%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWC067+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:51:44 AM UTC 2026
% Result : Theorem 15.84s 2.95s
% Output : CNFRefutation 15.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 96
% Syntax : Number of formulae : 1923 ( 448 unt; 0 typ; 0 def)
% Number of atoms : 22288 (7791 equ; 0 cnn)
% Maximal formula atoms : 33 ( 11 avg)
% Number of connectives : 37280 (9369 ~;8288 |; 233 &;18592 @)
% ( 78 <=>; 720 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 11 con; 0-2 aty)
% Number of variables : 5533 ( 0 ^;5431 !; 102 ?;5533 :)
% 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_SY262,type,
sK10_SY262: $i > $i ).
thf(tp_sK11_SY277,type,
sK11_SY277: $i > $i ).
thf(tp_sK12_SY309,type,
sK12_SY309: $i > $i ).
thf(tp_sK13_SY323,type,
sK13_SY323: $i > $i ).
thf(tp_sK14_SY338,type,
sK14_SY338: $i > $i ).
thf(tp_sK15_SY366,type,
sK15_SY366: $i > $i ).
thf(tp_sK16_SY383,type,
sK16_SY383: $i > $i ).
thf(tp_sK17_SY249,type,
sK17_SY249: $i > $i ).
thf(tp_sK18_SY468,type,
sK18_SY468: $i > $i ).
thf(tp_sK19_SY476,type,
sK19_SY476: $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK20_SY484,type,
sK20_SY484: $i > $i ).
thf(tp_sK21_SY492,type,
sK21_SY492: $i > $i ).
thf(tp_sK22_SY500,type,
sK22_SY500: $i > $i ).
thf(tp_sK23_SY450,type,
sK23_SY450: $i ).
thf(tp_sK24_SY507,type,
sK24_SY507: $i > $i ).
thf(tp_sK25_SY514,type,
sK25_SY514: $i > $i ).
thf(tp_sK26_SY449,type,
sK26_SY449: $i > $i ).
thf(tp_sK27_SY403,type,
sK27_SY403: $i > $i > $i ).
thf(tp_sK28_SY406,type,
sK28_SY406: $i > $i > $i ).
thf(tp_sK29_SY408,type,
sK29_SY408: $i > $i > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK30_SY518,type,
sK30_SY518: $i > $i ).
thf(tp_sK31_SY521,type,
sK31_SY521: $i > $i ).
thf(tp_sK32_SY415,type,
sK32_SY415: $i > $i > $i ).
thf(tp_sK33_SY524,type,
sK33_SY524: $i > $i ).
thf(tp_sK34_SY527,type,
sK34_SY527: $i > $i ).
thf(tp_sK35_SY530,type,
sK35_SY530: $i > $i ).
thf(tp_sK36_SY533,type,
sK36_SY533: $i ).
thf(tp_sK37_SY542,type,
sK37_SY542: $i > $i ).
thf(tp_sK38_SY544,type,
sK38_SY544: $i > $i ).
thf(tp_sK39_SY569,type,
sK39_SY569: $i > $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK40_SY571,type,
sK40_SY571: $i > $i ).
thf(tp_sK41_SY575,type,
sK41_SY575: $i > $i ).
thf(tp_sK42_SY577,type,
sK42_SY577: $i > $i ).
thf(tp_sK43_SY579,type,
sK43_SY579: $i > $i ).
thf(tp_sK44_SY589,type,
sK44_SY589: $i > $i ).
thf(tp_sK45_SY590,type,
sK45_SY590: $i > $i ).
thf(tp_sK46_SY594,type,
sK46_SY594: $i > $i ).
thf(tp_sK47_SY597,type,
sK47_SY597: $i > $i ).
thf(tp_sK48_SY600,type,
sK48_SY600: $i > $i ).
thf(tp_sK49_SY603,type,
sK49_SY603: $i > $i ).
thf(tp_sK4_SY389,type,
sK4_SY389: $i ).
thf(tp_sK50_SY606,type,
sK50_SY606: $i > $i ).
thf(tp_sK51_SY610,type,
sK51_SY610: $i > $i ).
thf(tp_sK52_SY567,type,
sK52_SY567: $i > $i > $i ).
thf(tp_sK53_SY573,type,
sK53_SY573: $i > $i > $i ).
thf(tp_sK5_SY328,type,
sK5_SY328: $i > $i ).
thf(tp_sK6_SY428,type,
sK6_SY428: $i ).
thf(tp_sK7_SY315,type,
sK7_SY315: $i > $i ).
thf(tp_sK8_SY402,type,
sK8_SY402: $i ).
thf(tp_sK9_SY388,type,
sK9_SY388: $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(1,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( gt @ U @ V )
& ( gt @ V @ W ) )
=> ( gt @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
thf(2,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
=> ~ ( gt @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
thf(3,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
<=> ( ( U != V )
& ( leq @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
thf(4,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( leq @ U @ V )
=> ( ( U = V )
| ( lt @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
thf(5,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
thf(6,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ~ ( lt @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(7,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( geq @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(8,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ W ) )
=> ( geq @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
thf(9,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
thf(10,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax85) ).
thf(12,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax79) ).
thf(18,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax77) ).
thf(20,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(21,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssItem @ V )
& ( ( hd @ U )
= V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
thf(22,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(23,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( equalelemsP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(24,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(25,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( duplicatefreeP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(26,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( strictorderedP @ ( cons @ U @ V ) )
<=> ( ( nil = V )
| ( ( nil != V )
& ( strictorderedP @ V )
& ( lt @ U @ ( hd @ V ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
thf(27,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(28,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( strictorderedP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(29,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( totalorderedP @ ( cons @ U @ V ) )
<=> ( ( nil = V )
| ( ( nil != V )
& ( totalorderedP @ V )
& ( leq @ U @ ( hd @ V ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
thf(30,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(31,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( totalorderedP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(32,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(33,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( strictorderP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(34,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(35,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( totalorderP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(36,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(37,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( cyclefreeP @ ( cons @ U @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(38,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(39,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax56) ).
thf(41,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(44,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(45,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(47,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(50,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(51,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(54,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(57,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(58,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(61,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
<=> ( lt @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(62,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( lt @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(63,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
=> ~ ( lt @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(64,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( geq @ U @ V )
<=> ( leq @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(65,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( leq @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(66,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ W ) )
=> ( leq @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(67,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(68,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(70,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(71,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(72,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(73,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(74,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(75,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(78,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(79,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(80,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(81,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(82,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( equalelemsP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ( ( ( app @ X @ ( cons @ V @ ( cons @ W @ Y ) ) )
= U )
=> ( V = W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(83,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( duplicatefreeP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( V != W ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(84,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( strictorderedP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( lt @ V @ W ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(85,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( totalorderedP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( leq @ V @ W ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(86,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( strictorderP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( ( lt @ V @ W )
| ( lt @ W @ V ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(87,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( totalorderP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( ( leq @ V @ W )
| ( leq @ W @ V ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(88,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( cyclefreeP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ~ ( ( leq @ V @ W )
& ( leq @ W @ V ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(92,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ssItem @ V )
& ( ( cons @ V @ nil )
= U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(93,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( memberP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ W @ ( cons @ V @ X ) )
= U ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(94,axiom,
? [U: $i] :
( ( ssItem @ U )
& ? [V: $i] :
( ( ssItem @ V )
& ( U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(95,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox/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 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ W ) @ Z )
!= X )
| ~ ( strictorderedP @ W )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= W )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= W )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != X )
& ( nil = W ) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ~ ( neq @ V @ nil )
| ? [X9: $i] :
( ( ssList @ X9 )
& ( neq @ X9 @ nil )
& ( segmentP @ V @ X9 )
& ( segmentP @ U @ X9 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ W ) @ Z )
!= X )
| ~ ( strictorderedP @ W )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= W )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= W )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != X )
& ( nil = W ) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ~ ( neq @ V @ nil )
| ? [X9: $i] :
( ( ssList @ X9 )
& ( neq @ X9 @ nil )
& ( segmentP @ V @ X9 )
& ( segmentP @ U @ X9 ) ) ) ) ) ) ) ) ) )
= $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 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ W ) @ Z )
!= X )
| ~ ( strictorderedP @ W )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= W )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= W )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != X )
& ( nil = W ) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ~ ( neq @ V @ nil )
| ? [X9: $i] :
( ( ssList @ X9 )
& ( neq @ X9 @ nil )
& ( segmentP @ V @ X9 )
& ( segmentP @ U @ X9 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( gt @ U @ V )
& ( gt @ V @ W ) )
=> ( gt @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(100,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
=> ~ ( gt @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(101,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
<=> ( ( U != V )
& ( leq @ U @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( leq @ U @ V )
=> ( ( U = V )
| ( lt @ U @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(103,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(104,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( lt @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(105,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( geq @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(106,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ W ) )
=> ( geq @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(107,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(108,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(109,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(110,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(111,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(112,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(113,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(114,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(115,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(116,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(117,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(118,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(119,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssItem @ V )
& ( ( hd @ U )
= V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(120,plain,
( ( equalelemsP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(121,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( equalelemsP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(122,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(123,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( duplicatefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(124,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( strictorderedP @ ( cons @ U @ V ) )
<=> ( ( nil = V )
| ( ( nil != V )
& ( strictorderedP @ V )
& ( lt @ U @ ( hd @ V ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(125,plain,
( ( strictorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(126,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(127,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( totalorderedP @ ( cons @ U @ V ) )
<=> ( ( nil = V )
| ( ( nil != V )
& ( totalorderedP @ V )
& ( leq @ U @ ( hd @ V ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(128,plain,
( ( totalorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(129,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(130,plain,
( ( strictorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(131,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(132,plain,
( ( totalorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(134,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(135,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( cyclefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(136,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(137,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(138,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(139,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(140,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(141,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(142,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(143,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(144,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(145,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(146,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(147,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(148,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(149,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(150,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(151,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(152,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(153,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(154,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(155,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(156,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(157,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(158,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(159,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
<=> ( lt @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(160,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( lt @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(161,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
=> ~ ( lt @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(162,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( geq @ U @ V )
<=> ( leq @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(163,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( leq @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(164,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ W ) )
=> ( leq @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(165,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(166,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(167,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(168,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(169,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(170,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(171,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(172,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(173,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(174,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(175,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(176,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(177,plain,
( ( ssList @ nil )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(178,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(179,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(180,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( equalelemsP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ( ( ( app @ X @ ( cons @ V @ ( cons @ W @ Y ) ) )
= U )
=> ( V = W ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(181,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( duplicatefreeP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( V != W ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(182,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( strictorderedP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( lt @ V @ W ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(183,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( totalorderedP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( leq @ V @ W ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(184,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( strictorderP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( ( lt @ V @ W )
| ( lt @ W @ V ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(185,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( totalorderP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( ( leq @ V @ W )
| ( leq @ W @ V ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(186,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( cyclefreeP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ~ ( ( leq @ V @ W )
& ( leq @ W @ V ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(187,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(188,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(189,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(190,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ssItem @ V )
& ( ( cons @ V @ nil )
= U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(191,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( memberP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ W @ ( cons @ V @ X ) )
= U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(192,plain,
( ( ? [U: $i] :
( ( ssItem @ U )
& ? [V: $i] :
( ( ssItem @ V )
& ( U != V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(193,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(194,plain,
( ( ( ssList @ sK1_U )
=> ! [SY218: $i] :
( ( ssList @ SY218 )
=> ! [SY219: $i] :
( ( ssList @ SY219 )
=> ! [SY220: $i] :
( ( ssList @ SY220 )
=> ( ( SY218 != SY220 )
| ( sK1_U != SY219 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ SY219 ) @ Z )
!= SY220 )
| ~ ( strictorderedP @ SY219 )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= SY219 )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= SY219 )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != SY220 )
& ( nil = SY219 ) )
| ( ( ( nil != SY218 )
| ( nil = sK1_U ) )
& ( ~ ( neq @ SY218 @ nil )
| ? [SY231: $i] :
( ( ssList @ SY231 )
& ( neq @ SY231 @ nil )
& ( segmentP @ SY218 @ SY231 )
& ( segmentP @ sK1_U @ SY231 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(195,plain,
( ( ssList @ sK1_U )
= $true ),
inference(standard_cnf,[status(thm)],[194]) ).
