TSTP Solution File: SWC388+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC388+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pV1tkGsfuB true
% Computer : n006.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 21:31:14 EDT 2023
% Result : Theorem 251.14s 36.56s
% Output : Refutation 251.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 49
% Syntax : Number of formulae : 377 ( 93 unt; 22 typ; 0 def)
% Number of atoms : 1038 ( 340 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 2699 ( 495 ~; 602 |; 17 &;1521 @)
% ( 7 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 6 con; 0-2 aty)
% Number of variables : 295 ( 0 ^; 285 !; 10 ?; 295 :)
% Comments :
%------------------------------------------------------------------------------
thf(frontsegP_type,type,
frontsegP: $i > $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(nil_type,type,
nil: $i ).
thf(app_type,type,
app: $i > $i > $i ).
thf(sk__49_type,type,
sk__49: $i ).
thf(sk__44_type,type,
sk__44: $i > $i ).
thf(sk__5_type,type,
sk__5: $i > $i > $i ).
thf(hd_type,type,
hd: $i > $i ).
thf(ssList_type,type,
ssList: $i > $o ).
thf(tl_type,type,
tl: $i > $i ).
thf(sk__7_type,type,
sk__7: $i > $i > $i ).
thf(sk__47_type,type,
sk__47: $i ).
thf(sk__4_type,type,
sk__4: $i > $i ).
thf(sk__50_type,type,
sk__50: $i ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(sk__8_type,type,
sk__8: $i > $i > $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(sk__48_type,type,
sk__48: $i ).
thf(sk__43_type,type,
sk__43: $i > $i ).
thf(ax57,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) ).
thf(zip_derived_cl136,plain,
! [X0: $i] :
( ( segmentP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax57]) ).
thf(co1,conjecture,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ~ ( segmentP @ X @ W )
| ? [Y: $i] :
( ( memberP @ V @ Y )
& ( ( cons @ Y @ nil )
= U )
& ( ssItem @ Y ) )
| ( ~ ( singletonP @ W )
& ( neq @ X @ nil ) )
| ( ( nil = V )
& ( nil = U ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ~ ( segmentP @ X @ W )
| ? [Y: $i] :
( ( memberP @ V @ Y )
& ( ( cons @ Y @ nil )
= U )
& ( ssItem @ Y ) )
| ( ~ ( singletonP @ W )
& ( neq @ X @ nil ) )
| ( ( nil = V )
& ( nil = U ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[co1]) ).
thf(zip_derived_cl196,plain,
segmentP @ sk__50 @ sk__49,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197,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_cl202,plain,
segmentP @ sk__48 @ sk__47,
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl197,zip_derived_cl194]) ).
thf(ax54,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) ).
thf(zip_derived_cl133,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( X1 = X0 )
| ~ ( segmentP @ X0 @ X1 )
| ~ ( segmentP @ X1 @ X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax54]) ).
thf(zip_derived_cl592,plain,
( ~ ( ssList @ sk__48 )
| ( sk__47 = sk__48 )
| ~ ( segmentP @ sk__47 @ sk__48 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl202,zip_derived_cl133]) ).
thf(zip_derived_cl198,plain,
ssList @ sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_001,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_cl190,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl597,plain,
( ( sk__47 = sk__48 )
| ~ ( segmentP @ sk__47 @ sk__48 ) ),
inference(demod,[status(thm)],[zip_derived_cl592,zip_derived_cl201,zip_derived_cl190]) ).
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(zip_derived_cl195,plain,
( ( singletonP @ sk__49 )
| ~ ( neq @ sk__50 @ nil ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl194_002,plain,
sk__47 = sk__49,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl197_003,plain,
sk__48 = sk__50,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl203,plain,
( ( singletonP @ sk__47 )
| ~ ( neq @ sk__48 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl195,zip_derived_cl194,zip_derived_cl197]) ).
thf(zip_derived_cl451,plain,
( ~ ( ssList @ sk__48 )
| ( sk__48 = nil )
| ~ ( ssList @ nil )
| ( singletonP @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl203]) ).
thf(zip_derived_cl201_004,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(ax17,axiom,
ssList @ nil ).
thf(zip_derived_cl83,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl454,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl202_005,plain,
segmentP @ sk__48 @ sk__47,
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl197,zip_derived_cl194]) ).
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_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_cl429,plain,
( ~ ( ssList @ sk__47 )
| ( ( app @ ( app @ ( sk__7 @ sk__47 @ sk__48 ) @ sk__47 ) @ ( sk__8 @ sk__47 @ sk__48 ) )
= sk__48 )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl202,zip_derived_cl19]) ).
thf(zip_derived_cl190_006,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl201_007,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl435,plain,
( ( app @ ( app @ ( sk__7 @ sk__47 @ sk__48 ) @ sk__47 ) @ ( sk__8 @ sk__47 @ sk__48 ) )
= sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl429,zip_derived_cl190,zip_derived_cl201]) ).
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_cl4447,plain,
( ~ ( ssList @ sk__47 )
| ( sk__48
= ( app @ ( sk__7 @ sk__47 @ sk__48 ) @ ( app @ sk__47 @ ( sk__8 @ sk__47 @ sk__48 ) ) ) )
| ~ ( ssList @ ( sk__8 @ sk__47 @ sk__48 ) )
| ~ ( ssList @ ( sk__7 @ sk__47 @ sk__48 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl435,zip_derived_cl172]) ).
thf(zip_derived_cl190_008,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl202_009,plain,
segmentP @ sk__48 @ sk__47,
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl197,zip_derived_cl194]) ).
