%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET031-4 : 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 : n008.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 08:47:04 AM UTC 2026 % Result : Unsatisfiable 0.38s 0.66s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET031-4 : TPTP v9.2.1. Released v1.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n008.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 14:43:03 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.27/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.66 % SZS status Unsatisfiable % 0.38/0.66 % SZS output start Proof % 0.38/0.67 ( % 0.38/0.67 (declare-sort $$unsorted 0) % 0.38/0.67 (declare-const tptp.b $$unsorted) % 0.38/0.67 (declare-const tptp.f32 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f31 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f29 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.closed (-> $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f28 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.apply_to_two_arguments (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f10 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f7 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f8 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.single_valued_set (-> $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f25 $$unsorted) % 0.38/0.67 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.infinity $$unsorted) % 0.38/0.67 (declare-const tptp.rotate_right (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f24 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.converse (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f2 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f30 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.non_ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.a $$unsorted) % 0.38/0.67 (declare-const tptp.estin $$unsorted) % 0.38/0.67 (declare-const tptp.singleton_set (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f26 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.flip_range_of (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f11 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.little_set (-> $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f3 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f12 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.ordered_pair_predicate (-> $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f20 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f9 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f18 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f14 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f22 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.empty_set $$unsorted) % 0.38/0.67 (declare-const tptp.universal_set $$unsorted) % 0.38/0.67 (declare-const tptp.f16 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.sigma (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.one_to_one_function (-> $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f17 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f13 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f33 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f19 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.identity_relation $$unsorted) % 0.38/0.67 (declare-const tptp.f21 (-> $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.67 (declare-const tptp.f23 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (declare-const tptp.f27 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.67 (define @t1 () (@var "X" $$unsorted)) % 0.38/0.67 (define @t2 () (tptp.little_set @t1)) % 0.38/0.67 (define @t3 () (@var "Y" $$unsorted)) % 0.38/0.67 (define @t4 () (@list @t1 @t3)) % 0.38/0.67 (define @t5 () (= @t1 @t3)) % 0.38/0.67 (define @t6 () (tptp.f1 @t1 @t3)) % 0.38/0.67 (define @t7 () (tptp.member @t6 @t3)) % 0.38/0.67 (define @t8 () (tptp.member @t6 @t1)) % 0.38/0.67 (define @t9 () (@var "U" $$unsorted)) % 0.38/0.67 (define @t10 () (= @t9 @t3)) % 0.38/0.67 (define @t11 () (= @t9 @t1)) % 0.38/0.67 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.38/0.67 (define @t13 () (tptp.member @t9 @t12)) % 0.38/0.67 (define @t14 () (@list @t9 @t1 @t3)) % 0.38/0.67 (define @t15 () (not (tptp.little_set @t9))) % 0.38/0.67 (define @t16 () (tptp.singleton_set @t1)) % 0.38/0.67 (define @t17 () (@list @t1)) % 0.38/0.67 (define @t18 () (tptp.ordered_pair @t1 @t3)) % 0.38/0.67 (define @t19 () (tptp.f2 @t1)) % 0.38/0.67 (define @t20 () (tptp.ordered_pair_predicate @t1)) % 0.38/0.67 (define @t21 () (not @t20)) % 0.38/0.67 (define @t22 () (tptp.f3 @t1)) % 0.38/0.67 (define @t23 () (@var "Z" $$unsorted)) % 0.38/0.67 (define @t24 () (tptp.ordered_pair @t3 @t23)) % 0.38/0.67 (define @t25 () (not (= @t1 @t24))) % 0.38/0.67 (define @t26 () (not (tptp.little_set @t23))) % 0.38/0.67 (define @t27 () (not (tptp.little_set @t3))) % 0.38/0.67 (define @t28 () (or @t20 @t27 @t26 @t25)) % 0.38/0.67 (define @t29 () (forall (@list @t1 @t3 @t23) @t28)) % 0.38/0.67 (define @t30 () (tptp.f4 @t23 @t1)) % 0.38/0.67 (define @t31 () (tptp.member @t23 (tptp.first @t1))) % 0.38/0.67 (define @t32 () (not @t31)) % 0.38/0.67 (define @t33 () (@list @t23 @t1)) % 0.38/0.67 (define @t34 () (tptp.f5 @t23 @t1)) % 0.38/0.67 (define @t35 () (@var "V" $$unsorted)) % 0.38/0.67 (define @t36 () (tptp.ordered_pair @t9 @t35)) % 0.38/0.67 (define @t37 () (not (= @t1 @t36))) % 0.38/0.67 (define @t38 () (not (tptp.little_set @t35))) % 0.38/0.67 (define @t39 () (@list @t23 @t1 @t9 @t35)) % 0.38/0.67 (define @t40 () (tptp.f6 @t23 @t1)) % 0.38/0.67 (define @t41 () (tptp.member @t23 (tptp.second @t1))) % 0.38/0.67 (define @t42 () (not @t41)) % 0.38/0.67 (define @t43 () (tptp.f7 @t23 @t1)) % 0.38/0.67 (define @t44 () (tptp.ordered_pair_predicate @t23)) % 0.38/0.67 (define @t45 () (tptp.member @t23 tptp.estin)) % 0.38/0.67 (define @t46 () (not @t45)) % 0.38/0.67 (define @t47 () (@list @t23)) % 0.38/0.67 (define @t48 () (tptp.second @t23)) % 0.38/0.67 (define @t49 () (tptp.first @t23)) % 0.38/0.67 (define @t50 () (tptp.member @t49 @t48)) % 0.38/0.67 (define @t51 () (not @t44)) % 0.38/0.67 (define @t52 () (tptp.member @t23 @t1)) % 0.38/0.67 (define @t53 () (tptp.member @t23 (tptp.intersection @t1 @t3))) % 0.38/0.67 (define @t54 () (not @t53)) % 0.38/0.67 (define @t55 () (@list @t23 @t1 @t3)) % 0.38/0.67 (define @t56 () (tptp.member @t23 @t3)) % 0.38/0.67 (define @t57 () (not @t56)) % 0.38/0.67 (define @t58 () (not @t52)) % 0.38/0.67 (define @t59 () (tptp.complement @t1)) % 0.38/0.67 (define @t60 () (tptp.member @t23 @t59)) % 0.38/0.67 (define @t61 () (tptp.f8 @t23 @t1)) % 0.38/0.67 (define @t62 () (tptp.member @t23 (tptp.domain_of @t1))) % 0.38/0.67 (define @t63 () (not @t62)) % 0.38/0.67 (define @t64 () (@var "Xp" $$unsorted)) % 0.38/0.67 (define @t65 () (not (tptp.member @t64 @t1))) % 0.38/0.67 (define @t66 () (not (tptp.ordered_pair_predicate @t64))) % 0.38/0.67 (define @t67 () (@list @t23 @t1 @t64)) % 0.38/0.67 (define @t68 () (tptp.member @t23 (tptp.cross_product @t1 @t3))) % 0.38/0.67 (define @t69 () (not @t68)) % 0.38/0.67 (define @t70 () (tptp.member @t49 @t1)) % 0.38/0.67 (define @t71 () (tptp.member @t48 @t3)) % 0.38/0.67 (define @t72 () (tptp.member @t23 (tptp.converse @t1))) % 0.38/0.67 (define @t73 () (not @t72)) % 0.38/0.67 (define @t74 () (tptp.member (tptp.ordered_pair @t48 @t49) @t1)) % 0.38/0.67 (define @t75 () (tptp.f9 @t23 @t1)) % 0.38/0.67 (define @t76 () (tptp.member @t23 (tptp.rotate_right @t1))) % 0.38/0.67 (define @t77 () (not @t76)) % 0.38/0.67 (define @t78 () (tptp.f10 @t23 @t1)) % 0.38/0.67 (define @t79 () (tptp.f11 @t23 @t1)) % 