%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU935^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 3.60s 3.77s % Output : Proof 3.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU935^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 06:17:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.60/3.77 SZS status Theorem for theBenchmark.p % 3.60/3.77 SZS output start Proof for theBenchmark.p % 3.60/3.77 Clause #0 (by assumption #[]): Eq % 3.60/3.77 (Not % 3.60/3.77 (∀ (F : a → b) (G : b → c), % 3.60/3.77 And (∀ (Y : b), Exists fun X => Eq (F X) Y) (∀ (Y : c), Exists fun X => Eq (G X) Y) → % 3.60/3.77 ∀ (Y : c), Exists fun X => Eq (G (F X)) Y)) % 3.60/3.77 True % 3.60/3.77 Clause #1 (by clausification #[0]): Eq % 3.60/3.77 (∀ (F : a → b) (G : b → c), % 3.60/3.77 And (∀ (Y : b), Exists fun X => Eq (F X) Y) (∀ (Y : c), Exists fun X => Eq (G X) Y) → % 3.60/3.77 ∀ (Y : c), Exists fun X => Eq (G (F X)) Y) % 3.60/3.77 False % 3.60/3.77 Clause #2 (by clausification #[1]): ∀ (a_1 : a → b), % 3.60/3.77 Eq % 3.60/3.77 (Not % 3.60/3.77 (∀ (G : b → c), % 3.60/3.77 And (∀ (Y : b), Exists fun X => Eq (skS.0 0 a_1 X) Y) (∀ (Y : c), Exists fun X => Eq (G X) Y) → % 3.60/3.77 ∀ (Y : c), Exists fun X => Eq (G (skS.0 0 a_1 X)) Y)) % 3.60/3.77 True % 3.60/3.77 Clause #3 (by clausification #[2]): ∀ (a_1 : a → b), % 3.60/3.77 Eq % 3.60/3.77 (∀ (G : b → c), % 3.60/3.77 And (∀ (Y : b), Exists fun X => Eq (skS.0 0 a_1 X) Y) (∀ (Y : c), Exists fun X => Eq (G X) Y) → % 3.60/3.77 ∀ (Y : c), Exists fun X => Eq (G (skS.0 0 a_1 X)) Y) % 3.60/3.77 False % 3.60/3.77 Clause #4 (by clausification #[3]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.60/3.77 Eq % 3.60/3.77 (Not % 3.60/3.77 (And (∀ (Y : b), Exists fun X => Eq (skS.0 0 a_1 X) Y) (∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 X) Y) → % 3.60/3.77 ∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 X)) Y)) % 3.60/3.77 True % 3.60/3.77 Clause #5 (by clausification #[4]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.60/3.77 Eq % 3.60/3.77 (And (∀ (Y : b), Exists fun X => Eq (skS.0 0 a_1 X) Y) (∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 X) Y) → % 3.60/3.77 ∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 X)) Y) % 3.60/3.77 False % 3.60/3.77 Clause #6 (by clausification #[5]): ∀ (a_1 : a → b) (a_2 : b → c), % 3.60/3.77 Eq (And (∀ (Y : b), Exists fun X => Eq (skS.0 0 a_1 X) Y) (∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 X) Y)) True % 3.60/3.77 Clause #7 (by clausification #[5]): ∀ (a_1 : a → b) (a_2 : b → c), Eq (∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 X)) Y) False % 3.60/3.77 Clause #8 (by clausification #[6]): ∀ (a_1 : a → b) (a_2 : b → c), Eq (∀ (Y : c), Exists fun X => Eq (skS.0 1 a_1 a_2 X) Y) True % 3.60/3.77 Clause #9 (by clausification #[6]): ∀ (a_1 : a → b), Eq (∀ (Y : b), Exists fun X => Eq (skS.0 0 a_1 X) Y) True % 3.60/3.77 Clause #10 (by clausification #[8]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : c), Eq (Exists fun X => Eq (skS.0 1 a_1 a_2 X) a_3) True % 3.60/3.77 Clause #11 (by clausification #[10]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : c) (a_4 : b), Eq (Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 a_4)) a_3) True % 3.60/3.77 Clause #12 (by clausification #[11]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : c) (a_4 : b), Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 a_4)) a_3 % 3.60/3.77 Clause #13 (by clausification #[9]): ∀ (a_1 : a → b) (a_2 : b), Eq (Exists fun X => Eq (skS.0 0 a_1 X) a_2) True % 3.60/3.77 Clause #14 (by clausification #[13]): ∀ (a_1 : a → b) (a_2 : b) (a_3 : a), Eq (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) a_2) True % 3.60/3.77 Clause #15 (by clausification #[14]): ∀ (a_1 : a → b) (a_2 : b) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) a_2 % 3.60/3.77 Clause #16 (by clausification #[7]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : c), % 3.60/3.77 Eq (Not (Exists fun X => Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 X)) (skS.0 4 a_1 a_2 a_3))) True % 3.60/3.77 Clause #17 (by clausification #[16]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : c), % 3.60/3.77 Eq (Exists fun X => Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 X)) (skS.0 4 a_1 a_2 a_3)) False % 3.60/3.77 Clause #18 (by clausification #[17]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : a) (a_4 : c), % 3.60/3.77 Eq (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 a_3)) (skS.0 4 a_1 a_2 a_4)) False % 3.60/3.77 Clause #19 (by clausification #[18]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : a) (a_4 : c), Ne (skS.0 1 a_1 a_2 (skS.0 0 a_1 a_3)) (skS.0 4 a_1 a_2 a_4) % 3.60/3.77 Clause #20 (by superposition #[19, 15]): ∀ (a_1 : a → b) (a_2 : b → c) (a_3 : b) (a_4 : c), Ne (skS.0 1 a_1 a_2 a_3) (skS.0 4 a_1 a_2 a_4) % 3.60/3.77 Clause #21 (by superposition #[20, 12]): ∀ (a_1 : c) (a_2 : a → b) (a_3 : b → c) (a_4 : c), Ne a_1 (skS.0 4 a_2 a_3 a_4) % 3.60/3.77 Clause #22 (by destructive equality resolution #[21]): False % 3.60/3.77 SZS output end Proof for theBenchmark.p 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