%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET023-3 : TPTP v9.2.1. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:47:00 AM UTC 2026 % Result : Unsatisfiable 0.45s 0.67s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET023-3 : TPTP v9.2.1. Released v1.0.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n004.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % 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 14:41:22 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.32/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.67 % SZS status Unsatisfiable % 0.45/0.67 % SZS output start Proof % 0.45/0.67 ( % 0.45/0.67 (declare-sort $$unsorted 0) % 0.45/0.67 (declare-const tptp.f32 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f31 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f29 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.closed (-> $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f28 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.apply_to_two_arguments (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f10 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f7 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f8 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.single_valued_set (-> $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f25 $$unsorted) % 0.45/0.67 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.infinity $$unsorted) % 0.45/0.67 (declare-const tptp.rotate_right (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f24 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.converse (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.a $$unsorted) % 0.45/0.67 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f2 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f30 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.non_ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.estin $$unsorted) % 0.45/0.67 (declare-const tptp.singleton_set (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f26 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.flip_range_of (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f11 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.little_set (-> $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f3 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f12 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.ordered_pair_predicate (-> $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f20 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f9 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f18 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f14 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f22 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.empty_set $$unsorted) % 0.45/0.67 (declare-const tptp.universal_set $$unsorted) % 0.45/0.67 (declare-const tptp.f16 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.sigma (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.one_to_one_function (-> $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.function (-> $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f17 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f13 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f33 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f19 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.identity_relation $$unsorted) % 0.45/0.67 (declare-const tptp.f21 (-> $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.45/0.67 (declare-const tptp.f23 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (declare-const tptp.f27 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.67 (define @t1 () (@var "X" $$unsorted)) % 0.45/0.67 (define @t2 () (tptp.little_set @t1)) % 0.45/0.67 (define @t3 () (@var "Y" $$unsorted)) % 0.45/0.67 (define @t4 () (@list @t1 @t3)) % 0.45/0.67 (define @t5 () (= @t1 @t3)) % 0.45/0.67 (define @t6 () (tptp.f1 @t1 @t3)) % 0.45/0.67 (define @t7 () (tptp.member @t6 @t3)) % 0.45/0.67 (define @t8 () (tptp.member @t6 @t1)) % 0.45/0.67 (define @t9 () (@var "U" $$unsorted)) % 0.45/0.67 (define @t10 () (= @t9 @t3)) % 0.45/0.67 (define @t11 () (= @t9 @t1)) % 0.45/0.67 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.45/0.67 (define @t13 () (tptp.member @t9 @t12)) % 0.45/0.67 (define @t14 () (@list @t9 @t1 @t3)) % 0.45/0.67 (define @t15 () (not (tptp.little_set @t9))) % 0.45/0.67 (define @t16 () (tptp.singleton_set @t1)) % 0.45/0.67 (define @t17 () (@list @t1)) % 0.45/0.67 (define @t18 () (tptp.ordered_pair @t1 @t3)) % 0.45/0.67 (define @t19 () (tptp.f2 @t1)) % 0.45/0.67 (define @t20 () (tptp.ordered_pair_predicate @t1)) % 0.45/0.67 (define @t21 () (not @t20)) % 0.45/0.67 (define @t22 () (tptp.f3 @t1)) % 0.45/0.67 (define @t23 () (@var "Z" $$unsorted)) % 0.45/0.67 (define @t24 () (not (tptp.little_set @t23))) % 0.45/0.67 (define @t25 () (not (tptp.little_set @t3))) % 0.45/0.67 (define @t26 () (@list @t1 @t3 @t23)) % 0.45/0.67 (define @t27 () (tptp.f4 @t23 @t1)) % 0.45/0.67 (define @t28 () (tptp.first @t1)) % 0.45/0.67 (define @t29 () (tptp.member @t23 @t28)) % 0.45/0.67 (define @t30 () (not @t29)) % 0.45/0.67 (define @t31 () (@list @t23 @t1)) % 0.45/0.67 (define @t32 () (tptp.f5 @t23 @t1)) % 0.45/0.67 (define @t33 () (@var "V" $$unsorted)) % 0.45/0.67 (define @t34 () (tptp.ordered_pair @t9 @t33)) % 0.45/0.67 (define @t35 () (not (= @t1 @t34))) % 0.45/0.67 (define @t36 () (not (tptp.little_set @t33))) % 0.45/0.67 (define @t37 () (@list @t23 @t1 @t9 @t33)) % 0.45/0.67 (define @t38 () (tptp.f6 @t23 @t1)) % 0.45/0.67 (define @t39 () (tptp.member @t23 (tptp.second @t1))) % 0.45/0.67 (define @t40 () (not @t39)) % 0.45/0.67 (define @t41 () (tptp.f7 @t23 @t1)) % 0.45/0.67 (define @t42 () (tptp.ordered_pair_predicate @t23)) % 0.45/0.67 (define @t43 () (tptp.member @t23 tptp.estin)) % 0.45/0.67 (define @t44 () (not @t43)) % 0.45/0.67 (define @t45 () (@list @t23)) % 0.45/0.67 (define @t46 () (tptp.second @t23)) % 0.45/0.67 (define @t47 () (tptp.first @t23)) % 0.45/0.67 (define @t48 () (tptp.member @t47 @t46)) % 0.45/0.67 (define @t49 () (not @t42)) % 0.45/0.67 (define @t50 () (tptp.member @t23 @t1)) % 0.45/0.67 (define @t51 () (tptp.member @t23 (tptp.intersection @t1 @t3))) % 0.45/0.67 (define @t52 () (not @t51)) % 0.45/0.67 (define @t53 () (@list @t23 @t1 @t3)) % 0.45/0.67 (define @t54 () (tptp.member @t23 @t3)) % 0.45/0.67 (define @t55 () (not @t54)) % 0.45/0.67 (define @t56 () (not @t50)) % 0.45/0.67 (define @t57 () (tptp.complement @t1)) % 0.45/0.67 (define @t58 () (tptp.member @t23 @t57)) % 0.45/0.67 (define @t59 () (tptp.f8 @t23 @t1)) % 0.45/0.67 (define @t60 () (tptp.member @t23 (tptp.domain_of @t1))) % 0.45/0.67 (define @t61 () (not @t60)) % 0.45/0.67 (define @t62 () (@var "Xp" $$unsorted)) % 0.45/0.67 (define @t63 () (not (tptp.member @t62 @t1))) % 0.45/0.67 (define @t64 () (not (tptp.ordered_pair_predicate @t62))) % 0.45/0.67 (define @t65 () (@list @t23 @t1 @t62)) % 0.45/0.67 (define @t66 () (tptp.member @t23 (tptp.cross_product @t1 @t3))) % 0.45/0.67 (define @t67 () (not @t66)) % 0.45/0.67 (define @t68 () (tptp.member @t47 @t1)) % 0.45/0.67 (define @t69 () (tptp.member @t46 @t3)) % 0.45/0.67 (define @t70 () (tptp.member @t23 (tptp.converse @t1))) % 0.45/0.67 (define @t71 () (not @t70)) % 