%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET589^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:00:11 PM UTC 2025 % Result : Theorem 3.67s 3.84s % Output : Proof 3.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET589^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.14/0.36 % Computer : n007.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 15:01:53 EDT 2025 % 0.14/0.36 % CPUTime : % 3.67/3.84 SZS status Theorem for theBenchmark.p % 3.67/3.84 SZS output start Proof for theBenchmark.p % 3.67/3.84 Clause #0 (by assumption #[]): Eq % 3.67/3.84 (Not % 3.67/3.84 (∀ (X Y Z V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (X Xx) (Not (V Xx)) → And (Y Xx) (Not (Z Xx)))) % 3.67/3.84 True % 3.67/3.84 Clause #1 (by clausification #[0]): Eq % 3.67/3.84 (∀ (X Y Z V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (X Xx) (Not (V Xx)) → And (Y Xx) (Not (Z Xx))) % 3.67/3.84 False % 3.67/3.84 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (Not % 3.67/3.84 (∀ (Y Z V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (V Xx)) → And (Y Xx) (Not (Z Xx)))) % 3.67/3.84 True % 3.67/3.84 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (∀ (Y Z V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (V Xx)) → And (Y Xx) (Not (Z Xx))) % 3.67/3.84 False % 3.67/3.84 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (Not % 3.67/3.84 (∀ (Z V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (V Xx)) → And (skS.0 1 a_1 a_2 Xx) (Not (Z Xx)))) % 3.67/3.84 True % 3.67/3.84 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (∀ (Z V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (V Xx)) → And (skS.0 1 a_1 a_2 Xx) (Not (Z Xx))) % 3.67/3.84 False % 3.67/3.84 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (Not % 3.67/3.84 (∀ (V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (V Xx)) → And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)))) % 3.67/3.84 True % 3.67/3.84 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (∀ (V : a → Prop), % 3.67/3.84 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → V Xx) → % 3.67/3.84 ∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (V Xx)) → And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx))) % 3.67/3.84 False % 3.67/3.84 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (Not % 3.67/3.84 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.67/3.84 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) → % 3.67/3.84 ∀ (Xx : a), % 3.67/3.84 And (skS.0 0 a_1 Xx) (Not (skS.0 3 a_1 a_2 a_3 a_4 Xx)) → % 3.67/3.84 And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)))) % 3.67/3.84 True % 3.67/3.84 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.67/3.84 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) → % 3.67/3.84 ∀ (Xx : a), % 3.67/3.84 And (skS.0 0 a_1 Xx) (Not (skS.0 3 a_1 a_2 a_3 a_4 Xx)) → % 3.67/3.84 And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx))) % 3.67/3.84 False % 3.67/3.84 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.67/3.84 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx)) % 3.67/3.84 True % 3.67/3.84 Clause #11 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.67/3.84 Eq % 3.67/3.84 (∀ (Xx : a), % 3.67/3.84 And (skS.0 0 a_1 Xx) (Not (skS.0 3 a_1 a_2 a_3 a_4 Xx)) → And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx))) % 3.67/3.84 False % 3.67/3.84 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), Eq (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) True % 3.67/3.84 Clause #13 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True % 3.67/3.84 Clause #14 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), Eq (skS.0 2 a_1 a_2 a_3 a_4 → skS.0 3 a_1 a_2 a_3 a_5 a_4) True % 3.67/3.86 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.67/3.86 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (skS.0 3 a_1 a_2 a_3 a_5 a_4) True) % 3.67/3.86 Clause #16 (by clausification #[13]): ∀ (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 % 3.67/3.86 Clause #17 (by clausification #[16]): ∀ (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) % 3.67/3.86 Clause #18 (by clausification #[11]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Eq % 3.67/3.86 (Not % 3.67/3.86 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (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))) → % 3.67/3.86 And (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5))))) % 3.67/3.86 True % 3.67/3.86 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Eq % 3.67/3.86 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (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))) → % 3.67/3.86 And (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)))) % 3.67/3.86 False % 3.67/3.86 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (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)))) % 3.67/3.86 True % 3.67/3.86 Clause #21 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Eq (And (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)))) % 3.67/3.86 False % 3.67/3.86 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), 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))) True % 3.67/3.86 Clause #23 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True % 3.67/3.86 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), 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)) False % 3.67/3.86 Clause #25 (by superposition #[23, 17]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.67/3.86 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) % 3.67/3.86 Clause #26 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) True % 3.67/3.86 Clause #27 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False) % 3.67/3.86 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) False) % 3.67/3.86 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False) % 3.67/3.86 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 3.67/3.86 Clause #29 (by forward demodulation #[28, 26]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.67/3.86 Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 3.67/3.86 Clause #30 (by clausification #[29]): ∀ (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 4 a_1 a_2 a_3 a_4 a_5)) True % 3.67/3.86 Clause #31 (by superposition #[30, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.67/3.86 Or (Eq True False) (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_5 a_6)) True) % 3.67/3.86 Clause #32 (by clausification #[31]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_5 a_6)) True % 3.67/3.86 Clause #33 (by superposition #[32, 24]): Eq True False % 3.67/3.86 Clause #34 (by clausification #[33]): False % 3.67/3.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------