%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET232-6 : 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 : n006.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 08:47:41 AM UTC 2026 % Result : Unsatisfiable 0.37s 0.74s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET232-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n006.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 15:13:04 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.29/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.74 % SZS status Unsatisfiable % 0.37/0.74 % SZS output start Proof % 0.37/0.75 ( % 0.37/0.75 (declare-sort $$unsorted 0) % 0.37/0.75 (declare-const tptp.y $$unsorted) % 0.37/0.75 (declare-const tptp.z $$unsorted) % 0.37/0.75 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.application_function $$unsorted) % 0.37/0.75 (declare-const tptp.singleton_relation $$unsorted) % 0.37/0.75 (declare-const tptp.x $$unsorted) % 0.37/0.75 (declare-const tptp.single_valued1 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.single_valued3 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.element_relation $$unsorted) % 0.37/0.75 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.single_valued2 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.universal_class $$unsorted) % 0.37/0.75 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.successor_relation $$unsorted) % 0.37/0.75 (declare-const tptp.choice $$unsorted) % 0.37/0.75 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.subset_relation $$unsorted) % 0.37/0.75 (declare-const tptp.null_class $$unsorted) % 0.37/0.75 (declare-const tptp.compose_class (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.omega $$unsorted) % 0.37/0.75 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.composition_function $$unsorted) % 0.37/0.75 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.identity_relation $$unsorted) % 0.37/0.75 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.domain_relation $$unsorted) % 0.37/0.75 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.37/0.75 (define @t1 () (@var "Y" $$unsorted)) % 0.37/0.75 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.75 (define @t3 () (@var "X" $$unsorted)) % 0.37/0.75 (define @t4 () (tptp.member @t2 @t3)) % 0.37/0.75 (define @t5 () (not @t4)) % 0.37/0.75 (define @t6 () (tptp.subclass @t3 @t1)) % 0.37/0.75 (define @t7 () (not @t6)) % 0.37/0.75 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.37/0.75 (define @t9 () (@list @t3 @t1)) % 0.37/0.75 (define @t10 () (@list @t3)) % 0.37/0.75 (define @t11 () (= @t3 @t1)) % 0.37/0.75 (define @t12 () (not @t11)) % 0.37/0.75 (define @t13 () (tptp.subclass @t1 @t3)) % 0.37/0.75 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.37/0.75 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 0.37/0.75 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 0.37/0.75 (define @t17 () (tptp.singleton @t3)) % 0.37/0.75 (define @t18 () (tptp.ordered_pair @t3 @t1)) % 0.37/0.75 (define @t19 () (tptp.singleton @t1)) % 0.37/0.75 (define @t20 () (tptp.cross_product @t3 @t1)) % 0.37/0.75 (define @t21 () (@var "V" $$unsorted)) % 0.37/0.75 (define @t22 () (tptp.ordered_pair @t2 @t21)) % 0.37/0.75 (define @t23 () (tptp.member @t22 @t20)) % 0.37/0.75 (define @t24 () (not @t23)) % 0.37/0.75 (define @t25 () (@list @t2 @t21 @t3 @t1)) % 0.37/0.75 (define @t26 () (tptp.member @t21 @t1)) % 0.37/0.75 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.75 (define @t28 () (tptp.ordered_pair (tptp.first @t27) (tptp.second @t27))) % 0.37/0.75 (define @t29 () (not (tptp.member @t27 @t20))) % 0.37/0.75 (define @t30 () (or @t29 (= @t28 @t27))) % 0.37/0.75 (define @t31 () (@list @t27 @t3 @t1)) % 0.37/0.75 (define @t32 () (forall @t31 @t30)) % 0.37/0.75 (define @t33 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.37/0.75 (define @t34 () (tptp.member @t3 @t1)) % 0.37/0.75 (define @t35 () (tptp.member @t18 tptp.element_relation)) % 0.37/0.75 (define @t36 () (not (tptp.member @t18 @t33))) % 0.37/0.75 (define @t37 () (tptp.member @t27 @t3)) % 0.37/0.75 (define @t38 () (tptp.intersection @t3 @t1)) % 0.37/0.75 (define @t39 () (tptp.member @t27 @t38)) % 0.37/0.75 (define @t40 () (not @t39)) % 0.37/0.75 (define @t41 () (tptp.member @t27 @t1)) % 0.37/0.75 (define @t42 () (not @t37)) % 0.37/0.75 (define @t43 () (tptp.complement @t3)) % 0.37/0.75 (define @t44 () (tptp.member @t27 @t43)) % 0.37/0.75 (define @t45 () (@list @t27 @t3)) % 0.37/0.75 (define @t46 () (not (tptp.member @t27 tptp.universal_class))) % 0.37/0.75 (define @t47 () (tptp.complement (tptp.intersection @t43 (tptp.complement @t1)))) % 0.37/0.75 (define @t48 () (@var "Xr" $$unsorted)) % 0.37/0.75 (define @t49 () (tptp.restrict @t48 @t3 @t1)) % 0.37/0.75 (define @t50 () (tptp.domain_of @t3)) % 0.37/0.75 (define @t51 () (tptp.member @t27 @t50)) % 0.37/0.75 (define @t52 () (= (tptp.restrict @t3 (tptp.singleton @t27) tptp.universal_class) tptp.null_class)) % 0.37/0.75 (define @t53 () (tptp.cross_product @t33 tptp.universal_class)) % 0.37/0.75 (define @t54 () (tptp.rotate @t3)) % 0.37/0.75 (define @t55 () (@var "W" $$unsorted)) % 0.37/0.75 (define @t56 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t55) @t2) @t3)) % 0.37/0.75 (define @t57 () (tptp.ordered_pair @t22 @t55)) % 0.37/0.75 (define @t58 () (tptp.member @t57 @t54)) % 0.37/0.75 (define @t59 () (@list @t2 @t21 @t55 @t3)) % 0.37/0.75 (define @t60 () (not (tptp.member @t57 @t53))) % 0.37/0.75 (define @t61 () (tptp.flip @t3)) % 0.37/0.75 (define @t62 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t55) @t3)) % 0.37/0.75 (define @t63 () (tptp.member @t57 @t61)) % 0.37/0.75 (define @t64 () (@list @t1)) % 0.37/0.75 (define @t65 () (tptp.successor @t3)) % 0.37/0.75 (define @t66 () (= @t65 @t1)) % 0.37/0.75 (define @t67 () (tptp.member @t18 tptp.successor_relation)) % 0.37/0.75 (define @t68 () (tptp.member tptp.null_class @t3)) % 0.37/0.75 (define @t69 () (tptp.inductive @t3)) % 0.37/0.75 (define @t70 () (not @t69)) % 0.37/0.75 (define @t71 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.37/0.75 (define @t72 () (tptp.sum_class @t3)) % 0.37/0.75 (define @t73 () (@var "Yr" $$unsorted)) % 0.37/0.75 (define @t74 () (tptp.compose @t73 @t48)) % 0.37/0.75 (define @t75 () (tptp.member @t27 (tptp.image @t73 (tptp.image @t48 @t19)))) % 0.37/0.75 (define @t76 () (tptp.ordered_pair @t1 @t27)) % 0.37/0.75 (define @t77 () (tptp.member @t76 @t74)) % 0.37/0.75 (define @t78 () (not (tptp.member @t76 @t33))) % 0.37/0.75 (define @t79 () (tptp.inverse @t3)) % 0.37/0.75 (define @t80 () (tptp.compose @t3 @t79)) % 0.37/0.75 (define @t81 () (tptp.subclass @t80 tptp.identity_relation)) % 0.37/0.75 (define @t82 () (tptp.single_valued_class @t3)) % 0.37/0.75 (define @t83 () (@var "Xf" $$unsorted)) % 0.37/0.75 (define @t84 () (tptp.subclass @t83 @t33)) % 0.37/0.75 (define @t85 () (tptp.function @t83)) % 0.37/0.75 (define @t86 () (not @t85)) % 0.37/0.75 (define @t87 () (@list @t83)) % 0.37/0.75 (define @t88 () (tptp.inverse @t83)) % 0.37/0.75 (define @t89 () (tptp.subclass (tptp.compose @t83 @t88) tptp.identity_relation)) % 0.37/0.75 (define @t90 () (tptp.regular @t3)) % 0.37/0.75 (define @t91 () (= @t3 tptp.null_class)) % 0.37/0.75 (define @t92 () (@list @t83 @t1)) % 0.37/0.75 (define @t93 () (tptp.one_to_one @t83)) % 0.37/0.75 (define @t94 () (not @t93)) % 0.37/0.75 (define @t95 () (tptp.function @t88)) % 0.37/0.75 (define @t96 () (tptp.inverse tptp.element_relation)) % 0.37/0.75 (define @t97 () (tptp.operation @t83)) % 0.37/0.75 (define @t98 () (not @t97)) % 0.37/0.75 (define @t99 () (tptp.domain_of @t83)) % 0.37/0.75 (define @t100 () (tptp.domain_of @t99)) % 0.37/0.75 (define @t101 () (= (tptp.cross_product @t100 @t100) @t99)) % 0.37/0.75 (define @t102 () (tptp.range_of @t83)) % 0.37/0.75 (define @t103 () (tptp.subclass @t102 @t100)) % 0.37/0.75 (define @t104 () (@var "Xh" $$unsorted)) % 0.37/0.75 (define @t105 () (tptp.function @t104)) % 0.37/0.75 (define @t106 () (@var "Xf2" $$unsorted)) % 0.37/0.75 (define @t107 () (@var "Xf1" $$unsorted)) % 0.37/0.75 (define @t108 () (tptp.compatible @t104 @t107 @t106)) % 0.37/0.75 (define @t109 () (not @t108)) % 0.37/0.75 (define @t110 () (@list @t104 @t107 @t106)) % 0.37/0.75 (define @t111 () (tptp.domain_of @t107)) % 0.37/0.75 (define @t112 () (= (tptp.domain_of @t111) (tptp.domain_of @t104))) % 0.37/0.75 (define @t113 () (tptp.subclass (tptp.range_of @t104) (tptp.domain_of (tptp.domain_of @t106)))) % 0.37/0.75 (define @t114 () (tptp.operation @t107)) % 0.37/0.75 (define @t115 () (tptp.homomorphism @t104 @t107 @t106)) % 0.37/0.75 (define @t116 () (not @t115)) % 0.37/0.75 (define @t117 () (tptp.operation @t106)) % 0.37/0.75 (define @t118 () (tptp.not_homomorphism2 @t104 @t107 @t106)) % 0.37/0.75 (define @t119 () (tptp.not_homomorphism1 @t104 @t107 @t106)) % 0.37/0.75 (define @t120 () (tptp.ordered_pair @t119 @t118)) % 0.37/0.75 (define @t121 () (not @t117)) % 0.37/0.75 (define @t122 () (not @t114)) % 0.37/0.75 (define @t123 () (@list @t107 @t106 @t104)) % 0.37/0.75 (define @t124 () (tptp.compose_class @t3)) % 0.37/0.75 (define @t125 () (tptp.compose @t3 @t1)) % 0.37/0.75 (define @t126 () (= @t125 @t27)) % 0.37/0.75 (define @t127 () (tptp.member @t76 @t124)) % 0.37/0.75 (define @t128 () (@list @t1 @t27 @t3)) % 0.37/0.75 (define @t129 () (tptp.cross_product tptp.universal_class @t33)) % 0.37/0.75 (define @t130 () (tptp.ordered_pair @t3 @t76)) % 0.37/0.75 (define @t131 () (@list @t3 @t1 @t27)) % 0.37/0.75 (define @t132 () (tptp.single_valued1 @t3)) % 0.37/0.75 (define @t133 () (tptp.not_subclass_element @t80 tptp.identity_relation)) % 0.37/0.75 (define @t134 () (tptp.single_valued2 @t3)) % 0.37/0.75 (define @t135 () (tptp.member @t1 @t50)) % 0.37/0.75 (define @t136 () (not (tptp.member @t130 tptp.application_function))) % 0.37/0.75 (define @t137 () (tptp.apply @t3 @t1)) % 0.37/0.75 (define @t138 () (not (tptp.maps @t83 @t3 @t1))) % 0.37/0.75 (define @t139 () (@list @t83 @t3 @t1)) % 0.37/0.75 (define @t140 () (tptp.subclass @t102 @t1)) % 0.37/0.75 (define @t141 () (tptp.cross_product tptp.x tptp.y)) % 0.37/0.75 (define @t142 () (tptp.subclass @t141 tptp.z)) % 0.37/0.75 (define @t143 () (tptp.not_subclass_element @t141 tptp.z)) % 0.37/0.75 (define @t144 () (tptp.first @t143)) % 0.37/0.75 (define @t145 () (tptp.member @t144 tptp.x)) % 0.37/0.75 (define @t146 () (tptp.second @t143)) % 0.37/0.75 (define @t147 () (tptp.ordered_pair @t144 @t146)) % 0.37/0.75 (define @t148 () (not (tptp.member @t147 @t141))) % 0.37/0.75 (define @t149 () (or @t148 @t145)) % 0.37/0.75 (define @t150 () (@list true false)) % 0.37/0.75 (define @t151 () (tptp.member @t143 @t141)) % 0.37/0.75 (define @t152 () (or @t151 @t142)) % 0.37/0.75 (define @t153 () (= @t143 @t147)) % 0.37/0.75 (define @t154 () (not @t151)) % 0.37/0.75 (define @t155 () (or @t154 @t153)) % 0.37/0.75 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.37/0.75 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.37/0.75 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.37/0.75 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.37/0.75 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.37/0.75 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.37/0.75 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.37/0.75 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 0.37/0.75 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 0.37/0.75 (assume @p10 (forall (@list @t1 @t3) (or @t16 (tptp.member @t1 @t14)))) % 0.37/0.75 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.37/0.75 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t17))) % 0.37/0.75 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t17 (tptp.unordered_pair @t3 @t19)) @t18))) % 0.37/0.75 (assume @p14 (forall @t25 (or @t24 @t4))) % 0.37/0.75 (assume @p15 (forall @t25 (or @t24 @t26))) % 0.37/0.75 (assume @p16 (forall (@list @t2 @t3 @t21 @t1) (or @t5 (not @t26) @t23))) % 0.37/0.75 (assume @p17 @t32) % 0.37/0.75 (assume @p18 (tptp.subclass tptp.element_relation @t33)) % 0.37/0.75 (assume @p19 (forall @t9 (or (not @t35) @t34))) % 0.37/0.75 (assume @p20 (forall @t9 (or @t36 (not @t34) @t35))) % 0.37/0.75 (assume @p21 (forall @t31 (or @t40 @t37))) % 0.37/0.75 (assume @p22 (forall @t31 (or @t40 @t41))) % 0.37/0.75 (assume @p23 (forall @t31 (or @t42 (not @t41) @t39))) % 0.37/0.75 (assume @p24 (forall @t45 (or (not @t44) @t42))) % 0.37/0.75 (assume @p25 (forall @t45 (or @t46 @t44 @t37))) % 0.37/0.75 (assume @p26 (forall @t9 (= @t47 (tptp.union @t3 @t1)))) % 0.37/0.75 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t38) @t47) (tptp.symmetric_difference @t3 @t1)))) % 0.37/0.75 (assume @p28 (forall (@list @t48 @t3 @t1) (= (tptp.intersection @t48 @t20) @t49))) % 0.37/0.75 (assume @p29 (forall (@list @t3 @t1 @t48) (= (tptp.intersection @t20 @t48) @t49))) % 0.37/0.75 (assume @p30 (forall (@list @t3 @t27) (or (not @t52) (not @t51)))) % 0.37/0.75 (assume @p31 (forall @t45 (or @t46 @t52 @t51))) % 0.37/0.75 (assume @p32 (forall @t10 (tptp.subclass @t54 @t53))) % 0.37/0.75 (assume @p33 (forall @t59 (or (not @t58) @t56))) % 0.37/0.75 (assume @p34 (forall (@list @t21 @t55 @t2 @t3) (or (not @t56) @t60 @t58))) % 0.37/0.75 (assume @p35 (forall @t10 (tptp.subclass @t61 @t53))) % 0.37/0.75 (assume @p36 (forall @t59 (or (not @t63) @t62))) % 0.37/0.75 (assume @p37 (forall (@list @t21 @t2 @t55 @t3) (or (not @t62) @t60 @t63))) % 0.37/0.75 (assume @p38 (forall @t64 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.37/0.75 (assume @p39 (forall (@list @t27) (= (tptp.domain_of (tptp.inverse @t27)) (tptp.range_of @t27)))) % 0.37/0.75 (assume @p40 (forall @t31 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t27 @t3 @t19) tptp.null_class)) (tptp.domain @t27 @t3 @t1)))) % 0.37/0.75 (assume @p41 (forall @t31 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t27 @t17 @t1) tptp.null_class)) (tptp.range @t27 @t3 @t1)))) % 0.37/0.75 (assume @p42 (forall (@list @t48 @t3) (= (tptp.range_of (tptp.restrict @t48 @t3 tptp.universal_class)) (tptp.image @t48 @t3)))) % 0.37/0.75 (assume @p43 (forall @t10 (= (tptp.union @t3 @t17) @t65))) % 0.37/0.75 (assume @p44 (tptp.subclass tptp.successor_relation @t33)) % 0.37/0.75 (assume @p45 (forall @t9 (or (not @t67) @t66))) % 0.37/0.75 (assume @p46 (forall @t9 (or (not @t66) @t36 @t67))) % 0.37/0.75 (assume @p47 (forall @t10 (or @t70 @t68))) % 0.37/0.75 (assume @p48 (forall @t10 (or @t70 @t71))) % 0.37/0.75 (assume @p49 (forall @t10 (or (not @t68) (not @t71) @t69))) % 0.37/0.75 (assume @p50 (tptp.inductive tptp.omega)) % 0.37/0.75 (assume @p51 (forall @t64 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.37/0.75 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.37/0.75 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t72))) % 0.37/0.75 (assume @p54 (forall @t10 (or @t15 (tptp.member @t72 tptp.universal_class)))) % 0.37/0.75 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t43)) (tptp.power_class @t3)))) % 0.37/0.75 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.37/0.75 (assume @p57 (forall (@list @t73 @t48) (tptp.subclass @t74 @t33))) % 0.37/0.75 (assume @p58 (forall (@list @t1 @t27 @t73 @t48) (or (not @t77) @t75))) % 0.37/0.75 (assume @p59 (forall (@list @t27 @t73 @t48 @t1) (or (not @t75) @t78 @t77))) % 0.37/0.75 (assume @p60 (forall @t10 (or (not @t82) @t81))) % 0.37/0.75 (assume @p61 (forall @t10 (or (not @t81) @t82))) % 0.37/0.75 (assume @p62 (forall @t87 (or @t86 @t84))) % 0.37/0.75 (assume @p63 (forall @t87 (or @t86 @t89))) % 0.37/0.75 (assume @p64 (forall @t87 (or (not @t84) (not @t89) @t85))) % 0.37/0.75 (assume @p65 (forall (@list @t83 @t3) (or @t86 @t15 (tptp.member (tptp.image @t83 @t3) tptp.universal_class)))) % 0.37/0.75 (assume @p66 (forall @t10 (or @t91 (tptp.member @t90 @t3)))) % 0.37/0.75 (assume @p67 (forall @t10 (or @t91 (= (tptp.intersection @t3 @t90) tptp.null_class)))) % 0.37/0.75 (assume @p68 (forall @t92 (= (tptp.sum_class (tptp.image @t83 @t19)) (tptp.apply @t83 @t1)))) % 0.37/0.75 (assume @p69 (tptp.function tptp.choice)) % 0.37/0.75 (assume @p70 (forall @t64 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.37/0.75 (assume @p71 (forall @t87 (or @t94 @t85))) % 0.37/0.75 (assume @p72 (forall @t87 (or @t94 @t95))) % 0.37/0.75 (assume @p73 (forall @t87 (or (not @t95) @t86 @t93))) % 0.37/0.75 (assume @p74 (= (tptp.intersection @t33 (tptp.intersection @t33 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t96)))) tptp.subset_relation)) % 0.37/0.75 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.37/0.75 (assume @p76 (forall (@list @t48) (= (tptp.complement (tptp.domain_of (tptp.intersection @t48 tptp.identity_relation))) (tptp.diagonalise @t48)))) % 0.37/0.75 (assume @p77 (forall @t10 (= (tptp.intersection @t50 (tptp.diagonalise (tptp.compose @t96 @t3))) (tptp.cantor @t3)))) % 0.37/0.75 (assume @p78 (forall @t87 (or @t98 @t85))) % 0.37/0.75 (assume @p79 (forall @t87 (or @t98 @t101))) % 0.37/0.75 (assume @p80 (forall @t87 (or @t98 @t103))) % 0.37/0.75 (assume @p81 (forall @t87 (or @t86 (not @t101) (not @t103) @t97))) % 0.37/0.75 (assume @p82 (forall @t110 (or @t109 @t105))) % 0.37/0.75 (assume @p83 (forall @t110 (or @t109 @t112))) % 0.37/0.75 (assume @p84 (forall @t110 (or @t109 @t113))) % 0.37/0.75 (assume @p85 (forall @t110 (or (not @t105) (not @t112) (not @t113) @t108))) % 0.37/0.75 (assume @p86 (forall @t110 (or @t116 @t114))) % 0.37/0.75 (assume @p87 (forall @t110 (or @t116 @t117))) % 0.37/0.75 (assume @p88 (forall @t110 (or @t116 @t108))) % 0.37/0.75 (assume @p89 (forall (@list @t104 @t107 @t106 @t3 @t1) (or @t116 (not (tptp.member @t18 @t111)) (= (tptp.apply @t106 (tptp.ordered_pair (tptp.apply @t104 @t3) (tptp.apply @t104 @t1))) (tptp.apply @t104 (tptp.apply @t107 @t18)))))) % 0.37/0.75 (assume @p90 (forall @t123 (or @t122 @t121 @t109 (tptp.member @t120 @t111) @t115))) % 0.37/0.75 (assume @p91 (forall @t123 (or @t122 @t121 @t109 (not (= (tptp.apply @t106 (tptp.ordered_pair (tptp.apply @t104 @t119) (tptp.apply @t104 @t118))) (tptp.apply @t104 (tptp.apply @t107 @t120)))) @t115))) % 0.37/0.75 (assume @p92 (forall @t10 (tptp.subclass @t124 @t33))) % 0.37/0.75 (assume @p93 (forall @t128 (or (not @t127) @t126))) % 0.37/0.75 (assume @p94 (forall @t128 (or @t78 (not @t126) @t127))) % 0.37/0.75 (assume @p95 (tptp.subclass tptp.composition_function @t129)) % 0.37/0.75 (assume @p96 (forall @t131 (or (not (tptp.member @t130 tptp.composition_function)) @t126))) % 0.37/0.75 (assume @p97 (forall @t9 (or @t36 (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t125)) tptp.composition_function)))) % 0.37/0.75 (assume @p98 (tptp.subclass tptp.domain_relation @t33)) % 0.37/0.75 (assume @p99 (forall @t9 (or (not (tptp.member @t18 tptp.domain_relation)) (= @t50 @t1)))) % 0.37/0.75 (assume @p100 (forall @t10 (or @t15 (tptp.member (tptp.ordered_pair @t3 @t50) tptp.domain_relation)))) % 0.37/0.75 (assume @p101 (forall @t10 (= (tptp.first @t133) @t132))) % 0.37/0.75 (assume @p102 (forall @t10 (= (tptp.second @t133) @t134))) % 0.37/0.75 (assume @p103 (forall @t10 (= (tptp.domain @t3 (tptp.image @t79 (tptp.singleton @t132)) @t134) (tptp.single_valued3 @t3)))) % 0.37/0.75 (assume @p104 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation)) % 0.37/0.75 (assume @p105 (tptp.subclass tptp.application_function @t129)) % 0.37/0.75 (assume @p106 (forall @t131 (or @t136 @t135))) % 0.37/0.75 (assume @p107 (forall @t131 (or @t136 (= @t137 @t27)))) % 0.37/0.75 (assume @p108 (forall @t131 (or (not (tptp.member @t130 @t129)) (not @t135) (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t137)) tptp.application_function)))) % 0.37/0.75 (assume @p109 (forall @t139 (or @t138 @t85))) % 0.37/0.75 (assume @p110 (forall @t139 (or @t138 (= @t99 @t3)))) % 0.37/0.75 (assume @p111 (forall @t139 (or @t138 @t140))) % 0.37/0.75 (assume @p112 (forall @t92 (or @t86 (not @t140) (tptp.maps @t83 @t99 @t1)))) % 0.37/0.75 (assume @p113 (not @t142)) % 0.37/0.75 (assume @p114 (not @t145)) % 0.37/0.75 (step @p115 :rule evaluate :args ((= true false))) % 0.37/0.75 (step @p116 :rule instantiate :premises (@p14) :args ((@list @t144 @t146 tptp.x tptp.y))) % 0.37/0.75 (step @p117 :rule cnf_or_pos :args (@t149)) % 0.37/0.75 (step @p118 :rule reordering :premises (@p117) :args ((or @t145 @t148 (not @t149)))) % 0.37/0.75 (step @p119 :rule chain_m_resolution :premises (@p118 @p114 @p116) :args (@t148 @t150 (@list @t145 @t149))) % 0.37/0.75 (step @p120 :rule false_intro :premises (@p119)) % 0.37/0.75 (step @p121 :rule refl :args (@t141)) % 0.37/0.75 (step @p122 :rule eq-symm :args (@t28 @t27)) % 0.37/0.75 (step @p123 :rule refl :args (@t29)) % 0.37/0.75 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t30)) % 0.37/0.75 (step @p125 :rule cong :premises (@p124) :args (@t32)) % 0.37/0.75 (step @p126 :rule eq_resolve :premises (@p17 @p125)) % 0.37/0.75 (step @p127 :rule instantiate :premises (@p126) :args ((@list @t143 tptp.x tptp.y))) % 0.37/0.75 (step @p128 :rule instantiate :premises (@p2) :args ((@list @t141 tptp.z))) % 0.37/0.75 (step @p129 :rule cnf_or_pos :args (@t152)) % 0.37/0.75 (step @p130 :rule reordering :premises (@p129) :args ((or @t142 @t151 (not @t152)))) % 0.37/0.75 (step @p131 :rule chain_m_resolution :premises (@p130 @p113 @p128) :args (@t151 @t150 (@list @t142 @t152))) % 0.37/0.75 (step @p132 :rule cnf_or_pos :args (@t155)) % 0.37/0.75 (step @p133 :rule reordering :premises (@p132) :args ((or @t154 @t153 (not @t155)))) % 0.37/0.75 (step @p134 :rule chain_m_resolution :premises (@p133 @p131 @p127) :args (@t153 (@list false false) (@list @t151 @t155))) % 0.37/0.75 (step @p135 :rule cong :premises (@p134 @p121) :args (@t151)) % 0.37/0.75 (step @p136 :rule true_intro :premises (@p131)) % 0.37/0.75 (step @p137 :rule symm :premises (@p136)) % 0.37/0.75 (step @p138 :rule trans :premises (@p137 @p135 @p120)) % 0.37/0.75 (step @p139 false :rule eq_resolve :premises (@p138 @p115)) % 0.37/0.75 ) % 0.37/0.75 % SZS output end Proof % 0.37/0.75 % cvc5 exiting %------------------------------------------------------------------------------