%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET103-6 : 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 : n026.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 08:47:24 AM UTC 2026 % Result : Unsatisfiable 34.98s 35.18s % Output : Proof 34.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET103-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n026.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 14:56:10 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.27/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.52/15.72 --- Run --no-e-matching --full-saturate-quant at 6... % 21.53/21.78 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.64/27.83 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.63/33.88 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.98/35.18 % SZS status Unsatisfiable % 34.98/35.18 % SZS output start Proof % 34.98/35.19 ( % 34.98/35.19 (declare-sort $$unsorted 0) % 34.98/35.19 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.operation (-> $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.function (-> $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.element_relation $$unsorted) % 34.98/35.19 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.universal_class $$unsorted) % 34.98/35.19 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.successor_relation $$unsorted) % 34.98/35.19 (declare-const tptp.choice $$unsorted) % 34.98/35.19 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.y $$unsorted) % 34.98/35.19 (declare-const tptp.subset_relation $$unsorted) % 34.98/35.19 (declare-const tptp.null_class $$unsorted) % 34.98/35.19 (declare-const tptp.x $$unsorted) % 34.98/35.19 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.omega $$unsorted) % 34.98/35.19 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 34.98/35.19 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.identity_relation $$unsorted) % 34.98/35.19 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 34.98/35.19 (declare-const tptp.inductive (-> $$unsorted Bool)) % 34.98/35.19 (define @t1 () (@var "Y" $$unsorted)) % 34.98/35.19 (define @t2 () (@var "U" $$unsorted)) % 34.98/35.19 (define @t3 () (@var "X" $$unsorted)) % 34.98/35.19 (define @t4 () (tptp.member @t2 @t3)) % 34.98/35.19 (define @t5 () (not @t4)) % 34.98/35.19 (define @t6 () (tptp.subclass @t3 @t1)) % 34.98/35.19 (define @t7 () (not @t6)) % 34.98/35.19 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 34.98/35.19 (define @t9 () (@list @t3 @t1)) % 34.98/35.19 (define @t10 () (@list @t3)) % 34.98/35.19 (define @t11 () (= @t3 @t1)) % 34.98/35.19 (define @t12 () (not @t11)) % 34.98/35.19 (define @t13 () (tptp.subclass @t1 @t3)) % 34.98/35.19 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 34.98/35.19 (define @t15 () (not (tptp.member @t2 @t14))) % 34.98/35.19 (define @t16 () (or @t15 (= @t2 @t3) (= @t2 @t1))) % 34.98/35.19 (define @t17 () (forall (@list @t2 @t3 @t1) @t16)) % 34.98/35.19 (define @t18 () (not (tptp.member @t3 tptp.universal_class))) % 34.98/35.19 (define @t19 () (not (tptp.member @t1 tptp.universal_class))) % 34.98/35.19 (define @t20 () (tptp.singleton @t3)) % 34.98/35.19 (define @t21 () (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t20))) % 34.98/35.19 (define @t22 () (tptp.ordered_pair @t3 @t1)) % 34.98/35.19 (define @t23 () (tptp.singleton @t1)) % 34.98/35.19 (define @t24 () (forall @t9 (= (tptp.unordered_pair @t20 (tptp.unordered_pair @t3 @t23)) @t22))) % 34.98/35.19 (define @t25 () (tptp.cross_product @t3 @t1)) % 34.98/35.19 (define @t26 () (@var "V" $$unsorted)) % 34.98/35.19 (define @t27 () (tptp.ordered_pair @t2 @t26)) % 34.98/35.19 (define @t28 () (tptp.member @t27 @t25)) % 34.98/35.19 (define @t29 () (not @t28)) % 34.98/35.19 (define @t30 () (@list @t2 @t26 @t3 @t1)) % 34.98/35.19 (define @t31 () (tptp.member @t26 @t1)) % 34.98/35.19 (define @t32 () (@var "Z" $$unsorted)) % 