TSTP Solution File: LCL494+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:09:57 EDT 2023
% Result : Theorem 7.44s 7.62s
% Output : Proof 7.49s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 05:07:58 EDT 2023
% 0.20/0.34 % CPUTime :
% 7.44/7.62 SZS status Theorem for theBenchmark.p
% 7.44/7.62 SZS output start Proof for theBenchmark.p
% 7.44/7.62 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
% 7.44/7.62 Clause #13 (by assumption #[]): Eq (Iff equivalence_2 (∀ (X Y : Iota), is_a_theorem (implies (equiv X Y) (implies Y X)))) True
% 7.44/7.62 Clause #22 (by assumption #[]): Eq (Iff r2 (∀ (P Q : Iota), is_a_theorem (implies Q (or P Q)))) True
% 7.44/7.62 Clause #23 (by assumption #[]): Eq (Iff r3 (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P)))) True
% 7.44/7.62 Clause #28 (by assumption #[]): Eq (op_implies_and → ∀ (X Y : Iota), Eq (implies X Y) (not (and X (not Y)))) True
% 7.44/7.62 Clause #29 (by assumption #[]): Eq (op_implies_or → ∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True
% 7.44/7.62 Clause #30 (by assumption #[]): Eq (op_equiv → ∀ (X Y : Iota), Eq (equiv X Y) (and (implies X Y) (implies Y X))) True
% 7.44/7.62 Clause #31 (by assumption #[]): Eq op_implies_or True
% 7.44/7.62 Clause #33 (by assumption #[]): Eq op_equiv True
% 7.44/7.62 Clause #34 (by assumption #[]): Eq modus_ponens True
% 7.44/7.62 Clause #36 (by assumption #[]): Eq r2 True
% 7.44/7.62 Clause #37 (by assumption #[]): Eq r3 True
% 7.44/7.62 Clause #42 (by assumption #[]): Eq op_implies_and True
% 7.44/7.62 Clause #43 (by assumption #[]): Eq (Not equivalence_2) True
% 7.44/7.62 Clause #45 (by clausification #[0]): Or (Eq modus_ponens False)
% 7.44/7.62 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 7.44/7.62 Clause #64 (by clausification #[43]): Eq equivalence_2 False
% 7.44/7.62 Clause #65 (by clausification #[45]): ∀ (a : Iota),
% 7.44/7.62 Or (Eq modus_ponens False)
% 7.44/7.62 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 7.44/7.62 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota),
% 7.44/7.62 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 7.44/7.62 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota),
% 7.44/7.62 Or (Eq modus_ponens False)
% 7.44/7.62 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 7.44/7.62 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota),
% 7.44/7.62 Or (Eq modus_ponens False)
% 7.44/7.62 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 7.44/7.62 Clause #69 (by forward demodulation #[68, 34]): ∀ (a a_1 : Iota),
% 7.44/7.62 Or (Eq True False)
% 7.44/7.62 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 7.44/7.62 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 7.44/7.62 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 7.44/7.62 Clause #121 (by clausification #[22]): Or (Eq r2 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies Q (or P Q))) True)
% 7.44/7.62 Clause #133 (by clausification #[121]): ∀ (a : Iota), Or (Eq r2 False) (Eq (∀ (Q : Iota), is_a_theorem (implies Q (or a Q))) True)
% 7.44/7.62 Clause #134 (by clausification #[133]): ∀ (a a_1 : Iota), Or (Eq r2 False) (Eq (is_a_theorem (implies a (or a_1 a))) True)
% 7.44/7.62 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)
% 7.44/7.62 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies a (or a_1 a))) True
% 7.44/7.62 Clause #138 (by superposition #[136, 70]): ∀ (a a_1 a_2 : Iota),
% 7.44/7.62 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))
% 7.44/7.62 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)
% 7.44/7.62 Clause #197 (by clausification #[195]): ∀ (a : Iota),
% 7.44/7.62 Or (Eq equivalence_2 True)
% 7.44/7.62 (Eq (Not (∀ (Y : Iota), is_a_theorem (implies (equiv (skS.0 32 a) Y) (implies Y (skS.0 32 a))))) True)
% 7.44/7.62 Clause #198 (by clausification #[197]): ∀ (a : Iota),
% 7.44/7.62 Or (Eq equivalence_2 True)
% 7.44/7.62 (Eq (∀ (Y : Iota), is_a_theorem (implies (equiv (skS.0 32 a) Y) (implies Y (skS.0 32 a)))) False)
% 7.44/7.62 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota),
% 7.44/7.62 Or (Eq equivalence_2 True)
% 7.44/7.62 (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)))))
% 7.44/7.64 True)
% 7.44/7.64 Clause #200 (by clausification #[199]): ∀ (a a_1 : Iota),
% 7.44/7.64 Or (Eq equivalence_2 True)
% 7.44/7.64 (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)
% 7.44/7.64 Clause #201 (by forward demodulation #[200, 64]): ∀ (a a_1 : Iota),
% 7.44/7.64 Or (Eq False True)
% 7.44/7.64 (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)
% 7.44/7.64 Clause #202 (by clausification #[201]): ∀ (a a_1 : Iota),
% 7.44/7.64 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
% 7.44/7.64 Clause #224 (by clausification #[29]): Or (Eq op_implies_or False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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))
% 7.44/7.64 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))
% 7.44/7.64 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Eq (implies a a_1) (or (not a) a_1)
% 7.44/7.64 Clause #244 (by clausification #[23]): Or (Eq r3 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P))) True)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True
% 7.44/7.64 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
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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))))
% 7.44/7.64 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))))
% 7.44/7.64 Clause #274 (by clausification #[273]): ∀ (a a_1 : Iota), Eq (implies a a_1) (not (and a (not a_1)))
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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)
% 7.44/7.64 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)))
% 7.44/7.64 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)))
% 7.44/7.64 Clause #508 (by clausification #[507]): ∀ (a a_1 : Iota), Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a))
% 7.49/7.65 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)
% 7.49/7.65 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)
% 7.49/7.65 Clause #697 (by clausification #[681]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (or a a_1) (not a_1))) True
% 7.49/7.65 Clause #704 (by superposition #[697, 229]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (implies a a_1) (not a_1))) True
% 7.49/7.65 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
% 7.49/7.65 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
% 7.49/7.65 Clause #1667 (by superposition #[1661, 508]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (equiv a a_1) (implies a_1 a))) True
% 7.49/7.65 Clause #1668 (by superposition #[1667, 202]): Eq True False
% 7.49/7.65 Clause #1691 (by clausification #[1668]): False
% 7.49/7.65 SZS output end Proof for theBenchmark.p
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