%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV019^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:02:45 PM UTC 2025 % Result : Theorem 15.22s 15.41s % Output : Proof 15.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEV019^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.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 : Fri Oct 3 00:59:38 EDT 2025 % 0.13/0.34 % CPUTime : % 15.22/15.41 SZS status Theorem for theBenchmark.p % 15.22/15.41 SZS output start Proof for theBenchmark.p % 15.22/15.41 Clause #0 (by assumption #[]): Eq % 15.22/15.41 (Not % 15.22/15.41 ((∀ (Xx : a), % 15.22/15.41 Exists fun Xp => % 15.22/15.41 And (And (Exists fun Xz => Xp Xz) (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy))) (Xp Xx)) → % 15.22/15.41 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 15.22/15.41 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))) % 15.22/15.41 True % 15.22/15.41 Clause #1 (by betaEtaReduce #[0]): Eq % 15.22/15.41 (Not % 15.22/15.41 ((∀ (Xx : a), % 15.22/15.41 Exists fun Xp => And (And (Exists Xp) (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy))) (Xp Xx)) → % 15.22/15.41 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 15.22/15.41 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))) % 15.22/15.41 True % 15.22/15.41 Clause #2 (by clausification #[1]): Eq % 15.22/15.41 ((∀ (Xx : a), % 15.22/15.41 Exists fun Xp => And (And (Exists Xp) (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy))) (Xp Xx)) → % 15.22/15.41 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 15.22/15.41 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 15.22/15.41 False % 15.22/15.41 Clause #3 (by clausification #[2]): Eq % 15.22/15.41 (∀ (Xx : a), % 15.22/15.41 Exists fun Xp => And (And (Exists Xp) (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy))) (Xp Xx)) % 15.22/15.41 True % 15.22/15.41 Clause #4 (by clausification #[2]): Eq % 15.22/15.41 (And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 15.22/15.41 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 15.22/15.41 False % 15.22/15.41 Clause #5 (by clausification #[3]): ∀ (a_1 : a), % 15.22/15.41 Eq (Exists fun Xp => And (And (Exists Xp) (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy))) (Xp a_1)) True % 15.22/15.41 Clause #6 (by clausification #[5]): ∀ (a_1 : a) (a_2 : a → Prop), % 15.22/15.41 Eq % 15.22/15.41 (And % 15.22/15.41 (And (Exists (skS.0 0 a_1 a_2)) % 15.22/15.41 (∀ (Xx0 : a), skS.0 0 a_1 a_2 Xx0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx0 Xy))) % 15.22/15.41 (skS.0 0 a_1 a_2 a_1)) % 15.22/15.41 True % 15.22/15.41 Clause #7 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (skS.0 0 a_1 a_2 a_1) True % 15.22/15.41 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → Prop), % 15.22/15.41 Eq % 15.22/15.41 (And (Exists (skS.0 0 a_1 a_2)) % 15.22/15.41 (∀ (Xx0 : a), skS.0 0 a_1 a_2 Xx0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx0 Xy))) % 15.22/15.41 True % 15.22/15.41 Clause #9 (by clausification #[4]): Or (Eq (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) False) % 15.22/15.41 (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False) % 15.22/15.41 Clause #10 (by clausification #[9]): Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False) % 15.22/15.41 (Or (Eq (∀ (Xx : a), cQ Xx Xx) False) (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)) % 15.22/15.41 Clause #11 (by clausification #[10]): ∀ (a_1 : a), % 15.22/15.41 Or (Eq (∀ (Xx : a), cQ Xx Xx) False) % 15.22/15.41 (Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False) % 15.22/15.41 (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True)) % 15.22/15.41 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : a), % 15.22/15.41 Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False) % 15.22/15.41 (Or (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True) % 15.22/15.41 (Eq (Not (cQ (skS.0 2 a_2) (skS.0 2 a_2))) True)) % 15.22/15.41 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a), % 15.22/15.41 Or (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True) % 15.22/15.41 (Or (Eq (Not (cQ (skS.0 2 a_2) (skS.0 2 a_2))) True) % 15.22/15.41 (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_3) Xy → cQ Xy (skS.0 3 a_3))) True)) % 15.22/15.41 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a), % 15.22/15.41 Or (Eq (Not (cQ (skS.0 2 a_1) (skS.0 2 a_1))) True) % 15.22/15.41 (Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2))) True) % 15.22/15.41 (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_3) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_3) Xz) False)) % 15.22/15.41 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a), % 