%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL674+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 11:36:23 AM UTC 2026 % Result : Theorem 5.26s 5.50s % Output : Proof 5.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL674+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.11/0.35 % Computer : n028.cluster.edu % 0.11/0.35 % Model : x86_64 x86_64 % 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.35 % Memory : 8046.5625MB % 0.11/0.35 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sat Sep 5 02:07:29 UTC 2026 % 0.11/0.36 % CPUTime : % 5.26/5.50 SZS status Theorem for theBenchmark.p % 5.26/5.50 SZS output start Proof for theBenchmark.p % 5.26/5.50 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True % 5.26/5.50 Clause #2 (by assumption #[]): Eq % 5.26/5.50 (Not % 5.26/5.50 (Not % 5.26/5.50 (Exists fun X => % 5.26/5.50 Not % 5.26/5.50 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 5.26/5.50 (Not % 5.26/5.50 (And % 5.26/5.50 (And % 5.26/5.50 (∀ (Y : Iota), % 5.26/5.50 Or (Not (r1 X Y)) % 5.26/5.50 (And % 5.26/5.50 (And % 5.26/5.50 (And % 5.26/5.50 (And % 5.26/5.50 (Or % 5.26/5.50 (And % 5.26/5.50 (Not % 5.26/5.50 (∀ (X : Iota), % 5.26/5.50 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.50 (Not % 5.26/5.50 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.50 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.51 (Or % 5.26/5.51 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.51 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.51 (Not (p101 Y)))) % 5.26/5.51 (Or % 5.26/5.51 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.51 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.51 (Not (p100 Y)))) % 5.26/5.51 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.51 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.51 (Not (p101 X))) % 5.26/5.51 (p100 X))))))) % 5.26/5.51 True % 5.26/5.51 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True % 5.26/5.51 Clause #11 (by clausification #[2]): Eq % 5.26/5.51 (Not % 5.26/5.51 (Exists fun X => % 5.26/5.51 Not % 5.26/5.51 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 5.26/5.51 (Not % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (∀ (Y : Iota), % 5.26/5.51 Or (Not (r1 X Y)) % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (Or % 5.26/5.51 (And % 5.26/5.51 (Not % 5.26/5.51 (∀ (X : Iota), % 5.26/5.51 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.51 (Not % 5.26/5.51 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.51 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.51 (Or % 5.26/5.51 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.51 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.51 (Not (p101 Y)))) % 5.26/5.51 (Or % 5.26/5.51 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.51 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.51 (Not (p100 Y)))) % 5.26/5.51 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.51 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.51 (Not (p101 X))) % 5.26/5.51 (p100 X)))))) % 5.26/5.51 False % 5.26/5.51 Clause #12 (by clausification #[11]): Eq % 5.26/5.51 (Exists fun X => % 5.26/5.51 Not % 5.26/5.51 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 5.26/5.51 (Not % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (∀ (Y : Iota), % 5.26/5.51 Or (Not (r1 X Y)) % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (And % 5.26/5.51 (Or % 5.26/5.51 (And % 5.26/5.51 (Not % 5.26/5.51 (∀ (X : Iota), % 5.26/5.51 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.53 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.53 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.53 (Or % 5.26/5.53 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.53 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.53 (Not (p101 Y)))) % 5.26/5.53 (Or % 5.26/5.53 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.53 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.53 (Not (p100 Y)))) % 5.26/5.53 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.53 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.53 (Not (p101 X))) % 5.26/5.53 (p100 X))))) % 5.26/5.53 True % 5.26/5.53 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 5.26/5.53 Eq % 5.26/5.53 (Not % 5.26/5.53 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 5.26/5.53 (Not % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (∀ (Y : Iota), % 5.26/5.53 Or (Not (r1 (skS.0 0 a) Y)) % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (Or % 5.26/5.53 (And % 5.26/5.53 (Not % 5.26/5.53 (∀ (X : Iota), % 5.26/5.53 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.53 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.53 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.53 (Or % 5.26/5.53 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.53 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.53 (Not (p101 Y)))) % 5.26/5.53 (Or % 5.26/5.53 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.53 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.53 (Not (p100 Y)))) % 5.26/5.53 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.53 