TSTP Solution File: LCL636+1.001 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL636+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n029.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 07:10:17 EDT 2023
% Result : Theorem 4.11s 4.28s
% Output : Proof 4.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL636+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 07:38:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.11/4.28 SZS status Theorem for theBenchmark.p
% 4.11/4.28 SZS output start Proof for theBenchmark.p
% 4.11/4.28 Clause #0 (by assumption #[]): Eq
% 4.11/4.28 (Not
% 4.11/4.28 (Not
% 4.11/4.28 (Exists fun X =>
% 4.11/4.28 Not
% 4.11/4.28 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 4.11/4.28 (Not
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (∀ (Y : Iota),
% 4.11/4.28 Or (Not (r1 X Y))
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (Or
% 4.11/4.28 (And
% 4.11/4.28 (Not
% 4.11/4.28 (∀ (X : Iota),
% 4.11/4.28 Or (Not (r1 Y X))
% 4.11/4.28 (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.11/4.28 (Not
% 4.11/4.28 (∀ (X : Iota),
% 4.11/4.28 Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.11/4.28 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.11/4.28 (Or
% 4.11/4.28 (And
% 4.11/4.28 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X)))
% 4.11/4.28 (p2 Y))
% 4.11/4.28 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X)))
% 4.11/4.28 (Not (p2 Y))))
% 4.11/4.28 (Not (p101 Y))))
% 4.11/4.28 (Or
% 4.11/4.28 (And
% 4.11/4.28 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.11/4.28 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X)))
% 4.11/4.28 (Not (p1 Y))))
% 4.11/4.28 (Not (p100 Y))))
% 4.11/4.28 (Or (p101 Y) (Not (p102 Y))))
% 4.11/4.28 (Or (p100 Y) (Not (p101 Y)))))
% 4.11/4.28 (Or
% 4.11/4.28 (And
% 4.11/4.28 (Not
% 4.11/4.28 (∀ (Y : Iota),
% 4.11/4.28 Or (Not (r1 X Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.11/4.28 (Not
% 4.11/4.28 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.11/4.28 (Not (And (Not (p101 X)) (p100 X)))))
% 4.11/4.28 (Or
% 4.11/4.28 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 X))
% 4.11/4.28 (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 X))))
% 4.11/4.28 (Not (p101 X))))
% 4.11/4.28 (Or
% 4.11/4.28 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 X))
% 4.11/4.28 (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 X))))
% 4.11/4.28 (Not (p100 X))))
% 4.11/4.28 (Or (p101 X) (Not (p102 X))))
% 4.11/4.28 (Or (p100 X) (Not (p101 X))))
% 4.11/4.28 (Not (p101 X)))
% 4.11/4.28 (p100 X)))))))
% 4.11/4.28 True
% 4.11/4.28 Clause #1 (by clausification #[0]): Eq
% 4.11/4.28 (Not
% 4.11/4.28 (Exists fun X =>
% 4.11/4.28 Not
% 4.11/4.28 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 4.11/4.28 (Not
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (And
% 4.11/4.28 (∀ (Y : Iota),
% 4.11/4.28 Or (Not (r1 X Y))
% 4.11/4.28 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (Or
% 4.11/4.30 (And
% 4.11/4.30 (Not
% 4.11/4.30 (∀ (X : Iota),
% 4.11/4.30 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.11/4.30 (Not
% 4.11/4.30 (∀ (X : Iota),
% 4.11/4.30 Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.11/4.30 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.11/4.30 (Or
% 4.11/4.30 (And
% 4.11/4.30 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.11/4.30 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X)))
% 4.11/4.30 (Not (p2 Y))))
% 4.11/4.30 (Not (p101 Y))))
% 4.11/4.30 (Or
% 4.11/4.30 (And
% 4.11/4.30 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.11/4.30 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.11/4.30 (Not (p100 Y))))
% 4.11/4.30 (Or (p101 Y) (Not (p102 Y))))
% 4.11/4.30 (Or (p100 Y) (Not (p101 Y)))))
% 4.11/4.30 (Or
% 4.11/4.30 (And
% 4.11/4.30 (Not
% 4.11/4.30 (∀ (Y : Iota),
% 4.11/4.30 Or (Not (r1 X Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.11/4.30 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.11/4.30 (Not (And (Not (p101 X)) (p100 X)))))
% 4.11/4.30 (Or
% 4.11/4.30 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 X))
% 4.11/4.30 (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 X))))
% 4.11/4.30 (Not (p101 X))))
% 4.11/4.30 (Or
% 4.11/4.30 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 X))
% 4.11/4.30 (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 X))))
% 4.11/4.30 (Not (p100 X))))
% 4.11/4.30 (Or (p101 X) (Not (p102 X))))
% 4.11/4.30 (Or (p100 X) (Not (p101 X))))
% 4.11/4.30 (Not (p101 X)))
% 4.11/4.30 (p100 X))))))
% 4.11/4.30 False
% 4.11/4.30 Clause #2 (by clausification #[1]): Eq
% 4.11/4.30 (Exists fun X =>
% 4.11/4.30 Not
