%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM009-1 : TPTP v9.2.1. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:38:21 AM UTC 2026 % Result : Unsatisfiable 0.43s 0.68s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM009-1 : TPTP v9.2.1. Bugfixed v1.2.1. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 10:17:55 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.31/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.68 % SZS status Unsatisfiable % 0.43/0.68 % SZS output start Proof % 0.43/0.68 ( % 0.43/0.68 (declare-sort $$unsorted 0) % 0.43/0.68 (declare-const tptp.f59 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.even_numbers $$unsorted) % 0.43/0.68 (declare-const tptp.twin_prime_numbers $$unsorted) % 0.43/0.68 (declare-const tptp.f56 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.prime_numbers $$unsorted) % 0.43/0.68 (declare-const tptp.f52 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.times $$unsorted) % 0.43/0.68 (declare-const tptp.f58 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f50 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f48 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f47 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f45 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.natural_numbers $$unsorted) % 0.43/0.68 (declare-const tptp.f41 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.inverse (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f43 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f35 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f32 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f31 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f29 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f57 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.closed (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f28 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f39 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.apply_to_two_arguments (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f10 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f7 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.commutes (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f8 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f36 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.single_valued_set (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f51 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f34 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f25 $$unsorted) % 0.43/0.68 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.infinity $$unsorted) % 0.43/0.68 (declare-const tptp.rotate_right (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.finite (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f24 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f38 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.converse (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f2 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.identity (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f30 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f42 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.non_ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.associative (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.estin $$unsorted) % 0.43/0.68 (declare-const tptp.f53 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.singleton_set (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f26 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.flip_range_of (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f44 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f55 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f40 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f11 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.plus $$unsorted) % 0.43/0.68 (declare-const tptp.f37 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.little_set (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f3 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f12 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.ordered_pair_predicate (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f20 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f9 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f18 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f14 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f22 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f46 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.empty_set $$unsorted) % 0.43/0.68 (declare-const tptp.f54 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.universal_set $$unsorted) % 0.43/0.68 (declare-const tptp.f16 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.sigma (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.one_to_one_function (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.function (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f49 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.group (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f17 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f13 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f33 