%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM228-1 : TPTP v9.2.1. Bugfixed v2.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n023.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 08:38:36 AM UTC 2026 % Result : Unsatisfiable 27.90s 28.97s % Output : Proof 27.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM228-1 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n023.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 10:51:43 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.28/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.74/15.90 --- Run --no-e-matching --full-saturate-quant at 6... % 21.75/21.97 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 21.82/28.04 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 27.90/28.97 % SZS status Unsatisfiable % 27.90/28.97 % SZS output start Proof % 27.90/28.97 ( % 27.90/28.97 (declare-sort $$unsorted 0) % 27.90/28.97 (declare-const tptp.integer_of (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.union_of_range_map $$unsorted) % 27.90/28.97 (declare-const tptp.rest_of (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.kind_1_ordinals $$unsorted) % 27.90/28.97 (declare-const tptp.section (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.not_well_ordering (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.asymmetric (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.transitive (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.irreflexive (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.limit_ordinals $$unsorted) % 27.90/28.97 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.ordinal_multiply (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.ordinal_numbers $$unsorted) % 27.90/28.97 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.identity_relation $$unsorted) % 27.90/28.97 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.composition_function $$unsorted) % 27.90/28.97 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.compose_class (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.well_ordering (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.domain_relation $$unsorted) % 27.90/28.97 (declare-const tptp.null_class $$unsorted) % 27.90/28.97 (declare-const tptp.rest_relation $$unsorted) % 27.90/28.97 (declare-const tptp.subset_relation $$unsorted) % 27.90/28.97 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.inductive (-> $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.connected (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.omega $$unsorted) % 27.90/28.97 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.universal_class $$unsorted) % 27.90/28.97 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.choice $$unsorted) % 27.90/28.97 (declare-const tptp.successor_relation $$unsorted) % 27.90/28.97 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.single_valued2 (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.element_relation $$unsorted) % 27.90/28.97 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.single_valued3 (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.z $$unsorted) % 27.90/28.97 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.function (-> $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.recursion_equation_functions (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.segment (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.operation (-> $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.recursion (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.single_valued1 (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.symmetrization_of (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.ordinal_add (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.singleton_relation $$unsorted) % 27.90/28.97 (declare-const tptp.add_relation $$unsorted) % 27.90/28.97 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 27.90/28.97 