%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET025-4 : 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 : n003.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 : SET025-4 : 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 % 0.17/0.35 % Computer : n003.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 14:41:59 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.28/0.55 --- 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 $$unsorted 0) % 0.38/0.66 (declare-const tptp.b $$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.a $$unsorted) % 0.38/0.66 (declare-const tptp.estin $$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" $$unsorted)) % 0.38/0.66 (define @t10 () (= @t9 @t3)) % 0.38/0.66 (define @t11 () (= @t9 @t1)) % 0.38/0.66 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.38/0.66 (define @t13 () (tptp.member @t9 @t12)) % 0.38/0.66 (define @t14 () (@list @t9 @t1 @t3)) % 0.38/0.66 (define @t15 () (not (tptp.little_set @t9))) % 0.38/0.66 (define @t16 () (tptp.singleton_set @t1)) % 0.38/0.66 (define @t17 () (@list @t1)) % 0.38/0.66 (define @t18 () (tptp.ordered_pair @t1 @t3)) % 0.38/0.66 (define @t19 () (tptp.f2 @t1)) % 0.38/0.66 (define @t20 () (tptp.ordered_pair_predicate @t1)) % 0.38/0.66 (define @t21 () (not @t20)) % 0.38/0.66 (define @t22 () (tptp.f3 @t1)) % 0.38/0.66 (define @t23 () (@var "Z" $$unsorted)) % 0.38/0.66 (define @t24 () (not (tptp.little_set @t23))) % 0.38/0.66 (define @t25 () (not (tptp.little_set @t3))) % 0.38/0.66 (define @t26 () (tptp.f4 @t23 @t1)) % 0.38/0.66 (define @t27 () (tptp.member @t23 (tptp.first @t1))) % 0.38/0.66 (define @t28 () (not @t27)) % 0.38/0.66 (define @t29 () (@list @t23 @t1)) % 0.38/0.66 (define @t30 () (tptp.f5 @t23 @t1)) % 0.38/0.66 (define @t31 () (@var "V" $$unsorted)) % 0.38/0.66 (define @t32 () (tptp.ordered_pair @t9 @t31)) % 0.38/0.66 (define @t33 () (not (= @t1 @t32))) % 0.38/0.66 (define @t34 () (not (tptp.little_set @t31))) % 0.38/0.66 (define @t35 () (@list @t23 @t1 @t9 @t31)) % 0.38/0.66 (define @t36 () (tptp.f6 @t23 @t1)) % 0.38/0.66 (define @t37 () (tptp.member @t23 (tptp.second @t1))) % 0.38/0.66 (define @t38 () (not @t37)) % 0.38/0.66 (define @t39 () (tptp.f7 @t23 @t1)) % 0.38/0.66 (define @t40 () (tptp.ordered_pair_predicate @t23)) % 0.38/0.66 (define @t41 () (tptp.member @t23 tptp.estin)) % 0.38/0.66 (define @t42 () (not @t41)) % 0.38/0.66 (define @t43 () (@list @t23)) % 0.38/0.66 (define @t44 () (tptp.second @t23)) % 0.38/0.66 (define @t45 () (tptp.first @t23)) % 0.38/0.66 (define @t46 () (tptp.member @t45 @t44)) % 0.38/0.66 (define @t47 () (not @t40)) % 0.38/0.66 (define @t48 () (tptp.member @t23 @t1)) % 0.38/0.66 (define @t49 () (tptp.member @t23 (tptp.intersection @t1 @t3))) % 0.38/0.66 (define @t50 () (not @t49)) % 0.38/0.66 (define @t51 () (@list @t23 @t1 @t3)) % 0.38/0.66 (define @t52 () (tptp.member @t23 @t3)) % 0.38/0.66 (define @t53 () (not @t52)) % 0.38/0.66 (define @t54 () (not @t48)) % 0.38/0.66 (define @t55 () (tptp.complement @t1)) % 0.38/0.66 (define @t56 () (tptp.member @t23 @t55)) % 0.38/0.66 (define @t57 () (tptp.f8 @t23 @t1)) % 0.38/0.66 (define @t58 () (tptp.member @t23 (tptp.domain_of @t1))) % 0.38/0.66 (define @t59 () (not @t58)) % 0.38/0.66 (define @t60 () (@var "Xp" $$unsorted)) % 0.38/0.66 (define @t61 () (not (tptp.member @t60 @t1))) % 0.38/0.66 (define @t62 () (not (tptp.ordered_pair_predicate @t60))) % 0.38/0.66 (define @t63 () (@list @t23 @t1 @t60)) % 0.38/0.66 (define @t64 () (tptp.member @t23 (tptp.cross_product @t1 @t3))) % 0.38/0.66 (define @t65 () (not @t64)) % 0.38/0.66 (define @t66 () (tptp.member @t45 @t1)) % 0.38/0.66 (define @t67 () (tptp.member @t44 @t3)) % 0.38/0.66 (define @t68 () (tptp.member @t23 (tptp.converse @t1))) % 0.38/0.66 (define @t69 () (not @t68)) % 0.38/0.66 (define @t70 () (tptp.member (tptp.ordered_pair @t44 @t45) @t1)) % 0.38/0.66 (define @t71 () (tptp.f9 @t23 @t1)) % 0.38/0.66 (define @t72 () (tptp.member @t23 (tptp.rotate_right @t1))) % 0.38/0.66 (define @t73 () (not @t72)) % 0.38/0.66 (define @t74 () (tptp.f10 @t23 @t1)) % 0.38/0.66 (define @t75 () (tptp.f11 @t23 @t1)) % 0.38/0.66 (define @t76 () (@var "W" $$unsorted)) % 0.38/0.66 (define @t77 () (not (= @t23 (tptp.ordered_pair @t9 (tptp.ordered_pair @t31 @t76))))) % 0.38/0.66 (define @t78 () (not (tptp.little_set @t76))) % 0.38/0.66 (define @t79 () (@list @t23 @t1 @t9 @t31 @t76)) % 0.38/0.66 (define @t80 () (tptp.f12 @t23 @t1)) % 0.38/0.66 (define @t81 () (tptp.member @t23 (tptp.flip_range_of @t1))) % 0.38/0.66 (define @t82 () (not @t81)) % 0.38/0.66 (define @t83 () (tptp.f13 @t23 @t1)) % 0.38/0.66 (define @t84 () (tptp.f14 @t23 @t1)) % 0.38/0.66 (define @t85 () (tptp.successor @t1)) % 0.38/0.66 (define @t86 () (tptp.f16 @t23 @t1)) % 0.38/0.66 (define @t87 () (tptp.member @t23 (tptp.sigma @t1))) % 0.38/0.66 (define @t88 () (not @t87)) % 0.38/0.66 (define @t89 () (@list @t9)) % 0.38/0.66 (define @t90 () (tptp.member @t9 @t3)) % 0.38/0.66 (define @t91 () (not (tptp.member @t9 @t1))) % 0.38/0.66 (define @t92 () (tptp.subset @t1 @t3)) % 0.38/0.66 (define @t93 () (not @t92)) % 0.38/0.66 (define @t94 () (@list @t1 @t3 @t9)) % 0.38/0.66 (define @t95 () (tptp.f17 @t1 @t3)) % 0.38/0.66 (define @t96 () (tptp.proper_subset @t1 @t3)) % 0.38/0.66 (define @t97 () (not @t96)) % 0.38/0.66 (define @t98 () (tptp.subset @t23 @t1)) % 0.38/0.66 (define @t99 () (tptp.member @t23 (tptp.powerset @t1))) % 