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f19 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.identity_relation $$unsorted) % 0.43/0.68 (declare-const tptp.f21 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.f23 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.f27 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (define @t1 () (@var "X" $$unsorted)) % 0.43/0.68 (define @t2 () (tptp.little_set @t1)) % 0.43/0.68 (define @t3 () (@var "Y" $$unsorted)) % 0.43/0.68 (define @t4 () (@list @t1 @t3)) % 0.43/0.68 (define @t5 () (= @t1 @t3)) % 0.43/0.68 (define @t6 () (tptp.f1 @t1 @t3)) % 0.43/0.68 (define @t7 () (tptp.member @t6 @t3)) % 0.43/0.68 (define @t8 () (tptp.member @t6 @t1)) % 0.43/0.68 (define @t9 () (@var "U" $$unsorted)) % 0.43/0.68 (define @t10 () (= @t9 @t3)) % 0.43/0.68 (define @t11 () (= @t9 @t1)) % 0.43/0.68 (define @t12 () (tptp.non_ordered_pair @t1 @t3)) % 0.43/0.68 (define @t13 () (tptp.member @t9 @t12)) % 0.43/0.68 (define @t14 () (@list @t9 @t1 @t3)) % 0.43/0.68 (define @t15 () (not (tptp.little_set @t9))) % 0.43/0.68 (define @t16 () (tptp.singleton_set @t1)) % 0.43/0.68 (define @t17 () (@list @t1)) % 0.43/0.68 (define @t18 () (tptp.ordered_pair @t1 @t3)) % 0.43/0.68 (define @t19 () (tptp.f2 @t1)) % 0.43/0.68 (define @t20 () (tptp.ordered_pair_predicate @t1)) % 0.43/0.68 (define @t21 () (not @t20)) % 0.43/0.68 (define @t22 () (tptp.f3 @t1)) % 0.43/0.68 (define @t23 () (@var "Z" $$unsorted)) % 0.43/0.68 (define @t24 () (not (tptp.little_set @t23))) % 0.43/0.68 (define @t25 () (not (tptp.little_set @t3))) % 0.43/0.68 (define @t26 () (tptp.f4 @t23 @t1)) % 0.43/0.68 (define @t27 () (tptp.member @t23 (tptp.first @t1))) % 0.43/0.68 (define @t28 () (not @t27)) % 0.43/0.68 (define @t29 () (@list @t23 @t1)) % 0.43/0.68 (define @t30 () (tptp.f5 @t23 @t1)) % 0.43/0.68 (define @t31 () (@var "V" $$unsorted)) % 0.43/0.68 (define @t32 () (tptp.ordered_pair @t9 @t31)) % 0.43/0.68 (define @t33 () (not (= @t1 @t32))) % 0.43/0.68 (define @t34 () (not (tptp.little_set @t31))) % 0.43/0.68 (define @t35 () (@list @t23 @t1 @t9 @t31)) % 0.43/0.68 (define @t36 () (tptp.f6 @t23 @t1)) % 0.43/0.68 (define @t37 () (tptp.member @t23 (tptp.second @t1))) % 0.43/0.68 (define @t38 () (not @t37)) % 0.43/0.68 (define @t39 () (tptp.f7 @t23 @t1)) % 0.43/0.68 (define @t40 () (tptp.ordered_pair_predicate @t23)) % 0.43/0.68 (define @t41 () (tptp.member @t23 tptp.estin)) % 0.43/0.68 (define @t42 () (not @t41)) % 0.43/0.68 (define @t43 () (@list @t23)) % 0.43/0.68 (define @t44 () (tptp.second @t23)) % 0.43/0.68 (define @t45 () (tptp.first @t23)) % 0.43/0.68 (define @t46 () (tptp.member @t45 @t44)) % 0.43/0.68 (define @t47 () (not @t40)) % 0.43/0.68 (define @t48 () (tptp.member @t23 @t1)) % 0.43/0.68 (define @t49 () (tptp.member @t23 (tptp.intersection @t1 @t3))) % 0.43/0.68 (define @t50 () (not @t49)) % 0.43/0.68 (define @t51 () (@list @t23 @t1 @t3)) % 0.43/0.68 (define @t52 () (tptp.member @t23 @t3)) % 0.43/0.68 (define @t53 () (not @t52)) % 0.43/0.68 (define @t54 () (not @t48)) % 0.43/0.68 (define @t55 () (tptp.complement @t1)) % 0.43/0.68 (define @t56 () (tptp.member @t23 @t55)) % 0.43/0.68 (define @t57 () (tptp.f8 @t23 @t1)) % 0.43/0.68 (define @t58 () (tptp.member @t23 (tptp.domain_of @t1))) % 0.43/0.68 (define @t59 () (not @t58)) % 0.43/0.68 (define @t60 () (@var "Xp" $$unsorted)) % 0.43/0.68 (define @t61 () (not (tptp.member @t60 @t1))) % 0.43/0.68 (define @t62 () (not (tptp.ordered_pair_predicate @t60))) % 0.43/0.68 (define @t63 () (@list @t23 @t1 @t60)) % 0.43/0.68 (define @t64 () (tptp.member @t23 (tptp.cross_product @t1 @t3))) % 0.43/0.68 (define @t65 () (not @t64)) % 0.43/0.68 (define @t66 () (tptp.member @t45 @t1)) % 0.43/0.68 (define @t67 () (tptp.member @t44 @t3)) % 0.43/0.68 (define @t68 () (tptp.member @t23 (tptp.converse @t1))) % 0.43/0.68 (define @t69 () (not @t68)) % 0.43/0.68 (define @t70 () (tptp.member (tptp.ordered_pair @t44 @t45) @t1)) % 0.43/0.68 (define @t71 () (tptp.f9 @t23 @t1)) % 0.43/0.68 (define @t72 () (tptp.member @t23 (tptp.rotate_right @t1))) % 0.43/0.68 (define @t73 () (not @t72)) % 0.43/0.68 (define @t74 () (tptp.f10 @t23 @t1)) % 0.43/0.68 (define @t75 () (tptp.f11 @t23 @t1)) % 0.43/0.68 (define @t76 () (@var "W" $$unsorted)) % 0.43/0.68 (define @t77 () (not (= @t23 (tptp.ordered_pair @t9 (tptp.ordered_pair @t31 @t76))))) % 0.43/0.68 (define @t78 () (not (tptp.little_set @t76))) % 0.43/0.68 (define @t79 () (@list @t23 @t1 @t9 @t31 @t76)) % 0.43/0.68 (define @t80 () (tptp.f12 @t23 @t1)) % 0.43/0.68 (define @t81 () (tptp.member @t23 (tptp.flip_range_of @t1))) % 0.43/0.68 (define @t82 () (not @t81)) % 0.43/0.68 (define @t83 () (tptp.f13 @t23 @t1)) % 0.43/0.68 (define @t84 () (tptp.f14 @t23 @t1)) % 0.43/0.68 (define @t85 () (tptp.successor @t1)) % 0.43/0.68 (define @t86 () (tptp.member tptp.empty_set tptp.infinity)) % 0.43/0.68 (define @t87 () (tptp.f16 @t23 @t1)) % 0.43/0.68 (define @t88 () (tptp.member @t23 (tptp.sigma @t1))) % 0.43/0.68 (define @t89 () (not @t88)) % 0.43/0.68 (define @t90 () (@list @t9)) % 0.43/0.68 (define @t91 () (tptp.member @t9 @t3)) % 0.43/0.68 (define @t92 () (not (tptp.member @t9 @t1))) % 0.43/0.68 (define @t93 () (tptp.subset @t1 @t3)) % 0.43/0.68 (define @t94 () (not @t93)) % 0.43/0.68 (define @t95 () (@list @t1 @t3 @t9)) % 0.43/0.68 (define @t96 () (tptp.f17 @t1 @t3)) % 0.43/0.68 (define @t97 () (tptp.proper_subset @t1 @t3)) % 0.43/0.68 (define @t98 () (not @t97)) % 0.43/0.68 (define @t99 () (tptp.subset @t23 @t1)) % 0.43/0.68 (define @t100 () (tptp.member @t23 (tptp.powerset @t1))) % 0.43/0.68 (define @t101 () (tptp.relation @t23)) % 0.43/0.68 (define @t102 () (tptp.f18 @t23)) % 0.43/0.68 (define @t103 () (tptp.single_valued_set @t1)) % 0.43/0.68 (define @t104 () (tptp.f19 @t1)) % 0.43/0.68 (define @t105 () (tptp.f20 @t1)) % 0.43/0.68 (define @t106 () (tptp.f21 @t1)) % 0.43/0.68 (define @t107 () (@var "Xf" $$unsorted)) % 0.43/0.68 (define @t108 () (tptp.relation @t107)) % 0.43/0.68 (define @t109 () (tptp.function @t107)) % 0.43/0.68 (define @t110 () (not @t109)) % 0.43/0.68 (define @t111 () (@list @t107)) % 0.43/0.68 (define @t112 () (tptp.single_valued_set @t107)) % 0.43/0.68 (define @t113 () (tptp.f22 @t23 @t1 @t107)) % 0.43/0.68 (define @t114 () (tptp.image @t1 @t107)) % 0.43/0.68 (define @t115 () (tptp.member @t23 @t114)) % 0.43/0.68 (define @t116 () (not @t115)) % 0.43/0.68 (define @t117 () (@list @t23 @t1 @t107)) % 0.43/0.68 (define @t118 () (not @t2)) % 0.43/0.68 (define @t119 () (tptp.disjoint @t1 @t3)) % 0.43/0.68 (define @t120 () (tptp.f23 @t1 @t3)) % 0.43/0.68 (define @t121 () (tptp.f24 @t1)) % 0.43/0.68 (define @t122 () (= @t1 tptp.empty_set)) % 0.43/0.68 (define @t123 () (tptp.f26 @t1)) % 0.43/0.68 (define @t124 () (tptp.f27 @t23 @t1)) % 0.43/0.68 (define @t125 () (tptp.member @t23 (tptp.range_of @t1))) % 0.43/0.68 (define @t126 () (not @t125)) % 0.43/0.68 (define @t127 () (tptp.member @t23 tptp.identity_relation)) % 0.43/0.68 (define @t128 () (not @t127)) % 0.43/0.68 (define @t129 () (= @t45 @t44)) % 0.43/0.68 (define @t130 () (tptp.one_to_one_function @t107)) % 0.43/0.68 (define @t131 () (not @t130)) % 0.43/0.68 (define @t132 () (tptp.function (tptp.converse @t107))) % 0.43/0.68 (define @t133 () (tptp.f28 @t23 @t107 @t3)) % 0.43/0.68 (define @t134 () (tptp.member @t23 (tptp.apply @t107 @t3))) % 0.43/0.68 (define @t135 () (not @t134)) % 0.43/0.68 (define @t136 () (@list @t23 @t107 @t3)) % 0.43/0.68 (define @t137 () (tptp.apply_to_two_arguments @t107 @t1 @t3)) % 0.43/0.68 (define @t138 () (@list @t107 @t1 @t3)) % 0.43/0.68 (define @t139 () (tptp.maps @t107 @t1 @t3)) % 0.43/0.69 (define @t140 () (not @t139)) % 0.43/0.69 (define @t141 () (= (tptp.domain_of @t107) @t1)) % 0.43/0.69 (define @t142 () (tptp.range_of @t107)) % 0.43/0.69 (define @t143 () (tptp.subset @t142 @t3)) % 0.43/0.69 (define @t144 () (@var "Xs" $$unsorted)) % 0.43/0.69 (define @t145 () (tptp.little_set @t144)) % 0.43/0.69 (define @t146 () (tptp.closed @t144 @t107)) % 0.43/0.69 (define @t147 () (not @t146)) % 0.43/0.69 (define @t148 () (@list @t144 @t107)) % 0.43/0.69 (define @t149 () (tptp.little_set @t107)) % 0.43/0.69 (define @t150 () (tptp.maps @t107 (tptp.cross_product @t144 @t144) @t144)) % 0.43/0.69 (define @t151 () (not @t145)) % 0.43/0.69 (define @t152 () (@var "Xg" $$unsorted)) % 0.43/0.69 (define @t153 () (tptp.f29 @t23 @t107 @t152)) % 0.43/0.69 (define @t154 () (tptp.member @t23 (tptp.compose @t107 @t152))) % 0.43/0.69 (define @t155 () (not @t154)) % 0.43/0.69 (define @t156 () (@list @t23 @t107 @t152)) % 0.43/0.69 (define @t157 () (tptp.f30 @t23 @t107 @t152)) % 0.43/0.69 (define @t158 () (tptp.f31 @t23 @t107 @t152)) % 0.43/0.69 (define @t159 () (@var "Xf1" $$unsorted)) % 0.43/0.69 (define @t160 () (@var "Xs1" $$unsorted)) % 0.43/0.69 (define @t161 () (tptp.closed @t160 @t159)) % 0.43/0.69 (define @t162 () (@var "Xf2" $$unsorted)) % 0.43/0.69 (define @t163 () (@var "Xs2" $$unsorted)) % 0.43/0.69 (define @t164 () (@var "Xh" $$unsorted)) % 0.43/0.69 (define @t165 () (tptp.homomorphism @t164 @t160 @t159 @t163 @t162)) % 0.43/0.69 (define @t166 () (not @t165)) % 0.43/0.69 (define @t167 () (@list @t164 @t160 @t159 @t163 @t162)) % 0.43/0.69 (define @t168 () (tptp.closed @t163 @t162)) % 0.43/0.69 (define @t169 () (tptp.maps @t164 @t160 @t163)) % 0.43/0.69 (define @t170 () (tptp.f32 @t164 @t160 @t159 @t163 @t162)) % 0.43/0.69 (define @t171 () (not @t169)) % 0.43/0.69 (define @t172 () (not @t168)) % 0.43/0.69 (define @t173 () (not @t161)) % 0.43/0.69 (define @t174 () (tptp.f33 @t164 @t160 @t159 @t163 @t162)) % 0.43/0.69 (define @t175 () (tptp.member @t23 @t144)) % 0.43/0.69 (define @t176 () (not (tptp.member @t3 @t144))) % 0.43/0.69 (define @t177 () (not (tptp.member @t1 @t144))) % 0.43/0.69 (define @t178 () (tptp.associative @t144 @t107)) % 0.43/0.69 (define @t179 () (not @t178)) % 0.43/0.69 (define @t180 () (tptp.f34 @t144 @t107)) % 0.43/0.69 (define @t181 () (tptp.f35 @t144 @t107)) % 0.43/0.69 (define @t182 () (tptp.f36 @t144 @t107)) % 0.43/0.69 (define @t183 () (@var "Xe" $$unsorted)) % 0.43/0.69 (define @t184 () (tptp.member @t183 @t144)) % 0.43/0.69 (define @t185 () (tptp.identity @t144 @t107 @t183)) % 0.43/0.69 (define @t186 () (not @t185)) % 0.43/0.69 (define @t187 () (@list @t144 @t107 @t183)) % 0.43/0.69 (define @t188 () (@list @t144 @t107 @t183 @t1)) % 0.43/0.69 (define @t189 () (tptp.f37 @t144 @t107 @t183)) % 0.43/0.69 (define @t190 () (not @t184)) % 0.43/0.69 (define @t191 () (tptp.maps @t152 @t144 @t144)) % 0.43/0.69 (define @t192 () (tptp.inverse @t144 @t107 @t183 @t152)) % 0.43/0.69 (define @t193 () (not @t192)) % 0.43/0.69 (define @t194 () (@list @t144 @t107 @t183 @t152)) % 0.43/0.69 (define @t195 () (tptp.apply @t152 @t1)) % 0.43/0.69 (define @t196 () (@list @t144 @t107 @t183 @t152 @t1)) % 0.43/0.69 (define @t197 () (tptp.f38 @t144 @t107 @t183 @t152)) % 0.43/0.69 (define @t198 () (not @t191)) % 0.43/0.69 (define @t199 () (tptp.apply @t152 @t197)) % 0.43/0.69 (define @t200 () (tptp.group @t144 @t107)) % 0.43/0.69 (define @t201 () (not @t200)) % 0.43/0.69 (define @t202 () (tptp.f39 @t144 @t107)) % 0.43/0.69 (define @t203 () (tptp.commutes @t144 @t107)) % 0.43/0.69 (define @t204 () (tptp.f41 @t144 @t107)) % 0.43/0.69 (define @t205 () (tptp.f42 @t144 @t107)) % 0.43/0.69 (define @t206 () (tptp.f43 @t23 @t144)) % 0.43/0.69 (define @t207 () (not (tptp.member tptp.empty_set @t144))) % 0.43/0.69 (define @t208 () (tptp.member @t23 tptp.natural_numbers)) % 0.43/0.69 (define @t209 () (not @t208)) % 0.43/0.69 (define @t210 () (@list @t23 @t144)) % 0.43/0.69 (define @t211 () (tptp.f44 @t23)) % 0.43/0.69 (define @t212 () (@var "Xk" $$unsorted)) % 0.43/0.69 (define @t213 () (tptp.successor @t212)) % 0.43/0.69 (define @t214 () (tptp.f46 @t23 @t144)) % 0.43/0.69 (define @t215 () (tptp.member @t214 tptp.natural_numbers)) % 0.43/0.69 (define @t216 () (tptp.f45 @t23 @t144)) % 0.43/0.69 (define @t217 () (tptp.member @t216 tptp.natural_numbers)) % 0.43/0.69 (define @t218 () (tptp.member @t23 tptp.plus)) % 0.43/0.69 (define @t219 () (not @t218)) % 0.43/0.69 (define @t220 () (tptp.f47 @t23 @t144)) % 0.43/0.69 (define @t221 () (tptp.member @t220 tptp.natural_numbers)) % 0.43/0.69 (define @t222 () (tptp.f48 @t23 @t144)) % 0.43/0.69 (define @t223 () (tptp.member @t222 tptp.natural_numbers)) % 0.43/0.69 (define @t224 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t214 @t220) @t222) @t144)) % 0.43/0.69 (define @t225 () (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor @t214) @t220) (tptp.successor @t222)) @t144))) % 0.43/0.69 (define @t226 () (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set @t216) @t216) @t144))) % 0.43/0.69 (define @t227 () (tptp.f49 @t23)) % 0.43/0.69 (define @t228 () (@var "Xi" $$unsorted)) % 0.43/0.69 (define @t229 () (tptp.ordered_pair tptp.empty_set @t228)) % 0.43/0.69 (define @t230 () (not (tptp.member @t228 tptp.natural_numbers))) % 0.43/0.69 (define @t231 () (@list @t23 @t228)) % 0.43/0.69 (define @t232 () (@var "Xj" $$unsorted)) % 0.43/0.69 (define @t233 () (@var "Uu1" $$unsorted)) % 0.43/0.69 (define @t234 () (not (tptp.member @t212 tptp.natural_numbers))) % 0.43/0.69 (define @t235 () (not (tptp.member @t232 tptp.natural_numbers))) % 0.43/0.69 (define @t236 () (tptp.f51 @t23 @t144)) % 0.43/0.69 (define @t237 () (tptp.member @t236 tptp.natural_numbers)) % 0.43/0.69 (define @t238 () (tptp.f50 @t23 @t144)) % 0.43/0.69 (define @t239 () (tptp.member @t238 tptp.natural_numbers)) % 0.43/0.69 (define @t240 () (tptp.member @t23 tptp.times)) % 0.43/0.69 (define @t241 () (not @t240)) % 0.43/0.69 (define @t242 () (tptp.f52 @t23 @t144)) % 0.43/0.69 (define @t243 () (tptp.member @t242 tptp.natural_numbers)) % 0.43/0.69 (define @t244 () (tptp.f53 @t23 @t144)) % 0.43/0.69 (define @t245 () (tptp.member @t244 tptp.natural_numbers)) % 0.43/0.69 (define @t246 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t236 @t242) @t244) @t144)) % 0.43/0.69 (define @t247 () (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor @t236) @t242) (tptp.apply_to_two_arguments tptp.plus @t244 @t242)) @t144))) % 0.43/0.69 (define @t248 () (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set @t238) tptp.empty_set) @t144))) % 0.43/0.69 (define @t249 () (tptp.f54 @t23)) % 0.43/0.69 (define @t250 () (@var "Uu2" $$unsorted)) % 0.43/0.69 (define @t251 () (tptp.member @t23 tptp.prime_numbers)) % 0.43/0.69 (define @t252 () (not @t251)) % 0.43/0.69 (define @t253 () (= @t23 tptp.empty_set)) % 0.43/0.69 (define @t254 () (tptp.successor tptp.empty_set)) % 0.43/0.69 (define @t255 () (= @t23 @t254)) % 0.43/0.69 (define @t256 () (tptp.non_ordered_pair @t254 @t23)) % 0.43/0.69 (define @t257 () (tptp.f55 @t23)) % 0.43/0.69 (define @t258 () (tptp.f56 @t23)) % 0.43/0.69 (define @t259 () (tptp.f57 @t1)) % 0.43/0.69 (define @t260 () (tptp.finite @t1)) % 0.43/0.69 (define @t261 () (not @t260)) % 0.43/0.69 (define @t262 () (tptp.f58 @t1)) % 0.43/0.69 (define @t263 () (@var "Xn" $$unsorted)) % 0.43/0.69 (define @t264 () (tptp.member @t23 tptp.twin_prime_numbers)) % 0.43/0.69 (define @t265 () (not @t264)) % 0.43/0.69 (define @t266 () (tptp.member (tptp.successor (tptp.successor @t23)) tptp.prime_numbers)) % 0.43/0.69 (define @t267 () (tptp.member @t23 tptp.even_numbers)) % 0.43/0.69 (define @t268 () (not @t267)) % 0.43/0.69 (define @t269 () (tptp.f59 @t23)) % 0.43/0.69 (define @t270 () (tptp.member tptp.empty_set tptp.natural_numbers)) % 0.43/0.69 (define @t271 () (@list tptp.empty_set)) % 0.43/0.69 (define @t272 () (tptp.little_set tptp.empty_set)) % 0.43/0.69 (define @t273 () (not @t86)) % 0.43/0.69 (define @t274 () (or @t273 @t272)) % 0.43/0.69 (define @t275 () (tptp.member tptp.empty_set (tptp.f44 tptp.empty_set))) % 0.43/0.69 (define @t276 () (not @t275)) % 