TSTP Solution File: LCL674+1.001 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL674+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 07:10:42 EDT 2023
% Result : Theorem 3.96s 4.19s
% Output : Proof 4.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL674+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n016.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 : Fri Aug 25 07:25:10 EDT 2023
% 0.14/0.35 % 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 (∀ (X : Iota), r1 X X) True
% 3.96/4.19 Clause #2 (by assumption #[]): Eq
% 3.96/4.19 (Not
% 3.96/4.19 (Not
% 3.96/4.19 (Exists fun X =>
% 3.96/4.19 Not
% 3.96/4.19 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 3.96/4.19 (Not
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (∀ (Y : Iota),
% 3.96/4.19 Or (Not (r1 X Y))
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (Or
% 3.96/4.19 (And
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X : Iota),
% 3.96/4.19 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.96/4.19 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.96/4.19 (Or
% 3.96/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.96/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.96/4.19 (Not (p101 Y))))
% 3.96/4.19 (Or
% 3.96/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.96/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.96/4.19 (Not (p100 Y))))
% 3.96/4.19 (Or (p101 Y) (Not (p102 Y))))
% 3.96/4.19 (Or (p100 Y) (Not (p101 Y)))))
% 3.96/4.19 (Not (p101 X)))
% 3.96/4.19 (p100 X)))))))
% 3.96/4.19 True
% 3.96/4.19 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True
% 3.96/4.19 Clause #11 (by clausification #[2]): Eq
% 3.96/4.19 (Not
% 3.96/4.19 (Exists fun X =>
% 3.96/4.19 Not
% 3.96/4.19 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 3.96/4.19 (Not
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (∀ (Y : Iota),
% 3.96/4.19 Or (Not (r1 X Y))
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (Or
% 3.96/4.19 (And
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X : Iota),
% 3.96/4.19 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 3.96/4.19 (Not (And (Not (p101 Y)) (p100 Y))))
% 3.96/4.19 (Or
% 3.96/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 3.96/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 3.96/4.19 (Not (p101 Y))))
% 3.96/4.19 (Or
% 3.96/4.19 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 3.96/4.19 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 3.96/4.19 (Not (p100 Y))))
% 3.96/4.19 (Or (p101 Y) (Not (p102 Y))))
% 3.96/4.19 (Or (p100 Y) (Not (p101 Y)))))
% 3.96/4.19 (Not (p101 X)))
% 3.96/4.19 (p100 X))))))
% 3.96/4.19 False
% 3.96/4.19 Clause #12 (by clausification #[11]): Eq
% 3.96/4.19 (Exists fun X =>
% 3.96/4.19 Not
% 3.96/4.19 (Or (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p2 Y)))
% 3.96/4.19 (Not
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (∀ (Y : Iota),
% 3.96/4.19 Or (Not (r1 X Y))
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (And
% 3.96/4.19 (Or
% 3.96/4.19 (And
% 3.96/4.19 (Not
% 3.96/4.19 (∀ (X : Iota),
% 3.96/4.19 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.22 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.22 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.22 (Or
% 4.05/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.22 (Not (p101 Y))))
% 4.05/4.22 (Or
% 4.05/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.22 (Not (p100 Y))))
% 4.05/4.22 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.22 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.22 (Not (p101 X)))
% 4.05/4.22 (p100 X)))))
% 4.05/4.22 True
% 4.05/4.22 Clause #13 (by clausification #[12]): ∀ (a : Iota),
% 4.05/4.22 Eq
% 4.05/4.22 (Not
% 4.05/4.22 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))
% 4.05/4.22 (Not
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (∀ (Y : Iota),
% 4.05/4.22 Or (Not (r1 (skS.0 0 a) Y))
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (Or
% 4.05/4.22 (And
% 4.05/4.22 (Not
% 4.05/4.22 (∀ (X : Iota),
% 4.05/4.22 Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.22 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.22 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.22 (Or
% 4.05/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.22 (Not (p101 Y))))
% 4.05/4.22 (Or
% 4.05/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.22 (Not (p100 Y))))
% 4.05/4.22 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.22 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.22 (Not (p101 (skS.0 0 a))))
% 4.05/4.22 (p100 (skS.0 0 a))))))
% 4.05/4.22 True
% 4.05/4.22 Clause #14 (by clausification #[13]): ∀ (a : Iota),
% 4.05/4.22 Eq
% 4.05/4.22 (Or (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)))
% 4.05/4.22 (Not
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (∀ (Y : Iota),
% 4.05/4.22 Or (Not (r1 (skS.0 0 a) Y))
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (And
% 4.05/4.22 (Or
% 4.05/4.22 (And
% 4.05/4.22 (Not
% 4.05/4.22 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.22 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.22 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.22 (Or
