%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET215-6 : 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 : n028.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 08:47:40 AM UTC 2026 % Result : Unsatisfiable 1.02s 1.26s % Output : Proof 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET215-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n028.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 15:12:20 EDT 2026 % 0.16/0.35 % 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... % 1.02/1.26 % SZS status Unsatisfiable % 1.02/1.26 % SZS output start Proof % 1.02/1.26 ( % 1.02/1.26 (declare-sort $$unsorted 0) % 1.02/1.26 (declare-const tptp.y $$unsorted) % 1.02/1.26 (declare-const tptp.z $$unsorted) % 1.02/1.26 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.application_function $$unsorted) % 1.02/1.26 (declare-const tptp.singleton_relation $$unsorted) % 1.02/1.26 (declare-const tptp.x $$unsorted) % 1.02/1.26 (declare-const tptp.single_valued1 (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.operation (-> $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.function (-> $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.single_valued3 (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.element_relation $$unsorted) % 1.02/1.26 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.single_valued2 (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.universal_class $$unsorted) % 1.02/1.26 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.successor_relation $$unsorted) % 1.02/1.26 (declare-const tptp.choice $$unsorted) % 1.02/1.26 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.subset_relation $$unsorted) % 1.02/1.26 (declare-const tptp.null_class $$unsorted) % 1.02/1.26 (declare-const tptp.compose_class (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.omega $$unsorted) % 1.02/1.26 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 1.02/1.26 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.composition_function $$unsorted) % 1.02/1.26 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.identity_relation $$unsorted) % 1.02/1.26 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.domain_relation $$unsorted) % 1.02/1.26 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 1.02/1.26 (declare-const tptp.inductive (-> $$unsorted Bool)) % 1.02/1.26 (define @t1 () (@var "Y" $$unsorted)) % 1.02/1.26 (define @t2 () (@var "U" $$unsorted)) % 1.02/1.26 (define @t3 () (@var "X" $$unsorted)) % 1.02/1.26 (define @t4 () (tptp.member @t2 @t3)) % 1.02/1.26 (define @t5 () (not @t4)) % 1.02/1.26 (define @t6 () (tptp.subclass @t3 @t1)) % 1.02/1.26 (define @t7 () (not @t6)) % 1.02/1.26 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 1.02/1.26 (define @t9 () (@list @t3 @t1)) % 1.02/1.26 (define @t10 () (@list @t3)) % 1.02/1.26 (define @t11 () (= @t3 @t1)) % 1.02/1.26 (define @t12 () (not @t11)) % 1.02/1.26 (define @t13 () (tptp.subclass @t1 @t3)) % 1.02/1.26 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 1.02/1.26 (define @t15 () (not (tptp.member @t3 tptp.universal_class))) % 1.02/1.26 (define @t16 () (not (tptp.member @t1 