%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET255-6 : TPTP v9.2.1. Bugfixed v2.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:47:43 AM UTC 2026 % Result : Unsatisfiable 5.39s 5.65s % Output : Proof 5.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.14 % Problem : SET255-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.12/0.15 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.36 % Computer : n005.cluster.edu % 0.17/0.36 % Model : x86_64 x86_64 % 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.36 % Memory : 8042.1875MB % 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Tue Jun 2 15:15:48 EDT 2026 % 0.17/0.36 % CPUTime : % 0.28/0.55 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 5.39/5.65 % SZS status Unsatisfiable % 5.39/5.65 % SZS output start Proof % 5.39/5.66 ( % 5.39/5.66 (declare-sort $$unsorted 0) % 5.39/5.66 (declare-const tptp.x $$unsorted) % 5.39/5.66 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.identity_relation $$unsorted) % 5.39/5.66 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.composition_function $$unsorted) % 5.39/5.66 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.compose_class (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.domain_relation $$unsorted) % 5.39/5.66 (declare-const tptp.null_class $$unsorted) % 5.39/5.66 (declare-const tptp.subset_relation $$unsorted) % 5.39/5.66 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.inductive (-> $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.omega $$unsorted) % 5.39/5.66 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.universal_class $$unsorted) % 5.39/5.66 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.choice $$unsorted) % 5.39/5.66 (declare-const tptp.successor_relation $$unsorted) % 5.39/5.66 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.single_valued2 (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.element_relation $$unsorted) % 5.39/5.66 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.single_valued3 (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.function (-> $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.operation (-> $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.single_valued1 (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.y1 $$unsorted) % 5.39/5.66 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.singleton_relation $$unsorted) % 5.39/5.66 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.application_function $$unsorted) % 5.39/5.66 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.39/5.66 (declare-const tptp.y2 $$unsorted) % 5.39/5.66 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 5.39/5.66 (declare-const tptp.z $$unsorted) % 5.39/5.66 (define @t1 () (@var "Y" $$unsorted)) % 5.39/5.66 (define @t2 () (@var "U" $$unsorted)) % 5.39/5.66 (define @t3 () (@var "X" $$unsorted)) % 5.39/5.66 (define @t4 () (tptp.member @t2 @t3)) % 5.39/5.66 (define @t5 () (not @t4)) % 5.39/5.66 (define @t6 () (tptp.subclass @t3 @t1)) % 5.39/5.66 (define @t7 () (not @t6)) % 5.39/5.66 (define @t8 () (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 5.39/5.66 (define @t9 () (tptp.not_subclass_element @t3 @t1)) % 5.39/5.66 (define @t10 () (@list @t3 @t1)) % 5.39/5.66 (define @t11 () (@list @t3)) % 5.39/5.66 (define @t12 () (= @t3 @t1)) % 5.39/5.66 (define @t13 () (not @t12)) % 5.39/5.66 (define @t14 () (tptp.subclass @t1 @t3)) % 5.39/5.66 (define @t15 () (tptp.unordered_pair @t3 @t1)) % 5.39/5.66 (define @t16 () (not (tptp.member @t3 tptp.universal_class))) % 5.39/5.66 (define @t17 () (not (tptp.member @t1 