%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV056^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:02:47 PM UTC 2025 % Result : Theorem 17.01s 17.24s % Output : Proof 17.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : SEV056^5 : TPTP v9.2.0. Released v4.0.0. % 0.02/0.11 % Command : duper %s % 0.16/0.31 % Computer : n004.cluster.edu % 0.16/0.31 % Model : x86_64 x86_64 % 0.16/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.31 % Memory : 8042.1875MB % 0.16/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.31 % CPULimit : 300 % 0.16/0.31 % WCLimit : 300 % 0.16/0.31 % DateTime : Fri Oct 3 01:11:53 EDT 2025 % 0.16/0.31 % CPUTime : % 17.01/17.24 SZS status Theorem for theBenchmark.p % 17.01/17.24 SZS output start Proof for theBenchmark.p % 17.01/17.24 Clause #0 (by assumption #[]): Eq % 17.01/17.24 (Not % 17.01/17.24 (∀ (Xr : a → a → Prop), % 17.01/17.24 Exists fun Xp => % 17.01/17.24 And (∀ (Xx Xy : a), Xr Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz))) % 17.01/17.24 True % 17.01/17.24 Clause #1 (by clausification #[0]): Eq % 17.01/17.24 (∀ (Xr : a → a → Prop), % 17.01/17.24 Exists fun Xp => And (∀ (Xx Xy : a), Xr Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)) % 17.01/17.24 False % 17.01/17.24 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 17.01/17.24 Eq % 17.01/17.24 (Not % 17.01/17.24 (Exists fun Xp => % 17.01/17.24 And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz))) % 17.01/17.24 True % 17.01/17.24 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 17.01/17.24 Eq % 17.01/17.24 (Exists fun Xp => % 17.01/17.24 And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)) % 17.01/17.24 False % 17.01/17.24 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → a → Prop), % 17.01/17.24 Eq (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → a_2 Xx Xy) (∀ (Xx Xy Xz : a), And (a_2 Xx Xy) (a_2 Xy Xz) → a_2 Xx Xz)) % 17.01/17.24 False % 17.01/17.24 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → a → Prop), % 17.01/17.24 Or (Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → a_2 Xx Xy) False) % 17.01/17.24 (Eq (∀ (Xx Xy Xz : a), And (a_2 Xx Xy) (a_2 Xy Xz) → a_2 Xx Xz) False) % 17.01/17.24 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a → a → Prop) (a_3 : a), % 17.01/17.24 Or (Eq (∀ (Xx Xy Xz : a), And (a_1 Xx Xy) (a_1 Xy Xz) → a_1 Xx Xz) False) % 17.01/17.24 (Eq (Not (∀ (Xy : a), skS.0 0 a_2 (skS.0 1 a_2 a_1 a_3) Xy → a_1 (skS.0 1 a_2 a_1 a_3) Xy)) True) % 17.01/17.24 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 : a), % 17.01/17.24 Or (Eq (Not (∀ (Xy : a), skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) Xy → a_2 (skS.0 1 a_1 a_2 a_3) Xy)) True) % 17.01/17.24 (Eq (Not (∀ (Xy Xz : a), And (a_2 (skS.0 2 a_2 a_4) Xy) (a_2 Xy Xz) → a_2 (skS.0 2 a_2 a_4) Xz)) True) % 17.01/17.24 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : a), % 17.01/17.24 Or (Eq (Not (∀ (Xy Xz : a), And (a_1 (skS.0 2 a_1 a_2) Xy) (a_1 Xy Xz) → a_1 (skS.0 2 a_1 a_2) Xz)) True) % 17.01/17.24 (Eq (∀ (Xy : a), skS.0 0 a_3 (skS.0 1 a_3 a_1 a_4) Xy → a_1 (skS.0 1 a_3 a_1 a_4) Xy) False) % 17.01/17.24 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 : a), % 17.01/17.24 Or (Eq (∀ (Xy : a), skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) Xy → a_2 (skS.0 1 a_1 a_2 a_3) Xy) False) % 17.01/17.24 (Eq (∀ (Xy Xz : a), And (a_2 (skS.0 2 a_2 a_4) Xy) (a_2 Xy Xz) → a_2 (skS.0 2 a_2 a_4) Xz) False) % 17.01/17.24 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a), % 17.01/17.24 Or (Eq (∀ (Xy Xz : a), And (a_1 (skS.0 2 a_1 a_2) Xy) (a_1 Xy Xz) → a_1 (skS.0 2 a_1 a_2) Xz) False) % 17.01/17.24 (Eq % 17.01/17.24 (Not % 17.01/17.24 (skS.0 0 a_3 (skS.0 1 a_3 a_1 a_4) (skS.0 3 a_3 a_1 a_4 a_5) → % 17.01/17.24 