%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV034^5 : 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 08:02:46 PM UTC 2025 % Result : Theorem 12.73s 12.90s % Output : Proof 12.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV034^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % 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 01:43:53 EDT 2025 % 0.13/0.34 % CPUTime : % 12.73/12.90 SZS status Theorem for theBenchmark.p % 12.73/12.90 SZS output start Proof for theBenchmark.p % 12.73/12.90 Clause #0 (by assumption #[]): Eq % 12.73/12.90 (Not % 12.73/12.90 (∀ (Xp : a → a → Prop) (Xq : a → b → b → Prop) (Xf Xg : a → b), % 12.73/12.90 (∀ (Xx : a), Xp Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) → % 12.73/12.90 (∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) → % 12.73/12.90 And (And (∀ (Xx Xy : a), Xp Xx Xy → Xp Xy Xx) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)) % 12.73/12.90 (Eq Xp Xp) → % 12.73/12.90 (∀ (Xx Xy : a), % 12.73/12.90 Xp Xx Xy → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0) % 12.73/12.90 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz)) % 12.73/12.90 (Eq (Xq Xx) (Xq Xy))) → % 12.73/12.90 ∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xg Xy))) % 12.73/12.90 True % 12.73/12.90 Clause #1 (by clausification #[0]): Eq % 12.73/12.90 (∀ (Xp : a → a → Prop) (Xq : a → b → b → Prop) (Xf Xg : a → b), % 12.73/12.90 (∀ (Xx : a), Xp Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) → % 12.73/12.90 (∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) → % 12.73/12.90 And (And (∀ (Xx Xy : a), Xp Xx Xy → Xp Xy Xx) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)) % 12.73/12.90 (Eq Xp Xp) → % 12.73/12.90 (∀ (Xx Xy : a), % 12.73/12.90 Xp Xx Xy → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0) % 12.73/12.90 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz)) % 12.73/12.90 (Eq (Xq Xx) (Xq Xy))) → % 12.73/12.90 ∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xg Xy)) % 12.73/12.90 False % 12.73/12.90 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 12.73/12.90 Eq % 12.73/12.90 (Not % 12.73/12.90 (∀ (Xq : a → b → b → Prop) (Xf Xg : a → b), % 12.73/12.90 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) → % 12.73/12.90 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.73/12.90 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.73/12.90 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.73/12.90 (∀ (Xx Xy : a), % 12.73/12.90 skS.0 0 a_1 Xx Xy → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0) % 12.73/12.90 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz)) % 12.73/12.90 (Eq (Xq Xx) (Xq Xy))) → % 12.73/12.90 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xg Xy))) % 12.73/12.90 True % 12.73/12.90 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 12.73/12.90 Eq % 12.73/12.90 (∀ (Xq : a → b → b → Prop) (Xf Xg : a → b), % 12.73/12.90 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) → % 12.73/12.90 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.73/12.90 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.73/12.90 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.73/12.90 (∀ (Xx Xy : a), % 12.73/12.90 skS.0 0 a_1 Xx Xy → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0) % 12.73/12.90 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz)) % 12.73/12.90 (Eq (Xq Xx) (Xq Xy))) → % 12.73/12.90 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xg Xy)) % 12.73/12.90 False % 12.73/12.90 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop), % 12.73/12.90 Eq % 12.73/12.90 (Not % 12.73/12.90 (∀ (Xf Xg : a → b), % 12.73/12.90 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xx)) → % 12.73/12.90 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xf Xy)) → % 12.73/12.90 And % 12.73/12.90 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.73/12.90 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.73/12.90 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.73/12.90 (∀ (Xx Xy : a), % 12.76/12.92 skS.0 0 a_1 Xx Xy → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.92 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.92 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.92 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.92 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xy))) % 12.76/12.92 