TSTP Solution File: LCL638+1.001 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL638+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 07:10:18 EDT 2023
% Result : Theorem 4.21s 4.38s
% Output : Proof 4.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL638+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 21:41:32 EDT 2023
% 0.14/0.34 % CPUTime :
% 4.21/4.38 SZS status Theorem for theBenchmark.p
% 4.21/4.38 SZS output start Proof for theBenchmark.p
% 4.21/4.38 Clause #0 (by assumption #[]): Eq
% 4.21/4.38 (Not
% 4.21/4.38 (Not
% 4.21/4.38 (Exists fun X =>
% 4.21/4.38 Not
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 4.21/4.38 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.21/4.38 (Not (p1 Y))))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 4.21/4.38 (And
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.21/4.38 (p1 Y))))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 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))
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.21/4.38 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 4.21/4.38 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.21/4.38 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.38 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))))
% 4.21/4.38 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))))))))
% 4.21/4.38 True
% 4.21/4.38 Clause #1 (by clausification #[0]): Eq
% 4.21/4.38 (Not
% 4.21/4.38 (Exists fun X =>
% 4.21/4.38 Not
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Or
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 4.21/4.38 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.21/4.38 (Not (p1 Y))))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 4.21/4.38 (And
% 4.21/4.38 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.21/4.38 (p1 Y))))))
% 4.21/4.38 (Not
% 4.21/4.38 (∀ (Y : Iota),
% 4.21/4.38 Or (Not (r1 X Y))
% 4.21/4.38 (Not
% 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))
% 4.21/4.39 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.21/4.39 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.21/4.39 (Not
% 4.21/4.39 (∀ (Y : Iota),
% 4.21/4.39 Or (Not (r1 X Y))
% 4.21/4.39 (Not
% 4.21/4.39 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.21/4.39 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.39 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))))
% 4.21/4.39 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.39 False
% 4.21/4.39 Clause #2 (by clausification #[1]): Eq
% 4.21/4.39 (Exists fun X =>
% 4.21/4.39 Not
% 4.21/4.39 (Or
% 4.21/4.39 (Or
% 4.21/4.39 (Or
% 4.21/4.39 (Or
% 4.21/4.39 (Or
% 4.21/4.39 (Not
% 4.21/4.39 (∀ (Y : Iota),
% 4.21/4.39 Or (Not (r1 X Y))
% 4.21/4.39 (Not
% 4.21/4.40 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.21/4.40 (Not (p1 Y))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 X Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And
% 4.21/4.40 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.21/4.40 (p1 Y))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 X Y))
% 4.21/4.40 (Not
% 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))
% 4.21/4.40 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.21/4.40 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 X Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.21/4.40 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.40 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))))
% 4.21/4.40 (∀ (Y : Iota), Or (Or (Not (r1 X Y)) (p1 Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))))))
% 4.21/4.40 True
% 4.21/4.40 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 4.21/4.40 Eq
% 4.21/4.40 (Not
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.21/4.40 (Not (p1 Y))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And
% 4.21/4.40 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.21/4.40 (p1 Y))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 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))
% 4.21/4.40 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.21/4.40 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.21/4.40 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.40 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))))
