245.87 (step @p72 :rule refl :args (tptp.emptyset)) % 245.63/245.87 (step @p73 :rule refl :args ((tptp.setadjoin @t2 @t33))) % 245.63/245.87 (step @p74 :rule refl :args (@t82)) % 245.63/245.87 (step @p75 :rule refl :args (@t2)) % 245.63/245.87 (step @p76 :rule cong :premises (@p75 @p74) :args (@t83)) % 245.63/245.87 (step @p77 :rule trans :premises (@p76 @p73)) % 245.63/245.87 (step @p78 :rule cong :premises (@p77 @p72) :args (@t84)) % 245.63/245.87 (step @p79 :rule trans :premises (@p78 @p71)) % 245.63/245.87 (step @p80 :rule refl :args (@t52)) % 245.63/245.87 (step @p81 :rule cong :premises (@p80 @p79) :args (@t85)) % 245.63/245.87 (step @p82 :rule trans :premises (@p81 @p70)) % 245.63/245.87 (step @p83 :rule refl :args (tptp.setadjoin)) % 245.63/245.87 (step @p84 :rule ho_cong :premises (@p83 @p80)) % 245.63/245.87 (step @p85 :rule ho_cong :premises (@p84 @p79)) % 245.63/245.87 (step @p86 :rule cong :premises (@p85 @p82) :args ((= (_ (_ tptp.setadjoin @t52) @t84) @t85))) % 245.63/245.87 (step @p87 :rule symm :premises (@p86)) % 245.63/245.87 (step @p88 :rule refl :args (@t38)) % 245.63/245.87 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 245.63/245.87 (step @p90 :rule ho_cong :premises (@p83 @p77)) % 245.63/245.87 (step @p91 :rule ho_cong :premises (@p90 @p72)) % 245.63/245.87 (step @p92 :rule cong :premises (@p91 @p79) :args ((= (_ (_ tptp.setadjoin @t83) tptp.emptyset) @t84))) % 245.63/245.87 (step @p93 :rule symm :premises (@p92)) % 245.63/245.87 (step @p94 :rule refl :args (@t36)) % 245.63/245.87 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 245.63/245.87 (step @p96 :rule refl :args (@t34)) % 245.63/245.87 (step @p97 :rule ho_cong :premises (@p96 @p74)) % 245.63/245.87 (step @p98 :rule cong :premises (@p97 @p77) :args ((= (_ @t34 @t82) @t83))) % 245.63/245.87 (step @p99 :rule symm :premises (@p98)) % 245.63/245.87 (step @p100 :rule refl :args (@t35)) % 245.63/245.87 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 245.63/245.87 (step @p102 :rule refl :args (@t33)) % 245.63/245.87 (step @p103 :rule cong :premises (@p102 @p74) :args ((= @t33 @t82))) % 245.63/245.87 (step @p104 :rule symm :premises (@p103)) % 245.63/245.87 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 245.63/245.87 (step @p106 :rule ho_cong :premises (@p96 @p105)) % 245.63/245.87 (step @p107 :rule trans :premises (@p106 @p101)) % 245.63/245.87 (step @p108 :rule ho_cong :premises (@p83 @p107)) % 245.63/245.87 (step @p109 :rule ho_cong :premises (@p108 @p72)) % 245.63/245.87 (step @p110 :rule trans :premises (@p109 @p95)) % 245.63/245.87 (step @p111 :rule refl :args (@t37)) % 245.63/245.87 (step @p112 :rule cong :premises (@p111 @p80) :args ((= @t37 @t52))) % 245.63/245.87 (step @p113 :rule symm :premises (@p112)) % 245.63/245.87 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 245.63/245.87 (step @p115 :rule ho_cong :premises (@p83 @p114)) % 245.63/245.87 (step @p116 :rule ho_cong :premises (@p115 @p110)) % 245.63/245.87 (step @p117 :rule trans :premises (@p116 @p89)) % 245.63/245.87 (step @p118 :rule cong :premises (@p117 @p11) :args (@t94)) % 245.63/245.87 (step @p119 :rule cong :premises (@p118) :args (@t95)) % 245.63/245.87 (step @p120 :rule refl :args (@t86)) % 245.63/245.87 (step @p121 :rule refl :args (@t11)) % 245.63/245.87 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t11 @t86))) % 245.63/245.87 (step @p123 :rule symm :premises (@p122)) % 245.63/245.87 