%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL656+1.001 : TPTP v9.3.1. 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:17 AM UTC 2026 % Result : Theorem 3.79s 4.13s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.05 % Command : duper %s % 0.12/0.37 % Computer : n008.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Sat Sep 5 02:16:23 UTC 2026 % 0.12/0.37 % CPUTime : % 3.79/4.13 SZS status Theorem for theBenchmark.p % 3.79/4.13 SZS output start Proof for theBenchmark.p % 3.79/4.13 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True % 3.79/4.13 Clause #1 (by assumption #[]): Eq % 3.79/4.13 (Not % 3.79/4.13 (Not % 3.79/4.13 (Exists fun X => % 3.79/4.13 Not % 3.79/4.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 3.79/4.13 (Not % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (∀ (Y : Iota), % 3.79/4.13 Or (Not (r1 X Y)) % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (Or % 3.79/4.13 (And % 3.79/4.13 (Not % 3.79/4.13 (∀ (X : Iota), % 3.79/4.13 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.79/4.13 (Not % 3.79/4.13 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.79/4.13 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.79/4.13 (Or % 3.79/4.13 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.79/4.13 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.79/4.13 (Not (p101 Y)))) % 3.79/4.13 (Or % 3.79/4.13 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.79/4.13 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.79/4.13 (Not (p100 Y)))) % 3.79/4.13 (Or (p101 Y) (Not (p102 Y)))) % 3.79/4.13 (Or (p100 Y) (Not (p101 Y))))) % 3.79/4.13 (Not (p101 X))) % 3.79/4.13 (p100 X))))))) % 3.79/4.13 True % 3.79/4.13 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True % 3.79/4.13 Clause #3 (by clausification #[1]): Eq % 3.79/4.13 (Not % 3.79/4.13 (Exists fun X => % 3.79/4.13 Not % 3.79/4.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 3.79/4.13 (Not % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (∀ (Y : Iota), % 3.79/4.13 Or (Not (r1 X Y)) % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (Or % 3.79/4.13 (And % 3.79/4.13 (Not % 3.79/4.13 (∀ (X : Iota), % 3.79/4.13 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.79/4.13 (Not % 3.79/4.13 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.79/4.13 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.79/4.13 (Or % 3.79/4.13 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.79/4.13 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.79/4.13 (Not (p101 Y)))) % 3.79/4.13 (Or % 3.79/4.13 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.79/4.13 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.79/4.13 (Not (p100 Y)))) % 3.79/4.13 (Or (p101 Y) (Not (p102 Y)))) % 3.79/4.13 (Or (p100 Y) (Not (p101 Y))))) % 3.79/4.13 (Not (p101 X))) % 3.79/4.13 (p100 X)))))) % 3.79/4.13 False % 3.79/4.13 Clause #4 (by clausification #[3]): Eq % 3.79/4.13 (Exists fun X => % 3.79/4.13 Not % 3.79/4.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 3.79/4.13 (Not % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (∀ (Y : Iota), % 3.79/4.13 Or (Not (r1 X Y)) % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (And % 3.79/4.13 (Or % 3.79/4.13 (And % 3.79/4.13 (Not % 3.79/4.13 (∀ (X : Iota), % 3.79/4.13 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.15 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.15 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.15 (Or % 3.89/4.15 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.15 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.15 (Not (p101 Y)))) % 3.89/4.15 (Or % 3.89/4.15 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.15 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.15 (Not (p100 Y)))) % 3.89/4.15 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.15 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.15 (Not (p101 X))) % 3.89/4.15 (p100 X))))) % 3.89/4.15 True % 3.89/4.15 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 3.89/4.15 Eq % 3.89/4.15 (Not % 3.89/4.15 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 3.89/4.15 (Not % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (∀ (Y : Iota), % 3.89/4.15 Or (Not (r1 (skS.0 0 a) Y)) % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (Or % 3.89/4.15 (And % 3.89/4.15 (Not % 3.89/4.15 (∀ (X : Iota), % 3.89/4.15 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.15 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.15 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.15 (Or % 3.89/4.15 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.15 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.15 (Not (p101 Y)))) % 3.89/4.15 (Or % 3.89/4.15 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.15 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.15 (Not (p100 Y)))) % 3.89/4.15 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.15 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.15 (Not (p101 (skS.0 