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 27.90/28.97 (declare-const tptp.application_function $$unsorted) % 27.90/28.97 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.90/28.97 (define @t1 () (@var "Y" $$unsorted)) % 27.90/28.97 (define @t2 () (@var "U" $$unsorted)) % 27.90/28.97 (define @t3 () (@var "X" $$unsorted)) % 27.90/28.97 (define @t4 () (tptp.member @t2 @t3)) % 27.90/28.97 (define @t5 () (not @t4)) % 27.90/28.97 (define @t6 () (tptp.subclass @t3 @t1)) % 27.90/28.97 (define @t7 () (not @t6)) % 27.90/28.97 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 27.90/28.97 (define @t9 () (@list @t3 @t1)) % 27.90/28.97 (define @t10 () (@list @t3)) % 27.90/28.97 (define @t11 () (= @t3 @t1)) % 27.90/28.97 (define @t12 () (not @t11)) % 27.90/28.97 (define @t13 () (tptp.subclass @t1 @t3)) % 27.90/28.97 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 27.90/28.97 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 27.90/28.97 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 27.90/28.97 (define @t17 () (@list @t1 @t3)) % 27.90/28.97 (define @t18 () (tptp.singleton @t3)) % 27.90/28.97 (define @t19 () (tptp.ordered_pair @t3 @t1)) % 27.90/28.97 (define @t20 () (tptp.singleton @t1)) % 27.90/28.97 (define @t21 () (tptp.cross_product @t3 @t1)) % 27.90/28.97 (define @t22 () (@var "V" $$unsorted)) % 27.90/28.97 (define @t23 () (tptp.ordered_pair @t2 @t22)) % 27.90/28.97 (define @t24 () (tptp.member @t23 @t21)) % 27.90/28.97 (define @t25 () (not @t24)) % 27.90/28.97 (define @t26 () (@list @t2 @t22 @t3 @t1)) % 27.90/28.97 (define @t27 () (tptp.member @t22 @t1)) % 27.90/28.97 (define @t28 () (@var "Z" $$unsorted)) % 27.90/28.97 (define @t29 () (@list @t28 @t3 @t1)) % 27.90/28.97 (define @t30 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 27.90/28.97 (define @t31 () (tptp.member @t3 @t1)) % 27.90/28.97 (define @t32 () (tptp.member @t19 tptp.element_relation)) % 27.90/28.97 (define @t33 () (not (tptp.member @t19 @t30))) % 27.90/28.97 (define @t34 () (tptp.member @t28 @t3)) % 27.90/28.97 (define @t35 () (tptp.intersection @t3 @t1)) % 27.90/28.97 (define @t36 () (tptp.member @t28 @t35)) % 27.90/28.97 (define @t37 () (not @t36)) % 27.90/28.97 (define @t38 () (tptp.member @t28 @t1)) % 27.90/28.97 (define @t39 () (not @t34)) % 27.90/28.97 (define @t40 () (tptp.complement @t3)) % 27.90/28.97 (define @t41 () (tptp.member @t28 @t40)) % 27.90/28.97 (define @t42 () (@list @t28 @t3)) % 27.90/28.97 (define @t43 () (not (tptp.member @t28 tptp.universal_class))) % 27.90/28.97 (define @t44 () (tptp.complement (tptp.intersection @t40 (tptp.complement @t1)))) % 27.90/28.97 (define @t45 () (@var "Xr" $$unsorted)) % 27.90/28.97 (define @t46 () (tptp.restrict @t45 @t3 @t1)) % 27.90/28.97 (define @t47 () (tptp.domain_of @t3)) % 27.90/28.97 (define @t48 () (tptp.member @t28 @t47)) % 27.90/28.97 (define @t49 () (tptp.singleton @t28)) % 27.90/28.97 (define @t50 () (= (tptp.restrict @t3 @t49 tptp.universal_class) tptp.null_class)) % 27.90/28.97 (define @t51 () (@list @t3 @t28)) % 27.90/28.97 (define @t52 () (tptp.cross_product @t30 tptp.universal_class)) % 27.90/28.97 (define @t53 () (tptp.rotate @t3)) % 27.90/28.97 (define @t54 () (@var "W" $$unsorted)) % 27.90/28.97 (define @t55 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t54) @t2) @t3)) % 27.90/28.97 (define @t56 () (tptp.ordered_pair @t23 @t54)) % 27.90/28.97 (define @t57 () (tptp.member @t56 @t53)) % 27.90/28.97 (define @t58 () (@list @t2 @t22 @t54 @t3)) % 27.90/28.97 (define @t59 () (not (tptp.member @t56 @t52))) % 27.90/28.97 (define @t60 () (tptp.flip @t3)) % 27.90/28.97 (define @t61 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t2) @t54) @t3)) % 27.90/28.97 (define @t62 () (tptp.member @t56 @t60)) % 27.90/28.97 (define @t63 () (@list @t1)) % 27.90/28.97 (define @t64 () (tptp.successor @t3)) % 27.90/28.97 (define @t65 () (= @t64 @t1)) % 27.90/28.97 (define @t66 () (tptp.member @t19 