%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET080-6 : 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 : n012.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 0.25s 0.49s % Output : Proof 0.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET080-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 14:51:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.25/0.49 % SZS status Unsatisfiable % 0.25/0.49 % SZS output start Proof % 0.25/0.50 ( % 0.25/0.50 (declare-sort $$unsorted 0) % 0.25/0.50 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.function (-> $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.element_relation $$unsorted) % 0.25/0.50 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.universal_class $$unsorted) % 0.25/0.50 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.successor_relation $$unsorted) % 0.25/0.50 (declare-const tptp.choice $$unsorted) % 0.25/0.50 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.subset_relation $$unsorted) % 0.25/0.50 (declare-const tptp.null_class $$unsorted) % 0.25/0.50 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.omega $$unsorted) % 0.25/0.50 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.25/0.50 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.identity_relation $$unsorted) % 0.25/0.50 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.25/0.50 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.25/0.50 (define @t1 () (@var "Y" $$unsorted)) % 0.25/0.50 (define @t2 () (@var "U" $$unsorted)) % 0.25/0.50 (define @t3 () (@var "X" $$unsorted)) % 0.25/0.50 (define @t4 () (tptp.member @t2 @t3)) % 0.25/0.50 (define @t5 () (not @t4)) % 0.25/0.50 (define @t6 () (tptp.subclass @t3 @t1)) % 0.25/0.50 (define @t7 () (not @t6)) % 0.25/0.50 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.25/0.50 (define @t9 () (@list @t3 @t1)) % 0.25/0.50 (define @t10 () (@list @t3)) % 0.25/0.50 (define @t11 () (= @t3 @t1)) % 0.25/0.50 (define @t12 () (not @t11)) % 0.25/0.50 (define @t13 () (tptp.subclass @t1 @t3)) % 0.25/0.50 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.25/0.50 (define @t15 () (not (tptp.member @t2 @t14))) % 0.25/0.50 (define @t16 () (or @t15 (= @t2 @t3) (= @t2 @t1))) % 0.25/0.50 (define @t17 () (forall (@list @t2 @t3 @t1) @t16)) % 0.25/0.50 (define @t18 () (not (tptp.member @t3 tptp.universal_class))) % 0.25/0.50 (define @t19 () (not (tptp.member @t1 tptp.universal_class))) % 0.25/0.50 (define @t20 () (tptp.singleton @t3)) % 0.25/0.50 (define @t21 () (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t20))) % 0.25/0.50 (define @t22 () (tptp.ordered_pair @t3 @t1)) % 0.25/0.50 (define @t23 () (tptp.singleton @t1)) % 0.25/0.50 (define @t24 () (tptp.cross_product @t3 @t1)) % 0.25/0.50 (define @t25 () (@var "V" $$unsorted)) % 0.25/0.50 (define @t26 () (tptp.ordered_pair @t2 @t25)) % 0.25/0.50 (define @t27 () (tptp.member @t26 @t24)) % 0.25/0.50 (define @t28 () (not @t27)) % 0.25/0.50 (define @t29 () (@list @t2 @t25 @t3 @t1)) % 0.25/0.50 (define @t30 () (tptp.member @t25 @t1)) % 0.25/0.50 (define @t31 () (@var "Z" $$unsorted)) % 0.25/0.50 (define @t32 () (@list @t31 @t3 @t1)) % 0.25/0.50 (define @t33 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.25/0.50 (define @t34 () (tptp.member @t3 @t1)) % 0.25/0.50 (define @t35 () (tptp.member @t22 tptp.element_relation)) % 0.25/0.50 (define @t36 () (not (tptp.member @t22 @t33))) % 0.25/0.50 (define @t37 () (tptp.member @t31 @t3)) % 0.25/0.50 (define @t38 () (tptp.intersection @t3 @t1)) % 0.25/0.50 (define @t39 () (tptp.member @t31 @t38)) % 0.25/0.50 (define @t40 () (not @t39)) % 0.25/0.50 (define @t41 () (tptp.member @t31 @t1)) % 0.25/0.50 (define @t42 () (not @t37)) % 0.25/0.50 (define @t43 () (tptp.complement @t3)) % 0.25/0.50 (define @t44 () (tptp.member @t31 @t43)) % 0.25/0.50 (define @t45 () (@list @t31 @t3)) % 0.25/0.50 (define @t46 () (not (tptp.member @t31 tptp.universal_class))) % 0.25/0.50 (define @t47 () (tptp.complement (tptp.intersection @t43 (tptp.complement @t1)))) % 0.25/0.50 (define @t48 () (@var "Xr" $$unsorted)) % 0.25/0.50 (define @t49 () (tptp.restrict @t48 @t3 @t1)) % 0.25/0.50 (define @t50 () (tptp.domain_of @t3)) % 0.25/0.50 (define @t51 () (tptp.member @t31 @t50)) % 0.25/0.50 (define @t52 () (= (tptp.restrict @t3 (tptp.singleton @t31) tptp.universal_class) tptp.null_class)) % 0.25/0.50 (define @t53 () (tptp.cross_product @t33 tptp.universal_class)) % 0.25/0.50 (define @t54 () (tptp.rotate @t3)) % 0.25/0.50 (define @t55 () (@var "W" $$unsorted)) % 0.25/0.50 (define @t56 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t25 @t55) @t2) @t3)) % 0.25/0.50 (define @t57 () (tptp.ordered_pair @t26 @t55)) % 0.25/0.50 (define @t58 () (tptp.member @t57 @t54)) % 0.25/0.50 (define @t59 () (@list @t2 @t25 @t55 @t3)) % 0.25/0.50 (define @t60 () (not (tptp.member @t57 @t53))) % 0.25/0.50 (define @t61 () (tptp.flip @t3)) % 0.25/0.50 (define @t62 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t25 @t2) @t55) @t3)) % 0.25/0.50 (define @t63 () (tptp.member @t57 @t61)) % 0.25/0.50 (define @t64 () (@list @t1)) % 0.25/0.50 (define @t65 () (tptp.successor @t3)) % 0.25/0.50 (define @t66 () (= @t65 @t1)) % 0.25/0.50 (define @t67 () (tptp.member @t22 tptp.successor_relation)) % 0.25/0.50 (define @t68 () (tptp.member tptp.null_class @t3)) % 0.25/0.50 (define @t69 () (tptp.inductive @t3)) % 0.25/0.50 (define @t70 () (not @t69)) % 0.25/0.50 (define @t71 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.25/0.50 (define @t72 () (tptp.sum_class @t3)) % 0.25/0.50 (define @t73 () (@var "Yr" $$unsorted)) % 0.25/0.50 (define @t74 () (tptp.compose @t73 @t48)) % 0.25/0.50 (define @t75 () (tptp.member @t31 (tptp.image @t73 (tptp.image @t48 @t23)))) % 0.25/0.50 (define @t76 () (tptp.ordered_pair @t1 @t31)) % 0.25/0.50 (define @t77 () (tptp.member @t76 @t74)) % 0.25/0.50 (define @t78 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.25/0.50 (define @t79 () (tptp.single_valued_class @t3)) % 0.25/0.50 (define @t80 () (@var "Xf" $$unsorted)) % 0.25/0.50 (define @t81 () (tptp.subclass @t80 @t33)) % 0.25/0.50 (define @t82 () (tptp.function @t80)) % 0.25/0.50 (define @t83 () (not @t82)) % 0.25/0.50 (define @t84 () (@list @t80)) % 0.25/0.50 (define @t85 () (tptp.inverse @t80)) % 0.25/0.50 (define @t86 () (tptp.subclass (tptp.compose @t80 @t85) tptp.identity_relation)) % 0.25/0.50 (define @t87 () (tptp.regular @t3)) % 0.25/0.50 (define @t88 () (= @t3 tptp.null_class)) % 0.25/0.50 (define @t89 () (forall @t64 (or @t19 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.25/0.50 (define @t90 () (tptp.one_to_one @t80)) % 0.25/0.50 (define @t91 () (not @t90)) % 0.25/0.50 (define @t92 () (tptp.function @t85)) % 0.25/0.50 (define @t93 () (tptp.inverse tptp.element_relation)) % 0.25/0.50 (define @t94 () (tptp.operation @t80)) % 0.25/0.50 (define @t95 () (not @t94)) % 0.25/0.50 (define @t96 () (tptp.domain_of @t80)) % 0.25/0.50 (define @t97 () (tptp.domain_of @t96)) % 0.25/0.50 (define @t98 () (= (tptp.cross_product @t97 @t97) @t96)) % 0.25/0.50 (define @t99 () (tptp.subclass (tptp.range_of @t80) @t97)) % 0.25/0.50 (define @t100 () (@var "Xh" $$unsorted)) % 0.25/0.50 (define @t101 () (tptp.function @t100)) % 0.25/0.50 (define @t102 () (@var "Xf2" $$unsorted)) % 0.25/0.50 (define @t103 () (@var "Xf1" $$unsorted)) % 0.25/0.50 (define @t104 () (tptp.compatible @t100 @t103 @t102)) % 0.25/0.50 (define @t105 () (not @t104)) % 0.25/0.50 (define @t106 () (@list @t100 @t103 @t102)) % 0.25/0.50 (define @t107 () (tptp.domain_of @t103)) % 0.25/0.50 (define @t108 () (= (tptp.domain_of @t107) (tptp.domain_of @t100))) % 0.25/0.50 (define @t109 () (tptp.subclass (tptp.range_of @t100) (tptp.domain_of (tptp.domain_of @t102)))) % 0.25/0.50 (define @t110 () (tptp.operation @t103)) % 0.25/0.50 (define @t111 () (tptp.homomorphism @t100 @t103 @t102)) % 0.25/0.50 (define @t112 () (not @t111)) % 0.25/0.50 (define @t113 () (tptp.operation @t102)) % 0.25/0.50 (define @t114 () (tptp.not_homomorphism2 @t100 @t103 @t102)) % 0.25/0.50 (define @t115 () (tptp.not_homomorphism1 @t100 @t103 @t102)) % 0.25/0.50 (define @t116 () (tptp.ordered_pair @t115 @t114)) % 0.25/0.50 (define @t117 () (not @t113)) % 0.25/0.50 (define @t118 () (not @t110)) % 0.25/0.50 (define @t119 () (@list @t103 @t102 @t100)) % 0.25/0.50 (define @t120 () (tptp.singleton tptp.null_class)) % 0.25/0.50 (define @t121 () (tptp.member tptp.null_class @t120)) % 0.25/0.50 (define @t122 () (not @t121)) % 0.25/0.50 (define @t123 () (tptp.unordered_pair tptp.null_class tptp.null_class)) % 0.25/0.50 (define @t124 () (= @t123 @t120)) % 0.25/0.50 (define @t125 () (@list tptp.null_class)) % 0.25/0.50 (define @t126 () (= @t120 @t123)) % 0.25/0.50 (define @t127 () (@list false)) % 0.25/0.50 (define @t128 () (tptp.apply tptp.choice @t123)) % 0.25/0.50 (define @t129 () (tptp.member @t128 @t123)) % 0.25/0.50 (define @t130 () (tptp.member @t123 tptp.universal_class)) % 0.25/0.50 (define @t131 () (not @t130)) % 0.25/0.50 (define @t132 () (or @t131 (= @t123 tptp.null_class) @t129)) % 0.25/0.50 (define @t133 () (= tptp.null_class @t123)) % 0.25/0.50 (define @t134 () (or @t131 @t133 @t129)) % 0.25/0.50 (define @t135 () (@list tptp.null_class tptp.null_class)) % 0.25/0.50 (define @t136 () (tptp.member tptp.null_class @t123)) % 0.25/0.50 (define @t137 () (tptp.member tptp.null_class tptp.universal_class)) % 0.25/0.50 (define @t138 () (not @t137)) % 0.25/0.50 (define @t139 () (or @t138 @t136)) % 0.25/0.50 (define @t140 () (not @t133)) % 0.25/0.50 (define @t141 () (not @t126)) % 0.25/0.50 (define @t142 () (= true false)) % 0.25/0.50 (define @t143 () (and @t138 @t133 @t126 @t130)) % 0.25/0.50 (define @t144 () (@list false true false)) % 0.25/0.50 (define @t145 () (= tptp.null_class @t128)) % 0.25/0.50 (define @t146 () (not @t129)) % 0.25/0.50 (define @t147 () (or @t146 @t145 @t145)) % 0.25/0.50 (define @t148 () (not @t145)) % 0.25/0.50 (define @t149 () (and @t122 @t145 @t126 @t129)) % 0.25/0.50 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.25/0.50 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.25/0.50 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.25/0.50 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.25/0.50 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.25/0.50 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.25/0.50 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.25/0.50 (assume @p8 @t17) % 0.25/0.50 (assume @p9 (forall @t9 (or @t18 (tptp.member @t3 @t14)))) % 0.25/0.50 (assume @p10 (forall (@list @t1 @t3) (or @t19 (tptp.member @t1 @t14)))) % 0.25/0.50 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.25/0.50 (assume @p12 @t21) % 0.25/0.50 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t20 (tptp.unordered_pair @t3 @t23)) @t22))) % 0.25/0.50 (assume @p14 (forall @t29 (or @t28 @t4))) % 0.25/0.50 (assume @p15 (forall @t29 (or @t28 @t30))) % 0.25/0.50 (assume @p16 (forall (@list @t2 @t3 @t25 @t1) (or @t5 (not @t30) @t27))) % 0.25/0.50 (assume @p17 (forall @t32 (or (not (tptp.member @t31 @t24)) (= (tptp.ordered_pair (tptp.first @t31) (tptp.second @t31)) @t31)))) % 0.25/0.50 (assume @p18 (tptp.subclass tptp.element_relation @t33)) % 0.25/0.50 (assume @p19 (forall @t9 (or (not @t35) @t34))) % 0.25/0.50 (assume @p20 (forall @t9 (or @t36 (not @t34) @t35))) % 0.25/0.50 (assume @p21 (forall @t32 (or @t40 @t37))) % 0.25/0.50 (assume @p22 (forall @t32 (or @t40 @t41))) % 0.25/0.50 (assume @p23 (forall @t32 (or @t42 (not @t41) @t39))) % 0.25/0.50 (assume @p24 (forall @t45 (or (not @t44) @t42))) % 0.25/0.50 (assume @p25 (forall @t45 (or @t46 @t44 @t37))) % 0.25/0.50 (assume @p26 (forall @t9 (= @t47 (tptp.union @t3 @t1)))) % 0.25/0.50 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t38) @t47) (tptp.symmetric_difference @t3 @t1)))) % 0.25/0.50 (assume @p28 (forall (@list @t48 @t3 @t1) (= (tptp.intersection @t48 @t24) @t49))) % 0.25/0.50 (assume @p29 (forall (@list @t3 @t1 @t48) (= (tptp.intersection @t24 @t48) @t49))) % 0.25/0.50 (assume @p30 (forall (@list @t3 @t31) (or (not @t52) (not @t51)))) % 0.25/0.50 (assume @p31 (forall @t45 (or @t46 @t52 @t51))) % 0.25/0.50 (assume @p32 (forall @t10 (tptp.subclass @t54 @t53))) % 0.25/0.50 (assume @p33 (forall @t59 (or (not @t58) @t56))) % 0.25/0.50 (assume @p34 (forall (@list @t25 @t55 @t2 @t3) (or (not @t56) @t60 @t58))) % 0.25/0.50 (assume @p35 (forall @t10 (tptp.subclass @t61 @t53))) % 0.25/0.50 (assume @p36 (forall @t59 (or (not @t63) @t62))) % 0.25/0.50 (assume @p37 (forall (@list @t25 @t2 @t55 @t3) (or (not @t62) @t60 @t63))) % 0.25/0.50 (assume @p38 (forall @t64 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.25/0.50 (assume @p39 (forall (@list @t31) (= (tptp.domain_of (tptp.inverse @t31)) (tptp.range_of @t31)))) % 0.25/0.50 (assume @p40 (forall @t32 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t31 @t3 @t23) tptp.null_class)) (tptp.domain @t31 @t3 @t1)))) % 0.25/0.50 (assume @p41 (forall @t32 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t31 @t20 @t1) tptp.null_class)) (tptp.range @t31 @t3 @t1)))) % 0.25/0.50 (assume @p42 (forall (@list @t48 @t3) (= (tptp.range_of (tptp.restrict @t48 @t3 tptp.universal_class)) (tptp.image @t48 @t3)))) % 0.25/0.50 (assume @p43 (forall @t10 (= (tptp.union @t3 @t20) @t65))) % 0.25/0.50 (assume @p44 (tptp.subclass tptp.successor_relation @t33)) % 0.25/0.50 (assume @p45 (forall @t9 (or (not @t67) @t66))) % 0.25/0.50 (assume @p46 (forall @t9 (or (not @t66) @t36 @t67))) % 0.25/0.50 (assume @p47 (forall @t10 (or @t70 @t68))) % 0.25/0.50 (assume @p48 (forall @t10 (or @t70 @t71))) % 0.25/0.50 (assume @p49 (forall @t10 (or (not @t68) (not @t71) @t69))) % 0.25/0.50 (assume @p50 (tptp.inductive tptp.omega)) % 0.25/0.50 (assume @p51 (forall @t64 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.25/0.50 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.25/0.50 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t72))) % 0.25/0.50 (assume @p54 (forall @t10 (or @t18 (tptp.member @t72 tptp.universal_class)))) % 0.25/0.50 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t43)) (tptp.power_class @t3)))) % 0.25/0.50 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.25/0.50 (assume @p57 (forall (@list @t73 @t48) (tptp.subclass @t74 @t33))) % 0.25/0.50 (assume @p58 (forall (@list @t1 @t31 @t73 @t48) (or (not @t77) @t75))) % 0.25/0.50 (assume @p59 (forall (@list @t31 @t73 @t48 @t1) (or (not @t75) (not (tptp.member @t76 @t33)) @t77))) % 0.25/0.50 (assume @p60 (forall @t10 (or (not @t79) @t78))) % 0.25/0.50 (assume @p61 (forall @t10 (or (not @t78) @t79))) % 0.25/0.50 (assume @p62 (forall @t84 (or @t83 @t81))) % 0.25/0.50 (assume @p63 (forall @t84 (or @t83 @t86))) % 0.25/0.50 (assume @p64 (forall @t84 (or (not @t81) (not @t86) @t82))) % 0.25/0.50 (assume @p65 (forall (@list @t80 @t3) (or @t83 @t18 (tptp.member (tptp.image @t80 @t3) tptp.universal_class)))) % 0.25/0.50 (assume @p66 (forall @t10 (or @t88 (tptp.member @t87 @t3)))) % 0.25/0.50 (assume @p67 (forall @t10 (or @t88 (= (tptp.intersection @t3 @t87) tptp.null_class)))) % 0.25/0.50 (assume @p68 (forall (@list @t80 @t1) (= (tptp.sum_class (tptp.image @t80 @t23)) (tptp.apply @t80 @t1)))) % 0.25/0.50 (assume @p69 (tptp.function tptp.choice)) % 0.25/0.50 (assume @p70 @t89) % 0.25/0.50 (assume @p71 (forall @t84 (or @t91 @t82))) % 0.25/0.50 (assume @p72 (forall @t84 (or @t91 @t92))) % 0.25/0.50 (assume @p73 (forall @t84 (or (not @t92) @t83 @t90))) % 0.25/0.50 (assume @p74 (= (tptp.intersection @t33 (tptp.intersection @t33 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t93)))) tptp.subset_relation)) % 0.25/0.50 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.25/0.50 (assume @p76 (forall (@list @t48) (= (tptp.complement (tptp.domain_of (tptp.intersection @t48 tptp.identity_relation))) (tptp.diagonalise @t48)))) % 0.25/0.50 (assume @p77 (forall @t10 (= (tptp.intersection @t50 (tptp.diagonalise (tptp.compose @t93 @t3))) (tptp.cantor @t3)))) % 0.25/0.50 (assume @p78 (forall @t84 (or @t95 @t82))) % 0.25/0.50 (assume @p79 (forall @t84 (or @t95 @t98))) % 0.25/0.50 (assume @p80 (forall @t84 (or @t95 @t99))) % 0.25/0.50 (assume @p81 (forall @t84 (or @t83 (not @t98) (not @t99) @t94))) % 0.25/0.50 (assume @p82 (forall @t106 (or @t105 @t101))) % 0.25/0.50 (assume @p83 (forall @t106 (or @t105 @t108))) % 0.25/0.50 (assume @p84 (forall @t106 (or @t105 @t109))) % 0.25/0.50 (assume @p85 (forall @t106 (or (not @t101) (not @t108) (not @t109) @t104))) % 0.25/0.50 (assume @p86 (forall @t106 (or @t112 @t110))) % 0.25/0.50 (assume @p87 (forall @t106 (or @t112 @t113))) % 0.25/0.50 (assume @p88 (forall @t106 (or @t112 @t104))) % 0.25/0.50 (assume @p89 (forall (@list @t100 @t103 @t102 @t3 @t1) (or @t112 (not (tptp.member @t22 @t107)) (= (tptp.apply @t102 (tptp.ordered_pair (tptp.apply @t100 @t3) (tptp.apply @t100 @t1))) (tptp.apply @t100 (tptp.apply @t103 @t22)))))) % 0.25/0.50 (assume @p90 (forall @t119 (or @t118 @t117 @t105 (tptp.member @t116 @t107) @t111))) % 0.25/0.50 (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))) % 0.25/0.50 (assume @p92 @t122) % 0.25/0.50 (step @p93 :rule eq-symm :args (@t123 @t120)) % 0.25/0.50 (step @p94 :rule refl :args (@t21)) % 0.25/0.50 (step @p95 :rule cong :premises (@p94 @p93) :args ((=> @t21 @t124))) % 0.25/0.50 (assume-push @p213 @t21) % 0.25/0.50 (step @p97 :rule instantiate :premises (@p12) :args (@t125)) % 0.25/0.50 (step-pop @p214 :rule scope :premises (@p97)) % 0.25/0.50 (step @p98 :rule process_scope :premises (@p214) :args (@t124)) % 0.25/0.50 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 0.25/0.50 (step @p101 :rule implies_elim :premises (@p100)) % 0.25/0.50 (step @p102 :rule chain_m_resolution :premises (@p101 @p12) :args (@t126 @t127 (@list @t21))) % 0.25/0.50 (step @p103 :rule refl :args (@t129)) % 0.25/0.50 (step @p104 :rule eq-symm :args (@t123 tptp.null_class)) % 0.25/0.50 (step @p105 :rule refl :args (@t131)) % 0.25/0.50 (step @p106 :rule nary_cong :premises (@p105 @p104 @p103) :args (@t132)) % 0.25/0.50 (step @p107 :rule refl :args (@t89)) % 0.25/0.50 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t89 @t132))) % 0.25/0.50 (assume-push @p215 @t89) % 0.25/0.50 (step @p110 :rule instantiate :premises (@p70) :args ((@list @t123))) % 0.25/0.50 (step-pop @p216 :rule scope :premises (@p110)) % 0.25/0.50 (step @p111 :rule process_scope :premises (@p216) :args (@t132)) % 0.25/0.50 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 0.25/0.50 (step @p114 :rule implies_elim :premises (@p113)) % 0.25/0.50 (step @p115 :rule chain_m_resolution :premises (@p114 @p70) :args (@t134 @t127 (@list @t89))) % 0.25/0.50 (step @p116 :rule instantiate :premises (@p11) :args (@t135)) % 0.25/0.50 (step @p117 :rule instantiate :premises (@p9) :args (@t135)) % 0.25/0.50 (step @p118 :rule false_intro :premises (@p92)) % 0.25/0.50 (step @p97 :rule instantiate :premises (@p12) :args (@t125)) % 0.25/0.50 (step @p119 :rule refl :args (tptp.null_class)) % 0.25/0.50 (step @p120 :rule cong :premises (@p119 @p97) :args (@t136)) % 0.25/0.50 (step @p121 :rule trans :premises (@p120 @p118)) % 0.25/0.50 (step @p122 :rule false_elim :premises (@p121)) % 0.25/0.50 (step @p123 :rule cnf_or_pos :args (@t139)) % 0.25/0.50 (step @p124 :rule reordering :premises (@p123) :args ((or @t138 @t136 (not @t139)))) % 0.25/0.50 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p117) :args (@t138 (@list true false) (@list @t136 @t139))) % 0.25/0.50 (step @p126 :rule refl :args (@t140)) % 0.25/0.50 (step @p127 :rule bool-double-not-elim :args (@t137)) % 0.25/0.50 (step @p128 :rule refl :args (@t141)) % 0.25/0.50 (step @p129 :rule nary_cong :premises (@p128 @p127 @p105 @p126) :args ((or @t141 (not @t138) @t131 @t140))) % 0.25/0.50 (assume-push @p217 @t138) % 0.25/0.50 (assume-push @p218 @t133) % 0.25/0.50 (assume-push @p219 @t126) % 0.25/0.50 (assume-push @p220 @t130) % 0.25/0.50 (step @p134 :rule evaluate :args (@t142)) % 0.25/0.50 (step @p135 :rule false_intro :premises (@p125)) % 0.25/0.50 (step @p136 :rule refl :args (tptp.universal_class)) % 0.25/0.50 (step @p137 :rule symm :premises (@p218)) % 0.25/0.50 (step @p138 :rule trans :premises (@p102 @p137)) % 0.25/0.50 (step @p139 :rule cong :premises (@p138 @p136) :args ((tptp.member @t120 tptp.universal_class))) % 0.25/0.50 (step @p140 :rule cong :premises (@p97 @p136) :args (@t130)) % 0.25/0.50 (step @p141 :rule true_intro :premises (@p116)) % 0.25/0.50 (step @p142 :rule symm :premises (@p141)) % 0.25/0.50 (step @p143 :rule trans :premises (@p142 @p140 @p139 @p135)) % 0.25/0.50 (step @p144 false :rule eq_resolve :premises (@p143 @p134)) % 0.25/0.50 (step-pop @p221 :rule scope :premises (@p144)) % 0.25/0.50 (step-pop @p222 :rule scope :premises (@p221)) % 0.25/0.50 (step-pop @p223 :rule scope :premises (@p222)) % 0.25/0.50 (step-pop @p224 :rule scope :premises (@p223)) % 0.25/0.50 (step @p145 :rule process_scope :premises (@p224) :args (false)) % 0.25/0.50 (assume-push @p225 @t126) % 0.25/0.50 (assume-push @p226 @t138) % 0.25/0.50 (assume-push @p227 @t130) % 0.25/0.50 (assume-push @p228 @t133) % 0.25/0.50 (step @p154 :rule and_intro :premises (@p125 @p228 @p102 @p116)) % 0.25/0.50 (step-pop @p229 :rule scope :premises (@p154)) % 0.25/0.50 (step-pop @p230 :rule scope :premises (@p229)) % 0.25/0.50 (step-pop @p231 :rule scope :premises (@p230)) % 0.25/0.50 (step-pop @p232 :rule scope :premises (@p231)) % 0.25/0.50 (step @p155 :rule process_scope :premises (@p232) :args (@t143)) % 0.25/0.50 (step @p160 :rule implies_elim :premises (@p155)) % 0.25/0.50 (step @p161 :rule resolution :premises (@p160 @p145) :args (true @t143)) % 0.25/0.50 (step @p162 :rule not_and :premises (@p161)) % 0.25/0.50 (step @p163 :rule eq_resolve :premises (@p162 @p129)) % 0.25/0.50 (step @p164 :rule chain_m_resolution :premises (@p163 @p102 @p125 @p116) :args (@t140 @t144 (@list @t126 @t137 @t130))) % 0.25/0.50 (step @p165 :rule cnf_or_pos :args (@t134)) % 0.25/0.50 (step @p166 :rule reordering :premises (@p165) :args ((or @t131 @t129 @t133 (not @t134)))) % 0.25/0.50 (step @p167 :rule chain_m_resolution :premises (@p166 @p116 @p164 @p115) :args (@t129 @t144 (@list @t130 @t133 @t134))) % 