%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET723+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 : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:31 AM UTC 2026 % Result : Theorem 0.44s 0.64s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET723+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n002.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 16:10:18 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.64 % SZS status Theorem % 0.44/0.64 % SZS output start Proof % 0.44/0.64 ( % 0.44/0.64 (declare-sort $$unsorted 0) % 0.44/0.64 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.empty_set $$unsorted) % 0.44/0.64 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (define @t1 () (@var "B" $$unsorted)) % 0.44/0.64 (define @t2 () (@var "X" $$unsorted)) % 0.44/0.64 (define @t3 () (tptp.member @t2 @t1)) % 0.44/0.64 (define @t4 () (@var "A" $$unsorted)) % 0.44/0.64 (define @t5 () (tptp.member @t2 @t4)) % 0.44/0.64 (define @t6 () (@list @t2)) % 0.44/0.64 (define @t7 () (tptp.subset @t4 @t1)) % 0.44/0.64 (define @t8 () (@list @t4 @t1)) % 0.44/0.64 (define @t9 () (@list @t2 @t4)) % 0.44/0.64 (define @t10 () (@list @t2 @t4 @t1)) % 0.44/0.64 (define @t11 () (@var "E" $$unsorted)) % 0.44/0.64 (define @t12 () (= @t2 @t4)) % 0.44/0.64 (define @t13 () (@var "Y" $$unsorted)) % 0.44/0.64 (define @t14 () (tptp.member @t2 @t13)) % 0.44/0.64 (define @t15 () (tptp.member @t13 @t4)) % 0.44/0.64 (define @t16 () (@list @t13)) % 0.44/0.64 (define @t17 () (@var "Y2" $$unsorted)) % 0.44/0.64 (define @t18 () (@var "Y1" $$unsorted)) % 0.44/0.64 (define @t19 () (= @t18 @t17)) % 0.44/0.64 (define @t20 () (@var "F" $$unsorted)) % 0.44/0.64 (define @t21 () (tptp.apply @t20 @t2 @t17)) % 0.44/0.64 (define @t22 () (tptp.apply @t20 @t2 @t18)) % 0.44/0.64 (define @t23 () (and @t22 @t21)) % 0.44/0.64 (define @t24 () (=> @t23 @t19)) % 0.44/0.64 (define @t25 () (tptp.member @t17 @t1)) % 0.44/0.64 (define @t26 () (tptp.member @t18 @t1)) % 0.44/0.64 (define @t27 () (and @t5 @t26 @t25)) % 0.44/0.64 (define @t28 () (@list @t2 @t18 @t17)) % 0.44/0.64 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.44/0.64 (define @t30 () (tptp.apply @t20 @t2 @t13)) % 0.44/0.64 (define @t31 () (tptp.member @t13 @t1)) % 0.44/0.64 (define @t32 () (and @t31 @t30)) % 0.44/0.64 (define @t33 () (exists @t16 @t32)) % 0.44/0.64 (define @t34 () (=> @t5 @t33)) % 0.44/0.64 (define @t35 () (forall @t6 @t34)) % 0.44/0.64 (define @t36 () (and @t35 @t29)) % 0.44/0.64 (define @t37 () (tptp.maps @t20 @t4 @t1)) % 0.44/0.64 (define @t38 () (= @t37 @t36)) % 0.44/0.64 (define @t39 () (@list @t20 @t4 @t1)) % 0.44/0.64 (define @t40 () (forall @t39 @t38)) % 0.44/0.64 (define @t41 () (@var "Z" $$unsorted)) % 0.44/0.64 (define @t42 () (@var "G" $$unsorted)) % 0.44/0.64 (define @t43 () (tptp.apply @t42 @t13 @t41)) % 0.44/0.64 (define @t44 () (and @t31 @t30 @t43)) % 0.44/0.64 (define @t45 () (exists @t16 @t44)) % 0.44/0.64 (define @t46 () (@var "H" $$unsorted)) % 0.44/0.64 (define @t47 () (@var "C" $$unsorted)) % 0.44/0.64 (define @t48 () (tptp.member @t41 @t47)) % 0.44/0.64 (define @t49 () (and @t5 @t48)) % 0.44/0.64 (define @t50 () (tptp.apply (tptp.compose_function @t42 @t20 @t4 @t1 @t47) @t2 @t41)) % 0.44/0.64 (define @t51 () (=> @t49 (= @t50 @t45))) % 0.44/0.64 (define @t52 () (@list @t42 @t20 @t4 @t1 @t47 @t2 @t41)) % 0.44/0.64 (define @t53 () (forall @t52 @t51)) % 0.44/0.64 (define @t54 () (tptp.apply @t42 @t2 @t17)) % 0.44/0.64 (define @t55 () (and @t22 @t54)) % 0.44/0.64 (define @t56 () (=> @t55 @t19)) % 0.44/0.64 (define @t57 () (forall @t28 (=> @t27 @t56))) % 0.44/0.64 (define @t58 () (tptp.equal_maps @t20 @t42 @t4 @t1)) % 0.44/0.64 (define @t59 () (= @t58 @t57)) % 0.44/0.64 (define @t60 () (forall (@list @t20 @t42 @t4 @t1) @t59)) % 0.44/0.64 (define @t61 () (@var "X2" $$unsorted)) % 0.44/0.64 (define @t62 () (@var "X1" $$unsorted)) % 0.44/0.64 (define @t63 () (= @t62 @t61)) % 0.44/0.64 (define @t64 () (tptp.apply @t20 @t61 @t13)) % 0.44/0.64 (define @t65 () (tptp.apply @t20 @t62 @t13)) % 0.44/0.64 (define @t66 () (and @t65 @t64)) % 0.44/0.64 (define @t67 () (=> @t66 @t63)) % 0.44/0.64 (define @t68 () (tptp.member @t61 @t4)) % 0.44/0.64 (define @t69 () (tptp.member @t62 @t4)) % 0.44/0.64 (define @t70 () (and @t69 @t68 @t31)) % 0.44/0.64 (define @t71 () (@list @t62 @t61 @t13)) % 0.44/0.64 (define @t72 () (forall @t71 (=> @t70 @t67))) % 0.44/0.64 (define @t73 () (tptp.injective @t20 @t4 @t1)) % 0.44/0.64 (define @t74 () (= @t73 @t72)) % 0.44/0.64 (define @t75 () (forall @t39 @t74)) % 0.44/0.64 (define @t76 () (tptp.surjective @t20 @t4 @t1)) % 0.44/0.64 (define @t77 () (tptp.one_to_one @t20 @t4 @t1)) % 0.44/0.64 (define @t78 () (and @t5 @t31)) % 0.44/0.64 (define @t79 () (exists @t6 (and @t5 @t30))) % 0.44/0.64 (define @t80 () (@var "S" $$unsorted)) % 0.44/0.64 (define @t81 () (tptp.apply @t80 @t18 @t17)) % 0.44/0.64 (define @t82 () (tptp.apply @t20 @t61 @t17)) % 0.44/0.64 (define @t83 () (tptp.apply @t20 @t62 @t18)) % 0.44/0.64 (define @t84 () (@var "R" $$unsorted)) % 0.44/0.64 (define @t85 () (tptp.apply @t84 @t62 @t61)) % 0.44/0.64 (define @t86 () (and @t69 @t26 @t68 @t25 @t85 @t83 @t82)) % 0.44/0.64 (define @t87 () (@list @t62 @t18 @t61 @t17)) % 0.44/0.64 (define @t88 () (@list @t20 @t4 @t84 @t1 @t80)) % 0.44/0.64 (define @t89 () (tptp.equal_maps @t42 @t46 @t4 @t1)) % 0.44/0.64 (define @t90 () (tptp.equal_maps (tptp.compose_function @t20 @t42 @t4 @t1 @t47) (tptp.compose_function @t20 @t46 @t4 @t1 @t47) @t4 @t47)) % 0.44/0.64 (define @t91 () (tptp.injective @t20 @t1 @t47)) % 0.44/0.64 (define @t92 () (tptp.maps @t46 @t4 @t1)) % 0.44/0.64 (define @t93 () (tptp.maps @t42 @t4 @t1)) % 0.44/0.64 (define @t94 () (tptp.maps @t20 @t1 @t47)) % 0.44/0.64 (define @t95 () (and @t94 @t93 @t92 @t91 @t90)) % 0.44/0.64 (define @t96 () (@list @t20 @t42 @t46 @t4 @t1 @t47)) % 0.44/0.64 (define @t97 () (forall @t96 (=> @t95 @t89))) % 0.44/0.64 (define @t98 () (not @t97)) % 0.44/0.64 (define @t99 () (not @t21)) % 0.44/0.64 (define @t100 () (not @t22)) % 0.44/0.64 (define @t101 () (not @t25)) % 0.44/0.64 (define @t102 () (not @t26)) % 0.44/0.64 (define @t103 () (not @t5)) % 0.44/0.64 (define @t104 () (or @t100 @t99 @t19)) % 0.44/0.64 (define @t105 () (or @t103 @t102 @t101)) % 0.44/0.64 (define @t106 () (not @t27)) % 0.44/0.64 (define @t107 () (not @t30)) % 0.44/0.64 (define @t108 () (not @t31)) % 0.44/0.64 (define @t109 () (not (forall @t16 (or @t108 @t107)))) % 0.44/0.64 (define @t110 () (forall @t16 (not @t32))) % 0.44/0.64 (define @t111 () (not @t110)) % 0.44/0.64 (define @t112 () (not @t90)) % 0.44/0.64 (define @t113 () (not @t91)) % 0.44/0.64 (define @t114 () (not @t92)) % 0.44/0.64 (define @t115 () (not @t93)) % 0.44/0.64 (define @t116 () (not @t94)) % 0.44/0.64 (define @t117 () (or @t116 @t115 @t114 @t113 @t112 @t89)) % 0.44/0.64 (define @t118 () (forall @t96 @t117)) % 0.44/0.64 (define @t119 () (@quantifiers_skolemize @t118 5)) % 0.44/0.64 (define @t120 () (@quantifiers_skolemize @t118 4)) % 0.44/0.64 (define @t121 () (@quantifiers_skolemize @t118 0)) % 0.44/0.64 (define @t122 () (@list @t121 @t120 @t119)) % 0.44/0.64 (define @t123 () (or @t116 @t115 @t114 @t113 @t112)) % 0.44/0.64 (define @t124 () (tptp.maps @t121 @t120 @t119)) % 0.44/0.64 (define @t125 () (@quantifiers_skolemize @t118 3)) % 0.44/0.64 (define @t126 () (@quantifiers_skolemize @t118 2)) % 0.44/0.64 (define @t127 () (@quantifiers_skolemize @t118 1)) % 0.44/0.64 (define @t128 () (tptp.equal_maps @t127 @t126 @t125 @t120)) % 0.44/0.64 (define @t129 () (tptp.compose_function @t121 @t126 @t125 @t120 @t119)) % 0.44/0.64 (define @t130 () (tptp.compose_function @t121 @t127 @t125 @t120 @t119)) % 0.44/0.64 (define @t131 () (tptp.equal_maps @t130 @t129 @t125 @t119)) % 0.44/0.64 (define @t132 () (not @t131)) % 0.44/0.64 (define @t133 () (tptp.injective @t121 @t120 @t119)) % 0.44/0.64 (define @t134 () (not @t133)) % 0.44/0.64 (define @t135 () (not @t124)) % 0.44/0.64 (define @t136 () (or @t135 (not (tptp.maps @t127 @t125 @t120)) (not (tptp.maps @t126 @t125 @t120)) @t134 @t132 @t128)) % 0.44/0.64 (define @t137 () (@list true)) % 0.44/0.64 (define @t138 () (@list @t136)) % 0.44/0.64 (define @t139 () (not (tptp.member @t17 @t119))) % 0.44/0.64 (define @t140 () (not (tptp.member @t18 @t119))) % 0.44/0.64 (define @t141 () (not (tptp.member @t2 @t120))) % 0.44/0.64 (define @t142 () (not (tptp.member @t13 @t119))) % 0.44/0.64 (define @t143 () (forall @t6 (or @t141 (not (forall @t16 (or @t142 (not (tptp.apply @t121 @t2 @t13)))))))) % 0.44/0.64 (define @t144 () (and @t143 (forall @t28 (or @t141 @t140 @t139 (not (tptp.apply @t121 @t2 @t18)) (not (tptp.apply @t121 @t2 @t17)) @t19)))) % 0.44/0.64 (define @t145 () (= @t124 @t144)) % 0.44/0.64 (define @t146 () (@list false false)) % 0.44/0.64 (define @t147 () (@list false)) % 0.44/0.64 (define @t148 () (not (tptp.member @t2 @t125))) % 0.44/0.64 (define @t149 () (forall @t28 (or @t148 (not (tptp.member @t18 @t120)) (not (tptp.member @t17 @t120)) (not (tptp.apply @t127 @t2 @t18)) (not (tptp.apply @t126 @t2 @t17)) @t19))) % 0.44/0.64 (define @t150 () (@quantifiers_skolemize @t149 1)) % 0.44/0.64 (define @t151 () (@list @t150)) % 0.44/0.64 (define @t152 () (not @t54)) % 0.44/0.64 (define @t153 () (or @t100 @t152 @t19)) % 0.44/0.64 (define @t154 () (= @t128 @t149)) % 0.44/0.64 (define @t155 () (not @t149)) % 0.44/0.64 (define @t156 () (@list true false)) % 0.44/0.64 (define @t157 () (tptp.member @t150 @t120)) % 0.44/0.64 (define @t158 () (@quantifiers_skolemize @t149 2)) % 0.44/0.64 (define @t159 () (= @t150 @t158)) % 0.44/0.64 (define @t160 () (@quantifiers_skolemize @t149 0)) % 0.44/0.64 (define @t161 () (tptp.apply @t126 @t160 @t158)) % 0.44/0.64 (define @t162 () (not @t161)) % 0.44/0.64 (define @t163 () (tptp.apply @t127 @t160 @t150)) % 0.44/0.64 (define @t164 () (not @t163)) % 0.44/0.64 (define @t165 () (tptp.member @t158 @t120)) % 0.44/0.64 (define @t166 () (not @t165)) % 0.44/0.64 (define @t167 () (not @t157)) % 0.44/0.64 (define @t168 () (tptp.member @t160 @t125)) % 0.44/0.64 (define @t169 () (not @t168)) % 0.44/0.64 (define @t170 () (or @t169 @t167 @t166 @t164 @t162 @t159)) % 0.44/0.64 (define @t171 () (@list @t170)) % 0.44/0.64 (define @t172 () (forall @t16 (or @t142 (not (tptp.apply @t121 @t150 @t13))))) % 0.44/0.64 (define @t173 () (not @t172)) % 0.44/0.64 (define @t174 () (or @t167 @t173)) % 0.44/0.64 (define @t175 () (@quantifiers_skolemize @t172 0)) % 0.44/0.64 (define @t176 () (tptp.apply @t121 @t150 @t175)) % 0.44/0.64 (define @t177 () (not @t176)) % 0.44/0.64 (define @t178 () (tptp.member @t175 @t119)) % 0.44/0.64 (define @t179 () (not @t178)) % 0.44/0.64 (define @t180 () (or @t179 @t177)) % 0.44/0.64 (define @t181 () (@list @t180)) % 0.44/0.64 (define @t182 () (not @t64)) % 0.44/0.64 (define @t183 () (not @t65)) % 0.44/0.64 (define @t184 () (not @t68)) % 0.44/0.64 (define @t185 () (not @t69)) % 0.44/0.64 (define @t186 () (or @t183 @t182 @t63)) % 0.44/0.64 (define @t187 () (or @t185 @t184 @t108)) % 0.44/0.64 (define @t188 () (forall @t71 (or (not (tptp.member @t62 @t120)) (not (tptp.member @t61 @t120)) @t142 (not (tptp.apply @t121 @t62 @t13)) (not (tptp.apply @t121 @t61 @t13)) @t63))) % 0.44/0.64 (define @t189 () (= @t133 @t188)) % 0.44/0.64 (define @t190 () (forall @t16 (or @t142 (not (tptp.apply @t121 @t158 @t13))))) % 0.44/0.64 (define @t191 () (@quantifiers_skolemize @t190 0)) % 0.44/0.64 (define @t192 () (tptp.apply @t121 @t150 @t191)) % 0.44/0.64 (define @t193 () (not @t192)) % 0.44/0.64 (define @t194 () (tptp.apply @t121 @t158 @t191)) % 0.44/0.64 (define @t195 () (not @t194)) % 0.44/0.64 (define @t196 () (tptp.member @t191 @t119)) % 0.44/0.64 (define @t197 () (not @t196)) % 0.44/0.64 (define @t198 () (or @t166 @t167 @t197 @t195 @t193 (= @t158 @t150))) % 0.44/0.64 (define @t199 () (or @t166 @t167 @t197 @t195 @t193 @t159)) % 0.44/0.64 (define @t200 () (@list @t188)) % 0.44/0.64 (define @t201 () (@list @t158)) % 0.44/0.64 (define @t202 () (not @t190)) % 0.44/0.64 (define @t203 () (or @t166 @t202)) % 0.44/0.64 (define @t204 () (or @t197 @t195)) % 0.44/0.64 (define @t205 () (@list @t204)) % 0.44/0.64 (define @t206 () (not (tptp.member @t13 @t120))) % 0.44/0.64 (define @t207 () (forall @t16 (or @t206 (not (tptp.apply @t127 @t160 @t13)) (not (tptp.apply @t121 @t13 @t175))))) % 0.44/0.64 (define @t208 () (@quantifiers_skolemize @t207 0)) % 0.44/0.64 (define @t209 () (tptp.apply @t121 @t208 @t175)) % 0.44/0.64 (define @t210 () (not @t209)) % 0.44/0.64 (define @t211 () (tptp.member @t208 @t120)) % 0.44/0.64 (define @t212 () (not @t211)) % 0.44/0.64 (define @t213 () (or @t212 @t167 @t179 @t210 @t177 (= @t208 @t150))) % 0.44/0.64 (define @t214 () (= @t150 @t208)) % 0.44/0.64 (define @t215 () (or @t212 @t167 @t179 @t210 @t177 @t214)) % 0.44/0.64 (define @t216 () (or @t167 @t164 @t177)) % 0.44/0.64 (define @t217 () (not @t216)) % 0.44/0.64 (define @t218 () (@list false false false)) % 0.44/0.64 (define @t219 () (not @t207)) % 0.44/0.64 (define @t220 () (or @t212 (not (tptp.apply @t127 @t160 @t208)) @t210)) % 0.44/0.64 (define @t221 () (not @t220)) % 0.44/0.64 (define @t222 () (not @t219)) % 0.44/0.64 (define @t223 () (@list @t220)) % 0.44/0.64 (define @t224 () (@list false false false false false false)) % 0.44/0.64 (define @t225 () (forall @t28 (or @t148 @t140 @t139 (not (tptp.apply @t130 @t2 @t18)) (not (tptp.apply @t129 @t2 @t17)) @t19))) % 0.44/0.64 (define @t226 () (= @t131 @t225)) % 0.44/0.64 (define @t227 () (not @t43)) % 0.44/0.64 (define @t228 () (or @t108 @t107 @t227)) % 0.44/0.64 (define @t229 () (not (forall @t16 @t228))) % 0.44/0.64 (define @t230 () (= @t50 @t229)) % 0.44/0.64 (define @t231 () (not @t48)) % 0.44/0.64 (define @t232 () (forall @t16 (not @t44))) % 0.44/0.64 (define @t233 () (not @t232)) % 0.44/0.64 (define @t234 () (forall @t16 (or @t206 (not (tptp.apply @t126 @t160 @t13)) (not (tptp.apply @t121 @t13 @t191))))) % 0.44/0.64 (define @t235 () (not @t234)) % 0.44/0.64 (define @t236 () (tptp.apply @t129 @t160 @t191)) % 0.44/0.64 (define @t237 () (= @t236 @t235)) % 0.44/0.64 (define @t238 () (or @t169 @t197 @t237)) % 0.44/0.64 (define @t239 () (or @t166 @t162 @t195)) % 0.44/0.64 (define @t240 () (not @t239)) % 0.44/0.64 (define @t241 () (not @t237)) % 0.44/0.64 (define @t242 () (tptp.apply @t130 @t160 @t175)) % 0.44/0.64 (define @t243 () (= @t242 @t219)) % 0.44/0.64 (define @t244 () (or @t169 @t179 @t243)) % 0.44/0.64 (define @t245 () (not @t243)) % 0.44/0.64 (define @t246 () (= @t175 @t191)) % 0.44/0.64 (define @t247 () (not @t236)) % 0.44/0.64 (define @t248 () (not @t242)) % 0.44/0.64 (define @t249 () (or @t169 @t179 @t197 @t248 @t247 @t246)) % 0.44/0.64 (define @t250 () (not @t214)) % 0.44/0.64 (define @t251 () (not @t246)) % 0.44/0.64 (define @t252 () (and @t176 @t214 @t246 @t193)) % 0.44/0.64 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.44/0.64 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.44/0.64 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.44/0.64 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.44/0.64 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.44/0.64 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.44/0.64 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.44/0.64 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.44/0.64 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.44/0.64 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.44/0.64 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.44/0.64 (assume @p12 @t40) % 0.44/0.64 (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)))))) % 0.44/0.64 (assume @p14 @t53) % 0.44/0.64 (assume @p15 @t60) % 0.44/0.64 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.44/0.64 (assume @p17 @t75) % 0.44/0.64 (assume @p18 (forall @t39 (= @t76 (forall @t16 (=> @t31 (exists (@list @t11) (and (tptp.member @t11 @t4) (tptp.apply @t20 @t11 @t13)))))))) % 0.44/0.64 (assume @p19 (forall @t39 (= @t77 (and @t73 @t76)))) % 0.44/0.64 (assume @p20 (forall (@list @t42 @t20 @t4 @t1) (= (tptp.inverse_predicate @t42 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t78 (= @t30 (tptp.apply @t42 @t13 @t2))))))) % 0.44/0.64 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t78 (= @t30 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.44/0.64 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t79))) % 0.44/0.64 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t31 @t79)))) % 0.44/0.64 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t33))) % 0.44/0.64 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t33)))) % 0.44/0.64 (assume @p26 (forall @t88 (= (tptp.increasing @t20 @t4 @t84 @t1 @t80) (forall @t87 (=> @t86 @t81))))) % 0.44/0.64 (assume @p27 (forall @t88 (= (tptp.decreasing @t20 @t4 @t84 @t1 @t80) (forall @t87 (=> @t86 (tptp.apply @t80 @t17 @t18)))))) % 0.44/0.64 (assume @p28 (forall @t88 (= (tptp.isomorphism @t20 @t4 @t84 @t1 @t80) (and @t37 @t77 (forall @t87 (=> (and @t69 @t26 @t68 @t25 @t83 @t82) (= @t85 @t81))))))) % 0.44/0.64 (assume @p29 @t98) % 0.44/0.64 (assume @p30 true) % 0.44/0.64 (step @p31 :rule aci_norm :args ((= (or @t105 @t104) (or @t103 @t102 @t101 @t100 @t99 @t19)))) % 0.44/0.64 (step @p32 :rule aci_norm :args ((= (or (or @t100 @t99) @t19) @t104))) % 0.44/0.64 (step @p33 :rule refl :args (@t19)) % 0.44/0.64 (step @p34 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.44/0.64 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or (not @t23) @t19))) % 0.44/0.64 (step @p36 :rule