TSTP Solution File: SEV034^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV034^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 : Thu Aug 31 19:24:06 EDT 2023
% Result : Theorem 11.86s 12.04s
% Output : Proof 11.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV034^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.16/0.35 % Computer : n012.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 24 02:23:57 EDT 2023
% 0.16/0.35 % CPUTime :
% 11.86/12.04 SZS status Theorem for theBenchmark.p
% 11.86/12.04 SZS output start Proof for theBenchmark.p
% 11.86/12.04 Clause #0 (by assumption #[]): Eq
% 11.86/12.04 (Not
% 11.86/12.04 (∀ (Xp : a → a → Prop) (Xq : a → b → b → Prop) (Xf Xg : a → b),
% 11.86/12.04 (∀ (Xx : a), Xp Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) →
% 11.86/12.04 (∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) →
% 11.86/12.04 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))
% 11.86/12.04 (Eq Xp Xp) →
% 11.86/12.04 (∀ (Xx Xy : a),
% 11.86/12.04 Xp Xx Xy →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0)
% 11.86/12.04 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz))
% 11.86/12.04 (Eq (Xq Xx) (Xq Xy))) →
% 11.86/12.04 ∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xg Xy)))
% 11.86/12.04 True
% 11.86/12.04 Clause #1 (by clausification #[0]): Eq
% 11.86/12.04 (∀ (Xp : a → a → Prop) (Xq : a → b → b → Prop) (Xf Xg : a → b),
% 11.86/12.04 (∀ (Xx : a), Xp Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) →
% 11.86/12.04 (∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) →
% 11.86/12.04 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))
% 11.86/12.04 (Eq Xp Xp) →
% 11.86/12.04 (∀ (Xx Xy : a),
% 11.86/12.04 Xp Xx Xy →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0)
% 11.86/12.04 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz))
% 11.86/12.04 (Eq (Xq Xx) (Xq Xy))) →
% 11.86/12.04 ∀ (Xx Xy : a), Xp Xx Xy → Xq Xx (Xf Xx) (Xg Xy))
% 11.86/12.04 False
% 11.86/12.04 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop),
% 11.86/12.04 Eq
% 11.86/12.04 (Not
% 11.86/12.04 (∀ (Xq : a → b → b → Prop) (Xf Xg : a → b),
% 11.86/12.04 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) →
% 11.86/12.04 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.04 (∀ (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))
% 11.86/12.04 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.04 (∀ (Xx Xy : a),
% 11.86/12.04 skS.0 0 a_1 Xx Xy →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0)
% 11.86/12.04 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz))
% 11.86/12.04 (Eq (Xq Xx) (Xq Xy))) →
% 11.86/12.04 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xg Xy)))
% 11.86/12.04 True
% 11.86/12.04 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop),
% 11.86/12.04 Eq
% 11.86/12.04 (∀ (Xq : a → b → b → Prop) (Xf Xg : a → b),
% 11.86/12.04 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → Xq Xx (Xf Xx) (Xg Xx)) →
% 11.86/12.04 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xf Xy)) →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.04 (∀ (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))
% 11.86/12.04 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.04 (∀ (Xx Xy : a),
% 11.86/12.04 skS.0 0 a_1 Xx Xy →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx0 Xy0 : b), Xq Xx Xx0 Xy0 → Xq Xx Xy0 Xx0)
% 11.86/12.04 (∀ (Xx0 Xy0 Xz : b), And (Xq Xx Xx0 Xy0) (Xq Xx Xy0 Xz) → Xq Xx Xx0 Xz))
% 11.86/12.04 (Eq (Xq Xx) (Xq Xy))) →
% 11.86/12.04 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xq Xx (Xf Xx) (Xg Xy))
% 11.86/12.04 False
% 11.86/12.04 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop),
% 11.86/12.04 Eq
% 11.86/12.04 (Not
% 11.86/12.04 (∀ (Xf Xg : a → b),
% 11.86/12.04 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xx)) →
% 11.86/12.04 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xf Xy)) →
% 11.86/12.04 And
% 11.86/12.04 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.04 (∀ (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))
% 11.86/12.04 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.04 (∀ (Xx Xy : a),
% 11.86/12.06 skS.0 0 a_1 Xx Xy →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.06 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.06 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))
% 11.86/12.06 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.06 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xy)))
% 11.86/12.06 True
% 11.86/12.06 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop),
% 11.86/12.06 Eq
% 11.86/12.06 (∀ (Xf Xg : a → b),
% 11.86/12.06 (∀ (Xx : a), skS.0 0 a_1 Xx Xx → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xx)) →
% 11.86/12.06 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xf Xy)) →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.06 (∀ (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))
% 11.86/12.06 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.06 (∀ (Xx Xy : a),
% 11.86/12.06 skS.0 0 a_1 Xx Xy →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.06 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.06 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))
