%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL664+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 11:36:20 AM UTC 2026 % Result : Theorem 8.90s 9.13s % Output : Proof 8.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL664+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.11/0.36 % Computer : n004.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 : Sun Sep 6 01:40:00 UTC 2026 % 0.11/0.36 % CPUTime : % 8.90/9.13 SZS status Theorem for theBenchmark.p % 8.90/9.13 SZS output start Proof for theBenchmark.p % 8.90/9.13 Clause #1 (by assumption #[]): Eq % 8.90/9.13 (Not % 8.90/9.13 (Not % 8.90/9.13 (Exists fun X => % 8.90/9.13 Not % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p16 Y))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p14 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y)))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p15 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p13 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p11 Y)))))) % 8.90/9.13 True % 8.90/9.13 Clause #3 (by clausification #[1]): Eq % 8.90/9.13 (Not % 8.90/9.13 (Exists fun X => % 8.90/9.13 Not % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p16 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p14 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y)))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p15 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p13 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p11 Y))))) % 8.90/9.13 False % 8.90/9.13 Clause #4 (by clausification #[3]): Eq % 8.90/9.13 (Exists fun X => % 8.90/9.13 Not % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p16 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p14 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y)))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p15 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p13 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p12 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 X Y)) (p11 Y)))) % 8.90/9.13 True % 8.90/9.13 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 8.90/9.13 Eq % 8.90/9.13 (Not % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p16 Y))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p14 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p15 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p13 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p11 Y)))) % 8.90/9.13 True % 8.90/9.13 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 8.90/9.13 Eq % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p16 Y))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p14 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p15 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p13 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p11 Y))) % 8.90/9.13 False % 8.90/9.13 Clause #8 (by clausification #[6]): ∀ (a : Iota), % 8.90/9.13 Eq % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or % 8.90/9.13 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p16 Y))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p14 Y)))) % 8.90/9.13 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p15 Y))) % 8.90/9.13 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p13 Y))) % 8.90/9.18 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y))) % 8.90/9.18 False % 8.90/9.18 Clause #14 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)) False % 8.90/9.18 Clause #15 (by clausification #[8]): ∀ (a : Iota), % 8.90/9.18 Eq % 8.90/9.18 (Or % 8.90/9.18 (Or % 8.90/9.18 (Or % 8.90/9.18 (Or % 8.90/9.18 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p16 Y))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p14 Y)))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.18 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p15 Y))) % 8.90/9.18 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p13 Y))) % 8.90/9.18 False % 8.90/9.18 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Not (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) (p12 (skS.0 2 a a_1)))) True % 8.90/9.18 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) (p12 (skS.0 2 a a_1))) False % 8.90/9.18 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (p12 (skS.0 2 a a_1)) False % 8.90/9.18 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) False % 8.90/9.18 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True % 8.90/9.18 Clause #22 (by clausification #[15]): ∀ (a : Iota), % 8.90/9.18 Eq % 8.90/9.18 (Or % 8.90/9.18 (Or % 8.90/9.18 (Or % 8.90/9.18 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p16 Y))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p14 Y)))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.18 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p15 Y))) % 8.90/9.18 False % 8.90/9.18 Clause #29 (by clausification #[22]): ∀ (a : Iota), % 8.90/9.18 Eq % 8.90/9.18 (Or % 8.90/9.18 (Or % 8.90/9.18 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p16 Y))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p14 Y)))) % 8.90/9.18 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)))) % 8.90/9.18 False % 8.90/9.18 Clause #35 (by clausification #[29]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y))) False % 8.90/9.18 Clause #37 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p12 Y)) True % 8.90/9.18 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p12 a_1)) True % 8.90/9.18 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p12 a_1) True) % 8.90/9.18 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (p12 a) True) (Eq (r1 (skS.0 0 a_1) a) False) % 8.90/9.18 Clause #42 (by superposition #[40, 20]): ∀ (a a_1 : Iota), Or (Eq (p12 (skS.0 2 a a_1)) True) (Eq False True) % 8.90/9.18 Clause #66 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (p12 (skS.0 2 a a_1)) True % 8.90/9.18 Clause #67 (by superposition #[66, 18]): Eq True False % 8.90/9.18 Clause #68 (by clausification #[67]): False % 8.90/9.18 SZS output end Proof for theBenchmark.p 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