%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET733+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 : n020.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 08:48:32 AM UTC 2026 % Result : Theorem 0.39s 0.66s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SET733+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n020.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 16:11:26 EDT 2026 % 0.14/0.35 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.66 % SZS status Theorem % 0.39/0.66 % SZS output start Proof % 0.39/0.66 ( % 0.39/0.66 (declare-sort $$unsorted 0) % 0.39/0.66 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.empty_set $$unsorted) % 0.39/0.66 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.66 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.66 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.66 (define @t2 () (@var "X" $$unsorted)) % 0.39/0.66 (define @t3 () (tptp.member @t2 @t1)) % 0.39/0.66 (define @t4 () (@var "A" $$unsorted)) % 0.39/0.66 (define @t5 () (tptp.member @t2 @t4)) % 0.39/0.66 (define @t6 () (@list @t2)) % 0.39/0.66 (define @t7 () (tptp.subset @t4 @t1)) % 0.39/0.66 (define @t8 () (@list @t4 @t1)) % 0.39/0.66 (define @t9 () (@list @t2 @t4)) % 0.39/0.66 (define @t10 () (@list @t2 @t4 @t1)) % 0.39/0.66 (define @t11 () (@var "E" $$unsorted)) % 0.39/0.66 (define @t12 () (= @t2 @t4)) % 0.39/0.66 (define @t13 () (@var "Y" $$unsorted)) % 0.39/0.66 (define @t14 () (tptp.member @t2 @t13)) % 0.39/0.66 (define @t15 () (tptp.member @t13 @t4)) % 0.39/0.66 (define @t16 () (@list @t13)) % 0.39/0.66 (define @t17 () (@var "Y2" $$unsorted)) % 0.39/0.66 (define @t18 () (@var "Y1" $$unsorted)) % 0.39/0.66 (define @t19 () (= @t18 @t17)) % 0.39/0.66 (define @t20 () (@var "F" $$unsorted)) % 0.39/0.66 (define @t21 () (tptp.apply @t20 @t2 @t17)) % 0.39/0.66 (define @t22 () (tptp.apply @t20 @t2 @t18)) % 0.39/0.66 (define @t23 () (and @t22 @t21)) % 0.39/0.66 (define @t24 () (=> @t23 @t19)) % 0.39/0.66 (define @t25 () (tptp.member @t17 @t1)) % 0.39/0.66 (define @t26 () (tptp.member @t18 @t1)) % 0.39/0.66 (define @t27 () (and @t5 @t26 @t25)) % 0.39/0.66 (define @t28 () (@list @t2 @t18 @t17)) % 0.39/0.66 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.39/0.66 (define @t30 () (tptp.apply @t20 @t2 @t13)) % 0.39/0.66 (define @t31 () (tptp.member @t13 @t1)) % 0.39/0.66 (define @t32 () (and @t31 @t30)) % 0.39/0.66 (define @t33 () (exists @t16 @t32)) % 0.39/0.66 (define @t34 () (=> @t5 @t33)) % 0.39/0.66 (define @t35 () (forall @t6 @t34)) % 0.39/0.66 (define @t36 () (and @t35 @t29)) % 0.39/0.66 (define @t37 () (tptp.maps @t20 @t4 @t1)) % 0.39/0.66 (define @t38 () (= @t37 @t36)) % 0.39/0.66 (define @t39 () (@list @t20 @t4 @t1)) % 0.39/0.66 (define @t40 () (forall @t39 @t38)) % 0.39/0.66 (define @t41 () (@var "Z" $$unsorted)) % 0.39/0.66 (define @t42 () (@var "G" $$unsorted)) % 0.39/0.66 (define @t43 () (tptp.apply @t42 @t13 @t41)) % 0.39/0.66 (define @t44 () (and @t31 @t30 @t43)) % 0.39/0.66 (define @t45 () (exists @t16 @t44)) % 0.39/0.66 (define @t46 () (@var "H" $$unsorted)) % 0.39/0.66 (define @t47 () (@var "C" $$unsorted)) % 0.39/0.66 (define @t48 () (tptp.member @t41 @t47)) % 0.39/0.66 (define @t49 () (and @t5 @t48)) % 0.39/0.66 (define @t50 () (tptp.apply (tptp.compose_function @t42 @t20 @t4 @t1 @t47) @t2 @t41)) % 