%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET709+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:48:29 AM UTC 2026 % Result : Theorem 0.46s 0.66s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET709+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n015.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:10:04 EDT 2026 % 0.18/0.35 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.66 % SZS status Theorem % 0.46/0.66 % SZS output start Proof % 0.46/0.66 ( % 0.46/0.66 (declare-sort $$unsorted 0) % 0.46/0.66 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.empty_set $$unsorted) % 0.46/0.66 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (define @t1 () (@var "B" $$unsorted)) % 0.46/0.66 (define @t2 () (@var "X" $$unsorted)) % 0.46/0.66 (define @t3 () (tptp.member @t2 @t1)) % 0.46/0.66 (define @t4 () (@var "A" $$unsorted)) % 0.46/0.66 (define @t5 () (tptp.member @t2 @t4)) % 0.46/0.66 (define @t6 () (@list @t2)) % 0.46/0.66 (define @t7 () (tptp.subset @t4 @t1)) % 0.46/0.66 (define @t8 () (@list @t4 @t1)) % 0.46/0.66 (define @t9 () (@list @t2 @t4)) % 0.46/0.66 (define @t10 () (@list @t2 @t4 @t1)) % 0.46/0.66 (define @t11 () (@var "E" $$unsorted)) % 0.46/0.66 (define @t12 () (= @t2 @t4)) % 0.46/0.66 (define @t13 () (@var "Y" $$unsorted)) % 0.46/0.66 (define @t14 () (tptp.member @t2 @t13)) % 0.46/0.66 (define @t15 () (tptp.member @t13 @t4)) % 0.46/0.66 (define @t16 () (@list @t13)) % 0.46/0.66 (define @t17 () (@var "Y2" $$unsorted)) % 0.46/0.66 (define @t18 () (@var "Y1" $$unsorted)) % 0.46/0.66 (define @t19 () (= @t18 @t17)) % 0.46/0.66 (define @t20 () (@var "F" $$unsorted)) % 0.46/0.66 (define @t21 () (tptp.apply @t20 @t2 @t17)) % 0.46/0.66 (define @t22 () (tptp.apply @t20 @t2 @t18)) % 0.46/0.66 (define @t23 () (and @t22 @t21)) % 0.46/0.66 (define @t24 () (=> @t23 @t19)) % 0.46/0.66 (define @t25 () (tptp.member @t17 @t1)) % 0.46/0.66 (define @t26 () (tptp.member @t18 @t1)) % 0.46/0.66 (define @t27 () (and @t5 @t26 @t25)) % 0.46/0.66 (define @t28 () (@list @t2 @t18 @t17)) % 0.46/0.66 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.46/0.66 (define @t30 () (tptp.apply @t20 @t2 @t13)) % 0.46/0.66 (define @t31 () (tptp.member @t13 @t1)) % 0.46/0.66 (define @t32 () (and @t31 @t30)) % 0.46/0.66 (define @t33 () (exists @t16 @t32)) % 0.46/0.66 (define @t34 () (=> @t5 @t33)) % 0.46/0.66 (define @t35 () (forall @t6 @t34)) % 0.46/0.66 (define @t36 () (and @t35 @t29)) % 0.46/0.66 (define @t37 () (tptp.maps @t20 @t4 @t1)) % 0.46/0.66 (define @t38 () (= @t37 @t36)) % 0.46/0.66 (define @t39 () (@list @t20 @t4 @t1)) % 0.46/0.66 (define @t40 () (forall @t39 @t38)) % 0.46/0.66 (define @t41 () (@var "Z" $$unsorted)) % 0.46/0.66 (define @t42 () (@var "G" $$unsorted)) % 0.46/0.66 (define @t43 () (tptp.apply @t42 @t13 @t41)) % 0.46/0.66 (define @t44 () (and @t31 @t30 @t43)) % 0.46/0.66 (define @t45 () (exists @t16 @t44)) % 0.46/0.66 (define @t46 () (@var "H" $$unsorted)) % 0.46/0.66 (define @t47 () (@var "C" $$unsorted)) % 0.46/0.66 (define @t48 () (tptp.member @t41 @t47)) % 0.46/0.66 (define @t49 () (and @t5 @t48)) % 0.46/0.66 (define @t50 () (tptp.compose_function @t42 @t20 @t4 @t1 @t47)) % 0.46/0.66 (define @t51 () (tptp.apply @t50 @t2 @t41)) % 0.46/0.66 (define @t52 () (=> @t49 (= @t51 @t45))) % 0.46/0.66 (define @t53 () (@list @t42 @t20 @t4 @t1 @t47 @t2 @t41)) % 0.46/0.66 (define @t54 () (forall @t53 @t52)) % 0.46/0.66 (define @t55 () (@var "X2" $$unsorted)) % 0.46/0.66 (define @t56 () (@var "X1" $$unsorted)) % 0.46/0.66 (define @t57 () (tptp.member @t55 @t4)) % 0.46/0.66 (define @t58 () (tptp.member @t56 @t4)) % 0.46/0.66 (define @t59 () (tptp.injective @t20 @t4 @t1)) % 0.46/0.66 (define @t60 () (tptp.surjective @t20 @t4 @t1)) % 0.46/0.66 (define @t61 () (tptp.one_to_one @t20 @t4 @t1)) % 0.46/0.66 (define @t62 () (and @t5 @t31)) % 0.46/0.66 (define @t63 () (exists @t6 (and @t5 @t30))) % 0.46/0.66 (define @t64 () (@var "S" $$unsorted)) % 0.46/0.66 (define @t65 () (tptp.apply @t64 @t18 @t17)) % 0.46/0.66 (define @t66 () (tptp.apply @t20 @t55 @t17)) % 0.46/0.66 (define @t67 () (tptp.apply @t20 @t56 @t18)) % 0.46/0.66 (define @t68 () (@var "R" $$unsorted)) % 0.46/0.66 (define @t69 () (tptp.apply @t68 @t56 @t55)) % 0.46/0.66 (define @t70 () (and @t58 @t26 @t57 @t25 @t69 @t67 @t66)) % 0.46/0.66 (define @t71 () (@list @t56 @t18 @t55 @t17)) % 0.46/0.66 (define @t72 () (@list @t20 @t4 @t68 @t1 @t64)) % 0.46/0.66 (define @t73 () (tptp.maps @t50 @t4 @t47)) % 0.46/0.66 (define @t74 () (tptp.maps @t42 @t1 @t47)) % 0.46/0.66 (define @t75 () (and @t37 @t74)) % 0.46/0.66 (define @t76 () (@list @t20 @t42 @t4 @t1 @t47)) % 0.46/0.66 (define @t77 () (forall @t76 (=> @t75 @t73))) % 0.46/0.66 (define @t78 () (not @t77)) % 0.46/0.66 (define @t79 () (not @t21)) % 0.46/0.66 (define @t80 () (not @t22)) % 0.46/0.66 (define @t81 () (not @t25)) % 0.46/0.66 (define @t82 () (not @t26)) % 0.46/0.66 (define @t83 () (not @t5)) % 0.46/0.66 (define @t84 () (or @t80 @t79 @t19)) % 0.46/0.66 (define @t85 () (or @t83 @t82 @t81)) % 0.46/0.66 (define @t86 () (not @t30)) % 0.46/0.66 (define @t87 () (not @t31)) % 0.46/0.66 (define @t88 () (not (forall @t16 (or @t87 @t86)))) % 0.46/0.66 (define @t89 () (forall @t16 (not @t32))) % 0.46/0.66 (define @t90 () (not @t89)) % 0.46/0.66 (define @t91 () (not @t74)) % 0.46/0.66 (define @t92 () (not @t37)) % 0.46/0.66 (define @t93 () (or @t92 @t91 @t73)) % 0.46/0.66 (define @t94 () (forall @t76 @t93)) % 0.46/0.66 (define @t95 () (@quantifiers_skolemize @t94 4)) % 0.46/0.66 (define @t96 () (@quantifiers_skolemize @t94 3)) % 0.46/0.66 (define @t97 () (@quantifiers_skolemize @t94 1)) % 0.46/0.66 (define @t98 () (tptp.maps @t97 @t96 @t95)) % 0.46/0.66 (define @t99 () (@quantifiers_skolemize @t94 2)) % 0.46/0.66 (define @t100 () (@quantifiers_skolemize @t94 0)) % 0.46/0.66 (define @t101 () (tptp.compose_function @t97 @t100 @t99 @t96 @t95)) % 0.46/0.66 (define @t102 () (tptp.maps @t101 @t99 @t95)) % 0.46/0.66 (define @t103 () (not @t98)) % 0.46/0.66 (define @t104 () (tptp.maps @t100 @t99 @t96)) % 0.46/0.66 (define @t105 () (not @t104)) % 0.46/0.66 (define @t106 () (or @t105 @t103 @t102)) % 0.46/0.66 (define @t107 () (@list true)) % 0.46/0.66 (define @t108 () (@list @t106)) % 0.46/0.66 (define @t109 () (not (tptp.member @t17 @t95))) % 0.46/0.66 (define @t110 () (not (tptp.member @t18 @t95))) % 0.46/0.66 (define @t111 () (not (tptp.member @t2 @t96))) % 0.46/0.66 (define @t112 () (forall @t28 (or @t111 @t110 @t109 (not (tptp.apply @t97 @t2 @t18)) (not (tptp.apply @t97 @t2 @t17)) @t19))) % 0.46/0.66 (define @t113 () (not (tptp.member @t13 @t95))) % 0.46/0.66 (define @t114 () (forall @t6 (or @t111 (not (forall @t16 (or @t113 (not (tptp.apply @t97 @t2 @t13)))))))) % 0.46/0.66 (define @t115 () (and @t114 @t112)) % 0.46/0.66 (define @t116 () (= @t98 @t115)) % 0.46/0.66 (define @t117 () (@list false false)) % 0.46/0.66 (define @t118 () (not @t115)) % 0.46/0.66 (define @t119 () (@list false)) % 0.46/0.66 (define @t120 () (@list @t115)) % 0.46/0.66 (define @t121 () (not (tptp.member @t2 @t99))) % 0.46/0.66 (define @t122 () (forall @t28 (or @t121 @t110 @t109 (not (tptp.apply @t101 @t2 @t18)) (not (tptp.apply @t101 @t2 @t17)) @t19))) % 0.46/0.66 (define @t123 () (@quantifiers_skolemize @t122 1)) % 0.46/0.66 (define @t124 () (@quantifiers_skolemize @t122 0)) % 