%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU275+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:01:16 PM UTC 2025 % Result : Theorem 3.70s 3.89s % Output : Proof 3.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU275+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 06:14:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.70/3.89 SZS status Theorem for theBenchmark.p % 3.70/3.89 SZS output start Proof for theBenchmark.p % 3.70/3.89 Clause #2 (by assumption #[]): Eq % 3.70/3.89 (∀ (A : Iota), % 3.70/3.89 relation A → % 3.70/3.89 Iff (well_ordering A) % 3.70/3.89 (And (And (And (And (reflexive A) (transitive A)) (antisymmetric A)) (connected A)) (well_founded_relation A))) % 3.70/3.89 True % 3.70/3.89 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), relation (inclusion_relation A)) True % 3.70/3.89 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), reflexive (inclusion_relation A)) True % 3.70/3.89 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), transitive (inclusion_relation A)) True % 3.70/3.89 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), ordinal A → connected (inclusion_relation A)) True % 3.70/3.89 Clause #8 (by assumption #[]): Eq (∀ (A : Iota), antisymmetric (inclusion_relation A)) True % 3.70/3.89 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), ordinal A → well_founded_relation (inclusion_relation A)) True % 3.70/3.89 Clause #10 (by assumption #[]): Eq (Not (∀ (A : Iota), ordinal A → well_ordering (inclusion_relation A))) True % 3.70/3.89 Clause #11 (by clausification #[8]): ∀ (a : Iota), Eq (antisymmetric (inclusion_relation a)) True % 3.70/3.89 Clause #12 (by clausification #[6]): ∀ (a : Iota), Eq (transitive (inclusion_relation a)) True % 3.70/3.89 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (relation (inclusion_relation a)) True % 3.70/3.89 Clause #14 (by clausification #[5]): ∀ (a : Iota), Eq (reflexive (inclusion_relation a)) True % 3.70/3.89 Clause #22 (by clausification #[7]): ∀ (a : Iota), Eq (ordinal a → connected (inclusion_relation a)) True % 3.70/3.89 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (connected (inclusion_relation a)) True) % 3.70/3.89 Clause #24 (by clausification #[9]): ∀ (a : Iota), Eq (ordinal a → well_founded_relation (inclusion_relation a)) True % 3.70/3.89 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (well_founded_relation (inclusion_relation a)) True) % 3.70/3.89 Clause #26 (by clausification #[10]): Eq (∀ (A : Iota), ordinal A → well_ordering (inclusion_relation A)) False % 3.70/3.89 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 0 a) → well_ordering (inclusion_relation (skS.0 0 a)))) True % 3.70/3.89 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (ordinal (skS.0 0 a) → well_ordering (inclusion_relation (skS.0 0 a))) False % 3.70/3.89 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (ordinal (skS.0 0 a)) True % 3.70/3.89 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (well_ordering (inclusion_relation (skS.0 0 a))) False % 3.70/3.89 Clause #32 (by superposition #[29, 23]): ∀ (a : Iota), Or (Eq True False) (Eq (connected (inclusion_relation (skS.0 0 a))) True) % 3.70/3.89 Clause #34 (by superposition #[29, 25]): ∀ (a : Iota), Or (Eq True False) (Eq (well_founded_relation (inclusion_relation (skS.0 0 a))) True) % 3.70/3.89 Clause #35 (by clausification #[2]): ∀ (a : Iota), % 3.70/3.89 Eq % 3.70/3.89 (relation a → % 3.70/3.89 Iff (well_ordering a) % 3.70/3.89 (And (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) (well_founded_relation a))) % 3.70/3.89 True % 3.70/3.89 Clause #36 (by clausification #[35]): ∀ (a : Iota), % 3.70/3.89 Or (Eq (relation a) False) % 3.70/3.89 (Eq % 3.70/3.89 (Iff (well_ordering a) % 3.70/3.89 (And (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) (well_founded_relation a))) % 3.70/3.89 True) % 3.70/3.89 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 3.70/3.89 Or (Eq (relation a) False) % 3.70/3.89 (Or (Eq (well_ordering a) True) % 3.70/3.89 (Eq (And (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) (well_founded_relation