%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET081-6 : 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 : n016.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 08:47:18 AM UTC 2026 % Result : Unsatisfiable 0.41s 0.62s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET081-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n016.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % 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 14:51:54 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.33/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.62 % SZS status Unsatisfiable % 0.41/0.62 % SZS output start Proof % 0.47/0.63 ( % 0.47/0.63 (declare-sort $$unsorted 0) % 0.47/0.63 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.function (-> $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.element_relation $$unsorted) % 0.47/0.63 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.universal_class $$unsorted) % 0.47/0.63 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.successor_relation $$unsorted) % 0.47/0.63 (declare-const tptp.choice $$unsorted) % 0.47/0.63 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.x $$unsorted) % 0.47/0.63 (declare-const tptp.subset_relation $$unsorted) % 0.47/0.63 (declare-const tptp.null_class $$unsorted) % 0.47/0.63 (declare-const tptp.y $$unsorted) % 0.47/0.63 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.omega $$unsorted) % 0.47/0.63 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.47/0.63 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.identity_relation $$unsorted) % 0.47/0.63 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.47/0.63 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.47/0.63 (define @t1 () (@var "Y" $$unsorted)) % 0.47/0.63 (define @t2 () (@var "U" $$unsorted)) % 0.47/0.63 (define @t3 () (@var "X" $$unsorted)) % 0.47/0.63 (define @t4 () (tptp.member @t2 @t3)) % 0.47/0.63 (define @t5 () (not @t4)) % 0.47/0.63 (define @t6 () (tptp.subclass @t3 @t1)) % 0.47/0.63 (define @t7 () (not @t6)) % 0.47/0.63 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.47/0.63 (define @t9 () (@list @t3 @t1)) % 0.47/0.63 (define @t10 () (@list @t3)) % 0.47/0.63 (define @t11 () (= @t3 @t1)) % 0.47/0.63 (define @t12 () (not @t11)) % 0.47/0.63 (define @t13 () (tptp.subclass @t1 @t3)) % 0.47/0.63 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.47/0.63 (define @t15 () (not (tptp.member @t2 @t14))) % 0.47/0.63 (define @t16 () (or @t15 (= @t2 @t3) (= @t2 @t1))) % 0.47/0.63 (define @t17 () (@list @t2 @t3 @t1)) % 0.47/0.63 (define @t18 () (forall @t17 @t16)) % 0.47/0.63 (define @t19 () (not (tptp.member @t3 tptp.universal_class))) % 0.47/0.63 (define @t20 () (not (tptp.member @t1 tptp.universal_class))) % 0.47/0.63 (define @t21 () (tptp.singleton @t3)) % 0.47/0.63 (define @t22 () (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t21))) % 0.47/0.63 (define @t23 () (tptp.ordered_pair @t3 @t1)) % 0.47/0.63 (define @t24 () (tptp.singleton @t1)) % 0.47/0.63 (define @t25 () (tptp.cross_product @t3 @t1)) % 0.47/0.63 (define @t26 () (@var "V" $$unsorted)) % 0.47/0.63 (define @t27 () (tptp.ordered_pair @t2 @t26)) % 0.47/0.63 (define @t28 () (tptp.member @t27 @t25)) % 