%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET009^5 : 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 07:59:20 PM UTC 2025 % Result : Theorem 3.53s 3.75s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SET009^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % 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 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 14:04:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.53/3.75 SZS status Theorem for theBenchmark.p % 3.53/3.75 SZS output start Proof for theBenchmark.p % 3.53/3.75 Clause #0 (by assumption #[]): Eq % 3.53/3.75 (Not % 3.53/3.75 (∀ (X Y Z : a → Prop), (∀ (Xx : a), X Xx → Y Xx) → ∀ (Xx : a), And (Z Xx) (Not (Y Xx)) → And (Z Xx) (Not (X Xx)))) % 3.53/3.75 True % 3.53/3.75 Clause #1 (by clausification #[0]): Eq (∀ (X Y Z : a → Prop), (∀ (Xx : a), X Xx → Y Xx) → ∀ (Xx : a), And (Z Xx) (Not (Y Xx)) → And (Z Xx) (Not (X Xx))) % 3.53/3.75 False % 3.53/3.75 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 (Not % 3.53/3.75 (∀ (Y Z : a → Prop), % 3.53/3.75 (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) → ∀ (Xx : a), And (Z Xx) (Not (Y Xx)) → And (Z Xx) (Not (skS.0 0 a_1 Xx)))) % 3.53/3.75 True % 3.53/3.75 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 (∀ (Y Z : a → Prop), % 3.53/3.75 (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) → ∀ (Xx : a), And (Z Xx) (Not (Y Xx)) → And (Z Xx) (Not (skS.0 0 a_1 Xx))) % 3.53/3.75 False % 3.53/3.75 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 (Not % 3.53/3.75 (∀ (Z : a → Prop), % 3.53/3.75 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.53/3.75 ∀ (Xx : a), And (Z Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (Z Xx) (Not (skS.0 0 a_1 Xx)))) % 3.53/3.75 True % 3.53/3.75 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 (∀ (Z : a → Prop), % 3.53/3.75 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.53/3.75 ∀ (Xx : a), And (Z Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (Z Xx) (Not (skS.0 0 a_1 Xx))) % 3.53/3.75 False % 3.53/3.75 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 (Not % 3.53/3.75 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.53/3.75 ∀ (Xx : a), % 3.53/3.75 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → % 3.53/3.75 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))) % 3.53/3.75 True % 3.53/3.75 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 ((∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.53/3.75 ∀ (Xx : a), % 3.53/3.75 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 3.53/3.75 False % 3.53/3.75 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 % 3.53/3.75 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.53/3.75 Eq % 3.53/3.75 (∀ (Xx : a), % 3.53/3.75 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 3.53/3.75 False % 3.53/3.75 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 % 3.53/3.75 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) % 3.53/3.75 Clause #12 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.75 Eq % 3.53/3.75 (Not % 3.53/3.75 (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 3.53/3.75 And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))))) % 3.53/3.75 True % 3.53/3.75 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.75 Eq % 3.53/3.75 (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 3.53/3.75 And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.53/3.75 False % 3.53/3.75 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.75 Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)))) True % 3.53/3.75 Clause #15 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.75 Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))) False % 3.53/3.75 Clause #16 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True % 3.53/3.75 Clause #17 (by clausification #[14]): ∀ (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)) True % 3.53/3.75 Clause #18 (by clausification #[16]): ∀ (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 % 3.53/3.76 Clause #19 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.76 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) False) % 3.53/3.76 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.76 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 3.53/3.76 Clause #21 (by superposition #[20, 17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.53/3.76 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) % 3.53/3.76 (Eq False True) % 3.53/3.76 Clause #22 (by betaEtaReduce #[21]): ∀ (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) % 3.53/3.76 Clause #23 (by clausification #[22]): ∀ (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 % 3.53/3.76 Clause #25 (by superposition #[23, 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) % 3.53/3.76 Clause #26 (by clausification #[25]): ∀ (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 % 3.53/3.76 Clause #27 (by superposition #[26, 18]): Eq True False % 3.53/3.76 Clause #28 (by clausification #[27]): False % 3.53/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------