thf(196,plain,
( ( ! [SY218: $i] :
( ( ssList @ SY218 )
=> ! [SY219: $i] :
( ( ssList @ SY219 )
=> ! [SY220: $i] :
( ( ssList @ SY220 )
=> ( ( SY218 != SY220 )
| ( sK1_U != SY219 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ SY219 ) @ Z )
!= SY220 )
| ~ ( strictorderedP @ SY219 )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= SY219 )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= SY219 )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != SY220 )
& ( nil = SY219 ) )
| ( ( ( nil != SY218 )
| ( nil = sK1_U ) )
& ( ~ ( neq @ SY218 @ nil )
| ? [SY231: $i] :
( ( ssList @ SY231 )
& ( neq @ SY231 @ nil )
& ( segmentP @ SY218 @ SY231 )
& ( segmentP @ sK1_U @ SY231 ) ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[194]) ).
thf(197,plain,
( ( ~ ! [SY218: $i] :
( ( ssList @ SY218 )
=> ! [SY219: $i] :
( ( ssList @ SY219 )
=> ! [SY220: $i] :
( ( ssList @ SY220 )
=> ( ( SY218 != SY220 )
| ( sK1_U != SY219 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ SY219 ) @ Z )
!= SY220 )
| ~ ( strictorderedP @ SY219 )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= SY219 )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= SY219 )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != SY220 )
& ( nil = SY219 ) )
| ( ( ( nil != SY218 )
| ( nil = sK1_U ) )
& ( ~ ( neq @ SY218 @ nil )
| ? [SY231: $i] :
( ( ssList @ SY231 )
& ( neq @ SY231 @ nil )
& ( segmentP @ SY218 @ SY231 )
& ( segmentP @ sK1_U @ SY231 ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[196]) ).
thf(198,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(199,plain,
( ( ? [U: $i] :
( ( ssItem @ U )
& ? [V: $i] :
( ( ssItem @ V )
& ( U != V ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(200,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( memberP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ W @ ( cons @ V @ X ) )
= U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(201,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( singletonP @ U )
<=> ? [V: $i] :
( ( ssItem @ V )
& ( ( cons @ V @ nil )
= U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(202,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)],[189]) ).
thf(203,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)],[188]) ).
thf(204,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)],[187]) ).
thf(205,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( cyclefreeP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ~ ( ( leq @ V @ W )
& ( leq @ W @ V ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(206,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( totalorderP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( ( leq @ V @ W )
| ( leq @ W @ V ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(207,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( strictorderP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( ( lt @ V @ W )
| ( lt @ W @ V ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(208,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( totalorderedP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( leq @ V @ W ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(209,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( strictorderedP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( lt @ V @ W ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(210,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( duplicatefreeP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
= U )
=> ( V != W ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(211,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( equalelemsP @ U )
<=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ! [Y: $i] :
( ( ssList @ Y )
=> ( ( ( app @ X @ ( cons @ V @ ( cons @ W @ Y ) ) )
= U )
=> ( V = W ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(212,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(213,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(214,plain,
( ( ssList @ nil )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(215,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(216,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)],[175]) ).
thf(217,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil = U )
| ? [V: $i] :
( ( ssList @ V )
& ? [W: $i] :
( ( ssItem @ W )
& ( ( cons @ W @ V )
= U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(218,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( nil
!= ( cons @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(219,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssItem @ ( hd @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(220,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( hd @ ( cons @ V @ U ) )
= V ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(221,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(222,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( tl @ ( cons @ V @ U ) )
= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(223,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(224,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)],[167]) ).
thf(225,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(226,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(227,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ W ) )
=> ( leq @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(228,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( leq @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(229,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( geq @ U @ V )
<=> ( leq @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(230,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
=> ~ ( lt @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(231,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( lt @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(232,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
<=> ( lt @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(233,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)],[158]) ).
thf(234,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)],[157]) ).
thf(235,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(236,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(237,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)],[154]) ).
thf(238,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(239,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(240,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)],[151]) ).
thf(241,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)],[150]) ).
thf(242,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(243,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(244,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)],[147]) ).
thf(245,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(246,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(247,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)],[144]) ).
thf(248,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(249,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(250,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)],[141]) ).
thf(251,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(252,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(253,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)],[138]) ).
thf(254,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(255,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(256,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( cyclefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(257,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(258,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(259,plain,
( ( totalorderP @ nil )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(260,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(261,plain,
( ( strictorderP @ nil )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(262,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( totalorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(263,plain,
( ( totalorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(264,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( totalorderedP @ ( cons @ U @ V ) )
<=> ( ( nil = V )
| ( ( nil != V )
& ( totalorderedP @ V )
& ( leq @ U @ ( hd @ V ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(265,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( strictorderedP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(266,plain,
( ( strictorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(267,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( strictorderedP @ ( cons @ U @ V ) )
<=> ( ( nil = V )
| ( ( nil != V )
& ( strictorderedP @ V )
& ( lt @ U @ ( hd @ V ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(268,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( duplicatefreeP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(269,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(270,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( equalelemsP @ ( cons @ U @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(271,plain,
( ( equalelemsP @ nil )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(272,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssItem @ V )
& ( ( hd @ U )
= V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(273,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(274,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)],[117]) ).
thf(275,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(276,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)],[115]) ).
thf(277,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)],[114]) ).
thf(278,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
= ( app @ ( cons @ V @ nil ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(279,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)],[112]) ).
thf(280,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(281,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(282,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(283,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(284,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(285,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ W ) )
=> ( geq @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(286,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( geq @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(287,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( lt @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(288,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(289,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( leq @ U @ V )
=> ( ( U = V )
| ( lt @ U @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(290,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
<=> ( ( U != V )
& ( leq @ U @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(291,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
=> ~ ( gt @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(292,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( gt @ U @ V )
& ( gt @ V @ W ) )
=> ( gt @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(293,plain,
( ( ssList @ sK1_U )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(294,plain,
( ( ~ ! [SY218: $i] :
( ( ssList @ SY218 )
=> ! [SY219: $i] :
( ( ssList @ SY219 )
=> ! [SY220: $i] :
( ( ssList @ SY220 )
=> ( ( SY218 != SY220 )
| ( sK1_U != SY219 )
| ! [Y: $i] :
( ( ssList @ Y )
=> ! [Z: $i] :
( ( ssList @ Z )
=> ( ( ( app @ ( app @ Y @ SY219 ) @ Z )
!= SY220 )
| ~ ( strictorderedP @ SY219 )
| ? [X1: $i] :
( ( ssItem @ X1 )
& ? [X2: $i] :
( ( ssList @ X2 )
& ( ( app @ X2 @ ( cons @ X1 @ nil ) )
= Y )
& ? [X3: $i] :
( ( ssItem @ X3 )
& ? [X4: $i] :
( ( ssList @ X4 )
& ( ( app @ ( cons @ X3 @ nil ) @ X4 )
= SY219 )
& ( lt @ X1 @ X3 ) ) ) ) )
| ? [X5: $i] :
( ( ssItem @ X5 )
& ? [X6: $i] :
( ( ssList @ X6 )
& ( ( app @ ( cons @ X5 @ nil ) @ X6 )
= Z )
& ? [X7: $i] :
( ( ssItem @ X7 )
& ? [X8: $i] :
( ( ssList @ X8 )
& ( ( app @ X8 @ ( cons @ X7 @ nil ) )
= SY219 )
& ( lt @ X7 @ X5 ) ) ) ) ) ) ) )
| ( ( nil != SY220 )
& ( nil = SY219 ) )
| ( ( ( nil != SY218 )
| ( nil = sK1_U ) )
& ( ~ ( neq @ SY218 @ nil )
| ? [SY231: $i] :
( ( ssList @ SY231 )
& ( neq @ SY231 @ nil )
& ( segmentP @ SY218 @ SY231 )
& ( segmentP @ sK1_U @ SY231 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(295,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ( frontsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(296,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ~ ( lt @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(297,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( ~ ( ~ ( lt @ SX0 @ SX1 )
| ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( leq @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( leq @ SX0 @ SX1 ) )
| ( lt @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(298,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( ~ ( ~ ( gt @ SX0 @ SX1 )
| ( lt @ SX1 @ SX0 ) )
| ~ ( ~ ( lt @ SX1 @ SX0 )
| ( gt @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(299,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)],[198]) ).
thf(300,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(301,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( strictorderedP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(302,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ( nil != SX0 ) )
| ( ( hd @ ( app @ SX0 @ SX1 ) )
= ( hd @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(303,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( strictorderP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(304,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SX0 @ SX1 ) )
| ( nil = SX1 )
| ~ ( ~ ~ ( ~ ( ( nil != SX1 ) )
| ~ ( strictorderedP @ SX1 ) )
| ~ ( lt @ SX0 @ ( hd @ SX1 ) ) ) )
| ~ ( ~ ( ( nil = SX1 )
| ~ ( ~ ~ ( ~ ( ( nil != SX1 ) )
| ~ ( strictorderedP @ SX1 ) )
| ~ ( lt @ SX0 @ ( hd @ SX1 ) ) ) )
| ( strictorderedP @ ( cons @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(305,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( segmentP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(306,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ SX0 )
= ( app @ ( cons @ SX1 @ nil ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(307,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ( ssList @ ( app @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(308,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( duplicatefreeP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(309,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( hd @ ( cons @ SX1 @ SX0 ) )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(310,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)],[202]) ).
thf(311,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( lt @ SX1 @ SX2 ) )
| ( lt @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(312,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)],[203]) ).
thf(313,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)],[201]) ).
thf(314,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ~ ( ~ ( geq @ SX0 @ SX1 )
| ~ ( geq @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( ~ ( ~ ( memberP @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ssList @ SX3 )
| ( ( app @ SX2 @ ( cons @ SX1 @ SX3 ) )
!= SX0 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( ssList @ SX2 )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ssList @ SX3 )
| ( ( app @ SX2 @ ( cons @ SX1 @ SX3 ) )
!= SX0 ) ) )
| ( memberP @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(316,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( strictorderP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( lt @ SX1 @ SX2 )
| ( lt @ SX2 @ SX1 ) ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( lt @ SX1 @ SX2 )
| ( lt @ SX2 @ SX1 ) ) ) ) ) )
| ( strictorderP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(317,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(318,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)],[233]) ).
thf(319,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ SX0 @ nil )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(320,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)],[274]) ).
thf(321,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( frontsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(322,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)],[244]) ).
thf(323,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( totalorderedP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( leq @ SX1 @ SX2 ) ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( leq @ SX1 @ SX2 ) ) ) ) ) )
| ( totalorderedP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(324,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( leq @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(325,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(326,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ nil @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(327,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ssList @ ( cons @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(328,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)],[204]) ).
thf(329,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)],[216]) ).
thf(330,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ( cons @ ( hd @ SX0 ) @ ( tl @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(331,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( totalorderP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(332,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(333,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(334,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)],[253]) ).
thf(335,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)],[283]) ).
thf(336,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(337,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( lt @ SX0 @ SX1 )
| ~ ( lt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(338,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( nil
!= ( cons @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(339,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)],[240]) ).
thf(340,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)],[234]) ).
thf(341,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( cyclefreeP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(342,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( duplicatefreeP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( SX1 != SX2 ) ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( SX1 != SX2 ) ) ) ) ) )
| ( duplicatefreeP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(343,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( rearsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(344,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( rearsegP @ SX0 @ SX1 )
| ~ ( rearsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(345,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssList @ SX1 )
| ( ( tl @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(346,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( geq @ SX0 @ SX1 )
| ~ ( geq @ SX1 @ SX2 ) )
| ( geq @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(347,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( strictorderedP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( lt @ SX1 @ SX2 ) ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( lt @ SX1 @ SX2 ) ) ) ) ) )
| ( strictorderedP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(348,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( equalelemsP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(349,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)],[217]) ).
thf(350,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(351,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)],[277]) ).
thf(352,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( totalorderP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( leq @ SX1 @ SX2 )
| ( leq @ SX2 @ SX1 ) ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ( leq @ SX1 @ SX2 )
| ( leq @ SX2 @ SX1 ) ) ) ) ) )
| ( totalorderP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(353,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)],[250]) ).