tptp.universal_class))) % 1.02/1.26 (define @t17 () (tptp.singleton @t3)) % 1.02/1.26 (define @t18 () (tptp.ordered_pair @t3 @t1)) % 1.02/1.26 (define @t19 () (tptp.singleton @t1)) % 1.02/1.26 (define @t20 () (tptp.cross_product @t3 @t1)) % 1.02/1.26 (define @t21 () (@var "V" $$unsorted)) % 1.02/1.26 (define @t22 () (tptp.ordered_pair @t2 @t21)) % 1.02/1.26 (define @t23 () (tptp.member @t22 @t20)) % 1.02/1.26 (define @t24 () (not @t23)) % 1.02/1.26 (define @t25 () (@list @t2 @t21 @t3 @t1)) % 1.02/1.26 (define @t26 () (tptp.member @t21 @t1)) % 1.02/1.26 (define @t27 () (@var "Z" $$unsorted)) % 1.02/1.26 (define @t28 () (tptp.ordered_pair (tptp.first @t27) (tptp.second @t27))) % 1.02/1.26 (define @t29 () (not (tptp.member @t27 @t20))) % 1.02/1.26 (define @t30 () (or @t29 (= @t28 @t27))) % 1.02/1.26 (define @t31 () (@list @t27 @t3 @t1)) % 1.02/1.26 (define @t32 () (forall @t31 @t30)) % 1.02/1.26 (define @t33 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 1.02/1.26 (define @t34 () (tptp.member @t3 @t1)) % 1.02/1.26 (define @t35 () (tptp.member @t18 tptp.element_relation)) % 1.02/1.26 (define @t36 () (not (tptp.member @t18 @t33))) % 1.02/1.26 (define @t37 () (tptp.member @t27 @t3)) % 1.02/1.26 (define @t38 () (tptp.intersection @t3 @t1)) % 1.02/1.26 (define @t39 () (tptp.member @t27 @t38)) % 1.02/1.26 (define @t40 () (not @t39)) % 1.02/1.26 (define @t41 () (tptp.member @t27 @t1)) % 1.02/1.26 (define @t42 () (forall @t31 (or @t40 @t41))) % 1.02/1.26 (define @t43 () (not @t37)) % 1.02/1.26 (define @t44 () (tptp.complement @t3)) % 1.02/1.26 (define @t45 () (tptp.member @t27 @t44)) % 1.02/1.26 (define @t46 () (@list @t27 @t3)) % 1.02/1.26 (define @t47 () (not (tptp.member @t27 tptp.universal_class))) % 1.02/1.26 (define @t48 () (tptp.complement (tptp.intersection @t44 (tptp.complement @t1)))) % 1.02/1.26 (define @t49 () (@var "Xr" $$unsorted)) % 1.02/1.26 (define @t50 () (tptp.restrict @t49 @t3 @t1)) % 1.02/1.26 (define @t51 () (tptp.domain_of @t3)) % 1.02/1.26 (define @t52 () (tptp.member @t27 @t51)) % 1.02/1.26 (define @t53 () (= (tptp.restrict @t3 (tptp.singleton @t27) tptp.universal_class) tptp.null_class)) % 1.02/1.26 (define @t54 () (tptp.cross_product @t33 tptp.universal_class)) % 1.02/1.26 (define @t55 () (tptp.rotate @t3)) % 1.02/1.26 (define @t56 () (@var "W" $$unsorted)) % 1.02/1.26 (define @t57 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t56) @t2) @t3)) % 1.02/1.26 (define @t58 () (tptp.ordered_pair @t22 @t56)) % 1.02/1.26 (define @t59 () (tptp.member @t58 @t55)) % 1.02/1.26 (define @t60 () (@list @t2 @t21 @t56 @t3)) % 1.02/1.26 (define @t61 () (not (tptp.member @t58 @t54))) % 1.02/1.26 (define @t62 () (tptp.flip @t3)) % 1.02/1.26 (define @t63 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t56) @t3)) % 1.02/1.26 (define @t64 () (tptp.member @t58 @t62)) % 1.02/1.26 (define @t65 () (@list @t1)) % 1.02/1.26 (define @t66 () (tptp.successor @t3)) % 1.02/1.26 (define @t67 () (= @t66 @t1)) % 1.02/1.26 (define @t68 () (tptp.member @t18 tptp.successor_relation)) % 1.02/1.26 (define @t69 () (tptp.member tptp.null_class @t3)) % 1.02/1.26 (define @t70 () (tptp.inductive @t3)) % 