%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 11:36:13 AM UTC 2026 % Result : Theorem 8.35s 8.66s % Output : Proof 8.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.11/0.36 % Computer : n011.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % 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 05:00:13 UTC 2026 % 0.11/0.37 % CPUTime : % 8.35/8.66 SZS status Theorem for theBenchmark.p % 8.35/8.66 SZS output start Proof for theBenchmark.p % 8.35/8.66 Clause #0 (by assumption #[]): Eq % 8.35/8.66 (Not % 8.35/8.66 (Not % 8.35/8.66 (Exists fun X => % 8.35/8.66 Not % 8.35/8.66 (Or % 8.35/8.66 (Or % 8.35/8.66 (Not % 8.35/8.66 (Or % 8.35/8.66 (Or % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Not (r1 X Y)) (p2 Y)) % 8.35/8.66 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y))))) % 8.35/8.66 (Not % 8.35/8.66 (And % 8.35/8.66 (And % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or % 8.35/8.66 (Or % 8.35/8.66 (Or (Not (r1 X Y)) % 8.35/8.66 (∀ (X : Iota), % 8.35/8.66 Or (Or (Not (r1 Y X)) (Not (And (p2 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))))) % 8.35/8.66 (p1 X))) % 8.35/8.66 (p2 Y)) % 8.35/8.66 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.35/8.66 (∀ (X : Iota), % 8.35/8.66 Or (Or (Not (r1 Y X)) (p2 X)) % 8.35/8.66 (Not (And (And (p1 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (p1 X)))))) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or % 8.35/8.66 (Or % 8.35/8.66 (Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.35/8.66 (p2 Y)) % 8.35/8.66 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))))))) % 8.35/8.66 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Not (r1 X Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y)))))))) % 8.35/8.66 True % 8.35/8.66 Clause #1 (by clausification #[0]): Eq % 8.35/8.66 (Not % 8.35/8.66 (Exists fun X => % 8.35/8.66 Not % 8.35/8.66 (Or % 8.35/8.66 (Or % 8.35/8.66 (Not % 8.35/8.66 (Or % 8.35/8.66 (Or % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Not (r1 X Y)) (p2 Y)) % 8.35/8.66 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y))))) % 8.35/8.66 (Not % 8.35/8.66 (And % 8.35/8.66 (And % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or % 8.35/8.66 (Or % 8.35/8.66 (Or (Not (r1 X Y)) % 8.35/8.66 (∀ (X : Iota), % 8.35/8.66 Or (Or (Not (r1 Y X)) (Not (And (p2 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))))) % 8.35/8.66 (p1 X))) % 8.35/8.66 (p2 Y)) % 8.35/8.66 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or (Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.35/8.66 (∀ (X : Iota), % 8.35/8.66 Or (Or (Not (r1 Y X)) (p2 X)) % 8.35/8.66 (Not (And (And (p1 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (p1 X)))))) % 8.35/8.66 (∀ (Y : Iota), % 8.35/8.66 Or % 8.35/8.66 (Or (Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.35/8.66 (p2 Y)) % 8.35/8.66 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))))))) % 8.35/8.66 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))) % 8.35/8.66 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))))) % 8.45/8.72 False % 8.45/8.72 Clause #2 (by clausification #[1]): Eq % 8.45/8.72 (Exists fun X => % 8.45/8.72 Not % 8.45/8.72 (Or % 8.45/8.72 (Or % 8.45/8.72 (Not % 8.45/8.72 (Or % 8.45/8.72 (Or % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Not (r1 X Y)) (p2 Y)) % 8.45/8.72 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y))))) % 8.45/8.72 (Not % 8.45/8.72 (And % 8.45/8.72 (And % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or % 8.45/8.72 (Or % 8.45/8.72 (Or (Not (r1 X Y)) % 8.45/8.72 (∀ (X : Iota), % 8.45/8.72 Or (Or (Not (r1 Y X)) (Not (And (p2 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))))) % 8.45/8.72 (p1 X))) % 8.45/8.72 (p2 Y)) % 8.45/8.72 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.45/8.72 (∀ (X : Iota), % 8.45/8.72 Or (Or (Not (r1 Y X)) (p2 X)) % 8.45/8.72 (Not (And (And (p1 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (p1 X)))))) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or % 8.45/8.72 (Or (Or (Or (Not (r1 X Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.45/8.72 (p2 Y)) % 8.45/8.72 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))))))) % 8.45/8.72 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))) % 8.45/8.72 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y)))))) % 8.45/8.72 True % 8.45/8.72 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 8.45/8.72 Eq % 8.45/8.72 (Not % 8.45/8.72 (Or % 8.45/8.72 (Or % 8.45/8.72 (Not % 8.45/8.72 (Or % 8.45/8.72 (Or % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) % 8.45/8.72 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y))))) % 8.45/8.72 (Not % 8.45/8.72 (And % 8.45/8.72 (And % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or % 8.45/8.72 (Or % 8.45/8.72 (Or (Not (r1 (skS.0 0 a) Y)) % 8.45/8.72 (∀ (X : Iota), % 8.45/8.72 Or (Or (Not (r1 Y X)) (Not (And (p2 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))))) % 8.45/8.72 (p1 X))) % 8.45/8.72 (p2 Y)) % 8.45/8.72 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or % 8.45/8.72 (Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) % 8.45/8.72 (p1 Y)) % 8.45/8.72 (∀ (X : Iota), % 8.45/8.72 Or (Or (Not (r1 Y X)) (p2 X)) % 8.45/8.72 (Not (And (And (p1 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (p1 X)))))) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or % 8.45/8.72 (Or % 8.45/8.72 (Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) % 8.45/8.72 (p1 Y)) % 8.45/8.72 (p2 Y)) % 8.45/8.72 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))))))) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))) % 8.45/8.72 (∀ (Y : Iota), % 8.45/8.72 Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y)))))) % 8.45/8.72 True % 8.45/8.77 Clause #4 (by clausification #[3]): ∀ (a : Iota), % 8.45/8.77 Eq % 8.45/8.77 (Or % 8.45/8.77 (Or % 8.45/8.77 (Not % 8.45/8.77 (Or % 8.45/8.77 (Or % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) (p1 Y)) % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) % 8.45/8.77 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y))))) % 8.45/8.77 (Not % 8.45/8.77 (And % 8.45/8.77 (And % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or % 8.45/8.77 (Or % 8.45/8.77 (Or (Not (r1 (skS.0 0 a) Y)) % 8.45/8.77 (∀ (X : Iota), % 8.45/8.77 Or (Or (Not (r1 Y X)) (Not (And (p2 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))))) (p1 X))) % 8.45/8.77 (p2 Y)) % 8.45/8.77 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))) % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or % 8.45/8.77 (Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) % 8.45/8.77 (p1 Y)) % 8.45/8.77 (∀ (X : Iota), % 8.45/8.77 Or (Or (Not (r1 Y X)) (p2 X)) % 8.45/8.77 (Not (And (And (p1 X) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (p1 X)))))) % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or % 8.45/8.77 (Or % 8.45/8.77 (Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p2 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p2 X))))) % 8.45/8.77 (p1 Y)) % 8.45/8.77 (p2 Y)) % 8.45/8.77 (Not (And (And (p1 Y) (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))) (p1 Y)))))))) % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))) % 8.45/8.77 (∀ (Y : Iota), % 8.45/8.77 Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y))))) % 8.45/8.77 False % 8.45/8.77 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 8.45/8.77 Eq (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (And (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)) (p1 Y)))) % 8.45/8.77 False % 8.45/8.77 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), % 8.45/8.77 Eq % 8.45/8.77 (Not % 8.45/8.77 (Or (Or (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) (p1 (skS.0 1 a a_1))) % 8.45/8.77 (Not (And (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X)) (p1 (skS.0 1 a a_1)))))) % 8.45/8.77 True % 8.45/8.77 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 8.45/8.77 Eq % 8.45/8.77 (Or (Or (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) (p1 (skS.0 1 a a_1))) % 8.45/8.77 (Not (And (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X)) (p1 (skS.0 1 a a_1))))) % 8.45/8.77 False % 8.45/8.77 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Not (And (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X)) (p1 (skS.0 1 a a_1)))) False % 8.45/8.77 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) (p1 (skS.0 1 a a_1))) False % 8.45/8.77 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (And (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X)) (p1 (skS.0 1 a a_1))) True % 8.45/8.77 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (p1 (skS.0 1 a a_1)) True % 8.45/8.77 Clause #17 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (p1 (skS.0 1 a a_1)) False % 8.45/8.77 Clause #19 (by superposition #[17, 12]): Eq False True % 8.45/8.77 Clause #20 (by clausification #[19]): False % 8.45/8.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------