%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU941^5 : 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 08:02:40 PM UTC 2025 % Result : Theorem 3.58s 3.77s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU941^5 : TPTP v9.2.0. Released v4.0.0. % 0.14/0.14 % Command : duper %s % 0.14/0.35 % Computer : n017.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 06:29:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.58/3.77 SZS status Theorem for theBenchmark.p % 3.58/3.77 SZS output start Proof for theBenchmark.p % 3.58/3.77 Clause #0 (by assumption #[]): Eq % 3.58/3.77 (Not % 3.58/3.77 (∀ (F : a → b) (G : b → c), % 3.58/3.77 And (∀ (Xx Xy : a), Eq (F Xx) (F Xy) → Eq Xx Xy) (∀ (Xx Xy : b), Eq (G Xx) (G Xy) → Eq Xx Xy) → % 3.58/3.77 ∀ (Xx Xy : a), Eq (G (F Xx)) (G (F Xy)) → Eq Xx Xy)) % 3.58/3.77 True % 3.58/3.77 Clause #1 (by clausification #[0]): Eq % 3.58/3.77 (∀ (F : a → b) (G : b → c), % 3.58/3.77 And (∀ (Xx Xy : a), Eq (F Xx) (F Xy) → Eq Xx Xy) (∀ (Xx Xy : b), Eq (G Xx) (G Xy) → Eq Xx Xy) → % 3.58/3.77 ∀ (Xx Xy : a), Eq (G (F Xx)) (G (F Xy)) → Eq Xx Xy) % 3.58/3.77 False % 3.58/3.77 Clause #2 (by clausification #[1]): ∀ (a_1 : a → b), % 3.58/3.77 Eq % 3.58/3.77 (Not % 3.58/3.77 (∀ (G : b → c), % 3.58/3.77 And (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy) → Eq Xx Xy) % 3.58/3.77 (∀ (Xx Xy : b), Eq (G Xx) (G Xy) → Eq Xx Xy) → % 3.58/3.77 ∀ (Xx Xy : a), Eq (G (skS.0 0 a_1 Xx)) (G (skS.0 0 a_1 Xy)) → Eq Xx Xy)) % 3.58/3.77 True % 3.58/3.77 Clause #3 (by clausification #[2]): ∀ (a_1 : a → b), % 3.58/3.77 Eq % 3.58/3.77 (∀ (G : b → c), % 3.58/3.77 And (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy) → Eq Xx Xy) % 3.58/3.77 (∀ (Xx Xy : b), Eq (G Xx) (G Xy) → Eq Xx Xy) → % 3.58/3.77 ∀ (Xx Xy : a), Eq (G (skS.0 0 a_1 Xx)) (G (skS.0 0 a_1 Xy)) → Eq Xx Xy) % 3.58/3.77 False % 3.58/3.77 Clause #4 (by clausification #[3]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.58/3.77 Eq % 3.58/3.77 (Not % 3.58/3.77 (And (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy) → Eq Xx Xy) % 3.58/3.77 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy) → Eq Xx Xy) → % 3.58/3.77 ∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)) → Eq Xx Xy)) % 3.58/3.77 True % 3.58/3.77 Clause #5 (by clausification #[4]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.58/3.77 Eq % 3.58/3.77 (And (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy) → Eq Xx Xy) % 3.58/3.77 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy) → Eq Xx Xy) → % 3.58/3.77 ∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)) → Eq Xx Xy) % 3.58/3.77 False % 3.58/3.77 Clause #6 (by clausification #[5]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.58/3.77 Eq % 3.58/3.77 (And (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy) → Eq Xx Xy) % 3.58/3.77 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy) → Eq Xx Xy)) % 3.58/3.77 True % 3.58/3.77 Clause #7 (by clausification #[5]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.58/3.77 Eq (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)) → Eq Xx Xy) False % 3.58/3.77 Clause #8 (by clausification #[6]): ∀ (a_1 : a → b) (a_2 : b → c), Eq (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy) → Eq Xx Xy) True % 3.58/3.77 Clause #9 (by clausification #[6]): ∀ (a_1 : a → b), Eq (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy) → Eq Xx Xy) True % 3.58/3.77 Clause #10 (by clausification #[8]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : b), Eq (∀ (Xy : b), Eq (skS.0 1 a_1 a_2 a_3) (skS.0 1 a_1 a_2 Xy) → Eq a_3 Xy) True % 3.58/3.77 Clause #11 (by clausification #[10]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : b), Eq (Eq (skS.0 1 a_1 a_2 a_3) (skS.0 1 a_1 a_2 a_4) → Eq a_3 a_4) True % 3.58/3.77 Clause #12 (by clausification #[11]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : b), % 3.58/3.77 Or (Eq (Eq (skS.0 1 a_1 a_2 a_3) (skS.0 1 a_1 a_2 a_4)) False) (Eq (Eq a_3 a_4) True) % 3.58/3.77 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : b) (a_3 : a → b) (a_4 : b → c), Or (Eq (Eq a_1 a_2) True) (Ne (skS.0 1 a_3 a_4 a_1) (skS.0 1 a_3 a_4 a_2)) % 3.58/3.77 Clause #14 (by clausification #[13]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : b), Or (Ne (skS.0 1 a_1 a_2 a_3) (skS.0 1 a_1 a_2 a_4)) (Eq a_3 a_4) % 3.58/3.77 Clause #16 (by clausification #[9]): ∀ (a_1 : a → b) (a_2 : a), Eq (∀ (Xy : a), Eq (skS.0 0 a_1 a_2) (skS.0 0 a_1 Xy) → Eq a_2 Xy) True % 3.58/3.77 Clause #17 (by clausification #[16]): ∀ (a_1 : a → b) (a_2 a_3 : a), Eq (Eq (skS.0 0 a_1 a_2) (skS.0 0 a_1 a_3) → Eq a_2 a_3) True % 3.58/3.77 Clause #18 (by clausification #[17]): ∀ (a_1 : a → b) (a_2 a_3 : a), Or (Eq (Eq (skS.0 0 a_1 a_2) (skS.0 0 a_1 a_3)) False) (Eq (Eq a_2 a_3) True) % 3.58/3.77 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a) (a_3 : a → b), Or (Eq (Eq a_1 a_2) True) (Ne (skS.0 0 a_3 a_1) (skS.0 0 a_3 a_2)) % 3.63/3.79 Clause #20 (by clausification #[19]): ∀ (a_1 : a → b) (a_2 a_3 : a), Or (Ne (skS.0 0 a_1 a_2) (skS.0 0 a_1 a_3)) (Eq a_2 a_3) % 3.63/3.79 Clause #22 (by clausification #[7]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : a), % 3.63/3.79 Eq % 3.63/3.79 (Not % 3.63/3.79 (∀ (Xy : a), % 3.63/3.79 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)) → % 3.63/3.79 Eq (skS.0 2 a_1 a_2 a_3) Xy)) % 3.63/3.79 True % 3.63/3.79 Clause #23 (by clausification #[22]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : a), % 3.63/3.79 Eq % 3.63/3.79 (∀ (Xy : a), % 3.63/3.79 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)) → % 3.63/3.79 Eq (skS.0 2 a_1 a_2 a_3) Xy) % 3.63/3.79 False % 3.63/3.79 Clause #24 (by clausification #[23]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), % 3.63/3.79 Eq % 3.63/3.79 (Not % 3.63/3.79 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) % 3.63/3.79 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) → % 3.63/3.79 Eq (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) % 3.63/3.79 True % 3.63/3.79 Clause #25 (by clausification #[24]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), % 3.63/3.79 Eq % 3.63/3.79 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) % 3.63/3.79 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) → % 3.63/3.79 Eq (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) % 3.63/3.79 False % 3.63/3.79 Clause #26 (by clausification #[25]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), % 3.63/3.79 Eq % 3.63/3.79 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.63/3.79 True % 3.63/3.79 Clause #27 (by clausification #[25]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), Eq (Eq (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) False % 3.63/3.79 Clause #28 (by clausification #[26]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), % 3.63/3.79 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) % 3.63/3.79 Clause #29 (by superposition #[28, 14]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : a) (a_4 : b) (a_5 : a), % 3.63/3.79 Or (Ne (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) (skS.0 1 a_1 a_2 a_4)) % 3.63/3.79 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) a_4) % 3.63/3.79 Clause #31 (by clausification #[27]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), Ne (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) % 3.63/3.79 Clause #32 (by equality resolution #[29]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), % 3.63/3.79 Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) % 3.63/3.79 Clause #37 (by superposition #[32, 20]): ∀ (a_1 : a → b) (a_2 : a) (a_3 : b → c) (a_4 a_5 : a), % 3.63/3.79 Or (Ne (skS.0 0 a_1 a_2) (skS.0 0 a_1 (skS.0 2 a_1 a_3 a_4))) (Eq a_2 (skS.0 3 a_1 a_3 a_4 a_5)) % 3.63/3.79 Clause #38 (by equality resolution #[37]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 a_4 : a), Eq (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) % 3.63/3.79 Clause #40 (by forward contextual literal cutting #[38, 31]): False % 3.63/3.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------