% 4.21/4.40 (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))))))
% 4.21/4.40 True
% 4.21/4.40 Clause #4 (by clausification #[3]): ∀ (a : Iota),
% 4.21/4.40 Eq
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Or
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.21/4.40 (Not (p1 Y))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.21/4.40 (p1 Y))))))
% 4.21/4.40 (Not
% 4.21/4.40 (∀ (Y : Iota),
% 4.21/4.40 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.40 (Not
% 4.21/4.40 (And
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (X : Iota),
% 4.21/4.42 Or (Not (r1 Y X))
% 4.21/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.21/4.42 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.42 (Not
% 4.21/4.42 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.21/4.42 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.42 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))))
% 4.21/4.42 (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))
% 4.21/4.42 False
% 4.21/4.42 Clause #5 (by clausification #[4]): ∀ (a : Iota),
% 4.21/4.42 Eq (∀ (Y : Iota), Or (Or (Not (r1 (skS.0 0 a) Y)) (p1 Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))) False
% 4.21/4.42 Clause #6 (by clausification #[4]): ∀ (a : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (Or
% 4.21/4.42 (Or
% 4.21/4.42 (Or
% 4.21/4.42 (Or
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.42 (Not
% 4.21/4.42 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.21/4.42 (Not (p1 Y))))))
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.42 (Not
% 4.21/4.42 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.21/4.42 (p1 Y))))))
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.42 (Not
% 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))
% 4.21/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.21/4.42 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (Y : Iota),
% 4.21/4.42 Or (Not (r1 (skS.0 0 a) Y))
% 4.21/4.42 (Not
% 4.21/4.42 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.21/4.42 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.21/4.42 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))))
% 4.21/4.42 False
% 4.21/4.42 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (Not
% 4.21/4.42 (Or (Or (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) (p1 (skS.0 1 a a_1)))
% 4.21/4.42 (Not (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X)))))
% 4.21/4.42 True
% 4.21/4.42 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (Or (Or (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) (p1 (skS.0 1 a a_1)))
% 4.21/4.42 (Not (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X))))
% 4.21/4.42 False
% 4.21/4.42 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Not (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X))) False
% 4.21/4.42 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) (p1 (skS.0 1 a a_1))) False
% 4.21/4.42 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (X : Iota), Or (Not (r1 (skS.0 1 a a_1) X)) (p1 X)) True
% 4.21/4.42 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 1 a a_1) a_2)) (p1 a_2)) True
% 4.21/4.42 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r1 (skS.0 1 a a_1) a_2)) True) (Eq (p1 a_2) True)
% 4.21/4.42 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 a) True) (Eq (r1 (skS.0 1 a_1 a_2) a) False)
% 4.21/4.42 Clause #15 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (p1 (skS.0 1 a a_1)) False
% 4.21/4.42 Clause #16 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a) (skS.0 1 a a_1))) False
% 4.21/4.42 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 1 a a_1)) True
% 4.21/4.42 Clause #18 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False)))) False
% 4.30/4.45 Clause #19 (by clausification #[6]): ∀ (a : Iota),
% 4.30/4.45 Eq
% 4.30/4.45 (Or
% 4.30/4.45 (Or
% 4.30/4.45 (Or
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.30/4.45 (Not (p1 Y))))))
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.30/4.45 (p1 Y))))))
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (X : Iota),
% 4.30/4.45 Or (Not (r1 Y X))
% 4.30/4.45 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.30/4.45 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.45 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))))