True % 12.76/12.92 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop), % 12.76/12.92 Eq % 12.76/12.92 (∀ (Xf Xg : a → b), % 12.76/12.92 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xx)) → % 12.76/12.92 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xf Xy)) → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.92 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.92 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.92 (∀ (Xx Xy : a), % 12.76/12.92 skS.0 0 a_1 Xx Xy → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.92 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.92 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.92 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.92 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xy)) % 12.76/12.92 False % 12.76/12.92 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 : a → b), % 12.76/12.92 Eq % 12.76/12.92 (Not % 12.76/12.92 (∀ (Xg : a → b), % 12.76/12.92 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (Xg Xx)) → % 12.76/12.92 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 2 a_1 a_2 a_3 Xy)) → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.92 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.92 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.92 (∀ (Xx Xy : a), % 12.76/12.92 skS.0 0 a_1 Xx Xy → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.92 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.92 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.92 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.92 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (Xg Xy))) % 12.76/12.92 True % 12.76/12.92 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 : a → b), % 12.76/12.92 Eq % 12.76/12.92 (∀ (Xg : a → b), % 12.76/12.92 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (Xg Xx)) → % 12.76/12.92 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 2 a_1 a_2 a_3 Xy)) → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.92 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.92 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.92 (∀ (Xx Xy : a), % 12.76/12.92 skS.0 0 a_1 Xx Xy → % 12.76/12.92 And % 12.76/12.92 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.92 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.92 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.92 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.92 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (Xg Xy)) % 12.76/12.92 False % 12.76/12.92 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.92 Eq % 12.76/12.92 (Not % 12.76/12.92 ((∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx)) → % 12.76/12.94 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 2 a_1 a_2 a_3 Xy)) → % 12.76/12.94 And % 12.76/12.94 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.94 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.94 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.94 (∀ (Xx Xy : a), % 12.76/12.94 skS.0 0 a_1 Xx Xy → % 12.76/12.94 And % 12.76/12.94 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.94 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.94 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.94 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.94 ∀ (Xx Xy : a), % 12.76/12.94 skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xy))) % 12.76/12.94 True % 12.76/12.94 Clause #9 (by clausification #[8]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.94 Eq % 12.76/12.94 ((∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx)) → % 12.76/12.94 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 2 a_1 a_2 a_3 Xy)) → % 12.76/12.94 And % 12.76/12.94 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.94 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.94 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.94 (∀ (Xx Xy : a), % 12.76/12.94 skS.0 0 a_1 Xx Xy → % 12.76/12.94 And % 12.76/12.94 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.94 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.94 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.94 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.94 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xy)) % 12.76/12.94 False % 12.76/12.94 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.94 Eq (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx)) True % 12.76/12.94 Clause #11 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.94 Eq % 12.76/12.94 ((∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 2 a_1 a_2 a_3 Xy)) → % 12.76/12.94 And % 12.76/12.94 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.94 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.94 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.94 (∀ (Xx Xy : a), % 12.76/12.94 skS.0 0 a_1 Xx Xy → % 12.76/12.94 And % 12.76/12.94 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.94 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.94 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.94 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.94 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xy)) % 12.76/12.94 False % 12.76/12.94 Clause #12 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → b → b → Prop) (a_4 a_5 : a → b), % 12.76/12.94 Eq (skS.0 0 a_1 a_2 a_2 → skS.0 1 a_1 a_3 a_2 (skS.0 2 a_1 a_3 a_4 a_2) (skS.0 3 a_1 a_3 a_4 a_5 a_2)) True % 12.76/12.94 Clause #13 (by clausification #[12]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → b → b → Prop) (a_4 a_5 : a → b), % 12.76/12.94 Or (Eq (skS.0 0 a_1 a_2 a_2) False) % 12.76/12.94 (Eq (skS.0 1 a_1 a_3 a_2 (skS.0 2 a_1 a_3 a_4 a_2) (skS.0 3 a_1 a_3 a_4 a_5 a_2)) True) % 12.76/12.94 Clause #14 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 : a → b), % 12.76/12.94 Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 2 a_1 a_2 a_3 Xy)) True % 12.76/12.97 Clause #15 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.97 Eq % 12.76/12.97 (And % 12.76/12.97 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.97 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.97 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) → % 12.76/12.97 (∀ (Xx Xy : a), % 12.76/12.97 skS.0 0 a_1 Xx Xy → % 12.76/12.97 And % 12.76/12.97 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.97 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.97 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.97 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.97 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xy)) % 12.76/12.97 False % 12.76/12.97 Clause #16 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → b → b → Prop) (a_4 : a → b), % 12.76/12.97 Eq (∀ (Xy : a), skS.0 0 a_1 a_2 Xy → skS.0 1 a_1 a_3 a_2 (skS.0 2 a_1 a_3 a_4 a_2) (skS.0 2 a_1 a_3 a_4 Xy)) True % 12.76/12.97 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 : a → b), % 12.76/12.97 Eq (skS.0 0 a_1 a_2 a_3 → skS.0 1 a_1 a_4 a_2 (skS.0 2 a_1 a_4 a_5 a_2) (skS.0 2 a_1 a_4 a_5 a_3)) True % 12.76/12.97 Clause #18 (by clausification #[17]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 : a → b), % 12.76/12.97 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.76/12.97 (Eq (skS.0 1 a_1 a_4 a_2 (skS.0 2 a_1 a_4 a_5 a_2) (skS.0 2 a_1 a_4 a_5 a_3)) True) % 12.76/12.97 Clause #19 (by clausification #[15]): ∀ (a_1 : a → a → Prop), % 12.76/12.97 Eq % 12.76/12.97 (And % 12.76/12.97 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.97 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.97 (Eq (skS.0 0 a_1) (skS.0 0 a_1))) % 12.76/12.97 True % 12.76/12.97 Clause #20 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.97 Eq % 12.76/12.97 ((∀ (Xx Xy : a), % 12.76/12.97 skS.0 0 a_1 Xx Xy → % 12.76/12.97 And % 12.76/12.97 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.97 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.97 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.97 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) → % 12.76/12.97 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xy)) % 12.76/12.97 False % 12.76/12.97 Clause #22 (by clausification #[19]): ∀ (a_1 : a → a → Prop), % 12.76/12.97 Eq % 12.76/12.97 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) % 12.76/12.97 (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)) % 12.76/12.97 True % 12.76/12.97 Clause #24 (by clausification #[22]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) True % 12.76/12.97 Clause #25 (by clausification #[22]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx) True % 12.76/12.97 Clause #26 (by clausification #[24]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 12.76/12.97 Eq (∀ (Xy Xz : a), And (skS.0 0 a_1 a_2 Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 a_2 Xz) True % 12.76/12.97 Clause #27 (by clausification #[26]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 12.76/12.97 Eq (∀ (Xz : a), And (skS.0 0 a_1 a_2 a_3) (skS.0 0 a_1 a_3 Xz) → skS.0 0 a_1 a_2 Xz) True % 12.76/12.97 Clause #28 (by clausification #[27]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 12.76/12.97 Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 0 a_1 a_3 a_4) → skS.0 0 a_1 a_2 a_4) True % 12.76/12.97 Clause #29 (by clausification #[28]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 12.76/12.97 Or (Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 0 a_1 a_3 a_4)) False) (Eq (skS.0 0 a_1 a_2 a_4) True) % 12.76/12.97 Clause #30 (by clausification #[29]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), % 12.76/12.97 Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Or (Eq (skS.0 0 a_1 a_2 a_4) False) (Eq (skS.0 0 a_1 a_4 a_3) False)) % 12.76/12.97 Clause #31 (by clausification #[25]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (∀ (Xy : a), skS.0 0 a_1 a_2 Xy → skS.0 0 a_1 Xy a_2) True % 12.76/12.99 Clause #32 (by clausification #[31]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 a_2 a_3 → skS.0 0 a_1 a_3 a_2) True % 12.76/12.99 Clause #33 (by clausification #[32]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (skS.0 0 a_1 a_3 a_2) True) % 12.76/12.99 Clause #34 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop), % 12.76/12.99 Eq % 12.76/12.99 (∀ (Xx Xy : a), % 12.76/12.99 skS.0 0 a_1 Xx Xy → % 12.76/12.99 And % 12.76/12.99 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0) % 12.76/12.99 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.99 And (skS.0 1 a_1 a_2 Xx Xx0 Xy0) (skS.0 1 a_1 a_2 Xx Xy0 Xz) → skS.0 1 a_1 a_2 Xx Xx0 Xz)) % 12.76/12.99 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) % 12.76/12.99 True % 12.76/12.99 Clause #35 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b), % 12.76/12.99 Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (skS.0 2 a_1 a_2 a_3 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xy)) False % 12.76/12.99 Clause #36 (by clausification #[34]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → b → b → Prop), % 12.76/12.99 Eq % 12.76/12.99 (∀ (Xy : a), % 12.76/12.99 skS.0 0 a_1 a_2 Xy → % 12.76/12.99 And % 12.76/12.99 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_3 a_2 Xx0 Xy0 → skS.0 1 a_1 a_3 a_2 Xy0 Xx0) % 12.76/12.99 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.99 And (skS.0 1 a_1 a_3 a_2 Xx0 Xy0) (skS.0 1 a_1 a_3 a_2 Xy0 Xz) → skS.0 1 a_1 a_3 a_2 Xx0 Xz)) % 12.76/12.99 (Eq (skS.0 1 a_1 a_3 a_2) (skS.0 1 a_1 a_3 Xy))) % 12.76/12.99 True % 12.76/12.99 Clause #37 (by clausification #[36]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop), % 12.76/12.99 Eq % 12.76/12.99 (skS.0 0 a_1 a_2 a_3 → % 12.76/12.99 And % 12.76/12.99 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_4 a_2 Xx0 Xy0 → skS.0 1 a_1 a_4 a_2 Xy0 Xx0) % 12.76/12.99 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.99 And (skS.0 1 a_1 a_4 a_2 Xx0 Xy0) (skS.0 1 a_1 a_4 a_2 Xy0 Xz) → skS.0 1 a_1 a_4 a_2 Xx0 Xz)) % 12.76/12.99 (Eq (skS.0 1 a_1 a_4 a_2) (skS.0 1 a_1 a_4 a_3))) % 12.76/12.99 True % 12.76/12.99 Clause #38 (by clausification #[37]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop), % 12.76/12.99 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.76/12.99 (Eq % 12.76/12.99 (And % 12.76/12.99 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_4 a_2 Xx0 Xy0 → skS.0 1 a_1 a_4 a_2 Xy0 Xx0) % 12.76/12.99 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.99 And (skS.0 1 a_1 a_4 a_2 Xx0 Xy0) (skS.0 1 a_1 a_4 a_2 Xy0 Xz) → skS.0 1 a_1 a_4 a_2 Xx0 Xz)) % 12.76/12.99 (Eq (skS.0 1 a_1 a_4 a_2) (skS.0 1 a_1 a_4 a_3))) % 12.76/12.99 True) % 12.76/12.99 Clause #39 (by clausification #[38]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop), % 12.76/12.99 Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (Eq (skS.0 1 a_1 a_4 a_2) (skS.0 1 a_1 a_4 a_3)) True) % 12.76/12.99 Clause #40 (by clausification #[38]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop), % 12.76/12.99 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.76/12.99 (Eq % 12.76/12.99 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_4 a_2 Xx0 Xy0 → skS.0 1 a_1 a_4 a_2 Xy0 Xx0) % 12.76/12.99 (∀ (Xx0 Xy0 Xz : b), % 