tptp.universal_class))) % 5.39/5.66 (define @t18 () (tptp.singleton @t3)) % 5.39/5.66 (define @t19 () (tptp.ordered_pair @t3 @t1)) % 5.39/5.66 (define @t20 () (tptp.singleton @t1)) % 5.39/5.66 (define @t21 () (tptp.cross_product @t3 @t1)) % 5.39/5.66 (define @t22 () (@var "V" $$unsorted)) % 5.39/5.66 (define @t23 () (tptp.ordered_pair @t2 @t22)) % 5.39/5.66 (define @t24 () (tptp.member @t23 @t21)) % 5.39/5.66 (define @t25 () (not @t24)) % 5.39/5.66 (define @t26 () (@list @t2 @t22 @t3 @t1)) % 5.39/5.66 (define @t27 () (tptp.member @t22 @t1)) % 5.39/5.66 (define @t28 () (@var "Z" $$unsorted)) % 5.39/5.66 (define @t29 () (tptp.ordered_pair (tptp.first @t28) (tptp.second @t28))) % 5.39/5.66 (define @t30 () (not (tptp.member @t28 @t21))) % 5.39/5.66 (define @t31 () (or @t30 (= @t29 @t28))) % 5.39/5.66 (define @t32 () (@list @t28 @t3 @t1)) % 5.39/5.66 (define @t33 () (forall @t32 @t31)) % 5.39/5.66 (define @t34 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 5.39/5.66 (define @t35 () (tptp.member @t3 @t1)) % 5.39/5.66 (define @t36 () (tptp.member @t19 tptp.element_relation)) % 5.39/5.66 (define @t37 () (not (tptp.member @t19 @t34))) % 5.39/5.66 (define @t38 () (tptp.member @t28 @t3)) % 5.39/5.66 (define @t39 () (tptp.intersection @t3 @t1)) % 5.39/5.66 (define @t40 () (tptp.member @t28 @t39)) % 5.39/5.66 (define @t41 () (not @t40)) % 5.39/5.66 (define @t42 () (tptp.member @t28 @t1)) % 5.39/5.66 (define @t43 () (not @t38)) % 5.39/5.66 (define @t44 () (tptp.complement @t3)) % 5.39/5.66 (define @t45 () (tptp.member @t28 @t44)) % 5.39/5.66 (define @t46 () (@list @t28 @t3)) % 5.39/5.66 (define @t47 () (not (tptp.member @t28 tptp.universal_class))) % 5.39/5.66 (define @t48 () (tptp.complement (tptp.intersection @t44 (tptp.complement @t1)))) % 5.39/5.66 (define @t49 () (@var "Xr" $$unsorted)) % 5.39/5.66 (define @t50 () (tptp.restrict @t49 @t3 @t1)) % 5.39/5.66 (define @t51 () (tptp.intersection @t21 @t49)) % 5.39/5.66 (define @t52 () (forall (@list @t3 @t1 @t49) (= @t51 @t50))) % 5.39/5.66 (define @t53 () (tptp.domain_of @t3)) % 5.39/5.66 (define @t54 () (tptp.member @t28 @t53)) % 5.39/5.66 (define @t55 () (= (tptp.restrict @t3 (tptp.singleton @t28) tptp.universal_class) tptp.null_class)) % 5.39/5.66 (define @t56 () (tptp.cross_product @t34 tptp.universal_class)) % 5.39/5.66 (define @t57 () (tptp.rotate @t3)) % 5.39/5.66 (define @t58 () (@var "W" $$unsorted)) % 5.39/5.66 (define @t59 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t58) @t2) @t3)) % 5.39/5.66 (define @t60 () (tptp.ordered_pair @t23 @t58)) % 5.39/5.66 (define @t61 () (tptp.member @t60 @t57)) % 5.39/5.66 (define @t62 () (@list @t2 @t22 @t58 @t3)) % 5.39/5.66 (define @t63 () (not (tptp.member @t60 @t56))) % 5.39/5.66 (define @t64 () (tptp.flip @t3)) % 5.39/5.66 (define @t65 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t2) @t58) @t3)) % 5.39/5.66 (define @t66 () (tptp.member @t60 @t64)) % 5.39/5.66 (define @t67 () (@list @t1)) % 5.39/5.66 (define @t68 () (tptp.successor @t3)) % 5.39/5.66 (define @t69 () (= @t68 @t1)) % 5.39/5.66 (define @t70 () (tptp.member @t19 tptp.successor_relation)) % 5.39/5.66 (define @t71 () (tptp.member tptp.null_class @t3)) % 5.39/5.66 (define @t72 () (tptp.inductive @t3)) % 5.39/5.66 (define @t73 () (not @t72)) % 5.39/5.66 (define @t74 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 5.39/5.66 (define @t75 () (tptp.sum_class @t3)) % 5.39/5.66 (define @t76 () (@var "Yr" $$unsorted)) % 5.39/5.66 (define @t77 () (tptp.compose @t76 @t49)) % 5.39/5.66 (define @t78 () (tptp.member @t28 (tptp.image @t76 (tptp.image @t49 @t20)))) % 5.39/5.66 (define @t79 () (tptp.ordered_pair @t1 @t28)) % 5.39/5.66 (define @t80 () (tptp.member @t79 @t77)) % 5.39/5.66 (define @t81 () (not (tptp.member @t79 @t34))) % 5.39/5.66 (define @t82 () (tptp.inverse @t3)) % 5.39/5.66 (define @t83 () (tptp.compose @t3 @t82)) % 5.39/5.66 (define @t84 () (tptp.subclass @t83 tptp.identity_relation)) % 5.39/5.66 (define @t85 () (tptp.single_valued_class @t3)) % 5.39/5.66 (define @t86 () (@var "Xf" $$unsorted)) % 5.39/5.66 (define @t87 () (tptp.subclass @t86 @t34)) % 5.39/5.66 (define @t88 () (tptp.function @t86)) % 5.39/5.66 (define @t89 () (not @t88)) % 5.39/5.66 (define @t90 () (@list @t86)) % 5.39/5.66 (define @t91 () (tptp.inverse @t86)) % 5.39/5.66 (define @t92 () (tptp.subclass (tptp.compose @t86 @t91) tptp.identity_relation)) % 5.39/5.66 (define @t93 () (tptp.regular @t3)) % 5.39/5.66 (define @t94 () (= @t3 tptp.null_class)) % 5.39/5.66 (define @t95 () (@list @t86 @t1)) % 5.39/5.66 (define @t96 () (tptp.one_to_one @t86)) % 5.39/5.66 (define @t97 () (not @t96)) % 5.39/5.66 (define @t98 () (tptp.function @t91)) % 5.39/5.66 (define @t99 () (tptp.inverse tptp.element_relation)) % 5.39/5.66 (define @t100 () (tptp.operation @t86)) % 5.39/5.66 (define @t101 () (not @t100)) % 5.39/5.66 (define @t102 () (tptp.domain_of @t86)) % 5.39/5.66 (define @t103 () (tptp.domain_of @t102)) % 5.39/5.66 (define @t104 () (= (tptp.cross_product @t103 @t103) @t102)) % 5.39/5.66 (define @t105 () (tptp.range_of @t86)) % 5.39/5.66 (define @t106 () (tptp.subclass @t105 @t103)) % 5.39/5.66 (define @t107 () (@var "Xh" $$unsorted)) % 5.39/5.66 (define @t108 () (tptp.function @t107)) % 5.39/5.66 (define @t109 () (@var "Xf2" $$unsorted)) % 5.39/5.66 (define @t110 () (@var "Xf1" $$unsorted)) % 5.39/5.66 (define @t111 () (tptp.compatible @t107 @t110 @t109)) % 5.39/5.66 (define @t112 () (not @t111)) % 5.39/5.66 (define @t113 () (@list @t107 @t110 @t109)) % 5.39/5.66 (define @t114 () (tptp.domain_of @t110)) % 5.39/5.66 (define @t115 () (= (tptp.domain_of @t114) (tptp.domain_of @t107))) % 5.39/5.66 (define @t116 () (tptp.subclass (tptp.range_of @t107) (tptp.domain_of (tptp.domain_of @t109)))) % 5.39/5.66 (define @t117 () (tptp.operation @t110)) % 5.39/5.66 (define @t118 () (tptp.homomorphism @t107 @t110 @t109)) % 5.39/5.66 (define @t119 () (not @t118)) % 5.39/5.66 (define @t120 () (tptp.operation @t109)) % 5.39/5.66 (define @t121 () (tptp.not_homomorphism2 @t107 @t110 @t109)) % 5.39/5.66 (define @t122 () (tptp.not_homomorphism1 @t107 @t110 @t109)) % 5.39/5.66 (define @t123 () (tptp.ordered_pair @t122 @t121)) % 5.39/5.66 (define @t124 () (not @t120)) % 5.39/5.66 (define @t125 () (not @t117)) % 5.39/5.66 (define @t126 () (@list @t110 @t109 @t107)) % 5.39/5.66 (define @t127 () (tptp.compose_class @t3)) % 5.39/5.66 (define @t128 () (tptp.compose @t3 @t1)) % 5.39/5.66 (define @t129 () (= @t128 @t28)) % 5.39/5.66 (define @t130 () (tptp.member @t79 @t127)) % 5.39/5.66 (define @t131 () (@list @t1 @t28 @t3)) % 5.39/5.66 (define @t132 () (tptp.cross_product tptp.universal_class @t34)) % 5.39/5.66 (define @t133 () (tptp.ordered_pair @t3 @t79)) % 5.39/5.66 (define @t134 () (@list @t3 @t1 @t28)) % 5.39/5.66 (define @t135 () (tptp.single_valued1 @t3)) % 5.39/5.66 (define @t136 () (tptp.not_subclass_element @t83 tptp.identity_relation)) % 5.39/5.66 (define @t137 () (tptp.single_valued2 @t3)) % 5.39/5.66 (define @t138 () (tptp.member @t1 @t53)) % 5.39/5.66 (define @t139 () (not (tptp.member @t133 tptp.application_function))) % 5.39/5.66 (define @t140 () (tptp.apply @t3 @t1)) % 5.39/5.66 (define @t141 () (not (tptp.maps @t86 @t3 @t1))) % 5.39/5.66 (define @t142 () (@list @t86 @t3 @t1)) % 5.39/5.66 (define @t143 () (tptp.subclass @t105 @t1)) % 5.39/5.66 (define @t144 () (tptp.subclass tptp.y1 tptp.y2)) % 5.39/5.66 (define @t145 () (tptp.restrict tptp.x tptp.y2 tptp.z)) % 5.39/5.66 (define @t146 () (tptp.restrict tptp.x tptp.y1 tptp.z)) % 5.39/5.66 (define @t147 () (tptp.subclass @t146 @t145)) % 5.39/5.66 (define @t148 () (tptp.not_subclass_element @t146 @t145)) % 5.39/5.66 (define @t149 () (tptp.second @t148)) % 5.39/5.66 (define @t150 () (tptp.first @t148)) % 5.39/5.66 (define @t151 () (@list @t150 @t149 tptp.y1 tptp.z)) % 5.39/5.66 (define @t152 () (tptp.cross_product tptp.y1 tptp.z)) % 5.39/5.66 (define @t153 () (@list @t148 @t152 tptp.x)) % 5.39/5.66 (define @t154 () (@list @t146 @t145)) % 5.39/5.66 (define @t155 () (tptp.member @t148 @t146)) % 5.39/5.66 (define @t156 () (or @t155 @t147)) % 5.39/5.66 (define @t157 () (@list true false)) % 5.39/5.66 (define @t158 () (tptp.member @t148 (tptp.intersection @t152 tptp.x))) % 5.39/5.66 (define @t159 () (tptp.member @t148 @t152)) % 5.39/5.66 (define @t160 () (not @t158)) % 5.39/5.66 (define @t161 () (or @t160 @t159)) % 5.39/5.66 (define @t162 () (@list false false)) % 5.39/5.66 (define @t163 () (tptp.ordered_pair @t150 @t149)) % 5.39/5.66 (define @t164 () (= @t148 @t163)) % 5.39/5.66 (define @t165 () (not @t159)) % 5.39/5.66 (define @t166 () (or @t165 @t164)) % 5.39/5.66 (define @t167 () (tptp.member @t163 @t152)) % 5.39/5.66 (define @t168 () (tptp.member @t150 tptp.y1)) % 5.39/5.66 (define @t169 () (not @t167)) % 5.39/5.66 (define @t170 () (or @t169 @t168)) % 5.39/5.66 (define @t171 () (tptp.cross_product tptp.y2 tptp.z)) % 5.39/5.66 (define @t172 () (not (tptp.member @t148 @t145))) % 5.39/5.66 (define @t173 () (or @t172 @t147)) % 5.39/5.66 (define @t174 () (tptp.member @t148 (tptp.intersection @t171 tptp.x))) % 5.39/5.66 (define @t175 () (tptp.member @t148 tptp.x)) % 5.39/5.66 (define @t176 () (or @t160 @t175)) % 5.39/5.66 (define @t177 () (not @t175)) % 5.39/5.66 (define @t178 () (not (tptp.member @t148 @t171))) % 5.39/5.66 (define @t179 () (or @t178 @t177 @t174)) % 5.39/5.66 (define @t180 () (@list false true false)) % 5.39/5.66 (define @t181 () (tptp.member @t163 @t171)) % 5.39/5.66 (define @t182 () (tptp.member @t149 tptp.z)) % 5.39/5.66 (define @t183 () (or @t169 @t182)) % 5.39/5.66 (define @t184 () (not @t182)) % 5.39/5.66 (define @t185 () (tptp.member @t150 tptp.y2)) % 5.39/5.66 (define @t186 () (not @t185)) % 5.39/5.66 (define @t187 () (or @t186 @t184 @t181)) % 5.39/5.66 (define @t188 () (not @t168)) % 5.39/5.66 (define @t189 () (not @t144)) % 5.39/5.66 (define @t190 () (or @t189 @t188 @t185)) % 5.39/5.66 (define @t191 () (not @t190)) % 5.39/5.66 (assume @p1 @t8) % 5.39/5.66 (assume @p2 (forall @t10 (or (tptp.member @t9 @t3) @t6))) % 5.39/5.66 (assume @p3 (forall @t10 (or (not (tptp.member @t9 @t1)) @t6))) % 5.39/5.66 (assume @p4 (forall @t11 (tptp.subclass @t3 tptp.universal_class))) % 5.39/5.66 (assume @p5 (forall @t10 (or @t13 @t6))) % 5.39/5.66 (assume @p6 (forall @t10 (or @t13 @t14))) % 5.39/5.66 (assume @p7 (forall @t10 (or @t7 (not @t14) @t12))) % 5.39/5.66 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t15)) (= @t2 @t3) (= @t2 @t1)))) % 5.39/5.66 (assume @p9 (forall @t10 (or @t16 (tptp.member @t3 @t15)))) % 5.39/5.66 (assume @p10 (forall (@list @t1 @t3) (or @t17 (tptp.member @t1 @t15)))) % 5.39/5.66 (assume @p11 (forall @t10 (tptp.member @t15 tptp.universal_class))) % 5.39/5.66 (assume @p12 (forall @t11 (= (tptp.unordered_pair @t3 @t3) @t18))) % 5.39/5.66 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t18 (tptp.unordered_pair @t3 @t20)) @t19))) % 5.39/5.66 (assume @p14 (forall @t26 (or @t25 @t4))) % 5.39/5.66 (assume @p15 (forall @t26 (or @t25 @t27))) % 5.39/5.66 (assume @p16 (forall (@list @t2 @t3 @t22 @t1) (or @t5 (not @t27) @t24))) % 5.39/5.66 (assume @p17 @t33) % 5.39/5.66 (assume @p18 (tptp.subclass tptp.element_relation @t34)) % 5.39/5.66 (assume @p19 (forall @t10 (or (not @t36) @t35))) % 5.39/5.66 (assume @p20 (forall @t10 (or @t37 (not @t35) @t36))) % 5.39/5.66 (assume @p21 (forall @t32 (or @t41 @t38))) % 5.39/5.66 (assume @p22 (forall @t32 (or @t41 @t42))) % 5.39/5.66 (assume @p23 (forall @t32 (or @t43 (not @t42) @t40))) % 5.39/5.66 (assume @p24 (forall @t46 (or (not @t45) @t43))) % 5.39/5.66 (assume @p25 (forall @t46 (or @t47 @t45 @t38))) % 5.39/5.66 (assume @p26 (forall @t10 (= @t48 (tptp.union @t3 @t1)))) % 5.39/5.66 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t39) @t48) (tptp.symmetric_difference @t3 @t1)))) % 5.39/5.66 (assume @p28 (forall (@list @t49 @t3 @t1) (= (tptp.intersection @t49 @t21) @t50))) % 5.39/5.66 (assume @p29 @t52) % 5.39/5.66 (assume @p30 (forall (@list @t3 @t28) (or (not @t55) (not @t54)))) % 5.39/5.66 (assume @p31 (forall @t46 (or @t47 @t55 @t54))) % 5.39/5.66 (assume @p32 (forall @t11 (tptp.subclass @t57 @t56))) % 5.39/5.66 (assume @p33 (forall @t62 (or (not @t61) @t59))) % 5.39/5.66 (assume @p34 (forall (@list @t22 @t58 @t2 @t3) (or (not @t59) @t63 @t61))) % 5.39/5.66 (assume @p35 (forall @t11 (tptp.subclass @t64 @t56))) % 5.39/5.66 (assume @p36 (forall @t62 (or (not @t66) @t65))) % 5.39/5.66 (assume @p37 (forall (@list @t22 @t2 @t58 @t3) (or (not @t65) @t63 @t66))) % 5.39/5.66 (assume @p38 (forall @t67 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 5.39/5.66 (assume @p39 (forall (@list @t28) (= (tptp.domain_of (tptp.inverse @t28)) (tptp.range_of @t28)))) % 5.39/5.66 (assume @p40 (forall @t32 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t28 @t3 @t20) tptp.null_class)) (tptp.domain @t28 @t3 @t1)))) % 5.39/5.66 (assume @p41 (forall @t32 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t28 @t18 @t1) tptp.null_class)) (tptp.range @t28 @t3 @t1)))) % 5.39/5.66 (assume @p42 (forall (@list @t49 @t3) (= (tptp.range_of (tptp.restrict @t49 @t3 tptp.universal_class)) (tptp.image @t49 @t3)))) % 5.39/5.66 (assume @p43 (forall @t11 (= (tptp.union @t3 @t18) @t68))) % 5.39/5.66 (assume @p44 (tptp.subclass tptp.successor_relation @t34)) % 5.39/5.66 (assume @p45 (forall @t10 (or (not @t70) @t69))) % 5.39/5.66 (assume @p46 (forall @t10 (or (not @t69) @t37 @t70))) % 5.39/5.66 (assume @p47 (forall @t11 (or @t73 @t71))) % 5.39/5.66 (assume @p48 (forall @t11 (or @t73 @t74))) % 5.39/5.66 (assume @p49 (forall @t11 (or (not @t71) (not @t74) @t72))) % 5.39/5.66 (assume @p50 (tptp.inductive tptp.omega)) % 5.39/5.66 (assume @p51 (forall @t67 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 5.39/5.66 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 5.39/5.66 (assume @p53 (forall @t11 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t75))) % 5.39/5.66 (assume @p54 (forall @t11 (or @t16 (tptp.member @t75 tptp.universal_class)))) % 5.39/5.66 (assume @p55 (forall @t11 (= (tptp.complement (tptp.image tptp.element_relation @t44)) (tptp.power_class @t3)))) % 5.39/5.66 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 5.39/5.66 (assume @p57 (forall (@list @t76 @t49) (tptp.subclass @t77 @t34))) % 5.39/5.66 (assume @p58 (forall (@list @t1 @t28 @t76 @t49) (or (not @t80) @t78))) % 5.39/5.66 (assume @p59 (forall (@list @t28 @t76 @t49 @t1) (or (not @t78) @t81 @t80))) % 5.39/5.66 (assume @p60 (forall @t11 (or (not @t85) @t84))) % 5.39/5.66 (assume @p61 (forall @t11 (or (not @t84) @t85))) % 5.39/5.66 (assume @p62 (forall @t90 (or @t89 @t87))) % 5.39/5.66 (assume @p63 (forall @t90 (or @t89 @t92))) % 5.39/5.66 (assume @p64 (forall @t90 (or (not @t87) (not @t92) @t88))) % 5.39/5.66 (assume @p65 (forall (@list @t86 @t3) (or @t89 @t16 (tptp.member (tptp.image @t86 @t3) tptp.universal_class)))) % 5.39/5.66 (assume @p66 (forall @t11 (or @t94 (tptp.member @t93 @t3)))) % 5.39/5.66 (assume @p67 (forall @t11 (or @t94 (= (tptp.intersection @t3 @t93) tptp.null_class)))) % 5.39/5.66 (assume @p68 (forall @t95 (= (tptp.sum_class (tptp.image @t86 @t20)) (tptp.apply @t86 @t1)))) % 5.39/5.66 (assume @p69 (tptp.function tptp.choice)) % 5.39/5.66 (assume @p70 (forall @t67 (or @t17 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 5.39/5.66 (assume @p71 (forall @t90 (or @t97 @t88))) % 5.39/5.66 (assume @p72 (forall @t90 (or @t97 @t98))) % 5.39/5.66 (assume @p73 (forall @t90 (or (not @t98) @t89 @t96))) % 5.39/5.66 (assume @p74 (= (tptp.intersection @t34 (tptp.intersection @t34 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t99)))) tptp.subset_relation)) % 5.39/5.66 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 5.39/5.66 (assume @p76 (forall (@list @t49) (= (tptp.complement (tptp.domain_of (tptp.intersection @t49 tptp.identity_relation))) (tptp.diagonalise @t49)))) % 5.39/5.66 (assume @p77 (forall @t11 (= (tptp.intersection @t53 (tptp.diagonalise (tptp.compose @t99 @t3))) (tptp.cantor @t3)))) % 5.39/5.66 (assume @p78 (forall @t90 (or @t101 @t88))) % 5.39/5.66 (assume @p79 (forall @t90 (or @t101 @t104))) % 5.39/5.66 (assume @p80 (forall @t90 (or @t101 @t106))) % 5.39/5.66 (assume @p81 (forall @t90 (or @t89 (not @t104) (not @t106) @t100))) % 5.39/5.66 (assume @p82 (forall @t113 (or @t112 @t108))) % 5.39/5.66 (assume @p83 (forall @t113 (or @t112 @t115))) % 5.39/5.66 (assume @p84 (forall @t113 (or @t112 @t116))) % 5.39/5.66 (assume @p85 (forall @t113 (or (not @t108) (not @t115) (not @t116) @t111))) % 5.39/5.66 (assume @p86 (forall @t113 (or @t119 @t117))) % 5.39/5.66 (assume @p87 (forall @t113 (or @t119 @t120))) % 5.39/5.66 (assume @p88 (forall @t113 (or @t119 @t111))) % 5.39/5.66 (assume @p89 (forall (@list @t107 @t110 @t109 @t3 @t1) (or @t119 (not (tptp.member @t19 @t114)) (= (tptp.apply @t109 (tptp.ordered_pair (tptp.apply @t107 @t3) (tptp.apply @t107 @t1))) (tptp.apply @t107 (tptp.apply @t110 @t19)))))) % 5.39/5.66 (assume @p90 (forall @t126 (or @t125 @t124 @t112 (tptp.member @t123 @t114) @t118))) % 5.39/5.66 (assume @p91 (forall @t126 (or @t125 @t124 @t112 (not (= (tptp.apply @t109 (tptp.ordered_pair (tptp.apply @t107 @t122) (tptp.apply @t107 @t121))) (tptp.apply @t107 (tptp.apply @t110 @t123)))) @t118))) % 5.39/5.66 (assume @p92 (forall @t11 (tptp.subclass @t127 @t34))) % 5.39/5.66 (assume @p93 (forall @t131 (or (not @t130) @t129))) % 5.39/5.66 (assume @p94 (forall @t131 (or @t81 (not @t129) @t130))) % 5.39/5.66 (assume @p95 (tptp.subclass tptp.composition_function @t132)) % 5.39/5.66 (assume @p96 (forall @t134 (or (not (tptp.member @t133 tptp.composition_function)) @t129))) % 5.39/5.66 (assume @p97 (forall @t10 (or @t37 (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t128)) tptp.composition_function)))) % 5.39/5.66 (assume @p98 (tptp.subclass tptp.domain_relation @t34)) % 5.39/5.66 (assume @p99 (forall @t10 (or (not (tptp.member @t19 tptp.domain_relation)) (= @t53 @t1)))) % 5.39/5.66 (assume @p100 (forall @t11 (or @t16 (tptp.member (tptp.ordered_pair @t3 @t53) tptp.domain_relation)))) % 5.39/5.66 (assume @p101 (forall @t11 (= (tptp.first @t136) @t135))) % 5.39/5.66 (assume @p102 (forall @t11 (= (tptp.second @t136) @t137))) % 5.39/5.66 (assume @p103 (forall @t11 (= (tptp.domain @t3 (tptp.image @t82 (tptp.singleton @t135)) @t137) (tptp.single_valued3 @t3)))) % 5.39/5.66 (assume @p104 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation)) % 5.39/5.66 (assume @p105 (tptp.subclass tptp.application_function @t132)) % 5.39/5.66 (assume @p106 (forall @t134 (or @t139 @t138))) % 5.39/5.66 (assume @p107 (forall @t134 (or @t139 (= @t140 @t28)))) % 5.39/5.66 (assume @p108 (forall @t134 (or (not (tptp.member @t133 @t132)) (not @t138) (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t140)) tptp.application_function)))) % 5.39/5.66 (assume @p109 (forall @t142 (or @t141 @t88))) % 5.39/5.66 (assume @p110 (forall @t142 (or @t141 (= @t102 @t3)))) % 5.39/5.66 (assume @p111 (forall @t142 (or @t141 @t143))) % 5.39/5.66 (assume @p112 (forall @t95 (or @t89 (not @t143) (tptp.maps @t86 @t102 @t1)))) % 5.39/5.66 (assume @p113 @t144) % 5.39/5.66 (assume @p114 (not @t147)) % 5.39/5.66 (step @p115 :rule instantiate :premises (@p14) :args (@t151)) % 5.39/5.66 (step @p116 :rule instantiate :premises (@p21) :args (@t153)) % 5.39/5.66 (step @p117 :rule instantiate :premises (@p2) :args (@t154)) % 5.39/5.66 (step @p118 :rule cnf_or_pos :args (@t156)) % 5.39/5.66 (step @p119 :rule reordering :premises (@p118) :args ((or @t147 @t155 (not @t156)))) % 5.39/5.66 (step @p120 :rule chain_m_resolution :premises (@p119 @p114 @p117) :args (@t155 @t157 (@list @t147 @t156))) % 5.39/5.66 (step @p121 :rule true_intro :premises (@p120)) % 5.39/5.66 (step @p122 :rule eq-symm :args (@t51 @t50)) % 5.39/5.66 (step @p123 :rule cong :premises (@p122) :args (@t52)) % 5.39/5.66 (step @p124 :rule eq_resolve :premises (@p29 @p123)) % 5.39/5.66 (step @p125 :rule instantiate :premises (@p124) :args ((@list tptp.y1 tptp.z tptp.x))) % 5.39/5.66 (step @p126 :rule symm :premises (@p125)) % 5.39/5.66 (step @p127 :rule refl :args (@t148)) % 5.39/5.66 (step @p128 :rule cong :premises (@p127 @p126) :args (@t158)) % 5.39/5.66 (step @p129 :rule trans :premises (@p128 @p121)) % 5.39/5.66 (step @p130 :rule true_elim :premises (@p129)) % 5.39/5.66 (step @p131 :rule cnf_or_pos :args (@t161)) % 5.39/5.66 (step @p132 :rule reordering :premises (@p131) :args ((or @t160 @t159 (not @t161)))) % 5.39/5.66 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p116) :args (@t159 @t162 (@list @t158 @t161))) % 5.39/5.66 (step @p134 :rule true_intro :premises (@p133)) % 5.39/5.66 (step @p135 :rule refl :args (@t152)) % 5.39/5.66 (step @p136 :rule eq-symm :args (@t29 @t28)) % 5.39/5.66 (step @p137 :rule refl :args (@t30)) % 5.39/5.66 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t31)) % 5.39/5.66 (step @p139 :rule cong :premises (@p138) :args (@t33)) % 5.39/5.66 (step @p140 :rule eq_resolve :premises (@p17 @p139)) % 5.39/5.66 (step @p141 :rule instantiate :premises (@p140) :args ((@list @t148 tptp.y1 tptp.z))) % 5.39/5.66 (step @p142 :rule cnf_or_pos :args (@t166)) % 5.39/5.66 (step @p143 :rule reordering :premises (@p142) :args ((or @t165 @t164 (not @t166)))) % 5.39/5.66 (step @p144 :rule chain_m_resolution :premises (@p143 @p133 @p141) :args (@t164 @t162 (@list @t159 @t166))) % 5.39/5.66 (step @p145 :rule symm :premises (@p144)) % 5.39/5.66 (step @p146 :rule cong :premises (@p145 @p135) :args (@t167)) % 5.39/5.66 (step @p147 :rule trans :premises (@p146 @p134)) % 5.39/5.66 (step @p148 :rule true_elim :premises (@p147)) % 5.39/5.66 (step @p149 :rule cnf_or_pos :args (@t170)) % 5.39/5.66 (step @p150 :rule reordering :premises (@p149) :args ((or @t169 @t168 (not @t170)))) % 5.39/5.66 (step @p151 :rule chain_m_resolution :premises (@p150 @p148 @p115) :args (@t168 @t162 (@list @t167 @t170))) % 5.39/5.66 (step @p152 :rule instantiate :premises (@p16) :args ((@list @t150 tptp.y2 @t149 tptp.z))) % 5.39/5.66 (step @p153 :rule instantiate :premises (@p23) :args ((@list @t148 @t171 tptp.x))) % 5.39/5.66 (step @p154 :rule instantiate :premises (@p3) :args (@t154)) % 5.39/5.66 (step @p155 :rule cnf_or_pos :args (@t173)) % 5.39/5.66 (step @p156 :rule reordering :premises (@p155) :args ((or @t147 @t172 (not @t173)))) % 5.39/5.66 (step @p157 :rule chain_m_resolution :premises (@p156 @p114 @p154) :args (@t172 @t157 (@list @t147 @t173))) % 5.39/5.66 (step @p158 :rule false_intro :premises (@p157)) % 5.39/5.66 (step @p159 :rule instantiate :premises (@p124) :args ((@list tptp.y2 tptp.z tptp.x))) % 5.39/5.66 (step @p160 :rule symm :premises (@p159)) % 5.39/5.66 (step @p161 :rule cong :premises (@p127 @p160) :args (@t174)) % 5.39/5.66 (step @p162 :rule trans :premises (@p161 @p158)) % 5.39/5.66 (step @p163 :rule false_elim :premises (@p162)) % 5.39/5.66 (step @p164 :rule instantiate :premises (@p22) :args (@t153)) % 5.39/5.66 (step @p165 :rule cnf_or_pos :args (@t176)) % 5.39/5.66 (step @p166 :rule reordering :premises (@p165) :args ((or @t160 @t175 (not @t176)))) % 5.39/5.66 (step @p167 :rule chain_m_resolution :premises (@p166 @p130 @p164) :args (@t175 @t162 (@list @t158 @t176))) % 5.39/5.66 (step @p168 :rule cnf_or_pos :args (@t179)) % 5.39/5.66 (step @p169 :rule reordering :premises (@p168) :args ((or @t178 @t177 @t174 (not @t179)))) % 5.39/5.66 (step @p170 :rule chain_m_resolution :premises (@p169 @p167 @p163 @p153) :args (@t178 @t180 (@list @t175 @t174 @t179))) % 5.39/5.66 (step @p171 :rule false_intro :premises (@p170)) % 5.39/5.66 (step @p172 :rule refl :args (@t171)) % 5.39/5.66 (step @p173 :rule cong :premises (@p145 @p172) :args (@t181)) % 5.39/5.66 (step @p174 :rule trans :premises (@p173 @p171)) % 5.39/5.66 (step @p175 :rule false_elim :premises (@p174)) % 5.39/5.66 (step @p176 :rule instantiate :premises (@p15) :args (@t151)) % 5.39/5.66 (step @p177 :rule cnf_or_pos :args (@t183)) % 5.39/5.66 (step @p178 :rule reordering :premises (@p177) :args ((or @t169 @t182 (not @t183)))) % 5.39/5.66 (step @p179 :rule chain_m_resolution :premises (@p178 @p148 @p176) :args (@t182 @t162 (@list @t167 @t183))) % 5.39/5.66 (step @p180 :rule cnf_or_pos :args (@t187)) % 5.39/5.66 (step @p181 :rule reordering :premises (@p180) :args ((or @t186 @t184 @t181 (not @t187)))) % 5.39/5.66 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p175 @p152) :args (@t186 @t180 (@list @t182 @t181 @t187))) % 5.39/5.66 (step @p183 :rule cnf_or_pos :args (@t190)) % 5.39/5.66 (step @p184 :rule reordering :premises (@p183) :args ((or @t189 @t185 @t188 @t191))) % 5.39/5.66 (step @p185 :rule chain_m_resolution :premises (@p184 @p113 @p182 @p151) :args (@t191 @t180 (@list @t144 @t185 @t168))) % 5.39/5.66 (assume-push @p192 @t8) % 5.39/5.66 (step @p187 :rule instantiate :premises (@p1) :args ((@list tptp.y1 tptp.y2 @t150))) % 5.39/5.66 (step-pop @p193 :rule scope :premises (@p187)) % 5.39/5.66 (step @p188 :rule process_scope :premises (@p193) :args (@t190)) % 5.39/5.66 (step @p190 :rule implies_elim :premises (@p188)) % 5.39/5.66 (step @p191 false :rule chain_m_resolution :premises (@p190 @p185 @p1) :args (false @t157 (@list @t190 @t8))) % 5.39/5.66 ) % 5.39/5.68 % SZS output end Proof % 5.39/5.68 % cvc5 exiting %------------------------------------------------------------------------------