%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET108-7 : 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 : n014.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 08:47:25 AM UTC 2026 % Result : Unsatisfiable 0.35s 0.64s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET108-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n014.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 14:56:58 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... % 0.35/0.64 % SZS status Unsatisfiable % 0.35/0.64 % SZS output start Proof % 0.35/0.64 ( % 0.35/0.64 (declare-sort $$unsorted 0) % 0.35/0.64 (declare-const tptp.z $$unsorted) % 0.35/0.64 (declare-const tptp.member_of1 (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.member_of (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.y $$unsorted) % 0.35/0.64 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.element_relation $$unsorted) % 0.35/0.64 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.universal_class $$unsorted) % 0.35/0.64 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.successor_relation $$unsorted) % 0.35/0.64 (declare-const tptp.choice $$unsorted) % 0.35/0.64 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.subset_relation $$unsorted) % 0.35/0.64 (declare-const tptp.null_class $$unsorted) % 0.35/0.64 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.omega $$unsorted) % 0.35/0.64 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.64 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.identity_relation $$unsorted) % 0.35/0.64 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.35/0.64 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.35/0.64 (define @t1 () (@var "Y" $$unsorted)) % 0.35/0.64 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.64 (define @t3 () (@var "X" $$unsorted)) % 0.35/0.64 (define @t4 () (tptp.member @t2 @t3)) % 0.35/0.64 (define @t5 () (not @t4)) % 0.35/0.64 (define @t6 () (tptp.subclass @t3 @t1)) % 0.35/0.64 (define @t7 () (not @t6)) % 0.35/0.64 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.35/0.64 (define @t9 () (tptp.member @t8 @t3)) % 0.35/0.64 (define @t10 () (@list @t3 @t1)) % 0.35/0.64 (define @t11 () (not (tptp.member @t8 @t1))) % 0.35/0.64 (define @t12 () (@list @t3)) % 0.35/0.64 (define @t13 () (= @t3 @t1)) % 0.35/0.64 (define @t14 () (not @t13)) % 0.35/0.64 (define @t15 () (tptp.subclass @t1 @t3)) % 0.35/0.64 (define @t16 () (tptp.unordered_pair @t3 @t1)) % 0.35/0.64 (define @t17 () (tptp.member @t3 @t16)) % 0.35/0.64 (define @t18 () (tptp.member @t3 tptp.universal_class)) % 0.35/0.64 (define @t19 () (not @t18)) % 0.35/0.64 (define @t20 () (tptp.member @t1 @t16)) % 0.35/0.64 (define @t21 () (tptp.member @t1 tptp.universal_class)) % 0.35/0.64 (define @t22 () (not @t21)) % 0.35/0.64 (define @t23 () (@list @t1 @t3)) % 0.35/0.64 (define @t24 () (tptp.singleton @t3)) % 0.35/0.64 (define @t25 () (tptp.ordered_pair @t3 @t1)) % 0.35/0.64 (define @t26 () (tptp.singleton @t1)) % 0.35/0.64 (define @t27 () (tptp.unordered_pair @t3 @t26)) % 0.35/0.64 (define @t28 () (tptp.cross_product @t3 @t1)) % 0.35/0.64 (define @t29 () (@var "V" $$unsorted)) % 0.35/0.64 (define @t30 () (tptp.ordered_pair @t2 @t29)) % 0.35/0.64 (define @t31 () (tptp.member @t30 @t28)) % 0.35/0.64 (define @t32 () (not @t31)) % 0.35/0.64 (define @t33 () (@list @t2 @t29 @t3 @t1)) % 0.35/0.64 (define @t34 () (tptp.member @t29 @t1)) % 0.35/0.64 (define @t35 () (@var "Z" $$unsorted)) % 0.35/0.64 (define @t36 () (tptp.ordered_pair (tptp.first @t35) (tptp.second @t35))) % 0.35/0.64 (define @t37 () (not (tptp.member @t35 @t28))) % 0.35/0.64 (define @t38 () (or @t37 (= @t36 @t35))) % 0.35/0.64 (define @t39 () (@list @t35 @t3 @t1)) % 0.35/0.64 (define @t40 () (forall @t39 @t38)) % 0.35/0.64 (define @t41 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.35/0.64 (define @t42 () (tptp.member @t3 @t1)) % 0.35/0.64 (define @t43 () (tptp.member @t25 tptp.element_relation)) % 0.35/0.64 (define @t44 () (not @t42)) % 0.35/0.64 (define @t45 () (not (tptp.member @t25 @t41))) % 0.35/0.64 (define @t46 () (tptp.member @t35 @t3)) % 0.35/0.64 (define @t47 () (tptp.intersection @t3 @t1)) % 0.35/0.64 (define @t48 () (tptp.member @t35 @t47)) % 0.35/0.64 (define @t49 () (not @t48)) % 0.35/0.64 (define @t50 () (tptp.member @t35 @t1)) % 0.35/0.64 (define @t51 () (not @t46)) % 0.35/0.64 (define @t52 () (tptp.complement @t3)) % 0.35/0.64 (define @t53 () (tptp.member @t35 @t52)) % 0.35/0.64 (define @t54 () (@list @t35 @t3)) % 0.35/0.64 (define @t55 () (not (tptp.member @t35 tptp.universal_class))) % 0.35/0.64 (define @t56 () (tptp.complement (tptp.intersection @t52 (tptp.complement @t1)))) % 0.35/0.64 (define @t57 () (@var "Xr" $$unsorted)) % 0.35/0.64 (define @t58 () (tptp.restrict @t57 @t3 @t1)) % 0.35/0.64 (define @t59 () (tptp.domain_of @t3)) % 0.35/0.64 (define @t60 () (tptp.member @t35 @t59)) % 0.35/0.64 (define @t61 () (= (tptp.restrict @t3 (tptp.singleton @t35) tptp.universal_class) tptp.null_class)) % 0.35/0.64 (define @t62 () (tptp.cross_product @t41 tptp.universal_class)) % 0.35/0.64 (define @t63 () (tptp.rotate @t3)) % 0.35/0.64 (define @t64 () (@var "W" $$unsorted)) % 0.35/0.64 (define @t65 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t29 @t64) @t2) @t3)) % 0.35/0.64 (define @t66 () (tptp.ordered_pair @t30 @t64)) % 0.35/0.64 (define @t67 () (tptp.member @t66 @t63)) % 0.35/0.64 (define @t68 () (@list @t2 @t29 @t64 @t3)) % 0.35/0.64 (define @t69 () (not (tptp.member @t66 @t62))) % 0.35/0.64 (define @t70 () (tptp.flip @t3)) % 0.35/0.64 (define @t71 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t29 @t2) @t64) @t3)) % 0.35/0.64 (define @t72 () (tptp.member @t66 @t70)) % 0.35/0.64 (define @t73 () (@list @t1)) % 0.35/0.64 (define @t74 () (@list @t35)) % 0.35/0.64 (define @t75 () (tptp.successor @t3)) % 0.35/0.64 (define @t76 () (= @t75 @t1)) % 0.35/0.64 (define @t77 () (tptp.member @t25 tptp.successor_relation)) % 0.35/0.64 (define @t78 () (tptp.member tptp.null_class @t3)) % 0.35/0.64 (define @t79 () (tptp.inductive @t3)) % 0.35/0.64 (define @t80 () (not @t79)) % 0.35/0.64 (define @t81 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.35/0.64 (define @t82 () (tptp.sum_class @t3)) % 0.35/0.64 (define @t83 () (tptp.member @t2 tptp.universal_class)) % 0.35/0.64 (define @t84 () (not @t83)) % 0.35/0.64 (define @t85 () (@list @t2)) % 0.35/0.64 (define @t86 () (@var "Yr" $$unsorted)) % 0.35/0.64 (define @t87 () (tptp.compose @t86 @t57)) % 0.35/0.64 (define @t88 () (tptp.member @t35 (tptp.image @t86 (tptp.image @t57 @t26)))) % 0.35/0.64 (define @t89 () (tptp.ordered_pair @t1 @t35)) % 0.35/0.64 (define @t90 () (tptp.member @t89 @t87)) % 0.35/0.64 (define @t91 () (not (tptp.member @t89 @t41))) % 0.35/0.64 (define @t92 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.35/0.64 (define @t93 () (tptp.single_valued_class @t3)) % 0.35/0.64 (define @t94 () (@var "Xf" $$unsorted)) % 0.35/0.64 (define @t95 () (tptp.subclass @t94 @t41)) % 0.35/0.64 (define @t96 () (tptp.function @t94)) % 0.35/0.64 (define @t97 () (not @t96)) % 0.35/0.64 (define @t98 () (@list @t94)) % 0.35/0.64 (define @t99 () (tptp.inverse @t94)) % 0.35/0.64 (define @t100 () (tptp.subclass (tptp.compose @t94 @t99) tptp.identity_relation)) % 0.35/0.64 (define @t101 () (tptp.regular @t3)) % 0.35/0.64 (define @t102 () (= @t3 tptp.null_class)) % 0.35/0.64 (define @t103 () (tptp.one_to_one @t94)) % 0.35/0.64 (define @t104 () (not @t103)) % 0.35/0.64 (define @t105 () (tptp.function @t99)) % 0.35/0.64 (define @t106 () (tptp.inverse tptp.element_relation)) % 0.35/0.64 (define @t107 () (tptp.operation @t94)) % 0.35/0.64 (define @t108 () (not @t107)) % 0.35/0.64 (define @t109 () (tptp.domain_of @t94)) % 0.35/0.64 (define @t110 () (tptp.domain_of @t109)) % 0.35/0.64 (define @t111 () (= (tptp.cross_product @t110 @t110) @t109)) % 0.35/0.64 (define @t112 () (tptp.subclass (tptp.range_of @t94) @t110)) % 0.35/0.64 (define @t113 () (@var "Xh" $$unsorted)) % 0.35/0.64 (define @t114 () (tptp.function @t113)) % 0.35/0.64 (define @t115 () (@var "Xf2" $$unsorted)) % 0.35/0.64 (define @t116 () (@var "Xf1" $$unsorted)) % 0.35/0.64 (define @t117 () (tptp.compatible @t113 @t116 @t115)) % 0.35/0.64 (define @t118 () (not @t117)) % 0.35/0.64 (define @t119 () (@list @t113 @t116 @t115)) % 0.35/0.64 (define @t120 () (tptp.domain_of @t116)) % 0.35/0.64 (define @t121 () (= (tptp.domain_of @t120) (tptp.domain_of @t113))) % 0.35/0.64 (define @t122 () (tptp.subclass (tptp.range_of @t113) (tptp.domain_of (tptp.domain_of @t115)))) % 0.35/0.64 (define @t123 () (tptp.operation @t116)) % 0.35/0.64 (define @t124 () (tptp.homomorphism @t113 @t116 @t115)) % 0.35/0.64 (define @t125 () (not @t124)) % 0.35/0.64 (define @t126 () (tptp.operation @t115)) % 0.35/0.64 (define @t127 () (tptp.not_homomorphism2 @t113 @t116 @t115)) % 0.35/0.64 (define @t128 () (tptp.not_homomorphism1 @t113 @t116 @t115)) % 0.35/0.64 (define @t129 () (tptp.ordered_pair @t128 @t127)) % 0.35/0.64 (define @t130 () (not @t126)) % 0.35/0.64 (define @t131 () (not @t123)) % 0.35/0.64 (define @t132 () (@list @t116 @t115 @t113)) % 0.35/0.64 (define @t133 () (not (tptp.member @t25 (tptp.cross_product @t2 @t29)))) % 0.35/0.64 (define @t134 () (@list @t3 @t1 @t2 @t29)) % 0.35/0.64 (define @t135 () (@list @t3 @t1 @t35)) % 0.35/0.64 (define @t136 () (tptp.not_subclass_element @t1 @t3)) % 0.35/0.64 (define @t137 () (tptp.member @t136 @t1)) % 0.35/0.64 (define @t138 () (not (tptp.member @t136 @t3))) % 0.35/0.64 (define @t139 () (= @t16 tptp.null_class)) % 0.35/0.64 (define @t140 () (tptp.unordered_pair @t3 @t35)) % 0.35/0.64 (define @t141 () (tptp.unordered_pair @t1 @t35)) % 0.35/0.64 (define @t142 () (@list @t3 @t35 @t1)) % 0.35/0.64 (define @t143 () (not @t139)) % 0.35/0.64 (define @t144 () (= @t24 tptp.null_class)) % 0.35/0.64 (define @t145 () (tptp.singleton tptp.null_class)) % 0.35/0.64 (define @t146 () (not (= @t24 @t26))) % 0.35/0.64 (define @t147 () (= @t3 @t35)) % 0.35/0.64 (define @t148 () (tptp.member_of @t26)) % 0.35/0.64 (define @t149 () (tptp.member_of @t3)) % 0.35/0.64 (define @t150 () (= @t149 @t3)) % 0.35/0.64 (define @t151 () (= (tptp.singleton @t149) @t3)) % 0.35/0.64 (define @t152 () (tptp.member_of1 @t3)) % 0.35/0.64 (define @t153 () (not @t151)) % 0.35/0.64 (define @t154 () (tptp.not_subclass_element @t3 tptp.null_class)) % 0.35/0.64 (define @t155 () (tptp.singleton @t154)) % 0.35/0.64 (define @t156 () (= @t155 @t3)) % 0.35/0.64 (define @t157 () (tptp.intersection (tptp.complement @t155) @t3)) % 0.35/0.64 (define @t158 () (tptp.not_subclass_element @t157 tptp.null_class)) % 0.35/0.64 (define @t159 () (not (= (tptp.ordered_pair @t64 @t3) @t89))) % 0.35/0.64 (define @t160 () (@list @t64 @t3 @t1 @t35)) % 0.35/0.64 (define @t161 () (tptp.ordered_pair tptp.y tptp.z)) % 0.35/0.64 (define @t162 () (tptp.member @t161 @t41)) % 0.35/0.64 (define @t163 () (tptp.ordered_pair (tptp.first @t161) (tptp.second @t161))) % 0.35/0.64 (define @t164 () (= @t161 @t163)) % 0.35/0.64 (define @t165 () (not @t162)) % 0.35/0.64 (define @t166 () (or @t165 @t164)) % 0.35/0.64 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.35/0.64 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.35/0.64 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.35/0.64 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.35/0.64 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.35/0.64 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.35/0.64 (assume @p7 (forall @t10 (or @t7 (not @t15) @t13))) % 0.35/0.64 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t16)) (= @t2 @t3) (= @t2 @t1)))) % 0.35/0.64 (assume @p9 (forall @t10 (or @t19 @t17))) % 0.35/0.64 (assume @p10 (forall @t23 (or @t22 @t20))) % 0.35/0.64 (assume @p11 (forall @t10 (tptp.member @t16 tptp.universal_class))) % 0.35/0.64 (assume @p12 (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t24))) % 0.35/0.64 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t24 @t27) @t25))) % 0.35/0.64 (assume @p14 (forall @t33 (or @t32 @t4))) % 0.35/0.64 (assume @p15 (forall @t33 (or @t32 @t34))) % 0.35/0.64 (assume @p16 (forall (@list @t2 @t3 @t29 @t1) (or @t5 (not @t34) @t31))) % 0.35/0.64 (assume @p17 @t40) % 0.35/0.64 (assume @p18 (tptp.subclass tptp.element_relation @t41)) % 0.35/0.64 (assume @p19 (forall @t10 (or (not @t43) @t42))) % 