% 4.05/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.22 (Not (p101 Y))))
% 4.05/4.22 (Or
% 4.05/4.22 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.22 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.22 (Not (p100 Y))))
% 4.05/4.22 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.22 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.22 (Not (p101 (skS.0 0 a))))
% 4.05/4.22 (p100 (skS.0 0 a)))))
% 4.05/4.22 False
% 4.05/4.22 Clause #15 (by clausification #[14]): ∀ (a : Iota),
% 4.05/4.23 Eq
% 4.05/4.23 (Not
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (∀ (Y : Iota),
% 4.05/4.23 Or (Not (r1 (skS.0 0 a) Y))
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (Or
% 4.05/4.23 (And
% 4.05/4.23 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.23 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.23 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.23 (Or
% 4.05/4.23 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.23 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.23 (Not (p101 Y))))
% 4.05/4.23 (Or
% 4.05/4.23 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.23 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.23 (Not (p100 Y))))
% 4.05/4.23 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.23 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.23 (Not (p101 (skS.0 0 a))))
% 4.05/4.23 (p100 (skS.0 0 a))))
% 4.05/4.23 False
% 4.05/4.23 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y))) False
% 4.05/4.23 Clause #17 (by clausification #[15]): ∀ (a : Iota),
% 4.05/4.23 Eq
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (∀ (Y : Iota),
% 4.05/4.23 Or (Not (r1 (skS.0 0 a) Y))
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (Or
% 4.05/4.23 (And
% 4.05/4.23 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.23 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.23 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.23 (Or
% 4.05/4.23 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.23 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.23 (Not (p101 Y))))
% 4.05/4.23 (Or
% 4.05/4.23 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.23 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.23 (Not (p100 Y))))
% 4.05/4.23 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.23 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.23 (Not (p101 (skS.0 0 a))))
% 4.05/4.23 (p100 (skS.0 0 a)))
% 4.05/4.23 True
% 4.05/4.23 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (p100 (skS.0 0 a)) True
% 4.05/4.23 Clause #19 (by clausification #[17]): ∀ (a : Iota),
% 4.05/4.23 Eq
% 4.05/4.23 (And
% 4.05/4.23 (∀ (Y : Iota),
% 4.05/4.23 Or (Not (r1 (skS.0 0 a) Y))
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (And
% 4.05/4.23 (Or
% 4.05/4.23 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.23 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.23 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.23 (Or
% 4.05/4.23 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.23 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.23 (Not (p101 Y))))
% 4.05/4.23 (Or
% 4.05/4.23 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.23 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.23 (Not (p100 Y))))
% 4.05/4.23 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.23 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.23 (Not (p101 (skS.0 0 a))))
% 4.05/4.23 True
% 4.05/4.23 Clause #20 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (p2 Y)) True
% 4.05/4.26 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (p2 a_1)) True
% 4.05/4.26 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (p2 a_1) True)
% 4.05/4.26 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (p2 a) True) (Eq (r1 (skS.0 0 a_1) a) False)
% 4.05/4.26 Clause #25 (by clausification #[19]): ∀ (a : Iota), Eq (Not (p101 (skS.0 0 a))) True
% 4.05/4.26 Clause #26 (by clausification #[19]): ∀ (a : Iota),
% 4.05/4.26 Eq
% 4.05/4.26 (∀ (Y : Iota),
% 4.05/4.26 Or (Not (r1 (skS.0 0 a) Y))
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (Or
% 4.05/4.26 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.26 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.26 (Not (And (Not (p101 Y)) (p100 Y))))
% 4.05/4.26 (Or
% 4.05/4.26 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p2 X))) (Not (p101 X))) (p2 Y))
% 4.05/4.26 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p2 X)) (Not (p101 X))) (Not (p2 Y))))
% 4.05/4.26 (Not (p101 Y))))
% 4.05/4.26 (Or
% 4.05/4.26 (And (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (Not (p1 X))) (Not (p100 X))) (p1 Y))
% 4.05/4.26 (Or (∀ (X : Iota), Or (Or (Not (r1 Y X)) (p1 X)) (Not (p100 X))) (Not (p1 Y))))
% 4.05/4.26 (Not (p100 Y))))
% 4.05/4.26 (Or (p101 Y) (Not (p102 Y))))
% 4.05/4.26 (Or (p100 Y) (Not (p101 Y)))))
% 4.05/4.26 True
% 4.05/4.26 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (p101 (skS.0 0 a)) False
% 4.05/4.26 Clause #29 (by clausification #[26]): ∀ (a a_1 : Iota),
% 4.05/4.26 Eq
% 4.05/4.26 (Or (Not (r1 (skS.0 0 a) a_1))
