%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV218^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:02:57 PM UTC 2025 % Result : Theorem 11.41s 11.62s % Output : Proof 11.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEV218^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 01:13:38 EDT 2025 % 0.13/0.35 % CPUTime : % 11.41/11.62 SZS status Theorem for theBenchmark.p % 11.41/11.62 SZS output start Proof for theBenchmark.p % 11.41/11.62 Clause #0 (by assumption #[]): Eq % 11.41/11.62 (Not % 11.41/11.62 ((Exists fun Xf => % 11.41/11.62 ∀ (Xx : a), % 11.41/11.62 And (And (Exists fun Xz => Xf Xx Xz) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) % 11.41/11.62 (Xf Xx Xx)) → % 11.41/11.62 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 11.41/11.62 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))) % 11.41/11.62 True % 11.41/11.62 Clause #1 (by betaEtaReduce #[0]): Eq % 11.41/11.62 (Not % 11.41/11.62 ((Exists fun Xf => % 11.41/11.62 ∀ (Xx : a), % 11.41/11.62 And (And (Exists (Xf Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) (Xf Xx Xx)) → % 11.41/11.62 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 11.41/11.62 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))) % 11.41/11.62 True % 11.41/11.62 Clause #2 (by clausification #[1]): Eq % 11.41/11.62 ((Exists fun Xf => % 11.41/11.62 ∀ (Xx : a), % 11.41/11.62 And (And (Exists (Xf Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) (Xf Xx Xx)) → % 11.41/11.62 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 11.41/11.62 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 11.41/11.62 False % 11.41/11.62 Clause #3 (by clausification #[2]): Eq % 11.41/11.62 (Exists fun Xf => % 11.41/11.62 ∀ (Xx : a), % 11.41/11.62 And (And (Exists (Xf Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) (Xf Xx Xx)) % 11.41/11.62 True % 11.41/11.62 Clause #4 (by clausification #[2]): Eq % 11.41/11.62 (And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) % 11.41/11.62 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 11.41/11.62 False % 11.41/11.62 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → Prop), % 11.41/11.62 Eq % 11.41/11.62 (∀ (Xx : a), % 11.41/11.62 And % 11.41/11.62 (And (Exists (skS.0 0 a_1 Xx)) % 11.41/11.62 (∀ (Xx_0 : a), skS.0 0 a_1 Xx Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 Xx Xy) (cQ Xx_0 Xy))) % 11.41/11.62 (skS.0 0 a_1 Xx Xx)) % 11.41/11.62 True % 11.41/11.62 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 11.41/11.62 Eq % 11.41/11.62 (And % 11.41/11.62 (And (Exists (skS.0 0 a_1 a_2)) % 11.41/11.62 (∀ (Xx_0 : a), skS.0 0 a_1 a_2 Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx_0 Xy))) % 11.41/11.62 (skS.0 0 a_1 a_2 a_2)) % 11.41/11.62 True % 11.41/11.62 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 a_2 a_2) True % 11.41/11.62 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 11.41/11.62 Eq % 11.41/11.62 (And (Exists (skS.0 0 a_1 a_2)) % 11.41/11.62 (∀ (Xx_0 : a), skS.0 0 a_1 a_2 Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx_0 Xy))) % 11.41/11.62 True % 11.41/11.62 Clause #9 (by clausification #[4]): Or (Eq (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) False) % 11.41/11.62 (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False) % 11.41/11.62 Clause #10 (by clausification #[9]): Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False) % 11.41/11.62 (Or (Eq (∀ (Xx : a), cQ Xx Xx) False) (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)) % 11.41/11.62 Clause #11 (by clausification #[10]): ∀ (a_1 : a), % 11.41/11.62 Or (Eq (∀ (Xx : a), cQ Xx Xx) False) % 11.41/11.62 (Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False) % 11.41/11.62 (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True)) % 11.41/11.62 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : a), % 11.41/11.62 Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False) % 11.41/11.62 (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) % 11.41/11.62 (Eq (Not (cQ (skS.0 2 a_2) (skS.0 2 a_2))) True)) % 11.41/11.62 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a), % 11.41/11.62 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) % 11.41/11.62 (Or (Eq (Not (cQ (skS.0 2 a_2) (skS.0 2 a_2))) True) % 11.41/11.62 (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_3) Xy → cQ Xy (skS.0 3 a_3))) True)) % 11.41/11.62 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a), % 11.41/11.62 Or (Eq (Not (cQ (skS.0 2 a_1) (skS.0 2 a_1))) True) % 11.41/11.62 (Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2))) True) % 11.41/11.62 (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_3) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_3) Xz) False)) % 11.41/11.62 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a), % 11.41/11.62 Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_1) Xy → cQ Xy (skS.0 3 a_1))) True) % 11.48/11.65 (Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_2) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_2) Xz) False) % 11.48/11.65 (Eq (cQ (skS.0 2 a_3) (skS.0 2 a_3)) False)) % 11.48/11.65 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a), % 11.48/11.65 Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz) False) % 