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 245.63/245.87 (step @p125 :rule cong :premises (@p124) :args (@t96)) % 245.63/245.87 (step @p126 :rule nary_cong :premises (@p125 @p119) :args (@t97)) % 245.63/245.87 (step @p127 :rule cong :premises (@p126) :args ((forall @t13 @t97))) % 245.63/245.87 (step @p128 :rule bool-and-de-morgan :args (@t11 @t94 true)) % 245.63/245.87 (step @p129 :rule cong :premises (@p128) :args (@t99)) % 245.63/245.87 (step @p130 :rule trans :premises (@p129 @p127)) % 245.63/245.87 (step @p131 :rule cong :premises (@p130) :args (@t100)) % 245.63/245.87 (step @p132 :rule exists-elim :args ((= (exists @t13 @t98) @t100))) % 245.63/245.87 (step @p133 :rule trans :premises (@p132 @p131)) % 245.63/245.87 (step @p134 :rule eq-symm :args (@t7 @t38)) % 245.63/245.87 (step @p135 :rule beta-reduce :args ((= (_ @t101 @t1) @t38))) % 245.63/245.87 (step @p136 :rule refl :args (@t1)) % 245.63/245.87 (step @p137 :rule beta-reduce :args ((= @t102 @t101))) % 245.63/245.87 (step @p138 :rule ho_cong :premises (@p137 @p136)) % 245.63/245.87 (step @p139 :rule trans :premises (@p138 @p135)) % 245.63/245.87 (step @p140 :rule refl :args (@t7)) % 245.63/245.87 (step @p141 :rule cong :premises (@p140 @p139) :args (@t104)) % 245.63/245.87 (step @p142 :rule trans :premises (@p141 @p134)) % 245.63/245.87 (step @p143 :rule refl :args (@t11)) % 245.63/245.87 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t105)) % 245.63/245.87 (step @p145 :rule cong :premises (@p144) :args (@t106)) % 245.63/245.87 (step @p146 :rule trans :premises (@p145 @p133)) % 245.63/245.87 (step @p147 :rule refl :args (@t17)) % 245.63/245.87 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t107)) % 245.63/245.87 (step @p149 :rule cong :premises (@p148) :args (@t108)) % 245.63/245.87 (step @p150 :rule trans :premises (@p149 @p69)) % 245.63/245.87 (step @p151 :rule refl :args (@t23)) % 245.63/245.87 (step @p152 :rule cong :premises (@p151 @p150) :args (@t109)) % 245.63/245.87 (step @p153 :rule cong :premises (@p152) :args (@t110)) % 245.63/245.87 (step @p154 :rule trans :premises (@p153 @p31)) % 245.63/245.87 (step @p155 :rule refl :args (tptp.cartprodmempair1)) % 245.63/245.87 (step @p156 :rule cong :premises (@p155 @p154) :args ((= tptp.cartprodmempair1 @t110))) % 245.63/245.87 (step @p157 :rule refl :args (@t2)) % 245.63/245.87 (step @p158 :rule ho_cong :premises (@p6 @p157)) % 245.63/245.87 (step @p159 :rule ho_cong :premises (@p158 @p136)) % 245.63/245.87 (step @p160 :rule cong :premises (@p140 @p159) :args (@t8)) % 245.63/245.87 (step @p161 :rule nary_cong :premises (@p143 @p160) :args (@t12)) % 245.63/245.87 (step @p162 :rule cong :premises (@p161) :args (@t14)) % 245.63/245.87 (step @p163 :rule nary_cong :premises (@p147 @p162) :args (@t18)) % 245.63/245.87 (step @p164 :rule cong :premises (@p163) :args (@t20)) % 245.63/245.87 (step @p165 :rule cong :premises (@p151 @p164) :args (@t24)) % 245.63/245.87 (step @p166 :rule cong :premises (@p165) :args (@t26)) % 245.63/245.87 (step @p167 :rule cong :premises (@p155 @p166) :args (@t27)) % 245.63/245.87 (step @p168 :rule trans :premises (@p167 @p156)) % 245.63/245.87 (step @p169 :rule eq_resolve :premises (@p2 @p168)) % 245.63/245.87 (step @p170 :rule cong :premises (@p169 @p7) :args (@t111)) % 245.63/245.87 (step @p171 :rule refl :args (@t113)) % 245.63/245.87 (step @p172 :rule cong :premises (@p117 @p171) :args (@t114)) % 245.63/245.87 (step @p173 :rule cong :premises (@p172) :args (@t115)) % 245.63/245.87 (step @p174 :rule cong :premises (@p117) :args (@t116)) % 245.63/245.87 (step @p175 :rule refl :args (@t50)) % 245.63/245.87 (step @p176 :rule cong :premises (@p175 @p174) :args (@t117)) % 245.63/245.87 (step @p177 :rule cong :premises (@p176) :args (@t118)) % 245.63/245.87 (step @p178 :rule refl :args (@t112)) % 245.63/245.87 (step @p179 :rule cong :premises (@p178 @p174) :args (@t119)) % 245.63/245.87 (step @p180 :rule cong :premises (@p179) :args (@t120)) % 245.63/245.87 (step @p181 :rule nary_cong :premises (@p180 @p177 @p173) :args (@t121)) % 245.63/245.87 (step @p182 :rule cong :premises (@p181) :args (@t123)) % 245.63/245.87 (step @p183 :rule cong :premises (@p182) :args (@t124)) % 245.63/245.87 (step @p184 :rule beta-reduce :args ((= (_ (lambda @t47 (not (forall @t122 (or (not (tptp.in @t112 @t125)) @t126 (not (= @t15 @t113)))))) @t38) @t124))) % 245.63/245.87 (step @p185 :rule trans :premises (@p184 @p183)) % 245.63/245.87 (step @p186 :rule alpha_equiv :args (@t131 (@list @t2) (@list @t112))) % 245.63/245.87 (step @p187 :rule cong :premises (@p186) :args (@t132)) % 245.63/245.87 (step @p188 :rule cong :premises (@p187) :args (@t133)) % 245.63/245.87 (step @p189 :rule ho_cong :premises (@p188 @p88)) % 245.63/245.87 (step @p190 :rule trans :premises (@p189 @p185)) % 245.63/245.87 (step @p191 :rule refl :args (@t133)) % 245.63/245.87 (step @p192 :rule ho_cong :premises (@p191 @p139)) % 245.63/245.87 (step @p193 :rule trans :premises (@p192 @p190)) % 245.63/245.87 (step @p194 :rule cong :premises (@p193) :args (@t134)) % 245.63/245.87 (step @p195 :rule refl :args (tptp.kpairp)) % 245.63/245.87 (step @p196 :rule cong :premises (@p195 @p194) :args ((= tptp.kpairp @t134))) % 245.63/245.87 (step @p197 :rule aci_norm :args ((= @t136 @t130))) % 245.63/245.87 (step @p198 :rule cong :premises (@p197) :args (@t137)) % 245.63/245.87 (step @p199 :rule quant-merge-prenex :args ((= (forall @t19 @t139) @t137))) % 245.63/245.87 (step @p200 :rule alpha_equiv :args (@t140 (@list @t50) @t80)) % 245.63/245.87 (step @p201 :rule refl :args (@t129)) % 245.63/245.87 (step @p202 :rule nary_cong :premises (@p201 @p200) :args (@t141)) % 245.63/245.87 (step @p203 :rule quant-miniscope-or :args ((= @t139 @t141))) % 245.63/245.87 (step @p204 :rule trans :premises (@p203 @p202)) % 245.63/245.87 (step @p205 :rule symm :premises (@p204)) % 245.63/245.87 (step @p206 :rule cong :premises (@p205) :args ((forall @t19 (or @t129 @t143)))) % 245.63/245.87 (step @p207 :rule trans :premises (@p206 @p199)) % 245.63/245.87 (step @p208 :rule trans :premises (@p207 @p198)) % 245.63/245.87 (step @p209 :rule refl :args (@t143)) % 245.63/245.87 (step @p210 :rule refl :args ((tptp.in @t2 @t40))) % 245.63/245.87 (step @p211 :rule refl :args (@t125)) % 245.63/245.87 (step @p212 :rule cong :premises (@p75 @p211) :args (@t128)) % 245.63/245.87 (step @p213 :rule trans :premises (@p212 @p210)) % 245.63/245.87 (step @p214 :rule refl :args (@t16)) % 245.63/245.87 (step @p215 :rule ho_cong :premises (@p214 @p211)) % 245.63/245.87 (step @p216 :rule cong :premises (@p215 @p213) :args ((= (_ @t16 @t125) @t128))) % 245.63/245.87 (step @p217 :rule symm :premises (@p216)) % 245.63/245.87 (step @p218 :rule refl :args (@t44)) % 245.63/245.87 (step @p219 :rule eq_resolve :premises (@p218 @p217)) % 245.63/245.87 (step @p220 :rule refl :args (@t40)) % 245.63/245.87 (step @p221 :rule cong :premises (@p220 @p211) :args ((= @t40 @t125))) % 245.63/245.87 (step @p222 :rule symm :premises (@p221)) % 245.63/245.87 (step @p223 :rule eq_resolve :premises (@p220 @p222)) % 245.63/245.87 (step @p224 :rule ho_cong :premises (@p214 @p223)) % 245.63/245.87 (step @p225 :rule trans :premises (@p224 @p219)) % 245.63/245.87 (step @p226 :rule cong :premises (@p225) :args (@t144)) % 245.63/245.87 (step @p227 :rule nary_cong :premises (@p226 @p209) :args (@t145)) % 245.63/245.87 (step @p228 :rule cong :premises (@p227) :args ((forall @t19 @t145))) % 245.63/245.87 (step @p229 :rule trans :premises (@p228 @p208)) % 245.63/245.87 (step @p230 :rule bool-double-not-elim :args (@t143)) % 245.63/245.87 (step @p231 :rule refl :args (@t144)) % 245.63/245.87 (step @p232 :rule nary_cong :premises (@p231 @p230) :args ((or @t144 (not @t146)))) % 245.63/245.87 (step @p233 :rule bool-and-de-morgan :args (@t44 @t146 true)) % 245.63/245.87 (step @p234 :rule trans :premises (@p233 @p232)) % 245.63/245.87 (step @p235 :rule cong :premises (@p234) :args (@t148)) % 245.63/245.87 (step @p236 :rule trans :premises (@p235 @p229)) % 245.63/245.87 (step @p237 :rule cong :premises (@p236) :args (@t149)) % 245.63/245.87 (step @p238 :rule exists-elim :args ((= (exists @t19 @t147) @t149))) % 245.63/245.87 (step @p239 :rule trans :premises (@p238 @p237)) % 245.63/245.87 (step @p240 :rule refl :args (@t15)) % 245.63/245.87 (step @p241 :rule cong :premises (@p240 @p117) :args (@t39)) % 245.63/245.87 (step @p242 :rule cong :premises (@p241) :args (@t150)) % 245.63/245.87 (step @p243 :rule refl :args ((tptp.in @t1 @t40))) % 245.63/245.87 (step @p244 :rule refl :args (@t1)) % 245.63/245.87 (step @p245 :rule cong :premises (@p244 @p211) :args (@t142)) % 245.63/245.87 (step @p246 :rule trans :premises (@p245 @p243)) % 245.63/245.87 (step @p247 :rule refl :args (@t10)) % 245.63/245.87 (step @p248 :rule ho_cong :premises (@p247 @p211)) % 245.63/245.87 (step @p249 :rule cong :premises (@p248 @p246) :args ((= (_ @t10 @t125) @t142))) % 245.63/245.87 (step @p250 :rule symm :premises (@p249)) % 245.63/245.87 (step @p251 :rule refl :args (@t41)) % 245.63/245.87 (step @p252 :rule eq_resolve :premises (@p251 @p250)) % 245.63/245.87 (step @p253 :rule ho_cong :premises (@p247 @p223)) % 245.63/245.87 (step @p254 :rule trans :premises (@p253 @p252)) % 245.63/245.87 (step @p255 :rule cong :premises (@p254) :args (@t151)) % 245.63/245.87 (step @p256 :rule nary_cong :premises (@p255 @p242) :args (@t152)) % 245.63/245.87 (step @p257 :rule cong :premises (@p256) :args ((forall @t13 @t152))) % 245.63/245.87 (step @p258 :rule bool-and-de-morgan :args (@t41 @t39 true)) % 245.63/245.87 (step @p259 :rule cong :premises (@p258) :args (@t153)) % 245.63/245.87 (step @p260 :rule trans :premises (@p259 @p257)) % 245.63/245.87 (step @p261 :rule cong :premises (@p260) :args (@t154)) % 245.63/245.87 (step @p262 :rule exists-elim :args ((= @t43 @t154))) % 245.63/245.87 (step @p263 :rule trans :premises (@p262 @p261)) % 245.63/245.87 (step @p264 :rule refl :args (@t44)) % 245.63/245.87 (step @p265 :rule nary_cong :premises (@p264 @p263) :args (@t45)) % 245.63/245.87 (step @p266 :rule cong :premises (@p265) :args (@t46)) % 245.63/245.87 (step @p267 :rule trans :premises (@p266 @p239)) % 245.63/245.87 (step @p268 :rule cong :premises (@p267) :args (@t48)) % 245.63/245.87 (step @p269 :rule trans :premises (@p5 @p268)) % 245.63/245.87 (step @p270 :rule ho_cong :premises (@p269 @p159)) % 245.63/245.87 (step @p271 :rule cong :premises (@p270) :args (@t5)) % 245.63/245.87 (step @p272 :rule cong :premises (@p195 @p271) :args (@t6)) % 245.63/245.87 (step @p273 :rule trans :premises (@p272 @p196)) % 245.63/245.87 (step @p274 :rule eq_resolve :premises (@p1 @p273)) % 245.63/245.87 (step @p275 :rule cong :premises (@p274 @p170) :args (@t155)) % 245.63/245.87 (step @p276 :rule cong :premises (@p275) :args ((not @t155))) % 245.63/245.87 (step @p277 :rule refl :args (@t58)) % 245.63/245.87 (step @p278 :rule nary_cong :premises (@p26 @p277) :args (@t156)) % 245.63/245.87 (step @p279 :rule cong :premises (@p278) :args ((forall @t25 @t156))) % 245.63/245.87 (step @p280 :rule bool-impl-elim :args (@t23 @t58)) % 245.63/245.87 (step @p281 :rule cong :premises (@p280) :args ((forall @t25 (=> @t23 @t58)))) % 245.63/245.87 (step @p282 :rule trans :premises (@p281 @p279)) % 245.63/245.87 (step @p283 :rule eq-symm :args (@t7 @t53)) % 245.63/245.87 (step @p284 :rule cong :premises (@p283) :args (@t157)) % 245.63/245.87 (step @p285 :rule refl :args (@t55)) % 245.63/245.87 (step @p286 :rule refl :args (@t56)) % 245.63/245.87 (step @p287 :rule nary_cong :premises (@p286 @p285 @p284) :args (@t158)) % 245.63/245.87 (step @p288 :rule cong :premises (@p287) :args (@t159)) % 245.63/245.87 (step @p289 :rule cong :premises (@p288) :args (@t160)) % 245.63/245.87 (step @p290 :rule beta-reduce :args ((= @t161 @t160))) % 245.63/245.87 (step @p291 :rule trans :premises (@p290 @p289)) % 245.63/245.87 (step @p292 :rule cong :premises (@p151 @p291) :args (@t162)) % 245.63/245.87 (step @p293 :rule cong :premises (@p292) :args (@t163)) % 245.63/245.87 (step @p294 :rule trans :premises (@p293 @p282)) % 245.63/245.87 (step @p295 :rule cong :premises (@p155 @p294) :args (@t164)) % 245.63/245.87 (step @p296 :rule cong :premises (@p195 @p295) :args (@t165)) % 245.63/245.87 (step @p297 :rule cong :premises (@p296) :args ((not @t165))) % 245.63/245.87 (step @p298 :rule ho_cong :premises (@p269 @p140)) % 245.63/245.87 (step @p299 :rule cong :premises (@p151 @p298) :args (@t28)) % 245.63/245.87 (step @p300 :rule cong :premises (@p299) :args (@t29)) % 245.63/245.87 (step @p301 :rule cong :premises (@p155 @p300) :args (@t30)) % 245.63/245.87 (step @p302 :rule cong :premises (@p195 @p301) :args (@t31)) % 245.63/245.87 (step @p303 :rule cong :premises (@p302) :args (@t32)) % 245.63/245.87 (step @p304 :rule trans :premises (@p303 @p297)) % 245.63/245.87 (step @p305 :rule trans :premises (@p304 @p276)) % 245.63/245.87 (step @p306 :rule eq_resolve :premises (@p3 @p305)) % 245.63/245.87 (step @p307 :rule not_implies_elim1 :premises (@p306)) % 245.63/245.87 (step @p308 :rule eq-symm :args (@t174 @t113)) % 245.63/245.87 (step @p309 :rule cong :premises (@p308) :args (@t175)) % 245.63/245.87 (step @p310 :rule refl :args (@t177)) % 245.63/245.87 (step @p311 :rule refl :args (@t178)) % 245.63/245.87 (step @p312 :rule nary_cong :premises (@p311 @p310 @p309) :args (@t179)) % 245.63/245.87 (step @p313 :rule cong :premises (@p312) :args (@t180)) % 245.63/245.87 (step @p314 :rule cong :premises (@p313) :args (@t181)) % 245.63/245.87 (step @p315 :rule refl :args (@t183)) % 245.63/245.87 (step @p316 :rule cong :premises (@p315 @p314) :args ((=> @t183 @t181))) % 245.63/245.87 (assume-push @p455 @t183) % 245.63/245.87 (step @p318 :rule instantiate :premises (@p307) :args ((@list @t173 @t172))) % 245.63/245.87 (step-pop @p456 :rule scope :premises (@p318)) % 245.63/245.87 (step @p319 :rule process_scope :premises (@p456) :args (@t181)) % 245.63/245.87 (step @p321 :rule eq_resolve :premises (@p319 @p316)) % 245.63/245.87 (step @p322 :rule implies_elim :premises (@p321)) % 245.63/245.87 (step @p323 :rule chain_m_resolution :premises (@p322 @p307) :args (@t185 @t186 (@list @t183))) % 245.63/245.87 (step @p324 :rule refl :args (@t197)) % 245.63/245.87 (step @p325 :rule bool-double-not-elim :args (@t184)) % 245.63/245.87 (step @p326 :rule nary_cong :premises (@p325 @p324) :args ((or (not @t185) @t197))) % 245.63/245.87 (step @p327 :rule eq-symm :args (@t189 @t174)) % 245.63/245.87 (step @p328 :rule cong :premises (@p327) :args (@t198)) % 245.63/245.87 (step @p329 :rule refl :args (@t193)) % 245.63/245.87 (step @p330 :rule refl :args (@t195)) % 245.63/245.87 (step @p331 :rule nary_cong :premises (@p330 @p329 @p328) :args (@t199)) % 245.63/245.87 (step @p332 :rule cong :premises (@p331) :args (@t200)) % 245.63/245.87 (step @p333 :rule refl :args (@t185)) % 245.63/245.87 (step @p334 :rule cong :premises (@p333 @p332) :args ((=> @t185 @t200))) % 245.63/245.87 (assume-push @p457 @t185) % 245.63/245.87 (step @p336 :rule skolemize :premises (@p323)) % 245.63/245.87 (step-pop @p458 :rule scope :premises (@p336)) % 245.63/245.87 (step @p337 :rule process_scope :premises (@p458) :args (@t200)) % 245.63/245.87 (step @p339 :rule eq_resolve :premises (@p337 @p334)) % 245.63/245.87 (step @p340 :rule implies_elim :premises (@p339)) % 245.63/245.87 (step @p341 :rule eq_resolve :premises (@p340 @p326)) % 245.63/245.87 (step @p342 :rule chain_m_resolution :premises (@p341 @p323) :args (@t197 @t201 (@list @t184))) % 245.63/245.87 (step @p343 :rule bool-double-not-elim :args (@t194)) % 245.63/245.87 (step @p344 :rule refl :args (@t196)) % 245.63/245.87 (step @p345 :rule nary_cong :premises (@p344 @p343) :args ((or @t196 (not @t195)))) % 245.63/245.87 (step @p346 :rule cnf_or_neg :args (@t196 0)) % 245.63/245.87 (step @p347 :rule eq_resolve :premises (@p346 @p345)) % 245.63/245.87 (step @p348 :rule reordering :premises (@p347) :args ((or @t194 @t196))) % 245.63/245.87 (step @p349 :rule chain_m_resolution :premises (@p348 @p342) :args (@t194 @t201 @t202)) % 245.63/245.87 (step @p350 :rule true_intro :premises (@p349)) % 245.63/245.87 (step @p351 :rule not_implies_elim2 :premises (@p306)) % 245.63/245.87 (step @p352 :rule not_implies_elim1 :premises (@p351)) % 245.63/245.87 (step @p353 :rule eq-symm :args (@t166 @t64)) % 245.63/245.87 (step @p354 :rule cong :premises (@p353) :args (@t203)) % 245.63/245.87 (step @p355 :rule refl :args (@t168)) % 245.63/245.87 (step @p356 :rule refl :args (@t170)) % 245.63/245.87 (step @p357 :rule nary_cong :premises (@p356 @p355 @p354) :args (@t204)) % 245.63/245.87 (step @p358 :rule cong :premises (@p357) :args (@t205)) % 245.63/245.87 (step @p359 :rule cong :premises (@p358) :args (@t206)) % 245.63/245.87 (step @p360 :rule refl :args (@t208)) % 245.63/245.87 (step @p361 :rule nary_cong :premises (@p360 @p359) :args (@t209)) % 245.63/245.87 (step @p362 :rule refl :args (@t210)) % 245.63/245.87 (step @p363 :rule cong :premises (@p362 @p361) :args ((=> @t210 @t209))) % 245.63/245.87 (assume-push @p459 @t210) % 245.63/245.87 (step @p365 :rule instantiate :premises (@p352) :args ((@list @t169 @t167 @t166))) % 245.63/245.87 (step-pop @p460 :rule scope :premises (@p365)) % 245.63/245.87 (step @p366 :rule