%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET743+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 : n026.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 08:48:33 AM UTC 2026 % Result : Theorem 0.71s 0.94s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET743+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 % 0.16/0.35 % Computer : n026.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:11:25 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.71/0.94 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.71/0.94 % SZS status Theorem % 0.71/0.94 % SZS output start Proof % 0.71/0.94 ( % 0.71/0.94 (declare-sort $$unsorted 0) % 0.71/0.94 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.empty_set $$unsorted) % 0.71/0.94 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.71/0.94 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.71/0.94 (define @t1 () (@var "B" $$unsorted)) % 0.71/0.94 (define @t2 () (@var "X" $$unsorted)) % 0.71/0.94 (define @t3 () (tptp.member @t2 @t1)) % 0.71/0.94 (define @t4 () (@var "A" $$unsorted)) % 0.71/0.94 (define @t5 () (tptp.member @t2 @t4)) % 0.71/0.94 (define @t6 () (@list @t2)) % 0.71/0.94 (define @t7 () (tptp.subset @t4 @t1)) % 0.71/0.94 (define @t8 () (@list @t4 @t1)) % 0.71/0.94 (define @t9 () (@list @t2 @t4)) % 0.71/0.94 (define @t10 () (@list @t2 @t4 @t1)) % 0.71/0.94 (define @t11 () (@var "E" $$unsorted)) % 0.71/0.94 (define @t12 () (= @t2 @t4)) % 0.71/0.94 (define @t13 () (@var "Y" $$unsorted)) % 0.71/0.94 (define @t14 () (tptp.member @t2 @t13)) % 0.71/0.94 (define @t15 () (tptp.member @t13 @t4)) % 0.71/0.94 (define @t16 () (@list @t13)) % 0.71/0.94 (define @t17 () (@var "Y2" $$unsorted)) % 0.71/0.94 (define @t18 () (@var "Y1" $$unsorted)) % 0.71/0.94 (define @t19 () (= @t18 @t17)) % 0.71/0.94 (define @t20 () (@var "F" $$unsorted)) % 0.71/0.94 (define @t21 () (tptp.apply @t20 @t2 @t17)) % 0.71/0.94 (define @t22 () (tptp.apply @t20 @t2 @t18)) % 0.71/0.94 (define @t23 () (and @t22 @t21)) % 0.71/0.94 (define @t24 () (=> @t23 @t19)) % 0.71/0.94 (define @t25 () (tptp.member @t17 @t1)) % 0.71/0.94 (define @t26 () (tptp.member @t18 @t1)) % 0.71/0.94 (define @t27 () (and @t5 @t26 @t25)) % 0.71/0.94 (define @t28 () (@list @t2 @t18 @t17)) % 0.71/0.94 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.71/0.94 (define @t30 () (tptp.apply @t20 @t2 @t13)) % 0.71/0.94 (define @t31 () (tptp.member @t13 @t1)) % 0.71/0.94 (define @t32 () (and @t31 @t30)) % 0.71/0.94 (define @t33 () (exists @t16 @t32)) % 0.71/0.94 (define @t34 () (=> @t5 @t33)) % 0.71/0.94 (define @t35 () (forall @t6 @t34)) % 0.71/0.94 (define @t36 () (and @t35 @t29)) % 0.71/0.94 (define @t37 () (tptp.maps @t20 @t4 @t1)) % 0.71/0.94 (define @t38 () (= @t37 @t36)) % 0.71/0.94 (define @t39 () (@list @t20 @t4 @t1)) % 0.71/0.94 (define @t40 () (forall @t39 @t38)) % 0.71/0.94 (define @t41 () (@var "Z" $$unsorted)) % 0.71/0.94 (define @t42 () (@var "G" $$unsorted)) % 0.71/0.94 (define @t43 () (tptp.apply @t42 @t13 @t41)) % 0.71/0.94 (define @t44 () (and @t31 @t30 @t43)) % 0.71/0.94 (define @t45 () (exists @t16 @t44)) % 0.71/0.94 (define @t46 () (@var "H" $$unsorted)) % 0.71/0.94 (define @t47 () (@var "C" $$unsorted)) % 0.71/0.94 (define @t48 () (tptp.member @t41 @t47)) % 0.71/0.94 (define @t49 () (and @t5 @t48)) % 0.71/0.94 (define @t50 () (tptp.compose_function @t42 @t20 @t4 @t1 @t47)) % 0.71/0.94 (define @t51 () (tptp.apply @t50 @t2 @t41)) % 0.71/0.94 (define @t52 () (=> @t49 (= @t51 @t45))) % 0.71/0.94 (define @t53 () (@list @t42 @t20 @t4 @t1 @t47 @t2 @t41)) % 0.71/0.94 (define @t54 () (forall @t53 @t52)) % 0.71/0.94 (define @t55 () (@var "X2" $$unsorted)) % 0.71/0.94 (define @t56 () (@var "X1" $$unsorted)) % 0.71/0.94 (define @t57 () (= @t56 @t55)) % 0.71/0.94 (define @t58 () (tptp.apply @t20 @t55 @t13)) % 0.71/0.94 (define @t59 () (tptp.apply @t20 @t56 @t13)) % 0.71/0.94 (define @t60 () (and @t59 @t58)) % 0.71/0.94 (define @t61 () (=> @t60 @t57)) % 0.71/0.94 (define @t62 () (tptp.member @t55 @t4)) % 0.71/0.94 (define @t63 () (tptp.member @t56 @t4)) % 0.71/0.94 (define @t64 () (and @t63 @t62 @t31)) % 0.71/0.94 (define @t65 () (@list @t56 @t55 @t13)) % 0.71/0.94 (define @t66 () (forall @t65 (=> @t64 @t61))) % 0.71/0.94 (define @t67 () (tptp.injective @t20 @t4 @t1)) % 0.71/0.94 (define @t68 () (= @t67 @t66)) % 0.71/0.94 (define @t69 () (forall @t39 @t68)) % 0.71/0.94 (define @t70 () (tptp.apply @t20 @t11 @t13)) % 0.71/0.94 (define @t71 () (tptp.member @t11 @t4)) % 0.71/0.94 (define @t72 () (and @t71 @t70)) % 0.71/0.94 (define @t73 () (@list @t11)) % 0.71/0.94 (define @t74 () (exists @t73 @t72)) % 0.71/0.94 (define @t75 () (=> @t31 @t74)) % 0.71/0.94 (define @t76 () (forall @t16 @t75)) % 0.71/0.94 (define @t77 () (tptp.surjective @t20 @t4 @t1)) % 0.71/0.94 (define @t78 () (= @t77 @t76)) % 0.71/0.94 (define @t79 () (forall @t39 @t78)) % 0.71/0.94 (define @t80 () (tptp.one_to_one @t20 @t4 @t1)) % 0.71/0.94 (define @t81 () (and @t5 @t31)) % 0.71/0.94 (define @t82 () (exists @t6 (and @t5 @t30))) % 0.71/0.94 (define @t83 () (@var "S" $$unsorted)) % 0.71/0.94 (define @t84 () (tptp.apply @t83 @t18 @t17)) % 0.71/0.94 (define @t85 () (tptp.apply @t20 @t55 @t17)) % 0.71/0.94 (define @t86 () (tptp.apply @t20 @t56 @t18)) % 0.71/0.94 (define @t87 () (@var "R" $$unsorted)) % 0.71/0.94 (define @t88 () (tptp.apply @t87 @t56 @t55)) % 0.71/0.94 (define @t89 () (and @t63 @t26 @t62 @t25 @t88 @t86 @t85)) % 0.71/0.94 (define @t90 () (@list @t56 @t18 @t55 @t17)) % 0.71/0.94 (define @t91 () (@list @t20 @t4 @t87 @t1 @t83)) % 0.71/0.94 (define @t92 () (tptp.one_to_one @t42 @t1 @t47)) % 0.71/0.94 (define @t93 () (tptp.one_to_one (tptp.compose_function @t46 @t42 @t1 @t47 @t4) @t1 @t4)) % 0.71/0.94 (define @t94 () (tptp.one_to_one @t50 @t4 @t47)) % 0.71/0.94 (define @t95 () (tptp.maps @t46 @t47 @t4)) % 0.71/0.94 (define @t96 () (tptp.maps @t42 @t1 @t47)) % 0.71/0.94 (define @t97 () (and @t37 @t96 @t95 @t94 @t93)) % 0.71/0.94 (define @t98 () (@list @t20 @t42 @t46 @t4 @t1 @t47)) % 0.71/0.94 (define @t99 () (forall @t98 (=> @t97 @t92))) % 0.71/0.94 (define @t100 () (not @t99)) % 0.71/0.94 (define @t101 () (not (forall @t73 (or (not @t71) (not @t70))))) % 0.71/0.94 (define @t102 () (forall @t73 (not @t72))) % 0.71/0.94 (define @t103 () (not @t102)) % 0.71/0.94 (define @t104 () (not @t93)) % 0.71/0.94 (define @t105 () (not @t94)) % 0.71/0.94 (define @t106 () (not @t95)) % 0.71/0.94 (define @t107 () (not @t96)) % 0.71/0.94 (define @t108 () (not @t37)) % 0.71/0.94 (define @t109 () (or @t108 @t107 @t106 @t105 @t104 @t92)) % 0.71/0.94 (define @t110 () (forall @t98 @t109)) % 0.71/0.94 (define @t111 () (@quantifiers_skolemize @t110 5)) % 0.71/0.94 (define @t112 () (@quantifiers_skolemize @t110 4)) % 0.71/0.94 (define @t113 () (@quantifiers_skolemize @t110 1)) % 0.71/0.94 (define @t114 () (@list @t113 @t112 @t111)) % 0.71/0.94 (define @t115 () (not @t58)) % 0.71/0.94 (define @t116 () (not @t59)) % 0.71/0.94 (define @t117 () (not @t31)) % 0.71/0.94 (define @t118 () (not @t62)) % 0.71/0.94 (define @t119 () (not @t63)) % 0.71/0.94 (define @t120 () (or @t116 @t115 @t57)) % 0.71/0.94 (define @t121 () (or @t119 @t118 @t117)) % 0.71/0.94 (define @t122 () (not (tptp.member @t13 @t111))) % 0.71/0.94 (define @t123 () (not (tptp.member @t55 @t112))) % 0.71/0.94 (define @t124 () (not (tptp.member @t56 @t112))) % 0.71/0.94 (define @t125 () (forall @t65 (or @t124 @t123 @t122 (not (tptp.apply @t113 @t56 @t13)) (not (tptp.apply @t113 @t55 @t13)) @t57))) % 