TSTP Solution File: COM007+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n025.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 : Wed Aug 30 18:38:05 EDT 2023
% Result : Theorem 5.29s 5.52s
% Output : Proof 5.39s
% 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 : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 13:44:25 EDT 2023
% 0.13/0.33 % CPUTime :
% 5.29/5.52 SZS status Theorem for theBenchmark.p
% 5.29/5.52 SZS output start Proof for theBenchmark.p
% 5.29/5.52 Clause #0 (by assumption #[]): Eq (And (reflexive_rewrite a b) (reflexive_rewrite a c)) True
% 5.29/5.52 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), And (reflexive_rewrite b A) (reflexive_rewrite c A) → goal) True
% 5.29/5.52 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), equalish A A) True
% 5.29/5.52 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), equalish A B → equalish B A) True
% 5.29/5.52 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), And (equalish A B) (reflexive_rewrite B C) → reflexive_rewrite A C) True
% 5.29/5.52 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), equalish A B → reflexive_rewrite A B) True
% 5.29/5.52 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), rewrite A B → reflexive_rewrite A B) True
% 5.29/5.52 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), reflexive_rewrite A B → Or (equalish A B) (rewrite A B)) True
% 5.29/5.52 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), And (rewrite A B) (rewrite A C) → Exists fun D => And (rewrite B D) (rewrite C D)) True
% 5.29/5.52 Clause #9 (by assumption #[]): Eq (Not goal) True
% 5.29/5.52 Clause #10 (by clausification #[9]): Eq goal False
% 5.29/5.52 Clause #11 (by clausification #[1]): ∀ (a : Iota), Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a) → goal) True
% 5.29/5.52 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a)) False) (Eq goal True)
% 5.29/5.52 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq goal True) (Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False))
% 5.29/5.52 Clause #14 (by forward demodulation #[13, 10]): ∀ (a : Iota), Or (Eq False True) (Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False))
% 5.29/5.52 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False)
% 5.29/5.52 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (equalish a a) True
% 5.29/5.52 Clause #17 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), equalish a B → equalish B a) True
% 5.29/5.52 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (equalish a a_1 → equalish a_1 a) True
% 5.29/5.52 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (equalish a a_1) False) (Eq (equalish a_1 a) True)
% 5.29/5.52 Clause #21 (by clausification #[0]): Eq (reflexive_rewrite a c) True
% 5.29/5.52 Clause #22 (by clausification #[0]): Eq (reflexive_rewrite a b) True
% 5.29/5.52 Clause #23 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), rewrite a B → reflexive_rewrite a B) True
% 5.29/5.52 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (rewrite a a_1 → reflexive_rewrite a a_1) True
% 5.29/5.52 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (rewrite a a_1) False) (Eq (reflexive_rewrite a a_1) True)
% 5.29/5.52 Clause #26 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), equalish a B → reflexive_rewrite a B) True
% 5.29/5.52 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (equalish a a_1 → reflexive_rewrite a a_1) True
% 5.29/5.52 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (equalish a a_1) False) (Eq (reflexive_rewrite a a_1) True)
% 5.29/5.52 Clause #29 (by superposition #[28, 16]): ∀ (a : Iota), Or (Eq (reflexive_rewrite a a) True) (Eq False True)
% 5.29/5.52 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (reflexive_rewrite a a) True
% 5.29/5.52 Clause #31 (by superposition #[30, 15]): Or (Eq True False) (Eq (reflexive_rewrite c b) False)
% 5.29/5.52 Clause #32 (by clausification #[31]): Eq (reflexive_rewrite c b) False
% 5.29/5.52 Clause #33 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (equalish a B) (reflexive_rewrite B C) → reflexive_rewrite a C) True