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_cl415,plain,
( ~ ( ssList @ sk__47 )
| ( ssList @ ( sk__8 @ sk__47 @ sk__48 ) )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl202,zip_derived_cl18]) ).
thf(zip_derived_cl190_010,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl201_011,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl420,plain,
ssList @ ( sk__8 @ sk__47 @ sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl415,zip_derived_cl190,zip_derived_cl201]) ).
thf(zip_derived_cl202_012,plain,
segmentP @ sk__48 @ sk__47,
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl197,zip_derived_cl194]) ).
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_cl482,plain,
( ~ ( ssList @ sk__47 )
| ( ssList @ ( sk__7 @ sk__47 @ sk__48 ) )
| ~ ( ssList @ sk__48 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl202,zip_derived_cl20]) ).
thf(zip_derived_cl190_013,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl201_014,plain,
ssList @ sk__48,
inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).
thf(zip_derived_cl487,plain,
ssList @ ( sk__7 @ sk__47 @ sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl482,zip_derived_cl190,zip_derived_cl201]) ).
thf(zip_derived_cl4477,plain,
( sk__48
= ( app @ ( sk__7 @ sk__47 @ sk__48 ) @ ( app @ sk__47 @ ( sk__8 @ sk__47 @ sk__48 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4447,zip_derived_cl190,zip_derived_cl420,zip_derived_cl487]) ).
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(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(zip_derived_cl764,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssItem @ ( sk__4 @ X0 ) )
| ( ( cons @ ( sk__4 @ X0 ) @ X1 )
= ( app @ X0 @ X1 ) )
| ~ ( ssList @ X1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl171]) ).
thf(zip_derived_cl10,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl8931,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( cons @ ( sk__4 @ X0 ) @ X1 )
= ( app @ X0 @ X1 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl764,zip_derived_cl10]) ).
thf(ax3,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( memberP @ U @ V )
<=> ? [W: $i] :
( ? [X: $i] :
( ( ( app @ W @ ( cons @ V @ X ) )
= U )
& ( ssList @ X ) )
& ( ssList @ W ) ) ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( ssItem @ X0 )
| ~ ( ssList @ X1 )
| ( ( app @ X3 @ ( cons @ X0 @ X1 ) )
!= X2 )
| ~ ( ssList @ X3 )
| ( memberP @ X2 @ X0 )
| ~ ( ssList @ X2 ) ),
inference(cnf,[status(esa)],[ax3]) ).
thf(zip_derived_cl238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( app @ X2 @ ( cons @ X1 @ X0 ) ) )
| ( memberP @ ( app @ X2 @ ( cons @ X1 @ X0 ) ) @ X1 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl8968,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X1 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
| ( memberP @ ( app @ X2 @ ( app @ X1 @ X0 ) ) @ ( sk__4 @ X1 ) )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssItem @ ( sk__4 @ X1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8931,zip_derived_cl238]) ).
thf(zip_derived_cl9087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssItem @ ( sk__4 @ X1 ) )
| ~ ( ssList @ X2 )
| ( memberP @ ( app @ X2 @ ( app @ X1 @ X0 ) ) @ ( sk__4 @ X1 ) )
| ~ ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
| ~ ( ssList @ X0 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8968]) ).
thf(zip_derived_cl10_015,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl250886,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X1 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
| ( memberP @ ( app @ X2 @ ( app @ X1 @ X0 ) ) @ ( sk__4 @ X1 ) )
| ~ ( ssList @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl9087,zip_derived_cl10]) ).
thf(zip_derived_cl172_016,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(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_cl2710,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_cl2808,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_cl2710]) ).
thf(zip_derived_cl95_017,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl73606,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_cl2808,zip_derived_cl95]) ).
thf(zip_derived_cl250887,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X2 )
| ( memberP @ ( app @ X2 @ ( app @ X1 @ X0 ) ) @ ( sk__4 @ X1 ) )
| ~ ( ssList @ X0 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl250886,zip_derived_cl73606]) ).
thf(zip_derived_cl250946,plain,
( ~ ( ssList @ ( sk__7 @ sk__47 @ sk__48 ) )
| ( memberP @ sk__48 @ ( sk__4 @ sk__47 ) )
| ~ ( ssList @ ( sk__8 @ sk__47 @ sk__48 ) )
| ~ ( singletonP @ sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4477,zip_derived_cl250887]) ).
thf(zip_derived_cl487_018,plain,
ssList @ ( sk__7 @ sk__47 @ sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl482,zip_derived_cl190,zip_derived_cl201]) ).
thf(zip_derived_cl420_019,plain,
ssList @ ( sk__8 @ sk__47 @ sk__48 ),
inference(demod,[status(thm)],[zip_derived_cl415,zip_derived_cl190,zip_derived_cl201]) ).
thf(zip_derived_cl190_020,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl251137,plain,
( ( memberP @ sk__48 @ ( sk__4 @ sk__47 ) )
| ~ ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl250946,zip_derived_cl487,zip_derived_cl420,zip_derived_cl190]) ).
thf(zip_derived_cl251262,plain,
( ( sk__48 = nil )
| ( memberP @ sk__48 @ ( sk__4 @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl454,zip_derived_cl251137]) ).
thf(zip_derived_cl193,plain,
! [X0: $i] :
( ~ ( memberP @ sk__48 @ X0 )
| ( ( cons @ X0 @ nil )
!= sk__47 )
| ~ ( ssItem @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl251286,plain,
( ( sk__48 = nil )
| ( ( cons @ ( sk__4 @ sk__47 ) @ nil )
!= sk__47 )
| ~ ( ssItem @ ( sk__4 @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl251262,zip_derived_cl193]) ).
thf(zip_derived_cl10_021,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
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(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_cl288,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( ( app @ nil @ ( sk__5 @ nil @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl12]) ).
thf(zip_derived_cl83_022,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl292,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ nil @ ( sk__5 @ nil @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl288,zip_derived_cl83]) ).
thf(zip_derived_cl293,plain,
! [X0: $i] :
( ( ( app @ nil @ ( sk__5 @ nil @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl292]) ).