% 4.11/4.30 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 4.11/4.30 (Not
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (∀ (Y : Iota),
% 4.11/4.30 Or (Not (r1 X Y))
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (And
% 4.11/4.30 (Or
% 4.11/4.30 (And
% 4.11/4.30 (Not
% 4.11/4.30 (∀ (X : Iota),
% 4.11/4.30 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.11/4.30 (Not
% 4.11/4.30 (∀ (X : Iota),
% 4.11/4.30 Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.11/4.30 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.11/4.30 (Or
% 4.11/4.30 (And
% 4.11/4.30 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.11/4.32 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.11/4.32 (Not (p101 Y))))
% 4.11/4.32 (Or
% 4.11/4.32 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.11/4.32 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.11/4.32 (Not (p100 Y))))
% 4.11/4.32 (Or (p101 Y) (Not (p102 Y))))
% 4.11/4.32 (Or (p100 Y) (Not (p101 Y)))))
% 4.11/4.32 (Or
% 4.11/4.32 (And
% 4.11/4.32 (Not
% 4.11/4.32 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.11/4.32 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.11/4.32 (Not (And (Not (p101 X)) (p100 X)))))
% 4.11/4.32 (Or
% 4.11/4.32 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 X))
% 4.11/4.32 (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 X))))
% 4.11/4.32 (Not (p101 X))))
% 4.11/4.32 (Or
% 4.11/4.32 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 X))
% 4.11/4.32 (Or (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 X))))
% 4.11/4.32 (Not (p100 X))))
% 4.11/4.32 (Or (p101 X) (Not (p102 X))))
% 4.11/4.32 (Or (p100 X) (Not (p101 X))))
% 4.11/4.32 (Not (p101 X)))
% 4.11/4.32 (p100 X)))))
% 4.11/4.32 True
% 4.11/4.32 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 4.11/4.32 Eq
% 4.11/4.32 (Not
% 4.11/4.32 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))
% 4.11/4.32 (Not
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (∀ (Y : Iota),
% 4.11/4.32 Or (Not (r1 (skS.0 0 a) Y))
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (And
% 4.11/4.32 (Or
% 4.11/4.32 (And
% 4.11/4.32 (Not
% 4.11/4.32 (∀ (X : Iota),
% 4.11/4.32 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.11/4.32 (Not
% 4.11/4.32 (∀ (X : Iota),
% 4.11/4.32 Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.11/4.32 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.11/4.32 (Or
% 4.11/4.32 (And
% 4.11/4.32 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.11/4.32 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.11/4.32 (Not (p101 Y))))
% 4.11/4.32 (Or
% 4.11/4.32 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.11/4.32 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.11/4.32 (Not (p100 Y))))
% 4.11/4.32 (Or (p101 Y) (Not (p102 Y))))
% 4.11/4.32 (Or (p100 Y) (Not (p101 Y)))))
% 4.11/4.32 (Or
% 4.11/4.32 (And
% 4.11/4.32 (Not
% 4.11/4.32 (∀ (Y : Iota),
% 4.11/4.32 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.11/4.32 (Not
% 4.18/4.34 (∀ (Y : Iota),
% 4.18/4.34 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.18/4.34 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.18/4.34 (Or
% 4.18/4.34 (And
% 4.18/4.34 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y)))
% 4.18/4.34 (p2 (skS.0 0 a)))
% 4.18/4.34 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y)))
% 4.18/4.34 (Not (p2 (skS.0 0 a)))))
% 4.18/4.34 (Not (p101 (skS.0 0 a)))))
% 4.18/4.34 (Or
% 4.18/4.34 (And
% 4.18/4.34 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y)))
% 4.18/4.34 (p1 (skS.0 0 a)))
% 4.18/4.34 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y)))
% 4.18/4.34 (Not (p1 (skS.0 0 a)))))
% 4.18/4.34 (Not (p100 (skS.0 0 a)))))
% 4.18/4.34 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.18/4.34 (Or (p100 (skS.0 0 a)) (Not (p101 (skS.0 0 a)))))
% 4.18/4.34 (Not (p101 (skS.0 0 a))))
% 4.18/4.34 (p100 (skS.0 0 a))))))
% 4.18/4.34 True
% 4.18/4.34 Clause #4 (by clausification #[3]): ∀ (a : Iota),
% 4.18/4.34 Eq
% 4.18/4.34 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))
% 4.18/4.34 (Not
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (∀ (Y : Iota),
% 4.18/4.34 Or (Not (r1 (skS.0 0 a) Y))
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (And
% 4.18/4.34 (Or
% 4.18/4.34 (And
% 4.18/4.34 (Not
% 4.18/4.34 (∀ (X : Iota),
% 4.18/4.34 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.18/4.34 (Not
% 4.18/4.34 (∀ (X : Iota),
% 4.18/4.34 Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.18/4.34 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.18/4.34 (Or
% 4.18/4.34 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.18/4.34 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.18/4.34 (Not (p101 Y))))
