%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU336+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:51:25 AM UTC 2026 % Result : Theorem 0.37s 0.89s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU336+1 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n029.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:58:32 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.89 % SZS status Theorem % 0.37/0.89 % SZS output start Proof % 0.37/0.89 ( % 0.37/0.89 (declare-sort $$unsorted 0) % 0.37/0.89 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.empty_set $$unsorted) % 0.37/0.89 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.89 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.89 (declare-const tptp.top_str (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.open_subsets (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.the_carrier (-> $$unsorted $$unsorted)) % 0.37/0.89 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.89 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v3_membered (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.natural (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v1_membered (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.one_sorted_str (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v1_xreal_0 (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.open_subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v5_membered (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v2_membered (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v1_rat_1 (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.closed_subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v1_xcmplx_0 (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v1_int_1 (-> $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.closed_subsets (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.37/0.89 (declare-const tptp.v4_membered (-> $$unsorted Bool)) % 0.37/0.89 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.89 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.89 (define @t3 () (tptp.in @t1 @t2)) % 0.37/0.89 (define @t4 () (@list @t1 @t2)) % 0.37/0.89 (define @t5 () (tptp.v1_xcmplx_0 @t2)) % 0.37/0.89 (define @t6 () (tptp.element @t2 @t1)) % 0.37/0.89 (define @t7 () (@list @t2)) % 0.37/0.89 (define @t8 () (tptp.v1_membered @t1)) % 0.37/0.89 (define @t9 () (@list @t1)) % 0.37/0.89 (define @t10 () (tptp.v1_xreal_0 @t2)) % 0.37/0.89 (define @t11 () (tptp.v2_membered @t1)) % 0.37/0.89 (define @t12 () (tptp.v1_rat_1 @t2)) % 0.37/0.89 (define @t13 () (tptp.v3_membered @t1)) % 0.37/0.89 (define @t14 () (tptp.v1_int_1 @t2)) % 0.37/0.89 (define @t15 () (tptp.v4_membered @t1)) % 0.37/0.89 (define @t16 () (tptp.v5_membered @t1)) % 0.37/0.89 (define @t17 () (tptp.empty @t1)) % 0.37/0.89 (define @t18 () (tptp.v1_membered @t2)) % 0.37/0.89 (define @t19 () (tptp.powerset @t1)) % 0.37/0.89 (define @t20 () (tptp.element @t2 @t19)) % 0.37/0.89 (define @t21 () (tptp.v2_membered @t2)) % 0.37/0.89 (define @t22 () (tptp.v3_membered @t2)) % 0.37/0.89 (define @t23 () (tptp.v4_membered @t2)) % 0.37/0.89 (define @t24 () (@var "C" $$unsorted)) % 0.37/0.89 (define @t25 () (tptp.open_subset @t24 @t1)) % 0.37/0.89 (define @t26 () (tptp.in @t24 @t2)) % 0.37/0.89 (define @t27 () (=> @t26 @t25)) % 0.37/0.89 (define @t28 () (tptp.the_carrier @t1)) % 0.37/0.89 (define @t29 () (tptp.powerset @t28)) % 0.37/0.89 (define @t30 () (tptp.element @t24 @t29)) % 0.37/0.89 (define @t31 () (@list @t24)) % 0.37/0.89 (define @t32 () (forall @t31 (=> @t30 @t27))) % 0.37/0.89 (define @t33 () (tptp.open_subsets @t2 @t1)) % 0.37/0.89 (define @t34 () (= @t33 @t32)) % 0.37/0.89 (define @t35 () (tptp.powerset @t29)) % 0.37/0.89 (define @t36 () (tptp.element @t2 @t35)) % 