tptp.successor_relation)) % 27.90/28.97 (define @t67 () (tptp.member tptp.null_class @t3)) % 27.90/28.97 (define @t68 () (tptp.inductive @t3)) % 27.90/28.97 (define @t69 () (not @t68)) % 27.90/28.97 (define @t70 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 27.90/28.97 (define @t71 () (tptp.sum_class @t3)) % 27.90/28.97 (define @t72 () (@var "Yr" $$unsorted)) % 27.90/28.97 (define @t73 () (tptp.compose @t72 @t45)) % 27.90/28.97 (define @t74 () (tptp.member @t28 (tptp.image @t72 (tptp.image @t45 @t20)))) % 27.90/28.97 (define @t75 () (tptp.ordered_pair @t1 @t28)) % 27.90/28.97 (define @t76 () (tptp.member @t75 @t73)) % 27.90/28.97 (define @t77 () (not (tptp.member @t75 @t30))) % 27.90/28.97 (define @t78 () (tptp.inverse @t3)) % 27.90/28.97 (define @t79 () (tptp.compose @t3 @t78)) % 27.90/28.97 (define @t80 () (tptp.subclass @t79 tptp.identity_relation)) % 27.90/28.97 (define @t81 () (tptp.single_valued_class @t3)) % 27.90/28.97 (define @t82 () (@var "Xf" $$unsorted)) % 27.90/28.97 (define @t83 () (tptp.subclass @t82 @t30)) % 27.90/28.97 (define @t84 () (tptp.function @t82)) % 27.90/28.97 (define @t85 () (not @t84)) % 27.90/28.97 (define @t86 () (@list @t82)) % 27.90/28.97 (define @t87 () (tptp.inverse @t82)) % 27.90/28.97 (define @t88 () (tptp.subclass (tptp.compose @t82 @t87) tptp.identity_relation)) % 27.90/28.97 (define @t89 () (tptp.regular @t3)) % 27.90/28.97 (define @t90 () (= @t3 tptp.null_class)) % 27.90/28.97 (define @t91 () (forall @t10 (or @t90 (tptp.member @t89 @t3)))) % 27.90/28.97 (define @t92 () (@list @t82 @t1)) % 27.90/28.97 (define @t93 () (tptp.one_to_one @t82)) % 27.90/28.97 (define @t94 () (not @t93)) % 27.90/28.97 (define @t95 () (tptp.function @t87)) % 27.90/28.97 (define @t96 () (tptp.inverse tptp.element_relation)) % 27.90/28.97 (define @t97 () (tptp.operation @t82)) % 27.90/28.97 (define @t98 () (not @t97)) % 27.90/28.97 (define @t99 () (tptp.domain_of @t82)) % 27.90/28.97 (define @t100 () (tptp.domain_of @t99)) % 27.90/28.97 (define @t101 () (= (tptp.cross_product @t100 @t100) @t99)) % 27.90/28.97 (define @t102 () (tptp.range_of @t82)) % 27.90/28.97 (define @t103 () (tptp.subclass @t102 @t100)) % 27.90/28.97 (define @t104 () (@var "Xh" $$unsorted)) % 27.90/28.97 (define @t105 () (tptp.function @t104)) % 27.90/28.97 (define @t106 () (@var "Xf2" $$unsorted)) % 27.90/28.97 (define @t107 () (@var "Xf1" $$unsorted)) % 27.90/28.97 (define @t108 () (tptp.compatible @t104 @t107 @t106)) % 27.90/28.97 (define @t109 () (not @t108)) % 27.90/28.97 (define @t110 () (@list @t104 @t107 @t106)) % 27.90/28.97 (define @t111 () (tptp.domain_of @t107)) % 27.90/28.97 (define @t112 () (= (tptp.domain_of @t111) (tptp.domain_of @t104))) % 27.90/28.97 (define @t113 () (tptp.subclass (tptp.range_of @t104) (tptp.domain_of (tptp.domain_of @t106)))) % 27.90/28.97 (define @t114 () (tptp.operation @t107)) % 27.90/28.97 (define @t115 () (tptp.homomorphism @t104 @t107 @t106)) % 27.90/28.97 (define @t116 () (not @t115)) % 27.90/28.97 (define @t117 () (tptp.operation @t106)) % 27.90/28.97 (define @t118 () (tptp.not_homomorphism2 @t104 @t107 @t106)) % 27.90/28.97 (define @t119 () (tptp.not_homomorphism1 @t104 @t107 @t106)) % 27.90/28.97 (define @t120 () (tptp.ordered_pair @t119 @t118)) % 27.90/28.97 (define @t121 () (not @t117)) % 27.90/28.97 (define @t122 () (not @t114)) % 27.90/28.97 (define @t123 () (@list @t107 @t106 @t104)) % 27.90/28.97 (define @t124 () (tptp.compose_class @t3)) % 27.90/28.97 (define @t125 () (tptp.compose @t3 @t1)) % 27.90/28.97 (define @t126 () (= @t125 @t28)) % 27.90/28.97 (define @t127 () (tptp.member @t75 @t124)) % 27.90/28.97 (define @t128 () (@list @t1 @t28 @t3)) % 27.90/28.97 (define @t129 () (tptp.cross_product tptp.universal_class @t30)) % 27.90/28.97 (define @t130 () (tptp.ordered_pair @t3 @t75)) % 27.90/28.97 (define @t131 () (@list @t3 @t1 @t28)) % 27.90/28.97 (define @t132 () (tptp.single_valued1 @t3)) % 27.90/28.97 (define @t133 () (tptp.not_subclass_element @t79 tptp.identity_relation)) % 27.90/28.97 (define @t134 () (tptp.single_valued2 @t3)) % 27.90/28.97 (define @t135 () (tptp.complement tptp.identity_relation)) % 27.90/28.97 (define @t136 () (tptp.member @t1 @t47)) % 27.90/28.97 (define @t137 () (not (tptp.member @t130 tptp.application_function))) % 27.90/28.97 (define @t138 () (tptp.apply @t3 @t1)) % 27.90/28.97 (define @t139 () (not (tptp.maps @t82 @t3 @t1))) % 27.90/28.97 (define @t140 () (@list @t82 @t3 @t1)) % 27.90/28.97 (define @t141 () (tptp.subclass @t102 @t1)) % 27.90/28.97 (define @t142 () (tptp.symmetrization_of @t3)) % 27.90/28.97 (define @t143 () (tptp.subclass (tptp.restrict @t3 @t1 @t1) @t135)) % 27.90/28.97 (define @t144 () (tptp.irreflexive @t3 @t1)) % 27.90/28.97 (define @t145 () (tptp.subclass (tptp.cross_product @t1 @t1) (tptp.union tptp.identity_relation @t142))) % 27.90/28.97 (define @t146 () (tptp.connected @t3 @t1)) % 27.90/28.97 (define @t147 () (tptp.restrict @t45 @t1 @t1)) % 27.90/28.97 (define @t148 () (tptp.subclass (tptp.compose @t147 @t147) @t147)) % 27.90/28.97 (define @t149 () (tptp.transitive @t45 @t1)) % 27.90/28.97 (define @t150 () (@list @t45 @t1)) % 27.90/28.97 (define @t151 () (= (tptp.restrict (tptp.intersection @t45 (tptp.inverse @t45)) @t1 @t1) tptp.null_class)) % 27.90/28.97 (define @t152 () (tptp.asymmetric @t45 @t1)) % 27.90/28.97 (define @t153 () (@list @t45 @t1 @t28)) % 27.90/28.97 (define @t154 () (tptp.least @t45 @t2)) % 27.90/28.97 (define @t155 () (tptp.member @t154 @t2)) % 27.90/28.97 (define @t156 () (not (tptp.subclass @t2 @t1))) % 27.90/28.97 (define @t157 () (tptp.well_ordering @t45 @t1)) % 27.90/28.97 (define @t158 () (not @t157)) % 27.90/28.97 (define @t159 () (@list @t45 @t1 @t2)) % 27.90/28.97 (define @t160 () (not (tptp.member @t22 @t2))) % 27.90/28.97 (define @t161 () (@list @t45 @t1 @t2 @t22)) % 27.90/28.97 (define @t162 () (tptp.not_well_ordering @t45 @t1)) % 27.90/28.97 (define @t163 () (not (tptp.connected @t45 @t1))) % 27.90/28.97 (define @t164 () (tptp.subclass @t1 @t28)) % 27.90/28.97 (define @t165 () (tptp.section @t45 @t1 @t28)) % 27.90/28.97 (define @t166 () (not @t165)) % 27.90/28.97 (define @t167 () (tptp.subclass (tptp.domain_of (tptp.restrict @t45 @t28 @t1)) @t1)) % 27.90/28.97 (define @t168 () (tptp.well_ordering tptp.element_relation @t3)) % 27.90/28.97 (define @t169 () (tptp.member @t3 tptp.ordinal_numbers)) % 27.90/28.97 (define @t170 () (not @t169)) % 27.90/28.97 (define @t171 () (tptp.subclass @t71 @t3)) % 27.90/28.97 (define @t172 () (not @t171)) % 27.90/28.97 (define @t173 () (not @t168)) % 27.90/28.97 (define @t174 () (tptp.rest_of @t3)) % 27.90/28.97 (define @t175 () (tptp.member @t2 @t47)) % 27.90/28.97 (define @t176 () (tptp.member @t23 @t174)) % 27.90/28.97 (define @t177 () (not @t176)) % 27.90/28.97 (define @t178 () (@list @t2 @t22 @t3)) % 27.90/28.97 (define @t179 () (= (tptp.restrict @t3 @t2 tptp.universal_class) @t22)) % 27.90/28.97 (define @t180 () (tptp.function @t28)) % 27.90/28.97 (define @t181 () (tptp.member @t3 (tptp.recursion_equation_functions @t28))) % 27.90/28.97 (define @t182 () (not @t181)) % 27.90/28.97 (define @t183 () (forall @t51 (or @t182 @t180))) % 27.90/28.97 (define @t184 () (tptp.function @t3)) % 27.90/28.97 (define @t185 () (tptp.member @t47 tptp.ordinal_numbers)) % 27.90/28.97 (define @t186 () (= (tptp.compose @t28 @t174) @t3)) % 27.90/28.97 (define @t187 () (= (tptp.sum_class (tptp.range_of @t3)) @t1)) % 27.90/28.97 (define @t188 () (tptp.member @t19 tptp.union_of_range_map)) % 27.90/28.97 (define @t189 () (tptp.integer_of @t3)) % 27.90/28.97 (define @t190 () (tptp.member @t3 tptp.omega)) % 27.90/28.97 (define @t191 () (tptp.function tptp.z)) % 27.90/28.97 (define @t192 () (tptp.recursion_equation_functions tptp.z)) % 27.90/28.97 (define @t193 () (= @t192 tptp.null_class)) % 27.90/28.97 (define @t194 () (tptp.regular @t192)) % 27.90/28.97 (define @t195 () (tptp.member @t194 @t192)) % 27.90/28.97 (define @t196 () (or @t193 @t195)) % 27.90/28.97 (define @t197 () (= tptp.null_class @t192)) % 27.90/28.97 (define @t198 () (or @t197 @t195)) % 27.90/28.97 (define @t199 () (@list true false)) % 27.90/28.97 (define @t200 () (not @t195)) % 27.90/28.97 (define @t201 () (or @t200 @t191)) % 27.90/28.97 (define @t202 () (not @t201)) % 27.90/28.97 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 27.90/28.97 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 27.90/28.97 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 27.90/28.97 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 27.90/28.97 (assume @p5 (forall @t9 (or @t12 @t6))) % 27.90/28.97 (assume @p6 (forall @t9 (or @t12 @t13))) % 27.90/28.97 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 27.90/28.97 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 27.90/28.97 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 27.90/28.97 (assume @p10 (forall @t17 (or @t16 (tptp.member @t1 @t14)))) % 27.90/28.97 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 27.90/28.97 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t18))) % 27.90/28.97 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t18 (tptp.unordered_pair @t3 @t20)) @t19))) % 27.90/28.97 (assume @p14 (forall @t26 (or @t25 @t4))) % 27.90/28.97 (assume @p15 (forall @t26 (or @t25 @t27))) % 27.90/28.97 (assume @p16 (forall (@list @t2 @t3 @t22 @t1) (or @t5 (not @t27) @t24))) % 27.90/28.97 (assume @p17 (forall @t29 (or (not (tptp.member @t28 @t21)) (= (tptp.ordered_pair (tptp.first @t28) (tptp.second @t28)) @t28)))) % 27.90/28.97 (assume @p18 (tptp.subclass tptp.element_relation @t30)) % 27.90/28.97 (assume @p19 (forall @t9 (or (not @t32) @t31))) % 27.90/28.97 (assume @p20 (forall @t9 (or @t33 (not @t31) @t32))) % 27.90/28.97 (assume @p21 (forall @t29 (or @t37 @t34))) % 27.90/28.97 (assume @p22 (forall @t29 (or @t37 @t38))) % 27.90/28.97 (assume @p23 (forall @t29 (or @t39 (not @t38) @t36))) % 27.90/28.97 (assume @p24 (forall @t42 (or (not @t41) @t39))) % 27.90/28.97 (assume @p25 (forall @t42 (or @t43 @t41 @t34))) % 27.90/28.97 (assume @p26 (forall @t9 (= @t44 (tptp.union @t3 @t1)))) % 27.90/28.97 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t35) @t44) (tptp.symmetric_difference @t3 @t1)))) % 27.90/28.97 (assume @p28 (forall (@list @t45 @t3 @t1) (= (tptp.intersection @t45 @t21) @t46))) % 27.90/28.97 (assume @p29 (forall (@list @t3 @t1 @t45) (= (tptp.intersection @t21 @t45) @t46))) % 27.90/28.97 (assume @p30 (forall @t51 (or (not @t50) (not @t48)))) % 27.90/28.97 (assume @p31 (forall @t42 (or @t43 @t50 @t48))) % 27.90/28.97 (assume @p32 (forall @t10 (tptp.subclass @t53 @t52))) % 27.90/28.97 (assume @p33 (forall @t58 (or (not @t57) @t55))) % 27.90/28.97 (assume @p34 (forall (@list @t22 @t54 @t2 @t3) (or (not @t55) @t59 @t57))) % 27.90/28.97 (assume @p35 (forall @t10 (tptp.subclass @t60 @t52))) % 27.90/28.97 (assume @p36 (forall @t58 (or (not @t62) @t61))) % 27.90/28.97 (assume @p37 (forall (@list @t22 @t2 @t54 @t3) (or (not @t61) @t59 @t62))) % 27.90/28.97 (assume @p38 (forall @t63 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 27.90/28.97 (assume @p39 (forall (@list @t28) (= (tptp.domain_of (tptp.inverse @t28)) (tptp.range_of @t28)))) % 27.90/28.97 (assume @p40 (forall @t29 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t28 @t3 @t20) tptp.null_class)) (tptp.domain @t28 @t3 @t1)))) % 27.90/28.97 (assume @p41 (forall @t29 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t28 @t18 @t1) tptp.null_class)) (tptp.range @t28 @t3 @t1)))) % 27.90/28.97 (assume @p42 (forall (@list @t45 @t3) (= (tptp.range_of (tptp.restrict @t45 @t3 tptp.universal_class)) (tptp.image @t45 @t3)))) % 27.90/28.97 (assume @p43 (forall @t10 (= (tptp.union @t3 @t18) @t64))) % 27.90/28.97 (assume @p44 (tptp.subclass tptp.successor_relation @t30)) % 27.90/28.97 (assume @p45 (forall @t9 (or (not @t66) @t65))) % 