TSTP Solution File: SWC072+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC072+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.sbai3tWb3k true
% Computer : n028.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 21:28:57 EDT 2023
% Result : Theorem 260.58s 38.13s
% Output : Refutation 260.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 57
% Syntax : Number of formulae : 656 ( 226 unt; 23 typ; 0 def)
% Number of atoms : 1827 ( 579 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 5502 ( 985 ~;1070 |; 41 &;3323 @)
% ( 9 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 583 ( 0 ^; 566 !; 17 ?; 583 :)
% Comments :
%------------------------------------------------------------------------------
thf(frontsegP_type,type,
frontsegP: $i > $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(sk__50_type,type,
sk__50: $i ).
thf(sk__6_type,type,
sk__6: $i > $i > $i ).
thf(nil_type,type,
nil: $i ).
thf(app_type,type,
app: $i > $i > $i ).
thf(hd_type,type,
hd: $i > $i ).
thf(sk__4_type,type,
sk__4: $i > $i ).
thf(ssList_type,type,
ssList: $i > $o ).
thf(tl_type,type,
tl: $i > $i ).
thf(rearsegP_type,type,
rearsegP: $i > $i > $o ).
thf(sk__43_type,type,
sk__43: $i > $i ).
thf(sk__49_type,type,
sk__49: $i ).
thf(sk__47_type,type,
sk__47: $i ).
thf(sk__48_type,type,
sk__48: $i ).
thf(sk__7_type,type,
sk__7: $i > $i > $i ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(sk__44_type,type,
sk__44: $i > $i ).
thf(sk__5_type,type,
sk__5: $i > $i > $i ).
thf(sk__8_type,type,
sk__8: $i > $i > $i ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(ax15,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) ).
thf(zip_derived_cl81,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( X1 = X0 )
| ( neq @ X1 @ X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax15]) ).
thf(ax55,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) ).
thf(zip_derived_cl134,plain,
! [X0: $i] :
( ( segmentP @ X0 @ X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax55]) ).
thf(co1,conjecture,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ( neq @ X @ nil )
& ? [Z: $i] :
( ? [X1: $i] :
( ? [X2: $i] :
( ( neq @ nil @ X )
& ? [X3: $i] :
( ( neq @ nil @ X )
& ( ( hd @ X )
= X3 )
& ( ( cons @ X3 @ nil )
= X2 )
& ( ssItem @ X3 ) )
& ( ( app @ X1 @ X2 )
= Z )
& ( ( tl @ X )
= X1 )
& ( ssList @ X2 ) )
& ( ssList @ X1 ) )
& ( W != Z )
& ( ssList @ Z ) ) )
| ( ( nil = U )
& ( nil = V ) )
| ( ( nil = X )
& ( nil != W ) )
| ? [Y: $i] :
( ( segmentP @ U @ Y )
& ( segmentP @ V @ Y )
& ( neq @ Y @ nil )
& ( ssList @ Y ) )
| ( U != W )
| ( V != X )
| ~ ( ssList @ X ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ( neq @ X @ nil )
& ? [Z: $i] :
( ? [X1: $i] :
( ? [X2: $i] :
( ( neq @ nil @ X )
& ? [X3: $i] :
( ( neq @ nil @ X )
& ( ( hd @ X )
= X3 )
& ( ( cons @ X3 @ nil )
= X2 )
& ( ssItem @ X3 ) )
& ( ( app @ X1 @ X2 )
= Z )
& ( ( tl @ X )
= X1 )
& ( ssList @ X2 ) )
& ( ssList @ X1 ) )
& ( W != Z )
& ( ssList @ Z ) ) )
| ( ( nil = U )
& ( nil = V ) )
| ( ( nil = X )
& ( nil != W ) )
| ? [Y: $i] :
( ( segmentP @ U @ Y )
& ( segmentP @ V @ Y )
& ( neq @ Y @ nil )
& ( ssList @ Y ) )
| ( U != W )
| ( V != X )
| ~ ( ssList @ X ) ) ) ) ),
inference('cnf.neg',[status(esa)],[co1]) ).
thf(zip_derived_cl193,plain,
! [X0: $i] :
( ~ ( segmentP @ sk__47 @ X0 )
| ~ ( segmentP @ sk__48 @ X0 )
| ~ ( neq @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl238,plain,
( ~ ( ssList @ sk__47 )
| ~ ( segmentP @ sk__48 @ sk__47 )
| ~ ( neq @ sk__47 @ nil )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl134,zip_derived_cl193]) ).
thf(zip_derived_cl190,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl190_001,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl240,plain,
( ~ ( segmentP @ sk__48 @ sk__47 )
| ~ ( neq @ sk__47 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl238,zip_derived_cl190,zip_derived_cl190]) ).
thf(ax22,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ) ).
thf(zip_derived_cl91,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssItem @ ( hd @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax22]) ).
thf(ax16,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) ).
thf(zip_derived_cl82,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(zip_derived_cl91_002,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssItem @ ( hd @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax22]) ).
thf(ax24,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) ).
thf(zip_derived_cl93,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl81_003,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( X1 = X0 )
| ( neq @ X1 @ X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax15]) ).
thf(zip_derived_cl81_004,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( X1 = X0 )
| ( neq @ X1 @ X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax15]) ).
thf(zip_derived_cl195,plain,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( neq @ sk__50 @ nil )
| ~ ( ssList @ X1 )
| ( sk__49 = X1 )
| ~ ( ssList @ X2 )
| ( ( app @ X3 @ X2 )
!= X1 )
| ~ ( neq @ nil @ sk__50 )
| ( ( hd @ sk__50 )
!= X4 )
| ( ( cons @ X4 @ nil )
!= X2 )
| ~ ( ssItem @ X4 )
| ( ( tl @ sk__50 )
!= X3 )
| ~ ( neq @ nil @ sk__50 )
| ~ ( ssList @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl206,plain,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ssList @ X3 )
| ( ( tl @ sk__50 )
!= X3 )
| ~ ( ssItem @ X4 )
| ( ( cons @ X4 @ nil )
!= X2 )
| ( ( hd @ sk__50 )
!= X4 )
| ~ ( neq @ nil @ sk__50 )
| ( ( app @ X3 @ X2 )
!= X1 )
| ~ ( ssList @ X2 )
| ( sk__49 = X1 )
| ~ ( ssList @ X1 )
| ~ ( neq @ sk__50 @ nil ) ),
inference(simplify,[status(thm)],[zip_derived_cl195]) ).
thf(zip_derived_cl197,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_005,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_006,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl194,plain,
sk__47 = sk__49,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_007,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl207,plain,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ssList @ X3 )
| ( ( tl @ sk__48 )
!= X3 )
| ~ ( ssItem @ X4 )
| ( ( cons @ X4 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X4 )
| ~ ( neq @ nil @ sk__48 )
| ( ( app @ X3 @ X2 )
!= X1 )
| ~ ( ssList @ X2 )
| ( sk__47 = X1 )
| ~ ( ssList @ X1 )
| ~ ( neq @ sk__48 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl206,zip_derived_cl197,zip_derived_cl197,zip_derived_cl197,zip_derived_cl194,zip_derived_cl197]) ).
thf(zip_derived_cl1609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ nil )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 )
| ~ ( ssList @ X0 )
| ( ( tl @ sk__48 )
!= X0 )
| ~ ( ssItem @ X1 )
| ( ( cons @ X1 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X1 )
| ( ( app @ X0 @ X2 )
!= X3 )
| ~ ( ssList @ X2 )
| ( sk__47 = X3 )
| ~ ( ssList @ X3 )
| ~ ( neq @ sk__48 @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl207]) ).
thf(ax17,axiom,
ssList @ nil ).
thf(zip_derived_cl83,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl198,plain,
ssList @ sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_008,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl201,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl1611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( nil = sk__48 )
| ~ ( ssList @ X0 )
| ( ( tl @ sk__48 )
!= X0 )
| ~ ( ssItem @ X1 )
| ( ( cons @ X1 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X1 )
| ( ( app @ X0 @ X2 )
!= X3 )
| ~ ( ssList @ X2 )
| ( sk__47 = X3 )
| ~ ( ssList @ X3 )
| ~ ( neq @ sk__48 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl1609,zip_derived_cl83,zip_derived_cl201]) ).
thf(zip_derived_cl196,plain,
( ( nil != sk__50 )
| ( nil = sk__49 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_009,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl194_010,plain,
sk__47 = sk__49,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl202,plain,
( ( nil != sk__48 )
| ( nil = sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl197,zip_derived_cl194]) ).
thf(zip_derived_cl192,plain,
( ( nil != sk__47 )
| ( nil != sk__48 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl203,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl1612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ sk__48 )
!= X0 )
| ~ ( ssItem @ X1 )
| ( ( cons @ X1 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X1 )
| ( ( app @ X0 @ X2 )
!= X3 )
| ~ ( ssList @ X2 )
| ( sk__47 = X3 )
| ~ ( ssList @ X3 )
| ~ ( neq @ sk__48 @ nil ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1611,zip_derived_cl203]) ).
thf(zip_derived_cl1614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ sk__48 )
| ( sk__48 = nil )
| ~ ( ssList @ nil )
| ~ ( ssList @ X0 )
| ( ( tl @ sk__48 )
!= X0 )
| ~ ( ssItem @ X1 )
| ( ( cons @ X1 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X1 )
| ( ( app @ X0 @ X2 )
!= X3 )
| ~ ( ssList @ X2 )
| ( sk__47 = X3 )
| ~ ( ssList @ X3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl1612]) ).