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(zip_derived_cl363,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( X0
= ( sk__5 @ nil @ X0 ) )
| ~ ( ssList @ ( sk__5 @ nil @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl293,zip_derived_cl97]) ).
thf(zip_derived_cl122_023,plain,
! [X0: $i] :
( ( frontsegP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax45]) ).
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_cl304,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( ssList @ ( sk__5 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl13]) ).
thf(zip_derived_cl83_024,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl307,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( sk__5 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl304,zip_derived_cl83]) ).
thf(zip_derived_cl308,plain,
! [X0: $i] :
( ( ssList @ ( sk__5 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl307]) ).
thf(zip_derived_cl2253,plain,
! [X0: $i] :
( ( X0
= ( sk__5 @ nil @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl363,zip_derived_cl308]) ).
thf(zip_derived_cl454_025,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl11_026,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_cl458,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_027,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl459,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssItem @ ( sk__4 @ X0 ) )
| ( ( hd @ X0 )
= ( sk__4 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl458,zip_derived_cl83]) ).
thf(zip_derived_cl10_028,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl4557,plain,
! [X0: $i] :
( ( ( hd @ X0 )
= ( sk__4 @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl459,zip_derived_cl10]) ).
thf(zip_derived_cl11_029,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ( cons @ ( sk__4 @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl4559,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( singletonP @ X0 )
| ( ( cons @ ( hd @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4557,zip_derived_cl11]) ).
thf(zip_derived_cl4565,plain,
! [X0: $i] :
( ( ( cons @ ( hd @ X0 ) @ nil )
= X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl4559]) ).
thf(zip_derived_cl4599,plain,
( ( sk__48 = nil )
| ( ( cons @ ( hd @ sk__47 ) @ nil )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl454,zip_derived_cl4565]) ).
thf(zip_derived_cl190_030,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4600,plain,
( ( sk__48 = nil )
| ( ( cons @ ( hd @ sk__47 ) @ nil )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl4599,zip_derived_cl190]) ).
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_cl240,plain,
( ~ ( ssList @ nil )
| ( frontsegP @ nil @ nil ) ),
inference(eq_res,[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl83_031,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl241,plain,
frontsegP @ nil @ nil,
inference(demod,[status(thm)],[zip_derived_cl240,zip_derived_cl83]) ).
thf(zip_derived_cl12_032,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_cl289,plain,
( ~ ( ssList @ nil )
| ( ( app @ nil @ ( sk__5 @ nil @ nil ) )
= nil )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl241,zip_derived_cl12]) ).
thf(zip_derived_cl83_033,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_034,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl294,plain,
( ( app @ nil @ ( sk__5 @ nil @ nil ) )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl289,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl294_035,plain,
( ( app @ nil @ ( sk__5 @ nil @ nil ) )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl289,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl97_036,plain,
! [X0: $i] :
( ( ( app @ nil @ X0 )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax28]) ).
thf(zip_derived_cl298,plain,
( ( nil
= ( sk__5 @ nil @ nil ) )
| ~ ( ssList @ ( sk__5 @ nil @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl294,zip_derived_cl97]) ).
thf(zip_derived_cl241_037,plain,
frontsegP @ nil @ nil,
inference(demod,[status(thm)],[zip_derived_cl240,zip_derived_cl83]) ).
thf(zip_derived_cl13_038,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_cl305,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk__5 @ nil @ nil ) )
| ~ ( ssList @ nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl241,zip_derived_cl13]) ).
thf(zip_derived_cl83_039,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_040,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl309,plain,
ssList @ ( sk__5 @ nil @ nil ),
inference(demod,[status(thm)],[zip_derived_cl305,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl310,plain,
( nil
= ( sk__5 @ nil @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl298,zip_derived_cl309]) ).
thf(zip_derived_cl311,plain,
( ( app @ nil @ nil )
= nil ),
inference(demod,[status(thm)],[zip_derived_cl294,zip_derived_cl310]) ).
thf(ax27,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( cons @ W @ ( app @ V @ U ) )
= ( app @ ( cons @ W @ V ) @ U ) ) ) ) ) ).
thf(zip_derived_cl96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( cons @ X1 @ ( app @ X0 @ X2 ) )
= ( app @ ( cons @ X1 @ X0 ) @ X2 ) )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X2 ) ),
inference(cnf,[status(esa)],[ax27]) ).
thf(zip_derived_cl1591,plain,
! [X0: $i] :
( ~ ( ssList @ nil )
| ( ( cons @ X0 @ nil )
= ( app @ ( cons @ X0 @ nil ) @ nil ) )
| ~ ( ssItem @ X0 )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl311,zip_derived_cl96]) ).
thf(zip_derived_cl83_041,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl83_042,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1605,plain,
! [X0: $i] :
( ( ( cons @ X0 @ nil )
= ( app @ ( cons @ X0 @ nil ) @ nil ) )
| ~ ( ssItem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1591,zip_derived_cl83,zip_derived_cl83]) ).
thf(zip_derived_cl4666,plain,
( ( sk__48 = nil )
| ( sk__47
= ( app @ sk__47 @ nil ) )
| ~ ( ssItem @ ( hd @ sk__47 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4600,zip_derived_cl1605]) ).
thf(zip_derived_cl454_043,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl4557_044,plain,
! [X0: $i] :
( ( ( hd @ X0 )
= ( sk__4 @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl459,zip_derived_cl10]) ).
thf(zip_derived_cl10_045,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl4558,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( singletonP @ X0 )
| ( ssItem @ ( hd @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4557,zip_derived_cl10]) ).
thf(zip_derived_cl4564,plain,
! [X0: $i] :
( ( ssItem @ ( hd @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl4558]) ).
thf(zip_derived_cl4576,plain,
( ( sk__48 = nil )
| ( ssItem @ ( hd @ sk__47 ) )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl454,zip_derived_cl4564]) ).
thf(zip_derived_cl190_046,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4577,plain,
( ( sk__48 = nil )
| ( ssItem @ ( hd @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4576,zip_derived_cl190]) ).
thf(zip_derived_cl5442,plain,
( ( sk__47
= ( app @ sk__47 @ nil ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl4666,zip_derived_cl4577]) ).
thf(zip_derived_cl122_047,plain,
! [X0: $i] :
( ( frontsegP @ X0 @ nil )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax45]) ).