0.45/0.67 (define @t72 () (tptp.member (tptp.ordered_pair @t46 @t47) @t1)) % 0.45/0.67 (define @t73 () (tptp.f9 @t23 @t1)) % 0.45/0.67 (define @t74 () (tptp.member @t23 (tptp.rotate_right @t1))) % 0.45/0.67 (define @t75 () (not @t74)) % 0.45/0.67 (define @t76 () (tptp.f10 @t23 @t1)) % 0.45/0.67 (define @t77 () (tptp.f11 @t23 @t1)) % 0.45/0.67 (define @t78 () (@var "W" $$unsorted)) % 0.45/0.67 (define @t79 () (not (= @t23 (tptp.ordered_pair @t9 (tptp.ordered_pair @t33 @t78))))) % 0.45/0.67 (define @t80 () (not (tptp.little_set @t78))) % 0.45/0.67 (define @t81 () (@list @t23 @t1 @t9 @t33 @t78)) % 0.45/0.67 (define @t82 () (tptp.f12 @t23 @t1)) % 0.45/0.67 (define @t83 () (tptp.member @t23 (tptp.flip_range_of @t1))) % 0.45/0.67 (define @t84 () (not @t83)) % 0.45/0.67 (define @t85 () (tptp.f13 @t23 @t1)) % 0.45/0.67 (define @t86 () (tptp.f14 @t23 @t1)) % 0.45/0.67 (define @t87 () (tptp.successor @t1)) % 0.45/0.67 (define @t88 () (tptp.f16 @t23 @t1)) % 0.45/0.67 (define @t89 () (tptp.member @t23 (tptp.sigma @t1))) % 0.45/0.67 (define @t90 () (not @t89)) % 0.45/0.67 (define @t91 () (@list @t9)) % 0.45/0.67 (define @t92 () (tptp.member @t9 @t3)) % 0.45/0.67 (define @t93 () (not (tptp.member @t9 @t1))) % 0.45/0.67 (define @t94 () (tptp.subset @t1 @t3)) % 0.45/0.67 (define @t95 () (not @t94)) % 0.45/0.67 (define @t96 () (@list @t1 @t3 @t9)) % 0.45/0.67 (define @t97 () (tptp.f17 @t1 @t3)) % 0.45/0.67 (define @t98 () (tptp.proper_subset @t1 @t3)) % 0.45/0.67 (define @t99 () (not @t98)) % 0.45/0.67 (define @t100 () (tptp.subset @t23 @t1)) % 0.45/0.67 (define @t101 () (tptp.member @t23 (tptp.powerset @t1))) % 0.45/0.67 (define @t102 () (tptp.relation @t23)) % 0.45/0.67 (define @t103 () (tptp.f18 @t23)) % 0.45/0.67 (define @t104 () (tptp.single_valued_set @t1)) % 0.45/0.67 (define @t105 () (tptp.f19 @t1)) % 0.45/0.67 (define @t106 () (tptp.f20 @t1)) % 0.45/0.67 (define @t107 () (tptp.f21 @t1)) % 0.45/0.67 (define @t108 () (@var "Xf" $$unsorted)) % 0.45/0.67 (define @t109 () (tptp.relation @t108)) % 0.45/0.67 (define @t110 () (tptp.function @t108)) % 0.45/0.67 (define @t111 () (not @t110)) % 0.45/0.67 (define @t112 () (@list @t108)) % 0.45/0.67 (define @t113 () (tptp.single_valued_set @t108)) % 0.45/0.67 (define @t114 () (tptp.f22 @t23 @t1 @t108)) % 0.45/0.67 (define @t115 () (tptp.image @t1 @t108)) % 0.45/0.67 (define @t116 () (tptp.member @t23 @t115)) % 0.45/0.67 (define @t117 () (not @t116)) % 0.45/0.67 (define @t118 () (@list @t23 @t1 @t108)) % 0.45/0.67 (define @t119 () (not @t2)) % 0.45/0.67 (define @t120 () (tptp.disjoint @t1 @t3)) % 0.45/0.67 (define @t121 () (tptp.f23 @t1 @t3)) % 0.45/0.67 (define @t122 () (tptp.f24 @t1)) % 0.45/0.67 (define @t123 () (= @t1 tptp.empty_set)) % 0.45/0.67 (define @t124 () (tptp.f26 @t1)) % 0.45/0.67 (define @t125 () (tptp.f27 @t23 @t1)) % 0.45/0.67 (define @t126 () (tptp.member @t23 (tptp.range_of @t1))) % 0.45/0.67 (define @t127 () (not @t126)) % 0.45/0.67 (define @t128 () (tptp.member @t23 tptp.identity_relation)) % 0.45/0.67 (define @t129 () (not @t128)) % 0.45/0.67 (define @t130 () (= @t47 @t46)) % 0.45/0.67 (define @t131 () (tptp.one_to_one_function @t108)) % 0.45/0.67 (define @t132 () (not @t131)) % 0.45/0.67 (define @t133 () (tptp.function (tptp.converse @t108))) % 0.45/0.67 (define @t134 () (tptp.f28 @t23 @t108 @t3)) % 0.45/0.67 (define @t135 () (tptp.member @t23 (tptp.apply @t108 @t3))) % 0.45/0.67 (define @t136 () (not @t135)) % 0.45/0.67 (define @t137 () (@list @t23 @t108 @t3)) % 0.45/0.67 (define @t138 () (@list @t108 @t1 @t3)) % 0.45/0.67 (define @t139 () (tptp.maps @t108 @t1 @t3)) % 0.45/0.67 (define @t140 () (not @t139)) % 