%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU807^2 : 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 : n017.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 08:53:17 AM UTC 2026 % Result : Theorem 150.84s 151.10s % Output : Proof 150.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU807^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.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 17:51:31 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 150.84/151.10 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.84/151.10 --- 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... % 150.84/151.10 --- 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... % 150.84/151.10 --- Run --ho-elim --full-saturate-quant at 18s... % 150.84/151.10 % SZS status Theorem % 150.84/151.10 % SZS output start Proof % 150.84/151.10 ( % 150.84/151.10 (declare-sort $$unsorted 0) % 150.84/151.10 (declare-const tptp.upairset2E Bool) % 150.84/151.10 (declare-const tptp.emptyset $$unsorted) % 150.84/151.10 (declare-const tptp.setadjoinIL Bool) % 150.84/151.10 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 150.84/151.10 (declare-const tptp.setadjoinIR Bool) % 150.84/151.10 (declare-const tptp.foundationAx Bool) % 150.84/151.10 (declare-const tptp.in__Cong Bool) % 150.84/151.10 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 150.84/151.10 (define @t1 () (@var "A" $$unsorted)) % 150.84/151.10 (define @t2 () (@var "Xx" $$unsorted)) % 150.84/151.10 (define @t3 () (_ tptp.in @t2)) % 150.84/151.10 (define @t4 () (_ @t3 @t1)) % 150.84/151.10 (define @t5 () (@var "B" $$unsorted)) % 150.84/151.10 (define @t6 () (_ @t3 @t5)) % 150.84/151.10 (define @t7 () (and @t6 @t4)) % 150.84/151.10 (define @t8 () (@list @t2)) % 150.84/151.10 (define @t9 () (exists @t8 @t7)) % 150.84/151.10 (define @t10 () (not @t9)) % 150.84/151.10 (define @t11 () (_ (_ tptp.in @t5) @t1)) % 150.84/151.10 (define @t12 () (and @t11 @t10)) % 150.84/151.10 (define @t13 () (@list @t5)) % 150.84/151.10 (define @t14 () (exists @t13 @t12)) % 150.84/151.10 (define @t15 () (exists @t8 @t4)) % 150.84/151.10 (define @t16 () (=> @t15 @t14)) % 150.84/151.10 (define @t17 () (@list @t1)) % 150.84/151.10 (define @t18 () (forall @t17 @t16)) % 150.84/151.10 (define @t19 () (= tptp.foundationAx @t18)) % 150.84/151.10 (define @t20 () (@var "Xy" $$unsorted)) % 150.84/151.10 (define @t21 () (_ tptp.setadjoin @t2)) % 150.84/151.10 (define @t22 () (_ @t21 @t20)) % 150.84/151.10 (define @t23 () (_ @t3 @t22)) % 150.84/151.10 (define @t24 () (@list @t2 @t20)) % 150.84/151.10 (define @t25 () (forall @t24 @t23)) % 150.84/151.10 (define @t26 () (= tptp.setadjoinIL @t25)) % 150.84/151.10 (define @t27 () (_ @t21 @t1)) % 150.84/151.10 (define @t28 () (_ tptp.in @t20)) % 150.84/151.10 (define @t29 () (_ @t28 @t27)) % 150.84/151.10 (define @t30 () (_ @t28 @t1)) % 150.84/151.10 (define @t31 () (@list @t2 @t1 @t20)) % 150.84/151.10 (define @t32 () (forall @t31 (=> @t30 @t29))) % 150.84/151.10 (define @t33 () (= tptp.setadjoinIR @t32)) % 150.84/151.10 (define @t34 () (_ @t28 @t5)) % 150.84/151.10 (define @t35 () (= @t4 @t34)) % 150.84/151.10 (define @t36 () (= @t2 @t20)) % 150.84/151.10 (define @t37 () (forall @t24 (=> @t36 @t35))) % 150.84/151.10 (define @t38 () (= @t1 @t5)) % 150.84/151.10 (define @t39 () (=> @t38 @t37)) % 150.84/151.10 (define @t40 () (@list @t1 @t5)) % 150.84/151.10 (define @t41 () (forall @t40 @t39)) % 150.84/151.10 (define @t42 () (= tptp.in__Cong @t41)) % 150.84/151.10 (define @t43 () (@var "Xz" $$unsorted)) % 150.84/151.10 (define @t44 () (or (= @t43 @t2) (= @t43 @t20))) % 150.84/151.10 (define @t45 () (_ (_ tptp.setadjoin @t20) tptp.emptyset)) % 150.84/151.10 (define @t46 () (_ @t21 @t45)) % 