%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWV447^1 : TPTP v9.2.0. Released v3.7.0. % 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 08:05:07 PM UTC 2025 % Result : Theorem 16.84s 17.03s % Output : Proof 16.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWV447^1 : TPTP v9.2.0. Released v3.7.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n021.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 : Thu Oct 2 13:10:53 EDT 2025 % 0.14/0.34 % CPUTime : % 16.84/17.03 SZS status Theorem for theBenchmark.p % 16.84/17.03 SZS output start Proof for theBenchmark.p % 16.84/17.03 Clause #0 (by assumption #[]): Eq (∀ (F : Iota → Iota), Eq (map F nil) nil) True % 16.84/17.03 Clause #1 (by assumption #[]): Eq (∀ (F : Iota → Iota) (X Y : Iota), Eq (map F (cons X Y)) (cons (F X) (map F Y))) True % 16.84/17.03 Clause #2 (by assumption #[]): Eq (Not (∀ (A : Iota), Eq (map (fun X => X) (cons A nil)) (cons A nil))) True % 16.84/17.03 Clause #3 (by clausification #[0]): ∀ (a : Iota → Iota), Eq (Eq (map a nil) nil) True % 16.84/17.03 Clause #4 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (map a nil) nil % 16.84/17.03 Clause #5 (by clausification #[2]): Eq (∀ (A : Iota), Eq (map (fun X => X) (cons A nil)) (cons A nil)) False % 16.84/17.03 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (Eq (map (fun X => X) (cons (skS.0 0 a) nil)) (cons (skS.0 0 a) nil))) True % 16.84/17.03 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (map (fun X => X) (cons (skS.0 0 a) nil)) (cons (skS.0 0 a) nil)) False % 16.84/17.03 Clause #8 (by clausification #[7]): ∀ (a : Iota), Ne (map (fun X => X) (cons (skS.0 0 a) nil)) (cons (skS.0 0 a) nil) % 16.84/17.03 Clause #9 (by clausification #[1]): ∀ (a : Iota → Iota), Eq (∀ (X Y : Iota), Eq (map a (cons X Y)) (cons (a X) (map a Y))) True % 16.84/17.03 Clause #10 (by clausification #[9]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (∀ (Y : Iota), Eq (map a (cons a_1 Y)) (cons (a a_1) (map a Y))) True % 16.84/17.03 Clause #11 (by clausification #[10]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (Eq (map a (cons a_1 a_2)) (cons (a a_1) (map a a_2))) True % 16.84/17.03 Clause #12 (by clausification #[11]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (map a (cons a_1 a_2)) (cons (a a_1) (map a a_2)) % 16.84/17.03 Clause #15 (by superposition #[12, 4]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (map a (cons a_1 nil)) (cons (a a_1) nil) % 16.84/17.03 Clause #20 (by fluidSup #[12, 4]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota) (a_3 : Iota → Iota), % 16.84/17.03 Eq (map a (cons (a_1 nil) a_2)) (cons (a (a_1 (map a_3 nil))) (map a a_2)) % 16.84/17.03 Clause #2457 (by forward demodulation #[20, 4]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (map a (cons (a_1 nil) a_2)) (cons (a (a_1 nil)) (map a a_2)) % 16.84/17.03 Clause #2480 (by superposition #[2457, 2457]): ∀ (a : Iota) (a_1 : Iota → Iota) (a_2 : Iota) (a_3 : Iota → Iota), % 16.84/17.03 Eq (map (fun x => a) (cons (a_1 nil) a_2)) (map (fun x => a) (cons (a_3 nil) a_2)) % 16.84/17.03 Clause #2701 (by superposition #[2480, 15]): ∀ (a : Iota) (a_1 : Iota → Iota), Eq (map (fun x => a) (cons (a_1 nil) nil)) (cons a nil) % 16.84/17.03 Clause #2933 (by superposition #[2701, 12]): ∀ (a : Iota), Eq (cons a nil) (cons a (map (fun x => a) nil)) % 16.84/17.03 Clause #3227 (by superposition #[2933, 12]): ∀ (a a_1 : Iota), Eq (map (fun x => a) (cons a_1 nil)) (cons a nil) % 16.84/17.03 Clause #3393 (by superposition #[3227, 2480]): ∀ (a : Iota) (a_1 : Iota → Iota), Eq (cons a nil) (map (fun x => a) (cons (a_1 nil) nil)) % 16.84/17.03 Clause #3404 (by superposition #[3227, 15]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (map a (cons a_1 nil)) (map (fun x => a a_1) (cons a_2 nil)) % 16.84/17.03 Clause #6166 (by superposition #[3404, 3393]): ∀ (a : Iota), Eq (cons a nil) (map (fun x => x) (cons a nil)) % 16.84/17.03 Clause #6477 (by backward contextual literal cutting #[6166, 8]): False % 16.84/17.03 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------