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (Or
% 4.05/4.26 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.26 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.26 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.05/4.26 (Or
% 4.05/4.26 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.05/4.26 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.05/4.26 (Not (p101 a_1))))
% 4.05/4.26 (Or
% 4.05/4.26 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 4.05/4.26 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 4.05/4.26 (Not (p100 a_1))))
% 4.05/4.26 (Or (p101 a_1) (Not (p102 a_1))))
% 4.05/4.26 (Or (p100 a_1) (Not (p101 a_1)))))
% 4.05/4.26 True
% 4.05/4.26 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 4.05/4.26 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True)
% 4.05/4.26 (Eq
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (Or
% 4.05/4.26 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.26 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.05/4.26 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.05/4.26 (Or
% 4.05/4.26 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.05/4.26 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.05/4.26 (Not (p101 a_1))))
% 4.05/4.26 (Or
% 4.05/4.26 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 4.05/4.26 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 4.05/4.26 (Not (p100 a_1))))
% 4.05/4.26 (Or (p101 a_1) (Not (p102 a_1))))
% 4.05/4.26 (Or (p100 a_1) (Not (p101 a_1))))
% 4.05/4.26 True)
% 4.05/4.26 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 4.05/4.26 Or
% 4.05/4.26 (Eq
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (And
% 4.05/4.26 (Or
% 4.05/4.26 (And (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.05/4.26 (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.13/4.29 (Not (And (Not (p101 a)) (p100 a))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p2 X))) (Not (p101 X))) (p2 a))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p2 X)) (Not (p101 X))) (Not (p2 a))))
% 4.13/4.29 (Not (p101 a))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (Not (p1 X))) (Not (p100 X))) (p1 a))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a X)) (p1 X)) (Not (p100 X))) (Not (p1 a))))
% 4.13/4.29 (Not (p100 a))))
% 4.13/4.29 (Or (p101 a) (Not (p102 a))))
% 4.13/4.29 (Or (p100 a) (Not (p101 a))))
% 4.13/4.29 True)
% 4.13/4.29 (Eq (r1 (skS.0 0 a_1) a) False)
% 4.13/4.29 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota),
% 4.13/4.29 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.29 (Eq
% 4.13/4.29 (And
% 4.13/4.29 (And
% 4.13/4.29 (And
% 4.13/4.29 (Or
% 4.13/4.29 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.13/4.29 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.13/4.29 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.13/4.29 (Not (p101 a_1))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 4.13/4.29 (Not (p100 a_1))))
% 4.13/4.29 (Or (p101 a_1) (Not (p102 a_1))))
% 4.13/4.29 True)
% 4.13/4.29 Clause #40 (by clausification #[33]): ∀ (a a_1 : Iota),
% 4.13/4.29 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.29 (Eq
% 4.13/4.29 (And
% 4.13/4.29 (And
% 4.13/4.29 (Or
% 4.13/4.29 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.13/4.29 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.13/4.29 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.13/4.29 (Not (p101 a_1))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p1 X))) (Not (p100 X))) (p1 a_1))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p1 X)) (Not (p100 X))) (Not (p1 a_1))))
% 4.13/4.29 (Not (p100 a_1))))
% 4.13/4.29 True)
% 4.13/4.29 Clause #46 (by clausification #[40]): ∀ (a a_1 : Iota),
% 4.13/4.29 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.29 (Eq
% 4.13/4.29 (And
% 4.13/4.29 (Or
% 4.13/4.29 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.13/4.29 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.13/4.29 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.13/4.29 (Or
% 4.13/4.29 (And (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (Not (p2 X))) (Not (p101 X))) (p2 a_1))
% 4.13/4.29 (Or (∀ (X : Iota), Or (Or (Not (r1 a_1 X)) (p2 X)) (Not (p101 X))) (Not (p2 a_1))))
% 4.13/4.29 (Not (p101 a_1))))
% 4.13/4.29 True)
% 4.13/4.29 Clause #79 (by clausification #[46]): ∀ (a a_1 : Iota),
% 4.13/4.29 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.29 (Eq
% 4.13/4.29 (Or
% 4.13/4.29 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.13/4.29 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.13/4.29 (Not (And (Not (p101 a_1)) (p100 a_1))))
% 4.13/4.29 True)
% 4.13/4.29 Clause #102 (by clausification #[79]): ∀ (a a_1 : Iota),
% 4.13/4.29 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.29 (Or
% 4.13/4.29 (Eq
% 4.13/4.29 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))))
% 4.13/4.29 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (p2 X) (Not (p102 X))) (p101 X))))))
% 4.13/4.29 True)
% 4.13/4.29 (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True))
