%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWC021+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:51:14 AM UTC 2026
% Result : Theorem 16.95s 3.10s
% Output : CNFRefutation 16.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 69
% Syntax : Number of formulae : 1016 ( 313 unt; 0 typ; 0 def)
% Number of atoms : 9807 (3651 equ; 0 cnn)
% Maximal formula atoms : 19 ( 9 avg)
% Number of connectives : 14621 (3743 ~;3231 |; 119 &;7077 @)
% ( 39 <=>; 412 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 7 con; 0-2 aty)
% Number of variables : 2219 ( 0 ^;2178 !; 41 ?;2219 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_app,type,
app: $i > $i > $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_cyclefreeP,type,
cyclefreeP: $i > $o ).
thf(tp_duplicatefreeP,type,
duplicatefreeP: $i > $o ).
thf(tp_equalelemsP,type,
equalelemsP: $i > $o ).
thf(tp_frontsegP,type,
frontsegP: $i > $i > $o ).
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_gt,type,
gt: $i > $i > $o ).
thf(tp_hd,type,
hd: $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_lt,type,
lt: $i > $i > $o ).
thf(tp_memberP,type,
memberP: $i > $i > $o ).
thf(tp_neq,type,
neq: $i > $i > $o ).
thf(tp_nil,type,
nil: $i ).
thf(tp_rearsegP,type,
rearsegP: $i > $i > $o ).
thf(tp_sK10_SY204,type,
sK10_SY204: $i > $i > $i ).
thf(tp_sK11_SY212,type,
sK11_SY212: $i > $i > $i ).
thf(tp_sK12_SY215,type,
sK12_SY215: $i > $i > $i ).
thf(tp_sK13_SY231,type,
sK13_SY231: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY193,type,
sK3_SY193: $i ).
thf(tp_sK4_SY201,type,
sK4_SY201: $i ).
thf(tp_sK5_SY179,type,
sK5_SY179: $i > $i ).
thf(tp_sK6_SY172,type,
sK6_SY172: $i > $i ).
thf(tp_sK7_SY175,type,
sK7_SY175: $i > $i ).
thf(tp_sK8_SY173,type,
sK8_SY173: $i > $i ).
thf(tp_sK9_SY227,type,
sK9_SY227: $i > $i ).
thf(tp_segmentP,type,
segmentP: $i > $i > $o ).
thf(tp_singletonP,type,
singletonP: $i > $o ).
thf(tp_ssItem,type,
ssItem: $i > $o ).
thf(tp_ssList,type,
ssList: $i > $o ).
thf(tp_strictorderP,type,
strictorderP: $i > $o ).
thf(tp_strictorderedP,type,
strictorderedP: $i > $o ).
thf(tp_tl,type,
tl: $i > $i ).
thf(tp_totalorderP,type,
totalorderP: $i > $o ).
thf(tp_totalorderedP,type,
totalorderedP: $i > $o ).
thf(10,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
thf(11,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
thf(12,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(13,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
thf(14,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
thf(15,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
= ( app @ ( cons @ V @ nil ) @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
thf(16,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
thf(17,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ W @ V )
= ( app @ U @ V ) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
thf(18,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
thf(19,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( nil != V )
& ( nil != U )
& ( ( hd @ V )
= ( hd @ U ) )
& ( ( tl @ V )
= ( tl @ U ) ) )
=> ( V = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).
thf(20,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
thf(21,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssItem @ V )
& ( ( hd @ U )
= V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
thf(22,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(23,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( equalelemsP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(24,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(25,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( duplicatefreeP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
thf(27,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(28,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( strictorderedP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
thf(30,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(31,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( totalorderedP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
thf(32,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(33,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( strictorderP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
thf(34,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(35,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( totalorderP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(36,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(37,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( cyclefreeP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(38,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(39,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(40,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 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
thf(41,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(42,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(43,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ W ) )
=> ( segmentP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(44,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(45,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(46,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( rearsegP @ U @ V )
=> ( rearsegP @ ( app @ W @ U ) @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(47,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(48,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
thf(49,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ W ) )
=> ( rearsegP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
thf(50,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(51,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(52,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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
thf(53,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( frontsegP @ U @ V )
=> ( frontsegP @ ( app @ U @ W ) @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(54,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(55,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(56,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ W ) )
=> ( frontsegP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(57,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(58,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(59,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(60,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( app @ V @ W ) @ U )
<=> ( ( memberP @ V @ U )
| ( memberP @ W @ U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(68,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(69,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( cons @ W @ ( app @ V @ U ) )
= ( app @ ( cons @ W @ V ) @ U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(70,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(71,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(72,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(73,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(74,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(75,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(76,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil = U )
| ? [V: $i] :
( ( ssList @ V )
& ? [W: $i] :
( ( ssItem @ W )
& ( ( cons @ W @ V )
= U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(77,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssItem @ X )
=> ( ( ( cons @ W @ U )
= ( cons @ X @ V ) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(78,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(79,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(80,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(81,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(89,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( segmentP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ ( app @ W @ V ) @ X )
= U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(90,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( rearsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ W @ V )
= U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(91,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( frontsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ V @ W )
= U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(92,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ssItem @ V )
& ( ( cons @ V @ nil )
= U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(95,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(96,conjecture,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ~ ( frontsegP @ X @ W )
| ~ ( strictorderedP @ W )
| ? [Y: $i] :
( ( ssList @ Y )
& ( neq @ Y @ nil )
& ( frontsegP @ V @ Y )
& ( frontsegP @ U @ Y ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ W @ Z )
& ( frontsegP @ X @ Z )
& ( segmentP @ Z @ W )
& ( strictorderedP @ Z ) )
| ( ( nil = V )
& ( nil = U ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(97,negated_conjecture,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ~ ( frontsegP @ X @ W )
| ~ ( strictorderedP @ W )
| ? [Y: $i] :
( ( ssList @ Y )
& ( neq @ Y @ nil )
& ( frontsegP @ V @ Y )
& ( frontsegP @ U @ Y ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ W @ Z )
& ( frontsegP @ X @ Z )
& ( segmentP @ Z @ W )
& ( strictorderedP @ Z ) )
| ( ( nil = V )
& ( nil = U ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[96]) ).
thf(98,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ~ ( frontsegP @ X @ W )
| ~ ( strictorderedP @ W )
| ? [Y: $i] :
( ( ssList @ Y )
& ( neq @ Y @ nil )
& ( frontsegP @ V @ Y )
& ( frontsegP @ U @ Y ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ W @ Z )
& ( frontsegP @ X @ Z )
& ( segmentP @ Z @ W )
& ( strictorderedP @ Z ) )
| ( ( nil = V )
& ( nil = U ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(100,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(101,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(102,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(103,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(104,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
= ( app @ ( cons @ V @ nil ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(105,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(106,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ W @ V )
= ( app @ U @ V ) )
=> ( W = U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(107,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(108,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( nil != V )
& ( nil != U )
& ( ( hd @ V )
= ( hd @ U ) )
& ( ( tl @ V )
= ( tl @ U ) ) )
=> ( V = U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(109,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(110,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssItem @ V )
& ( ( hd @ U )
= V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(111,plain,
( ( equalelemsP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(112,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( equalelemsP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(113,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(114,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( duplicatefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(115,plain,
( ( strictorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(116,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(117,plain,
( ( totalorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(118,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(119,plain,
( ( strictorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(120,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(121,plain,
( ( totalorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(122,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(123,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(124,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( cyclefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(125,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(126,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(127,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(128,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(129,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(130,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ W ) )
=> ( segmentP @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(131,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(132,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( rearsegP @ U @ V )
=> ( rearsegP @ ( app @ W @ U ) @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(134,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(135,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(136,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ W ) )
=> ( rearsegP @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(137,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(138,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(139,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(140,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( frontsegP @ U @ V )
=> ( frontsegP @ ( app @ U @ W ) @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(141,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(142,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(143,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ W ) )
=> ( frontsegP @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(144,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(145,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(146,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(147,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( app @ V @ W ) @ U )
<=> ( ( memberP @ V @ U )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(148,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(149,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( cons @ W @ ( app @ V @ U ) )
= ( app @ ( cons @ W @ V ) @ U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(150,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(151,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(152,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(153,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(154,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(155,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(156,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil = U )
| ? [V: $i] :
( ( ssList @ V )
& ? [W: $i] :
( ( ssItem @ W )
& ( ( cons @ W @ V )
= U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(157,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssItem @ X )
=> ( ( ( cons @ W @ U )
= ( cons @ X @ V ) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(158,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(159,plain,
( ( ssList @ nil )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(160,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(161,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(162,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( segmentP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ ( app @ W @ V ) @ X )
= U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(163,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( rearsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ W @ V )
= U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(164,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( frontsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ V @ W )
= U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(165,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ssItem @ V )
& ( ( cons @ V @ nil )
= U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(166,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(167,plain,
( ( ( ssList @ sK1_U )
=> ! [SY124: $i] :
( ( ssList @ SY124 )
=> ! [SY125: $i] :
( ( ssList @ SY125 )
=> ! [SY126: $i] :
( ( ssList @ SY126 )
=> ( ( SY124 != SY126 )
| ( sK1_U != SY125 )
| ~ ( frontsegP @ SY126 @ SY125 )
| ~ ( strictorderedP @ SY125 )
| ? [SY127: $i] :
( ( ssList @ SY127 )
& ( neq @ SY127 @ nil )
& ( frontsegP @ SY124 @ SY127 )
& ( frontsegP @ sK1_U @ SY127 ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ SY125 @ Z )
& ( frontsegP @ SY126 @ Z )
& ( segmentP @ Z @ SY125 )
& ( strictorderedP @ Z ) )
| ( ( nil = SY124 )
& ( nil = sK1_U ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(168,plain,
( ( ssList @ sK1_U )
= $true ),
inference(standard_cnf,[status(thm)],[167]) ).
thf(169,plain,
( ( ! [SY124: $i] :
( ( ssList @ SY124 )
=> ! [SY125: $i] :
( ( ssList @ SY125 )
=> ! [SY126: $i] :
( ( ssList @ SY126 )
=> ( ( SY124 != SY126 )
| ( sK1_U != SY125 )
| ~ ( frontsegP @ SY126 @ SY125 )
| ~ ( strictorderedP @ SY125 )
| ? [SY127: $i] :
( ( ssList @ SY127 )
& ( neq @ SY127 @ nil )
& ( frontsegP @ SY124 @ SY127 )
& ( frontsegP @ sK1_U @ SY127 ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ SY125 @ Z )
& ( frontsegP @ SY126 @ Z )
& ( segmentP @ Z @ SY125 )
& ( strictorderedP @ Z ) )
| ( ( nil = SY124 )
& ( nil = sK1_U ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[167]) ).
thf(170,plain,
( ( ~ ! [SY124: $i] :
( ( ssList @ SY124 )
=> ! [SY125: $i] :
( ( ssList @ SY125 )
=> ! [SY126: $i] :
( ( ssList @ SY126 )
=> ( ( SY124 != SY126 )
| ( sK1_U != SY125 )
| ~ ( frontsegP @ SY126 @ SY125 )
| ~ ( strictorderedP @ SY125 )
| ? [SY127: $i] :
( ( ssList @ SY127 )
& ( neq @ SY127 @ nil )
& ( frontsegP @ SY124 @ SY127 )
& ( frontsegP @ sK1_U @ SY127 ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ SY125 @ Z )
& ( frontsegP @ SY126 @ Z )
& ( segmentP @ Z @ SY125 )
& ( strictorderedP @ Z ) )
| ( ( nil = SY124 )
& ( nil = sK1_U ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[169]) ).
thf(171,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(172,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ssItem @ V )
& ( ( cons @ V @ nil )
= U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(173,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( frontsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ V @ W )
= U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(174,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( rearsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ W @ V )
= U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(175,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( segmentP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ ( app @ W @ V ) @ X )
= U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(176,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(177,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(178,plain,
( ( ssList @ nil )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(179,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(180,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssItem @ X )
=> ( ( ( cons @ W @ U )
= ( cons @ X @ V ) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(181,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil = U )
| ? [V: $i] :
( ( ssList @ V )
& ? [W: $i] :
( ( ssItem @ W )
& ( ( cons @ W @ V )
= U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(182,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(183,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(184,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(185,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(186,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(187,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(188,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( cons @ W @ ( app @ V @ U ) )
= ( app @ ( cons @ W @ V ) @ U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(189,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(190,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( app @ V @ W ) @ U )
<=> ( ( memberP @ V @ U )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(191,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(192,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(193,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(194,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ W ) )
=> ( frontsegP @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(195,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(196,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(197,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( frontsegP @ U @ V )
=> ( frontsegP @ ( app @ U @ W ) @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(198,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(199,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(200,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(201,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ W ) )
=> ( rearsegP @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(202,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(203,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(204,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( rearsegP @ U @ V )
=> ( rearsegP @ ( app @ W @ U ) @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(205,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(206,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(207,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ W ) )
=> ( segmentP @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(208,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(209,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(210,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(211,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(212,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(213,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( cyclefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(214,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(215,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(216,plain,
( ( totalorderP @ nil )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(217,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(218,plain,
( ( strictorderP @ nil )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(219,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(220,plain,
( ( totalorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(221,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(222,plain,
( ( strictorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(223,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( duplicatefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(224,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(225,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( equalelemsP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(226,plain,
( ( equalelemsP @ nil )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(227,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssItem @ V )
& ( ( hd @ U )
= V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(228,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(229,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( nil != V )
& ( nil != U )
& ( ( hd @ V )
= ( hd @ U ) )
& ( ( tl @ V )
= ( tl @ U ) ) )
=> ( V = U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(230,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(231,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ W @ V )
= ( app @ U @ V ) )
=> ( W = U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(232,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(233,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
= ( app @ ( cons @ V @ nil ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(234,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(235,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(236,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(237,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(238,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(239,plain,
( ( ssList @ sK1_U )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(240,plain,
( ( ~ ! [SY124: $i] :
( ( ssList @ SY124 )
=> ! [SY125: $i] :
( ( ssList @ SY125 )
=> ! [SY126: $i] :
( ( ssList @ SY126 )
=> ( ( SY124 != SY126 )
| ( sK1_U != SY125 )
| ~ ( frontsegP @ SY126 @ SY125 )
| ~ ( strictorderedP @ SY125 )
| ? [SY127: $i] :
( ( ssList @ SY127 )
& ( neq @ SY127 @ nil )
& ( frontsegP @ SY124 @ SY127 )
& ( frontsegP @ sK1_U @ SY127 ) )
| ? [Z: $i] :
( ( ssList @ Z )
& ( neq @ SY125 @ Z )
& ( frontsegP @ SY126 @ Z )
& ( segmentP @ Z @ SY125 )
& ( strictorderedP @ Z ) )
| ( ( nil = SY124 )
& ( nil = sK1_U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(241,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ( nil != SX0 ) )
| ( ( tl @ ( app @ SX0 @ SX1 ) )
= ( app @ ( tl @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(242,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ssList @ ( cons @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(243,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SX1 ) )
| ~ ( ( nil != SX0 ) ) )
| ( ( hd @ SX1 )
!= ( hd @ SX0 ) ) )
| ( ( tl @ SX1 )
!= ( tl @ SX0 ) ) )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(244,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( ( app @ SX1 @ SX2 )
!= ( app @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(245,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SX0 @ SX2 ) @ ( cons @ SX1 @ SX3 ) )
| ~ ( ( SX0 != SX1 )