0.71/0.94 (define @t126 () (@quantifiers_skolemize @t125 0)) % 0.71/0.94 (define @t127 () (tptp.member @t126 @t112)) % 0.71/0.94 (define @t128 () (@quantifiers_skolemize @t125 1)) % 0.71/0.94 (define @t129 () (= @t126 @t128)) % 0.71/0.94 (define @t130 () (@quantifiers_skolemize @t125 2)) % 0.71/0.94 (define @t131 () (tptp.apply @t113 @t128 @t130)) % 0.71/0.94 (define @t132 () (not @t131)) % 0.71/0.94 (define @t133 () (tptp.apply @t113 @t126 @t130)) % 0.71/0.94 (define @t134 () (not @t133)) % 0.71/0.94 (define @t135 () (tptp.member @t130 @t111)) % 0.71/0.94 (define @t136 () (not @t135)) % 0.71/0.94 (define @t137 () (tptp.member @t128 @t112)) % 0.71/0.94 (define @t138 () (not @t137)) % 0.71/0.94 (define @t139 () (not @t127)) % 0.71/0.94 (define @t140 () (or @t139 @t138 @t136 @t134 @t132 @t129)) % 0.71/0.94 (define @t141 () (not @t21)) % 0.71/0.94 (define @t142 () (not @t22)) % 0.71/0.94 (define @t143 () (not @t25)) % 0.71/0.94 (define @t144 () (not @t26)) % 0.71/0.94 (define @t145 () (not @t5)) % 0.71/0.94 (define @t146 () (or @t142 @t141 @t19)) % 0.71/0.94 (define @t147 () (or @t145 @t144 @t143)) % 0.71/0.94 (define @t148 () (not @t30)) % 0.71/0.94 (define @t149 () (not (forall @t16 (or @t117 @t148)))) % 0.71/0.94 (define @t150 () (forall @t16 (not @t32))) % 0.71/0.94 (define @t151 () (not @t150)) % 0.71/0.94 (define @t152 () (@quantifiers_skolemize @t110 3)) % 0.71/0.94 (define @t153 () (@quantifiers_skolemize @t110 2)) % 0.71/0.94 (define @t154 () (or @t108 @t107 @t106 @t105 @t104)) % 0.71/0.94 (define @t155 () (tptp.maps @t153 @t111 @t152)) % 0.71/0.94 (define @t156 () (tptp.one_to_one @t113 @t112 @t111)) % 0.71/0.94 (define @t157 () (tptp.compose_function @t153 @t113 @t112 @t111 @t152)) % 0.71/0.94 (define @t158 () (tptp.one_to_one @t157 @t112 @t152)) % 0.71/0.94 (define @t159 () (not @t158)) % 0.71/0.94 (define @t160 () (@quantifiers_skolemize @t110 0)) % 0.71/0.94 (define @t161 () (tptp.compose_function @t113 @t160 @t152 @t112 @t111)) % 0.71/0.94 (define @t162 () (tptp.one_to_one @t161 @t152 @t111)) % 0.71/0.94 (define @t163 () (not @t162)) % 0.71/0.94 (define @t164 () (not @t155)) % 0.71/0.94 (define @t165 () (or (not (tptp.maps @t160 @t152 @t112)) (not (tptp.maps @t113 @t112 @t111)) @t164 @t163 @t159 @t156)) % 0.71/0.94 (define @t166 () (@list true)) % 0.71/0.94 (define @t167 () (@list @t165)) % 0.71/0.94 (define @t168 () (not (tptp.member @t2 @t111))) % 0.71/0.94 (define @t169 () (not (tptp.member @t13 @t152))) % 0.71/0.94 (define @t170 () (forall @t6 (or @t168 (not (forall @t16 (or @t169 (not (tptp.apply @t153 @t2 @t13)))))))) % 0.71/0.94 (define @t171 () (and @t170 (forall @t28 (or @t168 (not (tptp.member @t18 @t152)) (not (tptp.member @t17 @t152)) (not (tptp.apply @t153 @t2 @t18)) (not (tptp.apply @t153 @t2 @t17)) @t19)))) % 0.71/0.94 (define @t172 () (= @t155 @t171)) % 0.71/0.94 (define @t173 () (@list false false)) % 0.71/0.94 (define @t174 () (@list false)) % 0.71/0.94 (define @t175 () (@list @t130)) % 0.71/0.94 (define @t176 () (forall @t16 (or @t169 (not (tptp.apply @t153 @t130 @t13))))) % 0.71/0.94 (define @t177 () (not @t176)) % 0.71/0.94 (define @t178 () (or @t136 @t177)) % 0.71/0.94 (define @t179 () (@quantifiers_skolemize @t176 0)) % 0.71/0.94 (define @t180 () (tptp.apply @t153 @t130 @t179)) % 0.71/0.94 (define @t181 () (not @t180)) % 0.71/0.94 (define @t182 () (tptp.member @t179 @t152)) % 0.71/0.94 (define @t183 () (not @t182)) % 0.71/0.94 (define @t184 () (or @t183 @t181)) % 0.71/0.94 (define @t185 () (not @t184)) % 0.71/0.94 (define @t186 () (not @t43)) % 0.71/0.94 (define @t187 () (or @t117 @t148 @t186)) % 0.71/0.94 (define @t188 () (not (forall @t16 @t187))) % 0.71/0.94 (define @t189 () (= @t51 @t188)) % 0.71/0.94 (define @t190 () (not @t48)) % 