%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET063-7 : 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 : n007.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 08:47:13 AM UTC 2026 % Result : Unsatisfiable 0.38s 0.64s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET063-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 14:49:11 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.29/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.64 % SZS status Unsatisfiable % 0.38/0.64 % SZS output start Proof % 0.38/0.64 ( % 0.38/0.64 (declare-sort $$unsorted 0) % 0.38/0.64 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.element_relation $$unsorted) % 0.38/0.64 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.universal_class $$unsorted) % 0.38/0.64 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.successor_relation $$unsorted) % 0.38/0.64 (declare-const tptp.x $$unsorted) % 0.38/0.64 (declare-const tptp.choice $$unsorted) % 0.38/0.64 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.subset_relation $$unsorted) % 0.38/0.64 (declare-const tptp.null_class $$unsorted) % 0.38/0.64 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.omega $$unsorted) % 0.38/0.64 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.identity_relation $$unsorted) % 0.38/0.64 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.38/0.64 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.38/0.64 (define @t1 () (@var "Y" $$unsorted)) % 0.38/0.64 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.64 (define @t3 () (@var "X" $$unsorted)) % 0.38/0.64 (define @t4 () (tptp.member @t2 @t3)) % 0.38/0.64 (define @t5 () (not @t4)) % 0.38/0.64 (define @t6 () (tptp.subclass @t3 @t1)) % 0.38/0.64 (define @t7 () (not @t6)) % 0.38/0.64 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.38/0.64 (define @t9 () (tptp.member @t8 @t3)) % 0.38/0.64 (define @t10 () (@list @t3 @t1)) % 0.38/0.64 (define @t11 () (not (tptp.member @t8 @t1))) % 0.38/0.64 (define @t12 () (@list @t3)) % 0.38/0.64 (define @t13 () (= @t3 @t1)) % 0.38/0.64 (define @t14 () (not @t13)) % 0.38/0.64 (define @t15 () (tptp.subclass @t1 @t3)) % 0.38/0.64 (define @t16 () (forall @t10 (or @t7 (not @t15) @t13))) % 0.38/0.64 (define @t17 () (tptp.unordered_pair @t3 @t1)) % 0.38/0.64 (define @t18 () (tptp.member @t3 @t17)) % 0.38/0.64 (define @t19 () (not (tptp.member @t3 tptp.universal_class))) % 0.38/0.64 (define @t20 () (tptp.member @t1 @t17)) % 0.38/0.64 (define @t21 () (not (tptp.member @t1 tptp.universal_class))) % 0.38/0.64 (define @t22 () (@list @t1 @t3)) % 0.38/0.64 (define @t23 () (tptp.singleton @t3)) % 0.38/0.64 (define @t24 () (tptp.ordered_pair @t3 @t1)) % 0.38/0.64 (define @t25 () (tptp.singleton @t1)) % 0.38/0.64 (define @t26 () (tptp.cross_product @t3 @t1)) % 0.38/0.64 (define @t27 () (@var "V" $$unsorted)) % 0.38/0.64 (define @t28 () (tptp.ordered_pair @t2 @t27)) % 0.38/0.64 (define @t29 () (tptp.member @t28 @t26)) % 0.38/0.64 (define @t30 () (not @t29)) % 0.38/0.64 (define @t31 () (@list @t2 @t27 @t3 @t1)) % 0.38/0.64 (define @t32 () (tptp.member @t27 @t1)) % 0.38/0.64 (define @t33 () (@var "Z" $$unsorted)) % 0.38/0.64 (define @t34 () (@list @t33 @t3 @t1)) % 0.38/0.64 (define @t35 