% 4.18/4.34 (Or
% 4.18/4.34 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.18/4.34 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.18/4.34 (Not (p100 Y))))
% 4.18/4.34 (Or (p101 Y) (Not (p102 Y))))
% 4.18/4.34 (Or (p100 Y) (Not (p101 Y)))))
% 4.18/4.34 (Or
% 4.18/4.34 (And
% 4.18/4.34 (Not
% 4.18/4.34 (∀ (Y : Iota),
% 4.18/4.34 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.18/4.34 (Not
% 4.18/4.34 (∀ (Y : Iota),
% 4.18/4.34 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.18/4.34 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.18/4.34 (Or
% 4.18/4.34 (And
% 4.18/4.34 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y)))
% 4.18/4.34 (p2 (skS.0 0 a)))
% 4.18/4.34 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y)))
% 4.18/4.34 (Not (p2 (skS.0 0 a)))))
% 4.18/4.34 (Not (p101 (skS.0 0 a)))))
% 4.18/4.34 (Or
% 4.18/4.34 (And
% 4.21/4.38 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.38 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y)))
% 4.21/4.38 (Not (p1 (skS.0 0 a)))))
% 4.21/4.38 (Not (p100 (skS.0 0 a)))))
% 4.21/4.38 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.21/4.38 (Or (p100 (skS.0 0 a)) (Not (p101 (skS.0 0 a)))))
% 4.21/4.38 (Not (p101 (skS.0 0 a))))
% 4.21/4.38 (p100 (skS.0 0 a)))))
% 4.21/4.38 False
% 4.21/4.38 Clause #5 (by clausification #[4]): ∀ (a : Iota),
% 4.21/4.38 Eq
% 4.21/4.38 (Not
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (Or
% 4.21/4.38 (And
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (X : Iota),
% 4.21/4.38 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (X : Iota),
% 4.21/4.38 Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.38 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.38 (Or
% 4.21/4.38 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.38 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.38 (Not (p101 Y))))
% 4.21/4.38 (Or
% 4.21/4.38 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.38 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.38 (Not (p100 Y))))
% 4.21/4.38 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.38 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.38 (Or
% 4.21/4.38 (And
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.38 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.38 (Or
% 4.21/4.38 (And
% 4.21/4.38 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.38 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y)))
% 4.21/4.38 (Not (p2 (skS.0 0 a)))))
% 4.21/4.38 (Not (p101 (skS.0 0 a)))))
% 4.21/4.38 (Or
% 4.21/4.38 (And
% 4.21/4.38 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.38 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 (skS.0 0 a)))))
% 4.21/4.38 (Not (p100 (skS.0 0 a)))))
% 4.21/4.38 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.21/4.38 (Or (p100 (skS.0 0 a)) (Not (p101 (skS.0 0 a)))))
% 4.21/4.38 (Not (p101 (skS.0 0 a))))
% 4.21/4.38 (p100 (skS.0 0 a))))
% 4.21/4.38 False
% 4.21/4.38 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) False
% 4.21/4.38 Clause #7 (by clausification #[5]): ∀ (a : Iota),
% 4.21/4.38 Eq
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.38 (And
% 4.21/4.40 (Or
% 4.21/4.40 (And
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (X : Iota),
% 4.21/4.40 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.40 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.40 (Or
% 4.21/4.40 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.40 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.40 (Not (p101 Y))))
% 4.21/4.40 (Or
% 4.21/4.40 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.40 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.40 (Not (p100 Y))))
% 4.21/4.40 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.40 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.40 (Or
% 4.21/4.40 (And
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.40 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.40 (Or
% 4.21/4.40 (And
% 4.21/4.40 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.40 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 (skS.0 0 a)))))
% 4.21/4.40 (Not (p101 (skS.0 0 a)))))
% 4.21/4.40 (Or
% 4.21/4.40 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.40 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 (skS.0 0 a)))))
% 4.21/4.40 (Not (p100 (skS.0 0 a)))))
% 4.21/4.40 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.21/4.40 (Or (p100 (skS.0 0 a)) (Not (p101 (skS.0 0 a)))))
% 4.21/4.40 (Not (p101 (skS.0 0 a))))
% 4.21/4.40 (p100 (skS.0 0 a)))
% 4.21/4.40 True
