%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU933^5 : 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 08:02:39 PM UTC 2025 % Result : Theorem 112.17s 112.39s % Output : Proof 113.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU933^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n003.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 05:37:08 EDT 2025 % 0.14/0.35 % CPUTime : % 112.17/112.39 SZS status Theorem for theBenchmark.p % 112.17/112.39 SZS output start Proof for theBenchmark.p % 112.17/112.39 Clause #0 (by assumption #[]): Eq % 112.17/112.39 (Not % 112.17/112.39 (Ne a b → % 112.17/112.39 Not % 112.17/112.39 (∀ (Xj Xk : Iota → Iota), % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => Xj (Xj_2 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 112.17/112.39 ∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => Xj (Xj_3 Xx)) → Xp Xk))) % 112.17/112.39 True % 112.17/112.39 Clause #1 (by clausification #[0]): Eq % 112.17/112.39 (Ne a b → % 112.17/112.39 Not % 112.17/112.39 (∀ (Xj Xk : Iota → Iota), % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => Xj (Xj_2 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 112.17/112.39 ∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => Xj (Xj_3 Xx)) → Xp Xk)) % 112.17/112.39 False % 112.17/112.39 Clause #2 (by clausification #[1]): Eq (Ne a b) True % 112.17/112.39 Clause #3 (by clausification #[1]): Eq % 112.17/112.39 (Not % 112.17/112.39 (∀ (Xj Xk : Iota → Iota), % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => Xj (Xj_2 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 112.17/112.39 ∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => Xj (Xj_3 Xx)) → Xp Xk)) % 112.17/112.39 False % 112.17/112.39 Clause #4 (by clausification #[2]): Ne a b % 112.17/112.39 Clause #5 (by clausification #[3]): Eq % 112.17/112.39 (∀ (Xj Xk : Iota → Iota), % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp Xj) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => Xj (Xj_2 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 112.17/112.39 ∀ (Xp : (Iota → Iota) → Prop), And (Xp Xj) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => Xj (Xj_3 Xx)) → Xp Xk) % 112.17/112.39 True % 112.17/112.39 Clause #6 (by clausification #[5]): ∀ (a : Iota → Iota), % 112.17/112.39 Eq % 112.17/112.39 (∀ (Xk : Iota → Iota), % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp a) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => a (Xj_2 Xx)) → Xp fun Xx => Xk (a Xx)) → % 112.17/112.39 ∀ (Xp : (Iota → Iota) → Prop), And (Xp a) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => a (Xj_3 Xx)) → Xp Xk) % 112.17/112.39 True % 112.17/112.39 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota → Iota), % 112.17/112.39 Eq % 112.17/112.39 ((∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp a) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => a (Xj_2 Xx)) → Xp fun