%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV015^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:02:44 PM UTC 2025 % Result : Theorem 4.35s 4.53s % Output : Proof 4.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : SEV015^5 : TPTP v9.2.0. Released v4.0.0. % 0.09/0.15 % Command : duper %s % 0.15/0.37 % Computer : n007.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Fri Oct 3 01:03:23 EDT 2025 % 0.15/0.37 % CPUTime : % 4.35/4.53 SZS status Theorem for theBenchmark.p % 4.35/4.53 SZS output start Proof for theBenchmark.p % 4.35/4.53 Clause #0 (by assumption #[]): Eq % 4.35/4.53 (Not % 4.35/4.53 (∀ (Xp : a → a → Prop), % 4.35/4.53 And (And (∀ (Xx Xy : a), Xp Xx Xy → Xp Xy Xx) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)) % 4.35/4.53 (Eq Xp Xp) → % 4.35/4.53 ∀ (Xx Xy : a), Xp Xx Xy → Xp Xx Xx)) % 4.35/4.53 True % 4.35/4.53 Clause #1 (by clausification #[0]): Eq % 4.35/4.53 (∀ (Xp : a → a → Prop), % 4.35/4.53 And (And (∀ (Xx Xy : a), Xp Xx Xy → Xp Xy Xx) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)) (Eq Xp Xp) → % 4.35/4.53 ∀ (Xx Xy : a), Xp Xx Xy → Xp Xx Xx) % 4.35/4.53 False % 4.35/4.53 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 4.35/4.53 Eq % 4.35/4.53 (Not % 4.35/4.53 (And % 4.35/4.53 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 4.35/4.53 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 4.35/4.53 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 4.35/4.53 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xx Xx)) % 4.35/4.53 True % 4.35/4.53 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 4.35/4.53 Eq % 4.35/4.53 (And % 4.35/4.53 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 4.35/4.53 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 4.35/4.53 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 4.35/4.53 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xx Xx) % 4.35/4.53 False % 4.35/4.53 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop), % 4.35/4.53 Eq % 4.35/4.53 (And % 4.35/4.53 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 4.35/4.53 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 4.35/4.53 (Eq (skS.0 0 a_1) (skS.0 0 a_1))) % 4.35/4.53 True % 4.35/4.53 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xx Xx) False % 4.35/4.53 Clause #7 (by clausification #[4]): ∀ (a_1 : a → a → Prop), % 4.35/4.53 Eq % 4.35/4.53 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 4.35/4.53 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 4.35/4.53 True % 4.35/4.53 Clause #9 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 4.35/4.53 Eq (Not (∀ (Xy : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2))) True % 4.35/4.53 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 4.35/4.53 Eq (∀ (Xy : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) False % 4.35/4.53 Clause #11 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 4.35/4.53 Eq (Not (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2))) True % 4.35/4.53 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 4.35/4.53 Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) False % 4.35/4.53 Clause #13 (by clausification #[12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) True % 4.35/4.53 Clause #14 (by clausification #[12]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) False % 4.35/4.53 Clause #15 (by clausification #[7]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) True % 4.35/4.53 Clause #16 (by clausification #[7]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) True % 4.35/4.53 Clause #17 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 4.35/4.53 Eq (∀ (Xy Xz : a), And (skS.0 0 a_1 a_2 Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 a_2 Xz) True % 4.35/4.53 Clause #18 (by clausification #[17]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 4.35/4.53 Eq (∀ (Xz : a), And (skS.0 0 a_1 a_2 a_3) (skS.0 0 a_1 a_3 Xz) → skS.0 0 a_1 a_2 Xz) True % 4.35/4.53 Clause #19 (by clausification #[18]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 4.35/4.53 Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 0 a_1 a_3 a_4) → skS.0 0 a_1 a_2 a_4) True % 4.35/4.53 Clause #20 (by clausification #[19]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 4.35/4.53 Or (Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 0 a_1 a_3 a_4)) False) (Eq (skS.0 0 a_1 a_2 a_4) True) % 4.36/4.55 Clause #21 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 4.36/4.55 Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Or (Eq (skS.0 0 a_1 a_2 a_4) False) (Eq (skS.0 0 a_1 a_4 a_3) False)) % 4.36/4.55 Clause #22 (by superposition #[21, 13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 4.36/4.55 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) (skS.0 1 a_1 a_2) a_3) True) % 4.36/4.55 (Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) (skS.0 2 a_1 a_2 a_4) a_3) False) (Eq False True)) % 4.36/4.55 Clause #23 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (∀ (Xy : a), skS.0 0 a_1 a_2 Xy → skS.0 0 a_1 Xy a_2) True % 4.36/4.55 Clause #24 (by clausification #[23]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 a_2 a_3 → skS.0 0 a_1 a_3 a_2) True % 4.36/4.55 Clause #25 (by clausification #[24]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (skS.0 0 a_1 a_3 a_2) True) % 4.36/4.55 Clause #26 (by superposition #[25, 13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 4.36/4.55 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2)) True) (Eq False True) % 4.36/4.55 Clause #27 (by betaEtaReduce #[22]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 4.36/4.55 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) a_3) True) % 4.36/4.55 (Or (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_4) a_3) False) (Eq False True)) % 4.36/4.55 Clause #28 (by clausification #[27]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 4.36/4.55 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) a_3) True) (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_4) a_3) False) % 4.36/4.55 Clause #29 (by betaEtaReduce #[26]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2)) True) (Eq False True) % 4.36/4.55 Clause #30 (by clausification #[29]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 1 a_1 a_2)) True % 4.36/4.55 Clause #31 (by superposition #[30, 28]): ∀ (a_1 : a → a → Prop) (a_2 : a), Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) True) (Eq True False) % 4.36/4.55 Clause #34 (by clausification #[31]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) True % 4.36/4.55 Clause #35 (by superposition #[34, 14]): Eq True False % 4.36/4.55 Clause #37 (by clausification #[35]): False % 4.36/4.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------