% 5.29/5.52 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (equalish a a_1) (reflexive_rewrite a_1 C) → reflexive_rewrite a C) True
% 5.29/5.52 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (And (equalish a a_1) (reflexive_rewrite a_1 a_2) → reflexive_rewrite a a_2) True
% 5.29/5.52 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 5.29/5.52 Or (Eq (And (equalish a a_1) (reflexive_rewrite a_1 a_2)) False) (Eq (reflexive_rewrite a a_2) True)
% 5.29/5.52 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 5.37/5.56 Or (Eq (reflexive_rewrite a a_1) True) (Or (Eq (equalish a a_2) False) (Eq (reflexive_rewrite a_2 a_1) False))
% 5.37/5.56 Clause #40 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), reflexive_rewrite a B → Or (equalish a B) (rewrite a B)) True
% 5.37/5.56 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (reflexive_rewrite a a_1 → Or (equalish a a_1) (rewrite a a_1)) True
% 5.37/5.56 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) False) (Eq (Or (equalish a a_1) (rewrite a a_1)) True)
% 5.37/5.56 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) False) (Or (Eq (equalish a a_1) True) (Eq (rewrite a a_1) True))
% 5.37/5.56 Clause #44 (by superposition #[43, 21]): Or (Eq (equalish a c) True) (Or (Eq (rewrite a c) True) (Eq False True))
% 5.37/5.56 Clause #45 (by superposition #[43, 22]): Or (Eq (equalish a b) True) (Or (Eq (rewrite a b) True) (Eq False True))
% 5.37/5.56 Clause #48 (by clausification #[45]): Or (Eq (equalish a b) True) (Eq (rewrite a b) True)
% 5.37/5.56 Clause #49 (by superposition #[48, 19]): Or (Eq (rewrite a b) True) (Or (Eq True False) (Eq (equalish b a) True))
% 5.37/5.56 Clause #54 (by clausification #[8]): ∀ (a : Iota),
% 5.37/5.56 Eq (∀ (B C : Iota), And (rewrite a B) (rewrite a C) → Exists fun D => And (rewrite B D) (rewrite C D)) True
% 5.37/5.56 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota),
% 5.37/5.56 Eq (∀ (C : Iota), And (rewrite a a_1) (rewrite a C) → Exists fun D => And (rewrite a_1 D) (rewrite C D)) True
% 5.37/5.56 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 5.37/5.56 Eq (And (rewrite a a_1) (rewrite a a_2) → Exists fun D => And (rewrite a_1 D) (rewrite a_2 D)) True
% 5.37/5.56 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 5.37/5.56 Or (Eq (And (rewrite a a_1) (rewrite a a_2)) False) (Eq (Exists fun D => And (rewrite a_1 D) (rewrite a_2 D)) True)
% 5.37/5.56 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 5.37/5.56 Or (Eq (Exists fun D => And (rewrite a D) (rewrite a_1 D)) True)
% 5.37/5.56 (Or (Eq (rewrite a_2 a) False) (Eq (rewrite a_2 a_1) False))
% 5.37/5.56 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.37/5.56 Or (Eq (rewrite a a_1) False)
% 5.37/5.56 (Or (Eq (rewrite a a_2) False)
% 5.37/5.56 (Eq (And (rewrite a_1 (skS.0 0 a_1 a_2 a_3)) (rewrite a_2 (skS.0 0 a_1 a_2 a_3))) True))
% 5.37/5.56 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.37/5.56 Or (Eq (rewrite a a_1) False) (Or (Eq (rewrite a a_2) False) (Eq (rewrite a_2 (skS.0 0 a_1 a_2 a_3)) True))
% 5.37/5.56 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.37/5.56 Or (Eq (rewrite a a_1) False) (Or (Eq (rewrite a a_2) False) (Eq (rewrite a_1 (skS.0 0 a_1 a_2 a_3)) True))
% 5.37/5.56 Clause #62 (by clausification #[49]): Or (Eq (rewrite a b) True) (Eq (equalish b a) True)
% 5.37/5.56 Clause #65 (by superposition #[62, 37]): ∀ (a_1 : Iota),
% 5.37/5.56 Or (Eq (rewrite a b) True)
% 5.37/5.56 (Or (Eq (reflexive_rewrite b a_1) True) (Or (Eq True False) (Eq (reflexive_rewrite a a_1) False)))
% 5.37/5.56 Clause #71 (by clausification #[44]): Or (Eq (equalish a c) True) (Eq (rewrite a c) True)
% 5.37/5.56 Clause #72 (by superposition #[71, 19]): Or (Eq (rewrite a c) True) (Or (Eq True False) (Eq (equalish c a) True))
% 5.37/5.56 Clause #79 (by clausification #[72]): Or (Eq (rewrite a c) True) (Eq (equalish c a) True)
% 5.37/5.56 Clause #82 (by superposition #[79, 37]): ∀ (a_1 : Iota),
% 5.37/5.56 Or (Eq (rewrite a c) True)
% 5.37/5.56 (Or (Eq (reflexive_rewrite c a_1) True) (Or (Eq True False) (Eq (reflexive_rewrite a a_1) False)))
