%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET584^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:00:11 PM UTC 2025 % Result : Theorem 4.08s 4.31s % Output : Proof 4.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.14 % Problem : SET584^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.15 % Command : duper %s % 0.12/0.36 % Computer : n018.cluster.edu % 0.12/0.36 % Model : x86_64 x86_64 % 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.36 % Memory : 8042.1875MB % 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.36 % CPULimit : 300 % 0.12/0.36 % WCLimit : 300 % 0.12/0.36 % DateTime : Thu Oct 2 14:14:23 EDT 2025 % 0.12/0.36 % CPUTime : % 4.08/4.31 SZS status Theorem for theBenchmark.p % 4.08/4.31 SZS output start Proof for theBenchmark.p % 4.08/4.31 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y Z : a → Prop), (∀ (Xx : a), X Xx → Y Xx) → ∀ (Xx : a), Or (X Xx) (Z Xx) → Or (Y Xx) (Z Xx))) True % 4.08/4.31 Clause #1 (by clausification #[0]): Eq (∀ (X Y Z : a → Prop), (∀ (Xx : a), X Xx → Y Xx) → ∀ (Xx : a), Or (X Xx) (Z Xx) → Or (Y Xx) (Z Xx)) False % 4.08/4.31 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 4.08/4.31 Eq % 4.08/4.31 (Not % 4.08/4.31 (∀ (Y Z : a → Prop), % 4.08/4.31 (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) → ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (Y Xx) (Z Xx))) % 4.08/4.31 True % 4.08/4.31 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 4.08/4.31 Eq % 4.08/4.31 (∀ (Y Z : a → Prop), % 4.08/4.31 (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) → ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (Y Xx) (Z Xx)) % 4.08/4.31 False % 4.08/4.31 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 4.08/4.31 Eq % 4.08/4.31 (Not % 4.08/4.31 (∀ (Z : a → Prop), % 4.08/4.31 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 4.08/4.31 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (skS.0 1 a_1 a_2 Xx) (Z Xx))) % 4.08/4.31 True % 4.08/4.31 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 4.08/4.31 Eq % 4.08/4.31 (∀ (Z : a → Prop), % 4.08/4.31 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 4.08/4.31 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) % 4.08/4.31 False % 4.08/4.31 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.08/4.31 Eq % 4.08/4.31 (Not % 4.08/4.31 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 4.08/4.31 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) % 4.08/4.31 True % 4.08/4.31 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.08/4.31 Eq % 4.08/4.31 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 4.08/4.31 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) % 4.08/4.31 False % 4.08/4.31 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True % 4.08/4.31 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.08/4.31 Eq (∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) False % 4.08/4.31 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True % 4.08/4.31 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 1 a_1 a_3 a_2) True) % 4.08/4.31 Clause #12 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.08/4.31 Eq % 4.08/4.31 (Not % 4.08/4.31 (Or (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) → % 4.08/4.31 Or (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 (skS.0 3 a_1 a_2 a_3 a_4)))) % 4.08/4.31 True % 4.08/4.31 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.08/4.31 Eq % 4.08/4.31 (Or (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) → % 4.08/4.31 Or (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 (skS.0 3 a_1 a_2 a_3 a_4))) % 4.08/4.31 False % 4.08/4.31 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.08/4.31 Eq (Or (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) True % 4.08/4.31 Clause #15 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.08/4.31 Eq (Or (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 (skS.0 3 a_1 a_2 a_3 a_4))) False % 4.08/4.31 Clause #16 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.08/4.31 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.08/4.31 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False % 4.08/4.31 Clause #18 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False % 4.08/4.31 Clause #19 (by superposition #[17, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq False True) % 4.08/4.31 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True % 4.08/4.31 Clause #22 (by superposition #[20, 11]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True) % 4.08/4.31 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True % 4.08/4.31 Clause #24 (by superposition #[23, 18]): Eq True False % 4.08/4.31 Clause #25 (by clausification #[24]): False % 4.08/4.31 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------