% 4.30/4.45 False
% 4.30/4.45 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) False))) True
% 4.30/4.45 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a) a_1)) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) False))) True
% 4.30/4.45 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 (skS.0 0 a) a_1)) True) (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) False)) True)
% 4.30/4.45 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a X)) False)) True) (Eq (r1 (skS.0 0 a_1) a) False)
% 4.30/4.45 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) False) False)
% 4.30/4.45 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) False)) True)
% 4.30/4.45 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Or (Not (r1 a_1 (skS.0 2 a_1 a_2))) False) False)
% 4.30/4.45 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (r1 a_1 (skS.0 2 a_1 a_2))) False)
% 4.30/4.45 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (r1 a_1 (skS.0 2 a_1 a_2)) True)
% 4.30/4.45 Clause #30 (by superposition #[29, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) a_2)) True) (Eq False True)
% 4.30/4.45 Clause #31 (by clausification #[19]): ∀ (a : Iota),
% 4.30/4.45 Eq
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.45 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X))))))
% 4.30/4.45 False
% 4.30/4.45 Clause #32 (by clausification #[19]): ∀ (a : Iota),
% 4.30/4.45 Eq
% 4.30/4.45 (Or
% 4.30/4.45 (Or
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.30/4.45 (Not (p1 Y))))))
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.30/4.45 (p1 Y))))))
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (Y : Iota),
% 4.30/4.45 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.45 (Not
% 4.30/4.45 (And
% 4.30/4.45 (Not
% 4.30/4.45 (∀ (X : Iota),
% 4.30/4.45 Or (Not (r1 Y X))
% 4.30/4.45 (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (p1 X)))))))
% 4.30/4.47 (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))))))
% 4.30/4.47 False
% 4.30/4.47 Clause #33 (by clausification #[31]): ∀ (a : Iota),
% 4.30/4.47 Eq
% 4.30/4.47 (∀ (Y : Iota),
% 4.30/4.47 Or (Not (r1 (skS.0 0 a) Y))
% 4.30/4.47 (Not
% 4.30/4.47 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.47 (∀ (X : Iota), Or (Not (r1 Y X)) (p1 X)))))
% 4.30/4.47 True
% 4.30/4.47 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota),
% 4.30/4.47 Eq
% 4.30/4.47 (Or (Not (r1 (skS.0 0 a) a_1))
% 4.30/4.47 (Not
% 4.30/4.47 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.47 (∀ (X : Iota), Or (Not (r1 a_1 X)) (p1 X)))))
% 4.30/4.47 True
% 4.30/4.47 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 4.30/4.47 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True)
% 4.30/4.47 (Eq
% 4.30/4.47 (Not
% 4.30/4.47 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.47 (∀ (X : Iota), Or (Not (r1 a_1 X)) (p1 X))))
% 4.30/4.47 True)
% 4.30/4.47 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 4.30/4.47 Or
% 4.30/4.47 (Eq
% 4.30/4.47 (Not
% 4.30/4.47 (And (Not (∀ (X : Iota), Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.47 (∀ (X : Iota), Or (Not (r1 a X)) (p1 X))))
% 4.30/4.47 True)
% 4.30/4.47 (Eq (r1 (skS.0 0 a_1) a) False)
% 4.30/4.47 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Eq
% 4.30/4.47 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 4.30/4.47 (∀ (X : Iota), Or (Not (r1 a_1 X)) (p1 X)))
% 4.30/4.47 False)
% 4.30/4.47 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) False)
% 4.30/4.47 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (p1 X)) False))
% 4.30/4.47 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (p1 X)) False)
% 4.30/4.47 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) True))
% 4.30/4.47 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) True)
% 4.30/4.47 (Eq (Not (Or (Not (r1 a_1 (skS.0 3 a_1 a_2))) (p1 (skS.0 3 a_1 a_2)))) True))
% 4.30/4.47 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (Not (Or (Not (r1 a_1 (skS.0 3 a_1 a_2))) (p1 (skS.0 3 a_1 a_2)))) True)
% 4.30/4.47 (Eq (Or (Not (r1 a_1 a_3)) (∀ (Y : Iota), Or (Not (r1 a_3 Y)) (p1 Y))) True))
% 4.30/4.47 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (Or (Not (r1 a_1 a_2)) (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y))) True)
