%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 11:36:26 AM UTC 2026 % Result : Theorem 10.06s 10.36s % Output : Proof 10.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.09/0.35 % Computer : n002.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Fri Sep 4 16:09:05 UTC 2026 % 0.09/0.36 % CPUTime : % 10.06/10.36 SZS status Theorem for theBenchmark.p % 10.06/10.36 SZS output start Proof for theBenchmark.p % 10.06/10.36 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True % 10.06/10.36 Clause #1 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (r1 X Y) (r1 Y Z) → r1 X Z) True % 10.06/10.36 Clause #2 (by assumption #[]): Eq % 10.06/10.36 (Not % 10.06/10.36 (Not % 10.06/10.36 (Exists fun X => % 10.06/10.36 Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Not % 10.06/10.36 (∀ (Y : Iota), % 10.06/10.36 Or (Not (r1 X Y)) % 10.06/10.36 (Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X))))))) % 10.06/10.36 True % 10.06/10.36 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True % 10.06/10.36 Clause #4 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (r1 a Y) (r1 Y Z) → r1 a Z) True % 10.06/10.36 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (r1 a a_1) (r1 a_1 Z) → r1 a Z) True % 10.06/10.36 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 a a_1) (r1 a_1 a_2) → r1 a a_2) True % 10.06/10.36 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r1 a a_1) (r1 a_1 a_2)) False) (Eq (r1 a a_2) True) % 10.06/10.36 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a a_1) True) (Or (Eq (r1 a a_2) False) (Eq (r1 a_2 a_1) False)) % 10.06/10.36 Clause #11 (by clausification #[2]): Eq % 10.06/10.36 (Not % 10.06/10.36 (Exists fun X => % 10.06/10.36 Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Not % 10.06/10.36 (∀ (Y : Iota), % 10.06/10.36 Or (Not (r1 X Y)) % 10.06/10.36 (Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X)))))) % 10.06/10.36 False % 10.06/10.36 Clause #12 (by clausification #[11]): Eq % 10.06/10.36 (Exists fun X => % 10.06/10.36 Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Not % 10.06/10.36 (∀ (Y : Iota), % 10.06/10.36 Or (Not (r1 X Y)) % 10.06/10.36 (Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.06/10.36 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.06/10.36 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X))))) % 10.06/10.36 True % 10.06/10.36 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 10.06/10.36 Eq % 10.06/10.36 (Not % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.06/10.36 (Or % 10.16/10.41 (Not % 10.16/10.41 (∀ (Y : Iota), % 10.16/10.41 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.41 (Not % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X))))) % 10.16/10.41 True % 10.16/10.41 Clause #14 (by clausification #[13]): ∀ (a : Iota), % 10.16/10.41 Eq % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Not % 10.16/10.41 (∀ (Y : Iota), % 10.16/10.41 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.41 (Not % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X)))) % 10.16/10.41 False % 10.16/10.41 Clause #16 (by clausification #[14]): ∀ (a : Iota), % 10.16/10.41 Eq % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Not % 10.16/10.41 (∀ (Y : Iota), % 10.16/10.41 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.41 (Not % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 False % 10.16/10.41 Clause #27 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))) False % 10.16/10.41 Clause #28 (by clausification #[16]): ∀ (a : Iota), % 10.16/10.41 Eq % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Not % 10.16/10.41 (∀ (Y : Iota), % 10.16/10.41 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.41 (Not % 10.16/10.41 (Or % 10.16/10.41 (Or % 10.16/10.41 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.41 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.16/10.41 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X)))) % 10.16/10.41 False % 10.16/10.41 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), % 10.16/10.41 Eq (Not (Or (Not (r1 (skS.0 0 a) (skS.0 3 a a_1))) (∀ (X : Iota), Or (Not (r1 (skS.0 3 a a_1) X)) (p12 X)))) True % 10.16/10.41 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 10.16/10.41 Eq (Or (Not (r1 (skS.0 0 a) (skS.0 3 a a_1))) (∀ (X : Iota), Or (Not (r1 (skS.0 3 a a_1) X)) (p12 X))) False % 10.16/10.41 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (X : Iota), Or (Not (r1 (skS.0 3 a a_1) X)) (p12 X)) False % 10.16/10.41 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a) (skS.0 3 a a_1))) False % 10.16/10.47 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (Not (Or (Not (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) (p12 (skS.0 4 a a_1 a_2)))) True % 10.16/10.47 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) (p12 (skS.0 4 a a_1 a_2))) False % 10.16/10.47 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (p12 (skS.0 4 a a_1 a_2)) False % 10.16/10.47 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (Not (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False % 10.16/10.47 Clause #37 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 3 a a_1)) True % 10.16/10.47 Clause #38 (by superposition #[37, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) True) (Or (Eq True False) (Eq (r1 (skS.0 3 a a_2) a_1) False)) % 10.16/10.47 Clause #41 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True % 10.16/10.47 Clause #43 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) True) (Eq (r1 (skS.0 3 a a_2) a_1) False) % 10.16/10.47 Clause #44 (by superposition #[43, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) (skS.0 4 a a_1 a_2)) True) (Eq False True) % 10.16/10.47 Clause #51 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 0 a) (skS.0 4 a a_1 a_2)) True % 10.16/10.47 Clause #56 (by clausification #[28]): ∀ (a : Iota), % 10.16/10.47 Eq % 10.16/10.47 (Or % 10.16/10.47 (Not % 10.16/10.47 (∀ (Y : Iota), % 10.16/10.47 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.47 (Not % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.16/10.47 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X)))) % 10.16/10.47 False % 10.16/10.47 Clause #82 (by clausification #[56]): ∀ (a : Iota), % 10.16/10.47 Eq % 10.16/10.47 (Not % 10.16/10.47 (∀ (Y : Iota), % 10.16/10.47 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.47 (Not % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))) % 10.16/10.47 False % 10.16/10.47 Clause #103 (by clausification #[82]): ∀ (a : Iota), % 10.16/10.47 Eq % 10.16/10.47 (∀ (Y : Iota), % 10.16/10.47 Or (Not (r1 (skS.0 0 a) Y)) % 10.16/10.47 (Not % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))) % 10.16/10.47 True % 10.16/10.47 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), % 10.16/10.47 Eq % 10.16/10.47 (Or (Not (r1 (skS.0 0 a) a_1)) % 10.16/10.47 (Not % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p14 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)))))) % 10.16/10.47 True % 10.16/10.47 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), % 10.16/10.47 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) % 10.16/10.47 (Eq % 10.16/10.47 (Not % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p14 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))))) % 10.16/10.47 True) % 10.16/10.47 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), % 10.16/10.47 Or % 10.16/10.47 (Eq % 10.16/10.47 (Not % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a X)) (p12 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 a X)) (p14 X)))) % 10.16/10.47 (Not (∀ (X : Iota), Or (Not (r1 a X)) (p12 X))))) % 10.16/10.47 True) % 10.16/10.47 (Eq (r1 (skS.0 0 a_1) a) False) % 10.16/10.47 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), % 10.16/10.47 Or (Eq (r1 (skS.0 0 a) a_1) False) % 10.16/10.47 (Eq % 10.16/10.47 (Or % 10.16/10.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)))) % 10.16/10.50 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p14 X)))) % 10.16/10.50 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)))) % 10.16/10.50 False) % 10.16/10.50 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))) False) % 10.16/10.50 Clause #110 (by clausification #[108]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)) True) % 10.16/10.50 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Or (Not (r1 a_1 a_2)) (p12 a_2)) True) % 10.16/10.50 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (Not (r1 a_1 a_2)) True) (Eq (p12 a_2) True)) % 10.16/10.50 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (p12 a_2) True) (Eq (r1 a_1 a_2) False)) % 10.16/10.50 Clause #122 (by superposition #[113, 3]): ∀ (a a_1 : Iota), Or (Eq (p12 a) True) (Or (Eq (r1 (skS.0 0 a_1) a) False) (Eq False True)) % 10.16/10.50 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (p12 a) True) (Eq (r1 (skS.0 0 a_1) a) False) % 10.16/10.50 Clause #127 (by superposition #[123, 51]): ∀ (a a_1 a_2 : Iota), Or (Eq (p12 (skS.0 4 a a_1 a_2)) True) (Eq False True) % 10.16/10.50 Clause #173 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), Eq (p12 (skS.0 4 a a_1 a_2)) True % 10.16/10.50 Clause #174 (by superposition #[173, 35]): Eq True False % 10.16/10.50 Clause #176 (by clausification #[174]): False % 10.16/10.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------