27.90/28.97 (assume @p46 (forall @t9 (or (not @t65) @t33 @t66))) % 27.90/28.97 (assume @p47 (forall @t10 (or @t69 @t67))) % 27.90/28.97 (assume @p48 (forall @t10 (or @t69 @t70))) % 27.90/28.97 (assume @p49 (forall @t10 (or (not @t67) (not @t70) @t68))) % 27.90/28.97 (assume @p50 (tptp.inductive tptp.omega)) % 27.90/28.97 (assume @p51 (forall @t63 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 27.90/28.97 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 27.90/28.97 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t71))) % 27.90/28.97 (assume @p54 (forall @t10 (or @t15 (tptp.member @t71 tptp.universal_class)))) % 27.90/28.97 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t40)) (tptp.power_class @t3)))) % 27.90/28.97 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 27.90/28.97 (assume @p57 (forall (@list @t72 @t45) (tptp.subclass @t73 @t30))) % 27.90/28.97 (assume @p58 (forall (@list @t1 @t28 @t72 @t45) (or (not @t76) @t74))) % 27.90/28.97 (assume @p59 (forall (@list @t28 @t72 @t45 @t1) (or (not @t74) @t77 @t76))) % 27.90/28.97 (assume @p60 (forall @t10 (or (not @t81) @t80))) % 27.90/28.97 (assume @p61 (forall @t10 (or (not @t80) @t81))) % 27.90/28.97 (assume @p62 (forall @t86 (or @t85 @t83))) % 27.90/28.97 (assume @p63 (forall @t86 (or @t85 @t88))) % 27.90/28.97 (assume @p64 (forall @t86 (or (not @t83) (not @t88) @t84))) % 27.90/28.97 (assume @p65 (forall (@list @t82 @t3) (or @t85 @t15 (tptp.member (tptp.image @t82 @t3) tptp.universal_class)))) % 27.90/28.97 (assume @p66 @t91) % 27.90/28.97 (assume @p67 (forall @t10 (or @t90 (= (tptp.intersection @t3 @t89) tptp.null_class)))) % 27.90/28.97 (assume @p68 (forall @t92 (= (tptp.sum_class (tptp.image @t82 @t20)) (tptp.apply @t82 @t1)))) % 27.90/28.97 (assume @p69 (tptp.function tptp.choice)) % 27.90/28.97 (assume @p70 (forall @t63 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 27.90/28.97 (assume @p71 (forall @t86 (or @t94 @t84))) % 27.90/28.97 (assume @p72 (forall @t86 (or @t94 @t95))) % 27.90/28.97 (assume @p73 (forall @t86 (or (not @t95) @t85 @t93))) % 27.90/28.97 (assume @p74 (= (tptp.intersection @t30 (tptp.intersection @t30 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t96)))) tptp.subset_relation)) % 27.90/28.97 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 27.90/28.97 (assume @p76 (forall (@list @t45) (= (tptp.complement (tptp.domain_of (tptp.intersection @t45 tptp.identity_relation))) (tptp.diagonalise @t45)))) % 27.90/28.97 (assume @p77 (forall @t10 (= (tptp.intersection @t47 (tptp.diagonalise (tptp.compose @t96 @t3))) (tptp.cantor @t3)))) % 27.90/28.97 (assume @p78 (forall @t86 (or @t98 @t84))) % 27.90/28.97 (assume @p79 (forall @t86 (or @t98 @t101))) % 27.90/28.97 (assume @p80 (forall @t86 (or @t98 @t103))) % 27.90/28.97 (assume @p81 (forall @t86 (or @t85 (not @t101) (not @t103) @t97))) % 27.90/28.97 (assume @p82 (forall @t110 (or @t109 @t105))) % 27.90/28.97 (assume @p83 (forall @t110 (or @t109 @t112))) % 27.90/28.97 (assume @p84 (forall @t110 (or @t109 @t113))) % 27.90/28.97 (assume @p85 (forall @t110 (or (not @t105) (not @t112) (not @t113) @t108))) % 27.90/28.97 (assume @p86 (forall @t110 (or @t116 @t114))) % 27.90/28.97 (assume @p87 (forall @t110 (or @t116 @t117))) % 27.90/28.97 (assume @p88 (forall @t110 (or @t116 @t108))) % 27.90/28.97 (assume @p89 (forall (@list @t104 @t107 @t106 @t3 @t1) (or @t116 (not (tptp.member @t19 @t111)) (= (tptp.apply @t106 (tptp.ordered_pair (tptp.apply @t104 @t3) (tptp.apply @t104 @t1))) (tptp.apply @t104 (tptp.apply @t107 @t19)))))) % 27.90/28.97 (assume @p90 (forall @t123 (or @t122 @t121 @t109 (tptp.member @t120 @t111) @t115))) % 27.90/28.97 (assume @p91 (forall @t123 (or @t122 @t121 @t109 (not (= (tptp.apply @t106 (tptp.ordered_pair (tptp.apply @t104 @t119) (tptp.apply @t104 @t118))) (tptp.apply @t104 (tptp.apply @t107 @t120)))) @t115))) % 27.90/28.97 (assume @p92 (forall @t10 (tptp.subclass @t124 @t30))) % 27.90/28.97 (assume @p93 (forall @t128 (or (not @t127) @t126))) % 27.90/28.97 (assume @p94 (forall @t128 (or @t77 (not @t126) @t127))) % 27.90/28.97 (assume @p95 (tptp.subclass tptp.composition_function @t129)) % 27.90/28.97 (assume @p96 (forall @t131 (or (not (tptp.member @t130 tptp.composition_function)) @t126))) % 27.90/28.97 (assume @p97 (forall @t9 (or @t33 (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t125)) tptp.composition_function)))) % 27.90/28.97 (assume @p98 (tptp.subclass tptp.domain_relation @t30)) % 27.90/28.97 (assume @p99 (forall @t9 (or (not (tptp.member @t19 tptp.domain_relation)) (= @t47 @t1)))) % 27.90/28.97 (assume @p100 (forall @t10 (or @t15 (tptp.member (tptp.ordered_pair @t3 @t47) tptp.domain_relation)))) % 27.90/28.97 (assume @p101 (forall @t10 (= (tptp.first @t133) @t132))) % 27.90/28.97 (assume @p102 (forall @t10 (= (tptp.second @t133) @t134))) % 27.90/28.97 (assume @p103 (forall @t10 (= (tptp.domain @t3 (tptp.image @t78 (tptp.singleton @t132)) @t134) (tptp.single_valued3 @t3)))) % 27.90/28.97 (assume @p104 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation @t135)) tptp.element_relation) tptp.singleton_relation)) % 27.90/28.97 (assume @p105 (tptp.subclass tptp.application_function @t129)) % 27.90/28.97 (assume @p106 (forall @t131 (or @t137 @t136))) % 27.90/28.97 (assume @p107 (forall @t131 (or @t137 (= @t138 @t28)))) % 27.90/28.97 (assume @p108 (forall @t131 (or (not (tptp.member @t130 @t129)) (not @t136) (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t138)) tptp.application_function)))) % 27.90/28.97 (assume @p109 (forall @t140 (or @t139 @t84))) % 27.90/28.97 (assume @p110 (forall @t140 (or @t139 (= @t99 @t3)))) % 27.90/28.97 (assume @p111 (forall @t140 (or @t139 @t141))) % 27.90/28.97 (assume @p112 (forall @t92 (or @t85 (not @t141) (tptp.maps @t82 @t99 @t1)))) % 27.90/28.97 (assume @p113 (forall @t10 (= (tptp.union @t3 @t78) @t142))) % 27.90/28.97 (assume @p114 (forall @t9 (or (not @t144) @t143))) % 27.90/28.97 (assume @p115 (forall @t9 (or (not @t143) @t144))) % 27.90/28.97 (assume @p116 (forall @t9 (or (not @t146) @t145))) % 27.90/28.97 (assume @p117 (forall @t17 (or (not @t145) @t146))) % 27.90/28.97 (assume @p118 (forall @t150 (or (not @t149) @t148))) % 27.90/28.97 (assume @p119 (forall @t150 (or (not @t148) @t149))) % 27.90/28.97 (assume @p120 (forall @t150 (or (not @t152) @t151))) % 27.90/28.97 (assume @p121 (forall @t150 (or (not @t151) @t152))) % 27.90/28.97 (assume @p122 (forall @t153 (= (tptp.segment @t45 @t1 @t28) (tptp.domain_of (tptp.restrict @t45 @t1 @t49))))) % 27.90/28.97 (assume @p123 (forall @t9 (or (not (tptp.well_ordering @t3 @t1)) @t146))) % 27.90/28.97 (assume @p124 (forall @t159 (or @t158 @t156 (= @t2 tptp.null_class) @t155))) % 27.90/28.97 (assume @p125 (forall @t161 (or @t158 @t156 @t160 @t155))) % 27.90/28.97 (assume @p126 (forall @t159 (or @t158 @t156 (= (tptp.segment @t45 @t2 @t154) tptp.null_class)))) % 27.90/28.97 (assume @p127 (forall @t161 (or @t158 @t156 @t160 (not (tptp.member (tptp.ordered_pair @t22 @t154) @t45))))) % 27.90/28.97 (assume @p128 (forall @t150 (or @t163 (not (= @t162 tptp.null_class)) @t157))) % 27.90/28.97 (assume @p129 (forall @t150 (or @t163 (tptp.subclass @t162 @t1) @t157))) % 27.90/28.97 (assume @p130 (forall (@list @t22 @t45 @t1) (or (not (tptp.member @t22 @t162)) (not (= (tptp.segment @t45 @t162 @t22) tptp.null_class)) @t163 @t157))) % 27.90/28.97 (assume @p131 (forall @t153 (or @t166 @t164))) % 27.90/28.97 (assume @p132 (forall @t153 (or @t166 @t167))) % 27.90/28.97 (assume @p133 (forall (@list @t1 @t28 @t45) (or (not @t164) (not @t167) @t165))) % 27.90/28.97 (assume @p134 (forall @t10 (or @t170 @t168))) % 27.90/28.97 (assume @p135 (forall @t10 (or @t170 @t171))) % 27.90/28.97 (assume @p136 (forall @t10 (or @t173 @t172 @t15 @t169))) % 27.90/28.97 (assume @p137 (forall @t10 (or @t173 @t172 @t169 (= @t3 tptp.ordinal_numbers)))) % 27.90/28.97 (assume @p138 (= (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)) tptp.kind_1_ordinals)) % 27.90/28.97 (assume @p139 (= (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers) tptp.limit_ordinals)) % 27.90/28.97 (assume @p140 (forall @t10 (tptp.subclass @t174 @t30))) % 27.90/28.97 (assume @p141 (forall @t178 (or @t177 @t175))) % 27.90/28.97 (assume @p142 (forall @t178 (or @t177 @t179))) % 27.90/28.97 (assume @p143 (forall (@list @t2 @t3 @t22) (or (not @t175) (not @t179) @t176))) % 27.90/28.97 (assume @p144 (tptp.subclass tptp.rest_relation @t30)) % 27.90/28.97 (assume @p145 (forall @t9 (or (not (tptp.member @t19 tptp.rest_relation)) (= @t174 @t1)))) % 27.90/28.97 (assume @p146 (forall @t10 (or @t15 (tptp.member (tptp.ordered_pair @t3 @t174) tptp.rest_relation)))) % 27.90/28.97 (assume @p147 @t183) % 27.90/28.97 (assume @p148 (forall @t51 (or @t182 @t184))) % 27.90/28.97 (assume @p149 (forall @t51 (or @t182 @t185))) % 27.90/28.97 (assume @p150 (forall @t51 (or @t182 @t186))) % 27.90/28.97 (assume @p151 (forall @t42 (or (not @t180) (not @t184) (not @t185) (not @t186) @t181))) % 27.90/28.97 (assume @p152 (tptp.subclass tptp.union_of_range_map @t30)) % 27.90/28.97 (assume @p153 (forall @t9 (or (not @t188) @t187))) % 27.90/28.97 (assume @p154 (forall @t9 (or @t33 (not @t187) @t188))) % 27.90/28.97 (assume @p155 (forall @t9 (= (tptp.apply (tptp.recursion @t3 tptp.successor_relation tptp.union_of_range_map) @t1) (tptp.ordinal_add @t3 @t1)))) % 27.90/28.97 (assume @p156 (forall @t9 (= (tptp.recursion tptp.null_class (tptp.apply tptp.add_relation @t3) tptp.union_of_range_map) (tptp.ordinal_multiply @t3 @t1)))) % 27.90/28.97 (assume @p157 (forall @t10 (or (not @t190) (= @t189 @t3)))) % 27.90/28.97 (assume @p158 (forall @t10 (or @t190 (= @t189 tptp.null_class)))) % 27.90/28.97 (assume @p159 (not @t191)) % 27.90/28.97 (assume @p160 (not @t193)) % 27.90/28.97 (step @p161 :rule refl :args (@t195)) % 27.90/28.97 (step @p162 :rule eq-symm :args (@t192 tptp.null_class)) % 27.90/28.97 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t196)) % 27.90/28.97 (step @p164 :rule refl :args (@t91)) % 27.90/28.97 (step @p165 :rule cong :premises (@p164 @p163) :args ((=> @t91 @t196))) % 27.90/28.97 (assume-push @p186 @t91) % 27.90/28.97 (step @p167 :rule instantiate :premises (@p66) :args ((@list @t192))) % 27.90/28.97 (step-pop @p187 :rule scope :premises (@p167)) % 27.90/28.97 (step @p168 :rule process_scope :premises (@p187) :args (@t196)) % 27.90/28.97 (step @p170 :rule eq_resolve :premises (@p168 @p165)) % 27.90/28.97 (step @p171 :rule implies_elim :premises (@p170)) % 27.90/28.97 (step @p172 :rule chain_m_resolution :premises (@p171 @p66) :args (@t198 (@list false) (@list @t91))) % 27.90/28.97 (step @p173 :rule symm :premises (@p160)) % 27.90/28.97 (step @p174 :rule cnf_or_pos :args (@t198)) % 27.90/28.97 (step @p175 :rule reordering :premises (@p174) :args ((or @t197 @t195 (not @t198)))) % 27.90/28.97 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p172) :args (@t195 @t199 (@list @t197 @t198))) % 27.90/28.97 (step @p177 :rule cnf_or_pos :args (@t201)) % 27.90/28.97 (step @p178 :rule reordering :premises (@p177) :args ((or @t191 @t200 @t202))) % 27.90/28.97 (step @p179 :rule chain_m_resolution :premises (@p178 @p159 @p176) :args (@t202 @t199 (@list @t191 @t195))) % 27.90/28.97 (assume-push @p188 @t183) % 27.90/28.97 (step @p181 :rule instantiate :premises (@p147) :args ((@list @t194 tptp.z))) % 27.90/28.97 (step-pop @p189 :rule scope :premises (@p181)) % 27.90/28.97 (step @p182 :rule process_scope :premises (@p189) :args (@t201)) % 27.90/28.97 (step @p184 :rule implies_elim :premises (@p182)) % 27.90/28.97 (step @p185 false :rule chain_m_resolution :premises (@p184 @p179 @p147) :args (false @t199 (@list @t201 @t183))) % 27.90/28.97 ) % 27.90/28.98 % SZS output end Proof % 27.90/28.98 % cvc5 exiting %------------------------------------------------------------------------------