%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU996^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:02:43 PM UTC 2025 % Result : Theorem 7.41s 7.60s % Output : Proof 7.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU996^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n011.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 04:08:38 EDT 2025 % 0.13/0.34 % CPUTime : % 7.41/7.60 SZS status Theorem for theBenchmark.p % 7.41/7.60 SZS output start Proof for theBenchmark.p % 7.41/7.60 Clause #0 (by assumption #[]): Eq % 7.41/7.60 (Not % 7.41/7.60 (∀ (JOIN MEET : a → a → a), % 7.41/7.60 And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And (And (∀ (Xx : a), Eq (JOIN Xx Xx) Xx) (∀ (Xx : a), Eq (MEET Xx Xx) Xx)) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (JOIN (JOIN Xx Xy) Xz) (JOIN Xx (JOIN Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET (MEET Xx Xy) Xz) (MEET Xx (MEET Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (JOIN Xx Xy) (JOIN Xy Xx))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (MEET Xx Xy) (MEET Xy Xx))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (JOIN (MEET Xx Xy) Xy) Xy)) % 7.41/7.60 (∀ (Xx Xy : a), Eq (MEET (JOIN Xx Xy) Xy) Xy)) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (JOIN Xx (MEET Xy Xz)) (MEET (JOIN Xx Xy) (JOIN Xx Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET Xx (JOIN Xy Xz)) (JOIN (MEET Xx Xy) (MEET Xx Xz))) → % 7.41/7.60 ∀ (Xx Xy Xz : a), Eq (JOIN Xx Xz) Xz → Eq (JOIN Xx (MEET Xy Xz)) (MEET (JOIN Xx Xy) Xz))) % 7.41/7.60 True % 7.41/7.60 Clause #1 (by clausification #[0]): Eq % 7.41/7.60 (∀ (JOIN MEET : a → a → a), % 7.41/7.60 And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And (And (∀ (Xx : a), Eq (JOIN Xx Xx) Xx) (∀ (Xx : a), Eq (MEET Xx Xx) Xx)) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (JOIN (JOIN Xx Xy) Xz) (JOIN Xx (JOIN Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET (MEET Xx Xy) Xz) (MEET Xx (MEET Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (JOIN Xx Xy) (JOIN Xy Xx))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (MEET Xx Xy) (MEET Xy Xx))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (JOIN (MEET Xx Xy) Xy) Xy)) % 7.41/7.60 (∀ (Xx Xy : a), Eq (MEET (JOIN Xx Xy) Xy) Xy)) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (JOIN Xx (MEET Xy Xz)) (MEET (JOIN Xx Xy) (JOIN Xx Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET Xx (JOIN Xy Xz)) (JOIN (MEET Xx Xy) (MEET Xx Xz))) → % 7.41/7.60 ∀ (Xx Xy Xz : a), Eq (JOIN Xx Xz) Xz → Eq (JOIN Xx (MEET Xy Xz)) (MEET (JOIN Xx Xy) Xz)) % 7.41/7.60 False % 7.41/7.60 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → a), % 7.41/7.60 Eq % 7.41/7.60 (Not % 7.41/7.60 (∀ (MEET : a → a → a), % 7.41/7.60 And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And (And (∀ (Xx : a), Eq (skS.0 0 a_1 Xx Xx) Xx) (∀ (Xx : a), Eq (MEET Xx Xx) Xx)) % 7.41/7.60 (∀ (Xx Xy Xz : a), % 7.41/7.60 Eq (skS.0 0 a_1 (skS.0 0 a_1 Xx Xy) Xz) (skS.0 0 a_1 Xx (skS.0 0 a_1 Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET (MEET Xx Xy) Xz) (MEET Xx (MEET Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xx))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (MEET Xx Xy) (MEET Xy Xx))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 (MEET Xx Xy) Xy) Xy)) % 7.41/7.60 (∀ (Xx Xy : a), Eq (MEET (skS.0 0 a_1 Xx Xy) Xy) Xy)) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 Xx (MEET Xy Xz)) (MEET (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET Xx (skS.0 0 a_1 Xy Xz)) (skS.0 0 a_1 (MEET Xx Xy) (MEET Xx Xz))) → % 