%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET014^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 07:59:21 PM UTC 2025 % Result : Theorem 3.72s 3.90s % Output : Proof 3.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET014^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 13:44:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.72/3.90 SZS status Theorem for theBenchmark.p % 3.72/3.90 SZS output start Proof for theBenchmark.p % 3.72/3.90 Clause #0 (by assumption #[]): Eq % 3.72/3.90 (Not % 3.72/3.90 (∀ (X Y Z : a → Prop), % 3.72/3.90 And (∀ (Xx : a), X Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), Or (X Xx) (Y Xx) → Z Xx)) % 3.72/3.90 True % 3.72/3.90 Clause #1 (by clausification #[0]): Eq (∀ (X Y Z : a → Prop), And (∀ (Xx : a), X Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), Or (X Xx) (Y Xx) → Z Xx) % 3.72/3.90 False % 3.72/3.90 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (Not % 3.72/3.90 (∀ (Y Z : a → Prop), % 3.72/3.90 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → % 3.72/3.90 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Y Xx) → Z Xx)) % 3.72/3.90 True % 3.72/3.90 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (∀ (Y Z : a → Prop), % 3.72/3.90 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Y Xx) → Z Xx) % 3.72/3.90 False % 3.72/3.90 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (Not % 3.72/3.90 (∀ (Z : a → Prop), % 3.72/3.90 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Z Xx) → % 3.72/3.90 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → Z Xx)) % 3.72/3.90 True % 3.72/3.90 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (∀ (Z : a → Prop), % 3.72/3.90 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Z Xx) → % 3.72/3.90 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → Z Xx) % 3.72/3.90 False % 3.72/3.90 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (Not % 3.72/3.90 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.72/3.90 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 3.72/3.90 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 2 a_1 a_2 a_3 Xx)) % 3.72/3.90 True % 3.72/3.90 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.72/3.90 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 3.72/3.90 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 2 a_1 a_2 a_3 Xx) % 3.72/3.90 False % 3.72/3.90 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.72/3.90 Eq % 3.72/3.90 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.72/3.90 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.72/3.90 True % 3.72/3.90 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 2 a_1 a_2 a_3 Xx) False % 3.72/3.90 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) True % 3.72/3.90 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) True % 3.72/3.90 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), Eq (skS.0 1 a_1 a_2 a_3 → skS.0 2 a_1 a_2 a_4 a_3) True % 3.72/3.90 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 3.72/3.90 Or (Eq (skS.0 1 a_1 a_2 a_3) False) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) % 3.72/3.90 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.72/3.90 Eq % 3.72/3.90 (Not % 3.72/3.90 (Or (skS.0 0 a_1 (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)) → % 3.72/3.90 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) % 3.72/3.90 True % 3.72/3.90 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.72/3.90 Eq % 3.72/3.90 (Or (skS.0 0 a_1 (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)) → % 3.72/3.90 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) % 3.72/3.90 False % 3.72/3.90 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.72/3.90 Eq (Or (skS.0 0 a_1 (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))) True % 3.72/3.90 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 % 3.72/3.90 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.72/3.90 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 3.72/3.92 Clause #19 (by superposition #[18, 13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.72/3.92 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True) % 3.72/3.92 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True)) % 3.72/3.92 Clause #20 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 2 a_1 a_3 a_4 a_2) True % 3.72/3.92 Clause #21 (by clausification #[20]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True) % 3.72/3.92 Clause #22 (by betaEtaReduce #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.72/3.92 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 3.72/3.92 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True)) % 3.72/3.92 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.72/3.92 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_5 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 3.72/3.92 Clause #24 (by superposition #[23, 17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.72/3.92 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True) % 3.72/3.92 (Eq True False) % 3.72/3.92 Clause #25 (by betaEtaReduce #[24]): ∀ (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 True False) % 3.72/3.92 Clause #26 (by clausification #[25]): ∀ (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 % 3.72/3.92 Clause #29 (by superposition #[26, 21]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.72/3.92 Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True) % 3.72/3.92 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True % 3.72/3.92 Clause #31 (by superposition #[30, 17]): Eq True False % 3.72/3.92 Clause #32 (by clausification #[31]): False % 3.72/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------