%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 7.26s 7.56s % Output : Proof 7.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : duper %s % 0.11/0.36 % Computer : n016.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 : Fri Sep 4 19:05:43 UTC 2026 % 0.11/0.36 % CPUTime : % 7.26/7.56 SZS status Theorem for theBenchmark.p % 7.26/7.56 SZS output start Proof for theBenchmark.p % 7.26/7.56 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 % 7.26/7.56 Clause #13 (by assumption #[]): Eq (Iff equivalence_2 (∀ (X Y : Iota), is_a_theorem (implies (equiv X Y) (implies Y X)))) True % 7.26/7.56 Clause #22 (by assumption #[]): Eq (Iff r2 (∀ (P Q : Iota), is_a_theorem (implies Q (or P Q)))) True % 7.26/7.56 Clause #23 (by assumption #[]): Eq (Iff r3 (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P)))) True % 7.26/7.56 Clause #28 (by assumption #[]): Eq (op_implies_and → ∀ (X Y : Iota), Eq (implies X Y) (not (and X (not Y)))) True % 7.26/7.56 Clause #29 (by assumption #[]): Eq (op_implies_or → ∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True % 7.26/7.56 Clause #30 (by assumption #[]): Eq (op_equiv → ∀ (X Y : Iota), Eq (equiv X Y) (and (implies X Y) (implies Y X))) True % 7.26/7.56 Clause #31 (by assumption #[]): Eq op_implies_or True % 7.26/7.56 Clause #33 (by assumption #[]): Eq op_equiv True % 7.26/7.56 Clause #34 (by assumption #[]): Eq modus_ponens True % 7.26/7.56 Clause #36 (by assumption #[]): Eq r2 True % 7.26/7.56 Clause #37 (by assumption #[]): Eq r3 True % 7.26/7.56 Clause #42 (by assumption #[]): Eq op_implies_and True % 7.26/7.56 Clause #43 (by assumption #[]): Eq (Not equivalence_2) True % 7.26/7.56 Clause #45 (by clausification #[0]): Or (Eq modus_ponens False) % 7.26/7.56 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True) % 7.26/7.56 Clause #64 (by clausification #[43]): Eq equivalence_2 False % 7.26/7.56 Clause #65 (by clausification #[45]): ∀ (a : Iota), % 7.26/7.56 Or (Eq modus_ponens False) % 7.26/7.56 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True) % 7.26/7.56 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 7.26/7.56 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True) % 7.26/7.56 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 7.26/7.56 Or (Eq modus_ponens False) % 7.26/7.56 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True)) % 7.26/7.56 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), % 7.26/7.56 Or (Eq modus_ponens False) % 7.26/7.56 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))) % 7.26/7.56 Clause #69 (by forward demodulation #[68, 34]): ∀ (a a_1 : Iota), % 7.26/7.56 Or (Eq True False) % 7.26/7.56 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))) % 7.26/7.56 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 7.26/7.56 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)) % 7.26/7.56 Clause #121 (by clausification #[22]): Or (Eq r2 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies Q (or P Q))) True) % 7.26/7.56 Clause #133 (by clausification #[121]): ∀ (a : Iota), Or (Eq r2 False) (Eq (∀ (Q : Iota), is_a_theorem (implies Q (or a Q))) True) % 7.26/7.56 Clause #134 (by clausification #[133]): ∀ (a a_1 : Iota), Or (Eq r2 False) (Eq (is_a_theorem (implies a (or a_1 a))) True) % 7.26/7.56 Clause #135 (by forward demodulation #[134, 36]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies a (or a_1 a))) True) % 7.26/7.56 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies a (or a_1 a))) True % 7.26/7.56 Clause #138 (by superposition #[136, 70]): ∀ (a a_1 a_2 : Iota), % 7.26/7.56 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 (or a_2 a_1)) a)) False)) % 7.26/7.56 Clause #195 (by clausification #[13]): Or (Eq equivalence_2 True) (Eq (∀ (X Y : Iota), is_a_theorem (implies (equiv X Y) (implies Y X))) False) % 7.26/7.56 Clause #197 (by clausification #[195]): ∀ (a : Iota), % 7.26/7.56 Or (Eq equivalence_2 True) % 7.26/7.56 (Eq (Not (∀ (Y : Iota), is_a_theorem (implies (equiv (skS.0 32 a) Y) (implies Y (skS.0 32 a))))) True) % 7.26/7.56 Clause #198 (by clausification #[197]): ∀ (a : Iota), % 7.26/7.56 Or (Eq equivalence_2 True) % 7.26/7.56 (Eq (∀ (Y : Iota), is_a_theorem (implies (equiv (skS.0 32 a) Y) (implies Y (skS.0 32 a)))) False) % 7.26/7.56 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota), % 7.26/7.56 Or (Eq equivalence_2 True) % 7.26/7.56 (Eq (Not (is_a_theorem (implies (equiv (skS.0 32 a) (skS.0 33 a a_1)) (implies (skS.0 33 a a_1) (skS.0 32 a))))) % 7.26/7.59 True) % 7.26/7.59 Clause #200 (by clausification #[199]): ∀ (a a_1 : Iota), % 7.26/7.59 Or (Eq equivalence_2 True) % 7.26/7.59 (Eq (is_a_theorem (implies (equiv (skS.0 32 a) (skS.0 33 a a_1)) (implies (skS.0 33 a a_1) (skS.0 32 