TSTP Solution File: DAT056^1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : DAT056^1 : TPTP v8.1.2. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 : Wed Aug 30 22:12:09 EDT 2023
% Result : Theorem 4.25s 4.41s
% Output : Proof 4.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT056^1 : TPTP v8.1.2. Released v5.4.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.34 % Computer : n021.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 14:48:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 4.25/4.41 SZS status Theorem for theBenchmark.p
% 4.25/4.41 SZS output start Proof for theBenchmark.p
% 4.25/4.41 Clause #0 (by assumption #[]): Eq
% 4.25/4.41 (∀ (Lst : lst),
% 4.25/4.41 (∀ (Ys Zs : lst), Eq (ap nl (ap Ys Zs)) (ap (ap nl Ys) Zs)) →
% 4.25/4.41 (∀ (A : a) (Lst2 : lst),
% 4.25/4.41 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.41 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) →
% 4.25/4.41 ∀ (Ys3 Zs2 : lst), Eq (ap Lst (ap Ys3 Zs2)) (ap (ap Lst Ys3) Zs2))
% 4.25/4.41 True
% 4.25/4.41 Clause #1 (by assumption #[]): Eq (∀ (Ys2 Xs : lst) (X : a), Eq (ap (cns X Xs) Ys2) (cns X (ap Xs Ys2))) True
% 4.25/4.41 Clause #2 (by assumption #[]): Eq (∀ (Ys2 : lst), Eq (ap nl Ys2) Ys2) True
% 4.25/4.41 Clause #3 (by assumption #[]): Eq (Not (∀ (Ys Zs : lst), Eq (ap xs (ap Ys Zs)) (ap (ap xs Ys) Zs))) True
% 4.25/4.41 Clause #4 (by clausification #[2]): ∀ (a : lst), Eq (Eq (ap nl a) a) True
% 4.25/4.41 Clause #5 (by clausification #[4]): ∀ (a : lst), Eq (ap nl a) a
% 4.25/4.41 Clause #6 (by clausification #[3]): Eq (∀ (Ys Zs : lst), Eq (ap xs (ap Ys Zs)) (ap (ap xs Ys) Zs)) False
% 4.25/4.41 Clause #7 (by clausification #[6]): ∀ (a : lst), Eq (Not (∀ (Zs : lst), Eq (ap xs (ap (skS.0 0 a) Zs)) (ap (ap xs (skS.0 0 a)) Zs))) True
% 4.25/4.41 Clause #8 (by clausification #[7]): ∀ (a : lst), Eq (∀ (Zs : lst), Eq (ap xs (ap (skS.0 0 a) Zs)) (ap (ap xs (skS.0 0 a)) Zs)) False
% 4.25/4.41 Clause #9 (by clausification #[8]): ∀ (a a_1 : lst), Eq (Not (Eq (ap xs (ap (skS.0 0 a) (skS.0 1 a a_1))) (ap (ap xs (skS.0 0 a)) (skS.0 1 a a_1)))) True
% 4.25/4.41 Clause #10 (by clausification #[9]): ∀ (a a_1 : lst), Eq (Eq (ap xs (ap (skS.0 0 a) (skS.0 1 a a_1))) (ap (ap xs (skS.0 0 a)) (skS.0 1 a a_1))) False
% 4.25/4.41 Clause #11 (by clausification #[10]): ∀ (a a_1 : lst), Ne (ap xs (ap (skS.0 0 a) (skS.0 1 a a_1))) (ap (ap xs (skS.0 0 a)) (skS.0 1 a a_1))
% 4.25/4.41 Clause #12 (by clausification #[1]): ∀ (a_1 : lst), Eq (∀ (Xs : lst) (X : a), Eq (ap (cns X Xs) a_1) (cns X (ap Xs a_1))) True
% 4.25/4.41 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : lst), Eq (∀ (X : a), Eq (ap (cns X a_1) a_2) (cns X (ap a_1 a_2))) True
% 4.25/4.41 Clause #14 (by clausification #[13]): ∀ (a : a) (a_1 a_2 : lst), Eq (Eq (ap (cns a a_1) a_2) (cns a (ap a_1 a_2))) True
% 4.25/4.41 Clause #15 (by clausification #[14]): ∀ (a : a) (a_1 a_2 : lst), Eq (ap (cns a a_1) a_2) (cns a (ap a_1 a_2))
% 4.25/4.41 Clause #19 (by clausification #[0]): ∀ (a_1 : lst),
% 4.25/4.41 Eq
% 4.25/4.41 ((∀ (Ys Zs : lst), Eq (ap nl (ap Ys Zs)) (ap (ap nl Ys) Zs)) →
% 4.25/4.41 (∀ (A : a) (Lst2 : lst),
% 4.25/4.41 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.41 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) →
