%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO170^5 : 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 08:08:41 PM UTC 2025 % Result : Theorem 3.79s 3.95s % Output : Proof 3.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO170^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 13:17:23 EDT 2025 % 0.14/0.34 % CPUTime : % 3.79/3.95 SZS status Theorem for theBenchmark.p % 3.79/3.95 SZS output start Proof for theBenchmark.p % 3.79/3.95 Clause #0 (by assumption #[]): Eq % 3.79/3.95 (Not % 3.79/3.95 (And (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) % 3.79/3.95 (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cP Xx Xyz Xxyz)) → % 3.79/3.95 cP a b ab → cP b a ab)) % 3.79/3.95 True % 3.79/3.95 Clause #1 (by clausification #[0]): Eq % 3.79/3.95 (And (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) % 3.79/3.95 (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cP Xx Xyz Xxyz)) → % 3.79/3.95 cP a b ab → cP b a ab) % 3.79/3.95 False % 3.79/3.95 Clause #2 (by clausification #[1]): Eq % 3.79/3.95 (And (And (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) (∀ (Xz : Iota), cP Xz Xz e)) % 3.79/3.95 (∀ (Xx Xy Xz Xxy Xyz Xxyz : Iota), And (cP Xx Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cP Xx Xyz Xxyz))) % 3.79/3.95 True % 3.79/3.95 Clause #3 (by clausification #[1]): Eq (cP a b ab → cP b a ab) False % 3.79/3.95 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) (cP Xx Xyz Xxyz)) True % 3.79/3.95 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 % 3.79/3.95 Clause #6 (by clausification #[4]): ∀ (a : Iota), % 3.79/3.95 Eq (∀ (Xy Xz Xxy Xyz Xxyz : Iota), And (cP a Xy Xxy) (cP Xy Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cP a Xyz Xxyz)) True % 3.79/3.95 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.79/3.95 Eq (∀ (Xz Xxy Xyz Xxyz : Iota), And (cP a a_1 Xxy) (cP a_1 Xz Xyz) → Iff (cP Xxy Xz Xxyz) (cP a Xyz Xxyz)) True % 3.79/3.95 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.79/3.95 Eq (∀ (Xxy Xyz Xxyz : Iota), And (cP a a_1 Xxy) (cP a_1 a_2 Xyz) → Iff (cP Xxy a_2 Xxyz) (cP a Xyz Xxyz)) True % 3.79/3.95 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.79/3.95 Eq (∀ (Xyz Xxyz : Iota), And (cP a a_1 a_2) (cP a_1 a_3 Xyz) → Iff (cP a_2 a_3 Xxyz) (cP a Xyz Xxyz)) True % 3.79/3.95 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.79/3.95 Eq (∀ (Xxyz : Iota), And (cP a a_1 a_2) (cP a_1 a_3 a_4) → Iff (cP a_2 a_3 Xxyz) (cP a a_4 Xxyz)) True % 3.79/3.95 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) (cP a a_4 a_5)) True % 3.79/3.95 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.79/3.95 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) (cP a a_4 a_5)) True) % 3.79/3.95 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.79/3.95 Or (Eq (Iff (cP a a_1 a_2) (cP a_3 a_4 a_2)) True) (Or (Eq (cP a_3 a_5 a) False) (Eq (cP a_5 a_1 a_4) False)) % 3.79/3.95 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.79/3.95 Or (Eq (cP a a_1 a_2) False) % 3.79/3.95 (Or (Eq (cP a_1 a_3 a_4) False) (Or (Eq (cP a_2 a_3 a_5) True) (Eq (cP a a_4 a_5) False))) % 3.79/3.95 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.79/3.95 Or (Eq (cP a a_1 a_2) False) % 3.79/3.95 (Or (Eq (cP a_1 a_3 a_4) False) (Or (Eq (cP a_2 a_3 a_5) False) (Eq (cP a a_4 a_5) True))) % 