% 11.86/12.06 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.06 ∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 1 a_1 a_2 Xx (Xf Xx) (Xg Xy))
% 11.86/12.06 False
% 11.86/12.06 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 : a → b),
% 11.86/12.06 Eq
% 11.86/12.06 (Not
% 11.86/12.06 (∀ (Xg : a → b),
% 11.86/12.06 (∀ (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)) →
% 11.86/12.06 (∀ (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)) →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.06 (∀ (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))
% 11.86/12.06 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.06 (∀ (Xx Xy : a),
% 11.86/12.06 skS.0 0 a_1 Xx Xy →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.06 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.06 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))
% 11.86/12.06 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.06 ∀ (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)))
% 11.86/12.06 True
% 11.86/12.06 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 : a → b),
% 11.86/12.06 Eq
% 11.86/12.06 (∀ (Xg : a → b),
% 11.86/12.06 (∀ (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)) →
% 11.86/12.06 (∀ (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)) →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.06 (∀ (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))
% 11.86/12.06 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.06 (∀ (Xx Xy : a),
% 11.86/12.06 skS.0 0 a_1 Xx Xy →
% 11.86/12.06 And
% 11.86/12.06 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.06 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.06 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))
% 11.86/12.06 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.06 ∀ (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))
% 11.86/12.06 False
% 11.86/12.06 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.86/12.06 Eq
% 11.86/12.06 (Not
% 11.86/12.06 ((∀ (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)) →
% 11.86/12.08 (∀ (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)) →
% 11.86/12.08 And
% 11.86/12.08 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.08 (∀ (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))
% 11.86/12.08 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.08 (∀ (Xx Xy : a),
% 11.86/12.08 skS.0 0 a_1 Xx Xy →
% 11.86/12.08 And
% 11.86/12.08 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.08 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.08 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))
% 11.86/12.08 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.08 ∀ (Xx Xy : a),
% 11.86/12.08 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)))
% 11.86/12.08 True
% 11.86/12.08 Clause #9 (by clausification #[8]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.86/12.08 Eq
% 11.86/12.08 ((∀ (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)) →
% 11.86/12.08 (∀ (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)) →
% 11.86/12.08 And
% 11.86/12.08 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.08 (∀ (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))
% 11.86/12.08 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.08 (∀ (Xx Xy : a),
% 11.86/12.08 skS.0 0 a_1 Xx Xy →
% 11.86/12.08 And
% 11.86/12.08 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.08 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.08 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))
% 11.86/12.08 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.08 ∀ (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))
% 11.86/12.08 False
% 11.86/12.08 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.86/12.08 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
% 11.86/12.08 Clause #11 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.86/12.08 Eq
% 11.86/12.08 ((∀ (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)) →
% 11.86/12.08 And
% 11.86/12.08 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.86/12.08 (∀ (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))
% 11.86/12.08 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.86/12.08 (∀ (Xx Xy : a),
% 11.86/12.08 skS.0 0 a_1 Xx Xy →
% 11.86/12.08 And
% 11.86/12.08 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.86/12.08 (∀ (Xx0 Xy0 Xz : b),
% 11.86/12.08 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))
% 11.86/12.08 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.86/12.08 ∀ (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))
% 11.86/12.08 False
% 11.86/12.08 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),
% 11.86/12.08 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
% 11.86/12.08 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),
% 11.86/12.08 Or (Eq (skS.0 0 a_1 a_2 a_2) False)
% 11.86/12.08 (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)
% 11.86/12.08 Clause #14 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 : a → b),
% 11.86/12.08 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
% 11.94/12.10 Clause #15 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.94/12.10 Eq
% 11.94/12.10 (And
