TSTP Solution File: LCL656+1.001 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL656+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 07:10:30 EDT 2023
% Result : Theorem 3.93s 4.10s
% Output : Proof 4.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL656+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 20:31:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.93/4.10 SZS status Theorem for theBenchmark.p
% 3.93/4.10 SZS output start Proof for theBenchmark.p
% 3.93/4.10 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True
% 3.93/4.10 Clause #1 (by assumption #[]): Eq
% 3.93/4.10 (Not
% 3.93/4.10 (Not
% 3.93/4.10 (Exists fun X =>
% 3.93/4.10 Not
% 3.93/4.10 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 3.93/4.10 (Not
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (∀ (Y : Iota),
% 3.93/4.10 Or (Not (r1 X Y))
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (Or
% 3.93/4.10 (And
% 3.93/4.10 (Not
% 3.93/4.10 (∀ (X : Iota),
% 3.93/4.10 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.10 (Not
% 3.93/4.10 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.10 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.10 (Or
% 3.93/4.10 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.10 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.10 (Not (p101 Y))))
% 3.93/4.10 (Or
% 3.93/4.10 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.10 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.10 (Not (p100 Y))))
% 3.93/4.10 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.10 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.10 (Not (p101 X)))
% 3.93/4.10 (p100 X)))))))
% 3.93/4.10 True
% 3.93/4.10 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True
% 3.93/4.10 Clause #3 (by clausification #[1]): Eq
% 3.93/4.10 (Not
% 3.93/4.10 (Exists fun X =>
% 3.93/4.10 Not
% 3.93/4.10 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 3.93/4.10 (Not
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (∀ (Y : Iota),
% 3.93/4.10 Or (Not (r1 X Y))
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (Or
% 3.93/4.10 (And
% 3.93/4.10 (Not
% 3.93/4.10 (∀ (X : Iota),
% 3.93/4.10 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.10 (Not
% 3.93/4.10 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.10 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.10 (Or
% 3.93/4.10 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.10 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.10 (Not (p101 Y))))
% 3.93/4.10 (Or
% 3.93/4.10 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.10 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.10 (Not (p100 Y))))
% 3.93/4.10 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.10 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.10 (Not (p101 X)))
% 3.93/4.10 (p100 X))))))
% 3.93/4.10 False
% 3.93/4.10 Clause #4 (by clausification #[3]): Eq
% 3.93/4.10 (Exists fun X =>
% 3.93/4.10 Not
% 3.93/4.10 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 3.93/4.10 (Not
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (∀ (Y : Iota),
% 3.93/4.10 Or (Not (r1 X Y))
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (And
% 3.93/4.10 (Or
% 3.93/4.10 (And
% 3.93/4.10 (Not
% 3.93/4.10 (∀ (X : Iota),
% 3.93/4.10 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.12 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.12 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.12 (Or
% 3.93/4.12 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.12 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.12 (Not (p101 Y))))
% 3.93/4.12 (Or
% 3.93/4.12 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.12 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.12 (Not (p100 Y))))
% 3.93/4.12 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.12 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.12 (Not (p101 X)))
% 3.93/4.12 (p100 X)))))
% 3.93/4.12 True
% 3.93/4.12 Clause #5 (by clausification #[4]): ∀ (a : Iota),
% 3.93/4.12 Eq
% 3.93/4.12 (Not
% 3.93/4.12 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))
% 3.93/4.12 (Not
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (∀ (Y : Iota),
% 3.93/4.12 Or (Not (r1 (skS.0 0 a) Y))
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (Or
% 3.93/4.12 (And
% 3.93/4.12 (Not
% 3.93/4.12 (∀ (X : Iota),
% 3.93/4.12 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.12 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.12 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.12 (Or
% 3.93/4.12 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.12 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.12 (Not (p101 Y))))
% 3.93/4.12 (Or
% 3.93/4.12 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.12 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.12 (Not (p100 Y))))
% 3.93/4.12 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.12 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.12 (Not (p101 (skS.0 0 a))))
% 3.93/4.12 (p100 (skS.0 0 a))))))
% 3.93/4.12 True
% 3.93/4.12 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 3.93/4.12 Eq