0.47/0.63 (define @t29 () (not @t28)) % 0.47/0.63 (define @t30 () (@list @t2 @t26 @t3 @t1)) % 0.47/0.63 (define @t31 () (tptp.member @t26 @t1)) % 0.47/0.63 (define @t32 () (@var "Z" $$unsorted)) % 0.47/0.63 (define @t33 () (@list @t32 @t3 @t1)) % 0.47/0.63 (define @t34 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.47/0.63 (define @t35 () (tptp.member @t3 @t1)) % 0.47/0.63 (define @t36 () (tptp.member @t23 tptp.element_relation)) % 0.47/0.63 (define @t37 () (not (tptp.member @t23 @t34))) % 0.47/0.63 (define @t38 () (tptp.member @t32 @t3)) % 0.47/0.63 (define @t39 () (tptp.intersection @t3 @t1)) % 0.47/0.63 (define @t40 () (tptp.member @t32 @t39)) % 0.47/0.63 (define @t41 () (not @t40)) % 0.47/0.63 (define @t42 () (tptp.member @t32 @t1)) % 0.47/0.63 (define @t43 () (not @t38)) % 0.47/0.63 (define @t44 () (tptp.complement @t3)) % 0.47/0.63 (define @t45 () (tptp.member @t32 @t44)) % 0.47/0.63 (define @t46 () (@list @t32 @t3)) % 0.47/0.63 (define @t47 () (not (tptp.member @t32 tptp.universal_class))) % 0.47/0.63 (define @t48 () (tptp.complement (tptp.intersection @t44 (tptp.complement @t1)))) % 0.47/0.63 (define @t49 () (@var "Xr" $$unsorted)) % 0.47/0.63 (define @t50 () (tptp.restrict @t49 @t3 @t1)) % 0.47/0.63 (define @t51 () (tptp.domain_of @t3)) % 0.47/0.63 (define @t52 () (tptp.member @t32 @t51)) % 0.47/0.63 (define @t53 () (= (tptp.restrict @t3 (tptp.singleton @t32) tptp.universal_class) tptp.null_class)) % 0.47/0.63 (define @t54 () (tptp.cross_product @t34 tptp.universal_class)) % 0.47/0.63 (define @t55 () (tptp.rotate @t3)) % 0.47/0.63 (define @t56 () (@var "W" $$unsorted)) % 0.47/0.63 (define @t57 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t26 @t56) @t2) @t3)) % 0.47/0.63 (define @t58 () (tptp.ordered_pair @t27 @t56)) % 0.47/0.63 (define @t59 () (tptp.member @t58 @t55)) % 0.47/0.63 (define @t60 () (@list @t2 @t26 @t56 @t3)) % 0.47/0.63 (define @t61 () (not (tptp.member @t58 @t54))) % 0.47/0.63 (define @t62 () (tptp.flip @t3)) % 0.47/0.63 (define @t63 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t26 @t2) @t56) @t3)) % 0.47/0.63 (define @t64 () (tptp.member @t58 @t62)) % 0.47/0.63 (define @t65 () (@list @t1)) % 0.47/0.63 (define @t66 () (tptp.successor @t3)) % 0.47/0.63 (define @t67 () (= @t66 @t1)) % 0.47/0.63 (define @t68 () (tptp.member @t23 tptp.successor_relation)) % 0.47/0.63 (define @t69 () (tptp.member tptp.null_class @t3)) % 0.47/0.63 (define @t70 () (tptp.inductive @t3)) % 0.47/0.63 (define @t71 () (not @t70)) % 0.47/0.63 (define @t72 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.47/0.63 (define @t73 () (tptp.sum_class @t3)) % 0.47/0.63 (define @t74 () (@var "Yr" $$unsorted)) % 0.47/0.63 (define @t75 () (tptp.compose @t74 @t49)) % 0.47/0.63 (define @t76 () (tptp.member @t32 (tptp.image @t74 (tptp.image @t49 @t24)))) % 0.47/0.63 (define @t77 () (tptp.ordered_pair @t1 @t32)) % 0.47/0.63 (define @t78 () (tptp.member @t77 @t75)) % 0.47/0.63 (define @t79 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.47/0.63 (define @t80 () (tptp.single_valued_class @t3)) % 0.47/0.63 (define @t81 () (@var "Xf" $$unsorted)) % 0.47/0.63 (define @t82 () (tptp.subclass @t81 @t34)) % 0.47/0.63 (define @t83 () (tptp.function @t81)) % 