0.46/0.66 (define @t125 () (not (tptp.apply @t100 @t124 @t13))) % 0.46/0.66 (define @t126 () (not (tptp.member @t13 @t96))) % 0.46/0.66 (define @t127 () (forall @t16 (or @t126 @t125 (not (tptp.apply @t97 @t13 @t123))))) % 0.46/0.66 (define @t128 () (@quantifiers_skolemize @t127 0)) % 0.46/0.66 (define @t129 () (forall @t16 (or @t113 (not (tptp.apply @t97 @t128 @t13))))) % 0.46/0.66 (define @t130 () (@quantifiers_skolemize @t129 0)) % 0.46/0.66 (define @t131 () (not @t43)) % 0.46/0.66 (define @t132 () (or @t87 @t86 @t131)) % 0.46/0.66 (define @t133 () (not (forall @t16 @t132))) % 0.46/0.66 (define @t134 () (= @t51 @t133)) % 0.46/0.66 (define @t135 () (not @t48)) % 0.46/0.66 (define @t136 () (forall @t16 (not @t44))) % 0.46/0.66 (define @t137 () (not @t136)) % 0.46/0.66 (define @t138 () (forall @t6 (or @t121 (not (forall @t16 (or @t113 (not (tptp.apply @t101 @t2 @t13)))))))) % 0.46/0.66 (define @t139 () (@quantifiers_skolemize @t138 0)) % 0.46/0.66 (define @t140 () (tptp.member @t139 @t99)) % 0.46/0.66 (define @t141 () (forall @t16 (or @t113 (not (tptp.apply @t101 @t139 @t13))))) % 0.46/0.66 (define @t142 () (not @t141)) % 0.46/0.66 (define @t143 () (not @t140)) % 0.46/0.66 (define @t144 () (or @t143 @t142)) % 0.46/0.66 (define @t145 () (forall @t28 (or @t121 (not (tptp.member @t18 @t96)) (not (tptp.member @t17 @t96)) (not (tptp.apply @t100 @t2 @t18)) (not (tptp.apply @t100 @t2 @t17)) @t19))) % 0.46/0.66 (define @t146 () (forall @t6 (or @t121 (not (forall @t16 (or @t126 (not (tptp.apply @t100 @t2 @t13)))))))) % 0.46/0.66 (define @t147 () (and @t146 @t145)) % 0.46/0.66 (define @t148 () (= @t104 @t147)) % 0.46/0.66 (define @t149 () (not @t147)) % 0.46/0.66 (define @t150 () (@list @t147)) % 0.46/0.66 (define @t151 () (not (tptp.apply @t100 @t139 @t13))) % 0.46/0.66 (define @t152 () (forall @t16 (or @t126 @t151))) % 0.46/0.66 (define @t153 () (not @t152)) % 0.46/0.66 (define @t154 () (or @t143 @t153)) % 0.46/0.66 (define @t155 () (@quantifiers_skolemize @t152 0)) % 0.46/0.66 (define @t156 () (forall @t16 (or @t113 (not (tptp.apply @t97 @t155 @t13))))) % 0.46/0.66 (define @t157 () (@quantifiers_skolemize @t156 0)) % 0.46/0.66 (define @t158 () (tptp.apply @t101 @t139 @t157)) % 0.46/0.66 (define @t159 () (not @t158)) % 0.46/0.66 (define @t160 () (tptp.member @t157 @t95)) % 0.46/0.66 (define @t161 () (not @t160)) % 0.46/0.66 (define @t162 () (or @t161 @t159)) % 0.46/0.66 (define @t163 () (tptp.apply @t100 @t139 @t155)) % 0.46/0.66 (define @t164 () (not @t163)) % 0.46/0.66 (define @t165 () (tptp.member @t155 @t96)) % 0.46/0.66 (define @t166 () (not @t165)) % 0.46/0.66 (define @t167 () (or @t166 @t164)) % 0.46/0.66 (define @t168 () (not @t167)) % 0.46/0.66 (define @t169 () (@list @t155)) % 0.46/0.66 (define @t170 () (not @t156)) % 0.46/0.66 (define @t171 () (or @t166 @t170)) % 0.46/0.66 (define @t172 () (tptp.apply @t97 @t155 @t157)) % 0.46/0.66 (define @t173 () (not @t172)) % 0.46/0.66 (define @t174 () (or @t161 @t173)) % 0.46/0.66 (define @t175 () (not @t174)) % 0.46/0.66 (define @t176 () (forall @t16 (or @t126 @t151 (not (tptp.apply @t97 @t13 @t157))))) % 0.46/0.66 (define @t177 () (not @t176)) % 0.46/0.66 (define @t178 () (= @t158 @t177)) % 0.46/0.66 (define @t179 () (or @t143 @t161 @t178)) % 0.46/0.66 (define @t180 () (or @t166 @t164 @t173)) % 0.46/0.66 (define @t181 () (not @t178)) % 0.46/0.66 (define @t182 () (not @t144)) % 0.46/0.66 (define @t183 () (not @t138)) % 0.46/0.66 (define @t184 () (and @t138 @t122)) % 0.46/0.66 (define @t185 () (= @t102 @t184)) % 0.46/0.66 (define @t186 () (not @t184)) % 0.46/0.66 (define @t187 () (@list true false)) % 0.46/0.66 (define @t188 () (not @t122)) % 