%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET254-6 : 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 : n004.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 0.35s 0.75s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET254-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 15:15:37 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.29/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.75 % SZS status Unsatisfiable % 0.35/0.75 % SZS output start Proof % 0.35/0.76 ( % 0.35/0.76 (declare-sort $$unsorted 0) % 0.35/0.76 (declare-const tptp.y $$unsorted) % 0.35/0.76 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.identity_relation $$unsorted) % 0.35/0.76 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.composition_function $$unsorted) % 0.35/0.76 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.compose_class (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.domain_relation $$unsorted) % 0.35/0.76 (declare-const tptp.null_class $$unsorted) % 0.35/0.76 (declare-const tptp.subset_relation $$unsorted) % 0.35/0.76 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.omega $$unsorted) % 0.35/0.76 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.universal_class $$unsorted) % 0.35/0.76 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.choice $$unsorted) % 0.35/0.76 (declare-const tptp.successor_relation $$unsorted) % 0.35/0.76 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.single_valued2 (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.element_relation $$unsorted) % 0.35/0.76 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.single_valued3 (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.single_valued1 (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.x1 $$unsorted) % 0.35/0.76 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.singleton_relation $$unsorted) % 0.35/0.76 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.application_function $$unsorted) % 0.35/0.76 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.76 (declare-const tptp.x2 $$unsorted) % 0.35/0.76 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.35/0.76 (declare-const tptp.z $$unsorted) % 0.35/0.76 (define @t1 () (@var "Y" $$unsorted)) % 0.35/0.76 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.76 (define @t3 () (@var "X" $$unsorted)) % 0.35/0.76 (define @t4 () (tptp.member @t2 @t3)) % 0.35/0.76 (define @t5 () (not @t4)) % 0.35/0.76 (define @t6 () (tptp.subclass @t3 @t1)) % 0.35/0.76 (define @t7 () (not @t6)) % 0.35/0.76 (define @t8 () (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.35/0.76 (define @t9 () (tptp.not_subclass_element @t3 @t1)) % 0.35/0.76 (define @t10 () (@list @t3 @t1)) % 0.35/0.76 (define @t11 () (@list @t3)) % 0.35/0.76 (define @t12 () (= @t3 @t1)) % 0.35/0.76 (define @t13 () (not @t12)) % 0.35/0.76 (define @t14 () (tptp.subclass @t1 @t3)) % 0.35/0.76 (define @t15 () (tptp.unordered_pair @t3 @t1)) % 0.35/0.76 (define @t16 () (not (tptp.member @t3 tptp.universal_class))) % 0.35/0.76 (define @t17 () (not (tptp.member @t1 tptp.universal_class))) % 