%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL684+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 11:36:27 AM UTC 2026 % Result : Theorem 8.46s 8.76s % Output : Proof 8.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : duper %s % 0.12/0.38 % Computer : n007.cluster.edu % 0.12/0.38 % Model : x86_64 x86_64 % 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.38 % Memory : 8046.5625MB % 0.12/0.38 % OS : Linux 6.8.0-71-generic % 0.12/0.38 % CPULimit : 300 % 0.12/0.38 % WCLimit : 300 % 0.12/0.38 % DateTime : Sat Sep 5 16:31:24 UTC 2026 % 0.12/0.38 % CPUTime : % 8.46/8.76 SZS status Theorem for theBenchmark.p % 8.46/8.76 SZS output start Proof for theBenchmark.p % 8.46/8.76 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True % 8.46/8.76 Clause #2 (by assumption #[]): Eq % 8.46/8.76 (Not % 8.46/8.76 (Not % 8.46/8.76 (Exists fun X => % 8.46/8.76 Not % 8.46/8.76 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 (Not (And (p201 X) (p101 X))))))) % 8.46/8.76 True % 8.46/8.76 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True % 8.46/8.76 Clause #11 (by clausification #[2]): Eq % 8.46/8.76 (Not % 8.46/8.76 (Exists fun X => % 8.46/8.76 Not % 8.46/8.76 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 False % 8.46/8.76 Clause #12 (by clausification #[11]): Eq % 8.46/8.76 (Exists fun X => % 8.46/8.76 Not % 8.46/8.76 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 (Not (And (p201 X) (p101 X))))) % 8.46/8.76 True % 8.46/8.76 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 8.46/8.76 Eq % 8.46/8.76 (Not % 8.46/8.76 (Or % 8.46/8.76 (Not % 8.46/8.76 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 (Not (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a)))))) % 8.46/8.76 True % 8.46/8.76 Clause #14 (by clausification #[13]): ∀ (a : Iota), % 8.46/8.76 Eq % 8.46/8.76 (Or % 8.46/8.76 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 (Not (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a))))) % 8.46/8.76 False % 8.46/8.76 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (Not (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a)))) False % 8.46/8.76 Clause #16 (by clausification #[14]): ∀ (a : Iota), % 8.46/8.76 Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X)))))) % 8.46/8.76 False % 8.46/8.76 Clause #17 (by clausification #[15]): ∀ (a : Iota), Eq (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a))) True % 8.46/8.76 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) True % 8.46/8.76 Clause #19 (by clausification #[17]): ∀ (a : Iota), Eq (p201 (skS.0 0 a)) True % 8.46/8.76 Clause #20 (by clausification #[16]): ∀ (a : Iota), % 8.46/8.76 Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (p201 X) (p101 X))))) True % 8.46/8.76 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 8.46/8.76 Eq (Or (Not (r1 (skS.0 0 a) a_1)) (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (p201 X) (p101 X))))) True % 8.46/8.76 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 8.46/8.76 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (p201 X) (p101 X)))) True) % 8.46/8.76 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 8.46/8.76 Or (Eq (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (p201 X) (p101 X)))) True) (Eq (r1 (skS.0 0 a_1) a) False) % 8.46/8.76 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 8.46/8.76 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Or (Not (r1 a_1 a_2)) (Not (And (p201 a_2) (p101 a_2)))) True) % 8.46/8.76 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 8.46/8.76 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (Not (r1 a_1 a_2)) True) (Eq (Not (And (p201 a_2) (p101 a_2))) True)) % 8.46/8.76 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 8.46/8.76 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (Not (And (p201 a_2) (p101 a_2))) True) (Eq (r1 a_1 a_2) False)) % 8.46/8.76 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 8.46/8.76 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (r1 a_1 a_2) False) (Eq (And (p201 a_2) (p101 a_2)) False)) % 8.46/8.76 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 8.46/8.76 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (r1 a_1 a_2) False) (Or (Eq (p201 a_2) False) (Eq (p101 a_2) False))) % 8.46/8.76 Clause #29 (by superposition #[28, 3]): ∀ (a a_1 : Iota), % 8.46/8.76 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (p201 a_1) False) (Or (Eq (p101 a_1) False) (Eq False True))) % 8.46/8.76 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (p201 a_1) False) (Eq (p101 a_1) False)) % 8.46/8.76 Clause #31 (by superposition #[30, 3]): ∀ (a : Iota), Or (Eq (p201 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) False) (Eq False True)) % 8.46/8.76 Clause #32 (by clausification #[31]): ∀ (a : Iota), Or (Eq (p201 (skS.0 0 a)) False) (Eq (p101 (skS.0 0 a)) False) % 8.46/8.77 Clause #33 (by forward demodulation #[32, 19]): ∀ (a : Iota), Or (Eq True False) (Eq (p101 (skS.0 0 a)) False) % 8.46/8.77 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False % 8.46/8.77 Clause #35 (by superposition #[34, 18]): Eq False True % 8.46/8.77 Clause #36 (by clausification #[35]): False % 8.46/8.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------