% 11.94/12.10 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.94/12.10 (∀ (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))
% 11.94/12.10 (Eq (skS.0 0 a_1) (skS.0 0 a_1)) →
% 11.94/12.10 (∀ (Xx Xy : a),
% 11.94/12.10 skS.0 0 a_1 Xx Xy →
% 11.94/12.10 And
% 11.94/12.10 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.94/12.10 (∀ (Xx0 Xy0 Xz : b),
% 11.94/12.10 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))
% 11.94/12.10 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.94/12.10 ∀ (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))
% 11.94/12.10 False
% 11.94/12.10 Clause #16 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → b → b → Prop) (a_4 : a → b),
% 11.94/12.10 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
% 11.94/12.10 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),
% 11.94/12.10 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
% 11.94/12.10 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),
% 11.94/12.10 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.94/12.10 (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)
% 11.94/12.10 Clause #19 (by clausification #[15]): ∀ (a_1 : a → a → Prop),
% 11.94/12.10 Eq
% 11.94/12.10 (And
% 11.94/12.10 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.94/12.10 (∀ (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))
% 11.94/12.10 (Eq (skS.0 0 a_1) (skS.0 0 a_1)))
% 11.94/12.10 True
% 11.94/12.10 Clause #20 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.94/12.10 Eq
% 11.94/12.10 ((∀ (Xx Xy : a),
% 11.94/12.10 skS.0 0 a_1 Xx Xy →
% 11.94/12.10 And
% 11.94/12.10 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.94/12.10 (∀ (Xx0 Xy0 Xz : b),
% 11.94/12.10 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))
% 11.94/12.10 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 11.94/12.10 ∀ (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))
% 11.94/12.10 False
% 11.94/12.10 Clause #22 (by clausification #[19]): ∀ (a_1 : a → a → Prop),
% 11.94/12.10 Eq
% 11.94/12.10 (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 Xy Xx)
% 11.94/12.10 (∀ (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))
% 11.94/12.10 True
% 11.94/12.10 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
% 11.94/12.10 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
% 11.94/12.10 Clause #26 (by clausification #[24]): ∀ (a_1 : a → a → Prop) (a_2 : a),
% 11.94/12.10 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
% 11.94/12.10 Clause #27 (by clausification #[26]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 11.94/12.10 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
% 11.94/12.10 Clause #28 (by clausification #[27]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 11.94/12.10 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
% 11.94/12.10 Clause #29 (by clausification #[28]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 11.94/12.10 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)
% 11.94/12.10 Clause #30 (by clausification #[29]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 11.94/12.10 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))
% 11.94/12.10 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
% 11.97/12.13 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
% 11.97/12.13 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)
% 11.97/12.13 Clause #34 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop),
% 11.97/12.13 Eq
% 11.97/12.13 (∀ (Xx Xy : a),
% 11.97/12.13 skS.0 0 a_1 Xx Xy →
% 11.97/12.13 And
% 11.97/12.13 (And (∀ (Xx0 Xy0 : b), skS.0 1 a_1 a_2 Xx Xx0 Xy0 → skS.0 1 a_1 a_2 Xx Xy0 Xx0)
% 11.97/12.13 (∀ (Xx0 Xy0 Xz : b),
% 11.97/12.13 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))
% 11.97/12.13 (Eq (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy)))
% 11.97/12.13 True
% 11.97/12.13 Clause #35 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 : a → b → b → Prop) (a_3 a_4 : a → b),
% 11.97/12.13 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
% 11.97/12.13 Clause #36 (by clausification #[34]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → b → b → Prop),
% 11.97/12.13 Eq
% 11.97/12.13 (∀ (Xy : a),
% 11.97/12.13 skS.0 0 a_1 a_2 Xy →
% 11.97/12.13 And
% 11.97/12.13 (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)
% 11.97/12.13 (∀ (Xx0 Xy0 Xz : b),
% 11.97/12.13 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))
% 11.97/12.13 (Eq (skS.0 1 a_1 a_3 a_2) (skS.0 1 a_1 a_3 Xy)))
% 11.97/12.13 True
% 11.97/12.13 Clause #37 (by clausification #[36]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop),
% 11.97/12.13 Eq
% 11.97/12.13 (skS.0 0 a_1 a_2 a_3 →
% 11.97/12.13 And
% 11.97/12.13 (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)
% 11.97/12.13 (∀ (Xx0 Xy0 Xz : b),
% 11.97/12.13 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))
% 11.97/12.13 (Eq (skS.0 1 a_1 a_4 a_2) (skS.0 1 a_1 a_4 a_3)))
% 11.97/12.13 True
% 11.97/12.13 Clause #38 (by clausification #[37]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop),
% 11.97/12.13 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.13 (Eq
% 11.97/12.13 (And
% 11.97/12.13 (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)
% 11.97/12.13 (∀ (Xx0 Xy0 Xz : b),