thf(354,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ( ( app @ ( app @ SX3 @ SX1 ) @ SX4 )
!= SX2 )
| ~ ( strictorderedP @ SX1 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ SX6 @ ( cons @ SX5 @ nil ) )
!= SX3 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ ( cons @ SX7 @ nil ) @ SX8 )
!= SX1 ) )
| ~ ( lt @ SX5 @ SX7 ) ) ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ ( cons @ SX5 @ nil ) @ SX6 )
!= SX4 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ SX8 @ ( cons @ SX7 @ nil ) )
!= SX1 ) )
| ~ ( lt @ SX7 @ SX5 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != SX2 ) )
| ( nil != SX1 ) )
| ~ ( ~ ( ( nil != SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ SX0 @ nil )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX3 @ nil ) )
| ~ ( segmentP @ SX0 @ SX3 ) )
| ~ ( segmentP @ sK1_U @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(355,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)],[224]) ).
thf(356,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)],[276]) ).
thf(357,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX2 ) )
| ( gt @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(358,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)],[280]) ).
thf(359,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( geq @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(360,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( tl @ ( cons @ SX1 @ SX0 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(361,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ SX0 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(362,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ( segmentP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(363,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)],[241]) ).
thf(364,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)],[212]) ).
thf(365,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( leq @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( lt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(366,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( totalorderedP @ ( cons @ SX0 @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(367,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SX0 @ SX1 ) )
| ( nil = SX1 )
| ~ ( ~ ~ ( ~ ( ( nil != SX1 ) )
| ~ ( totalorderedP @ SX1 ) )
| ~ ( leq @ SX0 @ ( hd @ SX1 ) ) ) )
| ~ ( ~ ( ( nil = SX1 )
| ~ ( ~ ~ ( ~ ( ( nil != SX1 ) )
| ~ ( totalorderedP @ SX1 ) )
| ~ ( leq @ SX0 @ ( hd @ SX1 ) ) ) )
| ( totalorderedP @ ( cons @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(368,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( ssItem @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(369,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(370,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( equalelemsP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ( ( app @ SX3 @ ( cons @ SX1 @ ( cons @ SX2 @ SX4 ) ) )
!= SX0 )
| ( SX1 = SX2 ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ( ( app @ SX3 @ ( cons @ SX1 @ ( cons @ SX2 @ SX4 ) ) )
!= SX0 )
| ( SX1 = SX2 ) ) ) ) )
| ( equalelemsP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(371,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)],[279]) ).
thf(372,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)],[247]) ).
thf(373,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)],[237]) ).
thf(374,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( lt @ SX0 @ SX1 )
| ~ ( lt @ SX1 @ SX2 ) )
| ( lt @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(375,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(376,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(377,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ~ ( memberP @ nil @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(378,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( cyclefreeP @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ~ ~ ( ~ ( leq @ SX1 @ SX2 )
| ~ ( leq @ SX2 @ SX1 ) ) ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ ( cons @ SX1 @ SX4 ) ) @ ( cons @ SX2 @ SX5 ) )
!= SX0 )
| ~ ~ ( ~ ( leq @ SX1 @ SX2 )
| ~ ( leq @ SX2 @ SX1 ) ) ) ) ) ) )
| ( cyclefreeP @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(379,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ssList @ ( tl @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(380,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ( ( hd @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(381,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ssItem @ ( hd @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(382,plain,
( ( singletonP @ nil )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(383,plain,
! [SV1: $i] :
( ( ~ ( ssList @ SV1 )
| ! [SY232: $i] :
( ~ ( ssList @ SY232 )
| ~ ~ ( ~ ( frontsegP @ SV1 @ SY232 )
| ~ ( frontsegP @ SY232 @ SV1 ) )
| ( SV1 = SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(384,plain,
! [SV2: $i] :
( ( ~ ( ssItem @ SV2 )
| ~ ( lt @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(385,plain,
! [SV3: $i] :
( ( ~ ( ssItem @ SV3 )
| ! [SY233: $i] :
( ~ ( ssItem @ SY233 )
| ~ ( ~ ( ~ ( lt @ SV3 @ SY233 )
| ~ ( ~ ( ( SV3 != SY233 ) )
| ~ ( leq @ SV3 @ SY233 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SY233 ) )
| ~ ( leq @ SV3 @ SY233 ) )
| ( lt @ SV3 @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(386,plain,
! [SV4: $i] :
( ( ~ ( ssItem @ SV4 )
| ! [SY234: $i] :
( ~ ( ssItem @ SY234 )
| ~ ( ~ ( ~ ( gt @ SV4 @ SY234 )
| ( lt @ SY234 @ SV4 ) )
| ~ ( ~ ( lt @ SY234 @ SV4 )
| ( gt @ SV4 @ SY234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(387,plain,
! [SV5: $i] :
( ( ~ ( ssItem @ SV5 )
| ! [SY235: $i] :
( ~ ( ssItem @ SY235 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SY235 )
| ( SV5 != SY235 ) )
| ~ ( ~ ( ( SV5 != SY235 ) )
| ( neq @ SV5 @ SY235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(388,plain,
! [SV6: $i] :
( ( ~ ( ssList @ SV6 )
| ( rearsegP @ SV6 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(389,plain,
! [SV7: $i] :
( ( ~ ( ssItem @ SV7 )
| ( strictorderedP @ ( cons @ SV7 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(390,plain,
! [SV8: $i] :
( ( ~ ( ssList @ SV8 )
| ! [SY236: $i] :
( ~ ( ssList @ SY236 )
| ~ ( ( nil != SV8 ) )
| ( ( hd @ ( app @ SV8 @ SY236 ) )
= ( hd @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(391,plain,
! [SV9: $i] :
( ( ~ ( ssItem @ SV9 )
| ( strictorderP @ ( cons @ SV9 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(392,plain,
! [SV10: $i] :
( ( ~ ( ssItem @ SV10 )
| ! [SY237: $i] :
( ~ ( ssList @ SY237 )
| ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SY237 ) )
| ( nil = SY237 )
| ~ ( ~ ~ ( ~ ( ( nil != SY237 ) )
| ~ ( strictorderedP @ SY237 ) )
| ~ ( lt @ SV10 @ ( hd @ SY237 ) ) ) )
| ~ ( ~ ( ( nil = SY237 )
| ~ ( ~ ~ ( ~ ( ( nil != SY237 ) )
| ~ ( strictorderedP @ SY237 ) )
| ~ ( lt @ SV10 @ ( hd @ SY237 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SY237 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(393,plain,
! [SV11: $i] :
( ( ~ ( ssList @ SV11 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( segmentP @ nil @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(394,plain,
! [SV12: $i] :
( ( ~ ( ssList @ SV12 )
| ! [SY238: $i] :
( ~ ( ssItem @ SY238 )
| ( ( cons @ SY238 @ SV12 )
= ( app @ ( cons @ SY238 @ nil ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(395,plain,
! [SV13: $i] :
( ( ~ ( ssList @ SV13 )
| ! [SY239: $i] :
( ~ ( ssList @ SY239 )
| ( ssList @ ( app @ SV13 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(396,plain,
! [SV14: $i] :
( ( ~ ( ssItem @ SV14 )
| ( duplicatefreeP @ ( cons @ SV14 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(397,plain,
! [SV15: $i] :
( ( ~ ( ssList @ SV15 )
| ! [SY240: $i] :
( ~ ( ssItem @ SY240 )
| ( ( hd @ ( cons @ SY240 @ SV15 ) )
= SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(398,plain,
! [SV16: $i] :
( ( ~ ( ssList @ SV16 )
| ! [SY241: $i] :
( ~ ( ssList @ SY241 )
| ~ ( ~ ( ~ ( frontsegP @ SV16 @ SY241 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( ssList @ SY242 )
| ( ( app @ SY241 @ SY242 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( ssList @ SY243 )
| ( ( app @ SY241 @ SY243 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SY241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(399,plain,
! [SV17: $i] :
( ( ~ ( ssItem @ SV17 )
| ! [SY244: $i] :
( ~ ( ssItem @ SY244 )
| ! [SY245: $i] :
( ~ ( ssItem @ SY245 )
| ~ ~ ( ~ ( leq @ SV17 @ SY244 )
| ~ ( lt @ SY244 @ SY245 ) )
| ( lt @ SV17 @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(400,plain,
! [SV18: $i] :
( ( ~ ( ssList @ SV18 )
| ! [SY246: $i] :
( ~ ( ssList @ SY246 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SY246 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ( ssList @ SY247 )
| ( ( app @ SY247 @ SY246 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ( ssList @ SY248 )
| ( ( app @ SY248 @ SY246 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SY246 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(401,plain,
! [SV19: $i] :
( ( ~ ( ssList @ SV19 )
| ~ ( ~ ( ~ ( singletonP @ SV19 )
| ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
| ~ ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) )
| ( singletonP @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(402,plain,
! [SV20: $i] :
( ( ~ ( ssItem @ SV20 )
| ! [SY251: $i] :
( ~ ( ssItem @ SY251 )
| ~ ~ ( ~ ( geq @ SV20 @ SY251 )
| ~ ( geq @ SY251 @ SV20 ) )
| ( SV20 = SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(403,plain,
! [SV21: $i] :
( ( ~ ( ssList @ SV21 )
| ! [SY252: $i] :
( ~ ( ssItem @ SY252 )
| ~ ( ~ ( ~ ( memberP @ SV21 @ SY252 )
| ~ ! [SY253: $i] :
~ ~ ( ~ ( ssList @ SY253 )
| ~ ~ ! [SY254: $i] :
~ ~ ( ~ ( ssList @ SY254 )
| ( ( app @ SY253 @ ( cons @ SY252 @ SY254 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY255: $i] :
~ ~ ( ~ ( ssList @ SY255 )
| ~ ~ ! [SY256: $i] :
~ ~ ( ~ ( ssList @ SY256 )
| ( ( app @ SY255 @ ( cons @ SY252 @ SY256 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SY252 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(404,plain,
! [SV22: $i] :
( ( ~ ( ssList @ SV22 )
| ~ ( ~ ( ~ ( strictorderP @ SV22 )
| ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
| ~ ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) )
| ( strictorderP @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(405,plain,
! [SV23: $i] :
( ( ~ ( ssList @ SV23 )
| ( segmentP @ SV23 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(406,plain,
! [SV24: $i] :
( ( ~ ( ssItem @ SV24 )
| ! [SY267: $i] :
( ~ ( ssList @ SY267 )
| ! [SY268: $i] :
( ~ ( ssList @ SY268 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY267 @ SY268 ) @ SV24 )
