%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET633^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 4.33s 4.51s % Output : Proof 4.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SET633^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : duper %s % 0.14/0.36 % Computer : n001.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 14:40:38 EDT 2025 % 0.14/0.36 % CPUTime : % 4.33/4.51 SZS status Theorem for theBenchmark.p % 4.33/4.51 SZS output start Proof for theBenchmark.p % 4.33/4.51 Clause #0 (by assumption #[]): Eq % 4.33/4.51 (Not % 4.33/4.51 (∀ (X Y Z : a → Prop), % 4.33/4.51 And (∀ (Xx : a), And (X Xx) (Not (Y Xx)) → Z Xx) (∀ (Xx : a), And (Y Xx) (Not (X Xx)) → Z Xx) → % 4.33/4.51 ∀ (Xx : a), Or (And (X Xx) (Not (Y Xx))) (And (Y Xx) (Not (X Xx))) → Z Xx)) % 4.33/4.51 True % 4.33/4.51 Clause #1 (by clausification #[0]): Eq % 4.33/4.51 (∀ (X Y Z : a → Prop), % 4.33/4.51 And (∀ (Xx : a), And (X Xx) (Not (Y Xx)) → Z Xx) (∀ (Xx : a), And (Y Xx) (Not (X Xx)) → Z Xx) → % 4.33/4.51 ∀ (Xx : a), Or (And (X Xx) (Not (Y Xx))) (And (Y Xx) (Not (X Xx))) → Z Xx) % 4.33/4.51 False % 4.33/4.51 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (Not % 4.33/4.51 (∀ (Y Z : a → Prop), % 4.33/4.51 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Y Xx)) → Z Xx) % 4.33/4.51 (∀ (Xx : a), And (Y Xx) (Not (skS.0 0 a_1 Xx)) → Z Xx) → % 4.33/4.51 ∀ (Xx : a), Or (And (skS.0 0 a_1 Xx) (Not (Y Xx))) (And (Y Xx) (Not (skS.0 0 a_1 Xx))) → Z Xx)) % 4.33/4.51 True % 4.33/4.51 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (∀ (Y Z : a → Prop), % 4.33/4.51 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Y Xx)) → Z Xx) % 4.33/4.51 (∀ (Xx : a), And (Y Xx) (Not (skS.0 0 a_1 Xx)) → Z Xx) → % 4.33/4.51 ∀ (Xx : a), Or (And (skS.0 0 a_1 Xx) (Not (Y Xx))) (And (Y Xx) (Not (skS.0 0 a_1 Xx))) → Z Xx) % 4.33/4.51 False % 4.33/4.51 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (Not % 4.33/4.51 (∀ (Z : a → Prop), % 4.33/4.51 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → Z Xx) % 4.33/4.51 (∀ (Xx : a), And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx)) → Z Xx) → % 4.33/4.51 ∀ (Xx : a), % 4.33/4.51 Or (And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx))) (And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx))) → % 4.33/4.51 Z Xx)) % 4.33/4.51 True % 4.33/4.51 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (∀ (Z : a → Prop), % 4.33/4.51 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → Z Xx) % 4.33/4.51 (∀ (Xx : a), And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx)) → Z Xx) → % 4.33/4.51 ∀ (Xx : a), % 4.33/4.51 Or (And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx))) (And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx))) → Z Xx) % 4.33/4.51 False % 4.33/4.51 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (Not % 4.33/4.51 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) % 4.33/4.51 (∀ (Xx : a), And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) → % 4.33/4.51 ∀ (Xx : a), % 4.33/4.51 Or (And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx))) (And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx))) → % 4.33/4.51 skS.0 2 a_1 a_2 a_3 Xx)) % 4.33/4.51 True % 4.33/4.51 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) % 4.33/4.51 (∀ (Xx : a), And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) → % 4.33/4.51 ∀ (Xx : a), % 4.33/4.51 Or (And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx))) (And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx))) → % 4.33/4.51 skS.0 2 a_1 a_2 a_3 Xx) % 4.33/4.51 False % 4.33/4.51 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) % 4.33/4.51 (∀ (Xx : a), And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx)) → skS.0 2 a_1 a_2 a_3 Xx)) % 4.33/4.51 True % 4.33/4.51 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.33/4.51 Eq % 4.33/4.51 (∀ (Xx : a), % 4.33/4.51 Or (And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx))) (And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx))) → % 4.33/4.51 skS.0 2 a_1 a_2 a_3 Xx) % 4.33/4.51 False % 4.33/4.51 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.33/4.51 Eq (∀ (Xx : a), And (skS.0 1 a_1 a_2 Xx) (Not (skS.0 0 a_1 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) True % 4.33/4.51 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.33/4.51 Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) True % 4.33/4.51 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.38/4.54 Eq (And (skS.0 1 a_1 a_2 a_3) (Not (skS.0 0 a_1 a_3)) → skS.0 2 a_1 a_2 a_4 a_3) True % 4.38/4.54 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.38/4.54 Or (Eq (And (skS.0 1 a_1 a_2 a_3) (Not (skS.0 0 a_1 a_3))) False) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) % 4.38/4.54 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (skS.0 1 a_1 a_2 a_4) False) (Eq (Not (skS.0 0 a_1 a_4)) False)) % 4.38/4.54 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (skS.0 1 a_1 a_2 a_4) False) (Eq (skS.0 0 a_1 a_4) True)) % 4.38/4.54 Clause #16 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Eq % 4.38/4.54 (Not % 4.38/4.54 (Or (And (skS.0 0 a_1 (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)))) % 4.38/4.54 (And (skS.0 1 a_1 a_2 (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)))) → % 4.38/4.54 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) % 4.38/4.54 True % 4.38/4.54 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Eq % 4.38/4.54 (Or (And (skS.0 0 a_1 (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)))) % 4.38/4.54 (And (skS.0 1 a_1 a_2 (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)))) → % 4.38/4.54 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) % 4.38/4.54 False % 4.38/4.54 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Eq % 4.38/4.54 (Or (And (skS.0 0 a_1 (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)))) % 4.38/4.54 (And (skS.0 1 a_1 a_2 (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))))) % 4.38/4.54 True % 4.38/4.54 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 % 4.38/4.54 Clause #20 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (And (skS.0 0 a_1 (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) % 4.38/4.54 (Eq (And (skS.0 1 a_1 a_2 (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)))) True) % 4.38/4.54 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (And (skS.0 1 a_1 a_2 (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)))) True) % 4.38/4.54 (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True) % 4.38/4.54 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (And (skS.0 1 a_1 a_2 (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)))) True) % 4.38/4.54 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.38/4.54 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True) (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True) % 4.38/4.54 Clause #25 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False) % 4.38/4.54 Clause #26 (by clausification #[25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (skS.0 1 a_1 a_2 (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)) False) % 4.38/4.54 Clause #27 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 4.38/4.54 Eq (And (skS.0 0 a_1 a_2) (Not (skS.0 1 a_1 a_3 a_2)) → skS.0 2 a_1 a_3 a_4 a_2) True % 4.38/4.54 Clause #28 (by clausification #[27]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 4.38/4.54 Or (Eq (And (skS.0 0 a_1 a_2) (Not (skS.0 1 a_1 a_3 a_2))) False) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True) % 4.38/4.54 Clause #29 (by clausification #[28]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (skS.0 0 a_1 a_4) False) (Eq (Not (skS.0 1 a_1 a_2 a_4)) False)) % 4.38/4.54 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.38/4.54 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (skS.0 0 a_1 a_4) False) (Eq (skS.0 1 a_1 a_2 a_4) True)) % 4.38/4.54 Clause #33 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.40/4.57 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.40/4.57 Clause #36 (by superposition #[33, 15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.40/4.57 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True) % 4.40/4.57 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.40/4.57 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True))) % 4.40/4.57 Clause #38 (by betaEtaReduce #[36]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.40/4.57 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.40/4.57 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.40/4.57 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True))) % 4.40/4.57 Clause #39 (by clausification #[38]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.40/4.57 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.40/4.57 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)) % 4.40/4.57 Clause #40 (by eliminate duplicate literals #[39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.40/4.57 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.40/4.57 Clause #41 (by superposition #[40, 19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.40/4.57 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) % 4.40/4.57 (Eq True False) % 4.40/4.57 Clause #42 (by betaEtaReduce #[41]): ∀ (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 True False) % 4.40/4.57 Clause #43 (by clausification #[42]): ∀ (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 % 4.40/4.57 Clause #44 (by backward demodulation #[43, 26]): ∀ (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_2 a_3 a_4)) False) (Eq True False) % 4.40/4.57 Clause #47 (by superposition #[43, 30]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 4.40/4.57 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True) % 4.40/4.57 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_4 a_5 a_6)) True)) % 4.40/4.57 Clause #48 (by clausification #[44]): ∀ (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 % 4.40/4.57 Clause #49 (by clausification #[47]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 4.40/4.57 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_4 a_5 a_6)) True) % 4.40/4.57 Clause #50 (by superposition #[49, 19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 4.40/4.57 Or % 4.40/4.57 (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_2 x) (fun x => a_3 x) a_4)) % 4.40/4.57 True) % 4.40/4.57 (Eq True False) % 4.40/4.57 Clause #51 (by betaEtaReduce #[50]): ∀ (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_2 a_3 a_4)) True) (Eq True False) % 4.40/4.57 Clause #52 (by clausification #[51]): ∀ (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)) True % 4.40/4.57 Clause #53 (by superposition #[52, 48]): Eq True False % 4.40/4.57 Clause #55 (by clausification #[53]): False % 4.40/4.57 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------