34.98/35.19 (define @t33 () (@list @t32 @t3 @t1)) % 34.98/35.19 (define @t34 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 34.98/35.19 (define @t35 () (tptp.member @t3 @t1)) % 34.98/35.19 (define @t36 () (tptp.member @t22 tptp.element_relation)) % 34.98/35.19 (define @t37 () (not (tptp.member @t22 @t34))) % 34.98/35.19 (define @t38 () (tptp.member @t32 @t3)) % 34.98/35.19 (define @t39 () (tptp.intersection @t3 @t1)) % 34.98/35.19 (define @t40 () (tptp.member @t32 @t39)) % 34.98/35.19 (define @t41 () (not @t40)) % 34.98/35.19 (define @t42 () (tptp.member @t32 @t1)) % 34.98/35.19 (define @t43 () (not @t38)) % 34.98/35.19 (define @t44 () (tptp.complement @t3)) % 34.98/35.19 (define @t45 () (tptp.member @t32 @t44)) % 34.98/35.19 (define @t46 () (@list @t32 @t3)) % 34.98/35.19 (define @t47 () (not (tptp.member @t32 tptp.universal_class))) % 34.98/35.19 (define @t48 () (tptp.complement (tptp.intersection @t44 (tptp.complement @t1)))) % 34.98/35.19 (define @t49 () (@var "Xr" $$unsorted)) % 34.98/35.19 (define @t50 () (tptp.restrict @t49 @t3 @t1)) % 34.98/35.19 (define @t51 () (tptp.domain_of @t3)) % 34.98/35.19 (define @t52 () (tptp.member @t32 @t51)) % 34.98/35.19 (define @t53 () (= (tptp.restrict @t3 (tptp.singleton @t32) tptp.universal_class) tptp.null_class)) % 34.98/35.19 (define @t54 () (tptp.cross_product @t34 tptp.universal_class)) % 34.98/35.19 (define @t55 () (tptp.rotate @t3)) % 34.98/35.19 (define @t56 () (@var "W" $$unsorted)) % 34.98/35.19 (define @t57 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t26 @t56) @t2) @t3)) % 34.98/35.19 (define @t58 () (tptp.ordered_pair @t27 @t56)) % 34.98/35.19 (define @t59 () (tptp.member @t58 @t55)) % 34.98/35.19 (define @t60 () (@list @t2 @t26 @t56 @t3)) % 34.98/35.19 (define @t61 () (not (tptp.member @t58 @t54))) % 34.98/35.19 (define @t62 () (tptp.flip @t3)) % 34.98/35.19 (define @t63 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t26 @t2) @t56) @t3)) % 34.98/35.19 (define @t64 () (tptp.member @t58 @t62)) % 34.98/35.19 (define @t65 () (@list @t1)) % 34.98/35.19 (define @t66 () (tptp.successor @t3)) % 34.98/35.19 (define @t67 () (= @t66 @t1)) % 34.98/35.19 (define @t68 () (tptp.member @t22 tptp.successor_relation)) % 34.98/35.19 (define @t69 () (tptp.member tptp.null_class @t3)) % 34.98/35.19 (define @t70 () (tptp.inductive @t3)) % 34.98/35.19 (define @t71 () (not @t70)) % 34.98/35.19 (define @t72 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 34.98/35.19 (define @t73 () (tptp.sum_class @t3)) % 34.98/35.19 (define @t74 () (@var "Yr" $$unsorted)) % 34.98/35.19 (define @t75 () (tptp.compose @t74 @t49)) % 34.98/35.19 (define @t76 () (tptp.member @t32 (tptp.image @t74 (tptp.image @t49 @t23)))) % 34.98/35.19 (define @t77 () (tptp.ordered_pair @t1 @t32)) % 34.98/35.19 (define @t78 () (tptp.member @t77 @t75)) % 34.98/35.19 (define @t79 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 34.98/35.19 (define @t80 () (tptp.single_valued_class @t3)) % 34.98/35.19 (define @t81 () (@var "Xf" $$unsorted)) % 34.98/35.19 (define @t82 () (tptp.subclass @t81 @t34)) % 34.98/35.19 (define @t83 () (tptp.function @t81)) % 34.98/35.19 (define @t84 () (not @t83)) % 34.98/35.19 (define @t85 () (@list @t81)) % 34.98/35.19 (define @t86 () (tptp.inverse @t81)) % 34.98/35.19 (define @t87 () (tptp.subclass (tptp.compose @t81 @t86) tptp.identity_relation)) % 34.98/35.19 (define @t88 () (tptp.regular @t3)) % 34.98/35.19 (define @t89 () (= @t3 tptp.null_class)) % 34.98/35.19 (define @t90 () (forall (@list @t81 @t1) (= (tptp.sum_class (tptp.image @t81 @t23)) (tptp.apply @t81 @t1)))) % 34.98/35.19 (define @t91 () (tptp.function tptp.choice)) % 34.98/35.19 (define @t92 () (forall @t65 (or @t19 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 34.98/35.19 (define @t93 () (tptp.one_to_one @t81)) % 34.98/35.19 (define @t94 () (not @t93)) % 34.98/35.19 (define @t95 () (tptp.function @t86)) % 