| ( memberP @ SY267 @ SV24 )
| ( memberP @ SY268 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SY267 @ SV24 )
| ( memberP @ SY268 @ SV24 ) )
| ( memberP @ ( app @ SY267 @ SY268 ) @ SV24 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(407,plain,
! [SV25: $i] :
( ( ~ ( ssList @ SV25 )
| ( ( app @ SV25 @ nil )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(408,plain,
! [SV26: $i] :
( ( ~ ( ssList @ SV26 )
| ! [SY269: $i] :
( ~ ( ssList @ SY269 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SY269 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SY269 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SY269 )
!= ( tl @ SV26 ) ) )
| ( SY269 = SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(409,plain,
! [SV27: $i] :
( ( ~ ( ssList @ SV27 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SV27 )
| ( nil = SV27 ) )
| ~ ( ( nil != SV27 )
| ( frontsegP @ nil @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(410,plain,
! [SV28: $i] :
( ( ~ ( ssList @ SV28 )
| ! [SY270: $i] :
( ~ ( ssList @ SY270 )
| ! [SY271: $i] :
( ~ ( ssList @ SY271 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SY270 )
| ~ ( rearsegP @ SY270 @ SY271 ) )
| ( rearsegP @ SV28 @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(411,plain,
! [SV29: $i] :
( ( ~ ( ssList @ SV29 )
| ~ ( ~ ( ~ ( totalorderedP @ SV29 )
| ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
| ~ ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) )
| ( totalorderedP @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(412,plain,
! [SV30: $i] :
( ( ~ ( ssItem @ SV30 )
| ( leq @ SV30 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(413,plain,
! [SV31: $i] :
( ( ~ ( ssItem @ SV31 )
| ! [SY282: $i] :
( ~ ( ssItem @ SY282 )
| ! [SY283: $i] :
( ~ ( ssItem @ SY283 )
| ~ ~ ( ~ ( leq @ SV31 @ SY282 )
| ~ ( leq @ SY282 @ SY283 ) )
| ( leq @ SV31 @ SY283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(414,plain,
! [SV32: $i] :
( ( ~ ( ssList @ SV32 )
| ( ( app @ nil @ SV32 )
= SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(415,plain,
! [SV33: $i] :
( ( ~ ( ssList @ SV33 )
| ! [SY284: $i] :
( ~ ( ssItem @ SY284 )
| ( ssList @ ( cons @ SY284 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(416,plain,
! [SV34: $i] :
( ( ~ ( ssList @ SV34 )
| ! [SY285: $i] :
( ~ ( ssList @ SY285 )
| ~ ( ~ ( ~ ( segmentP @ SV34 @ SY285 )
| ~ ! [SY286: $i] :
~ ~ ( ~ ( ssList @ SY286 )
| ~ ~ ! [SY287: $i] :
~ ~ ( ~ ( ssList @ SY287 )
| ( ( app @ ( app @ SY286 @ SY285 ) @ SY287 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY288: $i] :
~ ~ ( ~ ( ssList @ SY288 )
| ~ ~ ! [SY289: $i] :
~ ~ ( ~ ( ssList @ SY289 )
| ( ( app @ ( app @ SY288 @ SY285 ) @ SY289 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SY285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(417,plain,
! [SV35: $i] :
( ( ~ ( ssList @ SV35 )
| ! [SY290: $i] :
( ~ ( ssList @ SY290 )
| ! [SY291: $i] :
( ~ ( ssItem @ SY291 )
| ! [SY292: $i] :
( ~ ( ssItem @ SY292 )
| ( ( cons @ SY291 @ SV35 )
!= ( cons @ SY292 @ SY290 ) )
| ~ ( ( SY291 != SY292 )
| ( SY290 != SV35 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(418,plain,
! [SV36: $i] :
( ( ~ ( ssList @ SV36 )
| ~ ( ( nil != SV36 ) )
| ( ( cons @ ( hd @ SV36 ) @ ( tl @ SV36 ) )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(419,plain,
! [SV37: $i] :
( ( ~ ( ssItem @ SV37 )
| ( totalorderP @ ( cons @ SV37 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(420,plain,
! [SV38: $i] :
( ( ~ ( ssList @ SV38 )
| ( frontsegP @ SV38 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(421,plain,
! [SV39: $i] :
( ( ~ ( ssItem @ SV39 )
| ! [SY293: $i] :
( ~ ( ssItem @ SY293 )
| ~ ( ~ ( ~ ( geq @ SV39 @ SY293 )
| ( leq @ SY293 @ SV39 ) )
| ~ ( ~ ( leq @ SY293 @ SV39 )
| ( geq @ SV39 @ SY293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(422,plain,
! [SV40: $i] :
( ( ~ ( ssList @ SV40 )
| ! [SY294: $i] :
( ~ ( ssList @ SY294 )
| ! [SY295: $i] :
( ~ ( ssList @ SY295 )
| ! [SY296: $i] :
( ~ ( ssList @ SY296 )
| ~ ( segmentP @ SV40 @ SY294 )
| ( segmentP @ ( app @ ( app @ SY295 @ SV40 ) @ SY296 ) @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(423,plain,
! [SV41: $i] :
( ( ~ ( ssList @ SV41 )
| ! [SY297: $i] :
( ~ ( ssList @ SY297 )
| ~ ( ( nil != SV41 ) )
| ( ( tl @ ( app @ SV41 @ SY297 ) )
= ( app @ ( tl @ SV41 ) @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(424,plain,
! [SV42: $i] :
( ( ~ ( ssList @ SV42 )
| ( segmentP @ SV42 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(425,plain,
! [SV43: $i] :
( ( ~ ( ssItem @ SV43 )
| ! [SY298: $i] :
( ~ ( ssItem @ SY298 )
| ~ ( lt @ SV43 @ SY298 )
| ~ ( lt @ SY298 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(426,plain,
! [SV44: $i] :
( ( ~ ( ssList @ SV44 )
| ! [SY299: $i] :
( ~ ( ssItem @ SY299 )
| ( nil
!= ( cons @ SY299 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(427,plain,
! [SV45: $i] :
( ( ~ ( ssList @ SV45 )
| ! [SY300: $i] :
( ~ ( ssList @ SY300 )
| ! [SY301: $i] :
( ~ ( ssList @ SY301 )
| ~ ( frontsegP @ SV45 @ SY300 )
| ( frontsegP @ ( app @ SV45 @ SY301 ) @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(428,plain,
! [SV46: $i] :
( ( ~ ( ssItem @ SV46 )
| ! [SY302: $i] :
( ~ ( ssItem @ SY302 )
| ! [SY303: $i] :
( ~ ( ssList @ SY303 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY302 @ SY303 ) @ SV46 )
| ( SV46 = SY302 )
| ( memberP @ SY303 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SY302 )
| ( memberP @ SY303 @ SV46 ) )
| ( memberP @ ( cons @ SY302 @ SY303 ) @ SV46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(429,plain,
! [SV47: $i] :
( ( ~ ( ssItem @ SV47 )
| ( cyclefreeP @ ( cons @ SV47 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(430,plain,
! [SV48: $i] :
( ( ~ ( ssList @ SV48 )
| ~ ( ~ ( ~ ( duplicatefreeP @ SV48 )
| ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
| ~ ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) )
| ( duplicatefreeP @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(431,plain,
! [SV49: $i] :
( ( ~ ( ssList @ SV49 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SV49 )
| ( nil = SV49 ) )
| ~ ( ( nil != SV49 )
| ( rearsegP @ nil @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(432,plain,
! [SV50: $i] :
( ( ~ ( ssList @ SV50 )
| ! [SY314: $i] :
( ~ ( ssList @ SY314 )
| ~ ~ ( ~ ( rearsegP @ SV50 @ SY314 )
| ~ ( rearsegP @ SY314 @ SV50 ) )
| ( SV50 = SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(433,plain,
! [SV51: $i] :
( ( ~ ( ssList @ SV51 )
| ~ ( ( nil != SV51 ) )
| ~ ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(434,plain,
! [SV52: $i] :
( ( ~ ( ssItem @ SV52 )
| ! [SY316: $i] :
( ~ ( ssItem @ SY316 )
| ! [SY317: $i] :
( ~ ( ssItem @ SY317 )
| ~ ~ ( ~ ( geq @ SV52 @ SY316 )
| ~ ( geq @ SY316 @ SY317 ) )
| ( geq @ SV52 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(435,plain,
! [SV53: $i] :
( ( ~ ( ssList @ SV53 )
| ~ ( ~ ( ~ ( strictorderedP @ SV53 )
| ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) )
| ( strictorderedP @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(436,plain,
! [SV54: $i] :
( ( ~ ( ssItem @ SV54 )
| ( equalelemsP @ ( cons @ SV54 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(437,plain,
! [SV55: $i] :
( ( ~ ( ssList @ SV55 )
| ( nil = SV55 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( ssList @ SY328 )
| ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( ssItem @ SY329 )
| ( ( cons @ SY329 @ SY328 )
!= SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(438,plain,
! [SV56: $i] :
( ( ~ ( ssItem @ SV56 )
| ! [SY330: $i] :
( ~ ( ssItem @ SY330 )
| ~ ( gt @ SV56 @ SY330 )
| ~ ( gt @ SY330 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(439,plain,
! [SV57: $i] :
( ( ~ ( ssList @ SV57 )
| ! [SY331: $i] :
( ~ ( ssList @ SY331 )
| ! [SY332: $i] :
( ~ ( ssList @ SY332 )
| ( ( app @ SY331 @ SY332 )
!= ( app @ SY331 @ SV57 ) )
| ( SY332 = SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(440,plain,
! [SV58: $i] :
( ( ~ ( ssList @ SV58 )
| ~ ( ~ ( ~ ( totalorderP @ SV58 )
| ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) )
| ( totalorderP @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(441,plain,
! [SV59: $i] :
( ( ~ ( ssList @ SV59 )
| ! [SY343: $i] :
( ~ ( ssList @ SY343 )
| ! [SY344: $i] :
( ~ ( ssList @ SY344 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SY343 )
| ~ ( segmentP @ SY343 @ SY344 ) )
| ( segmentP @ SV59 @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(442,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ( ( app @ ( app @ SX3 @ SX1 ) @ SX4 )
!= SX2 )
| ~ ( strictorderedP @ SX1 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ SX6 @ ( cons @ SX5 @ nil ) )
!= SX3 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ ( cons @ SX7 @ nil ) @ SX8 )
!= SX1 ) )
| ~ ( lt @ SX5 @ SX7 ) ) ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ ( cons @ SX5 @ nil ) @ SX6 )
!= SX4 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ SX8 @ ( cons @ SX7 @ nil ) )
!= SX1 ) )
| ~ ( lt @ SX7 @ SX5 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != SX2 ) )
| ( nil != SX1 ) )
| ~ ( ~ ( ( nil != SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ SX0 @ nil )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX3 @ nil ) )
| ~ ( segmentP @ SX0 @ SX3 ) )
| ~ ( segmentP @ sK1_U @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(443,plain,
! [SV60: $i] :
( ( ~ ( ssList @ SV60 )
| ! [SY345: $i] :
( ~ ( ssList @ SY345 )
| ! [SY346: $i] :
( ~ ( ssItem @ SY346 )
| ( ( cons @ SY346 @ ( app @ SY345 @ SV60 ) )
= ( app @ ( cons @ SY346 @ SY345 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(444,plain,
! [SV61: $i] :
( ( ~ ( ssList @ SV61 )
| ! [SY347: $i] :
( ~ ( ssList @ SY347 )
| ! [SY348: $i] :
( ~ ( ssList @ SY348 )
| ( ( app @ SY348 @ SY347 )
!= ( app @ SV61 @ SY347 ) )
| ( SY348 = SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(445,plain,
! [SV62: $i] :
( ( ~ ( ssItem @ SV62 )
| ! [SY349: $i] :
( ~ ( ssItem @ SY349 )
| ! [SY350: $i] :
( ~ ( ssItem @ SY350 )
| ~ ~ ( ~ ( gt @ SV62 @ SY349 )
| ~ ( gt @ SY349 @ SY350 ) )
| ( gt @ SV62 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(446,plain,
! [SV63: $i] :
( ( ~ ( ssList @ SV63 )
| ! [SY351: $i] :
( ~ ( ssList @ SY351 )
| ~ ( ~ ( ( nil
!= ( app @ SV63 @ SY351 ) )
| ~ ( ( nil != SY351 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SY351 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SY351 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(447,plain,
! [SV64: $i] :
( ( ~ ( ssItem @ SV64 )
| ( geq @ SV64 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(448,plain,
! [SV65: $i] :
( ( ~ ( ssList @ SV65 )
| ! [SY352: $i] :
