%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO383^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:08:58 PM UTC 2025 % Result : Theorem 4.32s 4.48s % Output : Proof 4.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO383^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n017.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 14:01:23 EDT 2025 % 0.12/0.34 % CPUTime : % 4.32/4.48 SZS status Theorem for theBenchmark.p % 4.32/4.48 SZS output start Proof for theBenchmark.p % 4.32/4.48 Clause #0 (by assumption #[]): Eq % 4.32/4.48 (Not % 4.32/4.48 (Not % 4.32/4.48 (And % 4.32/4.48 (And % 4.32/4.48 (And (And (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) (∀ (Xx : Iota), cP_1 d Xx)) % 4.32/4.48 (∀ (Xx Xy : Iota), Or (Not (cP_1 Xx Xy)) (cP_1 (f Xx) Xy))) % 4.32/4.48 (∀ (Xx Xy Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 Xx Xy Xz)) (Not (cP_1 (f Xx) Xu))) (Not (cP_1 (f Xy) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw))) % 4.32/4.48 (∀ (Xx Xy Xz : Iota), Not (cQ_2 Xx Xy Xz))))) % 4.32/4.48 True % 4.32/4.48 Clause #1 (by clausification #[0]): Eq % 4.32/4.48 (Not % 4.32/4.48 (And % 4.32/4.48 (And % 4.32/4.48 (And (And (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) (∀ (Xx : Iota), cP_1 d Xx)) % 4.32/4.48 (∀ (Xx Xy : Iota), Or (Not (cP_1 Xx Xy)) (cP_1 (f Xx) Xy))) % 4.32/4.48 (∀ (Xx Xy Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 Xx Xy Xz)) (Not (cP_1 (f Xx) Xu))) (Not (cP_1 (f Xy) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw))) % 4.32/4.48 (∀ (Xx Xy Xz : Iota), Not (cQ_2 Xx Xy Xz)))) % 4.32/4.48 False % 4.32/4.48 Clause #2 (by clausification #[1]): Eq % 4.32/4.48 (And % 4.32/4.48 (And % 4.32/4.48 (And (And (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) (∀ (Xx : Iota), cP_1 d Xx)) % 4.32/4.48 (∀ (Xx Xy : Iota), Or (Not (cP_1 Xx Xy)) (cP_1 (f Xx) Xy))) % 4.32/4.48 (∀ (Xx Xy Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 Xx Xy Xz)) (Not (cP_1 (f Xx) Xu))) (Not (cP_1 (f Xy) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw))) % 4.32/4.48 (∀ (Xx Xy Xz : Iota), Not (cQ_2 Xx Xy Xz))) % 4.32/4.48 True % 4.32/4.48 Clause #3 (by clausification #[2]): Eq (∀ (Xx Xy Xz : Iota), Not (cQ_2 Xx Xy Xz)) True % 4.32/4.48 Clause #4 (by clausification #[2]): Eq % 4.32/4.48 (And % 4.32/4.48 (And (And (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) (∀ (Xx : Iota), cP_1 d Xx)) % 4.32/4.48 (∀ (Xx Xy : Iota), Or (Not (cP_1 Xx Xy)) (cP_1 (f Xx) Xy))) % 4.32/4.48 (∀ (Xx Xy Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 Xx Xy Xz)) (Not (cP_1 (f Xx) Xu))) (Not (cP_1 (f Xy) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw))) % 4.32/4.48 True % 4.32/4.48 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), Not (cQ_2 a Xy Xz)) True % 4.32/4.48 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), Not (cQ_2 a a_1 Xz)) True % 4.32/4.48 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Eq (Not (cQ_2 a a_1 a_2)) True % 4.32/4.48 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (cQ_2 a a_1 a_2) False % 4.32/4.48 Clause #9 (by clausification #[4]): Eq % 4.32/4.48 (∀ (Xx Xy Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 Xx Xy Xz)) (Not (cP_1 (f Xx) Xu))) (Not (cP_1 (f Xy) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw)) % 4.32/4.48 True % 4.32/4.48 Clause #10 (by clausification #[4]): Eq % 4.32/4.48 (And (And (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) (∀ (Xx : Iota), cP_1 d Xx)) % 4.32/4.48 (∀ (Xx Xy : Iota), Or (Not (cP_1 Xx Xy)) (cP_1 (f Xx) Xy))) % 4.32/4.48 True % 4.32/4.48 Clause #11 (by clausification #[9]): ∀ (a : Iota), % 4.32/4.48 Eq % 4.32/4.48 (∀ (Xy Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 a Xy Xz)) (Not (cP_1 (f a) Xu))) (Not (cP_1 (f Xy) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw)) % 4.32/4.48 True % 4.32/4.48 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 4.32/4.48 Eq % 4.32/4.48 (∀ (Xz Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 a a_1 Xz)) (Not (cP_1 (f a) Xu))) (Not (cP_1 (f a_1) Xv))) (Not (cP_1 (f Xz) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw)) % 4.32/4.48 True % 4.32/4.48 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.32/4.48 Eq % 4.32/4.48 (∀ (Xu Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 a a_1 a_2)) (Not (cP_1 (f a) Xu))) (Not (cP_1 (f a_1) Xv))) (Not (cP_1 (f a_2) Xw))) % 4.32/4.48 (cQ_2 Xu Xv Xw)) % 4.32/4.48 True % 4.32/4.48 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 4.32/4.48 Eq % 4.32/4.48 (∀ (Xv Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 a a_1 a_2)) (Not (cP_1 (f a) a_3))) (Not (cP_1 (f a_1) Xv))) (Not (cP_1 (f a_2) Xw))) % 4.32/4.48 (cQ_2 a_3 Xv Xw)) % 4.32/4.48 True % 4.32/4.48 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.32/4.48 Eq % 4.32/4.48 (∀ (Xw : Iota), % 4.32/4.48 Or (Or (Or (Or (Not (cQ_1 a a_1 a_2)) (Not (cP_1 (f a) a_3))) (Not (cP_1 (f a_1) a_4))) (Not (cP_1 (f a_2) Xw))) % 4.32/4.48 (cQ_2 a_3 a_4 Xw)) % 4.32/4.50 True % 4.32/4.50 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Eq % 4.32/4.50 (Or (Or (Or (Or (Not (cQ_1 a a_1 a_2)) (Not (cP_1 (f a) a_3))) (Not (cP_1 (f a_1) a_4))) (Not (cP_1 (f a_2) a_5))) % 4.32/4.50 (cQ_2 a_3 a_4 a_5)) % 4.32/4.50 True % 4.32/4.50 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or % 4.32/4.50 (Eq (Or (Or (Or (Not (cQ_1 a a_1 a_2)) (Not (cP_1 (f a) a_3))) (Not (cP_1 (f a_1) a_4))) (Not (cP_1 (f a_2) a_5))) % 4.32/4.50 True) % 4.32/4.50 (Eq (cQ_2 a_3 a_4 a_5) True) % 4.32/4.50 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (Or (Or (Not (cQ_1 a_3 a_4 a_5)) (Not (cP_1 (f a_3) a))) (Not (cP_1 (f a_4) a_1))) True) % 4.32/4.50 (Eq (Not (cP_1 (f a_5) a_2)) True)) % 4.32/4.50 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (Not (cP_1 (f a_3) a_2)) True) % 4.32/4.50 (Or (Eq (Or (Not (cQ_1 a_4 a_5 a_3)) (Not (cP_1 (f a_4) a))) True) (Eq (Not (cP_1 (f a_5) a_1)) True))) % 4.32/4.50 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (Or (Not (cQ_1 a_3 a_4 a_5)) (Not (cP_1 (f a_3) a))) True) % 4.32/4.50 (Or (Eq (Not (cP_1 (f a_4) a_1)) True) (Eq (cP_1 (f a_5) a_2) False))) % 4.32/4.50 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (Not (cP_1 (f a_3) a_1)) True) % 4.32/4.50 (Or (Eq (cP_1 (f a_4) a_2) False) (Or (Eq (Not (cQ_1 a_5 a_3 a_4)) True) (Eq (Not (cP_1 (f a_5) a)) True)))) % 4.32/4.50 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (cP_1 (f a_3) a_2) False) % 4.32/4.50 (Or (Eq (Not (cQ_1 a_4 a_5 a_3)) True) (Or (Eq (Not (cP_1 (f a_4) a)) True) (Eq (cP_1 (f a_5) a_1) False)))) % 4.32/4.50 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (cP_1 (f a_3) a_2) False) % 4.32/4.50 (Or (Eq (Not (cP_1 (f a_4) a)) True) (Or (Eq (cP_1 (f a_5) a_1) False) (Eq (cQ_1 a_4 a_5 a_3) False)))) % 4.32/4.50 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 a_2) True) % 4.32/4.50 (Or (Eq (cP_1 (f