%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV131^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:02:52 PM UTC 2025 % Result : Theorem 3.56s 3.77s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV131^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n022.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 01:29:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.56/3.77 SZS status Theorem for theBenchmark.p % 3.56/3.77 SZS output start Proof for theBenchmark.p % 3.56/3.77 Clause #0 (by assumption #[]): Eq % 3.56/3.77 (Not % 3.56/3.77 (∀ (Xr : a → a → Prop) (Xx Xy : a), % 3.56/3.77 Xr Xx Xy → ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (Xr Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy)) % 3.56/3.77 True % 3.56/3.77 Clause #1 (by clausification #[0]): Eq % 3.56/3.77 (∀ (Xr : a → a → Prop) (Xx Xy : a), % 3.56/3.77 Xr Xx Xy → ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (Xr Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy) % 3.56/3.77 False % 3.56/3.77 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 (∀ (Xx Xy : a), % 3.56/3.77 skS.0 0 a_1 Xx Xy → % 3.56/3.77 ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy)) % 3.56/3.77 True % 3.56/3.77 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 3.56/3.77 Eq % 3.56/3.77 (∀ (Xx Xy : a), % 3.56/3.77 skS.0 0 a_1 Xx Xy → % 3.56/3.77 ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy) % 3.56/3.77 False % 3.56/3.77 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 (∀ (Xy : a), % 3.56/3.77 skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → % 3.56/3.77 ∀ (Xx0 : a → Prop), % 3.56/3.77 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 (skS.0 1 a_1 a_2) → Xx0 Xy)) % 3.56/3.77 True % 3.56/3.77 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.56/3.77 Eq % 3.56/3.77 (∀ (Xy : a), % 3.56/3.77 skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → % 3.56/3.77 ∀ (Xx0 : a → Prop), % 3.56/3.77 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 (skS.0 1 a_1 a_2) → Xx0 Xy) % 3.56/3.77 False % 3.56/3.77 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.56/3.77 ∀ (Xx0 : a → Prop), % 3.56/3.77 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → % 3.56/3.77 Xx0 (skS.0 1 a_1 a_2) → Xx0 (skS.0 2 a_1 a_2 a_3))) % 3.56/3.77 True % 3.56/3.77 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.56/3.77 Eq % 3.56/3.77 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.56/3.77 ∀ (Xx0 : a → Prop), % 3.56/3.77 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → % 3.56/3.77 Xx0 (skS.0 1 a_1 a_2) → Xx0 (skS.0 2 a_1 a_2 a_3)) % 3.56/3.77 False % 3.56/3.77 Clause #8 (by clausification #[7]): ∀ (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 % 3.56/3.77 Clause #9 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.56/3.77 Eq % 3.56/3.77 (∀ (Xx0 : a → Prop), % 3.56/3.77 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 (skS.0 1 a_1 a_2) → Xx0 (skS.0 2 a_1 a_2 a_3)) % 3.56/3.77 False % 3.56/3.77 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 ((∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (skS.0 3 a_1 a_2 a_3 a_4 Xy0) → skS.0 3 a_1 a_2 a_3 a_4 Xz) → % 3.56/3.77 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2) → skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3))) % 3.56/3.77 True % 3.56/3.77 Clause #11 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.56/3.77 Eq % 3.56/3.77 ((∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (skS.0 3 a_1 a_2 a_3 a_4 Xy0) → skS.0 3 a_1 a_2 a_3 a_4 Xz) → % 3.56/3.77 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2) → skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) % 3.56/3.77 False % 3.56/3.77 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.56/3.77 Eq (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (skS.0 3 a_1 a_2 a_3 a_4 Xy0) → skS.0 3 a_1 a_2 a_3 a_4 Xz) True % 3.56/3.77 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.56/3.77 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2) → skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) False % 3.56/3.77 Clause #14 (by clausification #[12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a) (a_5 : a → Prop), % 3.56/3.77 Eq (∀ (Xz : a), And (skS.0 0 a_1 a_2 Xz) (skS.0 3 a_1 a_3 a_4 a_5 a_2) → skS.0 3 a_1 a_3 a_4 a_5 Xz) True % 3.56/3.77 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 a_5 : a) (a_6 : a → Prop), % 3.62/3.78 Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 3 a_1 a_4 a_5 a_6 a_2) → skS.0 3 a_1 a_4 a_5 a_6 a_3) True % 3.62/3.78 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 a_5 : a) (a_6 : a → Prop), % 3.62/3.78 Or (Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 3 a_1 a_4 a_5 a_6 a_2)) False) (Eq (skS.0 3 a_1 a_4 a_5 a_6 a_3) True) % 3.62/3.78 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 3.62/3.78 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5) True) % 3.62/3.78 (Or (Eq (skS.0 0 a_1 a_6 a_5) False) (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_6) False)) % 3.62/3.78 Clause #18 (by superposition #[17, 8]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 3.62/3.78 Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 a_4 (skS.0 2 a_1 a_5 a_6)) True) % 3.62/3.78 (Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 a_4 (skS.0 1 a_1 a_5)) False) (Eq False True)) % 3.62/3.78 Clause #19 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2)) True % 3.62/3.78 Clause #20 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) False % 3.62/3.78 Clause #21 (by betaEtaReduce #[18]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 3.62/3.78 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_5 a_6)) True) % 3.62/3.78 (Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_5)) False) (Eq False True)) % 3.62/3.78 Clause #22 (by clausification #[21]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 3.62/3.78 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_5 a_6)) True) (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_5)) False) % 3.62/3.78 Clause #23 (by superposition #[22, 19]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 3.62/3.78 Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 (fun x => a_4 x) (skS.0 2 (fun x x_1 => a_1 x x_1) a_2 a_5)) True) % 3.62/3.78 (Eq False True) % 3.62/3.78 Clause #24 (by betaEtaReduce #[23]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 3.62/3.78 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True) (Eq False True) % 3.62/3.78 Clause #25 (by clausification #[24]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True % 3.62/3.78 Clause #26 (by superposition #[25, 20]): Eq True False % 3.62/3.78 Clause #27 (by clausification #[26]): False % 3.62/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------