15.22/15.41 Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_1) Xy → cQ Xy (skS.0 3 a_1))) True) % 15.22/15.41 (Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_2) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_2) Xz) False) % 15.22/15.41 (Eq (cQ (skS.0 2 a_3) (skS.0 2 a_3)) False)) % 15.22/15.41 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a), % 15.27/15.43 Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 2 a_2) (skS.0 2 a_2)) False) (Eq (∀ (Xy : a), cQ (skS.0 3 a_3) Xy → cQ Xy (skS.0 3 a_3)) False)) % 15.27/15.43 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2)) False) % 15.27/15.43 (Eq (Not (∀ (Xz : a), And (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) (cQ (skS.0 4 a_3 a_4) Xz) → cQ (skS.0 1 a_3) Xz)) % 15.27/15.43 True)) % 15.27/15.43 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or % 15.27/15.43 (Eq (Not (∀ (Xz : a), And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) Xz) → cQ (skS.0 1 a_2) Xz)) % 15.27/15.43 True) % 15.27/15.43 (Eq (Not (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5) → cQ (skS.0 5 a_4 a_5) (skS.0 3 a_4))) True)) % 15.27/15.43 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (Not (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3) → cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2))) True) % 15.27/15.43 (Eq (∀ (Xz : a), And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) Xz) → cQ (skS.0 1 a_4) Xz) False)) % 15.27/15.43 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or % 15.27/15.43 (Eq (∀ (Xz : a), And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) Xz) → cQ (skS.0 1 a_2) Xz) False) % 15.27/15.43 (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5) → cQ (skS.0 5 a_4 a_5) (skS.0 3 a_4)) False)) % 15.27/15.43 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3) → cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) % 15.27/15.43 (Eq % 15.27/15.43 (Not % 15.27/15.43 (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) → % 15.27/15.43 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6))) % 15.27/15.43 True)) % 15.27/15.43 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or % 15.27/15.43 (Eq % 15.27/15.43 (Not % 15.27/15.43 (And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) → % 15.27/15.43 cQ (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4))) % 15.27/15.43 True) % 15.27/15.43 (Eq (cQ (skS.0 3 a_5) (skS.0 5 a_5 a_6)) True)) % 15.27/15.43 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or % 15.27/15.43 (Eq % 15.27/15.43 (Not % 15.27/15.43 (And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) → % 15.27/15.43 cQ (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4))) % 15.27/15.43 True) % 15.27/15.43 (Eq (cQ (skS.0 5 a_5 a_6) (skS.0 3 a_5)) False)) % 15.27/15.43 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) % 15.27/15.43 (Eq % 15.27/15.43 (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) → % 15.27/15.43 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) % 15.27/15.43 False)) % 15.27/15.43 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) % 15.27/15.43 (Eq (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6))) True)) % 15.27/15.43 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) False)) % 15.27/15.43 Clause #27 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True)) % 15.27/15.43 Clause #28 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.43 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.43 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) True)) % 15.27/15.46 Clause #29 (by clausification #[8]): ∀ (a_1 : a) (a_2 : a → Prop), % 15.27/15.46 Eq (∀ (Xx0 : a), skS.0 0 a_1 a_2 Xx0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx0 Xy)) True % 15.27/15.46 Clause #31 (by clausification #[29]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 a_2 a_3 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ a_3 Xy)) True % 15.27/15.46 Clause #32 (by clausification #[31]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), % 15.27/15.46 Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ a_3 Xy)) True) % 15.27/15.46 Clause #33 (by clausification #[32]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.27/15.46 Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (Iff (skS.0 0 a_1 a_2 a_4) (cQ a_3 a_4)) True) % 15.27/15.46 Clause #34 (by clausification #[33]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.27/15.46 Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (skS.0 0 a_1 a_2 a_4) True) (Eq (cQ a_3 a_4) False)) % 15.27/15.46 Clause #35 (by clausification #[33]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.27/15.46 Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (skS.0 