%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU961^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:02:41 PM UTC 2025 % Result : Theorem 61.02s 61.26s % Output : Proof 61.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU961^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n027.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 05:30:53 EDT 2025 % 0.14/0.35 % CPUTime : % 61.02/61.26 SZS status Theorem for theBenchmark.p % 61.02/61.26 SZS output start Proof for theBenchmark.p % 61.02/61.26 Clause #0 (by assumption #[]): Eq % 61.02/61.26 (Not % 61.02/61.26 (And (∀ (Xa Xb : Iota), Eq Xa Xb) (∀ (Xf Xg : Iota → Iota), (∀ (Xx : Iota), Eq (Xf Xx) (Xg Xx)) → Eq Xf Xg) → % 61.02/61.26 ∀ (Xj Xk : Iota → Iota), % 61.02/61.26 (∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp Xj) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => Xj (Xj_0 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 61.02/61.26 ∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp Xj) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => Xj (Xj_1 Xx)) → Xp Xk)) % 61.02/61.26 True % 61.02/61.26 Clause #1 (by clausification #[0]): Eq % 61.02/61.26 (And (∀ (Xa Xb : Iota), Eq Xa Xb) (∀ (Xf Xg : Iota → Iota), (∀ (Xx : Iota), Eq (Xf Xx) (Xg Xx)) → Eq Xf Xg) → % 61.02/61.26 ∀ (Xj Xk : Iota → Iota), % 61.02/61.26 (∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp Xj) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => Xj (Xj_0 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 61.02/61.26 ∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp Xj) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => Xj (Xj_1 Xx)) → Xp Xk) % 61.02/61.26 False % 61.02/61.26 Clause #2 (by clausification #[1]): Eq (And (∀ (Xa Xb : Iota), Eq Xa Xb) (∀ (Xf Xg : Iota → Iota), (∀ (Xx : Iota), Eq (Xf Xx) (Xg Xx)) → Eq Xf Xg)) True % 61.02/61.26 Clause #3 (by clausification #[1]): Eq % 61.02/61.26 (∀ (Xj Xk : Iota → Iota), % 61.02/61.26 (∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp Xj) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => Xj (Xj_0 Xx)) → Xp fun Xx => Xk (Xj Xx)) → % 61.02/61.26 ∀ (Xp : (Iota → Iota) → Prop), And (Xp Xj) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => Xj (Xj_1 Xx)) → Xp Xk) % 61.02/61.26 False % 61.02/61.26 Clause #4 (by clausification #[2]): Eq (∀ (Xf Xg : Iota → Iota), (∀ (Xx : Iota), Eq (Xf Xx) (Xg Xx)) → Eq Xf Xg) True % 61.02/61.26 Clause #5 (by clausification #[2]): Eq (∀ (Xa Xb : Iota), Eq Xa Xb) True % 61.02/61.26 Clause #6 (by clausification #[4]): ∀ (a : Iota → Iota), Eq (∀ (Xg : Iota → Iota), (∀ (Xx : Iota), Eq (a Xx) (Xg Xx)) → Eq a Xg) True % 61.02/61.26 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota → Iota), Eq ((∀ (Xx : Iota), Eq (a Xx) (a_1 Xx)) → Eq a a_1) True % 61.02/61.26 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota → Iota), Or (Eq (∀ (Xx : Iota), Eq (a Xx) (a_1 Xx)) False) (Eq (Eq a a_1) True) % 61.02/61.26 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), % 61.02/61.26 Or (Eq (Eq a a_1) True) (Eq (Not (Eq (a (skS.0 0 a a_1 a_2)) (a_1 (skS.0 0 a a_1 a_2)))) True) % 61.02/61.26 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), % 61.02/61.26 Or (Eq (Not (Eq (a (skS.0 0 a a_1 a_2)) (a_1 (skS.0 0 a a_1 a_2)))) True) (Eq a a_1) % 61.02/61.26 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Or (Eq a a_1) (Eq (Eq (a (skS.0 0 a a_1 a_2)) (a_1 (skS.0 0 a a_1 a_2))) False) % 61.02/61.26 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Or (Eq a a_1) (Ne (a (skS.0 0 a a_1 a_2)) (a_1 (skS.0 0 a a_1 a_2))) % 61.02/61.26 Clause #18 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Xb : Iota), Eq a Xb) True % 61.02/61.26 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Eq a a_1) True % 61.02/61.26 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq a a_1 % 61.02/61.26 Clause #28 (by fluidSup #[20, 12]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Eq a fun x => x) (Ne (a (skS.0 0 a (fun x => x) a_1)) ((fun _ => _) a_2)) % 61.02/61.26 Clause #30 (by clausification #[3]): ∀ (a : Iota → Iota), % 61.02/61.26 Eq % 61.02/61.26 (Not % 61.02/61.26 (∀ (Xk : Iota → Iota), % 61.02/61.26 (∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp (skS.0 1 