12.76/12.99 And (skS.0 1 a_1 a_4 a_2 Xx0 Xy0) (skS.0 1 a_1 a_4 a_2 Xy0 Xz) → skS.0 1 a_1 a_4 a_2 Xx0 Xz)) % 12.76/12.99 True) % 12.76/12.99 Clause #41 (by clausification #[39]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop), % 12.76/12.99 Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (skS.0 1 a_1 a_4 a_2) (skS.0 1 a_1 a_4 a_3)) % 12.76/12.99 Clause #42 (by clausification #[35]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 : a), % 12.76/12.99 Eq % 12.76/12.99 (Not % 12.76/12.99 (∀ (Xy : a), % 12.76/12.99 skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy → % 12.76/12.99 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 12.76/12.99 (skS.0 3 a_1 a_2 a_3 a_4 Xy))) % 12.76/12.99 True % 12.76/12.99 Clause #43 (by clausification #[42]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 : a), % 12.76/12.99 Eq % 12.76/12.99 (∀ (Xy : a), % 12.76/12.99 skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy → % 12.76/12.99 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 12.76/12.99 (skS.0 3 a_1 a_2 a_3 a_4 Xy)) % 12.76/12.99 False % 12.76/12.99 Clause #44 (by clausification #[43]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 : a), % 12.86/13.01 Eq % 12.86/13.01 (Not % 12.86/13.01 (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) → % 12.86/13.01 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 12.86/13.01 (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))) % 12.86/13.01 True % 12.86/13.01 Clause #45 (by clausification #[44]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 : a), % 12.86/13.01 Eq % 12.86/13.01 (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) → % 12.86/13.01 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 12.86/13.01 (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))) % 12.86/13.01 False % 12.86/13.01 Clause #46 (by clausification #[45]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 : a), % 12.86/13.01 Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True % 12.86/13.01 Clause #47 (by clausification #[45]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 : a), % 12.86/13.01 Eq % 12.86/13.01 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 12.86/13.01 (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))) % 12.86/13.01 False % 12.86/13.01 Clause #48 (by superposition #[46, 18]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 : a → b) (a_8 : a), % 12.86/13.01 Or (Eq True False) % 12.86/13.01 (Eq % 12.86/13.01 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) % 12.86/13.01 (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_8))) % 12.86/13.01 True) % 12.86/13.01 Clause #50 (by superposition #[46, 33]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 : a), % 12.86/13.01 Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) % 12.86/13.01 Clause #51 (by superposition #[46, 41]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 a_7 : a), % 12.86/13.01 Or (Eq True False) % 12.86/13.01 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7))) % 12.86/13.01 Clause #52 (by clausification #[50]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 : a), % 12.86/13.01 Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True % 12.86/13.01 Clause #54 (by superposition #[52, 30]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 a_7 : a), % 12.86/13.01 Or (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) a_7) True) % 12.86/13.01 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) a_7) False)) % 12.86/13.01 Clause #57 (by clausification #[40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop), % 12.86/13.01 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.86/13.01 (Eq % 12.86/13.01 (∀ (Xx0 Xy0 Xz : b), And (skS.0 1 a_1 a_4 a_2 Xx0 Xy0) (skS.0 1 a_1 a_4 a_2 Xy0 Xz) → skS.0 1 a_1 a_4 a_2 Xx0 Xz) % 12.86/13.01 True) % 12.86/13.01 Clause #59 (by clausification #[57]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 : b), % 12.86/13.01 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.86/13.01 (Eq (∀ (Xy0 Xz : b), And (skS.0 1 a_1 a_4 a_2 a_5 Xy0) (skS.0 1 a_1 a_4 a_2 Xy0 Xz) → skS.0 1 a_1 a_4 a_2 a_5 Xz) % 12.86/13.01 True) % 12.86/13.01 Clause #60 (by clausification #[59]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 a_6 : b), % 12.86/13.01 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.86/13.01 (Eq (∀ (Xz : b), And (skS.0 