0.46/0.66 (define @t189 () (@quantifiers_skolemize @t122 2)) % 0.46/0.66 (define @t190 () (= @t123 @t189)) % 0.46/0.66 (define @t191 () (tptp.apply @t101 @t124 @t189)) % 0.46/0.66 (define @t192 () (not @t191)) % 0.46/0.66 (define @t193 () (tptp.apply @t101 @t124 @t123)) % 0.46/0.66 (define @t194 () (not @t193)) % 0.46/0.66 (define @t195 () (tptp.member @t189 @t95)) % 0.46/0.66 (define @t196 () (not @t195)) % 0.46/0.66 (define @t197 () (tptp.member @t123 @t95)) % 0.46/0.66 (define @t198 () (not @t197)) % 0.46/0.66 (define @t199 () (tptp.member @t124 @t99)) % 0.46/0.66 (define @t200 () (not @t199)) % 0.46/0.66 (define @t201 () (or @t200 @t198 @t196 @t194 @t192 @t190)) % 0.46/0.66 (define @t202 () (not @t201)) % 0.46/0.66 (define @t203 () (@list @t201)) % 0.46/0.66 (define @t204 () (not @t127)) % 0.46/0.66 (define @t205 () (= @t193 @t204)) % 0.46/0.66 (define @t206 () (or @t200 @t198 @t205)) % 0.46/0.66 (define @t207 () (@list false false false)) % 0.46/0.66 (define @t208 () (tptp.apply @t97 @t128 @t123)) % 0.46/0.66 (define @t209 () (not @t208)) % 0.46/0.66 (define @t210 () (tptp.apply @t100 @t124 @t128)) % 0.46/0.66 (define @t211 () (not @t210)) % 0.46/0.66 (define @t212 () (tptp.member @t128 @t96)) % 0.46/0.66 (define @t213 () (not @t212)) % 0.46/0.66 (define @t214 () (or @t213 @t211 @t209)) % 0.46/0.66 (define @t215 () (not @t214)) % 0.46/0.66 (define @t216 () (@list @t214)) % 0.46/0.66 (define @t217 () (not @t129)) % 0.46/0.66 (define @t218 () (or @t213 @t217)) % 0.46/0.66 (define @t219 () (tptp.apply @t97 @t128 @t130)) % 0.46/0.66 (define @t220 () (not @t219)) % 0.46/0.66 (define @t221 () (tptp.member @t130 @t95)) % 0.46/0.66 (define @t222 () (not @t221)) % 0.46/0.66 (define @t223 () (or @t222 @t220)) % 0.46/0.66 (define @t224 () (not @t223)) % 0.46/0.66 (define @t225 () (@list @t223)) % 0.46/0.66 (define @t226 () (= @t123 @t130)) % 0.46/0.66 (define @t227 () (or @t213 @t198 @t222 @t209 @t220 @t226)) % 0.46/0.66 (define @t228 () (@list false false false false false false)) % 0.46/0.66 (define @t229 () (forall @t16 (or @t126 @t125 (not (tptp.apply @t97 @t13 @t189))))) % 0.46/0.66 (define @t230 () (@quantifiers_skolemize @t229 0)) % 0.46/0.66 (define @t231 () (not @t229)) % 0.46/0.66 (define @t232 () (= @t191 @t231)) % 0.46/0.66 (define @t233 () (or @t200 @t196 @t232)) % 0.46/0.66 (define @t234 () (tptp.apply @t97 @t230 @t189)) % 0.46/0.66 (define @t235 () (not @t234)) % 0.46/0.66 (define @t236 () (tptp.apply @t100 @t124 @t230)) % 0.46/0.66 (define @t237 () (not @t236)) % 0.46/0.66 (define @t238 () (tptp.member @t230 @t96)) % 0.46/0.66 (define @t239 () (not @t238)) % 0.46/0.66 (define @t240 () (or @t239 @t237 @t235)) % 0.46/0.66 (define @t241 () (not @t240)) % 0.46/0.66 (define @t242 () (@list @t240)) % 0.46/0.66 (define @t243 () (= @t230 @t128)) % 0.46/0.66 (define @t244 () (or @t200 @t239 @t213 @t237 @t211 @t243)) % 0.46/0.66 (define @t245 () (tptp.apply @t97 @t230 @t123)) % 0.46/0.66 (define @t246 () (and @t219 @t243 @t226)) % 0.46/0.66 (define @t247 () (not @t245)) % 0.46/0.66 (define @t248 () (or @t239 @t196 @t198 @t235 @t247 @t190)) % 0.46/0.66 (define @t249 () (not @t248)) % 0.46/0.66 (define @t250 () (or @t239 @t196 @t198 @t235 @t247 (= @t189 @t123))) % 0.46/0.66 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.46/0.66 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.46/0.66 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.46/0.66 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.46/0.66 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.46/0.66 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.46/0.66 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.46/0.66 