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.38/0.64 (define @t36 () (tptp.member @t3 @t1)) % 0.38/0.64 (define @t37 () (tptp.member @t24 tptp.element_relation)) % 0.38/0.64 (define @t38 () (not (tptp.member @t24 @t35))) % 0.38/0.64 (define @t39 () (tptp.member @t33 @t3)) % 0.38/0.64 (define @t40 () (tptp.intersection @t3 @t1)) % 0.38/0.64 (define @t41 () (tptp.member @t33 @t40)) % 0.38/0.64 (define @t42 () (not @t41)) % 0.38/0.64 (define @t43 () (tptp.member @t33 @t1)) % 0.38/0.64 (define @t44 () (not @t39)) % 0.38/0.64 (define @t45 () (tptp.complement @t3)) % 0.38/0.64 (define @t46 () (tptp.member @t33 @t45)) % 0.38/0.64 (define @t47 () (@list @t33 @t3)) % 0.38/0.64 (define @t48 () (not (tptp.member @t33 tptp.universal_class))) % 0.38/0.64 (define @t49 () (tptp.complement (tptp.intersection @t45 (tptp.complement @t1)))) % 0.38/0.64 (define @t50 () (@var "Xr" $$unsorted)) % 0.38/0.64 (define @t51 () (tptp.restrict @t50 @t3 @t1)) % 0.38/0.64 (define @t52 () (tptp.domain_of @t3)) % 0.38/0.64 (define @t53 () (tptp.member @t33 @t52)) % 0.38/0.64 (define @t54 () (= (tptp.restrict @t3 (tptp.singleton @t33) tptp.universal_class) tptp.null_class)) % 0.38/0.64 (define @t55 () (tptp.cross_product @t35 tptp.universal_class)) % 0.38/0.64 (define @t56 () (tptp.rotate @t3)) % 0.38/0.64 (define @t57 () (@var "W" $$unsorted)) % 0.38/0.64 (define @t58 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t27 @t57) @t2) @t3)) % 0.38/0.64 (define @t59 () (tptp.ordered_pair @t28 @t57)) % 0.38/0.64 (define @t60 () (tptp.member @t59 @t56)) % 0.38/0.64 (define @t61 () (@list @t2 @t27 @t57 @t3)) % 0.38/0.64 (define @t62 () (not (tptp.member @t59 @t55))) % 0.38/0.64 (define @t63 () (tptp.flip @t3)) % 0.38/0.64 (define @t64 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t27 @t2) @t57) @t3)) % 0.38/0.64 (define @t65 () (tptp.member @t59 @t63)) % 0.38/0.64 (define @t66 () (@list @t1)) % 0.38/0.64 (define @t67 () (@list @t33)) % 0.38/0.64 (define @t68 () (tptp.successor @t3)) % 0.38/0.64 (define @t69 () (= @t68 @t1)) % 0.38/0.64 (define @t70 () (tptp.member @t24 tptp.successor_relation)) % 0.38/0.64 (define @t71 () (tptp.member tptp.null_class @t3)) % 0.38/0.64 (define @t72 () (tptp.inductive @t3)) % 0.38/0.64 (define @t73 () (not @t72)) % 0.38/0.64 (define @t74 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.38/0.64 (define @t75 () (tptp.sum_class @t3)) % 0.38/0.64 (define @t76 () (tptp.member @t2 tptp.universal_class)) % 0.38/0.64 (define @t77 () (@var "Yr" $$unsorted)) % 0.38/0.64 (define @t78 () (tptp.compose @t77 @t50)) % 0.38/0.64 (define @t79 () (tptp.member @t33 (tptp.image @t77 (tptp.image @t50 @t25)))) % 0.38/0.64 (define @t80 () (tptp.ordered_pair @t1 @t33)) % 0.38/0.64 (define @t81 () (tptp.member @t80 @t78)) % 0.38/0.64 (define @t82 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.38/0.64 (define @t83 () (tptp.single_valued_class @t3)) % 0.38/0.64 (define @t84 () (@var "Xf" $$unsorted)) % 0.38/0.64 (define @t85 () (tptp.subclass @t84 @t35)) % 0.38/0.64 (define @t86 () (tptp.function @t84)) % 0.38/0.64 (define @t87 () (not @t86)) % 0.38/0.64 (define @t88 () (@list @t84)) % 0.38/0.64 (define @t89 () (tptp.inverse @t84)) % 0.38/0.64 (define @t90 () (tptp.subclass (tptp.compose @t84 @t89) tptp.identity_relation)) % 0.38/0.64 (define @t91 () (tptp.regular @t3)) % 0.38/0.64 (define @t92 () (= @t3 tptp.null_class)) % 0.38/0.64 (define @t93 () (tptp.one_to_one @t84)) % 0.38/0.64 (define @t94 () (not @t93)) % 0.38/0.64 (define @t95 () (tptp.function @t89)) % 0.38/0.64 (define @t96 () (tptp.inverse tptp.element_relation)) % 0.38/0.64 (define @t97 () (tptp.operation @t84)) % 0.38/0.64 (define @t98 () (not @t97)) % 0.38/0.64 (define @t99 () (tptp.domain_of @t84)) % 0.38/0.64 (define @t100 () (tptp.domain_of @t99)) % 0.38/0.64 (define @t101 () (= (tptp.cross_product @t100 @t100) @t99)) % 0.38/0.64 (define @t102 () (tptp.subclass (tptp.range_of @t84) @t100)) % 0.38/0.64 (define @t103 () (@var "Xh" $$unsorted)) % 0.38/0.64 (define @t104 () (tptp.function @t103)) % 0.38/0.64 (define @t105 () (@var "Xf2" $$unsorted)) % 0.38/0.64 (define @t106 () (@var "Xf1" $$unsorted)) % 0.38/0.64 (define @t107 () (tptp.compatible @t103 @t106 @t105)) % 0.38/0.64 (define @t108 () (not @t107)) % 0.38/0.64 (define @t109 () (@list @t103 @t106 @t105)) % 0.38/0.64 (define @t110 () (tptp.domain_of @t106)) % 0.38/0.64 (define @t111 () (= (tptp.domain_of @t110) (tptp.domain_of @t103))) % 0.38/0.64 (define @t112 () (tptp.subclass (tptp.range_of @t103) (tptp.domain_of (tptp.domain_of @t105)))) % 0.38/0.64 (define @t113 () (tptp.operation @t106)) % 0.38/0.64 (define @t114 () (tptp.homomorphism @t103 @t106 @t105)) % 0.38/0.64 (define @t115 () (not @t114)) % 0.38/0.64 (define @t116 () (tptp.operation @t105)) % 0.38/0.64 (define @t117 () (tptp.not_homomorphism2 @t103 @t106 @t105)) % 0.38/0.64 (define @t118 () (tptp.not_homomorphism1 @t103 @t106 @t105)) % 0.38/0.64 (define @t119 () (tptp.ordered_pair @t118 @t117)) % 0.38/0.64 (define @t120 () (not @t116)) % 0.38/0.64 (define @t121 () (not @t113)) % 0.38/0.64 (define @t122 () (@list @t106 @t105 @t103)) % 0.38/0.64 (define @t123 () (not (tptp.member @t24 (tptp.cross_product @t2 @t27)))) % 0.38/0.64 (define @t124 () (@list @t3 @t1 @t2 @t27)) % 0.38/0.64 (define @t125 () (tptp.not_subclass_element @t1 @t3)) % 0.38/0.64 (define @t126 () (tptp.member @t125 @t1)) % 0.38/0.64 (define @t127 () (not (tptp.member @t125 @t3))) % 0.38/0.64 (define @t128 () (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.38/0.64 (define @t129 () (tptp.subclass tptp.x tptp.null_class)) % 0.38/0.64 (define @t130 () (= tptp.x tptp.null_class)) % 0.38/0.64 (define @t131 () (tptp.subclass tptp.null_class tptp.x)) % 0.38/0.64 (define @t132 () (not @t131)) % 0.38/0.64 (define @t133 () (not @t129)) % 0.38/0.64 (define @t134 () (or @t133 @t132 @t130)) % 0.38/0.64 (define @t135 () (= tptp.null_class tptp.x)) % 0.38/0.64 (define @t136 () (or @t133 @t132 @t135)) % 0.38/0.64 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.38/0.64 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.38/0.64 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.38/0.64 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.38/0.64 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.38/0.64 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.38/0.64 (assume @p7 @t16) % 0.38/0.64 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t17)) (= @t2 @t3) (= @t2 @t1)))) % 0.38/0.64 (assume @p9 (forall @t10 (or @t19 @t18))) % 0.38/0.64 (assume @p10 (forall @t22 (or @t21 @t20))) % 0.38/0.64 (assume @p11 (forall @t10 (tptp.member @t17 tptp.universal_class))) % 0.38/0.64 (assume @p12 (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t23))) % 0.38/0.64 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t23 (tptp.unordered_pair @t3 @t25)) @t24))) % 0.38/0.64 (assume @p14 (forall @t31 (or @t30 @t4))) % 0.38/0.64 (assume @p15 (forall @t31 (or @t30 @t32))) % 0.38/0.64 (assume @p16 (forall (@list @t2 @t3 @t27 @t1) (or @t5 (not @t32) @t29))) % 0.38/0.64 (assume @p17 (forall @t34 (or (not (tptp.member @t33 @t26)) (= (tptp.ordered_pair (tptp.first @t33) (tptp.second @t33)) @t33)))) % 0.38/0.64 (assume @p18 (tptp.subclass tptp.element_relation @t35)) % 0.38/0.64 (assume @p19 (forall @t10 (or (not @t37) @t36))) % 0.38/0.64 (assume @p20 (forall @t10 (or @t38 (not @t36) @t37))) % 0.38/0.64 (assume @p21 (forall @t34 (or @t42 @t39))) % 0.38/0.64 (assume @p22 (forall @t34 (or @t42 @t43))) % 0.38/0.64 (assume @p23 (forall @t34 (or @t44 (not @t43) @t41))) % 0.38/0.64 (assume @p24 (forall @t47 (or (not @t46) @t44))) % 0.38/0.64 (assume @p25 (forall @t47 (or @t48 @t46 @t39))) % 0.38/0.64 (assume @p26 (forall @t10 (= @t49 (tptp.union @t3 @t1)))) % 0.38/0.64 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t40) @t49) (tptp.symmetric_difference @t3 @t1)))) % 0.38/0.64 (assume @p28 (forall (@list @t50 @t3 @t1) (= (tptp.intersection @t50 @t26) @t51))) % 0.38/0.64 (assume @p29 (forall (@list @t3 @t1 @t50) (= (tptp.intersection @t26 @t50) @t51))) % 0.38/0.64 (assume @p30 (forall (@list @t3 @t33) (or (not @t54) (not @t53)))) % 0.38/0.64 (assume @p31 (forall @t47 (or @t48 @t54 @t53))) % 0.38/0.64 (assume @p32 (forall @t12 (tptp.subclass @t56 @t55))) % 0.38/0.64 (assume @p33 (forall @t61 (or (not @t60) @t58))) % 0.38/0.64 (assume @p34 (forall (@list @t27 @t57 @t2 @t3) (or (not @t58) @t62 @t60))) % 0.38/0.64 (assume @p35 (forall @t12 (tptp.subclass @t63 @t55))) % 0.38/0.64 (assume @p36 (forall @t61 (or (not @t65) @t64))) % 0.38/0.64 (assume @p37 (forall (@list @t27 @t2 @t57 @t3) (or (not @t64) @t62 @t65))) % 0.38/0.64 (assume @p38 (forall @t66 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.38/0.64 (assume @p39 (forall @t67 (= (tptp.domain_of (tptp.inverse @t33)) (tptp.range_of @t33)))) % 0.38/0.64 (assume @p40 (forall @t34 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t33 @t3 @t25) tptp.null_class)) (tptp.domain @t33 @t3 @t1)))) % 0.38/0.64 (assume @p41 (forall @t34 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t33 @t23 @t1) tptp.null_class)) (tptp.range @t33 @t3 @t1)))) % 0.38/0.64 (assume @p42 (forall (@list @t50 @t3) (= (tptp.range_of (tptp.restrict @t50 @t3 tptp.universal_class)) (tptp.image @t50 @t3)))) % 0.38/0.64 (assume @p43 (forall @t12 (= (tptp.union @t3 @t23) @t68))) % 0.38/0.64 (assume @p44 (tptp.subclass tptp.successor_relation @t35)) % 0.38/0.64 (assume @p45 (forall @t10 (or (not @t70) @t69))) % 0.38/0.64 (assume @p46 (forall @t10 (or (not @t69) @t38 @t70))) % 0.38/0.64 (assume @p47 (forall @t12 (or @t73 @t71))) % 0.38/0.64 (assume @p48 (forall @t12 (or @t73 @t74))) % 0.38/0.64 (assume @p49 (forall @t12 (or (not @t71) (not @t74) @t72))) % 0.38/0.64 (assume @p50 (tptp.inductive tptp.omega)) % 0.38/0.64 (assume @p51 (forall @t66 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.38/0.64 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.38/0.64 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t75))) % 0.38/0.64 (assume @p54 (forall @t12 (or @t19 (tptp.member @t75 tptp.universal_class)))) % 0.38/0.64 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t45)) (tptp.power_class @t3)))) % 0.38/0.64 (assume @p56 (forall (@list @t2) (or (not @t76) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.38/0.64 (assume @p57 (forall (@list @t77 @t50) (tptp.subclass @t78 @t35))) % 0.38/0.64 (assume @p58 (forall (@list @t1 @t33 @t77 @t50) (or (not @t81) @t79))) % 0.38/0.64 (assume @p59 (forall (@list @t33 @t77 @t50 @t1) (or (not @t79) (not (tptp.member @t80 @t35)) @t81))) % 0.38/0.64 (assume @p60 (forall @t12 (or (not @t83) @t82))) % 0.38/0.64 (assume @p61 (forall @t12 (or (not @t82) @t83))) % 0.38/0.64 (assume @p62 (forall @t88 (or @t87 @t85))) % 0.38/0.64 (assume @p63 (forall @t88 (or @t87 @t90))) % 0.38/0.64 (assume @p64 (forall @t88 (or (not @t85) (not @t90) @t86))) % 0.38/0.64 (assume @p65 (forall (@list @t84 @t3) (or @t87 @t19 (tptp.member (tptp.image @t84 @t3) tptp.universal_class)))) % 0.38/0.64 (assume @p66 (forall @t12 (or @t92 (tptp.member @t91 @t3)))) % 0.38/0.64 (assume @p67 (forall @t12 (or @t92 (= (tptp.intersection @t3 @t91) tptp.null_class)))) % 0.38/0.64 (assume @p68 (forall (@list @t84 @t1) (= (tptp.sum_class (tptp.image @t84 @t25)) (tptp.apply @t84 @t1)))) % 0.38/0.64 (assume @p69 (tptp.function tptp.choice)) % 0.38/0.64 (assume @p70 (forall @t66 (or @t21 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.38/0.64 (assume @p71 (forall @t88 (or @t94 @t86))) % 0.38/0.64 (assume @p72 (forall @t88 (or @t94 @t95))) % 0.38/0.64 (assume @p73 (forall @t88 (or (not @t95) @t87 @t93))) % 0.38/0.64 (assume @p74 (= (tptp.intersection @t35 (tptp.intersection @t35 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t96)))) tptp.subset_relation)) % 0.38/0.64 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.38/0.64 (assume @p76 (forall (@list @t50) (= (tptp.complement (tptp.domain_of (tptp.intersection @t50 tptp.identity_relation))) (tptp.diagonalise @t50)))) % 0.38/0.64 (assume @p77 (forall @t12 (= (tptp.intersection @t52 (tptp.diagonalise (tptp.compose @t96 @t3))) (tptp.cantor @t3)))) % 0.38/0.64 (assume @p78 (forall @t88 (or @t98 @t86))) % 0.38/0.64 (assume @p79 (forall @t88 (or @t98 @t101))) % 0.38/0.64 (assume @p80 (forall @t88 (or @t98 @t102))) % 0.38/0.64 (assume @p81 (forall @t88 (or @t87 (not @t101) (not @t102) @t97))) % 0.38/0.64 (assume @p82 (forall @t109 (or @t108 @t104))) % 0.38/0.64 (assume @p83 (forall @t109 (or @t108 @t111))) % 0.38/0.64 (assume @p84 (forall @t109 (or @t108 @t112))) % 0.38/0.64 (assume @p85 (forall @t109 (or (not @t104) (not @t111) (not @t112) @t107))) % 0.38/0.64 (assume @p86 (forall @t109 (or @t115 @t113))) % 0.38/0.64 (assume @p87 (forall @t109 (or @t115 @t116))) % 0.38/0.64 (assume @p88 (forall @t109 (or @t115 @t107))) % 0.38/0.64 (assume @p89 (forall (@list @t103 @t106 @t105 @t3 @t1) (or @t115 (not (tptp.member @t24 @t110)) (= (tptp.apply @t105 (tptp.ordered_pair (tptp.apply @t103 @t3) (tptp.apply @t103 @t1))) (tptp.apply @t103 (tptp.apply @t106 @t24)))))) % 0.38/0.64 (assume @p90 (forall @t122 (or @t121 @t120 @t108 (tptp.member @t119 @t110) @t114))) % 0.38/0.64 (assume @p91 (forall @t122 (or @t121 @t120 @t108 (not (= (tptp.apply @t105 (tptp.ordered_pair (tptp.apply @t103 @t118) (tptp.apply @t103 @t117))) (tptp.apply @t103 (tptp.apply @t106 @t119)))) @t114))) % 0.38/0.64 (assume @p92 (forall @t124 (or @t123 @t18))) % 0.38/0.64 (assume @p93 (forall @t124 (or @t123 @t20))) % 0.38/0.64 (assume @p94 (forall @t31 (or @t30 @t76))) % 0.38/0.64 (assume @p95 (forall @t31 (or @t30 (tptp.member @t27 tptp.universal_class)))) % 0.38/0.64 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.38/0.64 (assume @p97 (forall (@list @t3 @t1 @t33) (or @t7 (not (tptp.subclass @t1 @t33)) (tptp.subclass @t3 @t33)))) % 0.38/0.64 (assume @p98 (forall @t10 (or @t13 @t9 @t126))) % 0.38/0.64 (assume @p99 (forall @t10 (or @t11 @t13 @t126))) % 0.38/0.64 (assume @p100 (forall @t22 (or @t127 @t13 @t9))) % 0.38/0.64 (assume @p101 (forall @t10 (or @t11 @t127 @t13))) % 0.38/0.64 (assume @p102 (forall @t22 (not (tptp.member @t1 (tptp.intersection @t45 @t3))))) % 0.38/0.64 (assume @p103 (forall @t67 (not (tptp.member @t33 tptp.null_class)))) % 0.38/0.64 (assume @p104 @t128) % 0.38/0.64 (assume @p105 @t129) % 0.38/0.64 (assume @p106 (not @t130)) % 0.38/0.64 (step @p107 :rule eq-symm :args (tptp.x tptp.null_class)) % 0.38/0.64 (step @p108 :rule refl :args (@t132)) % 0.38/0.64 (step @p109 :rule refl :args (@t133)) % 0.38/0.64 (step @p110 :rule nary_cong :premises (@p109 @p108 @p107) :args (@t134)) % 0.38/0.64 (step @p111 :rule refl :args (@t16)) % 0.38/0.64 (step @p112 :rule cong :premises (@p111 @p110) :args ((=> @t16 @t134))) % 0.38/0.64 (assume-push @p130 @t16) % 0.38/0.64 (step @p114 :rule instantiate :premises (@p7) :args ((@list tptp.x tptp.null_class))) % 0.38/0.64 (step-pop @p131 :rule scope :premises (@p114)) % 0.38/0.64 (step @p115 :rule process_scope :premises (@p131) :args (@t134)) % 0.38/0.64 (step @p117 :rule eq_resolve :premises (@p115 @p112)) % 0.38/0.64 (step @p118 :rule implies_elim :premises (@p117)) % 0.38/0.64 (step @p119 :rule chain_m_resolution :premises (@p118 @p7) :args (@t136 (@list false) (@list @t16))) % 0.38/0.64 (step @p120 :rule symm :premises (@p106)) % 0.38/0.64 (step @p121 :rule cnf_or_pos :args (@t136)) % 0.38/0.64 (step @p122 :rule reordering :premises (@p121) :args ((or @t135 @t133 @t132 (not @t136)))) % 0.38/0.64 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p105 @p119) :args (@t132 (@list true false false) (@list @t135 @t129 @t136))) % 0.38/0.64 (assume-push @p132 @t128) % 0.38/0.64 (step @p125 :rule instantiate :premises (@p104) :args ((@list tptp.x))) % 0.38/0.64 (step-pop @p133 :rule scope :premises (@p125)) % 0.38/0.64 (step @p126 :rule process_scope :premises (@p133) :args (@t131)) % 0.38/0.64 (step @p128 :rule implies_elim :premises (@p126)) % 0.38/0.64 (step @p129 false :rule chain_m_resolution :premises (@p128 @p123 @p104) :args (false (@list true false) (@list @t131 @t128))) % 0.38/0.64 ) % 0.38/0.65 % SZS output end Proof % 0.38/0.65 % cvc5 exiting %------------------------------------------------------------------------------