thf(zip_derived_cl201_011,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl83_012,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk__48 = nil )
| ~ ( ssList @ X0 )
| ( ( tl @ sk__48 )
!= X0 )
| ~ ( ssItem @ X1 )
| ( ( cons @ X1 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X1 )
| ( ( app @ X0 @ X2 )
!= X3 )
| ~ ( ssList @ X2 )
| ( sk__47 = X3 )
| ~ ( ssList @ X3 ) ),
inference(demod,[status(thm)],[zip_derived_cl1614,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl203_013,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl1617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ sk__48 )
!= X0 )
| ~ ( ssItem @ X1 )
| ( ( cons @ X1 @ nil )
!= X2 )
| ( ( hd @ sk__48 )
!= X1 )
| ( ( app @ X0 @ X2 )
!= X3 )
| ~ ( ssList @ X2 )
| ( sk__47 = X3 )
| ~ ( ssList @ X3 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1616,zip_derived_cl203]) ).
thf(zip_derived_cl1618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ~ ( ssList @ X1 )
| ( ( app @ ( tl @ sk__48 ) @ X1 )
!= X0 )
| ( ( hd @ sk__48 )
!= X2 )
| ( ( cons @ X2 @ nil )
!= X1 )
| ~ ( ssItem @ X2 )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1617]) ).
thf(zip_derived_cl1681,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ~ ( ssList @ X1 )
| ( ( app @ ( tl @ sk__48 ) @ X1 )
!= X0 )
| ( ( hd @ sk__48 )
!= X2 )
| ( ( cons @ X2 @ nil )
!= X1 )
| ~ ( ssItem @ X2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl1618]) ).
thf(zip_derived_cl201_014,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl1682,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( nil = sk__48 )
| ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ~ ( ssList @ X1 )
| ( ( app @ ( tl @ sk__48 ) @ X1 )
!= X0 )
| ( ( hd @ sk__48 )
!= X2 )
| ( ( cons @ X2 @ nil )
!= X1 )
| ~ ( ssItem @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1681,zip_derived_cl201]) ).
thf(zip_derived_cl203_015,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl1683,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ~ ( ssList @ X1 )
| ( ( app @ ( tl @ sk__48 ) @ X1 )
!= X0 )
| ( ( hd @ sk__48 )
!= X2 )
| ( ( cons @ X2 @ nil )
!= X1 )
| ~ ( ssItem @ X2 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1682,zip_derived_cl203]) ).
thf(zip_derived_cl1684,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ ( hd @ sk__48 ) )
| ( ( cons @ ( hd @ sk__48 ) @ nil )
!= X0 )
| ( ( app @ ( tl @ sk__48 ) @ X0 )
!= X1 )
| ~ ( ssList @ X0 )
| ( sk__47 = X1 )
| ~ ( ssList @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1683]) ).
thf(zip_derived_cl1685,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( ( cons @ ( hd @ sk__48 ) @ nil )
!= X0 )
| ( ( app @ ( tl @ sk__48 ) @ X0 )
!= X1 )
| ~ ( ssList @ X0 )
| ( sk__47 = X1 )
| ~ ( ssList @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl1684]) ).
thf(zip_derived_cl201_016,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl1686,plain,
! [X0: $i,X1: $i] :
( ( nil = sk__48 )
| ( ( cons @ ( hd @ sk__48 ) @ nil )
!= X0 )
| ( ( app @ ( tl @ sk__48 ) @ X0 )
!= X1 )
| ~ ( ssList @ X0 )
| ( sk__47 = X1 )
| ~ ( ssList @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1685,zip_derived_cl201]) ).
thf(zip_derived_cl203_017,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl1687,plain,
! [X0: $i,X1: $i] :
( ( ( cons @ ( hd @ sk__48 ) @ nil )
!= X0 )
| ( ( app @ ( tl @ sk__48 ) @ X0 )
!= X1 )
| ~ ( ssList @ X0 )
| ( sk__47 = X1 )
| ~ ( ssList @ X1 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1686,zip_derived_cl203]) ).
thf(zip_derived_cl1688,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
!= X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1687]) ).
thf(zip_derived_cl1689,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ ( hd @ sk__48 ) )
| ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
!= X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl1688]) ).
thf(zip_derived_cl83_018,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1690,plain,
! [X0: $i] :
( ~ ( ssItem @ ( hd @ sk__48 ) )
| ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
!= X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1689,zip_derived_cl83]) ).
thf(zip_derived_cl1720,plain,
! [X0: $i] :
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
!= X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl1690]) ).
thf(zip_derived_cl201_019,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl1721,plain,
! [X0: $i] :
( ( nil = sk__48 )
| ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
!= X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1720,zip_derived_cl201]) ).
thf(zip_derived_cl203_020,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl1722,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( sk__47 = X0 )
| ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
!= X0 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1721,zip_derived_cl203]) ).
thf(zip_derived_cl1723,plain,
( ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1722]) ).
thf(zip_derived_cl81_021,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( X1 = X0 )
| ( neq @ X1 @ X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax15]) ).
thf(zip_derived_cl93_022,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl93_023,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl93_024,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl93_025,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(ax42,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) ).
thf(zip_derived_cl117,plain,
! [X0: $i] :
( ( frontsegP @ X0 @ X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax42]) ).
thf(zip_derived_cl91_026,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssItem @ ( hd @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax22]) ).
thf(zip_derived_cl82_027,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(zip_derived_cl93_028,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl93_029,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl1723_030,plain,
( ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1722]) ).
thf(ax26,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) ).
thf(zip_derived_cl95,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl1823,plain,
( ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1723,zip_derived_cl95]) ).
thf(zip_derived_cl1825,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl1823]) ).
thf(zip_derived_cl201_031,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl1826,plain,
( ( nil = sk__48 )
| ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1825,zip_derived_cl201]) ).
thf(zip_derived_cl203_032,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl1827,plain,
( ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1826,zip_derived_cl203]) ).
thf(ax43,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( frontsegP @ U @ V )
=> ( frontsegP @ ( app @ U @ W ) @ V ) ) ) ) ) ).
thf(zip_derived_cl118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( frontsegP @ ( app @ X1 @ X2 ) @ X0 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax43]) ).
thf(zip_derived_cl1848,plain,
! [X0: $i] :
( ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ~ ( ssList @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1827,zip_derived_cl118]) ).
thf(zip_derived_cl1880,plain,
! [X0: $i] :
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1848]) ).
thf(zip_derived_cl2049,plain,
! [X0: $i] :
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl1880]) ).
thf(zip_derived_cl201_033,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl2050,plain,
! [X0: $i] :
( ( nil = sk__48 )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2049,zip_derived_cl201]) ).
thf(zip_derived_cl203_034,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl2051,plain,
! [X0: $i] :
( ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2050,zip_derived_cl203]) ).
thf(zip_derived_cl2052,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ ( hd @ sk__48 ) )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl2051]) ).
thf(zip_derived_cl83_035,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2053,plain,
! [X0: $i] :
( ~ ( ssItem @ ( hd @ sk__48 ) )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2052,zip_derived_cl83]) ).
thf(zip_derived_cl2054,plain,
! [X0: $i] :
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl2053]) ).
thf(zip_derived_cl201_036,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl2055,plain,
! [X0: $i] :
( ( nil = sk__48 )
| ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2054,zip_derived_cl201]) ).
thf(zip_derived_cl203_037,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl2056,plain,
! [X0: $i] :
( ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2055,zip_derived_cl203]) ).
thf(zip_derived_cl2057,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( frontsegP @ sk__47 @ ( tl @ sk__48 ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl117,zip_derived_cl2056]) ).
thf(zip_derived_cl2059,plain,
( ( frontsegP @ sk__47 @ ( tl @ sk__48 ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl2057]) ).
thf(zip_derived_cl2509,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( frontsegP @ sk__47 @ ( tl @ sk__48 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2059]) ).
thf(zip_derived_cl201_038,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl2510,plain,
( ( nil = sk__48 )
| ( frontsegP @ sk__47 @ ( tl @ sk__48 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2509,zip_derived_cl201]) ).
thf(zip_derived_cl203_039,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl2511,plain,
frontsegP @ sk__47 @ ( tl @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2510,zip_derived_cl203]) ).
thf(ax5,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( frontsegP @ U @ V )
<=> ? [W: $i] :
( ( ( app @ V @ W )
= U )
& ( ssList @ W ) ) ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( ( app @ X0 @ ( sk__5 @ X0 @ X1 ) )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl2512,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2511,zip_derived_cl12]) ).
thf(zip_derived_cl190_040,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2517,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl2512,zip_derived_cl190]) ).
thf(zip_derived_cl91848,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2517]) ).
thf(zip_derived_cl201_041,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl91849,plain,
( ( nil = sk__48 )
| ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl91848,zip_derived_cl201]) ).
thf(zip_derived_cl203_042,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl91850,plain,
( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl91849,zip_derived_cl203]) ).
thf(zip_derived_cl134_043,plain,
! [X0: $i] :
( ( segmentP @ X0 @ X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax55]) ).
thf(ax28,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) ).
thf(zip_derived_cl97,plain,
! [X0: $i] :
( ( ( app @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax28]) ).
thf(ax56,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( segmentP @ U @ V )
=> ( segmentP @ ( app @ ( app @ W @ U ) @ X ) @ V ) ) ) ) ) ) ).
thf(zip_derived_cl135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( segmentP @ ( app @ ( app @ X2 @ X3 ) @ X1 ) @ X0 )
| ~ ( segmentP @ X3 @ X0 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X3 ) ),
inference(cnf,[status(esa)],[ax56]) ).
thf(zip_derived_cl1477,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X2 )
| ( segmentP @ ( app @ X0 @ X2 ) @ X1 )
| ~ ( segmentP @ X0 @ X1 )
| ~ ( ssList @ nil )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl97,zip_derived_cl135]) ).
thf(zip_derived_cl83_044,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1492,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X2 )
| ( segmentP @ ( app @ X0 @ X2 ) @ X1 )
| ~ ( segmentP @ X0 @ X1 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1477,zip_derived_cl83]) ).