0.45/0.67 (define @t141 () (= (tptp.domain_of @t108) @t1)) % 0.45/0.67 (define @t142 () (tptp.subset (tptp.range_of @t108) @t3)) % 0.45/0.67 (define @t143 () (@var "Xs" $$unsorted)) % 0.45/0.67 (define @t144 () (tptp.little_set @t143)) % 0.45/0.68 (define @t145 () (tptp.closed @t143 @t108)) % 0.45/0.68 (define @t146 () (not @t145)) % 0.45/0.68 (define @t147 () (@list @t143 @t108)) % 0.45/0.68 (define @t148 () (tptp.little_set @t108)) % 0.45/0.68 (define @t149 () (tptp.maps @t108 (tptp.cross_product @t143 @t143) @t143)) % 0.45/0.68 (define @t150 () (@var "Xg" $$unsorted)) % 0.45/0.68 (define @t151 () (tptp.f29 @t23 @t108 @t150)) % 0.45/0.68 (define @t152 () (tptp.member @t23 (tptp.compose @t108 @t150))) % 0.45/0.68 (define @t153 () (not @t152)) % 0.45/0.68 (define @t154 () (@list @t23 @t108 @t150)) % 0.45/0.68 (define @t155 () (tptp.f30 @t23 @t108 @t150)) % 0.45/0.68 (define @t156 () (tptp.f31 @t23 @t108 @t150)) % 0.45/0.68 (define @t157 () (@var "Xf1" $$unsorted)) % 0.45/0.68 (define @t158 () (@var "Xs1" $$unsorted)) % 0.45/0.68 (define @t159 () (tptp.closed @t158 @t157)) % 0.45/0.68 (define @t160 () (@var "Xf2" $$unsorted)) % 0.45/0.68 (define @t161 () (@var "Xs2" $$unsorted)) % 0.45/0.68 (define @t162 () (@var "Xh" $$unsorted)) % 0.45/0.68 (define @t163 () (tptp.homomorphism @t162 @t158 @t157 @t161 @t160)) % 0.45/0.68 (define @t164 () (not @t163)) % 0.45/0.68 (define @t165 () (@list @t162 @t158 @t157 @t161 @t160)) % 0.45/0.68 (define @t166 () (tptp.closed @t161 @t160)) % 0.45/0.68 (define @t167 () (tptp.maps @t162 @t158 @t161)) % 0.45/0.68 (define @t168 () (tptp.f32 @t162 @t158 @t157 @t161 @t160)) % 0.45/0.68 (define @t169 () (not @t167)) % 0.45/0.68 (define @t170 () (not @t166)) % 0.45/0.68 (define @t171 () (not @t159)) % 0.45/0.68 (define @t172 () (tptp.f33 @t162 @t158 @t157 @t161 @t160)) % 0.45/0.68 (define @t173 () (not (= @t18 @t34))) % 0.45/0.68 (define @t174 () (tptp.second @t18)) % 0.45/0.68 (define @t175 () (or @t119 @t25 (= @t174 @t3))) % 0.45/0.68 (define @t176 () (forall @t4 @t175)) % 0.45/0.68 (define @t177 () (tptp.ordered_pair_predicate tptp.a)) % 0.45/0.68 (define @t178 () (@list tptp.a)) % 0.45/0.68 (define @t179 () (tptp.f3 tptp.a)) % 0.45/0.68 (define @t180 () (tptp.f2 tptp.a)) % 0.45/0.68 (define @t181 () (tptp.ordered_pair @t180 @t179)) % 0.45/0.68 (define @t182 () (= tptp.a @t181)) % 0.45/0.68 (define @t183 () (not @t177)) % 0.45/0.68 (define @t184 () (or @t183 @t182)) % 0.45/0.68 (define @t185 () (@list false false)) % 0.45/0.68 (define @t186 () (tptp.second @t181)) % 0.45/0.68 (define @t187 () (tptp.little_set @t179)) % 0.45/0.68 (define @t188 () (or @t183 @t187)) % 0.45/0.68 (define @t189 () (tptp.little_set @t180)) % 0.45/0.68 (define @t190 () (or @t183 @t189)) % 0.45/0.68 (define @t191 () (= @t179 @t186)) % 0.45/0.68 (define @t192 () (not @t187)) % 0.45/0.68 (define @t193 () (not @t189)) % 0.45/0.68 (define @t194 () (or @t193 @t192 @t191)) % 0.45/0.68 (assume @p1 (forall @t4 (or (not (tptp.member @t1 @t3)) @t2))) % 0.45/0.68 (assume @p2 (forall @t4 (or (tptp.little_set @t6) @t5))) % 0.45/0.68 (assume @p3 (forall @t4 (or @t8 @t7 @t5))) % 0.45/0.68 (assume @p4 (forall @t4 (or (not @t8) (not @t7) @t5))) % 0.45/0.68 (assume @p5 (forall @t14 (or (not @t13) @t11 @t10))) % 0.45/0.68 (assume @p6 (forall @t14 (or @t13 @t15 (not @t11)))) % 0.45/0.68 (assume @p7 (forall @t14 (or @t13 @t15 (not @t10)))) % 0.45/0.68 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.45/0.68 (assume @p9 (forall @t17 (= @t16 (tptp.non_ordered_pair @t1 @t1)))) % 0.45/0.68 (assume @p10 (forall @t4 (= @t18 (tptp.non_ordered_pair @t16 @t12)))) % 0.45/0.68 (assume @p11 (forall @t17 (or @t21 (tptp.little_set @t19)))) % 0.45/0.68 (assume @p12 (forall @t17 (or @t21 (tptp.little_set @t22)))) % 0.45/0.68 (assume @p13 (forall @t17 (or @t21 (= @t1 (tptp.ordered_pair @t19 @t22))))) % 0.45/0.68 (assume @p14 (forall @t26 (or @t20 @t25 @t24 (not (= @t1 (tptp.ordered_pair @t3 @t23)))))) % 0.45/0.68 (assume @p15 (forall @t31 (or @t30 (tptp.little_set @t27)))) % 0.45/0.68 (assume @p16 (forall @t31 (or @t30 (tptp.little_set @t32)))) % 0.45/0.68 (assume @p17 (forall @t31 (or @t30 (= @t1 (tptp.ordered_pair @t27 @t32))))) % 0.45/0.68 (assume @p18 (forall @t31 (or @t30 (tptp.member @t23 @t27)))) % 0.45/0.68 (assume @p19 (forall @t37 (or @t29 @t15 @t36 @t35 (not (tptp.member @t23 @t9))))) % 0.45/0.68 (assume @p20 (forall @t31 (or @t40 (tptp.little_set @t38)))) % 0.45/0.68 (assume @p21 (forall @t31 (or @t40 (tptp.little_set @t41)))) % 0.45/0.68 (assume @p22 (forall @t31 (or @t40 (= @t1 (tptp.ordered_pair @t38 @t41))))) % 0.45/0.68 (assume @p23 (forall @t31 (or @t40 (tptp.member @t23 @t41)))) % 0.45/0.68 (assume @p24 (forall @t37 (or @t39 @t15 @t36 @t35 (not (tptp.member @t23 @t33))))) % 0.45/0.68 (assume @p25 (forall @t45 (or @t44 @t42))) % 0.45/0.68 (assume @p26 (forall @t45 (or @t44 @t48))) % 0.45/0.68 (assume @p27 (forall @t45 (or @t43 @t24 @t49 (not @t48)))) % 0.45/0.68 (assume @p28 (forall @t53 (or @t52 @t50))) % 0.45/0.68 (assume @p29 (forall @t53 (or @t52 @t54))) % 0.45/0.68 (assume @p30 (forall @t53 (or @t51 @t56 @t55))) % 0.45/0.68 (assume @p31 (forall @t31 (or (not @t58) @t56))) % 0.45/0.68 (assume @p32 (forall @t31 (or @t58 @t24 @t50))) % 0.45/0.68 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t57 (tptp.complement @t3)))))) % 0.45/0.68 (assume @p34 (forall @t31 (or @t61 (tptp.ordered_pair_predicate @t59)))) % 0.45/0.68 (assume @p35 (forall @t31 (or @t61 (tptp.member @t59 @t1)))) % 0.45/0.68 (assume @p36 (forall @t31 (or @t61 (= @t23 (tptp.first @t59))))) % 0.45/0.68 (assume @p37 (forall @t65 (or @t60 @t24 @t64 @t63 (not (= @t23 (tptp.first @t62)))))) % 0.45/0.68 (assume @p38 (forall @t53 (or @t67 @t42))) % 0.45/0.68 (assume @p39 (forall @t53 (or @t67 @t68))) % 0.45/0.68 (assume @p40 (forall @t53 (or @t67 @t69))) % 0.45/0.68 (assume @p41 (forall @t53 (or @t66 @t24 @t49 (not @t68) (not @t69)))) % 0.45/0.68 (assume @p42 (forall @t31 (or @t71 @t42))) % 0.45/0.68 (assume @p43 (forall @t31 (or @t71 @t72))) % 0.45/0.68 (assume @p44 (forall @t31 (or @t70 @t24 @t49 (not @t72)))) % 0.45/0.68 (assume @p45 (forall @t31 (or @t75 (tptp.little_set @t73)))) % 0.45/0.68 (assume @p46 (forall @t31 (or @t75 (tptp.little_set @t76)))) % 0.45/0.68 (assume @p47 (forall @t31 (or @t75 (tptp.little_set @t77)))) % 0.45/0.68 (assume @p48 (forall @t31 (or @t75 (= @t23 (tptp.ordered_pair @t73 (tptp.ordered_pair @t76 @t77)))))) % 0.45/0.68 (assume @p49 (forall @t31 (or @t75 (tptp.member (tptp.ordered_pair @t76 (tptp.ordered_pair @t77 @t73)) @t1)))) % 0.45/0.68 (assume @p50 (forall @t81 (or @t74 @t24 @t15 @t36 @t80 @t79 (not (tptp.member (tptp.ordered_pair @t33 (tptp.ordered_pair @t78 @t9)) @t1))))) % 0.45/0.68 (assume @p51 (forall @t31 (or @t84 (tptp.little_set @t82)))) % 0.45/0.68 (assume @p52 (forall @t31 (or @t84 (tptp.little_set @t85)))) % 0.45/0.68 (assume @p53 (forall @t31 (or @t84 (tptp.little_set @t86)))) % 0.45/0.68 (assume @p54 (forall @t31 (or @t84 (= @t23 (tptp.ordered_pair @t82 (tptp.ordered_pair @t85 @t86)))))) % 0.45/0.68 (assume @p55 (forall @t31 (or @t84 (tptp.member (tptp.ordered_pair @t82 (tptp.ordered_pair @t86 @t85)) @t1)))) % 0.45/0.68 (assume @p56 (forall @t81 (or @t83 @t24 @t15 @t36 @t80 @t79 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t78 @t33)) @t1))))) % 0.45/0.68 (assume @p57 (forall @t17 (= @t87 (tptp.union @t1 @t16)))) % 0.45/0.68 (assume @p58 (forall @t45 (not (tptp.member @t23 tptp.empty_set)))) % 0.45/0.68 (assume @p59 (forall @t45 (or (tptp.member @t23 tptp.universal_set) @t24))) % 0.45/0.68 (assume @p60 (tptp.little_set tptp.infinity)) % 0.45/0.68 (assume @p61 (tptp.member tptp.empty_set tptp.infinity)) % 0.45/0.68 (assume @p62 (forall @t17 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t87 tptp.infinity)))) % 0.45/0.68 (assume @p63 (forall @t31 (or @t90 (tptp.member @t88 @t1)))) % 0.45/0.68 (assume @p64 (forall @t31 (or @t90 (tptp.member @t23 @t88)))) % 0.45/0.68 (assume @p65 (forall @t53 (or @t89 (not (tptp.member @t3 @t1)) @t55))) % 0.45/0.68 (assume @p66 (forall @t91 (or @t15 (tptp.little_set (tptp.sigma @t9))))) % 0.45/0.68 (assume @p67 (forall @t96 (or @t95 @t93 @t92))) % 0.45/0.68 (assume @p68 (forall @t4 (or @t94 (tptp.member @t97 @t1)))) % 0.45/0.68 (assume @p69 (forall @t4 (or @t94 (not (tptp.member @t97 @t3))))) % 0.45/0.68 (assume @p70 (forall @t4 (or @t99 @t94))) % 0.45/0.68 (assume @p71 (forall @t4 (or @t99 (not @t5)))) % 0.45/0.68 (assume @p72 (forall @t4 (or @t98 @t95 @t5))) % 0.45/0.68 (assume @p73 (forall @t31 (or (not @t101) @t100))) % 0.45/0.68 (assume @p74 (forall @t31 (or @t101 @t24 (not @t100)))) % 0.45/0.68 (assume @p75 (forall @t91 (or @t15 (tptp.little_set (tptp.powerset @t9))))) % 0.45/0.68 (assume @p76 (forall @t31 (or (not @t102) (not (tptp.member @t1 @t23)) @t20))) % 0.45/0.68 (assume @p77 (forall @t45 (or @t102 (tptp.member @t103 @t23)))) % 0.45/0.68 (assume @p78 (forall @t45 (or @t102 (not (tptp.ordered_pair_predicate @t103))))) % 0.45/0.68 (assume @p79 (forall (@list @t1 @t9 @t33 @t78) (or (not @t104) @t15 @t36 @t80 (not (tptp.member @t34 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t78) @t1)) (= @t33 @t78)))) % 0.45/0.68 (assume @p80 (forall @t17 (or @t104 (tptp.little_set @t105)))) % 0.45/0.68 (assume @p81 (forall @t17 (or @t104 (tptp.little_set @t106)))) % 0.45/0.68 (assume @p82 (forall @t17 (or @t104 (tptp.little_set @t107)))) % 0.45/0.68 (assume @p83 (forall @t17 (or @t104 (tptp.member (tptp.ordered_pair @t105 @t106) @t1)))) % 0.45/0.68 (assume @p84 (forall @t17 (or @t104 (tptp.member (tptp.ordered_pair @t105 @t107) @t1)))) % 0.45/0.68 (assume @p85 (forall @t17 (or @t104 (not (= @t106 @t107))))) % 0.45/0.68 (assume @p86 (forall @t112 (or @t111 @t109))) % 0.45/0.68 (assume @p87 (forall @t112 (or @t111 @t113))) % 0.45/0.68 (assume @p88 (forall @t112 (or @t110 (not @t109) (not @t113)))) % 0.45/0.68 (assume @p89 (forall @t118 (or @t117 (tptp.ordered_pair_predicate @t114)))) % 0.45/0.68 (assume @p90 (forall @t118 (or @t117 (tptp.member @t114 @t108)))) % 0.45/0.68 (assume @p91 (forall @t118 (or @t117 (tptp.member (tptp.first @t114) @t1)))) % 0.45/0.68 (assume @p92 (forall @t118 (or @t117 (= (tptp.second @t114) @t23)))) % 0.45/0.68 (assume @p93 (forall (@list @t23 @t1 @t108 @t3) (or @t116 @t24 (not (tptp.ordered_pair_predicate @t3)) (not (tptp.member @t3 @t108)) (not (tptp.member (tptp.first @t3) @t1)) (not (= (tptp.second @t3) @t23))))) % 0.45/0.68 (assume @p94 (forall (@list @t1 @t108) (or @t119 @t111 (tptp.little_set @t115)))) % 0.45/0.68 (assume @p95 (forall @t96 (or (not @t120) @t93 (not @t92)))) % 0.45/0.68 (assume @p96 (forall @t4 (or @t120 (tptp.member @t121 @t1)))) % 0.45/0.68 (assume @p97 (forall @t4 (or @t120 (tptp.member @t121 @t3)))) % 0.45/0.68 (assume @p98 (forall @t17 (or @t123 (tptp.member @t122 @t1)))) % 0.45/0.68 (assume @p99 (forall @t17 (or @t123 (tptp.disjoint @t122 @t1)))) % 0.45/0.68 (assume @p100 (tptp.function