TSTP Solution File: SYN334+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN334+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 Sep 1 02:11:14 EDT 2023
% Result : Theorem 5.02s 5.18s
% Output : Proof 5.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN334+1 : TPTP v8.1.2. Released v2.0.0.
% 0.14/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 18:47:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 5.02/5.18 SZS status Theorem for theBenchmark.p
% 5.02/5.18 SZS output start Proof for theBenchmark.p
% 5.02/5.18 Clause #0 (by assumption #[]): Eq
% 5.02/5.18 (Not
% 5.02/5.18 (Exists fun X =>
% 5.02/5.18 Exists fun Y =>
% 5.02/5.18 ∀ (Z : Iota),
% 5.02/5.18 (big_f X Y → Iff (big_f X Z) (big_g Y Z)) →
% 5.02/5.18 Iff (big_f X Y) (big_f Z Z → big_g Z Z) → Iff (big_g X Y) (big_g Z Z)))
% 5.02/5.18 True
% 5.02/5.18 Clause #1 (by clausification #[0]): Eq
% 5.02/5.18 (Exists fun X =>
% 5.02/5.18 Exists fun Y =>
% 5.02/5.18 ∀ (Z : Iota),
% 5.02/5.18 (big_f X Y → Iff (big_f X Z) (big_g Y Z)) →
% 5.02/5.18 Iff (big_f X Y) (big_f Z Z → big_g Z Z) → Iff (big_g X Y) (big_g Z Z))
% 5.02/5.18 False
% 5.02/5.18 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 5.02/5.18 Eq
% 5.02/5.18 (Exists fun Y =>
% 5.02/5.18 ∀ (Z : Iota),
% 5.02/5.18 (big_f a Y → Iff (big_f a Z) (big_g Y Z)) →
% 5.02/5.18 Iff (big_f a Y) (big_f Z Z → big_g Z Z) → Iff (big_g a Y) (big_g Z Z))
% 5.02/5.18 False
% 5.02/5.18 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota),
% 5.02/5.18 Eq
% 5.02/5.18 (∀ (Z : Iota),
% 5.02/5.18 (big_f a a_1 → Iff (big_f a Z) (big_g a_1 Z)) →
% 5.02/5.18 Iff (big_f a a_1) (big_f Z Z → big_g Z Z) → Iff (big_g a a_1) (big_g Z Z))
% 5.02/5.18 False
% 5.02/5.18 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Eq
% 5.02/5.18 (Not
% 5.02/5.18 ((big_f a a_1 → Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) →
% 5.02/5.18 Iff (big_f a a_1)
% 5.02/5.18 (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 5.02/5.18 Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))))
% 5.02/5.18 True
% 5.02/5.18 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Eq
% 5.02/5.18 ((big_f a a_1 → Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) →
% 5.02/5.18 Iff (big_f a a_1)
% 5.02/5.18 (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 5.02/5.18 Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)))
% 5.02/5.18 False
% 5.02/5.18 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (big_f a a_1 → Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) True
% 5.02/5.18 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Eq
% 5.02/5.18 (Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 5.02/5.18 Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)))
% 5.02/5.18 False
% 5.02/5.18 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Or (Eq (big_f a a_1) False) (Eq (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) True)
% 5.02/5.18 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Or (Eq (big_f a a_1) False) (Or (Eq (big_f a (skS.0 0 a a_1 a_2)) True) (Eq (big_g a_1 (skS.0 0 a a_1 a_2)) False))
% 5.02/5.18 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Or (Eq (big_f a a_1) False) (Or (Eq (big_f a (skS.0 0 a a_1 a_2)) False) (Eq (big_g a_1 (skS.0 0 a a_1 a_2)) True))
% 5.02/5.18 Clause #11 (by clausification #[7]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Eq (Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)))
% 5.02/5.18 True
% 5.02/5.18 Clause #12 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) False
% 5.02/5.18 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Or (Eq (big_f a a_1) True)
% 5.02/5.18 (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)
% 5.02/5.18 Clause #14 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.18 Or (Eq (big_f a a_1) False)
% 5.02/5.18 (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)
% 5.02/5.18 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)
% 5.02/5.18 Clause #16 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)
% 5.02/5.18 Clause #17 (by superposition #[15, 9]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.18 Or (Eq (big_f a a_1) True)
% 5.02/5.18 (Or (Eq True False)
% 5.02/5.18 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)
% 5.02/5.18 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False)))
% 5.02/5.21 Clause #18 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)
% 5.02/5.21 Clause #19 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)
% 5.02/5.21 Clause #20 (by superposition #[19, 16]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Or (Eq (big_f a a_1) True) (Eq True False))
% 5.02/5.21 Clause #21 (by superposition #[19, 18]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_g a a_1) True)
% 5.02/5.21 (Or (Eq True False)
% 5.02/5.21 (Eq
% 5.02/5.21 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)
% 5.02/5.21 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3))
% 5.02/5.21 False))
% 5.02/5.21 Clause #22 (by superposition #[10, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq True False)
% 5.02/5.21 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False)
% 5.02/5.21 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)))
% 5.02/5.21 Clause #23 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_f a a_1) True)