| ~ ( frontsegP @ SX2 @ SX3 ) ) )
| ~ ( ~ ~ ( ( SX0 != SX1 )
| ~ ( frontsegP @ SX2 @ SX3 ) )
| ( frontsegP @ ( cons @ SX0 @ SX2 ) @ ( cons @ SX1 @ SX3 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(246,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ( cons @ ( hd @ SX0 ) @ ( tl @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(247,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = SX1 )
| ( memberP @ SX2 @ SX0 ) )
| ~ ( ~ ( ( SX0 = SX1 )
| ( memberP @ SX2 @ SX0 ) )
| ( memberP @ ( cons @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(248,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( frontsegP @ SX2 @ SX1 )
| ~ ( strictorderedP @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX3 @ nil ) )
| ~ ( frontsegP @ SX0 @ SX3 ) )
| ~ ( frontsegP @ sK1_U @ SX3 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX1 @ SX3 ) )
| ~ ( frontsegP @ SX2 @ SX3 ) )
| ~ ( segmentP @ SX3 @ SX1 ) )
| ~ ( strictorderedP @ SX3 ) )
| ~ ( ( nil != SX0 )
| ( nil != sK1_U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(249,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ( ( app @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ( ( app @ SX1 @ SX2 )
!= SX0 ) )
| ( frontsegP @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(250,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( ( app @ ( app @ SX0 @ SX1 ) @ SX2 )
= ( app @ SX0 @ ( app @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(251,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( duplicatefreeP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(252,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(253,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ~ ( segmentP @ SX0 @ SX1 )
| ( segmentP @ ( app @ ( app @ SX2 @ SX0 ) @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(254,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( rearsegP @ SX0 @ SX1 )
| ~ ( rearsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(255,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ( frontsegP @ SX0 @ SX1 )
| ( frontsegP @ ( app @ SX0 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(256,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SX1 @ SX2 ) @ SX0 )
| ( memberP @ SX1 @ SX0 )
| ( memberP @ SX2 @ SX0 ) )
| ~ ( ~ ( ( memberP @ SX1 @ SX0 )
| ( memberP @ SX2 @ SX0 ) )
| ( memberP @ ( app @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(257,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ SX0 @ nil )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(258,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(259,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ~ ( ~ ( rearsegP @ SX0 @ SX1 )
| ~ ( rearsegP @ SX1 @ SX2 ) )
| ( rearsegP @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(260,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(261,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( strictorderP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(262,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( rearsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(263,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ssList @ ( tl @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(264,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( frontsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(265,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ SX0 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(266,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ~ ( rearsegP @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ( ( app @ SX2 @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ( ( app @ SX2 @ SX1 )
!= SX0 ) )
| ( rearsegP @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(267,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ( segmentP @ SX1 @ SX2 ) )
| ( segmentP @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(268,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ SX0 )
= ( app @ ( cons @ SX1 @ nil ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(269,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ssList @ SX3 )
| ( ( app @ ( app @ SX2 @ SX1 ) @ SX3 )
!= SX0 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ssList @ SX3 )
| ( ( app @ ( app @ SX2 @ SX1 ) @ SX3 )
!= SX0 ) ) )
| ( segmentP @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(270,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( hd @ ( cons @ SX1 @ SX0 ) )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(271,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( totalorderP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(272,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( ~ ( ~ ( neq @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ( ~ ( ( SX0 != SX1 ) )
| ( neq @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(273,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ssItem @ ( hd @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(274,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( segmentP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(275,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ( frontsegP @ SX1 @ SX2 ) )
| ( frontsegP @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(276,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ( ssList @ ( app @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(277,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ( segmentP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(278,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(279,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssList @ SX1 )
| ( ( tl @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(280,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( singletonP @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ nil )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ nil )
!= SX0 ) )
| ( singletonP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(281,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ( ( hd @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(282,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(283,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ~ ( memberP @ nil @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(284,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( tl @ ( cons @ SX1 @ SX0 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(285,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ~ ( neq @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ( ~ ( ( SX0 != SX1 ) )
| ( neq @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(286,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( equalelemsP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(287,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ( nil != SX0 ) )
| ( ( hd @ ( app @ SX0 @ SX1 ) )
= ( hd @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(288,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( nil = SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssList @ SX1 )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( ssItem @ SX2 )
| ( ( cons @ SX2 @ SX1 )
!= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(289,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( cyclefreeP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(290,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( ( app @ SX2 @ SX1 )
!= ( app @ SX0 @ SX1 ) )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(291,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ( frontsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(292,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ( nil
!= ( app @ SX0 @ SX1 ) )
| ~ ( ( nil != SX1 )
| ( nil != SX0 ) ) )
| ~ ( ~ ~ ( ( nil != SX1 )
| ( nil != SX0 ) )
| ( nil
= ( app @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(293,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ( rearsegP @ SX0 @ SX1 )
| ( rearsegP @ ( app @ SX2 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(294,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(295,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssItem @ SX3 )
| ( ( cons @ SX2 @ SX0 )
!= ( cons @ SX3 @ SX1 ) )
| ~ ( ( SX2 != SX3 )
| ( SX1 != SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(296,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( strictorderedP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(297,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ nil @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(298,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( totalorderedP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(299,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ( ( cons @ SX2 @ ( app @ SX1 @ SX0 ) )
= ( app @ ( cons @ SX2 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(300,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( nil
!= ( cons @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(301,plain,
( ( singletonP @ nil )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(302,plain,
! [SV1: $i] :
( ( ~ ( ssList @ SV1 )
| ! [SY129: $i] :
( ~ ( ssList @ SY129 )
| ~ ( ( nil != SV1 ) )
| ( ( tl @ ( app @ SV1 @ SY129 ) )
= ( app @ ( tl @ SV1 ) @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(303,plain,
! [SV2: $i] :
( ( ~ ( ssList @ SV2 )
| ! [SY130: $i] :
( ~ ( ssItem @ SY130 )
| ( ssList @ ( cons @ SY130 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(304,plain,
! [SV3: $i] :
( ( ~ ( ssList @ SV3 )
| ! [SY131: $i] :
( ~ ( ssList @ SY131 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SY131 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SY131 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SY131 )
!= ( tl @ SV3 ) ) )
| ( SY131 = SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(305,plain,
! [SV4: $i] :
( ( ~ ( ssList @ SV4 )
| ! [SY132: $i] :
( ~ ( ssList @ SY132 )
| ! [SY133: $i] :
( ~ ( ssList @ SY133 )
| ( ( app @ SY132 @ SY133 )
!= ( app @ SY132 @ SV4 ) )
| ( SY133 = SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(306,plain,
! [SV5: $i] :
( ( ~ ( ssItem @ SV5 )
| ! [SY134: $i] :
( ~ ( ssItem @ SY134 )
| ! [SY135: $i] :
( ~ ( ssList @ SY135 )
| ! [SY136: $i] :
( ~ ( ssList @ SY136 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SY135 ) @ ( cons @ SY134 @ SY136 ) )
| ~ ( ( SV5 != SY134 )
| ~ ( frontsegP @ SY135 @ SY136 ) ) )
| ~ ( ~ ~ ( ( SV5 != SY134 )
| ~ ( frontsegP @ SY135 @ SY136 ) )
| ( frontsegP @ ( cons @ SV5 @ SY135 ) @ ( cons @ SY134 @ SY136 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(307,plain,
! [SV6: $i] :
( ( ~ ( ssList @ SV6 )
| ~ ( ( nil != SV6 ) )
| ( ( cons @ ( hd @ SV6 ) @ ( tl @ SV6 ) )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(308,plain,
! [SV7: $i] :
( ( ~ ( ssItem @ SV7 )
| ! [SY137: $i] :
( ~ ( ssItem @ SY137 )
| ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY137 @ SY138 ) @ SV7 )
| ( SV7 = SY137 )
| ( memberP @ SY138 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SY137 )
| ( memberP @ SY138 @ SV7 ) )
| ( memberP @ ( cons @ SY137 @ SY138 ) @ SV7 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(309,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( frontsegP @ SX2 @ SX1 )
| ~ ( strictorderedP @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX3 @ nil ) )
| ~ ( frontsegP @ SX0 @ SX3 ) )
| ~ ( frontsegP @ sK1_U @ SX3 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX1 @ SX3 ) )
| ~ ( frontsegP @ SX2 @ SX3 ) )
| ~ ( segmentP @ SX3 @ SX1 ) )
| ~ ( strictorderedP @ SX3 ) )
| ~ ( ( nil != SX0 )
| ( nil != sK1_U ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(310,plain,
! [SV8: $i] :
( ( ~ ( ssList @ SV8 )
| ! [SY139: $i] :
( ~ ( ssList @ SY139 )
| ~ ( ~ ( ~ ( frontsegP @ SV8 @ SY139 )
| ~ ! [SY140: $i] :
~ ~ ( ~ ( ssList @ SY140 )
| ( ( app @ SY139 @ SY140 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( ssList @ SY141 )
| ( ( app @ SY139 @ SY141 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SY139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(311,plain,
! [SV9: $i] :
( ( ~ ( ssList @ SV9 )
| ! [SY142: $i] :
( ~ ( ssList @ SY142 )
| ! [SY143: $i] :
( ~ ( ssList @ SY143 )
| ( ( app @ ( app @ SV9 @ SY142 ) @ SY143 )
= ( app @ SV9 @ ( app @ SY142 @ SY143 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(312,plain,
! [SV10: $i] :
( ( ~ ( ssItem @ SV10 )
| ( duplicatefreeP @ ( cons @ SV10 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(313,plain,
! [SV11: $i] :
( ( ~ ( ssList @ SV11 )
| ( frontsegP @ SV11 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(314,plain,
! [SV12: $i] :
( ( ~ ( ssList @ SV12 )
| ! [SY144: $i] :
( ~ ( ssList @ SY144 )
| ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ! [SY146: $i] :
( ~ ( ssList @ SY146 )
| ~ ( segmentP @ SV12 @ SY144 )
| ( segmentP @ ( app @ ( app @ SY145 @ SV12 ) @ SY146 ) @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(315,plain,
! [SV13: $i] :
( ( ~ ( ssList @ SV13 )
| ! [SY147: $i] :
( ~ ( ssList @ SY147 )
| ~ ~ ( ~ ( rearsegP @ SV13 @ SY147 )
| ~ ( rearsegP @ SY147 @ SV13 ) )
| ( SV13 = SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(316,plain,
! [SV14: $i] :
( ( ~ ( ssList @ SV14 )
| ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ~ ( frontsegP @ SV14 @ SY148 )
| ( frontsegP @ ( app @ SV14 @ SY149 ) @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(317,plain,
! [SV15: $i] :
( ( ~ ( ssItem @ SV15 )
| ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY150 @ SY151 ) @ SV15 )
| ( memberP @ SY150 @ SV15 )
| ( memberP @ SY151 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SY150 @ SV15 )
| ( memberP @ SY151 @ SV15 ) )
| ( memberP @ ( app @ SY150 @ SY151 ) @ SV15 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(318,plain,
! [SV16: $i] :
( ( ~ ( ssList @ SV16 )
| ( ( app @ SV16 @ nil )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(319,plain,
! [SV17: $i] :
( ( ~ ( ssList @ SV17 )
| ( rearsegP @ SV17 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(320,plain,
! [SV18: $i] :
( ( ~ ( ssList @ SV18 )
| ! [SY152: $i] :
( ~ ( ssList @ SY152 )
| ! [SY153: $i] :
( ~ ( ssList @ SY153 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SY152 )
| ~ ( rearsegP @ SY152 @ SY153 ) )
| ( rearsegP @ SV18 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(321,plain,
! [SV19: $i] :
( ( ~ ( ssList @ SV19 )
| ( segmentP @ SV19 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(322,plain,
! [SV20: $i] :
( ( ~ ( ssItem @ SV20 )
| ( strictorderP @ ( cons @ SV20 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(323,plain,
! [SV21: $i] :
( ( ~ ( ssList @ SV21 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SV21 )
| ( nil = SV21 ) )
| ~ ( ( nil != SV21 )
| ( rearsegP @ nil @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(324,plain,
! [SV22: $i] :
( ( ~ ( ssList @ SV22 )
| ~ ( ( nil != SV22 ) )
| ( ssList @ ( tl @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(325,plain,
! [SV23: $i] :
( ( ~ ( ssList @ SV23 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(326,plain,
! [SV24: $i] :
( ( ~ ( ssList @ SV24 )
| ! [SY154: $i] :
( ~ ( ssItem @ SY154 )
| ( ( cons @ SY154 @ SV24 )
!= SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(327,plain,
! [SV25: $i] :
( ( ~ ( ssList @ SV25 )
| ! [SY155: $i] :
( ~ ( ssList @ SY155 )
| ~ ( ~ ( ~ ( rearsegP @ SV25 @ SY155 )
| ~ ! [SY156: $i] :
~ ~ ( ~ ( ssList @ SY156 )
| ( ( app @ SY156 @ SY155 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY157: $i] :
~ ~ ( ~ ( ssList @ SY157 )
| ( ( app @ SY157 @ SY155 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SY155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(328,plain,
! [SV26: $i] :
( ( ~ ( ssList @ SV26 )
| ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ! [SY159: $i] :
( ~ ( ssList @ SY159 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SY158 )
| ~ ( segmentP @ SY158 @ SY159 ) )
| ( segmentP @ SV26 @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(329,plain,
! [SV27: $i] :
( ( ~ ( ssList @ SV27 )
| ! [SY160: $i] :
( ~ ( ssItem @ SY160 )
| ( ( cons @ SY160 @ SV27 )
= ( app @ ( cons @ SY160 @ nil ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(330,plain,
! [SV28: $i] :
( ( ~ ( ssList @ SV28 )
| ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ~ ( ~ ( ~ ( segmentP @ SV28 @ SY161 )
| ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SY162 @ SY161 ) @ SY163 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( ssList @ SY164 )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( ssList @ SY165 )
| ( ( app @ ( app @ SY164 @ SY161 ) @ SY165 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SY161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(331,plain,
! [SV29: $i] :
( ( ~ ( ssList @ SV29 )
| ! [SY166: $i] :
( ~ ( ssItem @ SY166 )
| ( ( hd @ ( cons @ SY166 @ SV29 ) )
= SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(332,plain,
! [SV30: $i] :
( ( ~ ( ssItem @ SV30 )
| ( totalorderP @ ( cons @ SV30 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(333,plain,
! [SV31: $i] :
( ( ~ ( ssItem @ SV31 )
| ! [SY167: $i] :
( ~ ( ssItem @ SY167 )
| ~ ( ~ ( ~ ( neq @ SV31 @ SY167 )
| ( SV31 != SY167 ) )
| ~ ( ~ ( ( SV31 != SY167 ) )
| ( neq @ SV31 @ SY167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(334,plain,
! [SV32: $i] :
( ( ~ ( ssList @ SV32 )
| ~ ( ( nil != SV32 ) )
| ( ssItem @ ( hd @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(335,plain,
! [SV33: $i] :
( ( ~ ( ssList @ SV33 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SV33 )
| ( nil = SV33 ) )
| ~ ( ( nil != SV33 )
| ( segmentP @ nil @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(336,plain,
! [SV34: $i] :
( ( ~ ( ssList @ SV34 )
| ! [SY168: $i] :
( ~ ( ssList @ SY168 )
| ! [SY169: $i] :
( ~ ( ssList @ SY169 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SY168 )
| ~ ( frontsegP @ SY168 @ SY169 ) )
| ( frontsegP @ SV34 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(337,plain,
! [SV35: $i] :
( ( ~ ( ssList @ SV35 )
| ! [SY170: $i] :
( ~ ( ssList @ SY170 )
| ( ssList @ ( app @ SV35 @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(338,plain,
! [SV36: $i] :
( ( ~ ( ssList @ SV36 )
| ! [SY171: $i] :
( ~ ( ssList @ SY171 )
| ~ ~ ( ~ ( segmentP @ SV36 @ SY171 )
| ~ ( segmentP @ SY171 @ SV36 ) )
| ( SV36 = SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(339,plain,
! [SV37: $i] :
( ( ~ ( ssList @ SV37 )
| ( frontsegP @ SV37 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(340,plain,
! [SV38: $i] :
( ( ~ ( ssList @ SV38 )
| ~ ( ( nil != SV38 ) )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(341,plain,
! [SV39: $i] :
( ( ~ ( ssList @ SV39 )
| ~ ( ~ ( ~ ( singletonP @ SV39 )
| ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
| ~ ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) )
| ( singletonP @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(342,plain,
! [SV40: $i] :
( ( ~ ( ssList @ SV40 )
| ~ ( ( nil != SV40 ) )
| ~ ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(343,plain,
! [SV41: $i] :
( ( ~ ( ssList @ SV41 )
| ( segmentP @ SV41 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(344,plain,
! [SV42: $i] :
( ( ~ ( ssItem @ SV42 )
| ~ ( memberP @ nil @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(345,plain,
! [SV43: $i] :
( ( ~ ( ssList @ SV43 )
| ! [SY176: $i] :
( ~ ( ssItem @ SY176 )
| ( ( tl @ ( cons @ SY176 @ SV43 ) )
= SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(346,plain,
! [SV44: $i] :
( ( ~ ( ssList @ SV44 )
| ! [SY177: $i] :
( ~ ( ssList @ SY177 )
| ~ ( ~ ( ~ ( neq @ SV44 @ SY177 )
| ( SV44 != SY177 ) )
| ~ ( ~ ( ( SV44 != SY177 ) )
| ( neq @ SV44 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(347,plain,
! [SV45: $i] :
( ( ~ ( ssItem @ SV45 )
| ( equalelemsP @ ( cons @ SV45 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(348,plain,
! [SV46: $i] :
( ( ~ ( ssList @ SV46 )
| ! [SY178: $i] :
( ~ ( ssList @ SY178 )
| ~ ( ( nil != SV46 ) )
| ( ( hd @ ( app @ SV46 @ SY178 ) )
= ( hd @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(349,plain,
! [SV47: $i] :
( ( ~ ( ssList @ SV47 )
| ( nil = SV47 )
| ~ ! [SY179: $i] :
~ ~ ( ~ ( ssList @ SY179 )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ( ssItem @ SY180 )
| ( ( cons @ SY180 @ SY179 )
!= SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(350,plain,
! [SV48: $i] :
( ( ~ ( ssItem @ SV48 )
| ( cyclefreeP @ ( cons @ SV48 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(351,plain,
! [SV49: $i] :
( ( ~ ( ssList @ SV49 )
| ! [SY181: $i] :
( ~ ( ssList @ SY181 )
| ! [SY182: $i] :
( ~ ( ssList @ SY182 )
| ( ( app @ SY182 @ SY181 )
!= ( app @ SV49 @ SY181 ) )
| ( SY182 = SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(352,plain,
! [SV50: $i] :
( ( ~ ( ssList @ SV50 )
| ! [SY183: $i] :
( ~ ( ssList @ SY183 )
| ~ ~ ( ~ ( frontsegP @ SV50 @ SY183 )
| ~ ( frontsegP @ SY183 @ SV50 ) )
| ( SV50 = SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(353,plain,
! [SV51: $i] :
( ( ~ ( ssList @ SV51 )
| ! [SY184: $i] :
( ~ ( ssList @ SY184 )
| ~ ( ~ ( ( nil
!= ( app @ SV51 @ SY184 ) )
| ~ ( ( nil != SY184 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SY184 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SY184 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(354,plain,
! [SV52: $i] :
( ( ~ ( ssList @ SV52 )
| ! [SY185: $i] :
( ~ ( ssList @ SY185 )
| ! [SY186: $i] :
( ~ ( ssList @ SY186 )
| ~ ( rearsegP @ SV52 @ SY185 )
| ( rearsegP @ ( app @ SY186 @ SV52 ) @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(355,plain,
! [SV53: $i] :
( ( ~ ( ssList @ SV53 )
| ( rearsegP @ SV53 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(356,plain,
! [SV54: $i] :
( ( ~ ( ssList @ SV54 )
| ! [SY187: $i] :
( ~ ( ssList @ SY187 )
| ! [SY188: $i] :
( ~ ( ssItem @ SY188 )
| ! [SY189: $i] :
( ~ ( ssItem @ SY189 )
| ( ( cons @ SY188 @ SV54 )
!= ( cons @ SY189 @ SY187 ) )
| ~ ( ( SY188 != SY189 )
| ( SY187 != SV54 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(357,plain,
! [SV55: $i] :
( ( ~ ( ssItem @ SV55 )
| ( strictorderedP @ ( cons @ SV55 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(358,plain,
! [SV56: $i] :
( ( ~ ( ssList @ SV56 )
| ( ( app @ nil @ SV56 )
= SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(359,plain,
! [SV57: $i] :
( ( ~ ( ssItem @ SV57 )
| ( totalorderedP @ ( cons @ SV57 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(360,plain,
! [SV58: $i] :
( ( ~ ( ssList @ SV58 )
| ! [SY190: $i] :
( ~ ( ssList @ SY190 )
| ! [SY191: $i] :
( ~ ( ssItem @ SY191 )
| ( ( cons @ SY191 @ ( app @ SY190 @ SV58 ) )
= ( app @ ( cons @ SY191 @ SY190 ) @ SV58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(361,plain,
! [SV59: $i] :
( ( ~ ( ssList @ SV59 )
| ! [SY192: $i] :
( ~ ( ssItem @ SY192 )
| ( nil
!= ( cons @ SY192 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(362,plain,
! [SV1: $i] :
( ( ( ~ ( ssList @ SV1 ) )
= $true )
| ( ( ! [SY129: $i] :
( ~ ( ssList @ SY129 )
| ~ ( ( nil != SV1 ) )
| ( ( tl @ ( app @ SV1 @ SY129 ) )
= ( app @ ( tl @ SV1 ) @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(363,plain,
! [SV2: $i] :
( ( ( ~ ( ssList @ SV2 ) )
= $true )
| ( ( ! [SY130: $i] :
( ~ ( ssItem @ SY130 )
| ( ssList @ ( cons @ SY130 @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(364,plain,
! [SV3: $i] :
( ( ( ~ ( ssList @ SV3 ) )
= $true )
| ( ( ! [SY131: $i] :
( ~ ( ssList @ SY131 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SY131 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SY131 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SY131 )
!= ( tl @ SV3 ) ) )
| ( SY131 = SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(365,plain,
! [SV4: $i] :
( ( ( ~ ( ssList @ SV4 ) )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( ssList @ SY132 )
| ! [SY133: $i] :
( ~ ( ssList @ SY133 )
| ( ( app @ SY132 @ SY133 )
!= ( app @ SY132 @ SV4 ) )
| ( SY133 = SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(366,plain,
! [SV5: $i] :
( ( ( ~ ( ssItem @ SV5 ) )
= $true )
| ( ( ! [SY134: $i] :
( ~ ( ssItem @ SY134 )
| ! [SY135: $i] :
( ~ ( ssList @ SY135 )
| ! [SY136: $i] :
( ~ ( ssList @ SY136 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SY135 ) @ ( cons @ SY134 @ SY136 ) )
| ~ ( ( SV5 != SY134 )
| ~ ( frontsegP @ SY135 @ SY136 ) ) )
| ~ ( ~ ~ ( ( SV5 != SY134 )
| ~ ( frontsegP @ SY135 @ SY136 ) )
| ( frontsegP @ ( cons @ SV5 @ SY135 ) @ ( cons @ SY134 @ SY136 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(367,plain,
! [SV6: $i] :
( ( ( ~ ( ssList @ SV6 ) )
= $true )
| ( ( ~ ( ( nil != SV6 ) )
| ( ( cons @ ( hd @ SV6 ) @ ( tl @ SV6 ) )
= SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(368,plain,
! [SV7: $i] :
( ( ( ~ ( ssItem @ SV7 ) )
= $true )
| ( ( ! [SY137: $i] :
( ~ ( ssItem @ SY137 )
| ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY137 @ SY138 ) @ SV7 )
| ( SV7 = SY137 )
| ( memberP @ SY138 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SY137 )
| ( memberP @ SY138 @ SV7 ) )
| ( memberP @ ( cons @ SY137 @ SY138 ) @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(369,plain,
( ( ~ ( ssList @ sK2_SX0 )
| ! [SY193: $i] :
( ~ ( ssList @ SY193 )
| ! [SY194: $i] :
( ~ ( ssList @ SY194 )
| ( sK2_SX0 != SY194 )
| ( sK1_U != SY193 )
| ~ ( frontsegP @ SY194 @ SY193 )
| ~ ( strictorderedP @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SY193 @ SX3 ) )
| ~ ( frontsegP @ SY194 @ SX3 ) )
| ~ ( segmentP @ SX3 @ SY193 ) )
| ~ ( strictorderedP @ SX3 ) )
| ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[309]) ).
