%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET638^5 : 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 08:00:19 PM UTC 2025 % Result : Theorem 5.86s 6.12s % Output : Proof 5.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : SET638^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.10 % Command : duper %s % 0.09/0.29 % Computer : n031.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 300 % 0.09/0.29 % DateTime : Thu Oct 2 13:52:53 EDT 2025 % 0.09/0.29 % CPUTime : % 5.86/6.12 SZS status Theorem for theBenchmark.p % 5.86/6.12 SZS output start Proof for theBenchmark.p % 5.86/6.12 Clause #0 (by assumption #[]): Eq % 5.86/6.12 (Not % 5.86/6.12 (∀ (X Y Z : a → Prop), % 5.86/6.12 And (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) (Eq (fun Xx => And (X Xx) (Z Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), X Xx → Y Xx)) % 5.86/6.12 True % 5.86/6.12 Clause #1 (by clausification #[0]): Eq % 5.86/6.12 (∀ (X Y Z : a → Prop), % 5.86/6.12 And (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) (Eq (fun Xx => And (X Xx) (Z Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), X Xx → Y Xx) % 5.86/6.12 False % 5.86/6.12 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (Not % 5.86/6.12 (∀ (Y Z : a → Prop), % 5.86/6.12 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) % 5.86/6.12 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx)) % 5.86/6.12 True % 5.86/6.12 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (∀ (Y Z : a → Prop), % 5.86/6.12 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) % 5.86/6.12 False % 5.86/6.12 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (Not % 5.86/6.12 (∀ (Z : a → Prop), % 5.86/6.12 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) % 5.86/6.12 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)) % 5.86/6.12 True % 5.86/6.12 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (∀ (Z : a → Prop), % 5.86/6.12 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) % 5.86/6.12 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 5.86/6.12 False % 5.86/6.12 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (Not % 5.86/6.12 (And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) % 5.86/6.12 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)) % 5.86/6.12 True % 5.86/6.12 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) % 5.86/6.12 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False) → % 5.86/6.12 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 5.86/6.12 False % 5.86/6.12 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.86/6.12 Eq % 5.86/6.12 (And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) % 5.86/6.12 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False)) % 5.86/6.12 True % 5.86/6.12 Clause #9 (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) False % 5.86/6.12 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False) True % 5.86/6.12 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) True % 5.86/6.12 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False % 5.86/6.12 Clause #13 (by argument congruence #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 5.86/6.12 Eq ((fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) a_4) ((fun Xx => False) a_4) % 5.86/6.12 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 5.86/6.12 Eq (Not (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 % 5.86/6.12 Clause #15 (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) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False % 5.86/6.12 Clause #16 (by clausification #[15]): ∀ (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 % 5.86/6.12 Clause #17 (by clausification #[15]): ∀ (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)) False % 5.86/6.12 Clause #18 (by betaEtaReduce #[13]): ∀ (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 % 5.95/6.15 Clause #19 (by clausification #[18]): ∀ (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) % 5.95/6.15 Clause #20 (by superposition #[19, 16]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 5.95/6.15 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) % 5.95/6.15 Clause #21 (by betaEtaReduce #[20]): ∀ (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) % 5.95/6.15 Clause #22 (by clausification #[21]): ∀ (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 % 5.95/6.15 Clause #23 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 5.95/6.15 Eq (skS.0 0 a_1 a_2 → Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True % 5.95/6.15 Clause #24 (by clausification #[23]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 5.95/6.15 Or (Eq (skS.0 0 a_1 a_2) False) (Eq (Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True) % 5.95/6.15 Clause #25 (by clausification #[24]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 5.95/6.15 Or (Eq (skS.0 0 a_1 a_2) False) (Or (Eq (skS.0 1 a_1 a_3 a_2) True) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True)) % 5.95/6.15 Clause #26 (by superposition #[25, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 5.95/6.15 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_3 a_4)) True) % 5.95/6.15 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True)) % 5.95/6.15 Clause #27 (by betaEtaReduce #[26]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 5.95/6.15 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 5.95/6.15 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True)) % 5.95/6.15 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 5.95/6.15 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) % 5.95/6.15 Clause #29 (by superposition #[28, 22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 5.95/6.15 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) (fun x => a_3 x) a_4)) True) % 5.95/6.15 (Eq True False) % 5.95/6.15 Clause #30 (by betaEtaReduce #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq True False) % 5.95/6.15 Clause #31 (by clausification #[30]): ∀ (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_3 a_4)) True % 5.95/6.15 Clause #33 (by superposition #[31, 17]): Eq True False % 5.95/6.15 Clause #35 (by clausification #[33]): False % 5.95/6.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------