%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU898^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:02:36 PM UTC 2025 % Result : Theorem 4.09s 4.25s % Output : Proof 4.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU898^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : duper %s % 0.15/0.35 % Computer : n003.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 05:34:38 EDT 2025 % 0.15/0.35 % CPUTime : % 4.09/4.25 SZS status Theorem for theBenchmark.p % 4.09/4.25 SZS output start Proof for theBenchmark.p % 4.09/4.25 Clause #0 (by assumption #[]): Eq % 4.09/4.25 (Not % 4.09/4.25 (∀ (Xh : a → a) (Xs : a → Prop) (Xf : a → a), % 4.09/4.25 And (And (And (∀ (Xx : a), Xs Xx → Xs (Xf Xx)) (∀ (Xx : a), Xs Xx → Xs (Xf Xx))) (∀ (Xx : a), Xs Xx → Xs (Xh Xx))) % 4.09/4.25 (∀ (Xx : a), Xs Xx → Eq (Xh (Xf Xx)) (Xf (Xh Xx))) → % 4.09/4.25 ∀ (Xx : a), Xs Xx → Eq (Xh (Xh (Xf Xx))) (Xf (Xh (Xh Xx))))) % 4.09/4.25 True % 4.09/4.25 Clause #1 (by clausification #[0]): Eq % 4.09/4.25 (∀ (Xh : a → a) (Xs : a → Prop) (Xf : a → a), % 4.09/4.25 And (And (And (∀ (Xx : a), Xs Xx → Xs (Xf Xx)) (∀ (Xx : a), Xs Xx → Xs (Xf Xx))) (∀ (Xx : a), Xs Xx → Xs (Xh Xx))) % 4.09/4.25 (∀ (Xx : a), Xs Xx → Eq (Xh (Xf Xx)) (Xf (Xh Xx))) → % 4.09/4.25 ∀ (Xx : a), Xs Xx → Eq (Xh (Xh (Xf Xx))) (Xf (Xh (Xh Xx)))) % 4.09/4.25 False % 4.09/4.25 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a), % 4.09/4.25 Eq % 4.09/4.25 (Not % 4.09/4.25 (∀ (Xs : a → Prop) (Xf : a → a), % 4.09/4.25 And % 4.09/4.25 (And (And (∀ (Xx : a), Xs Xx → Xs (Xf Xx)) (∀ (Xx : a), Xs Xx → Xs (Xf Xx))) % 4.09/4.25 (∀ (Xx : a), Xs Xx → Xs (skS.0 0 a_1 Xx))) % 4.09/4.25 (∀ (Xx : a), Xs Xx → Eq (skS.0 0 a_1 (Xf Xx)) (Xf (skS.0 0 a_1 Xx))) → % 4.09/4.25 ∀ (Xx : a), Xs Xx → Eq (skS.0 0 a_1 (skS.0 0 a_1 (Xf Xx))) (Xf (skS.0 0 a_1 (skS.0 0 a_1 Xx))))) % 4.09/4.25 True % 4.09/4.25 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a), % 4.09/4.25 Eq % 4.09/4.25 (∀ (Xs : a → Prop) (Xf : a → a), % 4.09/4.25 And % 4.09/4.25 (And (And (∀ (Xx : a), Xs Xx → Xs (Xf Xx)) (∀ (Xx : a), Xs Xx → Xs (Xf Xx))) % 4.09/4.25 (∀ (Xx : a), Xs Xx → Xs (skS.0 0 a_1 Xx))) % 4.09/4.25 (∀ (Xx : a), Xs Xx → Eq (skS.0 0 a_1 (Xf Xx)) (Xf (skS.0 0 a_1 Xx))) → % 4.09/4.25 ∀ (Xx : a), Xs Xx → Eq (skS.0 0 a_1 (skS.0 0 a_1 (Xf Xx))) (Xf (skS.0 0 a_1 (skS.0 0 a_1 Xx)))) % 4.09/4.25 False % 4.09/4.25 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a) (a_2 : a → Prop), % 4.09/4.25 Eq % 4.09/4.25 (Not % 4.09/4.25 (∀ (Xf : a → a), % 4.09/4.25 And % 4.09/4.25 (And % 4.09/4.25 (And (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (Xf Xx)) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (Xf Xx))) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx))) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (Xf Xx)) (Xf (skS.0 0 a_1 Xx))) → % 4.09/4.25 ∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (skS.0 0 a_1 (Xf Xx))) (Xf (skS.0 0 a_1 (skS.0 0 a_1 Xx))))) % 4.09/4.25 True % 4.09/4.25 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a) (a_2 : a → Prop), % 4.09/4.25 Eq % 4.09/4.25 (∀ (Xf : a → a), % 4.09/4.25 And % 4.09/4.25 (And % 4.09/4.25 (And (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (Xf Xx)) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (Xf Xx))) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx))) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (Xf Xx)) (Xf (skS.0 0 a_1 Xx))) → % 4.09/4.25 ∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (skS.0 0 a_1 (Xf Xx))) (Xf (skS.0 0 a_1 (skS.0 0 a_1 Xx)))) % 4.09/4.25 False % 4.09/4.25 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a), % 4.09/4.25 Eq % 4.09/4.25 (Not % 4.09/4.25 (And % 4.09/4.25 (And % 4.09/4.25 (And (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx)) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx))) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx))) % 4.09/4.25 (∀ (Xx : a), % 4.09/4.25 skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx)) (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 Xx))) → % 4.09/4.25 ∀ (Xx : a), % 4.09/4.25 skS.0 1 a_1 a_2 Xx → % 4.09/4.25 Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx))) % 4.09/4.25 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 Xx))))) % 4.09/4.25 True % 4.09/4.25 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a), % 4.09/4.25 Eq % 4.09/4.25 (And % 4.09/4.25 (And % 4.09/4.25 (And (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx)) % 4.09/4.25 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx))) % 4.13/4.27 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx))) % 4.13/4.27 (∀ (Xx : a), % 4.13/4.27 skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx)) (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 Xx))) → % 4.13/4.27 ∀ (Xx : a), % 4.13/4.27 skS.0 1 a_1 a_2 Xx → % 4.13/4.27 Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx))) (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 Xx)))) % 4.13/4.27 False % 4.13/4.27 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a), % 4.13/4.27 Eq % 4.13/4.27 (And % 4.13/4.27 (And % 4.13/4.27 (And (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx)) % 4.13/4.27 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx))) % 4.13/4.27 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx))) % 4.13/4.27 (∀ (Xx : a), % 4.13/4.27 skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx)) (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 Xx)))) % 4.13/4.27 True % 4.13/4.27 Clause #9 (by clausification #[7]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a), % 4.13/4.27 