%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET076-7 : 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 : n013.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 08:47:17 AM UTC 2026 % Result : Unsatisfiable 0.35s 0.64s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET076-7 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n013.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 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:51:00 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.26/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.64 % SZS status Unsatisfiable % 0.35/0.64 % SZS output start Proof % 0.35/0.65 ( % 0.35/0.65 (declare-sort $$unsorted 0) % 0.35/0.65 (declare-const tptp.y $$unsorted) % 0.35/0.65 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.z $$unsorted) % 0.35/0.65 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.element_relation $$unsorted) % 0.35/0.65 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.universal_class $$unsorted) % 0.35/0.65 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.successor_relation $$unsorted) % 0.35/0.65 (declare-const tptp.choice $$unsorted) % 0.35/0.65 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.subset_relation $$unsorted) % 0.35/0.65 (declare-const tptp.null_class $$unsorted) % 0.35/0.65 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.omega $$unsorted) % 0.35/0.65 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.65 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.identity_relation $$unsorted) % 0.35/0.65 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.x $$unsorted) % 0.35/0.65 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.35/0.65 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.35/0.65 (define @t1 () (@var "Y" $$unsorted)) % 0.35/0.65 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.65 (define @t3 () (@var "X" $$unsorted)) % 0.35/0.65 (define @t4 () (tptp.member @t2 @t3)) % 0.35/0.65 (define @t5 () (not @t4)) % 0.35/0.65 (define @t6 () (tptp.subclass @t3 @t1)) % 0.35/0.65 (define @t7 () (not @t6)) % 0.35/0.65 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.35/0.65 (define @t9 () (tptp.member @t8 @t3)) % 0.35/0.65 (define @t10 () (@list @t3 @t1)) % 0.35/0.65 (define @t11 () (not (tptp.member @t8 @t1))) % 0.35/0.65 (define @t12 () (@list @t3)) % 0.35/0.65 (define @t13 () (= @t3 @t1)) % 0.35/0.65 (define @t14 () (not @t13)) % 0.35/0.65 (define @t15 () (tptp.subclass @t1 @t3)) % 0.35/0.65 (define @t16 () (tptp.unordered_pair @t3 @t1)) % 0.35/0.65 (define @t17 () (not (tptp.member @t2 @t16))) % 0.35/0.65 (define @t18 () (or @t17 (= @t2 @t3) (= @t2 @t1))) % 0.35/0.65 (define @t19 () (forall (@list @t2 @t3 @t1) @t18)) % 0.35/0.65 (define @t20 () (tptp.member @t3 @t16)) % 0.35/0.65 (define @t21 () (tptp.member @t3 tptp.universal_class)) % 0.35/0.65 (define @t22 () (not @t21)) % 0.35/0.65 (define @t23 () (tptp.member @t1 @t16)) % 0.35/0.65 (define @t24 () (tptp.member @t1 tptp.universal_class)) % 0.35/0.65 (define @t25 () (not @t24)) % 0.35/0.65 (define @t26 () (@list @t1 @t3)) % 0.35/0.65 (define @t27 () (tptp.singleton @t3)) % 0.35/0.65 (define @t28 () (tptp.ordered_pair @t3 @t1)) % 0.35/0.65 (define @t29 () (tptp.singleton @t1)) % 0.35/0.65 (define @t30 () (tptp.cross_product @t3 @t1)) % 0.35/0.65 (define @t31 () (@var "V" $$unsorted)) % 0.35/0.65 (define @t32 () (tptp.ordered_pair @t2 @t31)) % 0.35/0.65 (define @t33 () (tptp.member @t32 @t30)) % 0.35/0.65 (define @t34 () (not @t33)) % 0.35/0.65 (define @t35 () (@list @t2 @t31 @t3 @t1)) % 0.35/0.65 (define @t36 () (tptp.member @t31 @t1)) % 0.35/0.65 (define @t37 () (@var "Z" $$unsorted)) % 0.35/0.65 (define @t38 () (@list @t37 @t3 @t1)) % 0.35/0.65 (define @t39 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.35/0.65 (define @t40 () (tptp.member @t3 @t1)) % 0.35/0.65 (define @t41 () (tptp.member @t28 tptp.element_relation)) % 0.35/0.65 (define @t42 () (not (tptp.member @t28 @t39))) % 0.35/0.65 (define @t43 () (tptp.member @t37 @t3)) % 0.35/0.65 (define @t44 () (tptp.intersection @t3 @t1)) % 0.35/0.65 (define @t45 () (tptp.member @t37 @t44)) % 0.35/0.65 (define @t46 () (not @t45)) % 0.35/0.65 (define @t47 () (tptp.member @t37 @t1)) % 0.35/0.65 (define @t48 () (not @t43)) % 0.35/0.65 (define @t49 () (tptp.complement @t3)) % 0.35/0.65 (define @t50 () (tptp.member @t37 @t49)) % 0.35/0.65 (define @t51 () (@list @t37 @t3)) % 0.35/0.65 (define @t52 () (not (tptp.member @t37 tptp.universal_class))) % 0.35/0.65 (define @t53 () (tptp.complement (tptp.intersection @t49 (tptp.complement @t1)))) % 0.35/0.65 (define @t54 () (@var "Xr" $$unsorted)) % 0.35/0.65 (define @t55 () (tptp.restrict @t54 @t3 @t1)) % 0.35/0.65 (define @t56 () (tptp.domain_of @t3)) % 0.35/0.65 (define @t57 () (tptp.member @t37 @t56)) % 0.35/0.65 (define @t58 () (= (tptp.restrict @t3 (tptp.singleton @t37) tptp.universal_class) tptp.null_class)) % 0.35/0.65 (define @t59 () (tptp.cross_product @t39 tptp.universal_class)) % 0.35/0.65 (define @t60 () (tptp.rotate @t3)) % 0.35/0.65 (define @t61 () (@var "W" $$unsorted)) % 0.35/0.65 (define @t62 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t31 @t61) @t2) @t3)) % 0.35/0.65 (define @t63 () (tptp.ordered_pair @t32 @t61)) % 0.35/0.65 (define @t64 () (tptp.member @t63 @t60)) % 0.35/0.65 (define @t65 () (@list @t2 @t31 @t61 @t3)) % 0.35/0.65 (define @t66 () (not (tptp.member @t63 @t59))) % 0.35/0.65 (define @t67 () (tptp.flip @t3)) % 0.35/0.65 (define @t68 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t31 @t2) @t61) @t3)) % 0.35/0.65 (define @t69 () (tptp.member @t63 @t67)) % 0.35/0.65 (define @t70 () (@list @t1)) % 0.35/0.65 (define @t71 () (@list @t37)) % 0.35/0.65 (define @t72 () (tptp.successor @t3)) % 0.35/0.65 (define @t73 () (= @t72 @t1)) % 0.35/0.65 (define @t74 () (tptp.member @t28 tptp.successor_relation)) % 0.35/0.65 (define @t75 () (tptp.member tptp.null_class @t3)) % 0.35/0.65 (define @t76 () (tptp.inductive @t3)) % 0.35/0.65 (define @t77 () (not @t76)) % 0.35/0.65 (define @t78 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.35/0.65 (define @t79 () (tptp.sum_class @t3)) % 0.35/0.65 (define @t80 () (tptp.member @t2 tptp.universal_class)) % 0.35/0.65 (define @t81 () (@var "Yr" $$unsorted)) % 0.35/0.65 (define @t82 () (tptp.compose @t81 @t54)) % 0.35/0.65 (define @t83 () (tptp.member @t37 (tptp.image @t81 (tptp.image @t54 @t29)))) % 0.35/0.65 (define @t84 () (tptp.ordered_pair @t1 @t37)) % 