process_scope :premises (@p460) :args (@t209)) % 245.63/245.87 (step @p368 :rule eq_resolve :premises (@p366 @p363)) % 245.63/245.87 (step @p369 :rule implies_elim :premises (@p368)) % 245.63/245.87 (step @p370 :rule chain_m_resolution :premises (@p369 @p352) :args (@t212 @t186 (@list @t210))) % 245.63/245.87 (step @p371 :rule not_implies_elim2 :premises (@p351)) % 245.63/245.87 (step @p372 :rule skolemize :premises (@p371)) % 245.63/245.87 (step @p373 :rule bool-double-not-elim :args (@t207)) % 245.63/245.87 (step @p374 :rule refl :args (@t216)) % 245.63/245.87 (step @p375 :rule nary_cong :premises (@p374 @p373) :args ((or @t216 (not @t208)))) % 245.63/245.87 (step @p376 :rule cnf_or_neg :args (@t216 0)) % 245.63/245.87 (step @p377 :rule eq_resolve :premises (@p376 @p375)) % 245.63/245.87 (step @p378 :rule reordering :premises (@p377) :args ((or @t207 @t216))) % 245.63/245.87 (step @p379 :rule chain_m_resolution :premises (@p378 @p372) :args (@t207 @t201 @t217)) % 245.63/245.87 (step @p380 :rule cnf_or_pos :args (@t212)) % 245.63/245.87 (step @p381 :rule reordering :premises (@p380) :args ((or @t208 @t211 (not @t212)))) % 245.63/245.87 (step @p382 :rule chain_m_resolution :premises (@p381 @p379 @p370) :args (@t211 (@list false false) (@list @t207 @t212))) % 245.63/245.87 (step @p383 :rule refl :args (@t223)) % 245.63/245.87 (step @p384 :rule bool-double-not-elim :args (@t171)) % 245.63/245.87 (step @p385 :rule nary_cong :premises (@p384 @p383) :args ((or (not @t211) @t223))) % 245.63/245.87 (step @p386 :rule eq-symm :args (@t174 @t166)) % 245.63/245.87 (step @p387 :rule cong :premises (@p386) :args (@t224)) % 245.63/245.87 (step @p388 :rule refl :args (@t220)) % 245.63/245.87 (step @p389 :rule refl :args (@t221)) % 245.63/245.88 (step @p390 :rule nary_cong :premises (@p389 @p388 @p387) :args (@t225)) % 245.63/245.88 (step @p391 :rule cong :premises (@p390) :args (@t226)) % 245.63/245.88 (step @p392 :rule refl :args (@t211)) % 245.63/245.88 (step @p393 :rule cong :premises (@p392 @p391) :args ((=> @t211 @t226))) % 245.63/245.88 (assume-push @p461 @t211) % 245.63/245.88 (step @p395 :rule skolemize :premises (@p382)) % 245.63/245.88 (step-pop @p462 :rule scope :premises (@p395)) % 245.63/245.88 (step @p396 :rule process_scope :premises (@p462) :args (@t226)) % 245.63/245.88 (step @p398 :rule eq_resolve :premises (@p396 @p393)) % 245.63/245.88 (step @p399 :rule implies_elim :premises (@p398)) % 245.63/245.88 (step @p400 :rule eq_resolve :premises (@p399 @p385)) % 245.63/245.88 (step @p401 :rule chain_m_resolution :premises (@p400 @p382) :args (@t223 @t201 (@list @t171))) % 245.63/245.88 (step @p402 :rule bool-double-not-elim :args (@t218)) % 245.63/245.88 (step @p403 :rule refl :args (@t222)) % 245.63/245.88 (step @p404 :rule nary_cong :premises (@p403 @p402) :args ((or @t222 (not @t219)))) % 245.63/245.88 (step @p405 :rule cnf_or_neg :args (@t222 2)) % 245.63/245.88 (step @p406 :rule eq_resolve :premises (@p405 @p404)) % 245.63/245.88 (step @p407 :rule reordering :premises (@p406) :args ((or @t218 @t222))) % 245.63/245.88 (step @p408 :rule chain_m_resolution :premises (@p407 @p401) :args (@t218 @t201 (@list @t222))) % 245.63/245.88 (step @p409 :rule cong :premises (@p408) :args (@t213)) % 245.63/245.88 (step @p410 :rule refl :args (@t188)) % 245.63/245.88 (step @p411 :rule cong :premises (@p410 @p409) :args (@t227)) % 245.63/245.88 (step @p412 :rule trans :premises (@p411 @p350)) % 