%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET025-3 : 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 08:47:01 AM UTC 2026 % Result : Unsatisfiable 0.36s 0.64s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET025-3 : TPTP v9.2.1. Released v1.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 14:42:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.29/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.64 % SZS status Unsatisfiable % 0.36/0.64 % SZS output start Proof % 0.36/0.65 ( % 0.36/0.65 (declare-sort $$unsorted 0) % 0.36/0.65 (declare-const tptp.a $$unsorted) % 0.36/0.65 (declare-const tptp.f32 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f31 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f29 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.closed (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f28 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.apply_to_two_arguments (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f10 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f7 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f8 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.single_valued_set (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.f25 $$unsorted) % 0.36/0.65 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.infinity $$unsorted) % 0.36/0.65 (declare-const tptp.rotate_right (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f24 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.converse (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f2 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.f30 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.non_ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.estin $$unsorted) % 0.36/0.65 (declare-const tptp.singleton_set (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f26 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.flip_range_of (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f11 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.little_set (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.f3 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f12 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.ordered_pair_predicate (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f20 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f9 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f18 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f14 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f22 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.empty_set $$unsorted) % 0.36/0.65 (declare-const tptp.universal_set $$unsorted) % 0.36/0.65 (declare-const tptp.f16 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.sigma (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.one_to_one_function (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.function (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.f17 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f13 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f33 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.b $$unsorted) % 0.36/0.65 (declare-const tptp.f19 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.identity_relation $$unsorted) % 0.36/0.65 (declare-const