0.35/0.64 (assume @p20 (forall @t10 (or @t45 @t44 @t43))) % 0.35/0.64 (assume @p21 (forall @t39 (or @t49 @t46))) % 0.35/0.64 (assume @p22 (forall @t39 (or @t49 @t50))) % 0.35/0.64 (assume @p23 (forall @t39 (or @t51 (not @t50) @t48))) % 0.35/0.64 (assume @p24 (forall @t54 (or (not @t53) @t51))) % 0.35/0.64 (assume @p25 (forall @t54 (or @t55 @t53 @t46))) % 0.35/0.64 (assume @p26 (forall @t10 (= @t56 (tptp.union @t3 @t1)))) % 0.35/0.64 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t47) @t56) (tptp.symmetric_difference @t3 @t1)))) % 0.35/0.64 (assume @p28 (forall (@list @t57 @t3 @t1) (= (tptp.intersection @t57 @t28) @t58))) % 0.35/0.64 (assume @p29 (forall (@list @t3 @t1 @t57) (= (tptp.intersection @t28 @t57) @t58))) % 0.35/0.64 (assume @p30 (forall (@list @t3 @t35) (or (not @t61) (not @t60)))) % 0.35/0.64 (assume @p31 (forall @t54 (or @t55 @t61 @t60))) % 0.35/0.64 (assume @p32 (forall @t12 (tptp.subclass @t63 @t62))) % 0.35/0.64 (assume @p33 (forall @t68 (or (not @t67) @t65))) % 0.35/0.64 (assume @p34 (forall (@list @t29 @t64 @t2 @t3) (or (not @t65) @t69 @t67))) % 0.35/0.64 (assume @p35 (forall @t12 (tptp.subclass @t70 @t62))) % 0.35/0.64 (assume @p36 (forall @t68 (or (not @t72) @t71))) % 0.35/0.64 (assume @p37 (forall (@list @t29 @t2 @t64 @t3) (or (not @t71) @t69 @t72))) % 0.35/0.64 (assume @p38 (forall @t73 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.35/0.64 (assume @p39 (forall @t74 (= (tptp.domain_of (tptp.inverse @t35)) (tptp.range_of @t35)))) % 0.35/0.64 (assume @p40 (forall @t39 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t35 @t3 @t26) tptp.null_class)) (tptp.domain @t35 @t3 @t1)))) % 0.35/0.64 (assume @p41 (forall @t39 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t35 @t24 @t1) tptp.null_class)) (tptp.range @t35 @t3 @t1)))) % 0.35/0.64 (assume @p42 (forall (@list @t57 @t3) (= (tptp.range_of (tptp.restrict @t57 @t3 tptp.universal_class)) (tptp.image @t57 @t3)))) % 0.35/0.64 (assume @p43 (forall @t12 (= (tptp.union @t3 @t24) @t75))) % 0.35/0.64 (assume @p44 (tptp.subclass tptp.successor_relation @t41)) % 0.35/0.64 (assume @p45 (forall @t10 (or (not @t77) @t76))) % 0.35/0.64 (assume @p46 (forall @t10 (or (not @t76) @t45 @t77))) % 0.35/0.64 (assume @p47 (forall @t12 (or @t80 @t78))) % 0.35/0.64 (assume @p48 (forall @t12 (or @t80 @t81))) % 0.35/0.64 (assume @p49 (forall @t12 (or (not @t78) (not @t81) @t79))) % 0.35/0.64 (assume @p50 (tptp.inductive tptp.omega)) % 0.35/0.64 (assume @p51 (forall @t73 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.35/0.64 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.35/0.64 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t82))) % 0.35/0.64 (assume @p54 (forall @t12 (or @t19 (tptp.member @t82 tptp.universal_class)))) % 0.35/0.64 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t52)) (tptp.power_class @t3)))) % 0.35/0.64 (assume @p56 (forall @t85 (or @t84 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.35/0.64 (assume @p57 (forall (@list @t86 @t57) (tptp.subclass @t87 @t41))) % 0.35/0.64 (assume @p58 (forall (@list @t1 @t35 @t86 @t57) (or (not @t90) @t88))) % 0.35/0.64 (assume @p59 (forall (@list @t35 @t86 @t57 @t1) (or (not @t88) @t91 @t90))) % 0.35/0.64 (assume @p60 (forall @t12 (or (not @t93) @t92))) % 0.35/0.64 (assume @p61 (forall @t12 (or (not @t92) @t93))) % 0.35/0.64 (assume @p62 (forall @t98 (or @t97 @t95))) % 0.35/0.64 (assume @p63 (forall @t98 (or @t97 @t100))) % 0.35/0.64 (assume @p64 (forall @t98 (or (not @t95) (not @t100) @t96))) % 0.35/0.64 (assume @p65 (forall (@list @t94 @t3) (or @t97 @t19 (tptp.member (tptp.image @t94 @t3) tptp.universal_class)))) % 0.35/0.64 (assume @p66 (forall @t12 (or @t102 (tptp.member @t101 @t3)))) % 0.35/0.64 (assume @p67 (forall @t12 (or @t102 (= (tptp.intersection @t3 @t101) tptp.null_class)))) % 0.35/0.64 (assume @p68 (forall (@list @t94 @t1) (= (tptp.sum_class (tptp.image @t94 @t26)) (tptp.apply @t94 @t1)))) % 0.35/0.64 (assume @p69 (tptp.function tptp.choice)) % 0.35/0.64 (assume @p70 (forall @t73 (or @t22 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.35/0.64 (assume @p71 (forall @t98 (or @t104 @t96))) % 0.35/0.64 (assume @p72 (forall @t98 (or @t104 @t105))) % 0.35/0.64 (assume @p73 (forall @t98 (or (not @t105) @t97 @t103))) % 0.35/0.64 (assume @p74 (= (tptp.intersection @t41 (tptp.intersection @t41 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t106)))) tptp.subset_relation)) % 0.35/0.64 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.35/0.64 (assume @p76 (forall (@list @t57) (= (tptp.complement (tptp.domain_of (tptp.intersection @t57 tptp.identity_relation))) (tptp.diagonalise @t57)))) % 0.35/0.64 (assume @p77 (forall @t12 (= (tptp.intersection @t59 (tptp.diagonalise (tptp.compose @t106 @t3))) (tptp.cantor @t3)))) % 0.35/0.64 (assume @p78 (forall @t98 (or @t108 @t96))) % 0.35/0.64 (assume @p79 (forall @t98 (or @t108 @t111))) % 0.35/0.64 (assume @p80 (forall @t98 (or @t108 @t112))) % 0.35/0.64 (assume @p81 (forall @t98 (or @t97 (not @t111) (not @t112) @t107))) % 0.35/0.64 (assume @p82 (forall @t119 (or @t118 @t114))) % 0.35/0.64 (assume @p83 (forall @t119 (or @t118 @t121))) % 0.35/0.64 (assume @p84 (forall @t119 (or @t118 @t122))) % 0.35/0.64 (assume @p85 (forall @t119 (or (not @t114) (not @t121) (not @t122) @t117))) % 0.35/0.64 (assume @p86 (forall @t119 (or @t125 @t123))) % 0.35/0.64 (assume @p87 (forall @t119 (or @t125 @t126))) % 0.35/0.64 (assume @p88 (forall @t119 (or @t125 @t117))) % 0.35/0.64 (assume @p89 (forall (@list @t113 @t116 @t115 @t3 @t1) (or @t125 (not (tptp.member @t25 @t120)) (= (tptp.apply @t115 (tptp.ordered_pair (tptp.apply @t113 @t3) (tptp.apply @t113 @t1))) (tptp.apply @t113 (tptp.apply @t116 @t25)))))) % 0.35/0.64 (assume @p90 (forall @t132 (or @t131 @t130 @t118 (tptp.member @t129 @t120) @t124))) % 0.35/0.64 (assume @p91 (forall @t132 (or @t131 @t130 @t118 (not (= (tptp.apply @t115 (tptp.ordered_pair (tptp.apply @t113 @t128) (tptp.apply @t113 @t127))) (tptp.apply @t113 (tptp.apply @t116 @t129)))) @t124))) % 0.35/0.64 (assume @p92 (forall @t134 (or @t133 @t17))) % 0.35/0.64 (assume @p93 (forall @t134 (or @t133 @t20))) % 0.35/0.64 (assume @p94 (forall @t33 (or @t32 @t83))) % 0.35/0.64 (assume @p95 (forall @t33 (or @t32 (tptp.member @t29 tptp.universal_class)))) % 0.35/0.64 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.35/0.64 (assume @p97 (forall @t135 (or @t7 (not (tptp.subclass @t1 @t35)) (tptp.subclass @t3 @t35)))) % 0.35/0.64 (assume @p98 (forall @t10 (or @t13 @t9 @t137))) % 0.35/0.64 (assume @p99 (forall @t10 (or @t11 @t13 @t137))) % 0.35/0.64 (assume @p100 (forall @t23 (or @t138 @t13 @t9))) % 0.35/0.64 (assume @p101 (forall @t10 (or @t11 @t138 @t13))) % 0.35/0.64 (assume @p102 (forall @t23 (not (tptp.member @t1 (tptp.intersection @t52 @t3))))) % 0.35/0.64 (assume @p103 (forall @t74 (not (tptp.member @t35 tptp.null_class)))) % 0.35/0.64 (assume @p104 (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.35/0.64 (assume @p105 (forall @t12 (or (not (tptp.subclass @t3 tptp.null_class)) @t102))) % 0.35/0.64 (assume @p106 (forall @t74 (or (= @t35 tptp.null_class) (tptp.member (tptp.not_subclass_element @t35 tptp.null_class) @t35)))) % 0.35/0.64 (assume @p107 (tptp.member tptp.null_class tptp.universal_class)) % 0.35/0.64 (assume @p108 (forall @t10 (= @t16 (tptp.unordered_pair @t1 @t3)))) % 0.35/0.64 (assume @p109 (forall @t10 (tptp.subclass @t24 @t16))) % 0.35/0.64 (assume @p110 (forall @t23 (tptp.subclass @t26 @t16))) % 0.35/0.64 (assume @p111 (forall @t23 (or @t21 (= @t16 @t24)))) % 0.35/0.64 (assume @p112 (forall @t10 (or @t18 (= @t16 @t26)))) % 0.35/0.64 (assume @p113 (forall @t10 (or @t139 @t18 @t21))) % 0.35/0.64 (assume @p114 (forall @t135 (or (not (= @t16 @t140)) @t91 (= @t1 @t35)))) % 0.35/0.64 (assume @p115 (forall @t142 (or (not (= @t140 @t141)) @t45 @t13))) % 0.35/0.64 (assume @p116 (forall @t10 (or @t19 @t143))) % 0.35/0.64 (assume @p117 (forall @t23 (or @t22 @t143))) % 0.35/0.64 (assume @p118 (forall @t134 (or @t133 @t143))) % 0.35/0.64 (assume @p119 (forall @t142 (or (not (tptp.member @t3 @t35)) (not (tptp.member @t1 @t35)) (tptp.subclass @t16 @t35)))) % 0.35/0.64 (assume @p120 (forall @t12 (tptp.member @t24 tptp.universal_class))) % 0.35/0.64 (assume @p121 (forall @t23 (tptp.member @t26 @t27))) % 0.35/0.64 (assume @p122 (forall @t12 (or @t19 (tptp.member @t3 @t24)))) % 0.35/0.64 (assume @p123 (forall @t12 (or @t19 (not @t144)))) % 0.35/0.64 (assume @p124 (tptp.member tptp.null_class @t145)) % 0.35/0.64 (assume @p125 (forall @t23 (or (not (tptp.member @t1 @t24)) (= @t1 @t3)))) % 0.35/0.64 (assume @p126 (forall @t12 (or @t18 @t144))) % 0.35/0.64 (assume @p127 (forall @t10 (or @t146 @t19 @t13))) % 0.35/0.64 (assume @p128 (forall @t10 (or @t146 @t22 @t13))) % 0.35/0.64 (assume @p129 (forall (@list @t1 @t35 @t3) (or (not (= @t141 @t24)) @t19 @t13 @t147))) % 0.35/0.64 (assume @p130 (forall @t73 (or @t22 (tptp.member @t148 tptp.universal_class)))) % 0.35/0.64 (assume @p131 (forall @t73 (or @t22 (= (tptp.singleton @t148) @t26)))) % 0.35/0.64 (assume @p132 (forall @t12 (or (tptp.member @t149 tptp.universal_class) @t150))) % 0.35/0.64 (assume @p133 (forall @t12 (or @t151 @t150))) % 0.35/0.64 (assume @p134 (forall @t85 (or @t84 (= (tptp.member_of (tptp.singleton @t2)) @t2)))) % 0.35/0.64 (assume @p135 (forall @t12 (or (tptp.member @t152 tptp.universal_class) @t150))) % 0.35/0.64 (assume @p136 (forall @t12 (or (= (tptp.singleton @t152) @t3) @t150))) % 0.35/0.64 (assume @p137 (forall @t12 (or @t153 @t18))) % 0.35/0.64 (assume @p138 (forall @t10 (or @t153 (not (tptp.member @t1 @t3)) (= @t149 @t1)))) % 0.35/0.64 (assume @p139 (forall @t10 (or @t44 (tptp.subclass @t24 @t1)))) % 0.35/0.64 (assume @p140 (forall @t10 (or (not (tptp.subclass @t3 @t26)) @t102 (= @t26 @t3)))) % 0.35/0.64 (assume @p141 (forall @t12 (or (tptp.member @t158 @t157) @t156 @t102))) % 0.35/0.64 (assume @p142 (forall @t12 (or (tptp.member @t158 @t3) @t156 @t102))) % 0.35/0.64 (assume @p143 (forall @t12 (or (not (= @t158 @t154)) @t156 @t102))) % 0.35/0.64 (assume @p144 (forall @t10 (= @t16 (tptp.union @t24 @t26)))) % 0.35/0.64 (assume @p145 (forall @t10 (tptp.member @t25 tptp.universal_class))) % 0.35/0.64 (assume @p146 (forall @t10 (tptp.member @t24 @t25))) % 0.35/0.64 (assume @p147 (forall @t10 (tptp.member @t27 @t25))) % 0.35/0.64 (assume @p148 (forall @t10 (or (= (tptp.unordered_pair @t24 (tptp.unordered_pair @t3 tptp.null_class)) @t25) @t21))) % 0.35/0.64 (assume @p149 (forall @t23 (or @t22 (= (tptp.unordered_pair tptp.null_class (tptp.singleton @t26)) @t25) @t18))) % 0.35/0.64 (assume @p150 (forall @t10 (or (= (tptp.unordered_pair tptp.null_class @t145) @t25) @t18 @t21))) % 0.35/0.64 (assume @p151 (forall @t160 (or @t159 (not (tptp.member @t64 tptp.universal_class)) (= @t64 @t1)))) % 0.35/0.64 (assume @p152 (forall @t160 (or @t159 @t19 @t147))) % 0.35/0.64 (assume @p153 @t162) % 0.35/0.64 (assume @p154 (not (tptp.member @t163 @t41))) % 0.35/0.64 (step @p155 :rule evaluate :args ((= true false))) % 0.35/0.64 (step @p156 :rule false_intro :premises (@p154)) % 0.35/0.64 (step @p157 :rule refl :args (@t41)) % 0.35/0.64 (step @p158 :rule eq-symm :args (@t36 @t35)) % 0.35/0.64 (step @p159 :rule refl :args (@t37)) % 0.35/0.64 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t38)) % 0.35/0.64 (step @p161 :rule cong :premises (@p160) :args (@t40)) % 0.35/0.64 (step @p162 :rule eq_resolve :premises (@p17 @p161)) % 0.35/0.64 (step @p163 :rule instantiate :premises (@p162) :args ((@list @t161 tptp.universal_class tptp.universal_class))) % 0.35/0.64 (step @p164 :rule cnf_or_pos :args (@t166)) % 0.35/0.64 (step @p165 :rule reordering :premises (@p164) :args ((or @t165 @t164 (not @t166)))) % 0.35/0.64 (step @p166 :rule chain_m_resolution :premises (@p165 @p153 @p163) :args (@t164 (@list false false) (@list @t162 @t166))) % 0.35/0.64 (step @p167 :rule cong :premises (@p166 @p157) :args (@t162)) % 0.35/0.64 (step @p168 :rule true_intro :premises (@p153)) % 0.35/0.64 (step @p169 :rule symm :premises (@p168)) % 0.35/0.64 (step @p170 :rule trans :premises (@p169 @p167 @p156)) % 0.35/0.64 (step @p171 false :rule eq_resolve :premises (@p170 @p155)) % 0.35/0.64 ) % 0.35/0.64 % SZS output end Proof % 0.35/0.65 % cvc5 exiting %------------------------------------------------------------------------------