0.35/0.76 (define @t18 () (tptp.singleton @t3)) % 0.35/0.76 (define @t19 () (tptp.ordered_pair @t3 @t1)) % 0.35/0.76 (define @t20 () (tptp.singleton @t1)) % 0.35/0.76 (define @t21 () (tptp.cross_product @t3 @t1)) % 0.35/0.76 (define @t22 () (@var "V" $$unsorted)) % 0.35/0.76 (define @t23 () (tptp.ordered_pair @t2 @t22)) % 0.35/0.76 (define @t24 () (tptp.member @t23 @t21)) % 0.35/0.76 (define @t25 () (not @t24)) % 0.35/0.76 (define @t26 () (@list @t2 @t22 @t3 @t1)) % 0.35/0.76 (define @t27 () (tptp.member @t22 @t1)) % 0.35/0.76 (define @t28 () (@var "Z" $$unsorted)) % 0.35/0.76 (define @t29 () (@list @t28 @t3 @t1)) % 0.35/0.76 (define @t30 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.35/0.76 (define @t31 () (tptp.member @t3 @t1)) % 0.35/0.76 (define @t32 () (tptp.member @t19 tptp.element_relation)) % 0.35/0.76 (define @t33 () (not (tptp.member @t19 @t30))) % 0.35/0.76 (define @t34 () (tptp.member @t28 @t3)) % 0.35/0.76 (define @t35 () (tptp.intersection @t3 @t1)) % 0.35/0.76 (define @t36 () (tptp.member @t28 @t35)) % 0.35/0.76 (define @t37 () (not @t36)) % 0.35/0.76 (define @t38 () (tptp.member @t28 @t1)) % 0.35/0.76 (define @t39 () (not @t34)) % 0.35/0.76 (define @t40 () (tptp.complement @t3)) % 0.35/0.76 (define @t41 () (tptp.member @t28 @t40)) % 0.35/0.76 (define @t42 () (@list @t28 @t3)) % 0.35/0.76 (define @t43 () (not (tptp.member @t28 tptp.universal_class))) % 0.35/0.76 (define @t44 () (tptp.complement (tptp.intersection @t40 (tptp.complement @t1)))) % 0.35/0.76 (define @t45 () (@var "Xr" $$unsorted)) % 0.35/0.76 (define @t46 () (tptp.restrict @t45 @t3 @t1)) % 0.35/0.76 (define @t47 () (tptp.intersection @t21 @t45)) % 0.35/0.76 (define @t48 () (forall (@list @t3 @t1 @t45) (= @t47 @t46))) % 0.35/0.76 (define @t49 () (tptp.domain_of @t3)) % 0.35/0.76 (define @t50 () (tptp.member @t28 @t49)) % 0.35/0.76 (define @t51 () (= (tptp.restrict @t3 (tptp.singleton @t28) tptp.universal_class) tptp.null_class)) % 0.35/0.76 (define @t52 () (tptp.cross_product @t30 tptp.universal_class)) % 0.35/0.76 (define @t53 () (tptp.rotate @t3)) % 0.35/0.76 (define @t54 () (@var "W" $$unsorted)) % 0.35/0.76 (define @t55 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t54) @t2) @t3)) % 0.35/0.76 (define @t56 () (tptp.ordered_pair @t23 @t54)) % 0.35/0.76 (define @t57 () (tptp.member @t56 @t53)) % 0.35/0.76 (define @t58 () (@list @t2 @t22 @t54 @t3)) % 0.35/0.76 (define @t59 () (not (tptp.member @t56 @t52))) % 0.35/0.76 (define @t60 () (tptp.flip @t3)) % 0.35/0.76 (define @t61 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t2) @t54) @t3)) % 0.35/0.76 (define @t62 () (tptp.member @t56 @t60)) % 0.35/0.76 (define @t63 () (@list @t1)) % 0.35/0.76 (define @t64 () (tptp.successor @t3)) % 0.35/0.76 (define @t65 () (= @t64 @t1)) % 0.35/0.76 (define @t66 () (tptp.member @t19 tptp.successor_relation)) % 0.35/0.76 (define @t67 () (tptp.member tptp.null_class @t3)) % 0.35/0.76 (define @t68 () (tptp.inductive @t3)) % 0.35/0.76 (define @t69 () (not @t68)) % 0.35/0.76 (define @t70 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.35/0.76 (define @t71 () (tptp.sum_class @t3)) % 0.35/0.76 (define @t72 () (@var "Yr" $$unsorted)) % 0.35/0.76 (define @t73 () (tptp.compose @t72 @t45)) % 0.35/0.76 (define @t74 () (tptp.member @t28 (tptp.image @t72 (tptp.image @t45 @t20)))) % 0.35/0.76 (define @t75 () (tptp.ordered_pair @t1 @t28)) % 0.35/0.76 (define @t76 () (tptp.member @t75 @t73)) % 0.35/0.76 (define @t77 () (not (tptp.member @t75 @t30))) % 0.35/0.76 (define @t78 () (tptp.inverse @t3)) % 0.35/0.76 (define @t79 () (tptp.compose @t3 @t78)) % 0.35/0.76 (define @t80 () (tptp.subclass @t79 tptp.identity_relation)) % 0.35/0.76 (define @t81 () (tptp.single_valued_class @t3)) % 0.35/0.76 (define @t82 () (@var "Xf" $$unsorted)) % 0.35/0.76 (define @t83 () (tptp.subclass @t82 @t30)) % 0.35/0.76 (define @t84 () (tptp.function @t82)) % 0.35/0.76 (define @t85 () (not @t84)) % 0.35/0.76 (define @t86 () (@list @t82)) % 0.35/0.76 (define @t87 () (tptp.inverse @t82)) % 0.35/0.76 (define @t88 () (tptp.subclass (tptp.compose @t82 @t87) tptp.identity_relation)) % 0.35/0.76 (define @t89 () (tptp.regular @t3)) % 0.35/0.76 (define @t90 () (= @t3 tptp.null_class)) % 0.35/0.76 (define @t91 () (@list @t82 @t1)) % 0.35/0.76 (define @t92 () (tptp.one_to_one @t82)) % 0.35/0.76 (define @t93 () (not @t92)) % 0.35/0.76 (define @t94 () (tptp.function @t87)) % 0.35/0.76 (define @t95 () (tptp.inverse tptp.element_relation)) % 0.35/0.76 (define @t96 () (tptp.operation @t82)) % 0.35/0.76 (define @t97 () (not @t96)) % 0.35/0.76 (define @t98 () (tptp.domain_of @t82)) % 0.35/0.76 (define @t99 () (tptp.domain_of @t98)) % 0.35/0.76 (define @t100 () (= (tptp.cross_product @t99 @t99) @t98)) % 0.35/0.76 (define @t101 () (tptp.range_of @t82)) % 0.35/0.76 (define @t102 () (tptp.subclass @t101 @t99)) % 0.35/0.76 (define @t103 () (@var "Xh" $$unsorted)) % 0.35/0.76 (define @t104 () (tptp.function @t103)) % 0.35/0.76 (define @t105 () (@var "Xf2" $$unsorted)) % 0.35/0.76 (define @t106 () (@var "Xf1" $$unsorted)) % 0.35/0.76 (define @t107 () (tptp.compatible @t103 @t106 @t105)) % 0.35/0.76 (define @t108 () (not @t107)) % 0.35/0.76 (define @t109 () (@list @t103 @t106 @t105)) % 0.35/0.76 (define @t110 () (tptp.domain_of @t106)) % 0.35/0.76 (define @t111 () (= (tptp.domain_of @t110) (tptp.domain_of @t103))) % 0.35/0.76 (define @t112 () (tptp.subclass (tptp.range_of @t103) (tptp.domain_of (tptp.domain_of @t105)))) % 0.35/0.76 (define @t113 () (tptp.operation @t106)) % 0.35/0.76 (define @t114 () (tptp.homomorphism @t103 @t106 @t105)) % 0.35/0.76 (define @t115 () (not @t114)) % 0.35/0.76 (define @t116 () (tptp.operation @t105)) % 0.35/0.76 (define @t117 () (tptp.not_homomorphism2 @t103 @t106 @t105)) % 0.35/0.76 (define @t118 () (tptp.not_homomorphism1 @t103 @t106 @t105)) % 0.35/0.76 (define @t119 () (tptp.ordered_pair @t118 @t117)) % 0.35/0.76 (define @t120 () (not @t116)) % 0.35/0.76 (define @t121 () (not @t113)) % 0.35/0.76 (define @t122 () (@list @t106 @t105 @t103)) % 0.35/0.76 (define @t123 () (tptp.compose_class @t3)) % 0.35/0.76 (define @t124 () (tptp.compose @t3 @t1)) % 0.35/0.76 (define @t125 () (= @t124 @t28)) % 0.35/0.76 (define @t126 () (tptp.member @t75 @t123)) % 0.35/0.76 (define @t127 () (@list @t1 @t28 @t3)) % 0.35/0.76 (define @t128 () (tptp.cross_product tptp.universal_class @t30)) % 0.35/0.76 (define @t129 () (tptp.ordered_pair @t3 @t75)) % 0.35/0.76 (define @t130 () (@list @t3 @t1 @t28)) % 0.35/0.76 (define @t131 () (tptp.single_valued1 @t3)) % 0.35/0.76 (define @t132 () (tptp.not_subclass_element @t79 tptp.identity_relation)) % 0.35/0.76 (define @t133 () (tptp.single_valued2 @t3)) % 0.35/0.76 (define @t134 () (tptp.member @t1 @t49)) % 0.35/0.76 (define @t135 () (not (tptp.member @t129 tptp.application_function))) % 0.35/0.76 (define @t136 () (tptp.apply @t3 @t1)) % 0.35/0.76 (define @t137 () (not (tptp.maps @t82 @t3 @t1))) % 0.35/0.76 (define @t138 () (@list @t82 @t3 @t1)) % 0.35/0.76 (define @t139 () (tptp.subclass @t101 @t1)) % 0.35/0.76 (define @t140 () (tptp.subclass tptp.x1 tptp.x2)) % 0.35/0.76 (define @t141 () (tptp.restrict tptp.x2 tptp.y tptp.z)) % 0.35/0.76 (define @t142 () (tptp.restrict tptp.x1 tptp.y tptp.z)) % 0.35/0.76 (define @t143 () (tptp.subclass @t142 @t141)) % 0.35/0.76 (define @t144 () (tptp.cross_product tptp.y tptp.z)) % 0.35/0.76 (define @t145 () (tptp.not_subclass_element @t142 @t141)) % 0.35/0.76 (define @t146 () (@list @t145 @t144 tptp.x1)) % 0.35/0.76 (define @t147 () (@list @t142 @t141)) % 0.35/0.76 (define @t148 () (tptp.member @t145 @t142)) % 0.35/0.76 (define @t149 () (or @t148 @t143)) % 0.35/0.76 (define @t150 () (@list true false)) % 0.35/0.76 (define @t151 () (tptp.member @t145 (tptp.intersection @t144 tptp.x1))) % 0.35/0.76 (define @t152 () (tptp.member @t145 tptp.x1)) % 0.35/0.76 (define @t153 () (not @t151)) % 0.35/0.76 (define @t154 () (or @t153 @t152)) % 0.35/0.76 (define @t155 () (@list false false)) % 0.35/0.76 (define @t156 () (not (tptp.member @t145 @t141))) % 0.35/0.76 (define @t157 () (or @t156 @t143)) % 0.35/0.76 (define @t158 () (tptp.member @t145 (tptp.intersection @t144 tptp.x2))) % 0.35/0.76 (define @t159 () (tptp.member @t145 @t144)) % 0.35/0.76 (define @t160 () (or @t153 @t159)) % 0.35/0.76 (define @t161 () (tptp.member @t145 tptp.x2)) % 0.35/0.76 (define @t162 () (not @t161)) % 0.35/0.76 (define @t163 () (not @t159)) % 0.35/0.76 (define @t164 () (or @t163 @t162 @t158)) % 0.35/0.76 (define @t165 () (@list false true false)) % 0.35/0.76 (define @t166 () (not @t152)) % 0.35/0.76 (define @t167 () (not @t140)) % 0.35/0.76 (define @t168 () (or @t167 @t166 @t161)) % 0.35/0.76 (define @t169 () (not @t168)) % 0.35/0.76 (assume @p1 @t8) % 0.35/0.76 (assume @p2 (forall @t10 (or (tptp.member @t9 @t3) @t6))) % 0.35/0.76 (assume @p3 (forall @t10 (or (not (tptp.member @t9 @t1)) @t6))) % 0.35/0.76 (assume @p4 (forall @t11 (tptp.subclass @t3 tptp.universal_class))) % 0.35/0.76 (assume @p5 (forall @t10 (or @t13 @t6))) % 0.35/0.76 (assume @p6 (forall @t10 (or @t13 @t14))) % 0.35/0.76 (assume @p7 (forall @t10 (or @t7 (not @t14) @t12))) % 0.35/0.76 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t15)) (= @t2 @t3) (= @t2 @t1)))) % 0.35/0.76 (assume @p9 (forall @t10 (or @t16 (tptp.member @t3 @t15)))) % 0.35/0.76 (assume @p10 (forall (@list @t1 @t3) (or @t17 (tptp.member @t1 @t15)))) % 0.35/0.76 (assume @p11 (forall @t10 (tptp.member @t15 tptp.universal_class))) % 0.35/0.76 (assume @p12 (forall @t11 (= (tptp.unordered_pair @t3 @t3) @t18))) % 0.35/0.76 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t18 (tptp.unordered_pair @t3 @t20)) @t19))) % 0.35/0.76 (assume @p14 (forall @t26 (or @t25 @t4))) % 0.35/0.76 (assume @p15 (forall @t26 (or @t25 @t27))) % 0.35/0.76 (assume @p16 (forall (@list @t2 @t3 @t22 @t1) (or @t5 (not @t27) @t24))) % 0.35/0.76 (assume @p17 (forall @t29 (or (not (tptp.member @t28 @t21)) (= (tptp.ordered_pair (tptp.first @t28) (tptp.second @t28)) @t28)))) % 0.35/0.76 (assume @p18 (tptp.subclass tptp.element_relation @t30)) % 0.35/0.76 (assume @p19 (forall @t10 (or (not @t32) @t31))) % 0.35/0.76 (assume @p20 (forall @t10 (or @t33 (not @t31) @t32))) % 0.35/0.76 (assume @p21 (forall @t29 (or @t37 @t34))) % 0.35/0.76 (assume @p22 (forall @t29 (or @t37 @t38))) % 0.35/0.76 (assume @p23 (forall @t29 (or @t39 (not @t38) @t36))) % 0.35/0.76 (assume @p24 (forall @t42 (or (not @t41) @t39))) % 0.35/0.76 (assume @p25 (forall @t42 (or @t43 @t41 @t34))) % 0.35/0.76 (assume @p26 (forall @t10 (= @t44 (tptp.union @t3 @t1)))) % 0.35/0.76 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t35) @t44) (tptp.symmetric_difference @t3 @t1)))) % 0.35/0.76 (assume @p28 (forall (@list @t45 @t3 @t1) (= (tptp.intersection @t45 @t21) @t46))) % 0.35/0.76 (assume @p29 @t48) % 0.35/0.76 (assume @p30 (forall (@list @t3 @t28) (or (not @t51) (not @t50)))) % 0.35/0.76 (assume @p31 (forall @t42 (or @t43 @t51 @t50))) % 0.35/0.76 (assume @p32 (forall @t11 (tptp.subclass @t53 @t52))) % 0.35/0.76 (assume @p33 (forall @t58 (or (not @t57) @t55))) % 0.35/0.76 (assume @p34 (forall (@list @t22 @t54 @t2 @t3) (or (not @t55) @t59 @t57))) % 0.35/0.76 (assume @p35 (forall @t11 (tptp.subclass @t60 @t52))) % 0.35/0.76 (assume @p36 (forall @t58 (or (not @t62) @t61))) % 0.35/0.76 (assume @p37 (forall (@list @t22 @t2 @t54 @t3) (or (not @t61) @t59 @t62))) % 0.35/0.76 (assume @p38 (forall @t63 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.35/0.76 (assume @p39 (forall (@list @t28) (= (tptp.domain_of (tptp.inverse @t28)) (tptp.range_of @t28)))) % 0.35/0.76 (assume @p40 (forall @t29 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t28 @t3 @t20) tptp.null_class)) (tptp.domain @t28 @t3 @t1)))) % 0.35/0.76 (assume @p41 (forall @t29 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t28 @t18 @t1) tptp.null_class)) (tptp.range @t28 @t3 @t1)))) % 0.35/0.76 (assume @p42 (forall (@list @t45 @t3) (= (tptp.range_of (tptp.restrict @t45 @t3 tptp.universal_class)) (tptp.image @t45 @t3)))) % 0.35/0.76 (assume @p43 (forall @t11 (= (tptp.union @t3 @t18) @t64))) % 0.35/0.76 (assume @p44 (tptp.subclass tptp.successor_relation @t30)) % 0.35/0.76 (assume @p45 (forall @t10 (or (not @t66) @t65))) % 0.35/0.76 (assume @p46 (forall @t10 (or (not @t65) @t33 @t66))) % 0.35/0.76 (assume @p47 (forall @t11 (or @t69 @t67))) % 0.35/0.76 (assume @p48 (forall @t11 (or @t69 @t70))) % 0.35/0.76 (assume @p49 (forall @t11 (or (not @t67) (not @t70) @t68))) % 0.35/0.76 (assume @p50 (tptp.inductive tptp.omega)) % 0.35/0.76 (assume @p51 (forall @t63 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.35/0.76 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.35/0.76 (assume @p53 (forall @t11 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t71))) % 0.35/0.76 (assume @p54 (forall @t11 (or @t16 (tptp.member @t71 tptp.universal_class)))) % 0.35/0.76 (assume @p55 (forall @t11 (= (tptp.complement (tptp.image tptp.element_relation @t40)) (tptp.power_class @t3)))) % 0.35/0.76 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.35/0.76 (assume @p57 (forall (@list @t72 @t45) (tptp.subclass @t73 @t30))) % 0.35/0.76 (assume @p58 (forall (@list @t1 @t28 @t72 @t45) (or (not @t76) @t74))) % 0.35/0.76 (assume @p59 (forall (@list @t28 @t72 @t45 @t1) (or (not @t74) @t77 @t76))) % 0.35/0.76 (assume @p60 (forall @t11 (or (not @t81) @t80))) % 0.35/0.76 (assume @p61 (forall @t11 (or (not @t80) @t81))) % 0.35/0.76 (assume @p62 (forall @t86 (or @t85 @t83))) % 0.35/0.76 (assume @p63 (forall @t86 (or @t85 @t88))) % 0.35/0.76 (assume @p64 (forall @t86 (or (not @t83) (not @t88) @t84))) % 0.35/0.76 (assume @p65 (forall (@list @t82 @t3) (or @t85 @t16 (tptp.member (tptp.image @t82 @t3) tptp.universal_class)))) % 0.35/0.76 (assume @p66 (forall @t11 (or @t90 (tptp.member @t89 @t3)))) % 0.35/0.76 (assume @p67 (forall @t11 (or @t90 (= (tptp.intersection @t3 @t89) tptp.null_class)))) % 0.35/0.76 (assume @p68 (forall @t91 (= (tptp.sum_class (tptp.image @t82 @t20)) (tptp.apply @t82 @t1)))) % 0.35/0.76 (assume @p69 (tptp.function tptp.choice)) % 0.35/0.76 (assume @p70 (forall @t63 (or @t17 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.35/0.76 (assume @p71 (forall @t86 (or @t93 @t84))) % 0.35/0.76 (assume @p72 (forall @t86 (or @t93 @t94))) % 0.35/0.76 (assume @p73 (forall @t86 (or (not @t94) @t85 @t92))) % 0.35/0.76 (assume @p74 (= (tptp.intersection @t30 (tptp.intersection @t30 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t95)))) tptp.subset_relation)) % 0.35/0.76 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.35/0.76 (assume @p76 (forall (@list @t45) (= (tptp.complement (tptp.domain_of (tptp.intersection @t45 tptp.identity_relation))) (tptp.diagonalise @t45)))) % 0.35/0.76 (assume @p77 (forall @t11 (= (tptp.intersection @t49 (tptp.diagonalise (tptp.compose @t95 @t3))) (tptp.cantor @t3)))) % 0.35/0.76 (assume @p78 (forall @t86 (or @t97 @t84))) % 0.35/0.76 (assume @p79 (forall @t86 (or @t97 @t100))) % 0.35/0.76 (assume @p80 (forall @t86 (or @t97 @t102))) % 0.35/0.76 (assume @p81 (forall @t86 (or @t85 (not @t100) (not @t102) @t96))) % 0.35/0.76 (assume @p82 (forall @t109 (or @t108 @t104))) % 0.35/0.76 (assume @p83 (forall @t109 (or @t108 @t111))) % 0.35/0.76 (assume @p84 (forall @t109 (or @t108 @t112))) % 0.35/0.76 (assume @p85 (forall @t109 (or (not @t104) (not @t111) (not @t112) @t107))) % 0.35/0.76 (assume @p86 (forall @t109 (or @t115 @t113))) % 0.35/0.76 (assume @p87 (forall @t109 (or @t115 @t116))) % 0.35/0.76 (assume @p88 (forall @t109 (or @t115 @t107))) % 0.35/0.76 (assume @p89 (forall (@list @t103 @t106 @t105 @t3 @t1) (or @t115 (not (tptp.member @t19 @t110)) (= (tptp.apply @t105 (tptp.ordered_pair (tptp.apply @t103 @t3) (tptp.apply @t103 @t1))) (tptp.apply @t103 (tptp.apply @t106 @t19)))))) % 0.35/0.76 (assume @p90 (forall @t122 (or @t121 @t120 @t108 (tptp.member @t119 @t110) @t114))) % 0.35/0.76 (assume @p91 (forall @t122 (or @t121 @t120 @t108 (not (= (tptp.apply @t105 (tptp.ordered_pair (tptp.apply @t103 @t118) (tptp.apply @t103 @t117))) (tptp.apply @t103 (tptp.apply @t106 @t119)))) @t114))) % 0.35/0.76 (assume @p92 (forall @t11 (tptp.subclass @t123 @t30))) % 0.35/0.76 (assume @p93 (forall @t127 (or (not @t126) @t125))) % 0.35/0.76 (assume @p94 (forall @t127 (or @t77 (not @t125) @t126))) % 0.35/0.76 (assume @p95 (tptp.subclass tptp.composition_function @t128)) % 0.35/0.76 (assume @p96 (forall @t130 (or (not (tptp.member @t129 tptp.composition_function)) @t125))) % 0.35/0.76 (assume @p97 (forall @t10 (or @t33 (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t124)) tptp.composition_function)))) % 0.35/0.76 (assume @p98 (tptp.subclass tptp.domain_relation @t30)) % 0.35/0.76 (assume @p99 (forall @t10 (or (not (tptp.member @t19 tptp.domain_relation)) (= @t49 @t1)))) % 0.35/0.76 (assume @p100 (forall @t11 (or @t16 (tptp.member (tptp.ordered_pair @t3 @t49) tptp.domain_relation)))) % 0.35/0.76 (assume @p101 (forall @t11 (= (tptp.first @t132) @t131))) % 0.35/0.76 (assume @p102 (forall @t11 (= (tptp.second @t132) @t133))) % 0.35/0.76 (assume @p103 (forall @t11 (= (tptp.domain @t3 (tptp.image @t78 (tptp.singleton @t131)) @t133) (tptp.single_valued3 @t3)))) % 0.35/0.76 (assume @p104 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation)) % 0.35/0.76 (assume @p105 (tptp.subclass tptp.application_function @t128)) % 0.35/0.76 (assume @p106 (forall @t130 (or @t135 @t134))) % 0.35/0.76 (assume @p107 (forall @t130 (or @t135 (= @t136 @t28)))) % 0.35/0.76 (assume @p108 (forall @t130 (or (not (tptp.member @t129 @t128)) (not @t134) (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t136)) tptp.application_function)))) % 0.35/0.76 (assume @p109 (forall @t138 (or @t137 @t84))) % 0.35/0.76 (assume @p110 (forall @t138 (or @t137 (= @t98 @t3)))) % 0.35/0.76 (assume @p111 (forall @t138 (or @t137 @t139))) % 0.35/0.76 (assume @p112 (forall @t91 (or @t85 (not @t139) (tptp.maps @t82 @t98 @t1)))) % 0.35/0.76 (assume @p113 @t140) % 0.35/0.76 (assume @p114 (not @t143)) % 0.35/0.76 (step @p115 :rule instantiate :premises (@p22) :args (@t146)) % 0.35/0.76 (step @p116 :rule instantiate :premises (@p2) :args (@t147)) % 0.35/0.76 (step @p117 :rule cnf_or_pos :args (@t149)) % 0.35/0.76 (step @p118 :rule reordering :premises (@p117) :args ((or @t143 @t148 (not @t149)))) % 0.35/0.76 (step @p119 :rule chain_m_resolution :premises (@p118 @p114 @p116) :args (@t148 @t150 (@list @t143 @t149))) % 0.35/0.76 (step @p120 :rule true_intro :premises (@p119)) % 0.35/0.76 (step @p121 :rule eq-symm :args (@t47 @t46)) % 0.35/0.76 (step @p122 :rule cong :premises (@p121) :args (@t48)) % 0.35/0.76 (step @p123 :rule eq_resolve :premises (@p29 @p122)) % 0.35/0.76 (step @p124 :rule instantiate :premises (@p123) :args ((@list tptp.y tptp.z tptp.x1))) % 0.35/0.76 (step @p125 :rule symm :premises (@p124)) % 0.35/0.76 (step @p126 :rule refl :args (@t145)) % 0.35/0.76 (step @p127 :rule cong :premises (@p126 @p125) :args (@t151)) % 0.35/0.76 (step @p128 :rule trans :premises (@p127 @p120)) % 0.35/0.76 (step @p129 :rule true_elim :premises (@p128)) % 0.35/0.76 (step @p130 :rule cnf_or_pos :args (@t154)) % 0.35/0.76 (step @p131 :rule reordering :premises (@p130) :args ((or @t153 @t152 (not @t154)))) % 0.35/0.76 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p115) :args (@t152 @t155 (@list @t151 @t154))) % 0.35/0.76 (step @p133 :rule instantiate :premises (@p23) :args ((@list @t145 @t144 tptp.x2))) % 0.35/0.76 (step @p134 :rule instantiate :premises (@p3) :args (@t147)) % 0.35/0.76 (step @p135 :rule cnf_or_pos :args (@t157)) % 0.35/0.76 (step @p136 :rule reordering :premises (@p135) :args ((or @t143 @t156 (not @t157)))) % 0.35/0.76 (step @p137 :rule chain_m_resolution :premises (@p136 @p114 @p134) :args (@t156 @t150 (@list @t143 @t157))) % 0.35/0.76 (step @p138 :rule false_intro :premises (@p137)) % 0.35/0.76 (step @p139 :rule instantiate :premises (@p123) :args ((@list tptp.y tptp.z tptp.x2))) % 0.35/0.76 (step @p140 :rule symm :premises (@p139)) % 0.35/0.76 (step @p141 :rule cong :premises (@p126 @p140) :args (@t158)) % 0.35/0.76 (step @p142 :rule trans :premises (@p141 @p138)) % 0.35/0.76 (step @p143 :rule false_elim :premises (@p142)) % 0.35/0.76 (step @p144 :rule instantiate :premises (@p21) :args (@t146)) % 0.35/0.76 (step @p145 :rule cnf_or_pos :args (@t160)) % 0.35/0.76 (step @p146 :rule reordering :premises (@p145) :args ((or @t153 @t159 (not @t160)))) % 0.35/0.76 (step @p147 :rule chain_m_resolution :premises (@p146 @p129 @p144) :args (@t159 @t155 (@list @t151 @t160))) % 0.35/0.76 (step @p148 :rule cnf_or_pos :args (@t164)) % 0.35/0.76 (step @p149 :rule reordering :premises (@p148) :args ((or @t163 @t162 @t158 (not @t164)))) % 0.35/0.76 (step @p150 :rule chain_m_resolution :premises (@p149 @p147 @p143 @p133) :args (@t162 @t165 (@list @t159 @t158 @t164))) % 0.35/0.76 (step @p151 :rule cnf_or_pos :args (@t168)) % 0.35/0.76 (step @p152 :rule reordering :premises (@p151) :args ((or @t167 @t161 @t166 @t169))) % 0.35/0.76 (step @p153 :rule chain_m_resolution :premises (@p152 @p113 @p150 @p132) :args (@t169 @t165 (@list @t140 @t161 @t152))) % 0.35/0.76 (assume-push @p160 @t8) % 0.35/0.76 (step @p155 :rule instantiate :premises (@p1) :args ((@list tptp.x1 tptp.x2 @t145))) % 0.35/0.76 (step-pop @p161 :rule scope :premises (@p155)) % 0.35/0.76 (step @p156 :rule process_scope :premises (@p161) :args (@t168)) % 0.35/0.76 (step @p158 :rule implies_elim :premises (@p156)) % 0.35/0.76 (step @p159 false :rule chain_m_resolution :premises (@p158 @p153 @p1) :args (false @t150 (@list @t168 @t8))) % 0.35/0.76 ) % 0.35/0.76 % SZS output end Proof % 0.35/0.76 % cvc5 exiting %------------------------------------------------------------------------------