thf(zip_derived_cl1493,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( segmentP @ X0 @ X1 )
| ( segmentP @ ( app @ X0 @ X2 ) @ X1 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1492]) ).
thf(zip_derived_cl54766,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( segmentP @ ( app @ X0 @ X1 ) @ X0 )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl134,zip_derived_cl1493]) ).
thf(zip_derived_cl54850,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( segmentP @ ( app @ X0 @ X1 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl54766]) ).
thf(zip_derived_cl92019,plain,
( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( segmentP @ sk__47 @ ( tl @ sk__48 ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl91850,zip_derived_cl54850]) ).
thf(zip_derived_cl93_045,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl2511_046,plain,
frontsegP @ sk__47 @ ( tl @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2510,zip_derived_cl203]) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( ssList @ ( sk__5 @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl2513,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2511,zip_derived_cl13]) ).
thf(zip_derived_cl190_047,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2518,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2513,zip_derived_cl190]) ).
thf(zip_derived_cl2651,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2518]) ).
thf(zip_derived_cl201_048,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl2652,plain,
( ( nil = sk__48 )
| ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2651,zip_derived_cl201]) ).
thf(zip_derived_cl203_049,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl2653,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl92205,plain,
( ( segmentP @ sk__47 @ ( tl @ sk__48 ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92019,zip_derived_cl2653]) ).
thf(zip_derived_cl92248,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( segmentP @ sk__47 @ ( tl @ sk__48 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl92205]) ).
thf(zip_derived_cl201_050,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl92249,plain,
( ( nil = sk__48 )
| ( segmentP @ sk__47 @ ( tl @ sk__48 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92248,zip_derived_cl201]) ).
thf(zip_derived_cl203_051,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl92250,plain,
segmentP @ sk__47 @ ( tl @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl92249,zip_derived_cl203]) ).
thf(zip_derived_cl193_052,plain,
! [X0: $i] :
( ~ ( segmentP @ sk__47 @ X0 )
| ~ ( segmentP @ sk__48 @ X0 )
| ~ ( neq @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl92265,plain,
( ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
| ~ ( neq @ ( tl @ sk__48 ) @ nil )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl92250,zip_derived_cl193]) ).
thf(zip_derived_cl92280,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
| ~ ( neq @ ( tl @ sk__48 ) @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl92265]) ).
thf(zip_derived_cl201_053,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl92281,plain,
( ( nil = sk__48 )
| ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
| ~ ( neq @ ( tl @ sk__48 ) @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl92280,zip_derived_cl201]) ).
thf(zip_derived_cl203_054,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl92282,plain,
( ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
| ~ ( neq @ ( tl @ sk__48 ) @ nil ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl92281,zip_derived_cl203]) ).
thf(zip_derived_cl91850_055,plain,
( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl91849,zip_derived_cl203]) ).
thf(ax86,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ) ).
thf(zip_derived_cl178,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(ax85,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ) ).
thf(zip_derived_cl177,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( hd @ ( app @ X1 @ X0 ) )
= ( hd @ X1 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax85]) ).
thf(ax78,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ) ).
thf(zip_derived_cl168,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax78]) ).
thf(zip_derived_cl528,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ X1 )
| ( nil
= ( app @ X0 @ X1 ) )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
= ( app @ X0 @ X1 ) )
| ~ ( ssList @ ( app @ X0 @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl177,zip_derived_cl168]) ).
thf(ax83,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) ).
thf(zip_derived_cl174,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil
!= ( app @ X1 @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax83]) ).
thf(zip_derived_cl4501,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ ( app @ X0 @ X1 ) )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
= ( app @ X0 @ X1 ) )
| ~ ( ssList @ X1 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl528,zip_derived_cl174]) ).
thf(zip_derived_cl95_056,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl4502,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ X1 )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
= ( app @ X0 @ X1 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl4501,zip_derived_cl95]) ).
thf(zip_derived_cl4546,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( nil = X1 )
| ~ ( ssList @ X0 )
| ( ( cons @ ( hd @ X1 ) @ ( app @ ( tl @ X1 ) @ X0 ) )
= ( app @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl4502]) ).
thf(zip_derived_cl4582,plain,
! [X0: $i,X1: $i] :
( ( ( cons @ ( hd @ X1 ) @ ( app @ ( tl @ X1 ) @ X0 ) )
= ( app @ X1 @ X0 ) )
| ~ ( ssList @ X0 )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl4546]) ).
thf(zip_derived_cl175202,plain,
( ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) )
| ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl91850,zip_derived_cl4582]) ).
thf(zip_derived_cl2653_057,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl201_058,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl175278,plain,
( ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl175202,zip_derived_cl2653,zip_derived_cl201]) ).
thf(zip_derived_cl203_059,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl175279,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).
thf(zip_derived_cl14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ X0 @ X2 )
!= X1 )
| ~ ( ssList @ X2 )
| ( frontsegP @ X1 @ X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl344,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( frontsegP @ ( app @ X1 @ X0 ) @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl95_060,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl2777,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ( frontsegP @ ( app @ X1 @ X0 ) @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl344,zip_derived_cl95]) ).
thf(zip_derived_cl196252,plain,
( ~ ( ssList @ sk__48 )
| ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( frontsegP @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl2777]) ).
thf(zip_derived_cl201_061,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl2653_062,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl196523,plain,
frontsegP @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl196252,zip_derived_cl201,zip_derived_cl2653]) ).
thf(ax20,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil = U )
| ? [V: $i] :
( ? [W: $i] :
( ( ( cons @ W @ V )
= U )
& ( ssItem @ W ) )
& ( ssList @ V ) ) ) ) ).
thf(zip_derived_cl88,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(ax44,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( frontsegP @ ( cons @ U @ W ) @ ( cons @ V @ X ) )
<=> ( ( U = V )
& ( frontsegP @ W @ X ) ) ) ) ) ) ) ).
thf(zip_derived_cl121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssItem @ X0 )
| ~ ( ssList @ X1 )
| ~ ( frontsegP @ ( cons @ X2 @ X3 ) @ ( cons @ X0 @ X1 ) )
| ( X2 = X0 )
| ~ ( ssList @ X3 )
| ~ ( ssItem @ X2 ) ),
inference(cnf,[status(esa)],[ax44]) ).
thf(zip_derived_cl969,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssItem @ ( sk__44 @ X0 ) )
| ~ ( ssList @ ( sk__43 @ X0 ) )
| ~ ( frontsegP @ ( cons @ X2 @ X1 ) @ X0 )
| ( X2
= ( sk__44 @ X0 ) )
| ~ ( ssList @ X1 )
| ~ ( ssItem @ X2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl88,zip_derived_cl121]) ).
thf(zip_derived_cl87,plain,
! [X0: $i] :
( ( ssItem @ ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl16177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssItem @ X2 )
| ~ ( ssList @ X1 )
| ( X2
= ( sk__44 @ X0 ) )
| ~ ( frontsegP @ ( cons @ X2 @ X1 ) @ X0 )
| ~ ( ssList @ ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl969,zip_derived_cl87]) ).
thf(zip_derived_cl89,plain,
! [X0: $i] :
( ( ssList @ ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl16178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( frontsegP @ ( cons @ X2 @ X1 ) @ X0 )
| ( X2
= ( sk__44 @ X0 ) )
| ~ ( ssList @ X1 )
| ~ ( ssItem @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl16177,zip_derived_cl89]) ).
thf(zip_derived_cl198778,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( ( hd @ sk__48 )
= ( sk__44 @ sk__48 ) )
| ~ ( ssList @ sk__47 )
| ~ ( ssItem @ ( hd @ sk__48 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl196523,zip_derived_cl16178]) ).
thf(zip_derived_cl201_063,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl190_064,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175279_065,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).
thf(zip_derived_cl177_066,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( hd @ ( app @ X1 @ X0 ) )
= ( hd @ X1 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax85]) ).
thf(zip_derived_cl196232,plain,
( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( ( hd @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
= ( hd @ sk__48 ) )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl177]) ).
thf(zip_derived_cl2653_067,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl201_068,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl196497,plain,
( ( ( hd @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
= ( hd @ sk__48 ) )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl196232,zip_derived_cl2653,zip_derived_cl201]) ).
thf(zip_derived_cl203_069,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl196498,plain,
( ( hd @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
= ( hd @ sk__48 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl196497,zip_derived_cl203]) ).
thf(zip_derived_cl91_070,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssItem @ ( hd @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax22]) ).
thf(zip_derived_cl197126,plain,
( ( nil
= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ( ssItem @ ( hd @ sk__48 ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl196498,zip_derived_cl91]) ).
thf(zip_derived_cl175279_071,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).
thf(zip_derived_cl95_072,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl196226,plain,
( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl95]) ).
thf(zip_derived_cl2653_073,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl201_074,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl196490,plain,
ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl196226,zip_derived_cl2653,zip_derived_cl201]) ).
thf(zip_derived_cl197272,plain,
( ( nil
= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ( ssItem @ ( hd @ sk__48 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl197126,zip_derived_cl196490]) ).
thf(zip_derived_cl175279_075,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).
thf(zip_derived_cl174_076,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil
!= ( app @ X1 @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax83]) ).
thf(zip_derived_cl196230,plain,
( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( nil
!= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl175279,zip_derived_cl174]) ).
thf(zip_derived_cl2653_077,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl201_078,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl196494,plain,
( ( nil
!= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl196230,zip_derived_cl2653,zip_derived_cl201]) ).
thf(zip_derived_cl203_079,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl196495,plain,
( nil
!= ( cons @ ( hd @ sk__48 ) @ sk__47 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl196494,zip_derived_cl203]) ).
thf(zip_derived_cl197273,plain,
ssItem @ ( hd @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).
thf(zip_derived_cl198791,plain,
( ( nil = sk__48 )
| ( ( hd @ sk__48 )
= ( sk__44 @ sk__48 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl198778,zip_derived_cl201,zip_derived_cl190,zip_derived_cl197273]) ).
