%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET124-6 : 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 : n024.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 08:47:28 AM UTC 2026 % Result : Unsatisfiable 0.51s 0.70s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET124-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 09:59:30 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.15/0.35 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.70 % SZS status Unsatisfiable % 0.51/0.70 % SZS output start Proof % 0.51/0.71 ( % 0.51/0.71 (declare-sort $$unsorted 0) % 0.51/0.71 (declare-const tptp.x $$unsorted) % 0.51/0.71 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.function (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.element_relation $$unsorted) % 0.51/0.71 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.universal_class $$unsorted) % 0.51/0.71 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.successor_relation $$unsorted) % 0.51/0.71 (declare-const tptp.choice $$unsorted) % 0.51/0.71 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.subset_relation $$unsorted) % 0.51/0.71 (declare-const tptp.null_class $$unsorted) % 0.51/0.71 (declare-const tptp.set_builder (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.omega $$unsorted) % 0.51/0.71 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.identity_relation $$unsorted) % 0.51/0.71 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.z $$unsorted) % 0.51/0.71 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.51/0.71 (define @t1 () (@var "Y" $$unsorted)) % 0.51/0.71 (define @t2 () (@var "U" $$unsorted)) % 0.51/0.71 (define @t3 () (@var "X" $$unsorted)) % 0.51/0.71 (define @t4 () (tptp.member @t2 @t3)) % 0.51/0.71 (define @t5 () (not @t4)) % 0.51/0.71 (define @t6 () (tptp.subclass @t3 @t1)) % 0.51/0.71 (define @t7 () (not @t6)) % 0.51/0.71 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.51/0.71 (define @t9 () (@list @t3 @t1)) % 0.51/0.71 (define @t10 () (@list @t3)) % 0.51/0.71 (define @t11 () (= @t3 @t1)) % 0.51/0.71 (define @t12 () (not @t11)) % 0.51/0.71 (define @t13 () (tptp.subclass @t1 @t3)) % 0.51/0.71 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.51/0.71 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 0.51/0.71 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 0.51/0.71 (define @t17 () (tptp.singleton @t3)) % 0.51/0.71 (define @t18 () (tptp.ordered_pair @t3 @t1)) % 0.51/0.71 (define @t19 () (tptp.singleton @t1)) % 0.51/0.71 (define @t20 () (tptp.cross_product @t3 @t1)) % 0.51/0.71 (define @t21 () (@var "V" $$unsorted)) % 0.51/0.71 (define @t22 () (tptp.ordered_pair @t2 @t21)) % 0.51/0.71 (define @t23 () (tptp.member @t22 @t20)) % 0.51/0.71 (define @t24 () (not @t23)) % 0.51/0.71 (define @t25 () (@list @t2 @t21 @t3 @t1)) % 0.51/0.71 (define @t26 () (tptp.member @t21 @t1)) % 0.51/0.71 (define @t27 () (@var "Z" $$unsorted)) % 0.51/0.71 (define @t28 () (@list @t27 @t3 @t1)) % 0.51/0.71 (define @t29 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.51/0.71 (define @t30 () (tptp.member @t3 @t1)) % 0.51/0.71 (define @t31 () (tptp.member @t18 tptp.element_relation)) % 0.51/0.71 (define @t32 () (not (tptp.member @t18 @t29))) % 0.51/0.71 (define @t33 () (tptp.member @t27 @t3)) % 0.51/0.71 (define @t34 () (tptp.intersection @t3 @t1)) % 0.51/0.71 (define @t35 () (tptp.member @t27 @t34)) % 0.51/0.71 (define @t36 () (not @t35)) % 0.51/0.71 (define @t37 () (tptp.member @t27 @t1)) % 0.51/0.71 (define @t38 () (not @t33)) % 0.51/0.71 (define @t39 () (tptp.complement @t3)) % 0.51/0.71 (define @t40 () (tptp.member @t27 @t39)) % 0.51/0.71 (define @t41 () (@list @t27 @t3)) % 0.51/0.71 (define @t42 () (not (tptp.member @t27 tptp.universal_class))) % 0.51/0.71 (define @t43 () (tptp.complement (tptp.intersection @t39 (tptp.complement @t1)))) % 0.51/0.71 (define @t44 () (@var "Xr" $$unsorted)) % 0.51/0.71 (define @t45 () (tptp.restrict @t44 @t3 @t1)) % 0.51/0.71 (define @t46 () (tptp.domain_of @t3)) % 0.51/0.71 (define @t47 () (tptp.member @t27 @t46)) % 0.51/0.71 (define @t48 () (= (tptp.restrict @t3 (tptp.singleton @t27) tptp.universal_class) tptp.null_class)) % 0.51/0.71 (define @t49 () (tptp.cross_product @t29 tptp.universal_class)) % 0.51/0.71 (define @t50 () (tptp.rotate @t3)) % 0.51/0.71 (define @t51 () (@var "W" $$unsorted)) % 0.51/0.71 (define @t52 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t51) @t2) @t3)) % 0.51/0.71 (define @t53 () (tptp.ordered_pair @t22 @t51)) % 0.51/0.71 (define @t54 () (tptp.member @t53 @t50)) % 0.51/0.71 (define @t55 () (@list @t2 @t21 @t51 @t3)) % 0.51/0.71 (define @t56 () (not (tptp.member @t53 @t49))) % 0.51/0.71 (define @t57 () (tptp.flip @t3)) % 0.51/0.71 (define @t58 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t51) @t3)) % 0.51/0.71 (define @t59 () (tptp.member @t53 @t57)) % 0.51/0.71 (define @t60 () (@list @t1)) % 0.51/0.71 (define @t61 () (tptp.successor @t3)) % 0.51/0.71 (define @t62 () (= @t61 @t1)) % 0.51/0.71 (define @t63 () (tptp.member @t18 tptp.successor_relation)) % 0.51/0.71 (define @t64 () (tptp.member tptp.null_class @t3)) % 0.51/0.71 (define @t65 () (tptp.inductive @t3)) % 0.51/0.71 (define @t66 () (not @t65)) % 0.51/0.71 (define @t67 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.51/0.71 (define @t68 () (tptp.sum_class @t3)) % 0.51/0.71 (define @t69 () (@var "Yr" $$unsorted)) % 0.51/0.71 (define @t70 () (tptp.compose @t69 @t44)) % 0.51/0.71 (define @t71 () (tptp.member @t27 (tptp.image @t69 (tptp.image @t44 @t19)))) % 0.51/0.71 (define @t72 () (tptp.ordered_pair @t1 @t27)) % 0.51/0.71 (define @t73 () (tptp.member @t72 @t70)) % 0.51/0.71 (define @t74 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.51/0.71 (define @t75 () (tptp.single_valued_class @t3)) % 0.51/0.71 (define @t76 () (@var "Xf" $$unsorted)) % 0.51/0.71 (define @t77 () (tptp.subclass @t76 @t29)) % 0.51/0.71 (define @t78 () (tptp.function @t76)) % 0.51/0.71 (define @t79 () (not @t78)) % 0.51/0.71 (define @t80 () (@list @t76)) % 0.51/0.71 (define @t81 () (tptp.inverse @t76)) % 0.51/0.71 (define @t82 () (tptp.subclass (tptp.compose @t76 @t81) tptp.identity_relation)) % 0.51/0.71 (define @t83 () (tptp.regular @t3)) % 0.51/0.71 (define @t84 () (= @t3 tptp.null_class)) % 0.51/0.71 (define @t85 () (tptp.one_to_one @t76)) % 0.51/0.71 (define @t86 () (not @t85)) % 0.51/0.71 (define @t87 () (tptp.function @t81)) % 