% 4.25/4.41 ∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2))
% 4.25/4.41 True
% 4.25/4.41 Clause #20 (by clausification #[19]): ∀ (a_1 : lst),
% 4.25/4.41 Or (Eq (∀ (Ys Zs : lst), Eq (ap nl (ap Ys Zs)) (ap (ap nl Ys) Zs)) False)
% 4.25/4.41 (Eq
% 4.25/4.41 ((∀ (A : a) (Lst2 : lst),
% 4.25/4.41 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.41 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) →
% 4.25/4.41 ∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2))
% 4.25/4.41 True)
% 4.25/4.41 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : lst),
% 4.25/4.41 Or
% 4.25/4.41 (Eq
% 4.25/4.41 ((∀ (A : a) (Lst2 : lst),
% 4.25/4.41 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.41 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) →
% 4.25/4.41 ∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2))
% 4.25/4.41 True)
% 4.25/4.41 (Eq (Not (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_2) Zs)) (ap (ap nl (skS.0 2 a_2)) Zs))) True)
% 4.25/4.41 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 : lst),
% 4.25/4.41 Or (Eq (Not (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_1) Zs)) (ap (ap nl (skS.0 2 a_1)) Zs))) True)
% 4.25/4.41 (Or
% 4.25/4.41 (Eq
% 4.25/4.41 (∀ (A : a) (Lst2 : lst),
% 4.25/4.41 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.41 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs))
% 4.25/4.41 False)
% 4.25/4.41 (Eq (∀ (Ys3 Zs2 : lst), Eq (ap a_2 (ap Ys3 Zs2)) (ap (ap a_2 Ys3) Zs2)) True))
% 4.25/4.43 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 : lst),
% 4.25/4.43 Or
% 4.25/4.43 (Eq
% 4.25/4.43 (∀ (A : a) (Lst2 : lst),
% 4.25/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.43 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs))
% 4.25/4.43 False)
% 4.25/4.43 (Or (Eq (∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) True)
% 4.25/4.43 (Eq (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_2) Zs)) (ap (ap nl (skS.0 2 a_2)) Zs)) False))
% 4.25/4.43 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 : lst) (a_3 : a),
% 4.25/4.43 Or (Eq (∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) True)
% 4.25/4.43 (Or (Eq (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_2) Zs)) (ap (ap nl (skS.0 2 a_2)) Zs)) False)
% 4.25/4.43 (Eq
% 4.25/4.43 (Not
% 4.25/4.43 (∀ (Lst2 : lst),
% 4.25/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.43 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_3) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_3) Lst2) Ys) Zs)))
% 4.25/4.43 True))
% 4.25/4.43 Clause #25 (by clausification #[24]): ∀ (a_1 : lst) (a_2 : a) (a_3 a_4 : lst),
% 4.25/4.43 Or (Eq (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_1) Zs)) (ap (ap nl (skS.0 2 a_1)) Zs)) False)
% 4.25/4.43 (Or
% 4.25/4.43 (Eq
% 4.25/4.43 (Not
% 4.25/4.43 (∀ (Lst2 : lst),
% 4.25/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.43 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_2) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_2) Lst2) Ys) Zs)))
% 4.25/4.43 True)
% 4.25/4.43 (Eq (∀ (Zs2 : lst), Eq (ap a_3 (ap a_4 Zs2)) (ap (ap a_3 a_4) Zs2)) True))
% 4.25/4.43 Clause #26 (by clausification #[25]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : lst),
% 4.25/4.43 Or