1.02/1.26 (define @t71 () (not @t70)) % 1.02/1.26 (define @t72 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 1.02/1.26 (define @t73 () (tptp.sum_class @t3)) % 1.02/1.26 (define @t74 () (@var "Yr" $$unsorted)) % 1.02/1.26 (define @t75 () (tptp.compose @t74 @t49)) % 1.02/1.26 (define @t76 () (tptp.member @t27 (tptp.image @t74 (tptp.image @t49 @t19)))) % 1.02/1.26 (define @t77 () (tptp.ordered_pair @t1 @t27)) % 1.02/1.26 (define @t78 () (tptp.member @t77 @t75)) % 1.02/1.26 (define @t79 () (not (tptp.member @t77 @t33))) % 1.02/1.26 (define @t80 () (tptp.inverse @t3)) % 1.02/1.26 (define @t81 () (tptp.compose @t3 @t80)) % 1.02/1.26 (define @t82 () (tptp.subclass @t81 tptp.identity_relation)) % 1.02/1.26 (define @t83 () (tptp.single_valued_class @t3)) % 1.02/1.26 (define @t84 () (@var "Xf" $$unsorted)) % 1.02/1.26 (define @t85 () (tptp.subclass @t84 @t33)) % 1.02/1.26 (define @t86 () (tptp.function @t84)) % 1.02/1.26 (define @t87 () (not @t86)) % 1.02/1.26 (define @t88 () (@list @t84)) % 1.02/1.26 (define @t89 () (tptp.inverse @t84)) % 1.02/1.26 (define @t90 () (tptp.subclass (tptp.compose @t84 @t89) tptp.identity_relation)) % 1.02/1.26 (define @t91 () (tptp.regular @t3)) % 1.02/1.26 (define @t92 () (= @t3 tptp.null_class)) % 1.02/1.26 (define @t93 () (@list @t84 @t1)) % 1.02/1.26 (define @t94 () (tptp.one_to_one @t84)) % 1.02/1.26 (define @t95 () (not @t94)) % 1.02/1.26 (define @t96 () (tptp.function @t89)) % 1.02/1.26 (define @t97 () (tptp.inverse tptp.element_relation)) % 1.02/1.26 (define @t98 () (tptp.operation @t84)) % 1.02/1.26 (define @t99 () (not @t98)) % 1.02/1.26 (define @t100 () (tptp.domain_of @t84)) % 1.02/1.26 (define @t101 () (tptp.domain_of @t100)) % 1.02/1.26 (define @t102 () (= (tptp.cross_product @t101 @t101) @t100)) % 1.02/1.26 (define @t103 () (tptp.range_of @t84)) % 1.02/1.26 (define @t104 () (tptp.subclass @t103 @t101)) % 1.02/1.26 (define @t105 () (@var "Xh" $$unsorted)) % 1.02/1.26 (define @t106 () (tptp.function @t105)) % 1.02/1.26 (define @t107 () (@var "Xf2" $$unsorted)) % 1.02/1.26 (define @t108 () (@var "Xf1" $$unsorted)) % 1.02/1.26 (define @t109 () (tptp.compatible @t105 @t108 @t107)) % 1.02/1.26 (define @t110 () (not @t109)) % 1.02/1.26 (define @t111 () (@list @t105 @t108 @t107)) % 1.02/1.26 (define @t112 () (tptp.domain_of @t108)) % 1.02/1.26 (define @t113 () (= (tptp.domain_of @t112) (tptp.domain_of @t105))) % 1.02/1.26 (define @t114 () (tptp.subclass (tptp.range_of @t105) (tptp.domain_of (tptp.domain_of @t107)))) % 1.02/1.26 (define @t115 () (tptp.operation @t108)) % 1.02/1.26 (define @t116 () (tptp.homomorphism @t105 @t108 @t107)) % 1.02/1.26 (define @t117 () (not @t116)) % 1.02/1.26 (define @t118 () (tptp.operation @t107)) % 1.02/1.26 (define @t119 () (tptp.not_homomorphism2 @t105 @t108 @t107)) % 1.02/1.26 (define @t120 () (tptp.not_homomorphism1 @t105 @t108 @t107)) % 1.02/1.26 (define @t121 () (tptp.ordered_pair @t120 @t119)) % 1.02/1.26 (define @t122 () (not @t118)) % 1.02/1.26 (define @t123 () (not @t115)) % 1.02/1.26 (define @t124 () (@list @t108 @t107 @t105)) % 1.02/1.26 (define @t125 () (tptp.compose_class @t3)) % 1.02/1.26 (define @t126 () (tptp.compose @t3 @t1)) % 1.02/1.26 (define @t127 () (= @t126 @t27)) % 1.02/1.26 (define @t128 () (tptp.member @t77 @t125)) % 1.02/1.26 (define @t129 () (@list @t1 @t27 @t3)) % 1.02/1.26 (define @t130 () (tptp.cross_product tptp.universal_class @t33)) % 1.02/1.26 (define @t131 () (tptp.ordered_pair @t3 @t77)) % 1.02/1.26 (define @t132 () (@list @t3 @t1 @t27)) % 1.02/1.26 (define @t133 () (tptp.single_valued1 @t3)) % 1.02/1.26 (define @t134 () (tptp.not_subclass_element @t81 tptp.identity_relation)) % 1.02/1.26 (define @t135 () (tptp.single_valued2 @t3)) % 1.02/1.26 (define @t136 () (tptp.member @t1 @t51)) % 1.02/1.26 (define @t137 () (not (tptp.member @t131 tptp.application_function))) % 1.02/1.26 (define @t138 () (tptp.apply @t3 @t1)) % 1.02/1.26 (define @t139 () (not (tptp.maps @t84 @t3 @t1))) % 1.02/1.26 (define @t140 () (@list @t84 @t3 @t1)) % 1.02/1.26 (define @t141 () (tptp.subclass @t103 @t1)) % 1.02/1.26 (define @t142 () (tptp.cross_product tptp.y tptp.z)) % 1.02/1.26 (define @t143 () (tptp.intersection tptp.x tptp.y)) % 1.02/1.26 (define @t144 () (tptp.cross_product @t143 tptp.z)) % 1.02/1.26 (define @t145 () (tptp.subclass @t144 @t142)) % 1.02/1.26 (define @t146 () (tptp.not_subclass_element @t144 @t142)) % 1.02/1.26 (define @t147 () (tptp.second @t146)) % 1.02/1.26 (define @t148 () (tptp.first @t146)) % 1.02/1.26 (define @t149 () (@list @t148 @t147 @t143 tptp.z)) % 1.02/1.26 (define @t150 () (@list @t144 @t142)) % 1.02/1.26 (define @t151 () (tptp.member @t146 @t144)) % 1.02/1.26 (define @t152 () (or @t151 @t145)) % 1.02/1.26 (define @t153 () (@list true false)) % 1.02/1.26 (define @t154 () (tptp.ordered_pair @t148 @t147)) % 1.02/1.26 (define @t155 () (= @t146 @t154)) % 1.02/1.26 (define @t156 () (not @t151)) % 1.02/1.26 (define @t157 () (or @t156 @t155)) % 1.02/1.26 (define @t158 () (@list false false)) % 1.02/1.26 (define @t159 () (tptp.member @t154 @t144)) % 1.02/1.26 (define @t160 () (tptp.member @t148 @t143)) % 1.02/1.26 (define @t161 () (not @t159)) % 1.02/1.26 (define @t162 () (or @t161 @t160)) % 1.02/1.26 (define @t163 () (not (tptp.member @t146 @t142))) % 1.02/1.26 (define @t164 () (or @t163 @t145)) % 1.02/1.26 (define @t165 () (tptp.member @t154 @t142)) % 1.02/1.26 (define @t166 () (tptp.member @t147 tptp.z)) % 1.02/1.26 (define @t167 () (or @t161 @t166)) % 1.02/1.26 (define @t168 () (not @t166)) % 1.02/1.26 (define @t169 () (tptp.member @t148 tptp.y)) % 1.02/1.26 (define @t170 () (not @t169)) % 1.02/1.26 (define @t171 () (or @t170 @t168 @t165)) % 1.02/1.26 (define @t172 () (not @t160)) % 1.02/1.26 (define @t173 () (or @t172 @t169)) % 1.02/1.26 (define @t174 () (not @t173)) % 1.02/1.26 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 1.02/1.26 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 1.02/1.26 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 1.02/1.26 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 1.02/1.26 (assume @p5 (forall @t9 (or @t12 @t6))) % 1.02/1.26 (assume @p6 (forall @t9 (or @t12 @t13))) % 1.02/1.26 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 1.02/1.26 (assume @p8 (forall (@list @t2 @t3 @t1) (or (not (tptp.member @t2 @t14)) (= @t2 @t3) (= @t2 @t1)))) % 1.02/1.26 (assume @p9 (forall @t9 (or @t15 (tptp.member @t3 @t14)))) % 1.02/1.26 (assume @p10 (forall (@list @t1 @t3) (or @t16 (tptp.member @t1 @t14)))) % 1.02/1.26 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 1.02/1.26 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t17))) % 1.02/1.26 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t17 (tptp.unordered_pair @t3 @t19)) @t18))) % 1.02/1.26 (assume @p14 (forall @t25 (or @t24 @t4))) % 1.02/1.26 (assume @p15 (forall @t25 (or @t24 @t26))) % 1.02/1.26 (assume @p16 (forall (@list @t2 @t3 @t21 @t1) (or @t5 (not @t26) @t23))) % 1.02/1.26 (assume @p17 @t32) % 1.02/1.26 (assume @p18 (tptp.subclass tptp.element_relation @t33)) % 1.02/1.26 (assume @p19 (forall @t9 (or (not @t35) @t34))) % 1.02/1.26 (assume @p20 (forall @t9 (or @t36 (not @t34) @t35))) % 1.02/1.26 (assume @p21 (forall @t31 (or @t40 @t37))) % 1.02/1.26 (assume @p22 @t42) % 1.02/1.26 (assume @p23 (forall @t31 (or @t43 (not @t41) @t39))) % 1.02/1.26 (assume @p24 (forall @t46 (or (not @t45) @t43))) % 1.02/1.26 (assume @p25 (forall @t46 (or @t47 @t45 @t37))) % 1.02/1.26 (assume @p26 (forall @t9 (= @t48 (tptp.union @t3 @t1)))) % 1.02/1.26 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t38) @t48) (tptp.symmetric_difference @t3 @t1)))) % 1.02/1.26 (assume @p28 (forall (@list @t49 @t3 @t1) (= (tptp.intersection @t49 @t20) @t50))) % 1.02/1.26 (assume @p29 (forall (@list @t3 @t1 @t49) (= (tptp.intersection @t20 @t49) @t50))) % 1.02/1.26 (assume @p30 (forall (@list @t3 @t27) (or (not @t53) (not @t52)))) % 1.02/1.26 (assume @p31 (forall @t46 (or @t47 @t53 @t52))) % 1.02/1.26 (assume @p32 (forall @t10 (tptp.subclass @t55 @t54))) % 1.02/1.26 (assume @p33 (forall @t60 (or (not @t59) @t57))) % 1.02/1.26 (assume @p34 (forall (@list @t21 @t56 @t2 @t3) (or (not @t57) @t61 @t59))) % 1.02/1.26 (assume @p35 (forall @t10 (tptp.subclass @t62 @t54))) % 1.02/1.26 (assume @p36 (forall @t60 (or (not @t64) @t63))) % 1.02/1.26 (assume @p37 (forall (@list @t21 @t2 @t56 @t3) (or (not @t63) @t61 @t64))) % 1.02/1.26 (assume @p38 (forall @t65 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 1.02/1.26 (assume @p39 (forall (@list @t27) (= (tptp.domain_of (tptp.inverse @t27)) (tptp.range_of @t27)))) % 1.02/1.26 (assume @p40 (forall @t31 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t27 @t3 @t19) tptp.null_class)) (tptp.domain @t27 @t3 @t1)))) % 1.02/1.26 (assume @p41 (forall @t31 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t27 @t17 @t1) tptp.null_class)) (tptp.range @t27 @t3 @t1)))) % 1.02/1.26 (assume @p42 (forall (@list @t49 @t3) (= (tptp.range_of (tptp.restrict @t49 @t3 tptp.universal_class)) (tptp.image @t49 @t3)))) % 1.02/1.26 (assume @p43 (forall @t10 (= (tptp.union @t3 @t17) @t66))) % 1.02/1.26 (assume @p44 (tptp.subclass tptp.successor_relation @t33)) % 1.02/1.26 (assume @p45 (forall @t9 (or (not @t68) @t67))) % 1.02/1.26 (assume @p46 (forall @t9 (or (not @t67) @t36 @t68))) % 1.02/1.26 (assume @p47 (forall @t10 (or @t71 @t69))) % 1.02/1.26 (assume @p48 (forall @t10 (or @t71 @t72))) % 1.02/1.26 (assume @p49 (forall @t10 (or (not @t69) (not @t72) @t70))) % 1.02/1.26 (assume @p50 (tptp.inductive tptp.omega)) % 1.02/1.26 (assume @p51 (forall @t65 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 1.02/1.26 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 1.02/1.26 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t73))) % 1.02/1.26 (assume @p54 (forall @t10 (or @t15 (tptp.member @t73 tptp.universal_class)))) % 1.02/1.26 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t44)) (tptp.power_class @t3)))) % 1.02/1.26 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 1.02/1.26 (assume @p57 (forall (@list @t74 @t49) (tptp.subclass @t75 @t33))) % 1.02/1.26 (assume @p58 (forall (@list @t1 @t27 @t74 @t49) (or (not @t78) @t76))) % 1.02/1.26 (assume @p59 (forall (@list @t27 @t74 @t49 @t1) (or (not @t76) @t79 @t78))) % 1.02/1.26 (assume @p60 (forall @t10 (or (not @t83) @t82))) % 1.02/1.26 (assume @p61 (forall @t10 (or (not @t82) @t83))) % 1.02/1.26 (assume @p62 (forall @t88 (or @t87 @t85))) % 1.02/1.26 (assume @p63 (forall @t88 (or @t87 @t90))) % 1.02/1.26 (assume @p64 (forall @t88 (or (not @t85) (not @t90) @t86))) % 1.02/1.26 (assume @p65 (forall (@list @t84 @t3) (or @t87 @t15 (tptp.member (tptp.image @t84 @t3) tptp.universal_class)))) % 1.02/1.26 (assume @p66 (forall @t10 (or @t92 (tptp.member @t91 @t3)))) % 1.02/1.26 (assume @p67 (forall @t10 (or @t92 (= (tptp.intersection @t3 @t91) tptp.null_class)))) % 1.02/1.26 (assume @p68 (forall @t93 (= (tptp.sum_class (tptp.image @t84 @t19)) (tptp.apply @t84 @t1)))) % 1.02/1.26 (assume @p69 (tptp.function tptp.choice)) % 1.02/1.26 (assume @p70 (forall @t65 (or @t16 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 1.02/1.26 (assume @p71 (forall @t88 (or @t95 @t86))) % 1.02/1.26 (assume @p72 (forall @t88 (or @t95 @t96))) % 1.02/1.26 (assume @p73 (forall @t88 (or (not @t96) @t87 @t94))) % 1.02/1.26 (assume @p74 (= (tptp.intersection @t33 (tptp.intersection @t33 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t97)))) tptp.subset_relation)) % 1.02/1.26 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 1.02/1.26 (assume @p76 (forall (@list @t49) (= (tptp.complement (tptp.domain_of (tptp.intersection @t49 tptp.identity_relation))) (tptp.diagonalise @t49)))) % 1.02/1.26 (assume @p77 (forall @t10 (= (tptp.intersection @t51 (tptp.diagonalise (tptp.compose @t97 @t3))) (tptp.cantor @t3)))) % 1.02/1.26 (assume @p78 (forall @t88 (or @t99 @t86))) % 1.02/1.26 (assume @p79 (forall @t88 (or @t99 @t102))) % 1.02/1.26 (assume @p80 (forall @t88 (or @t99 @t104))) % 1.02/1.26 (assume @p81 (forall @t88 (or @t87 (not @t102) (not @t104) @t98))) % 1.02/1.26 (assume @p82 (forall @t111 (or @t110 @t106))) % 1.02/1.26 (assume @p83 (forall @t111 (or @t110 @t113))) % 1.02/1.26 (assume @p84 (forall @t111 (or @t110 @t114))) % 1.02/1.26 (assume @p85 (forall @t111 (or (not @t106) (not @t113) (not @t114) @t109))) % 1.02/1.26 (assume @p86 (forall @t111 (or @t117 @t115))) % 1.02/1.26 (assume @p87 (forall @t111 (or @t117 @t118))) % 1.02/1.26 (assume @p88 (forall @t111 (or @t117 @t109))) % 1.02/1.26 (assume @p89 (forall (@list @t105 @t108 @t107 @t3 @t1) (or @t117 (not (tptp.member @t18 @t112)) (= (tptp.apply @t107 (tptp.ordered_pair (tptp.apply @t105 @t3) (tptp.apply @t105 @t1))) (tptp.apply @t105 (tptp.apply @t108 @t18)))))) % 1.02/1.27 (assume @p90 (forall @t124 (or @t123 @t122 @t110 (tptp.member @t121 @t112) @t116))) % 1.02/1.27 (assume @p91 (forall @t124 (or @t123 @t122 @t110 (not (= (tptp.apply @t107 (tptp.ordered_pair (tptp.apply @t105 @t120) (tptp.apply @t105 @t119))) (tptp.apply @t105 (tptp.apply @t108 @t121)))) @t116))) % 1.02/1.27 (assume @p92 (forall @t10 (tptp.subclass @t125 @t33))) % 1.02/1.27 (assume @p93 (forall @t129 (or (not @t128) @t127))) % 1.02/1.27 (assume @p94 (forall @t129 (or @t79 (not @t127) @t128))) % 1.02/1.27 (assume @p95 (tptp.subclass tptp.composition_function @t130)) % 1.02/1.27 (assume @p96 (forall @t132 (or (not (tptp.member @t131 tptp.composition_function)) @t127))) % 1.02/1.27 (assume @p97 (forall @t9 (or @t36 (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t126)) tptp.composition_function)))) % 1.02/1.27 (assume @p98 (tptp.subclass tptp.domain_relation @t33)) % 1.02/1.27 (assume @p99 (forall @t9 (or (not (tptp.member @t18 tptp.domain_relation)) (= @t51 @t1)))) % 1.02/1.27 (assume @p100 (forall @t10 (or @t15 (tptp.member (tptp.ordered_pair @t3 @t51) tptp.domain_relation)))) % 1.02/1.27 (assume @p101 (forall @t10 (= (tptp.first @t134) @t133))) % 1.02/1.27 (assume @p102 (forall @t10 (= (tptp.second @t134) @t135))) % 1.02/1.27 (assume @p103 (forall @t10 (= (tptp.domain @t3 (tptp.image @t80 (tptp.singleton @t133)) @t135) (tptp.single_valued3 @t3)))) % 1.02/1.27 (assume @p104 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation)) % 1.02/1.27 (assume @p105 (tptp.subclass tptp.application_function @t130)) % 1.02/1.27 (assume @p106 (forall @t132 (or @t137 @t136))) % 1.02/1.27 (assume @p107 (forall @t132 (or @t137 (= @t138 @t27)))) % 1.02/1.27 (assume @p108 (forall @t132 (or (not (tptp.member @t131 @t130)) (not @t136) (tptp.member (tptp.ordered_pair @t3 (tptp.ordered_pair @t1 @t138)) tptp.application_function)))) % 1.02/1.27 (assume @p109 (forall @t140 (or @t139 @t86))) % 1.02/1.27 (assume @p110 (forall @t140 (or @t139 (= @t100 @t3)))) % 1.02/1.27 (assume @p111 (forall @t140 (or @t139 @t141))) % 1.02/1.27 (assume @p112 (forall @t93 (or @t87 (not @t141) (tptp.maps @t84 @t100 @t1)))) % 1.02/1.27 (assume @p113 (not @t145)) % 1.02/1.27 (step @p114 :rule instantiate :premises (@p14) :args (@t149)) % 1.02/1.27 (step @p115 :rule instantiate :premises (@p2) :args (@t150)) % 1.02/1.27 (step @p116 :rule cnf_or_pos :args (@t152)) % 1.02/1.27 (step @p117 :rule reordering :premises (@p116) :args ((or @t145 @t151 (not @t152)))) % 1.02/1.27 (step @p118 :rule chain_m_resolution :premises (@p117 @p113 @p115) :args (@t151 @t153 (@list @t145 @t152))) % 1.02/1.27 (step @p119 :rule true_intro :premises (@p118)) % 1.02/1.27 (step @p120 :rule refl :args (@t144)) % 1.02/1.27 (step @p121 :rule eq-symm :args (@t28 @t27)) % 1.02/1.27 (step @p122 :rule refl :args (@t29)) % 1.02/1.27 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t30)) % 1.02/1.27 (step @p124 :rule cong :premises (@p123) :args (@t32)) % 1.02/1.27 (step @p125 :rule eq_resolve :premises (@p17 @p124)) % 1.02/1.27 (step @p126 :rule instantiate :premises (@p125) :args ((@list @t146 @t143 tptp.z))) % 1.02/1.27 (step @p127 :rule cnf_or_pos :args (@t157)) % 1.02/1.27 (step @p128 :rule reordering :premises (@p127) :args ((or @t156 @t155 (not @t157)))) % 1.02/1.27 (step @p129 :rule chain_m_resolution :premises (@p128 @p118 @p126) :args (@t155 @t158 (@list @t151 @t157))) % 1.02/1.27 (step @p130 :rule symm :premises (@p129)) % 1.02/1.27 (step @p131 :rule cong :premises (@p130 @p120) :args (@t159)) % 1.02/1.27 (step @p132 :rule trans :premises (@p131 @p119)) % 1.02/1.27 (step @p133 :rule true_elim :premises (@p132)) % 1.02/1.27 (step @p134 :rule cnf_or_pos :args (@t162)) % 1.02/1.27 (step @p135 :rule reordering :premises (@p134) :args ((or @t161 @t160 (not @t162)))) % 1.02/1.27 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p114) :args (@t160 @t158 (@list @t159 @t162))) % 1.02/1.27 (step @p137 :rule instantiate :premises (@p16) :args ((@list @t148 tptp.y @t147 tptp.z))) % 1.02/1.27 (step @p138 :rule instantiate :premises (@p3) :args (@t150)) % 1.02/1.27 (step @p139 :rule cnf_or_pos :args (@t164)) % 1.02/1.27 (step @p140 :rule reordering :premises (@p139) :args ((or @t145 @t163 (not @t164)))) % 1.02/1.27 (step @p141 :rule chain_m_resolution :premises (@p140 @p113 @p138) :args (@t163 @t153 (@list @t145 @t164))) % 1.02/1.27 (step @p142 :rule false_intro :premises (@p141)) % 1.02/1.27 (step @p143 :rule refl :args (@t142)) % 1.02/1.27 (step @p144 :rule cong :premises (@p130 @p143) :args (@t165)) % 1.02/1.27 (step @p145 :rule trans :premises (@p144 @p142)) % 1.02/1.27 (step @p146 :rule false_elim :premises (@p145)) % 1.02/1.27 (step @p147 :rule instantiate :premises (@p15) :args (@t149)) % 1.02/1.27 (step @p148 :rule cnf_or_pos :args (@t167)) % 1.02/1.27 (step @p149 :rule reordering :premises (@p148) :args ((or @t161 @t166 (not @t167)))) % 1.02/1.27 (step @p150 :rule chain_m_resolution :premises (@p149 @p133 @p147) :args (@t166 @t158 (@list @t159 @t167))) % 1.02/1.27 (step @p151 :rule cnf_or_pos :args (@t171)) % 1.02/1.27 (step @p152 :rule reordering :premises (@p151) :args ((or @t170 @t168 @t165 (not @t171)))) % 1.02/1.27 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p146 @p137) :args (@t170 (@list false true false) (@list @t166 @t165 @t171))) % 1.02/1.27 (step @p154 :rule cnf_or_pos :args (@t173)) % 1.02/1.27 (step @p155 :rule reordering :premises (@p154) :args ((or @t169 @t172 @t174))) % 1.02/1.27 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p136) :args (@t174 @t153 (@list @t169 @t160))) % 1.02/1.27 (assume-push @p163 @t42) % 1.02/1.27 (step @p158 :rule instantiate :premises (@p22) :args ((@list @t148 tptp.x tptp.y))) % 1.02/1.27 (step-pop @p164 :rule scope :premises (@p158)) % 1.02/1.27 (step @p159 :rule process_scope :premises (@p164) :args (@t173)) % 1.02/1.27 (step @p161 :rule implies_elim :premises (@p159)) % 1.02/1.27 (step @p162 false :rule chain_m_resolution :premises (@p161 @p156 @p22) :args (false @t153 (@list @t173 @t42))) % 1.02/1.27 ) % 1.02/1.27 % SZS output end Proof % 1.02/1.27 % cvc5 exiting %------------------------------------------------------------------------------