tptp.f25)) % 0.45/0.68 (assume @p101 (forall @t17 (or @t119 @t123 (tptp.member @t124 @t1)))) % 0.45/0.68 (assume @p102 (forall @t17 (or @t119 @t123 (tptp.member (tptp.ordered_pair @t1 @t124) tptp.f25)))) % 0.45/0.68 (assume @p103 (forall @t31 (or @t127 (tptp.ordered_pair_predicate @t125)))) % 0.45/0.68 (assume @p104 (forall @t31 (or @t127 (tptp.member @t125 @t1)))) % 0.45/0.68 (assume @p105 (forall @t31 (or @t127 (= @t23 (tptp.second @t125))))) % 0.45/0.68 (assume @p106 (forall @t65 (or @t126 @t24 @t64 @t63 (not (= @t23 (tptp.second @t62)))))) % 0.45/0.68 (assume @p107 (forall @t45 (or @t129 @t42))) % 0.45/0.68 (assume @p108 (forall @t45 (or @t129 @t130))) % 0.45/0.68 (assume @p109 (forall @t45 (or @t128 @t24 @t49 (not @t130)))) % 0.45/0.68 (assume @p110 (forall @t4 (= (tptp.restrict @t1 @t3) (tptp.intersection @t1 (tptp.cross_product @t3 tptp.universal_set))))) % 0.45/0.68 (assume @p111 (forall @t112 (or @t132 @t110))) % 0.45/0.68 (assume @p112 (forall @t112 (or @t132 @t133))) % 0.45/0.68 (assume @p113 (forall @t112 (or @t131 @t111 (not @t133)))) % 0.45/0.68 (assume @p114 (forall @t137 (or @t136 (tptp.ordered_pair_predicate @t134)))) % 0.45/0.68 (assume @p115 (forall @t137 (or @t136 (tptp.member @t134 @t108)))) % 0.45/0.68 (assume @p116 (forall @t137 (or @t136 (= (tptp.first @t134) @t3)))) % 0.45/0.68 (assume @p117 (forall @t137 (or @t136 (tptp.member @t23 (tptp.second @t134))))) % 0.45/0.68 (assume @p118 (forall (@list @t23 @t108 @t3 @t78) (or @t135 (not (tptp.ordered_pair_predicate @t78)) (not (tptp.member @t78 @t108)) (not (= (tptp.first @t78) @t3)) (not (tptp.member @t23 (tptp.second @t78)))))) % 0.45/0.68 (assume @p119 (forall @t138 (= (tptp.apply_to_two_arguments @t108 @t1 @t3) (tptp.apply @t108 @t18)))) % 0.45/0.68 (assume @p120 (forall @t138 (or @t140 @t110))) % 0.45/0.68 (assume @p121 (forall @t138 (or @t140 @t141))) % 0.45/0.68 (assume @p122 (forall @t138 (or @t140 @t142))) % 0.45/0.68 (assume @p123 (forall @t138 (or @t139 @t111 (not @t141) (not @t142)))) % 0.45/0.68 (assume @p124 (forall @t147 (or @t146 @t144))) % 0.45/0.68 (assume @p125 (forall @t147 (or @t146 @t148))) % 0.45/0.68 (assume @p126 (forall @t147 (or @t146 @t149))) % 0.45/0.68 (assume @p127 (forall @t147 (or @t145 (not @t144) (not @t148) (not @t149)))) % 0.45/0.68 (assume @p128 (forall @t154 (or @t153 (tptp.little_set @t151)))) % 0.45/0.68 (assume @p129 (forall @t154 (or @t153 (tptp.little_set @t155)))) % 0.45/0.68 (assume @p130 (forall @t154 (or @t153 (tptp.little_set @t156)))) % 0.45/0.68 (assume @p131 (forall @t154 (or @t153 (= @t23 (tptp.ordered_pair @t151 @t155))))) % 0.45/0.68 (assume @p132 (forall @t154 (or @t153 (tptp.member (tptp.ordered_pair @t151 @t156) @t108)))) % 0.45/0.68 (assume @p133 (forall @t154 (or @t153 (tptp.member (tptp.ordered_pair @t156 @t155) @t150)))) % 0.45/0.68 (assume @p134 (forall (@list @t23 @t108 @t150 @t1 @t3 @t78) (or @t152 @t24 @t119 @t25 @t80 (not (= @t23 @t18)) (not (tptp.member (tptp.ordered_pair @t1 @t78) @t108)) (not (tptp.member (tptp.ordered_pair @t78 @t3) @t150))))) % 0.45/0.68 (assume @p135 (forall @t165 (or @t164 @t159))) % 0.45/0.68 (assume @p136 (forall @t165 (or @t164 @t166))) % 0.45/0.68 (assume @p137 (forall @t165 (or @t164 @t167))) % 0.45/0.68 (assume @p138 (forall (@list @t162 @t158 @t157 @t161 @t160 @t1 @t3) (or @t164 (not (tptp.member @t1 @t158)) (not (tptp.member @t3 @t158)) (= (tptp.apply @t162 (tptp.apply_to_two_arguments @t157 @t1 @t3)) (tptp.apply_to_two_arguments @t160 (tptp.apply @t162 @t1) (tptp.apply @t162 @t3)))))) % 0.45/0.68 (assume @p139 (forall @t165 (or @t163 @t171 @t170 @t169 (tptp.member @t168 @t158)))) % 0.45/0.68 (assume @p140 (forall @t165 (or @t163 @t171 @t170 @t169 (tptp.member @t172 @t158)))) % 0.45/0.68 (assume @p141 (forall @t165 (or @t163 @t171 @t170 @t169 (not (= (tptp.apply @t162 (tptp.apply_to_two_arguments @t157 @t168 @t172)) (tptp.apply_to_two_arguments @t160 (tptp.apply @t162 @t168) (tptp.apply @t162 @t172))))))) % 0.45/0.68 (assume @p142 (forall (@list @t1 @t9 @t3 @t33) (or @t119 @t15 @t173 (= @t1 @t9)))) % 0.45/0.68 (assume @p143 (forall @t26 (or @t119 @t25 (not (= (tptp.non_ordered_pair @t23 @t1) (tptp.non_ordered_pair @t23 @t3))) @t5))) % 0.45/0.68 (assume @p144 (forall (@list @t1 @t3 @t9 @t33) (or @t119 @t25 @t15 @t36 @t173 (= @t3 @t33)))) % 0.45/0.68 (assume @p145 (forall @t4 (or @t95 (not (tptp.subset @t3 @t1)) @t5))) % 0.45/0.68 (assume @p146 (forall @t4 (or @t119 @t25 (= (tptp.first @t18) @t1)))) % 0.45/0.68 (assume @p147 @t176) % 0.45/0.68 (assume @p148 (forall @t17 (or @t21 (tptp.little_set @t28)))) % 0.45/0.68 (assume @p149 @t177) % 0.45/0.68 (assume @p150 (not (tptp.little_set (tptp.second tptp.a)))) % 0.45/0.68 (step @p151 :rule evaluate :args ((= true false))) % 0.45/0.68 (step @p152 :rule false_intro :premises (@p150)) % 0.45/0.68 (step @p153 :rule instantiate :premises (@p13) :args (@t178)) % 0.45/0.68 (step @p154 :rule cnf_or_pos :args (@t184)) % 0.45/0.68 (step @p155 :rule reordering :premises (@p154) :args ((or @t183 @t182 (not @t184)))) % 0.45/0.68 (step @p156 :rule chain_m_resolution :premises (@p155 @p149 @p153) :args (@t182 @t185 (@list @t177 @t184))) % 0.45/0.68 (step @p157 :rule symm :premises (@p156)) % 0.45/0.68 (step @p158 :rule cong :premises (@p157) :args (@t186)) % 0.45/0.68 (step @p159 :rule eq-symm :args (@t174 @t3)) % 0.45/0.68 (step @p160 :rule refl :args (@t25)) % 0.45/0.68 (step @p161 :rule refl :args (@t119)) % 0.45/0.68 (step @p162 :rule nary_cong :premises (@p161 @p160 @p159) :args (@t175)) % 0.45/0.68 (step @p163 :rule cong :premises (@p162) :args (@t176)) % 0.45/0.68 (step @p164 :rule eq_resolve :premises (@p147 @p163)) % 0.45/0.68 (step @p165 :rule instantiate :premises (@p164) :args ((@list @t180 @t179))) % 0.45/0.68 (step @p166 :rule instantiate :premises (@p12) :args (@t178)) % 0.45/0.68 (step @p167 :rule cnf_or_pos :args (@t188)) % 0.45/0.68 (step @p168 :rule reordering :premises (@p167) :args ((or @t183 @t187 (not @t188)))) % 0.45/0.68 (step @p169 :rule chain_m_resolution :premises (@p168 @p149 @p166) :args (@t187 @t185 (@list @t177 @t188))) % 0.45/0.68 (step @p170 :rule instantiate :premises (@p11) :args (@t178)) % 0.45/0.68 (step @p171 :rule cnf_or_pos :args (@t190)) % 0.45/0.68 (step @p172 :rule reordering :premises (@p171) :args ((or @t183 @t189 (not @t190)))) % 0.45/0.68 (step @p173 :rule chain_m_resolution :premises (@p172 @p149 @p170) :args (@t189 @t185 (@list @t177 @t190))) % 0.45/0.68 (step @p174 :rule cnf_or_pos :args (@t194)) % 0.45/0.68 (step @p175 :rule reordering :premises (@p174) :args ((or @t193 @t192 @t191 (not @t194)))) % 0.45/0.68 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p169 @p165) :args (@t191 (@list false false false) (@list @t189 @t187 @t194))) % 0.45/0.68 (step @p177 :rule trans :premises (@p176 @p158)) % 0.45/0.68 (step @p178 :rule cong :premises (@p177) :args (@t187)) % 0.45/0.68 (step @p179 :rule true_intro :premises (@p169)) % 0.45/0.68 (step @p180 :rule symm :premises (@p179)) % 0.45/0.68 (step @p181 :rule trans :premises (@p180 @p178 @p152)) % 0.45/0.68 (step @p182 false :rule eq_resolve :premises (@p181 @p151)) % 0.45/0.68 ) % 0.45/0.68 % SZS output end Proof % 0.45/0.68 % cvc5 exiting %------------------------------------------------------------------------------