% 4.25/4.43 (Eq
% 4.25/4.43 (Not
% 4.25/4.43 (∀ (Lst2 : lst),
% 4.25/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.25/4.43 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_1) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_1) Lst2) Ys) Zs)))
% 4.25/4.43 True)
% 4.25/4.43 (Or (Eq (∀ (Zs2 : lst), Eq (ap a_2 (ap a_3 Zs2)) (ap (ap a_2 a_3) Zs2)) True)
% 4.25/4.43 (Eq (Not (Eq (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))) True))
% 4.28/4.43 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 : lst) (a_5 : a),
% 4.28/4.43 Or (Eq (∀ (Zs2 : lst), Eq (ap a_1 (ap a_2 Zs2)) (ap (ap a_1 a_2) Zs2)) True)
% 4.28/4.43 (Or (Eq (Not (Eq (ap nl (ap (skS.0 2 a_3) (skS.0 4 a_3 a_4))) (ap (ap nl (skS.0 2 a_3)) (skS.0 4 a_3 a_4)))) True)
% 4.28/4.43 (Eq
% 4.28/4.43 (∀ (Lst2 : lst),
% 4.28/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.28/4.43 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_5) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_5) Lst2) Ys) Zs))
% 4.28/4.43 False))
% 4.28/4.43 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : lst) (a_3 : a) (a_4 a_5 a_6 : lst),
% 4.28/4.43 Or (Eq (Not (Eq (ap nl (ap (skS.0 2 a_1) (skS.0 4 a_1 a_2))) (ap (ap nl (skS.0 2 a_1)) (skS.0 4 a_1 a_2)))) True)
% 4.28/4.43 (Or
% 4.28/4.43 (Eq
% 4.28/4.43 (∀ (Lst2 : lst),
% 4.28/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.28/4.43 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_3) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_3) Lst2) Ys) Zs))
% 4.28/4.43 False)
% 4.28/4.43 (Eq (Eq (ap a_4 (ap a_5 a_6)) (ap (ap a_4 a_5) a_6)) True))
% 4.28/4.43 Clause #29 (by clausification #[28]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 a_6 : lst),
% 4.28/4.43 Or
% 4.28/4.43 (Eq
% 4.28/4.43 (∀ (Lst2 : lst),
% 4.28/4.43 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) →
% 4.28/4.43 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_1) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_1) Lst2) Ys) Zs))
% 4.28/4.43 False)
% 4.28/4.43 (Or (Eq (Eq (ap a_2 (ap a_3 a_4)) (ap (ap a_2 a_3) a_4)) True)
% 4.28/4.43 (Eq (Eq (ap nl (ap (skS.0 2 a_5) (skS.0 4 a_5 a_6))) (ap (ap nl (skS.0 2 a_5)) (skS.0 4 a_5 a_6))) False))
% 4.28/4.43 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst),
% 4.28/4.43 Or (Eq (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) True)
% 4.28/4.43 (Or (Eq (Eq (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) False)
% 4.28/4.43 (Eq
% 4.28/4.43 (Not
% 4.28/4.43 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_6 a_7) Ys3) Zs2)) →
% 4.28/4.45 ∀ (Ys Zs : lst),
% 4.28/4.45 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap Ys Zs))
% 4.28/4.45 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) Ys) Zs)))
% 4.28/4.45 True))
% 4.28/4.45 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 : lst) (a_3 : a) (a_4 a_5 a_6 a_7 : lst),
% 4.28/4.45 Or (Eq (Eq (ap nl (ap (skS.0 2 a_1) (skS.0 4 a_1 a_2))) (ap (ap nl (skS.0 2 a_1)) (skS.0 4 a_1 a_2))) False)
% 4.28/4.45 (Or
% 4.28/4.45 (Eq
% 4.28/4.45 (Not
% 4.28/4.45 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_3 a_4) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_3 a_4) Ys3) Zs2)) →
% 4.28/4.45 ∀ (Ys Zs : lst),
% 4.28/4.45 Eq (ap (cns (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ap Ys Zs))
