%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM410+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 7.34s 7.55s % Output : Proof 7.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM410+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 06:50:38 EDT 2025 % 0.14/0.34 % CPUTime : % 7.34/7.55 SZS status Theorem for theBenchmark.p % 7.34/7.55 SZS output start Proof for theBenchmark.p % 7.34/7.55 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), And (relation A) (function A) → Iff (transfinite_sequence A) (ordinal (relation_dom A))) True % 7.34/7.55 Clause #8 (by assumption #[]): Eq % 7.34/7.55 (∀ (A B : Iota), % 7.34/7.55 And (And (relation B) (function B)) (transfinite_sequence B) → % 7.34/7.55 Iff (transfinite_sequence_of B A) (subset (relation_rng B) A)) % 7.34/7.55 True % 7.34/7.55 Clause #35 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 7.34/7.55 Clause #39 (by assumption #[]): Eq % 7.34/7.55 (Not % 7.34/7.55 (∀ (A : Iota), % 7.34/7.55 And (relation A) (function A) → ordinal (relation_dom A) → transfinite_sequence_of A (relation_rng A))) % 7.34/7.55 True % 7.34/7.55 Clause #64 (by clausification #[35]): ∀ (a : Iota), Eq (Iota → subset a a) True % 7.34/7.55 Clause #65 (by clausification #[64]): ∀ (a : Iota), Iota → Eq (subset a a) True % 7.34/7.55 Clause #132 (by clausification #[7]): ∀ (a : Iota), Eq (And (relation a) (function a) → Iff (transfinite_sequence a) (ordinal (relation_dom a))) True % 7.34/7.55 Clause #133 (by clausification #[132]): ∀ (a : Iota), % 7.34/7.55 Or (Eq (And (relation a) (function a)) False) (Eq (Iff (transfinite_sequence a) (ordinal (relation_dom a))) True) % 7.34/7.55 Clause #134 (by clausification #[133]): ∀ (a : Iota), % 7.34/7.55 Or (Eq (Iff (transfinite_sequence a) (ordinal (relation_dom a))) True) % 7.34/7.55 (Or (Eq (relation a) False) (Eq (function a) False)) % 7.34/7.55 Clause #135 (by clausification #[134]): ∀ (a : Iota), % 7.34/7.55 Or (Eq (relation a) False) % 7.34/7.55 (Or (Eq (function a) False) (Or (Eq (transfinite_sequence a) True) (Eq (ordinal (relation_dom a)) False))) % 7.34/7.55 Clause #152 (by clausification #[8]): ∀ (a : Iota), % 7.34/7.55 Eq % 7.34/7.55 (∀ (B : Iota), % 7.34/7.55 And (And (relation B) (function B)) (transfinite_sequence B) → % 7.34/7.55 Iff (transfinite_sequence_of B a) (subset (relation_rng B) a)) % 7.34/7.55 True % 7.34/7.55 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), % 7.34/7.55 Eq % 7.34/7.55 (And (And (relation a) (function a)) (transfinite_sequence a) → % 7.34/7.55 Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) % 7.34/7.55 True % 7.34/7.55 Clause #154 (by clausification #[153]): ∀ (a a_1 : Iota), % 7.34/7.55 Or (Eq (And (And (relation a) (function a)) (transfinite_sequence a)) False) % 7.34/7.55 (Eq (Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) True) % 7.34/7.55 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota), % 7.34/7.55 Or (Eq (Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) True) % 7.34/7.55 (Or (Eq (And (relation a) (function a)) False) (Eq (transfinite_sequence a) False)) % 7.34/7.55 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota), % 7.34/7.55 Or (Eq (And (relation a) (function a)) False) % 7.34/7.55 (Or (Eq (transfinite_sequence a) False) % 7.34/7.55 (Or (Eq (transfinite_sequence_of a a_1) True) (Eq (subset (relation_rng a) a_1) False))) % 7.34/7.55 Clause #158 (by clausification #[156]): ∀ (a a_1 : Iota), % 7.34/7.55 Or (Eq (transfinite_sequence a) False) % 7.34/7.55 (Or (Eq (transfinite_sequence_of a a_1) True) % 7.34/7.55 (Or (Eq (subset (relation_rng a) a_1) False) (Or (Eq (relation a) False) (Eq (function a) False)))) % 7.34/7.55 Clause #160 (by clausification #[39]): Eq (∀ (A : Iota), And (relation A) (function A) → ordinal (relation_dom A) → transfinite_sequence_of A (relation_rng A)) % 7.34/7.55 False % 7.34/7.55 Clause #161 (by clausification #[160]): ∀ (a : Iota), % 7.34/7.55 Eq % 7.34/7.55 (Not % 7.34/7.55 (And (relation (skS.0 5 a)) (function (skS.0 5 a)) → % 7.34/7.55 ordinal (relation_dom (skS.0 5 