0.71/0.94 (define @t191 () (forall @t16 (not @t44))) % 0.71/0.94 (define @t192 () (not @t191)) % 0.71/0.94 (define @t193 () (not (tptp.apply @t153 @t13 @t179))) % 0.71/0.94 (define @t194 () (forall @t16 (or @t122 (not (tptp.apply @t113 @t128 @t13)) @t193))) % 0.71/0.94 (define @t195 () (not @t194)) % 0.71/0.94 (define @t196 () (tptp.apply @t157 @t128 @t179)) % 0.71/0.94 (define @t197 () (= @t196 @t195)) % 0.71/0.94 (define @t198 () (or @t138 @t183 @t197)) % 0.71/0.94 (define @t199 () (forall @t16 (or @t122 (not (tptp.apply @t113 @t126 @t13)) @t193))) % 0.71/0.94 (define @t200 () (not @t199)) % 0.71/0.94 (define @t201 () (tptp.apply @t157 @t126 @t179)) % 0.71/0.94 (define @t202 () (= @t201 @t200)) % 0.71/0.94 (define @t203 () (or @t139 @t183 @t202)) % 0.71/0.94 (define @t204 () (or @t136 @t132 @t181)) % 0.71/0.94 (define @t205 () (or @t136 @t134 @t181)) % 0.71/0.94 (define @t206 () (not @t197)) % 0.71/0.94 (define @t207 () (not @t202)) % 0.71/0.94 (define @t208 () (@list @t157 @t112 @t152)) % 0.71/0.94 (define @t209 () (tptp.injective @t157 @t112 @t152)) % 0.71/0.94 (define @t210 () (and @t209 (tptp.surjective @t157 @t112 @t152))) % 0.71/0.94 (define @t211 () (= @t158 @t210)) % 0.71/0.94 (define @t212 () (forall @t65 (or @t124 @t123 @t169 (not (tptp.apply @t157 @t56 @t13)) (not (tptp.apply @t157 @t55 @t13)) @t57))) % 0.71/0.94 (define @t213 () (= @t209 @t212)) % 0.71/0.94 (define @t214 () (not @t201)) % 0.71/0.94 (define @t215 () (not @t196)) % 0.71/0.94 (define @t216 () (or @t138 @t139 @t183 @t215 @t214 (= @t128 @t126))) % 0.71/0.94 (define @t217 () (or @t138 @t139 @t183 @t215 @t214 @t129)) % 0.71/0.94 (define @t218 () (not @t140)) % 0.71/0.94 (define @t219 () (not @t125)) % 0.71/0.94 (define @t220 () (tptp.injective @t113 @t112 @t111)) % 0.71/0.94 (define @t221 () (= @t220 @t125)) % 0.71/0.94 (define @t222 () (tptp.surjective @t113 @t112 @t111)) % 0.71/0.94 (define @t223 () (and @t220 @t222)) % 0.71/0.94 (define @t224 () (= @t156 @t223)) % 0.71/0.94 (define @t225 () (not @t223)) % 0.71/0.94 (define @t226 () (@list true false)) % 0.71/0.94 (define @t227 () (not (tptp.member @t11 @t112))) % 0.71/0.94 (define @t228 () (forall @t16 (or @t122 (not (forall @t73 (or @t227 (not (tptp.apply @t113 @t11 @t13)))))))) % 0.71/0.94 (define @t229 () (= @t222 @t228)) % 0.71/0.94 (define @t230 () (not @t228)) % 0.71/0.94 (define @t231 () (@quantifiers_skolemize @t228 0)) % 0.71/0.94 (define @t232 () (forall @t73 (or @t227 (not (tptp.apply @t113 @t11 @t231))))) % 0.71/0.94 (define @t233 () (not @t232)) % 0.71/0.94 (define @t234 () (tptp.member @t231 @t111)) % 0.71/0.94 (define @t235 () (not @t234)) % 0.71/0.94 (define @t236 () (or @t235 @t233)) % 0.71/0.94 (define @t237 () (not @t236)) % 0.71/0.94 (define @t238 () (@list @t236)) % 0.71/0.94 (define @t239 () (not (tptp.member @t11 @t152))) % 0.71/0.94 (define @t240 () (forall @t73 (or @t239 (not (tptp.apply @t161 @t11 @t231))))) % 0.71/0.94 (define @t241 () (@quantifiers_skolemize @t240 0)) % 0.71/0.94 (define @t242 () (forall @t16 (or (not (tptp.member @t13 @t112)) (not (tptp.apply @t160 @t241 @t13)) (not (tptp.apply @t113 @t13 @t231))))) % 0.71/0.94 (define @t243 () (@quantifiers_skolemize @t242 0)) % 0.71/0.94 (define @t244 () (tptp.apply @t113 @t243 @t231)) % 0.71/0.94 (define @t245 () (not @t244)) % 0.71/0.94 (define @t246 () (tptp.member @t243 @t112)) % 0.71/0.94 (define @t247 () (not @t246)) % 0.71/0.94 (define @t248 () (or @t247 @t245)) % 0.71/0.94 (define @t249 () (@list @t161 @t152 @t111)) % 0.71/0.94 (define @t250 () (tptp.surjective @t161 @t152 @t111)) % 0.71/0.94 (define @t251 () (and (tptp.injective @t161 @t152 @t111) @t250)) % 0.71/0.94 (define @t252 () (= @t162 @t251)) % 0.71/0.94 (define @t253 () (forall @t16 (or @t122 (not (forall @t73 (or @t239 (not (tptp.apply @t161 @t11 @t13)))))))) % 0.71/0.94 (define @t254 () (= @t250 @t253)) % 0.71/0.94 (define @t255 () (not @t240)) % 0.71/0.94 (define @t256 () (or @t235 @t255)) % 0.71/0.94 (define @t257 () (tptp.apply @t161 @t241 @t231)) % 0.71/0.94 (define @t258 () (not @t257)) % 0.71/0.94 (define @t259 () (tptp.member @t241 @t152)) % 0.71/0.94 (define @t260 () (not @t259)) % 0.71/0.94 (define @t261 () (or @t260 @t258)) % 0.71/0.94 (define @t262 () (not @t261)) % 0.71/0.94 (define @t263 () (@list @t261)) % 0.71/0.94 (define @t264 () (not @t242)) % 0.71/0.94 (define @t265 () (= @t257 @t264)) % 0.71/0.94 (define @t266 () (or @t260 @t235 @t265)) % 0.71/0.94 (define @t267 () (@list false false false)) % 0.71/0.94 (define @t268 () (or @t247 (not (tptp.apply @t160 @t241 @t243)) @t245)) % 0.71/0.94 (define @t269 () (not @t268)) % 0.71/0.94 (define @t270 () (@list @t268)) % 0.71/0.94 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.71/0.94 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.71/0.94 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.71/0.94 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.71/0.94 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.71/0.94 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.71/0.94 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.71/0.94 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.71/0.94 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.71/0.94 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.71/0.94 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.71/0.94 (assume @p12 @t40) % 0.71/0.94 (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)))))) % 0.71/0.94 (assume @p14 @t54) % 0.71/0.94 (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)))))) % 0.71/0.94 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.71/0.94 (assume @p17 @t69) % 0.71/0.94 (assume @p18 @t79) % 0.71/0.94 (assume @p19 (forall @t39 (= @t80 (and @t67 @t77)))) % 0.71/0.94 (assume @p20 (forall (@list @t42 @t20 @t4 @t1) (= (tptp.inverse_predicate @t42 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t81 (= @t30 (tptp.apply @t42 @t13 @t2))))))) % 0.71/0.94 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t81 (= @t30 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.71/0.94 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t82))) % 0.71/0.94 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t31 @t82)))) % 0.71/0.94 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t33))) % 0.71/0.94 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t33)))) % 0.71/0.94 (assume @p26 (forall @t91 (= (tptp.increasing @t20 @t4 @t87 @t1 @t83) (forall @t90 (=> @t89 @t84))))) % 0.71/0.94 (assume @p27 (forall @t91 (= (tptp.decreasing @t20 @t4 @t87 @t1 @t83) (forall @t90 (=> @t89 (tptp.apply @t83 @t17 @t18)))))) % 0.71/0.94 (assume @p28 (forall @t91 (= (tptp.isomorphism @t20 @t4 @t87 @t1 @t83) (and @t37 @t80 (forall @t90 (=> (and @t63 @t26 @t62 @t25 @t86 @t85) (= @t88 @t84))))))) % 0.71/0.94 (assume @p29 @t100) % 0.71/0.94 (assume @p30 true) % 0.71/0.94 (step @p31 :rule bool-impl-elim :args (@t31 @t101)) % 0.71/0.94 (step @p32 :rule cong :premises (@p31) :args ((forall @t16 (=> @t31 @t101)))) % 0.71/0.94 (step @p33 :rule bool-and-de-morgan :args (@t71 @t70 true)) % 0.71/0.94 (step @p34 :rule cong :premises (@p33) :args (@t102)) % 0.71/0.94 (step @p35 :rule cong :premises (@p34) :args (@t103)) % 0.71/0.94 (step @p36 :rule exists-elim :args ((= @t74 @t103))) % 0.71/0.94 (step @p37 :rule trans :premises (@p36 @p35)) % 0.71/0.94 (step @p38 :rule refl :args (@t31)) % 0.71/0.94 (step @p39 :rule cong :premises (@p38 @p37) :args (@t75)) % 0.71/0.94 (step @p40 :rule cong :premises (@p39) :args (@t76)) % 0.71/0.94 (step @p41 :rule trans :premises (@p40 @p32)) % 0.71/0.94 (step @p42 :rule refl :args (@t77)) % 0.71/0.94 (step @p43 :rule cong :premises (@p42 @p41) :args (@t78)) % 0.71/0.94 (step @p44 :rule cong :premises (@p43) :args (@t79)) % 0.71/0.94 (step @p45 :rule eq_resolve :premises (@p18 @p44)) % 0.71/0.94 (step @p46 :rule instantiate :premises (@p45) :args (@t114)) % 0.71/0.94 (step @p47 :rule aci_norm :args ((= (or @t121 @t120) (or @t119 @t118 @t117 @t116 @t115 @t57)))) % 0.71/0.94 (step @p48 :rule aci_norm :args ((= (or (or @t116 @t115) @t57) @t120))) % 0.71/0.94 (step @p49 :rule refl :args (@t57)) % 0.71/0.94 (step @p50 :rule bool-and-de-morgan :args (@t59 @t58 true)) % 0.71/0.94 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or (not @t60) @t57))) % 0.71/0.94 (step @p52 :rule trans :premises (@p51 @p48)) % 0.71/0.94 (step @p53 :rule bool-impl-elim :args (@t60 @t57)) % 0.71/0.94 (step @p54 :rule trans :premises (@p53 @p52)) % 0.71/0.94 (step @p55 :rule aci_norm :args ((= (or @t119 (or @t118 @t117)) @t121))) % 0.71/0.94 (step @p56 :rule bool-and-de-morgan :args (@t62 @t31 true)) % 0.71/0.94 (step @p57 :rule refl :args (@t119)) % 0.71/0.94 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or @t119 (not (and @t62 @t31))))) % 0.71/0.94 (step @p59 :rule bool-and-de-morgan :args (@t63 @t62 (and @t31))) % 0.71/0.94 (step @p60 :rule trans :premises (@p59 @p58)) % 0.71/0.94 (step @p61 :rule trans :premises (@p60 @p55)) % 0.71/0.94 (step @p62 :rule nary_cong :premises (@p61 @p54) :args ((or (not @t64) @t61))) % 0.71/0.94 (step @p63 :rule trans :premises (@p62 @p47)) % 0.71/0.94 (step @p64 :rule bool-impl-elim :args (@t64 @t61)) % 0.71/0.94 (step @p65 :rule trans :premises (@p64 @p63)) % 0.71/0.94 (step @p66 :rule cong :premises (@p65) :args (@t66)) % 0.71/0.94 (step @p67 :rule refl :args (@t67)) % 0.71/0.94 (step @p68 :rule cong :premises (@p67 @p66) :args (@t68)) % 0.71/0.94 (step @p69 :rule cong :premises (@p68) :args (@t69)) % 0.71/0.94 (step @p70 :rule eq_resolve :premises (@p17 @p69)) % 0.71/0.94 (step @p71 :rule instantiate :premises (@p70) :args (@t114)) % 0.71/0.94 (step @p72 :rule bool-double-not-elim :args (@t127)) % 0.71/0.94 (step @p73 :rule refl :args (@t140)) % 0.71/0.94 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t140 (not @t139)))) % 0.71/0.94 (step @p75 :rule cnf_or_neg :args (@t140 0)) % 0.71/0.94 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.71/0.94 (step @p77 :rule reordering :premises (@p76) :args ((or @t127 @t140))) % 0.71/0.94 (step @p78 :rule bool-double-not-elim :args (@t137)) % 0.71/0.94 (step @p79 :rule nary_cong :premises (@p73 @p78) :args ((or @t140 (not @t138)))) % 0.71/0.94 (step @p80 :rule cnf_or_neg :args (@t140 1)) % 0.71/0.94 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.71/0.94 (step @p82 :rule reordering :premises (@p81) :args ((or @t137 @t140))) % 0.71/0.94 (step @p83 :rule bool-double-not-elim :args (@t135)) % 0.71/0.94 (step @p84 :rule nary_cong :premises (@p73 @p83) :args ((or @t140 (not @t136)))) % 0.71/0.94 (step @p85 :rule cnf_or_neg :args (@t140 2)) % 0.71/0.94 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.71/0.94 (step @p87 :rule reordering :premises (@p86) :args ((or @t135 @t140))) % 0.71/0.94 (step @p88 :rule bool-double-not-elim :args (@t133)) % 0.71/0.94 (step @p89 :rule nary_cong :premises (@p73 @p88) :args ((or @t140 (not @t134)))) % 0.71/0.94 (step @p90 :rule cnf_or_neg :args (@t140 3)) % 0.71/0.94 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.71/0.94 (step @p92 :rule reordering :premises (@p91) :args ((or @t133 @t140))) % 0.71/0.94 (step @p93 :rule bool-double-not-elim :args (@t131)) % 0.71/0.94 (step @p94 :rule nary_cong :premises (@p73 @p93) :args ((or @t140 (not @t132)))) % 0.71/0.94 (step @p95 :rule cnf_or_neg :args (@t140 4)) % 0.71/0.94 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 0.71/0.94 (step @p97 :rule reordering :premises (@p96) :args ((or @t131 @t140))) % 0.71/0.94 (step @p98 :rule cnf_or_neg :args (@t140 5)) % 0.71/0.94 (step @p99 :rule aci_norm :args ((= (or @t147 @t146) (or @t145 @t144 @t143 @t142 @t141 @t19)))) % 0.71/0.94 (step @p100 :rule aci_norm :args ((= (or (or @t142 @t141) @t19) @t146))) % 0.71/0.94 (step @p101 :rule refl :args (@t19)) % 0.71/0.94 (step @p102 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.71/0.94 (step @p103 :rule nary_cong :premises (@p102 @p101) :args ((or (not @t23) @t19))) % 0.71/0.94 (step @p104 :rule trans :premises (@p103 @p100)) % 0.71/0.94 (step @p105 :rule bool-impl-elim :args (@t23 @t19)) % 0.71/0.94 (step @p106 :rule trans :premises (@p105 @p104)) % 0.71/0.94 (step @p107 :rule aci_norm :args ((= (or @t145 (or @t144 @t143)) @t147))) % 0.71/0.94 (step @p108 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.71/0.94 (step @p109 :rule refl :args (@t145)) % 0.71/0.94 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t145 (not (and @t26 @t25))))) % 0.71/0.94 (step @p111 :rule bool-and-de-morgan :args (@t5 @t26 (and @t25))) % 0.71/0.94 (step @p112 :rule trans :premises (@p111 @p110)) % 0.71/0.94 (step @p113 :rule trans :premises (@p112 @p107)) % 0.71/0.94 (step @p114 :rule nary_cong :premises (@p113 @p106) :args ((or (not @t27) @t24))) % 0.71/0.94 (step @p115 :rule trans :premises (@p114 @p99)) % 0.71/0.94 (step @p116 :rule bool-impl-elim :args (@t27 @t24)) % 0.71/0.94 (step @p117 :rule trans :premises (@p116 @p115)) % 0.71/0.94 (step @p118 :rule cong :premises (@p117) :args (@t29)) % 0.71/0.94 (step @p119 :rule bool-impl-elim :args (@t5 @t149)) % 0.71/0.94 (step @p120 :rule cong :premises (@p119) :args ((forall @t6 (=> @t5 @t149)))) % 0.71/0.94 (step @p121 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.71/0.94 (step @p122 :rule cong :premises (@p121) :args (@t150)) % 0.71/0.94 (step @p123 :rule cong :premises (@p122) :args (@t151)) % 0.71/0.94 (step @p124 :rule exists-elim :args ((= @t33 @t151))) % 0.71/0.94 (step @p125 :rule trans :premises (@p124 @p123)) % 0.71/0.94 (step @p126 :rule refl :args (@t5)) % 0.71/0.94 (step @p127 :rule cong :premises (@p126 @p125) :args (@t34)) % 0.71/0.94 (step @p128 :rule cong :premises (@p127) :args (@t35)) % 0.71/0.94 (step @p129 :rule trans :premises (@p128 @p120)) % 0.71/0.94 (step @p130 :rule nary_cong :premises (@p129 @p118) :args (@t36)) % 0.71/0.94 (step @p131 :rule refl :args (@t37)) % 0.71/0.94 (step @p132 :rule cong :premises (@p131 @p130) :args (@t38)) % 0.71/0.94 (step @p133 :rule cong :premises (@p132) :args (@t40)) % 0.71/0.94 (step @p134 :rule eq_resolve :premises (@p12 @p133)) % 0.71/0.94 (step @p135 :rule instantiate :premises (@p134) :args ((@list @t153 @t111 @t152))) % 0.71/0.94 (step @p136 :rule aci_norm :args ((= (or @t154 @t92) @t109))) % 0.71/0.94 (step @p137 :rule refl :args (@t92)) % 0.71/0.94 (step @p138 :rule 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0.71/0.94 (step @p372 :rule refl :args (@t262)) % 0.71/0.94 (step @p373 :rule bool-double-not-elim :args (@t240)) % 0.71/0.94 (step @p374 :rule nary_cong :premises (@p373 @p372) :args ((or (not @t255) @t262))) % 0.71/0.94 (assume-push @p441 @t255) % 0.71/0.94 (step @p376 :rule skolemize :premises (@p441)) % 0.71/0.94 (step-pop @p442 :rule scope :premises (@p376)) % 0.71/0.94 (step @p377 :rule process_scope :premises (@p442) :args (@t262)) % 0.71/0.94 (step @p379 :rule implies_elim :premises (@p377)) % 0.71/0.94 (step @p380 :rule eq_resolve :premises (@p379 @p374)) % 0.71/0.94 (step @p381 :rule chain_m_resolution :premises (@p380 @p371) :args (@t262 @t166 (@list @t240))) % 0.71/0.94 (step @p382 :rule bool-double-not-elim :args (@t259)) % 0.71/0.94 (step @p383 :rule refl :args (@t261)) % 0.71/0.94 (step @p384 :rule nary_cong :premises (@p383 @p382) :args ((or @t261 (not @t260)))) % 0.71/0.94 (step @p385 :rule cnf_or_neg :args (@t261 0)) % 0.71/0.94 (step @p386 :rule eq_resolve :premises (@p385 @p384)) % 0.71/0.94 (step @p387 :rule reordering :premises (@p386) :args ((or @t259 @t261))) % 0.71/0.94 (step @p388 :rule chain_m_resolution :premises (@p387 @p381) :args (@t259 @t166 @t263)) % 0.71/0.94 (step @p389 :rule cnf_or_pos :args (@t266)) % 0.71/0.94 (step @p390 :rule reordering :premises (@p389) :args ((or @t235 @t260 @t265 (not @t266)))) % 0.71/0.94 (step @p391 :rule chain_m_resolution :premises (@p390 @p368 @p388 @p344) :args (@t265 @t267 (@list @t234 @t259 @t266))) % 0.71/0.94 (step @p392 :rule bool-double-not-elim :args (@t257)) % 0.71/0.94 (step @p393 :rule nary_cong :premises (@p383 @p392) :args ((or @t261 (not @t258)))) % 0.71/0.94 (step @p394 :rule cnf_or_neg :args (@t261 1)) % 0.71/0.94 (step @p395 :rule eq_resolve :premises (@p394 @p393)) % 0.71/0.94 (step @p396 :rule reordering :premises (@p395) :args ((or @t257 @t261))) % 0.71/0.94 (step @p397 :rule chain_m_resolution :premises (@p396 @p381) :args (@t257 @t166 @t263)) % 0.71/0.94 (step @p398 :rule cnf_equiv_pos1 :args (@t265)) % 0.71/0.94 (step @p399 :rule reordering :premises (@p398) :args ((or @t258 @t264 (not @t265)))) % 0.71/0.94 (step @p400 :rule chain_m_resolution :premises (@p399 @p397 @p391) :args (@t264 @t173 (@list @t257 @t265))) % 0.71/0.94 (step @p401 :rule refl :args (@t269)) % 0.71/0.94 (step @p402 :rule bool-double-not-elim :args (@t242)) % 0.71/0.94 (step @p403 :rule nary_cong :premises (@p402 @p401) :args ((or (not @t264) @t269))) % 0.71/0.94 (assume-push @p443 @t264) % 0.71/0.94 (step @p405 :rule skolemize :premises (@p443)) % 0.71/0.94 (step-pop @p444 :rule scope :premises (@p405)) % 0.71/0.94 (step @p406 :rule process_scope :premises (@p444) :args (@t269)) % 0.71/0.94 (step @p408 :rule implies_elim :premises (@p406)) % 0.71/0.94 (step @p409 :rule eq_resolve :premises (@p408 @p403)) % 0.71/0.94 (step @p410 :rule chain_m_resolution :premises (@p409 @p400) :args (@t269 @t166 (@list @t242))) % 0.71/0.94 (step @p411 :rule bool-double-not-elim :args (@t246)) % 0.71/0.94 (step @p412 :rule refl :args (@t268)) % 0.71/0.94 (step @p413 :rule nary_cong :premises (@p412 @p411) :args ((or @t268 (not @t247)))) % 0.71/0.94 (step @p414 :rule cnf_or_neg :args (@t268 0)) % 0.71/0.94 (step @p415 :rule eq_resolve :premises (@p414 @p413)) % 0.71/0.94 (step @p416 :rule reordering :premises (@p415) :args ((or @t246 @t268))) % 0.71/0.94 (step @p417 :rule chain_m_resolution :premises (@p416 @p410) :args (@t246 @t166 @t270)) % 0.71/0.94 (step @p418 :rule bool-double-not-elim :args (@t244)) % 0.71/0.94 (step @p419 :rule nary_cong :premises (@p412 @p418) :args ((or @t268 (not @t245)))) % 0.71/0.94 (step @p420 :rule cnf_or_neg :args (@t268 2)) % 0.71/0.94 (step @p421 :rule eq_resolve :premises (@p420 @p419)) % 0.71/0.94 (step @p422 :rule reordering :premises (@p421) :args ((or @t244 @t268))) % 0.71/0.94 (step @p423 :rule chain_m_resolution :premises (@p422 @p410) :args (@t244 @t166 @t270)) % 0.71/0.94 (step @p424 :rule cnf_or_pos :args (@t248)) % 0.71/0.94 (step @p425 :rule reordering :premises (@p424) :args ((or @t247 @t245 (not @t248)))) % 0.71/0.94 (step @p426 false :rule chain_m_resolution :premises (@p425 @p423 @p417 @p343) :args (false @t267 (@list @t244 @t246 @t248))) % 0.71/0.94 ) % 0.71/0.94 % SZS output end Proof % 0.71/0.94 % cvc5 exiting %------------------------------------------------------------------------------