TSTP Solution File: COM007+2 by Duper---1.0
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% File : Duper---1.0
% Problem : COM007+2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 3.87s 4.10s
% Output : Proof 3.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM007+2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 13:03:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.87/4.10 SZS status Theorem for theBenchmark.p
% 3.87/4.10 SZS output start Proof for theBenchmark.p
% 3.87/4.10 Clause #0 (by assumption #[]): Eq (And (reflexive_rewrite a b) (reflexive_rewrite a c)) True
% 3.87/4.10 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), And (reflexive_rewrite b A) (reflexive_rewrite c A) → goal) True
% 3.87/4.10 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq A B → reflexive_rewrite A B) True
% 3.87/4.10 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), rewrite A B → reflexive_rewrite A B) True
% 3.87/4.10 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), reflexive_rewrite A B → Or (Eq A B) (rewrite A B)) True
% 3.87/4.10 Clause #5 (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
% 3.87/4.10 Clause #6 (by assumption #[]): Eq (Not goal) True
% 3.87/4.10 Clause #7 (by clausification #[6]): Eq goal False
% 3.87/4.10 Clause #8 (by clausification #[1]): ∀ (a : Iota), Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a) → goal) True
% 3.87/4.10 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a)) False) (Eq goal True)
% 3.87/4.10 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq goal True) (Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False))
% 3.87/4.10 Clause #11 (by forward demodulation #[10, 7]): ∀ (a : Iota), Or (Eq False True) (Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False))
% 3.87/4.10 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False)
% 3.87/4.10 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), rewrite a B → reflexive_rewrite a B) True
% 3.87/4.10 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (rewrite a a_1 → reflexive_rewrite a a_1) True
% 3.87/4.10 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (rewrite a a_1) False) (Eq (reflexive_rewrite a a_1) True)
% 3.87/4.10 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq a B → reflexive_rewrite a B) True
% 3.87/4.10 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq a a_1 → reflexive_rewrite a a_1) True
% 3.87/4.10 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) False) (Eq (reflexive_rewrite a a_1) True)
% 3.87/4.10 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) True) (Ne a a_1)
% 3.87/4.10 Clause #20 (by destructive equality resolution #[19]): ∀ (a : Iota), Eq (reflexive_rewrite a a) True
% 3.87/4.10 Clause #21 (by superposition #[20, 12]): Or (Eq True False) (Eq (reflexive_rewrite c b) False)
% 3.87/4.10 Clause #22 (by clausification #[21]): Eq (reflexive_rewrite c b) False
% 3.87/4.10 Clause #23 (by clausification #[0]): Eq (reflexive_rewrite a c) True
% 3.87/4.10 Clause #24 (by clausification #[0]): Eq (reflexive_rewrite a b) True
% 3.87/4.10 Clause #25 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), reflexive_rewrite a B → Or (Eq a B) (rewrite a B)) True
% 3.87/4.10 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (reflexive_rewrite a a_1 → Or (Eq a a_1) (rewrite a a_1)) True
% 3.87/4.10 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) False) (Eq (Or (Eq a a_1) (rewrite a a_1)) True)
% 3.87/4.10 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) False) (Or (Eq (Eq a a_1) True) (Eq (rewrite a a_1) True))
% 3.87/4.10 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) False) (Or (Eq (rewrite a a_1) True) (Eq a a_1))
% 3.87/4.10 Clause #30 (by superposition #[29, 23]): Or (Eq (rewrite a c) True) (Or (Eq a c) (Eq False True))
% 3.87/4.10 Clause #31 (by superposition #[29, 24]): Or (Eq (rewrite a b) True) (Or (Eq a b) (Eq False True))
% 3.87/4.10 Clause #34 (by clausification #[31]): Or (Eq (rewrite a b) True) (Eq a b)
% 3.87/4.10 Clause #37 (by clausification #[5]): ∀ (a : Iota),
% 3.87/4.10 Eq (∀ (B C : Iota), And (rewrite a B) (rewrite a C) → Exists fun D => And (rewrite B D) (rewrite C D)) True
% 3.87/4.10 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 3.87/4.10 Eq (∀ (C : Iota), And (rewrite a a_1) (rewrite a C) → Exists fun D => And (rewrite a_1 D) (rewrite C D)) True
