%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM411+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 : Fri Oct 3 07:56:26 PM UTC 2025 % Result : Theorem 8.60s 8.79s % Output : Proof 8.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM411+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 08:45:53 EDT 2025 % 0.13/0.35 % CPUTime : % 8.60/8.79 SZS status Theorem for theBenchmark.p % 8.60/8.79 SZS output start Proof for theBenchmark.p % 8.60/8.79 Clause #7 (by assumption #[]): Eq % 8.60/8.79 (∀ (A B : Iota), % 8.60/8.79 And (And (relation B) (function B)) (transfinite_sequence B) → % 8.60/8.79 Iff (transfinite_sequence_of B A) (subset (relation_rng B) A)) % 8.60/8.79 True % 8.60/8.79 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), transfinite_sequence_of B A → And (And (relation B) (function B)) (transfinite_sequence B)) True % 8.60/8.79 Clause #34 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True % 8.60/8.79 Clause #37 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset A B → ∀ (C : Iota), transfinite_sequence_of C A → transfinite_sequence_of C B)) True % 8.60/8.79 Clause #97 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True % 8.60/8.79 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True % 8.60/8.79 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 8.60/8.79 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True) % 8.60/8.79 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False)) % 8.60/8.79 Clause #128 (by clausification #[7]): ∀ (a : Iota), % 8.60/8.79 Eq % 8.60/8.79 (∀ (B : Iota), % 8.60/8.79 And (And (relation B) (function B)) (transfinite_sequence B) → % 8.60/8.79 Iff (transfinite_sequence_of B a) (subset (relation_rng B) a)) % 8.60/8.79 True % 8.60/8.79 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota), % 8.60/8.79 Eq % 8.60/8.79 (And (And (relation a) (function a)) (transfinite_sequence a) → % 8.60/8.79 Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) % 8.60/8.79 True % 8.60/8.79 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota), % 8.60/8.79 Or (Eq (And (And (relation a) (function a)) (transfinite_sequence a)) False) % 8.60/8.79 (Eq (Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) True) % 8.60/8.79 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota), % 8.60/8.79 Or (Eq (Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) True) % 8.60/8.79 (Or (Eq (And (relation a) (function a)) False) (Eq (transfinite_sequence a) False)) % 8.60/8.79 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), % 8.60/8.79 Or (Eq (And (relation a) (function a)) False) % 8.60/8.79 (Or (Eq (transfinite_sequence a) False) % 8.60/8.79 (Or (Eq (transfinite_sequence_of a a_1) True) (Eq (subset (relation_rng a) a_1) False))) % 8.60/8.79 Clause #133 (by clausification #[131]): ∀ (a a_1 : Iota), % 8.60/8.79 Or (Eq (And (relation a) (function a)) False) % 8.60/8.79 (Or (Eq (transfinite_sequence a) False) % 8.60/8.79 (Or (Eq (transfinite_sequence_of a a_1) False) (Eq (subset (relation_rng a) a_1) True))) % 8.60/8.79 Clause #134 (by clausification #[132]): ∀ (a a_1 : Iota), % 8.60/8.79 Or (Eq (transfinite_sequence a) False) % 8.60/8.79 (Or (Eq (transfinite_sequence_of a a_1) True) % 8.60/8.79 (Or (Eq (subset (relation_rng a) a_1) False) (Or (Eq (relation a) False) (Eq (function a) False)))) % 8.60/8.79 Clause #150 (by clausification #[8]): ∀ (a : Iota), % 8.60/8.79 Eq (∀ (B : Iota), transfinite_sequence_of B a → And (And (relation B) (function B)) (transfinite_sequence B)) True % 8.60/8.79 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (transfinite_sequence_of a a_1 → And (And (relation a) (function a)) (transfinite_sequence a)) True % 8.60/8.79 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota), % 8.60/8.79 Or (Eq (transfinite_sequence_of a a_1) False) (Eq (And (And (relation a) (function a)) (transfinite_sequence a)) True) % 8.60/8.79 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), Or (Eq (transfinite_sequence_of a a_1) False) (Eq (transfinite_sequence a) True) % 8.60/8.79 Clause #154 (by clausification #[152]): ∀ (a a_1 : Iota), Or (Eq (transfinite_sequence_of a a_1) False) (Eq (And (relation