%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET185^5 : 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 07:59:46 PM UTC 2025 % Result : Theorem 3.45s 3.66s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET185^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n018.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 : Thu Oct 2 13:38:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.45/3.66 SZS status Theorem for theBenchmark.p % 3.45/3.66 SZS output start Proof for theBenchmark.p % 3.45/3.66 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y : a → Prop), (∀ (Xx : a), X Xx → Y Xx) → ∀ (Xx : a), Or (X Xx) (Y Xx) → Y Xx)) True % 3.45/3.66 Clause #1 (by clausification #[0]): Eq (∀ (X Y : a → Prop), (∀ (Xx : a), X Xx → Y Xx) → ∀ (Xx : a), Or (X Xx) (Y Xx) → Y Xx) False % 3.45/3.66 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.45/3.66 Eq (Not (∀ (Y : a → Prop), (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) → ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Y Xx) → Y Xx)) True % 3.45/3.66 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.45/3.66 Eq (∀ (Y : a → Prop), (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) → ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Y Xx) → Y Xx) False % 3.45/3.66 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.45/3.66 Eq % 3.45/3.66 (Not % 3.45/3.66 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.45/3.66 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 1 a_1 a_2 Xx)) % 3.45/3.66 True % 3.45/3.66 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.45/3.66 Eq % 3.45/3.66 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.45/3.66 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 1 a_1 a_2 Xx) % 3.45/3.66 False % 3.45/3.66 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True % 3.45/3.66 Clause #7 (by clausification #[5]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 1 a_1 a_2 Xx) False % 3.45/3.66 Clause #8 (by clausification #[6]): ∀ (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 % 3.45/3.66 Clause #9 (by clausification #[8]): ∀ (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) % 3.45/3.66 Clause #10 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.45/3.66 Eq % 3.45/3.66 (Not % 3.45/3.66 (Or (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3)) → % 3.45/3.66 skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3))) % 3.45/3.66 True % 3.45/3.66 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.45/3.66 Eq % 3.45/3.66 (Or (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3)) → % 3.45/3.66 skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3)) % 3.45/3.66 False % 3.45/3.66 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.45/3.66 Eq (Or (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3))) True % 3.45/3.66 Clause #13 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3)) False % 3.45/3.66 Clause #14 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.45/3.66 Or (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3)) True) % 3.45/3.66 Clause #15 (by superposition #[13, 14]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.45/3.66 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 2 (fun x => a_1 x) (fun x => a_2 x) a_3)) True) (Eq True False) % 3.45/3.66 Clause #16 (by betaEtaReduce #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) True) (Eq True False) % 3.45/3.66 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) True % 3.45/3.66 Clause #19 (by superposition #[17, 9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_3 a_4)) True) % 3.45/3.66 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_3 a_4)) True % 3.45/3.66 Clause #21 (by superposition #[20, 13]): Eq True False % 3.45/3.66 Clause #22 (by clausification #[21]): False % 3.45/3.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------