( ~ ( ssItem @ SY352 )
| ( ( tl @ ( cons @ SY352 @ SV65 ) )
= SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(449,plain,
! [SV66: $i] :
( ( ~ ( ssList @ SV66 )
| ! [SY353: $i] :
( ~ ( ssItem @ SY353 )
| ( ( cons @ SY353 @ SV66 )
!= SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(450,plain,
! [SV67: $i] :
( ( ~ ( ssList @ SV67 )
| ! [SY354: $i] :
( ~ ( ssList @ SY354 )
| ~ ~ ( ~ ( segmentP @ SV67 @ SY354 )
| ~ ( segmentP @ SY354 @ SV67 ) )
| ( SV67 = SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(451,plain,
! [SV68: $i] :
( ( ~ ( ssItem @ SV68 )
| ! [SY355: $i] :
( ~ ( ssItem @ SY355 )
| ! [SY356: $i] :
( ~ ( ssList @ SY356 )
| ! [SY357: $i] :
( ~ ( ssList @ SY357 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SY356 ) @ ( cons @ SY355 @ SY357 ) )
| ~ ( ( SV68 != SY355 )
| ~ ( frontsegP @ SY356 @ SY357 ) ) )
| ~ ( ~ ~ ( ( SV68 != SY355 )
| ~ ( frontsegP @ SY356 @ SY357 ) )
| ( frontsegP @ ( cons @ SV68 @ SY356 ) @ ( cons @ SY355 @ SY357 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(452,plain,
! [SV69: $i] :
( ( ~ ( ssList @ SV69 )
| ! [SY358: $i] :
( ~ ( ssList @ SY358 )
| ~ ( ~ ( ~ ( neq @ SV69 @ SY358 )
| ( SV69 != SY358 ) )
| ~ ( ~ ( ( SV69 != SY358 ) )
| ( neq @ SV69 @ SY358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(453,plain,
! [SV70: $i] :
( ( ~ ( ssItem @ SV70 )
| ! [SY359: $i] :
( ~ ( ssItem @ SY359 )
| ~ ( leq @ SV70 @ SY359 )
| ( SV70 = SY359 )
| ( lt @ SV70 @ SY359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(454,plain,
! [SV71: $i] :
( ( ~ ( ssItem @ SV71 )
| ( totalorderedP @ ( cons @ SV71 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(455,plain,
! [SV72: $i] :
( ( ~ ( ssItem @ SV72 )
| ! [SY360: $i] :
( ~ ( ssList @ SY360 )
| ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SY360 ) )
| ( nil = SY360 )
| ~ ( ~ ~ ( ~ ( ( nil != SY360 ) )
| ~ ( totalorderedP @ SY360 ) )
| ~ ( leq @ SV72 @ ( hd @ SY360 ) ) ) )
| ~ ( ~ ( ( nil = SY360 )
| ~ ( ~ ~ ( ~ ( ( nil != SY360 ) )
| ~ ( totalorderedP @ SY360 ) )
| ~ ( leq @ SV72 @ ( hd @ SY360 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SY360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(456,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( ssItem @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(457,plain,
! [SV73: $i] :
( ( ~ ( ssItem @ SV73 )
| ! [SY361: $i] :
( ~ ( ssItem @ SY361 )
| ~ ~ ( ~ ( leq @ SV73 @ SY361 )
| ~ ( leq @ SY361 @ SV73 ) )
| ( SV73 = SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(458,plain,
! [SV74: $i] :
( ( ~ ( ssList @ SV74 )
| ~ ( ~ ( ~ ( equalelemsP @ SV74 )
| ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
| ~ ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) )
| ( equalelemsP @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(459,plain,
! [SV75: $i] :
( ( ~ ( ssList @ SV75 )
| ! [SY370: $i] :
( ~ ( ssList @ SY370 )
| ! [SY371: $i] :
( ~ ( ssList @ SY371 )
| ( ( app @ ( app @ SV75 @ SY370 ) @ SY371 )
= ( app @ SV75 @ ( app @ SY370 @ SY371 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(460,plain,
! [SV76: $i] :
( ( ~ ( ssList @ SV76 )
| ! [SY372: $i] :
( ~ ( ssList @ SY372 )
| ! [SY373: $i] :
( ~ ( ssList @ SY373 )
| ~ ( rearsegP @ SV76 @ SY372 )
| ( rearsegP @ ( app @ SY373 @ SV76 ) @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(461,plain,
! [SV77: $i] :
( ( ~ ( ssList @ SV77 )
| ! [SY374: $i] :
( ~ ( ssList @ SY374 )
| ! [SY375: $i] :
( ~ ( ssList @ SY375 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SY374 )
| ~ ( frontsegP @ SY374 @ SY375 ) )
| ( frontsegP @ SV77 @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(462,plain,
! [SV78: $i] :
( ( ~ ( ssItem @ SV78 )
| ! [SY376: $i] :
( ~ ( ssItem @ SY376 )
| ! [SY377: $i] :
( ~ ( ssItem @ SY377 )
| ~ ~ ( ~ ( lt @ SV78 @ SY376 )
| ~ ( lt @ SY376 @ SY377 ) )
| ( lt @ SV78 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(463,plain,
! [SV79: $i] :
( ( ~ ( ssList @ SV79 )
| ( frontsegP @ SV79 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(464,plain,
! [SV80: $i] :
( ( ~ ( ssList @ SV80 )
| ( rearsegP @ SV80 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(465,plain,
! [SV81: $i] :
( ( ~ ( ssItem @ SV81 )
| ~ ( memberP @ nil @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(466,plain,
! [SV82: $i] :
( ( ~ ( ssList @ SV82 )
| ~ ( ~ ( ~ ( cyclefreeP @ SV82 )
| ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) )
| ( cyclefreeP @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(467,plain,
! [SV83: $i] :
( ( ~ ( ssList @ SV83 )
| ~ ( ( nil != SV83 ) )
| ( ssList @ ( tl @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(468,plain,
! [SV84: $i] :
( ( ~ ( ssList @ SV84 )
| ~ ( ( nil != SV84 ) )
| ~ ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(469,plain,
! [SV85: $i] :
( ( ~ ( ssList @ SV85 )
| ~ ( ( nil != SV85 ) )
| ( ssItem @ ( hd @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(470,plain,
! [SV1: $i] :
( ( ( ~ ( ssList @ SV1 ) )
= $true )
| ( ( ! [SY232: $i] :
( ~ ( ssList @ SY232 )
| ~ ~ ( ~ ( frontsegP @ SV1 @ SY232 )
| ~ ( frontsegP @ SY232 @ SV1 ) )
| ( SV1 = SY232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(471,plain,
! [SV2: $i] :
( ( ( ~ ( ssItem @ SV2 ) )
= $true )
| ( ( ~ ( lt @ SV2 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(472,plain,
! [SV3: $i] :
( ( ( ~ ( ssItem @ SV3 ) )
= $true )
| ( ( ! [SY233: $i] :
( ~ ( ssItem @ SY233 )
| ~ ( ~ ( ~ ( lt @ SV3 @ SY233 )
| ~ ( ~ ( ( SV3 != SY233 ) )
| ~ ( leq @ SV3 @ SY233 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SY233 ) )
| ~ ( leq @ SV3 @ SY233 ) )
| ( lt @ SV3 @ SY233 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(473,plain,
! [SV4: $i] :
( ( ( ~ ( ssItem @ SV4 ) )
= $true )
| ( ( ! [SY234: $i] :
( ~ ( ssItem @ SY234 )
| ~ ( ~ ( ~ ( gt @ SV4 @ SY234 )
| ( lt @ SY234 @ SV4 ) )
| ~ ( ~ ( lt @ SY234 @ SV4 )
| ( gt @ SV4 @ SY234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(474,plain,
! [SV5: $i] :
( ( ( ~ ( ssItem @ SV5 ) )
= $true )
| ( ( ! [SY235: $i] :
( ~ ( ssItem @ SY235 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SY235 )
| ( SV5 != SY235 ) )
| ~ ( ~ ( ( SV5 != SY235 ) )
| ( neq @ SV5 @ SY235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(475,plain,
! [SV6: $i] :
( ( ( ~ ( ssList @ SV6 ) )
= $true )
| ( ( rearsegP @ SV6 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(476,plain,
! [SV7: $i] :
( ( ( ~ ( ssItem @ SV7 ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV7 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(477,plain,
! [SV8: $i] :
( ( ( ~ ( ssList @ SV8 ) )
= $true )
| ( ( ! [SY236: $i] :
( ~ ( ssList @ SY236 )
| ~ ( ( nil != SV8 ) )
| ( ( hd @ ( app @ SV8 @ SY236 ) )
= ( hd @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(478,plain,
! [SV9: $i] :
( ( ( ~ ( ssItem @ SV9 ) )
= $true )
| ( ( strictorderP @ ( cons @ SV9 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(479,plain,
! [SV10: $i] :
( ( ( ~ ( ssItem @ SV10 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( ssList @ SY237 )
| ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SY237 ) )
| ( nil = SY237 )
| ~ ( ~ ~ ( ~ ( ( nil != SY237 ) )
| ~ ( strictorderedP @ SY237 ) )
| ~ ( lt @ SV10 @ ( hd @ SY237 ) ) ) )
| ~ ( ~ ( ( nil = SY237 )
| ~ ( ~ ~ ( ~ ( ( nil != SY237 ) )
| ~ ( strictorderedP @ SY237 ) )
| ~ ( lt @ SV10 @ ( hd @ SY237 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SY237 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(480,plain,
! [SV11: $i] :
( ( ( ~ ( ssList @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( segmentP @ nil @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(481,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ SV12 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( ssItem @ SY238 )
| ( ( cons @ SY238 @ SV12 )
= ( app @ ( cons @ SY238 @ nil ) @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(482,plain,
! [SV13: $i] :
( ( ( ~ ( ssList @ SV13 ) )
= $true )
| ( ( ! [SY239: $i] :
( ~ ( ssList @ SY239 )
| ( ssList @ ( app @ SV13 @ SY239 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(483,plain,
! [SV14: $i] :
( ( ( ~ ( ssItem @ SV14 ) )
= $true )
| ( ( duplicatefreeP @ ( cons @ SV14 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(484,plain,
! [SV15: $i] :
( ( ( ~ ( ssList @ SV15 ) )
= $true )
| ( ( ! [SY240: $i] :
( ~ ( ssItem @ SY240 )
| ( ( hd @ ( cons @ SY240 @ SV15 ) )
= SY240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(485,plain,
! [SV16: $i] :
( ( ( ~ ( ssList @ SV16 ) )
= $true )
| ( ( ! [SY241: $i] :
( ~ ( ssList @ SY241 )
| ~ ( ~ ( ~ ( frontsegP @ SV16 @ SY241 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( ssList @ SY242 )
| ( ( app @ SY241 @ SY242 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( ssList @ SY243 )
| ( ( app @ SY241 @ SY243 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SY241 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(486,plain,
! [SV17: $i] :
( ( ( ~ ( ssItem @ SV17 ) )
= $true )
| ( ( ! [SY244: $i] :
( ~ ( ssItem @ SY244 )
| ! [SY245: $i] :
( ~ ( ssItem @ SY245 )
| ~ ~ ( ~ ( leq @ SV17 @ SY244 )
| ~ ( lt @ SY244 @ SY245 ) )
| ( lt @ SV17 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(487,plain,
! [SV18: $i] :
( ( ( ~ ( ssList @ SV18 ) )
= $true )
| ( ( ! [SY246: $i] :
( ~ ( ssList @ SY246 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SY246 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ( ssList @ SY247 )
| ( ( app @ SY247 @ SY246 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ( ssList @ SY248 )
| ( ( app @ SY248 @ SY246 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SY246 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(488,plain,
! [SV19: $i] :
( ( ( ~ ( ssList @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( singletonP @ SV19 )
| ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
| ~ ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) )
| ( singletonP @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(489,plain,
! [SV20: $i] :
( ( ( ~ ( ssItem @ SV20 ) )
= $true )
| ( ( ! [SY251: $i] :
( ~ ( ssItem @ SY251 )
| ~ ~ ( ~ ( geq @ SV20 @ SY251 )
| ~ ( geq @ SY251 @ SV20 ) )
| ( SV20 = SY251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(490,plain,
! [SV21: $i] :
( ( ( ~ ( ssList @ SV21 ) )
= $true )
| ( ( ! [SY252: $i] :
( ~ ( ssItem @ SY252 )
| ~ ( ~ ( ~ ( memberP @ SV21 @ SY252 )
| ~ ! [SY253: $i] :
~ ~ ( ~ ( ssList @ SY253 )
| ~ ~ ! [SY254: $i] :
~ ~ ( ~ ( ssList @ SY254 )
| ( ( app @ SY253 @ ( cons @ SY252 @ SY254 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY255: $i] :
~ ~ ( ~ ( ssList @ SY255 )
| ~ ~ ! [SY256: $i] :
~ ~ ( ~ ( ssList @ SY256 )