% 4.30/4.47 (Eq (Or (Not (r1 a_1 (skS.0 3 a_1 a_3))) (p1 (skS.0 3 a_1 a_3))) False))
% 4.30/4.47 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (Or (Not (r1 a_1 (skS.0 3 a_1 a_2))) (p1 (skS.0 3 a_1 a_2))) False)
% 4.30/4.47 (Or (Eq (Not (r1 a_1 a_3)) True) (Eq (∀ (Y : Iota), Or (Not (r1 a_3 Y)) (p1 Y)) True)))
% 4.30/4.47 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (Not (r1 a_1 a_2)) True)
% 4.30/4.47 (Or (Eq (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y)) True) (Eq (p1 (skS.0 3 a_1 a_3)) False)))
% 4.30/4.47 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (Not (r1 a_1 a_2)) True)
% 4.30/4.47 (Or (Eq (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y)) True) (Eq (Not (r1 a_1 (skS.0 3 a_1 a_3))) False)))
% 4.30/4.47 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y)) True)
% 4.30/4.47 (Or (Eq (p1 (skS.0 3 a_1 a_3)) False) (Eq (r1 a_1 a_2) False)))
% 4.30/4.47 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.30/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.30/4.47 (Or (Eq (p1 (skS.0 3 a_1 a_2)) False) (Or (Eq (r1 a_1 a_3) False) (Eq (Or (Not (r1 a_3 a_4)) (p1 a_4)) True)))
% 4.34/4.50 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (p1 (skS.0 3 a_1 a_2)) False)
% 4.34/4.50 (Or (Eq (r1 a_1 a_3) False) (Or (Eq (Not (r1 a_3 a_4)) True) (Eq (p1 a_4) True))))
% 4.34/4.50 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (p1 (skS.0 3 a_1 a_2)) False) (Or (Eq (r1 a_1 a_3) False) (Or (Eq (p1 a_4) True) (Eq (r1 a_3 a_4) False))))
% 4.34/4.50 Clause #50 (by superposition #[49, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (p1 (skS.0 3 (skS.0 1 a a_1) a_2)) False)
% 4.34/4.50 (Or (Eq (r1 (skS.0 1 a a_1) a_3) False) (Or (Eq (p1 a_4) True) (Or (Eq (r1 a_3 a_4) False) (Eq False True))))
% 4.34/4.50 Clause #51 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) a_2)) True
% 4.34/4.50 Clause #54 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y)) True)
% 4.34/4.50 (Or (Eq (Not (r1 a_1 (skS.0 3 a_1 a_3))) False) (Eq (r1 a_1 a_2) False)))
% 4.34/4.50 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (Not (r1 a_1 (skS.0 3 a_1 a_2))) False)
% 4.34/4.50 (Or (Eq (r1 a_1 a_3) False) (Eq (Or (Not (r1 a_3 a_4)) (p1 a_4)) True)))
% 4.34/4.50 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (r1 a_1 a_2) False) (Or (Eq (Or (Not (r1 a_2 a_3)) (p1 a_3)) True) (Eq (r1 a_1 (skS.0 3 a_1 a_4)) True)))
% 4.34/4.50 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (r1 a_1 a_2) False)
% 4.34/4.50 (Or (Eq (r1 a_1 (skS.0 3 a_1 a_3)) True) (Or (Eq (Not (r1 a_2 a_4)) True) (Eq (p1 a_4) True))))
% 4.34/4.50 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.50 (Or (Eq (r1 a_1 a_2) False)
% 4.34/4.50 (Or (Eq (r1 a_1 (skS.0 3 a_1 a_3)) True) (Or (Eq (p1 a_4) True) (Eq (r1 a_2 a_4) False))))
% 4.34/4.50 Clause #59 (by superposition #[58, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 1 a a_1) a_2) False)
% 4.34/4.50 (Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_3)) True)
% 4.34/4.50 (Or (Eq (p1 a_4) True) (Or (Eq (r1 a_2 a_4) False) (Eq False True))))
% 4.34/4.50 Clause #60 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (p1 (skS.0 3 (skS.0 1 a a_1) a_2)) False)
% 4.34/4.50 (Or (Eq (r1 (skS.0 1 a a_1) a_3) False) (Or (Eq (p1 a_4) True) (Eq (r1 a_3 a_4) False)))
% 4.34/4.50 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 1 a a_1) a_2) False)
% 4.34/4.50 (Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_3)) True) (Or (Eq (p1 a_4) True) (Eq (r1 a_2 a_4) False)))
% 4.34/4.50 Clause #62 (by superposition #[61, 51]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_2)) True)
% 4.34/4.50 (Or (Eq (p1 a_3) True) (Or (Eq (r1 (skS.0 2 (skS.0 1 a a_1) a_4) a_3) False) (Eq False True)))
% 4.34/4.50 Clause #64 (by clausification #[32]): ∀ (a : Iota),
% 4.34/4.50 Eq
% 4.34/4.50 (Or
% 4.34/4.50 (Not
% 4.34/4.50 (∀ (Y : Iota),
% 4.34/4.50 Or (Not (r1 (skS.0 0 a) Y))
% 4.34/4.50 (Not
% 4.34/4.50 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 4.34/4.50 (Not (p1 Y))))))
% 4.34/4.50 (Not
% 4.34/4.50 (∀ (Y : Iota),
% 4.34/4.50 Or (Not (r1 (skS.0 0 a) Y))
% 4.34/4.50 (Not
% 4.34/4.50 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (Not (p1 Y))))))
% 4.34/4.50 (p1 Y))))))
% 4.34/4.50 False