a)))) False) % 7.26/7.59 Clause #201 (by forward demodulation #[200, 64]): ∀ (a a_1 : Iota), % 7.26/7.59 Or (Eq False True) % 7.26/7.59 (Eq (is_a_theorem (implies (equiv (skS.0 32 a) (skS.0 33 a a_1)) (implies (skS.0 33 a a_1) (skS.0 32 a)))) False) % 7.26/7.59 Clause #202 (by clausification #[201]): ∀ (a a_1 : Iota), % 7.26/7.59 Eq (is_a_theorem (implies (equiv (skS.0 32 a) (skS.0 33 a a_1)) (implies (skS.0 33 a a_1) (skS.0 32 a)))) False % 7.26/7.59 Clause #224 (by clausification #[29]): Or (Eq op_implies_or False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True) % 7.26/7.59 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) % 7.26/7.59 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) % 7.26/7.59 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)) % 7.26/7.59 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)) % 7.26/7.59 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Eq (implies a a_1) (or (not a) a_1) % 7.26/7.59 Clause #244 (by clausification #[23]): Or (Eq r3 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P))) True) % 7.26/7.59 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) % 7.26/7.59 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) % 7.26/7.59 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) % 7.26/7.59 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True % 7.26/7.59 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 % 7.26/7.59 Clause #269 (by clausification #[28]): Or (Eq op_implies_and False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (not (and X (not Y)))) True) % 7.26/7.59 Clause #270 (by clausification #[269]): ∀ (a : Iota), Or (Eq op_implies_and False) (Eq (∀ (Y : Iota), Eq (implies a Y) (not (and a (not Y)))) True) % 7.26/7.59 Clause #271 (by clausification #[270]): ∀ (a a_1 : Iota), Or (Eq op_implies_and False) (Eq (Eq (implies a a_1) (not (and a (not a_1)))) True) % 7.26/7.59 Clause #272 (by clausification #[271]): ∀ (a a_1 : Iota), Or (Eq op_implies_and False) (Eq (implies a a_1) (not (and a (not a_1)))) % 7.26/7.59 Clause #273 (by forward demodulation #[272, 42]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (implies a a_1) (not (and a (not a_1)))) % 7.26/7.59 Clause #274 (by clausification #[273]): ∀ (a a_1 : Iota), Eq (implies a a_1) (not (and a (not a_1))) % 7.26/7.59 Clause #275 (by superposition #[274, 229]): ∀ (a a_1 a_2 : Iota), Eq (implies (and a (not a_1)) a_2) (or (implies a a_1) a_2) % 7.26/7.59 Clause #290 (by superposition #[275, 274]): ∀ (a a_1 a_2 a_3 : Iota), Eq (implies (and a (implies a_1 a_2)) a_3) (or (implies a (and a_1 (not a_2))) a_3) % 7.26/7.59 Clause #503 (by clausification #[30]): Or (Eq op_equiv False) (Eq (∀ (X Y : Iota), Eq (equiv X Y) (and (implies X Y) (implies Y X))) True) % 7.26/7.59 Clause #504 (by clausification #[503]): ∀ (a : Iota), Or (Eq op_equiv False) (Eq (∀ (Y : Iota), Eq (equiv a Y) (and (implies a Y) (implies Y a))) True) % 7.26/7.59 Clause #505 (by clausification #[504]): ∀ (a a_1 : Iota), Or (Eq op_equiv False) (Eq (Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a))) True) % 7.26/7.59 Clause #506 (by clausification #[505]): ∀ (a a_1 : Iota), Or (Eq op_equiv False) (Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a))) % 7.26/7.59 Clause #507 (by forward demodulation #[506, 33]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a))) % 7.26/7.59 Clause #508 (by clausification #[507]): ∀ (a a_1 : Iota), Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a)) % 7.36/7.60 Clause #678 (by clausification #[138]): ∀ (a a_1 a_2 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies a_1 (or a_2 a_1)) a)) False) % 7.36/7.60 Clause #681 (by superposition #[678, 256]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (or (or a a_1) (not a_1))) True) (Eq False True) % 7.36/7.60 Clause #697 (by clausification #[681]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (or a a_1) (not a_1))) True % 7.36/7.60 Clause #704 (by superposition #[697, 229]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (implies a a_1) (not a_1))) True % 7.36/7.60 Clause #708 (by superposition #[704, 274]): ∀ (a a_1 a_2 : Iota), Eq (is_a_theorem (or (implies a (and a_1 (not a_2))) (implies a_1 a_2))) True % 7.36/7.60 Clause #1661 (by forward demodulation #[708, 290]): ∀ (a a_1 a_2 : Iota), Eq (is_a_theorem (implies (and a (implies a_1 a_2)) (implies a_1 a_2))) True % 7.36/7.60 Clause #1667 (by superposition #[1661, 508]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (equiv a a_1) (implies a_1 a))) True % 7.36/7.60 Clause #1668 (by superposition #[1667, 202]): Eq True False % 7.36/7.60 Clause #1691 (by clausification #[1668]): False % 7.36/7.60 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------