%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET024-3 : TPTP v9.2.1. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:47:01 AM UTC 2026 % Result : Unsatisfiable 0.38s 0.65s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET024-3 : TPTP v9.2.1. Released v1.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.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 14:42:18 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.31/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.65 % SZS status Unsatisfiable % 0.38/0.65 % SZS output start Proof % 0.38/0.66 ( % 0.38/0.66 (declare-sort $$unsorted 0) % 0.38/0.66 (declare-const tptp.a $$unsorted) % 0.38/0.66 (declare-const tptp.f32 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f31 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f29 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.closed (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f28 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.apply_to_two_arguments (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f10 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f7 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f8 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.single_valued_set (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f25 $$unsorted) % 0.38/0.66 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.infinity $$unsorted) % 0.38/0.66 (declare-const tptp.rotate_right (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f24 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.converse (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f2 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f30 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.non_ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.estin $$unsorted) % 0.38/0.66 (declare-const tptp.singleton_set (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f26 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.flip_range_of (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f11 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.little_set (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f3 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f12 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.ordered_pair_predicate (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f20 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f9 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f18 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f14 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f22 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.empty_set $$unsorted) % 0.38/0.66 (declare-const tptp.universal_set $$unsorted) % 0.38/0.66 (declare-const tptp.f16 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.sigma (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.one_to_one_function (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f17 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f13 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f33 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f19 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.identity_relation $$unsorted) % 0.38/0.66 (declare-const tptp.f21 (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.f23 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.f27 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (define @t1 () (@var "X" $$unsorted)) % 0.38/0.66 (define @t2 () (tptp.little_set @t1)) % 0.38/0.66 (define @t3 () (@var "Y" $$unsorted)) % 0.38/0.66 (define @t4 () (@list @t1 @t3)) % 0.38/0.66 (define @t5 () (= @t1 @t3)) % 0.38/0.66 (define @t6 () (tptp.f1 @t1 @t3)) % 0.38/0.66 (define @t7 () (tptp.member @t6 @t3)) % 0.38/0.66 (define @t8 () (tptp.member @t6 @t1)) % 0.38/0.66 (define @t9 () (@var "U" $$unsorted)) % 0.38/0.66 (define @t10 () (= @t9 @t3)) % 0.38/0.66 (define @t11 () (= @t9 @t1)) % 0.38/0.66 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.38/0.66 (define @t13 () (tptp.member @t9 @t12)) % 0.38/0.66 (define @t14 () (@list @t9 @t1 @t3)) % 0.38/0.66 (define @t15 () (not @t11)) % 0.38/0.66 (define @t16 () (not (tptp.little_set @t9))) % 0.38/0.66 (define @t17 () (or @t13 @t16 @t15)) % 0.38/0.66 (define @t18 () (forall @t14 @t17)) % 0.38/0.66 (define @t19 () (tptp.singleton_set @t1)) % 0.38/0.66 (define @t20 () (@list @t1)) % 0.38/0.66 (define @t21 () (tptp.ordered_pair @t1 @t3)) % 0.38/0.66 (define @t22 () (tptp.f2 @t1)) % 0.38/0.66 (define @t23 () (tptp.ordered_pair_predicate @t1)) % 0.38/0.66 (define @t24 () (not @t23)) % 0.38/0.66 (define @t25 () (tptp.f3 @t1)) % 0.38/0.66 (define @t26 () (@var "Z" $$unsorted)) % 0.38/0.66 (define @t27 () (not (tptp.little_set @t26))) % 0.38/0.66 (define @t28 () (not (tptp.little_set @t3))) % 0.38/0.66 (define @t29 () (@list @t1 @t3 @t26)) % 0.38/0.66 (define @t30 () (tptp.f4 @t26 @t1)) % 0.38/0.66 (define @t31 () (tptp.first @t1)) % 0.38/0.66 (define @t32 () (tptp.member @t26 @t31)) % 0.38/0.66 (define @t33 () (not @t32)) % 0.38/0.66 (define @t34 () (@list @t26 @t1)) % 0.38/0.66 (define @t35 () (tptp.f5 @t26 @t1)) % 0.38/0.66 (define @t36 () (@var "V" $$unsorted)) % 0.38/0.66 (define @t37 () (tptp.ordered_pair @t9 @t36)) % 0.38/0.66 (define @t38 () (not (= @t1 @t37))) % 0.38/0.66 (define @t39 () (not (tptp.little_set @t36))) % 0.38/0.66 (define @t40 () (@list @t26 @t1 @t9 @t36)) % 0.38/0.66 (define @t41 () (tptp.f6 @t26 @t1)) % 0.38/0.66 (define @t42 () (tptp.second @t1)) % 0.38/0.66 (define @t43 () (tptp.member @t26 @t42)) % 0.38/0.66 (define @t44 () (not @t43)) % 0.38/0.66 (define @t45 () (tptp.f7 @t26 @t1)) % 0.38/0.66 (define @t46 () (tptp.ordered_pair_predicate @t26)) % 0.38/0.66 (define @t47 () (tptp.member @t26 tptp.estin)) % 0.38/0.66 (define @t48 () (not @t47)) % 0.38/0.66 (define @t49 () (@list @t26)) % 0.38/0.66 (define @t50 () (tptp.second @t26)) % 0.38/0.66 (define @t51 () (tptp.first @t26)) % 0.38/0.66 (define @t52 () (tptp.member @t51 @t50)) % 0.38/0.66 (define @t53 () (not @t46)) % 0.38/0.66 (define @t54 () (tptp.member @t26 @t1)) % 0.38/0.66 (define @t55 () (tptp.member @t26 (tptp.intersection @t1 @t3))) % 0.38/0.66 (define @t56 () (not @t55)) % 0.38/0.66 (define @t57 () (@list @t26 @t1 @t3)) % 0.38/0.66 (define @t58 () (tptp.member @t26 @t3)) % 0.38/0.66 (define @t59 () (not @t58)) % 0.38/0.66 (define @t60 () (not @t54)) % 0.38/0.66 (define @t61 () (tptp.complement @t1)) % 0.38/0.66 (define @t62 () (tptp.member @t26 @t61)) % 0.38/0.66 (define @t63 () (tptp.f8 @t26 @t1)) % 0.38/0.66 (define @t64 () (tptp.member @t26 (tptp.domain_of @t1))) % 0.38/0.66 (define @t65 () (not @t64)) % 0.38/0.66 (define @t66 () (@var "Xp" $$unsorted)) % 0.38/0.66 (define @t67 () (not (tptp.member @t66 @t1))) % 0.38/0.66 (define @t68 () (not (tptp.ordered_pair_predicate @t66))) % 0.38/0.66 (define @t69 () (@list @t26 @t1 @t66)) % 0.38/0.66 (define @t70 () (tptp.member @t26 (tptp.cross_product @t1 @t3))) % 0.38/0.66 (define @t71 () (not @t70)) % 0.38/0.66 (define @t72 () (tptp.member @t51 @t1)) % 0.38/0.66 (define @t73 () (tptp.member @t50 @t3)) % 0.38/0.66 (define @t74 () (tptp.member @t26 (tptp.converse @t1))) % 0.38/0.66 (define @t75 () (not @t74)) % 0.38/0.66 (define @t76 () (tptp.member (tptp.ordered_pair @t50 @t51) @t1)) % 0.38/0.66 (define @t77 () (tptp.f9 @t26 @t1)) % 0.38/0.66 (define @t78 () (tptp.member @t26 (tptp.rotate_right @t1))) % 0.38/0.66 (define @t79 () (not @t78)) % 0.38/0.66 (define @t80 () (tptp.f10 @t26 @t1)) % 0.38/0.66 (define @t81 () (tptp.f11 @t26 @t1)) % 0.38/0.66 (define @t82 () (@var "W" $$unsorted)) % 0.38/0.66 (define @t83 () (not (= @t26 (tptp.ordered_pair @t9 (tptp.ordered_pair @t36 @t82))))) % 0.38/0.66 (define @t84 () (not (tptp.little_set @t82))) % 0.38/0.66 (define @t85 () (@list @t26 @t1 @t9 @t36 @t82)) % 0.38/0.66 (define @t86 () (tptp.f12 @t26 @t1)) % 0.38/0.66 (define @t87 () (tptp.member @t26 (tptp.flip_range_of @t1))) % 0.38/0.66 (define @t88 () (not @t87)) % 0.38/0.66 (define @t89 () (tptp.f13 @t26 @t1)) % 0.38/0.66 (define @t90 () (tptp.f14 @t26 @t1)) % 0.38/0.66 (define @t91 () (tptp.successor @t1)) % 0.38/0.66 (define @t92 () (tptp.f16 @t26 @t1)) % 0.38/0.66 (define @t93 () (tptp.member @t26 (tptp.sigma @t1))) % 0.38/0.66 (define @t94 () (not @t93)) % 0.38/0.66 (define @t95 () (@list @t9)) % 0.38/0.66 (define @t96 () (tptp.member @t9 @t3)) % 0.38/0.66 (define @t97 () (not (tptp.member @t9 @t1))) % 0.38/0.66 (define @t98 () (tptp.subset @t1 @t3)) % 0.38/0.66 (define @t99 () (not @t98)) % 0.38/0.66 (define @t100 () (@list @t1 @t3 @t9)) % 0.38/0.66 (define @t101 () (tptp.f17 @t1 @t3)) % 0.38/0.66 (define @t102 () (tptp.proper_subset @t1 @t3)) % 0.38/0.66 (define @t103 () (not @t102)) % 0.38/0.66 (define @t104 () (tptp.subset @t26 @t1)) % 0.38/0.66 (define @t105 () (tptp.member @t26 (tptp.powerset @t1))) % 0.38/0.66 (define @t106 () (tptp.relation @t26)) % 0.38/0.66 (define @t107 () (tptp.f18 @t26)) % 0.38/0.66 (define @t108 () (tptp.single_valued_set @t1)) % 0.38/0.66 (define @t109 () (tptp.f19 @t1)) % 0.38/0.66 (define @t110 () (tptp.f20 @t1)) % 0.38/0.66 (define @t111 () (tptp.f21 @t1)) % 0.38/0.66 (define @t112 () (@var "Xf" $$unsorted)) % 0.38/0.66 (define @t113 () (tptp.relation @t112)) % 0.38/0.66 (define @t114 () (tptp.function @t112)) % 0.38/0.66 (define @t115 () (not @t114)) % 0.38/0.66 (define @t116 () (@list @t112)) % 0.38/0.66 (define @t117 () (tptp.single_valued_set @t112)) % 0.38/0.66 (define @t118 () (tptp.f22 @t26 @t1 @t112)) % 0.38/0.66 (define @t119 () (tptp.image @t1 @t112)) % 0.38/0.66 (define @t120 () (tptp.member @t26 @t119)) % 0.38/0.66 (define @t121 () (not @t120)) % 0.38/0.66 (define @t122 () (@list @t26 @t1 @t112)) % 0.38/0.66 (define @t123 () (not @t2)) % 0.38/0.66 (define @t124 () (tptp.disjoint @t1 @t3)) % 0.38/0.66 (define @t125 () (tptp.f23 @t1 @t3)) % 0.38/0.66 (define @t126 () (tptp.f24 @t1)) % 0.38/0.66 (define @t127 () (= @t1 tptp.empty_set)) % 0.38/0.66 (define @t128 () (tptp.f26 @t1)) % 0.38/0.66 (define @t129 () (tptp.f27 @t26 @t1)) % 0.38/0.66 (define @t130 () (tptp.member @t26 (tptp.range_of @t1))) % 0.38/0.66 (define @t131 () (not @t130)) % 0.38/0.66 (define @t132 () (tptp.member @t26 tptp.identity_relation)) % 0.38/0.66 (define @t133 () (not @t132)) % 0.38/0.66 (define @t134 () (= @t51 @t50)) % 0.38/0.66 (define @t135 () (tptp.one_to_one_function @t112)) % 0.38/0.66 (define @t136 () (not @t135)) % 0.38/0.66 (define @t137 () (tptp.function (tptp.converse @t112))) % 0.38/0.66 (define @t138 () (tptp.f28 @t26 @t112 @t3)) % 0.38/0.66 (define @t139 () (tptp.member @t26 (tptp.apply @t112 @t3))) % 0.38/0.66 (define @t140 () (not @t139)) % 0.38/0.66 (define @t141 () (@list @t26 @t112 @t3)) % 0.38/0.66 (define @t142 () (@list @t112 @t1 @t3)) % 0.38/0.66 (define @t143 () (tptp.maps @t112 @t1 @t3)) % 0.38/0.66 (define @t144 () (not @t143)) % 0.38/0.66 (define @t145 () (= (tptp.domain_of @t112) @t1)) % 0.38/0.66 (define @t146 () (tptp.subset (tptp.range_of @t112) @t3)) % 