%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET024-7 : 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 : n015.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 08:47:01 AM UTC 2026 % Result : Unsatisfiable 0.35s 0.65s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET024-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.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 14:42:04 EDT 2026 % 0.16/0.34 % 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... % 0.35/0.65 % SZS status Unsatisfiable % 0.35/0.65 % SZS output start Proof % 0.35/0.65 ( % 0.35/0.65 (declare-sort $$unsorted 0) % 0.35/0.65 (declare-const tptp.x $$unsorted) % 0.35/0.65 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.element_relation $$unsorted) % 0.35/0.65 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.universal_class $$unsorted) % 0.35/0.65 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.successor_relation $$unsorted) % 0.35/0.65 (declare-const tptp.choice $$unsorted) % 0.35/0.65 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.subset_relation $$unsorted) % 0.35/0.65 (declare-const tptp.null_class $$unsorted) % 0.35/0.65 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.omega $$unsorted) % 0.35/0.65 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.identity_relation $$unsorted) % 0.35/0.65 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.35/0.65 (define @t1 () (@var "Y" $$unsorted)) % 0.35/0.65 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.65 (define @t3 () (@var "X" $$unsorted)) % 0.35/0.65 (define @t4 () (tptp.member @t2 @t3)) % 0.35/0.65 (define @t5 () (not @t4)) % 0.35/0.65 (define @t6 () (tptp.subclass @t3 @t1)) % 0.35/0.65 (define @t7 () (not @t6)) % 0.35/0.65 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.35/0.65 (define @t9 () (tptp.member @t8 @t3)) % 0.35/0.65 (define @t10 () (@list @t3 @t1)) % 0.35/0.65 (define @t11 () (not (tptp.member @t8 @t1))) % 0.35/0.65 (define @t12 () (@list @t3)) % 0.35/0.65 (define @t13 () (= @t3 @t1)) % 0.35/0.65 (define @t14 () (not @t13)) % 0.35/0.65 (define @t15 () (tptp.subclass @t1 @t3)) % 0.35/0.65 (define @t16 () (tptp.unordered_pair @t3 @t1)) % 0.35/0.65 (define @t17 () (tptp.member @t3 @t16)) % 0.35/0.65 (define @t18 () (tptp.member @t3 tptp.universal_class)) % 0.35/0.65 (define @t19 () (not @t18)) % 0.35/0.65 (define @t20 () (tptp.member @t1 @t16)) % 0.35/0.65 (define @t21 () (tptp.member @t1 tptp.universal_class)) % 0.35/0.65 (define @t22 () (not @t21)) % 0.35/0.65 (define @t23 () (@list @t1 @t3)) % 0.35/0.65 (define @t24 () (tptp.singleton @t3)) % 0.35/0.65 (define @t25 () (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t24))) % 0.35/0.65 (define @t26 () (tptp.ordered_pair @t3 @t1)) % 0.35/0.65 (define @t27 () (tptp.singleton @t1)) % 0.35/0.65 (define @t28 () (tptp.unordered_pair @t3 @t27)) % 0.35/0.65 (define @t29 () (tptp.cross_product @t3 @t1)) % 0.35/0.65 (define @t30 () (@var "V" $$unsorted)) % 0.35/0.65 (define @t31 () (tptp.ordered_pair @t2 @t30)) % 0.35/0.65 (define @t32 () (tptp.member @t31 @t29)) % 0.35/0.65 (define @t33 () (not @t32)) % 0.35/0.65 (define @t34 () (@list @t2 @t30 @t3 @t1)) % 0.35/0.65 (define @t35 () (tptp.member @t30 @t1)) % 0.35/0.65 (define @t36 () (@var "Z" $$unsorted)) % 0.35/0.65 (define @t37 () (@list @t36 @t3 @t1)) % 0.35/0.65 (define @t38 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.35/0.65 (define @t39 () (tptp.member @t3 @t1)) % 0.35/0.65 (define @t40 () (tptp.member @t26 tptp.element_relation)) % 0.35/0.65 (define @t41 () (not (tptp.member @t26 @t38))) % 0.35/0.65 (define @t42 () (tptp.member @t36 @t3)) % 0.35/0.65 (define @t43 () (tptp.intersection @t3 @t1)) % 0.35/0.65 (define @t44 () (tptp.member @t36 @t43)) % 0.35/0.65 (define @t45 () (not @t44)) % 0.35/0.65 (define @t46 () (tptp.member @t36 @t1)) % 0.35/0.65 (define @t47 () (not @t42)) % 0.35/0.65 (define @t48 () (tptp.complement @t3)) % 0.35/0.65 (define @t49 () (tptp.member @t36 @t48)) % 0.35/0.65 (define @t50 () (@list @t36 @t3)) % 0.35/0.65 (define @t51 () (not (tptp.member @t36 tptp.universal_class))) % 0.35/0.65 (define @t52 () (tptp.complement (tptp.intersection @t48 (tptp.complement @t1)))) % 0.35/0.65 (define @t53 () (@var "Xr" $$unsorted)) % 0.35/0.65 (define @t54 () (tptp.restrict @t53 @t3 @t1)) % 0.35/0.65 (define @t55 () (tptp.domain_of @t3)) % 0.35/0.65 (define @t56 () (tptp.member @t36 @t55)) % 0.35/0.65 (define @t57 () (= (tptp.restrict @t3 (tptp.singleton @t36) tptp.universal_class) tptp.null_class)) % 0.35/0.65 (define @t58 () (tptp.cross_product @t38 tptp.universal_class)) % 0.35/0.65 (define @t59 () (tptp.rotate @t3)) % 0.35/0.65 (define @t60 () (@var "W" $$unsorted)) % 0.35/0.65 (define @t61 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t30 @t60) @t2) @t3)) % 0.35/0.65 (define @t62 () (tptp.ordered_pair @t31 @t60)) % 0.35/0.65 (define @t63 () (tptp.member @t62 @t59)) % 0.35/0.65 (define @t64 () (@list @t2 @t30 @t60 @t3)) % 0.35/0.65 (define @t65 () (not (tptp.member @t62 @t58))) % 0.35/0.65 (define @t66 () (tptp.flip @t3)) % 0.35/0.65 (define @t67 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t30 @t2) @t60) @t3)) % 0.35/0.65 (define @t68 () (tptp.member @t62 @t66)) % 0.35/0.65 (define @t69 () (@list @t1)) % 0.35/0.65 (define @t70 () (@list @t36)) % 0.35/0.65 (define @t71 () (tptp.successor @t3)) % 0.35/0.65 (define @t72 () (= @t71 @t1)) % 0.35/0.65 (define @t73 () (tptp.member @t26 tptp.successor_relation)) % 0.35/0.65 (define @t74 () (tptp.member tptp.null_class @t3)) % 0.35/0.65 (define @t75 () (tptp.inductive @t3)) % 0.35/0.65 (define @t76 () (not @t75)) % 0.35/0.65 (define @t77 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.35/0.65 (define @t78 () (tptp.sum_class @t3)) % 0.35/0.65 (define @t79 () (tptp.member @t2 tptp.universal_class)) % 0.35/0.65 (define @t80 () (@var "Yr" $$unsorted)) % 0.35/0.65 (define @t81 () (tptp.compose @t80 @t53)) % 0.35/0.65 (define @t82 () (tptp.member @t36 (tptp.image @t80 (tptp.image @t53 @t27)))) % 0.35/0.65 (define @t83 () (tptp.ordered_pair @t1 @t36)) % 0.35/0.65 (define @t84 () (tptp.member @t83 @t81)) % 0.35/0.65 (define @t85 () (not (tptp.member @t83 @t38))) % 0.35/0.65 (define @t86 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.35/0.65 (define @t87 () (tptp.single_valued_class @t3)) % 0.35/0.65 (define @t88 () (@var "Xf" $$unsorted)) % 0.35/0.65 (define @t89 () (tptp.subclass @t88 @t38)) % 0.35/0.65 (define @t90 () (tptp.function @t88)) % 0.35/0.65 (define @t91 () (not @t90)) % 0.35/0.65 (define @t92 () (@list @t88)) % 0.35/0.65 (define @t93 () (tptp.inverse @t88)) % 0.35/0.65 (define @t94 () (tptp.subclass (tptp.compose @t88 @t93) tptp.identity_relation)) % 0.35/0.65 (define @t95 () (tptp.regular @t3)) % 0.35/0.65 (define @t96 () (= @t3 tptp.null_class)) % 0.35/0.65 (define @t97 () (tptp.one_to_one @t88)) % 0.35/0.65 (define @t98 () (not @t97)) % 0.35/0.65 (define @t99 () (tptp.function @t93)) % 0.35/0.65 (define @t100 () (tptp.inverse tptp.element_relation)) % 0.35/0.65 (define @t101 () (tptp.operation @t88)) % 0.35/0.65 (define @t102 () (not @t101)) % 0.35/0.65 (define @t103 () (tptp.domain_of @t88)) % 0.35/0.65 (define @t104 () (tptp.domain_of @t103)) % 0.35/0.65 (define @t105 () (= (tptp.cross_product @t104 @t104) @t103)) % 0.35/0.65 (define @t106 () (tptp.subclass (tptp.range_of @t88) @t104)) % 0.35/0.65 (define @t107 () (@var "Xh" $$unsorted)) % 0.35/0.65 (define @t108 () (tptp.function @t107)) % 0.35/0.65 (define @t109 () (@var "Xf2" $$unsorted)) % 0.35/0.65 (define @t110 () (@var "Xf1" $$unsorted)) % 0.35/0.65 (define @t111 () (tptp.compatible @t107 @t110 @t109)) % 0.35/0.65 (define @t112 () (not @t111)) % 0.35/0.65 (define @t113 () (@list @t107 @t110 @t109)) % 0.35/0.65 (define @t114 () (tptp.domain_of @t110)) % 0.35/0.65 (define @t115 () (= (tptp.domain_of @t114) (tptp.domain_of @t107))) % 0.35/0.65 (define @t116 () (tptp.subclass (tptp.range_of @t107) (tptp.domain_of (tptp.domain_of @t109)))) % 0.35/0.65 (define @t117 () (tptp.operation @t110)) % 0.35/0.65 (define @t118 () (tptp.homomorphism @t107 @t110 @t109)) % 0.35/0.65 (define @t119 () (not @t118)) % 0.35/0.65 (define @t120 () (tptp.operation @t109)) % 0.35/0.65 (define @t121 () (tptp.not_homomorphism2 @t107 @t110 @t109)) % 0.35/0.65 (define @t122 () (tptp.not_homomorphism1 @t107 @t110 @t109)) % 0.35/0.65 (define @t123 () (tptp.ordered_pair @t122 @t121)) % 0.35/0.65 (define @t124 () (not @t120)) % 0.35/0.65 (define @t125 () (not @t117)) % 0.35/0.65 (define @t126 () (@list @t110 @t109 @t107)) % 0.35/0.65 (define @t127 () (not (tptp.member @t26 (tptp.cross_product @t2 @t30)))) % 0.35/0.65 (define @t128 () (@list @t3 @t1 @t2 @t30)) % 0.35/0.65 (define @t129 () (@list @t3 @t1 @t36)) % 0.35/0.65 (define @t130 () (tptp.not_subclass_element @t1 @t3)) % 0.35/0.65 (define @t131 () (tptp.member @t130 @t1)) % 0.35/0.65 (define @t132 () (not (tptp.member @t130 @t3))) % 0.35/0.65 (define @t133 () (= @t16 tptp.null_class)) % 0.35/0.65 (define @t134 () (tptp.unordered_pair @t3 @t36)) % 0.35/0.65 (define @t135 () (@list @t3 @t36 @t1)) % 0.35/0.65 (define @t136 () (not @t133)) % 0.35/0.65 (define @t137 () (tptp.member tptp.x tptp.universal_class)) % 0.35/0.65 (define @t138 () (tptp.singleton tptp.x)) % 0.35/0.65 (define @t139 () (tptp.member tptp.x @t138)) % 0.35/0.65 (define @t140 () (tptp.unordered_pair tptp.x tptp.x)) % 0.35/0.65 (define @t141 () (tptp.member tptp.x @t140)) % 0.35/0.65 (define @t142 () (not @t137)) % 0.35/0.65 (define @t143 () (or @t142 @t141)) % 0.35/0.65 (define @t144 () (= @t140 @t138)) % 0.35/0.65 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.35/0.65 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.35/0.65 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.35/0.65 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.35/0.65 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.35/0.65 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.35/0.65 (assume @p7 (forall @t10 (or @t7 (not @t15) @t13))) % 0.35/0.65 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t16)) (= @t2 @t3) (= @t2 @t1)))) % 0.35/0.65 (assume @p9 (forall @t10 (or @t19 @t17))) % 0.35/0.65 (assume @p10 (forall @t23 (or @t22 @t20))) % 0.35/0.65 (assume @p11 (forall @t10 (tptp.member @t16 tptp.universal_class))) % 0.35/0.65 (assume @p12 @t25) % 0.35/0.65 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t24 @t28) @t26))) % 0.35/0.65 (assume @p14 (forall @t34 (or @t33 @t4))) % 0.35/0.65 (assume @p15 (forall @t34 (or @t33 @t35))) % 0.35/0.65 (assume @p16 (forall (@list @t2 @t3 @t30 @t1) (or @t5 (not @t35) @t32))) % 0.35/0.65 (assume @p17 (forall @t37 (or (not (tptp.member @t36 @t29)) (= (tptp.ordered_pair (tptp.first @t36) (tptp.second @t36)) @t36)))) % 0.35/0.65 (assume @p18 (tptp.subclass tptp.element_relation @t38)) % 0.35/0.65 (assume @p19 (forall @t10 (or (not @t40) @t39))) % 0.35/0.65 (assume @p20 (forall @t10 (or @t41 (not @t39) @t40))) % 0.35/0.65 (assume @p21 (forall @t37 (or @t45 @t42))) % 0.35/0.65 (assume @p22 (forall @t37 (or @t45 @t46))) % 0.35/0.65 (assume @p23 (forall @t37 (or @t47 (not @t46) @t44))) % 0.35/0.65 (assume @p24 (forall @t50 (or (not @t49) @t47))) % 0.35/0.65 (assume @p25 (forall @t50 (or @t51 @t49 @t42))) % 0.35/0.65 (assume @p26 (forall @t10 (= @t52 (tptp.union @t3 @t1)))) % 0.35/0.65 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t43) @t52) (tptp.symmetric_difference @t3 @t1)))) % 0.35/0.65 (assume @p28 (forall (@list @t53 @t3 @t1) (= (tptp.intersection @t53 @t29) @t54))) % 0.35/0.65 (assume @p29 (forall (@list @t3 @t1 @t53) (= (tptp.intersection @t29 @t53) @t54))) % 0.35/0.65 (assume @p30 (forall (@list @t3 @t36) (or (not @t57) (not @t56)))) % 0.35/0.65 (assume @p31 (forall @t50 (or @t51 @t57 @t56))) % 0.35/0.65 (assume @p32 (forall @t12 (tptp.subclass @t59 @t58))) % 0.35/0.65 (assume @p33 (forall @t64 (or (not @t63) @t61))) % 0.35/0.65 (assume @p34 (forall (@list @t30 @t60 @t2 @t3) (or (not @t61) @t65 @t63))) % 0.35/0.65 (assume @p35 (forall @t12 (tptp.subclass @t66 @t58))) % 0.35/0.65 (assume @p36 (forall @t64 (or (not @t68) @t67))) % 0.35/0.65 (assume @p37 (forall (@list @t30 @t2 @t60 @t3) (or (not @t67) @t65 @t68))) % 0.35/0.65 (assume @p38 (forall @t69 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.35/0.65 (assume @p39 (forall @t70 (= (tptp.domain_of (tptp.inverse @t36)) (tptp.range_of @t36)))) % 0.35/0.65 (assume @p40 (forall @t37 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t36 @t3 @t27) tptp.null_class)) (tptp.domain @t36 @t3 @t1)))) % 0.35/0.65 (assume @p41 (forall @t37 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t36 @t24 @t1) tptp.null_class)) (tptp.range @t36 @t3 @t1)))) % 0.35/0.65 (assume @p42 (forall (@list @t53 @t3) (= (tptp.range_of (tptp.restrict @t53 @t3 tptp.universal_class)) (tptp.image @t53 @t3)))) % 0.35/0.65 (assume @p43 (forall @t12 (= (tptp.union @t3 @t24) @t71))) % 0.35/0.65 (assume @p44 (tptp.subclass tptp.successor_relation @t38)) % 0.35/0.65 (assume @p45 (forall @t10 (or (not @t73) @t72))) % 0.35/0.65 (assume @p46 (forall @t10 (or (not @t72) @t41 @t73))) % 0.35/0.65 (assume @p47 (forall @t12 (or @t76 @t74))) % 0.35/0.65 (assume @p48 (forall @t12 (or @t76 @t77))) % 0.35/0.65 (assume @p49 (forall @t12 (or (not @t74) (not @t77) @t75))) % 0.35/0.65 (assume @p50 (tptp.inductive tptp.omega)) % 0.35/0.65 (assume @p51 (forall @t69 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.35/0.65 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.35/0.65 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t78))) % 0.35/0.65 (assume @p54 (forall @t12 (or @t19 (tptp.member @t78 tptp.universal_class)))) % 0.35/0.65 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t48)) (tptp.power_class @t3)))) % 0.35/0.65 (assume @p56 (forall (@list @t2) (or (not @t79) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.35/0.65 (assume @p57 (forall (@list @t80 @t53) (tptp.subclass @t81 @t38))) % 0.35/0.65 (assume @p58 (forall (@list @t1 @t36 @t80 @t53) (or (not @t84) @t82))) % 0.35/0.65 (assume @p59 (forall (@list @t36 @t80 @t53 @t1) (or (not @t82) @t85 @t84))) % 0.35/0.65 (assume @p60 (forall @t12 (or (not @t87) @t86))) % 0.35/0.65 (assume @p61 (forall @t12 (or (not @t86) @t87))) % 0.35/0.65 (assume @p62 (forall @t92 (or @t91 @t89))) % 0.35/0.65 (assume @p63 (forall @t92 (or @t91 @t94))) % 0.35/0.65 (assume @p64 (forall @t92 (or (not @t89) (not @t94) @t90))) % 0.35/0.65 (assume @p65 (forall (@list @t88 @t3) (or @t91 @t19 (tptp.member (tptp.image @t88 @t3) tptp.universal_class)))) % 0.35/0.65 (assume @p66 (forall @t12 (or @t96 (tptp.member @t95 @t3)))) % 0.35/0.65 (assume @p67 (forall @t12 (or @t96 (= (tptp.intersection @t3 @t95) tptp.null_class)))) % 0.35/0.65 (assume @p68 (forall (@list @t88 @t1) (= (tptp.sum_class (tptp.image @t88 @t27)) (tptp.apply @t88 @t1)))) % 0.35/0.65 (assume @p69 (tptp.function tptp.choice)) % 0.35/0.65 (assume @p70 (forall @t69 (or @t22 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.35/0.65 (assume @p71 (forall @t92 (or @t98 @t90))) % 0.35/0.65 (assume @p72 (forall @t92 (or @t98 @t99))) % 0.35/0.65 (assume @p73 (forall @t92 (or (not @t99) @t91 @t97))) % 0.35/0.65 (assume @p74 (= (tptp.intersection @t38 (tptp.intersection @t38 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t100)))) tptp.subset_relation)) % 0.35/0.65 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.35/0.65 (assume @p76 (forall (@list @t53) (= (tptp.complement (tptp.domain_of (tptp.intersection @t53 tptp.identity_relation))) (tptp.diagonalise @t53)))) % 0.35/0.65 (assume @p77 (forall @t12 (= (tptp.intersection @t55 (tptp.diagonalise (tptp.compose @t100 @t3))) (tptp.cantor @t3)))) % 0.35/0.65 (assume @p78 (forall @t92 (or @t102 @t90))) % 0.35/0.65 (assume @p79 (forall @t92 (or @t102 @t105))) % 0.35/0.65 (assume @p80 (forall @t92 (or @t102 @t106))) % 0.35/0.65 (assume @p81 (forall @t92 (or @t91 (not @t105) (not @t106) @t101))) % 0.35/0.65 (assume @p82 (forall @t113 (or @t112 @t108))) % 0.35/0.65 (assume @p83 (forall @t113 (or @t112 @t115))) % 0.35/0.65 (assume @p84 (forall @t113 (or @t112 @t116))) % 0.35/0.65 (assume @p85 (forall @t113 (or (not @t108) (not @t115) (not @t116) @t111))) % 0.35/0.65 (assume @p86 (forall @t113 (or @t119 @t117))) % 0.35/0.65 (assume @p87 (forall @t113 (or @t119 @t120))) % 0.35/0.65 (assume @p88 (forall @t113 (or @t119 @t111))) % 0.35/0.65 (assume @p89 (forall (@list @t107 @t110 @t109 @t3 @t1) (or @t119 (not (tptp.member @t26 @t114)) (= (tptp.apply @t109 (tptp.ordered_pair (tptp.apply @t107 @t3) (tptp.apply @t107 @t1))) (tptp.apply @t107 (tptp.apply @t110 @t26)))))) % 0.35/0.65 (assume @p90 (forall @t126 (or @t125 @t124 @t112 (tptp.member @t123 @t114) @t118))) % 0.35/0.65 (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))) % 0.35/0.65 (assume @p92 (forall @t128 (or @t127 @t17))) % 0.35/0.65 (assume @p93 (forall @t128 (or @t127 @t20))) % 0.35/0.65 (assume @p94 (forall @t34 (or @t33 @t79))) % 0.35/0.65 (assume @p95 (forall @t34 (or @t33 (tptp.member @t30 tptp.universal_class)))) % 0.35/0.65 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.35/0.65 (assume @p97 (forall @t129 (or @t7 (not (tptp.subclass @t1 @t36)) (tptp.subclass @t3 @t36)))) % 0.35/0.65 (assume @p98 (forall @t10 (or @t13 @t9 @t131))) % 0.35/0.65 (assume @p99 (forall @t10 (or @t11 @t13 @t131))) % 0.35/0.65 (assume @p100 (forall @t23 (or @t132 @t13 @t9))) % 0.35/0.65 (assume @p101 (forall @t10 (or @t11 @t132 @t13))) % 0.35/0.65 (assume @p102 (forall @t23 (not (tptp.member @t1 (tptp.intersection @t48 @t3))))) % 0.35/0.65 (assume @p103 (forall @t70 (not (tptp.member @t36 tptp.null_class)))) % 0.35/0.65 (assume @p104 (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.35/0.65 (assume @p105 (forall @t12 (or (not (tptp.subclass @t3 tptp.null_class)) @t96))) % 0.35/0.65 (assume @p106 (forall @t70 (or (= @t36 tptp.null_class) (tptp.member (tptp.not_subclass_element @t36 tptp.null_class) @t36)))) % 0.35/0.65 (assume @p107 (tptp.member tptp.null_class tptp.universal_class)) % 0.35/0.65 (assume @p108 (forall @t10 (= @t16 (tptp.unordered_pair @t1 @t3)))) % 0.35/0.65 (assume @p109 (forall @t10 (tptp.subclass @t24 @t16))) % 0.35/0.65 (assume @p110 (forall @t23 (tptp.subclass @t27 @t16))) % 0.35/0.65 (assume @p111 (forall @t23 (or @t21 (= @t16 @t24)))) % 0.35/0.65 (assume @p112 (forall @t10 (or @t18 (= @t16 @t27)))) % 0.35/0.65 (assume @p113 (forall @t10 (or @t133 @t18 @t21))) % 0.35/0.65 (assume @p114 (forall @t129 (or (not (= @t16 @t134)) @t85 (= @t1 @t36)))) % 0.35/0.65 (assume @p115 (forall @t135 (or (not (= @t134 (tptp.unordered_pair @t1 @t36))) @t41 @t13))) % 0.35/0.65 (assume @p116 (forall @t10 (or @t19 @t136))) % 0.35/0.65 (assume @p117 (forall @t23 (or @t22 @t136))) % 0.35/0.65 (assume @p118 (forall @t128 (or @t127 @t136))) % 0.35/0.65 (assume @p119 (forall @t135 (or (not (tptp.member @t3 @t36)) (not (tptp.member @t1 @t36)) (tptp.subclass @t16 @t36)))) % 0.35/0.65 (assume @p120 (forall @t12 (tptp.member @t24 tptp.universal_class))) % 0.35/0.65 (assume @p121 (forall @t23 (tptp.member @t27 @t28))) % 0.35/0.65 (assume @p122 @t137) % 0.35/0.65 (assume @p123 (not @t139)) % 0.35/0.65 (step @p124 :rule evaluate :args ((= false true))) % 0.35/0.65 (step @p125 :rule instantiate :premises (@p9) :args ((@list tptp.x tptp.x))) % 0.35/0.65 (step @p126 :rule cnf_or_pos :args (@t143)) % 0.35/0.65 (step @p127 :rule reordering :premises (@p126) :args ((or @t142 @t141 (not @t143)))) % 0.35/0.65 (step @p128 :rule chain_m_resolution :premises (@p127 @p122 @p125) :args (@t141 (@list false false) (@list @t137 @t143))) % 0.35/0.65 (step @p129 :rule true_intro :premises (@p128)) % 0.35/0.65 (step @p130 :rule eq-symm :args (@t140 @t138)) % 0.35/0.65 (step @p131 :rule refl :args (@t25)) % 0.35/0.65 (step @p132 :rule cong :premises (@p131 @p130) :args ((=> @t25 @t144))) % 0.35/0.65 (assume-push @p146 @t25) % 0.35/0.65 (step @p134 :rule instantiate :premises (@p12) :args ((@list tptp.x))) % 0.35/0.65 (step-pop @p147 :rule scope :premises (@p134)) % 0.35/0.65 (step @p135 :rule process_scope :premises (@p147) :args (@t144)) % 0.35/0.65 (step @p137 :rule eq_resolve :premises (@p135 @p132)) % 0.35/0.65 (step @p138 :rule implies_elim :premises (@p137)) % 0.35/0.65 (step @p139 :rule chain_m_resolution :premises (@p138 @p12) :args ((= @t138 @t140) (@list false) (@list @t25))) % 0.35/0.65 (step @p140 :rule refl :args (tptp.x)) % 0.35/0.65 (step @p141 :rule cong :premises (@p140 @p139) :args (@t139)) % 0.35/0.65 (step @p142 :rule false_intro :premises (@p123)) % 0.35/0.65 (step @p143 :rule symm :premises (@p142)) % 0.35/0.65 (step @p144 :rule trans :premises (@p143 @p141 @p129)) % 0.35/0.65 (step @p145 false :rule eq_resolve :premises (@p144 @p124)) % 0.35/0.65 ) % 0.35/0.66 % SZS output end Proof % 0.35/0.66 % cvc5 exiting %------------------------------------------------------------------------------