TSTP Solution File: SYN345+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN345+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 02:11:18 EDT 2023
% Result : Theorem 3.96s 4.19s
% Output : Proof 3.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN345+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 18:30:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.96/4.19 SZS status Theorem for theBenchmark.p
% 3.96/4.19 SZS output start Proof for theBenchmark.p
% 3.96/4.19 Clause #0 (by assumption #[]): Eq
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X1 X2 : Iota),
% 3.96/4.19 Exists fun Y1 =>
% 3.96/4.19 Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f X1 X2 Y1 → big_f Y2 Y1 Z) → big_f X1 X1 X2 → big_f X1 X2 X2) →
% 3.96/4.19 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f X1 X2 X2 → big_f X1 X1 X2) →
% 3.96/4.19 big_f Y1 Y2 Z → And (big_f X2 X2 Y1) (Iff (big_f X1 X1 X2) (big_f X1 X2 X2))))
% 3.96/4.19 True
% 3.96/4.19 Clause #1 (by clausification #[0]): Eq
% 3.96/4.19 (∀ (X1 X2 : Iota),
% 3.96/4.19 Exists fun Y1 =>
% 3.96/4.19 Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f X1 X2 Y1 → big_f Y2 Y1 Z) → big_f X1 X1 X2 → big_f X1 X2 X2) →
% 3.96/4.19 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f X1 X2 X2 → big_f X1 X1 X2) →
% 3.96/4.19 big_f Y1 Y2 Z → And (big_f X2 X2 Y1) (Iff (big_f X1 X1 X2) (big_f X1 X2 X2)))
% 3.96/4.19 False
% 3.96/4.19 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 3.96/4.19 Eq
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X2 : Iota),
% 3.96/4.19 Exists fun Y1 =>
% 3.96/4.19 Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f (skS.0 0 a) X2 Y1 → big_f Y2 Y1 Z) → big_f (skS.0 0 a) (skS.0 0 a) X2 → big_f (skS.0 0 a) X2 X2) →
% 3.96/4.19 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f (skS.0 0 a) X2 X2 → big_f (skS.0 0 a) (skS.0 0 a) X2) →
% 3.96/4.19 big_f Y1 Y2 Z →
% 3.96/4.19 And (big_f X2 X2 Y1) (Iff (big_f (skS.0 0 a) (skS.0 0 a) X2) (big_f (skS.0 0 a) X2 X2))))
% 3.96/4.19 True
% 3.96/4.19 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 3.96/4.19 Eq
% 3.96/4.19 (∀ (X2 : Iota),
% 3.96/4.19 Exists fun Y1 =>
% 3.96/4.19 Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f (skS.0 0 a) X2 Y1 → big_f Y2 Y1 Z) → big_f (skS.0 0 a) (skS.0 0 a) X2 → big_f (skS.0 0 a) X2 X2) →
% 3.96/4.19 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f (skS.0 0 a) X2 X2 → big_f (skS.0 0 a) (skS.0 0 a) X2) →
% 3.96/4.19 big_f Y1 Y2 Z → And (big_f X2 X2 Y1) (Iff (big_f (skS.0 0 a) (skS.0 0 a) X2) (big_f (skS.0 0 a) X2 X2)))
% 3.96/4.19 False
% 3.96/4.19 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota),
% 3.96/4.19 Eq
% 3.96/4.19 (Not
% 3.96/4.19 (Exists fun Y1 =>
% 3.96/4.19 Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f (skS.0 0 a) (skS.0 1 a a_1) Y1 → big_f Y2 Y1 Z) →
% 3.96/4.19 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) →
% 3.96/4.19 ((big_f (skS.0 1 a a_1) Y1 Y2 → big_f Y1 Z Z) →
% 3.96/4.19 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.19 big_f Y1 Y2 Z →
% 3.96/4.19 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) Y1)
% 3.96/4.19 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1))
% 3.96/4.19 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))))
% 3.96/4.19 True
% 3.96/4.19 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota),
% 3.96/4.19 Eq
% 3.96/4.19 (Exists fun Y1 =>
% 3.96/4.19 Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f (skS.0 0 a) (skS.0 1 a a_1) Y1 → big_f Y2 Y1 Z) →
% 3.96/4.19 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) →
% 3.96/4.19 ((big_f (skS.0 1 a a_1) Y1 Y2 → big_f Y1 Z Z) →
% 3.96/4.19 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.19 big_f Y1 Y2 Z →
% 3.96/4.19 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) Y1)
% 3.96/4.19 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1))
% 3.96/4.19 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))
% 3.96/4.19 False
% 3.96/4.19 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 3.96/4.19 Eq
% 3.96/4.19 (Exists fun Y2 =>
% 3.96/4.19 ∀ (Z : Iota),
% 3.96/4.19 ((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f Y2 a_2 Z) →
% 3.96/4.19 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) →
% 3.96/4.19 ((big_f (skS.0 1 a a_1) a_2 Y2 → big_f a_2 Z Z) →
% 3.96/4.19 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.19 big_f a_2 Y2 Z →
% 3.96/4.19 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2)
% 3.96/4.22 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1))
% 3.96/4.22 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))
% 3.96/4.22 False
% 3.96/4.22 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.22 Eq
% 3.96/4.22 (∀ (Z : Iota),
% 3.96/4.22 ((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 Z) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) →
% 3.96/4.22 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 Z Z) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.22 big_f a_2 a_3 Z →
% 3.96/4.22 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2)
% 3.96/4.22 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))
% 3.96/4.22 False
% 3.96/4.22 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Eq
% 3.96/4.22 (Not
% 3.96/4.22 (((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) →
% 3.96/4.22 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.22 big_f a_2 a_3 (skS.0 2 a a_1 a_2 a_3 a_4) →
% 3.96/4.22 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2)
% 3.96/4.22 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1))
% 3.96/4.22 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))))
% 3.96/4.22 True
% 3.96/4.22 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Eq
% 3.96/4.22 (((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) →
% 3.96/4.22 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.22 big_f a_2 a_3 (skS.0 2 a a_1 a_2 a_3 a_4) →
% 3.96/4.22 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2)
% 3.96/4.22 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))
% 3.96/4.22 False
% 3.96/4.22 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Eq
% 3.96/4.22 ((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))
% 3.96/4.22 True
% 3.96/4.22 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Eq
% 3.96/4.22 (((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.22 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.96/4.22 big_f a_2 a_3 (skS.0 2 a a_1 a_2 a_3 a_4) →
% 3.96/4.22 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2)
% 3.96/4.22 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))
% 3.96/4.22 False
