%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 11:36:02 AM UTC 2026 % Result : Theorem 10.66s 10.92s % Output : Proof 10.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : duper %s % 0.11/0.37 % Computer : n006.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 02:53:01 UTC 2026 % 0.11/0.38 % CPUTime : % 10.66/10.92 SZS status Theorem for theBenchmark.p % 10.66/10.92 SZS output start Proof for theBenchmark.p % 10.66/10.92 Clause #0 (by assumption #[]): Eq (Iff modus_ponens (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y)) True % 10.66/10.92 Clause #15 (by assumption #[]): Eq (Iff kn1 (∀ (P : Iota), is_a_theorem (implies P (and P P)))) True % 10.66/10.92 Clause #21 (by assumption #[]): Eq (Iff r1 (∀ (P : Iota), is_a_theorem (implies (or P P) P))) True % 10.66/10.92 Clause #23 (by assumption #[]): Eq (Iff r3 (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P)))) True % 10.66/10.92 Clause #27 (by assumption #[]): Eq (op_and → ∀ (X Y : Iota), Eq (and X Y) (not (or (not X) (not Y)))) True % 10.66/10.92 Clause #29 (by assumption #[]): Eq (op_implies_or → ∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True % 10.66/10.92 Clause #31 (by assumption #[]): Eq op_implies_or True % 10.66/10.92 Clause #32 (by assumption #[]): Eq op_and True % 10.66/10.92 Clause #34 (by assumption #[]): Eq modus_ponens True % 10.66/10.92 Clause #35 (by assumption #[]): Eq r1 True % 10.66/10.92 Clause #37 (by assumption #[]): Eq r3 True % 10.66/10.92 Clause #43 (by assumption #[]): Eq (Not kn1) True % 10.66/10.92 Clause #45 (by clausification #[0]): Or (Eq modus_ponens False) % 10.66/10.92 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True) % 10.66/10.92 Clause #64 (by clausification #[43]): Eq kn1 False % 10.66/10.92 Clause #65 (by clausification #[45]): ∀ (a : Iota), % 10.66/10.92 Or (Eq modus_ponens False) % 10.66/10.92 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True) % 10.66/10.92 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 10.66/10.92 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True) % 10.66/10.92 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 10.66/10.92 Or (Eq modus_ponens False) % 10.66/10.92 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True)) % 10.66/10.92 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), % 10.66/10.92 Or (Eq modus_ponens False) % 10.66/10.92 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))) % 10.66/10.92 Clause #69 (by forward demodulation #[68, 34]): ∀ (a a_1 : Iota), % 10.66/10.92 Or (Eq True False) % 10.66/10.92 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))) % 10.66/10.92 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 10.66/10.92 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)) % 10.66/10.92 Clause #83 (by clausification #[15]): Or (Eq kn1 True) (Eq (∀ (P : Iota), is_a_theorem (implies P (and P P))) False) % 10.66/10.92 Clause #85 (by clausification #[83]): ∀ (a : Iota), Or (Eq kn1 True) (Eq (Not (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a))))) True) % 10.66/10.92 Clause #86 (by clausification #[85]): ∀ (a : Iota), Or (Eq kn1 True) (Eq (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a)))) False) % 10.66/10.92 Clause #87 (by forward demodulation #[86, 64]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a)))) False) % 10.66/10.92 Clause #88 (by clausification #[87]): ∀ (a : Iota), Eq (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a)))) False % 10.66/10.92 Clause #92 (by clausification #[21]): Or (Eq r1 False) (Eq (∀ (P : Iota), is_a_theorem (implies (or P P) P)) True) % 10.66/10.92 Clause #96 (by clausification #[92]): ∀ (a : Iota), Or (Eq r1 False) (Eq (is_a_theorem (implies (or a a) a)) True) % 10.66/10.92 Clause #97 (by forward demodulation #[96, 35]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (or a a) a)) True) % 