7.41/7.60 ∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 Xx Xz) Xz → Eq (skS.0 0 a_1 Xx (MEET Xy Xz)) (MEET (skS.0 0 a_1 Xx Xy) Xz))) % 7.41/7.60 True % 7.41/7.60 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → a), % 7.41/7.60 Eq % 7.41/7.60 (∀ (MEET : a → a → a), % 7.41/7.60 And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And % 7.41/7.60 (And (And (∀ (Xx : a), Eq (skS.0 0 a_1 Xx Xx) Xx) (∀ (Xx : a), Eq (MEET Xx Xx) Xx)) % 7.41/7.60 (∀ (Xx Xy Xz : a), % 7.41/7.60 Eq (skS.0 0 a_1 (skS.0 0 a_1 Xx Xy) Xz) (skS.0 0 a_1 Xx (skS.0 0 a_1 Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy Xz : a), Eq (MEET (MEET Xx Xy) Xz) (MEET Xx (MEET Xy Xz)))) % 7.41/7.60 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (MEET Xx Xy) (MEET Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 (MEET Xx Xy) Xy) Xy)) % 7.41/7.62 (∀ (Xx Xy : a), Eq (MEET (skS.0 0 a_1 Xx Xy) Xy) Xy)) % 7.41/7.62 (∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 Xx (MEET Xy Xz)) (MEET (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz)))) % 7.41/7.62 (∀ (Xx Xy Xz : a), Eq (MEET Xx (skS.0 0 a_1 Xy Xz)) (skS.0 0 a_1 (MEET Xx Xy) (MEET Xx Xz))) → % 7.41/7.62 ∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 Xx Xz) Xz → Eq (skS.0 0 a_1 Xx (MEET Xy Xz)) (MEET (skS.0 0 a_1 Xx Xy) Xz)) % 7.41/7.62 False % 7.41/7.62 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → a → a), % 7.41/7.62 Eq % 7.41/7.62 (Not % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And (And (∀ (Xx : a), Eq (skS.0 0 a_1 Xx Xx) Xx) (∀ (Xx : a), Eq (skS.0 1 a_1 a_2 Xx Xx) Xx)) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 0 a_1 (skS.0 0 a_1 Xx Xy) Xz) (skS.0 0 a_1 Xx (skS.0 0 a_1 Xy Xz)))) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 1 a_1 a_2 (skS.0 1 a_1 a_2 Xx Xy) Xz) (skS.0 1 a_1 a_2 Xx (skS.0 1 a_1 a_2 Xy Xz)))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) Xy) Xy)) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xy) Xy)) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz)))) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 1 a_1 a_2 Xx (skS.0 0 a_1 Xy Xz)) (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xx Xz))) → % 7.41/7.62 ∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 0 a_1 Xx Xz) Xz → % 7.41/7.62 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xz))) % 7.41/7.62 True % 7.41/7.62 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → a → a), % 7.41/7.62 Eq % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And (And (∀ (Xx : a), Eq (skS.0 0 a_1 Xx Xx) Xx) (∀ (Xx : a), Eq (skS.0 1 a_1 a_2 Xx Xx) Xx)) % 7.41/7.62 (∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 (skS.0 0 a_1 Xx Xy) Xz) (skS.0 0 a_1 Xx (skS.0 0 a_1 Xy Xz)))) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 1 a_1 a_2 (skS.0 1 a_1 a_2 Xx Xy) Xz) (skS.0 1 a_1 a_2 Xx (skS.0 1 a_1 a_2 Xy Xz)))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) Xy) Xy)) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xy) Xy)) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz)))) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 1 a_1 a_2 Xx (skS.0 0 a_1 Xy Xz)) (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xx Xz))) → % 7.41/7.62 ∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 0 a_1 Xx Xz) Xz → % 7.41/7.62 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xz)) % 7.41/7.62 False % 7.41/7.62 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a → a → a), % 7.41/7.62 Eq % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And % 7.41/7.62 (And (And (∀ (Xx : a), Eq (skS.0 0 a_1 Xx Xx) Xx) (∀ (Xx : a), Eq (skS.0 1 a_1 a_2 Xx Xx) Xx)) % 7.41/7.62 (∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 (skS.0 0 a_1 Xx Xy) Xz) (skS.0 0 a_1 Xx (skS.0 0 a_1 Xy Xz)))) % 7.41/7.62 (∀ (Xx Xy Xz : a), % 7.41/7.62 Eq (skS.0 1 a_1 a_2 (skS.0 1 a_1 a_2 Xx Xy) Xz) (skS.0 1 a_1 a_2 Xx (skS.0 1 a_1 a_2 Xy Xz)))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xx))) % 7.41/7.62 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xy Xx))) % 7.48/7.64 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) Xy) Xy)) % 7.48/7.64 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xy) Xy)) % 7.48/7.64 (∀ (Xx Xy Xz : a), % 7.48/7.64 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz)))) % 7.48/7.64 (∀ (Xx Xy Xz : a), % 7.48/7.64 Eq (skS.0 1 a_1 a_2 Xx (skS.0 0 a_1 Xy Xz)) (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xx Xz)))) % 7.48/7.64 True % 7.48/7.64 Clause #7 (by clausification #[5]): ∀ (a_1 a_2 : a → a → a), % 7.48/7.64 Eq % 7.48/7.64 (∀ (Xx Xy Xz : a), % 7.48/7.64 Eq (skS.0 0 a_1 Xx Xz) Xz → Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xz)) % 7.48/7.64 False % 7.48/7.64 Clause #9 (by clausification #[6]): ∀ (a_1 a_2 : a → a → a), % 7.48/7.64 Eq % 7.48/7.64 (And % 7.48/7.64 (And % 7.48/7.64 (And % 7.48/7.64 (And % 7.48/7.64 (And % 7.48/7.64 (And % 7.48/7.64 (And (And (∀ (Xx : a), Eq (skS.0 0 a_1 Xx Xx) Xx) (∀ (Xx : a), Eq (skS.0 1 a_1 a_2 Xx Xx) Xx)) % 7.48/7.64 (∀ (Xx Xy Xz : a), Eq (skS.0 0 a_1 (skS.0 0 a_1 Xx Xy) Xz) (skS.0 0 a_1 Xx (skS.0 0 a_1 Xy Xz)))) % 7.48/7.64 (∀ (Xx Xy Xz : a), % 7.48/7.64 Eq (skS.0 1 a_1 a_2 (skS.0 1 a_1 a_2 Xx Xy) Xz) (skS.0 1 a_1 a_2 Xx (skS.0 1 a_1 a_2 Xy Xz)))) % 7.48/7.64 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xx))) % 7.48/7.64 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 Xx Xy) (skS.0 1 a_1 a_2 Xy Xx))) % 7.48/7.64 (∀ (Xx Xy : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xx Xy) Xy) Xy)) % 7.48/7.64 (∀ (Xx Xy : a), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) Xy) Xy)) % 7.48/7.64 (∀ (Xx Xy Xz : a), % 7.48/7.64 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz)))) % 7.48/7.64 True % 7.48/7.64 Clause #14 (by clausification #[7]): ∀ (a_1 a_2 : a → a → a) (a_3 : a), % 7.48/7.64 Eq % 7.48/7.64 (Not % 7.48/7.64 (∀ (Xy Xz : a), % 7.48/7.64 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xz) Xz → % 7.48/7.64 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 Xy Xz)) % 7.48/7.64 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xy) Xz))) % 7.48/7.65 True % 7.48/7.65 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → a → a) (a_3 : a), % 7.48/7.65 Eq % 7.48/7.65 (∀ (Xy Xz : a), % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xz) Xz → % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 Xy Xz)) % 7.48/7.65 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xy) Xz)) % 7.48/7.65 False % 7.48/7.65 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 : a), % 7.48/7.65 Eq % 7.48/7.65 (Not % 7.48/7.65 (∀ (Xz : a), % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xz) Xz → % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) Xz)) % 7.48/7.65 (skS.0 1 a_1 a_2 (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)) Xz))) % 7.48/7.65 True % 7.48/7.65 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 : a), % 7.48/7.65 Eq % 7.48/7.65 (∀ (Xz : a), % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xz) Xz → % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) Xz)) % 7.48/7.65 (skS.0 1 a_1 a_2 (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)) Xz)) % 7.48/7.65 False % 