0.35/0.65 (define @t85 () (tptp.member @t84 @t82)) % 0.35/0.65 (define @t86 () (not (tptp.member @t84 @t39))) % 0.35/0.65 (define @t87 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.35/0.65 (define @t88 () (tptp.single_valued_class @t3)) % 0.35/0.65 (define @t89 () (@var "Xf" $$unsorted)) % 0.35/0.65 (define @t90 () (tptp.subclass @t89 @t39)) % 0.35/0.65 (define @t91 () (tptp.function @t89)) % 0.35/0.65 (define @t92 () (not @t91)) % 0.35/0.65 (define @t93 () (@list @t89)) % 0.35/0.65 (define @t94 () (tptp.inverse @t89)) % 0.35/0.65 (define @t95 () (tptp.subclass (tptp.compose @t89 @t94) tptp.identity_relation)) % 0.35/0.65 (define @t96 () (tptp.regular @t3)) % 0.35/0.65 (define @t97 () (= @t3 tptp.null_class)) % 0.35/0.65 (define @t98 () (tptp.one_to_one @t89)) % 0.35/0.65 (define @t99 () (not @t98)) % 0.35/0.65 (define @t100 () (tptp.function @t94)) % 0.35/0.65 (define @t101 () (tptp.inverse tptp.element_relation)) % 0.35/0.65 (define @t102 () (tptp.operation @t89)) % 0.35/0.65 (define @t103 () (not @t102)) % 0.35/0.65 (define @t104 () (tptp.domain_of @t89)) % 0.35/0.65 (define @t105 () (tptp.domain_of @t104)) % 0.35/0.65 (define @t106 () (= (tptp.cross_product @t105 @t105) @t104)) % 0.35/0.65 (define @t107 () (tptp.subclass (tptp.range_of @t89) @t105)) % 0.35/0.65 (define @t108 () (@var "Xh" $$unsorted)) % 0.35/0.65 (define @t109 () (tptp.function @t108)) % 0.35/0.65 (define @t110 () (@var "Xf2" $$unsorted)) % 0.35/0.65 (define @t111 () (@var "Xf1" $$unsorted)) % 0.35/0.65 (define @t112 () (tptp.compatible @t108 @t111 @t110)) % 0.35/0.65 (define @t113 () (not @t112)) % 0.35/0.65 (define @t114 () (@list @t108 @t111 @t110)) % 0.35/0.65 (define @t115 () (tptp.domain_of @t111)) % 0.35/0.65 (define @t116 () (= (tptp.domain_of @t115) (tptp.domain_of @t108))) % 0.35/0.65 (define @t117 () (tptp.subclass (tptp.range_of @t108) (tptp.domain_of (tptp.domain_of @t110)))) % 0.35/0.65 (define @t118 () (tptp.operation @t111)) % 0.35/0.65 (define @t119 () (tptp.homomorphism @t108 @t111 @t110)) % 0.35/0.65 (define @t120 () (not @t119)) % 0.35/0.65 (define @t121 () (tptp.operation @t110)) % 0.35/0.65 (define @t122 () (tptp.not_homomorphism2 @t108 @t111 @t110)) % 0.35/0.65 (define @t123 () (tptp.not_homomorphism1 @t108 @t111 @t110)) % 0.35/0.65 (define @t124 () (tptp.ordered_pair @t123 @t122)) % 0.35/0.65 (define @t125 () (not @t121)) % 0.35/0.65 (define @t126 () (not @t118)) % 0.35/0.65 (define @t127 () (@list @t111 @t110 @t108)) % 0.35/0.65 (define @t128 () (not (tptp.member @t28 (tptp.cross_product @t2 @t31)))) % 0.35/0.65 (define @t129 () (@list @t3 @t1 @t2 @t31)) % 0.35/0.65 (define @t130 () (@list @t3 @t1 @t37)) % 0.35/0.65 (define @t131 () (tptp.not_subclass_element @t1 @t3)) % 0.35/0.65 (define @t132 () (tptp.member @t131 @t1)) % 0.35/0.65 (define @t133 () (not (tptp.member @t131 @t3))) % 0.35/0.65 (define @t134 () (= @t16 tptp.null_class)) % 0.35/0.65 (define @t135 () (tptp.unordered_pair @t3 @t37)) % 0.35/0.65 (define @t136 () (not @t134)) % 0.35/0.65 (define @t137 () (tptp.member tptp.x tptp.z)) % 0.35/0.65 (define @t138 () (tptp.member tptp.y tptp.z)) % 0.35/0.65 (define @t139 () (tptp.unordered_pair tptp.x tptp.y)) % 0.35/0.65 (define @t140 () (tptp.subclass @t139 