% 11.97/12.13 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))
% 11.97/12.13 (Eq (skS.0 1 a_1 a_4 a_2) (skS.0 1 a_1 a_4 a_3)))
% 11.97/12.13 True)
% 11.97/12.13 Clause #39 (by clausification #[38]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop),
% 11.97/12.13 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)
% 11.97/12.13 Clause #40 (by clausification #[38]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop),
% 11.97/12.13 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.13 (Eq
% 11.97/12.13 (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)
% 11.97/12.13 (∀ (Xx0 Xy0 Xz : b),
% 11.97/12.13 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))
% 11.97/12.13 True)
% 11.97/12.13 Clause #41 (by clausification #[39]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop),
% 11.97/12.13 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))
% 11.97/12.13 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),
% 11.97/12.13 Eq
% 11.97/12.13 (Not
% 11.97/12.13 (∀ (Xy : a),
% 11.97/12.13 skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy →
% 11.97/12.13 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))
% 11.97/12.13 (skS.0 3 a_1 a_2 a_3 a_4 Xy)))
% 11.97/12.13 True
% 11.97/12.13 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),
% 11.97/12.13 Eq
% 11.97/12.13 (∀ (Xy : a),
% 11.97/12.13 skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy →
% 11.97/12.13 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))
% 11.97/12.13 (skS.0 3 a_1 a_2 a_3 a_4 Xy))
% 11.97/12.13 False
% 11.97/12.13 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),
% 11.97/12.15 Eq
% 11.97/12.15 (Not
% 11.97/12.15 (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) →
% 11.97/12.15 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))
% 11.97/12.15 (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))))
% 11.97/12.15 True
% 11.97/12.15 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),
% 11.97/12.15 Eq
% 11.97/12.15 (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) →
% 11.97/12.15 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))
% 11.97/12.15 (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)))
% 11.97/12.15 False
% 11.97/12.15 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),
% 11.97/12.15 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
% 11.97/12.15 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),
% 11.97/12.15 Eq
% 11.97/12.15 (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))
% 11.97/12.15 (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)))
% 11.97/12.15 False
% 11.97/12.15 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),
% 11.97/12.15 Or (Eq True False)
% 11.97/12.15 (Eq
% 11.97/12.15 (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))
% 11.97/12.15 (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_8)))
% 11.97/12.15 True)
% 11.97/12.15 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),
% 11.97/12.15 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)
% 11.97/12.15 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),
% 11.97/12.15 Or (Eq True False)
% 11.97/12.15 (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)))
% 11.97/12.15 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),
% 11.97/12.15 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
% 11.97/12.15 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),
% 11.97/12.15 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)
% 11.97/12.15 (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))
% 11.97/12.15 Clause #57 (by clausification #[40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop),
% 11.97/12.15 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.15 (Eq
% 11.97/12.15 (∀ (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)
% 11.97/12.15 True)
% 11.97/12.15 Clause #59 (by clausification #[57]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → b → b → Prop) (a_5 : b),
% 11.97/12.15 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.15 (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)
% 11.97/12.15 True)
% 11.97/12.15 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),
% 11.97/12.15 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.15 (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)
% 11.97/12.15 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),
% 11.97/12.15 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.15 (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)
% 11.97/12.15 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),
% 11.97/12.15 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.15 (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)
% 11.97/12.17 (Eq (skS.0 1 a_1 a_4 a_2 a_5 a_7) True))
% 11.97/12.17 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),
% 11.97/12.17 Or (Eq (skS.0 0 a_1 a_2 a_3) False)
% 11.97/12.17 (Or (Eq (skS.0 1 a_1 a_4 a_2 a_5 a_6) True)
% 11.97/12.17 (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)))
% 11.97/12.17 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),
% 11.97/12.17 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)
% 11.97/12.17 (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)
