%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET084-7 : 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 : n015.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 08:47:19 AM UTC 2026 % Result : Unsatisfiable 0.36s 0.82s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET084-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:51:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.31/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.82 % SZS status Unsatisfiable % 0.36/0.82 % SZS output start Proof % 0.36/0.83 ( % 0.36/0.83 (declare-sort $$unsorted 0) % 0.36/0.83 (declare-const tptp.x $$unsorted) % 0.36/0.83 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.function (-> $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.y $$unsorted) % 0.36/0.83 (declare-const tptp.element_relation $$unsorted) % 0.36/0.83 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.universal_class $$unsorted) % 0.36/0.83 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.successor_relation $$unsorted) % 0.36/0.83 (declare-const tptp.choice $$unsorted) % 0.36/0.83 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.subset_relation $$unsorted) % 0.36/0.83 (declare-const tptp.null_class $$unsorted) % 0.36/0.83 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.omega $$unsorted) % 0.36/0.83 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.83 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.identity_relation $$unsorted) % 0.36/0.83 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.36/0.83 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.36/0.83 (define @t1 () (@var "Y" $$unsorted)) % 0.36/0.83 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.83 (define @t3 () (@var "X" $$unsorted)) % 0.36/0.83 (define @t4 () (tptp.member @t2 @t3)) % 0.36/0.83 (define @t5 () (not @t4)) % 0.36/0.83 (define @t6 () (tptp.subclass @t3 @t1)) % 0.36/0.83 (define @t7 () (not @t6)) % 0.36/0.83 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.36/0.83 (define @t9 () (tptp.member @t8 @t3)) % 0.36/0.83 (define @t10 () (@list @t3 @t1)) % 0.36/0.83 (define @t11 () (not (tptp.member @t8 @t1))) % 0.36/0.83 (define @t12 () (@list @t3)) % 0.36/0.83 (define @t13 () (= @t3 @t1)) % 0.36/0.83 (define @t14 () (not @t13)) % 0.36/0.83 (define @t15 () (tptp.subclass @t1 @t3)) % 0.36/0.83 (define @t16 () (tptp.unordered_pair @t3 @t1)) % 0.36/0.83 (define @t17 () (not (tptp.member @t2 @t16))) % 0.36/0.83 (define @t18 () (or @t17 (= @t2 @t3) (= @t2 @t1))) % 0.36/0.83 (define @t19 () (forall (@list @t2 @t3 @t1) @t18)) % 0.36/0.83 (define @t20 () (tptp.member @t3 @t16)) % 0.36/0.83 (define @t21 () (tptp.member @t3 tptp.universal_class)) % 0.36/0.83 (define @t22 () (not @t21)) % 0.36/0.83 (define @t23 () (tptp.member @t1 @t16)) % 0.36/0.83 (define @t24 () (tptp.member @t1 tptp.universal_class)) % 0.36/0.83 (define @t25 () (not @t24)) % 0.36/0.83 (define @t26 () (@list @t1 @t3)) % 0.36/0.83 (define @t27 () (tptp.singleton @t3)) % 0.36/0.83 (define @t28 () (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t27))) % 0.36/0.83 (define @t29 () (tptp.ordered_pair @t3 @t1)) % 0.36/0.83 (define @t30 () (tptp.singleton @t1)) % 0.36/0.83 (define @t31 () (tptp.unordered_pair @t3 @t30)) % 0.36/0.83 (define @t32 () (tptp.cross_product @t3 @t1)) % 0.36/0.83 (define @t33 () (@var "V" $$unsorted)) % 0.36/0.83 (define @t34 () (tptp.ordered_pair @t2 @t33)) % 0.36/0.83 (define @t35 () (tptp.member @t34 @t32)) % 0.36/0.83 (define @t36 () (not @t35)) % 0.36/0.83 (define @t37 () (@list @t2 @t33 @t3 @t1)) % 0.36/0.83 (define @t38 () (tptp.member @t33 @t1)) % 0.36/0.83 (define @t39 () (@var "Z" $$unsorted)) % 0.36/0.83 (define @t40 () (@list @t39 @t3 @t1)) % 0.36/0.83 (define @t41 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.36/0.83 (define @t42 () (tptp.member @t3 @t1)) % 0.36/0.83 (define @t43 () (tptp.member @t29 tptp.element_relation)) % 0.36/0.83 (define @t44 () (not (tptp.member @t29 @t41))) % 0.36/0.83 (define @t45 () (tptp.member @t39 @t3)) % 0.36/0.83 (define @t46 () (tptp.intersection @t3 @t1)) % 0.36/0.83 (define @t47 () (tptp.member @t39 @t46)) % 0.36/0.83 (define @t48 () (not @t47)) % 0.36/0.83 (define @t49 () (tptp.member @t39 @t1)) % 0.36/0.83 (define @t50 () (not @t45)) % 0.36/0.83 (define @t51 () (tptp.complement @t3)) % 0.36/0.83 (define @t52 () (tptp.member @t39 @t51)) % 0.36/0.83 (define @t53 () (@list @t39 @t3)) % 0.36/0.83 (define @t54 () (not (tptp.member @t39 tptp.universal_class))) % 0.36/0.83 (define @t55 () (tptp.complement (tptp.intersection @t51 (tptp.complement @t1)))) % 0.36/0.83 (define @t56 () (@var "Xr" $$unsorted)) % 0.36/0.83 (define @t57 () (tptp.restrict @t56 @t3 @t1)) % 0.36/0.83 (define @t58 () (tptp.domain_of @t3)) % 0.36/0.83 (define @t59 () (tptp.member @t39 @t58)) % 0.36/0.83 (define @t60 () (= (tptp.restrict @t3 (tptp.singleton @t39) tptp.universal_class) tptp.null_class)) % 0.36/0.83 (define @t61 () (tptp.cross_product @t41 tptp.universal_class)) % 0.36/0.83 (define @t62 () (tptp.rotate @t3)) % 0.36/0.83 (define @t63 () (@var "W" $$unsorted)) % 0.36/0.83 (define @t64 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t33 @t63) @t2) @t3)) % 0.36/0.83 (define @t65 () (tptp.ordered_pair @t34 @t63)) % 0.36/0.83 (define @t66 () (tptp.member @t65 @t62)) % 0.36/0.83 (define @t67 () (@list @t2 @t33 @t63 @t3)) % 0.36/0.83 (define @t68 () (not (tptp.member @t65 @t61))) % 0.36/0.83 (define @t69 () (tptp.flip @t3)) % 0.36/0.83 (define @t70 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t33 @t2) @t63) @t3)) % 0.36/0.83 (define @t71 () (tptp.member @t65 @t69)) % 0.36/0.83 (define @t72 () (@list @t1)) % 0.36/0.83 (define @t73 () (@list @t39)) % 0.36/0.83 (define @t74 () (tptp.successor @t3)) % 0.36/0.83 (define @t75 () (= @t74 @t1)) % 0.36/0.83 (define @t76 () (tptp.member @t29 tptp.successor_relation)) % 0.36/0.83 (define @t77 () (tptp.member tptp.null_class @t3)) % 0.36/0.83 (define @t78 () (tptp.inductive @t3)) % 0.36/0.83 (define @t79 () (not @t78)) % 0.36/0.83 (define @t80 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.36/0.83 (define @t81 () (tptp.sum_class @t3)) % 0.36/0.83 (define @t82 () (tptp.member @t2 tptp.universal_class)) % 0.36/0.83 (define @t83 () (@var "Yr" $$unsorted)) % 0.36/0.83 (define @t84 () (tptp.compose @t83 @t56)) % 0.36/0.83 (define @t85 () (tptp.member @t39 (tptp.image @t83 (tptp.image @t56 @t30)))) % 0.36/0.83 (define @t86 () (tptp.ordered_pair @t1 @t39)) % 0.36/0.83 (define @t87 () (tptp.member @t86 @t84)) % 0.36/0.83 (define @t88 () (not (tptp.member @t86 @t41))) % 0.36/0.83 (define @t89 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.36/0.83 (define @t90 () (tptp.single_valued_class @t3)) % 0.36/0.83 (define @t91 () (@var "Xf" $$unsorted)) % 0.36/0.83 (define @t92 () (tptp.subclass @t91 @t41)) % 0.36/0.83 (define @t93 () (tptp.function @t91)) % 0.36/0.83 (define @t94 () (not @t93)) % 0.36/0.83 (define @t95 () (@list @t91)) % 0.36/0.83 (define @t96 () (tptp.inverse @t91)) % 0.36/0.83 (define @t97 () (tptp.subclass (tptp.compose @t91 @t96) tptp.identity_relation)) % 0.36/0.83 (define @t98 () (tptp.regular @t3)) % 0.36/0.83 (define @t99 () (= @t3 tptp.null_class)) % 0.36/0.83 (define @t100 () (tptp.one_to_one @t91)) % 0.36/0.83 (define @t101 () (not @t100)) % 0.36/0.83 (define @t102 () (tptp.function @t96)) % 0.36/0.83 (define @t103 () (tptp.inverse tptp.element_relation)) % 0.36/0.83 (define @t104 () (tptp.operation @t91)) % 0.36/0.83 (define @t105 () (not @t104)) % 0.36/0.83 (define @t106 () (tptp.domain_of @t91)) % 0.36/0.83 (define @t107 () (tptp.domain_of @t106)) % 0.36/0.83 (define @t108 () (= (tptp.cross_product @t107 @t107) @t106)) % 0.36/0.83 (define @t109 () (tptp.subclass (tptp.range_of @t91) @t107)) % 0.36/0.83 (define @t110 () (@var "Xh" $$unsorted)) % 0.36/0.83 (define @t111 () (tptp.function @t110)) % 0.36/0.83 (define @t112 () (@var "Xf2" $$unsorted)) % 0.36/0.83 (define @t113 () (@var "Xf1" $$unsorted)) % 0.36/0.83 (define @t114 () (tptp.compatible @t110 @t113 @t112)) % 0.36/0.83 (define @t115 () (not @t114)) % 0.36/0.83 (define @t116 () (@list @t110 @t113 @t112)) % 0.36/0.83 (define @t117 () (tptp.domain_of @t113)) % 0.36/0.83 (define @t118 () (= (tptp.domain_of @t117) (tptp.domain_of @t110))) % 0.36/0.83 (define @t119 () (tptp.subclass (tptp.range_of @t110) (tptp.domain_of (tptp.domain_of @t112)))) % 0.36/0.83 (define @t120 () (tptp.operation @t113)) % 0.36/0.83 (define @t121 () (tptp.homomorphism @t110 @t113 @t112)) % 0.36/0.83 (define @t122 () (not @t121)) % 0.36/0.83 (define @t123 () (tptp.operation @t112)) % 0.36/0.83 (define @t124 () (tptp.not_homomorphism2 @t110 @t113 @t112)) % 0.36/0.83 (define @t125 () (tptp.not_homomorphism1 @t110 @t113 @t112)) % 0.36/0.83 (define @t126 () (tptp.ordered_pair @t125 @t124)) % 0.36/0.83 (define @t127 () (not @t123)) % 0.36/0.83 (define @t128 () (not @t120)) % 0.36/0.83 (define @t129 () (@list @t113 @t112 @t110)) % 0.36/0.83 (define @t130 () (not (tptp.member @t29 (tptp.cross_product @t2 @t33)))) % 0.36/0.83 (define @t131 () (@list @t3 @t1 @t2 @t33)) % 0.36/0.83 (define @t132 () (@list @t3 @t1 @t39)) % 0.36/0.83 (define @t133 () (tptp.not_subclass_element @t1 @t3)) % 0.36/0.83 (define @t134 () (tptp.member @t133 @t1)) % 0.36/0.83 (define @t135 () (not (tptp.member @t133 @t3))) % 0.36/0.83 (define @t136 () (= @t16 tptp.null_class)) % 0.36/0.83 (define @t137 () (tptp.unordered_pair @t3 @t39)) % 0.36/0.83 (define @t138 () (@list @t3 @t39 @t1)) % 0.36/0.83 (define @t139 () (not @t136)) % 0.36/0.83 (define @t140 () (= @t27 tptp.null_class)) % 0.36/0.83 (define @t141 () (tptp.singleton tptp.y)) % 0.36/0.83 (define @t142 () (tptp.singleton tptp.x)) % 0.36/0.83 (define @t143 () (tptp.member tptp.y tptp.universal_class)) % 0.36/0.83 (define @t144 () (= tptp.x tptp.y)) % 0.36/0.83 (define @t145 () (tptp.unordered_pair tptp.x tptp.x)) % 0.36/0.83 (define @t146 () (not (tptp.member tptp.y @t145))) % 0.36/0.83 (define @t147 () (or @t146 @t144 @t144)) % 0.36/0.83 (define @t148 () (= @t145 @t142)) % 0.36/0.83 (define @t149 () (tptp.member tptp.y @t141)) % 0.36/0.83 (define @t150 () (not @t143)) % 0.36/0.83 (define @t151 () (or @t150 @t149)) % 0.36/0.83 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.36/0.83 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.36/0.83 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.36/0.83 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.36/0.83 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.36/0.83 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.36/0.83 (assume @p7 (forall @t10 (or @t7 (not @t15) @t13))) % 0.36/0.83 (assume @p8 @t19) % 0.36/0.83 (assume @p9 (forall @t10 (or @t22 @t20))) % 0.36/0.83 (assume @p10 (forall @t26 (or @t25 @t23))) % 0.36/0.83 (assume @p11 (forall @t10 (tptp.member @t16 tptp.universal_class))) % 0.36/0.83 (assume @p12 @t28) % 0.36/0.83 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t27 @t31) @t29))) % 0.36/0.83 (assume @p14 (forall @t37 (or @t36 @t4))) % 0.36/0.83 (assume @p15 (forall @t37 (or @t36 @t38))) % 0.36/0.83 (assume @p16 (forall (@list @t2 @t3 @t33 @t1) (or @t5 (not @t38) @t35))) % 0.36/0.83 (assume @p17 (forall @t40 (or (not (tptp.member @t39 @t32)) (= (tptp.ordered_pair (tptp.first @t39) (tptp.second @t39)) @t39)))) % 0.36/0.83 (assume @p18 (tptp.subclass tptp.element_relation @t41)) % 0.36/0.83 (assume @p19 (forall @t10 (or (not @t43) @t42))) % 0.36/0.83 (assume @p20 (forall @t10 (or @t44 (not @t42) @t43))) % 0.36/0.83 (assume @p21 (forall @t40 (or @t48 @t45))) % 0.36/0.83 (assume @p22 (forall @t40 (or @t48 @t49))) % 0.36/0.83 (assume @p23 (forall @t40 (or @t50 (not @t49) @t47))) % 0.36/0.83 (assume @p24 (forall @t53 (or (not @t52) @t50))) % 0.36/0.83 (assume @p25 (forall @t53 (or @t54 @t52 @t45))) % 0.36/0.83 (assume @p26 (forall @t10 (= @t55 (tptp.union @t3 @t1)))) % 0.36/0.83 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t46) @t55) (tptp.symmetric_difference @t3 @t1)))) % 0.36/0.83 (assume @p28 (forall (@list @t56 @t3 @t1) (= (tptp.intersection @t56 @t32) @t57))) % 0.36/0.83 (assume @p29 (forall (@list @t3 @t1 @t56) (= (tptp.intersection @t32 @t56) @t57))) % 0.36/0.83 (assume @p30 (forall (@list @t3 @t39) (or (not @t60) (not @t59)))) % 0.36/0.83 (assume @p31 (forall @t53 (or @t54 @t60 @t59))) % 0.36/0.83 (assume @p32 (forall @t12 (tptp.subclass @t62 @t61))) % 0.36/0.83 (assume @p33 (forall @t67 (or (not @t66) @t64))) % 0.36/0.83 (assume @p34 (forall (@list @t33 @t63 @t2 @t3) (or (not @t64) @t68 @t66))) % 0.36/0.83 (assume @p35 (forall @t12 (tptp.subclass @t69 @t61))) % 0.36/0.83 (assume @p36 (forall @t67 (or (not @t71) @t70))) % 0.36/0.83 (assume @p37 (forall (@list @t33 @t2 @t63 @t3) (or (not @t70) @t68 @t71))) % 0.36/0.83 (assume @p38 (forall @t72 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.36/0.83 (assume @p39 (forall @t73 (= (tptp.domain_of (tptp.inverse @t39)) (tptp.range_of @t39)))) % 0.36/0.83 (assume @p40 (forall @t40 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t39 @t3 @t30) tptp.null_class)) (tptp.domain @t39 @t3 @t1)))) % 0.36/0.83 (assume @p41 (forall @t40 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t39 @t27 @t1) tptp.null_class)) (tptp.range @t39 @t3 @t1)))) % 0.36/0.83 (assume @p42 (forall (@list @t56 @t3) (= (tptp.range_of (tptp.restrict @t56 @t3 tptp.universal_class)) (tptp.image @t56 @t3)))) % 0.36/0.83 (assume @p43 (forall @t12 (= (tptp.union @t3 @t27) @t74))) % 0.36/0.83 (assume @p44 (tptp.subclass tptp.successor_relation @t41)) % 0.36/0.83 (assume @p45 (forall @t10 (or (not @t76) @t75))) % 0.36/0.83 (assume @p46 (forall @t10 (or (not @t75) @t44 @t76))) % 0.36/0.83 (assume @p47 (forall @t12 (or @t79 @t77))) % 0.36/0.83 (assume @p48 (forall @t12 (or @t79 @t80))) % 0.36/0.83 (assume @p49 (forall @t12 (or (not @t77) (not @t80) @t78))) % 0.36/0.83 (assume @p50 (tptp.inductive tptp.omega)) % 0.36/0.83 (assume @p51 (forall @t72 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.36/0.83 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.36/0.83 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t81))) % 0.36/0.83 (assume @p54 (forall @t12 (or @t22 (tptp.member @t81 tptp.universal_class)))) % 0.36/0.83 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t51)) (tptp.power_class @t3)))) % 0.36/0.83 (assume @p56 (forall (@list @t2) (or (not @t82) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.36/0.83 (assume @p57 (forall (@list @t83 @t56) (tptp.subclass @t84 @t41))) % 0.36/0.83 (assume @p58 (forall (@list @t1 @t39 @t83 @t56) (or (not @t87) @t85))) % 0.36/0.83 (assume @p59 (forall (@list @t39 @t83 @t56 @t1) (or (not @t85) @t88 @t87))) % 0.36/0.83 (assume @p60 (forall @t12 (or (not @t90) @t89))) % 0.36/0.83 (assume @p61 (forall @t12 (or (not @t89) @t90))) % 0.36/0.83 (assume @p62 (forall @t95 (or @t94 @t92))) % 0.36/0.83 (assume @p63 (forall @t95 (or @t94 @t97))) % 0.36/0.83 (assume @p64 (forall @t95 (or (not @t92) (not @t97) @t93))) % 0.36/0.83 (assume @p65 (forall (@list @t91 @t3) (or @t94 @t22 (tptp.member (tptp.image @t91 @t3) tptp.universal_class)))) % 0.36/0.83 (assume @p66 (forall @t12 (or @t99 (tptp.member @t98 @t3)))) % 0.36/0.83 (assume @p67 (forall @t12 (or @t99 (= (tptp.intersection @t3 @t98) tptp.null_class)))) % 0.36/0.83 (assume @p68 (forall (@list @t91 @t1) (= (tptp.sum_class (tptp.image @t91 @t30)) (tptp.apply @t91 @t1)))) % 0.36/0.83 (assume @p69 (tptp.function tptp.choice)) % 0.36/0.83 (assume @p70 (forall @t72 (or @t25 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.36/0.83 (assume @p71 (forall @t95 (or @t101 @t93))) % 0.36/0.83 (assume @p72 (forall @t95 (or @t101 @t102))) % 0.36/0.83 (assume @p73 (forall @t95 (or (not @t102) @t94 @t100))) % 0.36/0.83 (assume @p74 (= (tptp.intersection @t41 (tptp.intersection @t41 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t103)))) tptp.subset_relation)) % 0.36/0.83 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.36/0.83 (assume @p76 (forall (@list @t56) (= (tptp.complement (tptp.domain_of (tptp.intersection @t56 tptp.identity_relation))) (tptp.diagonalise @t56)))) % 0.36/0.83 (assume @p77 (forall @t12 (= (tptp.intersection @t58 (tptp.diagonalise (tptp.compose @t103 @t3))) (tptp.cantor @t3)))) % 0.36/0.83 (assume @p78 (forall @t95 (or @t105 @t93))) % 0.36/0.83 (assume @p79 (forall @t95 (or @t105 @t108))) % 0.36/0.83 (assume @p80 (forall @t95 (or @t105 @t109))) % 0.36/0.83 (assume @p81 (forall @t95 (or @t94 (not @t108) (not @t109) @t104))) % 0.36/0.83 (assume @p82 (forall @t116 (or @t115 @t111))) % 0.36/0.83 (assume @p83 (forall @t116 (or @t115 @t118))) % 0.36/0.83 (assume @p84 (forall @t116 (or @t115 @t119))) % 0.36/0.83 (assume @p85 (forall @t116 (or (not @t111) (not @t118) (not @t119) @t114))) % 0.36/0.83 (assume @p86 (forall @t116 (or @t122 @t120))) % 0.36/0.83 (assume @p87 (forall @t116 (or @t122 @t123))) % 0.36/0.83 (assume @p88 (forall @t116 (or @t122 @t114))) % 0.36/0.83 (assume @p89 (forall (@list @t110 @t113 @t112 @t3 @t1) (or @t122 (not (tptp.member @t29 @t117)) (= (tptp.apply @t112 (tptp.ordered_pair (tptp.apply @t110 @t3) (tptp.apply @t110 @t1))) (tptp.apply @t110 (tptp.apply @t113 @t29)))))) % 0.36/0.83 (assume @p90 (forall @t129 (or @t128 @t127 @t115 (tptp.member @t126 @t117) @t121))) % 0.36/0.83 (assume @p91 (forall @t129 (or @t128 @t127 @t115 (not (= (tptp.apply @t112 (tptp.ordered_pair (tptp.apply @t110 @t125) (tptp.apply @t110 @t124))) (tptp.apply @t110 (tptp.apply @t113 @t126)))) @t121))) % 0.36/0.83 (assume @p92 (forall @t131 (or @t130 @t20))) % 0.36/0.83 (assume @p93 (forall @t131 (or @t130 @t23))) % 0.36/0.83 (assume @p94 (forall @t37 (or @t36 @t82))) % 0.36/0.83 (assume @p95 (forall @t37 (or @t36 (tptp.member @t33 tptp.universal_class)))) % 0.36/0.83 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.36/0.83 (assume @p97 (forall @t132 (or @t7 (not (tptp.subclass @t1 @t39)) (tptp.subclass @t3 @t39)))) % 0.36/0.83 (assume @p98 (forall @t10 (or @t13 @t9 @t134))) % 0.36/0.83 (assume @p99 (forall @t10 (or @t11 @t13 @t134))) % 0.36/0.83 (assume @p100 (forall @t26 (or @t135 @t13 @t9))) % 0.36/0.83 (assume @p101 (forall @t10 (or @t11 @t135 @t13))) % 0.36/0.83 (assume @p102 (forall @t26 (not (tptp.member @t1 (tptp.intersection @t51 @t3))))) % 0.36/0.83 (assume @p103 (forall @t73 (not (tptp.member @t39 tptp.null_class)))) % 0.36/0.83 (assume @p104 (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.36/0.83 (assume @p105 (forall @t12 (or (not (tptp.subclass @t3 tptp.null_class)) @t99))) % 0.36/0.83 (assume @p106 (forall @t73 (or (= @t39 tptp.null_class) (tptp.member (tptp.not_subclass_element @t39 tptp.null_class) @t39)))) % 0.36/0.83 (assume @p107 (tptp.member tptp.null_class tptp.universal_class)) % 0.36/0.83 (assume @p108 (forall @t10 (= @t16 (tptp.unordered_pair @t1 @t3)))) % 0.36/0.83 (assume @p109 (forall @t10 (tptp.subclass @t27 @t16))) % 0.36/0.83 (assume @p110 (forall @t26 (tptp.subclass @t30 @t16))) % 0.36/0.83 (assume @p111 (forall @t26 (or @t24 (= @t16 @t27)))) % 0.36/0.83 (assume @p112 (forall @t10 (or @t21 (= @t16 @t30)))) % 0.36/0.83 (assume @p113 (forall @t10 (or @t136 @t21 @t24))) % 0.36/0.83 (assume @p114 (forall @t132 (or (not (= @t16 @t137)) @t88 (= @t1 @t39)))) % 0.36/0.83 (assume @p115 (forall @t138 (or (not (= @t137 (tptp.unordered_pair @t1 @t39))) @t44 @t13))) % 0.36/0.83 (assume @p116 (forall @t10 (or @t22 @t139))) % 0.36/0.83 (assume @p117 (forall @t26 (or @t25 @t139))) % 0.36/0.83 (assume @p118 (forall @t131 (or @t130 @t139))) % 0.36/0.83 (assume @p119 (forall @t138 (or (not (tptp.member @t3 @t39)) (not (tptp.member @t1 @t39)) (tptp.subclass @t16 @t39)))) % 0.36/0.83 (assume @p120 (forall @t12 (tptp.member @t27 tptp.universal_class))) % 0.36/0.83 (assume @p121 (forall @t26 (tptp.member @t30 @t31))) % 0.36/0.83 (assume @p122 (forall @t12 (or @t22 (tptp.member @t3 @t27)))) % 0.36/0.83 (assume @p123 (forall @t12 (or @t22 (not @t140)))) % 0.36/0.83 (assume @p124 (tptp.member tptp.null_class (tptp.singleton tptp.null_class))) % 0.36/0.83 (assume @p125 (forall @t26 (or (not (tptp.member @t1 @t27)) (= @t1 @t3)))) % 0.36/0.83 (assume @p126 (forall @t12 (or @t21 @t140))) % 0.36/0.83 (assume @p127 (= @t142 @t141)) % 0.36/0.83 (assume @p128 @t143) % 0.36/0.83 (assume @p129 (not @t144)) % 0.36/0.83 (step @p130 :rule evaluate :args ((= true false))) % 0.36/0.83 (step @p131 :rule eq-symm :args (@t2 @t1)) % 0.36/0.83 (step @p132 :rule eq-symm :args (@t2 @t3)) % 0.36/0.83 (step @p133 :rule refl :args (@t17)) % 0.36/0.83 (step @p134 :rule nary_cong :premises (@p133 @p132 @p131) :args (@t18)) % 0.36/0.83 (step @p135 :rule cong :premises (@p134) :args (@t19)) % 0.36/0.83 (step @p136 :rule eq_resolve :premises (@p8 @p135)) % 0.36/0.83 (step @p137 :rule instantiate :premises (@p136) :args ((@list tptp.y tptp.x tptp.x))) % 0.36/0.83 (step @p138 :rule cnf_or_pos :args (@t147)) % 0.36/0.83 (step @p139 :rule factoring :premises (@p138)) % 0.36/0.83 (step @p140 :rule reordering :premises (@p139) :args ((or @t144 @t146 (not @t147)))) % 0.36/0.83 (step @p141 :rule chain_m_resolution :premises (@p140 @p129 @p137) :args (@t146 (@list true false) (@list @t144 @t147))) % 0.36/0.83 (step @p142 :rule false_intro :premises (@p141)) % 0.36/0.83 (step @p143 :rule eq-symm :args (@t145 @t142)) % 0.36/0.83 (step @p144 :rule refl :args (@t28)) % 0.36/0.83 (step @p145 :rule cong :premises (@p144 @p143) :args ((=> @t28 @t148))) % 0.36/0.83 (assume-push @p165 @t28) % 0.36/0.83 (step @p147 :rule instantiate :premises (@p12) :args ((@list tptp.x))) % 0.36/0.83 (step-pop @p166 :rule scope :premises (@p147)) % 0.36/0.83 (step @p148 :rule process_scope :premises (@p166) :args (@t148)) % 0.36/0.83 (step @p150 :rule eq_resolve :premises (@p148 @p145)) % 0.36/0.83 (step @p151 :rule implies_elim :premises (@p150)) % 0.36/0.83 (step @p152 :rule chain_m_resolution :premises (@p151 @p12) :args ((= @t142 @t145) (@list false) (@list @t28))) % 0.36/0.83 (step @p153 :rule symm :premises (@p127)) % 0.36/0.83 (step @p154 :rule trans :premises (@p153 @p152)) % 0.36/0.83 (step @p155 :rule refl :args (tptp.y)) % 0.36/0.83 (step @p156 :rule cong :premises (@p155 @p154) :args (@t149)) % 0.36/0.83 (step @p157 :rule instantiate :premises (@p122) :args ((@list tptp.y))) % 0.36/0.83 (step @p158 :rule cnf_or_pos :args (@t151)) % 0.36/0.83 (step @p159 :rule reordering :premises (@p158) :args ((or @t150 @t149 (not @t151)))) % 0.36/0.83 (step @p160 :rule chain_m_resolution :premises (@p159 @p128 @p157) :args (@t149 (@list false false) (@list @t143 @t151))) % 0.36/0.83 (step @p161 :rule true_intro :premises (@p160)) % 0.36/0.83 (step @p162 :rule symm :premises (@p161)) % 0.36/0.83 (step @p163 :rule trans :premises (@p162 @p156 @p142)) % 0.36/0.83 (step @p164 false :rule eq_resolve :premises (@p163 @p130)) % 0.36/0.83 ) % 0.36/0.83 % SZS output end Proof % 0.36/0.83 % cvc5 exiting %------------------------------------------------------------------------------