%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET080-7 : 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 : n017.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 0.37s 0.62s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET080-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.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 14:50:01 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.62 % SZS status Unsatisfiable % 0.37/0.62 % SZS output start Proof % 0.37/0.63 ( % 0.37/0.63 (declare-sort $$unsorted 0) % 0.37/0.63 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.element_relation $$unsorted) % 0.37/0.63 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.universal_class $$unsorted) % 0.37/0.63 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.successor_relation $$unsorted) % 0.37/0.63 (declare-const tptp.choice $$unsorted) % 0.37/0.63 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.subset_relation $$unsorted) % 0.37/0.63 (declare-const tptp.null_class $$unsorted) % 0.37/0.63 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.omega $$unsorted) % 0.37/0.63 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.identity_relation $$unsorted) % 0.37/0.63 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.37/0.63 (define @t1 () (@var "Y" $$unsorted)) % 0.37/0.63 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.63 (define @t3 () (@var "X" $$unsorted)) % 0.37/0.63 (define @t4 () (tptp.member @t2 @t3)) % 0.37/0.63 (define @t5 () (not @t4)) % 0.37/0.63 (define @t6 () (tptp.subclass @t3 @t1)) % 0.37/0.63 (define @t7 () (not @t6)) % 0.37/0.63 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.37/0.63 (define @t9 () (tptp.member @t8 @t3)) % 0.37/0.63 (define @t10 () (@list @t3 @t1)) % 0.37/0.63 (define @t11 () (not (tptp.member @t8 @t1))) % 0.37/0.63 (define @t12 () (@list @t3)) % 0.37/0.63 (define @t13 () (= @t3 @t1)) % 0.37/0.63 (define @t14 () (not @t13)) % 0.37/0.63 (define @t15 () (tptp.subclass @t1 @t3)) % 0.37/0.63 (define @t16 () (tptp.unordered_pair @t3 @t1)) % 0.37/0.63 (define @t17 () (tptp.member @t3 @t16)) % 0.37/0.63 (define @t18 () (tptp.member @t3 tptp.universal_class)) % 0.37/0.63 (define @t19 () (not @t18)) % 0.37/0.63 (define @t20 () (tptp.member @t1 @t16)) % 0.37/0.63 (define @t21 () (tptp.member @t1 tptp.universal_class)) % 0.37/0.63 (define @t22 () (not @t21)) % 0.37/0.63 (define @t23 () (@list @t1 @t3)) % 0.37/0.63 (define @t24 () (tptp.singleton @t3)) % 0.37/0.63 (define @t25 () (tptp.ordered_pair @t3 @t1)) % 0.37/0.63 (define @t26 () (tptp.singleton @t1)) % 0.37/0.63 (define @t27 () (tptp.unordered_pair @t3 @t26)) % 0.37/0.63 (define @t28 () (tptp.cross_product @t3 @t1)) % 0.37/0.63 (define @t29 () (@var "V" $$unsorted)) % 0.37/0.63 (define @t30 () (tptp.ordered_pair @t2 @t29)) % 0.37/0.63 (define @t31 () (tptp.member @t30 @t28)) % 0.37/0.63 (define @t32 () (not @t31)) % 0.37/0.63 (define @t33 () (@list @t2 @t29 @t3 @t1)) % 0.37/0.63 (define @t34 () (tptp.member @t29 @t1)) % 0.37/0.63 (define @t35 () (@var "Z" $$unsorted)) % 0.37/0.63 (define @t36 () (@list @t35 @t3 @t1)) % 0.37/0.63 (define @t37 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.37/0.63 (define @t38 () (tptp.member @t3 @t1)) % 0.37/0.63 (define @t39 () (tptp.member @t25 tptp.element_relation)) % 0.37/0.63 (define @t40 () (not (tptp.member @t25 @t37))) % 0.37/0.63 (define @t41 () (tptp.member @t35 @t3)) % 0.37/0.63 (define @t42 () (tptp.intersection @t3 @t1)) % 0.37/0.63 (define @t43 () (tptp.member @t35 @t42)) % 0.37/0.63 (define @t44 () (not @t43)) % 0.37/0.63 (define @t45 () (tptp.member @t35 @t1)) % 0.37/0.63 (define @t46 () (not @t41)) % 0.37/0.63 (define @t47 () (tptp.complement @t3)) % 0.37/0.63 (define @t48 () (tptp.member @t35 @t47)) % 0.37/0.63 (define @t49 () (@list @t35 @t3)) % 0.37/0.63 (define @t50 () (not (tptp.member @t35 tptp.universal_class))) % 0.37/0.63 (define @t51 () (tptp.complement (tptp.intersection @t47 (tptp.complement @t1)))) % 0.37/0.63 (define @t52 () (@var "Xr" $$unsorted)) % 0.37/0.63 (define @t53 () (tptp.restrict @t52 @t3 @t1)) % 0.37/0.63 (define @t54 () (tptp.domain_of @t3)) % 0.37/0.63 (define @t55 () (tptp.member @t35 @t54)) % 0.37/0.63 (define @t56 () (= (tptp.restrict @t3 (tptp.singleton @t35) tptp.universal_class) tptp.null_class)) % 0.37/0.63 (define @t57 () (tptp.cross_product @t37 tptp.universal_class)) % 0.37/0.63 (define @t58 () (tptp.rotate @t3)) % 0.37/0.63 (define @t59 () (@var "W" $$unsorted)) % 0.37/0.63 (define @t60 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t29 @t59) @t2) @t3)) % 0.37/0.63 (define @t61 () (tptp.ordered_pair @t30 @t59)) % 0.37/0.63 (define @t62 () (tptp.member @t61 @t58)) % 0.37/0.63 (define @t63 () (@list @t2 @t29 @t59 @t3)) % 0.37/0.63 (define @t64 () (not (tptp.member @t61 @t57))) % 0.37/0.63 (define @t65 () (tptp.flip @t3)) % 0.37/0.63 (define @t66 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t29 @t2) @t59) @t3)) % 0.37/0.63 (define @t67 () (tptp.member @t61 @t65)) % 0.37/0.63 (define @t68 () (@list @t1)) % 0.37/0.63 (define @t69 () (@list @t35)) % 0.37/0.63 (define @t70 () (tptp.successor @t3)) % 0.37/0.63 (define @t71 () (= @t70 @t1)) % 0.37/0.63 (define @t72 () (tptp.member @t25 tptp.successor_relation)) % 0.37/0.63 (define @t73 () (tptp.member tptp.null_class @t3)) % 0.37/0.63 (define @t74 () (tptp.inductive @t3)) % 0.37/0.63 (define @t75 () (not @t74)) % 0.37/0.63 (define @t76 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.37/0.63 (define @t77 () (tptp.sum_class @t3)) % 0.37/0.63 (define @t78 () (tptp.member @t2 tptp.universal_class)) % 0.37/0.63 (define @t79 () (@var "Yr" $$unsorted)) % 0.37/0.63 (define @t80 () (tptp.compose @t79 @t52)) % 0.37/0.63 (define @t81 () (tptp.member @t35 (tptp.image @t79 (tptp.image @t52 @t26)))) % 0.37/0.63 (define @t82 () (tptp.ordered_pair @t1 @t35)) % 0.37/0.63 (define @t83 () (tptp.member @t82 @t80)) % 0.37/0.63 (define @t84 () (not (tptp.member @t82 @t37))) % 0.37/0.63 (define @t85 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.37/0.63 (define @t86 () (tptp.single_valued_class @t3)) % 0.37/0.63 (define @t87 () (@var "Xf" $$unsorted)) % 0.37/0.63 (define @t88 () (tptp.subclass @t87 @t37)) % 0.37/0.63 (define @t89 () (tptp.function @t87)) % 0.37/0.63 (define @t90 () (not @t89)) % 0.37/0.63 (define @t91 () (@list @t87)) % 0.37/0.63 (define @t92 () (tptp.inverse @t87)) % 0.37/0.63 (define @t93 () (tptp.subclass (tptp.compose @t87 @t92) tptp.identity_relation)) % 0.37/0.63 (define @t94 () (tptp.regular @t3)) % 0.37/0.63 (define @t95 () (= @t3 tptp.null_class)) % 0.37/0.63 (define @t96 () (tptp.one_to_one @t87)) % 0.37/0.63 (define @t97 () (not @t96)) % 0.37/0.63 (define @t98 () (tptp.function @t92)) % 0.37/0.63 (define @t99 () (tptp.inverse tptp.element_relation)) % 0.37/0.63 (define @t100 () (tptp.operation @t87)) % 0.37/0.63 (define @t101 () (not @t100)) % 0.37/0.63 (define @t102 () (tptp.domain_of @t87)) % 0.37/0.63 (define @t103 () (tptp.domain_of @t102)) % 0.37/0.63 (define @t104 () (= (tptp.cross_product @t103 @t103) @t102)) % 0.37/0.63 (define @t105 () (tptp.subclass (tptp.range_of @t87) @t103)) % 0.37/0.63 (define @t106 () (@var "Xh" $$unsorted)) % 0.37/0.63 (define @t107 () (tptp.function @t106)) % 0.37/0.63 (define @t108 () (@var "Xf2" $$unsorted)) % 0.37/0.63 (define @t109 () (@var "Xf1" $$unsorted)) % 0.37/0.63 (define @t110 () (tptp.compatible @t106 @t109 @t108)) % 0.37/0.63 (define @t111 () (not @t110)) % 0.37/0.63 (define @t112 () (@list @t106 @t109 @t108)) % 0.37/0.63 (define @t113 () (tptp.domain_of @t109)) % 0.37/0.63 (define @t114 () (= (tptp.domain_of @t113) (tptp.domain_of @t106))) % 0.37/0.63 (define @t115 () (tptp.subclass (tptp.range_of @t106) (tptp.domain_of (tptp.domain_of @t108)))) % 0.37/0.63 (define @t116 () (tptp.operation @t109)) % 0.37/0.63 (define @t117 () (tptp.homomorphism @t106 @t109 @t108)) % 0.37/0.63 (define @t118 () (not @t117)) % 0.37/0.63 (define @t119 () (tptp.operation @t108)) % 0.37/0.63 (define @t120 () (tptp.not_homomorphism2 @t106 @t109 @t108)) % 0.37/0.63 (define @t121 () (tptp.not_homomorphism1 @t106 @t109 @t108)) % 0.37/0.63 (define @t122 () (tptp.ordered_pair @t121 @t120)) % 0.37/0.63 (define @t123 () (not @t119)) % 0.37/0.63 (define @t124 () (not @t116)) % 0.37/0.63 (define @t125 () (@list @t109 @t108 @t106)) % 0.37/0.63 (define @t126 () (not (tptp.member @t25 (tptp.cross_product @t2 @t29)))) % 0.37/0.63 (define @t127 () (@list @t3 @t1 @t2 @t29)) % 0.37/0.63 (define @t128 () (@list @t3 @t1 @t35)) % 0.37/0.63 (define @t129 () (tptp.not_subclass_element @t1 @t3)) % 0.37/0.63 (define @t130 () (tptp.member @t129 @t1)) % 0.37/0.63 (define @t131 () (not (tptp.member @t129 @t3))) % 0.37/0.63 (define @t132 () (tptp.member tptp.null_class tptp.universal_class)) % 0.37/0.63 (define @t133 () (= @t16 tptp.null_class)) % 0.37/0.63 (define @t134 () (tptp.unordered_pair @t3 @t35)) % 0.37/0.63 (define @t135 () (@list @t3 @t35 @t1)) % 0.37/0.63 (define @t136 () (not @t133)) % 0.37/0.63 (define @t137 () (forall @t12 (or @t19 (tptp.member @t3 @t24)))) % 0.37/0.63 (define @t138 () (tptp.member tptp.null_class (tptp.singleton tptp.null_class))) % 0.37/0.63 (define @t139 () (not @t132)) % 0.37/0.63 (define @t140 () (or @t139 @t138)) % 0.37/0.63 (define @t141 () (not @t140)) % 0.37/0.63 (define @t142 () (@list true false)) % 0.37/0.63 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.37/0.63 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.37/0.63 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.37/0.63 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.37/0.63 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.37/0.63 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.37/0.63 (assume @p7 (forall @t10 (or @t7 (not @t15) @t13))) % 0.37/0.63 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t16)) (= @t2 @t3) (= @t2 @t1)))) % 0.37/0.63 (assume @p9 (forall @t10 (or @t19 @t17))) % 0.37/0.63 (assume @p10 (forall @t23 (or @t22 @t20))) % 0.37/0.63 (assume @p11 (forall @t10 (tptp.member @t16 tptp.universal_class))) % 0.37/0.63 (assume @p12 (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t24))) % 0.37/0.63 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t24 @t27) @t25))) % 0.37/0.63 (assume @p14 (forall @t33 (or @t32 @t4))) % 0.37/0.63 (assume @p15 (forall @t33 (or @t32 @t34))) % 0.37/0.63 (assume @p16 (forall (@list @t2 @t3 @t29 @t1) (or @t5 (not @t34) @t31))) % 0.37/0.63 (assume @p17 (forall @t36 (or (not (tptp.member @t35 @t28)) (= (tptp.ordered_pair (tptp.first @t35) (tptp.second @t35)) @t35)))) % 0.37/0.63 (assume @p18 (tptp.subclass tptp.element_relation @t37)) % 0.37/0.63 (assume @p19 (forall @t10 (or (not @t39) @t38))) % 0.37/0.63 (assume @p20 (forall @t10 (or @t40 (not @t38) @t39))) % 0.37/0.63 (assume @p21 (forall @t36 (or @t44 @t41))) % 0.37/0.63 (assume @p22 (forall @t36 (or @t44 @t45))) % 0.37/0.63 (assume @p23 (forall @t36 (or @t46 (not @t45) @t43))) % 0.37/0.63 (assume @p24 (forall @t49 (or (not @t48) @t46))) % 0.37/0.63 (assume @p25 (forall @t49 (or @t50 @t48 @t41))) % 0.37/0.63 (assume @p26 (forall @t10 (= @t51 (tptp.union @t3 @t1)))) % 0.37/0.63 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t42) @t51) (tptp.symmetric_difference @t3 @t1)))) % 0.37/0.63 (assume @p28 (forall (@list @t52 @t3 @t1) (= (tptp.intersection @t52 @t28) @t53))) % 0.37/0.63 (assume @p29 (forall (@list @t3 @t1 @t52) (= (tptp.intersection @t28 @t52) @t53))) % 0.37/0.63 (assume @p30 (forall (@list @t3 @t35) (or (not @t56) (not @t55)))) % 0.37/0.63 (assume @p31 (forall @t49 (or @t50 @t56 @t55))) % 0.37/0.63 (assume @p32 (forall @t12 (tptp.subclass @t58 @t57))) % 0.37/0.63 (assume @p33 (forall @t63 (or (not @t62) @t60))) % 0.37/0.63 (assume @p34 (forall (@list @t29 @t59 @t2 @t3) (or (not @t60) @t64 @t62))) % 0.37/0.63 (assume @p35 (forall @t12 (tptp.subclass @t65 @t57))) % 0.37/0.63 (assume @p36 (forall @t63 (or (not @t67) @t66))) % 0.37/0.63 (assume @p37 (forall (@list @t29 @t2 @t59 @t3) (or (not @t66) @t64 @t67))) % 0.37/0.63 (assume @p38 (forall @t68 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.37/0.63 (assume @p39 (forall @t69 (= (tptp.domain_of (tptp.inverse @t35)) (tptp.range_of @t35)))) % 0.37/0.63 (assume @p40 (forall @t36 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t35 @t3 @t26) tptp.null_class)) (tptp.domain @t35 @t3 @t1)))) % 0.37/0.63 (assume @p41 (forall @t36 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t35 @t24 @t1) tptp.null_class)) (tptp.range @t35 @t3 @t1)))) % 0.37/0.63 (assume @p42 (forall (@list @t52 @t3) (= (tptp.range_of (tptp.restrict @t52 @t3 tptp.universal_class)) (tptp.image @t52 @t3)))) % 0.37/0.63 (assume @p43 (forall @t12 (= (tptp.union @t3 @t24) @t70))) % 0.37/0.63 (assume @p44 (tptp.subclass tptp.successor_relation @t37)) % 0.37/0.63 (assume @p45 (forall @t10 (or (not @t72) @t71))) % 0.37/0.63 (assume @p46 (forall @t10 (or (not @t71) @t40 @t72))) % 0.37/0.63 (assume @p47 (forall @t12 (or @t75 @t73))) % 0.37/0.63 (assume @p48 (forall @t12 (or @t75 @t76))) % 0.37/0.63 (assume @p49 (forall @t12 (or (not @t73) (not @t76) @t74))) % 0.37/0.63 (assume @p50 (tptp.inductive tptp.omega)) % 0.37/0.63 (assume @p51 (forall @t68 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.37/0.63 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.37/0.63 