thf(zip_derived_cl203_080,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl198792,plain,
( ( hd @ sk__48 )
= ( sk__44 @ sk__48 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl198791,zip_derived_cl203]) ).
thf(zip_derived_cl88_081,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(ax25,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ) ).
thf(zip_derived_cl94,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( tl @ ( cons @ X0 @ X1 ) )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax25]) ).
thf(zip_derived_cl491,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssItem @ ( sk__44 @ X0 ) )
| ( ( tl @ X0 )
= ( sk__43 @ X0 ) )
| ~ ( ssList @ ( sk__43 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl94]) ).
thf(zip_derived_cl87_082,plain,
! [X0: $i] :
( ( ssItem @ ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl4316,plain,
! [X0: $i] :
( ~ ( ssList @ ( sk__43 @ X0 ) )
| ( ( tl @ X0 )
= ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl491,zip_derived_cl87]) ).
thf(zip_derived_cl89_083,plain,
! [X0: $i] :
( ( ssList @ ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl4317,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ( ( tl @ X0 )
= ( sk__43 @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl4316,zip_derived_cl89]) ).
thf(zip_derived_cl88_084,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl4318,plain,
! [X0: $i] :
( ( nil = X0 )
| ~ ( ssList @ X0 )
| ( ( cons @ ( sk__44 @ X0 ) @ ( tl @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4317,zip_derived_cl88]) ).
thf(zip_derived_cl4321,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( tl @ X0 ) )
= X0 )
| ~ ( ssList @ X0 )
| ( nil = X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl4318]) ).
thf(zip_derived_cl198824,plain,
( ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
= sk__48 )
| ~ ( ssList @ sk__48 )
| ( nil = sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl198792,zip_derived_cl4321]) ).
thf(zip_derived_cl201_085,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl198886,plain,
( ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
= sk__48 )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl198824,zip_derived_cl201]) ).
thf(zip_derived_cl203_086,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl198887,plain,
( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
= sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl198886,zip_derived_cl203]) ).
thf(ax81,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
= ( app @ ( cons @ V @ nil ) @ U ) ) ) ) ).
thf(zip_derived_cl171,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( cons @ X0 @ X1 )
= ( app @ ( cons @ X0 @ nil ) @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax81]) ).
thf(ax84,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) ).
thf(zip_derived_cl176,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(ax7,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( segmentP @ U @ V )
<=> ? [W: $i] :
( ? [X: $i] :
( ( ( app @ ( app @ W @ V ) @ X )
= U )
& ( ssList @ X ) )
& ( ssList @ W ) ) ) ) ) ).
thf(zip_derived_cl21,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( ( app @ ( app @ X3 @ X0 ) @ X1 )
!= X2 )
| ~ ( ssList @ X3 )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ X2 ) ),
inference(cnf,[status(esa)],[ax7]) ).
thf(zip_derived_cl587,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( ( app @ X1 @ X0 )
!= X2 )
| ~ ( ssList @ X1 )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ X2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl21]) ).
thf(zip_derived_cl83_087,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl595,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X0 )
| ( ( app @ X1 @ X0 )
!= X2 )
| ~ ( ssList @ X1 )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl587,zip_derived_cl83]) ).
thf(zip_derived_cl95_088,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl5131,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ X1 )
| ( ( app @ X1 @ X0 )
!= X2 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl595,zip_derived_cl95]) ).
thf(zip_derived_cl5144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X2 )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ ( cons @ X1 @ nil ) )
| ( ( cons @ X1 @ X0 )
!= X2 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl171,zip_derived_cl5131]) ).
thf(zip_derived_cl5172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( cons @ X1 @ X0 )
!= X2 )
| ~ ( ssList @ ( cons @ X1 @ nil ) )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ X2 )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl5144]) ).
thf(zip_derived_cl82_089,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(ax4,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ( cons @ V @ nil )
= U )
& ( ssItem @ V ) ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ( cons @ ( sk__4 @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(ax23,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ) ).
thf(zip_derived_cl92,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( hd @ ( cons @ X0 @ X1 ) )
= X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax23]) ).
thf(zip_derived_cl359,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssItem @ ( sk__4 @ X0 ) )
| ( ( hd @ X0 )
= ( sk__4 @ X0 ) )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl92]) ).
thf(zip_derived_cl83_090,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl360,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssItem @ ( sk__4 @ X0 ) )
| ( ( hd @ X0 )
= ( sk__4 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl83]) ).
thf(zip_derived_cl10,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl3022,plain,
! [X0: $i] :
( ( ( hd @ X0 )
= ( sk__4 @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl360,zip_derived_cl10]) ).
thf(zip_derived_cl11_091,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ( cons @ ( sk__4 @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl3024,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( singletonP @ X0 )
| ( ( cons @ ( hd @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3022,zip_derived_cl11]) ).
thf(zip_derived_cl3028,plain,
! [X0: $i] :
( ( ( cons @ ( hd @ X0 ) @ nil )
= X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3024]) ).
thf(zip_derived_cl82_092,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i] :
( ( ( cons @ X1 @ nil )
!= X0 )
| ~ ( ssItem @ X1 )
| ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl261,plain,
! [X0: $i] :
( ~ ( ssList @ ( cons @ X0 @ nil ) )
| ( singletonP @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl2074,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ X0 )
| ( singletonP @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl261]) ).
thf(zip_derived_cl83_093,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2077,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ( singletonP @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2074,zip_derived_cl83]) ).
thf(zip_derived_cl2078,plain,
! [X0: $i] :
( ( singletonP @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2077]) ).
thf(zip_derived_cl3051,plain,
! [X0: $i] :
( ~ ( ssList @ ( cons @ X0 @ nil ) )
| ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
= ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3028,zip_derived_cl2078]) ).
thf(zip_derived_cl3729,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ X0 )
| ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
= ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3051]) ).
thf(zip_derived_cl83_094,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl3733,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
= ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3729,zip_derived_cl83]) ).
thf(zip_derived_cl3734,plain,
! [X0: $i] :
( ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
= ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3733]) ).
thf(zip_derived_cl82_095,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(zip_derived_cl3740,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ~ ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
| ( ssList @ ( cons @ X0 @ nil ) )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3734,zip_derived_cl82]) ).
thf(zip_derived_cl83_096,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl3806,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ~ ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
| ( ssList @ ( cons @ X0 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3740,zip_derived_cl83]) ).
thf(zip_derived_cl82_097,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(zip_derived_cl3022_098,plain,
! [X0: $i] :
( ( ( hd @ X0 )
= ( sk__4 @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl360,zip_derived_cl10]) ).
thf(zip_derived_cl10_099,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl3023,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( singletonP @ X0 )
| ( ssItem @ ( hd @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3022,zip_derived_cl10]) ).
thf(zip_derived_cl3027,plain,
! [X0: $i] :
( ( ssItem @ ( hd @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3023]) ).
thf(zip_derived_cl2078_100,plain,
! [X0: $i] :
( ( singletonP @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2077]) ).
thf(zip_derived_cl3047,plain,
! [X0: $i] :
( ~ ( ssList @ ( cons @ X0 @ nil ) )
| ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
| ~ ( ssItem @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3027,zip_derived_cl2078]) ).
thf(zip_derived_cl3054,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ X0 )
| ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
| ~ ( ssItem @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3047]) ).
thf(zip_derived_cl83_101,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl3058,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
| ~ ( ssItem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3054,zip_derived_cl83]) ).
thf(zip_derived_cl3059,plain,
! [X0: $i] :
( ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
| ~ ( ssItem @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3058]) ).
thf(zip_derived_cl3961,plain,
! [X0: $i] :
( ( ssList @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl3806,zip_derived_cl3059]) ).
thf(zip_derived_cl209900,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X2 )
| ( segmentP @ X2 @ X0 )
| ( ( cons @ X1 @ X0 )
!= X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl5172,zip_derived_cl3961]) ).
thf(zip_derived_cl209930,plain,
! [X0: $i] :
( ~ ( ssList @ ( tl @ sk__48 ) )
| ~ ( ssItem @ ( hd @ sk__48 ) )
| ~ ( ssList @ X0 )
| ( segmentP @ X0 @ ( tl @ sk__48 ) )
| ( sk__48 != X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl198887,zip_derived_cl209900]) ).
thf(zip_derived_cl198887_102,plain,
( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
= sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl198886,zip_derived_cl203]) ).
thf(zip_derived_cl177_103,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( hd @ ( app @ X1 @ X0 ) )
= ( hd @ X1 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax85]) ).
thf(zip_derived_cl176_104,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(zip_derived_cl178_105,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(zip_derived_cl785,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( ( tl @ X0 )
= ( app @ ( tl @ X0 ) @ nil ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl178]) ).
thf(zip_derived_cl83_106,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl792,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ X0 )
= ( app @ ( tl @ X0 ) @ nil ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl785,zip_derived_cl83]) ).
thf(zip_derived_cl793,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ( tl @ X0 )
= ( app @ ( tl @ X0 ) @ nil ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl792]) ).
thf(zip_derived_cl178_107,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(zip_derived_cl168_108,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax78]) ).
thf(zip_derived_cl783,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ~ ( ssList @ X0 )
| ( nil
= ( app @ X1 @ X0 ) )
| ( ( cons @ ( hd @ ( app @ X1 @ X0 ) ) @ ( app @ ( tl @ X1 ) @ X0 ) )
= ( app @ X1 @ X0 ) )
| ~ ( ssList @ ( app @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl168]) ).
thf(zip_derived_cl174_109,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil
!= ( app @ X1 @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax83]) ).
thf(zip_derived_cl8584,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( ( cons @ ( hd @ ( app @ X1 @ X0 ) ) @ ( app @ ( tl @ X1 ) @ X0 ) )
= ( app @ X1 @ X0 ) )
| ~ ( ssList @ X0 )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl783,zip_derived_cl174]) ).
