%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU928^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:02:39 PM UTC 2025 % Result : Theorem 3.58s 3.81s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU928^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 06:25:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.58/3.81 SZS status Theorem for theBenchmark.p % 3.58/3.81 SZS output start Proof for theBenchmark.p % 3.58/3.81 Clause #0 (by assumption #[]): Eq % 3.58/3.81 (Not % 3.58/3.81 (∀ (F : Iota → Iota), % 3.58/3.81 (∀ (Xx Xy : Iota), Eq (F Xx) (F Xy) → Eq Xx Xy) → ∀ (Xx Xy : Iota), Eq (F (F Xx)) (F (F Xy)) → Eq Xx Xy)) % 3.58/3.81 True % 3.58/3.81 Clause #1 (by clausification #[0]): Eq % 3.58/3.81 (∀ (F : Iota → Iota), % 3.58/3.81 (∀ (Xx Xy : Iota), Eq (F Xx) (F Xy) → Eq Xx Xy) → ∀ (Xx Xy : Iota), Eq (F (F Xx)) (F (F Xy)) → Eq Xx Xy) % 3.58/3.81 False % 3.58/3.81 Clause #2 (by clausification #[1]): ∀ (a : Iota → Iota), % 3.58/3.81 Eq % 3.58/3.81 (Not % 3.58/3.81 ((∀ (Xx Xy : Iota), Eq (skS.0 0 a Xx) (skS.0 0 a Xy) → Eq Xx Xy) → % 3.58/3.81 ∀ (Xx Xy : Iota), Eq (skS.0 0 a (skS.0 0 a Xx)) (skS.0 0 a (skS.0 0 a Xy)) → Eq Xx Xy)) % 3.58/3.81 True % 3.58/3.81 Clause #3 (by clausification #[2]): ∀ (a : Iota → Iota), % 3.58/3.81 Eq % 3.58/3.81 ((∀ (Xx Xy : Iota), Eq (skS.0 0 a Xx) (skS.0 0 a Xy) → Eq Xx Xy) → % 3.58/3.81 ∀ (Xx Xy : Iota), Eq (skS.0 0 a (skS.0 0 a Xx)) (skS.0 0 a (skS.0 0 a Xy)) → Eq Xx Xy) % 3.58/3.81 False % 3.58/3.81 Clause #4 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (∀ (Xx Xy : Iota), Eq (skS.0 0 a Xx) (skS.0 0 a Xy) → Eq Xx Xy) True % 3.58/3.81 Clause #5 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (∀ (Xx Xy : Iota), Eq (skS.0 0 a (skS.0 0 a Xx)) (skS.0 0 a (skS.0 0 a Xy)) → Eq Xx Xy) False % 3.58/3.81 Clause #6 (by clausification #[4]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (∀ (Xy : Iota), Eq (skS.0 0 a a_1) (skS.0 0 a Xy) → Eq a_1 Xy) True % 3.58/3.81 Clause #7 (by clausification #[6]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (Eq (skS.0 0 a a_1) (skS.0 0 a a_2) → Eq a_1 a_2) True % 3.58/3.81 Clause #8 (by clausification #[7]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Eq (Eq (skS.0 0 a a_1) (skS.0 0 a a_2)) False) (Eq (Eq a_1 a_2) True) % 3.58/3.81 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota), Or (Eq (Eq a a_1) True) (Ne (skS.0 0 a_2 a) (skS.0 0 a_2 a_1)) % 3.58/3.81 Clause #10 (by clausification #[9]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Ne (skS.0 0 a a_1) (skS.0 0 a a_2)) (Eq a_1 a_2) % 3.58/3.81 Clause #12 (by clausification #[5]): ∀ (a : Iota → Iota) (a_1 : Iota), % 3.58/3.81 Eq % 3.58/3.81 (Not (∀ (Xy : Iota), Eq (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a (skS.0 0 a Xy)) → Eq (skS.0 1 a a_1) Xy)) % 3.58/3.81 True % 3.58/3.81 Clause #13 (by clausification #[12]): ∀ (a : Iota → Iota) (a_1 : Iota), % 3.58/3.81 Eq (∀ (Xy : Iota), Eq (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a (skS.0 0 a Xy)) → Eq (skS.0 1 a a_1) Xy) % 3.58/3.81 False % 3.58/3.81 Clause #14 (by clausification #[13]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), % 3.58/3.81 Eq % 3.58/3.81 (Not % 3.58/3.81 (Eq (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a (skS.0 0 a (skS.0 2 a a_1 a_2))) → % 3.58/3.81 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.58/3.81 True % 3.58/3.81 Clause #15 (by clausification #[14]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), % 3.58/3.81 Eq % 3.58/3.81 (Eq (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a (skS.0 0 a (skS.0 2 a a_1 a_2))) → % 3.58/3.81 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.58/3.81 False % 3.58/3.81 Clause #16 (by clausification #[15]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), % 3.58/3.81 Eq (Eq (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a (skS.0 0 a (skS.0 2 a a_1 a_2)))) True % 3.58/3.81 Clause #17 (by clausification #[15]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 3.58/3.81 Clause #18 (by clausification #[16]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), % 3.58/3.81 Eq (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a (skS.0 0 a (skS.0 2 a a_1 a_2))) % 3.58/3.81 Clause #19 (by superposition #[18, 10]): ∀ (a : Iota → Iota) (a_1 a_2 a_3 : Iota), % 3.58/3.81 Or (Ne (skS.0 0 a (skS.0 0 a (skS.0 1 a a_1))) (skS.0 0 a a_2)) (Eq (skS.0 0 a (skS.0 2 a a_1 a_3)) a_2) % 3.58/3.81 Clause #21 (by clausification #[17]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Ne (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) % 3.58/3.81 Clause #22 (by equality resolution #[19]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 0 a (skS.0 1 a a_1)) % 3.58/3.81 Clause #27 (by superposition #[22, 10]): ∀ (a : Iota → Iota) (a_1 a_2 a_3 : Iota), % 3.58/3.81 Or (Ne (skS.0 0 a a_1) (skS.0 0 a (skS.0 1 a a_2))) (Eq a_1 (skS.0 2 a a_2 a_3)) % 3.58/3.81 Clause #28 (by equality resolution #[27]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) % 3.58/3.81 Clause #30 (by forward contextual literal cutting #[28, 21]): False % 3.58/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------