11.48/11.65 (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)) % 11.48/11.65 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or (Eq (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2)) False) % 11.48/11.65 (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)) % 11.48/11.65 True)) % 11.48/11.65 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or % 11.48/11.65 (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)) % 11.48/11.65 True) % 11.48/11.65 (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)) % 11.48/11.65 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (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) % 11.48/11.65 (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)) % 11.48/11.65 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or % 11.48/11.65 (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) % 11.48/11.65 (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)) % 11.48/11.65 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (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) % 11.48/11.65 (Eq % 11.48/11.65 (Not % 11.48/11.65 (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)) → % 11.48/11.65 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6))) % 11.48/11.65 True)) % 11.48/11.65 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or % 11.48/11.65 (Eq % 11.48/11.65 (Not % 11.48/11.65 (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)) → % 11.48/11.65 cQ (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4))) % 11.48/11.65 True) % 11.48/11.65 (Eq (cQ (skS.0 3 a_5) (skS.0 5 a_5 a_6)) True)) % 11.48/11.65 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or % 11.48/11.65 (Eq % 11.48/11.65 (Not % 11.48/11.65 (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)) → % 11.48/11.65 cQ (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4))) % 11.48/11.65 True) % 11.48/11.65 (Eq (cQ (skS.0 5 a_5 a_6) (skS.0 3 a_5)) False)) % 11.48/11.65 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) % 11.48/11.65 (Eq % 11.48/11.65 (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)) → % 11.48/11.65 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) % 11.48/11.65 False)) % 11.48/11.65 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) % 11.48/11.65 (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)) % 11.48/11.65 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (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)) % 11.48/11.65 Clause #27 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.48/11.65 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.48/11.65 (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)) % 11.50/11.68 Clause #28 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.68 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.50/11.68 (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)) % 11.50/11.68 Clause #29 (by clausification #[8]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 11.50/11.68 Eq (∀ (Xx_0 : a), skS.0 0 a_1 a_2 Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx_0 Xy)) True % 11.50/11.68 Clause #31 (by clausification #[29]): ∀ (a_1 : a → a → Prop) (a_2 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 % 11.50/11.68 Clause #32 (by clausification #[31]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 11.50/11.68 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) % 11.50/11.68 Clause #33 (by clausification #[32]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.50/11.68 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) % 11.50/11.68 Clause #34 (by clausification #[33]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.50/11.68 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)) % 11.50/11.68 Clause #35 (by clausification #[33]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.50/11.68 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)) % 11.50/11.68 Clause #36 (by superposition #[34, 7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 11.50/11.68 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) a_2 a_3) True) (Or (Eq (cQ a_2 a_3) False) (Eq False True)) % 11.50/11.68 Clause #39 (by betaEtaReduce #[36]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Or (Eq (cQ a_2 a_3) False) (Eq False True)) % 11.50/11.68 Clause #40 (by clausification #[39]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Eq (cQ a_2 a_3) False) % 11.50/11.68 Clause #41 (by clausification #[23]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.50/11.68 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.50/11.68 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) % 11.50/11.68 (Eq % 11.50/11.68 (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)) → % 11.50/11.68 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) % 11.50/11.68 False)) % 11.50/11.68 Clause #42 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.50/11.68 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.50/11.68 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) % 11.50/11.68 (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)) % 11.50/11.68 Clause #43 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.50/11.68 