0.37/0.89 (define @t37 () (=> @t36 @t34)) % 0.37/0.89 (define @t38 () (forall @t7 @t37)) % 0.37/0.89 (define @t39 () (tptp.top_str @t1)) % 0.37/0.89 (define @t40 () (=> @t39 @t38)) % 0.37/0.89 (define @t41 () (forall @t9 @t40)) % 0.37/0.89 (define @t42 () (tptp.closed_subset @t24 @t1)) % 0.37/0.89 (define @t43 () (=> @t26 @t42)) % 0.37/0.89 (define @t44 () (forall @t31 (=> @t30 @t43))) % 0.37/0.89 (define @t45 () (tptp.closed_subsets @t2 @t1)) % 0.37/0.89 (define @t46 () (= @t45 @t44)) % 0.37/0.89 (define @t47 () (=> @t36 @t46)) % 0.37/0.89 (define @t48 () (forall @t7 @t47)) % 0.37/0.89 (define @t49 () (=> @t39 @t48)) % 0.37/0.89 (define @t50 () (forall @t9 @t49)) % 0.37/0.89 (define @t51 () (@var "D" $$unsorted)) % 0.37/0.89 (define @t52 () (tptp.in (tptp.subset_complement @t1 @t51) @t2)) % 0.37/0.89 (define @t53 () (= (tptp.in @t51 @t24) @t52)) % 0.37/0.89 (define @t54 () (tptp.element @t51 @t19)) % 0.37/0.89 (define @t55 () (@list @t51)) % 0.37/0.89 (define @t56 () (forall @t55 (=> @t54 @t53))) % 0.37/0.89 (define @t57 () (tptp.complements_of_subsets @t1 @t2)) % 0.37/0.89 (define @t58 () (= @t24 @t57)) % 0.37/0.89 (define @t59 () (= @t58 @t56)) % 0.37/0.89 (define @t60 () (tptp.powerset @t19)) % 0.37/0.89 (define @t61 () (tptp.element @t24 @t60)) % 0.37/0.89 (define @t62 () (=> @t61 @t59)) % 0.37/0.89 (define @t63 () (forall @t31 @t62)) % 0.37/0.89 (define @t64 () (tptp.element @t2 @t60)) % 0.37/0.89 (define @t65 () (=> @t64 @t63)) % 0.37/0.89 (define @t66 () (forall @t4 @t65)) % 0.37/0.89 (define @t67 () (tptp.subset_complement @t1 @t2)) % 0.37/0.89 (define @t68 () (tptp.element @t67 @t19)) % 0.37/0.89 (define @t69 () (forall @t4 (=> @t20 @t68))) % 0.37/0.89 (define @t70 () (tptp.element @t57 @t60)) % 0.37/0.89 (define @t71 () (forall @t4 (=> @t64 @t70))) % 0.37/0.89 (define @t72 () (tptp.one_sorted_str @t1)) % 0.37/0.89 (define @t73 () (tptp.complements_of_subsets @t1 @t57)) % 0.37/0.89 (define @t74 () (=> @t64 (= @t73 @t2))) % 0.37/0.89 (define @t75 () (forall @t4 @t74)) % 0.37/0.89 (define @t76 () (not @t17)) % 0.37/0.89 (define @t77 () (tptp.empty @t2)) % 0.37/0.89 (define @t78 () (= @t45 (tptp.open_subsets (tptp.complements_of_subsets @t28 @t2) @t1))) % 0.37/0.89 (define @t79 () (forall @t7 (=> @t36 @t78))) % 0.37/0.89 (define @t80 () (=> @t39 @t79)) % 0.37/0.89 (define @t81 () (forall @t9 @t80)) % 0.37/0.89 (define @t82 () (not @t81)) % 0.37/0.89 (define @t83 () (tptp.element @t1 @t2)) % 0.37/0.89 (define @t84 () (tptp.subset_complement @t28 @t2)) % 0.37/0.89 (define @t85 () (= (tptp.closed_subset @t2 @t1) (tptp.open_subset @t84 @t1))) % 0.37/0.89 (define @t86 () (tptp.element @t2 @t29)) % 0.37/0.89 (define @t87 () (forall @t7 (=> @t86 @t85))) % 0.37/0.89 (define @t88 () (=> @t39 @t87)) % 0.37/0.89 (define @t89 () (forall @t9 @t88)) % 0.37/0.89 (define @t90 () (= (tptp.open_subset @t2 @t1) (tptp.closed_subset @t84 @t1))) % 0.37/0.89 (define @t91 () (forall @t7 (=> @t86 @t90))) % 0.37/0.89 (define @t92 () (=> @t39 @t91)) % 0.37/0.89 (define @t93 () (forall @t9 @t92)) % 0.37/0.89 (define @t94 () (tptp.element @t2 (tptp.powerset @t24))) % 0.37/0.89 (define @t95 () (@list @t1 @t2 @t24)) % 0.37/0.89 (define @t96 () (@var "BOUND_VARIABLE_8128" $$unsorted)) % 0.37/0.89 (define @t97 () (= (tptp.open_subset @t96 @t1) (tptp.closed_subset (tptp.subset_complement @t28 @t96) @t1))) % 0.37/0.89 (define @t98 () (not (tptp.element @t96 @t29))) % 0.37/0.89 (define @t99 () (not @t39)) % 0.37/0.89 (define @t100 () (or @t98 @t97)) % 0.37/0.89 (define @t101 () (or @t99 @t100)) % 0.37/0.89 (define @t102 () (forall (@list @t1 @t96) @t101)) % 0.37/0.89 (define @t103 () (@list @t96)) % 0.37/0.89 (define @t104 () (forall @t103 @t101)) % 0.37/0.89 (define @t105 () (forall @t103 @t100)) % 0.37/0.89 (define @t106 () (@list @t2)) % 0.37/0.89 (define @t107 () (or @t99 @t105)) % 0.37/0.89 (define @t108 () (not @t86)) % 0.37/0.89 (define @t109 () (forall @t7 (or @t108 @t90))) % 0.37/0.89 (define @t110 () (@var "BOUND_VARIABLE_8077" $$unsorted)) % 0.37/0.89 (define @t111 () (= (tptp.closed_subsets @t110 @t1) (tptp.open_subsets (tptp.complements_of_subsets @t28 @t110) @t1))) % 0.37/0.89 (define @t112 () (not (tptp.element @t110 @t35))) % 0.37/0.89 (define @t113 () (or @t99 @t112 @t111)) % 0.37/0.89 (define @t114 () (@list @t1 @t110)) % 0.37/0.89 (define @t115 () (forall @t114 @t113)) % 0.37/0.89 (define @t116 () (@quantifiers_skolemize @t115 0)) % 0.37/0.89 (define @t117 () (@quantifiers_skolemize @t115 1)) % 0.37/0.89 (define @t118 () (tptp.the_carrier @t116)) % 0.37/0.89 (define @t119 () (tptp.complements_of_subsets @t118 @t117)) % 0.37/0.89 (define @t120 () (tptp.powerset @t118)) % 0.37/0.89 (define @t121 () (not (tptp.element @t24 @t120))) % 0.37/0.89 (define @t122 () (forall @t31 (or @t121 (not (tptp.in @t24 @t119)) (tptp.open_subset @t24 @t116)))) % 0.37/0.89 (define @t123 () (@quantifiers_skolemize @t122 0)) % 0.37/0.89 (define @t124 () (@var "BOUND_VARIABLE_7928" $$unsorted)) % 0.37/0.89 (define @t125 () (not @t30)) % 0.37/0.89 (define @t126 () (= (tptp.open_subsets @t124 @t1) (forall @t31 (or @t125 (not (tptp.in @t24 @t124)) @t25)))) % 0.37/0.89 (define @t127 () (not (tptp.element @t124 @t35))) % 0.37/0.89 (define @t128 () (or @t127 @t126)) % 0.37/0.89 (define @t129 () (or @t99 @t128)) % 0.37/0.89 (define @t130 () (forall (@list @t1 @t124) @t129)) % 0.37/0.89 (define @t131 () (@list @t124)) % 0.37/0.89 (define @t132 () (forall @t131 @t129)) % 0.37/0.89 (define @t133 () (forall @t131 @t128)) % 0.37/0.89 (define @t134 () (or @t99 @t133)) % 0.37/0.89 (define @t135 () (not @t26)) % 0.37/0.89 (define @t136 () (or @t125 @t135 @t25)) % 0.37/0.89 (define @t137 () (= @t33 (forall @t31 @t136))) % 0.37/0.89 (define @t138 () (not @t36)) % 0.37/0.89 (define @t139 () (forall @t7 (or @t138 @t137))) % 0.37/0.89 (define @t140 () (@list @t118 @t117)) % 0.37/0.89 (define @t141 () (or @t112 @t111)) % 0.37/0.89 (define @t142 () (or @t99 @t141)) % 0.37/0.89 (define @t143 () (forall @t114 @t142)) % 0.37/0.89 (define @t144 () (@list @t110)) % 0.37/0.89 (define @t145 () (forall @t144 @t142)) % 0.37/0.89 (define @t146 () (forall @t144 @t141)) % 0.37/0.89 (define @t147 () (or @t99 @t146)) % 0.37/0.89 (define @t148 () (forall @t7 (or @t138 @t78))) % 0.37/0.89 (define @t149 () (tptp.powerset @t120)) % 0.37/0.89 (define @t150 () (tptp.element @t117 @t149)) % 0.37/0.89 (define @t151 () (tptp.open_subsets @t119 @t116)) % 0.37/0.89 (define @t152 () (tptp.closed_subsets @t117 @t116)) % 0.37/0.89 (define @t153 () (= @t152 @t151)) % 0.37/0.89 (define @t154 () (not @t150)) % 0.37/0.89 (define @t155 () (tptp.top_str @t116)) % 0.37/0.89 (define @t156 () (not @t155)) % 0.37/0.89 (define @t157 () (or @t156 @t154 @t153)) % 0.37/0.89 (define @t158 () (@list true)) % 0.37/0.89 (define @t159 () (@list @t157)) % 0.37/0.89 (define @t160 () (tptp.element @t119 @t149)) % 0.37/0.89 (define @t161 () (or @t154 @t160)) % 0.37/0.89 (define @t162 () (@list false false)) % 0.37/0.89 (define @t163 () (= @t151 @t122)) % 0.37/0.89 (define @t164 () (not @t160)) % 0.37/0.89 (define @t165 () (or @t156 @t164 @t163)) % 0.37/0.89 (define @t166 () (@list false false false)) % 0.37/0.89 (define @t167 () (@var "BOUND_VARIABLE_7957" $$unsorted)) % 0.37/0.89 (define @t168 () (= (tptp.closed_subsets @t167 @t1) (forall @t31 (or @t125 (not (tptp.in @t24 @t167)) @t42)))) % 0.37/0.89 (define @t169 () (not (tptp.element @t167 @t35))) % 0.37/0.89 (define @t170 () (or @t169 @t168)) % 0.37/0.89 (define @t171 () (or @t99 @t170)) % 0.37/0.89 (define @t172 () (forall (@list @t1 @t167) @t171)) % 0.37/0.89 (define @t173 () (@list @t167)) % 0.37/0.89 (define @t174 () (forall @t173 @t171)) % 0.37/0.89 (define @t175 () (forall @t173 @t170)) % 0.37/0.89 (define @t176 () (or @t99 @t175)) % 0.37/0.89 (define @t177 () (or @t125 @t135 @t42)) % 0.37/0.89 (define @t178 () (= @t45 (forall @t31 @t177))) % 0.37/0.89 (define @t179 () (forall @t7 (or @t138 @t178))) % 0.37/0.89 (define @t180 () (forall @t31 (or @t121 (not (tptp.in @t24 @t117)) (tptp.closed_subset @t24 @t116)))) % 0.37/0.89 (define @t181 () (= @t152 @t180)) % 0.37/0.89 (define @t182 () (or @t156 @t154 @t181)) % 0.37/0.89 (define @t183 () (not @t181)) % 0.37/0.89 (define @t184 () (not @t180)) % 0.37/0.89 (define @t185 () (not @t163)) % 0.37/0.89 (define @t186 () (not @t151)) % 0.37/0.89 (define @t187 () (@quantifiers_skolemize @t180 0)) % 0.37/0.89 (define @t188 () (tptp.closed_subset @t187 @t116)) % 0.37/0.89 (define @t189 () (tptp.in @t187 @t117)) % 0.37/0.89 (define @t190 () (not @t189)) % 0.37/0.89 (define @t191 () (tptp.element @t187 @t120)) % 0.37/0.89 (define @t192 () (not @t191)) % 0.37/0.89 (define @t193 () (or @t192 @t190 @t188)) % 0.37/0.89 (define @t194 () (not @t193)) % 0.37/0.89 (define @t195 () (tptp.subset_complement @t118 @t187)) % 0.37/0.89 (define @t196 () (tptp.open_subset @t195 @t116)) % 0.37/0.89 (define @t197 () (tptp.in @t195 @t119)) % 0.37/0.89 (define @t198 () (not @t197)) % 0.37/0.89 (define @t199 () (tptp.element @t195 @t120)) % 0.37/0.89 (define @t200 () (not @t199)) % 0.37/0.89 (define @t201 () (or @t200 @t198 @t196)) % 0.37/0.89 (define @t202 () (@var "BOUND_VARIABLE_8103" $$unsorted)) % 0.37/0.89 (define @t203 () (= (tptp.closed_subset @t202 @t1) (tptp.open_subset (tptp.subset_complement @t28 @t202) @t1))) % 0.37/0.89 (define @t204 () (not (tptp.element @t202 @t29))) % 0.37/0.89 (define @t205 () (or @t204 @t203)) % 0.37/0.89 (define @t206 () (or @t99 @t205)) % 0.37/0.89 (define @t207 () (forall (@list @t1 @t202) @t206)) % 0.37/0.89 (define @t208 () (@list @t202)) % 0.37/0.89 (define @t209 () (forall @t208 @t206)) % 0.37/0.89 (define @t210 () (forall @t208 @t205)) % 0.37/0.89 (define @t211 () (or @t99 @t210)) % 0.37/0.89 (define @t212 () (forall @t7 (or @t108 @t85))) % 0.37/0.89 (define @t213 () (= @t188 @t196)) % 0.37/0.89 (define @t214 () (or @t156 @t192 @t213)) % 0.37/0.89 (define @t215 () (or @t192 @t199)) % 0.37/0.89 (define @t216 () (@var "BOUND_VARIABLE_7988" $$unsorted)) % 0.37/0.89 (define @t217 () (tptp.in @t51 @t216)) % 0.37/0.89 (define @t218 () (not @t54)) % 0.37/0.89 (define @t219 () (or @t218 (= @t217 @t52))) % 0.37/0.89 (define @t220 () (forall @t55 @t219)) % 0.37/0.89 (define @t221 () (= (= @t216 @t57) @t220)) % 0.37/0.89 (define @t222 () (not (tptp.element @t216 @t60))) % 0.37/0.89 (define @t223 () (not @t64)) % 0.37/0.89 (define @t224 () (or @t223 @t222 @t221)) % 0.37/0.89 (define @t225 () (or @t222 @t221)) % 0.37/0.89 (define @t226 () (or @t223 @t225)) % 0.37/0.89 (define @t227 () (@list @t1 @t2 @t216)) % 0.37/0.89 (define @t228 () (forall @t227 @t226)) % 0.37/0.89 (define @t229 () (@list @t216)) % 0.37/0.89 (define @t230 () (forall @t229 @t226)) % 0.37/0.89 (define @t231 () (forall @t229 @t225)) % 0.37/0.89 (define @t232 () (or @t223 @t231)) % 0.37/0.89 (define @t233 () (= @t58 (forall @t55 (or @t218 @t53)))) % 0.37/0.89 (define @t234 () (forall @t31 (or (not @t61) @t233))) % 0.37/0.89 (define @t235 () (tptp.subset_complement @t118 @t51)) % 0.37/0.89 (define @t236 () (tptp.in @t235 @t119)) % 0.37/0.89 (define @t237 () (tptp.in @t51 @t117)) % 0.37/0.89 (define @t238 () (not (tptp.element @t51 @t120))) % 0.37/0.89 (define @t239 () (or @t238 (= @t236 @t237))) % 0.37/0.89 (define @t240 () (forall @t55 @t239)) % 0.37/0.89 (define @t241 () (tptp.complements_of_subsets @t118 @t119)) % 0.37/0.89 (define @t242 () (= (= @t241 @t117) @t240)) % 0.37/0.89 (define @t243 () (or @t164 @t154 @t242)) % 0.37/0.89 (define @t244 () (forall @t227 (or @t223 @t222 (= (= @t57 @t216) (forall @t55 (or @t218 (= @t52 @t217))))))) % 0.37/0.89 (define @t245 () (forall @t55 (or @t238 (= @t237 @t236)))) % 0.37/0.89 (define @t246 () (= @t117 @t241)) % 0.37/0.89 (define @t247 () (= @t246 @t245)) % 0.37/0.89 (define @t248 () (or @t164 @t154 @t247)) % 0.37/0.89 (define @t249 () (@list false)) % 0.37/0.89 (define @t250 () (@list @t244)) % 0.37/0.89 (define @t251 () (= @t2 @t73)) % 0.37/0.89 (define @t252 () (or @t154 @t246)) % 0.37/0.89 (define @t253 () (= @t189 @t197)) % 0.37/0.89 (define @t254 () (or @t192 @t253)) % 0.37/0.89 (define @t255 () (@list true false)) % 0.37/0.89 (define @t256 () (not @t122)) % 0.37/0.89 (define @t257 () (tptp.open_subset @t123 @t116)) % 0.37/0.89 (define @t258 () (tptp.in @t123 @t119)) % 0.37/0.89 (define @t259 () (not @t258)) % 0.37/0.89 (define @t260 () (tptp.element @t123 @t120)) % 0.37/0.89 (define @t261 () (not @t260)) % 0.37/0.89 (define @t262 () (or @t261 @t259 @t257)) % 0.37/0.89 (define @t263 () (not @t262)) % 0.37/0.89 (define @t264 () (@list @t262)) % 0.37/0.89 (define @t265 () (tptp.subset_complement @t118 @t123)) % 0.37/0.89 (define @t266 () (tptp.closed_subset @t265 @t116)) % 0.37/0.89 (define @t267 () (= @t257 @t266)) % 0.37/0.89 (define @t268 () (or @t156 @t261 @t267)) % 0.37/0.89 (define @t269 () (not @t266)) % 0.37/0.89 (define @t270 () (forall @t55 (or @t238 (= (tptp.in @t235 @t117) (tptp.in @t51 @t119))))) % 0.37/0.89 (define @t271 () (= (= @t119 @t119) @t270)) % 0.37/0.89 (define @t272 () (or @t154 @t164 @t271)) % 0.37/0.89 (define @t273 () (or @t154 @t164 @t270)) % 0.37/0.89 (define @t274 () (tptp.in @t265 @t117)) % 0.37/0.89 (define @t275 () (or @t261 (= @t274 @t258))) % 0.37/0.89 (define @t276 () (= @t258 @t274)) % 0.37/0.89 (define @t277 () (or @t261 @t276)) % 0.37/0.89 (define @t278 () (not @t274)) % 0.37/0.89 (define @t279 () (tptp.element @t265 @t120)) % 0.37/0.89 (define @t280 () (not @t279)) % 0.37/0.89 (define @t281 () (or @t280 @t278 @t266)) % 0.37/0.89 (define @t282 () (or @t261 @t279)) % 0.37/0.89 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.37/0.89 (assume @p2 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.89 (assume @p3 (forall @t9 (=> @t11 (forall @t7 (=> @t6 (and @t5 @t10)))))) % 0.37/0.89 (assume @p4 (forall @t9 (=> @t13 (forall @t7 (=> @t6 (and @t5 @t10 @t12)))))) % 0.37/0.89 (assume @p5 (forall @t9 (=> @t15 (forall @t7 (=> @t6 (and @t5 @t10 @t14 @t12)))))) % 0.37/0.89 (assume @p6 (forall @t9 (=> @t16 (forall @t7 (=> @t6 (and @t5 (tptp.natural @t2) @t10 @t14 @t12)))))) % 0.37/0.89 (assume @p7 (forall @t9 (=> @t17 (and @t8 @t11 @t13 @t15 @t16)))) % 0.37/0.89 (assume @p8 (forall @t9 (=> @t8 (forall @t7 (=> @t20 @t18))))) % 0.37/0.89 (assume @p9 (forall @t9 (=> @t11 (forall @t7 (=> @t20 (and @t18 @t21)))))) % 0.37/0.89 (assume @p10 (forall @t9 (=> @t13 (forall @t7 (=> @t20 (and @t18 @t21 @t22)))))) % 0.37/0.89 (assume @p11 (forall @t9 (=> @t15 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23)))))) % 0.37/0.89 (assume @p12 (forall @t9 (=> @t16 @t15))) % 0.37/0.89 (assume @p13 (forall @t9 (=> @t16 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23 (tptp.v5_membered @t2))))))) % 0.37/0.89 (assume @p14 (forall @t9 (=> @t15 @t13))) % 0.37/0.89 (assume @p15 (forall @t9 (=> @t13 @t11))) % 0.37/0.89 (assume @p16 (forall @t9 (=> @t11 @t8))) % 0.37/0.89 (assume @p17 @t41) % 0.37/0.89 (assume @p18 @t50) % 0.37/0.89 (assume @p19 @t66) % 0.37/0.89 (assume @p20 true) % 0.37/0.89 (assume @p21 @t69) % 0.37/0.89 (assume @p22 @t71) % 0.37/0.89 (assume @p23 (forall @t9 (=> @t39 @t72))) % 0.37/0.89 (assume @p24 (exists @t9 @t39)) % 0.37/0.89 (assume @p25 (exists @t9 @t72)) % 0.37/0.89 (assume @p26 (forall @t9 (exists @t7 @t6))) % 0.37/0.89 (assume @p27 (forall @t9 (not (tptp.empty @t19)))) % 0.37/0.89 (assume @p28 (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set))) % 0.37/0.89 (assume @p29 (forall @t4 (=> @t20 (= (tptp.subset_complement @t1 @t67) @t2)))) % 0.37/0.89 (assume @p30 @t75) % 0.37/0.89 (assume @p31 (exists @t9 (and @t76 @t8 @t11 @t13 @t15 @t16))) % 0.37/0.89 (assume @p32 (forall @t9 (=> @t76 (exists @t7 (and @t20 (not @t77)))))) % 0.37/0.89 (assume @p33 (forall @t9 (exists @t7 (and @t20 @t77)))) % 0.37/0.89 (assume @p34 (forall @t4 (tptp.subset @t1 @t1))) % 0.37/0.89 (assume @p35 @t82) % 0.37/0.89 (assume @p36 (forall @t4 (=> @t3 @t83))) % 0.37/0.89 (assume @p37 @t89) % 0.37/0.89 (assume @p38 (forall @t4 (=> @t83 (or @t77 @t3)))) % 0.37/0.89 (assume @p39 @t93) % 0.37/0.89 (assume @p40 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 0.37/0.89 (assume @p41 (forall @t95 (=> (and @t3 @t94) (tptp.element @t1 @t24)))) % 0.37/0.89 (assume @p42 (forall @t95 (not (and @t3 @t94 (tptp.empty @t24))))) % 0.37/0.89 (assume @p43 (forall @t9 (=> @t17 (= @t1 tptp.empty_set)))) % 0.37/0.89 (assume @p44 (forall @t4 (not (and @t3 @t77)))) % 0.37/0.89 (assume @p45 (forall @t4 (not (and @t17 (not (= @t1 @t2)) @t77)))) % 0.37/0.89 (step @p46 :rule aci_norm :args ((= @t101 (or @t99 @t98 @t97)))) % 0.37/0.89 (step @p47 :rule cong :premises (@p46) :args (@t102)) % 0.37/0.89 (step @p48 :rule quant-merge-prenex :args ((= (forall @t9 @t104) @t102))) % 0.37/0.89 (step @p49 :rule alpha_equiv :args (@t105 (@list @t96) @t106)) % 0.37/0.89 (step @p50 :rule refl :args (@t99)) % 0.37/0.89 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t107)) % 0.37/0.89 (step @p52 :rule quant-miniscope-or :args ((= @t104 @t107))) % 0.37/0.89 (step @p53 :rule trans :premises (@p52 @p51)) % 0.37/0.89 (step @p54 :rule symm :premises (@p53)) % 0.37/0.89 (step @p55 :rule cong :premises (@p54) :args ((forall @t9 (or @t99 @t109)))) % 0.37/0.89 (step @p56 :rule trans :premises (@p55 @p48)) % 0.37/0.89 (step @p57 :rule trans :premises (@p56 @p47)) % 0.37/0.89 (step @p58 :rule bool-impl-elim :args (@t39 @t109)) % 0.37/0.89 (step @p59 :rule cong :premises (@p58) :args ((forall @t9 (=> @t39 @t109)))) % 0.37/0.89 (step @p60 :rule trans :premises (@p59 @p57)) % 0.37/0.89 (step @p61 :rule bool-impl-elim :args (@t86 @t90)) % 0.37/0.89 (step @p62 :rule cong :premises (@p61) :args (@t91)) % 0.37/0.89 (step @p63 :rule refl :args (@t39)) % 0.37/0.89 (step @p64 :rule cong :premises (@p63 @p62) :args (@t92)) % 0.37/0.89 (step @p65 :rule cong :premises (@p64) :args (@t93)) % 0.37/0.89 (step @p66 :rule trans :premises (@p65 @p60)) % 0.37/0.89 (step @p67 :rule eq_resolve :premises (@p39 @p66)) % 0.37/0.89 (step @p68 :rule instantiate :premises (@p67) :args ((@list @t116 @t123))) % 0.37/0.89 (step @p69 :rule aci_norm :args ((= @t129 (or @t99 @t127 @t126)))) % 0.37/0.89 (step @p70 :rule cong :premises (@p69) :args (@t130)) % 0.37/0.89 (step @p71 :rule quant-merge-prenex :args ((= (forall @t9 @t132) @t130))) % 0.37/0.89 (step @p72 :rule alpha_equiv :args (@t133 (@list @t124) @t106)) % 0.37/0.89 (step @p73 :rule nary_cong :premises (@p50 @p72) :args (@t134)) % 0.37/0.89 (step @p74 :rule quant-miniscope-or :args ((= @t132 @t134))) % 0.37/0.89 (step @p75 :rule trans :premises (@p74 @p73)) % 0.37/0.89 (step @p76 :rule symm :premises (@p75)) % 0.37/0.89 (step @p77 :rule cong :premises (@p76) :args ((forall @t9 (or @t99 @t139)))) % 0.37/0.89 (step @p78 :rule trans :premises (@p77 @p71)) % 0.37/0.89 (step @p79 :rule trans :premises (@p78 @p70)) % 0.37/0.89 (step @p80 :rule bool-impl-elim :args (@t39 @t139)) % 0.37/0.89 (step @p81 :rule cong :premises (@p80) :args ((forall @t9 (=> @t39 @t139)))) % 0.37/0.89 (step @p82 :rule trans :premises (@p81 @p79)) % 0.37/0.89 (step @p83 :rule bool-impl-elim :args (@t36 @t137)) % 0.37/0.89 (step @p84 :rule cong :premises (@p83) :args ((forall @t7 (=> @t36 @t137)))) % 0.37/0.89 (step @p85 :rule aci_norm :args ((= (or @t125 (or @t135 @t25)) @t136))) % 0.37/0.89 (step @p86 :rule bool-impl-elim :args (@t26 @t25)) % 0.37/0.89 (step @p87 :rule refl :args (@t125)) % 0.37/0.89 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t125 @t27))) % 0.37/0.89 (step @p89 :rule trans :premises (@p88 @p85)) % 0.37/0.89 (step @p90 :rule bool-impl-elim :args (@t30 @t27)) % 0.37/0.89 (step @p91 :rule trans :premises (@p90 @p89)) % 0.37/0.89 (step @p92 :rule cong :premises (@p91) :args (@t32)) % 0.37/0.89 (step @p93 :rule refl :args (@t33)) % 0.37/0.89 (step @p94 :rule cong :premises (@p93 @p92) :args (@t34)) % 0.37/0.89 (step @p95 :rule refl :args (@t36)) % 0.37/0.89 (step @p96 :rule cong :premises (@p95 @p94) :args (@t37)) % 0.37/0.89 (step @p97 :rule cong :premises (@p96) :args (@t38)) % 0.37/0.89 (step @p98 :rule trans :premises (@p97 @p84)) % 0.37/0.89 (step @p99 :rule cong :premises (@p63 @p98) :args (@t40)) % 0.37/0.89 (step @p100 :rule cong :premises (@p99) :args (@t41)) % 0.37/0.89 (step @p101 :rule trans :premises (@p100 @p82)) % 0.37/0.89 (step @p102 :rule eq_resolve :premises (@p17 @p101)) % 0.37/0.89 (step @p103 :rule instantiate :premises (@p102) :args ((@list @t116 @t119))) % 0.37/0.89 (step @p104 :rule bool-impl-elim :args (@t64 @t70)) % 0.37/0.89 (step @p105 :rule cong :premises (@p104) :args (@t71)) % 0.37/0.89 (step @p106 :rule eq_resolve :premises (@p22 @p105)) % 0.37/0.89 (step @p107 :rule instantiate :premises (@p106) :args (@t140)) % 0.37/0.89 (step @p108 :rule aci_norm :args ((= @t142 @t113))) % 0.37/0.89 (step @p109 :rule cong :premises (@p108) :args (@t143)) % 0.37/0.89 (step @p110 :rule quant-merge-prenex :args ((= (forall @t9 @t145) @t143))) % 0.37/0.89 (step @p111 :rule alpha_equiv :args (@t146 (@list @t110) @t106)) % 0.37/0.89 (step @p112 :rule nary_cong :premises (@p50 @p111) :args (@t147)) % 0.37/0.89 (step @p113 :rule quant-miniscope-or :args ((= @t145 @t147))) % 0.37/0.89 (step @p114 :rule trans :premises (@p113 @p112)) % 0.37/0.89 (step @p115 :rule symm :premises (@p114)) % 0.37/0.89 (step @p116 :rule cong :premises (@p115) :args ((forall @t9 (or @t99 @t148)))) % 0.37/0.89 (step @p117 :rule trans :premises (@p116 @p110)) % 0.37/0.89 (step @p118 :rule trans :premises (@p117 @p109)) % 0.37/0.89 (step @p119 :rule bool-impl-elim :args (@t39 @t148)) % 0.37/0.89 (step @p120 :rule cong :premises (@p119) :args ((forall @t9 (=> @t39 @t148)))) % 0.37/0.89 (step @p121 :rule trans :premises (@p120 @p118)) % 0.37/0.89 (step @p122 :rule bool-impl-elim :args (@t36 @t78)) % 0.37/0.89 (step @p123 :rule cong :premises (@p122) :args (@t79)) % 0.37/0.89 (step @p124 :rule cong :premises (@p63 @p123) :args (@t80)) % 0.37/0.89 (step @p125 :rule cong :premises (@p124) :args (@t81)) % 0.37/0.89 (step @p126 :rule trans :premises (@p125 @p121)) % 0.37/0.89 (step @p127 :rule cong :premises (@p126) :args (@t82)) % 0.37/0.89 (step @p128 :rule eq_resolve :premises (@p35 @p127)) % 0.37/0.89 (step @p129 :rule skolemize :premises (@p128)) % 0.37/0.89 (step @p130 :rule bool-double-not-elim :args (@t150)) % 0.37/0.89 (step @p131 :rule refl :args (@t157)) % 0.37/0.89 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or @t157 (not @t154)))) % 0.37/0.89 (step @p133 :rule cnf_or_neg :args (@t157 1)) % 0.37/0.89 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.37/0.89 (step @p135 :rule reordering :premises (@p134) :args ((or @t150 @t157))) % 0.37/0.89 (step @p136 :rule chain_m_resolution :premises (@p135 @p129) :args (@t150 @t158 @t159)) % 0.37/0.89 (step @p137 :rule cnf_or_pos :args (@t161)) % 0.37/0.89 (step @p138 :rule reordering :premises (@p137) :args ((or @t154 @t160 (not @t161)))) % 0.37/0.89 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p107) :args (@t160 @t162 (@list @t150 @t161))) % 0.37/0.89 (step @p140 :rule bool-double-not-elim :args (@t155)) % 0.37/0.89 (step @p141 :rule nary_cong :premises (@p131 @p140) :args ((or @t157 (not @t156)))) % 0.37/0.89 (step @p142 :rule cnf_or_neg :args (@t157 0)) % 0.37/0.89 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.37/0.89 (step @p144 :rule reordering :premises (@p143) :args ((or @t155 @t157))) % 0.37/0.89 (step @p145 :rule chain_m_resolution :premises (@p144 @p129) :args (@t155 @t158 @t159)) % 0.37/0.89 (step @p146 :rule cnf_or_pos :args (@t165)) % 0.37/0.89 (step @p147 :rule reordering :premises (@p146) :args ((or @t156 @t164 @t163 (not @t165)))) % 0.37/0.89 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p139 @p103) :args (@t163 @t166 (@list @t155 @t160 @t165))) % 0.37/0.89 (step @p149 :rule cnf_or_neg :args (@t157 2)) % 0.37/0.89 (step @p150 :rule chain_m_resolution :premises (@p149 @p129) :args ((not @t153) @t158 @t159)) % 0.37/0.89 (step @p151 :rule cnf_equiv_neg1 :args (@t153)) % 0.37/0.89 (step @p152 :rule reordering :premises (@p151) :args ((or @t152 @t151 @t153))) % 0.37/0.89 (step @p153 :rule aci_norm :args ((= @t171 (or @t99 @t169 @t168)))) % 0.37/0.89 (step @p154 :rule cong :premises (@p153) :args (@t172)) % 0.37/0.89 (step @p155 :rule quant-merge-prenex :args ((= (forall @t9 @t174) @t172))) % 0.37/0.89 (step @p156 :rule alpha_equiv :args (@t175 (@list @t167) @t106)) % 0.37/0.89 (step @p157 :rule nary_cong :premises (@p50 @p156) :args (@t176)) % 0.37/0.89 (step @p158 :rule quant-miniscope-or :args ((= @t174 @t176))) % 0.37/0.89 (step @p159 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:args (@t258 @t158 @t264)) % 0.37/0.89 (step @p402 :rule cnf_equiv_pos1 :args (@t276)) % 0.37/0.89 (step @p403 :rule reordering :premises (@p402) :args ((or @t259 @t274 (not @t276)))) % 0.37/0.89 (step @p404 :rule chain_m_resolution :premises (@p403 @p401 @p395) :args (@t274 @t162 (@list @t258 @t276))) % 0.37/0.89 (step @p405 :rule cnf_equiv_pos1 :args (@t181)) % 0.37/0.89 (step @p406 :rule reordering :premises (@p405) :args ((or (not @t152) @t180 @t183))) % 0.37/0.89 (step @p407 :rule chain_m_resolution :premises (@p406 @p332 @p188) :args (@t180 @t162 (@list @t152 @t181))) % 0.37/0.89 (assume-push @p433 @t180) % 0.37/0.89 (step @p409 :rule instantiate :premises (@p433) :args ((@list @t265))) % 0.37/0.89 (step-pop @p434 :rule scope :premises (@p409)) % 0.37/0.89 (step @p410 :rule process_scope :premises (@p434) :args (@t281)) % 0.37/0.89 (step @p412 :rule implies_elim :premises (@p410)) % 0.37/0.89 (step @p413 :rule chain_m_resolution :premises (@p412 @p407) :args (@t281 @t249 (@list @t180))) % 0.37/0.89 (step @p414 :rule instantiate :premises (@p244) :args ((@list @t118 @t123))) % 0.37/0.89 (step @p415 :rule cnf_or_pos :args (@t282)) % 0.37/0.89 (step @p416 :rule reordering :premises (@p415) :args ((or @t261 @t279 (not @t282)))) % 0.37/0.89 (step @p417 :rule chain_m_resolution :premises (@p416 @p354 @p414) :args (@t279 @t162 (@list @t260 @t282))) % 0.37/0.89 (step @p418 :rule cnf_or_pos :args (@t281)) % 0.37/0.89 (step @p419 :rule reordering :premises (@p418) :args ((or @t266 @t278 @t280 (not @t281)))) % 0.37/0.89 (step @p420 false :rule chain_m_resolution :premises (@p419 @p417 @p413 @p404 @p362) :args (false (@list false false false true) (@list @t279 @t281 @t274 @t266))) % 0.37/0.89 ) % 0.37/0.89 % SZS output end Proof % 0.37/0.89 % cvc5 exiting %------------------------------------------------------------------------------