7.48/7.65 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 a_5 : a), % 7.48/7.65 Eq % 7.48/7.65 (Not % 7.48/7.65 (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 4 a_1 a_2 a_3 a_4 a_5) → % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 7.48/7.65 (skS.0 1 a_1 a_2 (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)) % 7.48/7.65 (skS.0 4 a_1 a_2 a_3 a_4 a_5)))) % 7.48/7.65 True % 7.48/7.65 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 a_5 : a), % 7.48/7.65 Eq % 7.48/7.65 (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 4 a_1 a_2 a_3 a_4 a_5) → % 7.48/7.65 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 7.48/7.65 (skS.0 1 a_1 a_2 (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)) (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 7.48/7.65 False % 7.48/7.65 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 a_5 : a), % 7.48/7.66 Eq (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True % 7.48/7.66 Clause #21 (by clausification #[19]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 a_5 : a), % 7.48/7.66 Eq % 7.48/7.66 (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 7.48/7.66 (skS.0 1 a_1 a_2 (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)) (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 7.48/7.66 False % 7.48/7.66 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 a_5 : a), % 7.48/7.66 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 4 a_1 a_2 a_3 a_4 a_5) % 7.48/7.66 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 : a → a → a) (a_3 a_4 a_5 : a), % 7.48/7.66 Ne (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 7.48/7.66 (skS.0 1 a_1 a_2 (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)) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 7.48/7.66 Clause #24 (by clausification #[9]): ∀ (a_1 a_2 : a → a → a), % 7.48/7.66 Eq % 7.48/7.66 (∀ (Xx Xy Xz : a), % 7.48/7.66 Eq (skS.0 0 a_1 Xx (skS.0 1 a_1 a_2 Xy Xz)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xx Xz))) % 7.48/7.66 True % 7.48/7.66 Clause #26 (by clausification #[24]): ∀ (a_1 : a → a → a) (a_2 : a) (a_3 : a → a → a), % 7.48/7.66 Eq % 7.48/7.66 (∀ (Xy Xz : a), % 7.48/7.66 Eq (skS.0 0 a_1 a_2 (skS.0 1 a_1 a_3 Xy Xz)) (skS.0 1 a_1 a_3 (skS.0 0 a_1 a_2 Xy) (skS.0 0 a_1 a_2 Xz))) % 7.48/7.66 True % 7.48/7.66 Clause #27 (by clausification #[26]): ∀ (a_1 : a → a → a) (a_2 : a) (a_3 : a → a → a) (a_4 : a), % 7.48/7.66 Eq % 7.48/7.66 (∀ (Xz : a), % 7.48/7.66 Eq (skS.0 0 a_1 a_2 (skS.0 1 a_1 a_3 a_4 Xz)) (skS.0 1 a_1 a_3 (skS.0 0 a_1 a_2 a_4) (skS.0 0 a_1 a_2 Xz))) % 7.48/7.66 True % 7.48/7.66 Clause #28 (by clausification #[27]): ∀ (a_1 : a → a → a) (a_2 : a) (a_3 : a → a → a) (a_4 a_5 : a), % 7.48/7.66 Eq (Eq (skS.0 0 a_1 a_2 (skS.0 1 a_1 a_3 a_4 a_5)) (skS.0 1 a_1 a_3 (skS.0 0 a_1 a_2 a_4) (skS.0 0 a_1 a_2 a_5))) True % 7.48/7.66 Clause #29 (by clausification #[28]): ∀ (a_1 : a → a → a) (a_2 : a) (a_3 : a → a → a) (a_4 a_5 : a), % 7.48/7.66 Eq (skS.0 0 a_1 a_2 (skS.0 1 a_1 a_3 a_4 a_5)) (skS.0 1 a_1 a_3 (skS.0 0 a_1 a_2 a_4) (skS.0 0 a_1 a_2 a_5)) % 7.48/7.66 Clause #33 (by superposition #[29, 22]): ∀ (a_1 a_2 : a → a → a) (a_3 : a) (a_4 : a → a → a) (a_5 a_6 a_7 : a), % 7.48/7.66 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_4 a_5 (skS.0 4 a_1 a_2 a_3 a_6 a_7))) % 7.48/7.66 (skS.0 1 a_1 a_4 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) a_5) (skS.0 4 a_1 a_2 a_3 a_6 a_7)) % 7.48/7.66 Clause #400 (by backward contextual literal cutting #[33, 23]): False % 7.48/7.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------