0.38/0.67 (define @t80 () (@var "W" $$unsorted)) % 0.38/0.67 (define @t81 () (not (= @t23 (tptp.ordered_pair @t9 (tptp.ordered_pair @t35 @t80))))) % 0.38/0.67 (define @t82 () (not (tptp.little_set @t80))) % 0.38/0.67 (define @t83 () (@list @t23 @t1 @t9 @t35 @t80)) % 0.38/0.67 (define @t84 () (tptp.f12 @t23 @t1)) % 0.38/0.67 (define @t85 () (tptp.member @t23 (tptp.flip_range_of @t1))) % 0.38/0.67 (define @t86 () (not @t85)) % 0.38/0.67 (define @t87 () (tptp.f13 @t23 @t1)) % 0.38/0.67 (define @t88 () (tptp.f14 @t23 @t1)) % 0.38/0.67 (define @t89 () (tptp.successor @t1)) % 0.38/0.67 (define @t90 () (tptp.f16 @t23 @t1)) % 0.38/0.67 (define @t91 () (tptp.member @t23 (tptp.sigma @t1))) % 0.38/0.67 (define @t92 () (not @t91)) % 0.38/0.67 (define @t93 () (@list @t9)) % 0.38/0.67 (define @t94 () (tptp.member @t9 @t3)) % 0.38/0.67 (define @t95 () (not (tptp.member @t9 @t1))) % 0.38/0.67 (define @t96 () (tptp.subset @t1 @t3)) % 0.38/0.67 (define @t97 () (not @t96)) % 0.38/0.67 (define @t98 () (@list @t1 @t3 @t9)) % 0.38/0.67 (define @t99 () (tptp.f17 @t1 @t3)) % 0.38/0.67 (define @t100 () (tptp.proper_subset @t1 @t3)) % 0.38/0.67 (define @t101 () (not @t100)) % 0.38/0.67 (define @t102 () (tptp.subset @t23 @t1)) % 0.38/0.67 (define @t103 () (tptp.member @t23 (tptp.powerset @t1))) % 0.38/0.67 (define @t104 () (tptp.relation @t23)) % 0.38/0.67 (define @t105 () (tptp.f18 @t23)) % 0.38/0.67 (define @t106 () (tptp.single_valued_set @t1)) % 0.38/0.67 (define @t107 () (tptp.f19 @t1)) % 0.38/0.67 (define @t108 () (tptp.f20 @t1)) % 0.38/0.67 (define @t109 () (tptp.f21 @t1)) % 0.38/0.67 (define @t110 () (@var "Xf" $$unsorted)) % 0.38/0.67 (define @t111 () (tptp.relation @t110)) % 0.38/0.67 (define @t112 () (tptp.function @t110)) % 0.38/0.67 (define @t113 () (not @t112)) % 0.38/0.67 (define @t114 () (@list @t110)) % 0.38/0.67 (define @t115 () (tptp.single_valued_set @t110)) % 0.38/0.67 (define @t116 () (tptp.f22 @t23 @t1 @t110)) % 0.38/0.67 (define @t117 () (tptp.image @t1 @t110)) % 0.38/0.67 (define @t118 () (tptp.member @t23 @t117)) % 0.38/0.67 (define @t119 () (not @t118)) % 0.38/0.67 (define @t120 () (@list @t23 @t1 @t110)) % 0.38/0.67 (define @t121 () (not @t2)) % 0.38/0.67 (define @t122 () (tptp.disjoint @t1 @t3)) % 0.38/0.67 (define @t123 () (tptp.f23 @t1 @t3)) % 0.38/0.67 (define @t124 () (tptp.f24 @t1)) % 0.38/0.67 (define @t125 () (= @t1 tptp.empty_set)) % 0.38/0.67 (define @t126 () (tptp.f26 @t1)) % 0.38/0.67 (define @t127 () (tptp.f27 @t23 @t1)) % 0.38/0.67 (define @t128 () (tptp.member @t23 (tptp.range_of @t1))) % 0.38/0.67 (define @t129 () (not @t128)) % 0.38/0.67 (define @t130 () (tptp.member @t23 tptp.identity_relation)) % 0.38/0.67 (define @t131 () (not @t130)) % 0.38/0.67 (define @t132 () (= @t49 @t48)) % 0.38/0.67 (define @t133 () (tptp.one_to_one_function @t110)) % 0.38/0.67 (define @t134 () (not @t133)) % 0.38/0.67 (define @t135 () (tptp.function (tptp.converse @t110))) % 0.38/0.67 (define @t136 () (tptp.f28 @t23 @t110 @t3)) % 0.38/0.67 (define @t137 () (tptp.member @t23 (tptp.apply @t110 @t3))) % 0.38/0.67 (define @t138 () (not @t137)) % 0.38/0.67 (define @t139 () (@list @t23 @t110 @t3)) % 0.38/0.67 (define @t140 () (@list @t110 @t1 @t3)) % 0.38/0.67 (define @t141 () (tptp.maps @t110 @t1 @t3)) % 0.38/0.67 (define @t142 () (not @t141)) % 0.38/0.67 (define @t143 () (= (tptp.domain_of @t110) @t1)) % 0.38/0.67 (define @t144 () (tptp.subset (tptp.range_of @t110) @t3)) % 0.38/0.67 (define @t145 () (@var "Xs" $$unsorted)) % 0.38/0.67 (define @t146 () (tptp.little_set @t145)) % 0.38/0.67 (define @t147 () (tptp.closed @t145 @t110)) % 0.38/0.67 (define @t148 () (not @t147)) % 0.38/0.67 (define @t149 () (@list @t145 @t110)) % 0.38/0.67 (define @t150 () (tptp.little_set @t110)) % 0.38/0.67 (define @t151 () (tptp.maps @t110 (tptp.cross_product @t145 @t145) @t145)) % 0.38/0.67 (define @t152 () (@var "Xg" $$unsorted)) % 0.38/0.67 (define @t153 () (tptp.f29 @t23 @t110 @t152)) % 0.38/0.67 (define @t154 () (tptp.member @t23 (tptp.compose @t110 @t152))) % 0.38/0.67 (define @t155 () (not @t154)) % 0.38/0.67 (define @t156 () (@list @t23 @t110 @t152)) % 0.38/0.67 (define @t157 () (tptp.f30 @t23 @t110 @t152)) % 0.38/0.67 (define @t158 () (tptp.f31 @t23 @t110 @t152)) % 0.38/0.67 (define @t159 () (@var "Xf1" $$unsorted)) % 0.38/0.67 (define @t160 () (@var "Xs1" $$unsorted)) % 0.38/0.67 (define @t161 () (tptp.closed @t160 @t159)) % 0.38/0.67 (define @t162 () (@var "Xf2" $$unsorted)) % 0.38/0.67 (define @t163 () (@var "Xs2" $$unsorted)) % 0.38/0.67 (define @t164 () (@var "Xh" $$unsorted)) % 0.38/0.67 (define @t165 () (tptp.homomorphism @t164 @t160 @t159 @t163 @t162)) % 0.38/0.67 (define @t166 () (not @t165)) % 0.38/0.67 (define @t167 () (@list @t164 @t160 @t159 @t163 @t162)) % 0.38/0.67 (define @t168 () (tptp.closed @t163 @t162)) % 0.38/0.67 (define @t169 () (tptp.maps @t164 @t160 @t163)) % 0.38/0.67 (define @t170 () (tptp.f32 @t164 @t160 @t159 @t163 @t162)) % 0.38/0.67 (define @t171 () (not @t169)) % 0.38/0.67 (define @t172 () (not @t168)) % 0.38/0.67 (define @t173 () (not @t161)) % 0.38/0.67 (define @t174 () (tptp.f33 @t164 @t160 @t159 @t163 @t162)) % 0.38/0.67 (define @t175 () (tptp.compose tptp.a tptp.b)) % 0.38/0.67 (define @t176 () (tptp.relation @t175)) % 0.38/0.67 (define @t177 () (tptp.ordered_pair_predicate @t24)) % 0.38/0.67 (define @t178 () (not (= @t24 @t24))) % 0.38/0.67 (define @t179 () (or @t177 @t27 @t26 @t178)) % 0.38/0.67 (define @t180 () (@list @t3 @t23)) % 0.38/0.67 (define @t181 () (or @t25 @t20 @t27 @t26 @t25)) % 0.38/0.67 (define @t182 () (forall @t17 @t28)) % 0.38/0.67 (define @t183 () (forall @t180 @t182)) % 0.38/0.67 (define @t184 () (forall (@list @t3 @t23 @t1) @t28)) % 0.38/0.67 (define @t185 () (tptp.f18 @t175)) % 0.38/0.67 (define @t186 () (tptp.f30 @t185 tptp.a tptp.b)) % 0.38/0.67 (define @t187 () (tptp.f29 @t185 tptp.a tptp.b)) % 0.38/0.67 (define @t188 () (@list @t185 tptp.a tptp.b)) % 0.38/0.67 (define @t189 () (@list @t175)) % 0.38/0.67 (define @t190 () (tptp.member @t185 @t175)) % 0.38/0.67 (define @t191 () (or @t176 @t190)) % 0.38/0.67 (define @t192 () (@list true false)) % 0.38/0.67 (define @t193 () (tptp.little_set @t186)) % 0.38/0.67 (define @t194 () (not @t190)) % 0.38/0.67 (define @t195 () (or @t194 @t193)) % 0.38/0.67 (define @t196 () (@list false false)) % 0.38/0.67 (define @t197 () (tptp.little_set @t187)) % 0.38/0.67 (define @t198 () (or @t194 @t197)) % 0.38/0.67 (define @t199 () (not @t193)) % 0.38/0.67 (define @t200 () (not @t197)) % 0.38/0.67 (define @t201 () (tptp.ordered_pair @t187 @t186)) % 0.38/0.67 (define @t202 () (tptp.ordered_pair_predicate @t201)) % 0.38/0.67 (define @t203 () (or @t202 @t200 @t199)) % 0.38/0.67 (define @t204 () (= @t185 @t201)) % 0.38/0.67 (define @t205 () (or @t194 @t204)) % 0.38/0.67 (define @t206 () (tptp.ordered_pair_predicate @t185)) % 0.38/0.67 (define @t207 () (not @t206)) % 0.38/0.67 (define @t208 () (or @t176 @t207)) % 0.38/0.67 (assume @p1 (forall @t4 (or (not (tptp.member @t1 @t3)) @t2))) % 0.38/0.67 (assume @p2 (forall @t4 (or (tptp.little_set @t6) @t5))) % 0.38/0.67 (assume @p3 (forall @t4 (or @t8 @t7 @t5))) % 0.38/0.67 (assume @p4 (forall @t4 (or (not @t8) (not @t7) @t5))) % 0.38/0.67 (assume @p5 (forall @t14 (or (not @t13) @t11 @t10))) % 0.38/0.67 (assume @p6 (forall @t14 (or @t13 @t15 (not @t11)))) % 0.38/0.67 (assume @p7 (forall @t14 (or @t13 @t15 (not @t10)))) % 0.38/0.67 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.38/0.67 (assume @p9 (forall @t17 (= @t16 (tptp.non_ordered_pair @t1 @t1)))) % 0.38/0.67 (assume @p10 (forall @t4 (= @t18 (tptp.non_ordered_pair @t16 @t12)))) % 0.38/0.67 (assume @p11 (forall @t17 (or @t21 (tptp.little_set @t19)))) % 