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.50/11.68 (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)) % 11.50/11.68 Clause #44 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 11.50/11.68 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.50/11.68 (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)) % 11.50/11.68 Clause #45 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.68 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False) % 11.50/11.68 (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)) % 11.50/11.68 Clause #46 (by superposition #[35, 7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 11.50/11.68 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) a_2 a_3) False) (Or (Eq (cQ a_2 a_3) True) (Eq False True)) % 11.50/11.68 Clause #48 (by betaEtaReduce #[46]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (cQ a_2 a_3) True) (Eq False True)) % 11.50/11.68 Clause #49 (by clausification #[48]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (cQ a_2 a_3) True) % 11.50/11.68 Clause #51 (by superposition #[49, 7]): ∀ (a : a), Or (Eq (cQ a a) True) (Eq False True) % 11.50/11.68 Clause #52 (by clausification #[51]): ∀ (a : a), Eq (cQ a a) True % 11.50/11.68 Clause #53 (by superposition #[52, 27]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.68 Or (Eq True False) % 11.50/11.68 (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)) % 11.50/11.68 Clause #54 (by superposition #[52, 44]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.68 Or (Eq True False) % 11.50/11.71 (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)) % 11.50/11.71 Clause #58 (by superposition #[26, 52]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.71 Or (Eq True False) % 11.50/11.71 (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)) % 11.50/11.71 Clause #73 (by superposition #[28, 52]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 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)) % 11.50/11.71 Clause #98 (by superposition #[43, 52]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.71 Or (Eq True False) % 11.50/11.71 (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)) % 11.50/11.71 Clause #112 (by superposition #[45, 52]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 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)) % 11.50/11.71 Clause #119 (by clausification #[53]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.71 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) % 11.50/11.71 Clause #122 (by superposition #[119, 40]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 11.50/11.71 (Or (Eq (skS.0 0 a_3 (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True) (Eq True False)) % 11.50/11.71 Clause #137 (by clausification #[54]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.71 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) % 11.50/11.71 Clause #141 (by clausification #[73]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 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) % 11.50/11.71 Clause #142 (by superposition #[141, 40]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) % 11.50/11.71 (Or (Eq (skS.0 0 a_3 (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) (Eq True False)) % 11.50/11.71 Clause #146 (by clausification #[112]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 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) % 11.50/11.71 Clause #151 (by clausification #[58]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.71 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) % 11.50/11.71 Clause #203 (by clausification #[98]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.50/11.71 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) % 11.50/11.71 Clause #228 (by clausification #[142]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq (skS.0 0 a_3 (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) % 11.50/11.71 Clause #233 (by superposition #[228, 35]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) % 11.50/11.71 (Or (Eq True False) (Or (Eq (skS.0 0 a_3 (skS.0 3 a_4) a_5) False) (Eq (cQ (skS.0 5 a_4 a_6) a_5) True))) % 11.50/11.71 Clause #269 (by clausification #[122]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 a_3 (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True) % 11.50/11.71 Clause #375 (by clausification #[233]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) % 11.50/11.71 (Or (Eq (skS.0 0 a_3 (skS.0 3 a_4) a_5) False) (Eq (cQ (skS.0 5 a_4 a_6) a_5) True)) % 11.50/11.71 Clause #382 (by superposition #[375, 7]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True) (Eq False True)) % 11.50/11.71 Clause #388 (by clausification #[382]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True) % 11.50/11.71 Clause #394 (by superposition #[388, 146]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)) % 11.50/11.71 Clause #400 (by clausification #[394]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.50/11.71 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True) % 11.50/11.71 Clause #405 (by equality factoring #[400]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) % 11.55/11.74 Clause #406 (by clausification #[405]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq True False)) % 11.55/11.74 Clause #408 (by clausification #[406]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq True False) % 11.55/11.74 Clause #409 (by clausification #[408]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True % 11.55/11.74 Clause #410 (by superposition #[409, 40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 4 a_2 a_3)) True) (Eq True False) % 11.55/11.74 Clause #414 (by clausification #[410]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 4 a_2 a_3)) True % 11.55/11.74 Clause #415 (by superposition #[414, 34]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) True) (Eq (cQ (skS.0 4 a_2 a_4) a_3) False)) % 11.55/11.74 Clause #416 (by superposition #[414, 35]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) False) (Eq (cQ (skS.0 4 a_2 a_4) a_3) True)) % 11.55/11.74 Clause #428 (by clausification #[415]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) True) (Eq (cQ (skS.0 4 a_2 a_4) a_3) False) % 11.55/11.74 Clause #437 (by clausification #[416]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) False) (Eq (cQ (skS.0 4 a_2 a_4) a_3) True) % 11.55/11.74 Clause #443 (by superposition #[437, 7]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq False True) % 11.55/11.74 Clause #449 (by clausification #[443]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True % 11.55/11.74 Clause #451 (by superposition #[449, 40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) (skS.0 1 a_2)) True) (Eq True False) % 11.55/11.74 Clause #461 (by clausification #[451]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) (skS.0 1 a_2)) True % 11.55/11.74 Clause #463 (by superposition #[461, 35]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) a_4) False) (Eq (cQ (skS.0 1 a_2) a_4) True)) % 11.55/11.74 Clause #495 (by clausification #[463]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) a_4) False) (Eq (cQ (skS.0 1 a_2) a_4) True) % 11.55/11.74 Clause #496 (by superposition #[495, 269]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.55/11.74 Or (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True) % 11.55/11.74 (Or (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) (Eq False True)) % 11.55/11.74 Clause #603 (by clausification #[496]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 11.55/11.74 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) % 11.55/11.74 Clause #604 (by superposition #[603, 151]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.55/11.74 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)) % 11.55/11.74 Clause #625 (by clausification #[604]): ∀ (a_1 a_2 a_3 a_4 : a), % 11.55/11.74 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) % 11.55/11.74 Clause #630 (by equality factoring #[625]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) % 11.55/11.74 Clause #631 (by clausification #[630]): ∀ (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)) % 11.55/11.74 Clause #633 (by clausification #[631]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq True False) % 11.55/11.74 Clause #634 (by clausification #[633]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True % 11.55/11.74 Clause #635 (by superposition #[634, 40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq True False) % 11.55/11.74 Clause #639 (by clausification #[635]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True % 11.55/11.74 Clause #641 (by superposition #[639, 35]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.55/11.74 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) a_3) False) (Eq (cQ (skS.0 5 a_2 a_4) a_3) True)) % 11.58/11.75 Clause #648 (by clausification #[641]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 11.58/11.75 Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) a_3) False) (Eq (cQ (skS.0 5 a_2 a_4) a_3) True) % 11.58/11.75 Clause #655 (by superposition #[648, 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) % 11.58/11.75 Clause #656 (by clausification #[655]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True % 11.58/11.75 Clause #657 (by superposition #[656, 137]): ∀ (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) % 11.58/11.75 Clause #658 (by superposition #[656, 203]): ∀ (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) % 11.58/11.75 Clause #663 (by clausification #[658]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) False % 11.58/11.75 Clause #680 (by clausification #[657]): ∀ (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 % 11.58/11.75 Clause #681 (by superposition #[680, 428]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4)) True) (Eq True False) % 11.58/11.75 Clause #709 (by clausification #[681]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4)) True % 11.58/11.75 Clause #713 (by superposition #[709, 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) % 11.58/11.75 Clause #717 (by clausification #[713]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True % 11.58/11.75 Clause #718 (by superposition #[717, 663]): Eq True False % 11.58/11.75 Clause #722 (by clausification #[718]): False % 11.58/11.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------