%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV017^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 3.74s 3.92s % Output : Proof 3.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEV017^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n026.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % 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 01:43:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.74/3.92 SZS status Theorem for theBenchmark.p % 3.74/3.92 SZS output start Proof for theBenchmark.p % 3.74/3.92 Clause #0 (by assumption #[]): Eq % 3.74/3.92 (Not % 3.74/3.92 (∀ (Xr : a → a → Prop), % 3.74/3.92 And (And (∀ (Xx : a), Xr Xx Xx) (∀ (Xx Xy : a), Xr Xx Xy → Xr Xy Xx)) % 3.74/3.92 (∀ (Xx Xy Xz : a), And (Xr Xx Xy) (Xr Xy Xz) → Xr Xx Xz) → % 3.74/3.92 ∀ (Xx Xy Xz : a), Xr Xx Xy → Xr Xy Xz → Xr Xx Xz)) % 3.74/3.92 True % 3.74/3.92 Clause #1 (by clausification #[0]): Eq % 3.74/3.92 (∀ (Xr : a → a → Prop), % 3.74/3.92 And (And (∀ (Xx : a), Xr Xx Xx) (∀ (Xx Xy : a), Xr Xx Xy → Xr Xy Xx)) % 3.74/3.92 (∀ (Xx Xy Xz : a), And (Xr Xx Xy) (Xr Xy Xz) → Xr Xx Xz) → % 3.74/3.92 ∀ (Xx Xy Xz : a), Xr Xx Xy → Xr Xy Xz → Xr Xx Xz) % 3.74/3.92 False % 3.74/3.92 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 3.74/3.92 Eq % 3.74/3.92 (Not % 3.74/3.92 (And (And (∀ (Xx : a), skS.0 0 a_1 Xx Xx) (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)) % 3.74/3.92 (∀ (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) → % 3.74/3.92 ∀ (Xx Xy Xz : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xz → skS.0 0 a_1 Xx Xz)) % 3.74/3.92 True % 3.74/3.92 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 3.74/3.92 Eq % 3.74/3.92 (And (And (∀ (Xx : a), skS.0 0 a_1 Xx Xx) (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)) % 3.74/3.92 (∀ (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) → % 3.74/3.92 ∀ (Xx Xy Xz : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xz → skS.0 0 a_1 Xx Xz) % 3.74/3.92 False % 3.74/3.92 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop), % 3.74/3.92 Eq % 3.74/3.92 (And (And (∀ (Xx : a), skS.0 0 a_1 Xx Xx) (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)) % 3.74/3.92 (∀ (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)) % 3.74/3.92 True % 3.74/3.92 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xx Xy Xz : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xz → skS.0 0 a_1 Xx Xz) False % 3.74/3.92 Clause #6 (by clausification #[4]): ∀ (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 % 3.74/3.92 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.74/3.92 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 % 3.74/3.92 Clause #9 (by clausification #[8]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.74/3.92 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 % 3.74/3.92 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.92 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 % 3.74/3.92 Clause #11 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.92 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) % 3.74/3.92 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.92 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)) % 3.74/3.92 Clause #13 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.74/3.92 Eq (Not (∀ (Xy Xz : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → skS.0 0 a_1 Xy Xz → skS.0 0 a_1 (skS.0 1 a_1 a_2) Xz)) True % 3.74/3.92 Clause #14 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.74/3.92 Eq (∀ (Xy Xz : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → skS.0 0 a_1 Xy Xz → skS.0 0 a_1 (skS.0 1 a_1 a_2) Xz) False % 3.74/3.92 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.74/3.92 Eq % 3.74/3.92 (Not % 3.74/3.92 (∀ (Xz : a), % 3.74/3.92 skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.74/3.92 skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xz → skS.0 0 a_1 (skS.0 1 a_1 a_2) Xz)) % 3.74/3.92 True % 3.74/3.92 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.74/3.92 Eq % 3.74/3.92 (∀ (Xz : a), % 3.74/3.92 skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.74/3.92 skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) Xz → skS.0 0 a_1 (skS.0 1 a_1 a_2) Xz) % 3.74/3.92 False % 3.74/3.92 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.92 Eq % 3.74/3.92 (Not % 3.74/3.92 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.74/3.92 skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) → % 3.74/3.94 skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 3 a_1 a_2 a_3 a_4))) % 3.74/3.94 True % 3.74/3.94 Clause #18 (by clausification #[17]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.94 Eq % 3.74/3.94 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.74/3.94 skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) → % 3.74/3.94 skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 3 a_1 a_2 a_3 a_4)) % 3.74/3.94 False % 3.74/3.94 Clause #19 (by clausification #[18]): ∀ (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 % 3.74/3.94 Clause #20 (by clausification #[18]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.94 Eq % 3.74/3.94 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) → % 3.74/3.94 skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 3 a_1 a_2 a_3 a_4)) % 3.74/3.94 False % 3.74/3.94 Clause #21 (by superposition #[19, 12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.94 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) a_3) True) % 3.74/3.94 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_4) a_3) False)) % 3.74/3.94 Clause #31 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.74/3.94 Clause #32 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 3 a_1 a_2 a_3 a_4)) False % 3.74/3.94 Clause #42 (by clausification #[21]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.94 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) % 3.74/3.94 Clause #43 (by superposition #[42, 31]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.94 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) (skS.0 1 (fun x x_1 => a_1 x x_1) a_2) (skS.0 3 a_1 a_2 a_3 a_4)) True) % 3.74/3.94 (Eq False True) % 3.74/3.94 Clause #48 (by betaEtaReduce #[43]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 3.74/3.94 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq False True) % 3.74/3.94 Clause #49 (by clausification #[48]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.74/3.94 Clause #50 (by superposition #[49, 32]): Eq True False % 3.74/3.94 Clause #53 (by clausification #[50]): False % 3.74/3.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------