% 3.93/4.12 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))
% 3.93/4.12 (Not
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (∀ (Y : Iota),
% 3.93/4.12 Or (Not (r1 (skS.0 0 a) Y))
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (And
% 3.93/4.12 (Or
% 3.93/4.12 (And
% 3.93/4.12 (Not
% 3.93/4.12 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.12 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.12 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.12 (Or
% 3.93/4.12 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.12 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.12 (Not (p101 Y))))
% 3.93/4.12 (Or
% 3.93/4.12 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.12 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.12 (Not (p100 Y))))
% 3.93/4.12 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.12 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.12 (Not (p101 (skS.0 0 a))))
% 3.93/4.12 (p100 (skS.0 0 a)))))
% 3.93/4.12 False
% 3.93/4.12 Clause #7 (by clausification #[6]): ∀ (a : Iota),
% 3.93/4.14 Eq
% 3.93/4.14 (Not
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (∀ (Y : Iota),
% 3.93/4.14 Or (Not (r1 (skS.0 0 a) Y))
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (Or
% 3.93/4.14 (And
% 3.93/4.14 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.14 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.14 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.14 (Or
% 3.93/4.14 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.14 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.14 (Not (p101 Y))))
% 3.93/4.14 (Or
% 3.93/4.14 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.14 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.14 (Not (p100 Y))))
% 3.93/4.14 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.14 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.14 (Not (p101 (skS.0 0 a))))
% 3.93/4.14 (p100 (skS.0 0 a))))
% 3.93/4.14 False
% 3.93/4.14 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) False
% 3.93/4.14 Clause #9 (by clausification #[7]): ∀ (a : Iota),
% 3.93/4.14 Eq
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (∀ (Y : Iota),
% 3.93/4.14 Or (Not (r1 (skS.0 0 a) Y))
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (Or
% 3.93/4.14 (And
% 3.93/4.14 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.14 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.14 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.14 (Or
% 3.93/4.14 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.14 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.14 (Not (p101 Y))))
% 3.93/4.14 (Or
% 3.93/4.14 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.14 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.14 (Not (p100 Y))))
% 3.93/4.14 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.14 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.14 (Not (p101 (skS.0 0 a))))
% 3.93/4.14 (p100 (skS.0 0 a)))
% 3.93/4.14 True
% 3.93/4.14 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (p100 (skS.0 0 a)) True
% 3.93/4.14 Clause #11 (by clausification #[9]): ∀ (a : Iota),
% 3.93/4.14 Eq
% 3.93/4.14 (And
% 3.93/4.14 (∀ (Y : Iota),
% 3.93/4.14 Or (Not (r1 (skS.0 0 a) Y))
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (And
% 3.93/4.14 (Or
% 3.93/4.14 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.14 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.14 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.14 (Or
% 3.93/4.14 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.14 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.14 (Not (p101 Y))))
% 3.93/4.14 (Or
% 3.93/4.14 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.14 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.14 (Not (p100 Y))))
% 3.93/4.14 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.14 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.14 (Not (p101 (skS.0 0 a))))
% 3.93/4.14 True
% 3.93/4.14 Clause #12 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) True
% 3.93/4.14 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p2 a_1)) True
% 3.93/4.17 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p2 a_1) True)
% 3.93/4.17 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (p2 a) True) (Eq (r1 (skS.0 0 a_1) a) False)
% 3.93/4.17 Clause #18 (by clausification #[11]): ∀ (a : Iota), Eq (Not (p101 (skS.0 0 a))) True
% 3.93/4.17 Clause #19 (by clausification #[11]): ∀ (a : Iota),
% 3.93/4.17 Eq
% 3.93/4.17 (∀ (Y : Iota),
% 3.93/4.17 Or (Not (r1 (skS.0 0 a) Y))
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (Or
% 3.93/4.17 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.17 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.17 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.93/4.17 (Or
% 3.93/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.93/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.93/4.17 (Not (p101 Y))))
% 3.93/4.17 (Or
% 3.93/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.93/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.93/4.17 (Not (p100 Y))))