245.63/245.88 (step @p413 :rule true_elim :premises (@p412)) % 245.63/245.88 (step @p414 :rule bool-double-not-elim :args (@t214)) % 245.63/245.88 (step @p415 :rule nary_cong :premises (@p374 @p414) :args ((or @t216 (not @t215)))) % 245.63/245.88 (step @p416 :rule cnf_or_neg :args (@t216 1)) % 245.63/245.88 (step @p417 :rule eq_resolve :premises (@p416 @p415)) % 245.63/245.88 (step @p418 :rule reordering :premises (@p417) :args ((or @t214 @t216))) % 245.63/245.88 (step @p419 :rule chain_m_resolution :premises (@p418 @p372) :args (@t214 @t201 @t217)) % 245.63/245.88 (step @p420 :rule eq-symm :args (@t189 @t166)) % 245.63/245.88 (step @p421 :rule cong :premises (@p420) :args (@t228)) % 245.63/245.88 (step @p422 :rule refl :args (@t230)) % 245.63/245.88 (step @p423 :rule refl :args (@t231)) % 245.63/245.88 (step @p424 :rule nary_cong :premises (@p423 @p422 @p421) :args (@t232)) % 245.63/245.88 (step @p425 :rule refl :args (@t214)) % 245.63/245.88 (step @p426 :rule cong :premises (@p425 @p424) :args ((=> @t214 @t232))) % 245.63/245.88 (assume-push @p463 @t214) % 245.63/245.88 (step @p428 :rule instantiate :premises (@p419) :args ((@list @t188 @t187))) % 245.63/245.88 (step-pop @p464 :rule scope :premises (@p428)) % 245.63/245.88 (step @p429 :rule process_scope :premises (@p464) :args (@t232)) % 245.63/245.88 (step @p431 :rule eq_resolve :premises (@p429 @p426)) % 245.63/245.88 (step @p432 :rule implies_elim :premises (@p431)) % 245.63/245.88 (step @p433 :rule chain_m_resolution :premises (@p432 @p419) :args (@t235 @t186 (@list @t214))) % 245.63/245.88 (step @p434 :rule bool-double-not-elim :args (@t190)) % 245.63/245.88 (step @p435 :rule nary_cong :premises (@p344 @p434) :args ((or @t196 (not @t191)))) % 245.63/245.88 (step @p436 :rule cnf_or_neg :args (@t196 2)) % 245.63/245.88 (step @p437 :rule eq_resolve :premises (@p436 @p435)) % 245.63/245.88 (step @p438 :rule reordering :premises (@p437) :args ((or @t190 @t196))) % 245.63/245.88 (step @p439 :rule chain_m_resolution :premises (@p438 @p342) :args (@t190 @t201 @t202)) % 245.63/245.88 (step @p440 :rule trans :premises (@p408 @p439)) % 245.63/245.88 (step @p441 :rule bool-double-not-elim :args (@t192)) % 245.63/245.88 (step @p442 :rule nary_cong :premises (@p344 @p441) :args ((or @t196 (not @t193)))) % 245.63/245.88 (step @p443 :rule cnf_or_neg :args (@t196 1)) % 245.63/245.88 (step @p444 :rule eq_resolve :premises (@p443 @p442)) % 245.63/245.88 (step @p445 :rule reordering :premises (@p444) :args ((or @t192 @t196))) % 245.63/245.88 (step @p446 :rule chain_m_resolution :premises (@p445 @p342) :args (@t192 @t201 @t202)) % 245.63/245.88 (step @p447 :rule true_intro :premises (@p446)) % 245.63/245.88 (step @p448 :rule refl :args (@t187)) % 245.63/245.88 (step @p449 :rule cong :premises (@p448 @p409) :args (@t229)) % 245.63/245.88 (step @p450 :rule trans :premises (@p449 @p447)) % 245.63/245.88 (step @p451 :rule true_elim :premises (@p450)) % 245.63/245.88 (step @p452 :rule cnf_or_pos :args (@t235)) % 245.63/245.88 (step @p453 :rule reordering :premises (@p452) :args ((or @t231 @t230 @t234 (not @t235)))) % 245.63/245.88 (step @p454 false :rule chain_m_resolution :premises (@p453 @p451 @p440 @p433 @p413) :args (false (@list false false false false) (@list @t229 @t233 @t235 @t227))) % 245.63/245.88 ) % 245.63/245.88 % SZS output end Proof % 245.63/245.88 % cvc5 exiting %------------------------------------------------------------------------------