TSTP Solution File: NUM830^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 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 10:57:52 EDT 2023
% Result : Theorem 3.89s 4.09s
% Output : Proof 3.89s
% 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 : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:35:59 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.89/4.09 SZS status Theorem for theBenchmark.p
% 3.89/4.09 SZS output start Proof for theBenchmark.p
% 3.89/4.09 Clause #0 (by assumption #[]): Eq (Eq cPA_1 (∀ (Xx : n), Eq (c_plus Xx c0) Xx)) True
% 3.89/4.09 Clause #1 (by assumption #[]): Eq (Eq cPA_2 (∀ (Xx Xy : n), Eq (c_plus Xx (cS Xy)) (cS (c_plus Xx Xy)))) True
% 3.89/4.09 Clause #2 (by assumption #[]): Eq (Eq cPA_3 (∀ (Xx : n), Eq (c_star Xx c0) c0)) True
% 3.89/4.09 Clause #3 (by assumption #[]): Eq (Eq cPA_4 (∀ (Xx Xy : n), Eq (c_star Xx (cS Xy)) (c_plus (c_star Xx Xy) Xx))) True
% 3.89/4.09 Clause #4 (by assumption #[]): Eq
% 3.89/4.09 (Not
% 3.89/4.09 (And (And (And cPA_1 cPA_2) cPA_3) cPA_4 →
% 3.89/4.09 Eq (c_star (cS (cS c0)) (cS (cS c0))) (c_plus (cS (cS c0)) (cS (cS c0)))))
% 3.89/4.09 True
% 3.89/4.09 Clause #5 (by clausification #[2]): Eq cPA_3 (∀ (Xx : n), Eq (c_star Xx c0) c0)
% 3.89/4.09 Clause #7 (by clausify Prop equality #[5]): Or (Eq cPA_3 False) (Eq (∀ (Xx : n), Eq (c_star Xx c0) c0) True)
% 3.89/4.09 Clause #9 (by clausification #[7]): ∀ (a : n), Or (Eq cPA_3 False) (Eq (Eq (c_star a c0) c0) True)
% 3.89/4.09 Clause #10 (by clausification #[9]): ∀ (a : n), Or (Eq cPA_3 False) (Eq (c_star a c0) c0)
% 3.89/4.09 Clause #14 (by clausification #[0]): Eq cPA_1 (∀ (Xx : n), Eq (c_plus Xx c0) Xx)
% 3.89/4.09 Clause #16 (by clausify Prop equality #[14]): Or (Eq cPA_1 False) (Eq (∀ (Xx : n), Eq (c_plus Xx c0) Xx) True)
% 3.89/4.09 Clause #18 (by clausification #[1]): Eq cPA_2 (∀ (Xx Xy : n), Eq (c_plus Xx (cS Xy)) (cS (c_plus Xx Xy)))
% 3.89/4.09 Clause #20 (by clausify Prop equality #[18]): Or (Eq cPA_2 False) (Eq (∀ (Xx Xy : n), Eq (c_plus Xx (cS Xy)) (cS (c_plus Xx Xy))) True)
% 3.89/4.09 Clause #22 (by clausification #[16]): ∀ (a : n), Or (Eq cPA_1 False) (Eq (Eq (c_plus a c0) a) True)
% 3.89/4.09 Clause #23 (by clausification #[22]): ∀ (a : n), Or (Eq cPA_1 False) (Eq (c_plus a c0) a)
% 3.89/4.09 Clause #32 (by clausification #[20]): ∀ (a : n), Or (Eq cPA_2 False) (Eq (∀ (Xy : n), Eq (c_plus a (cS Xy)) (cS (c_plus a Xy))) True)
% 3.89/4.09 Clause #33 (by clausification #[32]): ∀ (a a_1 : n), Or (Eq cPA_2 False) (Eq (Eq (c_plus a (cS a_1)) (cS (c_plus a a_1))) True)
% 3.89/4.09 Clause #34 (by clausification #[33]): ∀ (a a_1 : n), Or (Eq cPA_2 False) (Eq (c_plus a (cS a_1)) (cS (c_plus a a_1)))
% 3.89/4.09 Clause #35 (by clausification #[3]): Eq cPA_4 (∀ (Xx Xy : n), Eq (c_star Xx (cS Xy)) (c_plus (c_star Xx Xy) Xx))
