%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET108-6 : 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 : n020.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 08:47:25 AM UTC 2026 % Result : Unsatisfiable 0.37s 0.63s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.15 % Problem : SET108-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.13/0.16 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.37 % Computer : n020.cluster.edu % 0.17/0.37 % Model : x86_64 x86_64 % 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.37 % Memory : 8042.1875MB % 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.37 % CPULimit : 300 % 0.17/0.37 % WCLimit : 300 % 0.17/0.37 % DateTime : Tue Jun 2 14:56:40 EDT 2026 % 0.17/0.37 % CPUTime : % 0.28/0.54 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.63 % SZS status Unsatisfiable % 0.37/0.63 % SZS output start Proof % 0.37/0.64 ( % 0.37/0.64 (declare-sort $$unsorted 0) % 0.37/0.64 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.element_relation $$unsorted) % 0.37/0.64 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.universal_class $$unsorted) % 0.37/0.64 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.successor_relation $$unsorted) % 0.37/0.64 (declare-const tptp.choice $$unsorted) % 0.37/0.64 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.z $$unsorted) % 0.37/0.64 (declare-const tptp.subset_relation $$unsorted) % 0.37/0.64 (declare-const tptp.null_class $$unsorted) % 0.37/0.64 (declare-const tptp.y $$unsorted) % 0.37/0.64 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.omega $$unsorted) % 0.37/0.64 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.64 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.identity_relation $$unsorted) % 0.37/0.64 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.37/0.64 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.37/0.64 (define @t1 () (@var "Y" $$unsorted)) % 0.37/0.64 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.64 (define @t3 () (@var "X" $$unsorted)) % 0.37/0.64 (define @t4 () (tptp.member @t2 @t3)) % 0.37/0.64 (define @t5 () (not @t4)) % 0.37/0.64 (define @t6 () (tptp.subclass @t3 @t1)) % 0.37/0.64 (define @t7 () (not @t6)) % 0.37/0.64 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.37/0.64 (define @t9 () (@list @t3 @t1)) % 0.37/0.64 (define @t10 () (@list @t3)) % 0.37/0.64 (define @t11 () (= @t3 @t1)) % 0.37/0.64 (define @t12 () (not @t11)) % 0.37/0.64 (define @t13 () (tptp.subclass @t1 @t3)) % 0.37/0.64 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.37/0.64 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 0.37/0.64 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 0.37/0.64 (define @t17 () (tptp.singleton @t3)) % 0.37/0.64 (define @t18 () (tptp.ordered_pair @t3 @t1)) % 0.37/0.64 (define @t19 () (tptp.singleton @t1)) % 0.37/0.64 (define @t20 () (tptp.cross_product @t3 @t1)) % 0.37/0.64 (define @t21 () (@var "V" $$unsorted)) % 0.37/0.64 (define @t22 () (tptp.ordered_pair @t2 @t21)) % 0.37/0.64 (define @t23 () (tptp.member @t22 @t20)) % 0.37/0.64 (define @t24 () (not @t23)) % 0.37/0.64 (define @t25 () (@list @t2 @t21 @t3 @t1)) % 0.37/0.64 (define @t26 () (tptp.member @t21 @t1)) % 0.37/0.64 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.64 (define @t28 () (tptp.ordered_pair (tptp.first @t27) (tptp.second @t27))) % 0.37/0.64 (define @t29 () (not (tptp.member @t27 @t20))) % 0.37/0.64 (define @t30 () (or @t29 (= @t28 @t27))) % 0.37/0.64 (define @t31 () (@list @t27 @t3 @t1)) % 0.37/0.64 (define @t32 () (forall @t31 @t30)) % 0.37/0.64 (define @t33 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.37/0.64 (define @t34 () (tptp.member @t3 @t1)) % 0.37/0.64 (define @t35 () (tptp.member @t18 tptp.element_relation)) % 0.37/0.64 (define @t36 () (not (tptp.member @t18 @t33))) % 0.37/0.64 (define @t37 () (tptp.member @t27 @t3)) % 0.37/0.64 (define @t38 () (tptp.intersection @t3 @t1)) % 0.37/0.64 (define @t39 () (tptp.member @t27 @t38)) % 0.37/0.64 (define @t40 () (not @t39)) % 0.37/0.64 (define @t41 () (tptp.member @t27 @t1)) % 0.37/0.64 (define @t42 () (not @t37)) % 0.37/0.64 (define @t43 () (tptp.complement @t3)) % 0.37/0.64 (define @t44 () (tptp.member @t27 @t43)) % 0.37/0.64 (define @t45 () (@list @t27 @t3)) % 0.37/0.64 (define @t46 () (not (tptp.member @t27 tptp.universal_class))) % 0.37/0.64 (define @t47 () (tptp.complement (tptp.intersection @t43 (tptp.complement @t1)))) % 0.37/0.64 (define @t48 () (@var "Xr" $$unsorted)) % 0.37/0.64 (define @t49 () (tptp.restrict @t48 @t3 @t1)) % 0.37/0.64 (define @t50 () (tptp.domain_of @t3)) % 0.37/0.64 (define @t51 () (tptp.member @t27 @t50)) % 0.37/0.64 (define @t52 () (= (tptp.restrict @t3 (tptp.singleton @t27) tptp.universal_class) tptp.null_class)) % 0.37/0.64 (define @t53 () (tptp.cross_product @t33 tptp.universal_class)) % 0.37/0.64 (define @t54 () (tptp.rotate @t3)) % 0.37/0.64 (define @t55 () (@var "W" $$unsorted)) % 0.37/0.64 (define @t56 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t55) @t2) @t3)) % 0.37/0.64 (define @t57 () (tptp.ordered_pair @t22 @t55)) % 0.37/0.64 (define @t58 () (tptp.member @t57 @t54)) % 0.37/0.64 (define @t59 () (@list @t2 @t21 @t55 @t3)) % 0.37/0.64 (define @t60 () (not (tptp.member @t57 @t53))) % 0.37/0.64 (define @t61 () (tptp.flip @t3)) % 0.37/0.64 (define @t62 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t55) @t3)) % 0.37/0.64 (define @t63 () (tptp.member @t57 @t61)) % 0.37/0.64 (define @t64 () (@list @t1)) % 0.37/0.64 (define @t65 () (tptp.successor @t3)) % 0.37/0.64 (define @t66 () (= @t65 @t1)) % 0.37/0.64 (define @t67 () (tptp.member @t18 tptp.successor_relation)) % 0.37/0.64 (define @t68 () (tptp.member tptp.null_class @t3)) % 0.37/0.64 (define @t69 () (tptp.inductive @t3)) % 0.37/0.64 (define @t70 () (not @t69)) % 0.37/0.64 (define @t71 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.37/0.64 (define @t72 () (tptp.sum_class @t3)) % 0.37/0.64 (define @t73 () (@var "Yr" $$unsorted)) % 0.37/0.64 (define @t74 () (tptp.compose @t73 @t48)) % 0.37/0.64 (define @t75 () (tptp.member @t27 (tptp.image @t73 (tptp.image @t48 @t19)))) % 0.37/0.64 (define @t76 () (tptp.ordered_pair @t1 @t27)) % 0.37/0.64 (define @t77 () (tptp.member @t76 @t74)) % 0.37/0.64 (define @t78 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.37/0.64 (define @t79 () (tptp.single_valued_class @t3)) % 0.37/0.64 (define @t80 () (@var "Xf" $$unsorted)) % 0.37/0.64 (define @t81 () (tptp.subclass @t80 @t33)) % 0.37/0.64 (define @t82 () (tptp.function @t80)) % 0.37/0.64 (define @t83 () (not @t82)) % 0.37/0.64 (define @t84 () (@list @t80)) % 0.37/0.64 (define @t85 () (tptp.inverse @t80)) % 0.37/0.64 (define @t86 () (tptp.subclass (tptp.compose @t80 @t85) tptp.identity_relation)) % 0.37/0.64 (define @t87 () (tptp.regular @t3)) % 0.37/0.64 (define @t88 () (= @t3 tptp.null_class)) % 0.37/0.64 (define @t89 () (tptp.one_to_one @t80)) % 0.37/0.64 (define @t90 () (not @t89)) % 0.37/0.64 (define @t91 () (tptp.function @t85)) % 0.37/0.64 (define @t92 () (tptp.inverse