34.98/35.19 (define @t96 () (tptp.inverse tptp.element_relation)) % 34.98/35.19 (define @t97 () (tptp.operation @t81)) % 34.98/35.19 (define @t98 () (not @t97)) % 34.98/35.19 (define @t99 () (tptp.domain_of @t81)) % 34.98/35.19 (define @t100 () (tptp.domain_of @t99)) % 34.98/35.19 (define @t101 () (= (tptp.cross_product @t100 @t100) @t99)) % 34.98/35.19 (define @t102 () (tptp.subclass (tptp.range_of @t81) @t100)) % 34.98/35.19 (define @t103 () (@var "Xh" $$unsorted)) % 34.98/35.19 (define @t104 () (tptp.function @t103)) % 34.98/35.19 (define @t105 () (@var "Xf2" $$unsorted)) % 34.98/35.19 (define @t106 () (@var "Xf1" $$unsorted)) % 34.98/35.19 (define @t107 () (tptp.compatible @t103 @t106 @t105)) % 34.98/35.19 (define @t108 () (not @t107)) % 34.98/35.19 (define @t109 () (@list @t103 @t106 @t105)) % 34.98/35.19 (define @t110 () (tptp.domain_of @t106)) % 34.98/35.19 (define @t111 () (= (tptp.domain_of @t110) (tptp.domain_of @t103))) % 34.98/35.19 (define @t112 () (tptp.subclass (tptp.range_of @t103) (tptp.domain_of (tptp.domain_of @t105)))) % 34.98/35.19 (define @t113 () (tptp.operation @t106)) % 34.98/35.19 (define @t114 () (tptp.homomorphism @t103 @t106 @t105)) % 34.98/35.19 (define @t115 () (not @t114)) % 34.98/35.19 (define @t116 () (tptp.operation @t105)) % 34.98/35.19 (define @t117 () (tptp.not_homomorphism2 @t103 @t106 @t105)) % 34.98/35.19 (define @t118 () (tptp.not_homomorphism1 @t103 @t106 @t105)) % 34.98/35.19 (define @t119 () (tptp.ordered_pair @t118 @t117)) % 34.98/35.19 (define @t120 () (not @t116)) % 34.98/35.19 (define @t121 () (not @t113)) % 34.98/35.19 (define @t122 () (@list @t106 @t105 @t103)) % 34.98/35.19 (define @t123 () (tptp.ordered_pair tptp.x tptp.y)) % 34.98/35.19 (define @t124 () (tptp.unordered_pair tptp.x tptp.null_class)) % 34.98/35.19 (define @t125 () (tptp.singleton tptp.x)) % 34.98/35.19 (define @t126 () (tptp.unordered_pair @t125 @t124)) % 34.98/35.19 (define @t127 () (= @t126 @t123)) % 34.98/35.19 (define @t128 () (tptp.member tptp.y tptp.universal_class)) % 34.98/35.19 (define @t129 () (not @t128)) % 34.98/35.19 (define @t130 () (tptp.singleton tptp.y)) % 34.98/35.19 (define @t131 () (tptp.unordered_pair @t125 (tptp.unordered_pair tptp.x @t130))) % 34.98/35.19 (define @t132 () (= @t131 @t123)) % 34.98/35.19 (define @t133 () (@list tptp.x tptp.y)) % 34.98/35.19 (define @t134 () (= @t123 @t131)) % 34.98/35.19 (define @t135 () (@list false)) % 34.98/35.19 (define @t136 () (tptp.apply tptp.choice @t130)) % 34.98/35.19 (define @t137 () (tptp.member @t136 @t130)) % 34.98/35.19 (define @t138 () (tptp.member @t130 tptp.universal_class)) % 34.98/35.19 (define @t139 () (not @t138)) % 34.98/35.19 (define @t140 () (or @t139 (= @t130 tptp.null_class) @t137)) % 34.98/35.19 (define @t141 () (@list @t130)) % 34.98/35.19 (define @t142 () (= tptp.null_class @t130)) % 34.98/35.19 (define @t143 () (or @t139 @t142 @t137)) % 34.98/35.19 (define @t144 () (tptp.singleton @t130)) % 34.98/35.19 (define @t145 () (tptp.image tptp.choice @t144)) % 34.98/35.19 (define @t146 () (tptp.unordered_pair @t130 @t130)) % 34.98/35.19 (define @t147 () (= @t146 @t144)) % 34.98/35.19 (define @t148 () (@list @t21)) % 34.98/35.19 (define @t149 () (tptp.member @t144 tptp.universal_class)) % 34.98/35.19 (define @t150 () (tptp.member @t145 tptp.universal_class)) % 34.98/35.19 (define @t151 () (not @t149)) % 34.98/35.19 (define @t152 () (not @t91)) % 34.98/35.19 (define @t153 () (or @t152 @t151 @t150)) % 34.98/35.19 (define @t154 () (tptp.sum_class @t145)) % 34.98/35.19 (define @t155 () (tptp.member @t154 tptp.universal_class)) % 34.98/35.19 (define @t156 () (not @t150)) % 34.98/35.19 (define @t157 () (or @t156 @t155)) % 34.98/35.19 (define @t158 () (= @t154 @t136)) % 34.98/35.19 (define @t159 () (@list tptp.choice @t130)) % 34.98/35.19 (define @t160 () (= @t136 @t154)) % 34.98/35.19 (define @t161 () (not @t155)) % 34.98/35.19 (define @t162 () (not @t160)) % 34.98/35.19 (define @t163 () (= tptp.y @t136)) % 34.98/35.19 (define @t164 () (not @t163)) % 34.98/35.19 (define @t165 () (tptp.unordered_pair tptp.y tptp.y)) % 34.98/35.19 (define @t166 () (tptp.member @t136 @t165)) % 34.98/35.19 (define @t167 () (not @t166)) % 34.98/35.19 (define @t168 () (or @t167 @t163 @t163)) % 34.98/35.19 (define @t169 () (= @t165 @t130)) % 34.98/35.19 (define @t170 () (= @t130 @t165)) % 34.98/35.19 (define @t171 () (not @t137)) % 34.98/35.19 (define @t172 () (not @t170)) % 34.98/35.19 (define @t173 () (and @t170 @t167)) % 34.98/35.19 (define @t174 () (and @t134 @t142)) % 34.98/35.19 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 34.98/35.19 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 34.98/35.19 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 34.98/35.19 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 34.98/35.19 (assume @p5 (forall @t9 (or @t12 @t6))) % 34.98/35.19 (assume @p6 (forall @t9 (or @t12 @t13))) % 34.98/35.19 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 34.98/35.19 (assume @p8 @t17) % 34.98/35.19 (assume @p9 (forall @t9 (or @t18 (tptp.member @t3 @t14)))) % 34.98/35.19 (assume @p10 (forall (@list @t1 @t3) (or @t19 (tptp.member @t1 @t14)))) % 34.98/35.19 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 34.98/35.19 (assume @p12 @t21) % 34.98/35.19 (assume @p13 @t24) % 34.98/35.19 (assume @p14 (forall @t30 (or @t29 @t4))) % 34.98/35.19 (assume @p15 (forall @t30 (or @t29 @t31))) % 34.98/35.19 (assume @p16 (forall (@list @t2 @t3 @t26 @t1) (or @t5 (not @t31) @t28))) % 34.98/35.19 (assume @p17 (forall @t33 (or (not (tptp.member @t32 @t25)) (= (tptp.ordered_pair (tptp.first @t32) (tptp.second @t32)) @t32)))) % 34.98/35.19 (assume @p18 (tptp.subclass tptp.element_relation @t34)) % 34.98/35.19 (assume @p19 (forall @t9 (or (not @t36) @t35))) % 34.98/35.19 (assume @p20 (forall @t9 (or @t37 (not @t35) @t36))) % 34.98/35.19 (assume @p21 (forall @t33 (or @t41 @t38))) % 34.98/35.19 (assume @p22 (forall @t33 (or @t41 @t42))) % 34.98/35.19 (assume @p23 (forall @t33 (or @t43 (not @t42) @t40))) % 34.98/35.19 (assume @p24 (forall @t46 (or (not @t45) @t43))) % 34.98/35.19 (assume @p25 (forall @t46 (or @t47 @t45 @t38))) % 34.98/35.19 (assume @p26 (forall @t9 (= @t48 (tptp.union @t3 @t1)))) % 34.98/35.19 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t39) @t48) (tptp.symmetric_difference @t3 @t1)))) % 34.98/35.19 (assume @p28 (forall (@list @t49 @t3 @t1) (= (tptp.intersection @t49 @t25) @t50))) % 34.98/35.19 (assume @p29 (forall (@list @t3 @t1 @t49) (= (tptp.intersection @t25 @t49) @t50))) % 34.98/35.19 (assume @p30 (forall (@list @t3 @t32) (or (not @t53) (not @t52)))) % 34.98/35.19 (assume @p31 (forall @t46 (or @t47 @t53 @t52))) % 34.98/35.19 (assume @p32 (forall @t10 (tptp.subclass @t55 @t54))) % 34.98/35.19 (assume @p33 (forall @t60 (or (not @t59) @t57))) % 34.98/35.19 (assume @p34 (forall (@list @t26 @t56 @t2 @t3) (or (not @t57) @t61 @t59))) % 34.98/35.19 (assume @p35 (forall @t10 (tptp.subclass @t62 @t54))) % 34.98/35.19 (assume @p36 (forall @t60 (or (not @t64) @t63))) % 34.98/35.19 (assume @p37 (forall (@list @t26 @t2 @t56 @t3) (or (not @t63) @t61 @t64))) % 34.98/35.19 (assume @p38 (forall @t65 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 34.98/35.19 (assume @p39 (forall (@list @t32) (= (tptp.domain_of (tptp.inverse @t32)) (tptp.range_of @t32)))) % 34.98/35.19 (assume @p40 (forall @t33 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t32 @t3 @t23) tptp.null_class)) (tptp.domain @t32 @t3 @t1)))) % 34.98/35.19 (assume @p41 (forall @t33 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t32 @t20 @t1) tptp.null_class)) (tptp.range @t32 @t3 @t1)))) % 34.98/35.19 (assume @p42 (forall (@list @t49 @t3) (= (tptp.range_of (tptp.restrict @t49 @t3 tptp.universal_class)) (tptp.image @t49 @t3)))) % 34.98/35.19 (assume @p43 (forall @t10 (= (tptp.union @t3 @t20) @t66))) % 34.98/35.19 (assume @p44 (tptp.subclass tptp.successor_relation @t34)) % 34.98/35.19 (assume @p45 (forall @t9 (or (not @t68) @t67))) % 34.98/35.19 (assume @p46 (forall @t9 (or (not @t67) @t37 @t68))) % 34.98/35.19 (assume @p47 (forall @t10 (or @t71 @t69))) % 34.98/35.19 (assume @p48 (forall @t10 (or @t71 @t72))) % 34.98/35.19 (assume @p49 (forall @t10 (or (not @t69) (not @t72) @t70))) % 34.98/35.19 (assume @p50 (tptp.inductive tptp.omega)) % 34.98/35.19 (assume @p51 (forall @t65 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 34.98/35.19 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 34.98/35.19 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t73))) % 34.98/35.19 (assume @p54 (forall @t10 (or @t18 (tptp.member @t73 tptp.universal_class)))) % 34.98/35.19 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t44)) (tptp.power_class @t3)))) % 34.98/35.19 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 34.98/35.19 (assume @p57 (forall (@list @t74 @t49) (tptp.subclass @t75 @t34))) % 34.98/35.19 (assume @p58 (forall (@list @t1 @t32 @t74 @t49) (or (not @t78) @t76))) % 34.98/35.19 (assume @p59 (forall (@list @t32 @t74 @t49 @t1) (or (not @t76) (not (tptp.member @t77 @t34)) @t78))) % 34.98/35.19 (assume @p60 (forall @t10 (or (not @t80) @t79))) % 34.98/35.19 (assume @p61 (forall @t10 (or (not @t79) @t80))) % 34.98/35.19 (assume @p62 (forall @t85 (or @t84 @t82))) % 34.98/35.19 (assume @p63 (forall @t85 (or @t84 @t87))) % 34.98/35.19 (assume @p64 (forall @t85 (or (not @t82) (not @t87) @t83))) % 34.98/35.19 (assume @p65 (forall (@list @t81 @t3) (or @t84 @t18 (tptp.member (tptp.image @t81 @t3) tptp.universal_class)))) % 34.98/35.19 (assume @p66 (forall @t10 (or @t89 (tptp.member @t88 @t3)))) % 34.98/35.19 (assume @p67 (forall @t10 (or @t89 (= (tptp.intersection @t3 @t88) tptp.null_class)))) % 34.98/35.19 (assume @p68 @t90) % 34.98/35.19 (assume @p69 @t91) % 34.98/35.19 (assume @p70 @t92) % 34.98/35.19 (assume @p71 (forall @t85 (or @t94 @t83))) % 34.98/35.19 (assume @p72 (forall @t85 (or @t94 @t95))) % 34.98/35.19 (assume @p73 (forall @t85 (or (not @t95) @t84 @t93))) % 34.98/35.19 (assume @p74 (= (tptp.intersection @t34 (tptp.intersection @t34 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t96)))) tptp.subset_relation)) % 34.98/35.19 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 34.98/35.19 (assume @p76 (forall (@list @t49) (= (tptp.complement (tptp.domain_of (tptp.intersection @t49 tptp.identity_relation))) (tptp.diagonalise @t49)))) % 34.98/35.19 (assume @p77 (forall @t10 (= (tptp.intersection @t51 (tptp.diagonalise (tptp.compose @t96 @t3))) (tptp.cantor @t3)))) % 34.98/35.19 (assume @p78 (forall @t85 (or @t98 @t83))) % 34.98/35.19 (assume @p79 (forall @t85 (or @t98 @t101))) % 34.98/35.19 (assume @p80 (forall @t85 (or @t98 @t102))) % 34.98/35.19 (assume @p81 (forall @t85 (or @t84 (not @t101) (not @t102) @t97))) % 34.98/35.19 (assume @p82 (forall @t109 (or @t108 @t104))) % 34.98/35.19 (assume @p83 (forall @t109 (or @t108 @t111))) % 34.98/35.19 (assume @p84 (forall @t109 (or @t108 @t112))) % 34.98/35.19 (assume @p85 (forall @t109 (or (not @t104) (not @t111) (not @t112) @t107))) % 34.98/35.19 (assume @p86 (forall @t109 (or @t115 @t113))) % 34.98/35.19 (assume @p87 (forall @t109 (or @t115 @t116))) % 34.98/35.19 (assume @p88 (forall @t109 (or @t115 @t107))) % 34.98/35.19 (assume @p89 (forall (@list @t103 @t106 @t105 @t3 @t1) (or @t115 (not (tptp.member @t22 @t110)) (= (tptp.apply @t105 (tptp.ordered_pair (tptp.apply @t103 @t3) (tptp.apply @t103 @t1))) (tptp.apply @t103 (tptp.apply @t106 @t22)))))) % 34.98/35.19 (assume @p90 (forall @t122 (or @t121 @t120 @t108 (tptp.member @t119 @t110) @t114))) % 34.98/35.19 (assume @p91 (forall @t122 (or @t121 @t120 @t108 (not (= (tptp.apply @t105 (tptp.ordered_pair (tptp.apply @t103 @t118) (tptp.apply @t103 @t117))) (tptp.apply @t103 (tptp.apply @t106 @t119)))) @t114))) % 34.98/35.19 (assume @p92 (not @t127)) % 34.98/35.19 (assume @p93 @t129) % 34.98/35.19 (step @p94 :rule eq-symm :args (@t131 @t123)) % 34.98/35.19 (step @p95 :rule refl :args (@t24)) % 34.98/35.19 (step @p96 :rule cong :premises (@p95 @p94) :args ((=> @t24 @t132))) % 34.98/35.19 (assume-push @p254 @t24) % 34.98/35.19 (step @p98 :rule instantiate :premises (@p13) :args (@t133)) % 34.98/35.19 (step-pop @p255 :rule scope :premises (@p98)) % 34.98/35.19 (step @p99 :rule process_scope :premises (@p255) :args (@t132)) % 34.98/35.19 (step @p101 :rule eq_resolve :premises (@p99 @p96)) % 34.98/35.19 (step @p102 :rule implies_elim :premises (@p101)) % 34.98/35.19 (step @p103 :rule chain_m_resolution :premises (@p102 @p13) :args (@t134 @t135 (@list @t24))) % 34.98/35.19 (step @p104 :rule refl :args (@t137)) % 34.98/35.19 (step @p105 :rule eq-symm :args (@t130 tptp.null_class)) % 34.98/35.19 (step @p106 :rule refl :args (@t139)) % 34.98/35.19 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104) :args (@t140)) % 34.98/35.19 (step @p108 :rule refl :args (@t92)) % 34.98/35.19 (step @p109 :rule cong :premises (@p108 @p107) :args ((=> @t92 @t140))) % 34.98/35.19 (assume-push @p256 @t92) % 34.98/35.19 (step @p111 :rule instantiate :premises (@p70) :args (@t141)) % 34.98/35.19 (step-pop @p257 :rule scope :premises (@p111)) % 34.98/35.19 (step @p112 :rule process_scope :premises (@p257) :args (@t140)) % 34.98/35.19 (step @p114 :rule eq_resolve :premises (@p112 @p109)) % 34.98/35.19 (step @p115 :rule implies_elim :premises (@p114)) % 34.98/35.19 (step @p116 :rule chain_m_resolution :premises (@p115 @p70) :args (@t143 @t135 (@list @t92))) % 34.98/35.19 (step @p117 :rule eq-symm :args (@t2 @t1)) % 34.98/35.19 (step @p118 :rule eq-symm :args (@t2 @t3)) % 34.98/35.19 (step @p119 :rule refl :args (@t15)) % 34.98/35.19 (step @p120 :rule nary_cong :premises (@p119 @p118 @p117) :args (@t16)) % 34.98/35.19 (step @p121 :rule cong :premises (@p120) :args (@t17)) % 34.98/35.19 (step @p122 :rule eq_resolve :premises (@p8 @p121)) % 34.98/35.19 (step @p123 :rule instantiate :premises (@p122) :args ((@list @t136 tptp.y tptp.y))) % 34.98/35.19 (step @p124 :rule instantiate :premises (@p54) :args ((@list @t145))) % 34.98/35.19 (step @p125 :rule instantiate :premises (@p65) :args ((@list tptp.choice @t144))) % 34.98/35.19 (step @p126 :rule instantiate :premises (@p11) :args ((@list @t130 @t130))) % 34.98/35.19 (step @p127 :rule true_intro :premises (@p126)) % 34.98/35.19 (step @p128 :rule refl :args (tptp.universal_class)) % 34.98/35.19 (step @p129 :rule eq-symm :args (@t146 @t144)) % 34.98/35.19 (step @p130 :rule refl :args (@t21)) % 34.98/35.19 (step @p131 :rule cong :premises (@p130 @p129) :args ((=> @t21 @t147))) % 34.98/35.19 (assume-push @p258 @t21) % 34.98/35.19 (step @p133 :rule instantiate :premises (@p12) :args (@t141)) % 34.98/35.19 (step-pop @p259 :rule scope :premises (@p133)) % 34.98/35.19 (step @p134 :rule process_scope :premises (@p259) :args (@t147)) % 34.98/35.19 (step @p136 :rule eq_resolve :premises (@p134 @p131)) % 34.98/35.19 (step @p137 :rule implies_elim :premises (@p136)) % 34.98/35.19 (step @p138 :rule chain_m_resolution :premises (@p137 @p12) :args ((= @t144 @t146) @t135 @t148)) % 34.98/35.19 (step @p139 :rule cong :premises (@p138 @p128) :args (@t149)) % 34.98/35.19 (step @p140 :rule trans :premises (@p139 @p127)) % 34.98/35.19 (step @p141 :rule true_elim :premises (@p140)) % 34.98/35.19 (step @p142 :rule cnf_or_pos :args (@t153)) % 34.98/35.19 (step @p143 :rule reordering :premises (@p142) :args ((or @t152 @t151 @t150 (not @t153)))) % 34.98/35.19 (step @p144 :rule chain_m_resolution :premises (@p143 @p69 @p141 @p125) :args (@t150 (@list false false false) (@list @t91 @t149 @t153))) % 34.98/35.19 (step @p145 :rule cnf_or_pos :args (@t157)) % 34.98/35.19 (step @p146 :rule reordering :premises (@p145) :args ((or @t156 @t155 (not @t157)))) % 34.98/35.19 (step @p147 :rule chain_m_resolution :premises (@p146 @p144 @p124) :args (@t155 (@list false false) (@list @t150 @t157))) % 34.98/35.19 (step @p148 :rule eq-symm :args (@t154 @t136)) % 34.98/35.19 (step @p149 :rule refl :args (@t90)) % 34.98/35.19 (step @p150 :rule cong :premises (@p149 @p148) :args ((=> @t90 @t158))) % 34.98/35.19 (assume-push @p260 @t90) % 34.98/35.19 (step @p152 :rule instantiate :premises (@p68) :args (@t159)) % 34.98/35.19 (step-pop @p261 :rule scope :premises (@p152)) % 34.98/35.19 (step @p153 :rule process_scope :premises (@p261) :args (@t158)) % 34.98/35.19 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 34.98/35.19 (step @p156 :rule implies_elim :premises (@p155)) % 34.98/35.19 (step @p157 :rule chain_m_resolution :premises (@p156 @p68) :args (@t160 @t135 (@list @t90))) % 34.98/35.19 (step @p158 :rule refl :args (@t161)) % 34.98/35.19 (step @p159 :rule refl :args (@t162)) % 34.98/35.19 (step @p160 :rule refl :args (@t164)) % 34.98/35.19 (step @p161 :rule bool-double-not-elim :args (@t128)) % 34.98/35.19 (step @p162 :rule nary_cong :premises (@p161 @p160 @p159 @p158) :args ((or (not @t129) @t164 @t162 @t161))) % 34.98/35.19 (assume-push @p262 @t129) % 34.98/35.19 (assume-push @p263 @t163) % 34.98/35.19 (assume-push @p264 @t160) % 34.98/35.19 (assume-push @p265 @t155) % 34.98/35.19 (step @p167 :rule evaluate :args ((= true false))) % 34.98/35.19 (step @p168 :rule false_intro :premises (@p93)) % 34.98/35.19 (step @p169 :rule symm :premises (@p263)) % 34.98/35.19 (step @p152 :rule instantiate :premises (@p68) :args (@t159)) % 34.98/35.19 (step @p170 :rule trans :premises (@p152 @p169)) % 34.98/35.19 (step @p171 :rule cong :premises (@p170 @p128) :args (@t155)) % 34.98/35.19 (step @p172 :rule true_intro :premises (@p147)) % 34.98/35.19 (step @p173 :rule symm :premises (@p172)) % 34.98/35.19 (step @p174 :rule trans :premises (@p173 @p171 @p168)) % 34.98/35.19 (step @p175 false :rule eq_resolve :premises (@p174 @p167)) % 34.98/35.19 (step-pop @p266 :rule scope :premises (@p175)) % 34.98/35.19 (step-pop @p267 :rule scope :premises (@p266)) % 34.98/35.19 (step-pop @p268 :rule scope :premises (@p267)) % 34.98/35.19 (step-pop @p269 :rule scope :premises (@p268)) % 34.98/35.19 (step @p176 :rule process_scope :premises (@p269) :args (false)) % 34.98/35.19 (step @p181 :rule not_and :premises (@p176)) % 34.98/35.19 (step @p182 :rule eq_resolve :premises (@p181 @p162)) % 34.98/35.19 (step @p183 :rule chain_m_resolution :premises (@p182 @p93 @p157 @p147) :args (@t164 (@list true false false) (@list @t128 @t160 @t155))) % 34.98/35.19 (step @p184 :rule cnf_or_pos :args (@t168)) % 34.98/35.19 (step @p185 :rule factoring :premises (@p184)) % 34.98/35.19 (step @p186 :rule reordering :premises (@p185) :args ((or @t167 @t163 (not @t168)))) % 34.98/35.19 (step @p187 :rule chain_m_resolution :premises (@p186 @p183 @p123) :args (@t167 (@list true false) (@list @t163 @t168))) % 34.98/35.19 (step @p188 :rule eq-symm :args (@t165 @t130)) % 34.98/35.19 (step @p189 :rule cong :premises (@p130 @p188) :args ((=> @t21 @t169))) % 34.98/35.19 (assume-push @p270 @t21) % 34.98/35.19 (step @p191 :rule instantiate :premises (@p12) :args ((@list tptp.y))) % 34.98/35.19 (step-pop @p271 :rule scope :premises (@p191)) % 34.98/35.19 (step @p192 :rule process_scope :premises (@p271) :args (@t169)) % 34.98/35.19 (step @p194 :rule eq_resolve :premises (@p192 @p189)) % 34.98/35.19 (step @p195 :rule implies_elim :premises (@p194)) % 34.98/35.19 (step @p196 :rule chain_m_resolution :premises (@p195 @p12) :args (@t170 @t135 @t148)) % 34.98/35.19 (step @p197 :rule refl :args (@t171)) % 34.98/35.19 (step @p198 :rule bool-double-not-elim :args (@t166)) % 34.98/35.19 (step @p199 :rule refl :args (@t172)) % 34.98/35.19 (step @p200 :rule nary_cong :premises (@p199 @p198 @p197) :args ((or @t172 (not @t167) @t171))) % 34.98/35.19 (assume-push @p272 @t170) % 34.98/35.19 (assume-push @p273 @t167) % 34.98/35.19 (assume-push @p274 @t167) % 34.98/35.19 (assume-push @p275 @t170) % 34.98/35.19 (step @p205 :rule false_intro :premises (@p273)) % 34.98/35.19 (step @p206 :rule refl :args (@t136)) % 34.98/35.19 (step @p207 :rule cong :premises (@p206 @p196) :args (@t137)) % 34.98/35.19 (step @p208 :rule trans :premises (@p207 @p205)) % 34.98/35.19 (step @p209 :rule false_elim :premises (@p208)) % 34.98/35.19 (step-pop @p276 :rule scope :premises (@p209)) % 34.98/35.19 (step-pop @p277 :rule scope :premises (@p276)) % 34.98/35.19 (step @p210 :rule process_scope :premises (@p277) :args (@t171)) % 34.98/35.19 (step @p213 :rule and_intro :premises (@p273 @p196)) % 34.98/35.19 (step @p214 :rule modus_ponens :premises (@p213 @p210)) % 34.98/35.19 (step-pop @p278 :rule scope :premises (@p214)) % 34.98/35.19 (step-pop @p279 :rule scope :premises (@p278)) % 34.98/35.19 (step @p215 :rule process_scope :premises (@p279) :args (@t171)) % 34.98/35.19 (step @p218 :rule implies_elim :premises (@p215)) % 34.98/35.19 (step @p219 :rule cnf_and_neg :args (@t173)) % 34.98/35.19 (step @p220 :rule resolution :premises (@p219 @p218) :args (true @t173)) % 34.98/35.19 (step @p221 :rule eq_resolve :premises (@p220 @p200)) % 34.98/35.19 (step @p222 :rule reordering :premises (@p221) :args ((or @t172 @t171 @t166))) % 34.98/35.19 (step @p223 :rule chain_m_resolution :premises (@p222 @p196 @p187) :args (@t171 (@list false true) (@list @t170 @t166))) % 34.98/35.19 (step @p224 :rule instantiate :premises (@p11) :args ((@list tptp.y tptp.y))) % 34.98/35.19 (step @p225 :rule true_intro :premises (@p224)) % 34.98/35.19 (step @p226 :rule cong :premises (@p196 @p128) :args (@t138)) % 34.98/35.19 (step @p227 :rule trans :premises (@p226 @p225)) % 34.98/35.19 (step @p228 :rule true_elim :premises (@p227)) % 34.98/35.19 (step @p229 :rule cnf_or_pos :args (@t143)) % 34.98/35.19 (step @p230 :rule reordering :premises (@p229) :args ((or @t139 @t137 @t142 (not @t143)))) % 34.98/35.19 (step @p231 :rule chain_m_resolution :premises (@p230 @p228 @p223 @p116) :args (@t142 (@list false true false) (@list @t138 @t137 @t143))) % 34.98/35.19 (assume-push @p280 @t134) % 34.98/35.19 (assume-push @p281 @t142) % 34.98/35.19 (assume-push @p282 @t134) % 34.98/35.19 (assume-push @p283 @t142) % 34.98/35.19 (step @p98 :rule instantiate :premises (@p13) :args (@t133)) % 34.98/35.19 (step @p236 :rule refl :args (tptp.x)) % 34.98/35.19 (step @p237 :rule cong :premises (@p236 @p281) :args (@t124)) % 34.98/35.19 (step @p238 :rule refl :args (@t125)) % 34.98/35.19 (step @p239 :rule cong :premises (@p238 @p237) :args (@t126)) % 34.98/35.19 (step @p240 :rule trans :premises (@p239 @p98)) % 34.98/35.19 (step-pop @p284 :rule scope :premises (@p240)) % 34.98/35.19 (step-pop @p285 :rule scope :premises (@p284)) % 34.98/35.19 (step @p241 :rule process_scope :premises (@p285) :args (@t127)) % 34.98/35.19 (step @p244 :rule and_intro :premises (@p103 @p281)) % 34.98/35.19 (step @p245 :rule modus_ponens :premises (@p244 @p241)) % 34.98/35.19 (step-pop @p286 :rule scope :premises (@p245)) % 34.98/35.19 (step-pop @p287 :rule scope :premises (@p286)) % 34.98/35.19 (step @p246 :rule process_scope :premises (@p287) :args (@t127)) % 34.98/35.19 (step @p249 :rule implies_elim :premises (@p246)) % 34.98/35.19 (step @p250 :rule cnf_and_neg :args (@t174)) % 34.98/35.19 (step @p251 :rule resolution :premises (@p250 @p249) :args (true @t174)) % 34.98/35.19 (step @p252 :rule reordering :premises (@p251) :args ((or @t127 (not @t134) (not @t142)))) % 34.98/35.19 (step @p253 false :rule chain_m_resolution :premises (@p252 @p231 @p103 @p92) :args (false (@list false false true) (@list @t142 @t134 @t127))) % 34.98/35.19 ) % 34.98/35.19 % SZS output end Proof % 34.98/35.20 % cvc5 exiting %------------------------------------------------------------------------------