a)) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => skS.0 1 a (Xj_0 Xx)) → % 61.02/61.26 Xp fun Xx => Xk (skS.0 1 a Xx)) → % 61.02/61.26 ∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp (skS.0 1 a)) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => skS.0 1 a (Xj_1 Xx)) → Xp Xk)) % 61.02/61.26 True % 61.02/61.26 Clause #31 (by clausification #[30]): ∀ (a : Iota → Iota), % 61.02/61.26 Eq % 61.02/61.26 (∀ (Xk : Iota → Iota), % 61.02/61.26 (∀ (Xp : (Iota → Iota) → Prop), % 61.02/61.26 And (Xp (skS.0 1 a)) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => skS.0 1 a (Xj_0 Xx)) → % 61.02/61.26 Xp fun Xx => Xk (skS.0 1 a Xx)) → % 61.77/61.91 ∀ (Xp : (Iota → Iota) → Prop), % 61.77/61.91 And (Xp (skS.0 1 a)) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => skS.0 1 a (Xj_1 Xx)) → Xp Xk) % 61.77/61.91 False % 61.77/61.91 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota → Iota), % 61.77/61.91 Eq % 61.77/61.91 (Not % 61.77/61.91 ((∀ (Xp : (Iota → Iota) → Prop), % 61.77/61.91 And (Xp (skS.0 1 a)) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => skS.0 1 a (Xj_0 Xx)) → % 61.77/61.91 Xp fun Xx => skS.0 2 a a_1 (skS.0 1 a Xx)) → % 61.77/61.91 ∀ (Xp : (Iota → Iota) → Prop), % 61.77/61.91 And (Xp (skS.0 1 a)) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => skS.0 1 a (Xj_1 Xx)) → % 61.77/61.91 Xp (skS.0 2 a a_1))) % 61.77/61.91 True % 61.77/61.91 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota → Iota), % 61.77/61.91 Eq % 61.77/61.91 ((∀ (Xp : (Iota → Iota) → Prop), % 61.77/61.91 And (Xp (skS.0 1 a)) (∀ (Xj_0 : Iota → Iota), Xp Xj_0 → Xp fun Xx => skS.0 1 a (Xj_0 Xx)) → % 61.77/61.91 Xp fun Xx => skS.0 2 a a_1 (skS.0 1 a Xx)) → % 61.77/61.91 ∀ (Xp : (Iota → Iota) → Prop), % 61.77/61.91 And (Xp (skS.0 1 a)) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => skS.0 1 a (Xj_1 Xx)) → Xp (skS.0 2 a a_1)) % 61.77/61.91 False % 61.77/61.91 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota → Iota), % 61.77/61.91 Eq % 61.77/61.91 (∀ (Xp : (Iota → Iota) → Prop), % 61.77/61.91 And (Xp (skS.0 1 a)) (∀ (Xj_1 : Iota → Iota), Xp Xj_1 → Xp fun Xx => skS.0 1 a (Xj_1 Xx)) → Xp (skS.0 2 a a_1)) % 61.77/61.91 False % 61.77/61.91 Clause #51 (by clausification #[35]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), % 61.77/61.91 Eq % 61.77/61.91 (Not % 61.77/61.91 (And (skS.0 4 a a_1 a_2 (skS.0 1 a)) % 61.77/61.91 (∀ (Xj_1 : Iota → Iota), skS.0 4 a a_1 a_2 Xj_1 → skS.0 4 a a_1 a_2 fun Xx => skS.0 1 a (Xj_1 Xx)) → % 61.77/61.91 skS.0 4 a a_1 a_2 (skS.0 2 a a_1))) % 61.77/61.91 True % 61.77/61.91 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), % 61.77/61.91 Eq % 61.77/61.91 (And (skS.0 4 a a_1 a_2 (skS.0 1 a)) % 61.77/61.91 (∀ (Xj_1 : Iota → Iota), skS.0 4 a a_1 a_2 Xj_1 → skS.0 4 a a_1 a_2 fun Xx => skS.0 1 a (Xj_1 Xx)) → % 61.77/61.91 skS.0 4 a a_1 a_2 (skS.0 2 a a_1)) % 61.77/61.91 False % 61.77/61.91 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), % 61.77/61.91 Eq % 61.77/61.91 (And (skS.0 4 a a_1 a_2 (skS.0 1 a)) % 61.77/61.91 (∀ (Xj_1 : Iota → Iota), skS.0 4 a a_1 a_2 Xj_1 → skS.0 4 a a_1 a_2 fun Xx => skS.0 1 a (Xj_1 Xx))) % 61.77/61.91 True % 61.77/61.91 Clause #54 (by clausification #[52]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), Eq (skS.0 4 a a_1 a_2 (skS.0 2 a a_1)) False % 61.77/61.91 Clause #56 (by clausification #[53]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), Eq (skS.0 4 a a_1 a_2 (skS.0 1 a)) True % 61.77/61.91 Clause #3699 (by betaEtaReduce #[28]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Eq a fun x => x) (Ne (a (skS.0 0 a (fun x => x) a_1)) a_2) % 61.77/61.91 Clause #3700 (by equality resolution #[3699]): ∀ (a : Iota → Iota), Eq a fun x => x % 61.77/61.91 Clause #9662 (by forward demodulation #[54, 3700]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), Eq (skS.0 4 a a_1 a_2 fun x => x) False % 61.77/61.91 Clause #9956 (by forward demodulation #[56, 3700]): ∀ (a a_1 : Iota → Iota) (a_2 : (Iota → Iota) → Prop), Eq (skS.0 4 a a_1 a_2 fun x => x) True % 61.77/61.91 Clause #9957 (by superposition #[9956, 9662]): Eq True False % 61.77/61.91 Clause #10112 (by clausification #[9957]): False % 61.77/61.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------