%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET022-3 : 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 : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:47:00 AM UTC 2026 % Result : Unsatisfiable 0.37s 0.64s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET022-3 : 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 % 0.17/0.34 % Computer : n002.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:41:18 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.64 % SZS status Unsatisfiable % 0.37/0.64 % SZS output start Proof % 0.37/0.65 ( % 0.37/0.65 (declare-sort $$unsorted 0) % 0.37/0.65 (declare-const tptp.f32 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f31 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f29 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.closed (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f28 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.apply_to_two_arguments (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f10 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f7 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f8 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.single_valued_set (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f25 $$unsorted) % 0.37/0.65 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.infinity $$unsorted) % 0.37/0.65 (declare-const tptp.rotate_right (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f24 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.converse (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f2 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f30 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.non_ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.estin $$unsorted) % 0.37/0.65 (declare-const tptp.singleton_set (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f26 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.flip_range_of (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f11 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.little_set (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f3 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f12 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.ordered_pair_predicate (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f20 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f9 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f18 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f14 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f22 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.empty_set $$unsorted) % 0.37/0.65 (declare-const tptp.universal_set $$unsorted) % 0.37/0.65 (declare-const tptp.f16 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.sigma (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.one_to_one_function (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f17 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f13 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f33 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f19 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.identity_relation $$unsorted) % 0.37/0.65 (declare-const tptp.f21 (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.f23 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.a $$unsorted) % 0.37/0.65 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.f27 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (define @t1 () (@var "X" $$unsorted)) % 0.37/0.65 (define @t2 () (tptp.little_set @t1)) % 0.37/0.65 (define @t3 () (@var "Y" $$unsorted)) % 0.37/0.65 (define @t4 () (@list @t1 @t3)) % 0.37/0.65 (define @t5 () (= @t1 @t3)) % 0.37/0.65 (define @t6 () (tptp.f1 @t1 @t3)) % 0.37/0.65 (define @t7 () (tptp.member @t6 @t3)) % 0.37/0.65 (define @t8 () (tptp.member @t6 @t1)) % 0.37/0.65 (define @t9 () (@var "U" $$unsorted)) % 0.37/0.65 (define @t10 () (= @t9 @t3)) % 0.37/0.65 (define @t11 () (= @t9 @t1)) % 0.37/0.65 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.37/0.65 (define @t13 () (tptp.member @t9 @t12)) % 0.37/0.65 (define @t14 () (@list @t9 @t1 @t3)) % 0.37/0.65 (define @t15 () (not (tptp.little_set @t9))) % 0.37/0.65 (define @t16 () (tptp.singleton_set @t1)) % 0.37/0.65 (define @t17 () (@list @t1)) % 0.37/0.65 (define @t18 () (tptp.ordered_pair @t1 @t3)) % 0.37/0.65 (define @t19 () (tptp.f2 @t1)) % 0.37/0.65 (define @t20 () (tptp.ordered_pair_predicate @t1)) % 0.37/0.65 (define @t21 () (not @t20)) % 0.37/0.65 (define @t22 () (tptp.f3 @t1)) % 0.37/0.65 (define @t23 () (@var "Z" $$unsorted)) % 0.37/0.65 (define @t24 () (not (tptp.little_set @t23))) % 0.37/0.65 (define @t25 () (not (tptp.little_set @t3))) % 0.37/0.65 (define @t26 () (@list @t1 @t3 @t23)) % 0.37/0.65 (define @t27 () (tptp.f4 @t23 @t1)) % 0.37/0.65 (define @t28 () (tptp.member @t23 (tptp.first @t1))) % 0.37/0.65 (define @t29 () (not @t28)) % 0.37/0.65 (define @t30 () (@list @t23 @t1)) % 0.37/0.65 (define @t31 () (tptp.f5 @t23 @t1)) % 0.37/0.65 (define @t32 () (@var "V" $$unsorted)) % 0.37/0.65 (define @t33 () (tptp.ordered_pair @t9 @t32)) % 0.37/0.65 (define @t34 () (not (= @t1 @t33))) % 0.37/0.65 (define @t35 () (not (tptp.little_set @t32))) % 0.37/0.65 (define @t36 () (@list @t23 @t1 @t9 @t32)) % 0.37/0.65 (define @t37 () (tptp.f6 @t23 @t1)) % 0.37/0.65 (define @t38 () (tptp.member @t23 (tptp.second @t1))) % 0.37/0.65 (define @t39 () (not @t38)) % 0.37/0.65 (define @t40 () (tptp.f7 @t23 @t1)) % 0.37/0.65 (define @t41 () (tptp.ordered_pair_predicate @t23)) % 0.37/0.65 (define @t42 () (tptp.member @t23 tptp.estin)) % 0.37/0.65 (define @t43 () (not @t42)) % 0.37/0.65 (define @t44 () (@list @t23)) % 0.37/0.65 (define @t45 () (tptp.second @t23)) % 0.37/0.65 (define @t46 () (tptp.first @t23)) % 0.37/0.65 (define @t47 () (tptp.member @t46 @t45)) % 0.37/0.65 (define @t48 () (not @t41)) % 0.37/0.65 (define @t49 () (tptp.member @t23 @t1)) % 0.37/0.65 (define @t50 () (tptp.member @t23 (tptp.intersection @t1 @t3))) % 0.37/0.65 (define @t51 () (not @t50)) % 0.37/0.65 (define @t52 () (@list @t23 @t1 @t3)) % 0.37/0.65 (define @t53 () (tptp.member @t23 @t3)) % 0.37/0.65 (define @t54 () (not @t53)) % 0.37/0.65 (define @t55 () (not @t49)) % 0.37/0.65 (define @t56 () (tptp.complement @t1)) % 0.37/0.65 (define @t57 () (tptp.member @t23 @t56)) % 0.37/0.65 (define @t58 () (tptp.f8 @t23 @t1)) % 0.37/0.65 (define @t59 () (tptp.member @t23 (tptp.domain_of @t1))) % 0.37/0.65 (define @t60 () (not @t59)) % 0.37/0.65 (define @t61 () (@var "Xp" $$unsorted)) % 0.37/0.65 (define @t62 () (not (tptp.member @t61 @t1))) % 0.37/0.65 (define @t63 () (not (tptp.ordered_pair_predicate @t61))) % 0.37/0.65 (define @t64 () (@list @t23 @t1 @t61)) % 0.37/0.65 (define @t65 () (tptp.member @t23 (tptp.cross_product @t1 @t3))) % 0.37/0.65 (define @t66 () (not @t65)) % 0.37/0.65 (define @t67 () (tptp.member @t46 @t1)) % 0.37/0.65 (define @t68 () (tptp.member @t45 @t3)) % 0.37/0.65 (define @t69 () (tptp.member @t23 (tptp.converse @t1))) % 0.37/0.65 (define @t70 () (not @t69)) % 0.37/0.65 (define @t71 () (tptp.member (tptp.ordered_pair @t45 @t46) @t1)) % 0.37/0.65 (define @t72 () (tptp.f9 @t23 @t1)) % 0.37/0.65 (define @t73 () (tptp.member @t23 (tptp.rotate_right @t1))) % 0.37/0.65 (define @t74 () (not @t73)) % 0.37/0.65 (define @t75 () (tptp.f10 @t23 @t1)) % 0.37/0.65 (define @t76 () (tptp.f11 @t23 @t1)) % 0.37/0.65 (define @t77 () (@var "W" $$unsorted)) % 0.37/0.65 (define @t78 () (not (= @t23 (tptp.ordered_pair @t9 (tptp.ordered_pair @t32 @t77))))) % 0.37/0.65 (define @t79 () (not (tptp.little_set @t77))) % 0.37/0.65 (define @t80 () (@list @t23 @t1 @t9 @t32 @t77)) % 0.37/0.65 (define @t81 () (tptp.f12 @t23 @t1)) % 0.37/0.65 (define @t82 () (tptp.member @t23 (tptp.flip_range_of @t1))) % 0.37/0.65 (define @t83 () (not @t82)) % 0.37/0.65 (define @t84 () (tptp.f13 @t23 @t1)) % 0.37/0.65 (define @t85 () (tptp.f14 @t23 @t1)) % 0.37/0.65 (define @t86 () (tptp.successor @t1)) % 0.37/0.65 (define @t87 () (tptp.f16 @t23 @t1)) % 0.37/0.65 (define @t88 () (tptp.member @t23 (tptp.sigma @t1))) % 0.37/0.65 (define @t89 () (not @t88)) % 0.37/0.65 (define @t90 () (@list @t9)) % 0.37/0.65 (define @t91 () (tptp.member @t9 @t3)) % 0.37/0.65 (define @t92 () (not (tptp.member @t9 @t1))) % 0.37/0.65 (define @t93 () (tptp.subset @t1 @t3)) % 0.37/0.65 (define @t94 () (not @t93)) % 0.37/0.65 (define @t95 () (@list @t1 @t3 @t9)) % 0.37/0.65 (define @t96 () (tptp.f17 @t1 @t3)) % 0.37/0.65 (define @t97 () (tptp.proper_subset @t1 @t3)) % 0.37/0.65 (define @t98 () (not @t97)) % 0.37/0.65 (define @t99 () (tptp.subset @t23 @t1)) % 0.37/0.65 (define @t100 () (tptp.member @t23 (tptp.powerset @t1))) % 0.37/0.65 (define @t101 () (tptp.relation @t23)) % 0.37/0.65 (define @t102 () (tptp.f18 @t23)) % 0.37/0.65 (define @t103 () (tptp.single_valued_set @t1)) % 0.37/0.65 (define @t104 () (tptp.f19 @t1)) % 0.37/0.65 (define @t105 () (tptp.f20 @t1)) % 0.37/0.65 (define @t106 () (tptp.f21 @t1)) % 0.37/0.65 (define @t107 () (@var "Xf" $$unsorted)) % 0.37/0.65 (define @t108 () (tptp.relation @t107)) % 0.37/0.65 (define @t109 () (tptp.function @t107)) % 0.37/0.65 (define @t110 () (not @t109)) % 0.37/0.65 (define @t111 () (@list @t107)) % 0.37/0.65 (define @t112 () (tptp.single_valued_set @t107)) % 0.37/0.65 (define @t113 () (tptp.f22 @t23 @t1 @t107)) % 0.37/0.65 (define @t114 () (tptp.image @t1 @t107)) % 0.37/0.65 (define @t115 () (tptp.member @t23 @t114)) % 0.37/0.65 (define @t116 () (not @t115)) % 0.37/0.65 (define @t117 () (@list @t23 @t1 @t107)) % 0.37/0.65 (define @t118 () (not @t2)) % 0.37/0.65 (define @t119 () (tptp.disjoint @t1 @t3)) % 0.37/0.65 (define @t120 () (tptp.f23 @t1 @t3)) % 0.37/0.65 (define @t121 () (tptp.f24 @t1)) % 0.37/0.65 (define @t122 () (= @t1 tptp.empty_set)) % 0.37/0.65 (define @t123 () (tptp.f26 @t1)) % 0.37/0.65 (define @t124 () (tptp.f27 @t23 @t1)) % 0.37/0.65 (define @t125 () (tptp.member @t23 (tptp.range_of @t1))) % 0.37/0.65 (define @t126 () (not @t125)) % 0.37/0.65 (define @t127 () (tptp.member @t23 tptp.identity_relation)) % 0.37/0.65 (define @t128 () (not @t127)) % 0.37/0.65 (define @t129 () (= @t46 @t45)) % 0.37/0.65 (define @t130 () (tptp.one_to_one_function @t107)) % 0.37/0.65 (define @t131 () (not @t130)) % 0.37/0.65 (define @t132 () (tptp.function (tptp.converse @t107))) % 0.37/0.65 (define @t133 () (tptp.f28 @t23 @t107 @t3)) % 0.37/0.65 (define @t134 () (tptp.member @t23 (tptp.apply @t107 @t3))) % 0.37/0.65 (define @t135 () (not @t134)) % 0.37/0.65 (define @t136 () (@list @t23 @t107 @t3)) % 0.37/0.65 (define @t137 () (@list @t107 @t1 @t3)) % 0.37/0.65 (define @t138 () (tptp.maps @t107 @t1 @t3)) % 0.37/0.65 (define @t139 () (not @t138)) % 0.37/0.65 (define @t140 () (= (tptp.domain_of @t107) @t1)) % 0.37/0.65 (define @t141 () (tptp.subset (tptp.range_of @t107) @t3)) % 