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_cl2050,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ nil )
| ( frontsegP @ ( app @ X0 @ X1 ) @ nil )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl118]) ).
thf(zip_derived_cl83_048,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl2078,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( frontsegP @ ( app @ X0 @ X1 ) @ nil )
| ~ ( ssList @ X1 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2050,zip_derived_cl83]) ).
thf(zip_derived_cl2079,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( frontsegP @ ( app @ X0 @ X1 ) @ nil )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2078]) ).
thf(zip_derived_cl6466,plain,
( ( sk__48 = nil )
| ~ ( ssList @ nil )
| ( frontsegP @ sk__47 @ nil )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5442,zip_derived_cl2079]) ).
thf(zip_derived_cl83_049,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_050,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6496,plain,
( ( sk__48 = nil )
| ( frontsegP @ sk__47 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl6466,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl12_051,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_cl6504,plain,
( ( sk__48 = nil )
| ~ ( ssList @ nil )
| ( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl6496,zip_derived_cl12]) ).
thf(zip_derived_cl83_052,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl190_053,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6509,plain,
( ( sk__48 = nil )
| ( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl6504,zip_derived_cl83,zip_derived_cl190]) ).
thf(zip_derived_cl6563,plain,
( ~ ( ssList @ sk__47 )
| ( sk__48 = nil )
| ( ( app @ nil @ sk__47 )
= sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2253,zip_derived_cl6509]) ).
thf(zip_derived_cl190_054,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6564,plain,
( ( sk__48 = nil )
| ( ( app @ nil @ sk__47 )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl6563,zip_derived_cl190]) ).
thf(zip_derived_cl11_055,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ( cons @ ( sk__4 @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl238_056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ ( app @ X2 @ ( cons @ X1 @ X0 ) ) )
| ( memberP @ ( app @ X2 @ ( cons @ X1 @ X0 ) ) @ X1 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl3045,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( memberP @ ( app @ X1 @ X0 ) @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X1 )
| ~ ( ssList @ nil )
| ~ ( ssItem @ ( sk__4 @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl238]) ).
thf(zip_derived_cl83_057,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl3074,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ ( app @ X1 @ X0 ) )
| ( memberP @ ( app @ X1 @ X0 ) @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X1 )
| ~ ( ssItem @ ( sk__4 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3045,zip_derived_cl83]) ).
thf(zip_derived_cl95_058,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl91477,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X1 )
| ( memberP @ ( app @ X1 @ X0 ) @ ( sk__4 @ X0 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl3074,zip_derived_cl95]) ).
thf(zip_derived_cl10_059,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl91478,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ( memberP @ ( app @ X1 @ X0 ) @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl91477,zip_derived_cl10]) ).
thf(zip_derived_cl91561,plain,
( ( sk__48 = nil )
| ~ ( ssList @ sk__47 )
| ~ ( singletonP @ sk__47 )
| ( memberP @ sk__47 @ ( sk__4 @ sk__47 ) )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl6564,zip_derived_cl91478]) ).
thf(zip_derived_cl190_060,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl83_061,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl91663,plain,
( ( sk__48 = nil )
| ~ ( singletonP @ sk__47 )
| ( memberP @ sk__47 @ ( sk__4 @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl91561,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl454_062,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl151162,plain,
( ( memberP @ sk__47 @ ( sk__4 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl91663,zip_derived_cl454]) ).
thf(ax20,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil = U )
| ? [V: $i] :
( ? [W: $i] :
( ( ( cons @ W @ V )
= U )
& ( ssItem @ W ) )
& ( ssList @ V ) ) ) ) ).
thf(zip_derived_cl87,plain,
! [X0: $i] :
( ( ssItem @ ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl454_063,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl11_064,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ( cons @ ( sk__4 @ X0 ) @ nil )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
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_cl492,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssItem @ ( sk__4 @ X0 ) )
| ( ( tl @ X0 )
= nil )
| ~ ( ssList @ nil ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl94]) ).
thf(zip_derived_cl83_065,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl493,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( singletonP @ X0 )
| ~ ( ssItem @ ( sk__4 @ X0 ) )
| ( ( tl @ X0 )
= nil ) ),
inference(demod,[status(thm)],[zip_derived_cl492,zip_derived_cl83]) ).
thf(zip_derived_cl10_066,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl3177,plain,
! [X0: $i] :
( ( ( tl @ X0 )
= nil )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl493,zip_derived_cl10]) ).
thf(zip_derived_cl3183,plain,
( ( sk__48 = nil )
| ( ( tl @ sk__47 )
= nil )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl454,zip_derived_cl3177]) ).
thf(zip_derived_cl190_067,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3184,plain,
( ( sk__48 = nil )
| ( ( tl @ sk__47 )
= nil ) ),
inference(demod,[status(thm)],[zip_derived_cl3183,zip_derived_cl190]) ).