a)) % 3.70/3.89 False)) % 3.70/3.89 Clause #39 (by clausification #[37]): ∀ (a : Iota), % 3.70/3.89 Or (Eq (relation a) False) % 3.70/3.89 (Or (Eq (well_ordering a) True) % 3.70/3.89 (Or (Eq (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) False) % 3.70/3.89 (Eq (well_founded_relation a) False))) % 3.70/3.89 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 3.70/3.89 Or (Eq (relation a) False) % 3.70/3.89 (Or (Eq (well_ordering a) True) % 3.70/3.89 (Or (Eq (well_founded_relation a) False) % 3.70/3.89 (Or (Eq (And (And (reflexive a) (transitive a)) (antisymmetric a)) False) (Eq (connected a) False)))) % 3.70/3.89 Clause #41 (by clausification #[40]): ∀ (a : Iota), % 3.70/3.89 Or (Eq (relation a) False) % 3.70/3.91 (Or (Eq (well_ordering a) True) % 3.70/3.91 (Or (Eq (well_founded_relation a) False) % 3.70/3.91 (Or (Eq (connected a) False) (Or (Eq (And (reflexive a) (transitive a)) False) (Eq (antisymmetric a) False))))) % 3.70/3.91 Clause #42 (by clausification #[41]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (relation a) False) % 3.70/3.91 (Or (Eq (well_ordering a) True) % 3.70/3.91 (Or (Eq (well_founded_relation a) False) % 3.70/3.91 (Or (Eq (connected a) False) % 3.70/3.91 (Or (Eq (antisymmetric a) False) (Or (Eq (reflexive a) False) (Eq (transitive a) False)))))) % 3.70/3.91 Clause #43 (by superposition #[42, 13]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (antisymmetric (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (reflexive (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (transitive (inclusion_relation a)) False) (Eq False True)))))) % 3.70/3.91 Clause #47 (by clausification #[32]): ∀ (a : Iota), Eq (connected (inclusion_relation (skS.0 0 a))) True % 3.70/3.91 Clause #48 (by clausification #[34]): ∀ (a : Iota), Eq (well_founded_relation (inclusion_relation (skS.0 0 a))) True % 3.70/3.91 Clause #65 (by clausification #[43]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (antisymmetric (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (reflexive (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False))))) % 3.70/3.91 Clause #66 (by forward demodulation #[65, 11]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq True False) % 3.70/3.91 (Or (Eq (reflexive (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False))))) % 3.70/3.91 Clause #67 (by clausification #[66]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (reflexive (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False)))) % 3.70/3.91 Clause #68 (by forward demodulation #[67, 14]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq True False) (Eq (transitive (inclusion_relation a)) False)))) % 3.70/3.91 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False))) % 3.70/3.91 Clause #70 (by forward demodulation #[69, 12]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) % 3.70/3.91 (Or (Eq (connected (inclusion_relation a)) False) (Eq True False))) % 3.70/3.91 Clause #71 (by clausification #[70]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation a)) True) % 3.70/3.91 (Or (Eq (well_founded_relation (inclusion_relation a)) False) (Eq (connected (inclusion_relation a)) False)) % 3.70/3.91 Clause #72 (by superposition #[71, 48]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation (skS.0 0 a))) True) % 3.70/3.91 (Or (Eq (connected (inclusion_relation (skS.0 0 a))) False) (Eq False True)) % 3.70/3.91 Clause #82 (by clausification #[72]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (well_ordering (inclusion_relation (skS.0 0 a))) True) (Eq (connected (inclusion_relation (skS.0 0 a))) False) % 3.70/3.91 Clause #83 (by forward demodulation #[82, 30]): ∀ (a : Iota), Or (Eq False True) (Eq (connected (inclusion_relation (skS.0 0 a))) False) % 3.70/3.91 Clause #84 (by clausification #[83]): ∀ (a : Iota), Eq (connected (inclusion_relation (skS.0 0 a))) False % 3.70/3.91 Clause #85 (by superposition #[84, 47]): Eq False True % 3.70/3.91 Clause #86 (by clausification #[85]): False % 3.70/3.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------