trans :premises (@p35 @p32)) % 0.44/0.64 (step @p37 :rule bool-impl-elim :args (@t23 @t19)) % 0.44/0.64 (step @p38 :rule trans :premises (@p37 @p36)) % 0.44/0.64 (step @p39 :rule aci_norm :args ((= (or @t103 (or @t102 @t101)) @t105))) % 0.44/0.64 (step @p40 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.44/0.64 (step @p41 :rule refl :args (@t103)) % 0.44/0.64 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t103 (not (and @t26 @t25))))) % 0.44/0.64 (step @p43 :rule bool-and-de-morgan :args (@t5 @t26 (and @t25))) % 0.44/0.64 (step @p44 :rule trans :premises (@p43 @p42)) % 0.44/0.64 (step @p45 :rule trans :premises (@p44 @p39)) % 0.44/0.64 (step @p46 :rule nary_cong :premises (@p45 @p38) :args ((or @t106 @t24))) % 0.44/0.64 (step @p47 :rule trans :premises (@p46 @p31)) % 0.44/0.64 (step @p48 :rule bool-impl-elim :args (@t27 @t24)) % 0.44/0.64 (step @p49 :rule trans :premises (@p48 @p47)) % 0.44/0.64 (step @p50 :rule cong :premises (@p49) :args (@t29)) % 0.44/0.64 (step @p51 :rule bool-impl-elim :args (@t5 @t109)) % 0.44/0.64 (step @p52 :rule cong :premises (@p51) :args ((forall @t6 (=> @t5 @t109)))) % 0.44/0.64 (step @p53 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.44/0.64 (step @p54 :rule cong :premises (@p53) :args (@t110)) % 0.44/0.64 (step @p55 :rule cong :premises (@p54) :args (@t111)) % 0.44/0.64 (step @p56 :rule exists-elim :args ((= @t33 @t111))) % 0.44/0.64 (step @p57 :rule trans :premises (@p56 @p55)) % 0.44/0.64 (step @p58 :rule refl :args (@t5)) % 0.44/0.64 (step @p59 :rule cong :premises (@p58 @p57) :args (@t34)) % 0.44/0.64 (step @p60 :rule cong :premises (@p59) :args (@t35)) % 0.44/0.64 (step @p61 :rule trans :premises (@p60 @p52)) % 0.44/0.64 (step @p62 :rule nary_cong :premises (@p61 @p50) :args (@t36)) % 0.44/0.64 (step @p63 :rule refl :args (@t37)) % 0.44/0.64 (step @p64 :rule cong :premises (@p63 @p62) :args (@t38)) % 0.44/0.64 (step @p65 :rule cong :premises (@p64) :args (@t40)) % 0.44/0.64 (step @p66 :rule eq_resolve :premises (@p12 @p65)) % 0.44/0.64 (step @p67 :rule instantiate :premises (@p66) :args (@t122)) % 0.44/0.64 (step @p68 :rule aci_norm :args ((= (or @t123 @t89) @t117))) % 0.44/0.64 (step @p69 :rule refl :args (@t89)) % 0.44/0.64 (step @p70 :rule aci_norm :args ((= (or @t116 (or @t115 (or @t114 (or @t113 @t112)))) @t123))) % 0.44/0.64 (step @p71 :rule bool-and-de-morgan :args (@t91 @t90 true)) % 0.44/0.64 (step @p72 :rule refl :args (@t114)) % 0.44/0.64 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t114 (not (and @t91 @t90))))) % 0.44/0.64 (step @p74 :rule bool-and-de-morgan :args (@t92 @t91 (and @t90))) % 0.44/0.64 (step @p75 :rule trans :premises (@p74 @p73)) % 0.44/0.64 (step @p76 :rule refl :args (@t115)) % 0.44/0.64 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t115 (not (and @t92 @t91 @t90))))) % 0.44/0.64 (step @p78 :rule bool-and-de-morgan :args (@t93 @t92 (and @t91 @t90))) % 0.44/0.64 (step @p79 :rule trans :premises (@p78 @p77)) % 0.44/0.64 (step @p80 :rule refl :args (@t116)) % 0.44/0.64 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t116 (not (and @t93 @t92 @t91 @t90))))) % 0.44/0.64 (step @p82 :rule bool-and-de-morgan :args (@t94 @t93 (and @t92 @t91 @t90))) % 0.44/0.64 (step @p83 :rule trans :premises (@p82 @p81)) % 0.44/0.64 (step @p84 :rule trans :premises (@p83 @p70)) % 0.44/0.64 (step @p85 :rule nary_cong :premises (@p84 @p69) :args ((or (not @t95) @t89))) % 0.44/0.64 (step @p86 :rule trans :premises (@p85 @p68)) % 0.44/0.64 (step @p87 :rule bool-impl-elim :args (@t95 @t89)) % 0.44/0.64 (step @p88 :rule trans :premises (@p87 @p86)) % 0.44/0.64 (step @p89 :rule cong :premises (@p88) :args (@t97)) % 0.44/0.64 (step @p90 :rule cong :premises (@p89) :args (@t98)) % 0.44/0.64 (step @p91 :rule eq_resolve :premises (@p29 @p90)) % 0.44/0.64 (step @p92 :rule skolemize :premises (@p91)) % 0.44/0.64 (step @p93 :rule bool-double-not-elim :args (@t124)) % 0.44/0.64 (step @p94 :rule refl :args (@t136)) % 0.44/0.64 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or @t136 (not @t135)))) % 0.44/0.64 (step @p96 :rule cnf_or_neg :args (@t136 0)) % 0.44/0.64 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 0.44/0.64 (step @p98 :rule reordering :premises (@p97) :args ((or @t124 @t136))) % 0.44/0.64 (step @p99 :rule chain_m_resolution :premises (@p98 @p92) :args (@t124 @t137 @t138)) % 0.44/0.64 (step @p100 :rule cnf_equiv_pos1 :args (@t145)) % 0.44/0.64 (step @p101 :rule reordering :premises (@p100) :args ((or @t135 @t144 (not @t145)))) % 0.44/0.64 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p67) :args (@t144 @t146 (@list @t124 @t145))) % 0.44/0.64 (step @p103 :rule cnf_and_pos :args (@t144 0)) % 0.44/0.64 (step @p104 :rule reordering :premises (@p103) :args ((or @t143 (not @t144)))) % 0.44/0.64 (step @p105 :rule chain_m_resolution :premises (@p104 @p102) :args (@t143 @t147 (@list @t144))) % 0.44/0.64 (step @p106 :rule instantiate :premises (@p105) :args (@t151)) % 0.44/0.64 (step @p107 :rule aci_norm :args ((= (or @t105 @t153) (or @t103 @t102 @t101 @t100 @t152 @t19)))) % 0.44/0.64 (step @p108 :rule aci_norm :args ((= (or (or @t100 @t152) @t19) @t153))) % 0.44/0.64 (step @p109 :rule bool-and-de-morgan :args (@t22 @t54 true)) % 0.44/0.64 (step @p110 :rule nary_cong :premises (@p109 @p33) :args ((or (not @t55) @t19))) % 0.44/0.64 (step @p111 :rule trans :premises (@p110 @p108)) % 0.44/0.64 (step @p112 :rule bool-impl-elim :args (@t55 @t19)) % 0.44/0.64 (step @p113 :rule trans :premises (@p112 @p111)) % 0.44/0.64 (step @p114 :rule nary_cong :premises (@p45 @p113) :args ((or @t106 @t56))) % 0.44/0.64 (step @p115 :rule trans :premises (@p114 @p107)) % 0.44/0.64 (step @p116 :rule bool-impl-elim :args (@t27 @t56)) % 0.44/0.64 (step @p117 :rule trans :premises (@p116 @p115)) % 0.44/0.64 (step @p118 :rule cong :premises (@p117) :args (@t57)) % 0.44/0.64 (step @p119 :rule refl :args (@t58)) % 0.44/0.64 (step @p120 :rule cong :premises (@p119 @p118) :args (@t59)) % 0.44/0.64 (step @p121 :rule cong :premises (@p120) :args (@t60)) % 0.44/0.64 (step @p122 :rule eq_resolve :premises (@p15 @p121)) % 0.44/0.64 (step @p123 :rule instantiate :premises (@p122) :args ((@list @t127 @t126 @t125 @t120))) % 0.44/0.64 (step @p124 :rule cnf_or_neg :args (@t136 5)) % 0.44/0.64 (step @p125 :rule chain_m_resolution :premises (@p124 @p92) :args ((not @t128) @t137 @t138)) % 0.44/0.64 (step @p126 :rule cnf_equiv_pos2 :args (@t154)) % 0.44/0.64 (step @p127 :rule reordering :premises (@p126) :args ((or @t128 @t155 (not @t154)))) % 0.44/0.64 (step @p128 :rule chain_m_resolution :premises (@p127 @p125 @p123) :args (@t155 @t156 (@list @t128 @t154))) % 0.44/0.64 (step @p129 :rule skolemize :premises (@p128)) % 0.44/0.64 (step @p130 :rule bool-double-not-elim :args (@t157)) % 0.44/0.64 (step @p131 :rule refl :args (@t170)) % 0.44/0.64 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or @t170 (not @t167)))) % 0.44/0.64 (step @p133 :rule cnf_or_neg :args (@t170 1)) % 0.44/0.64 