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(zip_derived_cl94_068,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( tl @ ( cons @ X0 @ X1 ) )
= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax25]) ).
thf(zip_derived_cl542,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_069,plain,
! [X0: $i] :
( ( ssItem @ ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl5650,plain,
! [X0: $i] :
( ~ ( ssList @ ( sk__43 @ X0 ) )
| ( ( tl @ X0 )
= ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl542,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_cl5651,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ( ( tl @ X0 )
= ( sk__43 @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl5650,zip_derived_cl89]) ).
thf(zip_derived_cl88_070,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl5652,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_cl5651,zip_derived_cl88]) ).
thf(zip_derived_cl5655,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( tl @ X0 ) )
= X0 )
| ~ ( ssList @ X0 )
| ( nil = X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl5652]) ).
thf(zip_derived_cl6031,plain,
( ( sk__48 = nil )
| ( ( cons @ ( sk__44 @ sk__47 ) @ nil )
= sk__47 )
| ~ ( ssList @ sk__47 )
| ( nil = sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3184,zip_derived_cl5655]) ).
thf(zip_derived_cl190_071,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6033,plain,
( ( sk__48 = nil )
| ( ( cons @ ( sk__44 @ sk__47 ) @ nil )
= sk__47 )
| ( nil = sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl6031,zip_derived_cl190]) ).
thf(ax37,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ) ).
thf(zip_derived_cl110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssItem @ X0 )
| ~ ( memberP @ ( cons @ X0 @ X1 ) @ X2 )
| ( X2 = X0 )
| ( memberP @ X1 @ X2 )
| ~ ( ssList @ X1 )
| ~ ( ssItem @ X2 ) ),
inference(cnf,[status(esa)],[ax37]) ).
thf(zip_derived_cl6044,plain,
! [X0: $i] :
( ( nil = sk__47 )
| ( sk__48 = nil )
| ~ ( ssItem @ ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ( memberP @ nil @ X0 )
| ~ ( ssList @ nil )
| ~ ( ssItem @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl6033,zip_derived_cl110]) ).
thf(zip_derived_cl83_072,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl6122,plain,
! [X0: $i] :
( ( nil = sk__47 )
| ( sk__48 = nil )
| ~ ( ssItem @ ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ( memberP @ nil @ X0 )
| ~ ( ssItem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl6044,zip_derived_cl83]) ).
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_cl12_073,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_cl287,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( ( app @ X0 @ ( sk__5 @ X0 @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl117,zip_derived_cl12]) ).
thf(zip_derived_cl291,plain,
! [X0: $i] :
( ( ( app @ X0 @ ( sk__5 @ X0 @ X0 ) )
= X0 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl287]) ).
thf(zip_derived_cl5442_074,plain,
( ( sk__47
= ( app @ sk__47 @ nil ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl4666,zip_derived_cl4577]) ).
thf(ax80,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ) ).
thf(zip_derived_cl170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ X0 @ X2 )
!= ( app @ X0 @ X1 ) )
| ( X2 = X1 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax80]) ).
thf(zip_derived_cl5446,plain,
! [X0: $i] :
( ( sk__48 = nil )
| ~ ( ssList @ sk__47 )
| ( sk__47
!= ( app @ sk__47 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ nil )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5442,zip_derived_cl170]) ).
thf(zip_derived_cl190_075,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl83_076,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl5484,plain,
! [X0: $i] :
( ( sk__48 = nil )
| ( sk__47
!= ( app @ sk__47 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl5446,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl5665,plain,
( ~ ( ssList @ sk__47 )
| ( sk__48 = nil )
| ( sk__47 != sk__47 )
| ( nil
= ( sk__5 @ sk__47 @ sk__47 ) )
| ~ ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl291,zip_derived_cl5484]) ).
thf(zip_derived_cl190_077,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5669,plain,
( ( sk__48 = nil )
| ( sk__47 != sk__47 )
| ( nil
= ( sk__5 @ sk__47 @ sk__47 ) )
| ~ ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5665,zip_derived_cl190]) ).
thf(zip_derived_cl5670,plain,
( ~ ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) )
| ( nil
= ( sk__5 @ sk__47 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(simplify,[status(thm)],[zip_derived_cl5669]) ).
thf(zip_derived_cl5442_078,plain,
( ( sk__47
= ( app @ sk__47 @ nil ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl4666,zip_derived_cl4577]) ).
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_cl326,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_079,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ( ssList @ ( app @ X1 @ X0 ) )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax26]) ).
thf(zip_derived_cl3762,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ~ ( ssList @ X0 )
| ( frontsegP @ ( app @ X1 @ X0 ) @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl326,zip_derived_cl95]) ).
thf(zip_derived_cl5463,plain,
( ( sk__48 = nil )
| ~ ( ssList @ sk__47 )
| ~ ( ssList @ nil )
| ( frontsegP @ sk__47 @ sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5442,zip_derived_cl3762]) ).
thf(zip_derived_cl190_080,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl83_081,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl5502,plain,
( ( sk__48 = nil )
| ( frontsegP @ sk__47 @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl5463,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl13_082,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_cl5522,plain,
( ( sk__48 = nil )
| ~ ( ssList @ sk__47 )
| ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5502,zip_derived_cl13]) ).
thf(zip_derived_cl190_083,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl190_084,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5527,plain,
( ( sk__48 = nil )
| ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5522,zip_derived_cl190,zip_derived_cl190]) ).
thf(zip_derived_cl13439,plain,
( ( sk__48 = nil )
| ( nil
= ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl5670,zip_derived_cl5527]) ).
thf(zip_derived_cl5502_085,plain,
( ( sk__48 = nil )
| ( frontsegP @ sk__47 @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl5463,zip_derived_cl190,zip_derived_cl83]) ).
thf(zip_derived_cl12_086,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_cl5521,plain,
( ( sk__48 = nil )
| ~ ( ssList @ sk__47 )
| ( ( app @ sk__47 @ ( sk__5 @ sk__47 @ sk__47 ) )
= sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5502,zip_derived_cl12]) ).
thf(zip_derived_cl190_087,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl190_088,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5526,plain,
( ( sk__48 = nil )
| ( ( app @ sk__47 @ ( sk__5 @ sk__47 @ sk__47 ) )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl5521,zip_derived_cl190,zip_derived_cl190]) ).
