%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET024-6 : 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 : n004.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 0.36s 0.62s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET024-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.33 % Computer : n004.cluster.edu % 0.17/0.33 % Model : x86_64 x86_64 % 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.33 % Memory : 8042.1875MB % 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:42:22 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.29/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.62 % SZS status Unsatisfiable % 0.36/0.62 % SZS output start Proof % 0.43/0.63 ( % 0.43/0.63 (declare-sort $$unsorted 0) % 0.43/0.63 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.function (-> $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.element_relation $$unsorted) % 0.43/0.63 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.universal_class $$unsorted) % 0.43/0.63 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.successor_relation $$unsorted) % 0.43/0.63 (declare-const tptp.choice $$unsorted) % 0.43/0.63 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.subset_relation $$unsorted) % 0.43/0.63 (declare-const tptp.null_class $$unsorted) % 0.43/0.63 (declare-const tptp.x $$unsorted) % 0.43/0.63 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.omega $$unsorted) % 0.43/0.63 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.identity_relation $$unsorted) % 0.43/0.63 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.43/0.63 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.43/0.63 (define @t1 () (@var "Y" $$unsorted)) % 0.43/0.63 (define @t2 () (@var "U" $$unsorted)) % 0.43/0.63 (define @t3 () (@var "X" $$unsorted)) % 0.43/0.63 (define @t4 () (tptp.member @t2 @t3)) % 0.43/0.63 (define @t5 () (not @t4)) % 0.43/0.63 (define @t6 () (tptp.subclass @t3 @t1)) % 0.43/0.63 (define @t7 () (not @t6)) % 0.43/0.63 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.43/0.63 (define @t9 () (@list @t3 @t1)) % 0.43/0.63 (define @t10 () (@list @t3)) % 0.43/0.63 (define @t11 () (= @t3 @t1)) % 0.43/0.63 (define @t12 () (not @t11)) % 0.43/0.63 (define @t13 () (tptp.subclass @t1 @t3)) % 0.43/0.63 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.43/0.63 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 0.43/0.63 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 0.43/0.63 (define @t17 () (tptp.singleton @t3)) % 0.43/0.63 (define @t18 () (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t17))) % 0.43/0.63 (define @t19 () (tptp.ordered_pair @t3 @t1)) % 0.43/0.63 (define @t20 () (tptp.singleton @t1)) % 0.43/0.63 (define @t21 () (tptp.cross_product @t3 @t1)) % 0.43/0.63 (define @t22 () (@var "V" $$unsorted)) % 0.43/0.63 (define @t23 () (tptp.ordered_pair @t2 @t22)) % 0.43/0.63 (define @t24 () (tptp.member @t23 @t21)) % 0.43/0.63 (define @t25 () (not @t24)) % 0.43/0.63 (define @t26 () (@list @t2 @t22 @t3 @t1)) % 0.43/0.63 (define @t27 () (tptp.member @t22 @t1)) % 0.43/0.63 (define @t28 () (@var "Z" $$unsorted)) % 0.43/0.63 (define @t29 () (@list @t28 @t3 @t1)) % 0.43/0.63 (define @t30 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.43/0.63 (define @t31 () (tptp.member @t3 @t1)) % 0.43/0.63 (define @t32 () (tptp.member @t19 tptp.element_relation)) % 0.43/0.63 (define @t33 () (not (tptp.member @t19 @t30))) % 0.43/0.63 (define @t34 () (tptp.member @t28 @t3)) % 0.43/0.63 (define @t35 () (tptp.intersection @t3 @t1)) % 