%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : COM007+2 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 3.95s 4.13s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM007+2 : TPTP v9.2.0. Released v3.2.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n010.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 Oct 2 15:58:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.95/4.13 SZS status Theorem for theBenchmark.p % 3.95/4.13 SZS output start Proof for theBenchmark.p % 3.95/4.13 Clause #0 (by assumption #[]): Eq (And (reflexive_rewrite a b) (reflexive_rewrite a c)) True % 3.95/4.13 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), And (reflexive_rewrite b A) (reflexive_rewrite c A) → goal) True % 3.95/4.13 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq A B → reflexive_rewrite A B) True % 3.95/4.13 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), rewrite A B → reflexive_rewrite A B) True % 3.95/4.13 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), reflexive_rewrite A B → Or (Eq A B) (rewrite A B)) True % 3.95/4.13 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 % 3.95/4.13 Clause #6 (by assumption #[]): Eq (Not goal) True % 3.95/4.13 Clause #7 (by clausification #[6]): Eq goal False % 3.95/4.13 Clause #8 (by clausification #[1]): ∀ (a : Iota), Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a) → goal) True % 3.95/4.13 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (And (reflexive_rewrite b a) (reflexive_rewrite c a)) False) (Eq goal True) % 3.95/4.13 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq goal True) (Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False)) % 3.95/4.13 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)) % 3.95/4.13 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (reflexive_rewrite b a) False) (Eq (reflexive_rewrite c a) False) % 3.95/4.13 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), rewrite a B → reflexive_rewrite a B) True % 3.95/4.13 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (rewrite a a_1 → reflexive_rewrite a a_1) True % 3.95/4.13 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (rewrite a a_1) False) (Eq (reflexive_rewrite a a_1) True) % 3.95/4.13 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq a B → reflexive_rewrite a B) True % 3.95/4.13 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq a a_1 → reflexive_rewrite a a_1) True % 3.95/4.13 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) False) (Eq (reflexive_rewrite a a_1) True) % 3.95/4.13 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (reflexive_rewrite a a_1) True) (Ne a a_1) % 3.95/4.13 Clause #20 (by destructive equality resolution #[19]): ∀ (a : Iota), Eq (reflexive_rewrite a a) True % 3.95/4.13 Clause #21 (by superposition #[20, 12]): Or (Eq True False) (Eq (reflexive_rewrite c b) False) % 3.95/4.13 Clause #22 (by clausification #[21]): Eq (reflexive_rewrite c b) False % 3.95/4.13 Clause #23 (by clausification #[0]): Eq (reflexive_rewrite a c) True % 3.95/4.13 Clause #24 (by clausification #[0]): Eq (reflexive_rewrite a b) True % 3.95/4.13 Clause #25 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), reflexive_rewrite a B → Or (Eq a B) (rewrite a B)) True % 3.95/4.13 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 % 3.95/4.13 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) % 3.95/4.13 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)) % 3.95/4.13 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)) % 3.95/4.13 Clause #30 (by superposition #[29, 23]): Or (Eq (rewrite a c) True) (Or (Eq a c) (Eq False True)) % 3.95/4.13 Clause #31 (by superposition #[29, 24]): Or (Eq (rewrite a b) True) (Or (Eq a b) (Eq False True)) % 3.95/4.13 Clause #34 (by clausification #[31]): Or (Eq (rewrite a b) True) (Eq a b) % 3.95/4.13 Clause #37 (by clausification #[5]): ∀ (a : Iota), % 3.95/4.13 Eq (∀ (B C : Iota), And (rewrite a B) (rewrite a C) → Exists fun D => And (rewrite B D) (rewrite C D)) True % 3.95/4.13 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 3.95/4.13 Eq (∀ (C : Iota), And (rewrite a a_1) (rewrite a C) → Exists fun D => And (rewrite a_1 D) (rewrite C D)) True % 3.95/4.13 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.95/4.13 Eq (And (rewrite a a_1) (rewrite a a_2) → Exists fun D => And (rewrite a_1 D) (rewrite a_2 D)) True % 3.95/4.16 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 3.95/4.16 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) % 3.95/4.16 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.95/4.16 Or (Eq (Exists fun D => And (rewrite a D) (rewrite a_1 D)) True) % 3.95/4.16 (Or (Eq (rewrite a_2 a) False) (Eq (rewrite a_2 a_1) False)) % 3.95/4.16 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 3.95/4.16 Or (Eq (rewrite a a_1) False) % 3.95/4.16 (Or (Eq (rewrite a a_2) False) % 3.95/4.16 (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)) % 3.95/4.16 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 3.95/4.16 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)) % 3.95/4.16 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 3.95/4.16 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)) % 3.95/4.16 Clause #46 (by clausification #[30]): Or (Eq (rewrite a c) True) (Eq a c) % 3.95/4.16 Clause #48 (by superposition #[46, 43]): ∀ (a_1 a_2 : Iota), % 3.95/4.16 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))) % 3.95/4.16 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)) % 3.95/4.16 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))) % 3.95/4.16 Clause #60 (by superposition #[44, 46]): ∀ (a_1 a_2 : Iota), % 3.95/4.16 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))) % 3.95/4.16 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)) % 3.95/4.16 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))) % 3.95/4.16 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)) % 3.95/4.16 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))) % 3.95/4.16 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)) % 3.95/4.16 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)) % 3.95/4.16 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))) % 3.95/4.16 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)) % 3.95/4.16 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))) % 3.95/4.16 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)) % 3.95/4.16 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)))) % 3.95/4.16 Clause #102 (by clausification #[100]): Or (Eq a c) (Or (Eq a b) (Or (Eq a c) (Eq a b))) % 3.95/4.16 Clause #103 (by eliminate duplicate literals #[102]): Or (Eq a c) (Eq a b) % 3.95/4.16 Clause #104 (by superposition #[103, 23]): Or (Eq a c) (Eq (reflexive_rewrite b c) True) % 3.95/4.16 Clause #112 (by superposition #[104, 12]): Or (Eq a c) (Or (Eq True False) (Eq (reflexive_rewrite c c) False)) % 3.95/4.16 Clause #114 (by clausification #[112]): Or (Eq a c) (Eq (reflexive_rewrite c c) False) % 3.95/4.16 Clause #115 (by superposition #[114, 20]): Or (Eq a c) (Eq False True) % 3.95/4.16 Clause #116 (by clausification #[115]): Eq a c % 3.95/4.16 Clause #118 (by backward demodulation #[116, 24]): Eq (reflexive_rewrite c b) True % 3.95/4.16 Clause #134 (by superposition #[118, 22]): Eq True False % 3.95/4.16 Clause #138 (by clausification #[134]): False % 3.95/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------