a_3) a_2) False) % 4.32/4.50 (Or (Eq (cP_1 (f a_4) a_1) False) (Or (Eq (cQ_1 a_5 a_4 a_3) False) (Eq (cP_1 (f a_5) a) False)))) % 4.32/4.50 Clause #25 (by clausification #[10]): Eq (∀ (Xx Xy : Iota), Or (Not (cP_1 Xx Xy)) (cP_1 (f Xx) Xy)) True % 4.32/4.50 Clause #26 (by clausification #[10]): Eq (And (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) (∀ (Xx : Iota), cP_1 d Xx)) True % 4.32/4.50 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Or (Not (cP_1 a Xy)) (cP_1 (f a) Xy)) True % 4.32/4.50 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Or (Not (cP_1 a a_1)) (cP_1 (f a) a_1)) True % 4.32/4.50 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (Not (cP_1 a a_1)) True) (Eq (cP_1 (f a) a_1) True) % 4.32/4.50 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (cP_1 (f a) a_1) True) (Eq (cP_1 a a_1) False) % 4.32/4.50 Clause #32 (by clausification #[26]): Eq (And (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) (cP_1 c c)) True % 4.32/4.50 Clause #38 (by clausification #[32]): Eq (cP_1 c c) True % 4.32/4.50 Clause #39 (by clausification #[32]): Eq (And (And (cQ_1 a b c) (cP_1 a a)) (cP_1 b b)) True % 4.32/4.50 Clause #40 (by superposition #[38, 30]): Or (Eq (cP_1 (f c) c) True) (Eq True False) % 4.32/4.50 Clause #41 (by clausification #[40]): Eq (cP_1 (f c) c) True % 4.32/4.50 Clause #42 (by superposition #[41, 24]): ∀ (a a_1 a_2 a_3 : Iota), % 4.32/4.50 Or (Eq (cQ_2 a a_1 c) True) % 4.32/4.50 (Or (Eq True False) (Or (Eq (cP_1 (f a_2) a_1) False) (Or (Eq (cQ_1 a_3 a_2 c) False) (Eq (cP_1 (f a_3) a) False)))) % 4.32/4.50 Clause #83 (by clausification #[39]): Eq (cP_1 b b) True % 4.32/4.50 Clause #84 (by clausification #[39]): Eq (And (cQ_1 a b c) (cP_1 a a)) True % 4.32/4.50 Clause #85 (by superposition #[83, 30]): Or (Eq (cP_1 (f b) b) True) (Eq True False) % 4.32/4.50 Clause #86 (by clausification #[85]): Eq (cP_1 (f b) b) True % 4.32/4.50 Clause #98 (by clausification #[84]): Eq (cP_1 a a) True % 4.32/4.50 Clause #99 (by clausification #[84]): Eq (cQ_1 a b c) True % 4.32/4.50 Clause #100 (by superposition #[98, 30]): Or (Eq (cP_1 (f a) a) True) (Eq True False) % 4.32/4.51 Clause #101 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.32/4.51 Or (Eq (cQ_2 a a_1 c) True) % 4.32/4.51 (Or (Eq (cP_1 (f a_2) a_1) False) (Or (Eq (cQ_1 a_3 a_2 c) False) (Eq (cP_1 (f a_3) a) False))) % 4.32/4.51 Clause #107 (by superposition #[101, 86]): ∀ (a a_1 : Iota), % 4.32/4.51 Or (Eq (cQ_2 a b c) True) (Or (Eq (cQ_1 a_1 b c) False) (Or (Eq (cP_1 (f a_1) a) False) (Eq False True))) % 4.32/4.51 Clause #116 (by clausification #[100]): Eq (cP_1 (f a) a) True % 4.32/4.51 Clause #434 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (cQ_2 a b c) True) (Or (Eq (cQ_1 a_1 b c) False) (Eq (cP_1 (f a_1) a) False)) % 4.32/4.51 Clause #435 (by superposition #[434, 99]): ∀ (a_1 : Iota), Or (Eq (cQ_2 a_1 b c) True) (Or (Eq (cP_1 (f a) a_1) False) (Eq False True)) % 4.32/4.51 Clause #436 (by clausification #[435]): ∀ (a_1 : Iota), Or (Eq (cQ_2 a_1 b c) True) (Eq (cP_1 (f a) a_1) False) % 4.32/4.51 Clause #437 (by superposition #[436, 116]): Or (Eq (cQ_2 a b c) True) (Eq False True) % 4.32/4.51 Clause #438 (by clausification #[437]): Eq (cQ_2 a b c) True % 4.32/4.51 Clause #439 (by superposition #[438, 8]): Eq True False % 4.32/4.51 Clause #441 (by clausification #[439]): False % 4.32/4.51 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------