0.25/0.50 (step @p168 :rule eq-symm :args (@t2 @t1)) % 0.25/0.50 (step @p169 :rule eq-symm :args (@t2 @t3)) % 0.25/0.50 (step @p170 :rule refl :args (@t15)) % 0.25/0.50 (step @p171 :rule nary_cong :premises (@p170 @p169 @p168) :args (@t16)) % 0.25/0.50 (step @p172 :rule cong :premises (@p171) :args (@t17)) % 0.25/0.50 (step @p173 :rule eq_resolve :premises (@p8 @p172)) % 0.25/0.50 (step @p174 :rule instantiate :premises (@p173) :args ((@list @t128 tptp.null_class tptp.null_class))) % 0.25/0.50 (step @p175 :rule cnf_or_pos :args (@t147)) % 0.25/0.50 (step @p176 :rule factoring :premises (@p175)) % 0.25/0.50 (step @p177 :rule reordering :premises (@p176) :args ((or @t146 @t145 (not @t147)))) % 0.25/0.50 (step @p178 :rule chain_m_resolution :premises (@p177 @p167 @p174) :args (@t145 (@list false false) (@list @t129 @t147))) % 0.25/0.50 (step @p179 :rule refl :args (@t148)) % 0.25/0.50 (step @p180 :rule refl :args (@t146)) % 0.25/0.50 (step @p181 :rule bool-double-not-elim :args (@t121)) % 0.25/0.50 (step @p182 :rule nary_cong :premises (@p181 @p128 @p180 @p179) :args ((or (not @t122) @t141 @t146 @t148))) % 0.25/0.50 (assume-push @p233 @t122) % 0.25/0.50 (assume-push @p234 @t145) % 0.25/0.50 (assume-push @p235 @t126) % 0.25/0.50 (assume-push @p236 @t129) % 0.25/0.50 (step @p134 :rule evaluate :args (@t142)) % 0.25/0.50 (step @p187 :rule symm :premises (@p234)) % 0.25/0.50 (step @p188 :rule cong :premises (@p187 @p97) :args (@t129)) % 0.25/0.50 (step @p189 :rule true_intro :premises (@p236)) % 0.25/0.50 (step @p190 :rule symm :premises (@p189)) % 0.25/0.50 (step @p191 :rule trans :premises (@p190 @p188 @p118)) % 0.25/0.50 (step @p192 false :rule eq_resolve :premises (@p191 @p134)) % 0.25/0.50 (step-pop @p237 :rule scope :premises (@p192)) % 0.25/0.50 (step-pop @p238 :rule scope :premises (@p237)) % 0.25/0.50 (step-pop @p239 :rule scope :premises (@p238)) % 0.25/0.50 (step-pop @p240 :rule scope :premises (@p239)) % 0.25/0.50 (step @p193 :rule process_scope :premises (@p240) :args (false)) % 0.25/0.50 (assume-push @p241 @t122) % 0.25/0.50 (assume-push @p242 @t126) % 0.25/0.50 (assume-push @p243 @t129) % 0.25/0.50 (assume-push @p244 @t145) % 0.25/0.50 (step @p202 :rule and_intro :premises (@p92 @p244 @p102 @p243)) % 0.25/0.50 (step-pop @p245 :rule scope :premises (@p202)) % 0.25/0.50 (step-pop @p246 :rule scope :premises (@p245)) % 0.25/0.50 (step-pop @p247 :rule scope :premises (@p246)) % 0.25/0.50 (step-pop @p248 :rule scope :premises (@p247)) % 0.25/0.50 (step @p203 :rule process_scope :premises (@p248) :args (@t149)) % 0.25/0.50 (step @p208 :rule implies_elim :premises (@p203)) % 0.25/0.50 (step @p209 :rule resolution :premises (@p208 @p193) :args (true @t149)) % 0.25/0.50 (step @p210 :rule not_and :premises (@p209)) % 0.25/0.50 (step @p211 :rule eq_resolve :premises (@p210 @p182)) % 0.25/0.50 (step @p212 false :rule chain_m_resolution :premises (@p211 @p178 @p167 @p102 @p92) :args (false (@list false false false true) (@list @t145 @t129 @t126 @t121))) % 0.25/0.50 ) % 0.25/0.50 % SZS output end Proof % 0.25/0.50 % cvc5 exiting %------------------------------------------------------------------------------