%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 11:36:25 AM UTC 2026 % Result : Theorem 8.89s 9.18s % Output : Proof 8.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.10/0.36 % Computer : n027.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 23:59:43 UTC 2026 % 0.10/0.37 % CPUTime : % 8.89/9.18 SZS status Theorem for theBenchmark.p % 8.89/9.18 SZS output start Proof for theBenchmark.p % 8.89/9.18 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True % 8.89/9.18 Clause #2 (by assumption #[]): Eq % 8.89/9.18 (Not % 8.89/9.18 (Not % 8.89/9.18 (Exists fun X => % 8.89/9.18 Not % 8.89/9.18 (Or False % 8.89/9.18 (Not % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 X Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))))))) % 8.89/9.18 True % 8.89/9.18 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True % 8.89/9.18 Clause #11 (by clausification #[2]): Eq % 8.89/9.18 (Not % 8.89/9.18 (Exists fun X => % 8.89/9.18 Not % 8.89/9.18 (Or False % 8.89/9.18 (Not % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 X Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))))))) % 8.89/9.18 False % 8.89/9.18 Clause #12 (by clausification #[11]): Eq % 8.89/9.18 (Exists fun X => % 8.89/9.18 Not % 8.89/9.18 (Or False % 8.89/9.18 (Not % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 X Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))))) % 8.89/9.18 True % 8.89/9.18 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 8.89/9.18 Eq % 8.89/9.18 (Not % 8.89/9.18 (Or False % 8.89/9.18 (Not % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 (skS.0 0 a) Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))))) % 8.89/9.18 True % 8.89/9.18 Clause #14 (by clausification #[13]): ∀ (a : Iota), % 8.89/9.18 Eq % 8.89/9.18 (Or False % 8.89/9.18 (Not % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 (skS.0 0 a) Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))))) % 8.89/9.18 False % 8.89/9.18 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 8.89/9.18 Eq % 8.89/9.18 (Not % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 (skS.0 0 a) Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))) % 8.89/9.18 False % 8.89/9.18 Clause #17 (by clausification #[15]): ∀ (a : Iota), % 8.89/9.18 Eq % 8.89/9.18 (∀ (Y : Iota), % 8.89/9.18 Or (Or (Not (r1 (skS.0 0 a) Y)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))) % 8.89/9.18 True % 8.89/9.18 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 8.89/9.18 Eq % 8.89/9.18 (Or (Or (Not (r1 (skS.0 0 a) a_1)) False) % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))) % 8.89/9.18 True % 8.89/9.18 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 8.89/9.18 Or (Eq (Or (Not (r1 (skS.0 0 a) a_1)) False) True) % 8.89/9.18 (Eq % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) % 8.89/9.18 True) % 8.89/9.18 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 8.89/9.18 Or % 8.89/9.18 (Eq % 8.89/9.18 (Not % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) % 8.89/9.18 True) % 8.89/9.18 (Or (Eq (Not (r1 (skS.0 0 a_1) a)) True) (Eq False True)) % 8.89/9.18 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 8.89/9.18 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) % 8.89/9.18 (Or (Eq False True) % 8.89/9.18 (Eq % 8.89/9.18 (∀ (X : Iota), % 8.89/9.18 Or (Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.89/9.18 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) % 8.89/9.18 False)) % 8.96/9.25 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 8.96/9.25 Or (Eq False True) % 8.96/9.25 (Or % 8.96/9.25 (Eq % 8.96/9.25 (∀ (X : Iota), % 8.96/9.25 Or (Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) % 8.96/9.25 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) % 8.96/9.25 False) % 8.96/9.25 (Eq (r1 (skS.0 0 a_1) a) False)) % 8.96/9.25 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 8.96/9.25 Or % 8.96/9.25 (Eq % 8.96/9.25 (∀ (X : Iota), % 8.96/9.25 Or (Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) % 8.96/9.25 False) % 8.96/9.25 (Eq (r1 (skS.0 0 a_1) a) False) % 8.96/9.25 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 8.96/9.25 (Eq % 8.96/9.25 (Not % 8.96/9.25 (Or (Or (Not (r1 a_1 (skS.0 1 a_1 a_2))) (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))) % 8.96/9.25 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))))) % 8.96/9.25 True) % 8.96/9.25 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 8.96/9.25 (Eq % 8.96/9.25 (Or (Or (Not (r1 a_1 (skS.0 1 a_1 a_2))) (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))) % 8.96/9.25 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)))) % 8.96/9.25 False) % 8.96/9.25 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))) False) % 8.96/9.25 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 8.96/9.25 (Eq (Or (Not (r1 a_1 (skS.0 1 a_1 a_2))) (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))) False) % 8.96/9.25 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)) True) % 8.96/9.25 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Or (Not (r1 (skS.0 1 a_1 a_2) a_3)) (p1 a_3)) True) % 8.96/9.25 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (Not (r1 (skS.0 1 a_1 a_2) a_3)) True) (Eq (p1 a_3) True)) % 8.96/9.25 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (p1 a_2) True) (Eq (r1 (skS.0 1 a_1 a_3) a_2) False)) % 8.96/9.25 Clause #32 (by superposition #[31, 3]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 a) True) (Or (Eq (r1 (skS.0 1 (skS.0 0 a_1) a_2) a) False) (Eq False True)) % 8.96/9.25 Clause #33 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)) False) % 8.96/9.25 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 8.96/9.25 (Eq (Not (Or (Not (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) (p1 (skS.0 2 a_1 a_2 a_3)))) True) % 8.96/9.25 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) % 8.96/9.25 (Eq (Or (Not (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) (p1 (skS.0 2 a_1 a_2 a_3))) False) % 8.96/9.25 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (p1 (skS.0 2 a_1 a_2 a_3)) False) % 8.96/9.25 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 8.96/9.25 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) False) % 8.96/9.25 Clause #39 (by superposition #[37, 3]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) False) (Eq False True) % 8.96/9.25 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) False % 8.96/9.25 Clause #41 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 a) True) (Eq (r1 (skS.0 1 (skS.0 0 a_1) a_2) a) False) % 8.96/9.25 Clause #51 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) True) % 8.96/9.25 Clause #53 (by superposition #[51, 3]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 1 (skS.0 0 a) a_1) (skS.0 2 (skS.0 0 a) a_1 a_2)) True) (Eq False True) % 8.96/9.25 Clause #59 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 (skS.0 0 a) a_1) (skS.0 2 (skS.0 0 a) a_1 a_2)) True % 8.96/9.25 Clause #60 (by superposition #[59, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) True) (Eq True False) % 8.96/9.25 Clause #67 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) True % 8.96/9.25 Clause #68 (by superposition #[67, 40]): Eq True False % 8.96/9.25 Clause #69 (by clausification #[68]): False % 8.96/9.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------