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.46/0.66 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.46/0.66 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.46/0.66 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.46/0.66 (assume @p12 @t40) % 0.46/0.66 (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)))))) % 0.46/0.66 (assume @p14 @t54) % 0.46/0.66 (assume @p15 (forall (@list @t20 @t42 @t4 @t1) (= (tptp.equal_maps @t20 @t42 @t4 @t1) (forall @t28 (=> @t27 (=> (and @t22 (tptp.apply @t42 @t2 @t17)) @t19)))))) % 0.46/0.66 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.46/0.66 (assume @p17 (forall @t39 (= @t59 (forall (@list @t56 @t55 @t13) (=> (and @t58 @t57 @t31) (=> (and (tptp.apply @t20 @t56 @t13) (tptp.apply @t20 @t55 @t13)) (= @t56 @t55))))))) % 0.46/0.66 (assume @p18 (forall @t39 (= @t60 (forall @t16 (=> @t31 (exists (@list @t11) (and (tptp.member @t11 @t4) (tptp.apply @t20 @t11 @t13)))))))) % 0.46/0.66 (assume @p19 (forall @t39 (= @t61 (and @t59 @t60)))) % 0.46/0.66 (assume @p20 (forall (@list @t42 @t20 @t4 @t1) (= (tptp.inverse_predicate @t42 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t62 (= @t30 (tptp.apply @t42 @t13 @t2))))))) % 0.46/0.66 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t62 (= @t30 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.46/0.66 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t63))) % 0.46/0.66 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t31 @t63)))) % 0.46/0.66 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t33))) % 0.46/0.66 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t33)))) % 0.46/0.66 (assume @p26 (forall @t72 (= (tptp.increasing @t20 @t4 @t68 @t1 @t64) (forall @t71 (=> @t70 @t65))))) % 0.46/0.66 (assume @p27 (forall @t72 (= (tptp.decreasing @t20 @t4 @t68 @t1 @t64) (forall @t71 (=> @t70 (tptp.apply @t64 @t17 @t18)))))) % 0.46/0.66 (assume @p28 (forall @t72 (= (tptp.isomorphism @t20 @t4 @t68 @t1 @t64) (and @t37 @t61 (forall @t71 (=> (and @t58 @t26 @t57 @t25 @t67 @t66) (= @t69 @t65))))))) % 0.46/0.66 (assume @p29 @t78) % 0.46/0.66 (assume @p30 true) % 0.46/0.66 (step @p31 :rule aci_norm :args ((= (or @t85 @t84) (or @t83 @t82 @t81 @t80 @t79 @t19)))) % 0.46/0.66 (step @p32 :rule aci_norm :args ((= (or (or @t80 @t79) @t19) @t84))) % 0.46/0.66 (step @p33 :rule refl :args (@t19)) % 0.46/0.66 (step @p34 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.46/0.66 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or (not @t23) @t19))) % 0.46/0.66 (step @p36 :rule trans :premises (@p35 @p32)) % 0.46/0.66 (step @p37 :rule bool-impl-elim :args (@t23 @t19)) % 0.46/0.66 (step @p38 :rule trans :premises (@p37 @p36)) % 0.46/0.66 (step @p39 :rule aci_norm :args ((= (or @t83 (or @t82 @t81)) @t85))) % 0.46/0.66 (step @p40 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.46/0.66 (step @p41 :rule refl :args (@t83)) % 0.46/0.66 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t83 (not (and @t26 @t25))))) % 0.46/0.66 (step @p43 :rule bool-and-de-morgan :args (@t5 @t26 (and @t25))) % 0.46/0.66 (step @p44 :rule trans :premises (@p43 @p42)) % 0.46/0.66 (step @p45 :rule trans :premises (@p44 @p39)) % 0.46/0.66 (step @p46 :rule nary_cong :premises (@p45 @p38) :args ((or (not @t27) @t24))) % 0.46/0.66 (step @p47 :rule trans :premises (@p46 @p31)) % 0.46/0.66 (step @p48 :rule bool-impl-elim :args (@t27 @t24)) % 0.46/0.66 (step @p49 :rule trans :premises (@p48 @p47)) % 0.46/0.66 (step @p50 :rule cong :premises (@p49) :args (@t29)) % 0.46/0.66 (step @p51 :rule bool-impl-elim :args (@t5 @t88)) % 0.46/0.66 (step @p52 :rule cong :premises (@p51) :args ((forall @t6 (=> @t5 @t88)))) % 0.46/0.66 (step @p53 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.46/0.66 (step @p54 :rule cong :premises (@p53) :args (@t89)) % 0.46/0.66 (step @p55 :rule cong :premises (@p54) :args (@t90)) % 0.46/0.66 (step @p56 :rule exists-elim :args ((= @t33 @t90))) % 0.46/0.66 (step @p57 :rule trans :premises (@p56 @p55)) % 0.46/0.66 (step @p58 :rule refl :args (@t5)) % 0.46/0.66 (step @p59 :rule cong :premises (@p58 @p57) :args (@t34)) % 0.46/0.66 (step @p60 :rule cong :premises (@p59) :args (@t35)) % 0.46/0.66 (step @p61 :rule trans :premises (@p60 @p52)) % 0.46/0.66 (step @p62 :rule nary_cong :premises (@p61 @p50) :args (@t36)) % 0.46/0.66 (step @p63 :rule refl :args (@t37)) % 0.46/0.66 (step @p64 :rule cong :premises (@p63 @p62) :args (@t38)) % 0.46/0.66 (step @p65 :rule cong :premises (@p64) :args (@t40)) % 0.46/0.66 (step @p66 :rule eq_resolve :premises (@p12 @p65)) % 0.46/0.66 (step @p67 :rule instantiate :premises (@p66) :args ((@list @t97 @t96 @t95))) % 0.46/0.66 (step @p68 :rule aci_norm :args ((= (or (or @t92 @t91) @t73) @t93))) % 0.46/0.66 (step @p69 :rule refl :args (@t73)) % 0.46/0.66 (step @p70 :rule bool-and-de-morgan :args (@t37 @t74 true)) % 0.46/0.66 (step @p71 :rule nary_cong :premises (@p70 @p69) :args ((or (not @t75) @t73))) % 0.46/0.66 (step @p72 :rule trans :premises (@p71 @p68)) % 0.46/0.66 (step @p73 :rule bool-impl-elim :args (@t75 @t73)) % 0.46/0.66 (step @p74 :rule trans :premises (@p73 @p72)) % 0.46/0.66 (step @p75 :rule cong :premises (@p74) :args (@t77)) % 0.46/0.66 (step @p76 :rule cong :premises (@p75) :args (@t78)) % 0.46/0.66 (step @p77 :rule eq_resolve :premises (@p29 @p76)) % 0.46/0.66 (step @p78 :rule skolemize :premises (@p77)) % 0.46/0.66 (step @p79 :rule bool-double-not-elim :args (@t98)) % 0.46/0.66 (step @p80 :rule refl :args (@t106)) % 0.46/0.66 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t106 (not @t103)))) % 0.46/0.66 (step @p82 :rule cnf_or_neg :args (@t106 1)) % 0.46/0.66 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.46/0.66 (step @p84 :rule reordering :premises (@p83) :args ((or @t98 @t106))) % 0.46/0.66 (step @p85 :rule chain_m_resolution :premises (@p84 @p78) :args (@t98 @t107 @t108)) % 0.46/0.66 (step @p86 :rule cnf_equiv_pos1 :args (@t116)) % 0.46/0.66 (step @p87 :rule reordering :premises (@p86) :args ((or @t103 @t115 (not @t116)))) % 0.46/0.66 (step @p88 :rule chain_m_resolution :premises (@p87 @p85 @p67) :args (@t115 @t117 (@list @t98 @t116))) % 0.46/0.66 (step @p89 :rule cnf_and_pos :args (@t115 1)) % 0.46/0.66 (step @p90 :rule reordering :premises (@p89) :args ((or @t112 @t118))) % 0.46/0.66 (step @p91 :rule chain_m_resolution :premises (@p90 @p88) :args (@t112 @t119 @t120)) % 0.46/0.66 (step @p92 :rule instantiate :premises (@p91) :args ((@list @t128 @t123 @t130))) % 0.46/0.66 (step @p93 :rule cnf_and_pos :args (@t115 0)) % 0.46/0.66 (step @p94 :rule reordering :premises (@p93) :args ((or @t114 @t118))) % 0.46/0.66 (step @p95 :rule chain_m_resolution :premises (@p94 @p88) :args (@t114 @t119 @t120)) % 0.46/0.66 (step @p96 :rule instantiate :premises (@p95) :args ((@list @t128))) % 0.46/0.66 (step @p97 :rule aci_norm :args ((= (or (or @t83 @t135) @t134) (or @t83 @t135 @t134)))) % 0.46/0.66 (step @p98 :rule refl :args (@t134)) % 0.46/0.66 (step @p99 :rule bool-and-de-morgan :args (@t5 @t48 true)) % 0.46/0.66 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or (not @t49) @t134))) % 0.46/0.66 (step @p101 :rule trans :premises (@p100 @p97)) % 0.46/0.66 (step @p102 :rule bool-impl-elim :args (@t49 @t134)) % 0.46/0.66 (step @p103 :rule trans :premises (@p102 @p101)) % 0.46/0.66 (step @p104 :rule cong :premises (@p103) :args ((forall @t53 (=> @t49 @t134)))) % 0.46/0.66 (step @p105 :rule eq-symm :args (@t133 @t51)) % 0.46/0.66 (step @p106 :rule refl :args (@t51)) % 0.46/0.66 (step @p107 :rule aci_norm :args ((= (or @t87 (or @t86 @t131)) @t132))) % 0.46/0.66 (step @p108 :rule bool-and-de-morgan :args (@t30 @t43 true)) % 0.46/0.66 (step @p109 :rule refl :args (@t87)) % 0.46/0.66 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t87 (not (and @t30 @t43))))) % 0.46/0.66 (step @p111 :rule bool-and-de-morgan :args (@t31 @t30 (and @t43))) % 0.46/0.66 (step @p112 :rule trans :premises (@p111 @p110)) % 0.46/0.66 (step @p113 :rule trans :premises (@p112 @p107)) % 0.46/0.66 (step @p114 :rule cong :premises (@p113) :args (@t136)) % 0.46/0.66 (step @p115 :rule cong :premises (@p114) :args (@t137)) % 0.46/0.66 (step @p116 :rule exists-elim :args ((= @t45 @t137))) % 0.46/0.66 (step @p117 :rule trans :premises (@p116 @p115)) % 0.46/0.66 (step @p118 :rule cong :premises (@p117 @p106) :args ((= @t45 @t51))) % 0.46/0.66 (step @p119 :rule trans :premises (@p118 @p105)) % 0.46/0.66 (step @p120 :rule eq-symm :args (@t51 @t45)) % 0.46/0.66 (step @p121 :rule trans :premises (@p120 @p119)) % 0.46/0.66 (step @p122 :rule refl :args (@t49)) % 0.46/0.66 (step @p123 :rule cong :premises (@p122 @p121) :args (@t52)) % 0.46/0.66 (step @p124 :rule cong :premises (@p123) :args (@t54)) % 0.46/0.66 (step @p125 :rule trans :premises (@p124 @p104)) % 0.46/0.66 (step @p126 :rule eq_resolve :premises (@p14 @p125)) % 0.46/0.66 (step @p127 :rule instantiate :premises (@p126) :args ((@list @t97 @t100 @t99 @t96 @t95 @t124 @t123))) % 0.46/0.66 (step @p128 :rule bool-double-not-elim :args (@t140)) % 0.46/0.66 (step @p129 :rule refl :args (@t144)) % 0.46/0.66 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or @t144 (not @t143)))) % 0.46/0.66 (step @p131 :rule cnf_or_neg :args (@t144 0)) % 0.46/0.66 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 0.46/0.66 (step @p133 :rule reordering :premises (@p132) :args ((or @t140 @t144))) % 0.46/0.66 (step @p134 :rule bool-double-not-elim :args (@t141)) % 0.46/0.66 (step @p135 :rule nary_cong :premises (@p129 @p134) :args ((or @t144 (not @t142)))) % 0.46/0.66 (step @p136 :rule cnf_or_neg :args (@t144 1)) % 0.46/0.66 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.46/0.66 (step @p138 :rule reordering :premises (@p137) :args ((or @t141 @t144))) % 0.46/0.66 (step @p139 :rule instantiate :premises (@p66) :args ((@list @t100 @t99 @t96))) % 0.46/0.66 (step @p140 :rule bool-double-not-elim :args (@t104)) % 0.46/0.66 (step @p141 :rule nary_cong :premises (@p80 @p140) :args ((or @t106 (not @t105)))) % 0.46/0.66 (step @p142 :rule cnf_or_neg :args (@t106 0)) % 0.46/0.66 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.46/0.66 (step @p144 :rule reordering :premises (@p143) :args ((or @t104 @t106))) % 0.46/0.66 (step @p145 :rule chain_m_resolution :premises (@p144 @p78) :args (@t104 @t107 @t108)) % 0.46/0.66 (step @p146 :rule cnf_equiv_pos1 :args (@t148)) % 0.46/0.66 (step @p147 :rule reordering :premises (@p146) :args ((or @t105 @t147 (not @t148)))) % 0.46/0.66 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p139) :args (@t147 @t117 (@list @t104 @t148))) % 0.46/0.66 (step @p149 :rule cnf_and_pos :args (@t147 0)) % 0.46/0.66 (step @p150 :rule reordering :premises (@p149) :args ((or @t146 @t149))) % 0.46/0.66 (step @p151 :rule chain_m_resolution 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(assume-push @p455 @t243) % 0.46/0.66 (assume-push @p456 @t226) % 0.46/0.66 (assume-push @p457 @t219) % 0.46/0.66 (assume-push @p458 @t243) % 0.46/0.66 (assume-push @p459 @t226) % 0.46/0.66 (step @p389 :rule true_intro :premises (@p454)) % 0.46/0.66 (step @p390 :rule refl :args (@t97)) % 0.46/0.66 (step @p391 :rule cong :premises (@p390 @p455 @p456) :args (@t245)) % 0.46/0.66 (step @p392 :rule trans :premises (@p391 @p389)) % 0.46/0.66 (step @p393 :rule true_elim :premises (@p392)) % 0.46/0.66 (step-pop @p460 :rule scope :premises (@p393)) % 0.46/0.66 (step-pop @p461 :rule scope :premises (@p460)) % 0.46/0.66 (step-pop @p462 :rule scope :premises (@p461)) % 0.46/0.66 (step @p394 :rule process_scope :premises (@p462) :args (@t245)) % 0.46/0.66 (step @p398 :rule and_intro :premises (@p454 @p455 @p456)) % 0.46/0.66 (step @p399 :rule modus_ponens :premises (@p398 @p394)) % 0.46/0.66 (step-pop @p463 :rule scope :premises (@p399)) % 0.46/0.66 (step-pop @p464 :rule scope :premises (@p463)) % 0.46/0.66 (step-pop @p465 :rule scope :premises (@p464)) % 0.46/0.66 (step @p400 :rule process_scope :premises (@p465) :args (@t245)) % 0.46/0.66 (step @p404 :rule implies_elim :premises (@p400)) % 0.46/0.66 (step @p405 :rule cnf_and_neg :args (@t246)) % 0.46/0.66 (step @p406 :rule resolution :premises (@p405 @p404) :args (true @t246)) % 0.46/0.66 (step @p407 :rule reordering :premises (@p406) :args ((or @t220 @t245 (not @t243) (not @t226)))) % 0.46/0.66 (step @p408 :rule chain_m_resolution :premises (@p407 @p312 @p382 @p327) :args (@t245 @t207 (@list @t219 @t243 @t226))) % 0.46/0.66 (step @p409 :rule bool-double-not-elim :args (@t234)) % 0.46/0.66 (step @p410 :rule nary_cong :premises (@p368 @p409) :args ((or @t240 (not @t235)))) % 0.46/0.66 (step @p411 :rule cnf_or_neg :args (@t240 2)) % 0.46/0.66 (step @p412 :rule eq_resolve :premises (@p411 @p410)) % 0.46/0.66 (step @p413 :rule reordering :premises (@p412) :args ((or @t234 @t240))) % 0.46/0.66 (step @p414 :rule chain_m_resolution :premises (@p413 @p366) :args (@t234 @t107 @t242)) % 0.46/0.66 (step @p415 :rule cnf_or_neg :args (@t201 5)) % 0.46/0.66 (step @p416 :rule chain_m_resolution :premises (@p415 @p250) :args ((not @t190) @t107 @t203)) % 0.46/0.66 (step @p417 :rule cnf_or_pos :args (@t248)) % 0.46/0.66 (step @p418 :rule reordering :premises (@p417) :args ((or @t198 @t196 @t190 @t239 @t235 @t247 @t249))) % 0.46/0.66 (step @p419 :rule chain_m_resolution :premises (@p418 @p257 @p344 @p416 @p379 @p414 @p408) :args (@t249 (@list false false true false false false) (@list @t197 @t195 @t190 @t238 @t234 @t245))) % 0.46/0.66 (step @p420 :rule eq-symm :args (@t189 @t123)) % 0.46/0.66 (step @p421 :rule refl :args (@t247)) % 0.46/0.66 (step @p422 :rule refl :args (@t235)) % 0.46/0.66 (step @p423 :rule refl :args (@t198)) % 0.46/0.66 (step @p424 :rule refl :args (@t196)) % 0.46/0.66 (step @p425 :rule refl :args (@t239)) % 0.46/0.66 (step @p426 :rule nary_cong :premises (@p425 @p424 @p423 @p422 @p421 @p420) :args (@t250)) % 0.46/0.66 (step @p427 :rule refl :args (@t112)) % 0.46/0.66 (step @p428 :rule cong :premises (@p427 @p426) :args ((=> @t112 @t250))) % 0.46/0.66 (assume-push @p466 @t112) % 0.46/0.66 (step @p430 :rule instantiate :premises (@p91) :args ((@list @t230 @t189 @t123))) % 0.46/0.67 (step-pop @p467 :rule scope :premises (@p430)) % 0.46/0.67 (step @p431 :rule process_scope :premises (@p467) :args (@t250)) % 0.46/0.67 (step @p433 :rule eq_resolve :premises (@p431 @p428)) % 0.46/0.67 (step @p434 :rule implies_elim :premises (@p433)) % 0.46/0.67 (step @p435 false :rule chain_m_resolution :premises (@p434 @p419 @p91) :args (false @t187 (@list @t248 @t112))) % 0.46/0.67 ) % 0.46/0.67 % SZS output end Proof % 0.46/0.67 % cvc5 exiting %------------------------------------------------------------------------------