0.37/0.65 (define @t142 () (@var "Xs" $$unsorted)) % 0.37/0.65 (define @t143 () (tptp.little_set @t142)) % 0.37/0.65 (define @t144 () (tptp.closed @t142 @t107)) % 0.37/0.65 (define @t145 () (not @t144)) % 0.37/0.65 (define @t146 () (@list @t142 @t107)) % 0.37/0.65 (define @t147 () (tptp.little_set @t107)) % 0.37/0.65 (define @t148 () (tptp.maps @t107 (tptp.cross_product @t142 @t142) @t142)) % 0.37/0.65 (define @t149 () (@var "Xg" $$unsorted)) % 0.37/0.65 (define @t150 () (tptp.f29 @t23 @t107 @t149)) % 0.37/0.65 (define @t151 () (tptp.member @t23 (tptp.compose @t107 @t149))) % 0.37/0.65 (define @t152 () (not @t151)) % 0.37/0.65 (define @t153 () (@list @t23 @t107 @t149)) % 0.37/0.65 (define @t154 () (tptp.f30 @t23 @t107 @t149)) % 0.37/0.65 (define @t155 () (tptp.f31 @t23 @t107 @t149)) % 0.37/0.65 (define @t156 () (@var "Xf1" $$unsorted)) % 0.37/0.65 (define @t157 () (@var "Xs1" $$unsorted)) % 0.37/0.65 (define @t158 () (tptp.closed @t157 @t156)) % 0.37/0.65 (define @t159 () (@var "Xf2" $$unsorted)) % 0.37/0.65 (define @t160 () (@var "Xs2" $$unsorted)) % 0.37/0.65 (define @t161 () (@var "Xh" $$unsorted)) % 0.37/0.65 (define @t162 () (tptp.homomorphism @t161 @t157 @t156 @t160 @t159)) % 0.37/0.65 (define @t163 () (not @t162)) % 0.37/0.65 (define @t164 () (@list @t161 @t157 @t156 @t160 @t159)) % 0.37/0.65 (define @t165 () (tptp.closed @t160 @t159)) % 0.37/0.65 (define @t166 () (tptp.maps @t161 @t157 @t160)) % 0.37/0.65 (define @t167 () (tptp.f32 @t161 @t157 @t156 @t160 @t159)) % 0.37/0.65 (define @t168 () (not @t166)) % 0.37/0.65 (define @t169 () (not @t165)) % 0.37/0.65 (define @t170 () (not @t158)) % 0.37/0.65 (define @t171 () (tptp.f33 @t161 @t157 @t156 @t160 @t159)) % 0.37/0.65 (define @t172 () (not (= @t18 @t33))) % 0.37/0.65 (define @t173 () (tptp.first @t18)) % 0.37/0.65 (define @t174 () (or @t118 @t25 (= @t173 @t1))) % 0.37/0.65 (define @t175 () (forall @t4 @t174)) % 0.37/0.65 (define @t176 () (tptp.ordered_pair_predicate tptp.a)) % 0.37/0.65 (define @t177 () (@list tptp.a)) % 0.37/0.65 (define @t178 () (tptp.f3 tptp.a)) % 0.37/0.65 (define @t179 () (tptp.f2 tptp.a)) % 0.37/0.65 (define @t180 () (tptp.ordered_pair @t179 @t178)) % 0.37/0.65 (define @t181 () (= tptp.a @t180)) % 0.37/0.65 (define @t182 () (not @t176)) % 0.37/0.65 (define @t183 () (or @t182 @t181)) % 0.37/0.65 (define @t184 () (@list false false)) % 0.37/0.65 (define @t185 () (tptp.first @t180)) % 0.37/0.65 (define @t186 () (tptp.little_set @t178)) % 0.37/0.65 (define @t187 () (or @t182 @t186)) % 0.37/0.65 (define @t188 () (tptp.little_set @t179)) % 0.37/0.65 (define @t189 () (or @t182 @t188)) % 0.37/0.65 (define @t190 () (= @t179 @t185)) % 0.37/0.65 (define @t191 () (not @t186)) % 0.37/0.65 (define @t192 () (not @t188)) % 0.37/0.65 (define @t193 () (or @t192 @t191 @t190)) % 0.37/0.65 (assume @p1 (forall @t4 (or (not (tptp.member @t1 @t3)) @t2))) % 0.37/0.65 (assume @p2 (forall @t4 (or (tptp.little_set @t6) @t5))) % 0.37/0.65 (assume @p3 (forall @t4 (or @t8 @t7 @t5))) % 0.37/0.65 (assume @p4 (forall @t4 (or (not @t8) (not @t7) @t5))) % 0.37/0.65 (assume @p5 (forall @t14 (or (not @t13) @t11 @t10))) % 0.37/0.65 (assume @p6 (forall @t14 (or @t13 @t15 (not @t11)))) % 0.37/0.65 (assume @p7 (forall @t14 (or @t13 @t15 (not @t10)))) % 0.37/0.65 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.37/0.65 (assume @p9 (forall @t17 (= @t16 (tptp.non_ordered_pair @t1 @t1)))) % 0.37/0.65 (assume @p10 (forall @t4 (= @t18 (tptp.non_ordered_pair @t16 @t12)))) % 0.37/0.65 (assume @p11 (forall @t17 (or @t21 (tptp.little_set @t19)))) % 0.37/0.65 (assume @p12 (forall @t17 (or @t21 (tptp.little_set @t22)))) % 0.37/0.65 (assume @p13 (forall @t17 (or @t21 (= @t1 (tptp.ordered_pair @t19 @t22))))) % 0.37/0.65 (assume @p14 (forall @t26 (or @t20 @t25 @t24 (not (= @t1 (tptp.ordered_pair @t3 @t23)))))) % 0.37/0.65 (assume @p15 (forall @t30 (or @t29 (tptp.little_set @t27)))) % 0.37/0.65 (assume @p16 (forall @t30 (or @t29 (tptp.little_set @t31)))) % 0.37/0.65 (assume @p17 (forall @t30 (or @t29 (= @t1 (tptp.ordered_pair @t27 @t31))))) % 0.37/0.65 (assume @p18 (forall @t30 (or @t29 (tptp.member @t23 @t27)))) % 0.37/0.65 (assume @p19 (forall @t36 (or @t28 @t15 @t35 @t34 (not (tptp.member @t23 @t9))))) % 0.37/0.65 (assume @p20 (forall @t30 (or @t39 (tptp.little_set @t37)))) % 0.37/0.65 (assume @p21 (forall @t30 (or @t39 (tptp.little_set @t40)))) % 0.37/0.65 (assume @p22 (forall @t30 (or @t39 (= @t1 (tptp.ordered_pair @t37 @t40))))) % 0.37/0.65 (assume @p23 (forall @t30 (or @t39 (tptp.member @t23 @t40)))) % 0.37/0.65 (assume @p24 (forall @t36 (or @t38 @t15 @t35 @t34 (not (tptp.member @t23 @t32))))) % 0.37/0.65 (assume @p25 (forall @t44 (or @t43 @t41))) % 0.37/0.65 (assume @p26 (forall @t44 (or @t43 @t47))) % 0.37/0.65 (assume @p27 (forall @t44 (or @t42 @t24 @t48 (not @t47)))) % 0.37/0.65 (assume @p28 (forall @t52 (or @t51 @t49))) % 0.37/0.65 (assume @p29 (forall @t52 (or @t51 @t53))) % 0.37/0.65 (assume @p30 (forall @t52 (or @t50 @t55 @t54))) % 0.37/0.65 (assume @p31 (forall @t30 (or (not @t57) @t55))) % 0.37/0.65 (assume @p32 (forall @t30 (or @t57 @t24 @t49))) % 0.37/0.65 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t56 (tptp.complement @t3)))))) % 0.37/0.65 (assume @p34 (forall @t30 (or @t60 (tptp.ordered_pair_predicate @t58)))) % 0.37/0.65 (assume @p35 (forall @t30 (or @t60 (tptp.member @t58 @t1)))) % 0.37/0.65 (assume @p36 (forall @t30 (or @t60 (= @t23 (tptp.first @t58))))) % 0.37/0.65 (assume @p37 (forall @t64 (or @t59 @t24 @t63 @t62 (not (= @t23 (tptp.first @t61)))))) % 0.37/0.65 (assume @p38 (forall @t52 (or @t66 @t41))) % 0.37/0.65 (assume @p39 (forall @t52 (or @t66 @t67))) % 0.37/0.65 (assume @p40 (forall @t52 (or @t66 @t68))) % 0.37/0.65 (assume @p41 (forall @t52 (or @t65 @t24 @t48 (not @t67) (not @t68)))) % 0.37/0.65 (assume @p42 (forall @t30 (or @t70 @t41))) % 0.37/0.65 (assume @p43 (forall @t30 (or @t70 @t71))) % 0.37/0.65 (assume @p44 (forall @t30 (or @t69 @t24 @t48 (not @t71)))) % 0.37/0.65 (assume @p45 (forall @t30 (or @t74 (tptp.little_set @t72)))) % 0.37/0.65 (assume @p46 (forall @t30 (or @t74 (tptp.little_set @t75)))) % 0.37/0.65 (assume @p47 (forall @t30 (or @t74 (tptp.little_set @t76)))) % 0.37/0.65 (assume @p48 (forall @t30 (or @t74 (= @t23 (tptp.ordered_pair @t72 (tptp.ordered_pair @t75 @t76)))))) % 0.37/0.65 (assume @p49 (forall @t30 (or @t74 (tptp.member (tptp.ordered_pair @t75 (tptp.ordered_pair @t76 @t72)) @t1)))) % 0.37/0.65 (assume @p50 (forall @t80 (or @t73 @t24 @t15 @t35 @t79 @t78 (not (tptp.member (tptp.ordered_pair @t32 (tptp.ordered_pair @t77 @t9)) @t1))))) % 0.37/0.65 (assume @p51 (forall @t30 (or @t83 (tptp.little_set @t81)))) % 0.37/0.65 (assume @p52 (forall @t30 (or @t83 (tptp.little_set @t84)))) % 0.37/0.65 (assume @p53 (forall @t30 (or @t83 (tptp.little_set @t85)))) % 0.37/0.65 (assume @p54 (forall @t30 (or @t83 (= @t23 (tptp.ordered_pair @t81 (tptp.ordered_pair @t84 @t85)))))) % 0.37/0.65 (assume @p55 (forall @t30 (or @t83 (tptp.member (tptp.ordered_pair @t81 (tptp.ordered_pair @t85 @t84)) @t1)))) % 0.37/0.65 (assume @p56 (forall @t80 (or @t82 @t24 @t15 @t35 @t79 @t78 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t77 @t32)) @t1))))) % 0.37/0.65 (assume @p57 (forall @t17 (= @t86 (tptp.union @t1 @t16)))) % 0.37/0.65 (assume @p58 (forall @t44 (not (tptp.member @t23 tptp.empty_set)))) % 0.37/0.65 (assume @p59 (forall @t44 (or (tptp.member @t23 tptp.universal_set) @t24))) % 0.37/0.65 (assume @p60 (tptp.little_set tptp.infinity)) % 0.37/0.65 (assume @p61 (tptp.member tptp.empty_set tptp.infinity)) % 0.37/0.65 (assume @p62 (forall @t17 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t86 tptp.infinity)))) % 0.37/0.65 (assume @p63 (forall @t30 (or @t89 (tptp.member @t87 @t1)))) % 0.37/0.65 (assume @p64 (forall @t30 (or @t89 (tptp.member @t23 @t87)))) % 0.37/0.65 (assume @p65 (forall @t52 (or @t88 (not (tptp.member @t3 @t1)) @t54))) % 0.37/0.65 (assume @p66 (forall @t90 (or @t15 (tptp.little_set (tptp.sigma @t9))))) % 0.37/0.65 (assume @p67 (forall @t95 (or @t94 @t92 @t91))) % 0.37/0.65 (assume @p68 (forall @t4 (or @t93 (tptp.member @t96 @t1)))) % 0.37/0.65 (assume @p69 (forall @t4 (or @t93 (not (tptp.member @t96 @t3))))) % 0.37/0.65 (assume @p70 (forall @t4 (or @t98 @t93))) % 0.37/0.65 (assume @p71 (forall @t4 (or @t98 (not @t5)))) % 0.37/0.65 (assume @p72 (forall @t4 (or @t97 @t94 @t5))) % 0.37/0.65 (assume @p73 (forall @t30 (or (not @t100) @t99))) % 0.37/0.65 (assume @p74 (forall @t30 (or @t100 @t24 (not @t99)))) % 0.37/0.65 (assume @p75 (forall @t90 (or @t15 (tptp.little_set (tptp.powerset @t9))))) % 0.37/0.65 (assume @p76 (forall @t30 (or (not @t101) (not (tptp.member @t1 @t23)) @t20))) % 0.37/0.65 (assume @p77 (forall @t44 (or @t101 (tptp.member @t102 @t23)))) % 0.37/0.65 (assume @p78 (forall @t44 (or @t101 (not (tptp.ordered_pair_predicate @t102))))) % 0.37/0.65 (assume @p79 (forall (@list @t1 @t9 @t32 @t77) (or (not @t103) @t15 @t35 @t79 (not (tptp.member @t33 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t77) @t1)) (= @t32 @t77)))) % 0.37/0.65 (assume @p80 (forall @t17 (or @t103 (tptp.little_set @t104)))) % 0.37/0.65 (assume @p81 (forall @t17 (or @t103 (tptp.little_set @t105)))) % 0.37/0.65 (assume @p82 (forall @t17 (or @t103 (tptp.little_set @t106)))) % 0.37/0.65 (assume @p83 (forall @t17 (or @t103 (tptp.member (tptp.ordered_pair @t104 @t105) @t1)))) % 0.37/0.65 (assume @p84 (forall @t17 (or @t103 (tptp.member (tptp.ordered_pair @t104 @t106) @t1)))) % 0.37/0.65 (assume @p85 (forall @t17 (or @t103 (not (= @t105 @t106))))) % 0.37/0.65 (assume @p86 (forall @t111 (or @t110 @t108))) % 0.37/0.65 (assume @p87 (forall @t111 (or @t110 @t112))) % 0.37/0.65 (assume @p88 (forall @t111 (or @t109 (not @t108) (not @t112)))) % 0.37/0.65 (assume @p89 (forall @t117 (or @t116 (tptp.ordered_pair_predicate @t113)))) % 0.37/0.65 (assume @p90 (forall @t117 (or @t116 (tptp.member @t113 @t107)))) % 0.37/0.65 (assume @p91 (forall @t117 (or @t116 (tptp.member (tptp.first @t113) @t1)))) % 0.37/0.65 (assume @p92 (forall @t117 (or @t116 (= (tptp.second @t113) @t23)))) % 0.37/0.65 (assume @p93 (forall (@list @t23 @t1 @t107 @t3) (or @t115 @t24 (not (tptp.ordered_pair_predicate @t3)) (not (tptp.member @t3 @t107)) (not (tptp.member (tptp.first @t3) @t1)) (not (= (tptp.second @t3) @t23))))) % 0.37/0.65 (assume @p94 (forall (@list @t1 @t107) (or @t118 @t110 (tptp.little_set @t114)))) % 0.37/0.65 (assume @p95 (forall @t95 (or (not @t119) @t92 (not @t91)))) % 0.37/0.65 (assume @p96 (forall @t4 (or @t119 (tptp.member @t120 @t1)))) % 0.37/0.65 (assume @p97 (forall @t4 (or @t119 (tptp.member @t120 @t3)))) % 0.37/0.65 (assume @p98 (forall @t17 (or @t122 (tptp.member @t121 @t1)))) % 0.37/0.65 (assume @p99 (forall @t17 (or @t122 (tptp.disjoint @t121 @t1)))) % 0.37/0.65 (assume @p100 (tptp.function