%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : COM007+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 : Fri Oct 3 07:45:46 PM UTC 2025 % Result : Theorem 4.13s 4.29s % Output : Proof 4.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : COM007+1 : TPTP v9.2.0. Released v3.2.0. % 0.10/0.13 % Command : duper %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 16:04:38 EDT 2025 % 0.12/0.33 % CPUTime : % 4.13/4.29 SZS status Theorem for theBenchmark.p % 4.13/4.29 SZS output start Proof for theBenchmark.p % 4.13/4.29 Clause #0 (by assumption #[]): Eq (And (reflexive_rewrite a b) (reflexive_rewrite a c)) True % 4.13/4.29 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), And (reflexive_rewrite b A) (reflexive_rewrite c A) → goal) True % 4.13/4.29 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), equalish A A) True % 4.13/4.29 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), equalish A B → equalish B A) True % 4.13/4.29 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), And (equalish A B) (reflexive_rewrite B C) → reflexive_rewrite A C) True % 4.13/4.29 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), equalish A B → reflexive_rewrite A B) True % 4.13/4.29 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), rewrite A B → reflexive_rewrite A B) True % 4.13/4.29 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), reflexive_rewrite A B → Or (equalish A B) (rewrite A B)) True % 4.13/4.29 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 % 4.13/4.29 Clause #9 (by assumption #[]): Eq (Not goal) True % 4.13/4.29 Clause #10 (by clausification #[9]): Eq goal False % 4.13/4.29 Clause #11 (by clausification #[1]): ∀ (a : Iota), Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a) → goal) True % 4.13/4.29 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a)) False) (Eq goal True) % 4.13/4.29 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq goal True) (Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False)) % 4.13/4.29 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)) % 4.13/4.29 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False) % 4.13/4.29 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (equalish a a) True % 4.13/4.29 Clause #17 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), equalish a B → equalish B a) True % 4.13/4.29 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (equalish a a_1 → equalish a_1 a) True % 4.13/4.29 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (equalish a a_1) False) (Eq (equalish a_1 a) True) % 4.13/4.29 Clause #21 (by clausification #[0]): Eq (reflexive_rewrite a c) True % 4.13/4.29 Clause #22 (by clausification #[0]): Eq (reflexive_rewrite a b) True % 4.13/4.29 Clause #23 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), rewrite a B → reflexive_rewrite a B) True % 4.13/4.29 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (rewrite a a_1 → reflexive_rewrite a a_1) True % 4.13/4.29 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (rewrite a a_1) False) (Eq (reflexive_rewrite a a_1) True) % 4.13/4.29 Clause #26 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), equalish a B → reflexive_rewrite a B) True % 4.13/4.29 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (equalish a a_1 → reflexive_rewrite a a_1) True % 4.13/4.29 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (equalish a a_1) False) (Eq (reflexive_rewrite a a_1) True) % 4.13/4.29 Clause #29 (by superposition #[28, 16]): ∀ (a : Iota), Or (Eq (reflexive_rewrite a a) True) (Eq False True) % 4.13/4.29 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (reflexive_rewrite a a) True % 4.13/4.29 Clause #31 (by superposition #[30, 15]): Or (Eq True False) (Eq (reflexive_rewrite c b) False) % 4.13/4.29 Clause #32 (by clausification #[31]): Eq (reflexive_rewrite c b) False % 4.13/4.29 Clause #33 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (equalish a B) (reflexive_rewrite B C) → reflexive_rewrite a C) True % 4.13/4.29 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 % 4.13/4.29 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 % 4.13/4.29 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.13/4.29 Or (Eq (And (equalish a a_1) (reflexive_rewrite a_1 a_2)) False) (Eq (reflexive_rewrite a a_2) True) % 4.13/4.29 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 Or (Eq (reflexive_rewrite a a_1) True) (Or (Eq (equalish a a_2) False) (Eq (reflexive_rewrite a_2 a_1) False)) % 4.13/4.31 Clause #40 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), reflexive_rewrite a B → Or (equalish a B) (rewrite a B)) True % 4.13/4.31 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 % 4.13/4.31 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) % 4.13/4.31 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)) % 4.13/4.31 Clause #44 (by superposition #[43, 21]): Or (Eq (equalish a c) True) (Or (Eq (rewrite a c) True) (Eq False True)) % 4.13/4.31 Clause #45 (by superposition #[43, 22]): Or (Eq (equalish a b) True) (Or (Eq (rewrite a b) True) (Eq False True)) % 4.13/4.31 Clause #48 (by clausification #[45]): Or (Eq (equalish a b) True) (Eq (rewrite a b) True) % 4.13/4.31 Clause #49 (by superposition #[48, 19]): Or (Eq (rewrite a b) True) (Or (Eq True False) (Eq (equalish b a) True)) % 4.13/4.31 Clause #54 (by clausification #[8]): ∀ (a : Iota), % 4.13/4.31 Eq (∀ (B C : Iota), And (rewrite a B) (rewrite a C) → Exists fun D => And (rewrite B D) (rewrite C D)) True % 4.13/4.31 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 4.13/4.31 Eq (∀ (C : Iota), And (rewrite a a_1) (rewrite a C) → Exists fun D => And (rewrite a_1 D) (rewrite C D)) True % 4.13/4.31 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 Eq (And (rewrite a a_1) (rewrite a a_2) → Exists fun D => And (rewrite a_1 D) (rewrite a_2 D)) True % 4.13/4.31 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 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) % 4.13/4.31 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 Or (Eq (Exists fun D => And (rewrite a D) (rewrite a_1 D)) True) % 4.13/4.31 (Or (Eq (rewrite a_2 a) False) (Eq (rewrite a_2 a_1) False)) % 4.13/4.31 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 4.13/4.31 Or (Eq (rewrite a a_1) False) % 4.13/4.31 (Or (Eq (rewrite a a_2) False) % 4.13/4.31 (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)) % 4.13/4.31 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 4.13/4.31 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)) % 4.13/4.31 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 4.13/4.31 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)) % 4.13/4.31 Clause #62 (by clausification #[49]): Or (Eq (rewrite a b) True) (Eq (equalish b a) True) % 4.13/4.31 Clause #65 (by superposition #[62, 37]): ∀ (a_1 : Iota), % 4.13/4.31 Or (Eq (rewrite a b) True) % 4.13/4.31 (Or (Eq (reflexive_rewrite b a_1) True) (Or (Eq True False) (Eq (reflexive_rewrite a a_1) False))) % 4.13/4.31 Clause #71 (by clausification #[44]): Or (Eq (equalish a c) True) (Eq (rewrite a c) True) % 4.13/4.31 Clause #72 (by superposition #[71, 19]): Or (Eq (rewrite a c) True) (Or (Eq True False) (Eq (equalish c a) True)) % 4.13/4.31 Clause #79 (by clausification #[72]): Or (Eq (rewrite a c) True) (Eq (equalish c a) True) % 4.13/4.31 Clause #82 (by superposition #[79, 37]): ∀ (a_1 : Iota), % 4.13/4.31 Or (Eq (rewrite a c) True) % 4.13/4.31 (Or (Eq (reflexive_rewrite c a_1) True) (Or (Eq True False) (Eq (reflexive_rewrite a a_1) False))) % 4.13/4.31 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)) % 4.13/4.31 Clause #94 (by superposition #[92, 22]): Or (Eq (rewrite a c) True) (Or (Eq (reflexive_rewrite c b) True) (Eq False True)) % 4.13/4.31 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)) % 4.13/4.31 Clause #97 (by superposition #[96, 21]): Or (Eq (rewrite a b) True) (Or (Eq (reflexive_rewrite b c) True) (Eq False True)) % 4.13/4.31 Clause #101 (by clausification #[97]): Or (Eq (rewrite a b) True) (Eq (reflexive_rewrite b c) True) % 4.13/4.31 Clause #106 (by clausification #[94]): Or (Eq (rewrite a c) True) (Eq (reflexive_rewrite c b) True) % 4.16/4.33 Clause #107 (by forward demodulation #[106, 32]): Or (Eq (rewrite a c) True) (Eq False True) % 4.16/4.33 Clause #108 (by clausification #[107]): Eq (rewrite a c) True % 4.16/4.33 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)) % 4.16/4.33 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)) % 4.16/4.33 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) % 4.16/4.33 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)) % 4.16/4.33 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) % 4.16/4.33 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)) % 4.16/4.33 Clause #213 (by clausification #[138]): ∀ (a : Iota), Or (Eq (rewrite c (skS.0 0 c b a)) True) (Eq (reflexive_rewrite b c) True) % 4.16/4.33 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)) % 4.16/4.33 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) % 4.16/4.33 Clause #221 (by clausification #[121]): ∀ (a : Iota), Or (Eq (rewrite b (skS.0 0 c b a)) True) (Eq (reflexive_rewrite b c) True) % 4.16/4.33 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)) % 4.16/4.33 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) % 4.16/4.33 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)) % 4.16/4.33 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) % 4.16/4.33 Clause #231 (by superposition #[230, 217]): Or (Eq (reflexive_rewrite b c) True) (Or (Eq (reflexive_rewrite b c) True) (Eq False True)) % 4.16/4.33 Clause #232 (by clausification #[231]): Or (Eq (reflexive_rewrite b c) True) (Eq (reflexive_rewrite b c) True) % 4.16/4.33 Clause #233 (by eliminate duplicate literals #[232]): Eq (reflexive_rewrite b c) True % 4.16/4.33 Clause #238 (by superposition #[233, 15]): Or (Eq True False) (Eq (reflexive_rewrite c c) False) % 4.16/4.33 Clause #242 (by clausification #[238]): Eq (reflexive_rewrite c c) False % 4.16/4.33 Clause #243 (by superposition #[242, 30]): Eq False True % 4.16/4.33 Clause #246 (by clausification #[243]): False % 4.16/4.33 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------