% 4.21/4.40 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (p100 (skS.0 0 a)) True
% 4.21/4.40 Clause #9 (by clausification #[7]): ∀ (a : Iota),
% 4.21/4.40 Eq
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (And
% 4.21/4.40 (Or
% 4.21/4.40 (And
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (X : Iota),
% 4.21/4.40 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.40 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.40 (Or
% 4.21/4.40 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.40 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.40 (Not (p101 Y))))
% 4.21/4.40 (Or
% 4.21/4.40 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.40 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.40 (Not (p100 Y))))
% 4.21/4.40 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.42 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.42 (Or
% 4.21/4.42 (And
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.42 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.42 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.42 (Or
% 4.21/4.42 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.42 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 (skS.0 0 a)))))
% 4.21/4.42 (Not (p101 (skS.0 0 a)))))
% 4.21/4.42 (Or
% 4.21/4.42 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.42 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 (skS.0 0 a)))))
% 4.21/4.42 (Not (p100 (skS.0 0 a)))))
% 4.21/4.42 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.21/4.42 (Or (p100 (skS.0 0 a)) (Not (p101 (skS.0 0 a)))))
% 4.21/4.42 (Not (p101 (skS.0 0 a))))
% 4.21/4.42 True
% 4.21/4.42 Clause #10 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) True
% 4.21/4.42 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p2 a_1)) True
% 4.21/4.42 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p2 a_1) True)
% 4.21/4.42 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (p2 a) True) (Eq (r1 (skS.0 0 a_1) a) False)
% 4.21/4.42 Clause #14 (by clausification #[9]): ∀ (a : Iota), Eq (Not (p101 (skS.0 0 a))) True
% 4.21/4.42 Clause #15 (by clausification #[9]): ∀ (a : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (And
% 4.21/4.42 (Or
% 4.21/4.42 (And
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (X : Iota),
% 4.21/4.42 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.42 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.42 (Or
% 4.21/4.42 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.42 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.42 (Not (p101 Y))))
% 4.21/4.42 (Or
% 4.21/4.42 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.42 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.42 (Not (p100 Y))))
% 4.21/4.42 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.42 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.42 (Or
% 4.21/4.42 (And
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.42 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.42 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.42 (Or
% 4.21/4.42 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.42 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 (skS.0 0 a)))))
% 4.21/4.42 (Not (p101 (skS.0 0 a)))))
% 4.21/4.42 (Or
% 4.21/4.42 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.42 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 (skS.0 0 a)))))
% 4.21/4.45 (Not (p100 (skS.0 0 a)))))
% 4.21/4.45 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.21/4.45 (Or (p100 (skS.0 0 a)) (Not (p101 (skS.0 0 a)))))
% 4.21/4.45 True
% 4.21/4.45 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False
% 4.21/4.45 Clause #18 (by clausification #[15]): ∀ (a : Iota),
% 4.21/4.45 Eq
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (∀ (Y : Iota),
% 4.21/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (Or
% 4.21/4.45 (And
% 4.21/4.45 (Not
% 4.21/4.45 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.45 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.45 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.45 (Or
% 4.21/4.45 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.45 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.45 (Not (p101 Y))))
% 4.21/4.45 (Or
% 4.21/4.45 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.45 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.45 (Not (p100 Y))))
% 4.21/4.45 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.45 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.45 (Or
% 4.21/4.45 (And
% 4.21/4.45 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.45 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.45 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.45 (Or