% 4.28/4.45 (ap (ap (cns (skS.0 3 a_3) (skS.0 5 a_3 a_4)) Ys) Zs)))
% 4.28/4.45 True)
% 4.28/4.45 (Eq (ap a_5 (ap a_6 a_7)) (ap (ap a_5 a_6) a_7)))
% 4.28/4.45 Clause #32 (by clausification #[31]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 a_6 a_7 : lst),
% 4.28/4.45 Or
% 4.28/4.45 (Eq
% 4.28/4.45 (Not
% 4.28/4.45 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_1 a_2) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_1 a_2) Ys3) Zs2)) →
% 4.28/4.45 ∀ (Ys Zs : lst),
% 4.28/4.45 Eq (ap (cns (skS.0 3 a_1) (skS.0 5 a_1 a_2)) (ap Ys Zs))
% 4.28/4.45 (ap (ap (cns (skS.0 3 a_1) (skS.0 5 a_1 a_2)) Ys) Zs)))
% 4.28/4.45 True)
% 4.28/4.45 (Or (Eq (ap a_3 (ap a_4 a_5)) (ap (ap a_3 a_4) a_5))
% 4.28/4.45 (Ne (ap nl (ap (skS.0 2 a_6) (skS.0 4 a_6 a_7))) (ap (ap nl (skS.0 2 a_6)) (skS.0 4 a_6 a_7))))
% 4.28/4.45 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq
% 4.28/4.45 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_6 a_7) Ys3) Zs2)) →
% 4.28/4.45 ∀ (Ys Zs : lst),
% 4.28/4.45 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap Ys Zs))
% 4.28/4.45 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) Ys) Zs))
% 4.28/4.45 False))
% 4.28/4.45 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq (∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_6 a_7) Ys3) Zs2)) True))
% 4.28/4.45 Clause #35 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq
% 4.28/4.45 (∀ (Ys Zs : lst),
% 4.28/4.45 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap Ys Zs))
% 4.28/4.45 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) Ys) Zs))
% 4.28/4.45 False))
% 4.28/4.45 Clause #36 (by clausification #[34]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq (∀ (Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap a_8 Zs2)) (ap (ap (skS.0 5 a_6 a_7) a_8) Zs2)) True))
% 4.28/4.45 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9)) True))
% 4.28/4.45 Clause #38 (by clausification #[37]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9)))
% 4.28/4.45 Clause #39 (by forward demodulation #[38, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.45 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.45 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.45 (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9)))
% 4.28/4.48 Clause #40 (by forward demodulation #[39, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9)))
% 4.28/4.48 Clause #41 (by eliminate resolved literals #[40]): ∀ (a_1 a_2 a_3 : lst) (a_4 : a) (a_5 a_6 a_7 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Eq (ap (skS.0 5 a_4 a_5) (ap a_6 a_7)) (ap (ap (skS.0 5 a_4 a_5) a_6) a_7))
% 4.28/4.48 Clause #42 (by superposition #[41, 11]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 a_6 : lst),
% 4.28/4.48 Or (Eq (ap (skS.0 5 a_1 a_2) (ap a_3 a_4)) (ap (ap (skS.0 5 a_1 a_2) a_3) a_4))
% 4.28/4.48 (Ne (ap xs (ap (skS.0 0 a_5) (skS.0 1 a_5 a_6))) (ap xs (ap (skS.0 0 a_5) (skS.0 1 a_5 a_6))))
% 4.28/4.48 Clause #61 (by clausification #[35]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Eq
% 4.28/4.48 (Not
% 4.28/4.48 (∀ (Zs : lst),
% 4.28/4.48 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) Zs))
% 4.28/4.48 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) Zs)))