thf(zip_derived_cl8931_089,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( ( cons @ ( sk__4 @ X0 ) @ X1 )
= ( app @ X0 @ X1 ) )
| ~ ( singletonP @ X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl764,zip_derived_cl10]) ).
thf(ax18,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) ).
thf(zip_derived_cl84,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( cons @ X0 @ X1 )
!= X1 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax18]) ).
thf(zip_derived_cl8934,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X0 )
| ~ ( ssItem @ ( sk__4 @ X1 ) )
| ( ( app @ X1 @ X0 )
!= X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8931,zip_derived_cl84]) ).
thf(zip_derived_cl9053,plain,
! [X0: $i,X1: $i] :
( ( ( app @ X1 @ X0 )
!= X0 )
| ~ ( ssItem @ ( sk__4 @ X1 ) )
| ~ ( ssList @ X0 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8934]) ).
thf(zip_derived_cl10_090,plain,
! [X0: $i] :
( ~ ( singletonP @ X0 )
| ( ssItem @ ( sk__4 @ X0 ) )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax4]) ).
thf(zip_derived_cl10792,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ~ ( singletonP @ X1 )
| ~ ( ssList @ X0 )
| ( ( app @ X1 @ X0 )
!= X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl9053,zip_derived_cl10]) ).
thf(zip_derived_cl10835,plain,
( ( sk__48 = nil )
| ~ ( ssList @ sk__47 )
| ~ ( singletonP @ sk__47 )
| ~ ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) )
| ( sk__47
!= ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5526,zip_derived_cl10792]) ).
thf(zip_derived_cl190_091,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10879,plain,
( ( sk__48 = nil )
| ~ ( singletonP @ sk__47 )
| ~ ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) )
| ( sk__47
!= ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl10835,zip_derived_cl190]) ).
thf(zip_derived_cl454_092,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl10906,plain,
( ( sk__47
!= ( sk__5 @ sk__47 @ sk__47 ) )
| ~ ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl10879,zip_derived_cl454]) ).
thf(zip_derived_cl5527_093,plain,
( ( sk__48 = nil )
| ( ssList @ ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5522,zip_derived_cl190,zip_derived_cl190]) ).
thf(zip_derived_cl10907,plain,
( ( sk__48 = nil )
| ( sk__47
!= ( sk__5 @ sk__47 @ sk__47 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl10906,zip_derived_cl5527]) ).
thf(zip_derived_cl13454,plain,
( ( sk__48 = nil )
| ( sk__48 = nil )
| ( sk__47 != nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13439,zip_derived_cl10907]) ).
thf(zip_derived_cl13469,plain,
( ( sk__47 != nil )
| ( sk__48 = nil ) ),
inference(simplify,[status(thm)],[zip_derived_cl13454]) ).
thf(zip_derived_cl192,plain,
( ( nil != sk__48 )
| ( nil != sk__47 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13470,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl175805,plain,
! [X0: $i] :
( ( sk__48 = nil )
| ~ ( ssItem @ ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ( memberP @ nil @ X0 )
| ~ ( ssItem @ X0 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl6122,zip_derived_cl13470]) ).
thf(ax38,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) ).
thf(zip_derived_cl113,plain,
! [X0: $i] :
( ~ ( memberP @ nil @ X0 )
| ~ ( ssItem @ X0 ) ),
inference(cnf,[status(esa)],[ax38]) ).
thf(zip_derived_cl175806,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ~ ( ssItem @ ( sk__44 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl175805,zip_derived_cl113]) ).
thf(zip_derived_cl175807,plain,
! [X0: $i] :
( ~ ( ssList @ sk__47 )
| ( nil = sk__47 )
| ~ ( ssItem @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ( sk__48 = nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl175806]) ).
thf(zip_derived_cl190_094,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175810,plain,
! [X0: $i] :
( ( nil = sk__47 )
| ~ ( ssItem @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ( sk__48 = nil ) ),
inference(demod,[status(thm)],[zip_derived_cl175807,zip_derived_cl190]) ).
thf(zip_derived_cl13470_095,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl175811,plain,
! [X0: $i] :
( ~ ( ssItem @ X0 )
| ( X0
= ( sk__44 @ sk__47 ) )
| ~ ( memberP @ sk__47 @ X0 )
| ( sk__48 = nil ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl175810,zip_derived_cl13470]) ).
thf(zip_derived_cl184223,plain,
( ( sk__48 = nil )
| ~ ( ssItem @ ( sk__4 @ sk__47 ) )
| ( ( sk__4 @ sk__47 )
= ( sk__44 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl151162,zip_derived_cl175811]) ).
thf(zip_derived_cl184232,plain,
( ( ( sk__4 @ sk__47 )
= ( sk__44 @ sk__47 ) )
| ~ ( ssItem @ ( sk__4 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(simplify,[status(thm)],[zip_derived_cl184223]) ).
thf(zip_derived_cl184295,plain,
( ~ ( ssList @ sk__47 )
| ~ ( singletonP @ sk__47 )
| ( ( sk__4 @ sk__47 )
= ( sk__44 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl184232]) ).
thf(zip_derived_cl190_096,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl184299,plain,
( ~ ( singletonP @ sk__47 )
| ( ( sk__4 @ sk__47 )
= ( sk__44 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(demod,[status(thm)],[zip_derived_cl184295,zip_derived_cl190]) ).
thf(zip_derived_cl454_097,plain,
( ( sk__48 = nil )
| ( singletonP @ sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl451,zip_derived_cl201,zip_derived_cl83]) ).
thf(zip_derived_cl184310,plain,
( ( sk__48 = nil )
| ( ( sk__4 @ sk__47 )
= ( sk__44 @ sk__47 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl184299,zip_derived_cl454]) ).