1 a_1 a_4 a_2 a_5 a_6) (skS.0 1 a_1 a_4 a_2 a_6 Xz) → skS.0 1 a_1 a_4 a_2 a_5 Xz) True) % 12.86/13.01 Clause #61 (by clausification #[60]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 a_6 a_7 : b), % 12.86/13.01 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.86/13.01 (Eq (And (skS.0 1 a_1 a_4 a_2 a_5 a_6) (skS.0 1 a_1 a_4 a_2 a_6 a_7) → skS.0 1 a_1 a_4 a_2 a_5 a_7) True) % 12.86/13.01 Clause #62 (by clausification #[61]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 a_6 a_7 : b), % 12.86/13.01 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.86/13.01 (Or (Eq (And (skS.0 1 a_1 a_4 a_2 a_5 a_6) (skS.0 1 a_1 a_4 a_2 a_6 a_7)) False) % 12.86/13.04 (Eq (skS.0 1 a_1 a_4 a_2 a_5 a_7) True)) % 12.86/13.04 Clause #63 (by clausification #[62]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 a_6 a_7 : b), % 12.86/13.04 Or (Eq (skS.0 0 a_1 a_2 a_3) False) % 12.86/13.04 (Or (Eq (skS.0 1 a_1 a_4 a_2 a_5 a_6) True) % 12.86/13.04 (Or (Eq (skS.0 1 a_1 a_4 a_2 a_5 a_7) False) (Eq (skS.0 1 a_1 a_4 a_2 a_7 a_6) False))) % 12.86/13.04 Clause #64 (by superposition #[63, 46]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 a_9 : b), % 12.86/13.04 Or (Eq (skS.0 1 (fun x x_1 => a_1 x x_1) a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_8) True) % 12.86/13.04 (Or (Eq (skS.0 1 (fun x x_1 => a_1 x x_1) a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_9) False) % 12.86/13.04 (Or (Eq (skS.0 1 (fun x x_1 => a_1 x x_1) a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_9 a_8) False) (Eq False True))) % 12.86/13.04 Clause #73 (by clausification #[54]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 a_7 : a), % 12.86/13.04 Or (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) a_7) True) % 12.86/13.04 (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) a_7) False) % 12.86/13.04 Clause #74 (by superposition #[73, 46]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 a_7 : a), % 12.86/13.04 Or % 12.86/13.04 (Eq % 12.86/13.04 (skS.0 0 (fun x x_1 => a_1 x x_1) % 12.86/13.04 (skS.0 5 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_2 x x_1 x_2) (fun x => a_3 x) (fun x => a_4 x) a_5 a_6) % 12.86/13.04 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_7)) % 12.86/13.04 True) % 12.86/13.04 (Eq False True) % 12.86/13.04 Clause #75 (by clausification #[51]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 a_7 : a), % 12.86/13.04 Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7)) % 12.86/13.04 Clause #77 (by argument congruence #[75]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 : b) (a_9 : a), % 12.86/13.04 Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_8) (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9) a_7 a_8) % 12.86/13.04 Clause #79 (by clausification #[48]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 : a → b) (a_8 : a), % 12.86/13.04 Eq % 12.86/13.04 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) % 12.86/13.04 (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_8))) % 12.86/13.04 True % 12.86/13.04 Clause #98 (by betaEtaReduce #[74]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 a_7 : a), % 12.86/13.04 Or (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_7)) True) (Eq False True) % 12.86/13.04 Clause #99 (by clausification #[98]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b) (a_5 a_6 a_7 : a), % 12.86/13.04 Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_7)) True % 12.86/13.04 Clause #101 (by superposition #[99, 13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 a_7 : a) (a_8 a_9 : a → b), % 12.86/13.04 Or (Eq True False) % 12.86/13.04 (Eq % 12.86/13.04 (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7) (skS.0 2 a_1 a_2 a_8 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7)) % 12.86/13.04 (skS.0 3 a_1 a_2 a_8 a_9 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7))) % 12.86/13.04 True) % 12.86/13.04 Clause #108 (by betaEtaReduce #[64]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 a_9 : b), % 12.86/13.04 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_8) True) % 12.86/13.04 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_9) False) % 12.86/13.04 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_9 a_8) False) (Eq False True))) % 12.86/13.04 Clause #109 (by clausification #[108]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 