% 3.89/4.09 Clause #47 (by clausification #[4]): Eq (And (And (And cPA_1 cPA_2) cPA_3) cPA_4 → Eq (c_star (cS (cS c0)) (cS (cS c0))) (c_plus (cS (cS c0)) (cS (cS c0))))
% 3.89/4.09 False
% 3.89/4.09 Clause #48 (by clausification #[47]): Eq (And (And (And cPA_1 cPA_2) cPA_3) cPA_4) True
% 3.89/4.09 Clause #49 (by clausification #[47]): Eq (Eq (c_star (cS (cS c0)) (cS (cS c0))) (c_plus (cS (cS c0)) (cS (cS c0)))) False
% 3.89/4.09 Clause #50 (by clausification #[48]): Eq cPA_4 True
% 3.89/4.09 Clause #51 (by clausification #[48]): Eq (And (And cPA_1 cPA_2) cPA_3) True
% 3.89/4.09 Clause #52 (by backward demodulation #[50, 35]): Eq True (∀ (Xx Xy : n), Eq (c_star Xx (cS Xy)) (c_plus (c_star Xx Xy) Xx))
% 3.89/4.09 Clause #55 (by clausification #[49]): Ne (c_star (cS (cS c0)) (cS (cS c0))) (c_plus (cS (cS c0)) (cS (cS c0)))
% 3.89/4.09 Clause #56 (by clausification #[51]): Eq cPA_3 True
% 3.89/4.09 Clause #57 (by clausification #[51]): Eq (And cPA_1 cPA_2) True
% 3.89/4.09 Clause #59 (by backward demodulation #[56, 10]): ∀ (a : n), Or (Eq True False) (Eq (c_star a c0) c0)
% 3.89/4.09 Clause #61 (by clausification #[57]): Eq cPA_2 True
% 3.89/4.09 Clause #62 (by clausification #[57]): Eq cPA_1 True
% 3.89/4.09 Clause #65 (by backward demodulation #[61, 34]): ∀ (a a_1 : n), Or (Eq True False) (Eq (c_plus a (cS a_1)) (cS (c_plus a a_1)))
% 3.89/4.09 Clause #68 (by superposition #[62, 23]): ∀ (a : n), Or (Eq True False) (Eq (c_plus a c0) a)
% 3.89/4.09 Clause #69 (by clausification #[59]): ∀ (a : n), Eq (c_star a c0) c0
% 3.89/4.09 Clause #70 (by clausification #[68]): ∀ (a : n), Eq (c_plus a c0) a
% 3.89/4.09 Clause #71 (by clausification #[52]): ∀ (a : n), Eq (∀ (Xy : n), Eq (c_star a (cS Xy)) (c_plus (c_star a Xy) a)) True
% 3.89/4.09 Clause #72 (by clausification #[71]): ∀ (a a_1 : n), Eq (Eq (c_star a (cS a_1)) (c_plus (c_star a a_1) a)) True
% 3.89/4.09 Clause #73 (by clausification #[72]): ∀ (a a_1 : n), Eq (c_star a (cS a_1)) (c_plus (c_star a a_1) a)
% 3.89/4.09 Clause #82 (by clausification #[65]): ∀ (a a_1 : n), Eq (c_plus a (cS a_1)) (cS (c_plus a a_1))
% 3.89/4.09 Clause #84 (by superposition #[82, 70]): ∀ (a : n), Eq (c_plus a (cS c0)) (cS a)
% 3.89/4.09 Clause #87 (by superposition #[84, 82]): ∀ (a : n), Eq (c_plus a (cS (cS c0))) (cS (cS a))
% 3.89/4.09 Clause #88 (by backward demodulation #[87, 55]): Ne (c_star (cS (cS c0)) (cS (cS c0))) (cS (cS (cS (cS c0))))
% 3.89/4.09 Clause #89 (by superposition #[87, 73]): ∀ (a : n), Eq (c_star (cS (cS c0)) (cS a)) (cS (cS (c_star (cS (cS c0)) a)))
% 3.89/4.09 Clause #211 (by superposition #[89, 69]): Eq (c_star (cS (cS c0)) (cS c0)) (cS (cS c0))
% 3.89/4.09 Clause #213 (by superposition #[211, 89]): Eq (c_star (cS (cS c0)) (cS (cS c0))) (cS (cS (cS (cS c0))))
% 3.89/4.09 Clause #214 (by forward contextual literal cutting #[213, 88]): False
% 3.89/4.09 SZS output end Proof for theBenchmark.p
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