0 a)))) % 3.89/4.15 (p100 (skS.0 0 a)))))) % 3.89/4.15 True % 3.89/4.15 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 3.89/4.15 Eq % 3.89/4.15 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 3.89/4.15 (Not % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (∀ (Y : Iota), % 3.89/4.15 Or (Not (r1 (skS.0 0 a) Y)) % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (And % 3.89/4.15 (Or % 3.89/4.15 (And % 3.89/4.15 (Not % 3.89/4.15 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.15 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.15 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.15 (Or % 3.89/4.15 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.15 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.15 (Not (p101 Y)))) % 3.89/4.15 (Or % 3.89/4.15 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.15 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.15 (Not (p100 Y)))) % 3.89/4.15 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.15 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.15 (Not (p101 (skS.0 0 a)))) % 3.89/4.15 (p100 (skS.0 0 a))))) % 3.89/4.15 False % 3.89/4.15 Clause #7 (by clausification #[6]): ∀ (a : Iota), % 3.89/4.17 Eq % 3.89/4.17 (Not % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (∀ (Y : Iota), % 3.89/4.17 Or (Not (r1 (skS.0 0 a) Y)) % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (Or % 3.89/4.17 (And % 3.89/4.17 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.17 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.17 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.17 (Or % 3.89/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.17 (Not (p101 Y)))) % 3.89/4.17 (Or % 3.89/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.17 (Not (p100 Y)))) % 3.89/4.17 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.17 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.17 (Not (p101 (skS.0 0 a)))) % 3.89/4.17 (p100 (skS.0 0 a)))) % 3.89/4.17 False % 3.89/4.17 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) False % 3.89/4.17 Clause #9 (by clausification #[7]): ∀ (a : Iota), % 3.89/4.17 Eq % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (∀ (Y : Iota), % 3.89/4.17 Or (Not (r1 (skS.0 0 a) Y)) % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (Or % 3.89/4.17 (And % 3.89/4.17 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.17 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.17 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.17 (Or % 3.89/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.17 (Not (p101 Y)))) % 3.89/4.17 (Or % 3.89/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.17 (Not (p100 Y)))) % 3.89/4.17 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.17 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.17 (Not (p101 (skS.0 0 a)))) % 3.89/4.17 (p100 (skS.0 0 a))) % 3.89/4.17 True % 3.89/4.17 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (p100 (skS.0 0 a)) True % 3.89/4.17 Clause #11 (by clausification #[9]): ∀ (a : Iota), % 3.89/4.17 Eq % 3.89/4.17 (And % 3.89/4.17 (∀ (Y : Iota), % 3.89/4.17 Or (Not (r1 (skS.0 0 a) Y)) % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (And % 3.89/4.17 (Or % 3.89/4.17 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.17 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.17 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.17 (Or % 3.89/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.17 (Not (p101 Y)))) % 3.89/4.17 (Or % 3.89/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.17 (Not (p100 Y)))) % 3.89/4.17 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.17 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.17 (Not (p101 (skS.0 0 a)))) % 3.89/4.17 True % 3.89/4.17 Clause #12 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) True % 3.89/4.17 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p2 a_1)) True % 3.89/4.20 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p2 a_1) True) % 3.89/4.20 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (p2 a) True) (Eq (r1 (skS.0 0 a_1) a) False) % 3.89/4.20 Clause #18 (by clausification #[11]): ∀ (a : Iota), Eq (Not (p101 (skS.0 0 a))) True % 3.89/4.20 Clause #19 (by clausification #[11]): ∀ (a : Iota), % 3.89/4.20 Eq % 3.89/4.20 (∀ (Y : Iota), % 3.89/4.20 Or (Not (r1 (skS.0 0 a) Y)) % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (Or % 3.89/4.20 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.20 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.20 (Not (And (Not (p101 Y)) (p100 Y)))) % 3.89/4.20 (Or % 3.89/4.20 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 3.89/4.20 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 3.89/4.20 (Not (p101 Y)))) % 3.89/4.20 (Or % 3.89/4.20 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 3.89/4.20 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 3.89/4.20 (Not (p100 Y)))) % 3.89/4.20 (Or (p101 Y) (Not (p102 Y)))) % 3.89/4.20 (Or (p100 Y) (Not (p101 