a)) → transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a)))) % 7.34/7.55 True % 7.34/7.55 Clause #162 (by clausification #[161]): ∀ (a : Iota), % 7.34/7.55 Eq % 7.34/7.55 (And (relation (skS.0 5 a)) (function (skS.0 5 a)) → % 7.34/7.55 ordinal (relation_dom (skS.0 5 a)) → transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) % 7.34/7.55 False % 7.34/7.55 Clause #163 (by clausification #[162]): ∀ (a : Iota), Eq (And (relation (skS.0 5 a)) (function (skS.0 5 a))) True % 7.34/7.55 Clause #164 (by clausification #[162]): ∀ (a : Iota), % 7.34/7.55 Eq (ordinal (relation_dom (skS.0 5 a)) → transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) False % 7.34/7.55 Clause #165 (by clausification #[163]): ∀ (a : Iota), Eq (function (skS.0 5 a)) True % 7.34/7.55 Clause #166 (by clausification #[163]): ∀ (a : Iota), Eq (relation (skS.0 5 a)) True % 7.34/7.55 Clause #171 (by superposition #[166, 135]): ∀ (a : Iota), % 7.34/7.57 Or (Eq True False) % 7.34/7.57 (Or (Eq (function (skS.0 5 a)) False) % 7.34/7.57 (Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False))) % 7.34/7.57 Clause #493 (by clausification #[164]): ∀ (a : Iota), Eq (ordinal (relation_dom (skS.0 5 a))) True % 7.34/7.57 Clause #494 (by clausification #[164]): ∀ (a : Iota), Eq (transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) False % 7.34/7.57 Clause #548 (by clausification #[171]): ∀ (a : Iota), % 7.34/7.57 Or (Eq (function (skS.0 5 a)) False) % 7.34/7.57 (Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False)) % 7.34/7.57 Clause #549 (by forward demodulation #[548, 165]): ∀ (a : Iota), % 7.34/7.57 Or (Eq True False) (Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False)) % 7.34/7.57 Clause #550 (by clausification #[549]): ∀ (a : Iota), Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False) % 7.34/7.57 Clause #551 (by superposition #[550, 493]): ∀ (a : Iota), Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq False True) % 7.34/7.57 Clause #552 (by clausification #[551]): ∀ (a : Iota), Eq (transfinite_sequence (skS.0 5 a)) True % 7.34/7.57 Clause #554 (by superposition #[552, 158]): ∀ (a a_1 : Iota), % 7.34/7.57 Or (Eq True False) % 7.34/7.57 (Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) % 7.34/7.57 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) % 7.34/7.57 (Or (Eq (relation (skS.0 5 a)) False) (Eq (function (skS.0 5 a)) False)))) % 7.34/7.57 Clause #849 (by clausification #[554]): ∀ (a a_1 : Iota), % 7.34/7.57 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) % 7.34/7.57 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) % 7.34/7.57 (Or (Eq (relation (skS.0 5 a)) False) (Eq (function (skS.0 5 a)) False))) % 7.34/7.57 Clause #850 (by forward demodulation #[849, 166]): ∀ (a a_1 : Iota), % 7.34/7.57 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) % 7.34/7.57 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) (Or (Eq True False) (Eq (function (skS.0 5 a)) False))) % 7.34/7.57 Clause #851 (by clausification #[850]): ∀ (a a_1 : Iota), % 7.34/7.57 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) % 7.34/7.57 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) (Eq (function (skS.0 5 a)) False)) % 7.34/7.57 Clause #852 (by forward demodulation #[851, 165]): ∀ (a a_1 : Iota), % 7.34/7.57 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) % 7.34/7.57 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) (Eq True False)) % 7.34/7.57 Clause #853 (by clausification #[852]): ∀ (a a_1 : Iota), % 7.34/7.57 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) % 7.34/7.57 Clause #854 (by superposition #[853, 65]): ∀ (a : Iota), Or (Eq (transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) True) (Eq False True) % 7.34/7.57 Clause #926 (by clausification #[854]): ∀ (a : Iota), Eq (transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) True % 7.34/7.57 Clause #927 (by superposition #[926, 494]): Eq True False % 7.34/7.57 Clause #932 (by clausification #[927]): False % 7.34/7.57 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------