%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET727+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:48:31 AM UTC 2026 % Result : Theorem 0.53s 0.72s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET727+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n018.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:10:20 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.53/0.72 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.53/0.72 % SZS status Theorem % 0.53/0.72 % SZS output start Proof % 0.53/0.72 ( % 0.53/0.72 (declare-sort $$unsorted 0) % 0.53/0.72 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.empty_set $$unsorted) % 0.53/0.72 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (define @t1 () (@var "B" $$unsorted)) % 0.53/0.72 (define @t2 () (@var "X" $$unsorted)) % 0.53/0.72 (define @t3 () (tptp.member @t2 @t1)) % 0.53/0.72 (define @t4 () (@var "A" $$unsorted)) % 0.53/0.72 (define @t5 () (tptp.member @t2 @t4)) % 0.53/0.72 (define @t6 () (@list @t2)) % 0.53/0.72 (define @t7 () (tptp.subset @t4 @t1)) % 0.53/0.72 (define @t8 () (@list @t4 @t1)) % 0.53/0.72 (define @t9 () (@list @t2 @t4)) % 0.53/0.72 (define @t10 () (@list @t2 @t4 @t1)) % 0.53/0.72 (define @t11 () (@var "E" $$unsorted)) % 0.53/0.72 (define @t12 () (= @t2 @t4)) % 0.53/0.72 (define @t13 () (@var "Y" $$unsorted)) % 0.53/0.72 (define @t14 () (tptp.member @t2 @t13)) % 0.53/0.72 (define @t15 () (tptp.member @t13 @t4)) % 0.53/0.72 (define @t16 () (@list @t13)) % 0.53/0.72 (define @t17 () (@var "Y2" $$unsorted)) % 0.53/0.72 (define @t18 () (@var "Y1" $$unsorted)) % 0.53/0.72 (define @t19 () (= @t18 @t17)) % 0.53/0.72 (define @t20 () (@var "F" $$unsorted)) % 0.53/0.72 (define @t21 () (tptp.apply @t20 @t2 @t17)) % 0.53/0.72 (define @t22 () (tptp.apply @t20 @t2 @t18)) % 0.53/0.72 (define @t23 () (and @t22 @t21)) % 0.53/0.72 (define @t24 () (=> @t23 @t19)) % 0.53/0.72 (define @t25 () (tptp.member @t17 @t1)) % 0.53/0.72 (define @t26 () (tptp.member @t18 @t1)) % 0.53/0.72 (define @t27 () (and @t5 @t26 @t25)) % 0.53/0.72 (define @t28 () (@list @t2 @t18 @t17)) % 0.53/0.72 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.53/0.72 (define @t30 () (tptp.apply @t20 @t2 @t13)) % 0.53/0.72 (define @t31 () (tptp.member @t13 @t1)) % 0.53/0.72 (define @t32 () (and @t31 @t30)) % 0.53/0.72 (define @t33 () (exists @t16 @t32)) % 0.53/0.72 (define @t34 () (=> @t5 @t33)) % 0.53/0.72 (define @t35 () (forall @t6 @t34)) % 0.53/0.72 (define @t36 () (and @t35 @t29)) % 0.53/0.72 (define @t37 () (tptp.maps @t20 @t4 @t1)) % 0.53/0.72 (define @t38 () (= @t37 @t36)) % 0.53/0.72 (define @t39 () (@list @t20 @t4 @t1)) % 0.53/0.72 (define @t40 () (forall @t39 @t38)) % 0.53/0.72 (define @t41 () (@var "Z" $$unsorted)) % 0.53/0.72 (define @t42 () (@var "G" $$unsorted)) % 0.53/0.72 (define @t43 () (tptp.apply @t42 @t13 @t41)) % 0.53/0.72 (define @t44 () (and @t31 @t30 @t43)) % 0.53/0.72 (define @t45 () (exists @t16 @t44)) % 0.53/0.72 (define @t46 () (@var "H" $$unsorted)) % 0.53/0.72 (define @t47 () (@var "C" $$unsorted)) % 0.53/0.72 (define @t48 () (tptp.member @t41 @t47)) % 0.53/0.72 (define @t49 () (and @t5 @t48)) % 0.53/0.72 (define @t50 () (tptp.apply (tptp.compose_function @t42 @t20 @t4 @t1 @t47) @t2 @t41)) % 0.53/0.72 (define @t51 () (=> @t49 (= @t50 @t45))) % 0.53/0.72 (define @t52 () (@list @t42 @t20 @t4 @t1 @t47 @t2 @t41)) % 0.53/0.72 (define @t53 () (forall @t52 @t51)) % 0.53/0.72 (define @t54 () (tptp.apply @t42 @t2 @t17)) % 0.53/0.72 (define @t55 () (and @t22 @t54)) % 0.53/0.72 (define @t56 () (=> @t55 @t19)) % 0.53/0.72 (define @t57 () (forall @t28 (=> @t27 @t56))) % 0.53/0.72 (define @t58 () (tptp.equal_maps @t20 @t42 @t4 @t1)) % 0.53/0.72 (define @t59 () (= @t58 @t57)) % 0.53/0.72 (define @t60 () (forall (@list @t20 @t42 @t4 @t1) @t59)) % 0.53/0.72 (define @t61 () (tptp.apply @t20 @t2 @t2)) % 0.53/0.72 (define @t62 () (forall @t6 (=> @t5 @t61))) % 0.53/0.72 (define @t63 () (tptp.identity @t20 @t4)) % 0.53/0.72 (define @t64 () (= @t63 @t62)) % 0.53/0.72 (define @t65 () (forall (@list @t20 @t4) @t64)) % 0.53/0.72 (define @t66 () (@var "X2" $$unsorted)) % 0.53/0.72 (define @t67 () (@var "X1" $$unsorted)) % 0.53/0.72 (define @t68 () (tptp.member @t66 @t4)) % 0.53/0.72 (define @t69 () (tptp.member @t67 @t4)) % 0.53/0.72 (define @t70 () (tptp.injective @t20 @t4 @t1)) % 0.53/0.72 (define @t71 () (tptp.surjective @t20 @t4 @t1)) % 0.53/0.72 (define @t72 () (tptp.one_to_one @t20 @t4 @t1)) % 0.53/0.72 (define @t73 () (and @t5 @t31)) % 0.53/0.72 (define @t74 () (tptp.inverse_function @t20 @t4 @t1)) % 0.53/0.72 (define @t75 () (= @t30 (tptp.apply @t74 @t13 @t2))) % 0.53/0.72 (define @t76 () (@list @t20 @t4 @t1 @t2 @t13)) % 0.53/0.72 (define @t77 () (forall @t76 (=> @t73 @t75))) % 0.53/0.72 (define @t78 () (exists @t6 (and @t5 @t30))) % 0.53/0.72 (define @t79 () (@var "S" $$unsorted)) % 0.53/0.72 (define @t80 () (tptp.apply @t79 @t18 @t17)) % 0.53/0.72 (define @t81 () (tptp.apply @t20 @t66 @t17)) % 0.53/0.72 (define @t82 () (tptp.apply @t20 @t67 @t18)) % 0.53/0.72 (define @t83 () (@var "R" $$unsorted)) % 0.53/0.72 (define @t84 () (tptp.apply @t83 @t67 @t66)) % 0.53/0.72 (define @t85 () (and @t69 @t26 @t68 @t25 @t84 @t82 @t81)) % 0.53/0.72 (define @t86 () (@list @t67 @t18 @t66 @t17)) % 0.53/0.72 (define @t87 () (@list @t20 @t4 @t83 @t1 @t79)) % 0.53/0.72 (define @t88 () (tptp.equal_maps @t74 @t46 @t1 @t4)) % 0.53/0.72 (define @t89 () (tptp.identity (tptp.compose_function @t20 @t46 @t1 @t4 @t1) @t1)) % 0.53/0.72 (define @t90 () (tptp.identity (tptp.compose_function @t42 @t20 @t4 @t1 @t4) @t4)) % 0.53/0.72 (define @t91 () (tptp.maps @t46 @t1 @t4)) % 0.53/0.72 (define @t92 () (tptp.maps @t42 @t1 @t4)) % 0.53/0.72 (define @t93 () (and @t37 @t92 @t91 @t90 @t89)) % 0.53/0.72 (define @t94 () (@list @t20 @t42 @t46 @t4 @t1)) % 0.53/0.72 (define @t95 () (forall @t94 (=> @t93 @t88))) % 0.53/0.72 (define @t96 () (not @t95)) % 0.53/0.72 (define @t97 () (not @t21)) % 0.53/0.72 (define @t98 () (not @t22)) % 0.53/0.72 (define @t99 () (not @t25)) % 0.53/0.72 (define @t100 () (not @t26)) % 0.53/0.72 (define @t101 () (not @t5)) % 0.53/0.72 (define @t102 () (or @t98 @t97 @t19)) % 0.53/0.72 (define @t103 () (or @t101 @t100 @t99)) % 0.53/0.72 (define @t104 () (not @t27)) % 0.53/0.72 (define @t105 () (not @t30)) % 0.53/0.72 (define @t106 () (not @t31)) % 0.53/0.72 (define @t107 () (not (forall @t16 (or @t106 @t105)))) % 0.53/0.72 (define @t108 () (forall @t16 (not @t32))) % 0.53/0.72 (define @t109 () (not @t108)) % 0.53/0.72 (define @t110 () (not @t89)) % 0.53/0.72 (define @t111 () (not @t90)) % 0.53/0.72 (define @t112 () (not @t91)) % 0.53/0.72 (define @t113 () (not @t92)) % 0.53/0.72 (define @t114 () (not @t37)) % 0.53/0.72 (define @t115 () (or @t114 @t113 @t112 @t111 @t110 @t88)) % 0.53/0.72 (define @t116 () (forall @t94 @t115)) % 0.53/0.72 (define @t117 () (@quantifiers_skolemize @t116 3)) % 0.53/0.72 (define @t118 () (@quantifiers_skolemize @t116 4)) % 0.53/0.72 (define @t119 () (@quantifiers_skolemize @t116 1)) % 0.53/0.72 (define @t120 () (or @t114 @t113 @t112 @t111 @t110)) % 0.53/0.72 (define @t121 () (tptp.maps @t119 @t118 @t117)) % 0.53/0.72 (define @t122 () (@quantifiers_skolemize @t116 2)) % 