%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET200^5 : 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 07:59:48 PM UTC 2025 % Result : Theorem 3.83s 4.04s % Output : Proof 3.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET200^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 13:37:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.83/4.04 SZS status Theorem for theBenchmark.p % 3.83/4.04 SZS output start Proof for theBenchmark.p % 3.83/4.04 Clause #0 (by assumption #[]): Eq % 3.83/4.04 (Not % 3.83/4.04 (∀ (X Y Z V : a → Prop), % 3.83/4.04 And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → ∀ (Xx : a), Or (X Xx) (Z Xx) → Or (Y Xx) (V Xx))) % 3.83/4.04 True % 3.83/4.04 Clause #1 (by clausification #[0]): Eq % 3.83/4.04 (∀ (X Y Z V : a → Prop), % 3.83/4.04 And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → ∀ (Xx : a), Or (X Xx) (Z Xx) → Or (Y Xx) (V Xx)) % 3.83/4.04 False % 3.83/4.04 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (Not % 3.83/4.04 (∀ (Y Z V : a → Prop), % 3.83/4.04 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (Y Xx) (V Xx))) % 3.83/4.04 True % 3.83/4.04 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (∀ (Y Z V : a → Prop), % 3.83/4.04 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (Y Xx) (V Xx)) % 3.83/4.04 False % 3.83/4.04 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (Not % 3.83/4.04 (∀ (Z V : a → Prop), % 3.83/4.04 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx))) % 3.83/4.04 True % 3.83/4.04 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (∀ (Z V : a → Prop), % 3.83/4.04 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), Z Xx → V Xx) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx)) % 3.83/4.04 False % 3.83/4.04 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (Not % 3.83/4.04 (∀ (V : a → Prop), % 3.83/4.04 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) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx))) % 3.83/4.04 True % 3.83/4.04 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (∀ (V : a → Prop), % 3.83/4.04 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) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx)) % 3.83/4.04 False % 3.83/4.04 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (Not % 3.83/4.04 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.83/4.04 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) → % 3.83/4.04 ∀ (Xx : a), % 3.83/4.04 Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx))) % 3.83/4.04 True % 3.83/4.04 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.83/4.04 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) → % 3.83/4.04 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx)) % 3.83/4.04 False % 3.83/4.04 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.83/4.04 Eq % 3.83/4.04 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.83/4.04 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx)) % 3.83/4.04 True % 3.83/4.04 Clause #11 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), % 3.83/4.04 Eq (∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx)) % 3.83/4.04 False % 3.83/4.04 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 % 3.83/4.04 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 % 3.83/4.04 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 % 3.83/4.04 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.83/4.04 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) % 3.83/4.04 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 % 3.83/4.06 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) % 3.83/4.06 Clause #18 (by clausification #[11]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.83/4.06 Eq % 3.83/4.06 (Not % 3.83/4.06 (Or (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) → % 3.83/4.06 Or (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5)))) % 3.83/4.06 True % 3.83/4.06 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.83/4.06 Eq % 3.83/4.06 (Or (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) → % 3.83/4.06 Or (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 3.83/4.06 False % 3.83/4.06 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.83/4.06 Eq (Or (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) True % 3.83/4.06 Clause #21 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.83/4.06 Eq (Or (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (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 % 3.83/4.06 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.83/4.06 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 3.83/4.06 Clause #23 (by superposition #[22, 15]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 3.83/4.06 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4 a_5)) True) % 3.83/4.06 (Or (Eq True False) (Eq (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True)) % 3.83/4.06 Clause #24 (by clausification #[21]): ∀ (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 % 3.83/4.06 Clause #25 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False % 3.83/4.06 Clause #26 (by betaEtaReduce #[23]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 3.83/4.06 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 3.83/4.06 (Or (Eq True False) (Eq (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True)) % 3.83/4.06 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 3.83/4.06 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 3.83/4.06 (Eq (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 3.83/4.06 Clause #28 (by superposition #[27, 24]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 3.83/4.06 Or % 3.83/4.06 (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) (fun x => a_4 x) a_5)) % 3.83/4.06 True) % 3.83/4.06 (Eq True False) % 3.83/4.06 Clause #29 (by betaEtaReduce #[28]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) (Eq True False) % 3.83/4.06 Clause #30 (by clausification #[29]): ∀ (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 % 3.83/4.06 Clause #33 (by superposition #[30, 17]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.83/4.06 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) % 3.83/4.06 Clause #34 (by clausification #[33]): ∀ (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 % 3.83/4.06 Clause #35 (by superposition #[34, 25]): Eq True False % 3.83/4.06 Clause #36 (by clausification #[35]): False % 3.83/4.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------