0.47/0.63 (define @t84 () (not @t83)) % 0.47/0.63 (define @t85 () (@list @t81)) % 0.47/0.63 (define @t86 () (tptp.inverse @t81)) % 0.47/0.63 (define @t87 () (tptp.subclass (tptp.compose @t81 @t86) tptp.identity_relation)) % 0.47/0.63 (define @t88 () (tptp.regular @t3)) % 0.47/0.63 (define @t89 () (= @t3 tptp.null_class)) % 0.47/0.63 (define @t90 () (tptp.one_to_one @t81)) % 0.47/0.63 (define @t91 () (not @t90)) % 0.47/0.63 (define @t92 () (tptp.function @t86)) % 0.47/0.63 (define @t93 () (tptp.inverse tptp.element_relation)) % 0.47/0.63 (define @t94 () (tptp.operation @t81)) % 0.47/0.63 (define @t95 () (not @t94)) % 0.47/0.63 (define @t96 () (tptp.domain_of @t81)) % 0.47/0.63 (define @t97 () (tptp.domain_of @t96)) % 0.47/0.63 (define @t98 () (= (tptp.cross_product @t97 @t97) @t96)) % 0.47/0.63 (define @t99 () (tptp.subclass (tptp.range_of @t81) @t97)) % 0.47/0.63 (define @t100 () (@var "Xh" $$unsorted)) % 0.47/0.63 (define @t101 () (tptp.function @t100)) % 0.47/0.63 (define @t102 () (@var "Xf2" $$unsorted)) % 0.47/0.63 (define @t103 () (@var "Xf1" $$unsorted)) % 0.47/0.63 (define @t104 () (tptp.compatible @t100 @t103 @t102)) % 0.47/0.63 (define @t105 () (not @t104)) % 0.47/0.63 (define @t106 () (@list @t100 @t103 @t102)) % 0.47/0.63 (define @t107 () (tptp.domain_of @t103)) % 0.47/0.63 (define @t108 () (= (tptp.domain_of @t107) (tptp.domain_of @t100))) % 0.47/0.63 (define @t109 () (tptp.subclass (tptp.range_of @t100) (tptp.domain_of (tptp.domain_of @t102)))) % 0.47/0.63 (define @t110 () (tptp.operation @t103)) % 0.47/0.63 (define @t111 () (tptp.homomorphism @t100 @t103 @t102)) % 0.47/0.63 (define @t112 () (not @t111)) % 0.47/0.63 (define @t113 () (tptp.operation @t102)) % 0.47/0.63 (define @t114 () (tptp.not_homomorphism2 @t100 @t103 @t102)) % 0.47/0.63 (define @t115 () (tptp.not_homomorphism1 @t100 @t103 @t102)) % 0.47/0.63 (define @t116 () (tptp.ordered_pair @t115 @t114)) % 0.47/0.63 (define @t117 () (not @t113)) % 0.47/0.63 (define @t118 () (not @t110)) % 0.47/0.63 (define @t119 () (@list @t103 @t102 @t100)) % 0.47/0.63 (define @t120 () (tptp.singleton tptp.x)) % 0.47/0.63 (define @t121 () (tptp.member tptp.y @t120)) % 0.47/0.63 (define @t122 () (= tptp.y tptp.x)) % 0.47/0.63 (define @t123 () (tptp.unordered_pair tptp.x tptp.x)) % 0.47/0.63 (define @t124 () (not (tptp.member tptp.y @t123))) % 0.47/0.63 (define @t125 () (= tptp.x tptp.y)) % 0.47/0.63 (define @t126 () (or @t124 @t125 @t125)) % 0.47/0.63 (define @t127 () (forall @t17 (or @t15 (= @t3 @t2) (= @t1 @t2)))) % 0.47/0.63 (define @t128 () (or @t124 @t122 @t122)) % 0.47/0.63 (define @t129 () (@list false)) % 0.47/0.63 (define @t130 () (= @t123 @t120)) % 0.47/0.63 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.47/0.63 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.47/0.63 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.47/0.63 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.47/0.63 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.47/0.63 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.47/0.63 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.47/0.63 (assume @p8 @t18) % 0.47/0.63 (assume @p9 (forall @t9 (or @t19 (tptp.member @t3 @t14)))) % 0.47/0.63 (assume @p10 (forall (@list @t1 @t3) (or @t20 (tptp.member @t1 @t14)))) % 0.47/0.63 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.47/0.63 (assume @p12 @t22) % 0.47/0.63 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t21 (tptp.unordered_pair @t3 @t24)) @t23))) % 0.47/0.63 (assume @p14 (forall @t30 (or @t29 @t4))) % 0.47/0.63 (assume @p15 (forall @t30 (or @t29 @t31))) % 0.47/0.63 (assume @p16 (forall (@list @t2 @t3 @t26 @t1) (or @t5 (not @t31) @t28))) % 0.47/0.63 (assume @p17 (forall @t33 (or (not (tptp.member @t32 @t25)) (= (tptp.ordered_pair (tptp.first @t32) (tptp.second @t32)) @t32)))) % 0.47/0.63 (assume @p18 (tptp.subclass tptp.element_relation @t34)) % 0.47/0.63 (assume @p19 (forall @t9 (or (not @t36) @t35))) % 0.47/0.63 (assume @p20 (forall @t9 (or @t37 (not @t35) @t36))) % 0.47/0.63 (assume @p21 (forall @t33 (or @t41 @t38))) % 0.47/0.63 (assume @p22 (forall @t33 (or @t41 @t42))) % 0.47/0.63 (assume @p23 (forall @t33 (or @t43 (not @t42) @t40))) % 0.47/0.63 (assume @p24 (forall @t46 (or (not @t45) @t43))) % 0.47/0.63 (assume @p25 (forall @t46 (or @t47 @t45 @t38))) % 0.47/0.63 (assume @p26 (forall @t9 (= @t48 (tptp.union @t3 @t1)))) % 0.47/0.63 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t39) @t48) (tptp.symmetric_difference @t3 @t1)))) % 0.47/0.63 (assume @p28 (forall (@list @t49 @t3 @t1) (= (tptp.intersection @t49 @t25) @t50))) % 0.47/0.63 (assume @p29 (forall (@list @t3 @t1 @t49) (= (tptp.intersection @t25 @t49) @t50))) % 0.47/0.63 (assume @p30 (forall (@list @t3 @t32) (or (not @t53) (not @t52)))) % 0.47/0.63 (assume @p31 (forall @t46 (or @t47 @t53 @t52))) % 0.47/0.63 (assume @p32 (forall @t10 (tptp.subclass @t55 @t54))) % 0.47/0.63 (assume @p33 (forall @t60 (or (not @t59) @t57))) % 0.47/0.63 (assume @p34 (forall (@list @t26 @t56 @t2 @t3) (or (not @t57) @t61 @t59))) % 0.47/0.63 (assume @p35 (forall @t10 (tptp.subclass @t62 @t54))) % 0.47/0.63 (assume @p36 (forall @t60 (or (not @t64) @t63))) % 0.47/0.63 (assume @p37 (forall (@list @t26 @t2 @t56 @t3) (or (not @t63) @t61 @t64))) % 0.47/0.63 (assume @p38 (forall @t65 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.47/0.63 (assume @p39 (forall (@list @t32) (= (tptp.domain_of (tptp.inverse @t32)) (tptp.range_of @t32)))) % 0.47/0.63 (assume @p40 (forall @t33 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t32 @t3 @t24) tptp.null_class)) (tptp.domain @t32 @t3 @t1)))) % 0.47/0.63 (assume @p41 (forall @t33 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t32 @t21 @t1) tptp.null_class)) (tptp.range @t32 @t3 @t1)))) % 0.47/0.63 (assume @p42 (forall (@list @t49 @t3) (= (tptp.range_of (tptp.restrict @t49 @t3 tptp.universal_class)) (tptp.image @t49 @t3)))) % 0.47/0.63 (assume @p43 (forall @t10 (= (tptp.union @t3 @t21) @t66))) % 0.47/0.63 (assume @p44 (tptp.subclass tptp.successor_relation @t34)) % 0.47/0.63 (assume @p45 (forall @t9 (or (not @t68) @t67))) % 0.47/0.63 (assume @p46 (forall @t9 (or (not @t67) @t37 @t68))) % 0.47/0.63 (assume @p47 (forall @t10 (or @t71 @t69))) % 0.47/0.63 (assume @p48 (forall @t10 (or @t71 @t72))) % 0.47/0.63 (assume @p49 (forall @t10 (or (not @t69) (not @t72) @t70))) % 0.47/0.63 (assume @p50 (tptp.inductive tptp.omega)) % 0.47/0.63 (assume @p51 (forall @t65 