150.84/151.10 (define @t47 () (_ tptp.in @t43)) % 150.84/151.10 (define @t48 () (_ @t47 @t46)) % 150.84/151.10 (define @t49 () (=> @t48 @t44)) % 150.84/151.10 (define @t50 () (@list @t2 @t20 @t43)) % 150.84/151.10 (define @t51 () (forall @t50 @t49)) % 150.84/151.10 (define @t52 () (= tptp.upairset2E @t51)) % 150.84/151.10 (define @t53 () (not @t11)) % 150.84/151.10 (define @t54 () (_ (_ tptp.in @t1) @t5)) % 150.84/151.10 (define @t55 () (forall @t40 (=> @t54 @t53))) % 150.84/151.10 (define @t56 () (=> tptp.upairset2E @t55)) % 150.84/151.10 (define @t57 () (=> tptp.in__Cong @t56)) % 150.84/151.10 (define @t58 () (=> tptp.setadjoinIR @t57)) % 150.84/151.10 (define @t59 () (=> tptp.setadjoinIL @t58)) % 150.84/151.10 (define @t60 () (=> tptp.foundationAx @t59)) % 150.84/151.10 (define @t61 () (not @t60)) % 150.84/151.10 (define @t62 () (@const 0 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 150.84/151.10 (define @t63 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 150.84/151.10 (define @t64 () (_ @t63 @t62 @t5)) % 150.84/151.10 (define @t65 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 150.84/151.10 (define @t66 () (not (_ @t65 @t64 @t1))) % 150.84/151.10 (define @t67 () (forall @t40 (or (not (_ @t65 (_ @t63 @t62 @t1) @t5)) @t66))) % 150.84/151.10 (define @t68 () (= @t20 @t43)) % 150.84/151.10 (define @t69 () (= @t2 @t43)) % 150.84/151.10 (define @t70 () (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted $$unsorted)))) % 150.84/151.10 (define @t71 () (@const 4 (-> (@ho-elim-sort (-> $$unsorted $$unsorted $$unsorted)) $$unsorted (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 150.84/151.10 (define @t72 () (@const 5 (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))) % 150.84/151.10 (define @t73 () (_ @t71 @t70 @t2)) % 150.84/151.10 (define @t74 () (_ @t63 @t62 @t20)) % 150.84/151.10 (define @t75 () (_ @t63 @t62 @t2)) % 150.84/151.10 (define @t76 () (not (_ @t65 @t75 @t5))) % 150.84/151.10 (define @t77 () (@var "BOUND_VARIABLE_7523" $$unsorted)) % 150.84/151.10 (define @t78 () (@list @t1 @t77)) % 150.84/151.10 (define @t79 () (tptp.in @t5 @t1)) % 150.84/151.10 (define @t80 () (not @t79)) % 150.84/151.10 (define @t81 () (tptp.in @t1 @t5)) % 150.84/151.10 (define @t82 () (forall @t40 (or (not @t81) @t80))) % 150.84/151.10 (define @t83 () (tptp.setadjoin @t20 tptp.emptyset)) % 150.84/151.10 (define @t84 () (tptp.setadjoin @t2 @t83)) % 150.84/151.10 (define @t85 () (tptp.in @t43 @t84)) % 150.84/151.10 (define @t86 () (=> (forall @t50 (or (not @t85) @t69 @t68)) @t82)) % 150.84/151.10 (define @t87 () (tptp.setadjoin @t2 @t1)) % 150.84/151.10 (define @t88 () (tptp.in @t20 @t87)) % 150.84/151.10 (define @t89 () (tptp.in @t20 @t1)) % 150.84/151.10 (define @t90 () (forall @t31 (or (not @t89) @t88))) % 150.84/151.10 (define @t91 () (tptp.setadjoin @t2 @t20)) % 150.84/151.10 (define @t92 () (tptp.in @t2 @t91)) % 150.84/151.10 (define @t93 () (forall @t24 @t92)) % 150.84/151.10 (define @t94 () (tptp.in @t2 @t1)) % 150.84/151.10 (define @t95 () (not @t94)) % 150.84/151.10 (define @t96 () (tptp.in @t2 @t5)) % 150.84/151.10 (define @t97 () (forall @t8 (or (not @t96) @t95))) % 150.84/151.10 (define @t98 () (not @t97)) % 150.84/151.10 (define @t99 () (not (forall @t13 (or @t80 @t98)))) % 150.84/151.10 (define @t100 () (not (tptp.in @t77 @t1))) % 150.84/151.10 (define @t101 () (or @t100 @t99)) % 150.84/151.10 (define @t102 () (forall @t78 @t101)) % 150.84/151.10 (define @t103 () (=> @t90 (=> true @t86))) % 150.84/151.10 (define @t104 () (=> @t93 @t103)) % 150.84/151.10 (define @t105 () (=> @t102 @t104)) % 150.84/151.10 (define @t106 () (not @t48)) % 150.84/151.10 (define @t107 () (or @t106 @t69 @t68)) % 150.84/151.10 (define @t108 () (or @t69 @t68)) % 150.84/151.10 (define @t109 () (=> tptp.upairset2E @t82)) % 150.84/151.10 (define @t110 () (@var "BOUND_VARIABLE_7570" $$unsorted)) % 150.84/151.10 (define @t111 () (@list @t5 @t110)) % 150.84/151.10 (define @t112 () (tptp.in @t110 @t5)) % 150.84/151.10 (define @t113 () (not (= @t5 @t5))) % 150.84/151.10 (define @t114 () (or @t113 (= @t112 @t112))) % 150.84/151.10 (define @t115 () (= (tptp.in @t110 @t1) @t112)) % 150.84/151.10 (define @t116 () (not @t38)) % 150.84/151.10 (define @t117 () (or @t116 @t116 @t115)) % 150.84/151.10 (define @t118 () (or @t116 @t115)) % 150.84/151.10 (define @t119 () (forall @t17 @t118)) % 150.84/151.10 (define @t120 () (forall @t111 @t119)) % 150.84/151.10 (define @t121 () (forall (@list @t5 @t110 @t1) @t118)) % 150.84/151.10 (define @t122 () (forall (@list @t1 @t5 @t110) @t118)) % 150.84/151.10 (define @t123 () (@list @t110)) % 150.84/151.10 (define @t124 () (forall @t123 @t118)) % 150.84/151.10 (define @t125 () (forall @t123 @t115)) % 150.84/151.10 (define @t126 () (or @t116 @t125)) % 150.84/151.10 (define @t127 () (tptp.in @t20 @t5)) % 150.84/151.10 (define @t128 () (= @t89 @t127)) % 150.84/151.10 (define @t129 () (@list @t20)) % 150.84/151.10 (define @t130 () (forall @t129 @t128)) % 150.84/151.10 (define @t131 () (not (= @t20 @t20))) % 150.84/151.10 (define @t132 () (or @t131 @t128)) % 150.84/151.10 (define @t133 () (= @t94 @t127)) % 150.84/151.10 (define @t134 () (not @t36)) % 150.84/151.10 (define @t135 () (or @t134 @t134 @t133)) % 150.84/151.10 (define @t136 () (or @t134 @t133)) % 150.84/151.10 (define @t137 () (forall @t8 @t136)) % 150.84/151.10 (define @t138 () (forall @t129 @t137)) % 150.84/151.10 (define @t139 () (forall (@list @t20 @t2) @t136)) % 150.84/151.10 (define @t140 () (or @t134 @t35)) % 150.84/151.10 (define @t141 () (=> tptp.in__Cong @t109)) % 150.84/151.10 (define @t142 () (not @t30)) % 150.84/151.10 (define @t143 () (or @t142 @t29)) % 150.84/151.10 (define @t144 () (=> tptp.setadjoinIR @t141)) % 150.84/151.10 (define @t145 () (=> tptp.setadjoinIL @t144)) % 150.84/151.10 (define @t146 () (@list @t77)) % 150.84/151.10 (define @t147 () (forall @t146 @t101)) % 150.84/151.10 (define @t148 () (forall @t146 @t100)) % 150.84/151.10 (define @t149 () (or @t148 @t99)) % 150.84/151.10 (define @t150 () (forall @t8 @t95)) % 150.84/151.10 (define @t151 () (not @t150)) % 150.84/151.10 (define @t152 () (or @t53 @t98)) % 150.84/151.10 (define @t153 () (and @t11 @t97)) % 150.84/151.10 (define @t154 () (forall @t13 (not @t153))) % 150.84/151.10 (define @t155 () (not @t154)) % 150.84/151.10 (define @t156 () (not @t4)) % 150.84/151.10 (define @t157 () (not @t6)) % 150.84/151.10 (define @t158 () (or @t157 @t156)) % 150.84/151.10 (define @t159 () (forall @t8 (not @t7))) % 150.84/151.10 (define @t160 () (not @t159)) % 150.84/151.10 (define @t161 () (forall @t8 @t156)) % 150.84/151.10 (define @t162 () (not @t161)) % 150.84/151.10 (define @t163 () (=> tptp.foundationAx @t145)) % 150.84/151.10 (define @t164 () (not @t54)) % 150.84/151.10 (define @t165 () (or @t164 @t53)) % 150.84/151.10 (define @t166 () (@quantifiers_skolemize @t67 1)) % 150.84/151.10 (define @t167 () (@quantifiers_skolemize @t67 0)) % 150.84/151.10 (define @t168 () (_ @t63 @t62 @t167)) % 150.84/151.10 (define @t169 () (_ @t65 @t168 @t166)) % 150.84/151.10 (define @t170 () (_ @t63 @t62 @t166)) % 150.84/151.10 (define @t171 () (_ @t65 @t170 @t167)) % 150.84/151.10 (define @t172 () (not @t171)) % 150.84/151.10 (define @t173 () (not @t169)) % 150.84/151.10 (define @t174 () (or @t173 @t172)) % 150.84/151.10 (define @t175 () (@list true)) % 150.84/151.10 (define @t176 () (@list @t174)) % 150.84/151.10 (define @t177 () (_ @t72 (_ @t71 @t70 @t166) tptp.emptyset)) % 150.84/151.10 (define @t178 () (_ @t72 (_ @t71 @t70 @t167) @t177)) % 150.84/151.10 (define @t179 () (not (_ @t65 @t75 @t178))) % 150.84/151.10 (define @t180 () (forall @t13 (or (not (_ @t65 @t64 @t178)) (not (forall @t8 (or @t76 @t179)))))) % 150.84/151.10 (define @t181 () (@quantifiers_skolemize @t180 0)) % 150.84/151.10 (define @t182 () (_ @t65 @t170 @t178)) % 150.84/151.10 (define @t183 () (_ @t65 @t170 @t177)) % 150.84/151.10 (define @t184 () (not @t183)) % 150.84/151.10 (define @t185 () (or @t184 @t182)) % 150.84/151.10 (define @t186 () (@list false false)) % 150.84/151.10 (define @t187 () (not @t180)) % 150.84/151.10 (define @t188 () (not @t182)) % 150.84/151.10 (define @t189 () (or @t188 @t187)) % 150.84/151.10 (define @t190 () (forall @t8 (or (not (_ @t65 @t75 @t181)) @t179))) % 150.84/151.10 (define @t191 () (not @t190)) % 150.84/151.10 (define @t192 () (_ @t65 (_ @t63 @t62 @t181) @t178)) % 150.84/151.10 (define @t193 () (not @t192)) % 150.84/151.10 (define @t194 () (or @t193 @t191)) % 150.84/151.10 (define @t195 () (@list @t194)) % 150.84/151.10 (define @t196 () (_ @t65 @t170 @t181)) % 150.84/151.10 (define @t197 () (not @t196)) % 150.84/151.10 (define @t198 () (or @t197 @t188)) % 150.84/151.10 (define @t199 () (= @t167 @t181)) % 150.84/151.10 (define @t200 () (not @t199)) % 150.84/151.10 (define @t201 () (= @t166 @t181)) % 150.84/151.10 (define @t202 () (or @t193 @t199 @t201)) % 150.84/151.10 (define @t203 () (_ @t65 @t168 @t178)) % 150.84/151.10 (define @t204 () (not @t203)) % 150.84/151.10 (define @t205 () (_ @t65 @t168 @t181)) % 150.84/151.10 (define @t206 () (not @t205)) % 150.84/151.10 (define @t207 () (or @t206 @t204)) % 150.84/151.10 (define @t208 () (not @t201)) % 150.84/151.10 (define @t209 () (and @t206 @t201 @t169)) % 150.84/151.10 (assume @p1 @t19) % 150.84/151.10 (assume @p2 @t26) % 150.84/151.10 (assume @p3 @t33) % 150.84/151.10 (assume @p4 @t42) % 150.84/151.10 (assume @p5 @t52) % 150.84/151.10 (assume @p6 @t61) % 150.84/151.10 (assume @p7 true) % 150.84/151.10 ; WARNING: add trust step for TRUST % 150.84/151.10 ; trust TRUST PREPROCESS_HO_ELIM % 150.84/151.10 (step @p8 :rule trust :premises () :args ((= (not (=> @t102 (=> @t93 (=> @t90 @t86)))) (not (=> (forall @t78 (or (not (_ @t65 (_ @t63 @t62 @t77) @t1)) (not (forall @t13 (or @t66 (not (forall @t8 (or @t76 (not (_ @t65 @t75 @t1)))))))))) (=> (forall @t24 (_ @t65 @t75 (_ @t72 @t73 @t20))) (=> (forall @t31 (or (not (_ @t65 @t74 @t1)) (_ @t65 @t74 (_ @t72 @t73 @t1)))) (=> (forall @t50 (or (not (_ @t65 (_ @t63 @t62 @t43) (_ @t72 @t73 (_ @t72 (_ @t71 @t70 @t20) tptp.emptyset)))) @t69 @t68)) @t67)))))))) % 150.84/151.10 (step @p9 :rule bool-impl-true2 :args (@t86)) % 150.84/151.10 (step @p10 :rule refl :args (@t90)) % 150.84/151.10 (step @p11 :rule cong :premises (@p10 @p9) :args (@t103)) % 150.84/151.10 (step @p12 :rule refl :args (@t93)) % 150.84/151.10 (step @p13 :rule cong :premises (@p12 @p11) :args (@t104)) % 150.84/151.10 (step @p14 :rule refl :args (@t102)) % 150.84/151.10 (step @p15 :rule cong :premises (@p14 @p13) :args (@t105)) % 150.84/151.10 (step @p16 :rule cong :premises (@p15) :args ((not @t105))) % 150.84/151.10 (step @p17 :rule refl :args (@t82)) % 150.84/151.10 (step @p18 :rule refl :args (@t68)) % 150.84/151.10 (step @p19 :rule refl :args (@t69)) % 150.84/151.10 (step @p20 :rule refl :args ((tptp.in @t43 @t46))) % 150.84/151.10 (step @p21 :rule refl :args ((tptp.setadjoin @t2 @t45))) % 150.84/151.10 (step @p22 :rule refl :args (@t83)) % 150.84/151.10 (step @p23 :rule refl :args (@t2)) % 150.84/151.10 (step @p24 :rule cong :premises (@p23 @p22) :args (@t84)) % 150.84/151.10 (step @p25 :rule trans :premises (@p24 @p21)) % 150.84/151.10 (step @p26 :rule refl :args (@t43)) % 