thf(zip_derived_cl95_110,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl8585,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ~ ( ssList @ X0 )
| ( ( cons @ ( hd @ ( app @ X1 @ X0 ) ) @ ( app @ ( tl @ X1 ) @ X0 ) )
= ( app @ X1 @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl8584,zip_derived_cl95]) ).
thf(zip_derived_cl8641,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ nil )
| ( ( cons @ ( hd @ ( app @ X0 @ nil ) ) @ ( tl @ X0 ) )
= ( app @ X0 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl793,zip_derived_cl8585]) ).
thf(zip_derived_cl83_111,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl8687,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 )
| ( nil = X0 )
| ( ( cons @ ( hd @ ( app @ X0 @ nil ) ) @ ( tl @ X0 ) )
= ( app @ X0 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8641,zip_derived_cl83]) ).
thf(zip_derived_cl8688,plain,
! [X0: $i] :
( ( ( cons @ ( hd @ ( app @ X0 @ nil ) ) @ ( tl @ X0 ) )
= ( app @ X0 @ nil ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8687]) ).
thf(zip_derived_cl9796,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ nil )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
= ( app @ X0 @ nil ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl177,zip_derived_cl8688]) ).
thf(zip_derived_cl83_112,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl9813,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
= ( app @ X0 @ nil ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl9796,zip_derived_cl83]) ).
thf(zip_derived_cl9814,plain,
! [X0: $i] :
( ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
= ( app @ X0 @ nil ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl9813]) ).
thf(zip_derived_cl199185,plain,
( ( sk__48
= ( app @ sk__48 @ nil ) )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl198887,zip_derived_cl9814]) ).
thf(zip_derived_cl201_113,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl199442,plain,
( ( sk__48
= ( app @ sk__48 @ nil ) )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl199185,zip_derived_cl201]) ).
thf(zip_derived_cl203_114,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl199443,plain,
( sk__48
= ( app @ sk__48 @ nil ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl199442,zip_derived_cl203]) ).
thf(zip_derived_cl178_115,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(zip_derived_cl199540,plain,
( ~ ( ssList @ nil )
| ( ( tl @ sk__48 )
= ( app @ ( tl @ sk__48 ) @ nil ) )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl199443,zip_derived_cl178]) ).
thf(zip_derived_cl83_116,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl201_117,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl200024,plain,
( ( ( tl @ sk__48 )
= ( app @ ( tl @ sk__48 ) @ nil ) )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl199540,zip_derived_cl83,zip_derived_cl201]) ).
thf(zip_derived_cl203_118,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl200025,plain,
( ( tl @ sk__48 )
= ( app @ ( tl @ sk__48 ) @ nil ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl200024,zip_derived_cl203]) ).
thf(zip_derived_cl178_119,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(zip_derived_cl93_120,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(zip_derived_cl782,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ~ ( ssList @ X0 )
| ( nil
= ( app @ X1 @ X0 ) )
| ( ssList @ ( app @ ( tl @ X1 ) @ X0 ) )
| ~ ( ssList @ ( app @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl93]) ).
thf(zip_derived_cl174_121,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil
!= ( app @ X1 @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax83]) ).
thf(zip_derived_cl8514,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( ssList @ ( app @ ( tl @ X1 ) @ X0 ) )
| ~ ( ssList @ X0 )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl782,zip_derived_cl174]) ).
thf(zip_derived_cl95_122,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl8515,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ~ ( ssList @ X0 )
| ( ssList @ ( app @ ( tl @ X1 ) @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl8514,zip_derived_cl95]) ).
thf(zip_derived_cl202808,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ~ ( ssList @ nil )
| ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl200025,zip_derived_cl8515]) ).
thf(zip_derived_cl201_123,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl83_124,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl203153,plain,
( ( nil = sk__48 )
| ( ssList @ ( tl @ sk__48 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl202808,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl203_125,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl203154,plain,
ssList @ ( tl @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl203153,zip_derived_cl203]) ).
thf(zip_derived_cl197273_126,plain,
ssItem @ ( hd @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).
thf(zip_derived_cl209952,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( segmentP @ X0 @ ( tl @ sk__48 ) )
| ( sk__48 != X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl209930,zip_derived_cl203154,zip_derived_cl197273]) ).
thf(zip_derived_cl259913,plain,
( ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
| ~ ( ssList @ sk__48 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl209952]) ).
thf(zip_derived_cl201_127,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl259914,plain,
segmentP @ sk__48 @ ( tl @ sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl259913,zip_derived_cl201]) ).
thf(zip_derived_cl259940,plain,
~ ( neq @ ( tl @ sk__48 ) @ nil ),
inference(demod,[status(thm)],[zip_derived_cl92282,zip_derived_cl259914]) ).
thf(zip_derived_cl259969,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( ( tl @ sk__48 )
= nil )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl259940]) ).
thf(zip_derived_cl203154_128,plain,
ssList @ ( tl @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl203153,zip_derived_cl203]) ).
thf(zip_derived_cl83_129,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl259971,plain,
( ( tl @ sk__48 )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl259969,zip_derived_cl203154,zip_derived_cl83]) ).
thf(zip_derived_cl259971_130,plain,
( ( tl @ sk__48 )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl259969,zip_derived_cl203154,zip_derived_cl83]) ).
thf(zip_derived_cl259976,plain,
( ( sk__47
= ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1723,zip_derived_cl259971,zip_derived_cl259971]) ).
thf(zip_derived_cl198887_131,plain,
( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
= sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl198886,zip_derived_cl203]) ).
thf(zip_derived_cl259971_132,plain,
( ( tl @ sk__48 )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl259969,zip_derived_cl203154,zip_derived_cl83]) ).
thf(zip_derived_cl260001,plain,
( ( cons @ ( hd @ sk__48 ) @ nil )
= sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl198887,zip_derived_cl259971]) ).
thf(zip_derived_cl199443_133,plain,
( sk__48
= ( app @ sk__48 @ nil ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl199442,zip_derived_cl203]) ).
thf(zip_derived_cl97_134,plain,
! [X0: $i] :
( ( ( app @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax28]) ).
thf(ax82,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ) ).
thf(zip_derived_cl172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ ( app @ X1 @ X0 ) @ X2 )
= ( app @ X1 @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax82]) ).
thf(zip_derived_cl1219,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( ( app @ X0 @ X1 )
= ( app @ nil @ ( app @ X0 @ X1 ) ) )
| ~ ( ssList @ X1 )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl97,zip_derived_cl172]) ).
thf(zip_derived_cl83_135,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1230,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( ( app @ X0 @ X1 )
= ( app @ nil @ ( app @ X0 @ X1 ) ) )
| ~ ( ssList @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1219,zip_derived_cl83]) ).
thf(zip_derived_cl1231,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( app @ X0 @ X1 )
= ( app @ nil @ ( app @ X0 @ X1 ) ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1230]) ).
thf(zip_derived_cl199699,plain,
( ~ ( ssList @ nil )
| ( sk__48
= ( app @ nil @ sk__48 ) )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl199443,zip_derived_cl1231]) ).
thf(zip_derived_cl83_136,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl201_137,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl200246,plain,
( sk__48
= ( app @ nil @ sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl199699,zip_derived_cl83,zip_derived_cl201]) ).
thf(zip_derived_cl260001_138,plain,
( ( cons @ ( hd @ sk__48 ) @ nil )
= sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl198887,zip_derived_cl259971]) ).
thf(zip_derived_cl200246_139,plain,
( sk__48
= ( app @ nil @ sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl199699,zip_derived_cl83,zip_derived_cl201]) ).
thf(zip_derived_cl201_140,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl275627,plain,
sk__47 = sk__48,
inference(demod,[status(thm)],[zip_derived_cl259976,zip_derived_cl260001,zip_derived_cl200246,zip_derived_cl260001,zip_derived_cl200246,zip_derived_cl201]) ).
thf(zip_derived_cl176_141,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(zip_derived_cl93_142,plain,
! [X0: $i] :
( ( nil = X0 )
| ( ssList @ ( tl @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax24]) ).
thf(ax45,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) ).
thf(zip_derived_cl122,plain,
! [X0: $i] :
( ( frontsegP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax45]) ).
thf(zip_derived_cl2056_143,plain,
! [X0: $i] :
( ( frontsegP @ sk__47 @ X0 )
| ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
| ~ ( ssList @ X0 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2055,zip_derived_cl203]) ).
thf(zip_derived_cl2058,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( frontsegP @ sk__47 @ nil )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl2056]) ).
thf(zip_derived_cl83_144,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2060,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( frontsegP @ sk__47 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl2058,zip_derived_cl83]) ).
thf(zip_derived_cl2061,plain,
( ~ ( ssList @ sk__48 )
| ( nil = sk__48 )
| ( frontsegP @ sk__47 @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2060]) ).
thf(zip_derived_cl201_145,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl2062,plain,
( ( nil = sk__48 )
| ( frontsegP @ sk__47 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl2061,zip_derived_cl201]) ).
thf(zip_derived_cl203_146,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl2063,plain,
frontsegP @ sk__47 @ nil,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2062,zip_derived_cl203]) ).
thf(zip_derived_cl12_147,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( ( app @ X0 @ ( sk__5 @ X0 @ X1 ) )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl2064,plain,
( ~ ( ssList @ nil )
| ( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2063,zip_derived_cl12]) ).
thf(zip_derived_cl83_148,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_149,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2069,plain,
( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2064,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl2069_150,plain,
( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2064,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl97_151,plain,
! [X0: $i] :
( ( ( app @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax28]) ).
thf(zip_derived_cl2104,plain,
( ( sk__47
= ( sk__5 @ nil @ sk__47 ) )
| ~ ( ssList @ ( sk__5 @ nil @ sk__47 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2069,zip_derived_cl97]) ).