% 3.93/4.17 (Or (p101 Y) (Not (p102 Y))))
% 3.93/4.17 (Or (p100 Y) (Not (p101 Y)))))
% 3.93/4.17 True
% 3.93/4.17 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False
% 3.93/4.17 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota),
% 3.93/4.17 Eq
% 3.93/4.17 (Or (Not (r1 (skS.0 0 a) a_1))
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (Or
% 3.93/4.17 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.17 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.17 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 3.93/4.17 (Or
% 3.93/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 3.93/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 3.93/4.17 (Not (p101 a_1))))
% 3.93/4.17 (Or
% 3.93/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 3.93/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 3.93/4.17 (Not (p100 a_1))))
% 3.93/4.17 (Or (p101 a_1) (Not (p102 a_1))))
% 3.93/4.17 (Or (p100 a_1) (Not (p101 a_1)))))
% 3.93/4.17 True
% 3.93/4.17 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota),
% 3.93/4.17 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True)
% 3.93/4.17 (Eq
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (Or
% 3.93/4.17 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.17 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.93/4.17 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 3.93/4.17 (Or
% 3.93/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 3.93/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 3.93/4.17 (Not (p101 a_1))))
% 3.93/4.17 (Or
% 3.93/4.17 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 3.93/4.17 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 3.93/4.17 (Not (p100 a_1))))
% 3.93/4.17 (Or (p101 a_1) (Not (p102 a_1))))
% 3.93/4.17 (Or (p100 a_1) (Not (p101 a_1))))
% 3.93/4.17 True)
% 3.93/4.17 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 3.93/4.17 Or
% 3.93/4.17 (Eq
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (And
% 3.93/4.17 (Or
% 3.93/4.17 (And (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.93/4.17 (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.03/4.19 (Not (And (Not (p101 a)) (p100 a))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p2 X))) (Not (p101 X))) (p2 a))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p2 X)) (Not (p101 X))) (Not (p2 a))))
% 4.03/4.19 (Not (p101 a))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p1 X))) (Not (p100 X))) (p1 a))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p1 X)) (Not (p100 X))) (Not (p1 a))))
% 4.03/4.19 (Not (p100 a))))
% 4.03/4.19 (Or (p101 a) (Not (p102 a))))
% 4.03/4.19 (Or (p100 a) (Not (p101 a))))
% 4.03/4.19 True)
% 4.03/4.19 (Eq (r1 (skS.0 0 a_1) a) False)
% 4.03/4.19 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota),
% 4.03/4.19 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.03/4.19 (Eq
% 4.03/4.19 (And
% 4.03/4.19 (And
% 4.03/4.19 (And
% 4.03/4.19 (Or
% 4.03/4.19 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.03/4.19 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.03/4.19 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.03/4.19 (Not (p101 a_1))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 4.03/4.19 (Not (p100 a_1))))
% 4.03/4.19 (Or (p101 a_1) (Not (p102 a_1))))
% 4.03/4.19 True)
% 4.03/4.19 Clause #32 (by clausification #[25]): ∀ (a a_1 : Iota),
% 4.03/4.19 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.03/4.19 (Eq
% 4.03/4.19 (And
% 4.03/4.19 (And
% 4.03/4.19 (Or
% 4.03/4.19 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.03/4.19 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.03/4.19 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.03/4.19 (Not (p101 a_1))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 4.03/4.19 (Not (p100 a_1))))
% 4.03/4.19 True)
% 4.03/4.19 Clause #38 (by clausification #[32]): ∀ (a a_1 : Iota),
% 4.03/4.19 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.03/4.19 (Eq
% 4.03/4.19 (And
% 4.03/4.19 (Or
% 4.03/4.19 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.03/4.19 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.03/4.19 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.03/4.19 (Or
% 4.03/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.03/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.03/4.19 (Not (p101 a_1))))
% 4.03/4.19 True)
% 4.03/4.19 Clause #61 (by clausification #[38]): ∀ (a a_1 : Iota),
% 4.03/4.19 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.03/4.19 (Eq
% 4.03/4.19 (Or
% 4.03/4.19 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.03/4.19 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.03/4.19 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.03/4.19 True)
% 4.03/4.19 Clause #93 (by clausification #[61]): ∀ (a a_1 : Iota),
% 4.03/4.19 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.03/4.19 (Or
% 4.03/4.19 (Eq
% 4.03/4.19 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.03/4.19 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.03/4.19 True)
% 4.03/4.19 (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True))