a_1 (skS.0 1 a_3 a_1 a_4) (skS.0 3 a_3 a_1 a_4 a_5))) % 17.01/17.24 True) % 17.01/17.24 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 : a), % 17.01/17.24 Or % 17.01/17.24 (Eq % 17.01/17.24 (Not % 17.01/17.24 (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) → % 17.01/17.24 a_2 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) % 17.01/17.24 True) % 17.01/17.24 (Eq % 17.01/17.24 (Not % 17.01/17.24 (∀ (Xz : a), % 17.01/17.24 And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) Xz) → a_2 (skS.0 2 a_2 a_5) Xz)) % 17.01/17.24 True) % 17.01/17.24 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a), % 17.01/17.24 Or % 17.01/17.24 (Eq % 17.01/17.24 (Not % 17.01/17.24 (∀ (Xz : a), % 17.01/17.24 And (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) (a_1 (skS.0 4 a_1 a_2 a_3) Xz) → a_1 (skS.0 2 a_1 a_2) Xz)) % 17.01/17.24 True) % 17.01/17.24 (Eq % 17.01/17.24 (skS.0 0 a_4 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6) → % 17.01/17.24 a_1 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6)) % 17.01/17.24 False) % 17.01/17.24 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 : a), % 17.01/17.24 Or % 17.01/17.24 (Eq % 17.01/17.24 (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) → % 17.01/17.24 a_2 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) % 17.10/17.27 False) % 17.10/17.27 (Eq % 17.10/17.27 (∀ (Xz : a), % 17.10/17.27 And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) Xz) → a_2 (skS.0 2 a_2 a_5) Xz) % 17.10/17.27 False) % 17.10/17.27 Clause #14 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a), % 17.10/17.27 Or % 17.10/17.27 (Eq % 17.10/17.27 (∀ (Xz : a), % 17.10/17.27 And (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) (a_1 (skS.0 4 a_1 a_2 a_3) Xz) → a_1 (skS.0 2 a_1 a_2) Xz) % 17.10/17.27 False) % 17.10/17.27 (Eq (skS.0 0 a_4 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6)) True) % 17.10/17.27 Clause #15 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a), % 17.10/17.27 Or % 17.10/17.27 (Eq % 17.10/17.27 (∀ (Xz : a), % 17.10/17.27 And (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) (a_1 (skS.0 4 a_1 a_2 a_3) Xz) → a_1 (skS.0 2 a_1 a_2) Xz) % 17.10/17.27 False) % 17.10/17.27 (Eq (a_1 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6)) False) % 17.10/17.27 Clause #16 (by clausification #[14]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True) % 17.10/17.27 (Eq % 17.10/17.27 (Not % 17.10/17.27 (And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) (skS.0 5 a_2 a_5 a_6 a_7)) → % 17.10/17.27 a_2 (skS.0 2 a_2 a_5) (skS.0 5 a_2 a_5 a_6 a_7))) % 17.10/17.27 True) % 17.10/17.27 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True) % 17.10/17.27 (Eq % 17.10/17.27 (And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) (skS.0 5 a_2 a_5 a_6 a_7)) → % 17.10/17.27 a_2 (skS.0 2 a_2 a_5) (skS.0 5 a_2 a_5 a_6 a_7)) % 17.10/17.27 False) % 17.10/17.27 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True) % 17.10/17.27 (Eq (And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) (skS.0 5 a_2 a_5 a_6 a_7))) True) % 17.10/17.27 Clause #19 (by clausification #[17]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True) % 17.10/17.27 (Eq (a_2 (skS.0 2 a_2 a_5) (skS.0 5 a_2 a_5 a_6 a_7)) False) % 17.10/17.27 Clause #21 (by clausification #[18]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 : a), % 17.10/17.