%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET027^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 07:59:25 PM UTC 2025 % Result : Theorem 3.63s 3.86s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET027^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 14:46:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.63/3.86 SZS status Theorem for theBenchmark.p % 3.63/3.86 SZS output start Proof for theBenchmark.p % 3.63/3.86 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y Z : a → Prop), And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), X Xx → Z Xx)) True % 3.63/3.86 Clause #1 (by clausification #[0]): Eq (∀ (X Y Z : a → Prop), And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), X Xx → Z Xx) False % 3.63/3.86 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.63/3.86 Eq % 3.63/3.86 (Not % 3.63/3.86 (∀ (Y Z : a → Prop), % 3.63/3.86 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx)) % 3.63/3.86 True % 3.63/3.86 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.63/3.86 Eq % 3.63/3.86 (∀ (Y Z : a → Prop), % 3.63/3.86 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) % 3.63/3.86 False % 3.63/3.86 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.63/3.86 Eq % 3.63/3.86 (Not % 3.63/3.86 (∀ (Z : a → Prop), % 3.63/3.86 And (∀ (Xx : a), 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) → % 3.63/3.86 ∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx)) % 3.63/3.86 True % 3.63/3.86 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.63/3.86 Eq % 3.63/3.86 (∀ (Z : a → Prop), % 3.63/3.86 And (∀ (Xx : a), 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) → % 3.63/3.86 ∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) % 3.63/3.86 False % 3.63/3.86 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.63/3.86 Eq % 3.63/3.86 (Not % 3.63/3.86 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 3.63/3.86 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.63/3.86 True % 3.63/3.86 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.63/3.86 Eq % 3.63/3.86 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 3.63/3.86 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.63/3.86 False % 3.63/3.86 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.63/3.86 Eq (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.63/3.86 True % 3.63/3.86 Clause #9 (by clausification #[7]): ∀ (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) False % 3.63/3.86 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 % 3.63/3.86 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True % 3.63/3.86 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 % 3.63/3.86 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 3.63/3.86 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) % 3.63/3.86 Clause #14 (by clausification #[11]): ∀ (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 % 3.63/3.86 Clause #15 (by clausification #[14]): ∀ (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) % 3.63/3.86 Clause #16 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.63/3.86 Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) True % 3.63/3.86 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.63/3.86 Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False % 3.63/3.86 Clause #18 (by clausification #[17]): ∀ (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 % 3.63/3.86 Clause #19 (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_3 a_4)) False % 3.63/3.86 Clause #20 (by superposition #[18, 15]): ∀ (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) % 3.63/3.86 Clause #21 (by clausification #[20]): ∀ (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 % 3.63/3.87 Clause #22 (by superposition #[21, 13]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.63/3.87 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) % 3.63/3.87 Clause #23 (by clausification #[22]): ∀ (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 % 3.63/3.87 Clause #24 (by superposition #[23, 19]): Eq True False % 3.63/3.87 Clause #25 (by clausification #[24]): False % 3.63/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------