%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO169^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:08:41 PM UTC 2025 % Result : Theorem 3.83s 4.01s % Output : Proof 3.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYO169^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.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 : Fri Oct 3 14:24:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.83/4.01 SZS status Theorem for theBenchmark.p % 3.83/4.01 SZS output start Proof for theBenchmark.p % 3.83/4.01 Clause #0 (by assumption #[]): Eq % 3.83/4.01 (Not % 3.83/4.01 (And (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) % 3.83/4.01 (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cPx Xyz Xxyz)) → % 3.83/4.01 cP a b ab → cP b a ab)) % 3.83/4.01 True % 3.83/4.01 Clause #1 (by clausification #[0]): Eq % 3.83/4.01 (And (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) % 3.83/4.01 (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cPx Xyz Xxyz)) → % 3.83/4.01 cP a b ab → cP b a ab) % 3.83/4.01 False % 3.83/4.01 Clause #2 (by clausification #[1]): Eq % 3.83/4.01 (And (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) % 3.83/4.01 (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cPx Xyz Xxyz))) % 3.83/4.01 True % 3.83/4.01 Clause #3 (by clausification #[1]): Eq (cP a b ab → cP b a ab) False % 3.83/4.01 Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cPx Xyz Xxyz)) True % 3.83/4.01 Clause #5 (by clausification #[2]): Eq (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) True % 3.83/4.01 Clause #6 (by clausification #[4]): ∀ (a : Iota), % 3.83/4.01 Eq (∀ (Xy Xz Xxy Xyz Xxyz : Iota), And (cP a Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cPx Xyz Xxyz)) True % 3.83/4.01 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.83/4.01 Eq (∀ (Xz Xxy Xyz Xxyz : Iota), And (cP a a_1 Xxy) (cP a_1 Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cPx Xyz Xxyz)) True % 3.83/4.01 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.83/4.01 Eq (∀ (Xxy Xyz Xxyz : Iota), And (cP a a_1 Xxy) (cP a_1 a_2 Xyz) → Iff (cP Xxy a_2 Xxyz) (cPx Xyz Xxyz)) True % 3.83/4.01 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.83/4.01 Eq (∀ (Xyz Xxyz : Iota), And (cP a a_1 a_2) (cP a_1 a_3 Xyz) → Iff (cP a_2 a_3 Xxyz) (cPx Xyz Xxyz)) True % 3.83/4.01 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.83/4.01 Eq (∀ (Xxyz : Iota), And (cP a a_1 a_2) (cP a_1 a_3 a_4) → Iff (cP a_2 a_3 Xxyz) (cPx a_4 Xxyz)) True % 3.83/4.01 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (And (cP a a_1 a_2) (cP a_1 a_3 a_4) → Iff (cP a_2 a_3 a_5) (cPx a_4 a_5)) True % 3.83/4.01 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.83/4.01 Or (Eq (And (cP a a_1 a_2) (cP a_1 a_3 a_4)) False) (Eq (Iff (cP a_2 a_3 a_5) (cPx a_4 a_5)) True) % 3.83/4.01 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.83/4.01 Or (Eq (Iff (cP a a_1 a_2) (cPx a_3 a_2)) True) (Or (Eq (cP a_4 a_5 a) False) (Eq (cP a_5 a_1 a_3) False)) % 3.83/4.01 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.83/4.01 Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP a_1 a_3 a_4) False) (Or (Eq (cP a_2 a_3 a_5) True) (Eq (cPx a_4 a_5) False))) % 3.83/4.01 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.83/4.01 Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP a_1 a_3 a_4) False) (Or (Eq (cP a_2 a_3 a_5) False) (Eq (cPx a_4 a_5) True))) % 3.83/4.01 Clause #16 (by clausification #[3]): Eq (cP a b ab) True % 3.83/4.01 Clause #17 (by clausification #[3]): Eq (cP b a ab) False % 3.83/4.01 Clause #18 (by superposition #[16, 14]): ∀ (a a_1 a_2 : Iota), % 3.83/4.01 Or (Eq True False) (Or (Eq (cP b a a_1) False) (Or (Eq (cP ab a a_2) True) (Eq (cPx a_1 a_2) False))) % 3.83/4.01 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP b a a_1) False) (Or (Eq (cP ab a a_2) True) (Eq (cPx a_1 a_2) False)) % 3.83/4.01 Clause #20 (by clausification #[5]): Eq (∀ (Xz : Iota), cP Xz Xz e) True % 3.83/4.01 Clause #21 (by clausification #[5]): Eq (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) True % 3.83/4.01 Clause #22 (by clausification #[20]): ∀ (a : Iota), Eq (cP a a e) True % 3.83/4.01 Clause #23 (by superposition #[22, 14]): ∀ (a a_1 a_2 a_3 : Iota), % 3.83/4.01 Or (Eq True False) (Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP e a_1 a_3) True) (Eq (cPx a_2 a_3) False))) % 3.83/4.01 Clause #24 (by superposition #[22, 19]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (cP ab b a) True) (Eq (cPx e a) False)) % 3.83/4.04 Clause #25 (by superposition #[15, 16]): ∀ (a a_1 a_2 : Iota), % 3.83/4.04 Or (Eq True False) (Or (Eq (cP b a a_1) False) (Or (Eq (cP ab a a_2) False) (Eq (cPx a_1 a_2) True))) % 3.83/4.04 Clause #26 (by superposition #[15, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 3.83/4.04 Or (Eq True False) (Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP e a_1 a_3) False) (Eq (cPx a_2 a_3) True))) % 3.83/4.04 Clause #27 (by clausification #[24]): ∀ (a : Iota), Or (Eq (cP ab b a) True) (Eq (cPx e a) False) % 3.83/4.04 Clause #28 (by clausification #[21]): Eq (∀ (Xy : Iota), cP Xy e Xy) True % 3.83/4.04 Clause #29 (by clausification #[21]): Eq (∀ (Xx : Iota), cP e Xx Xx) True % 3.83/4.04 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (cP a e a) True % 3.83/4.04 Clause #31 (by superposition #[30, 14]): ∀ (a a_1 a_2 a_3 : Iota), % 3.83/4.04 Or (Eq True False) (Or (Eq (cP e a a_1) False) (Or (Eq (cP a_2 a a_3) True) (Eq (cPx a_1 a_3) False))) % 3.83/4.04 Clause #33 (by superposition #[30, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 3.83/4.04 Or (Eq True False) (Or (Eq (cP e a a_1) False) (Or (Eq (cP a_2 a a_3) False) (Eq (cPx a_1 a_3) True))) % 3.83/4.04 Clause #34 (by clausification #[29]): ∀ (a : Iota), Eq (cP e a a) True % 3.83/4.04 Clause #38 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP e a_1 a_3) True) (Eq (cPx a_2 a_3) False)) % 3.83/4.04 Clause #42 (by superposition #[38, 34]): ∀ (a a_1 : Iota), Or (Eq (cP e a a_1) True) (Or (Eq (cPx a a_1) False) (Eq False True)) % 3.83/4.04 Clause #43 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP b a a_1) False) (Or (Eq (cP ab a a_2) False) (Eq (cPx a_1 a_2) True)) % 3.83/4.04 Clause #45 (by superposition #[43, 30]): ∀ (a : Iota), Or (Eq (cP ab e a) False) (Or (Eq (cPx b a) True) (Eq False True)) % 3.83/4.04 Clause #46 (by clausification #[45]): ∀ (a : Iota), Or (Eq (cP ab e a) False) (Eq (cPx b a) True) % 3.83/4.04 Clause #52 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (cP e a a_1) True) (Eq (cPx a a_1) False) % 3.83/4.04 Clause #54 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP e a_1 a_3) False) (Eq (cPx a_2 a_3) True)) % 3.83/4.04 Clause #56 (by superposition #[54, 22]): ∀ (a a_1 : Iota), Or (Eq (cP e a a_1) False) (Or (Eq (cPx e a_1) True) (Eq False True)) % 3.83/4.04 Clause #62 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (cP e a a_1) False) (Eq (cPx e a_1) True) % 3.83/4.04 Clause #65 (by superposition #[62, 34]): ∀ (a : Iota), Or (Eq (cPx e a) True) (Eq False True) % 3.83/4.04 Clause #66 (by clausification #[65]): ∀ (a : Iota), Eq (cPx e a) True % 3.83/4.04 Clause #67 (by backward demodulation #[66, 27]): ∀ (a : Iota), Or (Eq (cP ab b a) True) (Eq True False) % 3.83/4.04 Clause #70 (by superposition #[66, 52]): ∀ (a : Iota), Or (Eq (cP e e a) True) (Eq True False) % 3.83/4.04 Clause #73 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP e a a_1) False) (Or (Eq (cP a_2 a a_3) True) (Eq (cPx a_1 a_3) False)) % 3.83/4.04 Clause #77 (by clausification #[67]): ∀ (a : Iota), Eq (cP ab b a) True % 3.83/4.04 Clause #82 (by clausification #[70]): ∀ (a : Iota), Eq (cP e e a) True % 3.83/4.04 Clause #85 (by superposition #[82, 73]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (cP a e a_1) True) (Eq (cPx a_2 a_1) False)) % 3.83/4.04 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a e a_1) True) (Eq (cPx a_2 a_1) False) % 3.83/4.04 Clause #88 (by superposition #[86, 66]): ∀ (a a_1 : Iota), Or (Eq (cP a e a_1) True) (Eq False True) % 3.83/4.04 Clause #89 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP e a a_1) False) (Or (Eq (cP a_2 a a_3) False) (Eq (cPx a_1 a_3) True)) % 3.83/4.04 Clause #94 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (cP a e a_1) True % 3.83/4.04 Clause #95 (by superposition #[94, 46]): ∀ (a : Iota), Or (Eq True False) (Eq (cPx b a) True) % 3.83/4.04 Clause #99 (by clausification #[95]): ∀ (a : Iota), Eq (cPx b a) True % 3.83/4.04 Clause #101 (by superposition #[99, 52]): ∀ (a : Iota), Or (Eq (cP e b a) True) (Eq True False) % 3.83/4.04 Clause #102 (by clausification #[101]): ∀ (a : Iota), Eq (cP e b a) True % 3.83/4.04 Clause #104 (by superposition #[102, 89]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (cP a b a_1) False) (Eq (cPx a_2 a_1) True)) % 3.83/4.04 Clause #112 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a b a_1) False) (Eq (cPx a_2 a_1) True) % 3.83/4.04 Clause #115 (by superposition #[112, 77]): ∀ (a a_1 : Iota), Or (Eq (cPx a a_1) True) (Eq False True) % 3.83/4.05 Clause #119 (by clausification #[115]): ∀ (a a_1 : Iota), Eq (cPx a a_1) True % 3.83/4.05 Clause #120 (by backward demodulation #[119, 52]): ∀ (a a_1 : Iota), Or (Eq (cP e a a_1) True) (Eq True False) % 3.83/4.05 Clause #128 (by clausification #[120]): ∀ (a a_1 : Iota), Eq (cP e a a_1) True % 3.83/4.05 Clause #130 (by superposition #[128, 73]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Or (Eq (cP a a_1 a_2) True) (Eq (cPx a_3 a_2) False)) % 3.83/4.05 Clause #155 (by clausification #[130]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a a_1 a_2) True) (Eq (cPx a_3 a_2) False) % 3.83/4.05 Clause #156 (by superposition #[155, 119]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1 a_2) True) (Eq False True) % 3.83/4.05 Clause #157 (by clausification #[156]): ∀ (a a_1 a_2 : Iota), Eq (cP a a_1 a_2) True % 3.83/4.05 Clause #158 (by superposition #[157, 17]): Eq True False % 3.83/4.05 Clause #159 (by clausification #[158]): False % 3.83/4.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------