0.38/0.66 (define @t147 () (@var "Xs" $$unsorted)) % 0.38/0.66 (define @t148 () (tptp.little_set @t147)) % 0.38/0.66 (define @t149 () (tptp.closed @t147 @t112)) % 0.38/0.66 (define @t150 () (not @t149)) % 0.38/0.66 (define @t151 () (@list @t147 @t112)) % 0.38/0.66 (define @t152 () (tptp.little_set @t112)) % 0.38/0.66 (define @t153 () (tptp.maps @t112 (tptp.cross_product @t147 @t147) @t147)) % 0.38/0.66 (define @t154 () (@var "Xg" $$unsorted)) % 0.38/0.66 (define @t155 () (tptp.f29 @t26 @t112 @t154)) % 0.38/0.66 (define @t156 () (tptp.member @t26 (tptp.compose @t112 @t154))) % 0.38/0.66 (define @t157 () (not @t156)) % 0.38/0.66 (define @t158 () (@list @t26 @t112 @t154)) % 0.38/0.66 (define @t159 () (tptp.f30 @t26 @t112 @t154)) % 0.38/0.66 (define @t160 () (tptp.f31 @t26 @t112 @t154)) % 0.38/0.66 (define @t161 () (@var "Xf1" $$unsorted)) % 0.38/0.66 (define @t162 () (@var "Xs1" $$unsorted)) % 0.38/0.66 (define @t163 () (tptp.closed @t162 @t161)) % 0.38/0.66 (define @t164 () (@var "Xf2" $$unsorted)) % 0.38/0.66 (define @t165 () (@var "Xs2" $$unsorted)) % 0.38/0.66 (define @t166 () (@var "Xh" $$unsorted)) % 0.38/0.66 (define @t167 () (tptp.homomorphism @t166 @t162 @t161 @t165 @t164)) % 0.38/0.66 (define @t168 () (not @t167)) % 0.38/0.66 (define @t169 () (@list @t166 @t162 @t161 @t165 @t164)) % 0.38/0.66 (define @t170 () (tptp.closed @t165 @t164)) % 0.38/0.66 (define @t171 () (tptp.maps @t166 @t162 @t165)) % 0.38/0.66 (define @t172 () (tptp.f32 @t166 @t162 @t161 @t165 @t164)) % 0.38/0.66 (define @t173 () (not @t171)) % 0.38/0.66 (define @t174 () (not @t170)) % 0.38/0.66 (define @t175 () (not @t163)) % 0.38/0.66 (define @t176 () (tptp.f33 @t166 @t162 @t161 @t165 @t164)) % 0.38/0.66 (define @t177 () (= @t1 @t9)) % 0.38/0.66 (define @t178 () (not (= @t21 @t37))) % 0.38/0.66 (define @t179 () (tptp.little_set tptp.a)) % 0.38/0.66 (define @t180 () (tptp.member tptp.a (tptp.singleton_set tptp.a))) % 0.38/0.66 (define @t181 () (tptp.member @t9 (tptp.non_ordered_pair @t9 @t3))) % 0.38/0.66 (define @t182 () (not (= @t9 @t9))) % 0.38/0.66 (define @t183 () (or @t181 @t16 @t182)) % 0.38/0.66 (define @t184 () (@list @t9 @t3)) % 0.38/0.66 (define @t185 () (not @t177)) % 0.38/0.66 (define @t186 () (or @t185 @t13 @t16 @t185)) % 0.38/0.66 (define @t187 () (or @t13 @t16 @t185)) % 0.38/0.66 (define @t188 () (forall @t20 @t187)) % 0.38/0.66 (define @t189 () (forall @t184 @t188)) % 0.38/0.66 (define @t190 () (forall (@list @t9 @t3 @t1) @t187)) % 0.38/0.66 (define @t191 () (not @t179)) % 0.38/0.66 (define @t192 () (tptp.member tptp.a (tptp.non_ordered_pair tptp.a tptp.a))) % 0.38/0.66 (define @t193 () (or @t192 @t191)) % 0.38/0.66 (assume @p1 (forall @t4 (or (not (tptp.member @t1 @t3)) @t2))) % 0.38/0.66 (assume @p2 (forall @t4 (or (tptp.little_set @t6) @t5))) % 0.38/0.66 (assume @p3 (forall @t4 (or @t8 @t7 @t5))) % 0.38/0.66 (assume @p4 (forall @t4 (or (not @t8) (not @t7) @t5))) % 0.38/0.66 (assume @p5 (forall @t14 (or (not @t13) @t11 @t10))) % 0.38/0.66 (assume @p6 @t18) % 0.38/0.66 (assume @p7 (forall @t14 (or @t13 @t16 (not @t10)))) % 0.38/0.66 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.38/0.66 (assume @p9 (forall @t20 (= @t19 (tptp.non_ordered_pair @t1 @t1)))) % 0.38/0.66 (assume @p10 (forall @t4 (= @t21 (tptp.non_ordered_pair @t19 @t12)))) % 0.38/0.66 (assume @p11 (forall @t20 (or @t24 (tptp.little_set @t22)))) % 0.38/0.66 (assume @p12 (forall @t20 (or @t24 (tptp.little_set @t25)))) % 0.38/0.66 (assume @p13 (forall @t20 (or @t24 (= @t1 (tptp.ordered_pair @t22 @t25))))) % 0.38/0.66 (assume @p14 (forall @t29 (or @t23 @t28 @t27 (not (= @t1 (tptp.ordered_pair @t3 @t26)))))) % 0.38/0.66 (assume @p15 (forall @t34 (or @t33 (tptp.little_set @t30)))) % 0.38/0.66 (assume @p16 (forall @t34 (or @t33 (tptp.little_set @t35)))) % 0.38/0.66 (assume @p17 (forall @t34 (or @t33 (= @t1 (tptp.ordered_pair @t30 @t35))))) % 0.38/0.66 (assume @p18 (forall @t34 (or @t33 (tptp.member @t26 @t30)))) % 0.38/0.66 (assume @p19 (forall @t40 (or @t32 @t16 @t39 @t38 (not (tptp.member @t26 @t9))))) % 0.38/0.66 (assume @p20 (forall @t34 (or @t44 (tptp.little_set @t41)))) % 0.38/0.66 (assume @p21 (forall @t34 (or @t44 (tptp.little_set @t45)))) % 0.38/0.66 (assume @p22 (forall @t34 (or @t44 (= @t1 (tptp.ordered_pair @t41 @t45))))) % 0.38/0.66 (assume @p23 (forall @t34 (or @t44 (tptp.member @t26 @t45)))) % 0.38/0.66 (assume @p24 (forall @t40 (or @t43 @t16 @t39 @t38 (not (tptp.member @t26 @t36))))) % 0.38/0.66 (assume @p25 (forall @t49 (or @t48 @t46))) % 0.38/0.66 (assume @p26 (forall @t49 (or @t48 @t52))) % 0.38/0.66 (assume @p27 (forall @t49 (or @t47 @t27 @t53 (not @t52)))) % 0.38/0.66 (assume @p28 (forall @t57 (or @t56 @t54))) % 0.38/0.66 (assume @p29 (forall @t57 (or @t56 @t58))) % 0.38/0.66 (assume @p30 (forall @t57 (or @t55 @t60 @t59))) % 0.38/0.66 (assume @p31 (forall @t34 (or (not @t62) @t60))) % 0.38/0.66 (assume @p32 (forall @t34 (or @t62 @t27 @t54))) % 0.38/0.66 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t61 (tptp.complement @t3)))))) % 0.38/0.66 (assume @p34 (forall @t34 (or @t65 (tptp.ordered_pair_predicate @t63)))) % 0.38/0.66 (assume @p35 (forall @t34 (or @t65 (tptp.member @t63 @t1)))) % 0.38/0.66 (assume @p36 (forall @t34 (or @t65 (= @t26 (tptp.first @t63))))) % 0.38/0.66 (assume @p37 (forall @t69 (or @t64 @t27 @t68 @t67 (not (= @t26 (tptp.first @t66)))))) % 0.38/0.66 (assume @p38 (forall @t57 (or @t71 @t46))) % 0.38/0.66 (assume @p39 (forall @t57 (or @t71 @t72))) % 0.38/0.66 (assume @p40 (forall @t57 (or @t71 @t73))) % 0.38/0.66 (assume @p41 (forall @t57 (or @t70 @t27 @t53 (not @t72) (not @t73)))) % 0.38/0.66 (assume @p42 (forall @t34 (or @t75 @t46))) % 0.38/0.66 (assume @p43 (forall @t34 (or @t75 @t76))) % 0.38/0.66 (assume @p44 (forall @t34 (or @t74 @t27 @t53 (not @t76)))) % 0.38/0.66 (assume @p45 (forall @t34 (or @t79 (tptp.little_set @t77)))) % 0.38/0.66 (assume @p46 (forall @t34 (or @t79 (tptp.little_set @t80)))) % 0.38/0.66 (assume @p47 (forall @t34 (or @t79 (tptp.little_set @t81)))) % 0.38/0.66 (assume @p48 (forall @t34 (or @t79 (= @t26 (tptp.ordered_pair @t77 (tptp.ordered_pair @t80 @t81)))))) % 0.38/0.66 (assume @p49 (forall @t34 (or @t79 (tptp.member (tptp.ordered_pair @t80 (tptp.ordered_pair @t81 @t77)) @t1)))) % 0.38/0.66 (assume @p50 (forall @t85 (or @t78 @t27 @t16 @t39 @t84 @t83 (not (tptp.member (tptp.ordered_pair @t36 (tptp.ordered_pair @t82 @t9)) @t1))))) % 0.38/0.66 (assume @p51 (forall @t34 (or @t88 (tptp.little_set @t86)))) % 0.38/0.66 (assume @p52 (forall @t34 (or @t88 (tptp.little_set @t89)))) % 0.38/0.66 (assume @p53 (forall @t34 (or @t88 (tptp.little_set @t90)))) % 0.38/0.66 (assume @p54 (forall @t34 (or @t88 (= @t26 (tptp.ordered_pair @t86 (tptp.ordered_pair @t89 @t90)))))) % 0.38/0.66 (assume @p55 (forall @t34 (or @t88 (tptp.member (tptp.ordered_pair @t86 (tptp.ordered_pair @t90 @t89)) @t1)))) % 0.38/0.66 (assume @p56 (forall @t85 (or @t87 @t27 @t16 @t39 @t84 @t83 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t82 @t36)) @t1))))) % 0.38/0.66 (assume @p57 (forall @t20 (= @t91 (tptp.union @t1 @t19)))) % 0.38/0.66 (assume @p58 (forall @t49 (not (tptp.member @t26 tptp.empty_set)))) % 0.38/0.66 (assume @p59 (forall @t49 (or (tptp.member @t26 tptp.universal_set) @t27))) % 0.38/0.66 (assume @p60 (tptp.little_set tptp.infinity)) % 0.38/0.66 (assume @p61 (tptp.member tptp.empty_set tptp.infinity)) % 0.38/0.66 (assume @p62 (forall @t20 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t91 tptp.infinity)))) % 0.38/0.66 (assume @p63 (forall @t34 (or @t94 (tptp.member @t92 @t1)))) % 0.38/0.66 (assume @p64 (forall @t34 (or @t94 (tptp.member @t26 @t92)))) % 0.38/0.66 (assume @p65 (forall @t57 (or @t93 (not (tptp.member @t3 @t1)) @t59))) % 0.38/0.66 (assume @p66 (forall @t95 (or @t16 (tptp.little_set (tptp.sigma @t9))))) % 0.38/0.66 (assume @p67 (forall @t100 (or @t99 @t97 @t96))) % 0.38/0.66 (assume @p68 (forall @t4 (or @t98 (tptp.member @t101 @t1)))) % 0.38/0.66 (assume @p69 (forall @t4 (or @t98 (not (tptp.member @t101 @t3))))) % 0.38/0.66 (assume @p70 (forall @t4 (or @t103 @t98))) % 0.38/0.66 (assume @p71 (forall @t4 (or @t103 (not @t5)))) % 0.38/0.66 (assume @p72 (forall @t4 (or @t102 @t99 @t5))) % 0.38/0.66 (assume @p73 (forall @t34 (or (not @t105) @t104))) % 0.38/0.66 (assume @p74 (forall @t34 (or @t105 @t27 (not @t104)))) % 0.38/0.66 (assume @p75 (forall @t95 (or @t16 (tptp.little_set (tptp.powerset @t9))))) % 0.38/0.66 (assume @p76 (forall @t34 (or (not @t106) (not (tptp.member @t1 @t26)) @t23))) % 0.38/0.66 (assume @p77 (forall @t49 (or @t106 (tptp.member @t107 @t26)))) % 0.38/0.66 (assume @p78 (forall @t49 (or @t106 (not (tptp.ordered_pair_predicate @t107))))) % 0.38/0.66 (assume @p79 (forall (@list @t1 @t9 @t36 @t82) (or (not @t108) @t16 @t39 @t84 (not (tptp.member @t37 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t82) @t1)) (= @t36 @t82)))) % 0.38/0.66 (assume @p80 (forall @t20 (or @t108 (tptp.little_set @t109)))) % 0.38/0.66 (assume @p81 (forall @t20 (or @t108 (tptp.little_set @t110)))) % 0.38/0.66 (assume @p82 (forall @t20 (or @t108 (tptp.little_set @t111)))) % 0.38/0.66 (assume @p83 (forall @t20 (or @t108 (tptp.member (tptp.ordered_pair @t109 @t110) @t1)))) % 0.38/0.66 (assume @p84 (forall @t20 (or @t108 (tptp.member (tptp.ordered_pair @t109 @t111) @t1)))) % 0.38/0.66 (assume @p85 (forall @t20 (or @t108 (not (= @t110 @t111))))) % 0.38/0.66 (assume @p86 (forall @t116 (or @t115 @t113))) % 0.38/0.66 (assume @p87 (forall @t116 (or @t115 @t117))) % 0.38/0.66 (assume @p88 (forall @t116 (or @t114 (not @t113) (not @t117)))) % 0.38/0.66 (assume @p89 (forall @t122 (or @t121 (tptp.ordered_pair_predicate @t118)))) % 0.38/0.66 (assume @p90 (forall @t122 (or @t121 (tptp.member @t118 @t112)))) % 0.38/0.66 (assume @p91 (forall @t122 (or @t121 (tptp.member (tptp.first @t118) @t1)))) % 0.38/0.66 (assume @p92 (forall @t122 (or @t121 (= (tptp.second @t118) @t26)))) % 0.38/0.66 (assume @p93 (forall (@list @t26 @t1 @t112 @t3) (or @t120 @t27 (not (tptp.ordered_pair_predicate @t3)) (not (tptp.member @t3 @t112)) (not (tptp.member (tptp.first @t3) @t1)) (not (= (tptp.second @t3) @t26))))) % 0.38/0.66 (assume @p94 (forall (@list @t1 @t112) (or @t123 @t115 (tptp.little_set @t119)))) % 0.38/0.66 (assume @p95 (forall @t100 (or (not @t124) @t97 (not @t96)))) % 0.38/0.66 (assume @p96 (forall @t4 (or @t124 (tptp.member @t125 @t1)))) % 0.38/0.66 (assume @p97 (forall @t4 (or @t124 (tptp.member @t125 @t3)))) % 0.38/0.66 (assume @p98 (forall @t20 (or @t127 (tptp.member @t126 @t1)))) % 0.38/0.66 (assume @p99 (forall @t20 (or @t127 (tptp.disjoint @t126 @t1)))) % 0.38/0.66 (assume @p100 (tptp.function tptp.f25)) % 0.38/0.66 (assume @p101 (forall @t20 (or @t123 @t127 (tptp.member @t128 @t1)))) % 0.38/0.66 (assume @p102 (forall @t20 (or @t123 @t127 (tptp.member (tptp.ordered_pair @t1 @t128) tptp.f25)))) % 0.38/0.66 (assume @p103 (forall @t34 (or @t131 (tptp.ordered_pair_predicate @t129)))) % 0.38/0.66 (assume @p104 (forall @t34 (or @t131 (tptp.member @t129 @t1)))) % 0.38/0.66 (assume @p105 (forall @t34 (or @t131 (= @t26 (tptp.second @t129))))) % 0.38/0.66 (assume @p106 (forall @t69 (or @t130 @t27 @t68 @t67 (not (= @t26 (tptp.second @t66)))))) % 0.38/0.66 (assume @p107 (forall @t49 (or @t133 @t46))) % 0.38/0.66 (assume @p108 (forall @t49 (or @t133 @t134))) % 0.38/0.66 (assume @p109 (forall @t49 (or @t132 @t27 @t53 (not @t134)))) % 0.38/0.66 (assume @p110 (forall @t4 (= (tptp.restrict @t1 @t3) (tptp.intersection @t1 (tptp.cross_product @t3 tptp.universal_set))))) % 0.38/0.66 (assume @p111 (forall @t116 (or @t136 @t114))) % 0.38/0.66 (assume @p112 (forall @t116 (or @t136 @t137))) % 0.38/0.66 (assume @p113 (forall @t116 (or @t135 @t115 (not @t137)))) % 0.38/0.66 (assume @p114 (forall @t141 (or @t140 (tptp.ordered_pair_predicate @t138)))) % 0.38/0.66 (assume @p115 (forall @t141 (or @t140 (tptp.member @t138 @t112)))) % 0.38/0.66 (assume @p116 (forall @t141 (or @t140 (= (tptp.first @t138) @t3)))) % 0.38/0.66 (assume @p117 (forall @t141 (or @t140 (tptp.member @t26 (tptp.second @t138))))) % 0.38/0.66 (assume @p118 (forall (@list @t26 @t112 @t3 @t82) (or @t139 (not (tptp.ordered_pair_predicate @t82)) (not (tptp.member @t82 @t112)) (not (= (tptp.first @t82) @t3)) (not (tptp.member @t26 (tptp.second @t82)))))) % 0.38/0.66 (assume @p119 (forall @t142 (= (tptp.apply_to_two_arguments @t112 @t1 @t3) (tptp.apply @t112 @t21)))) % 0.38/0.66 (assume @p120 (forall @t142 (or @t144 @t114))) % 0.38/0.66 (assume @p121 (forall @t142 (or @t144 @t145))) % 0.38/0.66 (assume @p122 (forall @t142 (or @t144 @t146))) % 0.38/0.66 (assume @p123 (forall @t142 (or @t143 @t115 (not @t145) (not @t146)))) % 0.38/0.66 (assume @p124 (forall @t151 (or @t150 @t148))) % 0.38/0.66 (assume @p125 (forall @t151 (or @t150 @t152))) % 0.38/0.66 (assume @p126 (forall @t151 (or @t150 @t153))) % 0.38/0.66 (assume @p127 (forall @t151 (or @t149 (not @t148) (not @t152) (not @t153)))) % 0.38/0.66 (assume @p128 (forall @t158 (or @t157 (tptp.little_set @t155)))) % 0.38/0.66 (assume @p129 (forall @t158 (or @t157 (tptp.little_set @t159)))) % 0.38/0.66 (assume @p130 (forall @t158 (or @t157 (tptp.little_set @t160)))) % 0.38/0.66 (assume @p131 (forall @t158 (or @t157 (= @t26 (tptp.ordered_pair @t155 @t159))))) % 0.38/0.66 (assume @p132 (forall @t158 (or @t157 (tptp.member (tptp.ordered_pair @t155 @t160) @t112)))) % 0.38/0.66 (assume @p133 (forall @t158 (or @t157 (tptp.member (tptp.ordered_pair @t160 @t159) @t154)))) % 0.38/0.66 (assume @p134 (forall (@list @t26 @t112 @t154 @t1 @t3 @t82) (or @t156 @t27 @t123 @t28 @t84 (not (= @t26 @t21)) (not (tptp.member (tptp.ordered_pair @t1 @t82) @t112)) (not (tptp.member (tptp.ordered_pair @t82 @t3) @t154))))) % 0.38/0.66 (assume @p135 (forall @t169 (or @t168 @t163))) % 0.38/0.66 (assume @p136 (forall @t169 (or @t168 @t170))) % 0.38/0.66 (assume @p137 (forall @t169 (or @t168 @t171))) % 0.38/0.66 (assume @p138 (forall (@list @t166 @t162 @t161 @t165 @t164 @t1 @t3) (or @t168 (not (tptp.member @t1 @t162)) (not (tptp.member @t3 @t162)) (= (tptp.apply @t166 (tptp.apply_to_two_arguments @t161 @t1 @t3)) (tptp.apply_to_two_arguments @t164 (tptp.apply @t166 @t1) (tptp.apply @t166 @t3)))))) % 0.38/0.66 (assume @p139 (forall @t169 (or @t167 @t175 @t174 @t173 (tptp.member @t172 @t162)))) % 0.38/0.66 (assume @p140 (forall @t169 (or @t167 @t175 @t174 @t173 (tptp.member @t176 @t162)))) % 0.38/0.66 (assume @p141 (forall @t169 (or @t167 @t175 @t174 @t173 (not (= (tptp.apply @t166 (tptp.apply_to_two_arguments @t161 @t172 @t176)) (tptp.apply_to_two_arguments @t164 (tptp.apply @t166 @t172) (tptp.apply @t166 @t176))))))) % 0.38/0.66 (assume @p142 (forall (@list @t1 @t9 @t3 @t36) (or @t123 @t16 @t178 @t177))) % 0.38/0.66 (assume @p143 (forall @t29 (or @t123 @t28 (not (= (tptp.non_ordered_pair @t26 @t1) (tptp.non_ordered_pair @t26 @t3))) @t5))) % 0.38/0.66 (assume @p144 (forall (@list @t1 @t3 @t9 @t36) (or @t123 @t28 @t16 @t39 @t178 (= @t3 @t36)))) % 0.38/0.66 (assume @p145 (forall @t4 (or @t99 (not (tptp.subset @t3 @t1)) @t5))) % 0.38/0.66 (assume @p146 (forall @t4 (or @t123 @t28 (= (tptp.first @t21) @t1)))) % 0.38/0.66 (assume @p147 (forall @t4 (or @t123 @t28 (= (tptp.second @t21) @t3)))) % 0.38/0.66 (assume @p148 (forall @t20 (or @t24 (tptp.little_set @t31)))) % 0.38/0.66 (assume @p149 (forall @t20 (or @t24 (tptp.little_set @t42)))) % 0.38/0.66 (assume @p150 @t179) % 0.38/0.66 (assume @p151 (not @t180)) % 0.38/0.66 (step @p152 :rule evaluate :args ((= false true))) % 0.38/0.66 (step @p153 :rule aci_norm :args ((= (or @t181 @t16 false) (or @t181 @t16)))) % 0.38/0.66 (step @p154 :rule evaluate :args ((not true))) % 0.38/0.66 (step @p155 :rule eq-refl :args (@t9)) % 0.38/0.66 (step @p156 :rule cong :premises (@p155) :args (@t182)) % 0.38/0.66 (step @p157 :rule trans :premises (@p156 @p154)) % 0.38/0.66 (step @p158 :rule refl :args (@t16)) % 0.38/0.66 (step @p159 :rule refl :args (@t181)) % 0.38/0.66 (step @p160 :rule nary_cong :premises (@p159 @p158 @p157) :args (@t183)) % 0.38/0.66 (step @p161 :rule trans :premises (@p160 @p153)) % 0.38/0.66 (step @p162 :rule cong :premises (@p161) :args ((forall @t184 @t183))) % 0.38/0.66 (step @p163 :rule quant-var-elim-eq :args ((= (forall @t20 @t186) @t183))) % 0.38/0.66 (step @p164 :rule aci_norm :args ((= @t187 @t186))) % 0.38/0.66 (step @p165 :rule cong :premises (@p164) :args (@t188)) % 0.38/0.66 (step @p166 :rule trans :premises (@p165 @p163)) % 0.38/0.66 (step @p167 :rule cong :premises (@p166) :args (@t189)) % 0.38/0.66 (step @p168 :rule quant-merge-prenex :args ((= @t189 @t190))) % 0.38/0.66 (step @p169 :rule symm :premises (@p168)) % 0.38/0.66 (step @p170 :rule quant_var_reordering :args ((= (forall @t14 @t187) @t190))) % 0.38/0.66 (step @p171 :rule trans :premises (@p170 @p169 @p167)) % 0.38/0.66 (step @p172 :rule trans :premises (@p171 @p162)) % 0.38/0.66 (step @p173 :rule eq-symm :args (@t9 @t1)) % 0.38/0.66 (step @p174 :rule cong :premises (@p173) :args (@t15)) % 0.38/0.66 (step @p175 :rule refl :args (@t13)) % 0.38/0.66 (step @p176 :rule nary_cong :premises (@p175 @p158 @p174) :args (@t17)) % 0.38/0.66 (step @p177 :rule cong :premises (@p176) :args (@t18)) % 0.38/0.66 (step @p178 :rule trans :premises (@p177 @p172)) % 0.38/0.66 (step @p179 :rule eq_resolve :premises (@p6 @p178)) % 0.38/0.66 (step @p180 :rule instantiate :premises (@p179) :args ((@list tptp.a tptp.a))) % 0.38/0.66 (step @p181 :rule cnf_or_pos :args (@t193)) % 0.38/0.66 (step @p182 :rule reordering :premises (@p181) :args ((or @t191 @t192 (not @t193)))) % 0.38/0.66 (step @p183 :rule chain_m_resolution :premises (@p182 @p150 @p180) :args (@t192 (@list false false) (@list @t179 @t193))) % 0.38/0.66 (step @p184 :rule true_intro :premises (@p183)) % 0.38/0.66 (step @p185 :rule instantiate :premises (@p9) :args ((@list tptp.a))) % 0.38/0.66 (step @p186 :rule refl :args (tptp.a)) % 0.38/0.66 (step @p187 :rule cong :premises (@p186 @p185) :args (@t180)) % 0.38/0.66 (step @p188 :rule false_intro :premises (@p151)) % 0.38/0.66 (step @p189 :rule symm :premises (@p188)) % 0.38/0.66 (step @p190 :rule trans :premises (@p189 @p187 @p184)) % 0.38/0.66 (step @p191 false :rule eq_resolve :premises (@p190 @p152)) % 0.38/0.66 ) % 0.38/0.66 % SZS output end Proof % 0.38/0.66 % cvc5 exiting %------------------------------------------------------------------------------