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.53 (Not (p101 (skS.0 0 a)))) % 5.26/5.53 (p100 (skS.0 0 a)))))) % 5.26/5.53 True % 5.26/5.53 Clause #14 (by clausification #[13]): ∀ (a : Iota), % 5.26/5.53 Eq % 5.26/5.53 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 5.26/5.53 (Not % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (∀ (Y : Iota), % 5.26/5.53 Or (Not (r1 (skS.0 0 a) Y)) % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (And % 5.26/5.53 (Or % 5.26/5.53 (And % 5.26/5.53 (Not % 5.26/5.53 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.53 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.53 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.53 (Or % 5.26/5.53 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.53 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.53 (Not (p101 Y)))) % 5.26/5.53 (Or % 5.26/5.53 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.53 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.53 (Not (p100 Y)))) % 5.26/5.53 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.53 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.53 (Not (p101 (skS.0 0 a)))) % 5.26/5.53 (p100 (skS.0 0 a))))) % 5.26/5.53 False % 5.26/5.53 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 5.26/5.54 Eq % 5.26/5.54 (Not % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (∀ (Y : Iota), % 5.26/5.54 Or (Not (r1 (skS.0 0 a) Y)) % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (Or % 5.26/5.54 (And % 5.26/5.54 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.54 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.54 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.54 (Or % 5.26/5.54 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.54 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.54 (Not (p101 Y)))) % 5.26/5.54 (Or % 5.26/5.54 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.54 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.54 (Not (p100 Y)))) % 5.26/5.54 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.54 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.54 (Not (p101 (skS.0 0 a)))) % 5.26/5.54 (p100 (skS.0 0 a)))) % 5.26/5.54 False % 5.26/5.54 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) False % 5.26/5.54 Clause #17 (by clausification #[15]): ∀ (a : Iota), % 5.26/5.54 Eq % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (∀ (Y : Iota), % 5.26/5.54 Or (Not (r1 (skS.0 0 a) Y)) % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (Or % 5.26/5.54 (And % 5.26/5.54 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.54 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.54 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.54 (Or % 5.26/5.54 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.54 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.54 (Not (p101 Y)))) % 5.26/5.54 (Or % 5.26/5.54 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.54 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.54 (Not (p100 Y)))) % 5.26/5.54 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.54 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.54 (Not (p101 (skS.0 0 a)))) % 5.26/5.54 (p100 (skS.0 0 a))) % 5.26/5.54 True % 5.26/5.54 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (p100 (skS.0 0 a)) True % 5.26/5.54 Clause #19 (by clausification #[17]): ∀ (a : Iota), % 5.26/5.54 Eq % 5.26/5.54 (And % 5.26/5.54 (∀ (Y : Iota), % 5.26/5.54 Or (Not (r1 (skS.0 0 a) Y)) % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (And % 5.26/5.54 (Or % 5.26/5.54 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.54 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.54 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.54 (Or % 5.26/5.54 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.54 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.54 (Not (p101 Y)))) % 5.26/5.54 (Or % 5.26/5.54 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.54 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.54 (Not (p100 Y)))) % 5.26/5.54 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.54 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.54 (Not (p101 (skS.0 0 a)))) % 5.26/5.54 True % 5.26/5.54 Clause #20 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) True % 5.26/5.57 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p2 a_1)) True % 5.26/5.57 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p2 a_1) True) % 5.26/5.57 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (p2 a) True) (Eq (r1 (skS.0 0 a_1) a) False) % 5.26/5.57 Clause #25 (by clausification #[19]): ∀ (a : Iota), Eq (Not (p101 (skS.0 0 a))) True % 5.26/5.57 Clause #26 (by clausification #[19]): ∀ (a : Iota), % 5.26/5.57 Eq % 5.26/5.57 (∀ (Y : Iota), % 5.26/5.57 Or (Not (r1 (skS.0 0 a) Y)) % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (Or % 5.26/5.57 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.57 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.57 (Not (And (Not (p101 Y)) (p100 Y)))) % 5.26/5.57 (Or % 5.26/5.57 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y)) % 5.26/5.57 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y)))) % 