%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU171+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n023.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 08:50:50 AM UTC 2026 % Result : Theorem 0.50s 0.79s % Output : Proof 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU171+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n023.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 16:34:28 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.50/0.79 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.50/0.79 % SZS status Theorem % 0.50/0.79 % SZS output start Proof % 0.50/0.79 ( % 0.50/0.79 (declare-sort $$unsorted 0) % 0.50/0.79 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (declare-const tptp.empty_set $$unsorted) % 0.50/0.79 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.50/0.79 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.79 (define @t1 () (@var "A" $$unsorted)) % 0.50/0.79 (define @t2 () (@var "B" $$unsorted)) % 0.50/0.79 (define @t3 () (tptp.in @t2 @t1)) % 0.50/0.79 (define @t4 () (not @t3)) % 0.50/0.79 (define @t5 () (tptp.in @t1 @t2)) % 0.50/0.79 (define @t6 () (@list @t1 @t2)) % 0.50/0.79 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.50/0.79 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.50/0.79 (define @t9 () (tptp.unordered_pair @t1 @t2)) % 0.50/0.79 (define @t10 () (tptp.set_union2 @t2 @t1)) % 0.50/0.79 (define @t11 () (tptp.set_union2 @t1 @t2)) % 0.50/0.79 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 0.50/0.79 (define @t13 () (tptp.subset @t1 @t2)) % 0.50/0.79 (define @t14 () (= @t1 @t2)) % 0.50/0.79 (define @t15 () (@var "C" $$unsorted)) % 0.50/0.79 (define @t16 () (tptp.in @t15 @t2)) % 0.50/0.79 (define @t17 () (@list @t15)) % 0.50/0.79 (define @t18 () (tptp.singleton @t1)) % 0.50/0.79 (define @t19 () (@list @t2)) % 0.50/0.79 (define @t20 () (= @t1 tptp.empty_set)) % 0.50/0.79 (define @t21 () (@list @t1)) % 0.50/0.79 (define @t22 () (tptp.powerset @t1)) % 0.50/0.79 (define @t23 () (tptp.empty @t2)) % 0.50/0.79 (define @t24 () (tptp.element @t2 @t1)) % 0.50/0.79 (define @t25 () (= @t24 @t23)) % 0.50/0.79 (define @t26 () (tptp.empty @t1)) % 0.50/0.79 (define @t27 () (=> @t26 @t25)) % 0.50/0.79 (define @t28 () (not @t26)) % 0.50/0.79 (define @t29 () (=> @t28 (= @t24 @t3))) % 0.50/0.79 (define @t30 () (and @t29 @t27)) % 0.50/0.79 (define @t31 () (forall @t6 @t30)) % 0.50/0.79 (define @t32 () (@var "D" $$unsorted)) % 0.50/0.79 (define @t33 () (tptp.in @t32 @t15)) % 0.50/0.79 (define @t34 () (@list @t32)) % 0.50/0.79 (define @t35 () (@list @t1 @t2 @t15)) % 0.50/0.79 (define @t36 () (tptp.in @t32 @t2)) % 0.50/0.79 (define @t37 () (tptp.in @t32 @t1)) % 0.50/0.79 (define @t38 () (@var "F" $$unsorted)) % 0.50/0.79 (define @t39 () (@var "E" $$unsorted)) % 0.50/0.79 (define @t40 () (tptp.in @t15 @t1)) % 0.50/0.79 (define @t41 () (tptp.set_difference @t1 @t2)) % 0.50/0.79 (define @t42 () (tptp.subset_complement @t1 @t2)) % 0.50/0.79 (define @t43 () (tptp.element @t2 @t22)) % 0.50/0.79 (define @t44 () (=> @t43 (= @t42 @t41))) % 0.50/0.79 (define @t45 () (forall @t6 @t44)) % 0.50/0.79 (define @t46 () (tptp.ordered_pair @t1 @t2)) % 0.50/0.79 (define @t47 () (tptp.disjoint @t1 @t2)) % 0.50/0.79 (define @t48 () (not @t14)) % 0.50/0.79 (define @t49 () (tptp.disjoint @t18 @t2)) % 0.50/0.79 (define @t50 () (not @t5)) % 0.50/0.79 (define @t51 () (forall @t6 (=> @t50 @t49))) % 0.50/0.79 (define @t52 () (tptp.subset @t18 @t2)) % 0.50/0.79 (define @t53 () (forall @t6 (= @t52 @t5))) % 0.50/0.79 (define @t54 () (tptp.singleton @t2)) % 0.50/0.79 (define @t55 () (tptp.in @t1 @t15)) % 0.50/0.79 (define @t56 () (@list @t1 @t2 @t15 @t32)) % 0.50/0.79 (define @t57 () (= @t1 @t15)) % 0.50/0.79 (define @t58 () (tptp.cartesian_product2 @t1 @t15)) % 0.50/0.79 (define @t59 () (not @t16)) % 0.50/0.79 (define @t60 () (tptp.subset @t15 @t2)) % 0.50/0.79 (define @t61 () (forall @t17 (not (and @t60 (not (tptp.are_equipotent @t15 @t2)) @t59)))) % 0.50/0.79 (define @t62 () (forall (@list @t15 @t32) (=> (and @t16 (tptp.subset @t32 @t15)) @t36))) % 0.50/0.79 (define @t63 () (tptp.set_intersection2 @t2 @t15)) % 0.50/0.79 (define @t64 () (tptp.subset @t1 @t15)) % 0.50/0.79 (define @t65 () (tptp.subset (tptp.set_difference @t1 @t15) (tptp.set_difference @t2 @t15))) % 0.50/0.79 (define @t66 () (forall @t35 (=> @t13 @t65))) % 0.50/0.79 (define @t67 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.50/0.79 (define @t68 () (and @t40 @t16)) % 0.50/0.79 (define @t69 () (exists @t17 @t68)) % 0.50/0.79 (define @t70 () (and @t69 @t47)) % 0.50/0.79 (define @t71 () (not @t70)) % 0.50/0.79 (define @t72 () (forall @t17 (not @t68))) % 0.50/0.79 (define @t73 () (not @t47)) % 0.50/0.79 (define @t74 () (and @t73 @t72)) % 0.50/0.79 (define @t75 () (not @t74)) % 0.50/0.79 (define @t76 () (and @t75 @t71)) % 0.50/0.79 (define @t77 () (forall @t6 @t76)) % 0.50/0.79 (define @t78 () (tptp.disjoint @t2 @t15)) % 0.50/0.79 (define @t79 () (tptp.in @t15 @t12)) % 0.50/0.79 (define @t80 () (tptp.in @t15 @t42)) % 0.50/0.79 (define @t81 () (=> @t59 @t80)) % 0.50/0.79 (define @t82 () (tptp.element @t15 @t1)) % 0.50/0.79 (define @t83 () (forall @t17 (=> @t82 @t81))) % 0.50/0.79 (define @t84 () (=> @t43 @t83)) % 0.50/0.79 (define @t85 () (forall @t19 @t84)) % 0.50/0.79 (define @t86 () (not @t20)) % 0.50/0.79 (define @t87 () (=> @t86 @t85)) % 0.50/0.79 (define @t88 () (forall @t21 @t87)) % 0.50/0.79 (define @t89 () (not @t88)) % 0.50/0.79 (define @t90 () (forall @t21 (=> @t26 @t20))) % 0.50/0.79 (define @t91 () (forall @t6 (not (and @t5 @t23)))) % 0.50/0.79 (define @t92 () (= @t47 (= @t41 @t1))) % 0.50/0.79 (define @t93 () (forall @t6 @t92)) % 0.50/0.79 (define @t94 () (= @t18 (tptp.unordered_pair @t2 @t15))) % 0.50/0.79 (define @t95 () (@var "BOUND_VARIABLE_8356" $$unsorted)) % 0.50/0.79 (define @t96 () (@var "BOUND_VARIABLE_8358" $$unsorted)) % 0.50/0.79 (define @t97 () (tptp.in @t96 (tptp.subset_complement @t1 @t95))) % 0.50/0.79 (define @t98 () (tptp.in @t96 @t95)) % 0.50/0.79 (define @t99 () (not (tptp.element @t96 @t1))) % 0.50/0.79 (define @t100 () (not (tptp.element @t95 @t22))) % 0.50/0.79 (define @t101 () (or @t20 @t100 @t99 @t98 @t97)) % 0.50/0.79 (define @t102 () (@list @t1 @t95 @t96)) % 0.50/0.79 (define @t103 () (forall @t102 @t101)) % 0.50/0.79 (define @t104 () (@quantifiers_skolemize @t103 1)) % 0.50/0.79 (define @t105 () (@quantifiers_skolemize @t103 0)) % 0.50/0.79 (define @t106 () (tptp.subset_complement @t105 @t104)) % 0.50/0.79 (define @t107 () (tptp.empty @t106)) % 0.50/0.79 (define @t108 () (not @t107)) % 0.50/0.79 (define @t109 () (or @t108 (= @t106 tptp.empty_set))) % 0.50/0.79 (define @t110 () (forall @t21 (or @t28 @t20))) % 0.50/0.79 (define @t111 () (= tptp.empty_set @t106)) % 0.50/0.79 (define @t112 () (or @t108 @t111)) % 0.50/0.79 (define @t113 () (@list false)) % 0.50/0.79 (define @t114 () (@list @t105 @t104)) % 0.50/0.79 (define @t115 () (@var "BOUND_VARIABLE_8221" $$unsorted)) % 0.50/0.79 (define @t116 () (@var "BOUND_VARIABLE_8235" $$unsorted)) % 0.50/0.79 (define @t117 () (not (tptp.in @t116 @t115))) % 0.50/0.79 (define @t118 () (@var "BOUND_VARIABLE_8219" $$unsorted)) % 0.50/0.79 (define @t119 () (not (tptp.in @t116 @t118))) % 0.50/0.79 (define @t120 () (not (tptp.disjoint @t118 @t115))) % 0.50/0.79 (define @t121 () (or @t119 @t117)) % 0.50/0.79 (define @t122 () (or @t121 @t120)) % 0.50/0.79 (define @t123 () (forall (@list @t118 @t115 @t116) @t122)) % 0.50/0.79 (define @t124 () (@list @t116)) % 0.50/0.79 (define @t125 () (forall @t124 @t122)) % 0.50/0.79 (define @t126 () (@list @t118 @t115)) % 0.50/0.79 (define @t127 () (forall @t124 @t121)) % 0.50/0.79 (define @t128 () (@list @t15)) % 0.50/0.79 (define @t129 () (or @t127 @t120)) % 0.50/0.79 (define @t130 () (forall @t126 (or (forall @t17 (or (not (tptp.in @t15 @t118)) (not (tptp.in @t15 @t115)))) @t120))) % 0.50/0.79 (define @t131 () (@var "BOUND_VARIABLE_8206" $$unsorted)) % 0.50/0.79 (define @t132 () (@var "BOUND_VARIABLE_8204" $$unsorted)) % 0.50/0.79 (define @t133 () (forall (@list @t132 @t131) (or (tptp.disjoint @t132 @t131) (not (forall @t17 (or (not (tptp.in @t15 @t132)) (not (tptp.in @t15 @t131)))))))) % 0.50/0.79 (define @t134 () (forall @t17 (or (not @t40) @t59))) % 0.50/0.79 (define @t135 () (or @t134 @t73)) % 0.50/0.79 (define @t136 () (forall @t6 @t135)) % 0.50/0.79 (define @t137 () (@list @t1 @t2)) % 0.50/0.79 (define @t138 () (not @t134)) % 0.50/0.79 (define @t139 () (or @t47 @t138)) % 0.50/0.79 (define @t140 () (forall @t6 @t139)) % 0.50/0.79 (define @t141 () (and @t140 @t136)) % 0.50/0.79 (define @t142 () (and (not (and @t73 @t134)) (not (and @t138 @t47)))) % 0.50/0.79 (define @t143 () (not @t72)) % 0.50/0.79 (define @t144 () (forall @t17 (or (not (tptp.in @t15 @t105)) (not (tptp.in @t15 @t104))))) % 0.50/0.79 (define @t145 () (@quantifiers_skolemize @t144 0)) % 0.50/0.79 (define @t146 () (or @t28 @t25)) % 0.50/0.79 (define @t147 () (forall @t6 @t146)) % 0.50/0.79 (define @t148 () (= @t3 @t24)) % 0.50/0.79 (define @t149 () (or @t26 @t148)) % 0.50/0.79 (define @t150 () (forall @t6 @t149)) % 0.50/0.79 (define @t151 () (@var "BOUND_VARIABLE_7911" $$unsorted)) % 0.50/0.79 (define @t152 () (@var "BOUND_VARIABLE_7909" $$unsorted)) % 0.50/0.79 (define @t153 () (and @t150 @t147)) % 0.50/0.79 (define @t154 () (and (=> @t28 @t148) @t27)) % 0.50/0.79 (define @t155 () (@quantifiers_skolemize @t103 2)) % 0.50/0.79 (define @t156 () (tptp.in @t155 @t105)) % 0.50/0.79 (define @t157 () (tptp.element @t155 @t105)) % 0.50/0.79 (define @t158 () (tptp.empty @t105)) % 0.50/0.79 (define @t159 () (or @t158 (= @t156 @t157))) % 0.50/0.79 (define @t160 () (forall (@list @t152 @t151) (or (tptp.empty @t152) (= (tptp.in @t151 @t152) (tptp.element @t151 @t152))))) % 0.50/0.79 (define @t161 () (= @t157 @t156)) % 0.50/0.79 (define @t162 () (or @t158 @t161)) % 0.50/0.79 (define @t163 () (tptp.singleton @t155)) % 0.50/0.79 (define @t164 () (or @t100 @t99 @t98 @t97)) % 0.50/0.79 (define @t165 () (or @t20 @t164)) % 0.50/0.79 (define @t166 () (forall @t102 @t165)) % 0.50/0.79 (define @t167 () (@list @t95 @t96)) % 0.50/0.79 (define @t168 () (forall @t167 @t165)) % 0.50/0.79 (define @t169 () (forall @t167 @t164)) % 0.50/0.79 (define @t170 () (@var "BOUND_VARIABLE_8340" $$unsorted)) % 0.50/0.79 (define @t171 () (or @t20 @t169)) % 0.50/0.79 (define @t172 () (tptp.in @t170 @t42)) % 0.50/0.79 (define @t173 () (tptp.in @t170 @t2)) % 0.50/0.79 (define @t174 () (not (tptp.element @t170 @t1))) % 0.50/0.79 (define @t175 () (not @t43)) % 0.50/0.79 (define @t176 () (or @t175 @t174 @t173 @t172)) % 0.50/0.79 (define @t177 () (@list @t2 @t170)) % 0.50/0.79 (define @t178 () (forall @t177 @t176)) % 0.50/0.79 (define @t179 () (or @t174 @t173 @t172)) % 0.50/0.79 (define @t180 () (or @t175 @t179)) % 0.50/0.79 (define @t181 () (forall @t177 @t180)) % 0.50/0.79 (define @t182 () (@list @t170)) % 0.50/0.79 (define @t183 () (forall @t182 @t180)) % 0.50/0.79 (define @t184 () (forall @t182 @t179)) % 0.50/0.79 (define @t185 () (or @t175 @t184)) % 0.50/0.79 (define @t186 () (not @t82)) % 0.50/0.79 (define @t187 () (or @t186 @t16 @t80)) % 0.50/0.79 (define @t188 () (forall @t17 @t187)) % 0.50/0.79 (define @t189 () (tptp.in @t155 @t106)) % 0.50/0.79 (define @t190 () (tptp.in @t155 @t104)) % 0.50/0.79 (define @t191 () (not @t157)) % 0.50/0.79 (define @t192 () (tptp.element @t104 (tptp.powerset @t105))) % 0.50/0.79 (define @t193 () (not @t192)) % 0.50/0.79 (define @t194 () (= tptp.empty_set @t105)) % 0.50/0.79 (define @t195 () (or @t194 @t193 @t191 @t190 @t189)) % 0.50/0.79 (define @t196 () (not @t195)) % 0.50/0.79 (define @t197 () (not @t103)) % 0.50/0.79 (define @t198 () (or (= @t105 tptp.empty_set) @t193 @t191 @t190 @t189)) % 0.50/0.79 (define @t199 () (not @t198)) % 0.50/0.79 (define @t200 () (@list true)) % 0.50/0.79 (define @t201 () (@list @t195)) % 0.50/0.79 (define @t202 () (tptp.subset @t163 @t106)) % 0.50/0.79 (define @t203 () (= @t189 @t202)) % 0.50/0.79 (define @t204 () (not @t202)) % 0.50/0.79 (define @t205 () (@list true false)) % 0.50/0.79 (define @t206 () (= @t41 @t42)) % 0.50/0.79 (define @t207 () (tptp.set_difference @t105 @t104)) % 0.50/0.79 (define @t208 () (or @t193 (= @t207 @t106))) % 0.50/0.79 (define @t209 () (forall @t6 (or @t175 @t206))) % 0.50/0.79 (define @t210 () (= @t106 @t207)) % 0.50/0.79 (define @t211 () (or @t193 @t210)) % 0.50/0.79 (define @t212 () (@list false false)) % 0.50/0.79 (define @t213 () (tptp.disjoint @t163 @t104)) % 0.50/0.79 (define @t214 () (or @t190 @t213)) % 0.50/0.79 (define @t215 () (tptp.set_difference @t163 @t104)) % 0.50/0.79 (define @t216 () (= @t163 @t215)) % 0.50/0.79 (define @t217 () (= @t213 @t216)) % 0.50/0.79 (define @t218 () (tptp.subset @t215 @t207)) % 0.50/0.79 (define @t219 () (tptp.subset @t163 @t105)) % 0.50/0.79 (define @t220 () (not @t219)) % 0.50/0.79 (define @t221 () (or @t220 @t218)) % 0.50/0.79 (define @t222 () (= @t156 @t219)) % 0.50/0.79 (define @t223 () (not @t156)) % 0.50/0.79 (define @t224 () (not @t161)) % 0.50/0.79 (define @t225 () (not @t158)) % 0.50/0.79 (define @t226 () (tptp.in @t145 @t105)) % 0.50/0.79 (define @t227 () (not @t226)) % 0.50/0.79 (define @t228 () (or @t227 @t225)) % 0.50/0.79 (define @t229 () (or @t227 (not (tptp.in @t145 @t104)))) % 0.50/0.79 (define @t230 () (not @t229)) % 0.50/0.79 (define @t231 () (not @t144)) % 0.50/0.79 (define @t232 () (tptp.disjoint @t105 @t104)) % 0.50/0.79 (define @t233 () (or @t232 @t231)) % 0.50/0.79 (define @t234 () (= @t105 @t207)) % 0.50/0.79 (define @t235 () (= @t232 @t234)) % 0.50/0.79 (define @t236 () (not @t194)) % 0.50/0.79 (define @t237 () (not @t111)) % 0.50/0.79 (define @t238 () (not @t234)) % 0.50/0.79 (define @t239 () (not @t210)) % 0.50/0.79 (define @t240 () (and @t236 @t210 @t234)) % 0.50/0.79 (define @t241 () (and @t158 @t210 @t234)) % 0.50/0.79 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.50/0.79 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.50/0.79 (assume @p3 (forall @t6 (= @t9 (tptp.unordered_pair @t2 @t1)))) % 0.50/0.79 (assume @p4 (forall @t6 (= @t11 @t10))) % 0.50/0.79 (assume @p5 (forall @t6 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 0.50/0.79 (assume @p6 (forall @t6 (= @t14 (and @t13 (tptp.subset @t2 @t1))))) % 0.50/0.79 (assume @p7 (forall @t6 (= (= @t2 @t18) (forall @t17 (= @t16 (= @t15 @t1)))))) % 0.50/0.79 (assume @p8 (forall @t21 (= @t20 (forall @t19 @t4)))) % 0.50/0.79 (assume @p9 (forall @t6 (= (= @t2 @t22) (forall @t17 (= @t16 (tptp.subset @t15 @t1)))))) % 0.50/0.79 (assume @p10 @t31) % 0.50/0.79 (assume @p11 (forall @t35 (= (= @t15 @t9) (forall @t34 (= @t33 (or (= @t32 @t1) (= @t32 @t2))))))) % 0.50/0.79 (assume @p12 (forall @t35 (= (= @t15 @t11) (forall @t34 (= @t33 (or @t37 @t36)))))) % 0.50/0.79 (assume @p13 (forall @t35 (= (= @t15 (tptp.cartesian_product2 @t1 @t2)) (forall @t34 (= @t33 (exists (@list @t39 @t38) (and (tptp.in @t39 @t1) (tptp.in @t38 @t2) (= @t32 (tptp.ordered_pair @t39 @t38))))))))) % 0.50/0.79 (assume @p14 (forall @t6 (= @t13 (forall @t17 (=> @t40 @t16))))) % 0.50/0.79 (assume @p15 (forall @t35 (= (= @t15 @t12) (forall @t34 (= @t33 (and @t37 @t36)))))) % 0.50/0.79 (assume @p16 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t17 (= @t16 (exists @t34 (and (tptp.in @t15 @t32) @t37))))))) % 0.50/0.79 (assume @p17 (forall @t35 (= (= @t15 @t41) (forall @t34 (= @t33 (and @t37 (not @t36))))))) % 0.50/0.79 (assume @p18 @t45) % 0.50/0.79 (assume @p19 (forall @t6 (= @t46 (tptp.unordered_pair @t9 @t18)))) % 0.50/0.79 (assume @p20 (forall @t6 (= @t47 (= @t12 tptp.empty_set)))) % 0.50/0.79 (assume @p21 (forall @t6 (= @t8 (and @t13 @t48)))) % 0.50/0.79 (assume @p22 true) % 0.50/0.79 (assume @p23 (forall @t6 (=> @t43 (tptp.element @t42 @t22)))) % 0.50/0.79 (assume @p24 (forall @t21 (exists @t19 @t24))) % 0.50/0.79 (assume @p25 (forall @t21 (not (tptp.empty @t22)))) % 0.50/0.79 (assume @p26 (tptp.empty tptp.empty_set)) % 0.50/0.79 (assume @p27 (forall @t6 (not (tptp.empty @t46)))) % 0.50/0.79 (assume @p28 (forall @t6 (=> @t28 (not (tptp.empty @t11))))) % 0.50/0.79 (assume @p29 (forall @t6 (=> @t28 (not (tptp.empty @t10))))) % 0.50/0.79 (assume @p30 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.50/0.79 (assume @p31 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.50/0.79 (assume @p32 (forall @t6 (=> @t43 (= (tptp.subset_complement @t1 @t42) @t2)))) % 0.50/0.79 (assume @p33 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.50/0.79 (assume @p34 (forall @t21 (not (= @t18 tptp.empty_set)))) % 0.50/0.79 (assume @p35 (forall @t6 (=> @t5 (= (tptp.set_union2 @t18 @t2) @t2)))) % 0.50/0.79 (assume @p36 (forall @t6 (not (and @t49 @t5)))) % 0.50/0.79 (assume @p37 @t51) % 0.50/0.79 (assume @p38 @t53) % 0.50/0.79 (assume @p39 (forall @t6 (= (= @t41 tptp.empty_set) @t13))) % 0.50/0.79 (assume @p40 (forall @t6 (=> @t43 (forall @t17 (=> @t16 @t40))))) % 0.50/0.79 (assume @p41 (forall @t35 (=> @t13 (or @t40 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t15))))))) % 0.50/0.79 (assume @p42 (forall @t6 (= (tptp.subset @t1 @t54) (or @t20 (= @t1 @t54))))) % 0.50/0.79 (assume @p43 (forall @t6 (=> @t5 (tptp.subset @t1 (tptp.union @t2))))) % 0.50/0.79 (assume @p44 (forall @t56 (= (tptp.in @t46 (tptp.cartesian_product2 @t15 @t32)) (and @t55 (tptp.in @t2 @t32))))) % 0.50/0.79 (assume @p45 (forall @t21 (=> @t28 (exists @t19 (and @t43 (not @t23)))))) % 0.50/0.79 (assume @p46 (exists @t21 @t26)) % 0.50/0.79 (assume @p47 (forall @t21 (exists @t19 (and @t43 @t23)))) % 0.50/0.79 (assume @p48 (exists @t21 @t28)) % 0.50/0.79 (assume @p49 (forall @t6 (tptp.subset @t1 @t1))) % 0.50/0.79 (assume @p50 (forall @t6 (=> @t47 (tptp.disjoint @t2 @t1)))) % 0.50/0.79 (assume @p51 (forall @t56 (not (and (= @t9 (tptp.unordered_pair @t15 @t32)) (not @t57) (not (= @t1 @t32)))))) % 0.50/0.79 (assume @p52 (forall @t35 (=> @t13 (and (tptp.subset @t58 (tptp.cartesian_product2 @t2 @t15)) (tptp.subset (tptp.cartesian_product2 @t15 @t1) (tptp.cartesian_product2 @t15 @t2)))))) % 0.50/0.79 (assume @p53 (forall @t56 (=> (and @t13 (tptp.subset @t15 @t32)) (tptp.subset @t58 (tptp.cartesian_product2 @t2 @t32))))) % 0.50/0.79 (assume @p54 (forall @t6 (=> @t13 (= @t11 @t2)))) % 0.50/0.79 (assume @p55 (forall @t21 (exists @t19 (and @t5 @t62 (forall @t17 (=> @t16 (tptp.in (tptp.powerset @t15) @t2))) @t61)))) % 0.50/0.79 (assume @p56 (forall @t6 (tptp.subset @t12 @t1))) % 0.50/0.79 (assume @p57 (forall @t35 (=> (and @t13 @t64) (tptp.subset @t1 @t63)))) % 0.50/0.79 (assume @p58 (forall @t21 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.50/0.79 (assume @p59 (forall @t35 (=> (and @t13 (tptp.subset @t2 @t15)) @t64))) % 0.50/0.79 (assume @p60 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.50/0.79 (assume @p61 (forall @t35 (=> @t13 (tptp.subset (tptp.set_intersection2 @t1 @t15) @t63)))) % 0.50/0.79 (assume @p62 (forall @t6 (=> @t13 (= @t12 @t1)))) % 0.50/0.79 (assume @p63 (forall @t21 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.50/0.79 (assume @p64 (forall @t6 (=> (forall @t17 (= @t40 @t16)) @t14))) % 0.50/0.79 (assume @p65 (forall @t21 (tptp.subset tptp.empty_set @t1))) % 0.50/0.79 (assume @p66 @t66) % 0.50/0.79 (assume @p67 (forall @t56 (=> (= @t46 (tptp.ordered_pair @t15 @t32)) (and @t57 (= @t2 @t32))))) % 0.50/0.79 (assume @p68 (forall @t6 (tptp.subset @t41 @t1))) % 0.50/0.79 (assume @p69 (forall @t35 (= (tptp.subset @t9 @t15) (and @t55 (tptp.in @t2 @t15))))) % 0.50/0.79 (assume @p70 (forall @t6 (= @t67 @t11))) % 0.50/0.79 (assume @p71 (forall @t21 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.50/0.79 (assume @p72 @t77) % 0.50/0.79 (assume @p73 (forall @t21 (=> (tptp.subset @t1 tptp.empty_set) @t20))) % 0.50/0.79 (assume @p74 (forall @t6 (= (tptp.set_difference @t11 @t2) @t41))) % 0.50/0.79 (assume @p75 (forall @t6 (=> @t43 (forall @t17 (=> (tptp.element @t15 @t22) (= @t78 (tptp.subset @t2 (tptp.subset_complement @t1 @t15)))))))) % 0.50/0.79 (assume @p76 (forall @t6 (=> @t13 (= @t2 @t67)))) % 0.50/0.79 (assume @p77 (forall @t6 (= (tptp.set_difference @t1 @t41) @t12))) % 0.50/0.79 (assume @p78 (forall @t21 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.50/0.79 (assume @p79 (forall @t6 (and (not (and @t73 (forall @t17 (not @t79)))) (not (and (exists @t17 @t79) @t47))))) % 0.50/0.79 (assume @p80 @t89) % 0.50/0.79 (assume @p81 (forall @t6 (not (and @t13 @t7)))) % 0.50/0.79 (assume @p82 (forall @t35 (=> (and @t13 @t78) (tptp.disjoint @t1 @t15)))) % 0.50/0.79 (assume @p83 (forall @t6 (= (= (tptp.set_difference @t1 @t54) @t1) @t4))) % 0.50/0.79 (assume @p84 (forall @t21 (= (tptp.unordered_pair @t1 @t1) @t18))) % 0.50/0.79 (assume @p85 @t90) % 0.50/0.79 (assume @p86 (forall @t6 (=> (tptp.subset @t18 @t54) @t14))) % 0.50/0.79 (assume @p87 @t91) % 0.50/0.79 (assume @p88 (forall @t6 (tptp.subset @t1 @t11))) % 0.50/0.79 (assume @p89 @t93) % 0.50/0.79 (assume @p90 (forall @t6 (not (and @t26 @t48 @t23)))) % 0.50/0.79 (assume @p91 (forall @t35 (=> (and @t13 @t60) (tptp.subset (tptp.set_union2 @t1 @t15) @t2)))) % 0.50/0.79 (assume @p92 (forall @t35 (=> @t94 @t14))) % 0.50/0.79 (assume @p93 (forall @t21 (= (tptp.union @t22) @t1))) % 0.50/0.79 (assume @p94 (forall @t21 (exists @t19 (and @t5 @t62 (forall @t17 (not (and @t16 (forall @t34 (not (and @t36 (forall (@list @t39) (=> (tptp.subset @t39 @t15) (tptp.in @t39 @t32))))))))) @t61)))) % 0.50/0.79 (assume @p95 (forall @t35 (=> @t94 (= @t2 @t15)))) % 0.50/0.79 (step @p96 :rule bool-impl-elim :args (@t26 @t20)) % 0.50/0.79 (step @p97 :rule cong :premises (@p96) :args (@t90)) % 0.50/0.79 (step @p98 :rule eq_resolve :premises (@p85 @p97)) % 0.50/0.79 (step @p99 :rule eq-symm :args (@t106 tptp.empty_set)) % 0.50/0.79 (step @p100 :rule refl :args (@t108)) % 0.50/0.79 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t109)) % 0.50/0.79 (step @p102 :rule refl :args (@t110)) % 0.50/0.79 (step @p103 :rule cong :premises (@p102 @p101) :args ((=> @t110 @t109))) % 0.50/0.79 (assume-push @p456 @t110) % 0.50/0.79 (step @p105 :rule instantiate :premises (@p98) :args ((@list @t106))) % 0.50/0.79 (step-pop @p457 :rule scope :premises (@p105)) % 0.50/0.79 (step @p106 :rule process_scope :premises (@p457) :args (@t109)) % 0.50/0.79 (step @p108 :rule eq_resolve :premises (@p106 @p103)) % 0.50/0.79 (step @p109 :rule implies_elim :premises (@p108)) % 0.50/0.79 (step @p110 :rule chain_m_resolution :premises (@p109 @p98) :args (@t112 @t113 (@list @t110))) % 0.50/0.79 (step @p111 :rule eq-symm :args (@t41 @t1)) % 0.50/0.79 (step @p112 :rule refl :args (@t47)) % 0.50/0.79 (step @p113 :rule cong :premises (@p112 @p111) :args (@t92)) % 0.50/0.79 (step @p114 :rule cong :premises (@p113) :args (@t93)) % 0.50/0.79 (step @p115 :rule eq_resolve :premises (@p89 @p114)) % 0.50/0.79 (step @p116 :rule instantiate :premises (@p115) :args (@t114)) % 0.50/0.79 (step @p117 :rule aci_norm :args ((= @t122 (or @t120 @t119 @t117)))) % 0.50/0.79 (step @p118 :rule cong :premises (@p117) :args (@t123)) % 0.50/0.79 (step @p119 :rule quant-merge-prenex :args ((= (forall @t126 @t125) @t123))) % 0.50/0.79 (step @p120 :rule refl :args (@t120)) % 0.50/0.79 (step @p121 :rule alpha_equiv :args (@t127 (@list @t116) @t128)) % 0.50/0.79 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t129)) % 0.50/0.79 (step @p123 :rule quant-miniscope-or :args ((= @t125 @t129))) % 0.50/0.79 (step @p124 :rule trans :premises (@p123 @p122)) % 0.50/0.79 (step @p125 :rule symm :premises (@p124)) % 0.50/0.79 (step @p126 :rule cong :premises (@p125) :args (@t130)) % 0.50/0.79 (step @p127 :rule trans :premises (@p126 @p119)) % 0.50/0.79 (step @p128 :rule trans :premises (@p127 @p118)) % 0.50/0.79 (step @p129 :rule refl :args (@t133)) % 0.50/0.79 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((and @t133 @t130))) % 0.50/0.79 (step @p131 :rule alpha_equiv :args (@t136 @t137 (@list @t118 @t115))) % 0.50/0.79 (step @p132 :rule alpha_equiv :args (@t140 @t137 (@list @t132 @t131))) % 0.50/0.79 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t141)) % 0.50/0.79 (step @p134 :rule quant-miniscope-and :args ((= (forall @t6 (and @t139 @t135)) @t141))) % 0.50/0.79 (step @p135 :rule trans :premises (@p134 @p133)) % 0.50/0.79 (step @p136 :rule trans :premises (@p135 @p130)) % 0.50/0.79 (step @p137 :rule refl :args (@t73)) % 0.50/0.79 (step @p138 :rule bool-double-not-elim :args (@t134)) % 0.50/0.79 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or (not @t138) @t73))) % 0.50/0.79 (step @p140 :rule bool-and-de-morgan :args (@t138 @t47 true)) % 0.50/0.79 (step @p141 :rule trans :premises (@p140 @p139)) % 0.50/0.79 (step @p142 :rule refl :args (@t138)) % 0.50/0.79 (step @p143 :rule bool-double-not-elim :args (@t47)) % 0.50/0.79 (step @p144 :rule nary_cong :premises (@p143 @p142) :args ((or (not @t73) @t138))) % 0.50/0.79 (step @p145 :rule bool-and-de-morgan :args (@t73 @t134 true)) % 0.50/0.79 (step @p146 :rule trans :premises (@p145 @p144)) % 0.50/0.79 (step @p147 :rule nary_cong :premises (@p146 @p141) :args (@t142)) % 0.50/0.79 (step @p148 :rule cong :premises (@p147) :args ((forall @t6 @t142))) % 0.50/0.79 (step @p149 :rule trans :premises (@p148 @p136)) % 0.50/0.79 (step @p150 :rule bool-and-de-morgan :args (@t40 @t16 true)) % 0.50/0.79 (step @p151 :rule cong :premises (@p150) :args (@t72)) % 0.50/0.79 (step @p152 :rule cong :premises (@p151) :args (@t143)) % 0.50/0.79 (step @p153 :rule exists-elim :args ((= @t69 @t143))) % 0.50/0.79 (step @p154 :rule trans :premises (@p153 @p152)) % 0.50/0.79 (step @p155 :rule nary_cong :premises (@p154 @p112) :args (@t70)) % 0.50/0.79 (step @p156 :rule cong :premises (@p155) :args (@t71)) % 0.50/0.79 (step @p157 :rule refl :args (@t73)) % 0.50/0.79 (step @p158 :rule nary_cong :premises (@p157 @p151) :args (@t74)) % 0.50/0.79 (step @p159 :rule cong :premises (@p158) :args (@t75)) % 0.50/0.79 (step @p160 :rule nary_cong :premises (@p159 @p156) :args (@t76)) % 0.50/0.79 (step @p161 :rule cong :premises (@p160) :args (@t77)) % 0.50/0.79 (step @p162 :rule trans :premises (@p161 @p149)) % 0.50/0.79 (step @p163 :rule eq_resolve :premises (@p72 @p162)) % 0.50/0.79 (step @p164 :rule and_elim :premises (@p163) :args (0)) % 0.50/0.79 (step @p165 :rule instantiate :premises (@p164) :args (@t114)) % 0.50/0.79 (step @p166 :rule bool-and-de-morgan :args (@t5 @t23 true)) % 0.50/0.79 (step @p167 :rule cong :premises (@p166) :args (@t91)) % 0.50/0.79 (step @p168 :rule eq_resolve :premises (@p87 @p167)) % 0.50/0.79 (step @p169 :rule instantiate :premises (@p168) :args ((@list @t145 @t105))) % 0.50/0.79 (step @p170 :rule alpha_equiv :args (@t147 @t137 (@list (@var "BOUND_VARIABLE_7920" $$unsorted) (@var "BOUND_VARIABLE_7922" $$unsorted)))) % 0.50/0.79 (step @p171 :rule alpha_equiv :args (@t150 @t137 (@list @t152 @t151))) % 0.50/0.79 (step @p172 :rule nary_cong :premises (@p171 @p170) :args (@t153)) % 0.50/0.79 (step @p173 :rule quant-miniscope-and :args ((= (forall @t6 (and @t149 @t146)) @t153))) % 0.50/0.79 (step @p174 :rule trans :premises (@p173 @p172)) % 0.50/0.79 (step @p175 :rule bool-impl-elim :args (@t26 @t25)) % 0.50/0.79 (step @p176 :rule refl :args (@t148)) % 0.50/0.79 (step @p177 :rule bool-double-not-elim :args (@t26)) % 0.50/0.79 (step @p178 :rule nary_cong :premises (@p177 @p176) :args ((or (not @t28) @t148))) % 0.50/0.79 (step @p179 :rule bool-impl-elim :args (@t28 @t148)) % 0.50/0.79 (step @p180 :rule trans :premises (@p179 @p178)) % 0.50/0.79 (step @p181 :rule nary_cong :premises (@p180 @p175) :args (@t154)) % 0.50/0.79 (step @p182 :rule cong :premises (@p181) :args ((forall @t6 @t154))) % 0.50/0.79 (step @p183 :rule trans :premises (@p182 @p174)) % 0.50/0.79 (step @p184 :rule refl :args (@t27)) % 0.50/0.79 (step @p185 :rule eq-symm :args (@t24 @t3)) 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@p396)) % 0.50/0.79 (step @p424 :rule reordering :premises (@p423) :args ((or @t194 @t239 @t237 @t238))) % 0.50/0.79 (step @p425 :rule chain_m_resolution :premises (@p424 @p391 @p323 @p389) :args (@t237 (@list true false false) (@list @t194 @t210 @t234))) % 0.50/0.79 (assume-push @p478 @t158) % 0.50/0.79 (assume-push @p479 @t210) % 0.50/0.79 (assume-push @p480 @t234) % 0.50/0.79 (assume-push @p481 @t158) % 0.50/0.79 (assume-push @p482 @t234) % 0.50/0.79 (assume-push @p483 @t210) % 0.50/0.79 (step @p432 :rule true_intro :premises (@p363)) % 0.50/0.79 (step @p433 :rule symm :premises (@p480)) % 0.50/0.79 (step @p434 :rule trans :premises (@p323 @p433)) % 0.50/0.79 (step @p435 :rule cong :premises (@p434) :args (@t107)) % 0.50/0.79 (step @p436 :rule trans :premises (@p435 @p432)) % 0.50/0.79 (step @p437 :rule true_elim :premises (@p436)) % 0.50/0.79 (step-pop @p484 :rule scope :premises (@p437)) % 0.50/0.79 (step-pop @p485 :rule scope :premises (@p484)) % 0.50/0.79 (step-pop @p486 :rule scope :premises (@p485)) % 0.50/0.79 (step @p438 :rule process_scope :premises (@p486) :args (@t107)) % 0.50/0.79 (step @p442 :rule and_intro :premises (@p363 @p480 @p323)) % 0.50/0.79 (step @p443 :rule modus_ponens :premises (@p442 @p438)) % 0.50/0.79 (step-pop @p487 :rule scope :premises (@p443)) % 0.50/0.79 (step-pop @p488 :rule scope :premises (@p487)) % 0.50/0.79 (step-pop @p489 :rule scope :premises (@p488)) % 0.50/0.79 (step @p444 :rule process_scope :premises (@p489) :args (@t107)) % 0.50/0.79 (step @p448 :rule implies_elim :premises (@p444)) % 0.50/0.79 (step @p449 :rule cnf_and_neg :args (@t241)) % 0.50/0.79 (step @p450 :rule resolution :premises (@p449 @p448) :args (true @t241)) % 0.50/0.79 (step @p451 :rule reordering :premises (@p450) :args ((or @t107 @t225 @t239 @t238))) % 0.50/0.79 (step @p452 :rule chain_m_resolution :premises (@p451 @p363 @p323 @p389) :args (@t107 (@list false false false) (@list @t158 @t210 @t234))) % 0.50/0.79 (step @p453 :rule cnf_or_pos :args (@t112)) % 0.50/0.79 (step @p454 :rule reordering :premises (@p453) :args ((or @t108 @t111 (not @t112)))) % 0.50/0.79 (step @p455 false :rule chain_m_resolution :premises (@p454 @p452 @p425 @p110) :args (false (@list false true false) (@list @t107 @t111 @t112))) % 0.50/0.79 ) % 0.50/0.79 % SZS output end Proof % 0.50/0.79 % cvc5 exiting %------------------------------------------------------------------------------