% 4.28/4.48 True))
% 4.28/4.48 Clause #62 (by clausification #[61]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Eq
% 4.28/4.48 (∀ (Zs : lst),
% 4.28/4.48 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) Zs))
% 4.28/4.48 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) Zs))
% 4.28/4.48 False))
% 4.28/4.48 Clause #63 (by clausification #[62]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Eq
% 4.28/4.48 (Not
% 4.28/4.48 (Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9)))
% 4.28/4.48 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9))))
% 4.28/4.48 True))
% 4.28/4.48 Clause #64 (by clausification #[63]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Eq
% 4.28/4.48 (Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9)))
% 4.28/4.48 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9)))
% 4.28/4.48 False))
% 4.28/4.48 Clause #65 (by clausification #[64]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Ne (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9)))
% 4.28/4.48 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9))))
% 4.28/4.48 Clause #66 (by forward demodulation #[65, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Ne (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9)))
% 4.28/4.48 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9))))
% 4.28/4.48 Clause #67 (by forward demodulation #[66, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst),
% 4.28/4.48 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.48 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)))
% 4.28/4.48 (Ne (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9)))
% 4.28/4.49 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9))))
% 4.28/4.49 Clause #68 (by eliminate resolved literals #[67]): ∀ (a_1 a_2 a_3 : lst) (a_4 : a) (a_5 a_6 a_7 : lst),
% 4.28/4.49 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3))
% 4.28/4.49 (Ne (ap (cns (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ap (skS.0 6 a_4 a_5 a_6) (skS.0 7 a_4 a_5 a_6 a_7)))
% 4.28/4.49 (ap (ap (cns (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (skS.0 6 a_4 a_5 a_6)) (skS.0 7 a_4 a_5 a_6 a_7)))
% 4.28/4.49 Clause #90 (by eliminate resolved literals #[42]): ∀ (a_1 : a) (a_2 a_3 a_4 : lst), Eq (ap (skS.0 5 a_1 a_2) (ap a_3 a_4)) (ap (ap (skS.0 5 a_1 a_2) a_3) a_4)
% 4.28/4.49 Clause #91 (by superposition #[90, 15]): ∀ (a_1 a_2 : a) (a_3 a_4 a_5 : lst),
% 4.28/4.49 Eq (ap (cns a_1 (ap (skS.0 5 a_2 a_3) a_4)) a_5) (cns a_1 (ap (skS.0 5 a_2 a_3) (ap a_4 a_5)))
% 4.28/4.49 Clause #92 (by forward demodulation #[91, 15]): ∀ (a_1 a_2 : a) (a_3 a_4 a_5 : lst),
% 4.28/4.49 Eq (ap (ap (cns a_1 (skS.0 5 a_2 a_3)) a_4) a_5) (cns a_1 (ap (skS.0 5 a_2 a_3) (ap a_4 a_5)))
% 4.28/4.49 Clause #93 (by superposition #[92, 15]): ∀ (a_1 a_2 : a) (a_3 a_4 a_5 : lst),
% 4.28/4.49 Eq (ap (cns a_1 (skS.0 5 a_2 a_3)) (ap a_4 a_5)) (ap (ap (cns a_1 (skS.0 5 a_2 a_3)) a_4) a_5)
% 4.28/4.49 Clause #109 (by backward contextual literal cutting #[93, 68]): ∀ (a a_1 a_2 : lst), Eq (ap a (ap a_1 a_2)) (ap (ap a a_1) a_2)
% 4.28/4.49 Clause #113 (by backward contextual literal cutting #[109, 11]): False
% 4.28/4.49 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------