Xx => a_1 (a Xx)) → % 112.17/112.39 ∀ (Xp : (Iota → Iota) → Prop), And (Xp a) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => a (Xj_3 Xx)) → Xp a_1) % 112.17/112.39 True % 112.17/112.39 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota → Iota), % 112.17/112.39 Or % 112.17/112.39 (Eq % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), % 112.17/112.39 And (Xp a) (∀ (Xj_2 : Iota → Iota), Xp Xj_2 → Xp fun Xx => a (Xj_2 Xx)) → Xp fun Xx => a_1 (a Xx)) % 112.17/112.39 False) % 112.17/112.39 (Eq % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), And (Xp a) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => a (Xj_3 Xx)) → Xp a_1) % 112.17/112.39 True) % 112.17/112.39 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), % 112.17/112.39 Or % 112.17/112.39 (Eq % 112.17/112.39 (∀ (Xp : (Iota → Iota) → Prop), And (Xp a) (∀ (Xj_3 : Iota → Iota), Xp Xj_3 → Xp fun Xx => a (Xj_3 Xx)) → Xp a_1) % 112.17/112.39 True) % 112.17/112.39 (Eq % 112.17/112.39 (Not % 112.17/112.39 (And (skS.0 0 a a_1 a_2 a) % 112.17/112.39 (∀ (Xj_2 : Iota → Iota), skS.0 0 a a_1 a_2 Xj_2 → skS.0 0 a a_1 a_2 fun Xx => a (Xj_2 Xx)) → % 112.17/112.39 skS.0 0 a a_1 a_2 fun Xx => a_1 (a Xx))) % 112.17/112.39 True) % 112.17/112.39 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : (Iota → Iota) → Prop), % 112.17/112.39 Or % 112.17/112.39 (Eq % 112.17/112.39 (Not % 112.17/112.39 (And (skS.0 0 a a_1 a_2 a) % 112.17/112.39 (∀ (Xj_2 : Iota → Iota), skS.0 0 a a_1 a_2 Xj_2 → skS.0 0 a a_1 a_2 fun Xx => a (Xj_2 Xx)) → % 112.17/112.39 skS.0 0 a a_1 a_2 fun Xx => a_1 (a Xx))) % 112.17/112.39 True) % 112.17/112.39 (Eq (And (a_3 a) (∀ (Xj_3 : Iota → Iota), a_3 Xj_3 → a_3 fun Xx => a (Xj_3 Xx)) → a_3 a_1) True) % 112.17/112.39 Clause #11 (by clausification #[10]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop), % 112.17/112.39 Or (Eq (And (a a_1) (∀ (Xj_3 : Iota → Iota), a Xj_3 → a fun Xx => a_1 (Xj_3 Xx)) → a a_2) True) % 112.24/112.42 (Eq % 112.24/112.42 (And (skS.0 0 a_1 a_2 a_3 a_1) % 112.24/112.42 (∀ (Xj_2 : Iota → Iota), skS.0 0 a_1 a_2 a_3 Xj_2 → skS.0 0 a_1 a_2 a_3 fun Xx => a_1 (Xj_2 Xx)) → % 112.24/112.42 skS.0 0 a_1 a_2 a_3 fun Xx => a_2 (a_1 Xx)) % 112.24/112.42 False) % 112.24/112.42 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : (Iota → Iota) → Prop), % 112.24/112.42 Or % 112.24/112.42 (Eq % 112.24/112.42 (And (skS.0 0 a a_1 a_2 a) % 112.24/112.42 (∀ (Xj_2 : Iota → Iota), skS.0 0 a a_1 a_2 Xj_2 → skS.0 0 a a_1 a_2 fun Xx => a (Xj_2 Xx)) → % 112.24/112.42 skS.0 0 a a_1 a_2 fun Xx => a_1 (a Xx)) % 112.24/112.42 False) % 112.24/112.42 (Or (Eq (And (a_3 a) (∀ (Xj_3 : Iota → Iota), a_3 Xj_3 → a_3 fun Xx => a (Xj_3 Xx))) False) (Eq (a_3 a_1) True)) % 112.24/112.42 Clause #13 (by clausification #[12]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop), % 112.24/112.42 Or (Eq (And (a a_1) (∀ (Xj_3 : Iota → Iota), a Xj_3 → a fun Xx => a_1 (Xj_3 Xx))) False) % 