Eq % 4.13/4.27 (∀ (Xx : a), % 4.13/4.27 skS.0 1 a_1 a_2 Xx → % 4.13/4.27 Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx))) (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 Xx)))) % 4.13/4.27 False % 4.13/4.27 Clause #10 (by clausification #[8]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a), % 4.13/4.27 Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx)) (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 Xx))) % 4.13/4.27 True % 4.13/4.27 Clause #11 (by clausification #[8]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a), % 4.13/4.27 Eq % 4.13/4.27 (And % 4.13/4.27 (And (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx)) % 4.13/4.27 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3 Xx))) % 4.13/4.27 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx))) % 4.13/4.27 True % 4.13/4.27 Clause #12 (by clausification #[10]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a) (a_4 : a → a), % 4.13/4.27 Eq (skS.0 1 a_1 a_2 a_3 → Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_4 a_3)) (skS.0 2 a_1 a_2 a_4 (skS.0 0 a_1 a_3))) True % 4.13/4.27 Clause #13 (by clausification #[12]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a) (a_4 : a → a), % 4.13/4.27 Or (Eq (skS.0 1 a_1 a_2 a_3) False) % 4.13/4.27 (Eq (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_4 a_3)) (skS.0 2 a_1 a_2 a_4 (skS.0 0 a_1 a_3))) True) % 4.13/4.27 Clause #14 (by clausification #[13]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a) (a_4 : a → a), % 4.13/4.27 Or (Eq (skS.0 1 a_1 a_2 a_3) False) % 4.13/4.27 (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_4 a_3)) (skS.0 2 a_1 a_2 a_4 (skS.0 0 a_1 a_3))) % 4.13/4.27 Clause #15 (by clausification #[9]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.27 Eq % 4.13/4.27 (Not % 4.13/4.27 (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) → % 4.13/4.27 Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))) % 4.13/4.27 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))))) % 4.13/4.27 True % 4.13/4.27 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.27 Eq % 4.13/4.27 (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) → % 4.13/4.27 Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))) % 4.13/4.27 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))))) % 4.13/4.27 False % 4.13/4.27 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True % 4.13/4.27 Clause #18 (by clausification #[16]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.27 Eq % 4.13/4.27 (Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))) % 4.13/4.27 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))))) % 4.13/4.27 False % 4.13/4.27 Clause #19 (by superposition #[17, 14]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 a_4 : a → a) (a_5 : a), % 4.13/4.27 Or (Eq True False) % 4.13/4.27 (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_4 a_5))) % 4.13/4.27 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)))) % 4.13/4.27 Clause #20 (by clausification #[19]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 a_4 : a → a) (a_5 : a), % 4.13/4.27 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_4 a_5))) % 4.13/4.27 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5))) % 4.13/4.29 Clause #21 (by clausification #[11]): ∀ (a_1 : a → a) (a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) True % 4.13/4.29 Clause #23 (by clausification #[21]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 a_3 → skS.0 1 a_1 a_2 (skS.0 0 a_1 a_3)) True % 4.13/4.29 Clause #24 (by clausification #[23]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a), % 4.13/4.29 Or (Eq (skS.0 1 a_1 a_2 a_3) False) (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 a_3)) True) % 4.13/4.29 Clause #25 (by superposition #[24, 17]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.29 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 0 (fun x => a_1 x) (skS.0 3 a_1 a_2 a_3 a_4))) True) % 4.13/4.29 (Eq False True) % 4.13/4.29 Clause #26 (by betaEtaReduce #[25]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.29 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True) (Eq False True) % 4.13/4.29 Clause #27 (by clausification #[26]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.29 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True % 4.13/4.29 Clause #28 (by superposition #[27, 14]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 a_4 : a → a) (a_5 : a), % 4.13/4.29 Or (Eq True False) % 4.13/4.29 (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)))) % 4.13/4.29 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5))))) % 4.13/4.29 Clause #30 (by clausification #[18]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 : a → a) (a_4 : a), % 4.13/4.29 Ne (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))) % 4.13/4.29 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))) % 4.13/4.29 Clause #53 (by clausification #[28]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 a_4 : a → a) (a_5 : a), % 4.13/4.29 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)))) % 4.13/4.29 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)))) % 4.13/4.29 Clause #54 (by forward demodulation #[53, 20]): ∀ (a_1 : a → a) (a_2 : a → Prop) (a_3 a_4 : a → a) (a_5 : a), % 4.13/4.29 Eq (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_4 a_5)))) % 4.13/4.29 (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)))) % 4.13/4.29 Clause #56 (by backward contextual literal cutting #[54, 30]): False % 4.13/4.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------