%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET083-7 : 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 : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:47:19 AM UTC 2026 % Result : Unsatisfiable 0.32s 0.58s % Output : Proof 0.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET083-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.06/0.25 % Computer : n012.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Tue Jun 2 14:51:33 EDT 2026 % 0.06/0.25 % CPUTime : % 0.14/0.35 %----Proving TF0_NAR, FOF, or CNF % 0.14/0.36 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.32/0.58 % SZS status Unsatisfiable % 0.32/0.58 % SZS output start Proof % 0.32/0.58 ( % 0.32/0.58 (declare-sort $$unsorted 0) % 0.32/0.58 (declare-const tptp.x $$unsorted) % 0.32/0.58 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.function (-> $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.y $$unsorted) % 0.32/0.58 (declare-const tptp.element_relation $$unsorted) % 0.32/0.58 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.universal_class $$unsorted) % 0.32/0.58 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.successor_relation $$unsorted) % 0.32/0.58 (declare-const tptp.choice $$unsorted) % 0.32/0.58 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.subset_relation $$unsorted) % 0.32/0.58 (declare-const tptp.null_class $$unsorted) % 0.32/0.58 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.omega $$unsorted) % 0.32/0.58 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.identity_relation $$unsorted) % 0.32/0.58 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.32/0.58 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.32/0.58 (define @t1 () (@var "Y" $$unsorted)) % 0.32/0.58 (define @t2 () (@var "U" $$unsorted)) % 0.32/0.58 (define @t3 () (@var "X" $$unsorted)) % 0.32/0.58 (define @t4 () (tptp.member @t2 @t3)) % 0.32/0.58 (define @t5 () (not @t4)) % 0.32/0.58 (define @t6 () (tptp.subclass @t3 @t1)) % 0.32/0.58 (define @t7 () (not @t6)) % 0.32/0.58 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.32/0.58 (define @t9 () (tptp.member @t8 @t3)) % 0.32/0.58 (define @t10 () (@list @t3 @t1)) % 0.32/0.58 (define @t11 () (not (tptp.member @t8 @t1))) % 0.32/0.58 (define @t12 () (@list @t3)) % 0.32/0.58 (define @t13 () (= @t3 @t1)) % 0.32/0.58 (define @t14 () (not @t13)) % 0.32/0.58 (define @t15 () (tptp.subclass @t1 @t3)) % 0.32/0.58 (define @t16 () (tptp.unordered_pair @t3 @t1)) % 0.32/0.58 (define @t17 () (not (tptp.member @t2 @t16))) % 0.32/0.58 (define @t18 () (or @t17 (= @t2 @t3) (= @t2 @t1))) % 0.32/0.58 (define @t19 () (@list @t2 @t3 @t1)) % 0.32/0.58 (define @t20 () (forall @t19 @t18)) % 0.32/0.58 (define @t21 () (tptp.member @t3 @t16)) % 0.32/0.58 (define @t22 () (tptp.member @t3 tptp.universal_class)) % 0.32/0.58 (define @t23 () (not @t22)) % 0.32/0.58 (define @t24 () (tptp.member @t1 @t16)) % 0.32/0.58 (define @t25 () (tptp.member @t1 tptp.universal_class)) % 0.32/0.58 (define @t26 () (not @t25)) % 0.32/0.58 (define @t27 () (@list @t1 @t3)) % 0.32/0.58 (define @t28 () (tptp.singleton @t3)) % 0.32/0.58 (define @t29 () (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t28))) % 0.32/0.58 (define @t30 () (tptp.ordered_pair @t3 @t1)) % 0.32/0.58 (define @t31 () (tptp.singleton @t1)) % 0.32/0.58 (define @t32 () (tptp.unordered_pair @t3 @t31)) % 0.32/0.58 (define @t33 () (tptp.cross_product @t3 @t1)) % 0.32/0.58 (define @t34 () (@var "V" $$unsorted)) % 0.32/0.58 (define @t35 () (tptp.ordered_pair @t2 @t34)) % 0.32/0.58 (define @t36 () (tptp.member @t35 @t33)) % 0.32/0.58 (define @t37 () (not @t36)) % 0.32/0.58 (define @t38 () (@list @t2 @t34 @t3 @t1)) % 0.32/0.58 (define @t39 () (tptp.member @t34 @t1)) % 0.32/0.58 (define @t40 () (@var "Z" $$unsorted)) % 0.32/0.58 (define @t41 () (@list @t40 @t3 @t1)) % 0.32/0.58 (define @t42 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.32/0.58 (define @t43 () (tptp.member @t3 @t1)) % 0.32/0.58 (define @t44 () (tptp.member @t30 tptp.element_relation)) % 0.32/0.58 (define @t45 () (not (tptp.member @t30 @t42))) % 0.32/0.58 (define @t46 () (tptp.member @t40 @t3)) % 0.32/0.58 (define @t47 () (tptp.intersection @t3 @t1)) % 0.32/0.58 (define @t48 () (tptp.member @t40 @t47)) % 0.32/0.58 (define @t49 () (not @t48)) % 0.32/0.58 (define @t50 () (tptp.member @t40 @t1)) % 0.32/0.58 (define @t51 () (not @t46)) % 0.32/0.58 (define @t52 () (tptp.complement @t3)) % 0.32/0.58 (define @t53 () (tptp.member @t40 @t52)) % 0.32/0.58 (define @t54 () (@list @t40 @t3)) % 0.32/0.58 (define @t55 () (not (tptp.member @t40 tptp.universal_class))) % 0.32/0.58 (define @t56 () (tptp.complement (tptp.intersection @t52 (tptp.complement @t1)))) % 0.32/0.58 (define @t57 () (@var "Xr" $$unsorted)) % 0.32/0.58 (define @t58 () (tptp.restrict @t57 @t3 @t1)) % 0.32/0.58 (define @t59 () (tptp.domain_of @t3)) % 0.32/0.58 (define @t60 () (tptp.member @t40 @t59)) % 0.32/0.58 (define @t61 () (= (tptp.restrict @t3 (tptp.singleton @t40) tptp.universal_class) tptp.null_class)) % 0.32/0.58 (define @t62 () (tptp.cross_product @t42 tptp.universal_class)) % 0.32/0.58 (define @t63 () (tptp.rotate @t3)) % 0.32/0.58 (define @t64 () (@var "W" $$unsorted)) % 0.32/0.58 (define @t65 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t34 @t64) @t2) @t3)) % 0.32/0.58 (define @t66 () (tptp.ordered_pair @t35 @t64)) % 0.32/0.58 (define @t67 () (tptp.member @t66 @t63)) % 0.32/0.58 (define @t68 () (@list @t2 @t34 @t64 @t3)) % 0.32/0.58 (define @t69 () (not (tptp.member @t66 @t62))) % 0.32/0.58 (define @t70 () (tptp.flip @t3)) % 0.32/0.58 (define @t71 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t34 @t2) @t64) @t3)) % 0.32/0.58 (define @t72 () (tptp.member @t66 @t70)) % 0.32/0.58 (define @t73 () (@list @t1)) % 0.32/0.58 (define @t74 () (@list @t40)) % 0.32/0.58 (define @t75 () (tptp.successor @t3)) % 0.32/0.58 (define @t76 () (= @t75 @t1)) % 0.32/0.58 (define @t77 () (tptp.member @t30 tptp.successor_relation)) % 0.32/0.58 (define @t78 () (tptp.member tptp.null_class @t3)) % 0.32/0.58 (define @t79 () (tptp.inductive @t3)) % 0.32/0.58 (define @t80 () (not @t79)) % 0.32/0.58 (define @t81 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.32/0.58 (define @t82 () (tptp.sum_class @t3)) % 0.32/0.58 (define @t83 () (tptp.member @t2 tptp.universal_class)) % 0.32/0.58 (define @t84 () (@var "Yr" $$unsorted)) % 0.32/0.58 (define @t85 () (tptp.compose @t84 @t57)) % 0.32/0.58 (define @t86 () (tptp.member @t40 (tptp.image @t84 (tptp.image @t57 @t31)))) % 0.32/0.58 (define @t87 () (tptp.ordered_pair @t1 @t40)) % 0.32/0.58 (define @t88 () (tptp.member @t87 @t85)) % 0.32/0.58 (define @t89 () (not (tptp.member @t87 @t42))) % 0.32/0.58 (define @t90 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.32/0.58 (define @t91 () (tptp.single_valued_class @t3)) % 0.32/0.58 (define @t92 () (@var "Xf" $$unsorted)) % 0.32/0.58 (define @t93 () (tptp.subclass @t92 @t42)) % 0.32/0.58 (define @t94 () (tptp.function @t92)) % 0.32/0.58 (define @t95 () (not @t94)) % 0.32/0.58 (define @t96 () (@list @t92)) % 0.32/0.58 (define @t97 () (tptp.inverse @t92)) % 0.32/0.58 (define @t98 () (tptp.subclass (tptp.compose @t92 @t97) tptp.identity_relation)) % 0.32/0.58 (define @t99 () (tptp.regular @t3)) % 0.32/0.58 (define @t100 () (= @t3 tptp.null_class)) % 0.32/0.58 (define @t101 () (tptp.one_to_one @t92)) % 0.32/0.58 (define @t102 () (not @t101)) % 0.32/0.58 (define @t103 () (tptp.function @t97)) % 0.32/0.58 (define @t104 () (tptp.inverse tptp.element_relation)) % 0.32/0.58 (define @t105 () (tptp.operation @t92)) % 0.32/0.58 (define @t106 () (not @t105)) % 0.32/0.58 (define @t107 () (tptp.domain_of @t92)) % 0.32/0.58 (define @t108 () (tptp.domain_of @t107)) % 0.32/0.58 (define @t109 () (= (tptp.cross_product @t108 @t108) @t107)) % 0.32/0.58 (define @t110 () (tptp.subclass (tptp.range_of @t92) @t108)) % 0.32/0.58 (define @t111 () (@var "Xh" $$unsorted)) % 0.32/0.58 (define @t112 () (tptp.function @t111)) % 0.32/0.58 (define @t113 () (@var "Xf2" $$unsorted)) % 0.32/0.58 (define @t114 () (@var "Xf1" $$unsorted)) % 0.32/0.58 (define @t115 () (tptp.compatible @t111 @t114 @t113)) % 0.32/0.58 (define @t116 () (not @t115)) % 0.32/0.58 (define @t117 () (@list @t111 @t114 @t113)) % 0.32/0.58 (define @t118 () (tptp.domain_of @t114)) % 0.32/0.58 (define @t119 () (= (tptp.domain_of @t118) (tptp.domain_of @t111))) % 0.32/0.58 (define @t120 () (tptp.subclass (tptp.range_of @t111) (tptp.domain_of (tptp.domain_of @t113)))) % 0.32/0.58 (define @t121 () (tptp.operation @t114)) % 0.32/0.58 (define @t122 () (tptp.homomorphism @t111 @t114 @t113)) % 0.32/0.58 (define @t123 () (not @t122)) % 0.32/0.58 (define @t124 () (tptp.operation @t113)) % 0.32/0.58 (define @t125 () (tptp.not_homomorphism2 @t111 @t114 @t113)) % 0.32/0.58 (define @t126 () (tptp.not_homomorphism1 @t111 @t114 @t113)) % 0.32/0.58 (define @t127 () (tptp.ordered_pair @t126 @t125)) % 0.32/0.58 (define @t128 () (not @t124)) % 0.32/0.58 (define @t129 () (not @t121)) % 0.32/0.58 (define @t130 () (@list @t114 @t113 @t111)) % 0.32/0.58 (define @t131 () (not (tptp.member @t30 (tptp.cross_product @t2 @t34)))) % 0.32/0.58 (define @t132 () (@list @t3 @t1 @t2 @t34)) % 0.32/0.58 (define @t133 () (@list @t3 @t1 @t40)) % 0.32/0.58 (define @t134 () (tptp.not_subclass_element @t1 @t3)) % 0.32/0.58 (define @t135 () (tptp.member @t134 @t1)) % 0.32/0.58 (define @t136 () (not (tptp.member @t134 @t3))) % 0.32/0.58 (define @t137 () (= @t16 tptp.null_class)) % 0.32/0.58 (define @t138 () (tptp.unordered_pair @t3 @t40)) % 0.32/0.58 (define @t139 () (@list @t3 @t40 @t1)) % 0.32/0.58 (define @t140 () (not @t137)) % 0.32/0.58 (define @t141 () (= @t28 tptp.null_class)) % 0.32/0.58 (define @t142 () (tptp.singleton tptp.y)) % 0.32/0.58 (define @t143 () (tptp.singleton tptp.x)) % 0.32/0.58 (define @t144 () (tptp.member tptp.x tptp.universal_class)) % 0.32/0.58 (define @t145 () (= tptp.x tptp.y)) % 0.32/0.58 (define @t146 () (tptp.unordered_pair tptp.y tptp.y)) % 0.32/0.58 (define @t147 () (not (tptp.member tptp.x @t146))) % 0.32/0.58 (define @t148 () (= tptp.y tptp.x)) % 0.32/0.58 (define @t149 () (or @t147 @t148 @t148)) % 0.32/0.58 (define @t150 () (forall @t19 (or @t17 (= @t3 @t2) (= @t1 @t2)))) % 0.32/0.58 (define @t151 () (or @t147 @t145 @t145)) % 0.32/0.58 (define @t152 () (@list false)) % 0.32/0.58 (define @t153 () (= @t146 @t142)) % 0.32/0.58 (define @t154 () (tptp.member tptp.x @t143)) % 0.32/0.58 (define @t155 () (not @t144)) % 0.32/0.58 (define @t156 () (or @t155 @t154)) % 0.32/0.58 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.32/0.58 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.32/0.58 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.32/0.58 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.32/0.58 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.32/0.58 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.32/0.58 (assume @p7 (forall @t10 (or @t7 (not @t15) @t13))) % 0.32/0.58 (assume @p8 @t20) % 0.32/0.58 (assume @p9 (forall @t10 (or @t23 @t21))) % 0.32/0.58 (assume @p10 (forall @t27 (or @t26 @t24))) % 0.32/0.58 (assume @p11 (forall @t10 (tptp.member @t16 tptp.universal_class))) % 0.32/0.58 (assume @p12 @t29) % 0.32/0.58 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t28 @t32) @t30))) % 0.32/0.58 (assume @p14 (forall @t38 (or @t37 @t4))) % 0.32/0.58 (assume @p15 (forall @t38 (or @t37 @t39))) % 0.32/0.58 (assume @p16 (forall (@list @t2 @t3 @t34 @t1) (or @t5 (not @t39) @t36))) % 0.32/0.58 (assume @p17 (forall @t41 (or (not (tptp.member @t40 @t33)) (= (tptp.ordered_pair (tptp.first @t40) (tptp.second @t40)) @t40)))) % 0.32/0.58 (assume @p18 (tptp.subclass tptp.element_relation @t42)) % 0.32/0.58 (assume @p19 (forall @t10 (or (not @t44) @t43))) % 0.32/0.58 (assume @p20 (forall @t10 (or @t45 (not @t43) @t44))) % 0.32/0.58 (assume @p21 (forall @t41 (or @t49 @t46))) % 0.32/0.58 (assume @p22 (forall @t41 (or @t49 @t50))) % 0.32/0.58 (assume @p23 (forall @t41 (or @t51 (not @t50) @t48))) % 0.32/0.58 (assume @p24 (forall @t54 (or (not @t53) @t51))) % 0.32/0.58 (assume @p25 (forall @t54 (or @t55 @t53 @t46))) % 0.32/0.58 (assume @p26 (forall @t10 (= @t56 (tptp.union @t3 @t1)))) % 0.32/0.58 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t47) @t56) (tptp.symmetric_difference @t3 @t1)))) % 0.32/0.58 (assume @p28 (forall (@list @t57 @t3 @t1) (= (tptp.intersection @t57 @t33) @t58))) % 0.32/0.58 (assume @p29 (forall (@list @t3 @t1 @t57) (= (tptp.intersection @t33 @t57) @t58))) % 0.32/0.58 (assume @p30 (forall (@list @t3 @t40) (or (not @t61) (not @t60)))) % 0.32/0.58 (assume @p31 (forall @t54 (or @t55 @t61 @t60))) % 0.32/0.58 (assume @p32 (forall @t12 (tptp.subclass @t63 @t62))) % 0.32/0.58 (assume @p33 (forall @t68 (or (not @t67) @t65))) % 0.32/0.58 (assume @p34 (forall (@list @t34 @t64 @t2 @t3) (or (not @t65) @t69 @t67))) % 0.32/0.58 (assume @p35 (forall @t12 (tptp.subclass @t70 @t62))) % 0.32/0.58 (assume @p36 (forall @t68 (or (not @t72) @t71))) % 0.32/0.58 (assume @p37 (forall (@list @t34 @t2 @t64 @t3) (or (not @t71) @t69 @t72))) % 0.32/0.58 (assume @p38 (forall @t73 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.32/0.58 (assume @p39 (forall @t74 (= (tptp.domain_of (tptp.inverse @t40)) (tptp.range_of @t40)))) % 0.32/0.58 (assume @p40 (forall @t41 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t40 @t3 @t31) tptp.null_class)) (tptp.domain @t40 @t3 @t1)))) % 0.32/0.58 (assume @p41 (forall @t41 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t40 @t28 @t1) tptp.null_class)) (tptp.range @t40 @t3 @t1)))) % 0.32/0.58 (assume @p42 (forall (@list @t57 @t3) (= (tptp.range_of (tptp.restrict @t57 @t3 tptp.universal_class)) (tptp.image @t57 @t3)))) % 0.32/0.58 (assume @p43 (forall @t12 (= (tptp.union @t3 @t28) @t75))) % 0.32/0.58 (assume @p44 (tptp.subclass tptp.successor_relation @t42)) % 0.32/0.58 (assume @p45 (forall @t10 (or (not @t77) @t76))) % 0.32/0.58 (assume @p46 (forall @t10 (or (not @t76) @t45 @t77))) % 0.32/0.58 (assume @p47 (forall @t12 (or @t80 @t78))) % 0.32/0.58 (assume @p48 (forall @t12 (or @t80 @t81))) % 0.32/0.58 (assume @p49 (forall @t12 (or (not @t78) (not @t81) @t79))) % 0.32/0.58 (assume @p50 (tptp.inductive tptp.omega)) % 0.32/0.58 (assume @p51 (forall @t73 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.32/0.58 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.32/0.58 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t82))) % 0.32/0.58 (assume @p54 (forall @t12 (or @t23 (tptp.member @t82 tptp.universal_class)))) % 0.32/0.58 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t52)) (tptp.power_class @t3)))) % 0.32/0.58 (assume @p56 (forall (@list @t2) (or (not @t83) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.32/0.58 (assume @p57 (forall (@list @t84 @t57) (tptp.subclass @t85 @t42))) % 0.32/0.58 (assume @p58 (forall (@list @t1 @t40 @t84 @t57) (or (not @t88) @t86))) % 0.32/0.58 (assume @p59 (forall (@list @t40 @t84 @t57 @t1) (or (not @t86) @t89 @t88))) % 0.32/0.58 (assume @p60 (forall @t12 (or (not @t91) @t90))) % 0.32/0.58 (assume @p61 (forall @t12 (or (not @t90) @t91))) % 0.32/0.58 (assume @p62 (forall @t96 (or @t95 @t93))) % 0.32/0.58 (assume @p63 (forall @t96 (or @t95 @t98))) % 0.32/0.58 (assume @p64 (forall @t96 (or (not @t93) (not @t98) @t94))) % 0.32/0.58 (assume @p65 (forall (@list @t92 @t3) (or @t95 @t23 (tptp.member (tptp.image @t92 @t3) tptp.universal_class)))) % 0.32/0.58 (assume @p66 (forall @t12 (or @t100 (tptp.member @t99 @t3)))) % 0.32/0.58 (assume @p67 (forall @t12 (or @t100 (= (tptp.intersection @t3 @t99) tptp.null_class)))) % 0.32/0.58 (assume @p68 (forall (@list @t92 @t1) (= (tptp.sum_class (tptp.image @t92 @t31)) (tptp.apply @t92 @t1)))) % 0.32/0.58 (assume @p69 (tptp.function tptp.choice)) % 0.32/0.58 (assume @p70 (forall @t73 (or @t26 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.32/0.58 (assume @p71 (forall @t96 (or @t102 @t94))) % 0.32/0.58 (assume @p72 (forall @t96 (or @t102 @t103))) % 0.32/0.58 (assume @p73 (forall @t96 (or (not @t103) @t95 @t101))) % 0.32/0.58 (assume @p74 (= (tptp.intersection @t42 (tptp.intersection @t42 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t104)))) tptp.subset_relation)) % 0.32/0.58 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.32/0.58 (assume @p76 (forall (@list @t57) (= (tptp.complement (tptp.domain_of (tptp.intersection @t57 tptp.identity_relation))) (tptp.diagonalise @t57)))) % 0.32/0.58 (assume @p77 (forall @t12 (= (tptp.intersection @t59 (tptp.diagonalise (tptp.compose @t104 @t3))) (tptp.cantor @t3)))) % 0.32/0.58 (assume @p78 (forall @t96 (or @t106 @t94))) % 0.32/0.58 (assume @p79 (forall @t96 (or @t106 @t109))) % 0.32/0.58 (assume @p80 (forall @t96 (or @t106 @t110))) % 0.32/0.58 (assume @p81 (forall @t96 (or @t95 (not @t109) (not @t110) @t105))) % 0.32/0.58 (assume @p82 (forall @t117 (or @t116 @t112))) % 0.32/0.58 (assume @p83 (forall @t117 (or @t116 @t119))) % 0.32/0.58 (assume @p84 (forall @t117 (or @t116 @t120))) % 0.32/0.58 (assume @p85 (forall @t117 (or (not @t112) (not @t119) (not @t120) @t115))) % 0.32/0.58 (assume @p86 (forall @t117 (or @t123 @t121))) % 0.32/0.58 (assume @p87 (forall @t117 (or @t123 @t124))) % 0.32/0.58 (assume @p88 (forall @t117 (or @t123 @t115))) % 0.32/0.58 (assume @p89 (forall (@list @t111 @t114 @t113 @t3 @t1) (or @t123 (not (tptp.member @t30 @t118)) (= (tptp.apply @t113 (tptp.ordered_pair (tptp.apply @t111 @t3) (tptp.apply @t111 @t1))) (tptp.apply @t111 (tptp.apply @t114 @t30)))))) % 0.32/0.58 (assume @p90 (forall @t130 (or @t129 @t128 @t116 (tptp.member @t127 @t118) @t122))) % 0.32/0.58 (assume @p91 (forall @t130 (or @t129 @t128 @t116 (not (= (tptp.apply @t113 (tptp.ordered_pair (tptp.apply @t111 @t126) (tptp.apply @t111 @t125))) (tptp.apply @t111 (tptp.apply @t114 @t127)))) @t122))) % 0.32/0.58 (assume @p92 (forall @t132 (or @t131 @t21))) % 0.32/0.58 (assume @p93 (forall @t132 (or @t131 @t24))) % 0.32/0.58 (assume @p94 (forall @t38 (or @t37 @t83))) % 0.32/0.58 (assume @p95 (forall @t38 (or @t37 (tptp.member @t34 tptp.universal_class)))) % 0.32/0.58 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.32/0.58 (assume @p97 (forall @t133 (or @t7 (not (tptp.subclass @t1 @t40)) (tptp.subclass @t3 @t40)))) % 0.32/0.58 (assume @p98 (forall @t10 (or @t13 @t9 @t135))) % 0.32/0.58 (assume @p99 (forall @t10 (or @t11 @t13 @t135))) % 0.32/0.58 (assume @p100 (forall @t27 (or @t136 @t13 @t9))) % 0.32/0.58 (assume @p101 (forall @t10 (or @t11 @t136 @t13))) % 0.32/0.58 (assume @p102 (forall @t27 (not (tptp.member @t1 (tptp.intersection @t52 @t3))))) % 0.32/0.58 (assume @p103 (forall @t74 (not (tptp.member @t40 tptp.null_class)))) % 0.32/0.58 (assume @p104 (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.32/0.58 (assume @p105 (forall @t12 (or (not (tptp.subclass @t3 tptp.null_class)) @t100))) % 0.32/0.58 (assume @p106 (forall @t74 (or (= @t40 tptp.null_class) (tptp.member (tptp.not_subclass_element @t40 tptp.null_class) @t40)))) % 0.32/0.58 (assume @p107 (tptp.member tptp.null_class tptp.universal_class)) % 0.32/0.58 (assume @p108 (forall @t10 (= @t16 (tptp.unordered_pair @t1 @t3)))) % 0.32/0.58 (assume @p109 (forall @t10 (tptp.subclass @t28 @t16))) % 0.32/0.58 (assume @p110 (forall @t27 (tptp.subclass @t31 @t16))) % 0.32/0.58 (assume @p111 (forall @t27 (or @t25 (= @t16 @t28)))) % 0.32/0.58 (assume @p112 (forall @t10 (or @t22 (= @t16 @t31)))) % 0.32/0.58 (assume @p113 (forall @t10 (or @t137 @t22 @t25))) % 0.32/0.58 (assume @p114 (forall @t133 (or (not (= @t16 @t138)) @t89 (= @t1 @t40)))) % 0.32/0.58 (assume @p115 (forall @t139 (or (not (= @t138 (tptp.unordered_pair @t1 @t40))) @t45 @t13))) % 0.32/0.58 (assume @p116 (forall @t10 (or @t23 @t140))) % 0.32/0.58 (assume @p117 (forall @t27 (or @t26 @t140))) % 0.32/0.58 (assume @p118 (forall @t132 (or @t131 @t140))) % 0.32/0.58 (assume @p119 (forall @t139 (or (not (tptp.member @t3 @t40)) (not (tptp.member @t1 @t40)) (tptp.subclass @t16 @t40)))) % 0.32/0.58 (assume @p120 (forall @t12 (tptp.member @t28 tptp.universal_class))) % 0.32/0.58 (assume @p121 (forall @t27 (tptp.member @t31 @t32))) % 0.32/0.58 (assume @p122 (forall @t12 (or @t23 (tptp.member @t3 @t28)))) % 0.32/0.58 (assume @p123 (forall @t12 (or @t23 (not @t141)))) % 0.32/0.58 (assume @p124 (tptp.member tptp.null_class (tptp.singleton tptp.null_class))) % 0.32/0.58 (assume @p125 (forall @t27 (or (not (tptp.member @t1 @t28)) (= @t1 @t3)))) % 0.32/0.58 (assume @p126 (forall @t12 (or @t22 @t141))) % 0.32/0.58 (assume @p127 (= @t143 @t142)) % 0.32/0.58 (assume @p128 @t144) % 0.32/0.58 (assume @p129 (not @t145)) % 0.32/0.58 (step @p130 :rule evaluate :args ((= true false))) % 0.32/0.58 (step @p131 :rule eq-symm :args (@t2 @t1)) % 0.32/0.58 (step @p132 :rule eq-symm :args (@t2 @t3)) % 0.32/0.58 (step @p133 :rule refl :args (@t17)) % 0.32/0.58 (step @p134 :rule nary_cong :premises (@p133 @p132 @p131) :args (@t18)) % 0.32/0.58 (step @p135 :rule cong :premises (@p134) :args (@t20)) % 0.32/0.58 (step @p136 :rule eq_resolve :premises (@p8 @p135)) % 0.32/0.58 (step @p137 :rule eq-symm :args (tptp.y tptp.x)) % 0.32/0.58 (step @p138 :rule refl :args (@t147)) % 0.32/0.58 (step @p139 :rule nary_cong :premises (@p138 @p137 @p137) :args (@t149)) % 0.32/0.58 (step @p140 :rule refl :args (@t150)) % 0.32/0.58 (step @p141 :rule cong :premises (@p140 @p139) :args ((=> @t150 @t149))) % 0.32/0.58 (assume-push @p175 @t150) % 0.32/0.58 (step @p143 :rule instantiate :premises (@p136) :args ((@list tptp.x tptp.y tptp.y))) % 0.32/0.58 (step-pop @p176 :rule scope :premises (@p143)) % 0.32/0.58 (step @p144 :rule process_scope :premises (@p176) :args (@t149)) % 0.32/0.58 (step @p146 :rule eq_resolve :premises (@p144 @p141)) % 0.32/0.58 (step @p147 :rule implies_elim :premises (@p146)) % 0.32/0.58 (step @p148 :rule chain_m_resolution :premises (@p147 @p136) :args (@t151 @t152 (@list @t150))) % 0.32/0.58 (step @p149 :rule cnf_or_pos :args (@t151)) % 0.32/0.58 (step @p150 :rule factoring :premises (@p149)) % 0.32/0.58 (step @p151 :rule reordering :premises (@p150) :args ((or @t145 @t147 (not @t151)))) % 0.32/0.58 (step @p152 :rule chain_m_resolution :premises (@p151 @p129 @p148) :args (@t147 (@list true false) (@list @t145 @t151))) % 0.32/0.58 (step @p153 :rule false_intro :premises (@p152)) % 0.32/0.58 (step @p154 :rule eq-symm :args (@t146 @t142)) % 0.32/0.58 (step @p155 :rule refl :args (@t29)) % 0.32/0.58 (step @p156 :rule cong :premises (@p155 @p154) :args ((=> @t29 @t153))) % 0.32/0.58 (assume-push @p177 @t29) % 0.32/0.58 (step @p158 :rule instantiate :premises (@p12) :args ((@list tptp.y))) % 0.32/0.58 (step-pop @p178 :rule scope :premises (@p158)) % 0.32/0.58 (step @p159 :rule process_scope :premises (@p178) :args (@t153)) % 0.32/0.58 (step @p161 :rule eq_resolve :premises (@p159 @p156)) % 0.32/0.58 (step @p162 :rule implies_elim :premises (@p161)) % 0.32/0.58 (step @p163 :rule chain_m_resolution :premises (@p162 @p12) :args ((= @t142 @t146) @t152 (@list @t29))) % 0.32/0.58 (step @p164 :rule trans :premises (@p127 @p163)) % 0.32/0.58 (step @p165 :rule refl :args (tptp.x)) % 0.32/0.58 (step @p166 :rule cong :premises (@p165 @p164) :args (@t154)) % 0.32/0.58 (step @p167 :rule instantiate :premises (@p122) :args ((@list tptp.x))) % 0.32/0.58 (step @p168 :rule cnf_or_pos :args (@t156)) % 0.32/0.58 (step @p169 :rule reordering :premises (@p168) :args ((or @t155 @t154 (not @t156)))) % 0.32/0.58 (step @p170 :rule chain_m_resolution :premises (@p169 @p128 @p167) :args (@t154 (@list false false) (@list @t144 @t156))) % 0.32/0.58 (step @p171 :rule true_intro :premises (@p170)) % 0.32/0.58 (step @p172 :rule symm :premises (@p171)) % 0.32/0.58 (step @p173 :rule trans :premises (@p172 @p166 @p153)) % 0.32/0.58 (step @p174 false :rule eq_resolve :premises (@p173 @p130)) % 0.32/0.58 ) % 0.32/0.59 % SZS output end Proof % 0.32/0.59 % cvc5 exiting %------------------------------------------------------------------------------