% 3.96/4.22 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) False)
% 3.96/4.22 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.96/4.22 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.96/4.22 (Eq (big_f a_2 a_3 (skS.0 2 a a_1 a_3 a_2 a_4)) False)
% 3.96/4.22 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.22 Or (Eq (big_f a a_1 (skS.0 2 a_2 a_3 a_1 a a_4)) False)
% 3.96/4.22 (Or (Eq (big_f (skS.0 0 a_2) (skS.0 0 a_2) (skS.0 1 a_2 a_3)) False)
% 3.96/4.22 (Eq (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 1 a_2 a_3)) True))
% 3.96/4.22 Clause #17 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.25 Eq
% 3.96/4.25 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.96/4.25 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1))
% 3.96/4.25 True
% 3.96/4.25 Clause #18 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.25 Eq
% 3.96/4.25 (big_f a a_1 (skS.0 2 a_2 a_3 a a_1 a_4) →
% 3.96/4.25 And (big_f (skS.0 1 a_2 a_3) (skS.0 1 a_2 a_3) a)
% 3.96/4.25 (Iff (big_f (skS.0 0 a_2) (skS.0 0 a_2) (skS.0 1 a_2 a_3))
% 3.96/4.25 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 1 a_2 a_3))))
% 3.96/4.25 False
% 3.96/4.25 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.25 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.25 (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.25 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.25 (Eq (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) False)
% 3.96/4.25 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True))
% 3.96/4.25 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.96/4.25 Or (Eq (big_f a (skS.0 2 a_1 a_2 a a_3 a_4) (skS.0 2 a_1 a_2 a a_3 a_4)) False)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a_1) (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a_1) (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True))
% 3.96/4.25 Clause #24 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f a a_1 (skS.0 2 a_2 a_3 a a_1 a_4)) True
% 3.96/4.25 Clause #25 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 3.96/4.25 Eq
% 3.96/4.25 (And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2)
% 3.96/4.25 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))
% 3.96/4.25 False
% 3.96/4.25 Clause #26 (by superposition #[24, 16]): ∀ (a a_1 : Iota),
% 3.96/4.25 Or (Eq True False)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True))
% 3.96/4.25 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) False)
% 3.96/4.25 (Eq (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))) False)
% 3.96/4.25 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) False)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False))
% 3.96/4.25 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) False)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True))
% 3.96/4.25 Clause #30 (by superposition #[28, 24]): ∀ (a a_1 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) (Eq False True))
% 3.96/4.25 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)
% 3.96/4.25 Clause #32 (by clausification #[26]): ∀ (a a_1 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False)
% 3.96/4.25 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.96/4.25 Clause #33 (by superposition #[29, 24]): ∀ (a a_1 : Iota),
% 3.96/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq False True))
% 3.96/4.25 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.27 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.96/4.27 Clause #35 (by superposition #[34, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.27 (Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.27 (Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)))
% 3.96/4.27 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.27 (Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True))
% 3.96/4.27 Clause #37 (by eliminate duplicate literals #[36]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.27 Clause #38 (by superposition #[37, 31]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.27 (Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False))
% 3.96/4.27 Clause #39 (by superposition #[37, 32]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.27 (Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True))
% 3.96/4.27 Clause #41 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)
% 3.96/4.27 Clause #44 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.96/4.27 Clause #46 (by superposition #[44, 41]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Or (Eq (big_f (skS.0 1 a a_1) a_4 a_5) True) (Eq True False))
% 3.96/4.27 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 1 a a_1) a_4 a_5) True)
% 3.96/4.27 Clause #49 (by equality factoring #[47]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne True True) (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True)
% 3.96/4.27 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Or (Eq True False) (Eq True False))
% 3.96/4.27 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq True False)
% 3.96/4.27 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_f (skS.0 1 a a_1) a_2 a_3) True
% 3.96/4.27 Clause #54 (by superposition #[53, 23]): ∀ (a a_1 : Iota),
% 3.96/4.27 Or (Eq True False)
% 3.96/4.27 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)
% 3.96/4.27 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True))
% 3.96/4.27 Clause #57 (by clausification #[54]): ∀ (a a_1 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)
% 3.96/4.27 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.27 Clause #58 (by superposition #[57, 34]): ∀ (a a_1 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.27 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True))
% 3.96/4.27 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota),
% 3.96/4.27 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 3.96/4.27 Clause #60 (by eliminate duplicate literals #[59]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True
% 3.96/4.27 Clause #61 (by backward demodulation #[60, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)
% 3.96/4.27 Clause #62 (by backward demodulation #[60, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.96/4.27 Clause #65 (by clausification #[62]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True
% 3.96/4.27 Clause #68 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False
% 3.96/4.27 Clause #69 (by superposition #[68, 65]): Eq False True
% 3.96/4.27 Clause #70 (by clausification #[69]): False
% 3.96/4.27 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------