%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV230^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:02:58 PM UTC 2025 % Result : Theorem 3.62s 3.85s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV230^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n031.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 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 01:49:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.62/3.85 SZS status Theorem for theBenchmark.p % 3.62/3.85 SZS output start Proof for theBenchmark.p % 3.62/3.85 Clause #0 (by assumption #[]): Eq % 3.62/3.85 (Not % 3.62/3.85 (∀ (U V : a → Prop), % 3.62/3.85 (∀ (Xx : a), U Xx → V Xx) → % 3.62/3.85 ∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → U Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → V Xx1)) % 3.62/3.85 True % 3.62/3.85 Clause #1 (by clausification #[0]): Eq % 3.62/3.85 (∀ (U V : a → Prop), % 3.62/3.85 (∀ (Xx : a), U Xx → V Xx) → % 3.62/3.85 ∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → U Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → V Xx1) % 3.62/3.85 False % 3.62/3.85 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.62/3.85 Eq % 3.62/3.85 (Not % 3.62/3.85 (∀ (V : a → Prop), % 3.62/3.85 (∀ (Xx : a), skS.0 0 a_1 Xx → V Xx) → % 3.62/3.85 ∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → V Xx1)) % 3.62/3.85 True % 3.62/3.85 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.62/3.85 Eq % 3.62/3.85 (∀ (V : a → Prop), % 3.62/3.85 (∀ (Xx : a), skS.0 0 a_1 Xx → V Xx) → % 3.62/3.85 ∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → V Xx1) % 3.62/3.85 False % 3.62/3.85 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.62/3.85 Eq % 3.62/3.85 (Not % 3.62/3.85 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.62/3.85 ∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 1 a_1 a_2 Xx1)) % 3.62/3.85 True % 3.62/3.85 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.62/3.85 Eq % 3.62/3.85 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.62/3.85 ∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 1 a_1 a_2 Xx1) % 3.62/3.85 False % 3.62/3.85 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 % 3.62/3.85 Clause #7 (by clausification #[5]): ∀ (a_1 a_2 : a → Prop), % 3.62/3.85 Eq % 3.62/3.85 (∀ (Xx : (a → Prop) → Prop), % 3.62/3.85 (∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), Xx Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 1 a_1 a_2 Xx1) % 3.62/3.85 False % 3.62/3.85 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 % 3.62/3.85 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) % 3.62/3.85 Clause #10 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop), % 3.62/3.85 Eq % 3.62/3.85 (Not % 3.62/3.85 ((∀ (Xx0 : a → Prop), skS.0 2 a_1 a_2 a_3 Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), skS.0 2 a_1 a_2 a_3 Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 1 a_1 a_2 Xx1)) % 3.62/3.85 True % 3.62/3.85 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop), % 3.62/3.85 Eq % 3.62/3.85 ((∀ (Xx0 : a → Prop), skS.0 2 a_1 a_2 a_3 Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) → % 3.62/3.85 ∀ (Xx0 : a → Prop), skS.0 2 a_1 a_2 a_3 Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 1 a_1 a_2 Xx1) % 3.62/3.85 False % 3.62/3.85 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop), % 3.62/3.85 Eq (∀ (Xx0 : a → Prop), skS.0 2 a_1 a_2 a_3 Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 0 a_1 Xx1) True % 3.62/3.85 Clause #13 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop), % 3.62/3.85 Eq (∀ (Xx0 : a → Prop), skS.0 2 a_1 a_2 a_3 Xx0 → ∀ (Xx1 : a), Xx0 Xx1 → skS.0 1 a_1 a_2 Xx1) False % 3.62/3.85 Clause #14 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 3.71/3.87 Eq (skS.0 2 a_1 a_2 a_3 a_4 → ∀ (Xx1 : a), a_4 Xx1 → skS.0 0 a_1 Xx1) True % 3.71/3.87 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 3.71/3.87 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (∀ (Xx1 : a), a_4 Xx1 → skS.0 0 a_1 Xx1) True) % 3.71/3.87 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (a_4 a_5 → skS.0 0 a_1 a_5) True) % 3.71/3.87 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Or (Eq (a_4 a_5) False) (Eq (skS.0 0 a_1 a_5) True)) % 3.71/3.87 Clause #18 (by clausification #[13]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 3.71/3.87 Eq % 3.71/3.87 (Not % 3.71/3.87 (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4) → ∀ (Xx1 : a), skS.0 3 a_1 a_2 a_3 a_4 Xx1 → skS.0 1 a_1 a_2 Xx1)) % 3.71/3.87 True % 3.71/3.87 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 3.71/3.87 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4) → ∀ (Xx1 : a), skS.0 3 a_1 a_2 a_3 a_4 Xx1 → skS.0 1 a_1 a_2 Xx1) % 3.71/3.87 False % 3.71/3.87 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 3.71/3.87 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.71/3.87 Clause #21 (by clausification #[19]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 3.71/3.87 Eq (∀ (Xx1 : a), skS.0 3 a_1 a_2 a_3 a_4 Xx1 → skS.0 1 a_1 a_2 Xx1) False % 3.71/3.87 Clause #22 (by superposition #[20, 17]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Or (Eq True False) (Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5) False) (Eq (skS.0 0 a_1 a_5) True)) % 3.71/3.87 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Eq (Not (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) True % 3.71/3.87 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False % 3.71/3.87 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True % 3.71/3.87 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False % 3.71/3.87 Clause #27 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5) False) (Eq (skS.0 0 a_1 a_5) True) % 3.71/3.87 Clause #28 (by superposition #[27, 25]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) (Eq False True) % 3.71/3.87 Clause #29 (by betaEtaReduce #[28]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) (Eq False True) % 3.71/3.87 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop) (a_5 : a), % 3.71/3.87 Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True % 3.71/3.87 Clause #31 (by superposition #[30, 9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : (a → Prop) → Prop) (a_5 : a → Prop) (a_6 : a), % 3.71/3.87 Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) True) % 3.71/3.87 Clause #32 (by clausification #[31]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : (a → Prop) → Prop) (a_5 : a → Prop) (a_6 : a), % 3.71/3.87 Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) True % 3.71/3.87 Clause #33 (by superposition #[32, 26]): Eq True False % 3.71/3.87 Clause #34 (by clausification #[33]): False % 3.71/3.87 SZS output end Proof for theBenchmark.p 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