tptp.z)) % 0.35/0.65 (define @t141 () (@list @t139 tptp.z)) % 0.35/0.65 (define @t142 () (tptp.not_subclass_element @t139 tptp.z)) % 0.35/0.65 (define @t143 () (tptp.member @t142 tptp.z)) % 0.35/0.65 (define @t144 () (not @t143)) % 0.35/0.65 (define @t145 () (or @t144 @t140)) % 0.35/0.65 (define @t146 () (@list true false)) % 0.35/0.65 (define @t147 () (= tptp.x @t142)) % 0.35/0.65 (define @t148 () (not @t147)) % 0.35/0.65 (define @t149 () (not @t137)) % 0.35/0.65 (define @t150 () (not @t144)) % 0.35/0.65 (define @t151 () (= false true)) % 0.35/0.65 (define @t152 () (and @t137 @t147 @t144)) % 0.35/0.65 (define @t153 () (tptp.member @t142 @t139)) % 0.35/0.65 (define @t154 () (or @t153 @t140)) % 0.35/0.65 (define @t155 () (= tptp.y @t142)) % 0.35/0.65 (define @t156 () (not @t153)) % 0.35/0.65 (define @t157 () (or @t156 @t147 @t155)) % 0.35/0.65 (define @t158 () (@list false true false)) % 0.35/0.65 (define @t159 () (not @t155)) % 0.35/0.65 (define @t160 () (not @t138)) % 0.35/0.65 (define @t161 () (and @t138 @t155 @t144)) % 0.35/0.65 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.35/0.65 (assume @p2 (forall @t10 (or @t9 @t6))) % 0.35/0.65 (assume @p3 (forall @t10 (or @t11 @t6))) % 0.35/0.65 (assume @p4 (forall @t12 (tptp.subclass @t3 tptp.universal_class))) % 0.35/0.65 (assume @p5 (forall @t10 (or @t14 @t6))) % 0.35/0.65 (assume @p6 (forall @t10 (or @t14 @t15))) % 0.35/0.65 (assume @p7 (forall @t10 (or @t7 (not @t15) @t13))) % 0.35/0.65 (assume @p8 @t19) % 0.35/0.65 (assume @p9 (forall @t10 (or @t22 @t20))) % 0.35/0.65 (assume @p10 (forall @t26 (or @t25 @t23))) % 0.35/0.65 (assume @p11 (forall @t10 (tptp.member @t16 tptp.universal_class))) % 0.35/0.65 (assume @p12 (forall @t12 (= (tptp.unordered_pair @t3 @t3) @t27))) % 0.35/0.65 (assume @p13 (forall @t10 (= (tptp.unordered_pair @t27 (tptp.unordered_pair @t3 @t29)) @t28))) % 0.35/0.65 (assume @p14 (forall @t35 (or @t34 @t4))) % 0.35/0.65 (assume @p15 (forall @t35 (or @t34 @t36))) % 0.35/0.65 (assume @p16 (forall (@list @t2 @t3 @t31 @t1) (or @t5 (not @t36) @t33))) % 0.35/0.65 (assume @p17 (forall @t38 (or (not (tptp.member @t37 @t30)) (= (tptp.ordered_pair (tptp.first @t37) (tptp.second @t37)) @t37)))) % 0.35/0.65 (assume @p18 (tptp.subclass tptp.element_relation @t39)) % 0.35/0.65 (assume @p19 (forall @t10 (or (not @t41) @t40))) % 0.35/0.65 (assume @p20 (forall @t10 (or @t42 (not @t40) @t41))) % 0.35/0.65 (assume @p21 (forall @t38 (or @t46 @t43))) % 0.35/0.65 (assume @p22 (forall @t38 (or @t46 @t47))) % 0.35/0.65 (assume @p23 (forall @t38 (or @t48 (not @t47) @t45))) % 0.35/0.65 (assume @p24 (forall @t51 (or (not @t50) @t48))) % 0.35/0.65 (assume @p25 (forall @t51 (or @t52 @t50 @t43))) % 0.35/0.65 (assume @p26 (forall @t10 (= @t53 (tptp.union @t3 @t1)))) % 0.35/0.65 (assume @p27 (forall @t10 (= (tptp.intersection (tptp.complement @t44) @t53) (tptp.symmetric_difference @t3 @t1)))) % 0.35/0.65 (assume @p28 (forall (@list @t54 @t3 @t1) (= (tptp.intersection @t54 @t30) @t55))) % 0.35/0.65 (assume @p29 (forall (@list @t3 @t1 @t54) (= (tptp.intersection @t30 @t54) @t55))) % 0.35/0.65 (assume @p30 (forall (@list @t3 @t37) (or (not @t58) (not @t57)))) % 0.35/0.65 (assume @p31 (forall @t51 (or @t52 @t58 @t57))) % 0.35/0.65 (assume @p32 (forall @t12 (tptp.subclass @t60 @t59))) % 0.35/0.65 (assume @p33 (forall @t65 (or (not @t64) @t62))) % 0.35/0.65 (assume @p34 (forall (@list @t31 @t61 @t2 @t3) (or (not @t62) @t66 @t64))) % 0.35/0.65 (assume @p35 (forall @t12 (tptp.subclass @t67 @t59))) % 0.35/0.65 (assume @p36 (forall @t65 (or (not @t69) @t68))) % 0.35/0.65 (assume @p37 (forall (@list @t31 @t2 @t61 @t3) (or (not @t68) @t66 @t69))) % 0.35/0.65 (assume @p38 (forall @t70 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.35/0.65 (assume @p39 (forall @t71 (= (tptp.domain_of (tptp.inverse @t37)) (tptp.range_of @t37)))) % 0.35/0.65 (assume @p40 (forall @t38 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t37 @t3 @t29) tptp.null_class)) (tptp.domain @t37 @t3 @t1)))) % 0.35/0.65 (assume @p41 (forall @t38 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t37 @t27 @t1) tptp.null_class)) (tptp.range @t37 @t3 @t1)))) % 0.35/0.65 (assume @p42 (forall (@list @t54 @t3) (= (tptp.range_of (tptp.restrict @t54 @t3 tptp.universal_class)) (tptp.image @t54 @t3)))) % 0.35/0.65 (assume @p43 (forall @t12 (= (tptp.union @t3 @t27) @t72))) % 0.35/0.65 (assume @p44 (tptp.subclass tptp.successor_relation @t39)) % 0.35/0.65 (assume @p45 (forall @t10 (or (not @t74) @t73))) % 0.35/0.65 (assume @p46 (forall @t10 (or (not @t73) @t42 @t74))) % 0.35/0.65 (assume @p47 (forall @t12 (or @t77 @t75))) % 0.35/0.65 (assume @p48 (forall @t12 (or @t77 @t78))) % 0.35/0.65 (assume @p49 (forall @t12 (or (not @t75) (not @t78) @t76))) % 0.35/0.65 (assume @p50 (tptp.inductive tptp.omega)) % 0.35/0.65 (assume @p51 (forall @t70 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.35/0.65 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.35/0.65 (assume @p53 (forall @t12 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t79))) % 0.35/0.65 (assume @p54 (forall @t12 (or @t22 (tptp.member @t79 tptp.universal_class)))) % 0.35/0.65 (assume @p55 (forall @t12 (= (tptp.complement (tptp.image tptp.element_relation @t49)) (tptp.power_class @t3)))) % 0.35/0.65 (assume @p56 (forall (@list @t2) (or (not @t80) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.35/0.65 (assume @p57 (forall (@list @t81 @t54) (tptp.subclass @t82 @t39))) % 0.35/0.65 (assume @p58 (forall (@list @t1 @t37 @t81 @t54) (or (not @t85) @t83))) % 0.35/0.65 (assume @p59 (forall (@list @t37 @t81 @t54 @t1) (or (not @t83) @t86 @t85))) % 0.35/0.65 (assume @p60 (forall @t12 (or (not @t88) @t87))) % 0.35/0.65 (assume @p61 (forall @t12 (or (not @t87) @t88))) % 0.35/0.65 (assume @p62 (forall @t93 (or @t92 @t90))) % 0.35/0.65 (assume @p63 (forall @t93 (or @t92 @t95))) % 0.35/0.65 (assume @p64 (forall @t93 (or (not @t90) (not @t95) @t91))) % 0.35/0.65 (assume @p65 (forall (@list @t89 @t3) (or @t92 @t22 (tptp.member (tptp.image @t89 @t3) tptp.universal_class)))) % 0.35/0.65 (assume @p66 (forall @t12 (or @t97 (tptp.member @t96 @t3)))) % 0.35/0.65 (assume @p67 (forall @t12 (or @t97 (= (tptp.intersection @t3 @t96) tptp.null_class)))) % 0.35/0.65 (assume @p68 (forall (@list @t89 @t1) (= (tptp.sum_class (tptp.image @t89 @t29)) (tptp.apply @t89 @t1)))) % 0.35/0.65 (assume @p69 (tptp.function tptp.choice)) % 0.35/0.65 (assume @p70 (forall @t70 (or @t25 