% 4.03/4.19 Clause #95 (by clausification #[93]): ∀ (a a_1 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True)
% 4.06/4.22 (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True))
% 4.06/4.22 Clause #121 (by clausification #[95]): ∀ (a a_1 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True)
% 4.06/4.22 (Eq (And (Not (p101 a_1)) (p100 a_1)) False))
% 4.06/4.22 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (And (Not (p101 a_1)) (p100 a_1)) False)
% 4.06/4.22 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False))
% 4.06/4.22 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False)
% 4.06/4.22 (Or (Eq (Not (p101 a_1)) False) (Eq (p100 a_1) False)))
% 4.06/4.22 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (Not (p101 a_1)) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False)
% 4.06/4.22 (Eq
% 4.06/4.22 (Not
% 4.06/4.22 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2)))
% 4.06/4.22 (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2))))))
% 4.06/4.22 True)))
% 4.06/4.22 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False)
% 4.06/4.22 (Or
% 4.06/4.22 (Eq
% 4.06/4.22 (Not
% 4.06/4.22 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2)))
% 4.06/4.22 (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2))))))
% 4.06/4.22 True)
% 4.06/4.22 (Eq (p101 a_1) True)))
% 4.06/4.22 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False)
% 4.06/4.22 (Or (Eq (p101 a_1) True)
% 4.06/4.22 (Eq
% 4.06/4.22 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2)))
% 4.06/4.22 (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2)))))
% 4.06/4.22 False)))
% 4.06/4.22 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False)
% 4.06/4.22 (Or (Eq (p101 a_1) True)
% 4.06/4.22 (Eq (Not (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2))))
% 4.06/4.22 False)))
% 4.06/4.22 Clause #128 (by clausification #[126]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (Not (r1 a_1 (skS.0 2 a_1 a_2))) False)))
% 4.06/4.22 Clause #129 (by clausification #[127]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False)
% 4.06/4.22 (Or (Eq (p101 a_1) True)
% 4.06/4.22 (Eq (And (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) (p101 (skS.0 2 a_1 a_2))) True)))
% 4.06/4.22 Clause #131 (by clausification #[129]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False)
% 4.06/4.22 (Or (Eq (p101 a_1) True) (Eq (And (Not (p2 (skS.0 2 a_1 a_2))) (Not (p102 (skS.0 2 a_1 a_2)))) True)))
% 4.06/4.22 Clause #133 (by clausification #[128]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (r1 a_1 (skS.0 2 a_1 a_2)) True)))
% 4.06/4.22 Clause #134 (by superposition #[133, 2]): ∀ (a a_1 : Iota),
% 4.06/4.22 Or (Eq (p100 (skS.0 0 a)) False)
% 4.06/4.22 (Or (Eq (p101 (skS.0 0 a)) True) (Or (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True) (Eq False True)))
% 4.06/4.22 Clause #151 (by clausification #[131]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (Not (p2 (skS.0 2 a_1 a_2))) True)))
% 4.06/4.22 Clause #172 (by clausification #[151]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.22 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.06/4.22 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (p2 (skS.0 2 a_1 a_2)) False)))
% 4.06/4.22 Clause #174 (by superposition #[172, 2]): ∀ (a a_1 : Iota),
% 4.06/4.22 Or (Eq (p100 (skS.0 0 a)) False)
% 4.06/4.22 (Or (Eq (p101 (skS.0 0 a)) True) (Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) (Eq False True)))
% 4.07/4.23 Clause #181 (by clausification #[174]): ∀ (a a_1 : Iota),
% 4.07/4.23 Or (Eq (p100 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False))
% 4.07/4.23 Clause #182 (by forward demodulation #[181, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False))
% 4.07/4.23 Clause #183 (by clausification #[182]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False)
% 4.07/4.23 Clause #184 (by forward demodulation #[183, 20]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False)
% 4.07/4.23 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False
% 4.07/4.23 Clause #186 (by clausification #[134]): ∀ (a a_1 : Iota),
% 4.07/4.23 Or (Eq (p100 (skS.0 0 a)) False)
% 4.07/4.23 (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True))
% 4.07/4.23 Clause #187 (by forward demodulation #[186, 10]): ∀ (a a_1 : Iota),
% 4.07/4.23 Or (Eq True False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True))
% 4.07/4.23 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True)
% 4.07/4.23 Clause #189 (by forward demodulation #[188, 20]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True)
% 4.07/4.23 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True
% 4.07/4.23 Clause #191 (by superposition #[190, 15]): ∀ (a a_1 : Iota), Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True) (Eq True False)
% 4.07/4.23 Clause #205 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True
% 4.07/4.23 Clause #206 (by superposition #[205, 185]): Eq True False
% 4.07/4.23 Clause #207 (by clausification #[206]): False
% 4.07/4.23 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------