thf(370,plain,
! [SV8: $i] :
( ( ( ~ ( ssList @ SV8 ) )
= $true )
| ( ( ! [SY139: $i] :
( ~ ( ssList @ SY139 )
| ~ ( ~ ( ~ ( frontsegP @ SV8 @ SY139 )
| ~ ! [SY140: $i] :
~ ~ ( ~ ( ssList @ SY140 )
| ( ( app @ SY139 @ SY140 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( ssList @ SY141 )
| ( ( app @ SY139 @ SY141 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SY139 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(371,plain,
! [SV9: $i] :
( ( ( ~ ( ssList @ SV9 ) )
= $true )
| ( ( ! [SY142: $i] :
( ~ ( ssList @ SY142 )
| ! [SY143: $i] :
( ~ ( ssList @ SY143 )
| ( ( app @ ( app @ SV9 @ SY142 ) @ SY143 )
= ( app @ SV9 @ ( app @ SY142 @ SY143 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(372,plain,
! [SV10: $i] :
( ( ( ~ ( ssItem @ SV10 ) )
= $true )
| ( ( duplicatefreeP @ ( cons @ SV10 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(373,plain,
! [SV11: $i] :
( ( ( ~ ( ssList @ SV11 ) )
= $true )
| ( ( frontsegP @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(374,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ SV12 ) )
= $true )
| ( ( ! [SY144: $i] :
( ~ ( ssList @ SY144 )
| ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ! [SY146: $i] :
( ~ ( ssList @ SY146 )
| ~ ( segmentP @ SV12 @ SY144 )
| ( segmentP @ ( app @ ( app @ SY145 @ SV12 ) @ SY146 ) @ SY144 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(375,plain,
! [SV13: $i] :
( ( ( ~ ( ssList @ SV13 ) )
= $true )
| ( ( ! [SY147: $i] :
( ~ ( ssList @ SY147 )
| ~ ~ ( ~ ( rearsegP @ SV13 @ SY147 )
| ~ ( rearsegP @ SY147 @ SV13 ) )
| ( SV13 = SY147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(376,plain,
! [SV14: $i] :
( ( ( ~ ( ssList @ SV14 ) )
= $true )
| ( ( ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ~ ( frontsegP @ SV14 @ SY148 )
| ( frontsegP @ ( app @ SV14 @ SY149 ) @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(377,plain,
! [SV15: $i] :
( ( ( ~ ( ssItem @ SV15 ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY150 @ SY151 ) @ SV15 )
| ( memberP @ SY150 @ SV15 )
| ( memberP @ SY151 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SY150 @ SV15 )
| ( memberP @ SY151 @ SV15 ) )
| ( memberP @ ( app @ SY150 @ SY151 ) @ SV15 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(378,plain,
! [SV16: $i] :
( ( ( ~ ( ssList @ SV16 ) )
= $true )
| ( ( ( app @ SV16 @ nil )
= SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(379,plain,
! [SV17: $i] :
( ( ( ~ ( ssList @ SV17 ) )
= $true )
| ( ( rearsegP @ SV17 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(380,plain,
! [SV18: $i] :
( ( ( ~ ( ssList @ SV18 ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( ssList @ SY152 )
| ! [SY153: $i] :
( ~ ( ssList @ SY153 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SY152 )
| ~ ( rearsegP @ SY152 @ SY153 ) )
| ( rearsegP @ SV18 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(381,plain,
! [SV19: $i] :
( ( ( ~ ( ssList @ SV19 ) )
= $true )
| ( ( segmentP @ SV19 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(382,plain,
! [SV20: $i] :
( ( ( ~ ( ssItem @ SV20 ) )
= $true )
| ( ( strictorderP @ ( cons @ SV20 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(383,plain,
! [SV21: $i] :
( ( ( ~ ( ssList @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV21 )
| ( nil = SV21 ) )
| ~ ( ( nil != SV21 )
| ( rearsegP @ nil @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(384,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ SV22 ) )
= $true )
| ( ( ~ ( ( nil != SV22 ) )
| ( ssList @ ( tl @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(385,plain,
! [SV23: $i] :
( ( ( ~ ( ssList @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(386,plain,
! [SV24: $i] :
( ( ( ~ ( ssList @ SV24 ) )
= $true )
| ( ( ! [SY154: $i] :
( ~ ( ssItem @ SY154 )
| ( ( cons @ SY154 @ SV24 )
!= SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(387,plain,
! [SV25: $i] :
( ( ( ~ ( ssList @ SV25 ) )
= $true )
| ( ( ! [SY155: $i] :
( ~ ( ssList @ SY155 )
| ~ ( ~ ( ~ ( rearsegP @ SV25 @ SY155 )
| ~ ! [SY156: $i] :
~ ~ ( ~ ( ssList @ SY156 )
| ( ( app @ SY156 @ SY155 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY157: $i] :
~ ~ ( ~ ( ssList @ SY157 )
| ( ( app @ SY157 @ SY155 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SY155 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(388,plain,
! [SV26: $i] :
( ( ( ~ ( ssList @ SV26 ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ! [SY159: $i] :
( ~ ( ssList @ SY159 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SY158 )
| ~ ( segmentP @ SY158 @ SY159 ) )
| ( segmentP @ SV26 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(389,plain,
! [SV27: $i] :
( ( ( ~ ( ssList @ SV27 ) )
= $true )
| ( ( ! [SY160: $i] :
( ~ ( ssItem @ SY160 )
| ( ( cons @ SY160 @ SV27 )
= ( app @ ( cons @ SY160 @ nil ) @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(390,plain,
! [SV28: $i] :
( ( ( ~ ( ssList @ SV28 ) )
= $true )
| ( ( ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ~ ( ~ ( ~ ( segmentP @ SV28 @ SY161 )
| ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SY162 @ SY161 ) @ SY163 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( ssList @ SY164 )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( ssList @ SY165 )
| ( ( app @ ( app @ SY164 @ SY161 ) @ SY165 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SY161 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(391,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ SV29 ) )
= $true )
| ( ( ! [SY166: $i] :
( ~ ( ssItem @ SY166 )
| ( ( hd @ ( cons @ SY166 @ SV29 ) )
= SY166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(392,plain,
! [SV30: $i] :
( ( ( ~ ( ssItem @ SV30 ) )
= $true )
| ( ( totalorderP @ ( cons @ SV30 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(393,plain,
! [SV31: $i] :
( ( ( ~ ( ssItem @ SV31 ) )
= $true )
| ( ( ! [SY167: $i] :
( ~ ( ssItem @ SY167 )
| ~ ( ~ ( ~ ( neq @ SV31 @ SY167 )
| ( SV31 != SY167 ) )
| ~ ( ~ ( ( SV31 != SY167 ) )
| ( neq @ SV31 @ SY167 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(394,plain,
! [SV32: $i] :
( ( ( ~ ( ssList @ SV32 ) )
= $true )
| ( ( ~ ( ( nil != SV32 ) )
| ( ssItem @ ( hd @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(395,plain,
! [SV33: $i] :
( ( ( ~ ( ssList @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV33 )
| ( nil = SV33 ) )
| ~ ( ( nil != SV33 )
| ( segmentP @ nil @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(396,plain,
! [SV34: $i] :
( ( ( ~ ( ssList @ SV34 ) )
= $true )
| ( ( ! [SY168: $i] :
( ~ ( ssList @ SY168 )
| ! [SY169: $i] :
( ~ ( ssList @ SY169 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SY168 )
| ~ ( frontsegP @ SY168 @ SY169 ) )
| ( frontsegP @ SV34 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(397,plain,
! [SV35: $i] :
( ( ( ~ ( ssList @ SV35 ) )
= $true )
| ( ( ! [SY170: $i] :
( ~ ( ssList @ SY170 )
| ( ssList @ ( app @ SV35 @ SY170 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(398,plain,
! [SV36: $i] :
( ( ( ~ ( ssList @ SV36 ) )
= $true )
| ( ( ! [SY171: $i] :
( ~ ( ssList @ SY171 )
| ~ ~ ( ~ ( segmentP @ SV36 @ SY171 )
| ~ ( segmentP @ SY171 @ SV36 ) )
| ( SV36 = SY171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(399,plain,
! [SV37: $i] :
( ( ( ~ ( ssList @ SV37 ) )
= $true )
| ( ( frontsegP @ SV37 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(400,plain,
! [SV38: $i] :
( ( ( ~ ( ssList @ SV38 ) )
= $true )
| ( ( ~ ( ( nil != SV38 ) )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(401,plain,
! [SV39: $i] :
( ( ( ~ ( ssList @ SV39 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( singletonP @ SV39 )
| ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
| ~ ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) )
| ( singletonP @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(402,plain,
! [SV40: $i] :
( ( ( ~ ( ssList @ SV40 ) )
= $true )
| ( ( ~ ( ( nil != SV40 ) )
| ~ ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(403,plain,
! [SV41: $i] :
( ( ( ~ ( ssList @ SV41 ) )
= $true )
| ( ( segmentP @ SV41 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(404,plain,
! [SV42: $i] :
( ( ( ~ ( ssItem @ SV42 ) )
= $true )
| ( ( ~ ( memberP @ nil @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(405,plain,
! [SV43: $i] :
( ( ( ~ ( ssList @ SV43 ) )
= $true )
| ( ( ! [SY176: $i] :
( ~ ( ssItem @ SY176 )
| ( ( tl @ ( cons @ SY176 @ SV43 ) )
= SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(406,plain,
! [SV44: $i] :
( ( ( ~ ( ssList @ SV44 ) )
= $true )
| ( ( ! [SY177: $i] :
( ~ ( ssList @ SY177 )
| ~ ( ~ ( ~ ( neq @ SV44 @ SY177 )
| ( SV44 != SY177 ) )
| ~ ( ~ ( ( SV44 != SY177 ) )
| ( neq @ SV44 @ SY177 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(407,plain,
! [SV45: $i] :
( ( ( ~ ( ssItem @ SV45 ) )
= $true )
| ( ( equalelemsP @ ( cons @ SV45 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(408,plain,
! [SV46: $i] :
( ( ( ~ ( ssList @ SV46 ) )
= $true )
| ( ( ! [SY178: $i] :
( ~ ( ssList @ SY178 )
| ~ ( ( nil != SV46 ) )
| ( ( hd @ ( app @ SV46 @ SY178 ) )
= ( hd @ SV46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(409,plain,
! [SV47: $i] :
( ( ( ~ ( ssList @ SV47 ) )
= $true )
| ( ( ( nil = SV47 )
| ~ ! [SY179: $i] :
~ ~ ( ~ ( ssList @ SY179 )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ( ssItem @ SY180 )
| ( ( cons @ SY180 @ SY179 )
!= SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(410,plain,
! [SV48: $i] :
( ( ( ~ ( ssItem @ SV48 ) )
= $true )
| ( ( cyclefreeP @ ( cons @ SV48 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(411,plain,
! [SV49: $i] :
( ( ( ~ ( ssList @ SV49 ) )
= $true )
| ( ( ! [SY181: $i] :
( ~ ( ssList @ SY181 )
| ! [SY182: $i] :
( ~ ( ssList @ SY182 )
| ( ( app @ SY182 @ SY181 )
!= ( app @ SV49 @ SY181 ) )
| ( SY182 = SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(412,plain,
! [SV50: $i] :
( ( ( ~ ( ssList @ SV50 ) )
= $true )
| ( ( ! [SY183: $i] :
( ~ ( ssList @ SY183 )
| ~ ~ ( ~ ( frontsegP @ SV50 @ SY183 )
| ~ ( frontsegP @ SY183 @ SV50 ) )
| ( SV50 = SY183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(413,plain,
! [SV51: $i] :
( ( ( ~ ( ssList @ SV51 ) )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( ssList @ SY184 )
| ~ ( ~ ( ( nil
!= ( app @ SV51 @ SY184 ) )
| ~ ( ( nil != SY184 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SY184 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SY184 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(414,plain,
! [SV52: $i] :
( ( ( ~ ( ssList @ SV52 ) )
= $true )
| ( ( ! [SY185: $i] :
( ~ ( ssList @ SY185 )
| ! [SY186: $i] :
( ~ ( ssList @ SY186 )
| ~ ( rearsegP @ SV52 @ SY185 )
| ( rearsegP @ ( app @ SY186 @ SV52 ) @ SY185 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(415,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ SV53 ) )
= $true )
| ( ( rearsegP @ SV53 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(416,plain,
! [SV54: $i] :
( ( ( ~ ( ssList @ SV54 ) )
= $true )
| ( ( ! [SY187: $i] :
( ~ ( ssList @ SY187 )
| ! [SY188: $i] :
( ~ ( ssItem @ SY188 )
| ! [SY189: $i] :
( ~ ( ssItem @ SY189 )
| ( ( cons @ SY188 @ SV54 )
!= ( cons @ SY189 @ SY187 ) )
| ~ ( ( SY188 != SY189 )
| ( SY187 != SV54 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(417,plain,
! [SV55: $i] :
( ( ( ~ ( ssItem @ SV55 ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV55 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(418,plain,
! [SV56: $i] :
( ( ( ~ ( ssList @ SV56 ) )
= $true )
| ( ( ( app @ nil @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(419,plain,
! [SV57: $i] :
( ( ( ~ ( ssItem @ SV57 ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV57 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(420,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ SV58 ) )
= $true )
| ( ( ! [SY190: $i] :
( ~ ( ssList @ SY190 )
| ! [SY191: $i] :
( ~ ( ssItem @ SY191 )
| ( ( cons @ SY191 @ ( app @ SY190 @ SV58 ) )
= ( app @ ( cons @ SY191 @ SY190 ) @ SV58 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(421,plain,
! [SV59: $i] :
( ( ( ~ ( ssList @ SV59 ) )
= $true )
| ( ( ! [SY192: $i] :
( ~ ( ssItem @ SY192 )
| ( nil
!= ( cons @ SY192 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(422,plain,
! [SV1: $i] :
( ( ( ssList @ SV1 )
= $false )
| ( ( ! [SY129: $i] :
( ~ ( ssList @ SY129 )
| ~ ( ( nil != SV1 ) )
| ( ( tl @ ( app @ SV1 @ SY129 ) )
= ( app @ ( tl @ SV1 ) @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(423,plain,
! [SV2: $i] :
( ( ( ssList @ SV2 )
= $false )
| ( ( ! [SY130: $i] :
( ~ ( ssItem @ SY130 )
| ( ssList @ ( cons @ SY130 @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(424,plain,
! [SV3: $i] :
( ( ( ssList @ SV3 )
= $false )
| ( ( ! [SY131: $i] :
( ~ ( ssList @ SY131 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SY131 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SY131 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SY131 )
!= ( tl @ SV3 ) ) )
| ( SY131 = SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(425,plain,
! [SV4: $i] :
( ( ( ssList @ SV4 )
= $false )
| ( ( ! [SY132: $i] :
( ~ ( ssList @ SY132 )
| ! [SY133: $i] :
( ~ ( ssList @ SY133 )
| ( ( app @ SY132 @ SY133 )
!= ( app @ SY132 @ SV4 ) )
| ( SY133 = SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(426,plain,
! [SV5: $i] :
( ( ( ssItem @ SV5 )
= $false )
| ( ( ! [SY134: $i] :
( ~ ( ssItem @ SY134 )
| ! [SY135: $i] :
( ~ ( ssList @ SY135 )
| ! [SY136: $i] :
( ~ ( ssList @ SY136 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SY135 ) @ ( cons @ SY134 @ SY136 ) )
| ~ ( ( SV5 != SY134 )
| ~ ( frontsegP @ SY135 @ SY136 ) ) )
| ~ ( ~ ~ ( ( SV5 != SY134 )
| ~ ( frontsegP @ SY135 @ SY136 ) )
| ( frontsegP @ ( cons @ SV5 @ SY135 ) @ ( cons @ SY134 @ SY136 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(427,plain,
! [SV6: $i] :
( ( ( ssList @ SV6 )
= $false )
| ( ( ~ ( ( nil != SV6 ) )
| ( ( cons @ ( hd @ SV6 ) @ ( tl @ SV6 ) )
= SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(428,plain,
! [SV7: $i] :
( ( ( ssItem @ SV7 )
= $false )
| ( ( ! [SY137: $i] :
( ~ ( ssItem @ SY137 )
| ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY137 @ SY138 ) @ SV7 )
| ( SV7 = SY137 )
| ( memberP @ SY138 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SY137 )
| ( memberP @ SY138 @ SV7 ) )
| ( memberP @ ( cons @ SY137 @ SY138 ) @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(429,plain,
( ( ~ ( ssList @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(430,plain,
( ( ! [SY193: $i] :
( ~ ( ssList @ SY193 )
| ! [SY194: $i] :
( ~ ( ssList @ SY194 )
| ( sK2_SX0 != SY194 )
| ( sK1_U != SY193 )
| ~ ( frontsegP @ SY194 @ SY193 )
| ~ ( strictorderedP @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SY193 @ SX3 ) )
| ~ ( frontsegP @ SY194 @ SX3 ) )
| ~ ( segmentP @ SX3 @ SY193 ) )
| ~ ( strictorderedP @ SX3 ) )
| ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(431,plain,
! [SV8: $i] :
( ( ( ssList @ SV8 )
= $false )
| ( ( ! [SY139: $i] :
( ~ ( ssList @ SY139 )
| ~ ( ~ ( ~ ( frontsegP @ SV8 @ SY139 )
| ~ ! [SY140: $i] :
~ ~ ( ~ ( ssList @ SY140 )
| ( ( app @ SY139 @ SY140 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( ssList @ SY141 )
| ( ( app @ SY139 @ SY141 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SY139 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(432,plain,
! [SV9: $i] :
( ( ( ssList @ SV9 )
= $false )
| ( ( ! [SY142: $i] :
( ~ ( ssList @ SY142 )
| ! [SY143: $i] :
( ~ ( ssList @ SY143 )
| ( ( app @ ( app @ SV9 @ SY142 ) @ SY143 )
= ( app @ SV9 @ ( app @ SY142 @ SY143 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(433,plain,
! [SV10: $i] :
( ( ( ssItem @ SV10 )
= $false )
| ( ( duplicatefreeP @ ( cons @ SV10 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(434,plain,
! [SV11: $i] :
( ( ( ssList @ SV11 )
= $false )
| ( ( frontsegP @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(435,plain,
! [SV12: $i] :
( ( ( ssList @ SV12 )
= $false )
| ( ( ! [SY144: $i] :
( ~ ( ssList @ SY144 )
| ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ! [SY146: $i] :
( ~ ( ssList @ SY146 )
| ~ ( segmentP @ SV12 @ SY144 )
| ( segmentP @ ( app @ ( app @ SY145 @ SV12 ) @ SY146 ) @ SY144 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(436,plain,
! [SV13: $i] :
( ( ( ssList @ SV13 )
= $false )
| ( ( ! [SY147: $i] :
( ~ ( ssList @ SY147 )
| ~ ~ ( ~ ( rearsegP @ SV13 @ SY147 )
| ~ ( rearsegP @ SY147 @ SV13 ) )
| ( SV13 = SY147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(437,plain,
! [SV14: $i] :
( ( ( ssList @ SV14 )
= $false )
| ( ( ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ~ ( frontsegP @ SV14 @ SY148 )
| ( frontsegP @ ( app @ SV14 @ SY149 ) @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(438,plain,
! [SV15: $i] :
( ( ( ssItem @ SV15 )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY150 @ SY151 ) @ SV15 )
| ( memberP @ SY150 @ SV15 )
| ( memberP @ SY151 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SY150 @ SV15 )
| ( memberP @ SY151 @ SV15 ) )
| ( memberP @ ( app @ SY150 @ SY151 ) @ SV15 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(439,plain,
! [SV16: $i] :
( ( ( ssList @ SV16 )
= $false )
| ( ( ( app @ SV16 @ nil )
= SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(440,plain,
! [SV17: $i] :
( ( ( ssList @ SV17 )
= $false )
| ( ( rearsegP @ SV17 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(441,plain,
! [SV18: $i] :
( ( ( ssList @ SV18 )
= $false )
| ( ( ! [SY152: $i] :
( ~ ( ssList @ SY152 )
| ! [SY153: $i] :
( ~ ( ssList @ SY153 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SY152 )
| ~ ( rearsegP @ SY152 @ SY153 ) )
| ( rearsegP @ SV18 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(442,plain,
! [SV19: $i] :
( ( ( ssList @ SV19 )
= $false )
| ( ( segmentP @ SV19 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(443,plain,
! [SV20: $i] :
( ( ( ssItem @ SV20 )
= $false )
| ( ( strictorderP @ ( cons @ SV20 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(444,plain,
! [SV21: $i] :
( ( ( ssList @ SV21 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV21 )
| ( nil = SV21 ) )
| ~ ( ( nil != SV21 )
| ( rearsegP @ nil @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(445,plain,
! [SV22: $i] :
( ( ( ssList @ SV22 )
= $false )
| ( ( ~ ( ( nil != SV22 ) )
| ( ssList @ ( tl @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(446,plain,
! [SV23: $i] :
( ( ( ssList @ SV23 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(447,plain,
! [SV24: $i] :
( ( ( ssList @ SV24 )
= $false )
| ( ( ! [SY154: $i] :
( ~ ( ssItem @ SY154 )
| ( ( cons @ SY154 @ SV24 )
!= SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(448,plain,
! [SV25: $i] :
( ( ( ssList @ SV25 )
= $false )
| ( ( ! [SY155: $i] :
( ~ ( ssList @ SY155 )
| ~ ( ~ ( ~ ( rearsegP @ SV25 @ SY155 )
| ~ ! [SY156: $i] :
~ ~ ( ~ ( ssList @ SY156 )
| ( ( app @ SY156 @ SY155 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY157: $i] :
~ ~ ( ~ ( ssList @ SY157 )
| ( ( app @ SY157 @ SY155 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SY155 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(449,plain,
! [SV26: $i] :
( ( ( ssList @ SV26 )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ! [SY159: $i] :
( ~ ( ssList @ SY159 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SY158 )
| ~ ( segmentP @ SY158 @ SY159 ) )
| ( segmentP @ SV26 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(450,plain,
! [SV27: $i] :
( ( ( ssList @ SV27 )
= $false )
| ( ( ! [SY160: $i] :
( ~ ( ssItem @ SY160 )
| ( ( cons @ SY160 @ SV27 )
= ( app @ ( cons @ SY160 @ nil ) @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(451,plain,
! [SV28: $i] :
( ( ( ssList @ SV28 )
= $false )
| ( ( ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ~ ( ~ ( ~ ( segmentP @ SV28 @ SY161 )
| ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SY162 @ SY161 ) @ SY163 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( ssList @ SY164 )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( ssList @ SY165 )
| ( ( app @ ( app @ SY164 @ SY161 ) @ SY165 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SY161 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(452,plain,
! [SV29: $i] :
( ( ( ssList @ SV29 )
= $false )
| ( ( ! [SY166: $i] :
( ~ ( ssItem @ SY166 )
| ( ( hd @ ( cons @ SY166 @ SV29 ) )
= SY166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(453,plain,
! [SV30: $i] :
( ( ( ssItem @ SV30 )
= $false )
| ( ( totalorderP @ ( cons @ SV30 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(454,plain,
! [SV31: $i] :
( ( ( ssItem @ SV31 )
= $false )
| ( ( ! [SY167: $i] :
( ~ ( ssItem @ SY167 )
| ~ ( ~ ( ~ ( neq @ SV31 @ SY167 )
| ( SV31 != SY167 ) )
| ~ ( ~ ( ( SV31 != SY167 ) )
| ( neq @ SV31 @ SY167 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(455,plain,
! [SV32: $i] :
( ( ( ssList @ SV32 )
= $false )
| ( ( ~ ( ( nil != SV32 ) )
| ( ssItem @ ( hd @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(456,plain,
! [SV33: $i] :
( ( ( ssList @ SV33 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV33 )
| ( nil = SV33 ) )
| ~ ( ( nil != SV33 )
| ( segmentP @ nil @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(457,plain,
! [SV34: $i] :
( ( ( ssList @ SV34 )
= $false )
| ( ( ! [SY168: $i] :
( ~ ( ssList @ SY168 )
| ! [SY169: $i] :
( ~ ( ssList @ SY169 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SY168 )
| ~ ( frontsegP @ SY168 @ SY169 ) )
| ( frontsegP @ SV34 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(458,plain,
! [SV35: $i] :
( ( ( ssList @ SV35 )
= $false )
| ( ( ! [SY170: $i] :
( ~ ( ssList @ SY170 )
| ( ssList @ ( app @ SV35 @ SY170 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(459,plain,
! [SV36: $i] :
( ( ( ssList @ SV36 )
= $false )
| ( ( ! [SY171: $i] :
( ~ ( ssList @ SY171 )
| ~ ~ ( ~ ( segmentP @ SV36 @ SY171 )
| ~ ( segmentP @ SY171 @ SV36 ) )
| ( SV36 = SY171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(460,plain,
! [SV37: $i] :
( ( ( ssList @ SV37 )
= $false )
| ( ( frontsegP @ SV37 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(461,plain,
! [SV38: $i] :
( ( ( ssList @ SV38 )
= $false )
| ( ( ~ ( ( nil != SV38 ) )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(462,plain,
! [SV39: $i] :
( ( ( ssList @ SV39 )
= $false )
| ( ( ~ ( ~ ( ~ ( singletonP @ SV39 )
| ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
| ~ ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) )
| ( singletonP @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(463,plain,
! [SV40: $i] :
( ( ( ssList @ SV40 )
= $false )
| ( ( ~ ( ( nil != SV40 ) )
| ~ ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(464,plain,
! [SV41: $i] :
( ( ( ssList @ SV41 )
= $false )
| ( ( segmentP @ SV41 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(465,plain,
! [SV42: $i] :
( ( ( ssItem @ SV42 )
= $false )
| ( ( ~ ( memberP @ nil @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(466,plain,
! [SV43: $i] :
( ( ( ssList @ SV43 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( ssItem @ SY176 )
| ( ( tl @ ( cons @ SY176 @ SV43 ) )
= SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(467,plain,
! [SV44: $i] :
( ( ( ssList @ SV44 )
= $false )
| ( ( ! [SY177: $i] :
( ~ ( ssList @ SY177 )
| ~ ( ~ ( ~ ( neq @ SV44 @ SY177 )
| ( SV44 != SY177 ) )
| ~ ( ~ ( ( SV44 != SY177 ) )
| ( neq @ SV44 @ SY177 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(468,plain,
! [SV45: $i] :
( ( ( ssItem @ SV45 )
= $false )
| ( ( equalelemsP @ ( cons @ SV45 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(469,plain,
! [SV46: $i] :
( ( ( ssList @ SV46 )
= $false )
| ( ( ! [SY178: $i] :
( ~ ( ssList @ SY178 )
| ~ ( ( nil != SV46 ) )
| ( ( hd @ ( app @ SV46 @ SY178 ) )
= ( hd @ SV46 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(470,plain,
! [SV47: $i] :
( ( ( ssList @ SV47 )
= $false )
| ( ( ( nil = SV47 )
| ~ ! [SY179: $i] :
~ ~ ( ~ ( ssList @ SY179 )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ( ssItem @ SY180 )
| ( ( cons @ SY180 @ SY179 )
!= SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(471,plain,
! [SV48: $i] :
( ( ( ssItem @ SV48 )
= $false )
| ( ( cyclefreeP @ ( cons @ SV48 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(472,plain,
! [SV49: $i] :
( ( ( ssList @ SV49 )
= $false )
| ( ( ! [SY181: $i] :
( ~ ( ssList @ SY181 )
| ! [SY182: $i] :
( ~ ( ssList @ SY182 )
| ( ( app @ SY182 @ SY181 )
!= ( app @ SV49 @ SY181 ) )
| ( SY182 = SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(473,plain,
! [SV50: $i] :
( ( ( ssList @ SV50 )
= $false )
| ( ( ! [SY183: $i] :
( ~ ( ssList @ SY183 )
| ~ ~ ( ~ ( frontsegP @ SV50 @ SY183 )
| ~ ( frontsegP @ SY183 @ SV50 ) )
| ( SV50 = SY183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(474,plain,
! [SV51: $i] :
( ( ( ssList @ SV51 )
= $false )
| ( ( ! [SY184: $i] :
( ~ ( ssList @ SY184 )
| ~ ( ~ ( ( nil
!= ( app @ SV51 @ SY184 ) )
| ~ ( ( nil != SY184 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SY184 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SY184 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(475,plain,
! [SV52: $i] :
( ( ( ssList @ SV52 )
= $false )
| ( ( ! [SY185: $i] :
( ~ ( ssList @ SY185 )
| ! [SY186: $i] :
( ~ ( ssList @ SY186 )
| ~ ( rearsegP @ SV52 @ SY185 )
| ( rearsegP @ ( app @ SY186 @ SV52 ) @ SY185 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(476,plain,
! [SV53: $i] :
( ( ( ssList @ SV53 )
= $false )
| ( ( rearsegP @ SV53 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(477,plain,
! [SV54: $i] :
( ( ( ssList @ SV54 )
= $false )
| ( ( ! [SY187: $i] :
( ~ ( ssList @ SY187 )
| ! [SY188: $i] :
( ~ ( ssItem @ SY188 )
| ! [SY189: $i] :
( ~ ( ssItem @ SY189 )
| ( ( cons @ SY188 @ SV54 )
!= ( cons @ SY189 @ SY187 ) )
| ~ ( ( SY188 != SY189 )
| ( SY187 != SV54 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(478,plain,
! [SV55: $i] :
( ( ( ssItem @ SV55 )
= $false )
| ( ( strictorderedP @ ( cons @ SV55 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(479,plain,
! [SV56: $i] :
( ( ( ssList @ SV56 )
= $false )
| ( ( ( app @ nil @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(480,plain,
! [SV57: $i] :
( ( ( ssItem @ SV57 )
= $false )
| ( ( totalorderedP @ ( cons @ SV57 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(481,plain,
! [SV58: $i] :
( ( ( ssList @ SV58 )
= $false )
| ( ( ! [SY190: $i] :
( ~ ( ssList @ SY190 )
| ! [SY191: $i] :
( ~ ( ssItem @ SY191 )
| ( ( cons @ SY191 @ ( app @ SY190 @ SV58 ) )
= ( app @ ( cons @ SY191 @ SY190 ) @ SV58 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(482,plain,
! [SV59: $i] :
( ( ( ssList @ SV59 )
= $false )
| ( ( ! [SY192: $i] :
( ~ ( ssItem @ SY192 )
| ( nil
!= ( cons @ SY192 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(483,plain,
! [SV1: $i,SV60: $i] :
( ( ( ~ ( ssList @ SV60 )
| ~ ( ( nil != SV1 ) )
| ( ( tl @ ( app @ SV1 @ SV60 ) )
= ( app @ ( tl @ SV1 ) @ SV60 ) ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(484,plain,
! [SV2: $i,SV61: $i] :
( ( ( ~ ( ssItem @ SV61 )
| ( ssList @ ( cons @ SV61 @ SV2 ) ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(485,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ssList @ SV62 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SV62 )
!= ( tl @ SV3 ) ) )
| ( SV62 = SV3 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(486,plain,
! [SV4: $i,SV63: $i] :
( ( ( ~ ( ssList @ SV63 )
| ! [SY197: $i] :
( ~ ( ssList @ SY197 )
| ( ( app @ SV63 @ SY197 )
!= ( app @ SV63 @ SV4 ) )
| ( SY197 = SV4 ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(487,plain,
! [SV5: $i,SV64: $i] :
( ( ( ~ ( ssItem @ SV64 )
| ! [SY198: $i] :
( ~ ( ssList @ SY198 )
| ! [SY199: $i] :
( ~ ( ssList @ SY199 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SY198 ) @ ( cons @ SV64 @ SY199 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SY198 @ SY199 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SY198 @ SY199 ) )
| ( frontsegP @ ( cons @ SV5 @ SY198 ) @ ( cons @ SV64 @ SY199 ) ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(488,plain,
! [SV6: $i] :
( ( ( ~ ( ( nil != SV6 ) ) )
= $true )
| ( ( ( cons @ ( hd @ SV6 ) @ ( tl @ SV6 ) )
= SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(489,plain,
! [SV7: $i,SV65: $i] :
( ( ( ~ ( ssItem @ SV65 )
| ! [SY200: $i] :
( ~ ( ssList @ SY200 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SY200 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SY200 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SY200 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SY200 ) @ SV7 ) ) ) ) )
= $true )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(490,plain,
( ( ssList @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(491,plain,
( ( ~ ( ssList @ sK3_SY193 )
| ! [SY201: $i] :
( ~ ( ssList @ SY201 )
| ( sK2_SX0 != SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SY203: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY203 )
| ~ ( neq @ sK3_SY193 @ SY203 ) )
| ~ ( frontsegP @ SY201 @ SY203 ) )
| ~ ( segmentP @ SY203 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY203 ) )
| ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[430]) ).