0.53/0.72 (define @t123 () (@quantifiers_skolemize @t116 0)) % 0.53/0.72 (define @t124 () (tptp.inverse_function @t123 @t117 @t118)) % 0.53/0.72 (define @t125 () (tptp.equal_maps @t124 @t122 @t118 @t117)) % 0.53/0.72 (define @t126 () (tptp.compose_function @t123 @t122 @t118 @t117 @t118)) % 0.53/0.72 (define @t127 () (tptp.identity @t126 @t118)) % 0.53/0.72 (define @t128 () (not @t127)) % 0.53/0.72 (define @t129 () (tptp.compose_function @t119 @t123 @t117 @t118 @t117)) % 0.53/0.72 (define @t130 () (tptp.identity @t129 @t117)) % 0.53/0.72 (define @t131 () (not @t130)) % 0.53/0.72 (define @t132 () (tptp.maps @t122 @t118 @t117)) % 0.53/0.72 (define @t133 () (not @t132)) % 0.53/0.72 (define @t134 () (not @t121)) % 0.53/0.72 (define @t135 () (tptp.maps @t123 @t117 @t118)) % 0.53/0.72 (define @t136 () (not @t135)) % 0.53/0.72 (define @t137 () (or @t136 @t134 @t133 @t131 @t128 @t125)) % 0.53/0.72 (define @t138 () (@list true)) % 0.53/0.72 (define @t139 () (@list @t137)) % 0.53/0.72 (define @t140 () (not (tptp.member @t17 @t117))) % 0.53/0.72 (define @t141 () (not (tptp.member @t18 @t117))) % 0.53/0.72 (define @t142 () (not (tptp.member @t2 @t118))) % 0.53/0.72 (define @t143 () (forall @t28 (or @t142 @t141 @t140 (not (tptp.apply @t119 @t2 @t18)) (not (tptp.apply @t119 @t2 @t17)) @t19))) % 0.53/0.72 (define @t144 () (not (tptp.member @t13 @t117))) % 0.53/0.72 (define @t145 () (and (forall @t6 (or @t142 (not (forall @t16 (or @t144 (not (tptp.apply @t119 @t2 @t13))))))) @t143)) % 0.53/0.72 (define @t146 () (= @t121 @t145)) % 0.53/0.72 (define @t147 () (@list false false)) % 0.53/0.72 (define @t148 () (@list false)) % 0.53/0.72 (define @t149 () (not (tptp.apply @t122 @t2 @t17))) % 0.53/0.72 (define @t150 () (forall @t28 (or @t142 @t141 @t140 (not (tptp.apply @t124 @t2 @t18)) @t149 @t19))) % 0.53/0.72 (define @t151 () (@quantifiers_skolemize @t150 2)) % 0.53/0.72 (define @t152 () (@quantifiers_skolemize @t150 1)) % 0.53/0.72 (define @t153 () (@quantifiers_skolemize @t150 0)) % 0.53/0.72 (define @t154 () (not (tptp.apply @t122 @t153 @t13))) % 0.53/0.72 (define @t155 () (forall @t16 (or @t144 @t154))) % 0.53/0.72 (define @t156 () (@quantifiers_skolemize @t155 0)) % 0.53/0.72 (define @t157 () (not (tptp.member @t13 @t118))) % 0.53/0.72 (define @t158 () (forall @t16 (or @t157 (not (tptp.apply @t123 @t156 @t13))))) % 0.53/0.72 (define @t159 () (@quantifiers_skolemize @t158 0)) % 0.53/0.72 (define @t160 () (not (tptp.apply @t119 @t159 @t152))) % 0.53/0.72 (define @t161 () (tptp.apply @t119 @t159 @t151)) % 0.53/0.72 (define @t162 () (not @t161)) % 0.53/0.72 (define @t163 () (tptp.member @t152 @t117)) % 0.53/0.72 (define @t164 () (not @t163)) % 0.53/0.72 (define @t165 () (tptp.member @t151 @t117)) % 0.53/0.72 (define @t166 () (not @t165)) % 0.53/0.72 (define @t167 () (tptp.member @t159 @t118)) % 0.53/0.72 (define @t168 () (not @t167)) % 0.53/0.72 (define @t169 () (or @t168 @t166 @t164 @t162 @t160 (= @t151 @t152))) % 0.53/0.72 (define @t170 () (= @t152 @t151)) % 0.53/0.72 (define @t171 () (or @t168 @t166 @t164 @t162 @t160 @t170)) % 0.53/0.72 (define @t172 () (not @t43)) % 0.53/0.72 (define @t173 () (or @t106 @t105 @t172)) % 0.53/0.72 (define @t174 () (not (forall @t16 @t173))) % 0.53/0.72 (define @t175 () (= @t50 @t174)) % 0.53/0.72 (define @t176 () (not @t48)) % 0.53/0.72 (define @t177 () (forall @t16 (not @t44))) % 0.53/0.72 (define @t178 () (not @t177)) % 0.53/0.72 (define @t179 () (not @t54)) % 0.53/0.72 (define @t180 () (or @t98 @t179 @t19)) % 0.53/0.72 (define @t181 () (= @t125 @t150)) % 0.53/0.72 (define @t182 () (not @t150)) % 0.53/0.72 (define @t183 () (tptp.apply @t122 @t153 @t151)) % 0.53/0.72 (define @t184 () (not @t183)) % 0.53/0.72 (define @t185 () (tptp.apply @t124 @t153 @t152)) % 0.53/0.72 (define @t186 () (not @t185)) % 0.53/0.72 (define @t187 () (tptp.member @t153 @t118)) % 0.53/0.72 (define @t188 () (not @t187)) % 0.53/0.72 (define @t189 () (or @t188 @t164 @t166 @t186 @t184 @t170)) % 0.53/0.72 (define @t190 () (@list @t189)) % 0.53/0.72 (define @t191 () (not (tptp.apply @t123 @t151 @t13))) % 0.53/0.72 (define @t192 () (forall @t16 (or @t157 @t191 (not (tptp.apply @t119 @t13 @t151))))) % 0.53/0.72 (define @t193 () (not @t192)) % 0.53/0.72 (define @t194 () (tptp.apply @t129 @t151 @t151)) % 0.53/0.72 (define @t195 () (= @t194 @t193)) % 0.53/0.72 (define @t196 () (or @t166 @t166 @t195)) % 0.53/0.72 (define @t197 () (not (tptp.member @t2 @t117))) % 0.53/0.72 (define @t198 () (forall @t6 (or @t197 (tptp.apply @t129 @t2 @t2)))) % 0.53/0.72 (define @t199 () (= @t130 @t198)) % 0.53/0.72 (define @t200 () (@list @t151)) % 0.53/0.72 (define @t201 () (or @t166 @t194)) % 0.53/0.72 (define @t202 () (@quantifiers_skolemize @t192 0)) % 0.53/0.72 (define @t203 () (tptp.apply @t119 @t202 @t151)) % 0.53/0.72 (define @t204 () (not @t203)) % 0.53/0.72 (define @t205 () (tptp.apply @t123 @t151 @t202)) % 0.53/0.72 (define @t206 () (not @t205)) % 0.53/0.72 (define @t207 () (tptp.member @t202 @t118)) % 0.53/0.72 (define @t208 () (not @t207)) % 0.53/0.72 (define @t209 () (or @t208 @t206 @t204)) % 0.53/0.72 (define @t210 () (@list @t209)) % 0.53/0.72 (define @t211 () (forall @t28 (or @t197 (not (tptp.member @t18 @t118)) (not (tptp.member @t17 @t118)) (not (tptp.apply @t123 @t2 @t18)) (not (tptp.apply @t123 @t2 @t17)) @t19))) % 0.53/0.72 (define @t212 () (forall @t6 (or @t197 (not (forall @t16 (or @t157 (not (tptp.apply @t123 @t2 @t13)))))))) % 0.53/0.72 (define @t213 () (and @t212 @t211)) % 0.53/0.72 (define @t214 () (= @t135 @t213)) % 0.53/0.72 (define @t215 () (not @t213)) % 0.53/0.72 (define @t216 () (@list @t213)) % 0.53/0.72 (define @t217 () (tptp.apply @t123 @t156 @t159)) % 0.53/0.72 (define @t218 () (not @t217)) % 0.53/0.72 (define @t219 () (tptp.apply @t123 @t156 @t202)) % 0.53/0.72 (define @t220 () (not @t219)) % 0.53/0.72 (define @t221 () (tptp.member @t156 @t117)) % 0.53/0.72 (define @t222 () (not @t221)) % 0.53/0.72 (define @t223 () (or @t222 @t208 @t168 @t220 @t218 (= @t202 @t159))) % 0.53/0.72 (define @t224 () (= @t159 @t202)) % 0.53/0.72 (define @t225 () (or @t222 @t208 @t168 @t220 @t218 @t224)) % 0.53/0.72 (define @t226 () (@list @t211)) % 0.53/0.72 (define @t227 () (forall @t28 (or @t142 @t141 @t140 (not (tptp.apply @t122 @t2 @t18)) @t149 @t19))) % 0.53/0.72 (define @t228 () (forall @t6 (or @t142 (not (forall @t16 (or @t144 (not (tptp.apply @t122 @t2 @t13)))))))) % 0.53/0.72 (define @t229 () (and @t228 @t227)) % 0.53/0.72 (define @t230 () (= @t132 @t229)) % 0.53/0.72 (define @t231 () (not @t229)) % 0.53/0.72 (define @t232 () (@list @t229)) % 0.53/0.72 (define @t233 () (@list @t153)) % 0.53/0.72 (define @t234 () (not @t155)) % 0.53/0.72 (define @t235 () (or @t188 @t234)) % 0.53/0.72 (define @t236 () (tptp.apply @t122 @t153 @t156)) % 0.53/0.72 (define @t237 () (not @t236)) % 0.53/0.72 (define @t238 () (or @t222 @t237)) % 0.53/0.72 (define @t239 () (@list @t238)) % 0.53/0.72 (define @t240 () (= @t151 @t156)) % 0.53/0.72 (define @t241 () (or @t188 @t166 @t222 @t184 @t237 @t240)) % 0.53/0.72 (define @t242 () (@list false false false false false false)) % 0.53/0.72 (define @t243 () (not @t158)) % 0.53/0.72 (define @t244 () (or @t222 @t243)) % 0.53/0.72 (define @t245 () (or @t168 @t218)) % 0.53/0.72 (define @t246 () (@list @t245)) % 0.53/0.72 (define @t247 () (forall @t16 (or @t157 @t191))) % 0.53/0.72 (define @t248 () (@quantifiers_skolemize @t247 0)) % 0.53/0.72 (define @t249 () (tptp.apply @t123 @t151 @t248)) % 0.53/0.72 (define @t250 () (not @t249)) % 0.53/0.72 (define @t251 () (tptp.apply @t123 @t151 @t159)) % 0.53/0.72 (define @t252 () (not @t251)) % 0.53/0.72 (define @t253 () (tptp.member @t248 @t118)) % 0.53/0.72 (define @t254 () (not @t253)) % 0.53/0.72 (define @t255 () (or @t166 @t168 @t254 @t252 @t250 (= @t159 @t248))) % 0.53/0.72 (define @t256 () (= @t248 @t159)) % 0.53/0.72 (define @t257 () (or @t166 @t168 @t254 @t252 @t250 @t256)) % 0.53/0.72 (define @t258 () (not @t247)) % 0.53/0.72 (define @t259 () (or @t166 @t258)) % 0.53/0.72 (define @t260 () (or @t254 @t250)) % 0.53/0.72 (define @t261 () (@list @t260)) % 0.53/0.72 (define @t262 () (forall @t16 (or @t144 @t154 (not (tptp.apply @t123 @t13 @t153))))) % 0.53/0.72 (define @t263 () (@quantifiers_skolemize @t262 0)) % 0.53/0.72 (define @t264 () (tptp.apply @t123 @t263 @t153)) % 0.53/0.72 (define @t265 () (not @t264)) % 0.53/0.72 (define @t266 () (tptp.apply @t123 @t263 @t248)) % 0.53/0.72 (define @t267 () (not @t266)) % 0.53/0.72 (define @t268 () (tptp.member @t263 @t117)) % 0.53/0.72 (define @t269 () (not @t268)) % 0.53/0.72 (define @t270 () (or @t269 @t254 @t188 @t267 @t265 (= @t248 @t153))) % 0.53/0.72 (define @t271 () (= @t153 @t248)) % 0.53/0.72 (define @t272 () (or @t269 @t254 @t188 @t267 @t265 @t271)) % 0.53/0.72 (define @t273 () (tptp.apply @t122 @t153 @t263)) % 0.53/0.72 (define @t274 () (not @t273)) % 0.53/0.72 (define @t275 () (or @t188 @t269 @t166 @t274 @t184 (= @t263 @t151))) % 0.53/0.72 (define @t276 () (= @t151 @t263)) % 0.53/0.72 (define @t277 () (or @t188 @t269 @t166 @t274 @t184 @t276)) % 0.53/0.72 (define @t278 () (not @t262)) % 0.53/0.72 (define @t279 () (tptp.apply @t126 @t153 @t153)) % 0.53/0.72 (define @t280 () (= @t279 @t278)) % 0.53/0.72 (define @t281 () (or @t188 @t188 @t280)) % 0.53/0.72 (define @t282 () (forall @t6 (or @t142 (tptp.apply @t126 @t2 @t2)))) % 0.53/0.72 (define @t283 () (= @t127 @t282)) % 0.53/0.72 (define @t284 () (or @t188 @t279)) % 0.53/0.72 (define @t285 () (or @t269 @t274 @t265)) % 0.53/0.72 (define @t286 () (@list @t285)) % 0.53/0.72 (define @t287 () (forall @t16 (or @t157 (not (tptp.apply @t123 @t152 @t13)) (not (tptp.apply @t119 @t13 @t152))))) % 0.53/0.72 (define @t288 () (@quantifiers_skolemize @t287 0)) % 0.53/0.72 (define @t289 () (not @t287)) % 0.53/0.72 (define @t290 () (tptp.apply @t129 @t152 @t152)) % 0.53/0.72 (define @t291 () (= @t290 @t289)) % 0.53/0.72 (define @t292 () (or @t164 @t164 @t291)) % 0.53/0.72 (define @t293 () (or @t164 @t290)) % 0.53/0.72 (define @t294 () (tptp.apply @t123 @t152 @t288)) % 0.53/0.72 (define @t295 () (tptp.apply @t119 @t288 @t152)) % 0.53/0.72 (define @t296 () (not @t295)) % 0.53/0.72 (define @t297 () (not @t294)) % 0.53/0.72 (define @t298 () (tptp.member @t288 @t118)) % 0.53/0.72 (define @t299 () (not @t298)) % 0.53/0.72 (define @t300 () (or @t299 @t297 @t296)) % 0.53/0.72 (define @t301 () (@list @t300)) % 0.53/0.72 (define @t302 () (or @t101 @t106 @t75)) % 0.53/0.72 (define @t303 () (tptp.apply @t123 @t152 @t153)) % 0.53/0.72 (define @t304 () (or @t164 @t188 (= @t303 @t185))) % 0.53/0.72 (define @t305 () (forall @t76 @t302)) % 0.53/0.72 (define @t306 () (= @t185 @t303)) % 0.53/0.72 (define @t307 () (or @t164 @t188 @t306)) % 0.53/0.72 (define @t308 () (= @t153 @t288)) % 0.53/0.72 (define @t309 () (not @t303)) % 0.53/0.72 (define @t310 () (or @t164 @t188 @t299 @t309 @t297 @t308)) % 0.53/0.72 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.53/0.72 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.53/0.72 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.53/0.72 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.53/0.72 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.53/0.72 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.53/0.72 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.53/0.72 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.53/0.72 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.53/0.72 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.53/0.72 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.53/0.72 (assume @p12 @t40) % 0.53/0.72 (assume @p13 (forall (@list @t46 @t42 @t20 @t4 @t1 @t47) (= (tptp.compose_predicate @t46 @t42 @t20 @t4 @t1 @t47) (forall (@list @t2 @t41) (=> @t49 (= (tptp.apply @t46 @t2 @t41) @t45)))))) % 0.53/0.72 (assume @p14 @t53) % 0.53/0.72 (assume @p15 @t60) % 0.53/0.72 (assume @p16 @t65) % 0.53/0.72 (assume @p17 (forall @t39 (= @t70 (forall (@list @t67 @t66 @t13) (=> (and @t69 @t68 @t31) (=> (and (tptp.apply @t20 @t67 @t13) (tptp.apply @t20 @t66 @t13)) (= @t67 @t66))))))) % 0.53/0.72 (assume @p18 (forall @t39 (= @t71 (forall @t16 (=> @t31 (exists (@list @t11) (and (tptp.member @t11 @t4) (tptp.apply @t20 @t11 @t13)))))))) % 0.53/0.72 (assume @p19 (forall @t39 (= @t72 (and @t70 @t71)))) % 0.53/0.72 (assume @p20 (forall (@list @t42 @t20 @t4 @t1) (= (tptp.inverse_predicate @t42 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t73 (= @t30 (tptp.apply @t42 @t13 @t2))))))) % 0.53/0.72 (assume @p21 @t77) % 0.53/0.72 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t78))) % 0.53/0.72 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t31 @t78)))) % 0.53/0.72 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t33))) % 0.53/0.72 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t33)))) % 0.53/0.72 (assume @p26 (forall @t87 (= (tptp.increasing @t20 @t4 @t83 @t1 @t79) (forall @t86 (=> @t85 @t80))))) % 0.53/0.72 (assume @p27 (forall @t87 (= (tptp.decreasing @t20 @t4 @t83 @t1 @t79) (forall @t86 (=> @t85 (tptp.apply @t79 @t17 @t18)))))) % 0.53/0.72 (assume @p28 (forall @t87 (= (tptp.isomorphism @t20 @t4 @t83 @t1 @t79) (and @t37 @t72 (forall @t86 (=> (and @t69 @t26 @t68 @t25 @t82 @t81) (= @t84 @t80))))))) % 0.53/0.72 (assume @p29 @t96) % 0.53/0.72 (assume @p30 true) % 0.53/0.72 (step @p31 :rule evaluate :args ((= true false))) % 0.53/0.72 (step @p32 :rule aci_norm :args ((= (or @t103 @t102) (or @t101 @t100 @t99 @t98 @t97 @t19)))) % 0.53/0.72 (step @p33 :rule aci_norm :args ((= (or (or @t98 @t97) @t19) @t102))) % 0.53/0.72 (step @p34 :rule refl :args (@t19)) % 0.53/0.72 (step @p35 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.53/0.72 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((or (not @t23) @t19))) % 0.53/0.72 (step @p37 :rule trans :premises (@p36 @p33)) % 0.53/0.72 (step @p38 :rule bool-impl-elim :args (@t23 @t19)) % 0.53/0.72 (step @p39 :rule trans :premises (@p38 @p37)) % 0.53/0.72 (step @p40 :rule aci_norm :args ((= (or @t101 (or @t100 @t99)) @t103))) % 0.53/0.72 (step @p41 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.53/0.72 (step @p42 :rule refl :args (@t101)) % 0.53/0.72 (step @p43 :rule nary_cong :premises (@p42 @p41) :args ((or @t101 (not (and @t26 @t25))))) % 0.53/0.72 (step @p44 :rule bool-and-de-morgan :args (@t5 @t26 (and @t25))) % 0.53/0.72 (step @p45 :rule trans :premises (@p44 @p43)) % 0.53/0.72 (step @p46 :rule trans :premises (@p45 @p40)) % 