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t77))) % 0.37/0.63 (assume @p54 (forall @t12 (or @t19 (tptp.member @t77 tptp.universal_class)))) % 0.37/0.63 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t47)) (tptp.power_class @t3)))) % 0.37/0.63 (assume @p56 (forall (@list @t2) (or (not @t78) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.37/0.63 (assume @p57 (forall (@list @t79 @t52) (tptp.subclass @t80 @t37))) % 0.37/0.63 (assume @p58 (forall (@list @t1 @t35 @t79 @t52) (or (not @t83) @t81))) % 0.37/0.63 (assume @p59 (forall (@list @t35 @t79 @t52 @t1) (or (not @t81) @t84 @t83))) % 0.37/0.63 (assume @p60 (forall @t12 (or (not @t86) @t85))) % 0.37/0.63 (assume @p61 (forall @t12 (or (not @t85) @t86))) % 0.37/0.63 (assume @p62 (forall @t91 (or @t90 @t88))) % 0.37/0.63 (assume @p63 (forall @t91 (or @t90 @t93))) % 0.37/0.63 (assume @p64 (forall @t91 (or (not @t88) (not @t93) @t89))) % 0.37/0.63 (assume @p65 (forall (@list @t87 @t3) (or @t90 @t19 (tptp.member (tptp.image @t87 @t3) tptp.universal_class)))) % 0.37/0.63 (assume @p66 (forall @t12 (or @t95 (tptp.member @t94 @t3)))) % 0.37/0.63 (assume @p67 (forall @t12 (or @t95 (= (tptp.intersection @t3 @t94) tptp.null_class)))) % 0.37/0.63 (assume @p68 (forall (@list @t87 @t1) (= (tptp.sum_class (tptp.image @t87 @t26)) (tptp.apply @t87 @t1)))) % 0.37/0.63 (assume @p69 (tptp.function tptp.choice)) % 0.37/0.63 (assume @p70 (forall @t68 (or @t22 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.37/0.63 (assume @p71 (forall @t91 (or @t97 @t89))) % 0.37/0.63 (assume @p72 (forall @t91 (or @t97 @t98))) % 0.37/0.63 (assume @p73 (forall @t91 (or (not @t98) @t90 @t96))) % 0.37/0.63 (assume @p74 (= (tptp.intersection @t37 (tptp.intersection @t37 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t99)))) tptp.subset_relation)) % 0.37/0.63 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.37/0.63 (assume @p76 (forall (@list @t52) (= (tptp.complement (tptp.domain_of (tptp.intersection @t52 tptp.identity_relation))) (tptp.diagonalise @t52)))) % 0.37/0.63 (assume @p77 (forall @t12 (= (tptp.intersection @t54 (tptp.diagonalise (tptp.compose @t99 @t3))) (tptp.cantor @t3)))) % 0.37/0.63 (assume @p78 (forall @t91 (or @t101 @t89))) % 0.37/0.63 (assume @p79 (forall @t91 (or @t101 @t104))) % 0.37/0.63 (assume @p80 (forall @t91 (or @t101 @t105))) % 0.37/0.63 (assume @p81 (forall @t91 (or @t90 (not @t104) (not @t105) @t100))) % 0.37/0.63 (assume @p82 (forall @t112 (or @t111 @t107))) % 0.37/0.63 (assume @p83 (forall @t112 (or @t111 @t114))) % 0.37/0.63 (assume @p84 (forall @t112 (or @t111 @t115))) % 0.37/0.63 (assume @p85 (forall @t112 (or (not @t107) (not @t114) (not @t115) @t110))) % 0.37/0.63 (assume @p86 (forall @t112 (or @t118 @t116))) % 0.37/0.63 (assume @p87 (forall @t112 (or @t118 @t119))) % 0.37/0.63 (assume @p88 (forall @t112 (or @t118 @t110))) % 0.37/0.63 (assume @p89 (forall (@list @t106 @t109 @t108 @t3 @t1) (or @t118 (not (tptp.member @t25 @t113)) (= (tptp.apply @t108 (tptp.ordered_pair (tptp.apply @t106 @t3) (tptp.apply @t106 @t1))) (tptp.apply @t106 (tptp.apply @t109 @t25)))))) % 0.37/0.63 (assume @p90 (forall @t125 (or @t124 @t123 @t111 (tptp.member @t122 @t113) @t117))) % 0.37/0.63 (assume @p91 (forall @t125 (or @t124 @t123 @t111 (not (= (tptp.apply @t108 (tptp.ordered_pair (tptp.apply @t106 @t121) (tptp.apply @t106 @t120))) (tptp.apply @t106 (tptp.apply @t109 @t122)))) @t117))) % 0.37/0.63 (assume @p92 (forall @t127 (or @t126 @t17))) % 0.37/0.63 (assume @p93 (forall @t127 (or @t126 @t20))) % 0.37/0.63 (assume @p94 (forall @t33 (or @t32 @t78))) % 0.37/0.63 (assume @p95 (forall @t33 (or @t32 (tptp.member @t29 tptp.universal_class)))) % 0.37/0.63 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.37/0.63 (assume @p97 (forall @t128 (or @t7 (not (tptp.subclass @t1 @t35)) (tptp.subclass @t3 @t35)))) % 0.37/0.63 (assume @p98 (forall @t10 (or @t13 @t9 @t130))) % 0.37/0.63 (assume @p99 (forall @t10 (or @t11 @t13 @t130))) % 0.37/0.63 (assume @p100 (forall @t23 (or @t131 @t13 @t9))) % 0.37/0.63 (assume @p101 (forall @t10 (or @t11 @t131 @t13))) % 0.37/0.63 (assume @p102 (forall @t23 (not (tptp.member @t1 (tptp.intersection @t47 @t3))))) % 0.37/0.63 (assume @p103 (forall @t69 (not (tptp.member @t35 tptp.null_class)))) % 0.37/0.63 (assume @p104 (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.37/0.63 (assume @p105 (forall @t12 (or (not (tptp.subclass @t3 tptp.null_class)) @t95))) % 0.37/0.63 (assume @p106 (forall @t69 (or (= @t35 tptp.null_class) (tptp.member (tptp.not_subclass_element @t35 tptp.null_class) @t35)))) % 0.37/0.63 (assume @p107 @t132) % 0.37/0.63 (assume @p108 (forall @t10 (= @t16 (tptp.unordered_pair @t1 @t3)))) % 0.37/0.63 (assume @p109 (forall @t10 (tptp.subclass @t24 @t16))) % 0.37/0.63 (assume @p110 (forall @t23 (tptp.subclass @t26 @t16))) % 0.37/0.63 (assume @p111 (forall @t23 (or @t21 (= @t16 @t24)))) % 0.37/0.63 (assume @p112 (forall @t10 (or @t18 (= @t16 @t26)))) % 0.37/0.63 (assume @p113 (forall @t10 (or @t133 @t18 @t21))) % 0.37/0.63 (assume @p114 (forall @t128 (or (not (= @t16 @t134)) @t84 (= @t1 @t35)))) % 0.37/0.63 (assume @p115 (forall @t135 (or (not (= @t134 (tptp.unordered_pair @t1 @t35))) @t40 @t13))) % 0.37/0.63 (assume @p116 (forall @t10 (or @t19 @t136))) % 0.37/0.63 (assume @p117 (forall @t23 (or @t22 @t136))) % 0.37/0.63 (assume @p118 (forall @t127 (or @t126 @t136))) % 0.37/0.63 (assume @p119 (forall @t135 (or (not (tptp.member @t3 @t35)) (not (tptp.member @t1 @t35)) (tptp.subclass @t16 @t35)))) % 0.37/0.63 (assume @p120 (forall @t12 (tptp.member @t24 tptp.universal_class))) % 0.37/0.63 (assume @p121 (forall @t23 (tptp.member @t26 @t27))) % 0.37/0.63 (assume @p122 @t137) % 0.37/0.63 (assume @p123 (forall @t12 (or @t19 (not (= @t24 tptp.null_class))))) % 0.37/0.63 (assume @p124 (not @t138)) % 0.37/0.63 (step @p125 :rule cnf_or_pos :args (@t140)) % 0.37/0.63 (step @p126 :rule reordering :premises (@p125) :args ((or @t138 @t139 @t141))) % 0.37/0.63 (step @p127 :rule chain_m_resolution :premises (@p126 @p124 @p107) :args (@t141 @t142 (@list @t138 @t132))) % 0.37/0.63 (assume-push @p134 @t137) % 0.37/0.63 (step @p129 :rule instantiate :premises (@p122) :args ((@list tptp.null_class))) % 0.37/0.63 (step-pop @p135 :rule scope :premises (@p129)) % 0.37/0.63 (step @p130 :rule process_scope :premises (@p135) :args (@t140)) % 0.37/0.63 (step @p132 :rule implies_elim :premises (@p130)) % 0.37/0.63 (step @p133 false :rule chain_m_resolution :premises (@p132 @p127 @p122) :args (false @t142 (@list @t140 @t137))) % 0.37/0.63 ) % 0.37/0.63 % SZS output end Proof % 0.37/0.63 % cvc5 exiting %------------------------------------------------------------------------------