0.43/0.63 (define @t36 () (tptp.member @t28 @t35)) % 0.43/0.63 (define @t37 () (not @t36)) % 0.43/0.63 (define @t38 () (tptp.member @t28 @t1)) % 0.43/0.63 (define @t39 () (not @t34)) % 0.43/0.63 (define @t40 () (tptp.complement @t3)) % 0.43/0.63 (define @t41 () (tptp.member @t28 @t40)) % 0.43/0.63 (define @t42 () (@list @t28 @t3)) % 0.43/0.63 (define @t43 () (not (tptp.member @t28 tptp.universal_class))) % 0.43/0.63 (define @t44 () (tptp.complement (tptp.intersection @t40 (tptp.complement @t1)))) % 0.43/0.63 (define @t45 () (@var "Xr" $$unsorted)) % 0.43/0.63 (define @t46 () (tptp.restrict @t45 @t3 @t1)) % 0.43/0.63 (define @t47 () (tptp.domain_of @t3)) % 0.43/0.63 (define @t48 () (tptp.member @t28 @t47)) % 0.43/0.63 (define @t49 () (= (tptp.restrict @t3 (tptp.singleton @t28) tptp.universal_class) tptp.null_class)) % 0.43/0.63 (define @t50 () (tptp.cross_product @t30 tptp.universal_class)) % 0.43/0.63 (define @t51 () (tptp.rotate @t3)) % 0.43/0.63 (define @t52 () (@var "W" $$unsorted)) % 0.43/0.63 (define @t53 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t52) @t2) @t3)) % 0.43/0.63 (define @t54 () (tptp.ordered_pair @t23 @t52)) % 0.43/0.63 (define @t55 () (tptp.member @t54 @t51)) % 0.43/0.63 (define @t56 () (@list @t2 @t22 @t52 @t3)) % 0.43/0.63 (define @t57 () (not (tptp.member @t54 @t50))) % 0.43/0.63 (define @t58 () (tptp.flip @t3)) % 0.43/0.63 (define @t59 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t2) @t52) @t3)) % 0.43/0.63 (define @t60 () (tptp.member @t54 @t58)) % 0.43/0.63 (define @t61 () (@list @t1)) % 0.43/0.63 (define @t62 () (tptp.successor @t3)) % 0.43/0.63 (define @t63 () (= @t62 @t1)) % 0.43/0.63 (define @t64 () (tptp.member @t19 tptp.successor_relation)) % 0.43/0.63 (define @t65 () (tptp.member tptp.null_class @t3)) % 0.43/0.63 (define @t66 () (tptp.inductive @t3)) % 0.43/0.63 (define @t67 () (not @t66)) % 0.43/0.63 (define @t68 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.43/0.63 (define @t69 () (tptp.sum_class @t3)) % 0.43/0.63 (define @t70 () (@var "Yr" $$unsorted)) % 0.43/0.63 (define @t71 () (tptp.compose @t70 @t45)) % 0.43/0.63 (define @t72 () (tptp.member @t28 (tptp.image @t70 (tptp.image @t45 @t20)))) % 0.43/0.63 (define @t73 () (tptp.ordered_pair @t1 @t28)) % 0.43/0.63 (define @t74 () (tptp.member @t73 @t71)) % 0.43/0.63 (define @t75 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.43/0.63 (define @t76 () (tptp.single_valued_class @t3)) % 0.43/0.63 (define @t77 () (@var "Xf" $$unsorted)) % 0.43/0.63 (define @t78 () (tptp.subclass @t77 @t30)) % 0.43/0.63 (define @t79 () (tptp.function @t77)) % 0.43/0.63 (define @t80 () (not @t79)) % 0.43/0.63 (define @t81 () (@list @t77)) % 0.43/0.63 (define @t82 () (tptp.inverse @t77)) % 0.43/0.63 (define @t83 () (tptp.subclass (tptp.compose @t77 @t82) tptp.identity_relation)) % 0.43/0.63 (define @t84 () (tptp.regular @t3)) % 0.43/0.63 (define @t85 () (= @t3 tptp.null_class)) % 0.43/0.63 (define @t86 () (tptp.one_to_one @t77)) % 0.43/0.63 (define @t87 () (not @t86)) % 0.43/0.63 (define @t88 () (tptp.function @t82)) % 0.43/0.63 (define @t89 () (tptp.inverse tptp.element_relation)) % 0.43/0.63 (define @t90 () (tptp.operation @t77)) % 0.43/0.63 (define @t91 () (not @t90)) % 0.43/0.63 (define @t92 () (tptp.domain_of @t77)) % 0.43/0.63 (define @t93 () (tptp.domain_of @t92)) % 0.43/0.63 (define @t94 () (= (tptp.cross_product @t93 @t93) @t92)) % 0.43/0.63 (define @t95 () (tptp.subclass (tptp.range_of @t77) @t93)) % 0.43/0.63 (define @t96 () (@var "Xh" $$unsorted)) % 0.43/0.63 (define @t97 () (tptp.function @t96)) % 0.43/0.63 (define @t98 () (@var "Xf2" $$unsorted)) % 0.43/0.63 (define @t99 () (@var "Xf1" $$unsorted)) % 0.43/0.63 (define @t100 () (tptp.compatible @t96 @t99 @t98)) % 0.43/0.63 (define @t101 () (not @t100)) % 0.43/0.63 (define @t102 () (@list @t96 @t99 @t98)) % 0.43/0.63 (define @t103 () (tptp.domain_of @t99)) % 0.43/0.63 (define @t104 () (= (tptp.domain_of @t103) (tptp.domain_of @t96))) % 0.43/0.63 (define @t105 () (tptp.subclass (tptp.range_of @t96) (tptp.domain_of (tptp.domain_of @t98)))) % 0.43/0.63 (define @t106 () (tptp.operation @t99)) % 0.43/0.63 (define @t107 () (tptp.homomorphism @t96 @t99 @t98)) % 0.43/0.63 (define @t108 () (not @t107)) % 0.43/0.63 (define @t109 () (tptp.operation @t98)) % 0.43/0.63 (define @t110 () (tptp.not_homomorphism2 @t96 @t99 @t98)) % 0.43/0.63 (define @t111 () (tptp.not_homomorphism1 @t96 @t99 @t98)) % 0.43/0.63 (define @t112 () (tptp.ordered_pair @t111 @t110)) % 0.43/0.63 (define @t113 () (not @t109)) % 0.43/0.63 (define @t114 () (not @t106)) % 0.43/0.63 (define @t115 () (@list @t99 @t98 @t96)) % 0.43/0.63 (define @t116 () (tptp.member tptp.x tptp.universal_class)) % 0.43/0.63 (define @t117 () (tptp.singleton tptp.x)) % 0.43/0.63 (define @t118 () (tptp.member tptp.x @t117)) % 0.43/0.63 (define @t119 () (tptp.unordered_pair tptp.x tptp.x)) % 0.43/0.63 (define @t120 () (tptp.member tptp.x @t119)) % 0.43/0.63 (define @t121 () (not @t116)) % 0.43/0.63 (define @t122 () (or @t121 @t120)) % 0.43/0.63 (define @t123 () (= @t119 @t117)) % 0.43/0.63 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.43/0.63 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.43/0.63 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.43/0.63 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.43/0.63 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.43/0.63 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.43/0.63 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.43/0.63 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 0.43/0.63 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 0.43/0.63 (assume @p10 (forall (@list @t1 @t3) (or @t16 (tptp.member @t1 @t14)))) % 0.43/0.63 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.43/0.63 (assume @p12 @t18) % 0.43/0.63 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t17 (tptp.unordered_pair @t3 @t20)) @t19))) % 0.43/0.63 (assume @p14 (forall @t26 (or @t25 @t4))) % 0.43/0.63 (assume @p15 (forall @t26 (or @t25 @t27))) % 0.43/0.63 (assume @p16 (forall (@list @t2 @t3 @t22 @t1) (or @t5 (not @t27) @t24))) % 0.43/0.63 (assume @p17 (forall @t29 (or (not (tptp.member @t28 @t21)) (= (tptp.ordered_pair (tptp.first @t28) (tptp.second @t28)) @t28)))) % 0.43/0.63 (assume @p18 (tptp.subclass tptp.element_relation @t30)) % 0.43/0.63 (assume @p19 (forall @t9 (or (not @t32) @t31))) % 0.43/0.63 (assume @p20 (forall @t9 (or @t33 (not @t31) @t32))) % 0.43/0.63 (assume @p21 (forall @t29 (or @t37 @t34))) % 0.43/0.63 (assume @p22 (forall @t29 (or @t37 @t38))) % 0.43/0.63 (assume @p23 (forall @t29 (or @t39 (not @t38) @t36))) % 0.43/0.63 (assume @p24 (forall @t42 (or (not @t41) @t39))) % 0.43/0.63 (assume @p25 (forall @t42 (or @t43 @t41 @t34))) % 0.43/0.63 (assume @p26 (forall @t9 (= @t44 (tptp.union @t3 @t1)))) % 0.43/0.63 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t35) @t44) (tptp.symmetric_difference @t3 @t1)))) % 0.43/0.63 (assume @p28 (forall (@list @t45 @t3 @t1) (= (tptp.intersection @t45 @t21) @t46))) % 0.43/0.63 (assume @p29 (forall (@list @t3 @t1 @t45) (= (tptp.intersection @t21 @t45) @t46))) % 0.43/0.63 (assume @p30 (forall (@list @t3 @t28) (or (not @t49) (not @t48)))) % 0.43/0.63 (assume @p31 (forall @t42 (or @t43 @t49 @t48))) % 0.43/0.63 (assume @p32 (forall @t10 (tptp.subclass @t51 @t50))) % 0.43/0.63 (assume @p33 (forall @t56 (or (not @t55) @t53))) % 0.43/0.63 (assume @p34 (forall (@list @t22 @t52 @t2 @t3) (or (not @t53) @t57 @t55))) % 0.43/0.63 (assume @p35 (forall @t10 (tptp.subclass @t58 @t50))) % 0.43/0.63 (assume @p36 (forall @t56 (or (not @t60) @t59))) % 0.43/0.63 (assume @p37 (forall (@list @t22 @t2 @t52 @t3) (or (not @t59) @t57 @t60))) % 0.43/0.63 (assume @p38 (forall @t61 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.43/0.63 (assume @p39 (forall (@list @t28) (= (tptp.domain_of (tptp.inverse @t28)) (tptp.range_of @t28)))) % 0.43/0.63 (assume @p40 (forall @t29 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t28 @t3 @t20) tptp.null_class)) (tptp.domain @t28 @t3 @t1)))) % 0.43/0.63 (assume @p41 (forall @t29 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t28 @t17 @t1) tptp.null_class)) (tptp.range @t28 @t3 @t1)))) % 0.43/0.63 (assume @p42 (forall (@list @t45 @t3) (= (tptp.range_of (tptp.restrict @t45 @t3 tptp.universal_class)) (tptp.image @t45 @t3)))) % 0.43/0.63 (assume @p43 (forall @t10 (= (tptp.union @t3 @t17) @t62))) % 0.43/0.63 (assume @p44 (tptp.subclass tptp.successor_relation @t30)) % 0.43/0.63 (assume @p45 (forall @t9 (or (not @t64) @t63))) % 0.43/0.63 (assume @p46 (forall @t9 (or (not @t63) @t33 @t64))) % 0.43/0.63 (assume @p47 (forall @t10 (or @t67 @t65))) % 0.43/0.63 (assume @p48 (forall @t10 (or @t67 @t68))) % 0.43/0.63 (assume @p49 (forall @t10 (or (not @t65) (not @t68) @t66))) % 0.43/0.63 (assume @p50 (tptp.inductive tptp.omega)) % 0.43/0.63 (assume @p51 (forall @t61 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.43/0.63 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.43/0.63 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t69))) % 0.43/0.63 (assume @p54 (forall @t10 (or @t15 (tptp.member @t69 tptp.universal_class)))) % 0.43/0.63 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t40)) (tptp.power_class @t3)))) % 0.43/0.63 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.43/0.63 (assume @p57 (forall (@list @t70 @t45) (tptp.subclass @t71 @t30))) % 0.43/0.63 (assume @p58 (forall (@list @t1 @t28 @t70 @t45) (or (not @t74) @t72))) % 0.43/0.63 (assume @p59 (forall (@list @t28 @t70 @t45 @t1) (or (not @t72) (not (tptp.member @t73 @t30)) @t74))) % 0.43/0.63 (assume @p60 (forall @t10 (or (not @t76) @t75))) % 0.43/0.63 (assume @p61 (forall @t10 (or (not @t75) @t76))) % 0.43/0.63 (assume @p62 (forall @t81 (or @t80 @t78))) % 0.43/0.63 (assume @p63 (forall @t81 (or @t80 @t83))) % 0.43/0.63 (assume @p64 (forall @t81 (or (not @t78) (not @t83) @t79))) % 0.43/0.63 (assume @p65 (forall (@list @t77 @t3) (or @t80 @t15 (tptp.member (tptp.image @t77 @t3) tptp.universal_class)))) % 0.43/0.63 (assume @p66 (forall @t10 (or @t85 (tptp.member @t84 @t3)))) % 0.43/0.63 (assume @p67 (forall @t10 (or @t85 (= (tptp.intersection @t3 @t84) tptp.null_class)))) % 0.43/0.63 (assume @p68 (forall (@list @t77 @t1) (= (tptp.sum_class (tptp.image @t77 @t20)) (tptp.apply @t77 @t1)))) % 0.43/0.63 (assume @p69 (tptp.function tptp.choice)) % 0.43/0.63 (assume @p70 (forall @t61 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.43/0.63 (assume @p71 (forall @t81 (or @t87 @t79))) % 0.43/0.63 (assume @p72 (forall @t81 (or @t87 @t88))) % 0.43/0.63 (assume @p73 (forall @t81 (or (not @t88) @t80 @t86))) % 0.43/0.63 (assume @p74 (= (tptp.intersection @t30 (tptp.intersection @t30 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t89)))) tptp.subset_relation)) % 0.43/0.63 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.43/0.63 (assume @p76 (forall (@list @t45) (= (tptp.complement (tptp.domain_of (tptp.intersection @t45 tptp.identity_relation))) (tptp.diagonalise @t45)))) % 0.43/0.63 (assume @p77 (forall @t10 (= (tptp.intersection @t47 (tptp.diagonalise (tptp.compose @t89 @t3))) (tptp.cantor @t3)))) % 0.43/0.63 (assume @p78 (forall @t81 (or @t91 @t79))) % 0.43/0.63 (assume @p79 (forall @t81 (or @t91 @t94))) % 0.43/0.63 (assume @p80 (forall @t81 (or @t91 @t95))) % 0.43/0.63 (assume @p81 (forall @t81 (or @t80 (not @t94) (not @t95) @t90))) % 0.43/0.63 (assume @p82 (forall @t102 (or @t101 @t97))) % 0.43/0.63 (assume @p83 (forall @t102 (or @t101 @t104))) % 0.43/0.63 (assume @p84 (forall @t102 (or @t101 @t105))) % 0.43/0.63 (assume @p85 (forall @t102 (or (not @t97) (not @t104) (not @t105) @t100))) % 0.43/0.63 (assume @p86 (forall @t102 (or @t108 @t106))) % 0.43/0.63 (assume @p87 (forall @t102 (or @t108 @t109))) % 0.43/0.63 (assume @p88 (forall @t102 (or @t108 @t100))) % 0.43/0.63 (assume @p89 (forall (@list @t96 @t99 @t98 @t3 @t1) (or @t108 (not (tptp.member @t19 @t103)) (= (tptp.apply @t98 (tptp.ordered_pair (tptp.apply @t96 @t3) (tptp.apply @t96 @t1))) (tptp.apply @t96 (tptp.apply @t99 @t19)))))) % 0.43/0.63 (assume @p90 (forall @t115 (or @t114 @t113 @t101 (tptp.member @t112 @t103) @t107))) % 0.43/0.63 (assume @p91 (forall @t115 (or @t114 @t113 @t101 (not (= (tptp.apply @t98 (tptp.ordered_pair (tptp.apply @t96 @t111) (tptp.apply @t96 @t110))) (tptp.apply @t96 (tptp.apply @t99 @t112)))) @t107))) % 0.43/0.63 (assume @p92 @t116) % 0.43/0.63 (assume @p93 (not @t118)) % 0.43/0.63 (step @p94 :rule evaluate :args ((= false true))) % 0.43/0.63 (step @p95 :rule instantiate :premises (@p9) :args ((@list tptp.x tptp.x))) % 0.43/0.63 (step @p96 :rule cnf_or_pos :args (@t122)) % 0.43/0.63 (step @p97 :rule reordering :premises (@p96) :args ((or @t121 @t120 (not @t122)))) % 0.43/0.63 (step @p98 :rule chain_m_resolution :premises (@p97 @p92 @p95) :args (@t120 (@list false false) (@list @t116 @t122))) % 0.43/0.63 (step @p99 :rule true_intro :premises (@p98)) % 0.43/0.63 (step @p100 :rule eq-symm :args (@t119 @t117)) % 0.43/0.63 (step @p101 :rule refl :args (@t18)) % 0.43/0.63 (step @p102 :rule cong :premises (@p101 @p100) :args ((=> @t18 @t123))) % 0.43/0.63 (assume-push @p116 @t18) % 0.43/0.63 (step @p104 :rule instantiate :premises (@p12) :args ((@list tptp.x))) % 0.43/0.63 (step-pop @p117 :rule scope :premises (@p104)) % 0.43/0.63 (step @p105 :rule process_scope :premises (@p117) :args (@t123)) % 0.43/0.63 (step @p107 :rule eq_resolve :premises (@p105 @p102)) % 0.43/0.63 (step @p108 :rule implies_elim :premises (@p107)) % 0.43/0.63 (step @p109 :rule chain_m_resolution :premises (@p108 @p12) :args ((= @t117 @t119) (@list false) (@list @t18))) % 0.43/0.63 (step @p110 :rule refl :args (tptp.x)) % 0.43/0.63 (step @p111 :rule cong :premises (@p110 @p109) :args (@t118)) % 0.43/0.63 (step @p112 :rule false_intro :premises (@p93)) % 0.43/0.63 (step @p113 :rule symm :premises (@p112)) % 0.43/0.63 (step @p114 :rule trans :premises (@p113 @p111 @p99)) % 0.43/0.63 (step @p115 false :rule eq_resolve :premises (@p114 @p94)) % 0.43/0.63 ) % 0.43/0.63 % SZS output end Proof % 0.43/0.63 % cvc5 exiting %------------------------------------------------------------------------------