% 4.21/4.45 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.45 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 (skS.0 0 a)))))
% 4.21/4.45 (Not (p101 (skS.0 0 a)))))
% 4.21/4.45 (Or
% 4.21/4.45 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.45 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 (skS.0 0 a)))))
% 4.21/4.45 (Not (p100 (skS.0 0 a)))))
% 4.21/4.45 (Or (p101 (skS.0 0 a)) (Not (p102 (skS.0 0 a)))))
% 4.21/4.45 True
% 4.21/4.45 Clause #23 (by clausification #[18]): ∀ (a : Iota),
% 4.21/4.45 Eq
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (∀ (Y : Iota),
% 4.21/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (And
% 4.21/4.45 (Or
% 4.21/4.45 (And
% 4.21/4.45 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.45 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.45 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.45 (Or
% 4.21/4.45 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.45 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.45 (Not (p101 Y))))
% 4.21/4.45 (Or
% 4.21/4.45 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.45 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.45 (Not (p100 Y))))
% 4.21/4.45 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.45 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.45 (Or
% 4.21/4.45 (And
% 4.21/4.45 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.45 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.48 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.48 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 (skS.0 0 a)))))
% 4.21/4.48 (Not (p101 (skS.0 0 a)))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p1 Y))) (Not (p100 Y))) (p1 (skS.0 0 a)))
% 4.21/4.48 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (p100 Y))) (Not (p1 (skS.0 0 a)))))
% 4.21/4.48 (Not (p100 (skS.0 0 a)))))
% 4.21/4.48 True
% 4.21/4.48 Clause #27 (by clausification #[23]): ∀ (a : Iota),
% 4.21/4.48 Eq
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (∀ (Y : Iota),
% 4.21/4.48 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (Or
% 4.21/4.48 (And
% 4.21/4.48 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.48 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.48 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.48 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.48 (Not (p101 Y))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.48 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.48 (Not (p100 Y))))
% 4.21/4.48 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.48 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.48 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.48 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (Not (p2 Y))) (Not (p101 Y))) (p2 (skS.0 0 a)))
% 4.21/4.48 (Or (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) (Not (p101 Y))) (Not (p2 (skS.0 0 a)))))
% 4.21/4.48 (Not (p101 (skS.0 0 a)))))
% 4.21/4.48 True
% 4.21/4.48 Clause #54 (by clausification #[27]): ∀ (a : Iota),
% 4.21/4.48 Eq
% 4.21/4.48 (And
% 4.21/4.48 (∀ (Y : Iota),
% 4.21/4.48 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (And
% 4.21/4.48 (Or
% 4.21/4.48 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.21/4.48 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.21/4.48 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.21/4.48 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.21/4.48 (Not (p101 Y))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.21/4.48 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.21/4.48 (Not (p100 Y))))
% 4.21/4.48 (Or (p101 Y) (Not (p102 Y))))
% 4.21/4.48 (Or (p100 Y) (Not (p101 Y)))))
% 4.21/4.48 (Or
% 4.21/4.48 (And (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.48 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.48 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))))))
% 4.21/4.48 True
% 4.21/4.48 Clause #76 (by clausification #[54]): ∀ (a : Iota),
% 4.21/4.48 Eq
% 4.21/4.48 (Or
% 4.21/4.48 (And (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.52 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.52 (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a)))))
% 4.21/4.52 True
% 4.21/4.52 Clause #78 (by clausification #[76]): ∀ (a : Iota),
% 4.21/4.52 Or
% 4.21/4.52 (Eq
% 4.21/4.52 (And (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))))
% 4.21/4.52 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (p2 Y) (Not (p102 Y))) (p101 Y))))))
% 4.21/4.52 True)
% 4.21/4.52 (Eq (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a)))) True)
% 4.21/4.52 Clause #80 (by clausification #[78]): ∀ (a : Iota),