0.38/0.67 (assume @p12 (forall @t17 (or @t21 (tptp.little_set @t22)))) % 0.38/0.67 (assume @p13 (forall @t17 (or @t21 (= @t1 (tptp.ordered_pair @t19 @t22))))) % 0.38/0.67 (assume @p14 @t29) % 0.38/0.67 (assume @p15 (forall @t33 (or @t32 (tptp.little_set @t30)))) % 0.38/0.67 (assume @p16 (forall @t33 (or @t32 (tptp.little_set @t34)))) % 0.38/0.67 (assume @p17 (forall @t33 (or @t32 (= @t1 (tptp.ordered_pair @t30 @t34))))) % 0.38/0.67 (assume @p18 (forall @t33 (or @t32 (tptp.member @t23 @t30)))) % 0.38/0.67 (assume @p19 (forall @t39 (or @t31 @t15 @t38 @t37 (not (tptp.member @t23 @t9))))) % 0.38/0.67 (assume @p20 (forall @t33 (or @t42 (tptp.little_set @t40)))) % 0.38/0.67 (assume @p21 (forall @t33 (or @t42 (tptp.little_set @t43)))) % 0.38/0.67 (assume @p22 (forall @t33 (or @t42 (= @t1 (tptp.ordered_pair @t40 @t43))))) % 0.38/0.67 (assume @p23 (forall @t33 (or @t42 (tptp.member @t23 @t43)))) % 0.38/0.67 (assume @p24 (forall @t39 (or @t41 @t15 @t38 @t37 (not (tptp.member @t23 @t35))))) % 0.38/0.67 (assume @p25 (forall @t47 (or @t46 @t44))) % 0.38/0.67 (assume @p26 (forall @t47 (or @t46 @t50))) % 0.38/0.67 (assume @p27 (forall @t47 (or @t45 @t26 @t51 (not @t50)))) % 0.38/0.67 (assume @p28 (forall @t55 (or @t54 @t52))) % 0.38/0.67 (assume @p29 (forall @t55 (or @t54 @t56))) % 0.38/0.67 (assume @p30 (forall @t55 (or @t53 @t58 @t57))) % 0.38/0.67 (assume @p31 (forall @t33 (or (not @t60) @t58))) % 0.38/0.67 (assume @p32 (forall @t33 (or @t60 @t26 @t52))) % 0.38/0.67 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t59 (tptp.complement @t3)))))) % 0.38/0.67 (assume @p34 (forall @t33 (or @t63 (tptp.ordered_pair_predicate @t61)))) % 0.38/0.67 (assume @p35 (forall @t33 (or @t63 (tptp.member @t61 @t1)))) % 0.38/0.67 (assume @p36 (forall @t33 (or @t63 (= @t23 (tptp.first @t61))))) % 0.38/0.67 (assume @p37 (forall @t67 (or @t62 @t26 @t66 @t65 (not (= @t23 (tptp.first @t64)))))) % 0.38/0.67 (assume @p38 (forall @t55 (or @t69 @t44))) % 0.38/0.67 (assume @p39 (forall @t55 (or @t69 @t70))) % 0.38/0.67 (assume @p40 (forall @t55 (or @t69 @t71))) % 0.38/0.67 (assume @p41 (forall @t55 (or @t68 @t26 @t51 (not @t70) (not @t71)))) % 0.38/0.67 (assume @p42 (forall @t33 (or @t73 @t44))) % 0.38/0.67 (assume @p43 (forall @t33 (or @t73 @t74))) % 0.38/0.67 (assume @p44 (forall @t33 (or @t72 @t26 @t51 (not @t74)))) % 0.38/0.67 (assume @p45 (forall @t33 (or @t77 (tptp.little_set @t75)))) % 0.38/0.67 (assume @p46 (forall @t33 (or @t77 (tptp.little_set @t78)))) % 0.38/0.67 (assume @p47 (forall @t33 (or @t77 (tptp.little_set @t79)))) % 0.38/0.67 (assume @p48 (forall @t33 (or @t77 (= @t23 (tptp.ordered_pair @t75 (tptp.ordered_pair @t78 @t79)))))) % 0.38/0.67 (assume @p49 (forall @t33 (or @t77 (tptp.member (tptp.ordered_pair @t78 (tptp.ordered_pair @t79 @t75)) @t1)))) % 0.38/0.67 (assume @p50 (forall @t83 (or @t76 @t26 @t15 @t38 @t82 @t81 (not (tptp.member (tptp.ordered_pair @t35 (tptp.ordered_pair @t80 @t9)) @t1))))) % 0.38/0.67 (assume @p51 (forall @t33 (or @t86 (tptp.little_set @t84)))) % 0.38/0.67 (assume @p52 (forall @t33 (or @t86 (tptp.little_set @t87)))) % 0.38/0.67 (assume @p53 (forall @t33 (or @t86 (tptp.little_set @t88)))) % 0.38/0.67 (assume @p54 (forall @t33 (or @t86 (= @t23 (tptp.ordered_pair @t84 (tptp.ordered_pair @t87 @t88)))))) % 0.38/0.67 (assume @p55 (forall @t33 (or @t86 (tptp.member (tptp.ordered_pair @t84 (tptp.ordered_pair @t88 @t87)) @t1)))) % 0.38/0.67 (assume @p56 (forall @t83 (or @t85 @t26 @t15 @t38 @t82 @t81 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t80 @t35)) @t1))))) % 0.38/0.67 (assume @p57 (forall @t17 (= @t89 (tptp.union @t1 @t16)))) % 0.38/0.67 (assume @p58 (forall @t47 (not (tptp.member @t23 tptp.empty_set)))) % 0.38/0.67 (assume @p59 (forall @t47 (or (tptp.member @t23 tptp.universal_set) @t26))) % 0.38/0.67 (assume @p60 (tptp.little_set tptp.infinity)) % 