tptp.f21 (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.f23 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.f27 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (define @t1 () (@var "X" $$unsorted)) % 0.36/0.65 (define @t2 () (tptp.little_set @t1)) % 0.36/0.65 (define @t3 () (@var "Y" $$unsorted)) % 0.36/0.65 (define @t4 () (@list @t1 @t3)) % 0.36/0.65 (define @t5 () (= @t1 @t3)) % 0.36/0.65 (define @t6 () (tptp.f1 @t1 @t3)) % 0.36/0.65 (define @t7 () (tptp.member @t6 @t3)) % 0.36/0.65 (define @t8 () (tptp.member @t6 @t1)) % 0.36/0.65 (define @t9 () (@var "U" $$unsorted)) % 0.36/0.65 (define @t10 () (= @t9 @t3)) % 0.36/0.65 (define @t11 () (= @t9 @t1)) % 0.36/0.65 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.36/0.65 (define @t13 () (tptp.member @t9 @t12)) % 0.36/0.65 (define @t14 () (@list @t9 @t1 @t3)) % 0.36/0.65 (define @t15 () (not (tptp.little_set @t9))) % 0.36/0.65 (define @t16 () (tptp.singleton_set @t1)) % 0.36/0.65 (define @t17 () (@list @t1)) % 0.36/0.65 (define @t18 () (tptp.ordered_pair @t1 @t3)) % 0.36/0.65 (define @t19 () (tptp.f2 @t1)) % 0.36/0.65 (define @t20 () (tptp.ordered_pair_predicate @t1)) % 0.36/0.65 (define @t21 () (not @t20)) % 0.36/0.65 (define @t22 () (tptp.f3 @t1)) % 0.36/0.65 (define @t23 () (@var "Z" $$unsorted)) % 0.36/0.65 (define @t24 () (not (tptp.little_set @t23))) % 0.36/0.65 (define @t25 () (not (tptp.little_set @t3))) % 0.36/0.65 (define @t26 () (@list @t1 @t3 @t23)) % 0.36/0.65 (define @t27 () (tptp.f4 @t23 @t1)) % 0.36/0.65 (define @t28 () (tptp.first @t1)) % 0.36/0.65 (define @t29 () (tptp.member @t23 @t28)) % 0.36/0.65 (define @t30 () (not @t29)) % 0.36/0.65 (define @t31 () (@list @t23 @t1)) % 0.36/0.65 (define @t32 () (tptp.f5 @t23 @t1)) % 0.36/0.65 (define @t33 () (@var "V" $$unsorted)) % 0.36/0.65 (define @t34 () (tptp.ordered_pair @t9 @t33)) % 0.36/0.65 (define @t35 () (not (= @t1 @t34))) % 0.36/0.65 (define @t36 () (not (tptp.little_set @t33))) % 0.36/0.65 (define @t37 () (@list @t23 @t1 @t9 @t33)) % 0.36/0.65 (define @t38 () (tptp.f6 @t23 @t1)) % 0.36/0.65 (define @t39 () (tptp.second @t1)) % 0.36/0.65 (define @t40 () (tptp.member @t23 @t39)) % 0.36/0.65 (define @t41 () (not @t40)) % 0.36/0.65 (define @t42 () (tptp.f7 @t23 @t1)) % 0.36/0.65 (define @t43 () (tptp.ordered_pair_predicate @t23)) % 0.36/0.65 (define @t44 () (tptp.member @t23 tptp.estin)) % 0.36/0.65 (define @t45 () (not @t44)) % 0.36/0.65 (define @t46 () (@list @t23)) % 0.36/0.65 (define @t47 () (tptp.second @t23)) % 0.36/0.65 (define @t48 () (tptp.first @t23)) % 0.36/0.65 (define @t49 () (tptp.member @t48 @t47)) % 0.36/0.65 (define @t50 () (not @t43)) % 0.36/0.65 (define @t51 () (tptp.member @t23 @t1)) % 0.36/0.65 (define @t52 () (tptp.member @t23 (tptp.intersection @t1 @t3))) % 0.36/0.65 (define @t53 () (not @t52)) % 0.36/0.65 (define @t54 () (@list @t23 @t1 @t3)) % 0.36/0.65 (define @t55 () (tptp.member @t23 @t3)) % 0.36/0.65 (define @t56 () (not @t55)) % 0.36/0.65 (define @t57 () (not @t51)) % 0.36/0.65 (define @t58 () (tptp.complement @t1)) % 0.36/0.65 (define @t59 () (tptp.member @t23 @t58)) % 0.36/0.65 (define @t60 () (tptp.f8 @t23 @t1)) % 0.36/0.65 (define @t61 () (tptp.member @t23 (tptp.domain_of @t1))) % 0.36/0.65 (define @t62 () (not @t61)) % 0.36/0.65 (define @t63 () (@var "Xp" $$unsorted)) % 0.36/0.65 (define @t64 () (not (tptp.member @t63 @t1))) % 0.36/0.65 (define @t65 () (not (tptp.ordered_pair_predicate @t63))) % 0.36/0.65 (define @t66 () (@list @t23 @t1 @t63)) % 0.36/0.65 (define @t67 () (tptp.member @t23 (tptp.cross_product @t1 @t3))) % 0.36/0.65 (define @t68 () (not @t67)) % 0.36/0.65 (define @t69 () (tptp.member @t48 @t1)) % 0.36/0.65 (define @t70 () (tptp.member @t47 @t3)) % 0.36/0.65 (define @t71 () (tptp.member @t23 (tptp.converse @t1))) % 0.36/0.65 (define @t72 () (not @t71)) % 0.36/0.65 (define @t73 () (tptp.member (tptp.ordered_pair @t47 @t48) @t1)) % 0.36/0.65 (define @t74 () (tptp.f9 @t23 @t1)) % 0.36/0.65 (define @t75 () (tptp.member @t23 (tptp.rotate_right @t1))) % 0.36/0.65 (define @t76 () (not @t75)) % 0.36/0.65 (define @t77 () (tptp.f10 @t23 @t1)) % 0.36/0.65 (define @t78 () (tptp.f11 @t23 @t1)) % 0.36/0.65 (define @t79 () (@var "W" $$unsorted)) % 0.36/0.65 (define @t80 () (not (= @t23 (tptp.ordered_pair @t9 (tptp.ordered_pair @t33 @t79))))) % 0.36/0.65 (define @t81 () (not (tptp.little_set @t79))) % 0.36/0.65 (define @t82 () (@list @t23 @t1 @t9 @t33 @t79)) % 0.36/0.65 (define @t83 () (tptp.f12 @t23 @t1)) % 0.36/0.65 (define @t84 () (tptp.member @t23 (tptp.flip_range_of @t1))) % 0.36/0.65 (define @t85 () (not @t84)) % 0.36/0.65 (define @t86 () (tptp.f13 @t23 @t1)) % 0.36/0.65 (define @t87 () (tptp.f14 @t23 @t1)) % 0.36/0.65 (define @t88 () (tptp.successor @t1)) % 0.36/0.65 (define @t89 () (tptp.f16 @t23 @t1)) % 0.36/0.65 (define @t90 () (tptp.member @t23 (tptp.sigma @t1))) % 0.36/0.65 (define @t91 () (not @t90)) % 0.36/0.65 (define @t92 () (@list @t9)) % 0.36/0.65 (define @t93 () (tptp.member @t9 @t3)) % 0.36/0.65 (define @t94 () (not (tptp.member @t9 @t1))) % 0.36/0.65 (define @t95 () (tptp.subset @t1 @t3)) % 0.36/0.65 (define @t96 () (not @t95)) % 0.36/0.65 (define @t97 () (@list @t1 @t3 @t9)) % 0.36/0.65 (define @t98 () (tptp.f17 @t1 @t3)) % 0.36/0.65 (define @t99 () (tptp.proper_subset @t1 @t3)) % 0.36/0.65 (define @t100 () (not @t99)) % 0.36/0.65 (define @t101 () (tptp.subset @t23 @t1)) % 0.36/0.65 (define @t102 () (tptp.member @t23 (tptp.powerset @t1))) % 0.36/0.65 (define @t103 () (tptp.relation @t23)) % 0.36/0.65 (define @t104 () (tptp.f18 @t23)) % 0.36/0.65 (define @t105 () (tptp.single_valued_set @t1)) % 0.36/0.65 (define @t106 () (tptp.f19 @t1)) % 0.36/0.65 (define @t107 () (tptp.f20 @t1)) % 0.36/0.65 (define @t108 () (tptp.f21 @t1)) % 0.36/0.65 (define @t109 () (@var "Xf" $$unsorted)) % 0.36/0.65 (define @t110 () (tptp.relation @t109)) % 0.36/0.65 (define @t111 () (tptp.function @t109)) % 0.36/0.65 (define @t112 () (not @t111)) % 0.36/0.65 (define @t113 () (@list @t109)) % 0.36/0.65 (define @t114 () (tptp.single_valued_set @t109)) % 0.36/0.65 (define @t115 () (tptp.f22 @t23 @t1 @t109)) % 0.36/0.65 (define @t116 () (tptp.image @t1 @t109)) % 0.36/0.65 (define @t117 () (tptp.member @t23 @t116)) % 0.36/0.65 (define @t118 () (not @t117)) % 0.36/0.65 (define @t119 () (@list @t23 @t1 @t109)) % 0.36/0.65 (define @t120 () (not @t2)) % 0.36/0.65 (define @t121 () (tptp.disjoint @t1 @t3)) % 0.36/0.65 (define @t122 () (tptp.f23 @t1 @t3)) % 0.36/0.65 (define @t123 () (tptp.f24 @t1)) % 0.36/0.65 (define @t124 () (= @t1 tptp.empty_set)) % 0.36/0.65 (define @t125 () (tptp.f26 @t1)) % 0.36/0.65 (define @t126 () (tptp.f27 @t23 @t1)) % 0.36/0.65 (define @t127 () (tptp.member @t23 (tptp.range_of @t1))) % 0.36/0.65 (define @t128 () (not @t127)) % 0.36/0.65 (define @t129 () (tptp.member @t23 tptp.identity_relation)) % 0.36/0.65 (define @t130 () (not @t129)) % 0.36/0.65 (define @t131 () (= @t48 @t47)) % 0.36/0.65 (define @t132 () (tptp.one_to_one_function @t109)) % 0.36/0.65 (define @t133 () (not @t132)) % 0.36/0.65 (define @t134 () (tptp.function (tptp.converse @t109))) % 0.36/0.65 (define @t135 () (tptp.f28 @t23 @t109 @t3)) % 0.36/0.65 (define @t136 () (tptp.member @t23 (tptp.apply @t109 @t3))) % 0.36/0.65 (define @t137 () (not @t136)) % 0.36/0.65 (define @t138 () (@list @t23 @t109 @t3)) % 0.36/0.65 (define @t139 () (@list @t109 @t1 @t3)) % 0.36/0.65 (define @t140 () (tptp.maps @t109 @t1 @t3)) % 0.36/0.65 (define @t141 () (not @t140)) % 0.36/0.65 (define @t142 () (= (tptp.domain_of @t109) @t1)) % 0.36/0.65 (define @t143 () (tptp.subset (tptp.range_of @t109) @t3)) % 0.36/0.65 (define @t144 () (@var "Xs" $$unsorted)) % 0.36/0.65 (define @t145 () (tptp.little_set @t144)) % 0.36/0.65 (define @t146 () (tptp.closed @t144 @t109)) % 0.36/0.65 (define @t147 () (not @t146)) % 0.36/0.65 (define @t148 () (@list @t144 @t109)) % 0.36/0.65 (define @t149 () (tptp.little_set @t109)) % 0.36/0.65 (define @t150 () (tptp.maps @t109 (tptp.cross_product @t144 @t144) @t144)) % 0.36/0.65 (define @t151 () (@var "Xg" $$unsorted)) % 0.36/0.65 (define @t152 () (tptp.f29 @t23 @t109 @t151)) % 0.36/0.65 (define @t153 () (tptp.member @t23 (tptp.compose @t109 @t151))) % 0.36/0.65 (define @t154 () (not @t153)) % 0.36/0.65 (define @t155 () (@list @t23 @t109 @t151)) % 0.36/0.65 (define @t156 () (tptp.f30 @t23 @t109 @t151)) % 0.36/0.65 (define @t157 () (tptp.f31 @t23 @t109 @t151)) % 0.36/0.65 (define @t158 () (@var "Xf1" $$unsorted)) % 0.36/0.65 (define @t159 () (@var "Xs1" $$unsorted)) % 0.36/0.65 (define @t160 () (tptp.closed @t159 @t158)) % 0.36/0.65 (define @t161 () (@var "Xf2" $$unsorted)) % 0.36/0.65 (define @t162 () (@var "Xs2" $$unsorted)) % 0.36/0.65 (define @t163 () (@var "Xh" $$unsorted)) % 0.36/0.65 (define @t164 () (tptp.homomorphism @t163 @t159 @t158 @t162 @t161)) % 0.36/0.65 (define @t165 () (not @t164)) % 0.36/0.65 (define @t166 () (@list @t163 @t159 @t158 @t162 @t161)) % 0.36/0.65 (define @t167 () (tptp.closed @t162 @t161)) % 0.36/0.65 (define @t168 () (tptp.maps @t163 @t159 @t162)) % 0.36/0.65 (define @t169 () (tptp.f32 @t163 @t159 @t158 @t162 @t161)) % 0.36/0.65 (define @t170 () (not @t168)) % 0.36/0.65 (define @t171 () (not @t167)) % 0.36/0.65 (define @t172 () (not @t160)) % 0.36/0.65 (define @t173 () (tptp.f33 @t163 @t159 @t158 @t162 @t161)) % 0.36/0.65 (define @t174 () (not (= @t18 @t34))) % 0.36/0.65 (define @t175 () (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) % 0.36/0.65 (assume @p1 (forall @t4 (or (not (tptp.member @t1 @t3)) @t2))) % 0.36/0.65 (assume @p2 (forall @t4 (or (tptp.little_set @t6) @t5))) % 0.36/0.65 (assume @p3 (forall @t4 (or @t8 @t7 @t5))) % 0.36/0.65 (assume @p4 (forall @t4 (or (not @t8) (not @t7) @t5))) % 0.36/0.65 (assume @p5 (forall @t14 (or (not @t13) @t11 @t10))) % 0.36/0.65 (assume @p6 (forall @t14 (or @t13 @t15 (not @t11)))) % 0.36/0.65 (assume @p7 (forall @t14 (or @t13 @t15 (not @t10)))) % 0.36/0.65 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.36/0.65 (assume @p9 (forall @t17 (= @t16 (tptp.non_ordered_pair @t1 @t1)))) % 0.36/0.65 (assume @p10 (forall @t4 (= @t18 (tptp.non_ordered_pair @t16 @t12)))) % 0.36/0.65 (assume @p11 (forall @t17 (or @t21 (tptp.little_set @t19)))) % 0.36/0.65 (assume @p12 (forall @t17 (or @t21 (tptp.little_set @t22)))) % 0.36/0.65 (assume @p13 (forall @t17 (or @t21 (= @t1 (tptp.ordered_pair @t19 @t22))))) % 0.36/0.65 (assume @p14 (forall @t26 (or @t20 @t25 @t24 (not (= @t1 (tptp.ordered_pair @t3 @t23)))))) % 0.36/0.65 (assume @p15 (forall @t31 (or @t30 (tptp.little_set @t27)))) % 0.36/0.65 (assume @p16 (forall @t31 (or @t30 (tptp.little_set @t32)))) % 0.36/0.65 (assume @p17 (forall @t31 (or @t30 (= @t1 (tptp.ordered_pair @t27 @t32))))) % 0.36/0.65 (assume @p18 (forall @t31 (or @t30 (tptp.member @t23 @t27)))) % 0.36/0.65 (assume @p19 (forall @t37 (or @t29 @t15 @t36 @t35 (not (tptp.member @t23 @t9))))) % 0.36/0.65 (assume @p20 (forall @t31 (or @t41 (tptp.little_set @t38)))) % 0.36/0.65 (assume @p21 (forall @t31 (or @t41 (tptp.little_set @t42)))) % 0.36/0.65 (assume @p22 (forall @t31 (or @t41 (= @t1 (tptp.ordered_pair @t38 @t42))))) % 0.36/0.65 (assume @p23 (forall @t31 (or @t41 (tptp.member @t23 @t42)))) % 0.36/0.65 (assume @p24 (forall @t37 (or @t40 @t15 @t36 @t35 (not (tptp.member @t23 @t33))))) % 0.36/0.65 (assume @p25 (forall @t46 (or @t45 @t43))) % 0.36/0.65 (assume @p26 (forall @t46 (or @t45 @t49))) % 0.36/0.65 (assume @p27 (forall @t46 (or @t44 @t24 @t50 (not @t49)))) % 0.36/0.65 (assume @p28 (forall @t54 (or @t53 @t51))) % 0.36/0.65 (assume @p29 (forall @t54 (or @t53 @t55))) % 0.36/0.65 (assume @p30 (forall @t54 (or @t52 @t57 @t56))) % 0.36/0.65 (assume @p31 (forall @t31 (or (not @t59) @t57))) % 0.36/0.65 (assume @p32 (forall @t31 (or @t59 @t24 @t51))) % 0.36/0.65 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t58 (tptp.complement @t3)))))) % 0.36/0.65 (assume @p34 (forall @t31 (or @t62 (tptp.ordered_pair_predicate @t60)))) % 0.36/0.65 (assume @p35 (forall @t31 (or @t62 (tptp.member @t60 @t1)))) % 0.36/0.65 (assume @p36 (forall @t31 (or @t62 (= @t23 (tptp.first @t60))))) % 0.36/0.65 (assume @p37 (forall @t66 (or @t61 @t24 @t65 @t64 (not (= @t23 (tptp.first @t63)))))) % 0.36/0.65 (assume @p38 (forall @t54 (or @t68 @t43))) % 0.36/0.65 (assume @p39 (forall @t54 (or @t68 @t69))) % 0.36/0.65 (assume @p40 (forall @t54 (or @t68 @t70))) % 0.36/0.65 (assume @p41 (forall @t54 (or @t67 @t24 @t50 (not @t69) (not @t70)))) % 0.36/0.65 (assume @p42 (forall @t31 (or @t72 @t43))) % 0.36/0.65 (assume @p43 (forall @t31 (or @t72 @t73))) % 0.36/0.65 (assume @p44 (forall @t31 (or @t71 @t24 @t50 (not @t73)))) % 0.36/0.65 (assume @p45 (forall @t31 (or @t76 (tptp.little_set @t74)))) % 0.36/0.65 (assume @p46 (forall @t31 (or @t76 (tptp.little_set @t77)))) % 0.36/0.65 (assume @p47 (forall @t31 (or @t76 (tptp.little_set @t78)))) % 0.36/0.65 (assume @p48 (forall @t31 (or @t76 (= @t23 (tptp.ordered_pair @t74 (tptp.ordered_pair @t77 @t78)))))) % 0.36/0.65 (assume @p49 (forall @t31 (or @t76 (tptp.member (tptp.ordered_pair @t77 (tptp.ordered_pair @t78 @t74)) @t1)))) % 0.36/0.65 (assume @p50 (forall @t82 (or @t75 @t24 @t15 @t36 @t81 @t80 (not (tptp.member (tptp.ordered_pair @t33 (tptp.ordered_pair @t79 @t9)) @t1))))) % 0.36/0.65 (assume @p51 (forall @t31 (or @t85 (tptp.little_set @t83)))) % 0.36/0.65 (assume @p52 (forall @t31 (or @t85 (tptp.little_set @t86)))) % 0.36/0.65 (assume @p53 (forall @t31 (or @t85 (tptp.little_set @t87)))) % 0.36/0.65 (assume @p54 (forall @t31 (or @t85 (= @t23 (tptp.ordered_pair @t83 (tptp.ordered_pair @t86 @t87)))))) % 0.36/0.65 (assume @p55 (forall @t31 (or @t85 (tptp.member (tptp.ordered_pair @t83 (tptp.ordered_pair @t87 @t86)) @t1)))) % 0.36/0.65 (assume @p56 (forall @t82 (or @t84 @t24 @t15 @t36 @t81 @t80 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t79 @t33)) @t1))))) % 0.36/0.65 (assume @p57 (forall @t17 (= @t88 (tptp.union @t1 @t16)))) % 0.36/0.65 (assume @p58 (forall @t46 (not (tptp.member @t23 tptp.empty_set)))) % 0.36/0.65 (assume @p59 (forall @t46 (or (tptp.member @t23 tptp.universal_set) @t24))) % 0.36/0.65 (assume @p60 (tptp.little_set tptp.infinity)) % 0.36/0.65 (assume @p61 (tptp.member tptp.empty_set tptp.infinity)) % 0.36/0.65 (assume @p62 (forall @t17 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t88 tptp.infinity)))) % 0.36/0.65 (assume @p63 (forall @t31 (or @t91 (tptp.member @t89 @t1)))) % 0.36/0.65 (assume @p64 (forall @t31 (or @t91 (tptp.member @t23 @t89)))) % 0.36/0.65 (assume @p65 (forall @t54 (or @t90 (not (tptp.member @t3 @t1)) @t56))) % 0.36/0.65 (assume @p66 (forall @t92 (or @t15 (tptp.little_set (tptp.sigma @t9))))) % 0.36/0.65 (assume @p67 (forall @t97 (or @t96 @t94 @t93))) % 0.36/0.65 (assume @p68 (forall @t4 (or @t95 (tptp.member @t98 @t1)))) % 0.36/0.65 (assume @p69 (forall @t4 (or @t95 (not (tptp.member @t98 @t3))))) % 0.36/0.65 (assume @p70 (forall @t4 (or @t100 @t95))) % 0.36/0.65 (assume @p71 (forall @t4 (or @t100 (not @t5)))) % 0.36/0.65 (assume @p72 (forall @t4 (or @t99 @t96 @t5))) % 0.36/0.65 (assume @p73 (forall @t31 (or (not @t102) @t101))) % 0.36/0.65 (assume @p74 (forall @t31 (or @t102 @t24 (not @t101)))) % 0.36/0.65 (assume @p75 (forall @t92 (or @t15 (tptp.little_set (tptp.powerset @t9))))) % 0.36/0.65 (assume @p76 (forall @t31 (or (not @t103) (not (tptp.member @t1 @t23)) @t20))) % 0.36/0.65 (assume @p77 (forall @t46 (or @t103 (tptp.member @t104 @t23)))) % 0.36/0.65 (assume @p78 (forall @t46 (or @t103 (not (tptp.ordered_pair_predicate @t104))))) % 0.36/0.65 (assume @p79 (forall (@list @t1 @t9 @t33 @t79) (or (not @t105) @t15 @t36 @t81 (not (tptp.member @t34 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t79) @t1)) (= @t33 @t79)))) % 0.36/0.65 (assume @p80 (forall @t17 (or @t105 (tptp.little_set @t106)))) % 0.36/0.65 (assume @p81 (forall @t17 (or @t105 (tptp.little_set @t107)))) % 0.36/0.65 (assume @p82 (forall @t17 (or @t105 (tptp.little_set @t108)))) % 0.36/0.65 (assume @p83 (forall @t17 (or @t105 (tptp.member (tptp.ordered_pair @t106 @t107) @t1)))) % 0.36/0.65 (assume @p84 (forall @t17 (or @t105 (tptp.member (tptp.ordered_pair @t106 @t108) @t1)))) % 0.36/0.65 (assume @p85 (forall @t17 (or @t105 (not (= @t107 @t108))))) % 0.36/0.65 (assume @p86 (forall @t113 (or @t112 @t110))) % 0.36/0.65 (assume @p87 (forall @t113 (or @t112 @t114))) % 0.36/0.65 (assume @p88 (forall @t113 (or @t111 (not @t110) (not @t114)))) % 0.36/0.65 (assume @p89 (forall @t119 (or @t118 (tptp.ordered_pair_predicate @t115)))) % 0.36/0.65 (assume @p90 (forall @t119 (or @t118 (tptp.member @t115 @t109)))) % 0.36/0.65 (assume @p91 (forall @t119 (or @t118 (tptp.member (tptp.first @t115) @t1)))) % 0.36/0.65 (assume @p92 (forall @t119 (or @t118 (= (tptp.second @t115) @t23)))) % 0.36/0.65 (assume @p93 (forall (@list @t23 @t1 @t109 @t3) (or @t117 @t24 (not (tptp.ordered_pair_predicate @t3)) (not (tptp.member @t3 @t109)) (not (tptp.member (tptp.first @t3) @t1)) (not (= (tptp.second @t3) @t23))))) % 0.36/0.65 (assume @p94 (forall (@list @t1 @t109) (or @t120 @t112 (tptp.little_set @t116)))) % 0.36/0.65 (assume @p95 (forall @t97 (or (not @t121) @t94 (not @t93)))) % 0.36/0.65 (assume @p96 (forall @t4 (or @t121 (tptp.member @t122 @t1)))) % 0.36/0.65 (assume @p97 (forall @t4 (or @t121 (tptp.member @t122 @t3)))) % 0.36/0.65 (assume @p98 (forall @t17 (or @t124 (tptp.member @t123 @t1)))) % 0.36/0.65 (assume @p99 (forall @t17 (or @t124 (tptp.disjoint @t123 @t1)))) % 0.36/0.65 (assume @p100 (tptp.function tptp.f25)) % 0.36/0.65 (assume @p101 (forall @t17 (or @t120 @t124 (tptp.member @t125 @t1)))) % 0.36/0.65 (assume @p102 (forall @t17 (or @t120 @t124 (tptp.member (tptp.ordered_pair @t1 @t125) tptp.f25)))) % 0.36/0.65 (assume @p103 (forall @t31 (or @t128 (tptp.ordered_pair_predicate @t126)))) % 0.36/0.65 (assume @p104 (forall @t31 (or @t128 (tptp.member @t126 @t1)))) % 0.36/0.65 (assume @p105 (forall @t31 (or @t128 (= @t23 (tptp.second @t126))))) % 0.36/0.65 (assume @p106 (forall @t66 (or @t127 @t24 @t65 @t64 (not (= @t23 (tptp.second @t63)))))) % 0.36/0.65 (assume @p107 (forall @t46 (or @t130 @t43))) % 0.36/0.65 (assume @p108 (forall @t46 (or @t130 @t131))) % 0.36/0.65 (assume @p109 (forall @t46 (or @t129 @t24 @t50 (not @t131)))) % 0.36/0.65 (assume @p110 (forall @t4 (= (tptp.restrict @t1 @t3) (tptp.intersection @t1 (tptp.cross_product @t3 tptp.universal_set))))) % 0.36/0.65 (assume @p111 (forall @t113 (or @t133 @t111))) % 0.36/0.65 (assume @p112 (forall @t113 (or @t133 @t134))) % 0.36/0.65 (assume @p113 (forall @t113 (or @t132 @t112 (not @t134)))) % 0.36/0.65 (assume @p114 (forall @t138 (or @t137 (tptp.ordered_pair_predicate @t135)))) % 0.36/0.65 (assume @p115 (forall @t138 (or @t137 (tptp.member @t135 @t109)))) % 0.36/0.65 (assume @p116 (forall @t138 (or @t137 (= (tptp.first @t135) @t3)))) % 0.36/0.65 (assume @p117 (forall @t138 (or @t137 (tptp.member @t23 (tptp.second @t135))))) % 0.36/0.65 (assume @p118 (forall (@list @t23 @t109 @t3 @t79) (or @t136 (not (tptp.ordered_pair_predicate @t79)) (not (tptp.member @t79 @t109)) (not (= (tptp.first @t79) @t3)) (not (tptp.member @t23 (tptp.second @t79)))))) % 0.36/0.65 (assume @p119 (forall @t139 (= (tptp.apply_to_two_arguments @t109 @t1 @t3) (tptp.apply @t109 @t18)))) % 0.36/0.65 (assume @p120 (forall @t139 (or @t141 @t111))) % 0.36/0.65 (assume @p121 (forall @t139 (or @t141 @t142))) % 0.36/0.65 (assume @p122 (forall @t139 (or @t141 @t143))) % 0.36/0.65 (assume @p123 (forall @t139 (or @t140 @t112 (not @t142) (not @t143)))) % 0.36/0.65 (assume @p124 (forall @t148 (or @t147 @t145))) % 0.36/0.65 (assume @p125 (forall @t148 (or @t147 @t149))) % 0.36/0.65 (assume @p126 (forall @t148 (or @t147 @t150))) % 0.36/0.65 (assume @p127 (forall @t148 (or @t146 (not @t145) (not @t149) (not @t150)))) % 0.36/0.65 (assume @p128 (forall @t155 (or @t154 (tptp.little_set @t152)))) % 0.36/0.65 (assume @p129 (forall @t155 (or @t154 (tptp.little_set @t156)))) % 0.36/0.65 (assume @p130 (forall @t155 (or @t154 (tptp.little_set @t157)))) % 0.36/0.65 (assume @p131 (forall @t155 (or @t154 (= @t23 (tptp.ordered_pair @t152 @t156))))) % 0.36/0.65 (assume @p132 (forall @t155 (or @t154 (tptp.member (tptp.ordered_pair @t152 @t157) @t109)))) % 0.36/0.65 (assume @p133 (forall @t155 (or @t154 (tptp.member (tptp.ordered_pair @t157 @t156) @t151)))) % 0.36/0.65 (assume @p134 (forall (@list @t23 @t109 @t151 @t1 @t3 @t79) (or @t153 @t24 @t120 @t25 @t81 (not (= @t23 @t18)) (not (tptp.member (tptp.ordered_pair @t1 @t79) @t109)) (not (tptp.member (tptp.ordered_pair @t79 @t3) @t151))))) % 0.36/0.65 (assume @p135 (forall @t166 (or @t165 @t160))) % 0.36/0.65 (assume @p136 (forall @t166 (or @t165 @t167))) % 0.36/0.65 (assume @p137 (forall @t166 (or @t165 @t168))) % 0.36/0.65 (assume @p138 (forall (@list @t163 @t159 @t158 @t162 @t161 @t1 @t3) (or @t165 (not (tptp.member @t1 @t159)) (not (tptp.member @t3 @t159)) (= (tptp.apply @t163 (tptp.apply_to_two_arguments @t158 @t1 @t3)) (tptp.apply_to_two_arguments @t161 (tptp.apply @t163 @t1) (tptp.apply @t163 @t3)))))) % 0.36/0.65 (assume @p139 (forall @t166 (or @t164 @t172 @t171 @t170 (tptp.member @t169 @t159)))) % 0.36/0.65 (assume @p140 (forall @t166 (or @t164 @t172 @t171 @t170 (tptp.member @t173 @t159)))) % 0.36/0.65 (assume @p141 (forall @t166 (or @t164 @t172 @t171 @t170 (not (= (tptp.apply @t163 (tptp.apply_to_two_arguments @t158 @t169 @t173)) (tptp.apply_to_two_arguments @t161 (tptp.apply @t163 @t169) (tptp.apply @t163 @t173))))))) % 0.36/0.65 (assume @p142 (forall (@list @t1 @t9 @t3 @t33) (or @t120 @t15 @t174 (= @t1 @t9)))) % 0.36/0.65 (assume @p143 (forall @t26 (or @t120 @t25 (not (= (tptp.non_ordered_pair @t23 @t1) (tptp.non_ordered_pair @t23 @t3))) @t5))) % 0.36/0.65 (assume @p144 (forall (@list @t1 @t3 @t9 @t33) (or @t120 @t25 @t15 @t36 @t174 (= @t3 @t33)))) % 0.36/0.65 (assume @p145 (forall @t4 (or @t96 (not (tptp.subset @t3 @t1)) @t5))) % 0.36/0.65 (assume @p146 (forall @t4 (or @t120 @t25 (= (tptp.first @t18) @t1)))) % 0.36/0.65 (assume @p147 (forall @t4 (or @t120 @t25 (= (tptp.second @t18) @t3)))) % 0.36/0.65 (assume @p148 (forall @t17 (or @t21 (tptp.little_set @t28)))) % 0.36/0.65 (assume @p149 (forall @t17 (or @t21 (tptp.little_set @t39)))) % 0.36/0.65 (assume @p150 (forall @t17 (or @t120 (tptp.member @t1 @t16)))) % 0.36/0.65 (assume @p151 (not @t175)) % 0.36/0.65 (step @p152 :rule evaluate :args ((= false true))) % 0.36/0.65 (step @p153 :rule instantiate :premises (@p8) :args ((@list (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) % 0.36/0.65 (step @p154 :rule true_intro :premises (@p153)) % 0.36/0.65 (step @p155 :rule instantiate :premises (@p10) :args ((@list tptp.a tptp.b))) % 0.36/0.65 (step @p156 :rule cong :premises (@p155) :args (@t175)) % 0.36/0.65 (step @p157 :rule false_intro :premises (@p151)) % 0.36/0.65 (step @p158 :rule symm :premises (@p157)) % 0.36/0.65 (step @p159 :rule trans :premises (@p158 @p156 @p154)) % 0.36/0.65 (step @p160 false :rule eq_resolve :premises (@p159 @p152)) % 0.36/0.65 ) % 0.36/0.65 % SZS output end Proof % 0.36/0.65 % cvc5 exiting %------------------------------------------------------------------------------