Y))))) % 3.89/4.20 True % 3.89/4.20 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False % 3.89/4.20 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), % 3.89/4.20 Eq % 3.89/4.20 (Or (Not (r1 (skS.0 0 a) a_1)) % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (Or % 3.89/4.20 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.20 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.20 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 3.89/4.20 (Or % 3.89/4.20 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 3.89/4.20 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 3.89/4.20 (Not (p101 a_1)))) % 3.89/4.20 (Or % 3.89/4.20 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 3.89/4.20 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 3.89/4.20 (Not (p100 a_1)))) % 3.89/4.20 (Or (p101 a_1) (Not (p102 a_1)))) % 3.89/4.20 (Or (p100 a_1) (Not (p101 a_1))))) % 3.89/4.20 True % 3.89/4.20 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 3.89/4.20 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) % 3.89/4.20 (Eq % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (And % 3.89/4.20 (Or % 3.89/4.20 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.89/4.20 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.89/4.20 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 3.96/4.20 (Or % 3.96/4.20 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 3.96/4.20 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 3.96/4.20 (Not (p101 a_1)))) % 3.96/4.20 (Or % 3.96/4.20 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 3.96/4.20 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 3.96/4.20 (Not (p100 a_1)))) % 3.96/4.20 (Or (p101 a_1) (Not (p102 a_1)))) % 3.96/4.20 (Or (p100 a_1) (Not (p101 a_1)))) % 3.96/4.20 True) % 3.96/4.20 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.96/4.20 Or % 3.96/4.20 (Eq % 3.96/4.20 (And % 3.96/4.20 (And % 3.96/4.20 (And % 3.96/4.20 (And % 3.96/4.20 (Or % 3.96/4.20 (And (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.96/4.20 (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.96/4.22 (Not (And (Not (p101 a)) (p100 a)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p2 X))) (Not (p101 X))) (p2 a)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p2 X)) (Not (p101 X))) (Not (p2 a)))) % 3.96/4.22 (Not (p101 a)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p1 X))) (Not (p100 X))) (p1 a)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p1 X)) (Not (p100 X))) (Not (p1 a)))) % 3.96/4.22 (Not (p100 a)))) % 3.96/4.22 (Or (p101 a) (Not (p102 a)))) % 3.96/4.22 (Or (p100 a) (Not (p101 a)))) % 3.96/4.22 True) % 3.96/4.22 (Eq (r1 (skS.0 0 a_1) a) False) % 3.96/4.22 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), % 3.96/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.22 (Eq % 3.96/4.22 (And % 3.96/4.22 (And % 3.96/4.22 (And % 3.96/4.22 (Or % 3.96/4.22 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.96/4.22 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.96/4.22 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 3.96/4.22 (Not (p101 a_1)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 3.96/4.22 (Not (p100 a_1)))) % 3.96/4.22 (Or (p101 a_1) (Not (p102 a_1)))) % 3.96/4.22 True) % 3.96/4.22 Clause #32 (by clausification #[25]): ∀ (a a_1 : Iota), % 3.96/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.22 (Eq % 3.96/4.22 (And % 3.96/4.22 (And % 3.96/4.22 (Or % 3.96/4.22 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.96/4.22 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.96/4.22 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 3.96/4.22 (Not (p101 a_1)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 3.96/4.22 (Not (p100 a_1)))) % 3.96/4.22 True) % 3.96/4.22 Clause #38 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.96/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.22 (Eq % 3.96/4.22 (And % 3.96/4.22 (Or % 3.96/4.22 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.96/4.22 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.96/4.22 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 3.96/4.22 (Or % 3.96/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 3.96/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 3.96/4.22 (Not (p101 a_1)))) % 3.96/4.22 True) % 3.96/4.22 Clause #61 (by clausification #[38]): ∀ (a a_1 : Iota), % 3.96/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.22 (Eq % 3.96/4.22 (Or % 3.96/4.22 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.96/4.22 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.96/4.22 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 3.96/4.22 True) % 3.96/4.22 Clause #93 (by clausification #[61]): ∀ (a a_1 : Iota), % 3.96/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.22 (Or % 3.96/4.22 (Eq % 3.96/4.22 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 3.96/4.22 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 3.96/4.22 True) % 3.96/4.22 (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True)) % 3.96/4.22 Clause #95 (by clausification #[93]): ∀ (a a_1 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True) % 3.96/4.25 (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True)) % 3.96/4.25 Clause #121 (by clausification #[95]): ∀ (a a_1 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True) % 3.96/4.25 (Eq (And (Not (p101 a_1)) (p100 a_1)) False)) % 3.96/4.25 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (And (Not (p101 a_1)) (p100 a_1)) False) % 3.96/4.25 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False)) % 3.96/4.25 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False) % 3.96/4.25 (Or (Eq (Not (p101 a_1)) False) (Eq (p100 a_1) False))) % 3.96/4.25 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (Not (p101 a_1)) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) % 3.96/4.25 (Eq % 3.96/4.25 (Not % 3.96/4.25 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) % 3.96/4.25 (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2)))))) % 3.96/4.25 True))) % 3.96/4.25 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) % 3.96/4.25 (Or % 3.96/4.25 (Eq % 3.96/4.25 (Not % 3.96/4.25 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) % 3.96/4.25 (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2)))))) % 3.96/4.25 True) % 3.96/4.25 (Eq (p101 a_1) True))) % 3.96/4.25 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) % 3.96/4.25 (Or (Eq (p101 a_1) True) % 3.96/4.25 (Eq % 3.96/4.25 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) % 3.96/4.25 (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2))))) % 3.96/4.25 False))) % 3.96/4.25 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) % 3.96/4.25 (Or (Eq (p101 a_1) True) % 3.96/4.25 (Eq (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2)))) % 3.96/4.25 False))) % 3.96/4.25 Clause #128 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (Not (r1 a_1 (skS.0 2 a_1 a_2))) False))) % 3.96/4.25 Clause #129 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) % 3.96/4.25 (Or (Eq (p101 a_1) True) % 3.96/4.25 (Eq (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2))) True))) % 3.96/4.25 Clause #131 (by clausification #[129]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) % 3.96/4.25 (Or (Eq (p101 a_1) True) (Eq (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) True))) % 3.96/4.25 Clause #133 (by clausification #[128]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (r1 a_1 (skS.0 2 a_1 a_2)) True))) % 3.96/4.25 Clause #134 (by superposition #[133, 2]): ∀ (a a_1 : Iota), % 3.96/4.25 Or (Eq (p100 (skS.0 0 a)) False) % 3.96/4.25 (Or (Eq (p101 (skS.0 0 a)) True) (Or (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True) (Eq False True))) % 3.96/4.25 Clause #151 (by clausification #[131]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (Not (p2 (skS.0 2 a_1 a_2))) True))) % 3.96/4.25 Clause #172 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), % 3.96/4.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 3.96/4.25 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (p2 (skS.0 2 a_1 a_2)) False))) % 3.96/4.25 Clause #174 (by superposition #[172, 2]): ∀ (a a_1 : Iota), % 3.96/4.25 Or (Eq (p100 (skS.0 0 a)) False) % 3.96/4.25 (Or (Eq (p101 (skS.0 0 a)) True) (Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) (Eq False True))) % 3.96/4.26 Clause #181 (by clausification #[174]): ∀ (a a_1 : Iota), % 3.96/4.26 Or (Eq (p100 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False)) % 3.96/4.26 Clause #182 (by forward demodulation #[181, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False)) % 3.96/4.26 Clause #183 (by clausification #[182]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) % 3.96/4.26 Clause #184 (by forward demodulation #[183, 20]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) % 3.96/4.26 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False % 3.96/4.26 Clause #186 (by clausification #[134]): ∀ (a a_1 : Iota), % 3.96/4.26 Or (Eq (p100 (skS.0 0 a)) False) % 3.96/4.26 (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True)) % 3.96/4.26 Clause #187 (by forward demodulation #[186, 10]): ∀ (a a_1 : Iota), % 3.96/4.26 Or (Eq True False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True)) % 3.96/4.26 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True) % 3.96/4.26 Clause #189 (by forward demodulation #[188, 20]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True) % 3.96/4.26 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True % 3.96/4.26 Clause #191 (by superposition #[190, 15]): ∀ (a a_1 : Iota), Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True) (Eq True False) % 3.96/4.26 Clause #205 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True % 3.96/4.26 Clause #206 (by superposition #[205, 185]): Eq True False % 3.96/4.26 Clause #207 (by clausification #[206]): False % 3.96/4.26 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------