3.79/3.95 Clause #16 (by clausification #[3]): Eq (cP a b ab) True % 3.79/3.95 Clause #17 (by clausification #[3]): Eq (cP b a ab) False % 3.79/3.95 Clause #18 (by superposition #[16, 14]): ∀ (a_1 a_2 a_3 : Iota), % 3.79/3.95 Or (Eq True False) (Or (Eq (cP b a_1 a_2) False) (Or (Eq (cP ab a_1 a_3) True) (Eq (cP a a_2 a_3) False))) % 3.79/3.95 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 : Iota), Or (Eq (cP b a_1 a_2) False) (Or (Eq (cP ab a_1 a_3) True) (Eq (cP a a_2 a_3) False)) % 3.79/3.95 Clause #20 (by clausification #[5]): Eq (∀ (Xz : Iota), cP Xz Xz e) True % 3.79/3.95 Clause #21 (by clausification #[5]): Eq (And (∀ (Xx : Iota), cP e Xx Xx) (∀ (Xy : Iota), cP Xy e Xy)) True % 3.79/3.95 Clause #22 (by clausification #[20]): ∀ (a : Iota), Eq (cP a a e) True % 3.79/3.95 Clause #24 (by superposition #[22, 19]): ∀ (a_1 : Iota), Or (Eq True False) (Or (Eq (cP ab b a_1) True) (Eq (cP a e a_1) False)) % 3.79/3.95 Clause #26 (by superposition #[15, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 3.79/3.95 Or (Eq True False) (Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP e a_1 a_3) False) (Eq (cP a a_2 a_3) True))) % 3.79/3.96 Clause #27 (by clausification #[24]): ∀ (a_1 : Iota), Or (Eq (cP ab b a_1) True) (Eq (cP a e a_1) False) % 3.79/3.96 Clause #28 (by clausification #[21]): Eq (∀ (Xy : Iota), cP Xy e Xy) True % 3.79/3.96 Clause #29 (by clausification #[21]): Eq (∀ (Xx : Iota), cP e Xx Xx) True % 3.79/3.96 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (cP a e a) True % 3.79/3.96 Clause #31 (by superposition #[30, 27]): Or (Eq (cP ab b a) True) (Eq True False) % 3.79/3.96 Clause #35 (by clausification #[29]): ∀ (a : Iota), Eq (cP e a a) True % 3.79/3.96 Clause #38 (by clausification #[31]): Eq (cP ab b a) True % 3.79/3.96 Clause #64 (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 (cP a a_2 a_3) True)) % 3.79/3.96 Clause #66 (by superposition #[64, 38]): ∀ (a_1 : Iota), Or (Eq (cP e b a_1) False) (Or (Eq (cP ab a a_1) True) (Eq False True)) % 3.79/3.96 Clause #80 (by clausification #[66]): ∀ (a_1 : Iota), Or (Eq (cP e b a_1) False) (Eq (cP ab a a_1) True) % 3.79/3.96 Clause #81 (by superposition #[80, 35]): Or (Eq (cP ab a b) True) (Eq False True) % 3.79/3.96 Clause #82 (by clausification #[81]): Eq (cP ab a b) True % 3.79/3.96 Clause #83 (by superposition #[82, 14]): ∀ (a_1 a_2 a_3 : Iota), % 3.79/3.96 Or (Eq True False) (Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP b a_1 a_3) True) (Eq (cP ab a_2 a_3) False))) % 3.79/3.96 Clause #154 (by clausification #[83]): ∀ (a_1 a_2 a_3 : Iota), Or (Eq (cP a a_1 a_2) False) (Or (Eq (cP b a_1 a_3) True) (Eq (cP ab a_2 a_3) False)) % 3.79/3.96 Clause #157 (by superposition #[154, 22]): ∀ (a_1 : Iota), Or (Eq (cP b a a_1) True) (Or (Eq (cP ab e a_1) False) (Eq False True)) % 3.79/3.96 Clause #162 (by clausification #[157]): ∀ (a_1 : Iota), Or (Eq (cP b a a_1) True) (Eq (cP ab e a_1) False) % 3.79/3.96 Clause #163 (by superposition #[162, 30]): Or (Eq (cP b a ab) True) (Eq False True) % 3.79/3.96 Clause #164 (by clausification #[163]): Eq (cP b a ab) True % 3.79/3.96 Clause #165 (by superposition #[164, 17]): Eq True False % 3.79/3.96 Clause #176 (by clausification #[165]): False % 3.79/3.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------