% 5.02/5.21 Clause #26 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) False)
% 5.02/5.21 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)
% 5.02/5.21 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True))
% 5.02/5.21 Clause #30 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_g a a_1) True)
% 5.02/5.21 (Eq
% 5.02/5.21 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)
% 5.02/5.21 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3))
% 5.02/5.21 False)
% 5.02/5.21 Clause #33 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)
% 5.02/5.21 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False))
% 5.02/5.21 Clause #34 (by superposition #[33, 23]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)
% 5.02/5.21 (Or (Eq False True) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)))
% 5.02/5.21 Clause #39 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False)
% 5.02/5.21 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True))
% 5.02/5.21 Clause #40 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)
% 5.02/5.21 (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True))
% 5.02/5.21 Clause #41 (by eliminate duplicate literals #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)
% 5.02/5.21 Clause #42 (by superposition #[41, 39]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)))
% 5.02/5.21 Clause #45 (by superposition #[41, 26]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq True False)
% 5.02/5.21 (Or
% 5.02/5.21 (Eq
% 5.02/5.21 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.21 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.21 False)
% 5.02/5.21 (Eq
% 5.02/5.21 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.21 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.21 True)))
% 5.02/5.21 Clause #46 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.21 Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Or (Eq (big_f a a_1) True)
% 5.02/5.21 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True))
% 5.02/5.23 Clause #47 (by eliminate duplicate literals #[46]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)
% 5.02/5.23 Clause #48 (by superposition #[47, 18]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Or (Eq True False)
% 5.02/5.23 (Eq
% 5.02/5.23 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 False))
% 5.02/5.23 Clause #55 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Eq
% 5.02/5.23 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 False)
% 5.02/5.23 Clause #57 (by superposition #[55, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Or (Eq False True)
% 5.02/5.23 (Eq
% 5.02/5.23 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 True))
% 5.02/5.23 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Eq
% 5.02/5.23 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 True)
% 5.02/5.23 Clause #70 (by clausification #[45]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Or
% 5.02/5.23 (Eq
% 5.02/5.23 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 False)
% 5.02/5.23 (Eq
% 5.02/5.23 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 True))
% 5.02/5.23 Clause #72 (by superposition #[70, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Or
% 5.02/5.23 (Eq
% 5.02/5.23 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 True)
% 5.02/5.23 (Or (Eq (big_f a a_1) True) (Eq False True)))
% 5.02/5.23 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Or
% 5.02/5.23 (Eq
% 5.02/5.23 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 True)
% 5.02/5.23 (Eq (big_f a a_1) True))
% 5.02/5.23 Clause #74 (by eliminate duplicate literals #[73]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) True)
% 5.02/5.23 (Eq
% 5.02/5.23 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)
% 5.02/5.23 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4))
% 5.02/5.23 True)
% 5.02/5.23 Clause #77 (by superposition #[74, 55]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (big_f a a_1) True) (Eq True False))
% 5.02/5.23 Clause #81 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True)
% 5.02/5.23 Clause #82 (by eliminate duplicate literals #[81]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True
% 5.02/5.23 Clause #83 (by backward demodulation #[82, 26]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.23 Or (Eq (big_f a a_1) False) (Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True))
% 5.02/5.23 Clause #108 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)
% 5.02/5.23 Clause #109 (by forward demodulation #[108, 82]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)
% 5.02/5.23 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True
% 5.02/5.24 Clause #111 (by superposition #[110, 30]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq True False)
% 5.02/5.24 Clause #113 (by clausification #[111]): ∀ (a a_1 : Iota), Eq (big_g a a_1) True
% 5.02/5.24 Clause #114 (by backward demodulation #[113, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)
% 5.02/5.24 Clause #116 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False
% 5.02/5.24 Clause #117 (by superposition #[116, 113]): Eq False True
% 5.02/5.24 Clause #120 (by clausification #[117]): False
% 5.02/5.24 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------