0.38/0.66 (define @t100 () (tptp.relation @t23)) % 0.38/0.66 (define @t101 () (tptp.f18 @t23)) % 0.38/0.66 (define @t102 () (tptp.single_valued_set @t1)) % 0.38/0.66 (define @t103 () (tptp.f19 @t1)) % 0.38/0.66 (define @t104 () (tptp.f20 @t1)) % 0.38/0.66 (define @t105 () (tptp.f21 @t1)) % 0.38/0.66 (define @t106 () (@var "Xf" $$unsorted)) % 0.38/0.66 (define @t107 () (tptp.relation @t106)) % 0.38/0.66 (define @t108 () (tptp.function @t106)) % 0.38/0.66 (define @t109 () (not @t108)) % 0.38/0.66 (define @t110 () (@list @t106)) % 0.38/0.66 (define @t111 () (tptp.single_valued_set @t106)) % 0.38/0.66 (define @t112 () (tptp.f22 @t23 @t1 @t106)) % 0.38/0.66 (define @t113 () (tptp.image @t1 @t106)) % 0.38/0.66 (define @t114 () (tptp.member @t23 @t113)) % 0.38/0.66 (define @t115 () (not @t114)) % 0.38/0.66 (define @t116 () (@list @t23 @t1 @t106)) % 0.38/0.66 (define @t117 () (not @t2)) % 0.38/0.66 (define @t118 () (tptp.disjoint @t1 @t3)) % 0.38/0.66 (define @t119 () (tptp.f23 @t1 @t3)) % 0.38/0.66 (define @t120 () (tptp.f24 @t1)) % 0.38/0.66 (define @t121 () (= @t1 tptp.empty_set)) % 0.38/0.66 (define @t122 () (tptp.f26 @t1)) % 0.38/0.66 (define @t123 () (tptp.f27 @t23 @t1)) % 0.38/0.66 (define @t124 () (tptp.member @t23 (tptp.range_of @t1))) % 0.38/0.66 (define @t125 () (not @t124)) % 0.38/0.66 (define @t126 () (tptp.member @t23 tptp.identity_relation)) % 0.38/0.66 (define @t127 () (not @t126)) % 0.38/0.66 (define @t128 () (= @t45 @t44)) % 0.38/0.66 (define @t129 () (tptp.one_to_one_function @t106)) % 0.38/0.66 (define @t130 () (not @t129)) % 0.38/0.66 (define @t131 () (tptp.function (tptp.converse @t106))) % 0.38/0.66 (define @t132 () (tptp.f28 @t23 @t106 @t3)) % 0.38/0.66 (define @t133 () (tptp.member @t23 (tptp.apply @t106 @t3))) % 0.38/0.66 (define @t134 () (not @t133)) % 0.38/0.66 (define @t135 () (@list @t23 @t106 @t3)) % 0.38/0.66 (define @t136 () (@list @t106 @t1 @t3)) % 0.38/0.66 (define @t137 () (tptp.maps @t106 @t1 @t3)) % 0.38/0.66 (define @t138 () (not @t137)) % 0.38/0.66 (define @t139 () (= (tptp.domain_of @t106) @t1)) % 0.38/0.66 (define @t140 () (tptp.subset (tptp.range_of @t106) @t3)) % 0.38/0.66 (define @t141 () (@var "Xs" $$unsorted)) % 0.38/0.66 (define @t142 () (tptp.little_set @t141)) % 0.38/0.66 (define @t143 () (tptp.closed @t141 @t106)) % 0.38/0.66 (define @t144 () (not @t143)) % 0.38/0.66 (define @t145 () (@list @t141 @t106)) % 0.38/0.66 (define @t146 () (tptp.little_set @t106)) % 0.38/0.66 (define @t147 () (tptp.maps @t106 (tptp.cross_product @t141 @t141) @t141)) % 0.38/0.66 (define @t148 () (@var "Xg" $$unsorted)) % 0.38/0.66 (define @t149 () (tptp.f29 @t23 @t106 @t148)) % 0.38/0.66 (define @t150 () (tptp.member @t23 (tptp.compose @t106 @t148))) % 0.38/0.66 (define @t151 () (not @t150)) % 0.38/0.66 (define @t152 () (@list @t23 @t106 @t148)) % 0.38/0.66 (define @t153 () (tptp.f30 @t23 @t106 @t148)) % 0.38/0.66 (define @t154 () (tptp.f31 @t23 @t106 @t148)) % 0.38/0.66 (define @t155 () (@var "Xf1" $$unsorted)) % 0.38/0.66 (define @t156 () (@var "Xs1" $$unsorted)) % 0.38/0.66 (define @t157 () (tptp.closed @t156 @t155)) % 0.38/0.66 (define @t158 () (@var "Xf2" $$unsorted)) % 0.38/0.66 (define @t159 () (@var "Xs2" $$unsorted)) % 0.38/0.66 (define @t160 () (@var "Xh" $$unsorted)) % 0.38/0.66 (define @t161 () (tptp.homomorphism @t160 @t156 @t155 @t159 @t158)) % 0.38/0.66 (define @t162 () (not @t161)) % 0.38/0.66 (define @t163 () (@list @t160 @t156 @t155 @t159 @t158)) % 0.38/0.66 (define @t164 () (tptp.closed @t159 @t158)) % 0.38/0.66 (define @t165 () (tptp.maps @t160 @t156 @t159)) % 0.38/0.66 (define @t166 () (tptp.f32 @t160 @t156 @t155 @t159 @t158)) % 0.38/0.66 (define @t167 () (not @t165)) % 0.38/0.66 (define @t168 () (not @t164)) % 0.38/0.66 (define @t169 () (not @t157)) % 0.38/0.66 (define @t170 () (tptp.f33 @t160 @t156 @t155 @t159 @t158)) % 0.38/0.66 (define @t171 () (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) % 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 (forall @t14 (or @t13 @t15 (not @t11)))) % 0.38/0.66 (assume @p7 (forall @t14 (or @t13 @t15 (not @t10)))) % 0.38/0.66 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.38/0.66 (assume @p9 (forall @t17 (= @t16 (tptp.non_ordered_pair @t1 @t1)))) % 0.38/0.66 (assume @p10 (forall @t4 (= @t18 (tptp.non_ordered_pair @t16 @t12)))) % 0.38/0.66 (assume @p11 (forall @t17 (or @t21 (tptp.little_set @t19)))) % 0.38/0.66 (assume @p12 (forall @t17 (or @t21 (tptp.little_set @t22)))) % 0.38/0.66 (assume @p13 (forall @t17 (or @t21 (= @t1 (tptp.ordered_pair @t19 @t22))))) % 0.38/0.66 (assume @p14 (forall (@list @t1 @t3 @t23) (or @t20 @t25 @t24 (not (= @t1 (tptp.ordered_pair @t3 @t23)))))) % 0.38/0.66 (assume @p15 (forall @t29 (or @t28 (tptp.little_set @t26)))) % 0.38/0.66 (assume @p16 (forall @t29 (or @t28 (tptp.little_set @t30)))) % 0.38/0.66 (assume @p17 (forall @t29 (or @t28 (= @t1 (tptp.ordered_pair @t26 @t30))))) % 0.38/0.66 (assume @p18 (forall @t29 (or @t28 (tptp.member @t23 @t26)))) % 0.38/0.66 (assume @p19 (forall @t35 (or @t27 @t15 @t34 @t33 (not (tptp.member @t23 @t9))))) % 0.38/0.66 (assume @p20 (forall @t29 (or @t38 (tptp.little_set @t36)))) % 0.38/0.66 (assume @p21 (forall @t29 (or @t38 (tptp.little_set @t39)))) % 0.38/0.66 (assume @p22 (forall @t29 (or @t38 (= @t1 (tptp.ordered_pair @t36 @t39))))) % 0.38/0.66 (assume @p23 (forall @t29 (or @t38 (tptp.member @t23 @t39)))) % 0.38/0.66 (assume @p24 (forall @t35 (or @t37 @t15 @t34 @t33 (not (tptp.member @t23 @t31))))) % 0.38/0.66 (assume @p25 (forall @t43 (or @t42 @t40))) % 0.38/0.66 (assume @p26 (forall @t43 (or @t42 @t46))) % 0.38/0.66 (assume @p27 (forall @t43 (or @t41 @t24 @t47 (not @t46)))) % 0.38/0.66 (assume @p28 (forall @t51 (or @t50 @t48))) % 0.38/0.66 (assume @p29 (forall @t51 (or @t50 @t52))) % 0.38/0.66 (assume @p30 (forall @t51 (or @t49 @t54 @t53))) % 0.38/0.66 (assume @p31 (forall @t29 (or (not @t56) @t54))) % 0.38/0.66 (assume @p32 (forall @t29 (or @t56 @t24 @t48))) % 0.38/0.66 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t55 (tptp.complement @t3)))))) % 0.38/0.66 (assume @p34 (forall @t29 (or @t59 (tptp.ordered_pair_predicate @t57)))) % 0.38/0.66 (assume @p35 (forall @t29 (or @t59 (tptp.member @t57 @t1)))) % 0.38/0.66 (assume @p36 (forall @t29 (or @t59 (= @t23 (tptp.first @t57))))) % 0.38/0.66 (assume @p37 (forall @t63 (or @t58 @t24 @t62 @t61 (not (= @t23 (tptp.first @t60)))))) % 0.38/0.66 (assume @p38 (forall @t51 (or @t65 @t40))) % 0.38/0.66 (assume @p39 (forall @t51 (or @t65 @t66))) % 0.38/0.66 (assume @p40 (forall @t51 (or @t65 @t67))) % 0.38/0.66 (assume @p41 (forall @t51 (or @t64 @t24 @t47 (not @t66) (not @t67)))) % 0.38/0.66 (assume @p42 (forall @t29 (or @t69 @t40))) % 0.38/0.66 (assume @p43 (forall @t29 (or @t69 @t70))) % 0.38/0.66 (assume @p44 (forall @t29 (or @t68 @t24 @t47 (not @t70)))) % 0.38/0.66 (assume @p45 (forall @t29 (or @t73 (tptp.little_set @t71)))) % 0.38/0.66 (assume @p46 (forall @t29 (or @t73 (tptp.little_set @t74)))) % 0.38/0.66 (assume @p47 (forall @t29 (or @t73 (tptp.little_set @t75)))) % 0.38/0.66 (assume @p48 (forall @t29 (or @t73 (= @t23 (tptp.ordered_pair @t71 (tptp.ordered_pair @t74 @t75)))))) % 0.38/0.66 (assume @p49 (forall @t29 (or @t73 (tptp.member (tptp.ordered_pair @t74 (tptp.ordered_pair @t75 @t71)) @t1)))) % 0.38/0.66 (assume @p50 (forall @t79 (or @t72 @t24 @t15 @t34 @t78 @t77 (not (tptp.member (tptp.ordered_pair @t31 (tptp.ordered_pair @t76 @t9)) @t1))))) % 0.38/0.66 (assume @p51 (forall @t29 (or @t82 (tptp.little_set @t80)))) % 0.38/0.66 (assume @p52 (forall @t29 (or @t82 (tptp.little_set @t83)))) % 0.38/0.66 (assume @p53 (forall @t29 (or @t82 (tptp.little_set @t84)))) % 0.38/0.66 (assume @p54 (forall @t29 (or @t82 (= @t23 (tptp.ordered_pair @t80 (tptp.ordered_pair @t83 @t84)))))) % 0.38/0.66 (assume @p55 (forall @t29 (or @t82 (tptp.member (tptp.ordered_pair @t80 (tptp.ordered_pair @t84 @t83)) @t1)))) % 0.38/0.66 (assume @p56 (forall @t79 (or @t81 @t24 @t15 @t34 @t78 @t77 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t76 @t31)) @t1))))) % 0.38/0.66 (assume @p57 (forall @t17 (= @t85 (tptp.union @t1 @t16)))) % 0.38/0.66 (assume @p58 (forall @t43 (not (tptp.member @t23 tptp.empty_set)))) % 0.38/0.66 (assume @p59 (forall @t43 (or (tptp.member @t23 tptp.universal_set) @t24))) % 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 @t17 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t85 tptp.infinity)))) % 0.38/0.66 (assume @p63 (forall @t29 (or @t88 (tptp.member @t86 @t1)))) % 0.38/0.66 (assume @p64 (forall @t29 (or @t88 (tptp.member @t23 @t86)))) % 0.38/0.66 (assume @p65 (forall @t51 (or @t87 (not (tptp.member @t3 @t1)) @t53))) % 0.38/0.66 (assume @p66 (forall @t89 (or @t15 (tptp.little_set (tptp.sigma @t9))))) % 0.38/0.66 (assume @p67 (forall @t94 (or @t93 @t91 @t90))) % 0.38/0.66 (assume @p68 (forall @t4 (or @t92 (tptp.member @t95 @t1)))) % 0.38/0.66 (assume @p69 (forall @t4 (or @t92 (not (tptp.member @t95 @t3))))) % 0.38/0.66 (assume @p70 (forall @t4 (or @t97 @t92))) % 0.38/0.66 (assume @p71 (forall @t4 (or @t97 (not @t5)))) % 0.38/0.66 (assume @p72 (forall @t4 (or @t96 @t93 @t5))) % 0.38/0.66 (assume @p73 (forall @t29 (or (not @t99) @t98))) % 0.38/0.66 (assume @p74 (forall @t29 (or @t99 @t24 (not @t98)))) % 0.38/0.66 (assume @p75 (forall @t89 (or @t15 (tptp.little_set (tptp.powerset @t9))))) % 0.38/0.66 (assume @p76 (forall @t29 (or (not @t100) (not (tptp.member @t1 @t23)) @t20))) % 0.38/0.66 (assume @p77 (forall @t43 (or @t100 (tptp.member @t101 @t23)))) % 0.38/0.66 (assume @p78 (forall @t43 (or @t100 (not (tptp.ordered_pair_predicate @t101))))) % 0.38/0.66 (assume @p79 (forall (@list @t1 @t9 @t31 @t76) (or (not @t102) @t15 @t34 @t78 (not (tptp.member @t32 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t76) @t1)) (= @t31 @t76)))) % 0.38/0.66 (assume @p80 (forall @t17 (or @t102 (tptp.little_set @t103)))) % 0.38/0.66 (assume @p81 (forall @t17 (or @t102 (tptp.little_set @t104)))) % 0.38/0.66 (assume @p82 (forall @t17 (or @t102 (tptp.little_set @t105)))) % 0.38/0.66 (assume @p83 (forall @t17 (or @t102 (tptp.member (tptp.ordered_pair @t103 @t104) @t1)))) % 0.38/0.66 (assume @p84 (forall @t17 (or @t102 (tptp.member (tptp.ordered_pair @t103 @t105) @t1)))) % 0.38/0.66 (assume @p85 (forall @t17 (or @t102 (not (= @t104 @t105))))) % 0.38/0.66 (assume @p86 (forall @t110 (or @t109 @t107))) % 0.38/0.66 (assume @p87 (forall @t110 (or @t109 @t111))) % 0.38/0.66 (assume @p88 (forall @t110 (or @t108 (not @t107) (not @t111)))) % 0.38/0.66 (assume @p89 (forall @t116 (or @t115 (tptp.ordered_pair_predicate @t112)))) % 0.38/0.66 (assume @p90 (forall @t116 (or @t115 (tptp.member @t112 @t106)))) % 0.38/0.66 (assume @p91 (forall @t116 (or @t115 (tptp.member (tptp.first @t112) @t1)))) % 0.38/0.66 (assume @p92 (forall @t116 (or @t115 (= (tptp.second @t112) @t23)))) % 0.38/0.66 (assume @p93 (forall (@list @t23 @t1 @t106 @t3) (or @t114 @t24 (not (tptp.ordered_pair_predicate @t3)) (not (tptp.member @t3 @t106)) (not (tptp.member (tptp.first @t3) @t1)) (not (= (tptp.second @t3) @t23))))) % 0.38/0.66 (assume @p94 (forall (@list @t1 @t106) (or @t117 @t109 (tptp.little_set @t113)))) % 0.38/0.66 (assume @p95 (forall @t94 (or (not @t118) @t91 (not @t90)))) % 0.38/0.66 (assume @p96 (forall @t4 (or @t118 (tptp.member @t119 @t1)))) % 0.38/0.66 (assume @p97 (forall @t4 (or @t118 (tptp.member @t119 @t3)))) % 0.38/0.66 (assume @p98 (forall @t17 (or @t121 (tptp.member @t120 @t1)))) % 0.38/0.66 (assume @p99 (forall @t17 (or @t121 (tptp.disjoint @t120 @t1)))) % 0.38/0.66 (assume @p100 (tptp.function tptp.f25)) % 0.38/0.66 (assume @p101 (forall @t17 (or @t117 @t121 (tptp.member @t122 @t1)))) % 0.38/0.66 (assume @p102 (forall @t17 (or @t117 @t121 (tptp.member (tptp.ordered_pair @t1 @t122) tptp.f25)))) % 0.38/0.66 (assume @p103 (forall @t29 (or @t125 (tptp.ordered_pair_predicate @t123)))) % 0.38/0.66 (assume @p104 (forall @t29 (or @t125 (tptp.member @t123 @t1)))) % 0.38/0.66 (assume @p105 (forall @t29 (or @t125 (= @t23 (tptp.second @t123))))) % 0.38/0.66 (assume @p106 (forall @t63 (or @t124 @t24 @t62 @t61 (not (= @t23 (tptp.second @t60)))))) % 0.38/0.66 (assume @p107 (forall @t43 (or @t127 @t40))) % 0.38/0.66 (assume @p108 (forall @t43 (or @t127 @t128))) % 0.38/0.66 (assume @p109 (forall @t43 (or @t126 @t24 @t47 (not @t128)))) % 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 @t110 (or @t130 @t108))) % 0.38/0.66 (assume @p112 (forall @t110 (or @t130 @t131))) % 0.38/0.66 (assume @p113 (forall @t110 (or @t129 @t109 (not @t131)))) % 0.38/0.66 (assume @p114 (forall @t135 (or @t134 (tptp.ordered_pair_predicate @t132)))) % 0.38/0.66 (assume @p115 (forall @t135 (or @t134 (tptp.member @t132 @t106)))) % 0.38/0.66 (assume @p116 (forall @t135 (or @t134 (= (tptp.first @t132) @t3)))) % 0.38/0.66 (assume @p117 (forall @t135 (or @t134 (tptp.member @t23 (tptp.second @t132))))) % 0.38/0.66 (assume @p118 (forall (@list @t23 @t106 @t3 @t76) (or @t133 (not (tptp.ordered_pair_predicate @t76)) (not (tptp.member @t76 @t106)) (not (= (tptp.first @t76) @t3)) (not (tptp.member @t23 (tptp.second @t76)))))) % 0.38/0.66 (assume @p119 (forall @t136 (= (tptp.apply_to_two_arguments @t106 @t1 @t3) (tptp.apply @t106 @t18)))) % 0.38/0.66 (assume @p120 (forall @t136 (or @t138 @t108))) % 0.38/0.66 (assume @p121 (forall @t136 (or @t138 @t139))) % 0.38/0.66 (assume @p122 (forall @t136 (or @t138 @t140))) % 0.38/0.66 (assume @p123 (forall @t136 (or @t137 @t109 (not @t139) (not @t140)))) % 0.38/0.66 (assume @p124 (forall @t145 (or @t144 @t142))) % 0.38/0.66 (assume @p125 (forall @t145 (or @t144 @t146))) % 0.38/0.66 (assume @p126 (forall @t145 (or @t144 @t147))) % 0.38/0.66 (assume @p127 (forall @t145 (or @t143 (not @t142) (not @t146) (not @t147)))) % 0.38/0.66 (assume @p128 (forall @t152 (or @t151 (tptp.little_set @t149)))) % 0.38/0.66 (assume @p129 (forall @t152 (or @t151 (tptp.little_set @t153)))) % 0.38/0.66 (assume @p130 (forall @t152 (or @t151 (tptp.little_set @t154)))) % 0.38/0.66 (assume @p131 (forall @t152 (or @t151 (= @t23 (tptp.ordered_pair @t149 @t153))))) % 0.38/0.66 (assume @p132 (forall @t152 (or @t151 (tptp.member (tptp.ordered_pair @t149 @t154) @t106)))) % 0.38/0.66 (assume @p133 (forall @t152 (or @t151 (tptp.member (tptp.ordered_pair @t154 @t153) @t148)))) % 0.38/0.66 (assume @p134 (forall (@list @t23 @t106 @t148 @t1 @t3 @t76) (or @t150 @t24 @t117 @t25 @t78 (not (= @t23 @t18)) (not (tptp.member (tptp.ordered_pair @t1 @t76) @t106)) (not (tptp.member (tptp.ordered_pair @t76 @t3) @t148))))) % 0.38/0.66 (assume @p135 (forall @t163 (or @t162 @t157))) % 0.38/0.66 (assume @p136 (forall @t163 (or @t162 @t164))) % 0.38/0.66 (assume @p137 (forall @t163 (or @t162 @t165))) % 0.38/0.66 (assume @p138 (forall (@list @t160 @t156 @t155 @t159 @t158 @t1 @t3) (or @t162 (not (tptp.member @t1 @t156)) (not (tptp.member @t3 @t156)) (= (tptp.apply @t160 (tptp.apply_to_two_arguments @t155 @t1 @t3)) (tptp.apply_to_two_arguments @t158 (tptp.apply @t160 @t1) (tptp.apply @t160 @t3)))))) % 0.38/0.66 (assume @p139 (forall @t163 (or @t161 @t169 @t168 @t167 (tptp.member @t166 @t156)))) % 0.38/0.66 (assume @p140 (forall @t163 (or @t161 @t169 @t168 @t167 (tptp.member @t170 @t156)))) % 0.38/0.66 (assume @p141 (forall @t163 (or @t161 @t169 @t168 @t167 (not (= (tptp.apply @t160 (tptp.apply_to_two_arguments @t155 @t166 @t170)) (tptp.apply_to_two_arguments @t158 (tptp.apply @t160 @t166) (tptp.apply @t160 @t170))))))) % 0.38/0.66 (assume @p142 (not @t171)) % 0.38/0.66 (step @p143 :rule evaluate :args ((= false true))) % 0.38/0.66 (step @p144 :rule instantiate :premises (@p8) :args ((@list (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) % 0.38/0.66 (step @p145 :rule true_intro :premises (@p144)) % 0.38/0.66 (step @p146 :rule instantiate :premises (@p10) :args ((@list tptp.a tptp.b))) % 0.38/0.66 (step @p147 :rule cong :premises (@p146) :args (@t171)) % 0.38/0.66 (step @p148 :rule false_intro :premises (@p142)) % 0.38/0.66 (step @p149 :rule symm :premises (@p148)) % 0.38/0.66 (step @p150 :rule trans :premises (@p149 @p147 @p145)) % 0.38/0.66 (step @p151 false :rule eq_resolve :premises (@p150 @p143)) % 0.38/0.66 ) % 0.38/0.66 % SZS output end Proof % 0.38/0.66 % cvc5 exiting %------------------------------------------------------------------------------