% 3.87/4.10 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 3.87/4.10 Eq (And (rewrite a a_1) (rewrite a a_2) → Exists fun D => And (rewrite a_1 D) (rewrite a_2 D)) True
% 3.97/4.12 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.12 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)
% 3.97/4.12 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.12 Or (Eq (Exists fun D => And (rewrite a D) (rewrite a_1 D)) True)
% 3.97/4.12 (Or (Eq (rewrite a_2 a) False) (Eq (rewrite a_2 a_1) False))
% 3.97/4.12 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.12 Or (Eq (rewrite a a_1) False)
% 3.97/4.12 (Or (Eq (rewrite a a_2) False)
% 3.97/4.12 (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))
% 3.97/4.12 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.12 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))
% 3.97/4.12 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.12 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))
% 3.97/4.12 Clause #46 (by clausification #[30]): Or (Eq (rewrite a c) True) (Eq a c)
% 3.97/4.12 Clause #48 (by superposition #[46, 43]): ∀ (a_1 a_2 : Iota),
% 3.97/4.12 Or (Eq a c) (Or (Eq True False) (Or (Eq (rewrite a a_1) False) (Eq (rewrite a_1 (skS.0 0 c a_1 a_2)) True)))
% 3.97/4.12 Clause #50 (by clausification #[48]): ∀ (a_1 a_2 : Iota), Or (Eq a c) (Or (Eq (rewrite a a_1) False) (Eq (rewrite a_1 (skS.0 0 c a_1 a_2)) True))
% 3.97/4.12 Clause #51 (by superposition #[50, 34]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq (rewrite b (skS.0 0 c b a_1)) True) (Or (Eq False True) (Eq a b)))
% 3.97/4.12 Clause #60 (by superposition #[44, 46]): ∀ (a_1 a_2 : Iota),
% 3.97/4.12 Or (Eq a c) (Or (Eq True False) (Or (Eq (rewrite a a_1) False) (Eq (rewrite c (skS.0 0 c a_1 a_2)) True)))
% 3.97/4.12 Clause #62 (by clausification #[51]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq (rewrite b (skS.0 0 c b a_1)) True) (Eq a b))
% 3.97/4.12 Clause #63 (by superposition #[62, 15]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq a b) (Or (Eq True False) (Eq (reflexive_rewrite b (skS.0 0 c b a_1)) True)))
% 3.97/4.12 Clause #66 (by clausification #[63]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq a b) (Eq (reflexive_rewrite b (skS.0 0 c b a_1)) True))
% 3.97/4.12 Clause #67 (by superposition #[66, 12]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq a b) (Or (Eq True False) (Eq (reflexive_rewrite c (skS.0 0 c b a_1)) False)))
% 3.97/4.12 Clause #69 (by clausification #[67]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq a b) (Eq (reflexive_rewrite c (skS.0 0 c b a_1)) False))
% 3.97/4.12 Clause #91 (by clausification #[60]): ∀ (a_1 a_2 : Iota), Or (Eq a c) (Or (Eq (rewrite a a_1) False) (Eq (rewrite c (skS.0 0 c a_1 a_2)) True))
% 3.97/4.12 Clause #92 (by superposition #[91, 34]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq (rewrite c (skS.0 0 c b a_1)) True) (Or (Eq False True) (Eq a b)))
% 3.97/4.12 Clause #94 (by clausification #[92]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq (rewrite c (skS.0 0 c b a_1)) True) (Eq a b))
% 3.97/4.12 Clause #96 (by superposition #[94, 15]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq a b) (Or (Eq True False) (Eq (reflexive_rewrite c (skS.0 0 c b a_1)) True)))
% 3.97/4.12 Clause #99 (by clausification #[96]): ∀ (a_1 : Iota), Or (Eq a c) (Or (Eq a b) (Eq (reflexive_rewrite c (skS.0 0 c b a_1)) True))
% 3.97/4.12 Clause #100 (by superposition #[99, 69]): Or (Eq a c) (Or (Eq a b) (Or (Eq a c) (Or (Eq a b) (Eq True False))))
% 3.97/4.12 Clause #102 (by clausification #[100]): Or (Eq a c) (Or (Eq a b) (Or (Eq a c) (Eq a b)))
% 3.97/4.12 Clause #103 (by eliminate duplicate literals #[102]): Or (Eq a c) (Eq a b)
% 3.97/4.12 Clause #104 (by superposition #[103, 23]): Or (Eq a c) (Eq (reflexive_rewrite b c) True)
% 3.97/4.12 Clause #112 (by superposition #[104, 12]): Or (Eq a c) (Or (Eq True False) (Eq (reflexive_rewrite c c) False))
% 3.97/4.12 Clause #114 (by clausification #[112]): Or (Eq a c) (Eq (reflexive_rewrite c c) False)
% 3.97/4.12 Clause #115 (by superposition #[114, 20]): Or (Eq a c) (Eq False True)
% 3.97/4.12 Clause #116 (by clausification #[115]): Eq a c
% 3.97/4.12 Clause #118 (by backward demodulation #[116, 24]): Eq (reflexive_rewrite c b) True
% 3.97/4.12 Clause #134 (by superposition #[118, 22]): Eq True False
% 3.97/4.12 Clause #138 (by clausification #[134]): False
% 3.97/4.12 SZS output end Proof for theBenchmark.p
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