thf(zip_derived_cl2063_152,plain,
frontsegP @ sk__47 @ nil,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2062,zip_derived_cl203]) ).
thf(zip_derived_cl13_153,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( ssList @ ( sk__5 @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl2065,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk__5 @ nil @ sk__47 ) )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2063,zip_derived_cl13]) ).
thf(zip_derived_cl83_154,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_155,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2070,plain,
ssList @ ( sk__5 @ nil @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2065,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl2132,plain,
( sk__47
= ( sk__5 @ nil @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl2104,zip_derived_cl2070]) ).
thf(zip_derived_cl2136,plain,
( ( app @ nil @ sk__47 )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2069,zip_derived_cl2132]) ).
thf(zip_derived_cl21_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( ( app @ ( app @ X3 @ X0 ) @ X1 )
!= X2 )
| ~ ( ssList @ X3 )
| ( segmentP @ X2 @ X0 )
| ~ ( ssList @ X2 ) ),
inference(cnf,[status(esa)],[ax7]) ).
thf(zip_derived_cl2155,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ sk__47 )
| ~ ( ssList @ X1 )
| ( ( app @ sk__47 @ X1 )
!= X0 )
| ~ ( ssList @ nil )
| ( segmentP @ X0 @ sk__47 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2136,zip_derived_cl21]) ).
thf(zip_derived_cl190_157,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl83_158,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2181,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( app @ sk__47 @ X1 )
!= X0 )
| ( segmentP @ X0 @ sk__47 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2155,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl2597,plain,
! [X0: $i] :
( ~ ( ssList @ sk__47 )
| ~ ( ssList @ nil )
| ( sk__47 != X0 )
| ( segmentP @ X0 @ sk__47 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl2181]) ).
thf(zip_derived_cl190_159,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl83_160,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2600,plain,
! [X0: $i] :
( ( sk__47 != X0 )
| ( segmentP @ X0 @ sk__47 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2597,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl2602,plain,
( ~ ( ssList @ sk__47 )
| ( segmentP @ sk__47 @ sk__47 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl2600]) ).
thf(zip_derived_cl190_161,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2603,plain,
segmentP @ sk__47 @ sk__47,
inference(demod,[status(thm)],[zip_derived_cl2602,zip_derived_cl190]) ).
thf(zip_derived_cl275633,plain,
~ ( neq @ sk__47 @ nil ),
inference(demod,[status(thm)],[zip_derived_cl240,zip_derived_cl275627,zip_derived_cl2603]) ).
thf(zip_derived_cl276655,plain,
( ~ ( ssList @ sk__47 )
| ( sk__47 = nil )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl275633]) ).
thf(zip_derived_cl190_162,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl83_163,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl276657,plain,
sk__47 = nil,
inference(demod,[status(thm)],[zip_derived_cl276655,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl176_164,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(zip_derived_cl171_165,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( cons @ X0 @ X1 )
= ( app @ ( cons @ X0 @ nil ) @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax81]) ).
thf(zip_derived_cl172_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ ( app @ X1 @ X0 ) @ X2 )
= ( app @ X1 @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax82]) ).
thf(zip_derived_cl1217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X0 )
| ( ( app @ ( cons @ X1 @ X0 ) @ X2 )
= ( app @ ( cons @ X1 @ nil ) @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ ( cons @ X1 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl171,zip_derived_cl172]) ).
thf(zip_derived_cl1228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( cons @ X1 @ nil ) )
| ~ ( ssList @ X2 )
| ( ( app @ ( cons @ X1 @ X0 ) @ X2 )
= ( app @ ( cons @ X1 @ nil ) @ ( app @ X0 @ X2 ) ) )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1217]) ).
thf(zip_derived_cl3961_167,plain,
! [X0: $i] :
( ( ssList @ ( cons @ X0 @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl3806,zip_derived_cl3059]) ).
thf(zip_derived_cl33260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ( ( app @ ( cons @ X1 @ X0 ) @ X2 )
= ( app @ ( cons @ X1 @ nil ) @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1228,zip_derived_cl3961]) ).
thf(zip_derived_cl33382,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ( ( app @ ( cons @ X1 @ X0 ) @ nil )
= ( app @ ( cons @ X1 @ nil ) @ X0 ) )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl33260]) ).
thf(zip_derived_cl83_168,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl33446,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ( ( app @ ( cons @ X1 @ X0 ) @ nil )
= ( app @ ( cons @ X1 @ nil ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl33382,zip_derived_cl83]) ).
thf(zip_derived_cl33447,plain,
! [X0: $i,X1: $i] :
( ( ( app @ ( cons @ X1 @ X0 ) @ nil )
= ( app @ ( cons @ X1 @ nil ) @ X0 ) )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl33446]) ).
thf(zip_derived_cl175279_169,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).
thf(zip_derived_cl1231_170,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( app @ X0 @ X1 )
= ( app @ nil @ ( app @ X0 @ X1 ) ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1230]) ).
thf(zip_derived_cl196391,plain,
( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl1231]) ).
thf(zip_derived_cl2653_171,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl201_172,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl196698,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl196391,zip_derived_cl2653,zip_derived_cl201]) ).
thf(zip_derived_cl1231_173,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( app @ X0 @ X1 )
= ( app @ nil @ ( app @ X0 @ X1 ) ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1230]) ).
thf(zip_derived_cl172_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ ( app @ X1 @ X0 ) @ X2 )
= ( app @ X1 @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax82]) ).
thf(zip_derived_cl176_175,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(ax79,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ W @ V )
= ( app @ U @ V ) )
=> ( W = U ) ) ) ) ) ).
thf(zip_derived_cl169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ X2 @ X0 )
!= ( app @ X1 @ X0 ) )
| ( X2 = X1 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax79]) ).
thf(zip_derived_cl657,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( X0
!= ( app @ X1 @ nil ) )
| ( X0 = X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl169]) ).
thf(zip_derived_cl83_176,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl671,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( X0
!= ( app @ X1 @ nil ) )
| ( X0 = X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl657,zip_derived_cl83]) ).
thf(zip_derived_cl672,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( X0 = X1 )
| ( X0
!= ( app @ X1 @ nil ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl671]) ).
thf(zip_derived_cl1202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X1 )
| ~ ( ssList @ nil )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( X2
= ( app @ X1 @ X0 ) )
| ( X2
!= ( app @ X1 @ ( app @ X0 @ nil ) ) )
| ~ ( ssList @ X2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl172,zip_derived_cl672]) ).
thf(zip_derived_cl83_177,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( X2
= ( app @ X1 @ X0 ) )
| ( X2
!= ( app @ X1 @ ( app @ X0 @ nil ) ) )
| ~ ( ssList @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1202,zip_derived_cl83]) ).
thf(zip_derived_cl95_178,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl40036,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ( X2
!= ( app @ X1 @ ( app @ X0 @ nil ) ) )
| ( X2
= ( app @ X1 @ X0 ) )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl1254,zip_derived_cl95]) ).
thf(zip_derived_cl40043,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ~ ( ssList @ X1 )
| ( X1
!= ( app @ X0 @ nil ) )
| ( X1
= ( app @ nil @ X0 ) )
| ~ ( ssList @ X0 )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1231,zip_derived_cl40036]) ).
thf(zip_derived_cl83_179,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_180,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl40086,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( X1
!= ( app @ X0 @ nil ) )
| ( X1
= ( app @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl40043,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl40087,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( app @ nil @ X0 ) )
| ( X1
!= ( app @ X0 @ nil ) )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl40086]) ).
thf(zip_derived_cl40546,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ ( app @ X0 @ nil ) )
| ( ( app @ X0 @ nil )
= ( app @ nil @ X0 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl40087]) ).
thf(ax46,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) ).
thf(zip_derived_cl123,plain,
! [X0: $i] :
( ( nil != X0 )
| ( frontsegP @ nil @ X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax46]) ).
thf(zip_derived_cl262,plain,
( ~ ( ssList @ nil )
| ( frontsegP @ nil @ nil ) ),
inference(eq_res,[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl83_181,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl263,plain,
frontsegP @ nil @ nil,
inference(demod,[status(thm)],[zip_derived_cl262,zip_derived_cl83]) ).
thf(zip_derived_cl12_182,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( ( app @ X0 @ ( sk__5 @ X0 @ X1 ) )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl294,plain,
( ~ ( ssList @ nil )
| ( ( app @ nil @ ( sk__5 @ nil @ nil ) )
= nil )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl263,zip_derived_cl12]) ).
thf(zip_derived_cl83_183,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_184,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl299,plain,
( ( app @ nil @ ( sk__5 @ nil @ nil ) )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl294,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl299_185,plain,
( ( app @ nil @ ( sk__5 @ nil @ nil ) )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl294,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl97_186,plain,
! [X0: $i] :
( ( ( app @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax28]) ).
thf(zip_derived_cl303,plain,
( ( nil
= ( sk__5 @ nil @ nil ) )
| ~ ( ssList @ ( sk__5 @ nil @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl299,zip_derived_cl97]) ).
thf(zip_derived_cl263_187,plain,
frontsegP @ nil @ nil,
inference(demod,[status(thm)],[zip_derived_cl262,zip_derived_cl83]) ).
thf(zip_derived_cl13_188,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( frontsegP @ X1 @ X0 )
| ( ssList @ ( sk__5 @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax5]) ).
thf(zip_derived_cl320,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk__5 @ nil @ nil ) )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl263,zip_derived_cl13]) ).
thf(zip_derived_cl83_189,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_190,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl324,plain,
ssList @ ( sk__5 @ nil @ nil ),
inference(demod,[status(thm)],[zip_derived_cl320,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl325,plain,
( nil
= ( sk__5 @ nil @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl303,zip_derived_cl324]) ).
thf(zip_derived_cl326,plain,
( ( app @ nil @ nil )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl299,zip_derived_cl325]) ).