thf(492,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( ssList @ SV66 )
| ~ ( ~ ( ~ ( frontsegP @ SV8 @ SV66 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SV66 ) ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(493,plain,
! [SV9: $i,SV67: $i] :
( ( ( ~ ( ssList @ SV67 )
| ! [SY206: $i] :
( ~ ( ssList @ SY206 )
| ( ( app @ ( app @ SV9 @ SV67 ) @ SY206 )
= ( app @ SV9 @ ( app @ SV67 @ SY206 ) ) ) ) )
= $true )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(494,plain,
! [SV12: $i,SV68: $i] :
( ( ( ~ ( ssList @ SV68 )
| ! [SY207: $i] :
( ~ ( ssList @ SY207 )
| ! [SY208: $i] :
( ~ ( ssList @ SY208 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SY207 @ SV12 ) @ SY208 ) @ SV68 ) ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(495,plain,
! [SV13: $i,SV69: $i] :
( ( ( ~ ( ssList @ SV69 )
| ~ ~ ( ~ ( rearsegP @ SV13 @ SV69 )
| ~ ( rearsegP @ SV69 @ SV13 ) )
| ( SV13 = SV69 ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(496,plain,
! [SV14: $i,SV70: $i] :
( ( ( ~ ( ssList @ SV70 )
| ! [SY209: $i] :
( ~ ( ssList @ SY209 )
| ~ ( frontsegP @ SV14 @ SV70 )
| ( frontsegP @ ( app @ SV14 @ SY209 ) @ SV70 ) ) )
= $true )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(497,plain,
! [SV15: $i,SV71: $i] :
( ( ( ~ ( ssList @ SV71 )
| ! [SY210: $i] :
( ~ ( ssList @ SY210 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV71 @ SY210 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SY210 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SY210 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SY210 ) @ SV15 ) ) ) ) )
= $true )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(498,plain,
! [SV18: $i,SV72: $i] :
( ( ( ~ ( ssList @ SV72 )
| ! [SY211: $i] :
( ~ ( ssList @ SY211 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SY211 ) )
| ( rearsegP @ SV18 @ SY211 ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(499,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV21 )
| ( nil = SV21 ) )
| ~ ( ( nil != SV21 )
| ( rearsegP @ nil @ SV21 ) ) )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(500,plain,
! [SV22: $i] :
( ( ( ~ ( ( nil != SV22 ) ) )
= $true )
| ( ( ssList @ ( tl @ SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(501,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) )
= $false )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(502,plain,
! [SV24: $i,SV73: $i] :
( ( ( ~ ( ssItem @ SV73 )
| ( ( cons @ SV73 @ SV24 )
!= SV24 ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(503,plain,
! [SV25: $i,SV74: $i] :
( ( ( ~ ( ssList @ SV74 )
| ~ ( ~ ( ~ ( rearsegP @ SV25 @ SV74 )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SV74 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(504,plain,
! [SV26: $i,SV75: $i] :
( ( ( ~ ( ssList @ SV75 )
| ! [SY214: $i] :
( ~ ( ssList @ SY214 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SY214 ) )
| ( segmentP @ SV26 @ SY214 ) ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(505,plain,
! [SV27: $i,SV76: $i] :
( ( ( ~ ( ssItem @ SV76 )
| ( ( cons @ SV76 @ SV27 )
= ( app @ ( cons @ SV76 @ nil ) @ SV27 ) ) )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(506,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( ssList @ SV77 )
| ~ ( ~ ( ~ ( segmentP @ SV28 @ SV77 )
| ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SV77 ) ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(507,plain,
! [SV29: $i,SV78: $i] :
( ( ( ~ ( ssItem @ SV78 )
| ( ( hd @ ( cons @ SV78 @ SV29 ) )
= SV78 ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(508,plain,
! [SV31: $i,SV79: $i] :
( ( ( ~ ( ssItem @ SV79 )
| ~ ( ~ ( ~ ( neq @ SV31 @ SV79 )
| ( SV31 != SV79 ) )
| ~ ( ~ ( ( SV31 != SV79 ) )
| ( neq @ SV31 @ SV79 ) ) ) )
= $true )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(509,plain,
! [SV32: $i] :
( ( ( ~ ( ( nil != SV32 ) ) )
= $true )
| ( ( ssItem @ ( hd @ SV32 ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(510,plain,
! [SV33: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV33 )
| ( nil = SV33 ) )
| ~ ( ( nil != SV33 )
| ( segmentP @ nil @ SV33 ) ) )
= $false )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(511,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( ssList @ SV80 )
| ! [SY219: $i] :
( ~ ( ssList @ SY219 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SY219 ) )
| ( frontsegP @ SV34 @ SY219 ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(512,plain,
! [SV35: $i,SV81: $i] :
( ( ( ~ ( ssList @ SV81 )
| ( ssList @ ( app @ SV35 @ SV81 ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(513,plain,
! [SV36: $i,SV82: $i] :
( ( ( ~ ( ssList @ SV82 )
| ~ ~ ( ~ ( segmentP @ SV36 @ SV82 )
| ~ ( segmentP @ SV82 @ SV36 ) )
| ( SV36 = SV82 ) )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(514,plain,
! [SV38: $i] :
( ( ( ~ ( ( nil != SV38 ) ) )
= $true )
| ( ( ~ ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(515,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ( singletonP @ SV39 )
| ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
| ~ ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) )
| ( singletonP @ SV39 ) ) )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(516,plain,
! [SV40: $i] :
( ( ( ~ ( ( nil != SV40 ) ) )
= $true )
| ( ( ~ ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(517,plain,
! [SV42: $i] :
( ( ( memberP @ nil @ SV42 )
= $false )
| ( ( ssItem @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(518,plain,
! [SV43: $i,SV83: $i] :
( ( ( ~ ( ssItem @ SV83 )
| ( ( tl @ ( cons @ SV83 @ SV43 ) )
= SV43 ) )
= $true )
| ( ( ssList @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(519,plain,
! [SV44: $i,SV84: $i] :
( ( ( ~ ( ssList @ SV84 )
| ~ ( ~ ( ~ ( neq @ SV44 @ SV84 )
| ( SV44 != SV84 ) )
| ~ ( ~ ( ( SV44 != SV84 ) )
| ( neq @ SV44 @ SV84 ) ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(520,plain,
! [SV46: $i,SV85: $i] :
( ( ( ~ ( ssList @ SV85 )
| ~ ( ( nil != SV46 ) )
| ( ( hd @ ( app @ SV46 @ SV85 ) )
= ( hd @ SV46 ) ) )
= $true )
| ( ( ssList @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(521,plain,
! [SV47: $i] :
( ( ( nil = SV47 )
= $true )
| ( ( ~ ! [SY179: $i] :
~ ~ ( ~ ( ssList @ SY179 )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ( ssItem @ SY180 )
| ( ( cons @ SY180 @ SY179 )
!= SV47 ) ) ) )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(522,plain,
! [SV49: $i,SV86: $i] :
( ( ( ~ ( ssList @ SV86 )
| ! [SY220: $i] :
( ~ ( ssList @ SY220 )
| ( ( app @ SY220 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
| ( SY220 = SV49 ) ) )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(523,plain,
! [SV50: $i,SV87: $i] :
( ( ( ~ ( ssList @ SV87 )
| ~ ~ ( ~ ( frontsegP @ SV50 @ SV87 )
| ~ ( frontsegP @ SV87 @ SV50 ) )
| ( SV50 = SV87 ) )
= $true )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(524,plain,
! [SV51: $i,SV88: $i] :
( ( ( ~ ( ssList @ SV88 )
| ~ ( ~ ( ( nil
!= ( app @ SV51 @ SV88 ) )
| ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SV88 ) ) ) ) )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(525,plain,
! [SV52: $i,SV89: $i] :
( ( ( ~ ( ssList @ SV89 )
| ! [SY221: $i] :
( ~ ( ssList @ SY221 )
| ~ ( rearsegP @ SV52 @ SV89 )
| ( rearsegP @ ( app @ SY221 @ SV52 ) @ SV89 ) ) )
= $true )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(526,plain,
! [SV54: $i,SV90: $i] :
( ( ( ~ ( ssList @ SV90 )
| ! [SY222: $i] :
( ~ ( ssItem @ SY222 )
| ! [SY223: $i] :
( ~ ( ssItem @ SY223 )
| ( ( cons @ SY222 @ SV54 )
!= ( cons @ SY223 @ SV90 ) )
| ~ ( ( SY222 != SY223 )
| ( SV90 != SV54 ) ) ) ) )
= $true )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(527,plain,
! [SV58: $i,SV91: $i] :
( ( ( ~ ( ssList @ SV91 )
| ! [SY224: $i] :
( ~ ( ssItem @ SY224 )
| ( ( cons @ SY224 @ ( app @ SV91 @ SV58 ) )
= ( app @ ( cons @ SY224 @ SV91 ) @ SV58 ) ) ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(528,plain,
! [SV59: $i,SV92: $i] :
( ( ( ~ ( ssItem @ SV92 )
| ( nil
!= ( cons @ SV92 @ SV59 ) ) )
= $true )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(529,plain,
! [SV1: $i,SV60: $i] :
( ( ( ~ ( ssList @ SV60 ) )
= $true )
| ( ( ~ ( ( nil != SV1 ) )
| ( ( tl @ ( app @ SV1 @ SV60 ) )
= ( app @ ( tl @ SV1 ) @ SV60 ) ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(530,plain,
! [SV2: $i,SV61: $i] :
( ( ( ~ ( ssItem @ SV61 ) )
= $true )
| ( ( ssList @ ( cons @ SV61 @ SV2 ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(531,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ssList @ SV62 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SV62 )
!= ( tl @ SV3 ) ) )
| ( SV62 = SV3 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(532,plain,
! [SV4: $i,SV63: $i] :
( ( ( ~ ( ssList @ SV63 ) )
= $true )
| ( ( ! [SY197: $i] :
( ~ ( ssList @ SY197 )
| ( ( app @ SV63 @ SY197 )
!= ( app @ SV63 @ SV4 ) )
| ( SY197 = SV4 ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(533,plain,
! [SV5: $i,SV64: $i] :
( ( ( ~ ( ssItem @ SV64 ) )
= $true )
| ( ( ! [SY198: $i] :
( ~ ( ssList @ SY198 )
| ! [SY199: $i] :
( ~ ( ssList @ SY199 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SY198 ) @ ( cons @ SV64 @ SY199 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SY198 @ SY199 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SY198 @ SY199 ) )
| ( frontsegP @ ( cons @ SV5 @ SY198 ) @ ( cons @ SV64 @ SY199 ) ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(534,plain,
! [SV6: $i] :
( ( ( nil != SV6 )
= $false )
| ( ( ( cons @ ( hd @ SV6 ) @ ( tl @ SV6 ) )
= SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(535,plain,
! [SV7: $i,SV65: $i] :
( ( ( ~ ( ssItem @ SV65 ) )
= $true )
| ( ( ! [SY200: $i] :
( ~ ( ssList @ SY200 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SY200 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SY200 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SY200 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SY200 ) @ SV7 ) ) ) ) )
= $true )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(536,plain,
( ( ~ ( ssList @ sK3_SY193 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[491]) ).
thf(537,plain,
( ( ! [SY201: $i] :
( ~ ( ssList @ SY201 )
| ( sK2_SX0 != SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SY203: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY203 )
| ~ ( neq @ sK3_SY193 @ SY203 ) )
| ~ ( frontsegP @ SY201 @ SY203 ) )
| ~ ( segmentP @ SY203 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY203 ) )
| ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[491]) ).