% 5.37/5.56 Clause #92 (by clausification #[82]): ∀ (a_1 : Iota), Or (Eq (rewrite a c) True) (Or (Eq (reflexive_rewrite c a_1) True) (Eq (reflexive_rewrite a a_1) False))
% 5.37/5.56 Clause #94 (by superposition #[92, 22]): Or (Eq (rewrite a c) True) (Or (Eq (reflexive_rewrite c b) True) (Eq False True))
% 5.37/5.56 Clause #96 (by clausification #[65]): ∀ (a_1 : Iota), Or (Eq (rewrite a b) True) (Or (Eq (reflexive_rewrite b a_1) True) (Eq (reflexive_rewrite a a_1) False))
% 5.37/5.56 Clause #97 (by superposition #[96, 21]): Or (Eq (rewrite a b) True) (Or (Eq (reflexive_rewrite b c) True) (Eq False True))
% 5.37/5.56 Clause #101 (by clausification #[97]): Or (Eq (rewrite a b) True) (Eq (reflexive_rewrite b c) True)
% 5.37/5.56 Clause #106 (by clausification #[94]): Or (Eq (rewrite a c) True) (Eq (reflexive_rewrite c b) True)
% 5.39/5.58 Clause #107 (by forward demodulation #[106, 32]): Or (Eq (rewrite a c) True) (Eq False True)
% 5.39/5.58 Clause #108 (by clausification #[107]): Eq (rewrite a c) True
% 5.39/5.58 Clause #112 (by superposition #[108, 60]): ∀ (a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (rewrite a a_1) False) (Eq (rewrite a_1 (skS.0 0 c a_1 a_2)) True))
% 5.39/5.58 Clause #113 (by superposition #[108, 61]): ∀ (a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (rewrite a a_1) False) (Eq (rewrite c (skS.0 0 c a_1 a_2)) True))
% 5.39/5.58 Clause #119 (by clausification #[112]): ∀ (a_1 a_2 : Iota), Or (Eq (rewrite a a_1) False) (Eq (rewrite a_1 (skS.0 0 c a_1 a_2)) True)
% 5.39/5.58 Clause #121 (by superposition #[119, 101]): ∀ (a : Iota), Or (Eq (rewrite b (skS.0 0 c b a)) True) (Or (Eq False True) (Eq (reflexive_rewrite b c) True))
% 5.39/5.58 Clause #136 (by clausification #[113]): ∀ (a_1 a_2 : Iota), Or (Eq (rewrite a a_1) False) (Eq (rewrite c (skS.0 0 c a_1 a_2)) True)
% 5.39/5.58 Clause #138 (by superposition #[136, 101]): ∀ (a : Iota), Or (Eq (rewrite c (skS.0 0 c b a)) True) (Or (Eq False True) (Eq (reflexive_rewrite b c) True))
% 5.39/5.58 Clause #213 (by clausification #[138]): ∀ (a : Iota), Or (Eq (rewrite c (skS.0 0 c b a)) True) (Eq (reflexive_rewrite b c) True)
% 5.39/5.58 Clause #214 (by superposition #[213, 25]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b c) True) (Or (Eq True False) (Eq (reflexive_rewrite c (skS.0 0 c b a)) True))
% 5.39/5.58 Clause #217 (by clausification #[214]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b c) True) (Eq (reflexive_rewrite c (skS.0 0 c b a)) True)
% 5.39/5.58 Clause #221 (by clausification #[121]): ∀ (a : Iota), Or (Eq (rewrite b (skS.0 0 c b a)) True) (Eq (reflexive_rewrite b c) True)
% 5.39/5.58 Clause #222 (by superposition #[221, 25]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b c) True) (Or (Eq True False) (Eq (reflexive_rewrite b (skS.0 0 c b a)) True))
% 5.39/5.58 Clause #225 (by clausification #[222]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b c) True) (Eq (reflexive_rewrite b (skS.0 0 c b a)) True)
% 5.39/5.58 Clause #226 (by superposition #[225, 15]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b c) True) (Or (Eq True False) (Eq (reflexive_rewrite c (skS.0 0 c b a)) False))
% 5.39/5.58 Clause #230 (by clausification #[226]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b c) True) (Eq (reflexive_rewrite c (skS.0 0 c b a)) False)
% 5.39/5.58 Clause #231 (by superposition #[230, 217]): Or (Eq (reflexive_rewrite b c) True) (Or (Eq (reflexive_rewrite b c) True) (Eq False True))
% 5.39/5.58 Clause #232 (by clausification #[231]): Or (Eq (reflexive_rewrite b c) True) (Eq (reflexive_rewrite b c) True)
% 5.39/5.58 Clause #233 (by eliminate duplicate literals #[232]): Eq (reflexive_rewrite b c) True
% 5.39/5.58 Clause #238 (by superposition #[233, 15]): Or (Eq True False) (Eq (reflexive_rewrite c c) False)
% 5.39/5.58 Clause #242 (by clausification #[238]): Eq (reflexive_rewrite c c) False
% 5.39/5.58 Clause #243 (by superposition #[242, 30]): Eq False True
% 5.39/5.58 Clause #246 (by clausification #[243]): False
% 5.39/5.58 SZS output end Proof for theBenchmark.p
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