5.26/5.57 (Not (p101 Y)))) % 5.26/5.57 (Or % 5.26/5.57 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y)) % 5.26/5.57 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y)))) % 5.26/5.57 (Not (p100 Y)))) % 5.26/5.57 (Or (p101 Y) (Not (p102 Y)))) % 5.26/5.57 (Or (p100 Y) (Not (p101 Y))))) % 5.26/5.57 True % 5.26/5.57 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False % 5.26/5.57 Clause #29 (by clausification #[26]): ∀ (a a_1 : Iota), % 5.26/5.57 Eq % 5.26/5.57 (Or (Not (r1 (skS.0 0 a) a_1)) % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (Or % 5.26/5.57 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.57 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.57 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 5.26/5.57 (Or % 5.26/5.57 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 5.26/5.57 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 5.26/5.57 (Not (p101 a_1)))) % 5.26/5.57 (Or % 5.26/5.57 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 5.26/5.57 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 5.26/5.57 (Not (p100 a_1)))) % 5.26/5.57 (Or (p101 a_1) (Not (p102 a_1)))) % 5.26/5.57 (Or (p100 a_1) (Not (p101 a_1))))) % 5.26/5.57 True % 5.26/5.57 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 5.26/5.57 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) % 5.26/5.57 (Eq % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (Or % 5.26/5.57 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.57 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.26/5.57 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 5.26/5.57 (Or % 5.26/5.57 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 5.26/5.57 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 5.26/5.57 (Not (p101 a_1)))) % 5.26/5.57 (Or % 5.26/5.57 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 5.26/5.57 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 5.26/5.57 (Not (p100 a_1)))) % 5.26/5.57 (Or (p101 a_1) (Not (p102 a_1)))) % 5.26/5.57 (Or (p100 a_1) (Not (p101 a_1)))) % 5.26/5.57 True) % 5.26/5.57 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 5.26/5.57 Or % 5.26/5.57 (Eq % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (And % 5.26/5.57 (Or % 5.26/5.57 (And (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.26/5.57 (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.36/5.60 (Not (And (Not (p101 a)) (p100 a)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p2 X))) (Not (p101 X))) (p2 a)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p2 X)) (Not (p101 X))) (Not (p2 a)))) % 5.36/5.60 (Not (p101 a)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p1 X))) (Not (p100 X))) (p1 a)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p1 X)) (Not (p100 X))) (Not (p1 a)))) % 5.36/5.60 (Not (p100 a)))) % 5.36/5.60 (Or (p101 a) (Not (p102 a)))) % 5.36/5.60 (Or (p100 a) (Not (p101 a)))) % 5.36/5.60 True) % 5.36/5.60 (Eq (r1 (skS.0 0 a_1) a) False) % 5.36/5.60 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota), % 5.36/5.60 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.60 (Eq % 5.36/5.60 (And % 5.36/5.60 (And % 5.36/5.60 (And % 5.36/5.60 (Or % 5.36/5.60 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.36/5.60 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.36/5.60 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 5.36/5.60 (Not (p101 a_1)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 5.36/5.60 (Not (p100 a_1)))) % 5.36/5.60 (Or (p101 a_1) (Not (p102 a_1)))) % 5.36/5.60 True) % 5.36/5.60 Clause #40 (by clausification #[33]): ∀ (a a_1 : Iota), % 5.36/5.60 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.60 (Eq % 5.36/5.60 (And % 5.36/5.60 (And % 5.36/5.60 (Or % 5.36/5.60 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.36/5.60 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.36/5.60 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 5.36/5.60 (Not (p101 a_1)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1)))) % 5.36/5.60 (Not (p100 a_1)))) % 5.36/5.60 True) % 5.36/5.60 Clause #46 (by clausification #[40]): ∀ (a a_1 : Iota), % 5.36/5.60 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.60 (Eq % 5.36/5.60 (And % 5.36/5.60 (Or % 5.36/5.60 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.36/5.60 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.36/5.60 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 5.36/5.60 (Or % 5.36/5.60 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1)) % 5.36/5.60 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1)))) % 5.36/5.60 (Not (p101 a_1)))) % 5.36/5.60 True) % 5.36/5.60 Clause #79 (by clausification #[46]): ∀ (a a_1 : Iota), % 5.36/5.60 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.60 (Eq % 5.36/5.60 (Or % 5.36/5.60 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.36/5.60 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.36/5.60 (Not (And (Not (p101 a_1)) (p100 a_1)))) % 5.36/5.60 True) % 5.36/5.60 Clause #102 (by clausification #[79]): ∀ (a a_1 : Iota), % 5.36/5.60 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.60 (Or % 5.36/5.60 (Eq % 5.36/5.60 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) % 5.36/5.60 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X)))))) % 5.36/5.60 True) % 5.36/5.60 (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True)) % 5.36/5.60 Clause #104 (by clausification #[102]): ∀ (a a_1 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True) % 5.36/5.63 (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True)) % 5.36/5.63 Clause #124 (by clausification #[104]): ∀ (a a_1 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True) % 5.36/5.63 (Eq (And (Not (p101 a_1)) (p100 a_1)) False)) % 5.36/5.63 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (And (Not (p101 a_1)) (p100 a_1)) False) % 5.36/5.63 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False)) % 5.36/5.63 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False) % 5.36/5.63 (Or (Eq (Not (p101 a_1)) False) (Eq (p100 a_1) False))) % 5.36/5.63 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (Not (p101 a_1)) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) % 5.36/5.63 (Eq % 5.36/5.63 (Not % 5.36/5.63 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) % 5.36/5.63 (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)))))) % 5.36/5.63 True))) % 5.36/5.63 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) % 5.36/5.63 (Or % 5.36/5.63 (Eq % 5.36/5.63 (Not % 5.36/5.63 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) % 5.36/5.63 (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)))))) % 5.36/5.63 True) % 5.36/5.63 (Eq (p101 a_1) True))) % 5.36/5.63 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) % 5.36/5.63 (Or (Eq (p101 a_1) True) % 5.36/5.63 (Eq % 5.36/5.63 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) % 5.36/5.63 (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))))) % 5.36/5.63 False))) % 5.36/5.63 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) % 5.36/5.63 (Or (Eq (p101 a_1) True) % 5.36/5.63 (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)))) % 5.36/5.63 False))) % 5.36/5.63 Clause #131 (by clausification #[129]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (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))) % 5.36/5.63 Clause #132 (by clausification #[130]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) % 5.36/5.63 (Or (Eq (p101 a_1) True) % 5.36/5.63 (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))) % 5.36/5.63 Clause #134 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) % 5.36/5.63 (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))) % 5.36/5.63 Clause #136 (by clausification #[131]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (r1 a_1 (skS.0 2 a_1 a_2)) True))) % 5.36/5.63 Clause #137 (by superposition #[136, 3]): ∀ (a a_1 : Iota), % 5.36/5.63 Or (Eq (p100 (skS.0 0 a)) False) % 5.36/5.63 (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))) % 5.36/5.63 Clause #181 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (Not (p2 (skS.0 2 a_1 a_2))) True))) % 5.36/5.63 Clause #185 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 5.36/5.63 Or (Eq (r1 (skS.0 0 a) a_1) False) % 5.36/5.63 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (p2 (skS.0 2 a_1 a_2)) False))) % 5.36/5.63 Clause #187 (by superposition #[185, 3]): ∀ (a a_1 : Iota), % 5.36/5.63 Or (Eq (p100 (skS.0 0 a)) False) % 5.36/5.63 (Or (Eq (p101 (skS.0 0 a)) True) (Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) (Eq False True))) % 5.36/5.64 Clause #193 (by clausification #[187]): ∀ (a a_1 : Iota), % 5.36/5.64 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)) % 5.36/5.64 Clause #194 (by forward demodulation #[193, 18]): ∀ (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)) % 5.36/5.64 Clause #195 (by clausification #[194]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) % 5.36/5.64 Clause #196 (by forward demodulation #[195, 27]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) % 5.36/5.64 Clause #197 (by clausification #[196]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False % 5.36/5.64 Clause #202 (by clausification #[137]): ∀ (a a_1 : Iota), % 5.36/5.64 Or (Eq (p100 (skS.0 0 a)) False) % 5.36/5.64 (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True)) % 5.36/5.64 Clause #203 (by forward demodulation #[202, 18]): ∀ (a a_1 : Iota), % 5.36/5.64 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)) % 5.36/5.64 Clause #204 (by clausification #[203]): ∀ (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) % 5.36/5.64 Clause #205 (by forward demodulation #[204, 27]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True) % 5.36/5.64 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True % 5.36/5.64 Clause #207 (by superposition #[206, 23]): ∀ (a a_1 : Iota), Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True) (Eq True False) % 5.36/5.64 Clause #225 (by clausification #[207]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True % 5.36/5.64 Clause #226 (by superposition #[225, 197]): Eq True False % 5.36/5.64 Clause #227 (by clausification #[226]): False % 5.36/5.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------