| ( ( app @ SY255 @ ( cons @ SY252 @ SY256 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SY252 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(491,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ SV22 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( strictorderP @ SV22 )
| ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
| ~ ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) )
| ( strictorderP @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(492,plain,
! [SV23: $i] :
( ( ( ~ ( ssList @ SV23 ) )
= $true )
| ( ( segmentP @ SV23 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(493,plain,
! [SV24: $i] :
( ( ( ~ ( ssItem @ SV24 ) )
= $true )
| ( ( ! [SY267: $i] :
( ~ ( ssList @ SY267 )
| ! [SY268: $i] :
( ~ ( ssList @ SY268 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY267 @ SY268 ) @ SV24 )
| ( memberP @ SY267 @ SV24 )
| ( memberP @ SY268 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SY267 @ SV24 )
| ( memberP @ SY268 @ SV24 ) )
| ( memberP @ ( app @ SY267 @ SY268 ) @ SV24 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(494,plain,
! [SV25: $i] :
( ( ( ~ ( ssList @ SV25 ) )
= $true )
| ( ( ( app @ SV25 @ nil )
= SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(495,plain,
! [SV26: $i] :
( ( ( ~ ( ssList @ SV26 ) )
= $true )
| ( ( ! [SY269: $i] :
( ~ ( ssList @ SY269 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SY269 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SY269 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SY269 )
!= ( tl @ SV26 ) ) )
| ( SY269 = SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(496,plain,
! [SV27: $i] :
( ( ( ~ ( ssList @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV27 )
| ( nil = SV27 ) )
| ~ ( ( nil != SV27 )
| ( frontsegP @ nil @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(497,plain,
! [SV28: $i] :
( ( ( ~ ( ssList @ SV28 ) )
= $true )
| ( ( ! [SY270: $i] :
( ~ ( ssList @ SY270 )
| ! [SY271: $i] :
( ~ ( ssList @ SY271 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SY270 )
| ~ ( rearsegP @ SY270 @ SY271 ) )
| ( rearsegP @ SV28 @ SY271 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(498,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( totalorderedP @ SV29 )
| ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
| ~ ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) )
| ( totalorderedP @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(499,plain,
! [SV30: $i] :
( ( ( ~ ( ssItem @ SV30 ) )
= $true )
| ( ( leq @ SV30 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(500,plain,
! [SV31: $i] :
( ( ( ~ ( ssItem @ SV31 ) )
= $true )
| ( ( ! [SY282: $i] :
( ~ ( ssItem @ SY282 )
| ! [SY283: $i] :
( ~ ( ssItem @ SY283 )
| ~ ~ ( ~ ( leq @ SV31 @ SY282 )
| ~ ( leq @ SY282 @ SY283 ) )
| ( leq @ SV31 @ SY283 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(501,plain,
! [SV32: $i] :
( ( ( ~ ( ssList @ SV32 ) )
= $true )
| ( ( ( app @ nil @ SV32 )
= SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(502,plain,
! [SV33: $i] :
( ( ( ~ ( ssList @ SV33 ) )
= $true )
| ( ( ! [SY284: $i] :
( ~ ( ssItem @ SY284 )
| ( ssList @ ( cons @ SY284 @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(503,plain,
! [SV34: $i] :
( ( ( ~ ( ssList @ SV34 ) )
= $true )
| ( ( ! [SY285: $i] :
( ~ ( ssList @ SY285 )
| ~ ( ~ ( ~ ( segmentP @ SV34 @ SY285 )
| ~ ! [SY286: $i] :
~ ~ ( ~ ( ssList @ SY286 )
| ~ ~ ! [SY287: $i] :
~ ~ ( ~ ( ssList @ SY287 )
| ( ( app @ ( app @ SY286 @ SY285 ) @ SY287 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY288: $i] :
~ ~ ( ~ ( ssList @ SY288 )
| ~ ~ ! [SY289: $i] :
~ ~ ( ~ ( ssList @ SY289 )
| ( ( app @ ( app @ SY288 @ SY285 ) @ SY289 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SY285 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(504,plain,
! [SV35: $i] :
( ( ( ~ ( ssList @ SV35 ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( ssList @ SY290 )
| ! [SY291: $i] :
( ~ ( ssItem @ SY291 )
| ! [SY292: $i] :
( ~ ( ssItem @ SY292 )
| ( ( cons @ SY291 @ SV35 )
!= ( cons @ SY292 @ SY290 ) )
| ~ ( ( SY291 != SY292 )
| ( SY290 != SV35 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(505,plain,
! [SV36: $i] :
( ( ( ~ ( ssList @ SV36 ) )
= $true )
| ( ( ~ ( ( nil != SV36 ) )
| ( ( cons @ ( hd @ SV36 ) @ ( tl @ SV36 ) )
= SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(506,plain,
! [SV37: $i] :
( ( ( ~ ( ssItem @ SV37 ) )
= $true )
| ( ( totalorderP @ ( cons @ SV37 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(507,plain,
! [SV38: $i] :
( ( ( ~ ( ssList @ SV38 ) )
= $true )
| ( ( frontsegP @ SV38 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(508,plain,
! [SV39: $i] :
( ( ( ~ ( ssItem @ SV39 ) )
= $true )
| ( ( ! [SY293: $i] :
( ~ ( ssItem @ SY293 )
| ~ ( ~ ( ~ ( geq @ SV39 @ SY293 )
| ( leq @ SY293 @ SV39 ) )
| ~ ( ~ ( leq @ SY293 @ SV39 )
| ( geq @ SV39 @ SY293 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(509,plain,
! [SV40: $i] :
( ( ( ~ ( ssList @ SV40 ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( ssList @ SY294 )
| ! [SY295: $i] :
( ~ ( ssList @ SY295 )
| ! [SY296: $i] :
( ~ ( ssList @ SY296 )
| ~ ( segmentP @ SV40 @ SY294 )
| ( segmentP @ ( app @ ( app @ SY295 @ SV40 ) @ SY296 ) @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(510,plain,
! [SV41: $i] :
( ( ( ~ ( ssList @ SV41 ) )
= $true )
| ( ( ! [SY297: $i] :
( ~ ( ssList @ SY297 )
| ~ ( ( nil != SV41 ) )
| ( ( tl @ ( app @ SV41 @ SY297 ) )
= ( app @ ( tl @ SV41 ) @ SY297 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(511,plain,
! [SV42: $i] :
( ( ( ~ ( ssList @ SV42 ) )
= $true )
| ( ( segmentP @ SV42 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(512,plain,
! [SV43: $i] :
( ( ( ~ ( ssItem @ SV43 ) )
= $true )
| ( ( ! [SY298: $i] :
( ~ ( ssItem @ SY298 )
| ~ ( lt @ SV43 @ SY298 )
| ~ ( lt @ SY298 @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(513,plain,
! [SV44: $i] :
( ( ( ~ ( ssList @ SV44 ) )
= $true )
| ( ( ! [SY299: $i] :
( ~ ( ssItem @ SY299 )
| ( nil
!= ( cons @ SY299 @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(514,plain,
! [SV45: $i] :
( ( ( ~ ( ssList @ SV45 ) )
= $true )
| ( ( ! [SY300: $i] :
( ~ ( ssList @ SY300 )
| ! [SY301: $i] :
( ~ ( ssList @ SY301 )
| ~ ( frontsegP @ SV45 @ SY300 )
| ( frontsegP @ ( app @ SV45 @ SY301 ) @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(515,plain,
! [SV46: $i] :
( ( ( ~ ( ssItem @ SV46 ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( ssItem @ SY302 )
| ! [SY303: $i] :
( ~ ( ssList @ SY303 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY302 @ SY303 ) @ SV46 )
| ( SV46 = SY302 )
| ( memberP @ SY303 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SY302 )
| ( memberP @ SY303 @ SV46 ) )
| ( memberP @ ( cons @ SY302 @ SY303 ) @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(516,plain,
! [SV47: $i] :
( ( ( ~ ( ssItem @ SV47 ) )
= $true )
| ( ( cyclefreeP @ ( cons @ SV47 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(517,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( duplicatefreeP @ SV48 )
| ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
| ~ ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) )
| ( duplicatefreeP @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(518,plain,
! [SV49: $i] :
( ( ( ~ ( ssList @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV49 )
| ( nil = SV49 ) )
| ~ ( ( nil != SV49 )
| ( rearsegP @ nil @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(519,plain,
! [SV50: $i] :
( ( ( ~ ( ssList @ SV50 ) )
= $true )
| ( ( ! [SY314: $i] :
( ~ ( ssList @ SY314 )
| ~ ~ ( ~ ( rearsegP @ SV50 @ SY314 )
| ~ ( rearsegP @ SY314 @ SV50 ) )
| ( SV50 = SY314 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(520,plain,
! [SV51: $i] :
( ( ( ~ ( ssList @ SV51 ) )
= $true )
| ( ( ~ ( ( nil != SV51 ) )
| ~ ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(521,plain,
! [SV52: $i] :
( ( ( ~ ( ssItem @ SV52 ) )
= $true )
| ( ( ! [SY316: $i] :
( ~ ( ssItem @ SY316 )
| ! [SY317: $i] :
( ~ ( ssItem @ SY317 )
| ~ ~ ( ~ ( geq @ SV52 @ SY316 )
| ~ ( geq @ SY316 @ SY317 ) )
| ( geq @ SV52 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(522,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ SV53 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( strictorderedP @ SV53 )
| ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) )
| ( strictorderedP @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(523,plain,
! [SV54: $i] :
( ( ( ~ ( ssItem @ SV54 ) )
= $true )
| ( ( equalelemsP @ ( cons @ SV54 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(524,plain,
! [SV55: $i] :
( ( ( ~ ( ssList @ SV55 ) )
= $true )
| ( ( ( nil = SV55 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( ssList @ SY328 )
| ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( ssItem @ SY329 )
| ( ( cons @ SY329 @ SY328 )
!= SV55 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(525,plain,
! [SV56: $i] :
( ( ( ~ ( ssItem @ SV56 ) )
= $true )
| ( ( ! [SY330: $i] :
( ~ ( ssItem @ SY330 )
| ~ ( gt @ SV56 @ SY330 )
| ~ ( gt @ SY330 @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(526,plain,
! [SV57: $i] :
( ( ( ~ ( ssList @ SV57 ) )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( ssList @ SY331 )
| ! [SY332: $i] :
( ~ ( ssList @ SY332 )
| ( ( app @ SY331 @ SY332 )
!= ( app @ SY331 @ SV57 ) )
| ( SY332 = SV57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(527,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( totalorderP @ SV58 )
| ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) )
| ( totalorderP @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(528,plain,
! [SV59: $i] :
( ( ( ~ ( ssList @ SV59 ) )
= $true )
| ( ( ! [SY343: $i] :
( ~ ( ssList @ SY343 )
| ! [SY344: $i] :
( ~ ( ssList @ SY344 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SY343 )
| ~ ( segmentP @ SY343 @ SY344 ) )
| ( segmentP @ SV59 @ SY344 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(529,plain,
( ( ~ ( ssList @ sK2_SX0 )
| ! [SY389: $i] :
( ~ ( ssList @ SY389 )
| ! [SY390: $i] :
( ~ ( ssList @ SY390 )
| ( sK2_SX0 != SY390 )
| ( sK1_U != SY389 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ( ( app @ ( app @ SX3 @ SY389 ) @ SX4 )
!= SY390 )
| ~ ( strictorderedP @ SY389 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ SX6 @ ( cons @ SX5 @ nil ) )
!= SX3 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ ( cons @ SX7 @ nil ) @ SX8 )
!= SY389 ) )
| ~ ( lt @ SX5 @ SX7 ) ) ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ ( cons @ SX5 @ nil ) @ SX6 )
!= SX4 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ SX8 @ ( cons @ SX7 @ nil ) )
!= SY389 ) )
| ~ ( lt @ SX7 @ SX5 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != SY390 ) )
| ( nil != SY389 ) )
| ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[442]) ).