thf(538,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( ssList @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ SV8 @ SV66 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SV66 ) ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(539,plain,
! [SV9: $i,SV67: $i] :
( ( ( ~ ( ssList @ SV67 ) )
= $true )
| ( ( ! [SY206: $i] :
( ~ ( ssList @ SY206 )
| ( ( app @ ( app @ SV9 @ SV67 ) @ SY206 )
= ( app @ SV9 @ ( app @ SV67 @ SY206 ) ) ) ) )
= $true )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(540,plain,
! [SV12: $i,SV68: $i] :
( ( ( ~ ( ssList @ SV68 ) )
= $true )
| ( ( ! [SY207: $i] :
( ~ ( ssList @ SY207 )
| ! [SY208: $i] :
( ~ ( ssList @ SY208 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SY207 @ SV12 ) @ SY208 ) @ SV68 ) ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(541,plain,
! [SV13: $i,SV69: $i] :
( ( ( ~ ( ssList @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV13 @ SV69 )
| ~ ( rearsegP @ SV69 @ SV13 ) )
| ( SV13 = SV69 ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(542,plain,
! [SV14: $i,SV70: $i] :
( ( ( ~ ( ssList @ SV70 ) )
= $true )
| ( ( ! [SY209: $i] :
( ~ ( ssList @ SY209 )
| ~ ( frontsegP @ SV14 @ SV70 )
| ( frontsegP @ ( app @ SV14 @ SY209 ) @ SV70 ) ) )
= $true )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(543,plain,
! [SV15: $i,SV71: $i] :
( ( ( ~ ( ssList @ SV71 ) )
= $true )
| ( ( ! [SY210: $i] :
( ~ ( ssList @ SY210 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV71 @ SY210 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SY210 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SY210 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SY210 ) @ SV15 ) ) ) ) )
= $true )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(544,plain,
! [SV18: $i,SV72: $i] :
( ( ( ~ ( ssList @ SV72 ) )
= $true )
| ( ( ! [SY211: $i] :
( ~ ( ssList @ SY211 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SY211 ) )
| ( rearsegP @ SV18 @ SY211 ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(545,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV21 )
| ( nil = SV21 ) ) )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(546,plain,
! [SV21: $i] :
( ( ( ~ ( ( nil != SV21 )
| ( rearsegP @ nil @ SV21 ) ) )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(547,plain,
! [SV22: $i] :
( ( ( nil != SV22 )
= $false )
| ( ( ssList @ ( tl @ SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(548,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) ) )
= $false )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(549,plain,
! [SV23: $i] :
( ( ( ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) )
= $false )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(550,plain,
! [SV24: $i,SV73: $i] :
( ( ( ~ ( ssItem @ SV73 ) )
= $true )
| ( ( ( cons @ SV73 @ SV24 )
!= SV24 )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(551,plain,
! [SV25: $i,SV74: $i] :
( ( ( ~ ( ssList @ SV74 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ SV25 @ SV74 )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SV74 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(552,plain,
! [SV26: $i,SV75: $i] :
( ( ( ~ ( ssList @ SV75 ) )
= $true )
| ( ( ! [SY214: $i] :
( ~ ( ssList @ SY214 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SY214 ) )
| ( segmentP @ SV26 @ SY214 ) ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(553,plain,
! [SV27: $i,SV76: $i] :
( ( ( ~ ( ssItem @ SV76 ) )
= $true )
| ( ( ( cons @ SV76 @ SV27 )
= ( app @ ( cons @ SV76 @ nil ) @ SV27 ) )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(554,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( ssList @ SV77 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV28 @ SV77 )
| ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SV77 ) ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(555,plain,
! [SV29: $i,SV78: $i] :
( ( ( ~ ( ssItem @ SV78 ) )
= $true )
| ( ( ( hd @ ( cons @ SV78 @ SV29 ) )
= SV78 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(556,plain,
! [SV31: $i,SV79: $i] :
( ( ( ~ ( ssItem @ SV79 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV31 @ SV79 )
| ( SV31 != SV79 ) )
| ~ ( ~ ( ( SV31 != SV79 ) )
| ( neq @ SV31 @ SV79 ) ) ) )
= $true )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(557,plain,
! [SV32: $i] :
( ( ( nil != SV32 )
= $false )
| ( ( ssItem @ ( hd @ SV32 ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(558,plain,
! [SV33: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV33 )
| ( nil = SV33 ) ) )
= $false )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(559,plain,
! [SV33: $i] :
( ( ( ~ ( ( nil != SV33 )
| ( segmentP @ nil @ SV33 ) ) )
= $false )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(560,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( ssList @ SV80 ) )
= $true )
| ( ( ! [SY219: $i] :
( ~ ( ssList @ SY219 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SY219 ) )
| ( frontsegP @ SV34 @ SY219 ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(561,plain,
! [SV35: $i,SV81: $i] :
( ( ( ~ ( ssList @ SV81 ) )
= $true )
| ( ( ssList @ ( app @ SV35 @ SV81 ) )
= $true )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(562,plain,
! [SV36: $i,SV82: $i] :
( ( ( ~ ( ssList @ SV82 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV36 @ SV82 )
| ~ ( segmentP @ SV82 @ SV36 ) )
| ( SV36 = SV82 ) )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(563,plain,
! [SV38: $i] :
( ( ( nil != SV38 )
= $false )
| ( ( ~ ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(564,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ( singletonP @ SV39 )
| ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) ) )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(565,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) )
| ( singletonP @ SV39 ) ) )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(566,plain,
! [SV40: $i] :
( ( ( nil != SV40 )
= $false )
| ( ( ~ ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(567,plain,
! [SV43: $i,SV83: $i] :
( ( ( ~ ( ssItem @ SV83 ) )
= $true )
| ( ( ( tl @ ( cons @ SV83 @ SV43 ) )
= SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(568,plain,
! [SV44: $i,SV84: $i] :
( ( ( ~ ( ssList @ SV84 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV44 @ SV84 )
| ( SV44 != SV84 ) )
| ~ ( ~ ( ( SV44 != SV84 ) )
| ( neq @ SV44 @ SV84 ) ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(569,plain,
! [SV46: $i,SV85: $i] :
( ( ( ~ ( ssList @ SV85 ) )
= $true )
| ( ( ~ ( ( nil != SV46 ) )
| ( ( hd @ ( app @ SV46 @ SV85 ) )
= ( hd @ SV46 ) ) )
= $true )
| ( ( ssList @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(570,plain,
! [SV47: $i] :
( ( ( ! [SY179: $i] :
~ ~ ( ~ ( ssList @ SY179 )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ( ssItem @ SY180 )
| ( ( cons @ SY180 @ SY179 )
!= SV47 ) ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(571,plain,
! [SV49: $i,SV86: $i] :
( ( ( ~ ( ssList @ SV86 ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( ssList @ SY220 )
| ( ( app @ SY220 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
| ( SY220 = SV49 ) ) )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(572,plain,
! [SV50: $i,SV87: $i] :
( ( ( ~ ( ssList @ SV87 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV50 @ SV87 )
| ~ ( frontsegP @ SV87 @ SV50 ) )
| ( SV50 = SV87 ) )
= $true )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(573,plain,
! [SV51: $i,SV88: $i] :
( ( ( ~ ( ssList @ SV88 ) )
= $true )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV51 @ SV88 ) )
| ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SV88 ) ) ) ) )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(574,plain,
! [SV52: $i,SV89: $i] :
( ( ( ~ ( ssList @ SV89 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( ssList @ SY221 )
| ~ ( rearsegP @ SV52 @ SV89 )
| ( rearsegP @ ( app @ SY221 @ SV52 ) @ SV89 ) ) )
= $true )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(575,plain,
! [SV54: $i,SV90: $i] :
( ( ( ~ ( ssList @ SV90 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( ssItem @ SY222 )
| ! [SY223: $i] :
( ~ ( ssItem @ SY223 )
| ( ( cons @ SY222 @ SV54 )
!= ( cons @ SY223 @ SV90 ) )
| ~ ( ( SY222 != SY223 )
| ( SV90 != SV54 ) ) ) ) )
= $true )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(576,plain,
! [SV58: $i,SV91: $i] :
( ( ( ~ ( ssList @ SV91 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( ssItem @ SY224 )
| ( ( cons @ SY224 @ ( app @ SV91 @ SV58 ) )
= ( app @ ( cons @ SY224 @ SV91 ) @ SV58 ) ) ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(577,plain,
! [SV59: $i,SV92: $i] :
( ( ( ~ ( ssItem @ SV92 ) )
= $true )
| ( ( nil
!= ( cons @ SV92 @ SV59 ) )
= $true )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(578,plain,
! [SV1: $i,SV60: $i] :
( ( ( ssList @ SV60 )
= $false )
| ( ( ~ ( ( nil != SV1 ) )
| ( ( tl @ ( app @ SV1 @ SV60 ) )
= ( app @ ( tl @ SV1 ) @ SV60 ) ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(579,plain,
! [SV2: $i,SV61: $i] :
( ( ( ssItem @ SV61 )
= $false )
| ( ( ssList @ ( cons @ SV61 @ SV2 ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(580,plain,
! [SV3: $i,SV62: $i] :
( ( ( ssList @ SV62 )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SV62 )
!= ( tl @ SV3 ) ) )
| ( SV62 = SV3 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(581,plain,
! [SV4: $i,SV63: $i] :
( ( ( ssList @ SV63 )
= $false )
| ( ( ! [SY197: $i] :
( ~ ( ssList @ SY197 )
| ( ( app @ SV63 @ SY197 )
!= ( app @ SV63 @ SV4 ) )
| ( SY197 = SV4 ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(582,plain,
! [SV5: $i,SV64: $i] :
( ( ( ssItem @ SV64 )
= $false )
| ( ( ! [SY198: $i] :
( ~ ( ssList @ SY198 )
| ! [SY199: $i] :
( ~ ( ssList @ SY199 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SY198 ) @ ( cons @ SV64 @ SY199 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SY198 @ SY199 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SY198 @ SY199 ) )
| ( frontsegP @ ( cons @ SV5 @ SY198 ) @ ( cons @ SV64 @ SY199 ) ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(583,plain,
! [SV6: $i] :
( ( ( nil = SV6 )
= $true )
| ( ( ( cons @ ( hd @ SV6 ) @ ( tl @ SV6 ) )
= SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(584,plain,
! [SV7: $i,SV65: $i] :
( ( ( ssItem @ SV65 )
= $false )
| ( ( ! [SY200: $i] :
( ~ ( ssList @ SY200 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SY200 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SY200 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SY200 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SY200 ) @ SV7 ) ) ) ) )
= $true )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(585,plain,
( ( ssList @ sK3_SY193 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(586,plain,
( ( ~ ( ssList @ sK4_SY201 )
| ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY226 )
| ~ ( neq @ sK3_SY193 @ SY226 ) )
| ~ ( frontsegP @ sK4_SY201 @ SY226 ) )
| ~ ( segmentP @ SY226 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY226 ) )
| ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[537]) ).
thf(587,plain,
! [SV8: $i,SV66: $i] :
( ( ( ssList @ SV66 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ SV8 @ SV66 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SV66 ) ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(588,plain,
! [SV9: $i,SV67: $i] :
( ( ( ssList @ SV67 )
= $false )
| ( ( ! [SY206: $i] :
( ~ ( ssList @ SY206 )
| ( ( app @ ( app @ SV9 @ SV67 ) @ SY206 )
= ( app @ SV9 @ ( app @ SV67 @ SY206 ) ) ) ) )
= $true )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(589,plain,
! [SV12: $i,SV68: $i] :
( ( ( ssList @ SV68 )
= $false )
| ( ( ! [SY207: $i] :
( ~ ( ssList @ SY207 )
| ! [SY208: $i] :
( ~ ( ssList @ SY208 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SY207 @ SV12 ) @ SY208 ) @ SV68 ) ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(590,plain,
! [SV13: $i,SV69: $i] :
( ( ( ssList @ SV69 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV13 @ SV69 )
| ~ ( rearsegP @ SV69 @ SV13 ) )
| ( SV13 = SV69 ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(591,plain,
! [SV14: $i,SV70: $i] :
( ( ( ssList @ SV70 )
= $false )
| ( ( ! [SY209: $i] :
( ~ ( ssList @ SY209 )
| ~ ( frontsegP @ SV14 @ SV70 )
| ( frontsegP @ ( app @ SV14 @ SY209 ) @ SV70 ) ) )
= $true )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(592,plain,
! [SV15: $i,SV71: $i] :
( ( ( ssList @ SV71 )
= $false )
| ( ( ! [SY210: $i] :
( ~ ( ssList @ SY210 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV71 @ SY210 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SY210 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SY210 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SY210 ) @ SV15 ) ) ) ) )
= $true )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(593,plain,
! [SV18: $i,SV72: $i] :
( ( ( ssList @ SV72 )
= $false )
| ( ( ! [SY211: $i] :
( ~ ( ssList @ SY211 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SY211 ) )
| ( rearsegP @ SV18 @ SY211 ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(594,plain,
! [SV21: $i] :
( ( ( ~ ( rearsegP @ nil @ SV21 )
| ( nil = SV21 ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(595,plain,
! [SV21: $i] :
( ( ( ( nil != SV21 )
| ( rearsegP @ nil @ SV21 ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(596,plain,
! [SV22: $i] :
( ( ( nil = SV22 )
= $true )
| ( ( ssList @ ( tl @ SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(597,plain,
! [SV23: $i] :
( ( ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(598,plain,
! [SV23: $i] :
( ( ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(599,plain,
! [SV24: $i,SV73: $i] :
( ( ( ssItem @ SV73 )
= $false )
| ( ( ( cons @ SV73 @ SV24 )
!= SV24 )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(600,plain,
! [SV25: $i,SV74: $i] :
( ( ( ssList @ SV74 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ SV25 @ SV74 )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SV74 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(601,plain,
! [SV26: $i,SV75: $i] :
( ( ( ssList @ SV75 )
= $false )
| ( ( ! [SY214: $i] :
( ~ ( ssList @ SY214 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SY214 ) )
| ( segmentP @ SV26 @ SY214 ) ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(602,plain,
! [SV27: $i,SV76: $i] :
( ( ( ssItem @ SV76 )
= $false )
| ( ( ( cons @ SV76 @ SV27 )
= ( app @ ( cons @ SV76 @ nil ) @ SV27 ) )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(603,plain,
! [SV28: $i,SV77: $i] :
( ( ( ssList @ SV77 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV28 @ SV77 )
| ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SV77 ) ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(604,plain,
! [SV29: $i,SV78: $i] :
( ( ( ssItem @ SV78 )
= $false )
| ( ( ( hd @ ( cons @ SV78 @ SV29 ) )
= SV78 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(605,plain,
! [SV31: $i,SV79: $i] :
( ( ( ssItem @ SV79 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV31 @ SV79 )
| ( SV31 != SV79 ) )
| ~ ( ~ ( ( SV31 != SV79 ) )
| ( neq @ SV31 @ SV79 ) ) ) )
= $true )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(606,plain,
! [SV32: $i] :
( ( ( nil = SV32 )
= $true )
| ( ( ssItem @ ( hd @ SV32 ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(607,plain,
! [SV33: $i] :
( ( ( ~ ( segmentP @ nil @ SV33 )
| ( nil = SV33 ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(608,plain,
! [SV33: $i] :
( ( ( ( nil != SV33 )
| ( segmentP @ nil @ SV33 ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(609,plain,
! [SV34: $i,SV80: $i] :
( ( ( ssList @ SV80 )
= $false )
| ( ( ! [SY219: $i] :
( ~ ( ssList @ SY219 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SY219 ) )
| ( frontsegP @ SV34 @ SY219 ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(610,plain,
! [SV35: $i,SV81: $i] :
( ( ( ssList @ SV81 )
= $false )
| ( ( ssList @ ( app @ SV35 @ SV81 ) )
= $true )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(611,plain,
! [SV36: $i,SV82: $i] :
( ( ( ssList @ SV82 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV36 @ SV82 )
| ~ ( segmentP @ SV82 @ SV36 ) )
| ( SV36 = SV82 ) )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(612,plain,
! [SV38: $i] :
( ( ( nil = SV38 )
= $true )
| ( ( ~ ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(613,plain,
! [SV39: $i] :
( ( ( ~ ( singletonP @ SV39 )
| ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(614,plain,
! [SV39: $i] :
( ( ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) )
| ( singletonP @ SV39 ) )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(615,plain,
! [SV40: $i] :
( ( ( nil = SV40 )
= $true )
| ( ( ~ ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(616,plain,
! [SV43: $i,SV83: $i] :
( ( ( ssItem @ SV83 )
= $false )
| ( ( ( tl @ ( cons @ SV83 @ SV43 ) )
= SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(617,plain,
! [SV44: $i,SV84: $i] :
( ( ( ssList @ SV84 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV44 @ SV84 )
| ( SV44 != SV84 ) )
| ~ ( ~ ( ( SV44 != SV84 ) )
| ( neq @ SV44 @ SV84 ) ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(618,plain,
! [SV46: $i,SV85: $i] :
( ( ( ssList @ SV85 )
= $false )
| ( ( ~ ( ( nil != SV46 ) )
| ( ( hd @ ( app @ SV46 @ SV85 ) )
= ( hd @ SV46 ) ) )
= $true )
| ( ( ssList @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(619,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK5_SY179 @ SV47 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( ssItem @ SY227 )
| ( ( cons @ SY227 @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[570]) ).
thf(620,plain,
! [SV49: $i,SV86: $i] :
( ( ( ssList @ SV86 )
= $false )
| ( ( ! [SY220: $i] :
( ~ ( ssList @ SY220 )
| ( ( app @ SY220 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
| ( SY220 = SV49 ) ) )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(621,plain,
! [SV50: $i,SV87: $i] :
( ( ( ssList @ SV87 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV50 @ SV87 )
| ~ ( frontsegP @ SV87 @ SV50 ) )
| ( SV50 = SV87 ) )
= $true )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(622,plain,
! [SV51: $i,SV88: $i] :
( ( ( ssList @ SV88 )
= $false )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV51 @ SV88 ) )
| ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SV88 ) ) ) ) )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(623,plain,
! [SV52: $i,SV89: $i] :
( ( ( ssList @ SV89 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( ssList @ SY221 )
| ~ ( rearsegP @ SV52 @ SV89 )
| ( rearsegP @ ( app @ SY221 @ SV52 ) @ SV89 ) ) )
= $true )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(624,plain,
! [SV54: $i,SV90: $i] :
( ( ( ssList @ SV90 )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( ssItem @ SY222 )
| ! [SY223: $i] :
( ~ ( ssItem @ SY223 )
| ( ( cons @ SY222 @ SV54 )
!= ( cons @ SY223 @ SV90 ) )
| ~ ( ( SY222 != SY223 )
| ( SV90 != SV54 ) ) ) ) )
= $true )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(625,plain,
! [SV58: $i,SV91: $i] :
( ( ( ssList @ SV91 )
= $false )
| ( ( ! [SY224: $i] :
( ~ ( ssItem @ SY224 )
| ( ( cons @ SY224 @ ( app @ SV91 @ SV58 ) )
= ( app @ ( cons @ SY224 @ SV91 ) @ SV58 ) ) ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(626,plain,
! [SV59: $i,SV92: $i] :
( ( ( ssItem @ SV92 )
= $false )
| ( ( nil
!= ( cons @ SV92 @ SV59 ) )
= $true )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(627,plain,
! [SV60: $i,SV1: $i] :
( ( ( ~ ( ( nil != SV1 ) ) )
= $true )
| ( ( ( tl @ ( app @ SV1 @ SV60 ) )
= ( app @ ( tl @ SV1 ) @ SV60 ) )
= $true )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(628,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SV62 )
!= ( tl @ SV3 ) ) ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(629,plain,
! [SV4: $i,SV63: $i,SV93: $i] :
( ( ( ~ ( ssList @ SV93 )
| ( ( app @ SV63 @ SV93 )
!= ( app @ SV63 @ SV4 ) )
| ( SV93 = SV4 ) )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(630,plain,
! [SV64: $i,SV5: $i,SV94: $i] :
( ( ( ~ ( ssList @ SV94 )
| ! [SY228: $i] :
( ~ ( ssList @ SY228 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SY228 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SY228 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SY228 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SY228 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(631,plain,
! [SV7: $i,SV65: $i,SV95: $i] :
( ( ( ~ ( ssList @ SV95 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) ) ) )
= $true )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(632,plain,
( ( ~ ( ssList @ sK4_SY201 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(633,plain,
( ( ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY226 )
| ~ ( neq @ sK3_SY193 @ SY226 ) )
| ~ ( frontsegP @ sK4_SY201 @ SY226 ) )
| ~ ( segmentP @ SY226 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY226 ) )
| ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(634,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV8 @ SV66 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
| ~ ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SV66 ) ) )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(635,plain,
! [SV67: $i,SV9: $i,SV96: $i] :
( ( ( ~ ( ssList @ SV96 )
| ( ( app @ ( app @ SV9 @ SV67 ) @ SV96 )
= ( app @ SV9 @ ( app @ SV67 @ SV96 ) ) ) )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(636,plain,
! [SV68: $i,SV12: $i,SV97: $i] :
( ( ( ~ ( ssList @ SV97 )
| ! [SY229: $i] :
( ~ ( ssList @ SY229 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SY229 ) @ SV68 ) ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(637,plain,
! [SV69: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV13 @ SV69 )
| ~ ( rearsegP @ SV69 @ SV13 ) ) )
= $true )
| ( ( SV13 = SV69 )
= $true )
| ( ( ssList @ SV69 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(638,plain,
! [SV70: $i,SV14: $i,SV98: $i] :
( ( ( ~ ( ssList @ SV98 )
| ~ ( frontsegP @ SV14 @ SV70 )
| ( frontsegP @ ( app @ SV14 @ SV98 ) @ SV70 ) )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(639,plain,
! [SV15: $i,SV71: $i,SV99: $i] :
( ( ( ~ ( ssList @ SV99 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) ) ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(640,plain,
! [SV72: $i,SV18: $i,SV100: $i] :
( ( ( ~ ( ssList @ SV100 )
| ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SV100 ) )
| ( rearsegP @ SV18 @ SV100 ) )
= $true )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(641,plain,
! [SV21: $i] :
( ( ( ~ ( rearsegP @ nil @ SV21 ) )
= $true )
| ( ( nil = SV21 )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(642,plain,
! [SV21: $i] :
( ( ( nil != SV21 )
= $true )
| ( ( rearsegP @ nil @ SV21 )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(643,plain,
! [SV23: $i] :
( ( ( ~ ( frontsegP @ nil @ SV23 ) )
= $true )
| ( ( nil = SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(644,plain,
! [SV23: $i] :
( ( ( nil != SV23 )
= $true )
| ( ( frontsegP @ nil @ SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(645,plain,
! [SV24: $i,SV73: $i] :
( ( ( ( cons @ SV73 @ SV24 )
= SV24 )
= $false )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(646,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV25 @ SV74 )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
| ~ ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SV74 ) ) )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(647,plain,
! [SV75: $i,SV26: $i,SV101: $i] :
( ( ( ~ ( ssList @ SV101 )
| ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SV101 ) )
| ( segmentP @ SV26 @ SV101 ) )
= $true )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(648,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( ~ ( segmentP @ SV28 @ SV77 )
| ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SV77 ) ) )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(649,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( ~ ( neq @ SV31 @ SV79 )
| ( SV31 != SV79 ) )
| ~ ( ~ ( ( SV31 != SV79 ) )
| ( neq @ SV31 @ SV79 ) ) )
= $false )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(650,plain,
! [SV33: $i] :
( ( ( ~ ( segmentP @ nil @ SV33 ) )
= $true )
| ( ( nil = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(651,plain,
! [SV33: $i] :
( ( ( nil != SV33 )
= $true )
| ( ( segmentP @ nil @ SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(652,plain,
! [SV80: $i,SV34: $i,SV102: $i] :
( ( ( ~ ( ssList @ SV102 )
| ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SV102 ) )
| ( frontsegP @ SV34 @ SV102 ) )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(653,plain,
! [SV82: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV36 @ SV82 )
| ~ ( segmentP @ SV82 @ SV36 ) ) )
= $true )
| ( ( SV36 = SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(654,plain,
! [SV38: $i] :
( ( ( ! [SY172: $i] :
~ ~ ( ~ ( ssList @ SY172 )
| ( ( tl @ SV38 )
!= SY172 ) ) )
= $false )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(655,plain,
! [SV39: $i] :
( ( ( ~ ( singletonP @ SV39 ) )
= $true )
| ( ( ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(656,plain,
! [SV39: $i] :
( ( ( ~ ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) ) )
= $true )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(657,plain,
! [SV40: $i] :
( ( ( ! [SY175: $i] :
~ ~ ( ~ ( ssItem @ SY175 )
| ( ( hd @ SV40 )
!= SY175 ) ) )
= $false )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(658,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( ~ ( neq @ SV44 @ SV84 )
| ( SV44 != SV84 ) )
| ~ ( ~ ( ( SV44 != SV84 ) )
| ( neq @ SV44 @ SV84 ) ) )
= $false )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(659,plain,
! [SV85: $i,SV46: $i] :
( ( ( ~ ( ( nil != SV46 ) ) )
= $true )
| ( ( ( hd @ ( app @ SV46 @ SV85 ) )
= ( hd @ SV46 ) )
= $true )
| ( ( ssList @ SV85 )
= $false )
| ( ( ssList @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(660,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK5_SY179 @ SV47 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( ssItem @ SY227 )
| ( ( cons @ SY227 @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) ) )
= $true )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(661,plain,
! [SV49: $i,SV86: $i,SV103: $i] :
( ( ( ~ ( ssList @ SV103 )
| ( ( app @ SV103 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
| ( SV103 = SV49 ) )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(662,plain,
! [SV87: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV50 @ SV87 )
| ~ ( frontsegP @ SV87 @ SV50 ) ) )
= $true )
| ( ( SV50 = SV87 )
= $true )
| ( ( ssList @ SV87 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(663,plain,
! [SV88: $i,SV51: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV51 @ SV88 ) )
| ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
| ~ ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SV88 ) ) ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(664,plain,
! [SV89: $i,SV52: $i,SV104: $i] :
( ( ( ~ ( ssList @ SV104 )
| ~ ( rearsegP @ SV52 @ SV89 )
| ( rearsegP @ ( app @ SV104 @ SV52 ) @ SV89 ) )
= $true )
| ( ( ssList @ SV89 )
= $false )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(665,plain,
! [SV90: $i,SV54: $i,SV105: $i] :
( ( ( ~ ( ssItem @ SV105 )
| ! [SY230: $i] :
( ~ ( ssItem @ SY230 )
| ( ( cons @ SV105 @ SV54 )
!= ( cons @ SY230 @ SV90 ) )
| ~ ( ( SV105 != SY230 )
| ( SV90 != SV54 ) ) ) )
= $true )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(666,plain,
! [SV58: $i,SV91: $i,SV106: $i] :
( ( ( ~ ( ssItem @ SV106 )
| ( ( cons @ SV106 @ ( app @ SV91 @ SV58 ) )
= ( app @ ( cons @ SV106 @ SV91 ) @ SV58 ) ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(667,plain,
! [SV59: $i,SV92: $i] :
( ( ( nil
= ( cons @ SV92 @ SV59 ) )
= $false )
| ( ( ssItem @ SV92 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(668,plain,
! [SV60: $i,SV1: $i] :
( ( ( nil != SV1 )
= $false )
| ( ( ( tl @ ( app @ SV1 @ SV60 ) )
= ( app @ ( tl @ SV1 ) @ SV60 ) )
= $true )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(669,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SV62 )
!= ( tl @ SV3 ) ) ) )
= $false )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(670,plain,
! [SV4: $i,SV63: $i,SV93: $i] :
( ( ( ~ ( ssList @ SV93 ) )
= $true )
| ( ( ( ( app @ SV63 @ SV93 )
!= ( app @ SV63 @ SV4 ) )
| ( SV93 = SV4 ) )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(671,plain,
! [SV64: $i,SV5: $i,SV94: $i] :
( ( ( ~ ( ssList @ SV94 ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( ssList @ SY228 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SY228 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SY228 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SY228 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SY228 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(672,plain,
! [SV7: $i,SV65: $i,SV95: $i] :
( ( ( ~ ( ssList @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) ) ) )
= $true )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(673,plain,
( ( ssList @ sK4_SY201 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(674,plain,
( ( ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY226 )
| ~ ( neq @ sK3_SY193 @ SY226 ) )
| ~ ( frontsegP @ sK4_SY201 @ SY226 ) )
| ~ ( segmentP @ SY226 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY226 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(675,plain,
( ( ~ ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(676,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV8 @ SV66 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) ) )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(677,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SV66 ) ) )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(678,plain,
! [SV67: $i,SV9: $i,SV96: $i] :
( ( ( ~ ( ssList @ SV96 ) )
= $true )
| ( ( ( app @ ( app @ SV9 @ SV67 ) @ SV96 )
= ( app @ SV9 @ ( app @ SV67 @ SV96 ) ) )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(679,plain,
! [SV68: $i,SV12: $i,SV97: $i] :
( ( ( ~ ( ssList @ SV97 ) )
= $true )
| ( ( ! [SY229: $i] :
( ~ ( ssList @ SY229 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SY229 ) @ SV68 ) ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(680,plain,
! [SV69: $i,SV13: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV13 @ SV69 )
| ~ ( rearsegP @ SV69 @ SV13 ) ) )
= $false )
| ( ( SV13 = SV69 )
= $true )
| ( ( ssList @ SV69 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(681,plain,
! [SV70: $i,SV14: $i,SV98: $i] :
( ( ( ~ ( ssList @ SV98 ) )
= $true )
| ( ( ~ ( frontsegP @ SV14 @ SV70 )
| ( frontsegP @ ( app @ SV14 @ SV98 ) @ SV70 ) )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(682,plain,
! [SV15: $i,SV71: $i,SV99: $i] :
( ( ( ~ ( ssList @ SV99 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) ) ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(683,plain,
! [SV72: $i,SV18: $i,SV100: $i] :
( ( ( ~ ( ssList @ SV100 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SV100 ) )
| ( rearsegP @ SV18 @ SV100 ) )
= $true )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(684,plain,
! [SV21: $i] :
( ( ( rearsegP @ nil @ SV21 )
= $false )
| ( ( nil = SV21 )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(685,plain,
! [SV21: $i] :
( ( ( nil = SV21 )
= $false )
| ( ( rearsegP @ nil @ SV21 )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(686,plain,
! [SV23: $i] :
( ( ( frontsegP @ nil @ SV23 )
= $false )
| ( ( nil = SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(687,plain,
! [SV23: $i] :
( ( ( nil = SV23 )
= $false )
| ( ( frontsegP @ nil @ SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(688,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV25 @ SV74 )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) ) )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(689,plain,
! [SV25: $i,SV74: $i] :
( ( ( ~ ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SV74 ) ) )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(690,plain,
! [SV75: $i,SV26: $i,SV101: $i] :
( ( ( ~ ( ssList @ SV101 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SV101 ) )
| ( segmentP @ SV26 @ SV101 ) )
= $true )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(691,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( ~ ( segmentP @ SV28 @ SV77 )
| ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) ) )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(692,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SV77 ) ) )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(693,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( ~ ( neq @ SV31 @ SV79 )
| ( SV31 != SV79 ) ) )
= $false )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(694,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( ~ ( ( SV31 != SV79 ) )
| ( neq @ SV31 @ SV79 ) ) )
= $false )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(695,plain,
! [SV33: $i] :
( ( ( segmentP @ nil @ SV33 )
= $false )
| ( ( nil = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(696,plain,
! [SV33: $i] :
( ( ( nil = SV33 )
= $false )
| ( ( segmentP @ nil @ SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(697,plain,
! [SV80: $i,SV34: $i,SV102: $i] :
( ( ( ~ ( ssList @ SV102 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SV102 ) )
| ( frontsegP @ SV34 @ SV102 ) )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(698,plain,
! [SV82: $i,SV36: $i] :
( ( ( ~ ( ~ ( segmentP @ SV36 @ SV82 )
| ~ ( segmentP @ SV82 @ SV36 ) ) )
= $false )
| ( ( SV36 = SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(699,plain,
! [SV38: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK6_SY172 @ SV38 ) )
| ( ( tl @ SV38 )
!= ( sK6_SY172 @ SV38 ) ) ) )
= $false )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[654]) ).