% 4.21/4.52 Or (Eq (Not (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a)))) True)
% 4.21/4.52 (Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y))))) True)
% 4.21/4.52 Clause #118 (by clausification #[80]): ∀ (a : Iota),
% 4.21/4.52 Or (Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y))))) True)
% 4.21/4.52 (Eq (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))) False)
% 4.21/4.52 Clause #119 (by clausification #[118]): ∀ (a : Iota),
% 4.21/4.52 Or (Eq (And (Not (p101 (skS.0 0 a))) (p100 (skS.0 0 a))) False)
% 4.21/4.52 (Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))) False)
% 4.21/4.52 Clause #120 (by clausification #[119]): ∀ (a : Iota),
% 4.21/4.52 Or (Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (And (And (Not (p2 Y)) (Not (p102 Y))) (p101 Y)))) False)
% 4.21/4.52 (Or (Eq (Not (p101 (skS.0 0 a))) False) (Eq (p100 (skS.0 0 a)) False))
% 4.21/4.52 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (Not (p101 (skS.0 0 a))) False)
% 4.21/4.52 (Or (Eq (p100 (skS.0 0 a)) False)
% 4.21/4.52 (Eq
% 4.21/4.52 (Not
% 4.21/4.52 (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1)))
% 4.21/4.52 (Not (And (And (Not (p2 (skS.0 2 a a_1))) (Not (p102 (skS.0 2 a a_1)))) (p101 (skS.0 2 a a_1))))))
% 4.21/4.52 True))
% 4.21/4.52 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False)
% 4.21/4.52 (Or
% 4.21/4.52 (Eq
% 4.21/4.52 (Not
% 4.21/4.52 (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1)))
% 4.21/4.52 (Not (And (And (Not (p2 (skS.0 2 a a_1))) (Not (p102 (skS.0 2 a a_1)))) (p101 (skS.0 2 a a_1))))))
% 4.21/4.52 True)
% 4.21/4.52 (Eq (p101 (skS.0 0 a)) True))
% 4.21/4.52 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False)
% 4.21/4.52 (Or (Eq (p101 (skS.0 0 a)) True)
% 4.21/4.52 (Eq
% 4.21/4.52 (Or (Not (r1 (skS.0 0 a) (skS.0 2 a a_1)))
% 4.21/4.52 (Not (And (And (Not (p2 (skS.0 2 a a_1))) (Not (p102 (skS.0 2 a a_1)))) (p101 (skS.0 2 a a_1)))))
% 4.21/4.52 False))
% 4.21/4.52 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False)
% 4.21/4.52 (Or (Eq (p101 (skS.0 0 a)) True)
% 4.21/4.52 (Eq (Not (And (And (Not (p2 (skS.0 2 a a_1))) (Not (p102 (skS.0 2 a a_1)))) (p101 (skS.0 2 a a_1)))) False))
% 4.21/4.52 Clause #125 (by clausification #[123]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (Not (r1 (skS.0 0 a) (skS.0 2 a a_1))) False))
% 4.21/4.52 Clause #126 (by clausification #[124]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False)
% 4.21/4.52 (Or (Eq (p101 (skS.0 0 a)) True)
% 4.21/4.52 (Eq (And (And (Not (p2 (skS.0 2 a a_1))) (Not (p102 (skS.0 2 a a_1)))) (p101 (skS.0 2 a a_1))) True))
% 4.21/4.52 Clause #128 (by clausification #[126]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False)
% 4.21/4.52 (Or (Eq (p101 (skS.0 0 a)) True) (Eq (And (Not (p2 (skS.0 2 a a_1))) (Not (p102 (skS.0 2 a a_1)))) True))
% 4.21/4.52 Clause #133 (by clausification #[125]): ∀ (a a_1 : Iota),
% 4.21/4.52 Or (Eq (p100 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True))
% 4.21/4.52 Clause #134 (by forward demodulation #[133, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True))
% 4.21/4.52 Clause #135 (by clausification #[134]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True)
% 4.21/4.52 Clause #136 (by forward demodulation #[135, 16]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True)
% 4.21/4.52 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 a a_1)) True
% 4.21/4.53 Clause #138 (by superposition #[137, 13]): ∀ (a a_1 : Iota), Or (Eq (p2 (skS.0 2 a a_1)) True) (Eq True False)
% 4.21/4.53 Clause #140 (by clausification #[138]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 a a_1)) True
% 4.21/4.53 Clause #159 (by clausification #[128]): ∀ (a a_1 : Iota),
% 4.21/4.53 Or (Eq (p100 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (Not (p2 (skS.0 2 a a_1))) True))
% 4.21/4.53 Clause #165 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq (p100 (skS.0 0 a)) False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 a a_1)) False))
% 4.21/4.53 Clause #166 (by forward demodulation #[165, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 a a_1)) False))
% 4.21/4.53 Clause #167 (by clausification #[166]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 a a_1)) False)
% 4.21/4.53 Clause #168 (by forward demodulation #[167, 16]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (p2 (skS.0 2 a a_1)) False)
% 4.21/4.53 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 a a_1)) False
% 4.21/4.53 Clause #170 (by superposition #[169, 140]): Eq False True
% 4.21/4.53 Clause #171 (by clausification #[170]): False
% 4.21/4.53 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------