thf(zip_derived_cl89_098,plain,
! [X0: $i] :
( ( ssList @ ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl88_099,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl92_100,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( hd @ ( cons @ X0 @ X1 ) )
= X0 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax23]) ).
thf(zip_derived_cl541,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ~ ( ssItem @ ( sk__44 @ X0 ) )
| ( ( hd @ X0 )
= ( sk__44 @ X0 ) )
| ~ ( ssList @ ( sk__43 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl92]) ).
thf(zip_derived_cl87_101,plain,
! [X0: $i] :
( ( ssItem @ ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl5619,plain,
! [X0: $i] :
( ~ ( ssList @ ( sk__43 @ X0 ) )
| ( ( hd @ X0 )
= ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl541,zip_derived_cl87]) ).
thf(zip_derived_cl89_102,plain,
! [X0: $i] :
( ( ssList @ ( sk__43 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl5620,plain,
! [X0: $i] :
( ~ ( ssList @ X0 )
| ( nil = X0 )
| ( ( hd @ X0 )
= ( sk__44 @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl5619,zip_derived_cl89]) ).
thf(zip_derived_cl88_103,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl5622,plain,
! [X0: $i] :
( ( nil = X0 )
| ~ ( ssList @ X0 )
| ( ( cons @ ( hd @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5620,zip_derived_cl88]) ).
thf(zip_derived_cl5625,plain,
! [X0: $i] :
( ( ( cons @ ( hd @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ~ ( ssList @ X0 )
| ( nil = X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl5622]) ).
thf(zip_derived_cl4600_104,plain,
( ( sk__48 = nil )
| ( ( cons @ ( hd @ sk__47 ) @ nil )
= sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl4599,zip_derived_cl190]) ).
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_cl171_105,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(zip_derived_cl170_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( ssList @ X0 )
| ( ( app @ X0 @ X2 )
!= ( app @ X0 @ X1 ) )
| ( X2 = X1 )
| ~ ( ssList @ X2 )
| ~ ( ssList @ X1 ) ),
inference(cnf,[status(esa)],[ax80]) ).
thf(zip_derived_cl660,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( X0
!= ( app @ X0 @ X1 ) )
| ( nil = X1 )
| ~ ( ssList @ nil )
| ~ ( ssList @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl170]) ).
thf(zip_derived_cl83_107,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl674,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssList @ X0 )
| ( X0
!= ( app @ X0 @ X1 ) )
| ( nil = X1 )
| ~ ( ssList @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl83]) ).
thf(zip_derived_cl675,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ( X0
!= ( app @ X0 @ X1 ) )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl674]) ).
thf(zip_derived_cl1736,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X0 )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X0 )
| ( nil = X0 )
| ( ( cons @ X1 @ nil )
!= ( cons @ X1 @ X0 ) )
| ~ ( ssList @ ( cons @ X1 @ nil ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl171,zip_derived_cl675]) ).
thf(zip_derived_cl1750,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ ( cons @ X1 @ nil ) )
| ( ( cons @ X1 @ nil )
!= ( cons @ X1 @ X0 ) )
| ( nil = X0 )
| ~ ( ssItem @ X1 )
| ~ ( ssList @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1736]) ).
thf(zip_derived_cl1833,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ X0 )
| ( ( cons @ X0 @ nil )
!= ( cons @ X0 @ X1 ) )
| ( nil = X1 )
| ~ ( ssItem @ X0 )
| ~ ( ssList @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl1750]) ).
thf(zip_derived_cl83_108,plain,
ssList @ nil,
inference(cnf,[status(esa)],[ax17]) ).
thf(zip_derived_cl1835,plain,
! [X0: $i,X1: $i] :
( ~ ( ssItem @ X0 )
| ( ( cons @ X0 @ nil )
!= ( cons @ X0 @ X1 ) )
| ( nil = X1 )
| ~ ( ssItem @ X0 )
| ~ ( ssList @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1833,zip_derived_cl83]) ).
thf(zip_derived_cl1836,plain,
! [X0: $i,X1: $i] :
( ~ ( ssList @ X1 )
| ( nil = X1 )
| ( ( cons @ X0 @ nil )
!= ( cons @ X0 @ X1 ) )
| ~ ( ssItem @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1835]) ).
thf(zip_derived_cl4669,plain,
! [X0: $i] :
( ( sk__48 = nil )
| ~ ( ssList @ X0 )
| ( nil = X0 )
| ( sk__47
!= ( cons @ ( hd @ sk__47 ) @ X0 ) )
| ~ ( ssItem @ ( hd @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4600,zip_derived_cl1836]) ).
thf(zip_derived_cl4577_109,plain,
( ( sk__48 = nil )
| ( ssItem @ ( hd @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4576,zip_derived_cl190]) ).
thf(zip_derived_cl13837,plain,
! [X0: $i] :
( ( sk__47
!= ( cons @ ( hd @ sk__47 ) @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl4669,zip_derived_cl4577]) ).
thf(zip_derived_cl13841,plain,
( ( nil = sk__47 )
| ~ ( ssList @ sk__47 )
| ( sk__47 != sk__47 )
| ( nil
= ( sk__43 @ sk__47 ) )
| ~ ( ssList @ ( sk__43 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5625,zip_derived_cl13837]) ).
thf(zip_derived_cl190_110,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13847,plain,
( ( nil = sk__47 )
| ( sk__47 != sk__47 )
| ( nil
= ( sk__43 @ sk__47 ) )
| ~ ( ssList @ ( sk__43 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(demod,[status(thm)],[zip_derived_cl13841,zip_derived_cl190]) ).
thf(zip_derived_cl13848,plain,
( ( sk__48 = nil )
| ~ ( ssList @ ( sk__43 @ sk__47 ) )
| ( nil
= ( sk__43 @ sk__47 ) )
| ( nil = sk__47 ) ),
inference(simplify,[status(thm)],[zip_derived_cl13847]) ).