% 4.13/4.29 Clause #104 (by clausification #[102]): ∀ (a a_1 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (Not (And (Not (p101 a_1)) (p100 a_1))) True)
% 4.13/4.32 (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True))
% 4.13/4.32 Clause #124 (by clausification #[104]): ∀ (a a_1 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X))))) True)
% 4.13/4.32 (Eq (And (Not (p101 a_1)) (p100 a_1)) False))
% 4.13/4.32 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (And (Not (p101 a_1)) (p100 a_1)) False)
% 4.13/4.32 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False))
% 4.13/4.32 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (And (And (Not (p2 X)) (Not (p102 X))) (p101 X)))) False)
% 4.13/4.32 (Or (Eq (Not (p101 a_1)) False) (Eq (p100 a_1) False)))
% 4.13/4.32 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (Not (p101 a_1)) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False)
% 4.13/4.32 (Eq
% 4.13/4.32 (Not
% 4.13/4.32 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2)))
% 4.13/4.32 (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))))))
% 4.13/4.32 True)))
% 4.13/4.32 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False)
% 4.13/4.32 (Or
% 4.13/4.32 (Eq
% 4.13/4.32 (Not
% 4.13/4.32 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2)))
% 4.13/4.32 (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))))))
% 4.13/4.32 True)
% 4.13/4.32 (Eq (p101 a_1) True)))
% 4.13/4.32 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False)
% 4.13/4.32 (Or (Eq (p101 a_1) True)
% 4.13/4.32 (Eq
% 4.13/4.32 (Or (Not (r1 a_1 (skS.0 2 a_1 a_2)))
% 4.13/4.32 (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)))))
% 4.13/4.32 False)))
% 4.13/4.32 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False)
% 4.13/4.32 (Or (Eq (p101 a_1) True)
% 4.13/4.32 (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))))
% 4.13/4.32 False)))
% 4.13/4.32 Clause #131 (by clausification #[129]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (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)))
% 4.13/4.32 Clause #132 (by clausification #[130]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False)
% 4.13/4.32 (Or (Eq (p101 a_1) True)
% 4.13/4.32 (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)))
% 4.13/4.32 Clause #134 (by clausification #[132]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False)
% 4.13/4.32 (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)))
% 4.13/4.32 Clause #136 (by clausification #[131]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (r1 a_1 (skS.0 2 a_1 a_2)) True)))
% 4.13/4.32 Clause #137 (by superposition #[136, 3]): ∀ (a a_1 : Iota),
% 4.13/4.32 Or (Eq (p100 (skS.0 0 a)) False)
% 4.13/4.32 (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)))
% 4.13/4.32 Clause #181 (by clausification #[134]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (Not (p2 (skS.0 2 a_1 a_2))) True)))
% 4.13/4.32 Clause #185 (by clausification #[181]): ∀ (a a_1 a_2 : Iota),
% 4.13/4.32 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.13/4.32 (Or (Eq (p100 a_1) False) (Or (Eq (p101 a_1) True) (Eq (p2 (skS.0 2 a_1 a_2)) False)))
% 4.13/4.32 Clause #187 (by superposition #[185, 3]): ∀ (a a_1 : Iota),
% 4.13/4.32 Or (Eq (p100 (skS.0 0 a)) False)
% 4.13/4.32 (Or (Eq (p101 (skS.0 0 a)) True) (Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False) (Eq False True)))
% 4.13/4.33 Clause #193 (by clausification #[187]): ∀ (a a_1 : Iota),
% 4.13/4.33 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))
% 4.13/4.33 Clause #194 (by forward demodulation #[193, 18]): ∀ (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))
% 4.13/4.33 Clause #195 (by clausification #[194]): ∀ (a a_1 : Iota), Or (Eq (p101 (skS.0 0 a)) True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False)
% 4.13/4.33 Clause #196 (by forward demodulation #[195, 27]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False)
% 4.13/4.33 Clause #197 (by clausification #[196]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) False
% 4.13/4.33 Clause #202 (by clausification #[137]): ∀ (a a_1 : Iota),
% 4.13/4.33 Or (Eq (p100 (skS.0 0 a)) False)
% 4.13/4.33 (Or (Eq (p101 (skS.0 0 a)) True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True))
% 4.13/4.33 Clause #203 (by forward demodulation #[202, 18]): ∀ (a a_1 : Iota),
% 4.13/4.33 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))
% 4.13/4.33 Clause #204 (by clausification #[203]): ∀ (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)
% 4.13/4.33 Clause #205 (by forward demodulation #[204, 27]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True)
% 4.13/4.33 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 2 (skS.0 0 a) a_1)) True
% 4.13/4.33 Clause #207 (by superposition #[206, 23]): ∀ (a a_1 : Iota), Or (Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True) (Eq True False)
% 4.13/4.33 Clause #225 (by clausification #[207]): ∀ (a a_1 : Iota), Eq (p2 (skS.0 2 (skS.0 0 a) a_1)) True
% 4.13/4.33 Clause #226 (by superposition #[225, 197]): Eq True False
% 4.13/4.33 Clause #227 (by clausification #[226]): False
% 4.13/4.33 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------