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.44/0.64 (step @p135 :rule reordering :premises (@p134) :args ((or @t157 @t170))) % 0.44/0.64 (step @p136 :rule chain_m_resolution :premises (@p135 @p129) :args (@t157 @t137 @t171)) % 0.44/0.64 (step @p137 :rule cnf_or_pos :args (@t174)) % 0.44/0.64 (step @p138 :rule reordering :premises (@p137) :args ((or @t167 @t173 (not @t174)))) % 0.44/0.64 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p106) :args (@t173 @t146 (@list @t157 @t174))) % 0.44/0.64 (step @p140 :rule skolemize :premises (@p139)) % 0.44/0.64 (step @p141 :rule bool-double-not-elim :args (@t176)) % 0.44/0.64 (step @p142 :rule refl :args (@t180)) % 0.44/0.64 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t180 (not @t177)))) % 0.44/0.64 (step @p144 :rule cnf_or_neg :args (@t180 1)) % 0.44/0.64 (step @p145 :rule eq_resolve :premises (@p144 @p143)) % 0.44/0.64 (step @p146 :rule reordering :premises (@p145) :args ((or @t176 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0.44/0.64 (assume-push @p427 @t176) % 0.44/0.64 (assume-push @p428 @t214) % 0.44/0.64 (assume-push @p429 @t246) % 0.44/0.64 (assume-push @p430 @t193) % 0.44/0.64 (step @p384 :rule evaluate :args ((= false true))) % 0.44/0.64 (step @p385 :rule true_intro :premises (@p147)) % 0.44/0.64 (step @p386 :rule symm :premises (@p429)) % 0.44/0.64 (step @p387 :rule symm :premises (@p428)) % 0.44/0.64 (step @p388 :rule refl :args (@t121)) % 0.44/0.64 (step @p389 :rule cong :premises (@p388 @p387 @p386) :args ((tptp.apply @t121 @t208 @t191))) % 0.44/0.64 (step @p390 :rule refl :args (@t191)) % 0.44/0.64 (step @p391 :rule cong :premises (@p388 @p428 @p390) :args (@t192)) % 0.44/0.64 (step @p392 :rule false_intro :premises (@p226)) % 0.44/0.64 (step @p393 :rule symm :premises (@p392)) % 0.44/0.64 (step @p394 :rule trans :premises (@p393 @p391 @p389 @p385)) % 0.44/0.64 (step @p395 false :rule eq_resolve :premises (@p394 @p384)) % 0.44/0.64 (step-pop @p431 :rule scope :premises (@p395)) % 0.44/0.64 (step-pop @p432 :rule scope :premises (@p431)) % 0.44/0.64 (step-pop @p433 :rule scope :premises (@p432)) % 0.44/0.64 (step-pop @p434 :rule scope :premises (@p433)) % 0.44/0.64 (step @p396 :rule process_scope :premises (@p434) :args (false)) % 0.44/0.64 (assume-push @p435 @t176) % 0.44/0.64 (assume-push @p436 @t246) % 0.44/0.64 (assume-push @p437 @t193) % 0.44/0.64 (assume-push @p438 @t214) % 0.44/0.64 (step @p405 :rule and_intro :premises (@p147 @p438 @p436 @p226)) % 0.44/0.64 (step-pop @p439 :rule scope :premises (@p405)) % 0.44/0.64 (step-pop @p440 :rule scope :premises (@p439)) % 0.44/0.64 (step-pop @p441 :rule scope :premises (@p440)) % 0.44/0.64 (step-pop @p442 :rule scope :premises (@p441)) % 0.44/0.64 (step @p406 :rule process_scope :premises (@p442) :args (@t252)) % 0.44/0.64 (step @p411 :rule implies_elim :premises (@p406)) % 0.44/0.64 (step @p412 :rule resolution :premises (@p411 @p396) :args (true @t252)) % 0.44/0.64 (step @p413 :rule not_and :premises (@p412)) % 0.44/0.64 (step @p414 :rule eq_resolve :premises (@p413 @p379)) % 0.44/0.64 (step @p415 :rule reordering :premises (@p414) :args ((or @t177 @t192 @t251 @t250))) % 0.44/0.64 (step @p416 false :rule chain_m_resolution :premises (@p415 @p375 @p287 @p226 @p147) :args (false (@list false false true false) (@list @t246 @t214 @t192 @t176))) % 0.44/0.64 ) % 0.44/0.64 % SZS output end Proof % 0.44/0.64 % cvc5 exiting %------------------------------------------------------------------------------