tptp.element_relation)) % 0.37/0.64 (define @t93 () (tptp.operation @t80)) % 0.37/0.64 (define @t94 () (not @t93)) % 0.37/0.64 (define @t95 () (tptp.domain_of @t80)) % 0.37/0.64 (define @t96 () (tptp.domain_of @t95)) % 0.37/0.64 (define @t97 () (= (tptp.cross_product @t96 @t96) @t95)) % 0.37/0.64 (define @t98 () (tptp.subclass (tptp.range_of @t80) @t96)) % 0.37/0.64 (define @t99 () (@var "Xh" $$unsorted)) % 0.37/0.64 (define @t100 () (tptp.function @t99)) % 0.37/0.64 (define @t101 () (@var "Xf2" $$unsorted)) % 0.37/0.64 (define @t102 () (@var "Xf1" $$unsorted)) % 0.37/0.64 (define @t103 () (tptp.compatible @t99 @t102 @t101)) % 0.37/0.64 (define @t104 () (not @t103)) % 0.37/0.64 (define @t105 () (@list @t99 @t102 @t101)) % 0.37/0.64 (define @t106 () (tptp.domain_of @t102)) % 0.37/0.64 (define @t107 () (= (tptp.domain_of @t106) (tptp.domain_of @t99))) % 0.37/0.64 (define @t108 () (tptp.subclass (tptp.range_of @t99) (tptp.domain_of (tptp.domain_of @t101)))) % 0.37/0.64 (define @t109 () (tptp.operation @t102)) % 0.37/0.64 (define @t110 () (tptp.homomorphism @t99 @t102 @t101)) % 0.37/0.64 (define @t111 () (not @t110)) % 0.37/0.64 (define @t112 () (tptp.operation @t101)) % 0.37/0.64 (define @t113 () (tptp.not_homomorphism2 @t99 @t102 @t101)) % 0.37/0.64 (define @t114 () (tptp.not_homomorphism1 @t99 @t102 @t101)) % 0.37/0.64 (define @t115 () (tptp.ordered_pair @t114 @t113)) % 0.37/0.64 (define @t116 () (not @t112)) % 0.37/0.64 (define @t117 () (not @t109)) % 0.37/0.64 (define @t118 () (@list @t102 @t101 @t99)) % 0.37/0.64 (define @t119 () (tptp.ordered_pair tptp.y tptp.z)) % 0.37/0.64 (define @t120 () (tptp.member @t119 @t33)) % 0.37/0.64 (define @t121 () (tptp.ordered_pair (tptp.first @t119) (tptp.second @t119))) % 0.37/0.64 (define @t122 () (= @t119 @t121)) % 0.37/0.64 (define @t123 () (not @t120)) % 0.37/0.64 (define @t124 () (or @t123 @t122)) % 0.37/0.64 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.37/0.64 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.37/0.64 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.37/0.64 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.37/0.64 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.37/0.64 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.37/0.64 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.37/0.64 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 0.37/0.64 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 0.37/0.64 (assume @p10 (forall (@list @t1 @t3) (or @t16 (tptp.member @t1 @t14)))) % 0.37/0.64 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.37/0.64 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t17))) % 0.37/0.64 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t17 (tptp.unordered_pair @t3 @t19)) @t18))) % 0.37/0.64 (assume @p14 (forall @t25 (or @t24 @t4))) % 0.37/0.64 (assume @p15 (forall @t25 (or @t24 @t26))) % 0.37/0.64 (assume @p16 (forall (@list @t2 @t3 @t21 @t1) (or @t5 (not @t26) @t23))) % 0.37/0.64 (assume @p17 @t32) % 0.37/0.64 (assume @p18 (tptp.subclass tptp.element_relation @t33)) % 0.37/0.64 (assume @p19 (forall @t9 (or (not @t35) @t34))) % 0.37/0.64 (assume @p20 (forall @t9 (or @t36 (not @t34) @t35))) % 0.37/0.64 (assume @p21 (forall @t31 (or @t40 @t37))) % 0.37/0.64 (assume @p22 (forall @t31 (or @t40 @t41))) % 0.37/0.64 (assume @p23 (forall @t31 (or @t42 (not @t41) @t39))) % 0.37/0.64 (assume @p24 (forall @t45 (or (not @t44) @t42))) % 0.37/0.64 (assume @p25 (forall @t45 (or @t46 @t44 @t37))) % 0.37/0.64 (assume @p26 (forall @t9 (= @t47 (tptp.union @t3 @t1)))) % 0.37/0.64 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t38) @t47) (tptp.symmetric_difference @t3 @t1)))) % 0.37/0.64 (assume @p28 (forall (@list @t48 @t3 @t1) (= (tptp.intersection @t48 @t20) @t49))) % 0.37/0.64 (assume @p29 (forall (@list @t3 @t1 @t48) (= (tptp.intersection @t20 @t48) @t49))) % 0.37/0.64 (assume @p30 (forall (@list @t3 @t27) (or (not @t52) (not @t51)))) % 0.37/0.64 (assume @p31 (forall @t45 (or @t46 @t52 @t51))) % 0.37/0.64 (assume @p32 (forall @t10 (tptp.subclass @t54 @t53))) % 0.37/0.64 (assume @p33 (forall @t59 (or (not @t58) @t56))) % 0.37/0.64 (assume @p34 (forall (@list @t21 @t55 @t2 @t3) (or (not @t56) @t60 @t58))) % 0.37/0.64 (assume @p35 (forall @t10 (tptp.subclass @t61 @t53))) % 0.37/0.64 (assume @p36 (forall @t59 (or (not @t63) @t62))) % 0.37/0.64 (assume @p37 (forall (@list @t21 @t2 @t55 @t3) (or (not @t62) @t60 @t63))) % 0.37/0.64 (assume @p38 (forall @t64 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.37/0.64 (assume @p39 (forall (@list @t27) (= (tptp.domain_of (tptp.inverse @t27)) (tptp.range_of @t27)))) % 0.37/0.64 (assume @p40 (forall @t31 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t27 @t3 @t19) tptp.null_class)) (tptp.domain @t27 @t3 @t1)))) % 0.37/0.64 (assume @p41 (forall @t31 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t27 @t17 @t1) tptp.null_class)) (tptp.range @t27 @t3 @t1)))) % 0.37/0.64 (assume @p42 (forall (@list @t48 @t3) (= (tptp.range_of (tptp.restrict @t48 @t3 tptp.universal_class)) (tptp.image @t48 @t3)))) % 0.37/0.64 (assume @p43 (forall @t10 (= (tptp.union @t3 @t17) @t65))) % 0.37/0.64 (assume @p44 (tptp.subclass tptp.successor_relation @t33)) % 0.37/0.64 (assume @p45 (forall @t9 (or (not @t67) @t66))) % 0.37/0.64 (assume @p46 (forall @t9 (or (not @t66) @t36 @t67))) % 0.37/0.64 (assume @p47 (forall @t10 (or @t70 @t68))) % 0.37/0.64 (assume @p48 (forall @t10 (or @t70 @t71))) % 0.37/0.64 (assume @p49 (forall @t10 (or (not @t68) (not @t71) @t69))) % 0.37/0.64 (assume @p50 (tptp.inductive tptp.omega)) % 0.37/0.64 (assume @p51 (forall @t64 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.37/0.64 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.37/0.64 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t72))) % 0.37/0.64 (assume @p54 (forall @t10 (or @t15 (tptp.member @t72 tptp.universal_class)))) % 0.37/0.64 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t43)) (tptp.power_class @t3)))) % 0.37/0.64 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.37/0.64 (assume @p57 (forall (@list @t73 @t48) (tptp.subclass @t74 @t33))) % 0.37/0.64 (assume @p58 (forall (@list @t1 @t27 @t73 @t48) (or (not @t77) @t75))) % 0.37/0.64 (assume @p59 (forall (@list @t27 @t73 @t48 @t1) (or (not @t75) (not (tptp.member @t76 @t33)) @t77))) % 0.37/0.64 (assume @p60 (forall @t10 (or (not @t79) @t78))) % 0.37/0.64 (assume @p61 (forall @t10 (or (not @t78) @t79))) % 0.37/0.64 (assume @p62 (forall @t84 (or @t83 @t81))) % 0.37/0.64 (assume @p63 (forall @t84 (or @t83 @t86))) % 0.37/0.64 (assume @p64 (forall @t84 (or (not @t81) (not @t86) @t82))) % 0.37/0.64 (assume @p65 (forall (@list @t80 @t3) (or @t83 @t15 (tptp.member (tptp.image @t80 @t3) tptp.universal_class)))) % 0.37/0.64 (assume @p66 (forall @t10 (or @t88 (tptp.member @t87 @t3)))) % 0.37/0.64 (assume @p67 (forall @t10 (or @t88 (= (tptp.intersection @t3 @t87) tptp.null_class)))) % 0.37/0.64 (assume @p68 (forall (@list @t80 @t1) (= (tptp.sum_class (tptp.image @t80 @t19)) (tptp.apply @t80 @t1)))) % 0.37/0.64 (assume @p69 (tptp.function tptp.choice)) % 0.37/0.64 (assume @p70 (forall @t64 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.37/0.64 (assume @p71 (forall @t84 (or @t90 @t82))) % 0.37/0.64 (assume @p72 (forall @t84 (or @t90 @t91))) % 0.37/0.64 (assume @p73 (forall @t84 (or (not @t91) @t83 @t89))) % 0.37/0.64 (assume @p74 (= (tptp.intersection @t33 (tptp.intersection @t33 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t92)))) tptp.subset_relation)) % 0.37/0.64 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.37/0.64 (assume @p76 (forall (@list @t48) (= (tptp.complement (tptp.domain_of (tptp.intersection @t48 tptp.identity_relation))) (tptp.diagonalise @t48)))) % 0.37/0.64 (assume @p77 (forall @t10 (= (tptp.intersection @t50 (tptp.diagonalise (tptp.compose @t92 @t3))) (tptp.cantor @t3)))) % 0.37/0.64 (assume @p78 (forall @t84 (or @t94 @t82))) % 0.37/0.64 (assume @p79 (forall @t84 (or @t94 @t97))) % 0.37/0.64 (assume @p80 (forall @t84 (or @t94 @t98))) % 0.37/0.64 (assume @p81 (forall @t84 (or @t83 (not @t97) (not @t98) @t93))) % 0.37/0.64 (assume @p82 (forall @t105 (or @t104 @t100))) % 0.37/0.64 (assume @p83 (forall @t105 (or @t104 @t107))) % 0.37/0.64 (assume @p84 (forall @t105 (or @t104 @t108))) % 0.37/0.64 (assume @p85 (forall @t105 (or (not @t100) (not @t107) (not @t108) @t103))) % 0.37/0.64 (assume @p86 (forall @t105 (or @t111 @t109))) % 0.37/0.64 (assume @p87 (forall @t105 (or @t111 @t112))) % 0.37/0.64 (assume @p88 (forall @t105 (or @t111 @t103))) % 0.37/0.64 (assume @p89 (forall (@list @t99 @t102 @t101 @t3 @t1) (or @t111 (not (tptp.member @t18 @t106)) (= (tptp.apply @t101 (tptp.ordered_pair (tptp.apply @t99 @t3) (tptp.apply @t99 @t1))) (tptp.apply @t99 (tptp.apply @t102 @t18)))))) % 0.37/0.64 (assume @p90 (forall @t118 (or @t117 @t116 @t104 (tptp.member @t115 @t106) @t110))) % 0.37/0.64 (assume @p91 (forall @t118 (or @t117 @t116 @t104 (not (= (tptp.apply @t101 (tptp.ordered_pair (tptp.apply @t99 @t114) (tptp.apply @t99 @t113))) (tptp.apply @t99 (tptp.apply @t102 @t115)))) @t110))) % 0.37/0.64 (assume @p92 @t120) % 0.37/0.64 (assume @p93 (not (tptp.member @t121 @t33))) % 0.37/0.64 (step @p94 :rule evaluate :args ((= true false))) % 0.37/0.64 (step @p95 :rule false_intro :premises (@p93)) % 0.37/0.64 (step @p96 :rule refl :args (@t33)) % 0.37/0.64 (step @p97 :rule eq-symm :args (@t28 @t27)) % 0.37/0.64 (step @p98 :rule refl :args (@t29)) % 0.37/0.64 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t30)) % 0.37/0.64 (step @p100 :rule cong :premises (@p99) :args (@t32)) % 0.37/0.64 (step @p101 :rule eq_resolve :premises (@p17 @p100)) % 0.37/0.64 (step @p102 :rule instantiate :premises (@p101) :args ((@list @t119 tptp.universal_class tptp.universal_class))) % 0.37/0.64 (step @p103 :rule cnf_or_pos :args (@t124)) % 0.37/0.64 (step @p104 :rule reordering :premises (@p103) :args ((or @t123 @t122 (not @t124)))) % 0.37/0.64 (step @p105 :rule chain_m_resolution :premises (@p104 @p92 @p102) :args (@t122 (@list false false) (@list @t120 @t124))) % 0.37/0.64 (step @p106 :rule cong :premises (@p105 @p96) :args (@t120)) % 0.37/0.64 (step @p107 :rule true_intro :premises (@p92)) % 0.37/0.64 (step @p108 :rule symm :premises (@p107)) % 0.37/0.64 (step @p109 :rule trans :premises (@p108 @p106 @p95)) % 0.37/0.64 (step @p110 false :rule eq_resolve :premises (@p109 @p94)) % 0.37/0.64 ) % 0.37/0.64 % SZS output end Proof % 0.37/0.64 % cvc5 exiting %------------------------------------------------------------------------------