TSTP Solution File: LCL459+1 by Duper---1.0
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% File : Duper---1.0
% Problem : LCL459+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 07:09:51 EDT 2023
% Result : Theorem 5.49s 5.69s
% Output : Proof 5.49s
% 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 : LCL459+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n028.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 : Thu Aug 24 18:05:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.49/5.69 SZS status Theorem for theBenchmark.p
% 5.49/5.69 SZS output start Proof for theBenchmark.p
% 5.49/5.69 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
% 5.49/5.69 Clause #4 (by assumption #[]): Eq (Iff implies_2 (∀ (X Y : Iota), is_a_theorem (implies (implies X (implies X Y)) (implies X Y)))) True
% 5.49/5.69 Clause #8 (by assumption #[]): Eq (Iff and_3 (∀ (X Y : Iota), is_a_theorem (implies X (implies Y (and X Y))))) True
% 5.49/5.69 Clause #15 (by assumption #[]): Eq (Iff kn1 (∀ (P : Iota), is_a_theorem (implies P (and P P)))) True
% 5.49/5.69 Clause #34 (by assumption #[]): Eq modus_ponens True
% 5.49/5.69 Clause #37 (by assumption #[]): Eq implies_2 True
% 5.49/5.69 Clause #41 (by assumption #[]): Eq and_3 True
% 5.49/5.69 Clause #49 (by assumption #[]): Eq (Not kn1) True
% 5.49/5.69 Clause #51 (by clausification #[0]): Or (Eq modus_ponens False)
% 5.49/5.69 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 5.49/5.69 Clause #77 (by clausification #[49]): Eq kn1 False
% 5.49/5.69 Clause #78 (by clausification #[51]): ∀ (a : Iota),
% 5.49/5.69 Or (Eq modus_ponens False)
% 5.49/5.69 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 5.49/5.69 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 5.49/5.69 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq modus_ponens False)
% 5.49/5.69 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 5.49/5.69 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq modus_ponens False)
% 5.49/5.69 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 5.49/5.69 Clause #82 (by forward demodulation #[81, 34]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq True False)
% 5.49/5.69 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 5.49/5.69 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 5.49/5.69 Clause #96 (by clausification #[15]): Or (Eq kn1 True) (Eq (∀ (P : Iota), is_a_theorem (implies P (and P P))) False)
% 5.49/5.69 Clause #98 (by clausification #[96]): ∀ (a : Iota), Or (Eq kn1 True) (Eq (Not (is_a_theorem (implies (skS.0 9 a) (and (skS.0 9 a) (skS.0 9 a))))) True)
% 5.49/5.69 Clause #99 (by clausification #[98]): ∀ (a : Iota), Or (Eq kn1 True) (Eq (is_a_theorem (implies (skS.0 9 a) (and (skS.0 9 a) (skS.0 9 a)))) False)
% 5.49/5.69 Clause #100 (by forward demodulation #[99, 77]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (implies (skS.0 9 a) (and (skS.0 9 a) (skS.0 9 a)))) False)
% 5.49/5.69 Clause #101 (by clausification #[100]): ∀ (a : Iota), Eq (is_a_theorem (implies (skS.0 9 a) (and (skS.0 9 a) (skS.0 9 a)))) False
% 5.49/5.69 Clause #111 (by clausification #[4]): Or (Eq implies_2 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies (implies X (implies X Y)) (implies X Y))) True)
% 5.49/5.69 Clause #175 (by clausification #[8]): Or (Eq and_3 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies X (implies Y (and X Y)))) True)
% 5.49/5.69 Clause #255 (by clausification #[175]): ∀ (a : Iota), Or (Eq and_3 False) (Eq (∀ (Y : Iota), is_a_theorem (implies a (implies Y (and a Y)))) True)
% 5.49/5.69 Clause #256 (by clausification #[255]): ∀ (a a_1 : Iota), Or (Eq and_3 False) (Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True)
% 5.49/5.69 Clause #257 (by forward demodulation #[256, 41]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True)
% 5.49/5.69 Clause #258 (by clausification #[257]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True
% 5.49/5.69 Clause #259 (by superposition #[258, 83]): ∀ (a a_1 a_2 : Iota),
% 5.49/5.69 Or (Eq (is_a_theorem a) True)
% 5.49/5.69 (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 (implies a_2 (and a_1 a_2))) a)) False))
% 5.49/5.69 Clause #550 (by clausification #[111]): ∀ (a : Iota),
% 5.49/5.69 Or (Eq implies_2 False) (Eq (∀ (Y : Iota), is_a_theorem (implies (implies a (implies a Y)) (implies a Y))) True)
% 5.49/5.69 Clause #551 (by clausification #[550]): ∀ (a a_1 : Iota), Or (Eq implies_2 False) (Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True)
% 5.49/5.70 Clause #552 (by forward demodulation #[551, 37]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True)
% 5.49/5.70 Clause #553 (by clausification #[552]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True
% 5.49/5.70 Clause #775 (by clausification #[259]): ∀ (a a_1 a_2 : Iota),
% 5.49/5.70 Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies a_1 (implies a_2 (and a_1 a_2))) a)) False)
% 5.49/5.70 Clause #784 (by superposition #[775, 553]): ∀ (a : Iota), Or (Eq (is_a_theorem (implies a (and a a))) True) (Eq False True)
% 5.49/5.70 Clause #793 (by clausification #[784]): ∀ (a : Iota), Eq (is_a_theorem (implies a (and a a))) True
% 5.49/5.70 Clause #794 (by superposition #[793, 101]): Eq True False
% 5.49/5.70 Clause #805 (by clausification #[794]): False
% 5.49/5.70 SZS output end Proof for theBenchmark.p
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