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True) % 17.10/17.27 (Eq (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) True) % 17.10/17.27 Clause #47 (by clausification #[15]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (a_1 (skS.0 1 a_2 a_1 a_3) (skS.0 3 a_2 a_1 a_3 a_4)) False) % 17.10/17.27 (Eq % 17.10/17.27 (Not % 17.10/17.27 (And (a_1 (skS.0 2 a_1 a_5) (skS.0 4 a_1 a_5 a_6)) (a_1 (skS.0 4 a_1 a_5 a_6) (skS.0 6 a_1 a_5 a_6 a_7)) → % 17.10/17.27 a_1 (skS.0 2 a_1 a_5) (skS.0 6 a_1 a_5 a_6 a_7))) % 17.10/17.27 True) % 17.10/17.27 Clause #48 (by clausification #[47]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (a_1 (skS.0 1 a_2 a_1 a_3) (skS.0 3 a_2 a_1 a_3 a_4)) False) % 17.10/17.27 (Eq % 17.10/17.27 (And (a_1 (skS.0 2 a_1 a_5) (skS.0 4 a_1 a_5 a_6)) (a_1 (skS.0 4 a_1 a_5 a_6) (skS.0 6 a_1 a_5 a_6 a_7)) → % 17.10/17.27 a_1 (skS.0 2 a_1 a_5) (skS.0 6 a_1 a_5 a_6 a_7)) % 17.10/17.27 False) % 17.10/17.27 Clause #50 (by clausification #[48]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a), % 17.10/17.27 Or (Eq (a_1 (skS.0 1 a_2 a_1 a_3) (skS.0 3 a_2 a_1 a_3 a_4)) False) % 17.10/17.27 (Eq (a_1 (skS.0 2 a_1 a_5) (skS.0 6 a_1 a_5 a_6 a_7)) False) % 17.10/17.27 Clause #203 (by fluidSup #[21, 19]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 : Prop) (a_6 a_7 : a), % 17.10/17.27 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) % 17.10/17.27 (Or (Eq (skS.0 0 a_4 (skS.0 1 a_4 (fun x x => a_5) a_6) (skS.0 3 a_4 (fun x x => a_5) a_6 a_7)) True) % 17.10/17.27 (Eq ((fun _ => a_5) True) False)) % 17.10/17.27 Clause #315 (by betaEtaReduce #[203]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 : Prop) (a_6 a_7 : a), % 17.10/17.27 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) % 17.10/17.27 (Or (Eq (skS.0 0 a_4 (skS.0 1 a_4 (fun x x => a_5) a_6) (skS.0 3 a_4 (fun x x => a_5) a_6 a_7)) True) % 17.10/17.27 (Eq a_5 False)) % 17.10/17.27 Clause #318 (by falseElim #[315]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a), % 17.10/17.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) % 17.10/17.32 (Eq (skS.0 0 a_4 (skS.0 1 a_4 (fun x x => True) a_5) (skS.0 3 a_4 (fun x x => True) a_5 a_6)) True) % 17.10/17.32 Clause #426 (by fluidSup #[318, 50]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : Prop) (a_5 a_6 a_7 : a), % 17.10/17.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) % 17.10/17.32 (Or (Eq ((fun _ => a_4) True) False) % 17.10/17.32 (Eq ((fun x x => a_4) (skS.0 2 (fun x x => a_4) a_5) (skS.0 6 (fun x x => a_4) a_5 a_6 a_7)) False)) % 17.10/17.32 Clause #942 (by betaEtaReduce #[426]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : Prop), % 17.10/17.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) (Or (Eq a_4 False) (Eq a_4 False)) % 17.10/17.32 Clause #943 (by eliminate duplicate literals #[942]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : Prop), % 17.10/17.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) (Eq a_4 False) % 17.10/17.32 Clause #948 (by falseElim #[943]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True % 17.10/17.32 Clause #1073 (by fluidSup #[948, 21]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 : a) (a_6 : Prop → a), % 17.10/17.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) % 17.10/17.32 (Eq (a_4 (skS.0 2 a_4 a_5) (skS.0 4 a_4 a_5 (a_6 True))) True) % 17.10/17.32 Clause #1339 (by equality factoring #[1073]): ∀ (a_1 : Prop) (a_2 a_3 : a), % 17.10/17.32 Or (Ne True True) (Eq ((fun x x => a_1) (skS.0 2 (fun x x => a_1) a_2) (skS.0 4 (fun x x => a_1) a_2 a_3)) True) % 17.10/17.32 Clause #1650 (by betaEtaReduce #[1339]): ∀ (a : Prop), Or (Ne True True) (Eq a True) % 17.10/17.32 Clause #1651 (by clausification #[1650]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False)) % 17.10/17.32 Clause #1653 (by clausification #[1651]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 17.10/17.32 Clause #1654 (by clausification #[1653]): ∀ (a : Prop), Eq a True % 17.10/17.32 Clause #1655 (by falseElim #[1654]): False % 17.10/17.32 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------