a) (function a)) True) % 8.60/8.79 Clause #208 (by clausification #[37]): Eq (∀ (A B : Iota), subset A B → ∀ (C : Iota), transfinite_sequence_of C A → transfinite_sequence_of C B) False % 8.60/8.79 Clause #209 (by clausification #[208]): ∀ (a : Iota), % 8.60/8.79 Eq % 8.60/8.79 (Not % 8.60/8.79 (∀ (B : Iota), % 8.60/8.79 subset (skS.0 9 a) B → ∀ (C : Iota), transfinite_sequence_of C (skS.0 9 a) → transfinite_sequence_of C B)) % 8.60/8.81 True % 8.60/8.81 Clause #210 (by clausification #[209]): ∀ (a : Iota), % 8.60/8.81 Eq % 8.60/8.81 (∀ (B : Iota), % 8.60/8.81 subset (skS.0 9 a) B → ∀ (C : Iota), transfinite_sequence_of C (skS.0 9 a) → transfinite_sequence_of C B) % 8.60/8.81 False % 8.60/8.81 Clause #211 (by clausification #[210]): ∀ (a a_1 : Iota), % 8.60/8.81 Eq % 8.60/8.81 (Not % 8.60/8.81 (subset (skS.0 9 a) (skS.0 10 a a_1) → % 8.60/8.81 ∀ (C : Iota), transfinite_sequence_of C (skS.0 9 a) → transfinite_sequence_of C (skS.0 10 a a_1))) % 8.60/8.81 True % 8.60/8.81 Clause #212 (by clausification #[211]): ∀ (a a_1 : Iota), % 8.60/8.81 Eq % 8.60/8.81 (subset (skS.0 9 a) (skS.0 10 a a_1) → % 8.60/8.81 ∀ (C : Iota), transfinite_sequence_of C (skS.0 9 a) → transfinite_sequence_of C (skS.0 10 a a_1)) % 8.60/8.81 False % 8.60/8.81 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), Eq (subset (skS.0 9 a) (skS.0 10 a a_1)) True % 8.60/8.81 Clause #214 (by clausification #[212]): ∀ (a a_1 : Iota), % 8.60/8.81 Eq (∀ (C : Iota), transfinite_sequence_of C (skS.0 9 a) → transfinite_sequence_of C (skS.0 10 a a_1)) False % 8.60/8.81 Clause #239 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (transfinite_sequence_of a a_1) False) (Eq (function a) True) % 8.60/8.81 Clause #240 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (transfinite_sequence_of a a_1) False) (Eq (relation a) True) % 8.60/8.81 Clause #320 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), % 8.60/8.81 Eq % 8.60/8.81 (Not % 8.60/8.81 (transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 9 a) → % 8.60/8.81 transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 10 a a_1))) % 8.60/8.81 True % 8.60/8.81 Clause #321 (by clausification #[320]): ∀ (a a_1 a_2 : Iota), % 8.60/8.81 Eq % 8.60/8.81 (transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 9 a) → % 8.60/8.81 transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 10 a a_1)) % 8.60/8.81 False % 8.60/8.81 Clause #322 (by clausification #[321]): ∀ (a a_1 a_2 : Iota), Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 9 a)) True % 8.60/8.81 Clause #323 (by clausification #[321]): ∀ (a a_1 a_2 : Iota), Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 10 a a_1)) False % 8.60/8.81 Clause #324 (by superposition #[322, 153]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (transfinite_sequence (skS.0 18 a a_1 a_2)) True) % 8.60/8.81 Clause #325 (by superposition #[322, 239]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (function (skS.0 18 a a_1 a_2)) True) % 8.60/8.81 Clause #326 (by superposition #[322, 240]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (relation (skS.0 18 a a_1 a_2)) True) % 8.60/8.81 Clause #327 (by clausification #[326]): ∀ (a a_1 a_2 : Iota), Eq (relation (skS.0 18 a a_1 a_2)) True % 8.60/8.81 Clause #329 (by clausification #[325]): ∀ (a a_1 a_2 : Iota), Eq (function (skS.0 18 a a_1 a_2)) True % 8.60/8.81 Clause #339 (by clausification #[324]): ∀ (a a_1 a_2 : Iota), Eq (transfinite_sequence (skS.0 18 a a_1 a_2)) True % 8.60/8.81 Clause #340 (by superposition #[339, 134]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.81 Or (Eq True False) % 8.60/8.81 (Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) True) % 8.60/8.81 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) False) % 8.60/8.81 (Or (Eq (relation (skS.0 18 a a_1 a_2)) False) (Eq (function (skS.0 18 a a_1 a_2)) False)))) % 8.60/8.81 Clause #348 (by clausification #[133]): ∀ (a a_1 : Iota), % 8.60/8.81 Or (Eq (transfinite_sequence a) False) % 8.60/8.81 (Or (Eq (transfinite_sequence_of a a_1) False) % 8.60/8.81 (Or (Eq (subset (relation_rng a) a_1) True) (Or (Eq (relation a) False) (Eq (function a) False)))) % 8.60/8.81 Clause #351 (by