0.53/0.72 (step @p47 :rule nary_cong :premises (@p46 @p39) :args ((or @t104 @t24))) % 0.53/0.72 (step @p48 :rule trans :premises (@p47 @p32)) % 0.53/0.72 (step @p49 :rule bool-impl-elim :args (@t27 @t24)) % 0.53/0.72 (step @p50 :rule trans :premises (@p49 @p48)) % 0.53/0.72 (step @p51 :rule cong :premises (@p50) :args (@t29)) % 0.53/0.72 (step @p52 :rule bool-impl-elim :args (@t5 @t107)) % 0.53/0.72 (step @p53 :rule cong :premises (@p52) :args ((forall @t6 (=> @t5 @t107)))) % 0.53/0.72 (step @p54 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.53/0.72 (step @p55 :rule cong :premises (@p54) :args (@t108)) % 0.53/0.72 (step @p56 :rule cong :premises (@p55) :args (@t109)) % 0.53/0.72 (step @p57 :rule exists-elim :args ((= @t33 @t109))) % 0.53/0.72 (step @p58 :rule trans :premises (@p57 @p56)) % 0.53/0.72 (step @p59 :rule refl :args (@t5)) % 0.53/0.72 (step @p60 :rule cong :premises (@p59 @p58) :args (@t34)) % 0.53/0.72 (step @p61 :rule cong :premises (@p60) :args (@t35)) % 0.53/0.72 (step @p62 :rule trans :premises (@p61 @p53)) % 0.53/0.72 (step @p63 :rule nary_cong :premises (@p62 @p51) :args (@t36)) % 0.53/0.72 (step @p64 :rule refl :args (@t37)) % 0.53/0.72 (step @p65 :rule cong :premises (@p64 @p63) :args (@t38)) % 0.53/0.72 (step @p66 :rule cong :premises (@p65) :args (@t40)) % 0.53/0.72 (step @p67 :rule eq_resolve :premises (@p12 @p66)) % 0.53/0.72 (step @p68 :rule instantiate :premises (@p67) :args ((@list @t119 @t118 @t117))) % 0.53/0.72 (step @p69 :rule aci_norm :args ((= (or @t120 @t88) @t115))) % 0.53/0.72 (step @p70 :rule refl :args (@t88)) % 0.53/0.72 (step @p71 :rule aci_norm :args ((= (or @t114 (or @t113 (or @t112 (or @t111 @t110)))) @t120))) % 0.53/0.72 (step @p72 :rule bool-and-de-morgan :args (@t90 @t89 true)) % 0.53/0.72 (step @p73 :rule refl :args (@t112)) % 0.53/0.72 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t112 (not (and @t90 @t89))))) % 0.53/0.72 (step @p75 :rule bool-and-de-morgan :args (@t91 @t90 (and @t89))) % 0.53/0.72 (step @p76 :rule trans :premises (@p75 @p74)) % 0.53/0.72 (step @p77 :rule refl :args (@t113)) % 0.53/0.72 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t113 (not (and @t91 @t90 @t89))))) % 0.53/0.72 (step @p79 :rule bool-and-de-morgan :args (@t92 @t91 (and @t90 @t89))) % 0.53/0.72 (step @p80 :rule trans :premises (@p79 @p78)) % 0.53/0.72 (step @p81 :rule refl :args (@t114)) % 0.53/0.72 (step @p82 :rule nary_cong :premises (@p81 @p80) :args ((or @t114 (not (and @t92 @t91 @t90 @t89))))) % 0.53/0.72 (step @p83 :rule bool-and-de-morgan :args (@t37 @t92 (and @t91 @t90 @t89))) % 0.53/0.72 (step @p84 :rule trans :premises (@p83 @p82)) % 0.53/0.72 (step @p85 :rule trans :premises (@p84 @p71)) % 0.53/0.72 (step @p86 :rule nary_cong :premises (@p85 @p70) :args ((or (not @t93) @t88))) % 0.53/0.72 (step @p87 :rule trans :premises (@p86 @p69)) % 0.53/0.72 (step @p88 :rule bool-impl-elim :args (@t93 @t88)) % 0.53/0.72 (step @p89 :rule trans :premises (@p88 @p87)) % 0.53/0.72 (step @p90 :rule cong :premises (@p89) :args (@t95)) % 0.53/0.72 (step @p91 :rule cong :premises (@p90) :args (@t96)) % 0.53/0.72 (step @p92 :rule eq_resolve :premises (@p29 @p91)) % 0.53/0.72 (step @p93 :rule skolemize :premises (@p92)) % 0.53/0.72 (step @p94 :rule bool-double-not-elim :args (@t121)) % 0.53/0.72 (step @p95 :rule refl :args (@t137)) % 0.53/0.72 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or @t137 (not @t134)))) % 0.53/0.72 (step @p97 :rule cnf_or_neg :args (@t137 1)) % 0.53/0.72 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 0.53/0.72 (step @p99 :rule reordering :premises (@p98) :args ((or @t121 @t137))) % 0.53/0.72 (step @p100 :rule chain_m_resolution :premises (@p99 @p93) :args (@t121 @t138 @t139)) % 0.53/0.72 (step @p101 :rule cnf_equiv_pos1 :args (@t146)) % 0.53/0.72 (step @p102 :rule reordering :premises (@p101) :args ((or @t134 @t145 (not @t146)))) % 0.53/0.72 (step @p103 :rule chain_m_resolution :premises (@p102 @p100 @p68) :args (@t145 @t147 (@list @t121 @t146))) % 0.53/0.72 (step @p104 :rule cnf_and_pos :args (@t145 1)) % 0.53/0.72 (step @p105 :rule 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:args (@t305)) % 0.53/0.72 (step @p519 :rule cong :premises (@p518 @p517) :args ((=> @t305 @t304))) % 0.53/0.72 (assume-push @p564 @t305) % 0.53/0.72 (step @p521 :rule instantiate :premises (@p515) :args ((@list @t123 @t117 @t118 @t152 @t153))) % 0.53/0.72 (step-pop @p565 :rule scope :premises (@p521)) % 0.53/0.72 (step @p522 :rule process_scope :premises (@p565) :args (@t304)) % 0.53/0.72 (step @p524 :rule eq_resolve :premises (@p522 @p519)) % 0.53/0.72 (step @p525 :rule implies_elim :premises (@p524)) % 0.53/0.72 (step @p526 :rule chain_m_resolution :premises (@p525 @p515) :args (@t307 @t148 (@list @t305))) % 0.53/0.72 (step @p527 :rule cnf_or_pos :args (@t307)) % 0.53/0.72 (step @p528 :rule reordering :premises (@p527) :args ((or @t188 @t164 @t306 (not @t307)))) % 0.53/0.72 (step @p529 :rule chain_m_resolution :premises (@p528 @p280 @p353 @p526) :args (@t306 (@list false false false) (@list @t187 @t163 @t307))) % 0.53/0.72 (step @p530 :rule bool-double-not-elim :args (@t185)) % 0.53/0.72 (step @p531 :rule nary_cong :premises (@p178 @p530) :args ((or @t189 (not @t186)))) % 0.53/0.72 (step @p532 :rule cnf_or_neg :args (@t189 3)) % 0.53/0.72 (step @p533 :rule eq_resolve :premises (@p532 @p531)) % 0.53/0.72 (step @p534 :rule reordering :premises (@p533) :args ((or @t185 @t189))) % 0.53/0.72 (step @p535 :rule chain_m_resolution :premises (@p534 @p176) :args (@t185 @t138 @t190)) % 0.53/0.72 (step @p536 :rule cnf_equiv_pos1 :args (@t306)) % 0.53/0.72 (step @p537 :rule reordering :premises (@p536) :args ((or @t186 @t303 (not @t306)))) % 0.53/0.72 (step @p538 :rule chain_m_resolution :premises (@p537 @p535 @p529) :args (@t303 @t147 (@list @t185 @t306))) % 0.53/0.72 (step @p539 :rule cnf_or_pos :args (@t310)) % 0.53/0.72 (step @p540 :rule reordering :premises (@p539) :args ((or @t188 @t164 @t309 @t299 @t297 @t308 (not @t310)))) % 0.53/0.72 (step @p541 :rule chain_m_resolution :premises (@p540 @p280 @p353 @p538 @p506 @p500 @p480) :args (@t308 @t242 (@list @t187 @t163 @t303 @t298 @t294 @t310))) % 0.53/0.72 (step @p542 :rule symm :premises (@p541)) % 0.53/0.72 (step @p543 :rule cong :premises (@p342 @p542 @p358) :args (@t295)) % 0.53/0.72 (step @p544 :rule bool-double-not-elim :args (@t295)) % 0.53/0.72 (step @p545 :rule nary_cong :premises (@p495 @p544) :args ((or @t300 (not @t296)))) % 0.53/0.72 (step @p546 :rule cnf_or_neg :args (@t300 2)) % 0.53/0.72 (step @p547 :rule eq_resolve :premises (@p546 @p545)) % 0.53/0.72 (step @p548 :rule reordering :premises (@p547) :args ((or @t295 @t300))) % 0.53/0.72 (step @p549 :rule chain_m_resolution :premises (@p548 @p493) :args (@t295 @t138 @t301)) % 0.53/0.72 (step @p550 :rule true_intro :premises (@p549)) % 0.53/0.72 (step @p551 :rule symm :premises (@p550)) % 0.53/0.72 (step @p552 :rule trans :premises (@p551 @p543 @p479 @p357)) % 0.53/0.72 (step @p553 false :rule eq_resolve :premises (@p552 @p31)) % 0.53/0.72 ) % 0.53/0.72 % SZS output end Proof % 0.53/0.73 % cvc5 exiting %------------------------------------------------------------------------------