thf(zip_derived_cl172_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ ( app @ X1 @ X0 ) @ X2 )
= ( app @ X1 @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax82]) ).
thf(zip_derived_cl95_192,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl1188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
| ~ ( ssList @ ( app @ X2 @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl172,zip_derived_cl95]) ).
thf(zip_derived_cl1243,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( app @ X2 @ X1 ) )
| ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1188]) ).
thf(zip_derived_cl95_193,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl37007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1243,zip_derived_cl95]) ).
thf(zip_derived_cl37072,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ~ ( ssList @ nil )
| ( ssList @ ( app @ X0 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl326,zip_derived_cl37007]) ).
thf(zip_derived_cl83_194,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_195,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl37152,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X0 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl37072,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl40648,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= ( app @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl40546,zip_derived_cl37152]) ).
thf(zip_derived_cl1231_196,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( app @ X0 @ X1 )
= ( app @ nil @ ( app @ X0 @ X1 ) ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1230]) ).
thf(zip_derived_cl40736,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( ( app @ X0 @ nil )
= ( app @ nil @ ( app @ X0 @ nil ) ) )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl40648,zip_derived_cl1231]) ).
thf(zip_derived_cl83_197,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl41425,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( ( app @ X0 @ nil )
= ( app @ nil @ ( app @ X0 @ nil ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl40736,zip_derived_cl83]) ).
thf(zip_derived_cl41426,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= ( app @ nil @ ( app @ X0 @ nil ) ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl41425]) ).
thf(zip_derived_cl172_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ ( app @ X1 @ X0 ) @ X2 )
= ( app @ X1 @ ( app @ X0 @ X2 ) ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax82]) ).
thf(zip_derived_cl178_199,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(zip_derived_cl1194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
= ( app @ ( tl @ ( app @ X2 @ X1 ) ) @ X0 ) )
| ( nil
= ( app @ X2 @ X1 ) )
| ~ ( ssList @ ( app @ X2 @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl172,zip_derived_cl178]) ).
thf(zip_derived_cl1249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( app @ X2 @ X1 ) )
| ( nil
= ( app @ X2 @ X1 ) )
| ( ( tl @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
= ( app @ ( tl @ ( app @ X2 @ X1 ) ) @ X0 ) )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1194]) ).
thf(zip_derived_cl95_200,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl38127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( ( tl @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
= ( app @ ( tl @ ( app @ X2 @ X1 ) ) @ X0 ) )
| ( nil
= ( app @ X2 @ X1 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1249,zip_derived_cl95]) ).
thf(zip_derived_cl43040,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ~ ( ssList @ nil )
| ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X0 @ nil ) )
= ( app @ ( tl @ ( app @ nil @ X0 ) ) @ nil ) )
| ( nil
= ( app @ nil @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl41426,zip_derived_cl38127]) ).
thf(zip_derived_cl83_201,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_202,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl43300,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X0 @ nil ) )
= ( app @ ( tl @ ( app @ nil @ X0 ) ) @ nil ) )
| ( nil
= ( app @ nil @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl43040,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl43301,plain,
! [X0: $i] :
( ( nil
= ( app @ nil @ X0 ) )
| ( ( tl @ ( app @ X0 @ nil ) )
= ( app @ ( tl @ ( app @ nil @ X0 ) ) @ nil ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl43300]) ).
thf(zip_derived_cl237867,plain,
( ( nil
= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ nil ) )
= ( app @ ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) @ nil ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl196698,zip_derived_cl43301]) ).
thf(zip_derived_cl175279_203,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).
thf(zip_derived_cl178_204,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ( tl @ ( app @ X1 @ X0 ) )
= ( app @ ( tl @ X1 ) @ X0 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax86]) ).
thf(zip_derived_cl196233,plain,
( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
| ( ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
= ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) )
| ( nil = sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl178]) ).
thf(zip_derived_cl2653_205,plain,
ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).
thf(zip_derived_cl91850_206,plain,
( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
= sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl91849,zip_derived_cl203]) ).
thf(zip_derived_cl201_207,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl196499,plain,
( ( ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
= sk__47 )
| ( nil = sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl196233,zip_derived_cl2653,zip_derived_cl91850,zip_derived_cl201]) ).
thf(zip_derived_cl203_208,plain,
nil != sk__48,
inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).
thf(zip_derived_cl196500,plain,
( ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
= sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl196499,zip_derived_cl203]) ).
thf(zip_derived_cl176_209,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(ax6,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( rearsegP @ U @ V )
<=> ? [W: $i] :
( ( ( app @ W @ V )
= U )
& ( ssList @ W ) ) ) ) ) ).
thf(zip_derived_cl15,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( rearsegP @ X1 @ X0 )
| ( ( app @ ( sk__6 @ X0 @ X1 ) @ X0 )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax6]) ).
thf(zip_derived_cl364,plain,
! [X0: $i] :
( ~ ( ssList @ ( sk__6 @ nil @ X0 ) )
| ~ ( ssList @ nil )
| ~ ( rearsegP @ X0 @ nil )
| ( ( sk__6 @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl15]) ).
thf(zip_derived_cl83_210,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl369,plain,
! [X0: $i] :
( ~ ( ssList @ ( sk__6 @ nil @ X0 ) )
| ~ ( rearsegP @ X0 @ nil )
| ( ( sk__6 @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl364,zip_derived_cl83]) ).
thf(ax51,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) ).
thf(zip_derived_cl129,plain,
! [X0: $i] :
( ( rearsegP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax51]) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( rearsegP @ X1 @ X0 )
| ( ssList @ ( sk__6 @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax6]) ).
thf(zip_derived_cl393,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( ssList @ ( sk__6 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl16]) ).
thf(zip_derived_cl83_211,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl396,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( sk__6 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl393,zip_derived_cl83]) ).
thf(zip_derived_cl397,plain,
! [X0: $i] :
( ( ssList @ ( sk__6 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl396]) ).
thf(zip_derived_cl3064,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( ( sk__6 @ nil @ X0 )
= X0 )
| ~ ( rearsegP @ X0 @ nil ) ),
inference(clc,[status(thm)],[zip_derived_cl369,zip_derived_cl397]) ).
thf(zip_derived_cl129_212,plain,
! [X0: $i] :
( ( rearsegP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax51]) ).
thf(zip_derived_cl3065,plain,
! [X0: $i] :
( ( ( sk__6 @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl3064,zip_derived_cl129]) ).
thf(zip_derived_cl129_213,plain,
! [X0: $i] :
( ( rearsegP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax51]) ).
thf(zip_derived_cl176_214,plain,
! [X0: $i] :
( ( ( app @ X0 @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax84]) ).
thf(zip_derived_cl2136_215,plain,
( ( app @ nil @ sk__47 )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2069,zip_derived_cl2132]) ).
thf(zip_derived_cl97_216,plain,
! [X0: $i] :
( ( ( app @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax28]) ).
thf(ax58,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) ).
thf(zip_derived_cl137,plain,
! [X0: $i] :
( ( nil != X0 )
| ( segmentP @ nil @ X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax58]) ).
thf(zip_derived_cl222,plain,
( ~ ( ssList @ nil )
| ( segmentP @ nil @ nil ) ),
inference(eq_res,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl83_217,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl223,plain,
segmentP @ nil @ nil,
inference(demod,[status(thm)],[zip_derived_cl222,zip_derived_cl83]) ).
thf(zip_derived_cl135_218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X1 )
| ( segmentP @ ( app @ ( app @ X2 @ X3 ) @ X1 ) @ X0 )
| ~ ( segmentP @ X3 @ X0 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X3 ) ),
inference(cnf,[status(esa)],[ax56]) ).
thf(zip_derived_cl1484,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ nil )
| ~ ( ssList @ X0 )
| ( segmentP @ ( app @ ( app @ X1 @ nil ) @ X0 ) @ nil )
| ~ ( ssList @ X1 )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl135]) ).
thf(zip_derived_cl83_219,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_220,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1501,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( segmentP @ ( app @ ( app @ X1 @ nil ) @ X0 ) @ nil )
| ~ ( ssList @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1484,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl2733,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ~ ( ssList @ X0 )
| ( segmentP @ ( app @ nil @ X0 ) @ nil )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl97,zip_derived_cl1501]) ).
thf(zip_derived_cl83_221,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_222,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2744,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( segmentP @ ( app @ nil @ X0 ) @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl2733,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl2765,plain,
( ~ ( ssList @ sk__47 )
| ( segmentP @ sk__47 @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2136,zip_derived_cl2744]) ).
thf(zip_derived_cl190_223,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2770,plain,
segmentP @ sk__47 @ nil,
inference(demod,[status(thm)],[zip_derived_cl2765,zip_derived_cl190]) ).
thf(zip_derived_cl19,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( segmentP @ X1 @ X0 )
| ( ( app @ ( app @ ( sk__7 @ X0 @ X1 ) @ X0 ) @ ( sk__8 @ X0 @ X1 ) )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax7]) ).
thf(zip_derived_cl2828,plain,
( ~ ( ssList @ nil )
| ( ( app @ ( app @ ( sk__7 @ nil @ sk__47 ) @ nil ) @ ( sk__8 @ nil @ sk__47 ) )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2770,zip_derived_cl19]) ).
thf(zip_derived_cl83_224,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_225,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2835,plain,
( ( app @ ( app @ ( sk__7 @ nil @ sk__47 ) @ nil ) @ ( sk__8 @ nil @ sk__47 ) )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2828,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl2880,plain,
( ~ ( ssList @ ( sk__7 @ nil @ sk__47 ) )
| ( ( app @ ( sk__7 @ nil @ sk__47 ) @ ( sk__8 @ nil @ sk__47 ) )
= sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl2835]) ).
thf(zip_derived_cl2770_226,plain,
segmentP @ sk__47 @ nil,
inference(demod,[status(thm)],[zip_derived_cl2765,zip_derived_cl190]) ).