thf(700,plain,
! [SV39: $i] :
( ( ( singletonP @ SV39 )
= $false )
| ( ( ~ ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(701,plain,
! [SV39: $i] :
( ( ( ~ ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) ) )
= $false )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(702,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ ( sK7_SY175 @ SV40 ) )
| ( ( hd @ SV40 )
!= ( sK7_SY175 @ SV40 ) ) ) )
= $false )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[657]) ).
thf(703,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( ~ ( neq @ SV44 @ SV84 )
| ( SV44 != SV84 ) ) )
= $false )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(704,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( ~ ( ( SV44 != SV84 ) )
| ( neq @ SV44 @ SV84 ) ) )
= $false )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(705,plain,
! [SV85: $i,SV46: $i] :
( ( ( nil != SV46 )
= $false )
| ( ( ( hd @ ( app @ SV46 @ SV85 ) )
= ( hd @ SV46 ) )
= $true )
| ( ( ssList @ SV85 )
= $false )
| ( ( ssList @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(706,plain,
! [SV47: $i] :
( ( ( ~ ( ssList @ ( sK5_SY179 @ SV47 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( ssItem @ SY227 )
| ( ( cons @ SY227 @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(707,plain,
! [SV49: $i,SV86: $i,SV103: $i] :
( ( ( ~ ( ssList @ SV103 ) )
= $true )
| ( ( ( ( app @ SV103 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
| ( SV103 = SV49 ) )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(708,plain,
! [SV87: $i,SV50: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV50 @ SV87 )
| ~ ( frontsegP @ SV87 @ SV50 ) ) )
= $false )
| ( ( SV50 = SV87 )
= $true )
| ( ( ssList @ SV87 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(709,plain,
! [SV88: $i,SV51: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV51 @ SV88 ) )
| ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(710,plain,
! [SV51: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SV88 ) ) ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(711,plain,
! [SV89: $i,SV52: $i,SV104: $i] :
( ( ( ~ ( ssList @ SV104 ) )
= $true )
| ( ( ~ ( rearsegP @ SV52 @ SV89 )
| ( rearsegP @ ( app @ SV104 @ SV52 ) @ SV89 ) )
= $true )
| ( ( ssList @ SV89 )
= $false )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(712,plain,
! [SV90: $i,SV54: $i,SV105: $i] :
( ( ( ~ ( ssItem @ SV105 ) )
= $true )
| ( ( ! [SY230: $i] :
( ~ ( ssItem @ SY230 )
| ( ( cons @ SV105 @ SV54 )
!= ( cons @ SY230 @ SV90 ) )
| ~ ( ( SV105 != SY230 )
| ( SV90 != SV54 ) ) ) )
= $true )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(713,plain,
! [SV58: $i,SV91: $i,SV106: $i] :
( ( ( ~ ( ssItem @ SV106 ) )
= $true )
| ( ( ( cons @ SV106 @ ( app @ SV91 @ SV58 ) )
= ( app @ ( cons @ SV106 @ SV91 ) @ SV58 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(714,plain,
! [SV60: $i,SV1: $i] :
( ( ( nil = SV1 )
= $true )
| ( ( ( tl @ ( app @ SV1 @ SV60 ) )
= ( app @ ( tl @ SV1 ) @ SV60 ) )
= $true )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(715,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
| ( ( tl @ SV62 )
!= ( tl @ SV3 ) ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(716,plain,
! [SV4: $i,SV63: $i,SV93: $i] :
( ( ( ssList @ SV93 )
= $false )
| ( ( ( ( app @ SV63 @ SV93 )
!= ( app @ SV63 @ SV4 ) )
| ( SV93 = SV4 ) )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(717,plain,
! [SV64: $i,SV5: $i,SV94: $i] :
( ( ( ssList @ SV94 )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( ssList @ SY228 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SY228 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SY228 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SY228 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SY228 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(718,plain,
! [SV7: $i,SV65: $i,SV95: $i] :
( ( ( ssList @ SV95 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) ) ) )
= $true )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(719,plain,
( ( ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(720,plain,
( ( ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY226 )
| ~ ( neq @ sK3_SY193 @ SY226 ) )
| ~ ( frontsegP @ sK4_SY201 @ SY226 ) )
| ~ ( segmentP @ SY226 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY226 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(721,plain,
( ( ( nil != sK2_SX0 )
| ( nil != sK1_U ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(722,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( frontsegP @ SV8 @ SV66 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(723,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) )
| ( frontsegP @ SV8 @ SV66 ) )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(724,plain,
! [SV67: $i,SV9: $i,SV96: $i] :
( ( ( ssList @ SV96 )
= $false )
| ( ( ( app @ ( app @ SV9 @ SV67 ) @ SV96 )
= ( app @ SV9 @ ( app @ SV67 @ SV96 ) ) )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(725,plain,
! [SV68: $i,SV12: $i,SV97: $i] :
( ( ( ssList @ SV97 )
= $false )
| ( ( ! [SY229: $i] :
( ~ ( ssList @ SY229 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SY229 ) @ SV68 ) ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(726,plain,
! [SV69: $i,SV13: $i] :
( ( ( ~ ( rearsegP @ SV13 @ SV69 )
| ~ ( rearsegP @ SV69 @ SV13 ) )
= $true )
| ( ( SV13 = SV69 )
= $true )
| ( ( ssList @ SV69 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(727,plain,
! [SV70: $i,SV14: $i,SV98: $i] :
( ( ( ssList @ SV98 )
= $false )
| ( ( ~ ( frontsegP @ SV14 @ SV70 )
| ( frontsegP @ ( app @ SV14 @ SV98 ) @ SV70 ) )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(728,plain,
! [SV15: $i,SV71: $i,SV99: $i] :
( ( ( ssList @ SV99 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) ) ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(729,plain,
! [SV72: $i,SV18: $i,SV100: $i] :
( ( ( ssList @ SV100 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SV100 ) )
| ( rearsegP @ SV18 @ SV100 ) )
= $true )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(730,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( rearsegP @ SV25 @ SV74 )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(731,plain,
! [SV25: $i,SV74: $i] :
( ( ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) )
| ( rearsegP @ SV25 @ SV74 ) )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(732,plain,
! [SV75: $i,SV26: $i,SV101: $i] :
( ( ( ssList @ SV101 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SV101 ) )
| ( segmentP @ SV26 @ SV101 ) )
= $true )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(733,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( segmentP @ SV28 @ SV77 )
| ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(734,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) )
| ( segmentP @ SV28 @ SV77 ) )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(735,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( neq @ SV31 @ SV79 )
| ( SV31 != SV79 ) )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(736,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( ( SV31 != SV79 ) )
| ( neq @ SV31 @ SV79 ) )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(737,plain,
! [SV80: $i,SV34: $i,SV102: $i] :
( ( ( ssList @ SV102 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SV102 ) )
| ( frontsegP @ SV34 @ SV102 ) )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(738,plain,
! [SV82: $i,SV36: $i] :
( ( ( ~ ( segmentP @ SV36 @ SV82 )
| ~ ( segmentP @ SV82 @ SV36 ) )
= $true )
| ( ( SV36 = SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(739,plain,
! [SV38: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK6_SY172 @ SV38 ) )
| ( ( tl @ SV38 )
!= ( sK6_SY172 @ SV38 ) ) ) )
= $true )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(740,plain,
! [SV39: $i] :
( ( ( ! [SY173: $i] :
~ ~ ( ~ ( ssItem @ SY173 )
| ( ( cons @ SY173 @ nil )
!= SV39 ) ) )
= $false )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(741,plain,
! [SV39: $i] :
( ( ( ! [SY174: $i] :
~ ~ ( ~ ( ssItem @ SY174 )
| ( ( cons @ SY174 @ nil )
!= SV39 ) ) )
= $true )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(742,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( ssItem @ ( sK7_SY175 @ SV40 ) )
| ( ( hd @ SV40 )
!= ( sK7_SY175 @ SV40 ) ) ) )
= $true )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(743,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( neq @ SV44 @ SV84 )
| ( SV44 != SV84 ) )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(744,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( ( SV44 != SV84 ) )
| ( neq @ SV44 @ SV84 ) )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(745,plain,
! [SV85: $i,SV46: $i] :
( ( ( nil = SV46 )
= $true )
| ( ( ( hd @ ( app @ SV46 @ SV85 ) )
= ( hd @ SV46 ) )
= $true )
| ( ( ssList @ SV85 )
= $false )
| ( ( ssList @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(746,plain,
! [SV47: $i] :
( ( ( ~ ( ssList @ ( sK5_SY179 @ SV47 ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(747,plain,
! [SV47: $i] :
( ( ( ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( ssItem @ SY227 )
| ( ( cons @ SY227 @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(748,plain,
! [SV49: $i,SV86: $i,SV103: $i] :
( ( ( ssList @ SV103 )
= $false )
| ( ( ( ( app @ SV103 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
| ( SV103 = SV49 ) )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(749,plain,
! [SV87: $i,SV50: $i] :
( ( ( ~ ( frontsegP @ SV50 @ SV87 )
| ~ ( frontsegP @ SV87 @ SV50 ) )
= $true )
| ( ( SV50 = SV87 )
= $true )
| ( ( ssList @ SV87 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(750,plain,
! [SV88: $i,SV51: $i] :
( ( ( ( nil
!= ( app @ SV51 @ SV88 ) )
| ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(751,plain,
! [SV51: $i,SV88: $i] :
( ( ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) )
| ( nil
= ( app @ SV51 @ SV88 ) ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(752,plain,
! [SV89: $i,SV52: $i,SV104: $i] :
( ( ( ssList @ SV104 )
= $false )
| ( ( ~ ( rearsegP @ SV52 @ SV89 )
| ( rearsegP @ ( app @ SV104 @ SV52 ) @ SV89 ) )
= $true )
| ( ( ssList @ SV89 )
= $false )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(753,plain,
! [SV90: $i,SV54: $i,SV105: $i] :
( ( ( ssItem @ SV105 )
= $false )
| ( ( ! [SY230: $i] :
( ~ ( ssItem @ SY230 )
| ( ( cons @ SV105 @ SV54 )
!= ( cons @ SY230 @ SV90 ) )
| ~ ( ( SV105 != SY230 )
| ( SV90 != SV54 ) ) ) )
= $true )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(754,plain,
! [SV58: $i,SV91: $i,SV106: $i] :
( ( ( ssItem @ SV106 )
= $false )
| ( ( ( cons @ SV106 @ ( app @ SV91 @ SV58 ) )
= ( app @ ( cons @ SV106 @ SV91 ) @ SV58 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(755,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(756,plain,
! [SV4: $i,SV93: $i,SV63: $i] :
( ( ( ( app @ SV63 @ SV93 )
!= ( app @ SV63 @ SV4 ) )
= $true )
| ( ( SV93 = SV4 )
= $true )
| ( ( ssList @ SV93 )
= $false )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(757,plain,
! [SV64: $i,SV94: $i,SV5: $i,SV107: $i] :
( ( ( ~ ( ssList @ SV107 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) ) ) )
= $true )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(758,plain,
! [SV7: $i,SV95: $i,SV65: $i] :
( ( ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) ) )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(759,plain,
( ( ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 )
| ~ ( strictorderedP @ sK3_SY193 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(760,plain,
( ( ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(761,plain,
( ( ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY226 )
| ~ ( neq @ sK3_SY193 @ SY226 ) )
| ~ ( frontsegP @ sK4_SY201 @ SY226 ) )
| ~ ( segmentP @ SY226 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SY226 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(762,plain,
( ( ( nil != sK2_SX0 )
= $true )
| ( ( nil != sK1_U )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(763,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( frontsegP @ SV8 @ SV66 ) )
= $true )
| ( ( ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(764,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) ) )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(765,plain,
! [SV97: $i,SV68: $i,SV12: $i,SV108: $i] :
( ( ( ~ ( ssList @ SV108 )
| ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SV108 ) @ SV68 ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(766,plain,
! [SV69: $i,SV13: $i] :
( ( ( ~ ( rearsegP @ SV13 @ SV69 ) )
= $true )
| ( ( ~ ( rearsegP @ SV69 @ SV13 ) )
= $true )
| ( ( SV13 = SV69 )
= $true )
| ( ( ssList @ SV69 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(767,plain,
! [SV98: $i,SV70: $i,SV14: $i] :
( ( ( ~ ( frontsegP @ SV14 @ SV70 ) )
= $true )
| ( ( frontsegP @ ( app @ SV14 @ SV98 ) @ SV70 )
= $true )
| ( ( ssList @ SV98 )
= $false )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(768,plain,
! [SV15: $i,SV99: $i,SV71: $i] :
( ( ( ~ ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) ) )
= $false )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(769,plain,
! [SV100: $i,SV72: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SV100 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV100 )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(770,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( rearsegP @ SV25 @ SV74 ) )
= $true )
| ( ( ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(771,plain,
! [SV25: $i,SV74: $i] :
( ( ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(772,plain,
! [SV101: $i,SV75: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SV101 ) ) )
= $true )
| ( ( segmentP @ SV26 @ SV101 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(773,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( segmentP @ SV28 @ SV77 ) )
= $true )
| ( ( ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(774,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(775,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( neq @ SV31 @ SV79 ) )
= $true )
| ( ( SV31 != SV79 )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(776,plain,
! [SV79: $i,SV31: $i] :
( ( ( ~ ( ( SV31 != SV79 ) ) )
= $true )
| ( ( neq @ SV31 @ SV79 )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(777,plain,
! [SV102: $i,SV80: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SV102 ) ) )
= $true )
| ( ( frontsegP @ SV34 @ SV102 )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(778,plain,
! [SV82: $i,SV36: $i] :
( ( ( ~ ( segmentP @ SV36 @ SV82 ) )
= $true )
| ( ( ~ ( segmentP @ SV82 @ SV36 ) )
= $true )
| ( ( SV36 = SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(779,plain,
! [SV38: $i] :
( ( ( ~ ( ssList @ ( sK6_SY172 @ SV38 ) )
| ( ( tl @ SV38 )
!= ( sK6_SY172 @ SV38 ) ) )
= $false )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(780,plain,
! [SV39: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ ( sK8_SY173 @ SV39 ) )
| ( ( cons @ ( sK8_SY173 @ SV39 ) @ nil )
!= SV39 ) ) )
= $false )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[740]) ).