thf(530,plain,
! [SV60: $i] :
( ( ( ~ ( ssList @ SV60 ) )
= $true )
| ( ( ! [SY345: $i] :
( ~ ( ssList @ SY345 )
| ! [SY346: $i] :
( ~ ( ssItem @ SY346 )
| ( ( cons @ SY346 @ ( app @ SY345 @ SV60 ) )
= ( app @ ( cons @ SY346 @ SY345 ) @ SV60 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(531,plain,
! [SV61: $i] :
( ( ( ~ ( ssList @ SV61 ) )
= $true )
| ( ( ! [SY347: $i] :
( ~ ( ssList @ SY347 )
| ! [SY348: $i] :
( ~ ( ssList @ SY348 )
| ( ( app @ SY348 @ SY347 )
!= ( app @ SV61 @ SY347 ) )
| ( SY348 = SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(532,plain,
! [SV62: $i] :
( ( ( ~ ( ssItem @ SV62 ) )
= $true )
| ( ( ! [SY349: $i] :
( ~ ( ssItem @ SY349 )
| ! [SY350: $i] :
( ~ ( ssItem @ SY350 )
| ~ ~ ( ~ ( gt @ SV62 @ SY349 )
| ~ ( gt @ SY349 @ SY350 ) )
| ( gt @ SV62 @ SY350 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(533,plain,
! [SV63: $i] :
( ( ( ~ ( ssList @ SV63 ) )
= $true )
| ( ( ! [SY351: $i] :
( ~ ( ssList @ SY351 )
| ~ ( ~ ( ( nil
!= ( app @ SV63 @ SY351 ) )
| ~ ( ( nil != SY351 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SY351 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SY351 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(534,plain,
! [SV64: $i] :
( ( ( ~ ( ssItem @ SV64 ) )
= $true )
| ( ( geq @ SV64 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(535,plain,
! [SV65: $i] :
( ( ( ~ ( ssList @ SV65 ) )
= $true )
| ( ( ! [SY352: $i] :
( ~ ( ssItem @ SY352 )
| ( ( tl @ ( cons @ SY352 @ SV65 ) )
= SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(536,plain,
! [SV66: $i] :
( ( ( ~ ( ssList @ SV66 ) )
= $true )
| ( ( ! [SY353: $i] :
( ~ ( ssItem @ SY353 )
| ( ( cons @ SY353 @ SV66 )
!= SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(537,plain,
! [SV67: $i] :
( ( ( ~ ( ssList @ SV67 ) )
= $true )
| ( ( ! [SY354: $i] :
( ~ ( ssList @ SY354 )
| ~ ~ ( ~ ( segmentP @ SV67 @ SY354 )
| ~ ( segmentP @ SY354 @ SV67 ) )
| ( SV67 = SY354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(538,plain,
! [SV68: $i] :
( ( ( ~ ( ssItem @ SV68 ) )
= $true )
| ( ( ! [SY355: $i] :
( ~ ( ssItem @ SY355 )
| ! [SY356: $i] :
( ~ ( ssList @ SY356 )
| ! [SY357: $i] :
( ~ ( ssList @ SY357 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SY356 ) @ ( cons @ SY355 @ SY357 ) )
| ~ ( ( SV68 != SY355 )
| ~ ( frontsegP @ SY356 @ SY357 ) ) )
| ~ ( ~ ~ ( ( SV68 != SY355 )
| ~ ( frontsegP @ SY356 @ SY357 ) )
| ( frontsegP @ ( cons @ SV68 @ SY356 ) @ ( cons @ SY355 @ SY357 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(539,plain,
! [SV69: $i] :
( ( ( ~ ( ssList @ SV69 ) )
= $true )
| ( ( ! [SY358: $i] :
( ~ ( ssList @ SY358 )
| ~ ( ~ ( ~ ( neq @ SV69 @ SY358 )
| ( SV69 != SY358 ) )
| ~ ( ~ ( ( SV69 != SY358 ) )
| ( neq @ SV69 @ SY358 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(540,plain,
! [SV70: $i] :
( ( ( ~ ( ssItem @ SV70 ) )
= $true )
| ( ( ! [SY359: $i] :
( ~ ( ssItem @ SY359 )
| ~ ( leq @ SV70 @ SY359 )
| ( SV70 = SY359 )
| ( lt @ SV70 @ SY359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(541,plain,
! [SV71: $i] :
( ( ( ~ ( ssItem @ SV71 ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV71 @ nil ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(542,plain,
! [SV72: $i] :
( ( ( ~ ( ssItem @ SV72 ) )
= $true )
| ( ( ! [SY360: $i] :
( ~ ( ssList @ SY360 )
| ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SY360 ) )
| ( nil = SY360 )
| ~ ( ~ ~ ( ~ ( ( nil != SY360 ) )
| ~ ( totalorderedP @ SY360 ) )
| ~ ( leq @ SV72 @ ( hd @ SY360 ) ) ) )
| ~ ( ~ ( ( nil = SY360 )
| ~ ( ~ ~ ( ~ ( ( nil != SY360 ) )
| ~ ( totalorderedP @ SY360 ) )
| ~ ( leq @ SV72 @ ( hd @ SY360 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SY360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(543,plain,
( ( ~ ~ ( ~ ( ssItem @ sK3_SX0 )
| ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( ssItem @ SY402 )
| ~ ( ( sK3_SX0 != SY402 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[456]) ).
thf(544,plain,
! [SV73: $i] :
( ( ( ~ ( ssItem @ SV73 ) )
= $true )
| ( ( ! [SY361: $i] :
( ~ ( ssItem @ SY361 )
| ~ ~ ( ~ ( leq @ SV73 @ SY361 )
| ~ ( leq @ SY361 @ SV73 ) )
| ( SV73 = SY361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(545,plain,
! [SV74: $i] :
( ( ( ~ ( ssList @ SV74 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( equalelemsP @ SV74 )
| ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
| ~ ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) )
| ( equalelemsP @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(546,plain,
! [SV75: $i] :
( ( ( ~ ( ssList @ SV75 ) )
= $true )
| ( ( ! [SY370: $i] :
( ~ ( ssList @ SY370 )
| ! [SY371: $i] :
( ~ ( ssList @ SY371 )
| ( ( app @ ( app @ SV75 @ SY370 ) @ SY371 )
= ( app @ SV75 @ ( app @ SY370 @ SY371 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(547,plain,
! [SV76: $i] :
( ( ( ~ ( ssList @ SV76 ) )
= $true )
| ( ( ! [SY372: $i] :
( ~ ( ssList @ SY372 )
| ! [SY373: $i] :
( ~ ( ssList @ SY373 )
| ~ ( rearsegP @ SV76 @ SY372 )
| ( rearsegP @ ( app @ SY373 @ SV76 ) @ SY372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(548,plain,
! [SV77: $i] :
( ( ( ~ ( ssList @ SV77 ) )
= $true )
| ( ( ! [SY374: $i] :
( ~ ( ssList @ SY374 )
| ! [SY375: $i] :
( ~ ( ssList @ SY375 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SY374 )
| ~ ( frontsegP @ SY374 @ SY375 ) )
| ( frontsegP @ SV77 @ SY375 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(549,plain,
! [SV78: $i] :
( ( ( ~ ( ssItem @ SV78 ) )
= $true )
| ( ( ! [SY376: $i] :
( ~ ( ssItem @ SY376 )
| ! [SY377: $i] :
( ~ ( ssItem @ SY377 )
| ~ ~ ( ~ ( lt @ SV78 @ SY376 )
| ~ ( lt @ SY376 @ SY377 ) )
| ( lt @ SV78 @ SY377 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(550,plain,
! [SV79: $i] :
( ( ( ~ ( ssList @ SV79 ) )
= $true )
| ( ( frontsegP @ SV79 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(551,plain,
! [SV80: $i] :
( ( ( ~ ( ssList @ SV80 ) )
= $true )
| ( ( rearsegP @ SV80 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(552,plain,
! [SV81: $i] :
( ( ( ~ ( ssItem @ SV81 ) )
= $true )
| ( ( ~ ( memberP @ nil @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(553,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( cyclefreeP @ SV82 )
| ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) )
| ( cyclefreeP @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(554,plain,
! [SV83: $i] :
( ( ( ~ ( ssList @ SV83 ) )
= $true )
| ( ( ~ ( ( nil != SV83 ) )
| ( ssList @ ( tl @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(555,plain,
! [SV84: $i] :
( ( ( ~ ( ssList @ SV84 ) )
= $true )
| ( ( ~ ( ( nil != SV84 ) )
| ~ ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(556,plain,
! [SV85: $i] :
( ( ( ~ ( ssList @ SV85 ) )
= $true )
| ( ( ~ ( ( nil != SV85 ) )
| ( ssItem @ ( hd @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(557,plain,
! [SV1: $i] :
( ( ( ssList @ SV1 )
= $false )
| ( ( ! [SY232: $i] :
( ~ ( ssList @ SY232 )
| ~ ~ ( ~ ( frontsegP @ SV1 @ SY232 )
| ~ ( frontsegP @ SY232 @ SV1 ) )
| ( SV1 = SY232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(558,plain,
! [SV2: $i] :
( ( ( ssItem @ SV2 )
= $false )
| ( ( ~ ( lt @ SV2 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(559,plain,
! [SV3: $i] :
( ( ( ssItem @ SV3 )
= $false )
| ( ( ! [SY233: $i] :
( ~ ( ssItem @ SY233 )
| ~ ( ~ ( ~ ( lt @ SV3 @ SY233 )
| ~ ( ~ ( ( SV3 != SY233 ) )
| ~ ( leq @ SV3 @ SY233 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SY233 ) )
| ~ ( leq @ SV3 @ SY233 ) )
| ( lt @ SV3 @ SY233 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(560,plain,
! [SV4: $i] :
( ( ( ssItem @ SV4 )
= $false )
| ( ( ! [SY234: $i] :
( ~ ( ssItem @ SY234 )
| ~ ( ~ ( ~ ( gt @ SV4 @ SY234 )
| ( lt @ SY234 @ SV4 ) )
| ~ ( ~ ( lt @ SY234 @ SV4 )
| ( gt @ SV4 @ SY234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(561,plain,
! [SV5: $i] :
( ( ( ssItem @ SV5 )
= $false )
| ( ( ! [SY235: $i] :
( ~ ( ssItem @ SY235 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SY235 )
| ( SV5 != SY235 ) )
| ~ ( ~ ( ( SV5 != SY235 ) )
| ( neq @ SV5 @ SY235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(562,plain,
! [SV6: $i] :
( ( ( ssList @ SV6 )
= $false )
| ( ( rearsegP @ SV6 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(563,plain,
! [SV7: $i] :
( ( ( ssItem @ SV7 )
= $false )
| ( ( strictorderedP @ ( cons @ SV7 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(564,plain,
! [SV8: $i] :
( ( ( ssList @ SV8 )
= $false )
| ( ( ! [SY236: $i] :
( ~ ( ssList @ SY236 )
| ~ ( ( nil != SV8 ) )
| ( ( hd @ ( app @ SV8 @ SY236 ) )
= ( hd @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(565,plain,
! [SV9: $i] :
( ( ( ssItem @ SV9 )
= $false )
| ( ( strictorderP @ ( cons @ SV9 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(566,plain,
! [SV10: $i] :
( ( ( ssItem @ SV10 )
= $false )
| ( ( ! [SY237: $i] :
( ~ ( ssList @ SY237 )
| ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SY237 ) )
| ( nil = SY237 )
| ~ ( ~ ~ ( ~ ( ( nil != SY237 ) )
| ~ ( strictorderedP @ SY237 ) )
| ~ ( lt @ SV10 @ ( hd @ SY237 ) ) ) )
| ~ ( ~ ( ( nil = SY237 )
| ~ ( ~ ~ ( ~ ( ( nil != SY237 ) )
| ~ ( strictorderedP @ SY237 ) )
| ~ ( lt @ SV10 @ ( hd @ SY237 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SY237 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(567,plain,
! [SV11: $i] :
( ( ( ssList @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( segmentP @ nil @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(568,plain,
! [SV12: $i] :
( ( ( ssList @ SV12 )
= $false )
| ( ( ! [SY238: $i] :
( ~ ( ssItem @ SY238 )
| ( ( cons @ SY238 @ SV12 )
= ( app @ ( cons @ SY238 @ nil ) @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(569,plain,
! [SV13: $i] :
( ( ( ssList @ SV13 )
= $false )
| ( ( ! [SY239: $i] :
( ~ ( ssList @ SY239 )
| ( ssList @ ( app @ SV13 @ SY239 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(570,plain,
! [SV14: $i] :
( ( ( ssItem @ SV14 )
= $false )
| ( ( duplicatefreeP @ ( cons @ SV14 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(571,plain,
! [SV15: $i] :
( ( ( ssList @ SV15 )
= $false )
| ( ( ! [SY240: $i] :
( ~ ( ssItem @ SY240 )
| ( ( hd @ ( cons @ SY240 @ SV15 ) )
= SY240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(572,plain,
! [SV16: $i] :
( ( ( ssList @ SV16 )
= $false )
| ( ( ! [SY241: $i] :
( ~ ( ssList @ SY241 )
| ~ ( ~ ( ~ ( frontsegP @ SV16 @ SY241 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( ssList @ SY242 )
