%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL646+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 11:36:14 AM UTC 2026 % Result : Theorem 8.80s 9.06s % Output : Proof 8.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL646+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.11/0.36 % Computer : n007.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 11:39:09 UTC 2026 % 0.11/0.36 % CPUTime : % 8.80/9.06 SZS status Theorem for theBenchmark.p % 8.80/9.06 SZS output start Proof for theBenchmark.p % 8.80/9.06 Clause #0 (by assumption #[]): Eq % 8.80/9.06 (Not % 8.80/9.06 (Not % 8.80/9.06 (Exists fun X => % 8.80/9.06 Not % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p6 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p4 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p5 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p3 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))) % 8.80/9.06 True % 8.80/9.06 Clause #1 (by clausification #[0]): Eq % 8.80/9.06 (Not % 8.80/9.06 (Exists fun X => % 8.80/9.06 Not % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p6 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p4 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p5 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p3 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) % 8.80/9.06 False % 8.80/9.06 Clause #2 (by clausification #[1]): Eq % 8.80/9.06 (Exists fun X => % 8.80/9.06 Not % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p6 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p4 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p5 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p3 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) % 8.80/9.06 True % 8.80/9.06 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 8.80/9.06 Eq % 8.80/9.06 (Not % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p6 Y))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p4 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p5 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p3 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)))) % 8.80/9.06 True % 8.80/9.06 Clause #4 (by clausification #[3]): ∀ (a : Iota), % 8.80/9.06 Eq % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p6 Y))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p4 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p5 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p3 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p1 Y))) % 8.80/9.06 False % 8.80/9.06 Clause #6 (by clausification #[4]): ∀ (a : Iota), % 8.80/9.06 Eq % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or % 8.80/9.06 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p6 Y))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p4 Y)))) % 8.80/9.06 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p5 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p3 Y))) % 8.80/9.06 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) % 8.80/9.11 False % 8.80/9.11 Clause #12 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) False % 8.80/9.11 Clause #13 (by clausification #[6]): ∀ (a : Iota), % 8.80/9.11 Eq % 8.80/9.11 (Or % 8.80/9.11 (Or % 8.80/9.11 (Or % 8.80/9.11 (Or % 8.80/9.11 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p6 Y))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p4 Y)))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.11 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p5 Y))) % 8.80/9.11 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p3 Y))) % 8.80/9.11 False % 8.80/9.11 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) (p2 (skS.0 2 a a_1)))) True % 8.80/9.11 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) (p2 (skS.0 2 a a_1))) False % 8.80/9.11 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 a a_1)) False % 8.80/9.11 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) False % 8.80/9.11 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True % 8.80/9.11 Clause #20 (by clausification #[13]): ∀ (a : Iota), % 8.80/9.11 Eq % 8.80/9.11 (Or % 8.80/9.11 (Or % 8.80/9.11 (Or % 8.80/9.11 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p6 Y))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p4 Y)))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.11 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p5 Y))) % 8.80/9.11 False % 8.80/9.11 Clause #26 (by clausification #[20]): ∀ (a : Iota), % 8.80/9.11 Eq % 8.80/9.11 (Or % 8.80/9.11 (Or % 8.80/9.11 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p6 Y))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p4 Y)))) % 8.80/9.11 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))) % 8.80/9.11 False % 8.80/9.11 Clause #33 (by clausification #[26]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) False % 8.80/9.11 Clause #35 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) True % 8.80/9.11 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p2 a_1)) True % 8.80/9.11 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p2 a_1) True) % 8.80/9.11 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (p2 a) True) (Eq (r1 (skS.0 0 a_1) a) False) % 8.80/9.11 Clause #40 (by superposition #[38, 18]): ∀ (a a_1 : Iota), Or (Eq (p2 (skS.0 2 a a_1)) True) (Eq False True) % 8.80/9.11 Clause #60 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 a a_1)) True % 8.80/9.11 Clause #61 (by superposition #[60, 16]): Eq True False % 8.80/9.11 Clause #62 (by clausification #[61]): False % 8.80/9.11 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------