0.43/0.69 (define @t277 () (or @t270 @t276)) % 0.43/0.69 (define @t278 () (not @t272)) % 0.43/0.69 (define @t279 () (or @t270 @t278 @t275)) % 0.43/0.69 (assume @p1 (forall @t4 (or (not (tptp.member @t1 @t3)) @t2))) % 0.43/0.69 (assume @p2 (forall @t4 (or (tptp.little_set @t6) @t5))) % 0.43/0.69 (assume @p3 (forall @t4 (or @t8 @t7 @t5))) % 0.43/0.69 (assume @p4 (forall @t4 (or (not @t8) (not @t7) @t5))) % 0.43/0.69 (assume @p5 (forall @t14 (or (not @t13) @t11 @t10))) % 0.43/0.69 (assume @p6 (forall @t14 (or @t13 @t15 (not @t11)))) % 0.43/0.69 (assume @p7 (forall @t14 (or @t13 @t15 (not @t10)))) % 0.43/0.69 (assume @p8 (forall @t4 (tptp.little_set @t12))) % 0.43/0.69 (assume @p9 (forall @t17 (= @t16 (tptp.non_ordered_pair @t1 @t1)))) % 0.43/0.69 (assume @p10 (forall @t4 (= @t18 (tptp.non_ordered_pair @t16 @t12)))) % 0.43/0.69 (assume @p11 (forall @t17 (or @t21 (tptp.little_set @t19)))) % 0.43/0.69 (assume @p12 (forall @t17 (or @t21 (tptp.little_set @t22)))) % 0.43/0.69 (assume @p13 (forall @t17 (or @t21 (= @t1 (tptp.ordered_pair @t19 @t22))))) % 0.43/0.69 (assume @p14 (forall (@list @t1 @t3 @t23) (or @t20 @t25 @t24 (not (= @t1 (tptp.ordered_pair @t3 @t23)))))) % 0.43/0.69 (assume @p15 (forall @t29 (or @t28 (tptp.little_set @t26)))) % 0.43/0.69 (assume @p16 (forall @t29 (or @t28 (tptp.little_set @t30)))) % 0.43/0.69 (assume @p17 (forall @t29 (or @t28 (= @t1 (tptp.ordered_pair @t26 @t30))))) % 0.43/0.69 (assume @p18 (forall @t29 (or @t28 (tptp.member @t23 @t26)))) % 0.43/0.69 (assume @p19 (forall @t35 (or @t27 @t15 @t34 @t33 (not (tptp.member @t23 @t9))))) % 0.43/0.69 (assume @p20 (forall @t29 (or @t38 (tptp.little_set @t36)))) % 0.43/0.69 (assume @p21 (forall @t29 (or @t38 (tptp.little_set @t39)))) % 0.43/0.69 (assume @p22 (forall @t29 (or @t38 (= @t1 (tptp.ordered_pair @t36 @t39))))) % 0.43/0.69 (assume @p23 (forall @t29 (or @t38 (tptp.member @t23 @t39)))) % 0.43/0.69 (assume @p24 (forall @t35 (or @t37 @t15 @t34 @t33 (not (tptp.member @t23 @t31))))) % 0.43/0.69 (assume @p25 (forall @t43 (or @t42 @t40))) % 0.43/0.69 (assume @p26 (forall @t43 (or @t42 @t46))) % 0.43/0.69 (assume @p27 (forall @t43 (or @t41 @t24 @t47 (not @t46)))) % 0.43/0.69 (assume @p28 (forall @t51 (or @t50 @t48))) % 0.43/0.69 (assume @p29 (forall @t51 (or @t50 @t52))) % 0.43/0.69 (assume @p30 (forall @t51 (or @t49 @t54 @t53))) % 0.43/0.69 (assume @p31 (forall @t29 (or (not @t56) @t54))) % 0.43/0.69 (assume @p32 (forall @t29 (or @t56 @t24 @t48))) % 0.43/0.69 (assume @p33 (forall @t4 (= (tptp.union @t1 @t3) (tptp.complement (tptp.intersection @t55 (tptp.complement @t3)))))) % 0.43/0.69 (assume @p34 (forall @t29 (or @t59 (tptp.ordered_pair_predicate @t57)))) % 0.43/0.69 (assume @p35 (forall @t29 (or @t59 (tptp.member @t57 @t1)))) % 0.43/0.69 (assume @p36 (forall @t29 (or @t59 (= @t23 (tptp.first @t57))))) % 0.43/0.69 (assume @p37 (forall @t63 (or @t58 @t24 @t62 @t61 (not (= @t23 (tptp.first @t60)))))) % 0.43/0.69 (assume @p38 (forall @t51 (or @t65 @t40))) % 0.43/0.69 (assume @p39 (forall @t51 (or @t65 @t66))) % 0.43/0.69 (assume @p40 (forall @t51 (or @t65 @t67))) % 0.43/0.69 (assume @p41 (forall @t51 (or @t64 @t24 @t47 (not @t66) (not @t67)))) % 0.43/0.69 (assume @p42 (forall @t29 (or @t69 @t40))) % 0.43/0.69 (assume @p43 (forall @t29 (or @t69 @t70))) % 0.43/0.69 (assume @p44 (forall @t29 (or @t68 @t24 @t47 (not @t70)))) % 0.43/0.69 (assume @p45 (forall @t29 (or @t73 (tptp.little_set @t71)))) % 0.43/0.69 (assume @p46 (forall @t29 (or @t73 (tptp.little_set @t74)))) % 0.43/0.69 (assume @p47 (forall @t29 (or @t73 (tptp.little_set @t75)))) % 0.43/0.69 (assume @p48 (forall @t29 (or @t73 (= @t23 (tptp.ordered_pair @t71 (tptp.ordered_pair @t74 @t75)))))) % 0.43/0.69 (assume @p49 (forall @t29 (or @t73 (tptp.member (tptp.ordered_pair @t74 (tptp.ordered_pair @t75 @t71)) @t1)))) % 0.43/0.69 (assume @p50 (forall @t79 (or @t72 @t24 @t15 @t34 @t78 @t77 (not (tptp.member (tptp.ordered_pair @t31 (tptp.ordered_pair @t76 @t9)) @t1))))) % 0.43/0.69 (assume @p51 (forall @t29 (or @t82 (tptp.little_set @t80)))) % 0.43/0.69 (assume @p52 (forall @t29 (or @t82 (tptp.little_set @t83)))) % 0.43/0.69 (assume @p53 (forall @t29 (or @t82 (tptp.little_set @t84)))) % 0.43/0.69 (assume @p54 (forall @t29 (or @t82 (= @t23 (tptp.ordered_pair @t80 (tptp.ordered_pair @t83 @t84)))))) % 0.43/0.69 (assume @p55 (forall @t29 (or @t82 (tptp.member (tptp.ordered_pair @t80 (tptp.ordered_pair @t84 @t83)) @t1)))) % 0.43/0.69 (assume @p56 (forall @t79 (or @t81 @t24 @t15 @t34 @t78 @t77 (not (tptp.member (tptp.ordered_pair @t9 (tptp.ordered_pair @t76 @t31)) @t1))))) % 0.43/0.69 (assume @p57 (forall @t17 (= @t85 (tptp.union @t1 @t16)))) % 0.43/0.69 (assume @p58 (forall @t43 (not (tptp.member @t23 tptp.empty_set)))) % 0.43/0.69 (assume @p59 (forall @t43 (or (tptp.member @t23 tptp.universal_set) @t24))) % 0.43/0.69 (assume @p60 (tptp.little_set tptp.infinity)) % 0.43/0.69 (assume @p61 @t86) % 0.43/0.69 (assume @p62 (forall @t17 (or (not (tptp.member @t1 tptp.infinity)) (tptp.member @t85 tptp.infinity)))) % 0.43/0.69 (assume @p63 (forall @t29 (or @t89 (tptp.member @t87 @t1)))) % 0.43/0.69 (assume @p64 (forall @t29 (or @t89 (tptp.member @t23 @t87)))) % 0.43/0.69 (assume @p65 (forall @t51 (or @t88 (not (tptp.member @t3 @t1)) @t53))) % 0.43/0.69 (assume @p66 (forall @t90 (or @t15 (tptp.little_set (tptp.sigma @t9))))) % 0.43/0.69 (assume @p67 (forall @t95 (or @t94 @t92 @t91))) % 0.43/0.69 (assume @p68 (forall @t4 (or @t93 (tptp.member @t96 @t1)))) % 0.43/0.69 (assume @p69 (forall @t4 (or @t93 (not (tptp.member @t96 @t3))))) % 0.43/0.69 (assume @p70 (forall @t4 (or @t98 @t93))) % 0.43/0.69 (assume @p71 (forall @t4 (or @t98 (not @t5)))) % 0.43/0.69 (assume @p72 (forall @t4 (or @t97 @t94 @t5))) % 0.43/0.69 (assume @p73 (forall @t29 (or (not @t100) @t99))) % 0.43/0.69 (assume @p74 (forall @t29 (or @t100 @t24 (not @t99)))) % 0.43/0.69 (assume @p75 (forall @t90 (or @t15 (tptp.little_set (tptp.powerset @t9))))) % 0.43/0.69 (assume @p76 (forall @t29 (or (not @t101) (not (tptp.member @t1 @t23)) @t20))) % 0.43/0.69 (assume @p77 (forall @t43 (or @t101 (tptp.member @t102 @t23)))) % 0.43/0.69 (assume @p78 (forall @t43 (or @t101 (not (tptp.ordered_pair_predicate @t102))))) % 0.43/0.69 (assume @p79 (forall (@list @t1 @t9 @t31 @t76) (or (not @t103) @t15 @t34 @t78 (not (tptp.member @t32 @t1)) (not (tptp.member (tptp.ordered_pair @t9 @t76) @t1)) (= @t31 @t76)))) % 0.43/0.69 (assume @p80 (forall @t17 (or @t103 (tptp.little_set @t104)))) % 0.43/0.69 (assume @p81 (forall @t17 (or @t103 (tptp.little_set @t105)))) % 0.43/0.69 (assume @p82 (forall @t17 (or @t103 (tptp.little_set @t106)))) % 0.43/0.69 (assume @p83 (forall @t17 (or @t103 (tptp.member (tptp.ordered_pair @t104 @t105) @t1)))) % 0.43/0.69 (assume @p84 (forall @t17 (or @t103 (tptp.member (tptp.ordered_pair @t104 @t106) @t1)))) % 0.43/0.69 (assume @p85 (forall @t17 (or @t103 (not (= @t105 @t106))))) % 0.43/0.69 (assume @p86 (forall @t111 (or @t110 @t108))) % 0.43/0.69 (assume @p87 (forall @t111 (or @t110 @t112))) % 0.43/0.69 (assume @p88 (forall @t111 (or @t109 (not @t108) (not @t112)))) % 0.43/0.69 (assume @p89 (forall @t117 (or @t116 (tptp.ordered_pair_predicate @t113)))) % 0.43/0.69 (assume @p90 (forall @t117 (or @t116 (tptp.member @t113 @t107)))) % 0.43/0.69 (assume @p91 (forall @t117 (or @t116 (tptp.member (tptp.first @t113) @t1)))) % 0.43/0.69 (assume @p92 (forall @t117 (or @t116 (= (tptp.second @t113) @t23)))) % 0.43/0.69 (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))))) % 0.43/0.69 (assume @p94 (forall (@list @t1 @t107) (or @t118 @t110 (tptp.little_set @t114)))) % 0.43/0.69 (assume @p95 (forall @t95 (or (not @t119) @t92 (not @t91)))) % 0.43/0.69 (assume @p96 (forall @t4 (or @t119 (tptp.member @t120 @t1)))) % 0.43/0.69 (assume @p97 (forall @t4 (or @t119 (tptp.member @t120 @t3)))) % 0.43/0.69 (assume @p98 (forall @t17 (or @t122 (tptp.member @t121 @t1)))) % 0.43/0.69 (assume @p99 (forall @t17 (or @t122 (tptp.disjoint @t121 @t1)))) % 0.43/0.69 (assume @p100 (tptp.function tptp.f25)) % 0.43/0.69 (assume @p101 (forall @t17 (or @t118 @t122 (tptp.member @t123 @t1)))) % 0.43/0.69 (assume @p102 (forall @t17 (or @t118 @t122 (tptp.member (tptp.ordered_pair @t1 @t123) tptp.f25)))) % 0.43/0.69 (assume @p103 (forall @t29 (or @t126 (tptp.ordered_pair_predicate @t124)))) % 0.43/0.69 (assume @p104 (forall @t29 (or @t126 (tptp.member @t124 @t1)))) % 0.43/0.69 (assume @p105 (forall @t29 (or @t126 (= @t23 (tptp.second @t124))))) % 0.43/0.69 (assume @p106 (forall @t63 (or @t125 @t24 @t62 @t61 (not (= @t23 (tptp.second @t60)))))) % 0.43/0.69 (assume @p107 (forall @t43 (or @t128 @t40))) % 0.43/0.69 (assume @p108 (forall @t43 (or @t128 @t129))) % 0.43/0.69 (assume @p109 (forall @t43 (or @t127 @t24 @t47 (not @t129)))) % 0.43/0.69 (assume @p110 (forall @t4 (= (tptp.restrict @t1 @t3) (tptp.intersection @t1 (tptp.cross_product @t3 tptp.universal_set))))) % 0.43/0.69 (assume @p111 (forall @t111 (or @t131 @t109))) % 0.43/0.69 (assume @p112 (forall @t111 (or @t131 @t132))) % 0.43/0.69 (assume @p113 (forall @t111 (or @t130 @t110 (not @t132)))) % 0.43/0.69 (assume @p114 (forall @t136 (or @t135 (tptp.ordered_pair_predicate @t133)))) % 0.43/0.69 (assume @p115 (forall @t136 (or @t135 (tptp.member @t133 @t107)))) % 0.43/0.69 (assume @p116 (forall @t136 (or @t135 (= (tptp.first @t133) @t3)))) % 0.43/0.69 (assume @p117 (forall @t136 (or @t135 (tptp.member @t23 (tptp.second @t133))))) % 0.43/0.69 (assume @p118 (forall (@list @t23 @t107 @t3 @t76) (or @t134 (not (tptp.ordered_pair_predicate @t76)) (not (tptp.member @t76 @t107)) (not (= (tptp.first @t76) @t3)) (not (tptp.member @t23 (tptp.second @t76)))))) % 0.43/0.69 (assume @p119 (forall @t138 (= @t137 (tptp.apply @t107 @t18)))) % 0.43/0.69 (assume @p120 (forall @t138 (or @t140 @t109))) % 0.43/0.69 (assume @p121 (forall @t138 (or @t140 @t141))) % 0.43/0.69 (assume @p122 (forall @t138 (or @t140 @t143))) % 0.43/0.69 (assume @p123 (forall @t138 (or @t139 @t110 (not @t141) (not @t143)))) % 0.43/0.69 (assume @p124 (forall @t148 (or @t147 @t145))) % 0.43/0.69 (assume @p125 (forall @t148 (or @t147 @t149))) % 0.43/0.69 (assume @p126 (forall @t148 (or @t147 @t150))) % 0.43/0.69 (assume @p127 (forall @t148 (or @t146 @t151 (not @t149) (not @t150)))) % 0.43/0.69 (assume @p128 (forall @t156 (or @t155 (tptp.little_set @t153)))) % 0.43/0.69 (assume @p129 (forall @t156 (or @t155 (tptp.little_set @t157)))) % 0.43/0.69 (assume @p130 (forall @t156 (or @t155 (tptp.little_set @t158)))) % 0.43/0.69 (assume @p131 (forall @t156 (or @t155 (= @t23 (tptp.ordered_pair @t153 @t157))))) % 0.43/0.69 (assume @p132 (forall @t156 (or @t155 (tptp.member (tptp.ordered_pair @t153 @t158) @t107)))) % 0.43/0.69 (assume @p133 (forall @t156 (or @t155 (tptp.member (tptp.ordered_pair @t158 @t157) @t152)))) % 0.43/0.69 (assume @p134 (forall (@list @t23 @t107 @t152 @t1 @t3 @t76) (or @t154 @t24 @t118 @t25 @t78 (not (= @t23 @t18)) (not (tptp.member (tptp.ordered_pair @t1 @t76) @t107)) (not (tptp.member (tptp.ordered_pair @t76 @t3) @t152))))) % 0.43/0.69 (assume @p135 (forall @t167 (or @t166 @t161))) % 0.43/0.69 (assume @p136 (forall @t167 (or @t166 @t168))) % 0.43/0.69 (assume @p137 (forall @t167 (or @t166 @t169))) % 0.43/0.69 (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)))))) % 0.43/0.69 (assume @p139 (forall @t167 (or @t165 @t173 @t172 @t171 (tptp.member @t170 @t160)))) % 0.43/0.69 (assume @p140 (forall @t167 (or @t165 @t173 @t172 @t171 (tptp.member @t174 @t160)))) % 0.43/0.69 (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))))))) % 0.43/0.69 (assume @p142 (forall (@list @t144 @t107 @t1 @t3 @t23) (or @t179 @t177 @t176 (not @t175) (= (tptp.apply_to_two_arguments @t107 @t137 @t23) (tptp.apply_to_two_arguments @t107 @t1 (tptp.apply_to_two_arguments @t107 @t3 @t23)))))) % 0.43/0.69 (assume @p143 (forall @t148 (or @t178 (tptp.member @t180 @t144)))) % 0.43/0.69 (assume @p144 (forall @t148 (or @t178 (tptp.member @t181 @t144)))) % 0.43/0.69 (assume @p145 (forall @t148 (or @t178 (tptp.member @t182 @t144)))) % 0.43/0.69 (assume @p146 (forall @t148 (or @t178 (not (= (tptp.apply_to_two_arguments @t107 (tptp.apply_to_two_arguments @t107 @t180 @t181) @t182) (tptp.apply_to_two_arguments @t107 @t180 (tptp.apply_to_two_arguments @t107 @t181 @t182))))))) % 0.43/0.69 (assume @p147 (forall @t187 (or @t186 @t184))) % 0.43/0.69 (assume @p148 (forall @t188 (or @t186 @t177 (= (tptp.apply_to_two_arguments @t107 @t183 @t1) @t1)))) % 0.43/0.69 (assume @p149 (forall @t188 (or @t186 @t177 (= (tptp.apply_to_two_arguments @t107 @t1 @t183) @t1)))) % 0.43/0.69 (assume @p150 (forall @t187 (or @t185 @t190 (tptp.member @t189 @t144)))) % 0.43/0.69 (assume @p151 (forall @t187 (or @t185 @t190 (not (= (tptp.apply_to_two_arguments @t107 @t183 @t189) @t189)) (not (= (tptp.apply_to_two_arguments @t107 @t189 @t183) @t189))))) % 0.43/0.69 (assume @p152 (forall @t194 (or @t193 @t191))) % 0.43/0.69 (assume @p153 (forall @t196 (or @t193 @t177 (= (tptp.apply_to_two_arguments @t107 @t195 @t1) @t183)))) % 0.43/0.69 (assume @p154 (forall @t196 (or @t193 @t177 (= (tptp.apply_to_two_arguments @t107 @t1 @t195) @t183)))) % 0.43/0.69 (assume @p155 (forall @t194 (or @t192 @t198 (tptp.member @t197 @t144)))) % 0.43/0.69 (assume @p156 (forall @t194 (or @t192 @t198 (not (= (tptp.apply_to_two_arguments @t107 @t199 @t197) @t183)) (not (= (tptp.apply_to_two_arguments @t107 @t197 @t199) @t183))))) % 0.43/0.69 (assume @p157 (forall @t148 (or @t201 @t146))) % 0.43/0.69 (assume @p158 (forall @t148 (or @t201 @t178))) % 0.43/0.69 (assume @p159 (forall @t148 (or @t201 (tptp.identity @t144 @t107 @t202)))) % 0.43/0.69 (assume @p160 (forall @t148 (or @t201 (tptp.inverse @t144 @t107 @t202 (tptp.f40 @t144 @t107))))) % 0.43/0.69 (assume @p161 (forall @t194 (or @t200 @t147 @t179 @t186 @t193))) % 0.43/0.69 (assume @p162 (forall (@list @t144 @t107 @t1 @t3) (or (not @t203) @t177 @t176 (= @t137 (tptp.apply_to_two_arguments @t107 @t3 @t1))))) % 0.43/0.69 (assume @p163 (forall @t148 (or @t203 (tptp.member @t204 @t144)))) % 0.43/0.69 (assume @p164 (forall @t148 (or @t203 (tptp.member @t205 @t144)))) % 0.43/0.69 (assume @p165 (forall @t148 (or @t203 (not (= (tptp.apply_to_two_arguments @t107 @t204 @t205) (tptp.apply_to_two_arguments @t107 @t205 @t204)))))) % 0.43/0.69 (assume @p166 (forall @t210 (or @t209 @t151 @t207 (tptp.member @t206 @t144) @t175))) % 0.43/0.69 (assume @p167 (forall @t210 (or @t209 @t151 @t207 (not (tptp.member (tptp.successor @t206) @t144)) @t175))) % 0.43/0.69 (assume @p168 (forall @t43 (or @t208 @t24 (tptp.little_set @t211)))) % 0.43/0.69 (assume @p169 (forall @t43 (or @t208 @t24 (tptp.member tptp.empty_set @t211)))) % 0.43/0.69 (assume @p170 (forall (@list @t23 @t212) (or @t208 @t24 (not (tptp.member @t212 @t211)) (tptp.member @t213 @t211)))) % 0.43/0.69 (assume @p171 (forall @t43 (or @t208 (not (tptp.member @t23 @t211))))) % 0.43/0.69 (assume @p172 (forall @t210 (or @t219 @t151 @t217 @t215 @t175))) % 0.43/0.69 (assume @p173 (forall @t210 (or @t219 @t151 @t217 @t221 @t175))) % 0.43/0.69 (assume @p174 (forall @t210 (or @t219 @t151 @t217 @t223 @t175))) % 0.43/0.69 (assume @p175 (forall @t210 (or @t219 @t151 @t217 @t224 @t175))) % 0.43/0.69 (assume @p176 (forall @t210 (or @t219 @t151 @t217 @t225 @t175))) % 0.43/0.69 (assume @p177 (forall @t210 (or @t219 @t151 @t226 @t215 @t175))) % 0.43/0.69 (assume @p178 (forall @t210 (or @t219 @t151 @t226 @t221 @t175))) % 0.43/0.69 (assume @p179 (forall @t210 (or @t219 @t151 @t226 @t223 @t175))) % 0.43/0.69 (assume @p180 (forall @t210 (or @t219 @t151 @t226 @t224 @t175))) % 0.43/0.69 (assume @p181 (forall @t210 (or @t219 @t151 @t226 @t225 @t175))) % 0.43/0.69 (assume @p182 (forall @t43 (or @t218 @t24 (tptp.little_set @t227)))) % 0.43/0.69 (assume @p183 (forall @t231 (or @t218 @t24 @t230 (tptp.member (tptp.ordered_pair @t229 @t228) @t227)))) % 0.43/0.69 (assume @p184 (forall (@list @t23 @t233 @t232 @t212) (or @t218 @t24 (not (tptp.member @t233 tptp.natural_numbers)) @t235 @t234 (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t233 @t232) @t212) @t227)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor @t233) @t232) @t213) @t227)))) % 0.43/0.69 (assume @p185 (forall @t43 (or @t218 (not (tptp.member @t23 @t227))))) % 0.43/0.69 (assume @p186 (forall @t210 (or @t241 @t151 @t239 @t237 @t175))) % 0.43/0.69 (assume @p187 (forall @t210 (or @t241 @t151 @t239 @t243 @t175))) % 0.43/0.69 (assume @p188 (forall @t210 (or @t241 @t151 @t239 @t245 @t175))) % 0.43/0.69 (assume @p189 (forall @t210 (or @t241 @t151 @t239 @t246 @t175))) % 0.43/0.69 (assume @p190 (forall @t210 (or @t241 @t151 @t239 @t247 @t175))) % 0.43/0.69 (assume @p191 (forall @t210 (or @t241 @t151 @t248 @t237 @t175))) % 0.43/0.69 (assume @p192 (forall @t210 (or @t241 @t151 @t248 @t243 @t175))) % 0.43/0.69 (assume @p193 (forall @t210 (or @t241 @t151 @t248 @t245 @t175))) % 0.43/0.69 (assume @p194 (forall @t210 (or @t241 @t151 @t248 @t246 @t175))) % 0.43/0.69 (assume @p195 (forall @t210 (or @t241 @t151 @t248 @t247 @t175))) % 0.43/0.69 (assume @p196 (forall @t43 (or @t240 @t24 (tptp.little_set @t249)))) % 0.43/0.69 (assume @p197 (forall @t231 (or @t240 @t24 @t230 (tptp.member (tptp.ordered_pair @t229 tptp.empty_set) @t249)))) % 0.43/0.69 (assume @p198 (forall (@list @t23 @t250 @t232 @t212) (or @t240 @t24 (not (tptp.member @t250 tptp.natural_numbers)) @t235 @t234 (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t250 @t232) @t212) @t249)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor @t250) @t232) (tptp.apply_to_two_arguments tptp.plus @t212 @t232)) @t249)))) % 0.43/0.69 (assume @p199 (forall @t43 (or @t240 (not (tptp.member @t23 @t249))))) % 0.43/0.69 (assume @p200 (forall @t43 (or @t252 @t208))) % 0.43/0.69 (assume @p201 (forall @t43 (or @t252 (not @t253)))) % 0.43/0.69 (assume @p202 (forall @t43 (or @t252 (not @t255)))) % 0.43/0.69 (assume @p203 (forall (@list @t23 @t9 @t31) (or @t252 (not (tptp.member @t9 tptp.natural_numbers)) (not (tptp.member @t31 tptp.natural_numbers)) (not (= (tptp.apply_to_two_arguments tptp.times @t9 @t31) @t23)) (tptp.member @t9 @t256)))) % 0.43/0.69 (assume @p204 (forall @t43 (or @t251 @t209 @t253 @t255 (tptp.member @t257 tptp.natural_numbers)))) % 0.43/0.69 (assume @p205 (forall @t43 (or @t251 @t209 @t253 @t255 (tptp.member @t258 tptp.natural_numbers)))) % 0.43/0.69 (assume @p206 (forall @t43 (or @t251 @t209 @t253 @t255 (= (tptp.apply_to_two_arguments tptp.times @t257 @t258) @t23)))) % 0.43/0.69 (assume @p207 (forall @t43 (or @t251 @t209 @t253 @t255 (not (tptp.member @t257 @t256))))) % 0.43/0.69 (assume @p208 (forall @t17 (or @t261 (tptp.member @t259 tptp.natural_numbers)))) % 0.43/0.69 (assume @p209 (forall @t17 (or @t261 (tptp.maps @t262 @t259 @t1)))) % 0.43/0.69 (assume @p210 (forall @t17 (or @t261 (= (tptp.range_of @t262) @t1)))) % 0.43/0.69 (assume @p211 (forall @t17 (or @t261 (tptp.one_to_one_function @t262)))) % 0.43/0.69 (assume @p212 (forall (@list @t1 @t263 @t107) (or @t260 (not (tptp.member @t263 tptp.natural_numbers)) (not (tptp.maps @t107 @t263 @t1)) (not (= @t142 @t1)) @t131))) % 0.43/0.69 (assume @p213 (forall @t43 (or @t265 @t251))) % 0.43/0.69 (assume @p214 (forall @t43 (or @t265 @t266))) % 0.43/0.69 (assume @p215 (forall @t43 (or @t264 @t252 (not @t266)))) % 0.43/0.69 (assume @p216 (forall @t43 (or @t268 @t208))) % 0.43/0.69 (assume @p217 (forall @t43 (or @t268 (tptp.member @t269 tptp.natural_numbers)))) % 0.43/0.69 (assume @p218 (forall @t43 (or @t268 (= (tptp.apply_to_two_arguments tptp.plus @t269 @t269) @t23)))) % 0.43/0.69 (assume @p219 (forall @t29 (or @t267 @t209 (not (tptp.member @t1 tptp.natural_numbers)) (not (= (tptp.apply_to_two_arguments tptp.plus @t1 @t1) @t23))))) % 0.43/0.69 (assume @p220 (not @t270)) % 0.43/0.69 (step @p221 :rule instantiate :premises (@p169) :args (@t271)) % 0.43/0.69 (step @p222 :rule instantiate :premises (@p1) :args ((@list tptp.empty_set tptp.infinity))) % 0.43/0.69 (step @p223 :rule cnf_or_pos :args (@t274)) % 0.43/0.69 (step @p224 :rule reordering :premises (@p223) :args ((or @t273 @t272 (not @t274)))) % 0.43/0.69 (step @p225 :rule chain_m_resolution :premises (@p224 @p61 @p222) :args (@t272 (@list false false) (@list @t86 @t274))) % 0.43/0.69 (step @p226 :rule instantiate :premises (@p171) :args (@t271)) % 0.43/0.69 (step @p227 :rule cnf_or_pos :args (@t277)) % 0.43/0.69 (step @p228 :rule reordering :premises (@p227) :args ((or @t270 @t276 (not @t277)))) % 0.43/0.69 (step @p229 :rule chain_m_resolution :premises (@p228 @p220 @p226) :args (@t276 (@list true false) (@list @t270 @t277))) % 0.43/0.69 (step @p230 :rule cnf_or_pos :args (@t279)) % 0.43/0.69 (step @p231 :rule reordering :premises (@p230) :args ((or @t270 @t278 @t275 (not @t279)))) % 0.43/0.69 (step @p232 false :rule chain_m_resolution :premises (@p231 @p229 @p225 @p221 @p220) :args (false (@list true false false true) (@list @t275 @t272 @t279 @t270))) % 0.43/0.69 ) % 0.43/0.69 % SZS output end Proof % 0.43/0.69 % cvc5 exiting %------------------------------------------------------------------------------