%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 8.46s 8.72s % Output : Proof 8.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.05 % Command : duper %s % 0.12/0.37 % Computer : n019.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Sat Sep 5 21:18:53 UTC 2026 % 0.12/0.37 % CPUTime : % 8.46/8.72 SZS status Theorem for theBenchmark.p % 8.46/8.72 SZS output start Proof for theBenchmark.p % 8.46/8.72 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True % 8.46/8.72 Clause #1 (by assumption #[]): Eq % 8.46/8.72 (Not % 8.46/8.72 (Not % 8.46/8.72 (Exists fun X => % 8.46/8.72 Not (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (p201 Y) (p101 Y))))) (Not (And (p201 X) (p101 X))))))) % 8.46/8.72 True % 8.46/8.72 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True % 8.46/8.72 Clause #3 (by clausification #[1]): Eq % 8.46/8.72 (Not % 8.46/8.72 (Exists fun X => % 8.46/8.72 Not (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (p201 Y) (p101 Y))))) (Not (And (p201 X) (p101 X)))))) % 8.46/8.72 False % 8.46/8.72 Clause #4 (by clausification #[3]): Eq % 8.46/8.72 (Exists fun X => % 8.46/8.72 Not (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (p201 Y) (p101 Y))))) (Not (And (p201 X) (p101 X))))) % 8.46/8.72 True % 8.46/8.72 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 8.46/8.72 Eq % 8.46/8.72 (Not % 8.46/8.72 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p201 Y) (p101 Y))))) % 8.46/8.72 (Not (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a)))))) % 8.46/8.72 True % 8.46/8.72 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 8.46/8.72 Eq % 8.46/8.72 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p201 Y) (p101 Y))))) % 8.46/8.72 (Not (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a))))) % 8.46/8.72 False % 8.46/8.72 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (Not (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a)))) False % 8.46/8.72 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p201 Y) (p101 Y))))) False % 8.46/8.72 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (And (p201 (skS.0 0 a)) (p101 (skS.0 0 a))) True % 8.46/8.72 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) True % 8.46/8.72 Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (p201 (skS.0 0 a)) True % 8.46/8.72 Clause #12 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (p201 Y) (p101 Y)))) True % 8.46/8.72 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (Not (And (p201 a_1) (p101 a_1)))) True % 8.46/8.72 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (Not (And (p201 a_1) (p101 a_1))) True) % 8.46/8.72 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (Not (And (p201 a) (p101 a))) True) (Eq (r1 (skS.0 0 a_1) a) False) % 8.46/8.72 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (And (p201 a_1) (p101 a_1)) False) % 8.46/8.72 Clause #17 (by clausification #[16]): ∀ (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)) % 8.46/8.72 Clause #18 (by superposition #[17, 2]): ∀ (a : Iota), Or (Eq (p201 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) False) (Eq False True)) % 8.46/8.72 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (p201 (skS.0 0 a)) False) (Eq (p101 (skS.0 0 a)) False) % 8.46/8.72 Clause #20 (by forward demodulation #[19, 11]): ∀ (a : Iota), Or (Eq True False) (Eq (p101 (skS.0 0 a)) False) % 8.46/8.72 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False % 8.46/8.72 Clause #22 (by superposition #[21, 10]): Eq False True % 8.46/8.72 Clause #23 (by clausification #[22]): False % 8.46/8.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------