thf(zip_derived_cl20,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( segmentP @ X1 @ X0 )
| ( ssList @ ( sk__7 @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax7]) ).
thf(zip_derived_cl2829,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk__7 @ nil @ sk__47 ) )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2770,zip_derived_cl20]) ).
thf(zip_derived_cl83_227,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_228,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2836,plain,
ssList @ ( sk__7 @ nil @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2829,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl2881,plain,
( ( app @ ( sk__7 @ nil @ sk__47 ) @ ( sk__8 @ nil @ sk__47 ) )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2880,zip_derived_cl2836]) ).
thf(ax50,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( rearsegP @ U @ V )
=> ( rearsegP @ ( app @ W @ U ) @ V ) ) ) ) ) ).
thf(zip_derived_cl128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ~ ( rearsegP @ X1 @ X0 )
| ( rearsegP @ ( app @ X2 @ X1 ) @ X0 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax50]) ).
thf(zip_derived_cl2994,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( rearsegP @ ( sk__8 @ nil @ sk__47 ) @ X0 )
| ( rearsegP @ sk__47 @ X0 )
| ~ ( ssList @ ( sk__7 @ nil @ sk__47 ) )
| ~ ( ssList @ ( sk__8 @ nil @ sk__47 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2881,zip_derived_cl128]) ).
thf(zip_derived_cl2836_229,plain,
ssList @ ( sk__7 @ nil @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2829,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl2770_230,plain,
segmentP @ sk__47 @ nil,
inference(demod,[status(thm)],[zip_derived_cl2765,zip_derived_cl190]) ).
thf(zip_derived_cl18,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( segmentP @ X1 @ X0 )
| ( ssList @ ( sk__8 @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax7]) ).
thf(zip_derived_cl2827,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk__8 @ nil @ sk__47 ) )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2770,zip_derived_cl18]) ).
thf(zip_derived_cl83_231,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_232,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2834,plain,
ssList @ ( sk__8 @ nil @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2827,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl3020,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( rearsegP @ ( sk__8 @ nil @ sk__47 ) @ X0 )
| ( rearsegP @ sk__47 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2994,zip_derived_cl2836,zip_derived_cl2834]) ).
thf(zip_derived_cl3085,plain,
( ~ ( ssList @ ( sk__8 @ nil @ sk__47 ) )
| ~ ( ssList @ nil )
| ( rearsegP @ sk__47 @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl3020]) ).
thf(zip_derived_cl2834_233,plain,
ssList @ ( sk__8 @ nil @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl2827,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl83_234,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl3087,plain,
rearsegP @ sk__47 @ nil,
inference(demod,[status(thm)],[zip_derived_cl3085,zip_derived_cl2834,zip_derived_cl83]) ).
thf(zip_derived_cl15_235,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( rearsegP @ X1 @ X0 )
| ( ( app @ ( sk__6 @ X0 @ X1 ) @ X0 )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax6]) ).
thf(zip_derived_cl3088,plain,
( ~ ( ssList @ nil )
| ( ( app @ ( sk__6 @ nil @ sk__47 ) @ nil )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3087,zip_derived_cl15]) ).
thf(zip_derived_cl83_236,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_237,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3093,plain,
( ( app @ ( sk__6 @ nil @ sk__47 ) @ nil )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl3088,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl3132,plain,
( ~ ( ssList @ sk__47 )
| ( ( app @ sk__47 @ nil )
= sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3065,zip_derived_cl3093]) ).
thf(zip_derived_cl190_238,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3133,plain,
( ( app @ sk__47 @ nil )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl3132,zip_derived_cl190]) ).
thf(zip_derived_cl196490_239,plain,
ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl196226,zip_derived_cl2653,zip_derived_cl201]) ).
thf(zip_derived_cl238481,plain,
( ( nil
= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ nil ) )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl237867,zip_derived_cl196500,zip_derived_cl3133,zip_derived_cl196490]) ).
thf(zip_derived_cl196495_240,plain,
( nil
!= ( cons @ ( hd @ sk__48 ) @ sk__47 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl196494,zip_derived_cl203]) ).
thf(zip_derived_cl238482,plain,
( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ nil ) )
= sk__47 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl238481,zip_derived_cl196495]) ).
thf(zip_derived_cl239165,plain,
( ~ ( ssList @ sk__47 )
| ~ ( ssItem @ ( hd @ sk__48 ) )
| ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) )
= sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl33447,zip_derived_cl238482]) ).
thf(zip_derived_cl190_241,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197273_242,plain,
ssItem @ ( hd @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).
thf(zip_derived_cl239172,plain,
( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) )
= sk__47 ),
inference(demod,[status(thm)],[zip_derived_cl239165,zip_derived_cl190,zip_derived_cl197273]) ).
thf(zip_derived_cl92_243,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( hd @ ( cons @ X0 @ X1 ) )
= X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax23]) ).
thf(zip_derived_cl4502_244,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssList @ X1 )
| ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
= ( app @ X0 @ X1 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl4501,zip_derived_cl95]) ).
thf(zip_derived_cl4580,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ~ ( ssItem @ X0 )
| ~ ( ssList @ ( cons @ X0 @ X2 ) )
| ( nil
= ( cons @ X0 @ X2 ) )
| ~ ( ssList @ X1 )
| ( ( cons @ X0 @ ( tl @ ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) )
= ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl92,zip_derived_cl4502]) ).
thf(zip_derived_cl82_245,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ssList @ ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax16]) ).
thf(zip_derived_cl174275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( cons @ X0 @ ( tl @ ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) )
= ( app @ ( cons @ X0 @ X2 ) @ X1 ) )
| ~ ( ssList @ X1 )
| ( nil
= ( cons @ X0 @ X2 ) )
| ~ ( ssItem @ X0 )
| ~ ( ssList @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl4580,zip_derived_cl82]) ).
thf(ax21,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ) ).
thf(zip_derived_cl90,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( nil
!= ( cons @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax21]) ).
thf(zip_derived_cl174276,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ~ ( ssItem @ X0 )
| ~ ( ssList @ X1 )
| ( ( cons @ X0 @ ( tl @ ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) )
= ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl174275,zip_derived_cl90]) ).
thf(zip_derived_cl239602,plain,
( ~ ( ssList @ nil )
| ~ ( ssItem @ ( hd @ sk__48 ) )
| ~ ( ssList @ sk__47 )
| ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl239172,zip_derived_cl174276]) ).
thf(zip_derived_cl83_246,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl197273_247,plain,
ssItem @ ( hd @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).
thf(zip_derived_cl190_248,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl239756,plain,
( ( cons @ ( hd @ sk__48 ) @ sk__47 )
= ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl239602,zip_derived_cl83,zip_derived_cl197273,zip_derived_cl190]) ).
thf(zip_derived_cl175,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil != X0 )
| ( nil != X1 )
| ( nil
= ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax83]) ).
thf(zip_derived_cl243000,plain,
( ~ ( ssList @ sk__47 )
| ( nil != sk__47 )
| ( nil
!= ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( nil
= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl239756,zip_derived_cl175]) ).
thf(zip_derived_cl190_249,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl243437,plain,
( ( nil != sk__47 )
| ( nil
!= ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( nil
= ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl243000,zip_derived_cl190]) ).
thf(zip_derived_cl196495_250,plain,
( nil
!= ( cons @ ( hd @ sk__48 ) @ sk__47 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl196494,zip_derived_cl203]) ).
thf(zip_derived_cl243438,plain,
( ( nil != sk__47 )
| ( nil
!= ( cons @ ( hd @ sk__48 ) @ nil ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl243437,zip_derived_cl196495]) ).
thf(zip_derived_cl1827_251,plain,
( ( sk__47
= ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1826,zip_derived_cl203]) ).
thf(zip_derived_cl173,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( nil
!= ( app @ X1 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax83]) ).
thf(zip_derived_cl1838,plain,
( ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( nil != sk__47 )
| ( nil
= ( cons @ ( hd @ sk__48 ) @ nil ) )
| ~ ( ssList @ ( tl @ sk__48 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1827,zip_derived_cl173]) ).
thf(zip_derived_cl1870,plain,
( ~ ( ssList @ ( tl @ sk__48 ) )
| ( nil
= ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( nil != sk__47 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1838]) ).
thf(zip_derived_cl203154_252,plain,
ssList @ ( tl @ sk__48 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl203153,zip_derived_cl203]) ).
thf(zip_derived_cl203255,plain,
( ( nil
= ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( nil != sk__47 )
| ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1870,zip_derived_cl203154]) ).
thf(zip_derived_cl243808,plain,
( ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
| ( nil != sk__47 ) ),
inference(clc,[status(thm)],[zip_derived_cl243438,zip_derived_cl203255]) ).
thf(zip_derived_cl260001_253,plain,
( ( cons @ ( hd @ sk__48 ) @ nil )
= sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl198887,zip_derived_cl259971]) ).
thf(zip_derived_cl201_254,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl261676,plain,
nil != sk__47,
inference(demod,[status(thm)],[zip_derived_cl243808,zip_derived_cl260001,zip_derived_cl201]) ).
thf(zip_derived_cl276658,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl276657,zip_derived_cl261676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC072+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.sbai3tWb3k true
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 19:20:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.19/0.65 % Total configuration time : 435
% 0.19/0.65 % Estimated wc time : 1092
% 0.19/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.68 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.70 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.72/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.14/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.14/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.14/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.14/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 260.58/38.13 % Solved by fo/fo13.sh.
% 260.58/38.13 % done 23449 iterations in 37.345s
% 260.58/38.13 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 260.58/38.13 % SZS output start Refutation
% See solution above
% 260.58/38.14
% 260.58/38.14
% 260.58/38.14 % Terminating...
% 260.58/38.21 % Runner terminated.
% 260.58/38.23 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------