thf(zip_derived_cl13470_111,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl13849,plain,
( ( sk__48 = nil )
| ~ ( ssList @ ( sk__43 @ sk__47 ) )
| ( nil
= ( sk__43 @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl13848,zip_derived_cl13470]) ).
thf(zip_derived_cl13851,plain,
( ~ ( ssList @ sk__47 )
| ( nil = sk__47 )
| ( sk__48 = nil )
| ( nil
= ( sk__43 @ sk__47 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl13849]) ).
thf(zip_derived_cl190_112,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13853,plain,
( ( nil = sk__47 )
| ( sk__48 = nil )
| ( nil
= ( sk__43 @ sk__47 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl13851,zip_derived_cl190]) ).
thf(zip_derived_cl13470_113,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl13854,plain,
( ( sk__48 = nil )
| ( nil
= ( sk__43 @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl13853,zip_derived_cl13470]) ).
thf(zip_derived_cl88_114,plain,
! [X0: $i] :
( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
= X0 )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl13857,plain,
( ( sk__48 = nil )
| ( ( cons @ ( sk__44 @ sk__47 ) @ nil )
= sk__47 )
| ( nil = sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl13854,zip_derived_cl88]) ).
thf(zip_derived_cl190_115,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13867,plain,
( ( sk__48 = nil )
| ( ( cons @ ( sk__44 @ sk__47 ) @ nil )
= sk__47 )
| ( nil = sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl13857,zip_derived_cl190]) ).
thf(zip_derived_cl13470_116,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl13868,plain,
( ( sk__48 = nil )
| ( ( cons @ ( sk__44 @ sk__47 ) @ nil )
= sk__47 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl13867,zip_derived_cl13470]) ).
thf(zip_derived_cl184380,plain,
( ( sk__48 = nil )
| ( sk__48 = nil )
| ( ( cons @ ( sk__4 @ sk__47 ) @ nil )
= sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl184310,zip_derived_cl13868]) ).
thf(zip_derived_cl184566,plain,
( ( ( cons @ ( sk__4 @ sk__47 ) @ nil )
= sk__47 )
| ( sk__48 = nil ) ),
inference(simplify,[status(thm)],[zip_derived_cl184380]) ).
thf(zip_derived_cl251318,plain,
( ~ ( ssItem @ ( sk__4 @ sk__47 ) )
| ( sk__48 = nil ) ),
inference(clc,[status(thm)],[zip_derived_cl251286,zip_derived_cl184566]) ).
thf(zip_derived_cl184310_117,plain,
( ( sk__48 = nil )
| ( ( sk__4 @ sk__47 )
= ( sk__44 @ sk__47 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl184299,zip_derived_cl454]) ).
thf(zip_derived_cl87_118,plain,
! [X0: $i] :
( ( ssItem @ ( sk__44 @ X0 ) )
| ( nil = X0 )
| ~ ( ssList @ X0 ) ),
inference(cnf,[status(esa)],[ax20]) ).
thf(zip_derived_cl184311,plain,
( ( sk__48 = nil )
| ( ssItem @ ( sk__4 @ sk__47 ) )
| ( nil = sk__47 )
| ~ ( ssList @ sk__47 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl184310,zip_derived_cl87]) ).
thf(zip_derived_cl190_119,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl184432,plain,
( ( sk__48 = nil )
| ( ssItem @ ( sk__4 @ sk__47 ) )
| ( nil = sk__47 ) ),
inference(demod,[status(thm)],[zip_derived_cl184311,zip_derived_cl190]) ).
thf(zip_derived_cl13470_120,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl184433,plain,
( ( sk__48 = nil )
| ( ssItem @ ( sk__4 @ sk__47 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl184432,zip_derived_cl13470]) ).
thf(zip_derived_cl251319,plain,
sk__48 = nil,
inference(clc,[status(thm)],[zip_derived_cl251318,zip_derived_cl184433]) ).
thf(zip_derived_cl251319_121,plain,
sk__48 = nil,
inference(clc,[status(thm)],[zip_derived_cl251318,zip_derived_cl184433]) ).
thf(zip_derived_cl251328,plain,
( ( sk__47 = nil )
| ~ ( segmentP @ sk__47 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl597,zip_derived_cl251319,zip_derived_cl251319]) ).
thf(zip_derived_cl13470_122,plain,
sk__47 != nil,
inference(clc,[status(thm)],[zip_derived_cl13469,zip_derived_cl192]) ).
thf(zip_derived_cl251329,plain,
~ ( segmentP @ sk__47 @ nil ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl251328,zip_derived_cl13470]) ).
thf(zip_derived_cl253978,plain,
~ ( ssList @ sk__47 ),
inference('s_sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl251329]) ).
thf(zip_derived_cl190_123,plain,
ssList @ sk__47,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl253979,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl253978,zip_derived_cl190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.16 % Problem : SWC388+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.17 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pV1tkGsfuB true
% 0.16/0.38 % Computer : n006.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon Aug 28 16:13:51 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.16/0.38 % Running portfolio for 300 s
% 0.16/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.38 % Number of cores: 8
% 0.24/0.39 % Python version: Python 3.6.8
% 0.24/0.39 % Running in FO mode
% 0.35/0.67 % Total configuration time : 435
% 0.35/0.67 % Estimated wc time : 1092
% 0.35/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.38/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.38/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.38/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.38/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.38/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.38/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.38/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 251.14/36.56 % Solved by fo/fo13.sh.
% 251.14/36.56 % done 24681 iterations in 35.738s
% 251.14/36.56 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 251.14/36.56 % SZS output start Refutation
% See solution above
% 251.14/36.57
% 251.14/36.57
% 251.14/36.57 % Terminating...
% 251.66/36.66 % Runner terminated.
% 251.66/36.68 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------