112.24/112.42 (Or (Eq (a a_2) True) % 112.24/112.42 (Eq % 112.24/112.42 (And (skS.0 0 a_1 a_2 a_3 a_1) % 112.24/112.42 (∀ (Xj_2 : Iota → Iota), skS.0 0 a_1 a_2 a_3 Xj_2 → skS.0 0 a_1 a_2 a_3 fun Xx => a_1 (Xj_2 Xx))) % 112.24/112.42 True)) % 112.24/112.42 Clause #14 (by clausification #[12]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop), % 112.24/112.42 Or (Eq (And (a a_1) (∀ (Xj_3 : Iota → Iota), a Xj_3 → a fun Xx => a_1 (Xj_3 Xx))) False) % 112.24/112.42 (Or (Eq (a a_2) True) (Eq (skS.0 0 a_1 a_2 a_3 fun Xx => a_2 (a_1 Xx)) False)) % 112.24/112.42 Clause #15 (by clausification #[13]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or % 112.24/112.42 (Eq % 112.24/112.42 (And (skS.0 0 a_2 a_1 a_3 a_2) % 112.24/112.42 (∀ (Xj_2 : Iota → Iota), skS.0 0 a_2 a_1 a_3 Xj_2 → skS.0 0 a_2 a_1 a_3 fun Xx => a_2 (Xj_2 Xx))) % 112.24/112.42 True) % 112.24/112.42 (Or (Eq (a a_2) False) (Eq (∀ (Xj_3 : Iota → Iota), a Xj_3 → a fun Xx => a_2 (Xj_3 Xx)) False))) % 112.24/112.42 Clause #17 (by clausification #[15]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or (Eq (a a_2) False) % 112.24/112.42 (Or (Eq (∀ (Xj_3 : Iota → Iota), a Xj_3 → a fun Xx => a_2 (Xj_3 Xx)) False) (Eq (skS.0 0 a_2 a_1 a_3 a_2) True))) % 112.24/112.42 Clause #32 (by clausification #[17]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop) (a_4 : Iota → Iota), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or (Eq (a a_2) False) % 112.24/112.42 (Or (Eq (skS.0 0 a_2 a_1 a_3 a_2) True) % 112.24/112.42 (Eq (Not (a (skS.0 2 a a_2 a_4) → a fun Xx => a_2 (skS.0 2 a a_2 a_4 Xx))) True))) % 112.24/112.42 Clause #33 (by clausification #[32]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop) (a_4 : Iota → Iota), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or (Eq (a a_2) False) % 112.24/112.42 (Or (Eq (skS.0 0 a_2 a_1 a_3 a_2) True) % 112.24/112.42 (Eq (a (skS.0 2 a a_2 a_4) → a fun Xx => a_2 (skS.0 2 a a_2 a_4 Xx)) False))) % 112.24/112.42 Clause #35 (by clausification #[33]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop) (a_4 : Iota → Iota), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or (Eq (a a_2) False) (Or (Eq (skS.0 0 a_2 a_1 a_3 a_2) True) (Eq (a fun Xx => a_2 (skS.0 2 a a_2 a_4 Xx)) False))) % 112.24/112.42 Clause #45 (by clausification #[14]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or (Eq (skS.0 0 a_2 a_1 a_3 fun Xx => a_1 (a_2 Xx)) False) % 112.24/112.42 (Or (Eq (a a_2) False) (Eq (∀ (Xj_3 : Iota → Iota), a Xj_3 → a fun Xx => a_2 (Xj_3 Xx)) False))) % 112.24/112.42 Clause #46 (by clausification #[45]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop) (a_4 : Iota → Iota), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.42 (Or (Eq (skS.0 0 a_2 a_1 a_3 fun Xx => a_1 (a_2 Xx)) False) % 112.24/112.42 (Or (Eq (a a_2) False) (Eq (Not (a (skS.0 3 a a_2 a_4) → a fun Xx => a_2 (skS.0 3 a a_2 a_4 Xx))) True))) % 112.24/112.42 