0.51/0.71 (define @t88 () (tptp.inverse tptp.element_relation)) % 0.51/0.71 (define @t89 () (tptp.operation @t76)) % 0.51/0.71 (define @t90 () (not @t89)) % 0.51/0.71 (define @t91 () (tptp.domain_of @t76)) % 0.51/0.71 (define @t92 () (tptp.domain_of @t91)) % 0.51/0.71 (define @t93 () (= (tptp.cross_product @t92 @t92) @t91)) % 0.51/0.71 (define @t94 () (tptp.subclass (tptp.range_of @t76) @t92)) % 0.51/0.71 (define @t95 () (@var "Xh" $$unsorted)) % 0.51/0.71 (define @t96 () (tptp.function @t95)) % 0.51/0.71 (define @t97 () (@var "Xf2" $$unsorted)) % 0.51/0.71 (define @t98 () (@var "Xf1" $$unsorted)) % 0.51/0.71 (define @t99 () (tptp.compatible @t95 @t98 @t97)) % 0.51/0.71 (define @t100 () (not @t99)) % 0.51/0.71 (define @t101 () (@list @t95 @t98 @t97)) % 0.51/0.71 (define @t102 () (tptp.domain_of @t98)) % 0.51/0.71 (define @t103 () (= (tptp.domain_of @t102) (tptp.domain_of @t95))) % 0.51/0.71 (define @t104 () (tptp.subclass (tptp.range_of @t95) (tptp.domain_of (tptp.domain_of @t97)))) % 0.51/0.71 (define @t105 () (tptp.operation @t98)) % 0.51/0.71 (define @t106 () (tptp.homomorphism @t95 @t98 @t97)) % 0.51/0.71 (define @t107 () (not @t106)) % 0.51/0.71 (define @t108 () (tptp.operation @t97)) % 0.51/0.71 (define @t109 () (tptp.not_homomorphism2 @t95 @t98 @t97)) % 0.51/0.71 (define @t110 () (tptp.not_homomorphism1 @t95 @t98 @t97)) % 0.51/0.71 (define @t111 () (tptp.ordered_pair @t110 @t109)) % 0.51/0.71 (define @t112 () (not @t108)) % 0.51/0.71 (define @t113 () (not @t105)) % 0.51/0.71 (define @t114 () (@list @t98 @t97 @t95)) % 0.51/0.71 (define @t115 () (tptp.member tptp.x tptp.universal_class)) % 0.51/0.71 (define @t116 () (tptp.singleton tptp.x)) % 0.51/0.71 (define @t117 () (tptp.complement tptp.z)) % 0.51/0.71 (define @t118 () (tptp.complement @t116)) % 0.51/0.71 (define @t119 () (tptp.intersection @t118 @t117)) % 0.51/0.71 (define @t120 () (tptp.member tptp.x (tptp.complement @t119))) % 0.51/0.71 (define @t121 () (tptp.member tptp.x @t119)) % 0.51/0.71 (define @t122 () (not @t115)) % 0.51/0.71 (define @t123 () (or @t122 @t120 @t121)) % 0.51/0.71 (define @t124 () (tptp.member tptp.x @t118)) % 0.51/0.71 (define @t125 () (not @t121)) % 0.51/0.71 (define @t126 () (or @t125 @t124)) % 0.51/0.71 (define @t127 () (@list false false)) % 0.51/0.71 (define @t128 () (not (tptp.member tptp.x @t116))) % 0.51/0.71 (define @t129 () (not @t124)) % 0.51/0.71 (define @t130 () (or @t129 @t128)) % 0.51/0.71 (define @t131 () (tptp.member tptp.x (tptp.unordered_pair tptp.x tptp.x))) % 0.51/0.71 (define @t132 () (or @t122 @t131)) % 0.51/0.71 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.51/0.71 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.51/0.71 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.51/0.71 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.51/0.71 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.51/0.71 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.51/0.71 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.51/0.71 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 0.51/0.71 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 0.51/0.71 (assume @p10 (forall (@list @t1 @t3) (or @t16 (tptp.member @t1 @t14)))) % 0.51/0.71 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.51/0.71 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t17))) % 0.51/0.71 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t17 (tptp.unordered_pair @t3 @t19)) @t18))) % 0.51/0.71 (assume @p14 (forall @t25 (or @t24 @t4))) % 0.51/0.71 (assume @p15 (forall @t25 (or @t24 @t26))) % 0.51/0.71 (assume @p16 (forall (@list @t2 @t3 @t21 @t1) (or @t5 (not @t26) @t23))) % 0.51/0.71 (assume @p17 (forall @t28 (or (not (tptp.member @t27 @t20)) (= (tptp.ordered_pair (tptp.first @t27) (tptp.second @t27)) @t27)))) % 0.51/0.71 (assume @p18 (tptp.subclass tptp.element_relation @t29)) % 0.51/0.71 (assume @p19 (forall @t9 (or (not @t31) @t30))) % 0.51/0.71 (assume @p20 (forall @t9 (or @t32 (not @t30) @t31))) % 0.51/0.71 (assume @p21 (forall @t28 (or @t36 @t33))) % 0.51/0.71 (assume @p22 (forall @t28 (or @t36 @t37))) % 0.51/0.71 (assume @p23 (forall @t28 (or @t38 (not @t37) @t35))) % 0.51/0.71 (assume @p24 (forall @t41 (or (not @t40) @t38))) % 0.51/0.71 (assume @p25 (forall @t41 (or @t42 @t40 @t33))) % 0.51/0.71 (assume @p26 (forall @t9 (= @t43 (tptp.union @t3 @t1)))) % 0.51/0.71 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t34) @t43) (tptp.symmetric_difference @t3 @t1)))) % 0.51/0.71 (assume @p28 (forall (@list @t44 @t3 @t1) (= (tptp.intersection @t44 @t20) @t45))) % 0.51/0.71 (assume @p29 (forall (@list @t3 @t1 @t44) (= (tptp.intersection @t20 @t44) @t45))) % 0.51/0.71 (assume @p30 (forall (@list @t3 @t27) (or (not @t48) (not @t47)))) % 0.51/0.71 (assume @p31 (forall @t41 (or @t42 @t48 @t47))) % 0.51/0.71 (assume @p32 (forall @t10 (tptp.subclass @t50 @t49))) % 0.51/0.71 (assume @p33 (forall @t55 (or (not @t54) @t52))) % 0.51/0.71 (assume @p34 (forall (@list @t21 @t51 @t2 @t3) (or (not @t52) @t56 @t54))) % 0.51/0.71 (assume @p35 (forall @t10 (tptp.subclass @t57 @t49))) % 0.51/0.71 (assume @p36 (forall @t55 (or (not @t59) @t58))) % 0.51/0.71 (assume @p37 (forall (@list @t21 @t2 @t51 @t3) (or (not @t58) @t56 @t59))) % 0.51/0.71 (assume @p38 (forall @t60 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.51/0.71 (assume @p39 (forall (@list @t27) (= (tptp.domain_of (tptp.inverse @t27)) (tptp.range_of @t27)))) % 0.51/0.71 (assume @p40 (forall @t28 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t27 @t3 @t19) tptp.null_class)) (tptp.domain @t27 @t3 @t1)))) % 0.51/0.71 (assume @p41 (forall @t28 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t27 @t17 @t1) tptp.null_class)) (tptp.range @t27 @t3 @t1)))) % 0.51/0.71 (assume @p42 (forall (@list @t44 @t3) (= (tptp.range_of (tptp.restrict @t44 @t3 tptp.universal_class)) (tptp.image @t44 @t3)))) % 0.51/0.71 (assume @p43 (forall @t10 (= (tptp.union @t3 @t17) @t61))) % 0.51/0.71 (assume @p44 (tptp.subclass tptp.successor_relation @t29)) % 0.51/0.71 (assume @p45 (forall @t9 (or (not @t63) @t62))) % 0.51/0.71 (assume @p46 (forall @t9 (or (not @t62) @t32 @t63))) % 0.51/0.71 (assume @p47 (forall @t10 (or @t66 @t64))) % 0.51/0.71 (assume @p48 (forall @t10 (or @t66 @t67))) % 0.51/0.71 (assume @p49 (forall @t10 (or (not @t64) (not @t67) @t65))) % 0.51/0.71 (assume @p50 (tptp.inductive tptp.omega)) % 0.51/0.71 (assume @p51 (forall @t60 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.51/0.71 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.51/0.71 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t68))) % 0.51/0.71 (assume @p54 (forall @t10 (or @t15 (tptp.member @t68 tptp.universal_class)))) % 0.51/0.71 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t39)) (tptp.power_class @t3)))) % 0.51/0.71 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.51/0.71 (assume @p57 (forall (@list @t69 @t44) (tptp.subclass @t70 @t29))) % 0.51/0.71 (assume @p58 (forall (@list @t1 @t27 @t69 @t44) (or (not @t73) @t71))) % 0.51/0.71 (assume @p59 (forall (@list @t27 @t69 @t44 @t1) (or (not @t71) (not (tptp.member @t72 @t29)) @t73))) % 0.51/0.71 (assume @p60 (forall @t10 (or (not @t75) @t74))) % 0.51/0.71 (assume @p61 (forall @t10 (or (not @t74) @t75))) % 0.51/0.71 (assume @p62 (forall @t80 (or @t79 @t77))) % 0.51/0.71 (assume @p63 (forall @t80 (or @t79 @t82))) % 0.51/0.71 (assume @p64 (forall @t80 (or (not @t77) (not @t82) @t78))) % 0.51/0.71 (assume @p65 (forall (@list @t76 @t3) (or @t79 @t15 (tptp.member (tptp.image @t76 @t3) tptp.universal_class)))) % 0.51/0.71 (assume @p66 (forall @t10 (or @t84 (tptp.member @t83 @t3)))) % 0.51/0.71 (assume @p67 (forall @t10 (or @t84 (= (tptp.intersection @t3 @t83) tptp.null_class)))) % 0.51/0.71 (assume @p68 (forall (@list @t76 @t1) (= (tptp.sum_class (tptp.image @t76 @t19)) (tptp.apply @t76 @t1)))) % 0.51/0.71 (assume @p69 (tptp.function tptp.choice)) % 0.51/0.71 (assume @p70 (forall @t60 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.51/0.71 (assume @p71 (forall @t80 (or @t86 @t78))) % 0.51/0.71 (assume @p72 (forall @t80 (or @t86 @t87))) % 0.51/0.71 (assume @p73 (forall @t80 (or (not @t87) @t79 @t85))) % 0.51/0.71 (assume @p74 (= (tptp.intersection @t29 (tptp.intersection @t29 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t88)))) tptp.subset_relation)) % 0.51/0.71 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.51/0.71 (assume @p76 (forall (@list @t44) (= (tptp.complement (tptp.domain_of (tptp.intersection @t44 tptp.identity_relation))) (tptp.diagonalise @t44)))) % 0.51/0.71 (assume @p77 (forall @t10 (= (tptp.intersection @t46 (tptp.diagonalise (tptp.compose @t88 @t3))) (tptp.cantor @t3)))) % 0.51/0.71 (assume @p78 (forall @t80 (or @t90 @t78))) % 0.51/0.71 (assume @p79 (forall @t80 (or @t90 @t93))) % 0.51/0.71 (assume @p80 (forall @t80 (or @t90 @t94))) % 0.51/0.71 (assume @p81 (forall @t80 (or @t79 (not @t93) (not @t94) @t89))) % 0.51/0.71 (assume @p82 (forall @t101 (or @t100 @t96))) % 0.51/0.71 (assume @p83 (forall @t101 (or @t100 @t103))) % 0.51/0.71 (assume @p84 (forall @t101 (or @t100 @t104))) % 0.51/0.71 (assume @p85 (forall @t101 (or (not @t96) (not @t103) (not @t104) @t99))) % 0.51/0.71 (assume @p86 (forall @t101 (or @t107 @t105))) % 0.51/0.71 (assume @p87 (forall @t101 (or @t107 @t108))) % 0.51/0.71 (assume @p88 (forall @t101 (or @t107 @t99))) % 0.51/0.71 (assume @p89 (forall (@list @t95 @t98 @t97 @t3 @t1) (or @t107 (not (tptp.member @t18 @t102)) (= (tptp.apply @t97 (tptp.ordered_pair (tptp.apply @t95 @t3) (tptp.apply @t95 @t1))) (tptp.apply @t95 (tptp.apply @t98 @t18)))))) % 0.51/0.71 (assume @p90 (forall @t114 (or @t113 @t112 @t100 (tptp.member @t111 @t102) @t106))) % 0.51/0.71 (assume @p91 (forall @t114 (or @t113 @t112 @t100 (not (= (tptp.apply @t97 (tptp.ordered_pair (tptp.apply @t95 @t110) (tptp.apply @t95 @t109))) (tptp.apply @t95 (tptp.apply @t98 @t111)))) @t106))) % 0.51/0.71 (assume @p92 (forall @t9 (= (tptp.union @t17 @t1) (tptp.set_builder @t3 @t1)))) % 0.51/0.71 (assume @p93 @t115) % 0.51/0.71 (assume @p94 (not (tptp.member tptp.x (tptp.set_builder tptp.x tptp.z)))) % 0.51/0.71 (step @p95 :rule evaluate :args ((= true false))) % 0.51/0.71 (step @p96 :rule instantiate :premises (@p24) :args ((@list tptp.x @t116))) % 0.51/0.71 (step @p97 :rule instantiate :premises (@p21) :args ((@list tptp.x @t118 @t117))) % 0.51/0.71 (step @p98 :rule instantiate :premises (@p25) :args ((@list tptp.x @t119))) % 0.51/0.71 (step @p99 :rule false_intro :premises (@p94)) % 0.51/0.71 (step @p100 :rule instantiate :premises (@p92) :args ((@list tptp.x tptp.z))) % 0.51/0.71 (step @p101 :rule instantiate :premises (@p26) :args ((@list @t116 tptp.z))) % 0.51/0.71 (step @p102 :rule trans :premises (@p101 @p100)) % 0.51/0.71 (step @p103 :rule refl :args (tptp.x)) % 0.51/0.71 (step @p104 :rule cong :premises (@p103 @p102) :args (@t120)) % 0.51/0.71 (step @p105 :rule trans :premises (@p104 @p99)) % 0.51/0.71 (step @p106 :rule false_elim :premises (@p105)) % 0.51/0.71 (step @p107 :rule cnf_or_pos :args (@t123)) % 0.51/0.71 (step @p108 :rule reordering :premises (@p107) :args ((or @t122 @t120 @t121 (not @t123)))) % 0.51/0.71 (step @p109 :rule chain_m_resolution :premises (@p108 @p93 @p106 @p98) :args (@t121 (@list false true false) (@list @t115 @t120 @t123))) % 0.51/0.71 (step @p110 :rule cnf_or_pos :args (@t126)) % 0.51/0.71 (step @p111 :rule reordering :premises (@p110) :args ((or @t125 @t124 (not @t126)))) % 0.51/0.71 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p97) :args (@t124 @t127 (@list @t121 @t126))) % 0.51/0.71 (step @p113 :rule cnf_or_pos :args (@t130)) % 0.51/0.71 (step @p114 :rule reordering :premises (@p113) :args ((or @t129 @t128 (not @t130)))) % 0.51/0.71 (step @p115 :rule chain_m_resolution :premises (@p114 @p112 @p96) :args (@t128 @t127 (@list @t124 @t130))) % 0.51/0.71 (step @p116 :rule false_intro :premises (@p115)) % 0.51/0.71 (step @p117 :rule instantiate :premises (@p12) :args ((@list tptp.x))) % 0.51/0.71 (step @p118 :rule cong :premises (@p103 @p117) :args (@t131)) % 0.51/0.71 (step @p119 :rule instantiate :premises (@p9) :args ((@list tptp.x tptp.x))) % 0.51/0.71 (step @p120 :rule cnf_or_pos :args (@t132)) % 0.51/0.71 (step @p121 :rule reordering :premises (@p120) :args ((or @t122 @t131 (not @t132)))) % 0.51/0.71 (step @p122 :rule chain_m_resolution :premises (@p121 @p93 @p119) :args (@t131 @t127 (@list @t115 @t132))) % 0.51/0.71 (step @p123 :rule true_intro :premises (@p122)) % 0.51/0.71 (step @p124 :rule symm :premises (@p123)) % 0.51/0.71 (step @p125 :rule trans :premises (@p124 @p118 @p116)) % 0.51/0.71 (step @p126 false :rule eq_resolve :premises (@p125 @p95)) % 0.51/0.71 ) % 0.51/0.71 % SZS output end Proof % 0.51/0.71 % cvc5 exiting %------------------------------------------------------------------------------