0.39/0.66 (define @t51 () (=> @t49 (= @t50 @t45))) % 0.39/0.66 (define @t52 () (@list @t42 @t20 @t4 @t1 @t47 @t2 @t41)) % 0.39/0.66 (define @t53 () (forall @t52 @t51)) % 0.39/0.66 (define @t54 () (@list @t20 @t42 @t4 @t1)) % 0.39/0.66 (define @t55 () (tptp.apply @t20 @t2 @t2)) % 0.39/0.66 (define @t56 () (forall @t6 (=> @t5 @t55))) % 0.39/0.66 (define @t57 () (tptp.identity @t20 @t4)) % 0.39/0.66 (define @t58 () (= @t57 @t56)) % 0.39/0.66 (define @t59 () (forall (@list @t20 @t4) @t58)) % 0.39/0.66 (define @t60 () (@var "X2" $$unsorted)) % 0.39/0.66 (define @t61 () (@var "X1" $$unsorted)) % 0.39/0.66 (define @t62 () (= @t61 @t60)) % 0.39/0.66 (define @t63 () (tptp.apply @t20 @t60 @t13)) % 0.39/0.66 (define @t64 () (tptp.apply @t20 @t61 @t13)) % 0.39/0.66 (define @t65 () (and @t64 @t63)) % 0.39/0.66 (define @t66 () (=> @t65 @t62)) % 0.39/0.66 (define @t67 () (tptp.member @t60 @t4)) % 0.39/0.66 (define @t68 () (tptp.member @t61 @t4)) % 0.39/0.66 (define @t69 () (and @t68 @t67 @t31)) % 0.39/0.66 (define @t70 () (@list @t61 @t60 @t13)) % 0.39/0.66 (define @t71 () (forall @t70 (=> @t69 @t66))) % 0.39/0.66 (define @t72 () (tptp.injective @t20 @t4 @t1)) % 0.39/0.66 (define @t73 () (= @t72 @t71)) % 0.39/0.66 (define @t74 () (forall @t39 @t73)) % 0.39/0.66 (define @t75 () (tptp.surjective @t20 @t4 @t1)) % 0.39/0.66 (define @t76 () (tptp.one_to_one @t20 @t4 @t1)) % 0.39/0.66 (define @t77 () (and @t5 @t31)) % 0.39/0.66 (define @t78 () (exists @t6 (and @t5 @t30))) % 0.39/0.66 (define @t79 () (@var "S" $$unsorted)) % 0.39/0.66 (define @t80 () (tptp.apply @t79 @t18 @t17)) % 0.39/0.66 (define @t81 () (tptp.apply @t20 @t60 @t17)) % 0.39/0.66 (define @t82 () (tptp.apply @t20 @t61 @t18)) % 0.39/0.66 (define @t83 () (@var "R" $$unsorted)) % 0.39/0.66 (define @t84 () (tptp.apply @t83 @t61 @t60)) % 0.39/0.66 (define @t85 () (and @t68 @t26 @t67 @t25 @t84 @t82 @t81)) % 0.39/0.66 (define @t86 () (@list @t61 @t18 @t60 @t17)) % 0.39/0.66 (define @t87 () (@list @t20 @t4 @t83 @t1 @t79)) % 0.39/0.66 (define @t88 () (tptp.identity (tptp.compose_function @t42 @t20 @t4 @t1 @t4) @t4)) % 0.39/0.66 (define @t89 () (tptp.maps @t42 @t1 @t4)) % 0.39/0.66 (define @t90 () (and @t37 @t89 @t88)) % 0.39/0.66 (define @t91 () (forall @t54 (=> @t90 @t72))) % 0.39/0.66 (define @t92 () (not @t91)) % 0.39/0.66 (define @t93 () (not @t21)) % 0.39/0.66 (define @t94 () (not @t22)) % 0.39/0.66 (define @t95 () (not @t25)) % 0.39/0.66 (define @t96 () (not @t26)) % 0.39/0.66 (define @t97 () (not @t5)) % 0.39/0.66 (define @t98 () (or @t94 @t93 @t19)) % 0.39/0.66 (define @t99 () (or @t97 @t96 @t95)) % 0.39/0.66 (define @t100 () (not @t30)) % 0.39/0.66 (define @t101 () (not @t31)) % 0.39/0.66 (define @t102 () (not (forall @t16 (or @t101 @t100)))) % 0.39/0.66 (define @t103 () (forall @t16 (not @t32))) % 0.39/0.66 (define @t104 () (not @t103)) % 0.39/0.66 (define @t105 () (not @t88)) % 0.39/0.66 (define @t106 () (not @t89)) % 0.39/0.66 (define @t107 () (not @t37)) % 0.39/0.66 (define @t108 () (or @t107 @t106 @t105 @t72)) % 0.39/0.66 (define @t109 () (forall @t54 @t108)) % 0.39/0.66 (define @t110 () (@quantifiers_skolemize @t109 2)) % 0.39/0.66 (define @t111 () (@quantifiers_skolemize @t109 3)) % 0.39/0.66 (define @t112 () (@quantifiers_skolemize @t109 1)) % 0.39/0.66 (define @t113 () (or @t107 @t106 @t105)) % 0.39/0.66 (define @t114 () (tptp.maps @t112 @t111 @t110)) % 0.39/0.66 (define @t115 () (@quantifiers_skolemize @t109 0)) % 0.39/0.66 (define @t116 () (tptp.injective @t115 @t110 @t111)) % 0.39/0.66 (define @t117 () (tptp.compose_function @t112 @t115 @t110 @t111 @t110)) % 0.39/0.66 (define @t118 () (tptp.identity @t117 @t110)) % 0.39/0.66 (define @t119 () (not @t118)) % 0.39/0.66 (define @t120 () (not @t114)) % 0.39/0.66 (define @t121 () (tptp.maps @t115 @t110 @t111)) % 0.39/0.66 (define @t122 () (not @t121)) % 0.39/0.66 (define @t123 () (or @t122 @t120 @t119 @t116)) % 0.39/0.66 (define @t124 () (@list true)) % 0.39/0.66 (define @t125 () (@list @t123)) % 0.39/0.66 (define @t126 () (not (tptp.member @t2 @t111))) % 0.39/0.66 (define @t127 () (forall @t28 (or @t126 (not (tptp.member @t18 @t110)) (not (tptp.member @t17 @t110)) (not (tptp.apply @t112 @t2 @t18)) (not (tptp.apply @t112 @t2 @t17)) @t19))) % 0.39/0.66 (define @t128 () (not (tptp.member @t13 @t110))) % 0.39/0.66 (define @t129 () (forall @t6 (or @t126 (not (forall @t16 (or @t128 (not (tptp.apply @t112 @t2 @t13)))))))) % 0.39/0.66 (define @t130 () (and @t129 @t127)) % 0.39/0.66 (define @t131 () (= @t114 @t130)) % 0.39/0.66 (define @t132 () (@list false false)) % 0.39/0.66 (define @t133 () (not @t130)) % 0.39/0.66 (define @t134 () (@list false)) % 0.39/0.66 (define @t135 () (@list @t130)) % 0.39/0.66 (define @t136 () (not (tptp.member @t13 @t111))) % 0.39/0.66 (define @t137 () (forall @t70 (or (not (tptp.member @t61 @t110)) (not (tptp.member @t60 @t110)) @t136 (not (tptp.apply @t115 @t61 @t13)) (not (tptp.apply @t115 @t60 @t13)) @t62))) % 0.39/0.66 (define @t138 () (@quantifiers_skolemize @t137 1)) % 0.39/0.66 (define @t139 () (@quantifiers_skolemize @t137 0)) % 0.39/0.66 (define @t140 () (not (tptp.apply @t115 @t139 @t13))) % 0.39/0.66 (define @t141 () (forall @t16 (or @t136 @t140))) % 0.39/0.66 (define @t142 () (@quantifiers_skolemize @t141 0)) % 0.39/0.66 (define @t143 () (not @t43)) % 0.39/0.66 (define @t144 () (or @t101 @t100 @t143)) % 0.39/0.66 (define @t145 () (not (forall @t16 @t144))) % 0.39/0.66 (define @t146 () (= @t50 @t145)) % 0.39/0.66 (define @t147 () (not @t48)) % 0.39/0.66 (define @t148 () (forall @t16 (not @t44))) % 0.39/0.66 (define @t149 () (not @t148)) % 0.39/0.66 (define @t150 () (not @t63)) % 0.39/0.66 (define @t151 () (not @t64)) % 0.39/0.66 (define @t152 () (not @t67)) % 0.39/0.66 (define @t153 () (not @t68)) % 0.39/0.66 (define @t154 () (or @t151 @t150 @t62)) % 0.39/0.66 (define @t155 () (or @t153 @t152 @t101)) % 0.39/0.66 (define @t156 () (@list @t115 @t110 @t111)) % 0.39/0.66 (define @t157 () (= @t116 @t137)) % 0.39/0.66 (define @t158 () (not @t137)) % 0.39/0.66 (define @t159 () (tptp.member @t138 @t110)) % 0.39/0.66 (define @t160 () (= @t139 @t138)) % 0.39/0.66 (define @t161 () (@quantifiers_skolemize @t137 2)) % 0.39/0.66 (define @t162 () (tptp.apply @t115 @t138 @t161)) % 0.39/0.66 (define @t163 () (not @t162)) % 0.39/0.66 (define @t164 () (tptp.apply @t115 @t139 @t161)) % 0.39/0.66 (define @t165 () (not @t164)) % 0.39/0.66 (define @t166 () (tptp.member @t161 @t111)) % 0.39/0.66 (define @t167 () (not @t166)) % 0.39/0.66 (define @t168 () (not @t159)) % 0.39/0.66 (define @t169 () (tptp.member @t139 @t110)) % 0.39/0.66 (define @t170 () (not @t169)) % 0.39/0.66 (define @t171 () (or @t170 @t168 @t167 @t165 @t163 @t160)) % 0.39/0.66 (define @t172 () (@list @t171)) % 0.39/0.66 (define @t173 () (forall @t16 (or @t136 (not (tptp.apply @t115 @t138 @t13)) (not (tptp.apply @t112 @t13 @t138))))) % 0.39/0.66 (define @t174 () (not @t173)) % 0.39/0.66 (define @t175 () (tptp.apply @t117 @t138 @t138)) % 0.39/0.66 (define @t176 () (= @t175 @t174)) % 0.39/0.66 (define @t177 () (or @t168 @t168 @t176)) % 0.39/0.66 (define @t178 () (not (tptp.member @t2 @t110))) % 0.39/0.66 (define @t179 () (forall @t6 (or @t178 (tptp.apply @t117 @t2 @t2)))) % 0.39/0.66 (define @t180 () (= @t118 @t179)) % 0.39/0.66 (define @t181 () (or @t168 @t175)) % 0.39/0.66 (define @t182 () (@quantifiers_skolemize @t173 0)) % 0.39/0.66 (define @t183 () (tptp.apply @t112 @t182 @t138)) % 0.39/0.66 (define @t184 () (not @t183)) % 0.39/0.66 (define @t185 () (tptp.apply @t115 @t138 @t182)) % 0.39/0.66 (define @t186 () (not @t185)) % 0.39/0.66 (define @t187 () (tptp.member @t182 @t111)) % 0.39/0.66 (define @t188 () (not @t187)) % 0.39/0.66 (define @t189 () (or @t188 @t186 @t184)) % 0.39/0.66 (define @t190 () (@list @t189)) % 0.39/0.66 (define @t191 () (forall @t28 (or @t178 (not (tptp.member @t18 @t111)) (not (tptp.member @t17 @t111)) (not (tptp.apply @t115 @t2 @t18)) (not (tptp.apply @t115 @t2 @t17)) @t19))) % 0.39/0.66 (define @t192 () (forall @t6 (or @t178 (not (forall @t16 (or @t136 (not (tptp.apply @t115 @t2 @t13)))))))) % 0.39/0.66 (define @t193 () (and @t192 @t191)) % 0.39/0.66 (define @t194 () (= @t121 @t193)) % 0.39/0.66 (define @t195 () (not @t193)) % 0.39/0.66 (define @t196 () (@list @t193)) % 0.39/0.66 (define @t197 () (or @t168 @t188 @t167 @t186 @t163 (= @t182 @t161))) % 0.39/0.66 (define @t198 () (= @t161 @t182)) % 0.39/0.66 (define @t199 () (or @t168 @t188 @t167 @t186 @t163 @t198)) % 0.39/0.66 (define @t200 () (@list @t191)) % 0.39/0.66 (define @t201 () (@list false false false false false false)) % 0.39/0.66 (define @t202 () (@list @t139)) % 0.39/0.66 (define @t203 () (not @t141)) % 0.39/0.66 (define @t204 () (or @t170 @t203)) % 0.39/0.66 (define @t205 () (tptp.apply @t115 @t139 @t142)) % 0.39/0.66 (define @t206 () (not @t205)) % 0.39/0.66 (define @t207 () (tptp.member @t142 @t111)) % 0.39/0.66 (define @t208 () (not @t207)) % 0.39/0.66 (define @t209 () (or @t208 @t206)) % 0.39/0.66 (define @t210 () (@list @t209)) % 0.39/0.66 (define @t211 () (= @t161 @t142)) % 0.39/0.66 (define @t212 () (or @t170 @t167 @t208 @t165 @t206 @t211)) % 0.39/0.66 (define @t213 () (tptp.apply @t112 @t142 @t138)) % 0.39/0.66 (define @t214 () (not @t213)) % 0.39/0.66 (define @t215 () (not (tptp.apply @t112 @t142 @t139))) % 0.39/0.66 (define @t216 () (or @t208 @t170 @t168 @t215 @t214 @t160)) % 0.39/0.66 (define @t217 () (forall @t16 (or @t136 @t140 (not (tptp.apply @t112 @t13 @t139))))) % 0.39/0.66 (define @t218 () (@quantifiers_skolemize @t217 0)) % 0.39/0.66 (define @t219 () (forall @t16 (or @t128 (not (tptp.apply @t112 @t218 @t13))))) % 0.39/0.66 (define @t220 () (@quantifiers_skolemize @t219 0)) % 0.39/0.66 (define @t221 () (not @t217)) % 0.39/0.66 (define @t222 () (tptp.apply @t117 @t139 @t139)) % 0.39/0.66 (define @t223 () (= @t222 @t221)) % 0.39/0.66 (define @t224 () (or @t170 @t170 @t223)) % 0.39/0.66 (define @t225 () (or @t170 @t222)) % 0.39/0.66 (define @t226 () (tptp.member @t218 @t111)) % 0.39/0.66 (define @t227 () (tptp.apply @t112 @t218 @t139)) % 0.39/0.66 (define @t228 () (not @t227)) % 0.39/0.66 (define @t229 () (tptp.apply @t115 @t139 @t218)) % 0.39/0.66 (define @t230 () (not @t229)) % 0.39/0.66 (define @t231 () (not @t226)) % 0.39/0.66 (define @t232 () (or @t231 @t230 @t228)) % 0.39/0.66 (define @t233 () (@list @t232)) % 0.39/0.66 (define @t234 () (not @t219)) % 0.39/0.66 (define @t235 () (or @t231 @t234)) % 0.39/0.66 (define @t236 () (tptp.apply @t112 @t218 @t220)) % 0.39/0.66 (define @t237 () (not @t236)) % 0.39/0.66 (define @t238 () (tptp.member @t220 @t110)) % 0.39/0.66 (define @t239 () (not @t238)) % 0.39/0.66 (define @t240 () (or @t239 @t237)) % 0.39/0.66 (define @t241 () (@list @t240)) % 0.39/0.66 (define @t242 () (= @t139 @t220)) % 0.39/0.66 (define @t243 () (or @t231 @t170 @t239 @t228 @t237 @t242)) % 0.39/0.66 (define @t244 () (or @t170 @t231 @t167 @t230 @t165 (= @t218 @t161))) % 0.39/0.66 (define @t245 () (= @t161 @t218)) % 0.39/0.66 (define @t246 () (or @t170 @t231 @t167 @t230 @t165 @t245)) % 0.39/0.66 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.39/0.66 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.39/0.66 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.39/0.66 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.39/0.66 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.39/0.66 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.39/0.66 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.39/0.66 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.39/0.66 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.39/0.66 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.39/0.66 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.39/0.66 (assume @p12 @t40) % 0.39/0.66 (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)))))) % 0.39/0.66 (assume @p14 @t53) % 0.39/0.66 (assume @p15 (forall @t54 (= (tptp.equal_maps @t20 @t42 @t4 @t1) (forall @t28 (=> @t27 (=> (and @t22 (tptp.apply @t42 @t2 @t17)) @t19)))))) % 0.39/0.66 (assume @p16 @t59) % 0.39/0.67 (assume @p17 @t74) % 0.39/0.67 (assume @p18 (forall @t39 (= @t75 (forall @t16 (=> @t31 (exists (@list @t11) (and (tptp.member @t11 @t4) (tptp.apply @t20 @t11 @t13)))))))) % 0.39/0.67 (assume @p19 (forall @t39 (= @t76 (and @t72 @t75)))) % 0.39/0.67 (assume @p20 (forall (@list @t42 @t20 @t4 @t1) (= (tptp.inverse_predicate @t42 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t77 (= @t30 (tptp.apply @t42 @t13 @t2))))))) % 0.39/0.67 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t77 (= @t30 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.39/0.67 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t78))) % 0.39/0.67 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t31 @t78)))) % 0.39/0.67 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t33))) % 0.39/0.67 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t33)))) % 0.39/0.67 (assume @p26 (forall @t87 (= (tptp.increasing @t20 @t4 @t83 @t1 @t79) (forall @t86 (=> @t85 @t80))))) % 0.39/0.67 (assume @p27 (forall @t87 (= (tptp.decreasing @t20 @t4 @t83 @t1 @t79) (forall @t86 (=> @t85 (tptp.apply @t79 @t17 @t18)))))) % 0.39/0.67 (assume @p28 (forall @t87 (= (tptp.isomorphism @t20 @t4 @t83 @t1 @t79) (and @t37 @t76 (forall @t86 (=> (and @t68 @t26 @t67 @t25 @t82 @t81) (= @t84 @t80))))))) % 0.39/0.67 (assume @p29 @t92) % 0.39/0.67 (assume @p30 true) % 0.39/0.67 (step @p31 :rule evaluate :args ((= true false))) % 0.39/0.67 (step @p32 :rule aci_norm :args ((= (or @t99 @t98) (or @t97 @t96 @t95 @t94 @t93 @t19)))) % 0.39/0.67 (step @p33 :rule aci_norm :args ((= (or (or @t94 @t93) @t19) @t98))) % 0.39/0.67 (step @p34 :rule refl :args (@t19)) % 0.39/0.67 (step @p35 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.39/0.67 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((or (not @t23) @t19))) % 0.39/0.67 (step @p37 :rule trans :premises (@p36 @p33)) % 0.39/0.67 (step @p38 :rule bool-impl-elim :args (@t23 @t19)) % 0.39/0.67 (step @p39 :rule trans :premises (@p38 @p37)) % 0.39/0.67 (step @p40 :rule aci_norm :args ((= (or @t97 (or @t96 @t95)) @t99))) % 0.39/0.67 (step @p41 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.39/0.67 (step @p42 :rule refl :args (@t97)) % 0.39/0.67 (step @p43 :rule nary_cong :premises (@p42 @p41) :args ((or @t97 (not (and @t26 @t25))))) % 0.39/0.67 (step @p44 :rule bool-and-de-morgan :args (@t5 @t26 (and @t25))) % 0.39/0.67 (step @p45 :rule trans :premises (@p44 @p43)) % 0.39/0.67 (step @p46 :rule trans :premises (@p45 @p40)) % 0.39/0.67 (step @p47 :rule nary_cong :premises (@p46 @p39) :args ((or (not @t27) @t24))) % 0.39/0.67 (step @p48 :rule trans :premises (@p47 @p32)) % 0.39/0.67 (step @p49 :rule bool-impl-elim :args (@t27 @t24)) % 0.39/0.67 (step @p50 :rule trans :premises (@p49 @p48)) % 0.39/0.67 (step @p51 :rule cong :premises (@p50) :args (@t29)) % 0.39/0.67 (step @p52 :rule bool-impl-elim :args (@t5 @t102)) % 0.39/0.67 (step @p53 :rule cong :premises (@p52) :args ((forall @t6 (=> @t5 @t102)))) % 0.39/0.67 (step @p54 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.39/0.67 (step @p55 :rule cong :premises (@p54) :args (@t103)) % 0.39/0.67 (step @p56 :rule cong :premises (@p55) :args (@t104)) % 0.39/0.67 (step @p57 :rule exists-elim :args ((= @t33 @t104))) % 0.39/0.67 (step @p58 :rule trans :premises (@p57 @p56)) % 0.39/0.67 (step @p59 :rule refl :args (@t5)) % 0.39/0.67 (step @p60 :rule cong :premises (@p59 @p58) :args (@t34)) % 0.39/0.67 (step @p61 :rule cong :premises (@p60) :args (@t35)) % 0.39/0.67 (step @p62 :rule trans :premises (@p61 @p53)) % 0.39/0.67 (step @p63 :rule nary_cong :premises (@p62 @p51) :args (@t36)) % 0.39/0.67 (step @p64 :rule refl :args (@t37)) % 0.39/0.67 (step @p65 :rule cong :premises (@p64 @p63) :args (@t38)) % 0.39/0.67 (step @p66 :rule cong :premises (@p65) :args (@t40)) % 0.39/0.67 (step @p67 :rule eq_resolve :premises (@p12 @p66)) % 0.39/0.67 (step @p68 :rule instantiate :premises (@p67) :args ((@list @t112 @t111 @t110))) % 0.39/0.67 (step @p69 :rule aci_norm :args ((= (or @t113 @t72) @t108))) % 0.39/0.67 (step @p70 :rule refl :args (@t72)) % 0.39/0.67 (step @p71 :rule aci_norm :args ((= (or @t107 (or @t106 @t105)) @t113))) % 0.39/0.67 (step @p72 :rule bool-and-de-morgan :args (@t89 @t88 true)) % 0.39/0.67 (step @p73 :rule refl :args (@t107)) % 0.39/0.67 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t107 (not (and @t89 @t88))))) % 0.39/0.67 (step @p75 :rule bool-and-de-morgan :args (@t37 @t89 (and @t88))) % 0.39/0.67 (step @p76 :rule trans :premises (@p75 @p74)) % 0.39/0.67 (step @p77 :rule trans :premises (@p76 @p71)) % 0.39/0.67 (step @p78 :rule nary_cong :premises (@p77 @p70) :args ((or (not @t90) @t72))) % 0.39/0.67 (step @p79 :rule trans :premises (@p78 @p69)) % 0.39/0.67 (step @p80 :rule bool-impl-elim :args (@t90 @t72)) % 0.39/0.67 (step @p81 :rule trans :premises (@p80 @p79)) % 0.39/0.67 (step @p82 :rule cong :premises (@p81) :args (@t91)) % 0.39/0.67 (step @p83 :rule cong :premises (@p82) :args (@t92)) % 0.39/0.67 (step @p84 :rule eq_resolve :premises (@p29 @p83)) % 0.39/0.67 (step @p85 :rule skolemize :premises (@p84)) % 0.39/0.67 (step @p86 :rule bool-double-not-elim :args (@t114)) % 0.39/0.67 (step @p87 :rule refl :args (@t123)) % 0.39/0.67 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t123 (not @t120)))) % 0.39/0.67 (step @p89 :rule cnf_or_neg :args (@t123 1)) % 0.39/0.67 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 0.39/0.67 (step @p91 :rule reordering :premises (@p90) :args ((or @t114 @t123))) % 0.39/0.67 (step @p92 :rule chain_m_resolution :premises (@p91 @p85) :args (@t114 @t124 @t125)) % 0.39/0.67 (step @p93 :rule cnf_equiv_pos1 :args (@t131)) % 0.39/0.67 (step @p94 :rule reordering :premises (@p93) :args ((or @t120 @t130 (not @t131)))) % 0.39/0.67 (step @p95 :rule chain_m_resolution :premises (@p94 @p92 @p68) :args (@t130 @t132 (@list @t114 @t131))) % 0.39/0.67 (step @p96 :rule cnf_and_pos :args (@t130 1)) % 0.39/0.67 (step @p97 :rule reordering :premises (@p96) :args ((or @t127 @t133))) % 0.39/0.67 (step @p98 :rule chain_m_resolution :premises (@p97 @p95) :args (@t127 @t134 @t135)) % 0.39/0.67 (step @p99 :rule instantiate :premises (@p98) :args ((@list @t142 @t139 @t138))) % 0.39/0.67 (step @p100 :rule aci_norm :args ((= (or (or @t97 @t147) @t146) (or @t97 @t147 @t146)))) % 0.39/0.67 (step @p101 :rule refl :args (@t146)) % 0.39/0.67 (step @p102 :rule bool-and-de-morgan :args (@t5 @t48 true)) % 0.39/0.67 (step @p103 :rule nary_cong :premises (@p102 @p101) :args ((or (not @t49) @t146))) % 0.39/0.67 (step @p104 :rule trans :premises (@p103 @p100)) % 0.39/0.67 (step @p105 :rule bool-impl-elim :args (@t49 @t146)) % 0.39/0.67 (step @p106 :rule trans :premises (@p105 @p104)) % 0.39/0.67 (step @p107 :rule cong :premises (@p106) :args ((forall @t52 (=> @t49 @t146)))) % 0.39/0.67 (step @p108 :rule eq-symm :args (@t145 @t50)) % 0.39/0.67 (step @p109 :rule refl :args (@t50)) % 0.39/0.67 (step @p110 :rule aci_norm :args ((= (or @t101 (or @t100 @t143)) @t144))) % 0.39/0.67 (step @p111 :rule bool-and-de-morgan :args (@t30 @t43 true)) % 0.39/0.67 (step @p112 :rule refl :args (@t101)) % 0.39/0.67 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or @t101 (not (and @t30 @t43))))) % 0.39/0.67 (step @p114 :rule bool-and-de-morgan :args (@t31 @t30 (and @t43))) % 0.39/0.67 (step @p115 :rule trans :premises (@p114 @p113)) % 0.39/0.67 (step @p116 :rule trans :premises (@p115 @p110)) % 0.39/0.67 (step @p117 :rule cong :premises (@p116) :args (@t148)) % 0.39/0.67 (step @p118 :rule cong :premises (@p117) :args (@t149)) % 0.39/0.67 (step @p119 :rule exists-elim :args ((= @t45 @t149))) % 0.39/0.67 (step @p120 :rule trans :premises (@p119 @p118)) % 0.39/0.67 (step @p121 :rule cong :premises (@p120 @p109) :args ((= @t45 @t50))) % 0.39/0.67 (step @p122 :rule trans :premises (@p121 @p108)) % 0.39/0.67 (step @p123 :rule eq-symm :args (@t50 @t45)) % 0.39/0.67 (step @p124 :rule trans :premises (@p123 @p122)) % 0.39/0.67 (step @p125 :rule refl :args (@t49)) % 0.39/0.67 (step @p126 :rule cong :premises (@p125 @p124) :args (@t51)) % 0.39/0.67 (step @p127 :rule cong :premises (@p126) :args (@t53)) % 0.39/0.67 (step @p128 :rule trans :premises (@p127 @p107)) % 0.39/0.67 (step @p129 :rule eq_resolve :premises (@p14 @p128)) % 0.39/0.67 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t112 @t115 @t110 @t111 @t110 @t138 @t138))) % 0.39/0.67 (step @p131 :rule aci_norm :args ((= (or @t155 @t154) (or @t153 @t152 @t101 @t151 @t150 @t62)))) % 0.39/0.67 (step @p132 :rule aci_norm :args ((= (or (or @t151 @t150) @t62) @t154))) % 0.39/0.67 (step @p133 :rule refl :args (@t62)) % 0.39/0.67 (step @p134 :rule bool-and-de-morgan :args (@t64 @t63 true)) % 0.39/0.67 (step @p135 :rule nary_cong :premises (@p134 @p133) :args ((or (not @t65) @t62))) % 0.39/0.67 (step @p136 :rule trans :premises (@p135 @p132)) % 0.39/0.67 (step @p137 :rule bool-impl-elim :args (@t65 @t62)) % 0.39/0.67 (step @p138 :rule trans :premises (@p137 @p136)) % 0.39/0.67 (step @p139 :rule aci_norm :args ((= (or @t153 (or @t152 @t101)) @t155))) % 0.39/0.67 (step @p140 :rule bool-and-de-morgan :args (@t67 @t31 true)) % 0.39/0.67 (step @p141 :rule refl :args (@t153)) % 0.39/0.67 (step @p142 :rule nary_cong :premises (@p141 @p140) :args ((or @t153 (not (and @t67 @t31))))) % 0.39/0.67 (step @p143 :rule bool-and-de-morgan :args (@t68 @t67 (and @t31))) % 0.39/0.67 (step @p144 :rule trans :premises (@p143 @p142)) % 0.39/0.67 (step @p145 :rule trans :premises (@p144 @p139)) % 0.39/0.67 (step @p146 :rule nary_cong :premises (@p145 @p138) :args ((or (not @t69) @t66))) % 0.39/0.67 (step @p147 :rule trans :premises (@p146 @p131)) % 0.39/0.67 (step @p148 :rule bool-impl-elim :args (@t69 @t66)) % 0.39/0.67 (step @p149 :rule trans :premises (@p148 @p147)) % 0.39/0.67 (step @p150 :rule cong :premises (@p149) :args (@t71)) % 0.39/0.67 (step @p151 :rule refl :args (@t72)) % 0.39/0.67 (step @p152 :rule cong :premises (@p151 @p150) :args (@t73)) % 0.39/0.67 (step @p153 :rule cong :premises (@p152) :args (@t74)) % 0.39/0.67 (step @p154 :rule eq_resolve :premises (@p17 @p153)) % 0.39/0.67 (step @p155 :rule instantiate :premises (@p154) :args (@t156)) % 0.39/0.67 (step @p156 :rule cnf_or_neg :args (@t123 3)) % 0.39/0.67 (step @p157 :rule chain_m_resolution :premises (@p156 @p85) :args 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:premises (@p383 @p330) :args (@t229 @t124 @t233)) % 0.39/0.67 (step @p385 :rule cnf_or_pos :args (@t246)) % 0.39/0.67 (step @p386 :rule reordering :premises (@p385) :args ((or @t170 @t167 @t165 @t231 @t230 @t245 (not @t246)))) % 0.39/0.67 (step @p387 :rule chain_m_resolution :premises (@p386 @p274 @p258 @p297 @p337 @p384 @p378) :args (@t245 @t201 (@list @t169 @t166 @t164 @t226 @t229 @t246))) % 0.39/0.67 (step @p388 :rule symm :premises (@p387)) % 0.39/0.67 (step @p389 :rule cong :premises (@p262 @p388 @p364) :args (@t236)) % 0.39/0.67 (step @p390 :rule true_intro :premises (@p348)) % 0.39/0.67 (step @p391 :rule symm :premises (@p390)) % 0.39/0.67 (step @p392 :rule trans :premises (@p391 @p389 @p312 @p310)) % 0.39/0.67 (step @p393 false :rule eq_resolve :premises (@p392 @p31)) % 0.39/0.67 ) % 0.39/0.67 % SZS output end Proof % 0.39/0.67 % cvc5 exiting %------------------------------------------------------------------------------