superposition #[348, 339]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.81 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) False) % 8.60/8.81 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) % 8.60/8.81 (Or (Eq (relation (skS.0 18 a a_1 a_2)) False) (Or (Eq (function (skS.0 18 a a_1 a_2)) False) (Eq False True)))) % 8.60/8.81 Clause #606 (by clausification #[340]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.81 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) True) % 8.60/8.81 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) False) % 8.60/8.81 (Or (Eq (relation (skS.0 18 a a_1 a_2)) False) (Eq (function (skS.0 18 a a_1 a_2)) False))) % 8.60/8.81 Clause #607 (by forward demodulation #[606, 327]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.81 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) True) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) False) % 8.60/8.83 (Or (Eq True False) (Eq (function (skS.0 18 a a_1 a_2)) False))) % 8.60/8.83 Clause #608 (by clausification #[607]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) True) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) False) (Eq (function (skS.0 18 a a_1 a_2)) False)) % 8.60/8.83 Clause #609 (by forward demodulation #[608, 329]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) True) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) False) (Eq True False)) % 8.60/8.83 Clause #610 (by clausification #[609]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) True) % 8.60/8.83 (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) False) % 8.60/8.83 Clause #681 (by clausification #[351]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) False) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) % 8.60/8.83 (Or (Eq (relation (skS.0 18 a a_1 a_2)) False) (Eq (function (skS.0 18 a a_1 a_2)) False))) % 8.60/8.83 Clause #682 (by forward demodulation #[681, 327]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) False) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) % 8.60/8.83 (Or (Eq True False) (Eq (function (skS.0 18 a a_1 a_2)) False))) % 8.60/8.83 Clause #683 (by clausification #[682]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) False) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) (Eq (function (skS.0 18 a a_1 a_2)) False)) % 8.60/8.83 Clause #684 (by forward demodulation #[683, 329]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) False) % 8.60/8.83 (Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) (Eq True False)) % 8.60/8.83 Clause #685 (by clausification #[684]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) a_3) False) % 8.60/8.83 (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) % 8.60/8.83 Clause #686 (by superposition #[685, 322]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) (skS.0 9 a)) True) (Eq False True) % 8.60/8.83 Clause #792 (by clausification #[686]): ∀ (a a_1 a_2 : Iota), Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) (skS.0 9 a)) True % 8.60/8.83 Clause #794 (by superposition #[792, 101]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) (Or (Eq True False) (Eq (subset (skS.0 9 a) a_3) False)) % 8.60/8.83 Clause #899 (by clausification #[794]): ∀ (a a_1 a_2 a_3 : Iota), % 8.60/8.83 Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) a_3) True) (Eq (subset (skS.0 9 a) a_3) False) % 8.60/8.83 Clause #900 (by superposition #[899, 213]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) (skS.0 10 a a_3)) True) (Eq False True) % 8.60/8.83 Clause #901 (by clausification #[900]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (relation_rng (skS.0 18 a a_1 a_2)) (skS.0 10 a a_3)) True % 8.60/8.83 Clause #902 (by superposition #[901, 610]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 10 a a_3)) True) (Eq True False) % 8.60/8.83 Clause #917 (by clausification #[902]): ∀ (a a_1 a_2 a_3 : Iota), Eq (transfinite_sequence_of (skS.0 18 a a_1 a_2) (skS.0 10 a a_3)) True % 8.60/8.83 Clause #918 (by superposition #[917, 323]): Eq True False % 8.60/8.83 Clause #920 (by clausification #[918]): False % 8.60/8.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------