0.38/0.67 (assume @p61 (tptp.member tptp.empty_set tptp.infinity)) % 0.38/0.67 (assume @p62 (forall @t17 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t89 tptp.infinity)))) % 0.38/0.67 (assume @p63 (forall @t33 (or @t92 (tptp.member @t90 @t1)))) % 0.38/0.67 (assume @p64 (forall @t33 (or @t92 (tptp.member @t23 @t90)))) % 0.38/0.67 (assume @p65 (forall @t55 (or @t91 (not (tptp.member @t3 @t1)) @t57))) % 0.38/0.67 (assume @p66 (forall @t93 (or @t15 (tptp.little_set (tptp.sigma @t9))))) % 0.38/0.67 (assume @p67 (forall @t98 (or @t97 @t95 @t94))) % 0.38/0.67 (assume @p68 (forall @t4 (or @t96 (tptp.member @t99 @t1)))) % 0.38/0.67 (assume @p69 (forall @t4 (or @t96 (not (tptp.member @t99 @t3))))) % 0.38/0.67 (assume @p70 (forall @t4 (or @t101 @t96))) % 0.38/0.67 (assume @p71 (forall @t4 (or @t101 (not @t5)))) % 0.38/0.67 (assume @p72 (forall @t4 (or @t100 @t97 @t5))) % 0.38/0.67 (assume @p73 (forall @t33 (or (not @t103) @t102))) % 0.38/0.67 (assume @p74 (forall @t33 (or @t103 @t26 (not @t102)))) % 0.38/0.67 (assume @p75 (forall @t93 (or @t15 (tptp.little_set (tptp.powerset @t9))))) % 0.38/0.67 (assume @p76 (forall @t33 (or (not @t104) (not (tptp.member @t1 @t23)) @t20))) % 0.38/0.67 (assume @p77 (forall @t47 (or @t104 (tptp.member @t105 @t23)))) % 0.38/0.67 (assume @p78 (forall @t47 (or @t104 (not (tptp.ordered_pair_predicate @t105))))) % 0.38/0.67 (assume @p79 (forall (@list @t1 @t9 @t35 @t80) (or (not @t106) @t15 @t38 @t82 (not (tptp.member @t36 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t80) @t1)) (= @t35 @t80)))) % 0.38/0.67 (assume @p80 (forall @t17 (or @t106 (tptp.little_set @t107)))) % 0.38/0.67 (assume @p81 (forall @t17 (or @t106 (tptp.little_set @t108)))) % 0.38/0.67 (assume @p82 (forall @t17 (or @t106 (tptp.little_set @t109)))) % 0.38/0.67 (assume @p83 (forall @t17 (or @t106 (tptp.member (tptp.ordered_pair @t107 @t108) @t1)))) % 0.38/0.67 (assume @p84 (forall @t17 (or @t106 (tptp.member (tptp.ordered_pair @t107 @t109) @t1)))) % 0.38/0.67 (assume @p85 (forall @t17 (or @t106 (not (= @t108 @t109))))) % 0.38/0.67 (assume @p86 (forall @t114 (or @t113 @t111))) % 0.38/0.67 (assume @p87 (forall @t114 (or @t113 @t115))) % 0.38/0.67 (assume @p88 (forall @t114 (or @t112 (not @t111) (not @t115)))) % 0.38/0.67 (assume @p89 (forall @t120 (or @t119 (tptp.ordered_pair_predicate @t116)))) % 0.38/0.67 (assume @p90 (forall @t120 (or @t119 (tptp.member @t116 @t110)))) % 0.38/0.67 (assume @p91 (forall @t120 (or @t119 (tptp.member (tptp.first @t116) @t1)))) % 0.38/0.67 (assume @p92 (forall @t120 (or @t119 (= (tptp.second @t116) @t23)))) % 0.38/0.67 (assume @p93 (forall (@list @t23 @t1 @t110 @t3) (or @t118 @t26 (not (tptp.ordered_pair_predicate @t3)) (not (tptp.member @t3 @t110)) (not (tptp.member (tptp.first @t3) @t1)) (not (= (tptp.second @t3) @t23))))) % 0.38/0.67 (assume @p94 (forall (@list @t1 @t110) (or @t121 @t113 (tptp.little_set @t117)))) % 0.38/0.67 (assume @p95 (forall @t98 (or (not @t122) @t95 (not @t94)))) % 0.38/0.67 (assume @p96 (forall @t4 (or @t122 (tptp.member @t123 @t1)))) % 0.38/0.67 (assume @p97 (forall @t4 (or @t122 (tptp.member @t123 @t3)))) % 0.38/0.67 (assume @p98 (forall @t17 (or @t125 (tptp.member @t124 @t1)))) % 0.38/0.67 (assume @p99 (forall @t17 (or @t125 (tptp.disjoint @t124 @t1)))) % 0.38/0.67 (assume @p100 (tptp.function tptp.f25)) % 0.38/0.67 (assume @p101 (forall @t17 (or @t121 @t125 (tptp.member @t126 @t1)))) % 0.38/0.67 (assume @p102 (forall @t17 (or @t121 @t125 (tptp.member (tptp.ordered_pair @t1 @t126) tptp.f25)))) % 0.38/0.67 (assume @p103 (forall @t33 (or @t129 (tptp.ordered_pair_predicate @t127)))) % 0.38/0.67 (assume @p104 (forall @t33 (or @t129 (tptp.member @t127 @t1)))) % 0.38/0.67 (assume @p105 (forall @t33 (or @t129 (= @t23 (tptp.second @t127))))) % 0.38/0.67 (assume @p106 (forall @t67 (or @t128 @t26 @t66 @t65 (not (= @t23 (tptp.second @t64)))))) % 0.38/0.67 (assume @p107 (forall @t47 (or @t131 @t44))) % 0.38/0.67 (assume @p108 (forall @t47 (or @t131 @t132))) % 0.38/0.67 (assume @p109 (forall @t47 (or @t130 @t26 @t51 (not @t132)))) % 0.38/0.67 (assume @p110 (forall @t4 (= (tptp.restrict @t1 @t3) (tptp.intersection @t1 (tptp.cross_product @t3 tptp.universal_set))))) % 0.38/0.67 (assume @p111 (forall @t114 (or @t134 @t112))) % 0.38/0.67 (assume @p112 (forall @t114 (or @t134 @t135))) % 0.38/0.67 (assume @p113 (forall @t114 (or @t133 @t113 (not @t135)))) % 0.38/0.67 (assume @p114 (forall @t139 (or @t138 (tptp.ordered_pair_predicate @t136)))) % 0.38/0.67 (assume @p115 (forall @t139 (or @t138 (tptp.member @t136 @t110)))) % 0.38/0.67 (assume @p116 (forall @t139 (or @t138 (= (tptp.first @t136) @t3)))) % 0.38/0.67 (assume @p117 (forall @t139 (or @t138 (tptp.member @t23 (tptp.second @t136))))) % 0.38/0.67 (assume @p118 (forall (@list @t23 @t110 @t3 @t80) (or @t137 (not (tptp.ordered_pair_predicate @t80)) (not (tptp.member @t80 @t110)) (not (= (tptp.first @t80) @t3)) (not (tptp.member @t23 (tptp.second @t80)))))) % 0.38/0.67 (assume @p119 (forall @t140 (= (tptp.apply_to_two_arguments @t110 @t1 @t3) (tptp.apply @t110 @t18)))) % 0.38/0.67 (assume @p120 (forall @t140 (or @t142 @t112))) % 0.38/0.67 (assume @p121 (forall @t140 (or @t142 @t143))) % 0.38/0.67 (assume @p122 (forall @t140 (or @t142 @t144))) % 0.38/0.67 (assume @p123 (forall @t140 (or @t141 @t113 (not @t143) (not @t144)))) % 0.38/0.67 (assume @p124 (forall @t149 (or @t148 @t146))) % 0.38/0.67 (assume @p125 (forall @t149 (or @t148 @t150))) % 0.38/0.67 (assume @p126 (forall @t149 (or @t148 @t151))) % 0.38/0.67 (assume @p127 (forall @t149 (or @t147 (not @t146) (not @t150) (not @t151)))) % 0.38/0.67 (assume @p128 (forall @t156 (or @t155 (tptp.little_set @t153)))) % 0.38/0.67 (assume @p129 (forall @t156 (or @t155 (tptp.little_set @t157)))) % 0.38/0.67 (assume @p130 (forall @t156 (or @t155 (tptp.little_set @t158)))) % 0.38/0.67 (assume @p131 (forall @t156 (or @t155 (= @t23 (tptp.ordered_pair @t153 @t157))))) % 0.38/0.67 (assume @p132 (forall @t156 (or @t155 (tptp.member (tptp.ordered_pair @t153 @t158) @t110)))) % 0.38/0.67 (assume @p133 (forall @t156 (or @t155 (tptp.member (tptp.ordered_pair @t158 @t157) @t152)))) % 0.38/0.67 (assume @p134 (forall (@list @t23 @t110 @t152 @t1 @t3 @t80) (or @t154 @t26 @t121 @t27 @t82 (not (= @t23 @t18)) (not (tptp.member (tptp.ordered_pair @t1 @t80) @t110)) (not (tptp.member (tptp.ordered_pair @t80 @t3) @t152))))) % 0.38/0.67 (assume @p135 (forall @t167 (or @t166 @t161))) % 0.38/0.67 (assume @p136 (forall @t167 (or @t166 @t168))) % 0.38/0.67 (assume @p137 (forall @t167 (or @t166 @t169))) % 0.38/0.67 (assume @p138 (forall (@list @t164 @t160 @t159 @t163 @t162 @t1 @t3) (or @t166 (not (tptp.member @t1 @t160)) (not (tptp.member @t3 @t160)) (= (tptp.apply @t164 (tptp.apply_to_two_arguments @t159 @t1 @t3)) (tptp.apply_to_two_arguments @t162 (tptp.apply @t164 @t1) (tptp.apply @t164 @t3)))))) % 0.38/0.67 (assume @p139 (forall @t167 (or @t165 @t173 @t172 @t171 (tptp.member @t170 @t160)))) % 0.38/0.67 (assume @p140 (forall @t167 (or @t165 @t173 @t172 @t171 (tptp.member @t174 @t160)))) % 0.38/0.67 (assume @p141 (forall @t167 (or @t165 @t173 @t172 @t171 (not (= (tptp.apply @t164 (tptp.apply_to_two_arguments @t159 @t170 @t174)) (tptp.apply_to_two_arguments @t162 (tptp.apply @t164 @t170) (tptp.apply @t164 @t174))))))) % 0.38/0.67 (assume @p142 (not @t176)) % 0.38/0.67 (step @p143 :rule evaluate :args ((= false true))) % 0.38/0.67 (step @p144 :rule aci_norm :args ((= (or @t177 @t27 @t26 false) (or @t177 @t27 @t26)))) % 0.38/0.67 (step @p145 :rule evaluate :args ((not true))) % 0.38/0.67 (step @p146 :rule eq-refl :args (@t24)) % 0.38/0.67 (step @p147 :rule cong :premises (@p146) :args (@t178)) % 0.38/0.67 (step @p148 :rule trans :premises (@p147 @p145)) % 0.38/0.67 (step @p149 :rule refl :args (@t26)) % 0.38/0.67 (step @p150 :rule refl :args (@t27)) % 0.38/0.67 (step @p151 :rule refl :args (@t177)) % 0.38/0.67 (step @p152 :rule nary_cong :premises (@p151 @p150 @p149 @p148) :args (@t179)) % 0.38/0.67 (step @p153 :rule trans :premises (@p152 @p144)) % 0.38/0.67 (step @p154 :rule cong :premises (@p153) :args ((forall @t180 @t179))) % 0.38/0.67 (step @p155 :rule quant-var-elim-eq :args ((= (forall @t17 @t181) @t179))) % 0.38/0.67 (step @p156 :rule aci_norm :args ((= @t28 @t181))) % 0.38/0.67 (step @p157 :rule cong :premises (@p156) :args (@t182)) % 0.38/0.67 (step @p158 :rule trans :premises (@p157 @p155)) % 0.38/0.67 (step @p159 :rule cong :premises (@p158) :args (@t183)) % 0.38/0.67 (step @p160 :rule quant-merge-prenex :args ((= @t183 @t184))) % 0.38/0.67 (step @p161 :rule symm :premises (@p160)) % 0.38/0.67 (step @p162 :rule quant_var_reordering :args ((= @t29 @t184))) % 0.38/0.67 (step @p163 :rule trans :premises (@p162 @p161 @p159)) % 0.38/0.67 (step @p164 :rule trans :premises (@p163 @p154)) % 0.38/0.67 (step @p165 :rule eq_resolve :premises (@p14 @p164)) % 0.38/0.67 (step @p166 :rule instantiate :premises (@p165) :args ((@list @t187 @t186))) % 0.38/0.67 (step @p167 :rule instantiate :premises (@p129) :args (@t188)) % 0.38/0.67 (step @p168 :rule instantiate :premises (@p77) :args (@t189)) % 0.38/0.67 (step @p169 :rule cnf_or_pos :args (@t191)) % 0.38/0.67 (step @p170 :rule reordering :premises (@p169) :args ((or @t176 @t190 (not @t191)))) % 0.38/0.67 (step @p171 :rule chain_m_resolution :premises (@p170 @p142 @p168) :args (@t190 @t192 (@list @t176 @t191))) % 0.38/0.67 (step @p172 :rule cnf_or_pos :args (@t195)) % 0.38/0.67 (step @p173 :rule reordering :premises (@p172) :args ((or @t194 @t193 (not @t195)))) % 0.38/0.67 (step @p174 :rule chain_m_resolution :premises (@p173 @p171 @p167) :args (@t193 @t196 (@list @t190 @t195))) % 0.38/0.67 (step @p175 :rule instantiate :premises (@p128) :args (@t188)) % 0.38/0.67 (step @p176 :rule cnf_or_pos :args (@t198)) % 0.38/0.67 (step @p177 :rule reordering :premises (@p176) :args ((or @t194 @t197 (not @t198)))) % 0.38/0.67 (step @p178 :rule chain_m_resolution :premises (@p177 @p171 @p175) :args (@t197 @t196 (@list @t190 @t198))) % 0.38/0.67 (step @p179 :rule cnf_or_pos :args (@t203)) % 0.38/0.67 (step @p180 :rule reordering :premises (@p179) :args ((or @t200 @t199 @t202 (not @t203)))) % 0.38/0.67 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p174 @p166) :args (@t202 (@list false false false) (@list @t197 @t193 @t203))) % 0.38/0.67 (step @p182 :rule true_intro :premises (@p181)) % 0.38/0.67 (step @p183 :rule instantiate :premises (@p131) :args (@t188)) % 0.38/0.67 (step @p184 :rule cnf_or_pos :args (@t205)) % 0.38/0.67 (step @p185 :rule reordering :premises (@p184) :args ((or @t194 @t204 (not @t205)))) % 0.38/0.67 (step @p186 :rule chain_m_resolution :premises (@p185 @p171 @p183) :args (@t204 @t196 (@list @t190 @t205))) % 0.38/0.67 (step @p187 :rule cong :premises (@p186) :args (@t206)) % 0.38/0.67 (step @p188 :rule instantiate :premises (@p78) :args (@t189)) % 0.38/0.67 (step @p189 :rule cnf_or_pos :args (@t208)) % 0.38/0.67 (step @p190 :rule reordering :premises (@p189) :args ((or @t176 @t207 (not @t208)))) % 0.38/0.67 (step @p191 :rule chain_m_resolution :premises (@p190 @p142 @p188) :args (@t207 @t192 (@list @t176 @t208))) % 0.38/0.67 (step @p192 :rule false_intro :premises (@p191)) % 0.38/0.67 (step @p193 :rule symm :premises (@p192)) % 0.38/0.67 (step @p194 :rule trans :premises (@p193 @p187 @p182)) % 0.38/0.67 (step @p195 false :rule eq_resolve :premises (@p194 @p143)) % 0.38/0.67 ) % 0.38/0.67 % SZS output end Proof % 0.38/0.67 % cvc5 exiting %------------------------------------------------------------------------------