Clause #47 (by clausification #[46]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop) (a_4 : Iota → Iota), % 112.24/112.42 Or (Eq (a a_1) True) % 112.24/112.45 (Or (Eq (skS.0 0 a_2 a_1 a_3 fun Xx => a_1 (a_2 Xx)) False) % 112.24/112.45 (Or (Eq (a a_2) False) (Eq (a (skS.0 3 a a_2 a_4) → a fun Xx => a_2 (skS.0 3 a a_2 a_4 Xx)) False))) % 112.24/112.45 Clause #49 (by clausification #[47]): ∀ (a : (Iota → Iota) → Prop) (a_1 a_2 : Iota → Iota) (a_3 : (Iota → Iota) → Prop) (a_4 : Iota → Iota), % 112.24/112.45 Or (Eq (a a_1) True) % 112.24/112.45 (Or (Eq (skS.0 0 a_2 a_1 a_3 fun Xx => a_1 (a_2 Xx)) False) % 112.24/112.45 (Or (Eq (a a_2) False) (Eq (a fun Xx => a_2 (skS.0 3 a a_2 a_4 Xx)) False))) % 112.24/112.45 Clause #73 (by neHoist #[35]): ∀ (a : (Iota → Iota) → Sort _abstMVar.0) (a_1 a_2 : (x : Iota → Iota) → a x) (a_3 a_4 : Iota → Iota) % 112.24/112.45 (a_5 : (Iota → Iota) → Prop) (a_6 : Iota → Iota), % 112.24/112.45 Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) a_3) True) % 112.24/112.45 (Or (Eq (skS.0 0 a_4 a_3 a_5 a_4) True) % 112.24/112.45 (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) fun Xx => a_4 (skS.0 2 (fun x => Ne (a_1 x) (a_2 x)) a_4 a_6 Xx)) False) % 112.24/112.45 (Or (Eq True False) (Eq (a_1 a_4) (a_2 a_4))))) % 112.24/112.45 Clause #963 (by betaEtaReduce #[73]): ∀ (a : (Iota → Iota) → Sort _abstMVar.0) (a_1 : Iota → Iota) (a_2 a_3 : (x : Iota → Iota) → a x) (a_4 : Iota → Iota) % 112.24/112.45 (a_5 : (Iota → Iota) → Prop) (a_6 : Iota → Iota), % 112.24/112.45 Or (Eq (Ne (a_2 a_1) (a_3 a_1)) True) % 112.24/112.45 (Or (Eq (skS.0 0 a_4 a_1 a_5 a_4) True) % 112.24/112.45 (Or % 112.24/112.45 (Eq % 112.24/112.45 (Ne (a_2 fun Xx => a_4 (skS.0 2 (fun x => Ne (a_2 x) (a_3 x)) a_4 a_6 Xx)) % 112.24/112.45 (a_3 fun Xx => a_4 (skS.0 2 (fun x => Ne (a_2 x) (a_3 x)) a_4 a_6 Xx))) % 112.24/112.45 False) % 112.24/112.45 (Or (Eq True False) (Eq (a_2 a_4) (a_3 a_4))))) % 112.24/112.45 Clause #964 (by clausification #[963]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop) (a_3 : (Iota → Iota) → Sort _abstMVar.0) % 112.24/112.45 (a_4 a_5 : (x : Iota → Iota) → a_3 x) (a_6 : Iota → Iota), % 112.24/112.45 Or (Eq (skS.0 0 a a_1 a_2 a) True) % 112.24/112.45 (Or % 112.24/112.45 (Eq % 112.24/112.45 (Ne (a_4 fun Xx => a (skS.0 2 (fun x => Ne (a_4 x) (a_5 x)) a a_6 Xx)) % 112.24/112.45 (a_5 fun Xx => a (skS.0 2 (fun x => Ne (a_4 x) (a_5 x)) a a_6 Xx))) % 112.24/112.45 False) % 112.24/112.45 (Or (Eq True False) (Or (Eq (a_4 a) (a_5 a)) (Ne (a_4 a_1) (a_5 a_1))))) % 112.24/112.45 Clause #965 (by clausification #[964]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop) (a_3 : (Iota → Iota) → Sort _abstMVar.0) % 112.24/112.45 (a_4 a_5 : (x : Iota → Iota) → a_3 x) (a_6 : Iota → Iota), % 112.24/112.45 Or (Eq (skS.0 0 a a_1 a_2 a) True) % 112.24/112.45 (Or (Eq True False) % 112.24/112.45 (Or (Eq (a_4 a) (a_5 a)) % 112.24/112.45 (Or (Ne (a_4 