150.84/151.10 (step @p27 :rule cong :premises (@p26 @p25) :args (@t85)) % 150.84/151.10 (step @p28 :rule trans :premises (@p27 @p20)) % 150.84/151.10 (step @p29 :rule refl :args (@t47)) % 150.84/151.10 (step @p30 :rule ho_cong :premises (@p29 @p25)) % 150.84/151.10 (step @p31 :rule cong :premises (@p30 @p28) :args ((= (_ @t47 @t84) @t85))) % 150.84/151.10 (step @p32 :rule symm :premises (@p31)) % 150.84/151.10 (step @p33 :rule refl :args (@t48)) % 150.84/151.10 (step @p34 :rule eq_resolve :premises (@p33 @p32)) % 150.84/151.10 (step @p35 :rule refl :args (@t21)) % 150.84/151.10 (step @p36 :rule ho_cong :premises (@p35 @p22)) % 150.84/151.10 (step @p37 :rule cong :premises (@p36 @p25) :args ((= (_ @t21 @t83) @t84))) % 150.84/151.10 (step @p38 :rule symm :premises (@p37)) % 150.84/151.10 (step @p39 :rule refl :args (@t46)) % 150.84/151.10 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 150.84/151.10 (step @p41 :rule refl :args (@t45)) % 150.84/151.10 (step @p42 :rule cong :premises (@p41 @p22) :args ((= @t45 @t83))) % 150.84/151.10 (step @p43 :rule symm :premises (@p42)) % 150.84/151.10 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 150.84/151.10 (step @p45 :rule ho_cong :premises (@p35 @p44)) % 150.84/151.10 (step @p46 :rule trans :premises (@p45 @p40)) % 150.84/151.10 (step @p47 :rule ho_cong :premises (@p29 @p46)) % 150.84/151.10 (step @p48 :rule trans :premises (@p47 @p34)) % 150.84/151.10 (step @p49 :rule cong :premises (@p48) :args (@t106)) % 150.84/151.10 (step @p50 :rule nary_cong :premises (@p49 @p19 @p18) :args (@t107)) % 150.84/151.10 (step @p51 :rule cong :premises (@p50) :args ((forall @t50 @t107))) % 150.84/151.10 (step @p52 :rule aci_norm :args ((= (or @t106 @t108) @t107))) % 150.84/151.10 (step @p53 :rule bool-impl-elim :args (@t48 @t108)) % 150.84/151.10 (step @p54 :rule trans :premises (@p53 @p52)) % 150.84/151.10 (step @p55 :rule cong :premises (@p54) :args ((forall @t50 (=> @t48 @t108)))) % 150.84/151.10 (step @p56 :rule trans :premises (@p55 @p51)) % 150.84/151.10 (step @p57 :rule eq-symm :args (@t43 @t20)) % 150.84/151.10 (step @p58 :rule eq-symm :args (@t43 @t2)) % 150.84/151.10 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t44)) % 150.84/151.10 (step @p60 :rule refl :args (@t48)) % 150.84/151.10 (step @p61 :rule cong :premises (@p60 @p59) :args (@t49)) % 150.84/151.10 (step @p62 :rule cong :premises (@p61) :args (@t51)) % 150.84/151.10 (step @p63 :rule trans :premises (@p62 @p56)) % 150.84/151.10 (step @p64 :rule refl :args (tptp.upairset2E)) % 150.84/151.10 (step @p65 :rule cong :premises (@p64 @p63) :args (@t52)) % 150.84/151.10 (step @p66 :rule eq_resolve :premises (@p5 @p65)) % 150.84/151.10 (step @p67 :rule cong :premises (@p66 @p17) :args (@t109)) % 150.84/151.10 (step @p68 :rule bool-eq-true :args (tptp.in__Cong)) % 150.84/151.10 (step @p69 :rule symm :premises (@p68)) % 150.84/151.10 (step @p70 :rule quant-unused-vars :args ((= (forall @t111 true) true))) % 150.84/151.10 (step @p71 :rule evaluate :args ((or false true))) % 150.84/151.10 (step @p72 :rule eq-refl :args (@t112)) % 150.84/151.10 (step @p73 :rule evaluate :args ((not true))) % 150.84/151.10 (step @p74 :rule eq-refl :args (@t5)) % 150.84/151.10 (step @p75 :rule cong :premises (@p74) :args (@t113)) % 150.84/151.10 (step @p76 :rule trans :premises (@p75 @p73)) % 150.84/151.10 (step @p77 :rule nary_cong :premises (@p76 @p72) :args (@t114)) % 150.84/151.10 (step @p78 :rule trans :premises (@p77 @p71)) % 150.84/151.10 (step @p79 :rule cong :premises (@p78) :args ((forall @t111 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150.84/151.10 (step @p108 :rule trans :premises (@p107 @p73)) % 150.84/151.10 (step @p109 :rule nary_cong :premises (@p108 @p105) :args (@t132)) % 150.84/151.10 (step @p110 :rule trans :premises (@p109 @p104)) % 150.84/151.10 (step @p111 :rule cong :premises (@p110) :args ((forall @t129 @t132))) % 150.84/151.10 (step @p112 :rule quant-var-elim-eq :args ((= (forall @t8 @t135) @t132))) % 150.84/151.10 (step @p113 :rule aci_norm :args ((= @t136 @t135))) % 150.84/151.10 (step @p114 :rule cong :premises (@p113) :args (@t137)) % 150.84/151.10 (step @p115 :rule trans :premises (@p114 @p112)) % 150.84/151.10 (step @p116 :rule cong :premises (@p115) :args (@t138)) % 150.84/151.10 (step @p117 :rule quant-merge-prenex :args ((= @t138 @t139))) % 150.84/151.10 (step @p118 :rule symm :premises (@p117)) % 150.84/151.10 (step @p119 :rule quant_var_reordering :args ((= (forall @t24 @t136) @t139))) % 150.84/151.10 (step @p120 :rule trans :premises (@p119 @p118 @p116)) % 150.84/151.10 (step @p121 :rule 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(@p264 @p202) :args (@t163)) % 150.84/151.10 (step @p266 :rule cong :premises (@p265) :args ((not @t163))) % 150.84/151.10 (step @p267 :rule trans :premises (@p266 @p16)) % 150.84/151.10 (step @p268 :rule refl :args (@t81)) % 150.84/151.10 (step @p269 :rule refl :args (@t54)) % 150.84/151.10 (step @p270 :rule cong :premises (@p269 @p268) :args ((= @t54 @t81))) % 150.84/151.10 (step @p271 :rule symm :premises (@p270)) % 150.84/151.10 (step @p272 :rule eq_resolve :premises (@p269 @p271)) % 150.84/151.10 (step @p273 :rule cong :premises (@p272) :args (@t164)) % 150.84/151.10 (step @p274 :rule nary_cong :premises (@p273 @p224) :args (@t165)) % 150.84/151.10 (step @p275 :rule cong :premises (@p274) :args ((forall @t40 @t165))) % 150.84/151.10 (step @p276 :rule bool-impl-elim :args (@t54 @t53)) % 150.84/151.10 (step @p277 :rule cong :premises (@p276) :args (@t55)) % 150.84/151.10 (step @p278 :rule trans :premises (@p277 @p275)) % 150.84/151.10 (step @p279 :rule cong :premises (@p64 @p278) :args (@t56)) % 150.84/151.10 (step @p280 :rule cong :premises (@p144 @p279) :args (@t57)) % 150.84/151.10 (step @p281 :rule cong :premises (@p178 @p280) :args (@t58)) % 150.84/151.10 (step @p282 :rule cong :premises (@p199 @p281) :args (@t59)) % 150.84/151.10 (step @p283 :rule cong :premises (@p262 @p282) :args (@t60)) % 150.84/151.10 (step @p284 :rule cong :premises (@p283) :args (@t61)) % 150.84/151.10 (step @p285 :rule trans :premises (@p284 @p267 @p8)) % 150.84/151.10 (step @p286 :rule eq_resolve :premises (@p6 @p285)) % 150.84/151.10 (step @p287 :rule not_implies_elim2 :premises (@p286)) % 150.84/151.10 (step @p288 :rule not_implies_elim2 :premises (@p287)) % 150.84/151.10 (step @p289 :rule not_implies_elim2 :premises (@p288)) % 150.84/151.10 (step @p290 :rule not_implies_elim2 :premises (@p289)) % 150.84/151.10 (step @p291 :rule skolemize :premises (@p290)) % 150.84/151.10 (step @p292 :rule bool-double-not-elim :args (@t169)) % 150.84/151.10 (step @p293 :rule refl :args (@t174)) % 150.84/151.10 (step @p294 :rule nary_cong :premises (@p293 @p292) :args ((or @t174 (not @t173)))) % 150.84/151.10 (step @p295 :rule cnf_or_neg :args (@t174 0)) % 150.84/151.10 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 150.84/151.10 (step @p297 :rule reordering :premises (@p296) :args ((or @t169 @t174))) % 150.84/151.10 (step @p298 :rule chain_m_resolution :premises (@p297 @p291) :args (@t169 @t175 @t176)) % 150.84/151.10 (step @p299 :rule not_implies_elim1 :premises (@p289)) % 150.84/151.10 (step @p300 :rule instantiate :premises (@p299) :args ((@list @t167 @t166 @t181))) % 150.84/151.10 (step @p301 :rule not_implies_elim1 :premises (@p286)) % 150.84/151.10 (step @p302 :rule instantiate :premises (@p301) :args ((@list @t178 @t166))) % 150.84/151.10 (step @p303 :rule not_implies_elim1 :premises (@p288)) % 150.84/151.10 (step @p304 :rule instantiate :premises (@p303) :args ((@list @t167 @t177 @t166))) % 150.84/151.10 (step @p305 :rule not_implies_elim1 :premises (@p287)) % 150.84/151.10 (step @p306 :rule instantiate :premises (@p305) :args ((@list @t166 tptp.emptyset))) % 150.84/151.10 (step @p307 :rule cnf_or_pos :args (@t185)) % 150.84/151.10 (step @p308 :rule reordering :premises (@p307) :args ((or @t182 @t184 (not @t185)))) % 150.84/151.10 (step @p309 :rule chain_m_resolution :premises (@p308 @p306 @p304) :args (@t182 @t186 (@list @t183 @t185))) % 150.84/151.10 (step @p310 :rule cnf_or_pos :args (@t189)) % 150.84/151.10 (step @p311 :rule reordering :premises (@p310) :args ((or @t188 @t187 (not @t189)))) % 150.84/151.10 (step @p312 :rule chain_m_resolution :premises (@p311 @p309 @p302) :args (@t187 @t186 (@list @t182 @t189))) % 150.84/151.10 (step @p313 :rule skolemize :premises (@p312)) % 150.84/151.10 (step @p314 :rule bool-double-not-elim :args (@t190)) % 150.84/151.10 (step @p315 :rule refl :args (@t194)) % 150.84/151.10 (step @p316 :rule nary_cong :premises (@p315 @p314) :args ((or @t194 (not @t191)))) % 150.84/151.10 (step @p317 :rule cnf_or_neg :args (@t194 1)) % 150.84/151.10 (step @p318 :rule eq_resolve :premises (@p317 @p316)) % 150.84/151.10 (step @p319 :rule reordering :premises (@p318) :args ((or @t190 @t194))) % 150.84/151.10 (step @p320 :rule chain_m_resolution :premises (@p319 @p313) :args (@t190 @t175 @t195)) % 150.84/151.10 (step @p321 :rule instantiate :premises (@p320) :args ((@list @t166))) % 150.84/151.10 (step @p322 :rule cnf_or_pos :args (@t198)) % 150.84/151.10 (step @p323 :rule reordering :premises (@p322) :args ((or @t188 @t197 (not @t198)))) % 150.84/151.10 (step @p324 :rule chain_m_resolution :premises (@p323 @p309 @p321) :args (@t197 @t186 (@list @t182 @t198))) % 150.84/151.10 (step @p325 :rule bool-double-not-elim :args (@t171)) % 150.84/151.10 (step @p326 :rule nary_cong :premises (@p293 @p325) :args ((or @t174 (not @t172)))) % 150.84/151.10 (step @p327 :rule cnf_or_neg :args (@t174 1)) % 150.84/151.10 (step @p328 :rule eq_resolve :premises (@p327 @p326)) % 150.84/151.10 (step @p329 :rule reordering :premises (@p328) :args ((or @t171 @t174))) % 150.84/151.10 (step @p330 :rule chain_m_resolution :premises (@p329 @p291) :args (@t171 @t175 @t176)) % 150.84/151.10 (step @p331 :rule bool-double-not-elim :args (@t196)) % 150.84/151.10 (step @p332 :rule refl :args (@t200)) % 150.84/151.10 (step @p333 :rule refl :args (@t172)) % 150.84/151.10 (step @p334 :rule nary_cong :premises (@p333 @p332 @p331) :args ((or @t172 @t200 (not @t197)))) % 150.84/151.10 (assume-push @p400 @t171) % 150.84/151.10 (assume-push @p401 @t199) % 150.84/151.10 (assume-push @p402 @t197) % 150.84/151.10 (step @p338 :rule evaluate :args ((= false true))) % 150.84/151.10 (step @p339 :rule true_intro :premises (@p330)) % 150.84/151.10 (step @p340 :rule symm :premises (@p401)) % 150.84/151.10 (step @p341 :rule refl :args (@t170)) % 150.84/151.10 (step @p342 :rule cong :premises (@p341 @p340) :args (@t196)) % 150.84/151.10 (step @p343 :rule false_intro :premises (@p324)) % 150.84/151.10 (step @p344 :rule symm :premises (@p343)) % 150.84/151.10 (step @p345 :rule trans :premises (@p344 @p342 @p339)) % 150.84/151.10 (step @p346 false :rule eq_resolve :premises (@p345 @p338)) % 150.84/151.10 (step-pop @p403 :rule scope :premises (@p346)) % 150.84/151.10 (step-pop @p404 :rule scope :premises (@p403)) % 150.84/151.10 (step-pop @p405 :rule scope :premises (@p404)) % 150.84/151.10 (step @p347 :rule process_scope :premises (@p405) :args (false)) % 150.84/151.10 (step @p351 :rule not_and :premises (@p347)) % 150.84/151.10 (step @p352 :rule eq_resolve :premises (@p351 @p334)) % 150.84/151.10 (step @p353 :rule chain_m_resolution :premises (@p352 @p330 @p324) :args (@t200 (@list false true) (@list @t171 @t196))) % 150.84/151.10 (step @p354 :rule bool-double-not-elim :args (@t192)) % 150.84/151.10 (step @p355 :rule nary_cong :premises (@p315 @p354) :args ((or @t194 (not @t193)))) % 150.84/151.10 (step @p356 :rule cnf_or_neg :args (@t194 0)) % 150.84/151.10 (step @p357 :rule eq_resolve :premises (@p356 @p355)) % 150.84/151.10 (step @p358 :rule reordering :premises (@p357) :args ((or @t192 @t194))) % 150.84/151.10 (step @p359 :rule chain_m_resolution :premises (@p358 @p313) :args (@t192 @t175 @t195)) % 150.84/151.10 (step @p360 :rule cnf_or_pos :args (@t202)) % 150.84/151.10 (step @p361 :rule reordering :premises (@p360) :args ((or @t193 @t199 @t201 (not @t202)))) % 150.84/151.10 (step @p362 :rule chain_m_resolution :premises (@p361 @p359 @p353 @p300) :args (@t201 (@list false true false) (@list @t192 @t199 @t202))) % 150.84/151.10 (step @p363 :rule instantiate :premises (@p320) :args ((@list @t167))) % 150.84/151.10 (step @p364 :rule instantiate :premises (@p305) :args ((@list @t167 @t177))) % 150.84/151.10 (step @p365 :rule cnf_or_pos :args (@t207)) % 150.84/151.10 (step @p366 :rule reordering :premises (@p365) :args ((or @t204 @t206 (not @t207)))) % 150.84/151.10 (step @p367 :rule chain_m_resolution :premises (@p366 @p364 @p363) :args (@t206 @t186 (@list @t203 @t207))) % 150.84/151.10 (step @p368 :rule bool-double-not-elim :args (@t205)) % 150.84/151.10 (step @p369 :rule refl :args (@t208)) % 150.84/151.10 (step @p370 :rule refl :args (@t173)) % 150.84/151.10 (step @p371 :rule nary_cong :premises (@p370 @p369 @p368) :args ((or @t173 @t208 (not @t206)))) % 150.84/151.10 (assume-push @p406 @t206) % 150.84/151.10 (assume-push @p407 @t201) % 150.84/151.10 (assume-push @p408 @t169) % 150.84/151.10 (step @p375 :rule evaluate :args ((= true false))) % 150.84/151.10 (step @p376 :rule false_intro :premises (@p367)) % 150.84/151.10 (step @p377 :rule refl :args (@t168)) % 150.84/151.10 (step @p378 :rule cong :premises (@p377 @p407) :args (@t169)) % 150.84/151.10 (step @p379 :rule true_intro :premises (@p298)) % 150.84/151.10 (step @p380 :rule symm :premises (@p379)) % 150.84/151.10 (step @p381 :rule trans :premises (@p380 @p378 @p376)) % 150.84/151.10 (step @p382 false :rule eq_resolve :premises (@p381 @p375)) % 150.84/151.10 (step-pop @p409 :rule scope :premises (@p382)) % 150.84/151.10 (step-pop @p410 :rule scope :premises (@p409)) % 150.84/151.10 (step-pop @p411 :rule scope :premises (@p410)) % 150.84/151.10 (step @p383 :rule process_scope :premises (@p411) :args (false)) % 150.84/151.10 (assume-push @p412 @t169) % 150.84/151.10 (assume-push @p413 @t201) % 150.84/151.10 (assume-push @p414 @t206) % 150.84/151.10 (step @p390 :rule and_intro :premises (@p367 @p413 @p298)) % 150.84/151.10 (step-pop @p415 :rule scope :premises (@p390)) % 150.84/151.10 (step-pop @p416 :rule scope :premises (@p415)) % 150.84/151.10 (step-pop @p417 :rule scope :premises (@p416)) % 150.84/151.10 (step @p391 :rule process_scope :premises (@p417) :args (@t209)) % 150.84/151.10 (step @p395 :rule implies_elim :premises (@p391)) % 150.84/151.10 (step @p396 :rule resolution :premises (@p395 @p383) :args (true @t209)) % 150.84/151.10 (step @p397 :rule not_and :premises (@p396)) % 150.84/151.10 (step @p398 :rule eq_resolve :premises (@p397 @p371)) % 150.84/151.10 (step @p399 false :rule chain_m_resolution :premises (@p398 @p367 @p362 @p298) :args (false (@list true false false) (@list @t205 @t201 @t169))) % 150.84/151.10 ) % 150.84/151.10 % SZS output end Proof % 150.84/151.10 % cvc5 exiting %------------------------------------------------------------------------------