thf(781,plain,
! [SV39: $i,SV109: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ SV109 )
| ( ( cons @ SV109 @ nil )
!= SV39 ) ) )
= $true )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(782,plain,
! [SV40: $i] :
( ( ( ~ ( ssItem @ ( sK7_SY175 @ SV40 ) )
| ( ( hd @ SV40 )
!= ( sK7_SY175 @ SV40 ) ) )
= $false )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(783,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( neq @ SV44 @ SV84 ) )
= $true )
| ( ( SV44 != SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(784,plain,
! [SV84: $i,SV44: $i] :
( ( ( ~ ( ( SV44 != SV84 ) ) )
= $true )
| ( ( neq @ SV44 @ SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(785,plain,
! [SV47: $i] :
( ( ( ssList @ ( sK5_SY179 @ SV47 ) )
= $true )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(786,plain,
! [SV47: $i] :
( ( ( ~ ! [SY227: $i] :
~ ~ ( ~ ( ssItem @ SY227 )
| ( ( cons @ SY227 @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) )
= $true )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(787,plain,
! [SV49: $i,SV86: $i,SV103: $i] :
( ( ( ( app @ SV103 @ SV86 )
!= ( app @ SV49 @ SV86 ) )
= $true )
| ( ( SV103 = SV49 )
= $true )
| ( ( ssList @ SV103 )
= $false )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(788,plain,
! [SV87: $i,SV50: $i] :
( ( ( ~ ( frontsegP @ SV50 @ SV87 ) )
= $true )
| ( ( ~ ( frontsegP @ SV87 @ SV50 ) )
= $true )
| ( ( SV50 = SV87 )
= $true )
| ( ( ssList @ SV87 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(789,plain,
! [SV88: $i,SV51: $i] :
( ( ( nil
!= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(790,plain,
! [SV51: $i,SV88: $i] :
( ( ( ~ ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
= $true )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(791,plain,
! [SV104: $i,SV89: $i,SV52: $i] :
( ( ( ~ ( rearsegP @ SV52 @ SV89 ) )
= $true )
| ( ( rearsegP @ ( app @ SV104 @ SV52 ) @ SV89 )
= $true )
| ( ( ssList @ SV104 )
= $false )
| ( ( ssList @ SV89 )
= $false )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(792,plain,
! [SV90: $i,SV54: $i,SV105: $i,SV110: $i] :
( ( ( ~ ( ssItem @ SV110 )
| ( ( cons @ SV105 @ SV54 )
!= ( cons @ SV110 @ SV90 ) )
| ~ ( ( SV105 != SV110 )
| ( SV90 != SV54 ) ) )
= $true )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(793,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) ) )
= $false )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(794,plain,
! [SV4: $i,SV93: $i,SV63: $i] :
( ( ( ( app @ SV63 @ SV93 )
= ( app @ SV63 @ SV4 ) )
= $false )
| ( ( SV93 = SV4 )
= $true )
| ( ( ssList @ SV93 )
= $false )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(795,plain,
! [SV64: $i,SV94: $i,SV5: $i,SV107: $i] :
( ( ( ~ ( ssList @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) ) ) )
= $true )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(796,plain,
! [SV7: $i,SV95: $i,SV65: $i] :
( ( ( ~ ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) ) )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(797,plain,
! [SV95: $i,SV65: $i,SV7: $i] :
( ( ( ~ ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) ) )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(798,plain,
( ( ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 )
| ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(799,plain,
( ( ~ ( strictorderedP @ sK3_SY193 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(800,plain,
( ( ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY195 )
| ~ ( neq @ SY195 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SY195 ) )
| ~ ( frontsegP @ sK1_U @ SY195 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(801,plain,
! [SV111: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
| ~ ( segmentP @ SV111 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(802,plain,
( ( ( nil = sK2_SX0 )
= $false )
| ( ( nil != sK1_U )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(803,plain,
! [SV66: $i,SV8: $i] :
( ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ~ ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(804,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) ) )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(805,plain,
! [SV97: $i,SV68: $i,SV12: $i,SV108: $i] :
( ( ( ~ ( ssList @ SV108 ) )
= $true )
| ( ( ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SV108 ) @ SV68 ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(806,plain,
! [SV69: $i,SV13: $i] :
( ( ( rearsegP @ SV13 @ SV69 )
= $false )
| ( ( ~ ( rearsegP @ SV69 @ SV13 ) )
= $true )
| ( ( SV13 = SV69 )
= $true )
| ( ( ssList @ SV69 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(807,plain,
! [SV98: $i,SV70: $i,SV14: $i] :
( ( ( frontsegP @ SV14 @ SV70 )
= $false )
| ( ( frontsegP @ ( app @ SV14 @ SV98 ) @ SV70 )
= $true )
| ( ( ssList @ SV98 )
= $false )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(808,plain,
! [SV15: $i,SV99: $i,SV71: $i] :
( ( ( ~ ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) ) )
= $false )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(809,plain,
! [SV99: $i,SV15: $i,SV71: $i] :
( ( ( ~ ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) ) )
= $false )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(810,plain,
! [SV100: $i,SV72: $i,SV18: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SV100 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV100 )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(811,plain,
! [SV74: $i,SV25: $i] :
( ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ~ ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(812,plain,
! [SV25: $i,SV74: $i] :
( ( ( ~ ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) ) )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(813,plain,
! [SV101: $i,SV75: $i,SV26: $i] :
( ( ( ~ ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SV101 ) ) )
= $false )
| ( ( segmentP @ SV26 @ SV101 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(814,plain,
! [SV77: $i,SV28: $i] :
( ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ~ ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(815,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(816,plain,
! [SV79: $i,SV31: $i] :
( ( ( neq @ SV31 @ SV79 )
= $false )
| ( ( SV31 != SV79 )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(817,plain,
! [SV79: $i,SV31: $i] :
( ( ( SV31 != SV79 )
= $false )
| ( ( neq @ SV31 @ SV79 )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(818,plain,
! [SV102: $i,SV80: $i,SV34: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SV102 ) ) )
= $false )
| ( ( frontsegP @ SV34 @ SV102 )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(819,plain,
! [SV82: $i,SV36: $i] :
( ( ( segmentP @ SV36 @ SV82 )
= $false )
| ( ( ~ ( segmentP @ SV82 @ SV36 ) )
= $true )
| ( ( SV36 = SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(820,plain,
! [SV38: $i] :
( ( ( ~ ( ssList @ ( sK6_SY172 @ SV38 ) ) )
= $false )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(821,plain,
! [SV38: $i] :
( ( ( ( tl @ SV38 )
!= ( sK6_SY172 @ SV38 ) )
= $false )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(822,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ( ssItem @ ( sK8_SY173 @ SV39 ) )
| ( ( cons @ ( sK8_SY173 @ SV39 ) @ nil )
!= SV39 ) ) )
= $true )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(823,plain,
! [SV39: $i,SV109: $i] :
( ( ( ~ ( ~ ( ssItem @ SV109 )
| ( ( cons @ SV109 @ nil )
!= SV39 ) ) )
= $false )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(824,plain,
! [SV40: $i] :
( ( ( ~ ( ssItem @ ( sK7_SY175 @ SV40 ) ) )
= $false )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(825,plain,
! [SV40: $i] :
( ( ( ( hd @ SV40 )
!= ( sK7_SY175 @ SV40 ) )
= $false )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(826,plain,
! [SV84: $i,SV44: $i] :
( ( ( neq @ SV44 @ SV84 )
= $false )
| ( ( SV44 != SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(827,plain,
! [SV84: $i,SV44: $i] :
( ( ( SV44 != SV84 )
= $false )
| ( ( neq @ SV44 @ SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(828,plain,
! [SV47: $i] :
( ( ( ! [SY227: $i] :
~ ~ ( ~ ( ssItem @ SY227 )
| ( ( cons @ SY227 @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(829,plain,
! [SV49: $i,SV86: $i,SV103: $i] :
( ( ( ( app @ SV103 @ SV86 )
= ( app @ SV49 @ SV86 ) )
= $false )
| ( ( SV103 = SV49 )
= $true )
| ( ( ssList @ SV103 )
= $false )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(830,plain,
! [SV87: $i,SV50: $i] :
( ( ( frontsegP @ SV50 @ SV87 )
= $false )
| ( ( ~ ( frontsegP @ SV87 @ SV50 ) )
= $true )
| ( ( SV50 = SV87 )
= $true )
| ( ( ssList @ SV87 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(831,plain,
! [SV88: $i,SV51: $i] :
( ( ( nil
= ( app @ SV51 @ SV88 ) )
= $false )
| ( ( ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(832,plain,
! [SV51: $i,SV88: $i] :
( ( ( ~ ( ( nil != SV88 )
| ( nil != SV51 ) ) )
= $false )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(833,plain,
! [SV104: $i,SV89: $i,SV52: $i] :
( ( ( rearsegP @ SV52 @ SV89 )
= $false )
| ( ( rearsegP @ ( app @ SV104 @ SV52 ) @ SV89 )
= $true )
| ( ( ssList @ SV104 )
= $false )
| ( ( ssList @ SV89 )
= $false )
| ( ( ssList @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(834,plain,
! [SV90: $i,SV54: $i,SV105: $i,SV110: $i] :
( ( ( ~ ( ssItem @ SV110 ) )
= $true )
| ( ( ( ( cons @ SV105 @ SV54 )
!= ( cons @ SV110 @ SV90 ) )
| ~ ( ( SV105 != SV110 )
| ( SV90 != SV54 ) ) )
= $true )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(835,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
| ( ( hd @ SV62 )
!= ( hd @ SV3 ) ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(836,plain,
! [SV64: $i,SV94: $i,SV5: $i,SV107: $i] :
( ( ( ssList @ SV107 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) ) ) )
= $true )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(837,plain,
! [SV7: $i,SV95: $i,SV65: $i] :
( ( ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
| ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(838,plain,
! [SV95: $i,SV65: $i,SV7: $i] :
( ( ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
| ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(839,plain,
( ( ( sK2_SX0 != sK4_SY201 )
| ( sK1_U != sK3_SY193 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(840,plain,
( ( ~ ( frontsegP @ sK4_SY201 @ sK3_SY193 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(841,plain,
( ( strictorderedP @ sK3_SY193 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(842,plain,
! [SV112: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
| ~ ( frontsegP @ sK1_U @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(843,plain,
! [SV111: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
| ~ ( segmentP @ SV111 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SV111 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(844,plain,
( ( ( nil = sK1_U )
= $false )
| ( ( nil = sK2_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(845,plain,
! [SV8: $i,SV66: $i] :
( ( ( ! [SY204: $i] :
~ ~ ( ~ ( ssList @ SY204 )
| ( ( app @ SV66 @ SY204 )
!= SV8 ) ) )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(846,plain,
! [SV8: $i,SV66: $i] :
( ( ( ! [SY205: $i] :
~ ~ ( ~ ( ssList @ SY205 )
| ( ( app @ SV66 @ SY205 )
!= SV8 ) ) )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(847,plain,
! [SV97: $i,SV68: $i,SV12: $i,SV108: $i] :
( ( ( ssList @ SV108 )
= $false )
| ( ( ~ ( segmentP @ SV12 @ SV68 )
| ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SV108 ) @ SV68 ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(848,plain,
! [SV13: $i,SV69: $i] :
( ( ( rearsegP @ SV69 @ SV13 )
= $false )
| ( ( rearsegP @ SV13 @ SV69 )
= $false )
| ( ( SV13 = SV69 )
= $true )
| ( ( ssList @ SV69 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(849,plain,
! [SV15: $i,SV99: $i,SV71: $i] :
( ( ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
| ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(850,plain,
! [SV99: $i,SV15: $i,SV71: $i] :
( ( ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
| ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(851,plain,
! [SV100: $i,SV72: $i,SV18: $i] :
( ( ( ~ ( rearsegP @ SV18 @ SV72 )
| ~ ( rearsegP @ SV72 @ SV100 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV100 )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(852,plain,
! [SV25: $i,SV74: $i] :
( ( ( ! [SY212: $i] :
~ ~ ( ~ ( ssList @ SY212 )
| ( ( app @ SY212 @ SV74 )
!= SV25 ) ) )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(853,plain,
! [SV25: $i,SV74: $i] :
( ( ( ! [SY213: $i] :
~ ~ ( ~ ( ssList @ SY213 )
| ( ( app @ SY213 @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(854,plain,
! [SV101: $i,SV75: $i,SV26: $i] :
( ( ( ~ ( segmentP @ SV26 @ SV75 )
| ~ ( segmentP @ SV75 @ SV101 ) )
= $true )
| ( ( segmentP @ SV26 @ SV101 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(855,plain,
! [SV28: $i,SV77: $i] :
( ( ( ! [SY215: $i] :
~ ~ ( ~ ( ssList @ SY215 )
| ~ ~ ! [SY216: $i] :
~ ~ ( ~ ( ssList @ SY216 )
| ( ( app @ ( app @ SY215 @ SV77 ) @ SY216 )
!= SV28 ) ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(856,plain,
! [SV28: $i,SV77: $i] :
( ( ( ! [SY217: $i] :
~ ~ ( ~ ( ssList @ SY217 )
| ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( ssList @ SY218 )
| ( ( app @ ( app @ SY217 @ SV77 ) @ SY218 )
!= SV28 ) ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(857,plain,
! [SV79: $i,SV31: $i] :
( ( ( SV31 = SV79 )
= $false )
| ( ( neq @ SV31 @ SV79 )
= $false )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(858,plain,
! [SV79: $i,SV31: $i] :
( ( ( SV31 = SV79 )
= $true )
| ( ( neq @ SV31 @ SV79 )
= $true )
| ( ( ssItem @ SV79 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(859,plain,
! [SV102: $i,SV80: $i,SV34: $i] :
( ( ( ~ ( frontsegP @ SV34 @ SV80 )
| ~ ( frontsegP @ SV80 @ SV102 ) )
= $true )
| ( ( frontsegP @ SV34 @ SV102 )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(860,plain,
! [SV36: $i,SV82: $i] :
( ( ( segmentP @ SV82 @ SV36 )
= $false )
| ( ( segmentP @ SV36 @ SV82 )
= $false )
| ( ( SV36 = SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(861,plain,
! [SV38: $i] :
( ( ( ssList @ ( sK6_SY172 @ SV38 ) )
= $true )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(862,plain,
! [SV38: $i] :
( ( ( ( tl @ SV38 )
= ( sK6_SY172 @ SV38 ) )
= $true )
| ( ( nil = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(863,plain,
! [SV39: $i] :
( ( ( ~ ( ssItem @ ( sK8_SY173 @ SV39 ) )
| ( ( cons @ ( sK8_SY173 @ SV39 ) @ nil )
!= SV39 ) )
= $false )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(864,plain,
! [SV39: $i,SV109: $i] :
( ( ( ~ ( ssItem @ SV109 )
| ( ( cons @ SV109 @ nil )
!= SV39 ) )
= $true )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(865,plain,
! [SV40: $i] :
( ( ( ssItem @ ( sK7_SY175 @ SV40 ) )
= $true )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(866,plain,
! [SV40: $i] :
( ( ( ( hd @ SV40 )
= ( sK7_SY175 @ SV40 ) )
= $true )
| ( ( nil = SV40 )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(867,plain,
! [SV84: $i,SV44: $i] :
( ( ( SV44 = SV84 )
= $false )
| ( ( neq @ SV44 @ SV84 )
= $false )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(868,plain,
! [SV84: $i,SV44: $i] :
( ( ( SV44 = SV84 )
= $true )
| ( ( neq @ SV44 @ SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(869,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ ( sK9_SY227 @ SV47 ) )
| ( ( cons @ ( sK9_SY227 @ SV47 ) @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[828]) ).
thf(870,plain,
! [SV50: $i,SV87: $i] :
( ( ( frontsegP @ SV87 @ SV50 )
= $false )
| ( ( frontsegP @ SV50 @ SV87 )
= $false )
| ( ( SV50 = SV87 )
= $true )
| ( ( ssList @ SV87 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(871,plain,
! [SV51: $i,SV88: $i] :
( ( ( ( nil != SV88 )
| ( nil != SV51 ) )
= $false )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(872,plain,
! [SV51: $i,SV88: $i] :
( ( ( ( nil != SV88 )
| ( nil != SV51 ) )
= $true )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(873,plain,
! [SV90: $i,SV54: $i,SV105: $i,SV110: $i] :
( ( ( ssItem @ SV110 )
= $false )
| ( ( ( ( cons @ SV105 @ SV54 )
!= ( cons @ SV110 @ SV90 ) )
| ~ ( ( SV105 != SV110 )
| ( SV90 != SV54 ) ) )
= $true )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(874,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) ) )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(875,plain,
! [SV107: $i,SV64: $i,SV94: $i,SV5: $i] :
( ( ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
| ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(876,plain,
! [SV7: $i,SV95: $i,SV65: $i] :
( ( ( ~ ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 ) )
= $true )
| ( ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(877,plain,
! [SV95: $i,SV65: $i,SV7: $i] :
( ( ( ~ ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) ) )
= $true )
| ( ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(878,plain,
( ( sK2_SX0 != sK4_SY201 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(879,plain,
( ( sK1_U != sK3_SY193 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(880,plain,
( ( frontsegP @ sK4_SY201 @ sK3_SY193 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(881,plain,
! [SV112: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
| ~ ( frontsegP @ sK1_U @ SV112 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(882,plain,
! [SV111: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
| ~ ( segmentP @ SV111 @ sK3_SY193 ) )
| ~ ( strictorderedP @ SV111 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(883,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK10_SY204 @ SV8 @ SV66 ) )
| ( ( app @ SV66 @ ( sK10_SY204 @ SV8 @ SV66 ) )
!= SV8 ) ) )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[845]) ).
thf(884,plain,
! [SV8: $i,SV66: $i,SV113: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV113 )
| ( ( app @ SV66 @ SV113 )
!= SV8 ) ) )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(885,plain,
! [SV108: $i,SV97: $i,SV68: $i,SV12: $i] :
( ( ( ~ ( segmentP @ SV12 @ SV68 ) )
= $true )
| ( ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SV108 ) @ SV68 )
= $true )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(886,plain,
! [SV15: $i,SV99: $i,SV71: $i] :
( ( ( ~ ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 ) )
= $true )
| ( ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(887,plain,
! [SV99: $i,SV15: $i,SV71: $i] :
( ( ( ~ ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) ) )
= $true )
| ( ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(888,plain,
! [SV100: $i,SV72: $i,SV18: $i] :
( ( ( ~ ( rearsegP @ SV18 @ SV72 ) )
= $true )
| ( ( ~ ( rearsegP @ SV72 @ SV100 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV100 )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(889,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK11_SY212 @ SV25 @ SV74 ) )
| ( ( app @ ( sK11_SY212 @ SV25 @ SV74 ) @ SV74 )
!= SV25 ) ) )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[852]) ).
thf(890,plain,
! [SV25: $i,SV74: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV114 )
| ( ( app @ SV114 @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(891,plain,
! [SV101: $i,SV75: $i,SV26: $i] :
( ( ( ~ ( segmentP @ SV26 @ SV75 ) )
= $true )
| ( ( ~ ( segmentP @ SV75 @ SV101 ) )
= $true )
| ( ( segmentP @ SV26 @ SV101 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(892,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK12_SY215 @ SV28 @ SV77 ) )
| ~ ~ ! [SY231: $i] :
~ ~ ( ~ ( ssList @ SY231 )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ SY231 )
!= SV28 ) ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[855]) ).