a_1) (a_5 a_1)) % 112.24/112.45 (Eq (a_4 fun Xx => a (skS.0 2 (fun x => Ne (a_4 x) (a_5 x)) a a_6 Xx)) % 112.24/112.45 (a_5 fun Xx => a (skS.0 2 (fun x => Ne (a_4 x) (a_5 x)) a a_6 Xx)))))) % 112.24/112.45 Clause #966 (by clausification #[965]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop) (a_3 : (Iota → Iota) → Sort _abstMVar.0) % 112.24/112.45 (a_4 a_5 : (x : Iota → Iota) → a_3 x) (a_6 : Iota → Iota), % 112.24/112.45 Or (Eq (skS.0 0 a a_1 a_2 a) True) % 112.24/112.45 (Or (Eq (a_4 a) (a_5 a)) % 112.24/112.45 (Or (Ne (a_4 a_1) (a_5 a_1)) % 112.24/112.45 (Eq (a_4 fun Xx => a (skS.0 2 (fun x => Ne (a_4 x) (a_5 x)) a a_6 Xx)) % 112.24/112.45 (a_5 fun Xx => a (skS.0 2 (fun x => Ne (a_4 x) (a_5 x)) a a_6 Xx))))) % 112.24/112.45 Clause #968 (by equality resolution #[966]): ∀ (a : Iota → Iota) (a_1 : (Iota → Iota) → Prop) (a_2 : Iota → Iota), % 112.24/112.45 Or (Eq (skS.0 0 a (fun x => x) a_1 a) True) % 112.24/112.45 (Or (Eq ((fun x x => x) a) ((fun x => x) a)) % 112.24/112.45 (Eq ((fun x x => x) fun Xx => a (skS.0 2 (fun x => Ne ((fun x x => x) x) ((fun x => x) x)) a a_2 Xx)) % 112.24/112.45 ((fun x => x) fun Xx => a (skS.0 2 (fun x => Ne ((fun x x => x) x) ((fun x => x) x)) a a_2 Xx)))) % 112.24/112.45 Clause #5325 (by betaEtaReduce #[968]): ∀ (a : Iota → Iota) (a_1 : (Iota → Iota) → Prop) (a_2 : Iota → Iota), % 112.24/112.45 Or (Eq (skS.0 0 a (fun x => x) a_1 a) True) % 112.24/112.45 (Or (Eq (fun x => x) a) (Eq (fun x => x) fun Xx => a (skS.0 2 (Ne fun x => x) a a_2 Xx))) % 112.24/112.45 Clause #5387 (by argument congruence #[5325]): ∀ (a : Iota → Iota) (a_1 : (Iota → Iota) → Prop) (a_2 : Iota) (a_3 : Iota → Iota), % 112.24/112.45 Or (Eq (skS.0 0 a (fun x => x) a_1 a) True) % 112.24/112.45 (Or (Eq ((fun x => x) a_2) (a a_2)) (Eq (fun x => x) fun Xx => a (skS.0 2 (Ne fun x => x) a a_3 Xx))) % 112.24/112.45 Clause #6202 (by betaEtaReduce #[5387]): ∀ (a : Iota → Iota) (a_1 : (Iota → Iota) → Prop) (a_2 : Iota) (a_3 : Iota → Iota), % 113.23/113.41 Or (Eq (skS.0 0 a (fun x => x) a_1 a) True) % 113.23/113.41 (Or (Eq a_2 (a a_2)) (Eq (fun x => x) fun Xx => a (skS.0 2 (Ne fun x => x) a a_3 Xx))) % 113.23/113.41 Clause #6228 (by superposition #[6202, 4]): ∀ (a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop) (a_3 : Iota → Iota), % 113.23/113.41 Or (Eq (skS.0 0 a_1 (fun x => x) a_2 a_1) True) % 113.23/113.41 (Or (Eq (fun x => x) fun Xx => a_1 (skS.0 2 (Ne fun x => x) a_1 a_3 Xx)) (Ne a (a_1 b))) % 113.23/113.41 Clause #7128 (by equality resolution #[6228]): ∀ (a_1 : (Iota → Iota) → Prop) (a_2 : Iota → Iota), % 113.23/113.41 Or (Eq (skS.0 0 (fun x => a) (fun x => x) a_1 fun x => a) True) % 113.23/113.41 (Eq (fun x => x) fun Xx => (fun x => a) (skS.0 2 (Ne fun x => x) (fun x => a) a_2 Xx)) % 113.23/113.41 Clause #7150 (by betaEtaReduce #[7128]): ∀ (a_1 : (Iota → Iota) → Prop), % 113.23/113.41 Or (Eq (skS.0 0 (fun x => a) (fun x => x) a_1 fun x => a) True) (Eq (fun x => x) fun Xx => a) % 113.23/113.41 Clause #7152 (by superposition #[7150, 49]): ∀ (a_1 : (Iota → Iota) → Prop), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) % 113.23/113.41 (Or (Eq (a_1 fun x => x) True) (Or (Eq True False) (Or (Eq (a_1 fun x => a) False) (Eq (a_1 fun Xx => a) False)))) % 113.23/113.41 Clause #7339 (by clausification #[7152]): ∀ (a_1 : (Iota → Iota) → Prop), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) % 113.23/113.41 (Or (Eq (a_1 fun x => x) True) (Or (Eq (a_1 fun x => a) False) (Eq (a_1 fun Xx => a) False))) % 113.23/113.41 Clause #7340 (by eliminate duplicate literals #[7339]): ∀ (a_1 : (Iota → Iota) → Prop), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) (Or (Eq (a_1 fun x => x) True) (Eq (a_1 fun x => a) False)) % 113.23/113.41 Clause #7342 (by neHoist #[7340]): ∀ (a_1 : (Iota → Iota) → Sort _abstMVar.1) (a_2 a_3 : (x : Iota → Iota) → a_1 x), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) % 113.23/113.41 (Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) fun x => x) True) % 113.23/113.41 (Or (Eq True False) (Eq (a_2 fun x => a) (a_3 fun x => a)))) % 113.23/113.41 Clause #7569 (by betaEtaReduce #[7342]): ∀ (a_1 : (Iota → Iota) → Sort _abstMVar.1) (a_2 a_3 : (x : Iota → Iota) → a_1 x), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) % 113.23/113.41 (Or (Eq (Ne (a_2 fun x => x) (a_3 fun x => x)) True) (Or (Eq True False) (Eq (a_2 fun x => a) (a_3 fun x => a)))) % 113.23/113.41 Clause #7570 (by clausification #[7569]): ∀ (a_1 : (Iota → Iota) → Sort _abstMVar.1) (a_2 a_3 : (x : Iota → Iota) → a_1 x), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) % 113.23/113.41 (Or (Eq True False) (Or (Eq (a_2 fun x => a) (a_3 fun x => a)) (Ne (a_2 fun x => x) (a_3 fun x => x)))) % 113.23/113.41 Clause #7571 (by clausification #[7570]): ∀ (a_1 : (Iota → Iota) → Sort _abstMVar.1) (a_2 a_3 : (x : Iota → Iota) → a_1 x), % 113.23/113.41 Or (Eq (fun x => x) fun Xx => a) (Or (Eq (a_2 fun x => a) (a_3 fun x => a)) (Ne (a_2 fun x => x) (a_3 fun x => x))) % 113.23/113.41 Clause #7572 (by equality resolution #[7571]): Or (Eq (fun x => x) fun Xx => a) (Eq ((fun x => x) fun x => a) ((fun x x => x) fun x => a)) % 113.23/113.41 Clause #7602 (by betaEtaReduce #[7572]): Or (Eq (fun x => x) fun Xx => a) (Eq (fun x => a) fun x => x) % 113.23/113.41 Clause #7604 (by equality factoring #[7602]): Or (Ne (fun x => a) fun Xx => a) (Eq (fun x => x) fun Xx => a) % 113.23/113.41 Clause #7606 (by eliminate resolved literals #[7604]): Eq (fun x => x) fun Xx => a % 113.23/113.41 Clause #7647 (by argument congruence #[7606]): ∀ (a_1 : Iota), Eq ((fun x => x) a_1) ((fun Xx => a) a_1) % 113.23/113.41 Clause #7762 (by betaEtaReduce #[7647]): ∀ (a_1 : Iota), Eq a_1 a % 113.23/113.41 Clause #7763 (by backward contextual literal cutting #[7762, 4]): False % 113.23/113.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------