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.35/0.65 (assume @p71 (forall @t93 (or @t99 @t91))) % 0.35/0.65 (assume @p72 (forall @t93 (or @t99 @t100))) % 0.35/0.65 (assume @p73 (forall @t93 (or (not @t100) @t92 @t98))) % 0.35/0.65 (assume @p74 (= (tptp.intersection @t39 (tptp.intersection @t39 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t101)))) tptp.subset_relation)) % 0.35/0.65 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.35/0.65 (assume @p76 (forall (@list @t54) (= (tptp.complement (tptp.domain_of (tptp.intersection @t54 tptp.identity_relation))) (tptp.diagonalise @t54)))) % 0.35/0.65 (assume @p77 (forall @t12 (= (tptp.intersection @t56 (tptp.diagonalise (tptp.compose @t101 @t3))) (tptp.cantor @t3)))) % 0.35/0.65 (assume @p78 (forall @t93 (or @t103 @t91))) % 0.35/0.65 (assume @p79 (forall @t93 (or @t103 @t106))) % 0.35/0.65 (assume @p80 (forall @t93 (or @t103 @t107))) % 0.35/0.65 (assume @p81 (forall @t93 (or @t92 (not @t106) (not @t107) @t102))) % 0.35/0.65 (assume @p82 (forall @t114 (or @t113 @t109))) % 0.35/0.65 (assume @p83 (forall @t114 (or @t113 @t116))) % 0.35/0.65 (assume @p84 (forall @t114 (or @t113 @t117))) % 0.35/0.65 (assume @p85 (forall @t114 (or (not @t109) (not @t116) (not @t117) @t112))) % 0.35/0.65 (assume @p86 (forall @t114 (or @t120 @t118))) % 0.35/0.65 (assume @p87 (forall @t114 (or @t120 @t121))) % 0.35/0.65 (assume @p88 (forall @t114 (or @t120 @t112))) % 0.35/0.65 (assume @p89 (forall (@list @t108 @t111 @t110 @t3 @t1) (or @t120 (not (tptp.member @t28 @t115)) (= (tptp.apply @t110 (tptp.ordered_pair (tptp.apply @t108 @t3) (tptp.apply @t108 @t1))) (tptp.apply @t108 (tptp.apply @t111 @t28)))))) % 0.35/0.65 (assume @p90 (forall @t127 (or @t126 @t125 @t113 (tptp.member @t124 @t115) @t119))) % 0.35/0.65 (assume @p91 (forall @t127 (or @t126 @t125 @t113 (not (= (tptp.apply @t110 (tptp.ordered_pair (tptp.apply @t108 @t123) (tptp.apply @t108 @t122))) (tptp.apply @t108 (tptp.apply @t111 @t124)))) @t119))) % 0.35/0.65 (assume @p92 (forall @t129 (or @t128 @t20))) % 0.35/0.65 (assume @p93 (forall @t129 (or @t128 @t23))) % 0.35/0.65 (assume @p94 (forall @t35 (or @t34 @t80))) % 0.35/0.65 (assume @p95 (forall @t35 (or @t34 (tptp.member @t31 tptp.universal_class)))) % 0.35/0.65 (assume @p96 (forall @t12 (tptp.subclass @t3 @t3))) % 0.35/0.65 (assume @p97 (forall @t130 (or @t7 (not (tptp.subclass @t1 @t37)) (tptp.subclass @t3 @t37)))) % 0.35/0.65 (assume @p98 (forall @t10 (or @t13 @t9 @t132))) % 0.35/0.65 (assume @p99 (forall @t10 (or @t11 @t13 @t132))) % 0.35/0.65 (assume @p100 (forall @t26 (or @t133 @t13 @t9))) % 0.35/0.65 (assume @p101 (forall @t10 (or @t11 @t133 @t13))) % 0.35/0.65 (assume @p102 (forall @t26 (not (tptp.member @t1 (tptp.intersection @t49 @t3))))) % 0.35/0.65 (assume @p103 (forall @t71 (not (tptp.member @t37 tptp.null_class)))) % 0.35/0.65 (assume @p104 (forall @t12 (tptp.subclass tptp.null_class @t3))) % 0.35/0.65 (assume @p105 (forall @t12 (or (not (tptp.subclass @t3 tptp.null_class)) @t97))) % 0.35/0.65 (assume @p106 (forall @t71 (or (= @t37 tptp.null_class) (tptp.member (tptp.not_subclass_element @t37 tptp.null_class) @t37)))) % 0.35/0.65 (assume @p107 (tptp.member tptp.null_class tptp.universal_class)) % 0.35/0.65 (assume @p108 (forall @t10 (= @t16 (tptp.unordered_pair @t1 @t3)))) % 0.35/0.65 (assume @p109 (forall @t10 (tptp.subclass @t27 @t16))) % 0.35/0.65 (assume @p110 (forall @t26 (tptp.subclass @t29 @t16))) % 0.35/0.65 (assume @p111 (forall @t26 (or @t24 (= @t16 @t27)))) % 0.35/0.65 (assume @p112 (forall @t10 (or @t21 (= @t16 @t29)))) % 0.35/0.65 (assume @p113 (forall @t10 (or @t134 @t21 @t24))) % 0.35/0.65 (assume @p114 (forall @t130 (or (not (= @t16 @t135)) @t86 (= @t1 @t37)))) % 0.35/0.65 (assume @p115 (forall (@list @t3 @t37 @t1) (or (not (= @t135 (tptp.unordered_pair @t1 @t37))) @t42 @t13))) % 0.35/0.65 (assume @p116 (forall @t10 (or @t22 @t136))) % 0.35/0.65 (assume @p117 (forall @t26 (or @t25 @t136))) % 0.35/0.65 (assume @p118 (forall @t129 (or @t128 @t136))) % 0.35/0.65 (assume @p119 @t137) % 0.35/0.65 (assume @p120 @t138) % 0.35/0.65 (assume @p121 (not @t140)) % 0.35/0.65 (step @p122 :rule instantiate :premises (@p3) :args (@t141)) % 0.35/0.65 (step @p123 :rule cnf_or_pos :args (@t145)) % 0.35/0.65 (step @p124 :rule reordering :premises (@p123) :args ((or @t140 @t144 (not @t145)))) % 0.35/0.65 (step @p125 :rule chain_m_resolution :premises (@p124 @p121 @p122) :args (@t144 @t146 (@list @t140 @t145))) % 0.35/0.65 (step @p126 :rule eq-symm :args (@t2 @t1)) % 0.35/0.65 (step @p127 :rule eq-symm :args (@t2 @t3)) % 0.35/0.65 (step @p128 :rule refl :args (@t17)) % 0.35/0.65 (step @p129 :rule nary_cong :premises (@p128 @p127 @p126) :args (@t18)) % 0.35/0.65 (step @p130 :rule cong :premises (@p129) :args (@t19)) % 0.35/0.65 (step @p131 :rule eq_resolve :premises (@p8 @p130)) % 0.35/0.65 (step @p132 :rule instantiate :premises (@p131) :args ((@list @t142 tptp.x tptp.y))) % 0.35/0.65 (step @p133 :rule refl :args (@t148)) % 0.35/0.65 (step @p134 :rule bool-double-not-elim :args (@t143)) % 0.35/0.65 (step @p135 :rule refl :args (@t149)) % 0.35/0.65 (step @p136 :rule nary_cong :premises (@p135 @p134 @p133) :args ((or @t149 @t150 @t148))) % 0.35/0.65 (assume-push @p201 @t137) % 0.35/0.65 (assume-push @p202 @t147) % 0.35/0.65 (assume-push @p203 @t144) % 0.35/0.65 (step @p140 :rule evaluate :args (@t151)) % 0.35/0.65 (step @p141 :rule true_intro :premises (@p119)) % 0.35/0.65 (step @p142 :rule refl :args (tptp.z)) % 0.35/0.65 (step @p143 :rule symm :premises (@p202)) % 0.35/0.65 (step @p144 :rule cong :premises (@p143 @p142) :args (@t143)) % 0.35/0.65 (step @p145 :rule false_intro :premises (@p125)) % 0.35/0.65 (step @p146 :rule symm :premises (@p145)) % 0.35/0.65 (step @p147 :rule trans :premises (@p146 @p144 @p141)) % 0.35/0.65 (step @p148 false :rule eq_resolve :premises (@p147 @p140)) % 0.35/0.65 (step-pop @p204 :rule scope :premises (@p148)) % 0.35/0.65 (step-pop @p205 :rule scope :premises (@p204)) % 0.35/0.65 (step-pop @p206 :rule scope :premises (@p205)) % 0.35/0.65 (step @p149 :rule process_scope :premises (@p206) :args (false)) % 0.35/0.65 (assume-push @p207 @t137) % 0.35/0.65 (assume-push @p208 @t144) % 0.35/0.65 (assume-push @p209 @t147) % 0.35/0.65 (step @p156 :rule and_intro :premises (@p119 @p209 @p125)) % 0.35/0.65 (step-pop @p210 :rule scope :premises (@p156)) % 0.35/0.65 (step-pop @p211 :rule scope :premises (@p210)) % 0.35/0.65 (step-pop @p212 :rule scope :premises (@p211)) % 