% 4.34/4.50 Clause #110 (by clausification #[62]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.50 Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_2)) True)
% 4.34/4.50 (Or (Eq (p1 a_3) True) (Eq (r1 (skS.0 2 (skS.0 1 a a_1) a_4) a_3) False))
% 4.34/4.50 Clause #114 (by clausification #[64]): ∀ (a : Iota),
% 4.34/4.50 Eq
% 4.34/4.50 (Not
% 4.34/4.50 (∀ (Y : Iota),
% 4.34/4.50 Or (Not (r1 (skS.0 0 a) Y))
% 4.34/4.50 (Not
% 4.34/4.50 (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) (Not (p1 Y))))))
% 4.34/4.50 False
% 4.34/4.50 Clause #138 (by clausification #[114]): ∀ (a : Iota),
% 4.34/4.50 Eq
% 4.34/4.50 (∀ (Y : Iota),
% 4.34/4.53 Or (Not (r1 (skS.0 0 a) Y))
% 4.34/4.53 (Not (And (Not (∀ (X : Iota), Or (Not (r1 Y X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) (Not (p1 Y)))))
% 4.34/4.53 True
% 4.34/4.53 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota),
% 4.34/4.53 Eq
% 4.34/4.53 (Or (Not (r1 (skS.0 0 a) a_1))
% 4.34/4.53 (Not
% 4.34/4.53 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) (Not (p1 a_1)))))
% 4.34/4.53 True
% 4.34/4.53 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota),
% 4.34/4.53 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True)
% 4.34/4.53 (Eq
% 4.34/4.53 (Not
% 4.34/4.53 (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) (Not (p1 a_1))))
% 4.34/4.53 True)
% 4.34/4.53 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota),
% 4.34/4.53 Or
% 4.34/4.53 (Eq (Not (And (Not (∀ (X : Iota), Or (Not (r1 a X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) (Not (p1 a))))
% 4.34/4.53 True)
% 4.34/4.53 (Eq (r1 (skS.0 0 a_1) a) False)
% 4.34/4.53 Clause #142 (by clausification #[141]): ∀ (a a_1 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Eq (And (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) (Not (p1 a_1)))
% 4.34/4.53 False)
% 4.34/4.53 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))) False)
% 4.34/4.53 (Eq (Not (p1 a_1)) False))
% 4.34/4.53 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (Not (p1 a_1)) False)
% 4.34/4.53 (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) True))
% 4.34/4.53 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))) True) (Eq (p1 a_1) True))
% 4.34/4.53 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Eq (Or (Not (r1 a_1 a_2)) (Not (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y)))) True))
% 4.34/4.53 Clause #147 (by clausification #[146]): ∀ (a a_1 a_2 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Or (Eq (Not (r1 a_1 a_2)) True) (Eq (Not (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y))) True)))
% 4.34/4.53 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Or (Eq (Not (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y))) True) (Eq (r1 a_1 a_2) False)))
% 4.34/4.53 Clause #149 (by clausification #[148]): ∀ (a a_1 a_2 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Or (Eq (r1 a_1 a_2) False) (Eq (∀ (Y : Iota), Or (Not (r1 a_2 Y)) (p1 Y)) False)))
% 4.34/4.53 Clause #150 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True)
% 4.34/4.53 (Or (Eq (r1 a_1 a_2) False) (Eq (Not (Or (Not (r1 a_2 (skS.0 8 a_2 a_3))) (p1 (skS.0 8 a_2 a_3)))) True)))
% 4.34/4.53 Clause #151 (by clausification #[150]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True)
% 4.34/4.53 (Or (Eq (r1 a_1 a_2) False) (Eq (Or (Not (r1 a_2 (skS.0 8 a_2 a_3))) (p1 (skS.0 8 a_2 a_3))) False)))
% 4.34/4.53 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Or (Eq (r1 a_1 a_2) False) (Eq (p1 (skS.0 8 a_2 a_3)) False)))
% 4.34/4.53 Clause #153 (by clausification #[151]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Or (Eq (r1 a_1 a_2) False) (Eq (Not (r1 a_2 (skS.0 8 a_2 a_3))) False)))
% 4.34/4.53 Clause #154 (by superposition #[152, 17]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (p1 (skS.0 1 a a_1)) True)
% 4.34/4.53 (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Or (Eq (p1 (skS.0 8 a_2 a_3)) False) (Eq False True)))
% 4.34/4.53 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.34/4.53 (Or (Eq (p1 a_1) True) (Or (Eq (r1 a_1 a_2) False) (Eq (r1 a_2 (skS.0 8 a_2 a_3)) True)))
% 4.34/4.53 Clause #156 (by superposition #[155, 17]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.53 Or (Eq (p1 (skS.0 1 a a_1)) True)
% 4.34/4.55 (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Or (Eq (r1 a_2 (skS.0 8 a_2 a_3)) True) (Eq False True)))