10.66/10.92 Clause #98 (by clausification #[97]): ∀ (a : Iota), Eq (is_a_theorem (implies (or a a) a)) True % 10.66/10.92 Clause #99 (by superposition #[98, 70]): ∀ (a a_1 : Iota), % 10.66/10.92 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (implies (or a_1 a_1) a_1) a)) False)) % 10.66/10.92 Clause #224 (by clausification #[29]): Or (Eq op_implies_or False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True) % 10.66/10.92 Clause #225 (by clausification #[224]): ∀ (a : Iota), Or (Eq op_implies_or False) (Eq (∀ (Y : Iota), Eq (implies a Y) (or (not a) Y)) True) % 10.66/10.92 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq op_implies_or False) (Eq (Eq (implies a a_1) (or (not a) a_1)) True) % 10.66/10.96 Clause #227 (by clausification #[226]): ∀ (a a_1 : Iota), Or (Eq op_implies_or False) (Eq (implies a a_1) (or (not a) a_1)) % 10.66/10.96 Clause #228 (by forward demodulation #[227, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (implies a a_1) (or (not a) a_1)) % 10.66/10.96 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Eq (implies a a_1) (or (not a) a_1) % 10.66/10.96 Clause #244 (by clausification #[23]): Or (Eq r3 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P))) True) % 10.66/10.96 Clause #250 (by clausification #[244]): ∀ (a : Iota), Or (Eq r3 False) (Eq (∀ (Q : Iota), is_a_theorem (implies (or a Q) (or Q a))) True) % 10.66/10.96 Clause #251 (by clausification #[250]): ∀ (a a_1 : Iota), Or (Eq r3 False) (Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True) % 10.66/10.96 Clause #252 (by forward demodulation #[251, 37]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True) % 10.66/10.96 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True % 10.66/10.96 Clause #256 (by superposition #[253, 229]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies a a_1) (or a_1 (not a)))) True % 10.66/10.96 Clause #328 (by clausification #[99]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies (or a_1 a_1) a_1) a)) False) % 10.66/10.96 Clause #331 (by superposition #[328, 256]): ∀ (a : Iota), Or (Eq (is_a_theorem (or a (not (or a a)))) True) (Eq False True) % 10.66/10.96 Clause #334 (by clausification #[331]): ∀ (a : Iota), Eq (is_a_theorem (or a (not (or a a)))) True % 10.66/10.96 Clause #337 (by superposition #[334, 229]): ∀ (a : Iota), Eq (is_a_theorem (or (not a) (not (implies a (not a))))) True % 10.66/10.96 Clause #338 (by forward demodulation #[337, 229]): ∀ (a : Iota), Eq (is_a_theorem (implies a (not (implies a (not a))))) True % 10.66/10.96 Clause #425 (by clausification #[27]): Or (Eq op_and False) (Eq (∀ (X Y : Iota), Eq (and X Y) (not (or (not X) (not Y)))) True) % 10.66/10.96 Clause #426 (by clausification #[425]): ∀ (a : Iota), Or (Eq op_and False) (Eq (∀ (Y : Iota), Eq (and a Y) (not (or (not a) (not Y)))) True) % 10.66/10.96 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Or (Eq op_and False) (Eq (Eq (and a a_1) (not (or (not a) (not a_1)))) True) % 10.66/10.96 Clause #428 (by clausification #[427]): ∀ (a a_1 : Iota), Or (Eq op_and False) (Eq (and a a_1) (not (or (not a) (not a_1)))) % 10.66/10.96 Clause #429 (by forward demodulation #[428, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (and a a_1) (not (or (not a) (not a_1)))) % 10.66/10.96 Clause #430 (by clausification #[429]): ∀ (a a_1 : Iota), Eq (and a a_1) (not (or (not a) (not a_1))) % 10.66/10.96 Clause #431 (by forward demodulation #[430, 229]): ∀ (a a_1 : Iota), Eq (and a a_1) (not (implies a (not a_1))) % 10.66/10.96 Clause #432 (by backward demodulation #[431, 338]): ∀ (a : Iota), Eq (is_a_theorem (implies a (and a a))) True % 10.66/10.96 Clause #455 (by superposition #[432, 88]): Eq True False % 10.66/10.96 Clause #460 (by clausification #[455]): False % 10.66/10.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------