0 a_1 a_2 a_4) False) (Eq (cQ a_3 a_4) True)) % 15.27/15.46 Clause #36 (by superposition #[34, 7]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), % 15.27/15.46 Or (Eq (skS.0 0 a_1 (fun x => a_2 x) a_3) True) (Or (Eq (cQ a_1 a_3) False) (Eq False True)) % 15.27/15.46 Clause #39 (by betaEtaReduce #[36]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Or (Eq (cQ a_1 a_3) False) (Eq False True)) % 15.27/15.46 Clause #40 (by clausification #[39]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Eq (cQ a_1 a_3) False) % 15.27/15.46 Clause #41 (by clausification #[23]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.46 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.46 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) % 15.27/15.46 (Eq % 15.27/15.46 (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) → % 15.27/15.46 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) % 15.27/15.46 False)) % 15.27/15.46 Clause #42 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.46 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.46 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) % 15.27/15.46 (Eq (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6))) True)) % 15.27/15.46 Clause #43 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.46 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.46 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) False)) % 15.27/15.46 Clause #44 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 15.27/15.46 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.46 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True)) % 15.27/15.46 Clause #45 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.46 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 15.27/15.46 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) True)) % 15.27/15.46 Clause #46 (by superposition #[35, 7]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), % 15.27/15.46 Or (Eq (skS.0 0 a_1 (fun x => a_2 x) a_3) False) (Or (Eq (cQ a_1 a_3) True) (Eq False True)) % 15.27/15.46 Clause #48 (by betaEtaReduce #[46]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (cQ a_1 a_3) True) (Eq False True)) % 15.27/15.46 Clause #49 (by clausification #[48]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (cQ a_1 a_3) True) % 15.27/15.46 Clause #51 (by superposition #[49, 7]): ∀ (a : a), Or (Eq (cQ a a) True) (Eq False True) % 15.27/15.46 Clause #52 (by clausification #[51]): ∀ (a : a), Eq (cQ a a) True % 15.27/15.46 Clause #53 (by superposition #[52, 27]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.46 Or (Eq True False) % 15.27/15.46 (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True)) % 15.27/15.46 Clause #54 (by superposition #[52, 44]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.46 Or (Eq True False) % 15.27/15.46 (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True)) % 15.27/15.46 Clause #58 (by superposition #[26, 52]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.46 Or (Eq True False) % 15.27/15.46 (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False)) % 15.27/15.49 Clause #73 (by superposition #[28, 52]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.49 Or (Eq True False) (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)) % 15.27/15.49 Clause #98 (by superposition #[43, 52]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.49 Or (Eq True False) % 15.27/15.49 (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False)) % 15.27/15.49 Clause #112 (by superposition #[45, 52]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.49 Or (Eq True False) (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)) % 15.27/15.49 Clause #122 (by clausification #[53]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True) % 15.27/15.49 Clause #125 (by superposition #[122, 40]): ∀ (a_1 a_2 a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 15.27/15.49 (Or (Eq (skS.0 0 (skS.0 4 a_3 a_4) a_5 (skS.0 6 a_3 a_4 a_6)) True) (Eq True False)) % 15.27/15.49 Clause #140 (by clausification #[54]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True) % 15.27/15.49 Clause #141 (by clausification #[73]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True) % 15.27/15.49 Clause #144 (by superposition #[141, 40]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 15.27/15.49 (Or (Eq (skS.0 0 (skS.0 1 a_3) a_4 (skS.0 4 a_3 a_5)) True) (Eq True False)) % 15.27/15.49 Clause #146 (by clausification #[112]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True) % 15.27/15.49 Clause #162 (by clausification #[58]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False) % 15.27/15.49 Clause #196 (by clausification #[98]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False) % 15.27/15.49 Clause #211 (by clausification #[144]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 (skS.0 1 a_3) a_4 (skS.0 4 a_3 a_5)) True) % 15.27/15.49 Clause #216 (by superposition #[211, 35]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 15.27/15.49 (Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 1 a_3) a_4 a_5) False) (Eq (cQ (skS.0 4 a_3 a_6) a_5) True))) % 15.27/15.49 Clause #265 (by clausification #[125]): ∀ (a_1 a_2 a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 (skS.0 4 a_3 a_4) a_5 (skS.0 6 a_3 a_4 a_6)) True) % 15.27/15.49 Clause #408 (by clausification #[216]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 15.27/15.49 (Or (Eq (skS.0 0 (skS.0 1 a_3) a_4 a_5) False) (Eq (cQ (skS.0 4 a_3 a_6) a_5) True)) % 15.27/15.49 Clause #414 (by superposition #[408, 7]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 1 a_3)) True) (Eq False True)) % 15.27/15.49 Clause #415 (by clausification #[414]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 1 a_3)) True) % 15.27/15.49 Clause #416 (by superposition #[415, 40]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.27/15.49 (Or (Eq (skS.0 0 (skS.0 3 a_3) a_4 (skS.0 5 a_3 a_5)) True) (Eq True False)) % 15.27/15.49 Clause #425 (by clausification #[416]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq (skS.0 0 (skS.0 3 a_3) a_4 (skS.0 5 a_3 a_5)) True) % 15.27/15.49 Clause #432 (by superposition #[425, 35]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 15.27/15.49 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.27/15.49 (Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 3 a_3) a_4 a_5) False) (Eq (cQ (skS.0 5 a_3 a_6) a_5) True))) % 15.35/15.52 Clause #482 (by clausification #[432]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.35/15.52 (Or (Eq (skS.0 0 (skS.0 3 a_3) a_4 a_5) False) (Eq (cQ (skS.0 5 a_3 a_6) a_5) True)) % 15.35/15.52 Clause #490 (by superposition #[482, 7]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Or (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True) (Eq False True)) % 15.35/15.52 Clause #491 (by clausification #[490]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True) % 15.35/15.52 Clause #498 (by superposition #[491, 146]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Or (Eq True False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)) % 15.35/15.52 Clause #505 (by clausification #[498]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True) % 15.35/15.52 Clause #511 (by superposition #[505, 40]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.35/15.52 (Or (Eq (skS.0 0 (skS.0 1 a_3) a_4 (skS.0 4 a_3 a_5)) True) (Eq True False)) % 15.35/15.52 Clause #585 (by clausification #[511]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq (skS.0 0 (skS.0 1 a_3) a_4 (skS.0 4 a_3 a_5)) True) % 15.35/15.52 Clause #592 (by superposition #[585, 35]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.35/15.52 (Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 1 a_3) a_4 a_5) False) (Eq (cQ (skS.0 4 a_3 a_6) a_5) True))) % 15.35/15.52 Clause #715 (by clausification #[592]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.35/15.52 (Or (Eq (skS.0 0 (skS.0 1 a_3) a_4 a_5) False) (Eq (cQ (skS.0 4 a_3 a_6) a_5) True)) % 15.35/15.52 Clause #722 (by superposition #[715, 7]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Or (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 1 a_3)) True) (Eq False True)) % 15.35/15.52 Clause #727 (by clausification #[722]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 1 a_3)) True) % 15.35/15.52 Clause #733 (by equality factoring #[727]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) % 15.35/15.52 Clause #734 (by clausification #[733]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False)) % 15.35/15.52 Clause #736 (by clausification #[734]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq True False) % 15.35/15.52 Clause #737 (by clausification #[736]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True % 15.35/15.52 Clause #739 (by superposition #[737, 40]): ∀ (a_1 a_2 : a) (a_3 : a → Prop), Or (Eq (skS.0 0 (skS.0 4 a_1 a_2) a_3 (skS.0 1 a_1)) True) (Eq True False) % 15.35/15.52 Clause #743 (by clausification #[739]): ∀ (a_1 a_2 : a) (a_3 : a → Prop), Eq (skS.0 0 (skS.0 4 a_1 a_2) a_3 (skS.0 1 a_1)) True % 15.35/15.52 Clause #745 (by superposition #[743, 35]): ∀ (a_1 a_2 : a) (a_3 : a → Prop) (a_4 : a), % 15.35/15.52 Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 4 a_1 a_2) a_3 a_4) False) (Eq (cQ (skS.0 1 a_1) a_4) True)) % 15.35/15.52 Clause #757 (by clausification #[745]): ∀ (a_1 a_2 : a) (a_3 : a → Prop) (a_4 : a), % 15.35/15.52 Or (Eq (skS.0 0 (skS.0 4 a_1 a_2) a_3 a_4) False) (Eq (cQ (skS.0 1 a_1) a_4) True) % 15.35/15.52 Clause #761 (by superposition #[757, 265]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.35/15.52 Or (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True) % 15.35/15.52 (Or (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) (Eq False True)) % 15.35/15.52 Clause #764 (by superposition #[757, 7]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq False True) % 15.35/15.52 Clause #766 (by clausification #[764]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True % 15.35/15.52 Clause #768 (by superposition #[766, 40]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 (skS.0 1 a_1) a_2 (skS.0 4 a_1 a_3)) True) (Eq True False) % 15.35/15.52 Clause #772 (by clausification #[768]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 (skS.0 1 a_1) a_2 (skS.0 4 a_1 a_3)) True % 15.35/15.55 Clause #773 (by superposition #[772, 34]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.35/15.55 Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 1 a_1) a_2 a_3) True) (Eq (cQ (skS.0 4 a_1 a_4) a_3) False)) % 15.35/15.55 Clause #822 (by clausification #[773]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.35/15.55 Or (Eq (skS.0 0 (skS.0 1 a_1) a_2 a_3) True) (Eq (cQ (skS.0 4 a_1 a_4) a_3) False) % 15.35/15.55 Clause #903 (by clausification #[761]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 15.35/15.55 Or (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True) (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) % 15.35/15.55 Clause #904 (by superposition #[903, 162]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.55 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True) (Eq True False)) % 15.35/15.55 Clause #914 (by clausification #[904]): ∀ (a_1 a_2 a_3 a_4 : a), % 15.35/15.55 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True) % 15.35/15.55 Clause #919 (by equality factoring #[914]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 15.35/15.55 Clause #924 (by clausification #[919]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq True False) (Eq True False)) % 15.35/15.55 Clause #926 (by clausification #[924]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq True False) % 15.35/15.55 Clause #927 (by clausification #[926]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True % 15.35/15.55 Clause #928 (by superposition #[927, 40]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 (skS.0 3 a_1) a_2 (skS.0 5 a_1 a_3)) True) (Eq True False) % 15.35/15.55 Clause #932 (by clausification #[928]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 (skS.0 3 a_1) a_2 (skS.0 5 a_1 a_3)) True % 15.35/15.55 Clause #934 (by superposition #[932, 35]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.35/15.55 Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 3 a_1) a_2 a_3) False) (Eq (cQ (skS.0 5 a_1 a_4) a_3) True)) % 15.35/15.55 Clause #942 (by clausification #[934]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.35/15.55 Or (Eq (skS.0 0 (skS.0 3 a_1) a_2 a_3) False) (Eq (cQ (skS.0 5 a_1 a_4) a_3) True) % 15.35/15.55 Clause #948 (by superposition #[942, 7]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True) (Eq False True) % 15.35/15.55 Clause #949 (by clausification #[948]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True % 15.35/15.55 Clause #950 (by superposition #[949, 140]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 6 a_1 a_2 a_3)) True) % 15.35/15.55 Clause #951 (by superposition #[949, 196]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) False) % 15.35/15.55 Clause #956 (by clausification #[951]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) False % 15.35/15.55 Clause #962 (by clausification #[950]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 4 a_1 a_2) (skS.0 6 a_1 a_2 a_3)) True % 15.35/15.55 Clause #963 (by superposition #[962, 822]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), % 15.35/15.55 Or (Eq (skS.0 0 (skS.0 1 a_1) a_2 (skS.0 6 a_1 a_3 a_4)) True) (Eq True False) % 15.35/15.55 Clause #1012 (by clausification #[963]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), Eq (skS.0 0 (skS.0 1 a_1) a_2 (skS.0 6 a_1 a_3 a_4)) True % 15.35/15.55 Clause #1015 (by superposition #[1012, 49]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True) % 15.35/15.55 Clause #1020 (by clausification #[1015]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True % 15.35/15.55 Clause #1021 (by superposition #[1020, 956]): Eq True False % 15.35/15.55 Clause #1025 (by clausification #[1021]): False % 15.35/15.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------