% 4.34/4.55 Clause #159 (by clausification #[154]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.55 Or (Eq (p1 (skS.0 1 a a_1)) True) (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Eq (p1 (skS.0 8 a_2 a_3)) False))
% 4.34/4.55 Clause #160 (by forward demodulation #[159, 15]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq False True) (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Eq (p1 (skS.0 8 a_2 a_3)) False))
% 4.34/4.55 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Eq (p1 (skS.0 8 a_2 a_3)) False)
% 4.34/4.55 Clause #162 (by superposition #[161, 51]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p1 (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_2) a_3)) False) (Eq False True)
% 4.34/4.55 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota), Eq (p1 (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_2) a_3)) False
% 4.34/4.55 Clause #164 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.55 Or (Eq (p1 (skS.0 1 a a_1)) True) (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Eq (r1 a_2 (skS.0 8 a_2 a_3)) True))
% 4.34/4.55 Clause #165 (by forward demodulation #[164, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.55 Or (Eq False True) (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Eq (r1 a_2 (skS.0 8 a_2 a_3)) True))
% 4.34/4.55 Clause #166 (by clausification #[165]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Eq (r1 a_2 (skS.0 8 a_2 a_3)) True)
% 4.34/4.55 Clause #167 (by superposition #[166, 51]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.55 Or (Eq (r1 (skS.0 2 (skS.0 1 a a_1) a_2) (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_2) a_3)) True) (Eq False True)
% 4.34/4.55 Clause #168 (by clausification #[167]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r1 (skS.0 2 (skS.0 1 a a_1) a_2) (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_2) a_3)) True
% 4.34/4.55 Clause #169 (by superposition #[168, 110]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.55 Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_2)) True)
% 4.34/4.55 (Or (Eq (p1 (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_3) a_4)) True) (Eq True False))
% 4.34/4.55 Clause #174 (by clausification #[169]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.34/4.55 Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_2)) True)
% 4.34/4.55 (Eq (p1 (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_3) a_4)) True)
% 4.34/4.55 Clause #182 (by superposition #[174, 163]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_2)) True) (Eq True False)
% 4.34/4.55 Clause #183 (by clausification #[182]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) a_2)) True
% 4.34/4.55 Clause #184 (by superposition #[183, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 (skS.0 3 (skS.0 1 a a_1) a_2)) True) (Eq True False)
% 4.34/4.55 Clause #190 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Eq (p1 (skS.0 3 (skS.0 1 a a_1) a_2)) True
% 4.34/4.55 Clause #191 (by superposition #[190, 60]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.34/4.55 Or (Eq True False) (Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Or (Eq (p1 a_3) True) (Eq (r1 a_2 a_3) False)))
% 4.34/4.55 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 1 a a_1) a_2) False) (Or (Eq (p1 a_3) True) (Eq (r1 a_2 a_3) False))
% 4.34/4.55 Clause #193 (by superposition #[192, 51]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p1 a) True) (Or (Eq (r1 (skS.0 2 (skS.0 1 a_1 a_2) a_3) a) False) (Eq False True))
% 4.34/4.55 Clause #199 (by clausification #[193]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p1 a) True) (Eq (r1 (skS.0 2 (skS.0 1 a_1 a_2) a_3) a) False)
% 4.34/4.55 Clause #200 (by superposition #[199, 168]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p1 (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_2) a_3)) True) (Eq False True)
% 4.34/4.55 Clause #202 (by clausification #[200]): ∀ (a a_1 a_2 a_3 : Iota), Eq (p1 (skS.0 8 (skS.0 2 (skS.0 1 a a_1) a_2) a_3)) True
% 4.34/4.55 Clause #203 (by superposition #[202, 163]): Eq True False
% 4.34/4.55 Clause #204 (by clausification #[203]): False
% 4.34/4.55 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------