%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET625^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:00:17 PM UTC 2025 % Result : Theorem 3.42s 3.64s % Output : Proof 3.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET625^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 2 13:53:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.42/3.64 SZS status Theorem for theBenchmark.p % 3.42/3.64 SZS output start Proof for theBenchmark.p % 3.42/3.64 Clause #0 (by assumption #[]): Eq % 3.42/3.64 (Not % 3.42/3.64 (∀ (X Y Z : a → Prop), % 3.42/3.64 And (Exists fun Xx => And (X Xx) (Y Xx)) (∀ (Xx : a), Y Xx → Z Xx) → Exists fun Xx => And (X Xx) (Z Xx))) % 3.42/3.64 True % 3.42/3.64 Clause #1 (by clausification #[0]): Eq % 3.42/3.64 (∀ (X Y Z : a → Prop), % 3.42/3.64 And (Exists fun Xx => And (X Xx) (Y Xx)) (∀ (Xx : a), Y Xx → Z Xx) → Exists fun Xx => And (X Xx) (Z Xx)) % 3.42/3.64 False % 3.42/3.64 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (Not % 3.42/3.64 (∀ (Y Z : a → Prop), % 3.42/3.64 And (Exists fun Xx => And (skS.0 0 a_1 Xx) (Y Xx)) (∀ (Xx : a), Y Xx → Z Xx) → % 3.42/3.64 Exists fun Xx => And (skS.0 0 a_1 Xx) (Z Xx))) % 3.42/3.64 True % 3.42/3.64 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (∀ (Y Z : a → Prop), % 3.42/3.64 And (Exists fun Xx => And (skS.0 0 a_1 Xx) (Y Xx)) (∀ (Xx : a), Y Xx → Z Xx) → % 3.42/3.64 Exists fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) % 3.42/3.64 False % 3.42/3.64 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (Not % 3.42/3.64 (∀ (Z : a → Prop), % 3.42/3.64 And (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx)) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Z Xx) → % 3.42/3.64 Exists fun Xx => And (skS.0 0 a_1 Xx) (Z Xx))) % 3.42/3.64 True % 3.42/3.64 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (∀ (Z : a → Prop), % 3.42/3.64 And (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx)) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Z Xx) → % 3.42/3.64 Exists fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) % 3.42/3.64 False % 3.42/3.64 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (Not % 3.42/3.64 (And (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx)) % 3.42/3.64 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 3.42/3.64 Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) % 3.42/3.64 True % 3.42/3.64 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (And (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx)) % 3.42/3.64 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 3.42/3.64 Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) % 3.42/3.64 False % 3.42/3.64 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.42/3.64 Eq % 3.42/3.64 (And (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx)) % 3.42/3.64 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.42/3.64 True % 3.42/3.64 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) False % 3.42/3.64 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 % 3.42/3.64 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 : a → Prop), Eq (Exists fun Xx => And (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx)) True % 3.42/3.64 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 % 3.42/3.64 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 3.42/3.64 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) % 3.42/3.64 Clause #14 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.42/3.64 Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3))) True % 3.42/3.64 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) True % 3.42/3.64 Clause #16 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True % 3.42/3.64 Clause #17 (by superposition #[15, 13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_4)) True) % 3.42/3.64 Clause #18 (by clausification #[17]): ∀ (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_4)) True % 3.42/3.64 Clause #19 (by clausification #[9]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Eq (And (skS.0 0 a_1 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) False % 3.42/3.64 Clause #20 (by clausification #[19]): ∀ (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) False) % 3.42/3.65 Clause #21 (by superposition #[20, 16]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.42/3.65 Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_3 (skS.0 3 a_1 a_4 a_5)) False) (Eq False True) % 3.42/3.65 Clause #22 (by betaEtaReduce #[21]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) False) (Eq False True) % 3.42/3.65 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) False % 3.42/3.65 Clause #24 (by superposition #[23, 18]): Eq False True % 3.42/3.65 Clause #25 (by clausification #[24]): False % 3.42/3.65 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------