% 11.97/12.17 (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)))
% 11.97/12.17 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),
% 11.97/12.17 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)
% 11.97/12.17 (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5) a_7) False)
% 11.97/12.17 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),
% 11.97/12.17 Or
% 11.97/12.17 (Eq
% 11.97/12.17 (skS.0 0 (fun x x_1 => a_1 x x_1)
% 11.97/12.17 (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)
% 11.97/12.17 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_7))
% 11.97/12.17 True)
% 11.97/12.17 (Eq False True)
% 11.97/12.17 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),
% 11.97/12.17 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))
% 11.97/12.17 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),
% 11.97/12.17 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)
% 11.97/12.17 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),
% 11.97/12.17 Eq
% 11.97/12.17 (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))
% 11.97/12.17 (skS.0 2 a_1 a_2 a_7 (skS.0 5 a_1 a_3 a_4 a_5 a_6 a_8)))
% 11.97/12.17 True
% 11.97/12.17 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),
% 11.97/12.17 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)
% 11.97/12.17 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),
% 11.97/12.17 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
% 11.97/12.17 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),
% 11.97/12.17 Or (Eq True False)
% 11.97/12.17 (Eq
% 11.97/12.17 (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))
% 11.97/12.17 (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)))
% 11.97/12.17 True)
% 11.97/12.17 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),
% 11.97/12.17 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)
% 11.97/12.17 (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)
% 11.97/12.17 (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)))
% 11.97/12.17 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),
% 11.97/12.17 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)
% 11.97/12.17 (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)
% 11.97/12.17 (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))
% 11.97/12.17 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),
% 11.97/12.19 Or
% 11.97/12.19 (Eq
% 11.97/12.19 (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)
% 11.97/12.19 (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)
% 11.97/12.19 (skS.0 2 a_1 a_2 a_7 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) a_8)
% 11.97/12.19 True)
% 11.97/12.19 (Or
% 11.97/12.19 (Eq
% 11.97/12.19 (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)
% 11.97/12.19 (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)
% 11.97/12.19 (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)
% 11.97/12.19 False)
% 11.97/12.19 (Eq False True))
% 11.97/12.19 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),
% 11.97/12.19 Eq
% 11.97/12.19 (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))
% 11.97/12.19 (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)))
% 11.97/12.19 True
% 11.97/12.19 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),
% 11.97/12.19 Eq
% 11.97/12.19 (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))
% 11.97/12.19 (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)))
% 11.97/12.19 True
% 11.97/12.19 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),
% 11.97/12.19 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)
% 11.97/12.19 (Or
% 11.97/12.19 (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)
% 11.97/12.19 False)
% 11.97/12.19 (Eq False True))
% 11.97/12.19 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),
% 11.97/12.19 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)
% 11.97/12.19 (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)
% 11.97/12.19 False)
% 11.97/12.19 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),
% 11.97/12.19 Or
% 11.97/12.19 (Eq
% 11.97/12.19 (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)
% 11.97/12.19 (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)
% 11.97/12.19 (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)
% 11.97/12.19 (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))
% 11.97/12.19 (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)))
% 11.97/12.19 True)
% 11.97/12.19 (Eq False True)
% 11.97/12.19 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),
% 11.97/12.19 Or
% 11.97/12.19 (Eq
% 11.97/12.19 (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))
% 11.97/12.19 (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)))
% 11.97/12.19 True)
% 11.97/12.19 (Eq False True)
% 11.97/12.19 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),
% 11.97/12.19 Eq
% 11.97/12.19 (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))
% 11.97/12.19 (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)))
% 11.97/12.19 True
% 11.97/12.19 Clause #303 (by superposition #[289, 47]): Eq True False
% 11.97/12.19 Clause #304 (by clausification #[303]): False
% 11.97/12.19 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------