a_9 : b), % 12.86/13.04 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_8) True) % 12.86/13.04 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_7 a_9) False) % 12.86/13.04 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) a_9 a_8) False)) % 12.86/13.04 Clause #110 (by superposition #[109, 79]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 : a → b) (a_8 : b) (a_9 : a), % 12.86/13.07 Or % 12.86/13.07 (Eq % 12.86/13.07 (skS.0 1 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_2 x x_1 x_2) % 12.86/13.07 (skS.0 4 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_3 x x_1 x_2) (fun x => a_4 x) (fun x => a_5 x) a_6) % 12.86/13.07 (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) a_8) % 12.86/13.07 True) % 12.86/13.07 (Or % 12.86/13.07 (Eq % 12.86/13.07 (skS.0 1 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_2 x x_1 x_2) % 12.86/13.07 (skS.0 4 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_3 x x_1 x_2) (fun x => a_4 x) (fun x => a_5 x) a_6) % 12.86/13.07 (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9)) a_8) % 12.86/13.07 False) % 12.86/13.07 (Eq False True)) % 12.86/13.07 Clause #172 (by clausification #[101]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 a_7 : a) (a_8 a_9 : a → b), % 12.86/13.07 Eq % 12.86/13.07 (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7) (skS.0 2 a_1 a_2 a_8 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7)) % 12.86/13.07 (skS.0 3 a_1 a_2 a_8 a_9 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_7))) % 12.86/13.07 True % 12.86/13.07 Clause #173 (by superposition #[172, 77]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 : a → b) (a_8 : a) (a_9 : a → b), % 12.86/13.07 Eq % 12.86/13.07 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_8)) % 12.86/13.07 (skS.0 3 a_1 a_2 a_7 a_9 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_8))) % 12.86/13.07 True % 12.86/13.07 Clause #191 (by betaEtaReduce #[110]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 : a → b) (a_8 : b) (a_9 : a), % 12.86/13.07 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) a_8) True) % 12.86/13.07 (Or % 12.86/13.07 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9)) a_8) % 12.86/13.07 False) % 12.86/13.07 (Eq False True)) % 12.86/13.07 Clause #192 (by clausification #[191]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 : a → b) (a_8 : b) (a_9 : a), % 12.86/13.07 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) a_8) True) % 12.86/13.07 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9)) a_8) % 12.86/13.07 False) % 12.86/13.07 Clause #195 (by superposition #[192, 173]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 : a → b) (a_9 : a), % 12.86/13.07 Or % 12.86/13.07 (Eq % 12.86/13.07 (skS.0 1 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_2 x x_1 x_2) % 12.86/13.07 (skS.0 4 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_3 x x_1 x_2) (fun x => a_4 x) (fun x => a_5 x) a_6) % 12.86/13.07 (skS.0 2 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_2 x x_1 x_2) (fun x => a_7 x) % 12.86/13.07 (skS.0 4 (fun x x_1 => a_1 x x_1) (fun x x_1 x_2 => a_3 x x_1 x_2) (fun x => a_4 x) (fun x => a_5 x) a_6)) % 12.86/13.07 (skS.0 3 a_1 a_2 a_7 a_8 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9))) % 12.86/13.07 True) % 12.86/13.07 (Eq False True) % 12.86/13.07 Clause #288 (by betaEtaReduce #[195]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 : a → b) (a_9 : a), % 12.86/13.07 Or % 12.86/13.07 (Eq % 12.86/13.07 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) % 12.86/13.07 (skS.0 3 a_1 a_2 a_7 a_8 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9))) % 12.86/13.07 True) % 12.86/13.07 (Eq False True) % 12.86/13.07 Clause #289 (by clausification #[288]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a → b → b → Prop) (a_4 a_5 : a → b) (a_6 : a) (a_7 a_8 : a → b) (a_9 : a), % 12.86/13.07 Eq % 12.86/13.07 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6) (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) % 12.86/13.07 (skS.0 3 a_1 a_2 a_7 a_8 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_9))) % 12.86/13.07 True % 12.86/13.07 Clause #303 (by superposition #[289, 47]): Eq True False % 12.86/13.07 Clause #304 (by clausification #[303]): False % 12.86/13.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------