0.35/0.65 (step @p157 :rule process_scope :premises (@p212) :args (@t152)) % 0.35/0.65 (step @p161 :rule implies_elim :premises (@p157)) % 0.35/0.65 (step @p162 :rule resolution :premises (@p161 @p149) :args (true @t152)) % 0.35/0.65 (step @p163 :rule not_and :premises (@p162)) % 0.35/0.65 (step @p164 :rule eq_resolve :premises (@p163 @p136)) % 0.35/0.65 (step @p165 :rule chain_m_resolution :premises (@p164 @p119 @p125) :args (@t148 (@list false true) (@list @t137 @t143))) % 0.35/0.65 (step @p166 :rule instantiate :premises (@p2) :args (@t141)) % 0.35/0.65 (step @p167 :rule cnf_or_pos :args (@t154)) % 0.35/0.65 (step @p168 :rule reordering :premises (@p167) :args ((or @t140 @t153 (not @t154)))) % 0.35/0.65 (step @p169 :rule chain_m_resolution :premises (@p168 @p121 @p166) :args (@t153 @t146 (@list @t140 @t154))) % 0.35/0.65 (step @p170 :rule cnf_or_pos :args (@t157)) % 0.35/0.65 (step @p171 :rule reordering :premises (@p170) :args ((or @t156 @t147 @t155 (not @t157)))) % 0.35/0.65 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p165 @p132) :args (@t155 @t158 (@list @t153 @t147 @t157))) % 0.35/0.65 (step @p173 :rule refl :args (@t159)) % 0.35/0.65 (step @p174 :rule refl :args (@t160)) % 0.35/0.65 (step @p175 :rule nary_cong :premises (@p174 @p134 @p173) :args ((or @t160 @t150 @t159))) % 0.35/0.65 (assume-push @p213 @t138) % 0.35/0.65 (assume-push @p214 @t155) % 0.35/0.65 (assume-push @p215 @t144) % 0.35/0.65 (step @p140 :rule evaluate :args (@t151)) % 0.35/0.65 (step @p179 :rule true_intro :premises (@p120)) % 0.35/0.65 (step @p142 :rule refl :args (tptp.z)) % 0.35/0.65 (step @p180 :rule symm :premises (@p214)) % 0.35/0.65 (step @p181 :rule cong :premises (@p180 @p142) :args (@t143)) % 0.35/0.65 (step @p145 :rule false_intro :premises (@p125)) % 0.35/0.65 (step @p146 :rule symm :premises (@p145)) % 0.35/0.65 (step @p182 :rule trans :premises (@p146 @p181 @p179)) % 0.35/0.65 (step @p183 false :rule eq_resolve :premises (@p182 @p140)) % 0.35/0.65 (step-pop @p216 :rule scope :premises (@p183)) % 0.35/0.65 (step-pop @p217 :rule scope :premises (@p216)) % 0.35/0.65 (step-pop @p218 :rule scope :premises (@p217)) % 0.35/0.65 (step @p184 :rule process_scope :premises (@p218) :args (false)) % 0.35/0.65 (assume-push @p219 @t138) % 0.35/0.65 (assume-push @p220 @t144) % 0.35/0.65 (assume-push @p221 @t155) % 0.35/0.65 (step @p191 :rule and_intro :premises (@p120 @p221 @p125)) % 0.35/0.65 (step-pop @p222 :rule scope :premises (@p191)) % 0.35/0.65 (step-pop @p223 :rule scope :premises (@p222)) % 0.35/0.65 (step-pop @p224 :rule scope :premises (@p223)) % 0.35/0.65 (step @p192 :rule process_scope :premises (@p224) :args (@t161)) % 0.35/0.65 (step @p196 :rule implies_elim :premises (@p192)) % 0.35/0.65 (step @p197 :rule resolution :premises (@p196 @p184) :args (true @t161)) % 0.35/0.65 (step @p198 :rule not_and :premises (@p197)) % 0.35/0.65 (step @p199 :rule eq_resolve :premises (@p198 @p175)) % 0.35/0.65 (step @p200 false :rule chain_m_resolution :premises (@p199 @p172 @p125 @p120) :args (false @t158 (@list @t155 @t143 @t138))) % 0.35/0.65 ) % 0.35/0.65 % SZS output end Proof % 0.35/0.65 % cvc5 exiting %------------------------------------------------------------------------------