tptp.f25)) % 0.37/0.65 (assume @p101 (forall @t17 (or @t118 @t122 (tptp.member @t123 @t1)))) % 0.37/0.65 (assume @p102 (forall @t17 (or @t118 @t122 (tptp.member (tptp.ordered_pair @t1 @t123) tptp.f25)))) % 0.37/0.65 (assume @p103 (forall @t30 (or @t126 (tptp.ordered_pair_predicate @t124)))) % 0.37/0.65 (assume @p104 (forall @t30 (or @t126 (tptp.member @t124 @t1)))) % 0.37/0.65 (assume @p105 (forall @t30 (or @t126 (= @t23 (tptp.second @t124))))) % 0.37/0.65 (assume @p106 (forall @t64 (or @t125 @t24 @t63 @t62 (not (= @t23 (tptp.second @t61)))))) % 0.37/0.65 (assume @p107 (forall @t44 (or @t128 @t41))) % 0.37/0.65 (assume @p108 (forall @t44 (or @t128 @t129))) % 0.37/0.65 (assume @p109 (forall @t44 (or @t127 @t24 @t48 (not @t129)))) % 0.37/0.65 (assume @p110 (forall @t4 (= (tptp.restrict @t1 @t3) (tptp.intersection @t1 (tptp.cross_product @t3 tptp.universal_set))))) % 0.37/0.65 (assume @p111 (forall @t111 (or @t131 @t109))) % 0.37/0.65 (assume @p112 (forall @t111 (or @t131 @t132))) % 0.37/0.65 (assume @p113 (forall @t111 (or @t130 @t110 (not @t132)))) % 0.37/0.65 (assume @p114 (forall @t136 (or @t135 (tptp.ordered_pair_predicate @t133)))) % 0.37/0.65 (assume @p115 (forall @t136 (or @t135 (tptp.member @t133 @t107)))) % 0.37/0.65 (assume @p116 (forall @t136 (or @t135 (= (tptp.first @t133) @t3)))) % 0.37/0.65 (assume @p117 (forall @t136 (or @t135 (tptp.member @t23 (tptp.second @t133))))) % 0.37/0.65 (assume @p118 (forall (@list @t23 @t107 @t3 @t77) (or @t134 (not (tptp.ordered_pair_predicate @t77)) (not (tptp.member @t77 @t107)) (not (= (tptp.first @t77) @t3)) (not (tptp.member @t23 (tptp.second @t77)))))) % 0.37/0.65 (assume @p119 (forall @t137 (= (tptp.apply_to_two_arguments @t107 @t1 @t3) (tptp.apply @t107 @t18)))) % 0.37/0.65 (assume @p120 (forall @t137 (or @t139 @t109))) % 0.37/0.65 (assume @p121 (forall @t137 (or @t139 @t140))) % 0.37/0.65 (assume @p122 (forall @t137 (or @t139 @t141))) % 0.37/0.65 (assume @p123 (forall @t137 (or @t138 @t110 (not @t140) (not @t141)))) % 0.37/0.65 (assume @p124 (forall @t146 (or @t145 @t143))) % 0.37/0.65 (assume @p125 (forall @t146 (or @t145 @t147))) % 0.37/0.65 (assume @p126 (forall @t146 (or @t145 @t148))) % 0.37/0.65 (assume @p127 (forall @t146 (or @t144 (not @t143) (not @t147) (not @t148)))) % 0.37/0.65 (assume @p128 (forall @t153 (or @t152 (tptp.little_set @t150)))) % 0.37/0.65 (assume @p129 (forall @t153 (or @t152 (tptp.little_set @t154)))) % 0.37/0.65 (assume @p130 (forall @t153 (or @t152 (tptp.little_set @t155)))) % 0.37/0.65 (assume @p131 (forall @t153 (or @t152 (= @t23 (tptp.ordered_pair @t150 @t154))))) % 0.37/0.65 (assume @p132 (forall @t153 (or @t152 (tptp.member (tptp.ordered_pair @t150 @t155) @t107)))) % 0.37/0.65 (assume @p133 (forall @t153 (or @t152 (tptp.member (tptp.ordered_pair @t155 @t154) @t149)))) % 0.37/0.65 (assume @p134 (forall (@list @t23 @t107 @t149 @t1 @t3 @t77) (or @t151 @t24 @t118 @t25 @t79 (not (= @t23 @t18)) (not (tptp.member (tptp.ordered_pair @t1 @t77) @t107)) (not (tptp.member (tptp.ordered_pair @t77 @t3) @t149))))) % 0.37/0.65 (assume @p135 (forall @t164 (or @t163 @t158))) % 0.37/0.65 (assume @p136 (forall @t164 (or @t163 @t165))) % 0.37/0.65 (assume @p137 (forall @t164 (or @t163 @t166))) % 0.37/0.65 (assume @p138 (forall (@list @t161 @t157 @t156 @t160 @t159 @t1 @t3) (or @t163 (not (tptp.member @t1 @t157)) (not (tptp.member @t3 @t157)) (= (tptp.apply @t161 (tptp.apply_to_two_arguments @t156 @t1 @t3)) (tptp.apply_to_two_arguments @t159 (tptp.apply @t161 @t1) (tptp.apply @t161 @t3)))))) % 0.37/0.65 (assume @p139 (forall @t164 (or @t162 @t170 @t169 @t168 (tptp.member @t167 @t157)))) % 0.37/0.65 (assume @p140 (forall @t164 (or @t162 @t170 @t169 @t168 (tptp.member @t171 @t157)))) % 0.37/0.65 (assume @p141 (forall @t164 (or @t162 @t170 @t169 @t168 (not (= (tptp.apply @t161 (tptp.apply_to_two_arguments @t156 @t167 @t171)) (tptp.apply_to_two_arguments @t159 (tptp.apply @t161 @t167) (tptp.apply @t161 @t171))))))) % 0.37/0.65 (assume @p142 (forall (@list @t1 @t9 @t3 @t32) (or @t118 @t15 @t172 (= @t1 @t9)))) % 0.37/0.65 (assume @p143 (forall @t26 (or @t118 @t25 (not (= (tptp.non_ordered_pair @t23 @t1) (tptp.non_ordered_pair @t23 @t3))) @t5))) % 0.37/0.65 (assume @p144 (forall (@list @t1 @t3 @t9 @t32) (or @t118 @t25 @t15 @t35 @t172 (= @t3 @t32)))) % 0.37/0.65 (assume @p145 (forall @t4 (or @t94 (not (tptp.subset @t3 @t1)) @t5))) % 0.37/0.65 (assume @p146 @t175) % 0.37/0.65 (assume @p147 (forall @t4 (or @t118 @t25 (= (tptp.second @t18) @t3)))) % 0.37/0.65 (assume @p148 @t176) % 0.37/0.65 (assume @p149 (not (tptp.little_set (tptp.first tptp.a)))) % 0.37/0.65 (step @p150 :rule evaluate :args ((= true false))) % 0.37/0.65 (step @p151 :rule false_intro :premises (@p149)) % 0.37/0.65 (step @p152 :rule instantiate :premises (@p13) :args (@t177)) % 0.37/0.65 (step @p153 :rule cnf_or_pos :args (@t183)) % 0.37/0.65 (step @p154 :rule reordering :premises (@p153) :args ((or @t182 @t181 (not @t183)))) % 0.37/0.65 (step @p155 :rule chain_m_resolution :premises (@p154 @p148 @p152) :args (@t181 @t184 (@list @t176 @t183))) % 0.37/0.65 (step @p156 :rule symm :premises (@p155)) % 0.37/0.65 (step @p157 :rule cong :premises (@p156) :args (@t185)) % 0.37/0.65 (step @p158 :rule eq-symm :args (@t173 @t1)) % 0.37/0.65 (step @p159 :rule refl :args (@t25)) % 0.37/0.65 (step @p160 :rule refl :args (@t118)) % 0.37/0.65 (step @p161 :rule nary_cong :premises (@p160 @p159 @p158) :args (@t174)) % 0.37/0.65 (step @p162 :rule cong :premises (@p161) :args (@t175)) % 0.37/0.65 (step @p163 :rule eq_resolve :premises (@p146 @p162)) % 0.37/0.65 (step @p164 :rule instantiate :premises (@p163) :args ((@list @t179 @t178))) % 0.37/0.65 (step @p165 :rule instantiate :premises (@p12) :args (@t177)) % 0.37/0.65 (step @p166 :rule cnf_or_pos :args (@t187)) % 0.37/0.65 (step @p167 :rule reordering :premises (@p166) :args ((or @t182 @t186 (not @t187)))) % 0.37/0.65 (step @p168 :rule chain_m_resolution :premises (@p167 @p148 @p165) :args (@t186 @t184 (@list @t176 @t187))) % 0.37/0.65 (step @p169 :rule instantiate :premises (@p11) :args (@t177)) % 0.37/0.65 (step @p170 :rule cnf_or_pos :args (@t189)) % 0.37/0.65 (step @p171 :rule reordering :premises (@p170) :args ((or @t182 @t188 (not @t189)))) % 0.37/0.65 (step @p172 :rule chain_m_resolution :premises (@p171 @p148 @p169) :args (@t188 @t184 (@list @t176 @t189))) % 0.37/0.65 (step @p173 :rule cnf_or_pos :args (@t193)) % 0.37/0.65 (step @p174 :rule reordering :premises (@p173) :args ((or @t192 @t191 @t190 (not @t193)))) % 0.37/0.65 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p168 @p164) :args (@t190 (@list false false false) (@list @t188 @t186 @t193))) % 0.37/0.65 (step @p176 :rule trans :premises (@p175 @p157)) % 0.37/0.65 (step @p177 :rule cong :premises (@p176) :args (@t188)) % 0.37/0.65 (step @p178 :rule true_intro :premises (@p172)) % 0.37/0.65 (step @p179 :rule symm :premises (@p178)) % 0.37/0.65 (step @p180 :rule trans :premises (@p179 @p177 @p151)) % 0.37/0.65 (step @p181 false :rule eq_resolve :premises (@p180 @p150)) % 0.37/0.65 ) % 0.37/0.66 % SZS output end Proof % 0.37/0.66 % cvc5 exiting %------------------------------------------------------------------------------