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.47/0.63 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.47/0.63 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t73))) % 0.47/0.63 (assume @p54 (forall @t10 (or @t19 (tptp.member @t73 tptp.universal_class)))) % 0.47/0.63 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t44)) (tptp.power_class @t3)))) % 0.47/0.63 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.47/0.63 (assume @p57 (forall (@list @t74 @t49) (tptp.subclass @t75 @t34))) % 0.47/0.63 (assume @p58 (forall (@list @t1 @t32 @t74 @t49) (or (not @t78) @t76))) % 0.47/0.63 (assume @p59 (forall (@list @t32 @t74 @t49 @t1) (or (not @t76) (not (tptp.member @t77 @t34)) @t78))) % 0.47/0.63 (assume @p60 (forall @t10 (or (not @t80) @t79))) % 0.47/0.63 (assume @p61 (forall @t10 (or (not @t79) @t80))) % 0.47/0.63 (assume @p62 (forall @t85 (or @t84 @t82))) % 0.47/0.63 (assume @p63 (forall @t85 (or @t84 @t87))) % 0.47/0.63 (assume @p64 (forall @t85 (or (not @t82) (not @t87) @t83))) % 0.47/0.63 (assume @p65 (forall (@list @t81 @t3) (or @t84 @t19 (tptp.member (tptp.image @t81 @t3) tptp.universal_class)))) % 0.47/0.63 (assume @p66 (forall @t10 (or @t89 (tptp.member @t88 @t3)))) % 0.47/0.63 (assume @p67 (forall @t10 (or @t89 (= (tptp.intersection @t3 @t88) tptp.null_class)))) % 0.47/0.63 (assume @p68 (forall (@list @t81 @t1) (= (tptp.sum_class (tptp.image @t81 @t24)) (tptp.apply @t81 @t1)))) % 0.47/0.63 (assume @p69 (tptp.function tptp.choice)) % 0.47/0.63 (assume @p70 (forall @t65 (or @t20 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.47/0.63 (assume @p71 (forall @t85 (or @t91 @t83))) % 0.47/0.63 (assume @p72 (forall @t85 (or @t91 @t92))) % 0.47/0.63 (assume @p73 (forall @t85 (or (not @t92) @t84 @t90))) % 0.47/0.63 (assume @p74 (= (tptp.intersection @t34 (tptp.intersection @t34 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t93)))) tptp.subset_relation)) % 0.47/0.63 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.47/0.63 (assume @p76 (forall (@list @t49) (= (tptp.complement (tptp.domain_of (tptp.intersection @t49 tptp.identity_relation))) (tptp.diagonalise @t49)))) % 0.47/0.63 (assume @p77 (forall @t10 (= (tptp.intersection @t51 (tptp.diagonalise (tptp.compose @t93 @t3))) (tptp.cantor @t3)))) % 0.47/0.63 (assume @p78 (forall @t85 (or @t95 @t83))) % 0.47/0.63 (assume @p79 (forall @t85 (or @t95 @t98))) % 0.47/0.63 (assume @p80 (forall @t85 (or @t95 @t99))) % 0.47/0.63 (assume @p81 (forall @t85 (or @t84 (not @t98) (not @t99) @t94))) % 0.47/0.63 (assume @p82 (forall @t106 (or @t105 @t101))) % 0.47/0.63 (assume @p83 (forall @t106 (or @t105 @t108))) % 0.47/0.63 (assume @p84 (forall @t106 (or @t105 @t109))) % 0.47/0.63 (assume @p85 (forall @t106 (or (not @t101) (not @t108) (not @t109) @t104))) % 0.47/0.63 (assume @p86 (forall @t106 (or @t112 @t110))) % 0.47/0.63 (assume @p87 (forall @t106 (or @t112 @t113))) % 0.47/0.63 (assume @p88 (forall @t106 (or @t112 @t104))) % 0.47/0.63 (assume @p89 (forall (@list @t100 @t103 @t102 @t3 @t1) (or @t112 (not (tptp.member @t23 @t107)) (= (tptp.apply @t102 (tptp.ordered_pair (tptp.apply @t100 @t3) (tptp.apply @t100 @t1))) (tptp.apply @t100 (tptp.apply @t103 @t23)))))) % 0.47/0.63 (assume @p90 (forall @t119 (or @t118 @t117 @t105 (tptp.member @t116 @t107) @t111))) % 0.47/0.63 (assume @p91 (forall @t119 (or @t118 @t117 @t105 (not (= (tptp.apply @t102 (tptp.ordered_pair (tptp.apply @t100 @t115) (tptp.apply @t100 @t114))) (tptp.apply @t100 (tptp.apply @t103 @t116)))) @t111))) % 0.47/0.63 (assume @p92 @t121) % 0.47/0.63 (assume @p93 (not @t122)) % 0.47/0.63 (step @p94 :rule evaluate :args ((= true false))) % 0.47/0.63 (step @p95 :rule eq-symm :args (@t2 @t1)) % 0.47/0.63 (step @p96 :rule eq-symm :args (@t2 @t3)) % 0.47/0.63 (step @p97 :rule refl :args (@t15)) % 0.47/0.63 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95) :args (@t16)) % 0.47/0.63 (step @p99 :rule cong :premises (@p98) :args (@t18)) % 0.47/0.63 (step @p100 :rule eq_resolve :premises (@p8 @p99)) % 0.47/0.63 (step @p101 :rule eq-symm :args (tptp.x tptp.y)) % 0.47/0.63 (step @p102 :rule refl :args (@t124)) % 0.47/0.63 (step @p103 :rule nary_cong :premises (@p102 @p101 @p101) :args (@t126)) % 0.47/0.63 (step @p104 :rule refl :args (@t127)) % 0.47/0.63 (step @p105 :rule cong :premises (@p104 @p103) :args ((=> @t127 @t126))) % 0.47/0.63 (assume-push @p134 @t127) % 0.47/0.63 (step @p107 :rule instantiate :premises (@p100) :args ((@list tptp.y tptp.x tptp.x))) % 0.47/0.63 (step-pop @p135 :rule scope :premises (@p107)) % 0.47/0.63 (step @p108 :rule process_scope :premises (@p135) :args (@t126)) % 0.47/0.63 (step @p110 :rule eq_resolve :premises (@p108 @p105)) % 0.47/0.63 (step @p111 :rule implies_elim :premises (@p110)) % 0.47/0.63 (step @p112 :rule chain_m_resolution :premises (@p111 @p100) :args (@t128 @t129 (@list @t127))) % 0.47/0.63 (step @p113 :rule cnf_or_pos :args (@t128)) % 0.47/0.63 (step @p114 :rule factoring :premises (@p113)) % 0.47/0.63 (step @p115 :rule reordering :premises (@p114) :args ((or @t122 @t124 (not @t128)))) % 0.47/0.63 (step @p116 :rule chain_m_resolution :premises (@p115 @p93 @p112) :args (@t124 (@list true false) (@list @t122 @t128))) % 0.47/0.63 (step @p117 :rule false_intro :premises (@p116)) % 0.47/0.63 (step @p118 :rule eq-symm :args (@t123 @t120)) % 0.47/0.63 (step @p119 :rule refl :args (@t22)) % 0.47/0.63 (step @p120 :rule cong :premises (@p119 @p118) :args ((=> @t22 @t130))) % 0.47/0.63 (assume-push @p136 @t22) % 0.47/0.63 (step @p122 :rule instantiate :premises (@p12) :args ((@list tptp.x))) % 0.47/0.63 (step-pop @p137 :rule scope :premises (@p122)) % 0.47/0.63 (step @p123 :rule process_scope :premises (@p137) :args (@t130)) % 0.47/0.63 (step @p125 :rule eq_resolve :premises (@p123 @p120)) % 0.47/0.63 (step @p126 :rule implies_elim :premises (@p125)) % 0.47/0.63 (step @p127 :rule chain_m_resolution :premises (@p126 @p12) :args ((= @t120 @t123) @t129 (@list @t22))) % 0.47/0.63 (step @p128 :rule refl :args (tptp.y)) % 0.47/0.63 (step @p129 :rule cong :premises (@p128 @p127) :args (@t121)) % 0.47/0.63 (step @p130 :rule true_intro :premises (@p92)) % 0.47/0.63 (step @p131 :rule symm :premises (@p130)) % 0.47/0.63 (step @p132 :rule trans :premises (@p131 @p129 @p117)) % 0.47/0.63 (step @p133 false :rule eq_resolve :premises (@p132 @p94)) % 0.47/0.63 ) % 0.47/0.63 % SZS output end Proof % 0.47/0.63 % cvc5 exiting %------------------------------------------------------------------------------