thf(893,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV115 )
| ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(894,plain,
! [SV102: $i,SV80: $i,SV34: $i] :
( ( ( ~ ( frontsegP @ SV34 @ SV80 ) )
= $true )
| ( ( ~ ( frontsegP @ SV80 @ SV102 ) )
= $true )
| ( ( frontsegP @ SV34 @ SV102 )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(895,plain,
! [SV39: $i] :
( ( ( ~ ( ssItem @ ( sK8_SY173 @ SV39 ) ) )
= $false )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(896,plain,
! [SV39: $i] :
( ( ( ( cons @ ( sK8_SY173 @ SV39 ) @ nil )
!= SV39 )
= $false )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(897,plain,
! [SV39: $i,SV109: $i] :
( ( ( ~ ( ssItem @ SV109 ) )
= $true )
| ( ( ( cons @ SV109 @ nil )
!= SV39 )
= $true )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(898,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ( ssItem @ ( sK9_SY227 @ SV47 ) )
| ( ( cons @ ( sK9_SY227 @ SV47 ) @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) ) )
= $true )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(899,plain,
! [SV51: $i,SV88: $i] :
( ( ( nil != SV88 )
= $false )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(900,plain,
! [SV88: $i,SV51: $i] :
( ( ( nil != SV51 )
= $false )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(901,plain,
! [SV51: $i,SV88: $i] :
( ( ( nil != SV88 )
= $true )
| ( ( nil != SV51 )
= $true )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(902,plain,
! [SV90: $i,SV110: $i,SV54: $i,SV105: $i] :
( ( ( ( cons @ SV105 @ SV54 )
!= ( cons @ SV110 @ SV90 ) )
= $true )
| ( ( ~ ( ( SV105 != SV110 )
| ( SV90 != SV54 ) ) )
= $true )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(903,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) ) )
= $false )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(904,plain,
! [SV107: $i,SV64: $i,SV94: $i,SV5: $i] :
( ( ( ~ ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(905,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(906,plain,
! [SV7: $i,SV95: $i,SV65: $i] :
( ( ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
= $false )
| ( ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(907,plain,
! [SV95: $i,SV65: $i,SV7: $i] :
( ( ( ( SV7 = SV65 )
| ( memberP @ SV95 @ SV7 ) )
= $false )
| ( ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(908,plain,
( ( sK2_SX0 = sK4_SY201 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(909,plain,
( ( sK1_U = sK3_SY193 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(910,plain,
! [SV112: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
| ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(911,plain,
! [SV111: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
| ~ ( segmentP @ SV111 @ sK3_SY193 ) ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(912,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK10_SY204 @ SV8 @ SV66 ) )
| ( ( app @ SV66 @ ( sK10_SY204 @ SV8 @ SV66 ) )
!= SV8 ) ) )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(913,plain,
! [SV8: $i,SV66: $i,SV113: $i] :
( ( ( ~ ( ~ ( ssList @ SV113 )
| ( ( app @ SV66 @ SV113 )
!= SV8 ) ) )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(914,plain,
! [SV108: $i,SV97: $i,SV68: $i,SV12: $i] :
( ( ( segmentP @ SV12 @ SV68 )
= $false )
| ( ( segmentP @ ( app @ ( app @ SV97 @ SV12 ) @ SV108 ) @ SV68 )
= $true )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(915,plain,
! [SV15: $i,SV99: $i,SV71: $i] :
( ( ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
= $false )
| ( ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(916,plain,
! [SV99: $i,SV15: $i,SV71: $i] :
( ( ( ( memberP @ SV71 @ SV15 )
| ( memberP @ SV99 @ SV15 ) )
= $false )
| ( ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(917,plain,
! [SV100: $i,SV72: $i,SV18: $i] :
( ( ( rearsegP @ SV18 @ SV72 )
= $false )
| ( ( ~ ( rearsegP @ SV72 @ SV100 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV100 )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(918,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK11_SY212 @ SV25 @ SV74 ) )
| ( ( app @ ( sK11_SY212 @ SV25 @ SV74 ) @ SV74 )
!= SV25 ) ) )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(919,plain,
! [SV25: $i,SV74: $i,SV114: $i] :
( ( ( ~ ( ~ ( ssList @ SV114 )
| ( ( app @ SV114 @ SV74 )
!= SV25 ) ) )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(920,plain,
! [SV101: $i,SV75: $i,SV26: $i] :
( ( ( segmentP @ SV26 @ SV75 )
= $false )
| ( ( ~ ( segmentP @ SV75 @ SV101 ) )
= $true )
| ( ( segmentP @ SV26 @ SV101 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(921,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK12_SY215 @ SV28 @ SV77 ) )
| ~ ~ ! [SY231: $i] :
~ ~ ( ~ ( ssList @ SY231 )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ SY231 )
!= SV28 ) ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(922,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ~ ( ~ ( ssList @ SV115 )
| ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(923,plain,
! [SV102: $i,SV80: $i,SV34: $i] :
( ( ( frontsegP @ SV34 @ SV80 )
= $false )
| ( ( ~ ( frontsegP @ SV80 @ SV102 ) )
= $true )
| ( ( frontsegP @ SV34 @ SV102 )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(924,plain,
! [SV39: $i] :
( ( ( ssItem @ ( sK8_SY173 @ SV39 ) )
= $true )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(925,plain,
! [SV39: $i] :
( ( ( ( cons @ ( sK8_SY173 @ SV39 ) @ nil )
= SV39 )
= $true )
| ( ( singletonP @ SV39 )
= $false )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(926,plain,
! [SV39: $i,SV109: $i] :
( ( ( ssItem @ SV109 )
= $false )
| ( ( ( cons @ SV109 @ nil )
!= SV39 )
= $true )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(927,plain,
! [SV47: $i] :
( ( ( ~ ( ssItem @ ( sK9_SY227 @ SV47 ) )
| ( ( cons @ ( sK9_SY227 @ SV47 ) @ ( sK5_SY179 @ SV47 ) )
!= SV47 ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(928,plain,
! [SV51: $i,SV88: $i] :
( ( ( nil = SV88 )
= $true )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(929,plain,
! [SV88: $i,SV51: $i] :
( ( ( nil = SV51 )
= $true )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $false )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(930,plain,
! [SV51: $i,SV88: $i] :
( ( ( nil = SV88 )
= $false )
| ( ( nil != SV51 )
= $true )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(931,plain,
! [SV90: $i,SV110: $i,SV54: $i,SV105: $i] :
( ( ( ( cons @ SV105 @ SV54 )
= ( cons @ SV110 @ SV90 ) )
= $false )
| ( ( ~ ( ( SV105 != SV110 )
| ( SV90 != SV54 ) ) )
= $true )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(932,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ( nil != SV62 ) )
| ~ ( ( nil != SV3 ) ) )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(933,plain,
! [SV107: $i,SV64: $i,SV94: $i,SV5: $i] :
( ( ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
| ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(934,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
| ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(935,plain,
! [SV95: $i,SV65: $i,SV7: $i] :
( ( ( SV7 = SV65 )
= $true )
| ( ( memberP @ SV95 @ SV7 )
= $true )
| ( ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(936,plain,
! [SV95: $i,SV65: $i,SV7: $i] :
( ( ( SV7 = SV65 )
= $false )
| ( ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(937,plain,
! [SV65: $i,SV7: $i,SV95: $i] :
( ( ( memberP @ SV95 @ SV7 )
= $false )
| ( ( memberP @ ( cons @ SV65 @ SV95 ) @ SV7 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssItem @ SV65 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(938,plain,
! [SV112: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SV112 ) ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(939,plain,
! [SV111: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
| ~ ( segmentP @ SV111 @ sK3_SY193 ) ) )
= $false )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(940,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( ssList @ ( sK10_SY204 @ SV8 @ SV66 ) )
| ( ( app @ SV66 @ ( sK10_SY204 @ SV8 @ SV66 ) )
!= SV8 ) )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(941,plain,
! [SV8: $i,SV66: $i,SV113: $i] :
( ( ( ~ ( ssList @ SV113 )
| ( ( app @ SV66 @ SV113 )
!= SV8 ) )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(942,plain,
! [SV99: $i,SV15: $i,SV71: $i] :
( ( ( memberP @ SV71 @ SV15 )
= $true )
| ( ( memberP @ SV99 @ SV15 )
= $true )
| ( ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
= $false )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(943,plain,
! [SV99: $i,SV15: $i,SV71: $i] :
( ( ( memberP @ SV71 @ SV15 )
= $false )
| ( ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(944,plain,
! [SV71: $i,SV15: $i,SV99: $i] :
( ( ( memberP @ SV99 @ SV15 )
= $false )
| ( ( memberP @ ( app @ SV71 @ SV99 ) @ SV15 )
= $true )
| ( ( ssList @ SV99 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(945,plain,
! [SV18: $i,SV100: $i,SV72: $i] :
( ( ( rearsegP @ SV72 @ SV100 )
= $false )
| ( ( rearsegP @ SV18 @ SV72 )
= $false )
| ( ( rearsegP @ SV18 @ SV100 )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(946,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( ssList @ ( sK11_SY212 @ SV25 @ SV74 ) )
| ( ( app @ ( sK11_SY212 @ SV25 @ SV74 ) @ SV74 )
!= SV25 ) )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(947,plain,
! [SV25: $i,SV74: $i,SV114: $i] :
( ( ( ~ ( ssList @ SV114 )
| ( ( app @ SV114 @ SV74 )
!= SV25 ) )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(948,plain,
! [SV26: $i,SV101: $i,SV75: $i] :
( ( ( segmentP @ SV75 @ SV101 )
= $false )
| ( ( segmentP @ SV26 @ SV75 )
= $false )
| ( ( segmentP @ SV26 @ SV101 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV75 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(949,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( ssList @ ( sK12_SY215 @ SV28 @ SV77 ) )
| ~ ~ ! [SY231: $i] :
~ ~ ( ~ ( ssList @ SY231 )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ SY231 )
!= SV28 ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(950,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ~ ( ssList @ SV115 )
| ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(951,plain,
! [SV34: $i,SV102: $i,SV80: $i] :
( ( ( frontsegP @ SV80 @ SV102 )
= $false )
| ( ( frontsegP @ SV34 @ SV80 )
= $false )
| ( ( frontsegP @ SV34 @ SV102 )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(952,plain,
! [SV39: $i,SV109: $i] :
( ( ( ( cons @ SV109 @ nil )
= SV39 )
= $false )
| ( ( ssItem @ SV109 )
= $false )
| ( ( singletonP @ SV39 )
= $true )
| ( ( ssList @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(953,plain,
! [SV47: $i] :
( ( ( ~ ( ssItem @ ( sK9_SY227 @ SV47 ) ) )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(954,plain,
! [SV47: $i] :
( ( ( ( cons @ ( sK9_SY227 @ SV47 ) @ ( sK5_SY179 @ SV47 ) )
!= SV47 )
= $false )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(955,plain,
! [SV88: $i,SV51: $i] :
( ( ( nil = SV51 )
= $false )
| ( ( nil = SV88 )
= $false )
| ( ( nil
= ( app @ SV51 @ SV88 ) )
= $true )
| ( ( ssList @ SV88 )
= $false )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(956,plain,
! [SV54: $i,SV90: $i,SV110: $i,SV105: $i] :
( ( ( ( SV105 != SV110 )
| ( SV90 != SV54 ) )
= $false )
| ( ( ( cons @ SV105 @ SV54 )
= ( cons @ SV110 @ SV90 ) )
= $false )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(957,plain,
! [SV3: $i,SV62: $i] :
( ( ( ~ ( ( nil != SV62 ) ) )
= $true )
| ( ( ~ ( ( nil != SV3 ) ) )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(958,plain,
! [SV107: $i,SV64: $i,SV94: $i,SV5: $i] :
( ( ( ~ ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) ) )
= $true )
| ( ( ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(959,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
= $true )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(960,plain,
! [SV112: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SV112 ) ) )
= $false )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(961,plain,
! [SV111: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
| ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(962,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( ssList @ ( sK10_SY204 @ SV8 @ SV66 ) ) )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(963,plain,
! [SV8: $i,SV66: $i] :
( ( ( ( app @ SV66 @ ( sK10_SY204 @ SV8 @ SV66 ) )
!= SV8 )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(964,plain,
! [SV8: $i,SV66: $i,SV113: $i] :
( ( ( ~ ( ssList @ SV113 ) )
= $true )
| ( ( ( app @ SV66 @ SV113 )
!= SV8 )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(965,plain,
! [SV74: $i,SV25: $i] :
( ( ( ~ ( ssList @ ( sK11_SY212 @ SV25 @ SV74 ) ) )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(966,plain,
! [SV74: $i,SV25: $i] :
( ( ( ( app @ ( sK11_SY212 @ SV25 @ SV74 ) @ SV74 )
!= SV25 )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(967,plain,
! [SV25: $i,SV74: $i,SV114: $i] :
( ( ( ~ ( ssList @ SV114 ) )
= $true )
| ( ( ( app @ SV114 @ SV74 )
!= SV25 )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(968,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ( ssList @ ( sK12_SY215 @ SV28 @ SV77 ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(969,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ~ ! [SY231: $i] :
~ ~ ( ~ ( ssList @ SY231 )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ SY231 )
!= SV28 ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(970,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ~ ( ssList @ SV115 ) )
= $true )
| ( ( ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(971,plain,
! [SV47: $i] :
( ( ( ssItem @ ( sK9_SY227 @ SV47 ) )
= $true )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(972,plain,
! [SV47: $i] :
( ( ( ( cons @ ( sK9_SY227 @ SV47 ) @ ( sK5_SY179 @ SV47 ) )
= SV47 )
= $true )
| ( ( nil = SV47 )
= $true )
| ( ( ssList @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(973,plain,
! [SV90: $i,SV54: $i,SV110: $i,SV105: $i] :
( ( ( SV105 != SV110 )
= $false )
| ( ( ( cons @ SV105 @ SV54 )
= ( cons @ SV110 @ SV90 ) )
= $false )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(974,plain,
! [SV110: $i,SV105: $i,SV54: $i,SV90: $i] :
( ( ( SV90 != SV54 )
= $false )
| ( ( ( cons @ SV105 @ SV54 )
= ( cons @ SV110 @ SV90 ) )
= $false )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(975,plain,
! [SV3: $i,SV62: $i] :
( ( ( nil != SV62 )
= $false )
| ( ( ~ ( ( nil != SV3 ) ) )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(976,plain,
! [SV107: $i,SV64: $i,SV94: $i,SV5: $i] :
( ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $false )
| ( ( ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(977,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) ) )
= $false )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(978,plain,
! [SV112: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
| ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(979,plain,
! [SV111: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(980,plain,
! [SV66: $i,SV8: $i] :
( ( ( ssList @ ( sK10_SY204 @ SV8 @ SV66 ) )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(981,plain,
! [SV8: $i,SV66: $i] :
( ( ( ( app @ SV66 @ ( sK10_SY204 @ SV8 @ SV66 ) )
= SV8 )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $false )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(982,plain,
! [SV8: $i,SV66: $i,SV113: $i] :
( ( ( ssList @ SV113 )
= $false )
| ( ( ( app @ SV66 @ SV113 )
!= SV8 )
= $true )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(983,plain,
! [SV74: $i,SV25: $i] :
( ( ( ssList @ ( sK11_SY212 @ SV25 @ SV74 ) )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(984,plain,
! [SV74: $i,SV25: $i] :
( ( ( ( app @ ( sK11_SY212 @ SV25 @ SV74 ) @ SV74 )
= SV25 )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(985,plain,
! [SV25: $i,SV74: $i,SV114: $i] :
( ( ( ssList @ SV114 )
= $false )
| ( ( ( app @ SV114 @ SV74 )
!= SV25 )
= $true )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(986,plain,
! [SV77: $i,SV28: $i] :
( ( ( ssList @ ( sK12_SY215 @ SV28 @ SV77 ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(987,plain,
! [SV77: $i,SV28: $i] :
( ( ( ~ ! [SY231: $i] :
~ ~ ( ~ ( ssList @ SY231 )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ SY231 )
!= SV28 ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(988,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ssList @ SV115 )
= $false )
| ( ( ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(989,plain,
! [SV90: $i,SV54: $i,SV110: $i,SV105: $i] :
( ( ( SV105 = SV110 )
= $true )
| ( ( ( cons @ SV105 @ SV54 )
= ( cons @ SV110 @ SV90 ) )
= $false )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(990,plain,
! [SV110: $i,SV105: $i,SV54: $i,SV90: $i] :
( ( ( SV90 = SV54 )
= $true )
| ( ( ( cons @ SV105 @ SV54 )
= ( cons @ SV110 @ SV90 ) )
= $false )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV105 )
= $false )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(991,plain,
! [SV3: $i,SV62: $i] :
( ( ( nil = SV62 )
= $true )
| ( ( ~ ( ( nil != SV3 ) ) )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(992,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
= $false )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(993,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( ( SV5 != SV64 )
| ~ ( frontsegP @ SV94 @ SV107 ) )
= $true )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(994,plain,
! [SV112: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) ) )
= $true )
| ( ( ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(995,plain,
! [SV111: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) ) )
= $false )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(996,plain,
! [SV8: $i,SV113: $i,SV66: $i] :
( ( ( ( app @ SV66 @ SV113 )
= SV8 )
= $false )
| ( ( ssList @ SV113 )
= $false )
| ( ( frontsegP @ SV8 @ SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(997,plain,
! [SV25: $i,SV74: $i,SV114: $i] :
( ( ( ( app @ SV114 @ SV74 )
= SV25 )
= $false )
| ( ( ssList @ SV114 )
= $false )
| ( ( rearsegP @ SV25 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(998,plain,
! [SV77: $i,SV28: $i] :
( ( ( ! [SY231: $i] :
~ ~ ( ~ ( ssList @ SY231 )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ SY231 )
!= SV28 ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(999,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ~ ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) )
= $false )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1000,plain,
! [SV62: $i,SV3: $i] :
( ( ( nil != SV3 )
= $false )
| ( ( nil = SV62 )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1001,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( SV5 != SV64 )
= $false )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1002,plain,
! [SV64: $i,SV5: $i,SV107: $i,SV94: $i] :
( ( ( ~ ( frontsegP @ SV94 @ SV107 ) )
= $false )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1003,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( SV5 != SV64 )
= $true )
| ( ( ~ ( frontsegP @ SV94 @ SV107 ) )
= $true )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1004,plain,
! [SV112: $i] :
( ( ( ~ ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) ) )
= $false )
| ( ( ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1005,plain,
! [SV111: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
| ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1006,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK13_SY231 @ SV77 @ SV28 ) )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ ( sK13_SY231 @ SV77 @ SV28 ) )
!= SV28 ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[998]) ).
thf(1007,plain,
! [SV28: $i,SV77: $i,SV115: $i] :
( ( ( ! [SY232: $i] :
~ ~ ( ~ ( ssList @ SY232 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SY232 )
!= SV28 ) ) )
= $true )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1008,plain,
! [SV62: $i,SV3: $i] :
( ( ( nil = SV3 )
= $true )
| ( ( nil = SV62 )
= $true )
| ( ( ( hd @ SV62 )
!= ( hd @ SV3 ) )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1009,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( SV5 = SV64 )
= $true )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1010,plain,
! [SV64: $i,SV5: $i,SV107: $i,SV94: $i] :
( ( ( frontsegP @ SV94 @ SV107 )
= $true )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $false )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1011,plain,
! [SV107: $i,SV94: $i,SV64: $i,SV5: $i] :
( ( ( SV5 = SV64 )
= $false )
| ( ( ~ ( frontsegP @ SV94 @ SV107 ) )
= $true )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1012,plain,
! [SV112: $i] :
( ( ( ~ ( ssList @ SV112 )
| ~ ( neq @ SV112 @ nil ) )
= $true )
| ( ( ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1013,plain,
! [SV111: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) ) )
= $true )
| ( ( ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1014,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK13_SY231 @ SV77 @ SV28 ) )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ ( sK13_SY231 @ SV77 @ SV28 ) )
!= SV28 ) ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1015,plain,
! [SV28: $i,SV77: $i,SV115: $i,SV116: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV116 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SV116 )
!= SV28 ) ) )
= $true )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1016,plain,
! [SV3: $i,SV62: $i] :
( ( ( ( hd @ SV62 )
= ( hd @ SV3 ) )
= $false )
| ( ( nil = SV62 )
= $true )
| ( ( nil = SV3 )
= $true )
| ( ( ( tl @ SV62 )
!= ( tl @ SV3 ) )
= $true )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1017,plain,
! [SV64: $i,SV5: $i,SV107: $i,SV94: $i] :
( ( ( frontsegP @ SV94 @ SV107 )
= $false )
| ( ( SV5 = SV64 )
= $false )
| ( ( frontsegP @ ( cons @ SV5 @ SV94 ) @ ( cons @ SV64 @ SV107 ) )
= $true )
| ( ( ssList @ SV107 )
= $false )
| ( ( ssList @ SV94 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1018,plain,
! [SV112: $i] :
( ( ( ~ ( ssList @ SV112 ) )
= $true )
| ( ( ~ ( neq @ SV112 @ nil ) )
= $true )
| ( ( ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1019,plain,
! [SV111: $i] :
( ( ( ~ ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) ) )
= $false )
| ( ( ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1020,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( ssList @ ( sK13_SY231 @ SV77 @ SV28 ) )
| ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ ( sK13_SY231 @ SV77 @ SV28 ) )
!= SV28 ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1021,plain,
! [SV28: $i,SV77: $i,SV115: $i,SV116: $i] :
( ( ( ~ ( ~ ( ssList @ SV116 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SV116 )
!= SV28 ) ) )
= $false )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1022,plain,
! [SV3: $i,SV62: $i] :
( ( ( ( tl @ SV62 )
= ( tl @ SV3 ) )
= $false )
| ( ( nil = SV3 )
= $true )
| ( ( nil = SV62 )
= $true )
| ( ( ( hd @ SV62 )
= ( hd @ SV3 ) )
= $false )
| ( ( SV62 = SV3 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1023,plain,
! [SV112: $i] :
( ( ( ssList @ SV112 )
= $false )
| ( ( ~ ( neq @ SV112 @ nil ) )
= $true )
| ( ( ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1024,plain,
! [SV111: $i] :
( ( ( ~ ( ssList @ SV111 )
| ~ ( neq @ sK3_SY193 @ SV111 ) )
= $true )
| ( ( ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1025,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( ssList @ ( sK13_SY231 @ SV77 @ SV28 ) ) )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1026,plain,
! [SV77: $i,SV28: $i] :
( ( ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ ( sK13_SY231 @ SV77 @ SV28 ) )
!= SV28 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1027,plain,
! [SV28: $i,SV77: $i,SV115: $i,SV116: $i] :
( ( ( ~ ( ssList @ SV116 )
| ( ( app @ ( app @ SV115 @ SV77 ) @ SV116 )
!= SV28 ) )
= $true )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1028,plain,
! [SV112: $i] :
( ( ( neq @ SV112 @ nil )
= $false )
| ( ( ssList @ SV112 )
= $false )
| ( ( ~ ( frontsegP @ sK2_SX0 @ SV112 ) )
= $true )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1029,plain,
! [SV111: $i] :
( ( ( ~ ( ssList @ SV111 ) )
= $true )
| ( ( ~ ( neq @ sK3_SY193 @ SV111 ) )
= $true )
| ( ( ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1030,plain,
! [SV28: $i,SV77: $i] :
( ( ( ssList @ ( sK13_SY231 @ SV77 @ SV28 ) )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1031,plain,
! [SV77: $i,SV28: $i] :
( ( ( ( app @ ( app @ ( sK12_SY215 @ SV28 @ SV77 ) @ SV77 ) @ ( sK13_SY231 @ SV77 @ SV28 ) )
= SV28 )
= $true )
| ( ( segmentP @ SV28 @ SV77 )
= $false )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1032,plain,
! [SV28: $i,SV77: $i,SV115: $i,SV116: $i] :
( ( ( ~ ( ssList @ SV116 ) )
= $true )
| ( ( ( app @ ( app @ SV115 @ SV77 ) @ SV116 )
!= SV28 )
= $true )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1033,plain,
! [SV112: $i] :
( ( ( frontsegP @ sK2_SX0 @ SV112 )
= $false )
| ( ( ssList @ SV112 )
= $false )
| ( ( neq @ SV112 @ nil )
= $false )
| ( ( ~ ( frontsegP @ sK1_U @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1034,plain,
! [SV111: $i] :
( ( ( ssList @ SV111 )
= $false )
| ( ( ~ ( neq @ sK3_SY193 @ SV111 ) )
= $true )
| ( ( ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1035,plain,
! [SV28: $i,SV77: $i,SV115: $i,SV116: $i] :
( ( ( ssList @ SV116 )
= $false )
| ( ( ( app @ ( app @ SV115 @ SV77 ) @ SV116 )
!= SV28 )
= $true )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1036,plain,
! [SV112: $i] :
( ( ( frontsegP @ sK1_U @ SV112 )
= $false )
| ( ( neq @ SV112 @ nil )
= $false )
| ( ( ssList @ SV112 )
= $false )
| ( ( frontsegP @ sK2_SX0 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1037,plain,
! [SV111: $i] :
( ( ( neq @ sK3_SY193 @ SV111 )
= $false )
| ( ( ssList @ SV111 )
= $false )
| ( ( ~ ( frontsegP @ sK4_SY201 @ SV111 ) )
= $true )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1038,plain,
! [SV28: $i,SV116: $i,SV77: $i,SV115: $i] :
( ( ( ( app @ ( app @ SV115 @ SV77 ) @ SV116 )
= SV28 )
= $false )
| ( ( ssList @ SV116 )
= $false )
| ( ( ssList @ SV115 )
= $false )
| ( ( segmentP @ SV28 @ SV77 )
= $true )
| ( ( ssList @ SV77 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1039,plain,
! [SV111: $i] :
( ( ( frontsegP @ sK4_SY201 @ SV111 )
= $false )
| ( ( ssList @ SV111 )
= $false )
| ( ( neq @ sK3_SY193 @ SV111 )
= $false )
| ( ( ~ ( segmentP @ SV111 @ sK3_SY193 ) )
= $true )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1040,plain,
! [SV111: $i] :
( ( ( segmentP @ SV111 @ sK3_SY193 )
= $false )
| ( ( neq @ sK3_SY193 @ SV111 )
= $false )
| ( ( ssList @ SV111 )
= $false )
| ( ( frontsegP @ sK4_SY201 @ SV111 )
= $false )
| ( ( ~ ( strictorderedP @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1041,plain,
! [SV111: $i] :
( ( ( strictorderedP @ SV111 )
= $false )
| ( ( frontsegP @ sK4_SY201 @ SV111 )
= $false )
| ( ( ssList @ SV111 )
= $false )
| ( ( neq @ sK3_SY193 @ SV111 )
= $false )
| ( ( segmentP @ SV111 @ sK3_SY193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1042,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[178,1041,1038,1036,1031,1030,1022,1017,1010,1009,997,996,990,989,986,984,983,981,980,972,971,955,952,951,948,945,944,943,942,937,936,935,929,928,925,924,914,909,908,880,870,868,867,866,865,862,861,860,858,857,848,844,841,833,829,807,794,785,754,745,724,714,696,695,687,686,685,684,673,667,645,616,610,606,604,602,596,585,583,579,517,490,480,479,478,476,471,468,464,460,453,443,442,440,439,434,433,301,239,226,224,222,220,218,216,214]) ).
thf(1043,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC021+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.19 % Computer : n026.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 16:00:17 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.95/3.10 .
% 16.95/3.10
% 16.95/3.10 No.of.Axioms: 68
% 16.95/3.10
% 16.95/3.10 Length.of.Defs: 0
% 16.95/3.10
% 16.95/3.10 Contains.Choice.Funs: false
% 16.95/3.10 ...............................
% 16.95/3.10
% 16.95/3.10 ********************************
% 16.95/3.10 * All subproblems solved! *
% 16.95/3.10 ********************************
% 16.95/3.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:69,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1042,loop_count:0,foatp_calls:1,translation:fof_full)
% 16.95/3.10
% 16.95/3.10 %**** Beginning of derivation protocol ****
% 16.95/3.10 % SZS output start CNFRefutation
% See solution above
% 16.95/3.11
% 16.95/3.11 %**** End of derivation protocol ****
% 16.95/3.11 %**** no. of clauses in derivation: 1016 ****
% 16.95/3.11 %**** clause counter: 1042 ****
% 16.95/3.11
% 16.95/3.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:69,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1042,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------