%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET253-6 : 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 0.38s 0.66s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET253-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n005.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 15:15:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.66 % SZS status Unsatisfiable % 0.38/0.66 % SZS output start Proof % 0.38/0.66 ( % 0.38/0.66 (declare-sort $$unsorted 0) % 0.38/0.66 (declare-const tptp.y $$unsorted) % 0.38/0.66 (declare-const tptp.z $$unsorted) % 0.38/0.66 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.application_function $$unsorted) % 0.38/0.66 (declare-const tptp.singleton_relation $$unsorted) % 0.38/0.66 (declare-const tptp.x $$unsorted) % 0.38/0.66 (declare-const tptp.single_valued1 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.single_valued3 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.element_relation $$unsorted) % 0.38/0.66 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.single_valued2 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.universal_class $$unsorted) % 0.38/0.66 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.successor_relation $$unsorted) % 0.38/0.66 (declare-const tptp.choice $$unsorted) % 0.38/0.66 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.subset_relation $$unsorted) % 0.38/0.66 (declare-const tptp.null_class $$unsorted) % 0.38/0.66 (declare-const tptp.compose_class (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.omega $$unsorted) % 0.38/0.66 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.composition_function $$unsorted) % 0.38/0.66 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.identity_relation $$unsorted) % 0.38/0.66 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.domain_relation $$unsorted) % 0.38/0.66 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.38/0.66 (define @t1 () (@var "Y" $$unsorted)) % 0.38/0.66 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.66 (define @t3 () (@var "X" $$unsorted)) % 0.38/0.66 (define @t4 () (tptp.member @t2 @t3)) % 0.38/0.66 (define @t5 () (not @t4)) % 0.38/0.66 (define @t6 () (tptp.subclass @t3 @t1)) % 0.38/0.66 (define @t7 () (not @t6)) % 0.38/0.66 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.38/0.66 (define @t9 () (@list @t3 @t1)) % 0.38/0.66 (define @t10 () (@list @t3)) % 0.38/0.66 (define @t11 () (= @t3 @t1)) % 0.38/0.66 (define @t12 () (not @t11)) % 0.38/0.66 (define @t13 () (tptp.subclass @t1 @t3)) % 0.38/0.66 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.38/0.66 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 0.38/0.66 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 0.38/0.66 (define @t17 () (tptp.singleton @t3)) % 0.38/0.66 (define @t18 () (tptp.ordered_pair @t3 @t1)) % 0.38/0.66 (define @t19 () (tptp.singleton @t1)) % 0.38/0.66 (define @t20 () (tptp.cross_product @t3 @t1)) % 0.38/0.66 (define @t21 () (@var "V" $$unsorted)) % 0.38/0.66 (define @t22 () (tptp.ordered_pair @t2 @t21)) % 0.38/0.66 (define @t23 () (tptp.member @t22 @t20)) % 0.38/0.66 (define @t24 () (not @t23)) % 0.38/0.66 (define @t25 () (@list @t2 @t21 @t3 @t1)) % 0.38/0.66 (define @t26 () (tptp.member @t21 @t1)) % 0.38/0.66 (define @t27 () (@var "Z" $$unsorted)) % 0.38/0.66 (define @t28 () (@list @t27 @t3 @t1)) % 0.38/0.66 (define @t29 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.38/0.66 (define @t30 () (tptp.member @t3 @t1)) % 0.38/0.66 (define @t31 () (tptp.member @t18 tptp.element_relation)) % 0.38/0.66 (define @t32 () (not (tptp.member @t18 @t29))) % 0.38/0.66 (define @t33 () (tptp.member @t27 @t3)) % 0.38/0.66 (define @t34 () (tptp.intersection @t3 @t1)) % 0.38/0.66 (define @t35 () (tptp.member @t27 @t34)) % 0.38/0.66 (define @t36 () (not @t35)) % 0.38/0.66 (define @t37 () (tptp.member @t27 @t1)) % 0.38/0.66 (define @t38 () (not @t33)) % 0.38/0.66 (define @t39 () (tptp.complement @t3)) % 0.38/0.66 (define @t40 () (tptp.member @t27 @t39)) % 0.38/0.66 (define @t41 () (@list @t27 @t3)) % 0.38/0.66 (define @t42 () (not (tptp.member @t27 tptp.universal_class))) % 0.38/0.66 (define @t43 () (tptp.complement (tptp.intersection @t39 (tptp.complement @t1)))) % 0.38/0.66 (define @t44 () (@var "Xr" $$unsorted)) % 0.38/0.66 (define @t45 () (tptp.restrict @t44 @t3 @t1)) % 0.38/0.66 (define @t46 () (tptp.intersection @t20 @t44)) % 0.38/0.66 (define @t47 () (forall (@list @t3 @t1 @t44) (= @t46 @t45))) % 0.38/0.66 (define @t48 () (tptp.domain_of @t3)) % 0.38/0.66 (define @t49 () (tptp.member @t27 @t48)) % 0.38/0.66 (define @t50 () (= (tptp.restrict @t3 (tptp.singleton @t27) tptp.universal_class) tptp.null_class)) % 0.38/0.66 (define @t51 () (tptp.cross_product @t29 tptp.universal_class)) % 0.38/0.66 (define @t52 () (tptp.rotate @t3)) % 0.38/0.66 (define @t53 () (@var "W" $$unsorted)) % 0.38/0.66 (define @t54 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t53) @t2) @t3)) % 0.38/0.66 (define @t55 () (tptp.ordered_pair @t22 @t53)) % 0.38/0.66 (define @t56 () (tptp.member @t55 @t52)) % 0.38/0.66 (define @t57 () (@list @t2 @t21 @t53 @t3)) % 0.38/0.66 (define @t58 () (not (tptp.member @t55 @t51))) % 0.38/0.66 (define @t59 () (tptp.flip @t3)) % 0.38/0.66 (define @t60 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t53) @t3)) % 0.38/0.66 (define @t61 () (tptp.member @t55 @t59)) % 0.38/0.66 (define @t62 () (@list @t1)) % 0.38/0.66 (define @t63 () (tptp.successor @t3)) % 0.38/0.66 (define @t64 () (= @t63 @t1)) % 0.38/0.66 (define @t65 () (tptp.member @t18 tptp.successor_relation)) % 0.38/0.66 (define @t66 () (tptp.member tptp.null_class @t3)) % 0.38/0.66 (define @t67 () (tptp.inductive @t3)) % 0.38/0.66 (define @t68 () (not @t67)) % 0.38/0.66 (define @t69 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.38/0.66 (define @t70 () (tptp.sum_class @t3)) % 0.38/0.66 (define @t71 () (@var "Yr" $$unsorted)) % 0.38/0.66 (define @t72 () (tptp.compose @t71 @t44)) % 0.38/0.66 (define @t73 () (tptp.member @t27 (tptp.image @t71 (tptp.image @t44 @t19)))) % 0.38/0.66 (define @t74 () (tptp.ordered_pair @t1 @t27)) % 0.38/0.66 (define @t75 () (tptp.member @t74 @t72)) % 0.38/0.66 (define @t76 () (not (tptp.member @t74 @t29))) % 0.38/0.66 (define @t77 () (tptp.inverse @t3)) % 0.38/0.66 (define @t78 () (tptp.compose @t3 @t77)) % 0.38/0.66 (define @t79 () (tptp.subclass @t78 tptp.identity_relation)) % 0.38/0.66 (define @t80 () (tptp.single_valued_class @t3)) % 0.38/0.66 (define @t81 () (@var "Xf" $$unsorted)) % 0.38/0.66 (define @t82 () (tptp.subclass @t81 @t29)) % 0.38/0.66 (define @t83 () (tptp.function @t81)) % 0.38/0.66 (define @t84 () (not @t83)) % 0.38/0.66 (define @t85 () (@list @t81)) % 0.38/0.66 (define @t86 () (tptp.inverse @t81)) % 0.38/0.66 (define @t87 () (tptp.subclass (tptp.compose @t81 @t86) tptp.identity_relation)) % 0.38/0.66 (define @t88 () (tptp.regular @t3)) % 0.38/0.66 (define @t89 () (= @t3 tptp.null_class)) % 0.38/0.66 (define @t90 () (@list @t81 @t1)) % 0.38/0.66 (define @t91 () (tptp.one_to_one @t81)) % 0.38/0.66 (define @t92 () (not @t91)) % 0.38/0.66 (define @t93 () (tptp.function @t86)) % 0.38/0.66 (define @t94 () (tptp.inverse tptp.element_relation)) % 0.38/0.66 (define @t95 () (tptp.operation @t81)) % 0.38/0.66 (define @t96 () (not @t95)) % 0.38/0.66 (define @t97 () (tptp.domain_of @t81)) % 0.38/0.66 (define @t98 () (tptp.domain_of @t97)) % 0.38/0.66 (define @t99 () (= (tptp.cross_product @t98 @t98) @t97)) % 0.38/0.66 (define @t100 () (tptp.range_of @t81)) % 0.38/0.66 (define @t101 () (tptp.subclass @t100 @t98)) % 0.38/0.66 (define @t102 () (@var "Xh" $$unsorted)) % 0.38/0.66 (define @t103 () (tptp.function @t102)) % 0.38/0.66 (define @t104 () (@var "Xf2" $$unsorted)) % 0.38/0.66 (define @t105 () (@var "Xf1" $$unsorted)) % 0.38/0.66 (define @t106 () (tptp.compatible @t102 @t105 @t104)) % 0.38/0.66 (define @t107 () (not @t106)) % 0.38/0.66 (define @t108 () (@list @t102 @t105 @t104)) % 0.38/0.66 (define @t109 () (tptp.domain_of @t105)) % 0.38/0.66 (define @t110 () (= (tptp.domain_of @t109) (tptp.domain_of @t102))) % 0.38/0.66 (define @t111 () (tptp.subclass (tptp.range_of @t102) (tptp.domain_of (tptp.domain_of @t104)))) % 0.38/0.66 (define @t112 () (tptp.operation @t105)) % 0.38/0.66 (define @t113 () (tptp.homomorphism @t102 @t105 @t104)) % 0.38/0.66 (define @t114 () (not @t113)) % 0.38/0.66 (define @t115 () (tptp.operation @t104)) % 0.38/0.66 (define @t116 () (tptp.not_homomorphism2 @t102 @t105 @t104)) % 0.38/0.66 (define @t117 () (tptp.not_homomorphism1 @t102 @t105 @t104)) % 0.38/0.66 (define @t118 () (tptp.ordered_pair @t117 @t116)) % 0.38/0.66 (define @t119 () (not @t115)) % 0.38/0.66 (define @t120 () (not @t112)) % 0.38/0.66 (define @t121 () (@list @t105 @t104 @t102)) % 0.38/0.66 (define @t122 () (tptp.compose_class @t3)) % 0.38/0.66 (define @t123 () (tptp.compose @t3 @t1)) % 0.38/0.66 (define @t124 () (= @t123 @t27)) % 0.38/0.66 (define @t125 () (tptp.member @t74 @t122)) % 0.38/0.66 (define @t126 () (@list @t1 @t27 @t3)) % 0.38/0.66 (define @t127 () (tptp.cross_product tptp.universal_class @t29)) % 0.38/0.66 (define @t128 () (tptp.ordered_pair @t3 @t74)) % 0.38/0.66 (define @t129 () (@list @t3 @t1 @t27)) % 0.38/0.66 (define @t130 () (tptp.single_valued1 @t3)) % 0.38/0.66 (define @t131 () (tptp.not_subclass_element @t78 tptp.identity_relation)) % 0.38/0.66 (define @t132 () (tptp.single_valued2 @t3)) % 0.38/0.66 (define @t133 () (tptp.member @t1 @t48)) % 0.38/0.66 (define @t134 () (not (tptp.member @t128 tptp.application_function))) % 0.38/0.66 (define @t135 () (tptp.apply @t3 @t1)) % 0.38/0.66 (define @t136 () (not (tptp.maps @t81 @t3 @t1))) % 0.38/0.66 (define @t137 () (@list @t81 @t3 @t1)) % 0.38/0.66 (define @t138 () (tptp.subclass @t100 @t1)) % 0.38/0.66 (define @t139 () (tptp.cross_product tptp.y tptp.z)) % 0.38/0.66 (define @t140 () (tptp.restrict tptp.x tptp.y tptp.z)) % 0.38/0.66 (define @t141 () (tptp.subclass @t140 @t139)) % 0.38/0.66 (define @t142 () (tptp.not_subclass_element @t140 @t139)) % 0.38/0.66 (define @t143 () (@list @t140 @t139)) % 0.38/0.66 (define @t144 () (tptp.member @t142 @t139)) % 0.38/0.66 (define @t145 () (not @t144)) % 0.38/0.66 (define @t146 () (or @t145 @t141)) % 0.38/0.66 (define @t147 () (@list true false)) % 0.38/0.66 (define @t148 () (not (tptp.member @t142 (tptp.intersection @t139 tptp.x)))) % 0.38/0.66 (define @t149 () (or @t148 @t144)) % 0.38/0.66 (define @t150 () (tptp.member @t142 @t140)) % 0.38/0.66 (define @t151 () (or @t150 @t141)) % 0.38/0.66 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.38/0.66 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.38/0.66 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.38/0.66 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.38/0.66 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.38/0.66 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.38/0.66 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.38/0.66 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 0.38/0.66 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 0.38/0.66 (assume @p10 (forall (@list @t1 @t3) (or @t16 (tptp.member @t1 @t14)))) % 0.38/0.66 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.38/0.66 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t17))) % 0.38/0.66 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t17 (tptp.unordered_pair @t3 @t19)) @t18))) % 0.38/0.66 (assume @p14 (forall @t25 (or @t24 @t4))) % 0.38/0.66 (assume @p15 (forall @t25 (or @t24 @t26))) % 0.38/0.66 (assume @p16 (forall (@list @t2 @t3 @t21 @t1) (or @t5 (not @t26) @t23))) % 0.38/0.66 (assume @p17 (forall @t28 (or (not (tptp.member @t27 @t20)) (= (tptp.ordered_pair (tptp.first @t27) (tptp.second @t27)) @t27)))) % 0.38/0.66 (assume @p18 (tptp.subclass tptp.element_relation @t29)) % 0.38/0.66 (assume @p19 (forall @t9 (or (not @t31) @t30))) % 0.38/0.66 (assume @p20 (forall @t9 (or @t32 (not @t30) @t31))) % 0.38/0.66 (assume @p21 (forall @t28 (or @t36 @t33))) % 0.38/0.66 (assume @p22 (forall @t28 (or @t36 @t37))) % 0.38/0.66 (assume @p23 (forall @t28 (or @t38 (not @t37) @t35))) % 0.38/0.66 (assume @p24 (forall @t41 (or (not @t40) @t38))) % 0.38/0.66 (assume @p25 (forall @t41 (or @t42 @t40 @t33))) % 0.38/0.66 (assume @p26 (forall @t9 (= @t43 (tptp.union @t3 @t1)))) % 0.38/0.66 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t34) @t43) (tptp.symmetric_difference @t3 @t1)))) % 0.38/0.66 (assume @p28 (forall (@list @t44 @t3 @t1) (= (tptp.intersection @t44 @t20) @t45))) % 0.38/0.66 (assume @p29 @t47) % 0.38/0.66 (assume @p30 (forall (@list @t3 @t27) (or (not @t50) (not @t49)))) % 0.38/0.66 (assume @p31 (forall @t41 (or @t42 @t50 @t49))) % 0.38/0.66 (assume @p32 (forall @t10 (tptp.subclass @t52 @t51))) % 0.38/0.66 (assume @p33 (forall @t57 (or (not @t56) @t54))) % 0.38/0.66 (assume @p34 (forall (@list @t21 @t53 @t2 @t3) (or (not @t54) @t58 @t56))) % 0.38/0.66 (assume @p35 (forall @t10 (tptp.subclass @t59 @t51))) % 0.38/0.66 (assume @p36 (forall @t57 (or (not @t61) @t60))) % 0.38/0.66 (assume @p37 (forall (@list @t21 @t2 @t53 @t3) (or (not @t60) @t58 @t61))) % 0.38/0.66 (assume @p38 (forall @t62 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.38/0.66 (assume @p39 (forall (@list @t27) (= (tptp.domain_of (tptp.inverse @t27)) (tptp.range_of @t27)))) % 0.38/0.66 (assume @p40 (forall @t28 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t27 @t3 @t19) tptp.null_class)) (tptp.domain @t27 @t3 @t1)))) % 0.38/0.66 (assume @p41 (forall @t28 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t27 @t17 @t1) tptp.null_class)) (tptp.range @t27 @t3 @t1)))) % 0.38/0.66 (assume @p42 (forall (@list @t44 @t3) (= (tptp.range_of (tptp.restrict @t44 @t3 tptp.universal_class)) (tptp.image @t44 @t3)))) % 0.38/0.66 (assume @p43 (forall @t10 (= (tptp.union @t3 @t17) @t63))) % 0.38/0.66 (assume @p44 (tptp.subclass tptp.successor_relation @t29)) % 0.38/0.66 (assume @p45 (forall @t9 (or (not @t65) @t64))) % 0.38/0.66 (assume @p46 (forall @t9 (or (not @t64) @t32 @t65))) % 0.38/0.66 (assume @p47 (forall @t10 (or @t68 @t66))) % 0.38/0.66 (assume @p48 (forall @t10 (or @t68 @t69))) % 0.38/0.66 (assume @p49 (forall @t10 (or (not @t66) (not @t69) @t67))) % 0.38/0.66 (assume @p50 (tptp.inductive tptp.omega)) % 0.38/0.66 (assume @p51 (forall @t62 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.38/0.66 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.38/0.66 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t70))) % 0.38/0.66 (assume @p54 (forall @t10 (or @t15 (tptp.member @t70 tptp.universal_class)))) % 0.38/0.66 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t39)) (tptp.power_class @t3)))) % 0.38/0.66 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.38/0.66 (assume @p57 (forall (@list @t71 @t44) (tptp.subclass @t72 @t29))) % 0.38/0.66 (assume @p58 (forall (@list @t1 @t27 @t71 @t44) (or (not @t75) @t73))) % 0.38/0.66 (assume @p59 (forall (@list @t27 @t71 @t44 @t1) (or (not @t73) @t76 @t75))) % 0.38/0.66 (assume @p60 (forall @t10 (or (not @t80) @t79))) % 0.38/0.66 (assume @p61 (forall @t10 (or (not @t79) @t80))) % 0.38/0.66 (assume @p62 (forall @t85 (or @t84 @t82))) % 0.38/0.66 (assume @p63 (forall @t85 (or @t84 @t87))) % 0.38/0.66 (assume @p64 (forall @t85 (or (not @t82) (not @t87) @t83))) % 0.38/0.66 (assume @p65 (forall (@list @t81 @t3) (or @t84 @t15 (tptp.member (tptp.image @t81 @t3) tptp.universal_class)))) % 0.38/0.66 (assume @p66 (forall @t10 (or @t89 (tptp.member @t88 @t3)))) % 0.38/0.66 (assume @p67 (forall @t10 (or @t89 (= (tptp.intersection @t3 @t88) tptp.null_class)))) % 0.38/0.66 (assume @p68 (forall @t90 (= (tptp.sum_class (tptp.image @t81 @t19)) (tptp.apply @t81 @t1)))) % 0.38/0.66 (assume @p69 (tptp.function tptp.choice)) % 0.38/0.66 (assume @p70 (forall @t62 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.38/0.66 (assume @p71 (forall @t85 (or @t92 @t83))) % 0.38/0.66 (assume @p72 (forall @t85 (or @t92 @t93))) % 0.38/0.66 (assume @p73 (forall @t85 (or (not @t93) @t84 @t91))) % 0.38/0.66 (assume @p74 (= (tptp.intersection @t29 (tptp.intersection @t29 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t94)))) tptp.subset_relation)) % 0.38/0.66 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.38/0.66 (assume @p76 (forall (@list @t44) (= (tptp.complement (tptp.domain_of (tptp.intersection @t44 tptp.identity_relation))) (tptp.diagonalise @t44)))) % 0.38/0.66 (assume @p77 (forall @t10 (= (tptp.intersection @t48 (tptp.diagonalise (tptp.compose @t94 @t3))) (tptp.cantor @t3)))) % 0.38/0.66 (assume @p78 (forall @t85 (or @t96 @t83))) % 0.38/0.66 (assume @p79 (forall @t85 (or @t96 @t99))) % 0.38/0.66 (assume @p80 (forall @t85 (or @t96 @t101))) % 0.38/0.66 (assume @p81 (forall @t85 (or @t84 (not @t99) (not @t101) @t95))) % 0.38/0.66 (assume @p82 (forall @t108 (or @t107 @t103))) % 0.38/0.66 (assume @p83 (forall @t108 (or @t107 @t110))) % 0.38/0.66 (assume @p84 (forall @t108 (or @t107 @t111))) % 0.38/0.66 (assume @p85 (forall @t108 (or (not @t103) (not @t110) (not @t111) @t106))) % 0.38/0.66 (assume @p86 (forall @t108 (or @t114 @t112))) % 0.38/0.66 (assume @p87 (forall @t108 (or @t114 @t115))) % 0.38/0.66 (assume @p88 (forall @t108 (or @t114 @t106))) % 0.38/0.66 (assume @p89 (forall (@list @t102 @t105 @t104 @t3 @t1) (or @t114 (not (tptp.member @t18 @t109)) (= (tptp.apply @t104 (tptp.ordered_pair (tptp.apply @t102 @t3) (tptp.apply @t102 @t1))) (tptp.apply @t102 (tptp.apply @t105 @t18)))))) % 0.38/0.66 (assume @p90 (forall @t121 (or @t120 @t119 @t107 (tptp.member @t118 @t109) @t113))) % 0.38/0.66 (assume @p91 (forall @t121 (or @t120 @t119 @t107 (not (= (tptp.apply @t104 (tptp.ordered_pair (tptp.apply @t102 @t117) (tptp.apply @t102 @t116))) (tptp.apply @t102 (tptp.apply @t105 @t118)))) @t113))) % 0.38/0.66 (assume @p92 (forall @t10 (tptp.subclass @t122 @t29))) % 0.38/0.66 (assume @p93 (forall @t126 (or (not @t125) @t124))) % 0.38/0.66 (assume @p94 (forall @t126 (or @t76 (not @t124) @t125))) % 0.38/0.66 (assume @p95 (tptp.subclass tptp.composition_function @t127)) % 0.38/0.66 (assume @p96 (forall @t129 (or (not (tptp.member @t128 tptp.composition_function)) @t124))) % 0.38/0.66 (assume @p97 (forall @t9 (or @t32 (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t123)) tptp.composition_function)))) % 0.38/0.66 (assume @p98 (tptp.subclass tptp.domain_relation @t29)) % 0.38/0.66 (assume @p99 (forall @t9 (or (not (tptp.member @t18 tptp.domain_relation)) (= @t48 @t1)))) % 0.38/0.66 (assume @p100 (forall @t10 (or @t15 (tptp.member (tptp.ordered_pair @t3 @t48) tptp.domain_relation)))) % 0.38/0.66 (assume @p101 (forall @t10 (= (tptp.first @t131) @t130))) % 0.38/0.66 (assume @p102 (forall @t10 (= (tptp.second @t131) @t132))) % 0.38/0.66 (assume @p103 (forall @t10 (= (tptp.domain @t3 (tptp.image @t77 (tptp.singleton @t130)) @t132) (tptp.single_valued3 @t3)))) % 0.38/0.66 (assume @p104 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation)) % 0.38/0.66 (assume @p105 (tptp.subclass tptp.application_function @t127)) % 0.38/0.66 (assume @p106 (forall @t129 (or @t134 @t133))) % 0.38/0.66 (assume @p107 (forall @t129 (or @t134 (= @t135 @t27)))) % 0.38/0.66 (assume @p108 (forall @t129 (or (not (tptp.member @t128 @t127)) (not @t133) (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t135)) tptp.application_function)))) % 0.38/0.66 (assume @p109 (forall @t137 (or @t136 @t83))) % 0.38/0.66 (assume @p110 (forall @t137 (or @t136 (= @t97 @t3)))) % 0.38/0.66 (assume @p111 (forall @t137 (or @t136 @t138))) % 0.38/0.66 (assume @p112 (forall @t90 (or @t84 (not @t138) (tptp.maps @t81 @t97 @t1)))) % 0.38/0.66 (assume @p113 (not @t141)) % 0.38/0.66 (step @p114 :rule evaluate :args ((= true false))) % 0.38/0.66 (step @p115 :rule instantiate :premises (@p21) :args ((@list @t142 @t139 tptp.x))) % 0.38/0.66 (step @p116 :rule instantiate :premises (@p3) :args (@t143)) % 0.38/0.66 (step @p117 :rule cnf_or_pos :args (@t146)) % 0.38/0.66 (step @p118 :rule reordering :premises (@p117) :args ((or @t141 @t145 (not @t146)))) % 0.38/0.66 (step @p119 :rule chain_m_resolution :premises (@p118 @p113 @p116) :args (@t145 @t147 (@list @t141 @t146))) % 0.38/0.66 (step @p120 :rule cnf_or_pos :args (@t149)) % 0.38/0.66 (step @p121 :rule reordering :premises (@p120) :args ((or @t144 @t148 (not @t149)))) % 0.38/0.66 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p115) :args (@t148 @t147 (@list @t144 @t149))) % 0.38/0.66 (step @p123 :rule false_intro :premises (@p122)) % 0.38/0.66 (step @p124 :rule eq-symm :args (@t46 @t45)) % 0.38/0.66 (step @p125 :rule cong :premises (@p124) :args (@t47)) % 0.38/0.66 (step @p126 :rule eq_resolve :premises (@p29 @p125)) % 0.38/0.66 (step @p127 :rule instantiate :premises (@p126) :args ((@list tptp.y tptp.z tptp.x))) % 0.38/0.66 (step @p128 :rule refl :args (@t142)) % 0.38/0.66 (step @p129 :rule cong :premises (@p128 @p127) :args (@t150)) % 0.38/0.66 (step @p130 :rule instantiate :premises (@p2) :args (@t143)) % 0.38/0.66 (step @p131 :rule cnf_or_pos :args (@t151)) % 0.38/0.66 (step @p132 :rule reordering :premises (@p131) :args ((or @t141 @t150 (not @t151)))) % 0.38/0.66 (step @p133 :rule chain_m_resolution :premises (@p132 @p113 @p130) :args (@t150 @t147 (@list @t141 @t151))) % 0.38/0.66 (step @p134 :rule true_intro :premises (@p133)) % 0.38/0.66 (step @p135 :rule symm :premises (@p134)) % 0.38/0.66 (step @p136 :rule trans :premises (@p135 @p129 @p123)) % 0.38/0.66 (step @p137 false :rule eq_resolve :premises (@p136 @p114)) % 0.38/0.66 ) % 0.38/0.66 % SZS output end Proof % 0.38/0.67 % cvc5 exiting %------------------------------------------------------------------------------