| ( ( app @ SY241 @ SY242 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( ssList @ SY243 )
| ( ( app @ SY241 @ SY243 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SY241 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(573,plain,
! [SV17: $i] :
( ( ( ssItem @ SV17 )
= $false )
| ( ( ! [SY244: $i] :
( ~ ( ssItem @ SY244 )
| ! [SY245: $i] :
( ~ ( ssItem @ SY245 )
| ~ ~ ( ~ ( leq @ SV17 @ SY244 )
| ~ ( lt @ SY244 @ SY245 ) )
| ( lt @ SV17 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(574,plain,
! [SV18: $i] :
( ( ( ssList @ SV18 )
= $false )
| ( ( ! [SY246: $i] :
( ~ ( ssList @ SY246 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SY246 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ( ssList @ SY247 )
| ( ( app @ SY247 @ SY246 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ( ssList @ SY248 )
| ( ( app @ SY248 @ SY246 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SY246 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(575,plain,
! [SV19: $i] :
( ( ( ssList @ SV19 )
= $false )
| ( ( ~ ( ~ ( ~ ( singletonP @ SV19 )
| ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
| ~ ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) )
| ( singletonP @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(576,plain,
! [SV20: $i] :
( ( ( ssItem @ SV20 )
= $false )
| ( ( ! [SY251: $i] :
( ~ ( ssItem @ SY251 )
| ~ ~ ( ~ ( geq @ SV20 @ SY251 )
| ~ ( geq @ SY251 @ SV20 ) )
| ( SV20 = SY251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(577,plain,
! [SV21: $i] :
( ( ( ssList @ SV21 )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( ssItem @ SY252 )
| ~ ( ~ ( ~ ( memberP @ SV21 @ SY252 )
| ~ ! [SY253: $i] :
~ ~ ( ~ ( ssList @ SY253 )
| ~ ~ ! [SY254: $i] :
~ ~ ( ~ ( ssList @ SY254 )
| ( ( app @ SY253 @ ( cons @ SY252 @ SY254 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY255: $i] :
~ ~ ( ~ ( ssList @ SY255 )
| ~ ~ ! [SY256: $i] :
~ ~ ( ~ ( ssList @ SY256 )
| ( ( app @ SY255 @ ( cons @ SY252 @ SY256 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SY252 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(578,plain,
! [SV22: $i] :
( ( ( ssList @ SV22 )
= $false )
| ( ( ~ ( ~ ( ~ ( strictorderP @ SV22 )
| ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
| ~ ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) )
| ( strictorderP @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(579,plain,
! [SV23: $i] :
( ( ( ssList @ SV23 )
= $false )
| ( ( segmentP @ SV23 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(580,plain,
! [SV24: $i] :
( ( ( ssItem @ SV24 )
= $false )
| ( ( ! [SY267: $i] :
( ~ ( ssList @ SY267 )
| ! [SY268: $i] :
( ~ ( ssList @ SY268 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY267 @ SY268 ) @ SV24 )
| ( memberP @ SY267 @ SV24 )
| ( memberP @ SY268 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SY267 @ SV24 )
| ( memberP @ SY268 @ SV24 ) )
| ( memberP @ ( app @ SY267 @ SY268 ) @ SV24 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(581,plain,
! [SV25: $i] :
( ( ( ssList @ SV25 )
= $false )
| ( ( ( app @ SV25 @ nil )
= SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(582,plain,
! [SV26: $i] :
( ( ( ssList @ SV26 )
= $false )
| ( ( ! [SY269: $i] :
( ~ ( ssList @ SY269 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SY269 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SY269 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SY269 )
!= ( tl @ SV26 ) ) )
| ( SY269 = SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(583,plain,
! [SV27: $i] :
( ( ( ssList @ SV27 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV27 )
| ( nil = SV27 ) )
| ~ ( ( nil != SV27 )
| ( frontsegP @ nil @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(584,plain,
! [SV28: $i] :
( ( ( ssList @ SV28 )
= $false )
| ( ( ! [SY270: $i] :
( ~ ( ssList @ SY270 )
| ! [SY271: $i] :
( ~ ( ssList @ SY271 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SY270 )
| ~ ( rearsegP @ SY270 @ SY271 ) )
| ( rearsegP @ SV28 @ SY271 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(585,plain,
! [SV29: $i] :
( ( ( ssList @ SV29 )
= $false )
| ( ( ~ ( ~ ( ~ ( totalorderedP @ SV29 )
| ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
| ~ ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) )
| ( totalorderedP @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(586,plain,
! [SV30: $i] :
( ( ( ssItem @ SV30 )
= $false )
| ( ( leq @ SV30 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(587,plain,
! [SV31: $i] :
( ( ( ssItem @ SV31 )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( ssItem @ SY282 )
| ! [SY283: $i] :
( ~ ( ssItem @ SY283 )
| ~ ~ ( ~ ( leq @ SV31 @ SY282 )
| ~ ( leq @ SY282 @ SY283 ) )
| ( leq @ SV31 @ SY283 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(588,plain,
! [SV32: $i] :
( ( ( ssList @ SV32 )
= $false )
| ( ( ( app @ nil @ SV32 )
= SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(589,plain,
! [SV33: $i] :
( ( ( ssList @ SV33 )
= $false )
| ( ( ! [SY284: $i] :
( ~ ( ssItem @ SY284 )
| ( ssList @ ( cons @ SY284 @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(590,plain,
! [SV34: $i] :
( ( ( ssList @ SV34 )
= $false )
| ( ( ! [SY285: $i] :
( ~ ( ssList @ SY285 )
| ~ ( ~ ( ~ ( segmentP @ SV34 @ SY285 )
| ~ ! [SY286: $i] :
~ ~ ( ~ ( ssList @ SY286 )
| ~ ~ ! [SY287: $i] :
~ ~ ( ~ ( ssList @ SY287 )
| ( ( app @ ( app @ SY286 @ SY285 ) @ SY287 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY288: $i] :
~ ~ ( ~ ( ssList @ SY288 )
| ~ ~ ! [SY289: $i] :
~ ~ ( ~ ( ssList @ SY289 )
| ( ( app @ ( app @ SY288 @ SY285 ) @ SY289 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SY285 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(591,plain,
! [SV35: $i] :
( ( ( ssList @ SV35 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( ssList @ SY290 )
| ! [SY291: $i] :
( ~ ( ssItem @ SY291 )
| ! [SY292: $i] :
( ~ ( ssItem @ SY292 )
| ( ( cons @ SY291 @ SV35 )
!= ( cons @ SY292 @ SY290 ) )
| ~ ( ( SY291 != SY292 )
| ( SY290 != SV35 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(592,plain,
! [SV36: $i] :
( ( ( ssList @ SV36 )
= $false )
| ( ( ~ ( ( nil != SV36 ) )
| ( ( cons @ ( hd @ SV36 ) @ ( tl @ SV36 ) )
= SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(593,plain,
! [SV37: $i] :
( ( ( ssItem @ SV37 )
= $false )
| ( ( totalorderP @ ( cons @ SV37 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(594,plain,
! [SV38: $i] :
( ( ( ssList @ SV38 )
= $false )
| ( ( frontsegP @ SV38 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(595,plain,
! [SV39: $i] :
( ( ( ssItem @ SV39 )
= $false )
| ( ( ! [SY293: $i] :
( ~ ( ssItem @ SY293 )
| ~ ( ~ ( ~ ( geq @ SV39 @ SY293 )
| ( leq @ SY293 @ SV39 ) )
| ~ ( ~ ( leq @ SY293 @ SV39 )
| ( geq @ SV39 @ SY293 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(596,plain,
! [SV40: $i] :
( ( ( ssList @ SV40 )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( ssList @ SY294 )
| ! [SY295: $i] :
( ~ ( ssList @ SY295 )
| ! [SY296: $i] :
( ~ ( ssList @ SY296 )
| ~ ( segmentP @ SV40 @ SY294 )
| ( segmentP @ ( app @ ( app @ SY295 @ SV40 ) @ SY296 ) @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(597,plain,
! [SV41: $i] :
( ( ( ssList @ SV41 )
= $false )
| ( ( ! [SY297: $i] :
( ~ ( ssList @ SY297 )
| ~ ( ( nil != SV41 ) )
| ( ( tl @ ( app @ SV41 @ SY297 ) )
= ( app @ ( tl @ SV41 ) @ SY297 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(598,plain,
! [SV42: $i] :
( ( ( ssList @ SV42 )
= $false )
| ( ( segmentP @ SV42 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(599,plain,
! [SV43: $i] :
( ( ( ssItem @ SV43 )
= $false )
| ( ( ! [SY298: $i] :
( ~ ( ssItem @ SY298 )
| ~ ( lt @ SV43 @ SY298 )
| ~ ( lt @ SY298 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(600,plain,
! [SV44: $i] :
( ( ( ssList @ SV44 )
= $false )
| ( ( ! [SY299: $i] :
( ~ ( ssItem @ SY299 )
| ( nil
!= ( cons @ SY299 @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(601,plain,
! [SV45: $i] :
( ( ( ssList @ SV45 )
= $false )
| ( ( ! [SY300: $i] :
( ~ ( ssList @ SY300 )
| ! [SY301: $i] :
( ~ ( ssList @ SY301 )
| ~ ( frontsegP @ SV45 @ SY300 )
| ( frontsegP @ ( app @ SV45 @ SY301 ) @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(602,plain,
! [SV46: $i] :
( ( ( ssItem @ SV46 )
= $false )
| ( ( ! [SY302: $i] :
( ~ ( ssItem @ SY302 )
| ! [SY303: $i] :
( ~ ( ssList @ SY303 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY302 @ SY303 ) @ SV46 )
| ( SV46 = SY302 )
| ( memberP @ SY303 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SY302 )
| ( memberP @ SY303 @ SV46 ) )
| ( memberP @ ( cons @ SY302 @ SY303 ) @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(603,plain,
! [SV47: $i] :
( ( ( ssItem @ SV47 )
= $false )
| ( ( cyclefreeP @ ( cons @ SV47 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(604,plain,
! [SV48: $i] :
( ( ( ssList @ SV48 )
= $false )
| ( ( ~ ( ~ ( ~ ( duplicatefreeP @ SV48 )
| ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
| ~ ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) )
| ( duplicatefreeP @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(605,plain,
! [SV49: $i] :
( ( ( ssList @ SV49 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV49 )
| ( nil = SV49 ) )
| ~ ( ( nil != SV49 )
| ( rearsegP @ nil @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(606,plain,
! [SV50: $i] :
( ( ( ssList @ SV50 )
= $false )
| ( ( ! [SY314: $i] :
( ~ ( ssList @ SY314 )
| ~ ~ ( ~ ( rearsegP @ SV50 @ SY314 )
| ~ ( rearsegP @ SY314 @ SV50 ) )
| ( SV50 = SY314 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(607,plain,
! [SV51: $i] :
( ( ( ssList @ SV51 )
= $false )
| ( ( ~ ( ( nil != SV51 ) )
| ~ ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(608,plain,
! [SV52: $i] :
( ( ( ssItem @ SV52 )
= $false )
| ( ( ! [SY316: $i] :
( ~ ( ssItem @ SY316 )
| ! [SY317: $i] :
( ~ ( ssItem @ SY317 )
| ~ ~ ( ~ ( geq @ SV52 @ SY316 )
| ~ ( geq @ SY316 @ SY317 ) )
| ( geq @ SV52 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(609,plain,
! [SV53: $i] :
( ( ( ssList @ SV53 )
= $false )
| ( ( ~ ( ~ ( ~ ( strictorderedP @ SV53 )
| ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) )
| ( strictorderedP @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(610,plain,
! [SV54: $i] :
( ( ( ssItem @ SV54 )
= $false )
| ( ( equalelemsP @ ( cons @ SV54 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(611,plain,
! [SV55: $i] :
( ( ( ssList @ SV55 )
= $false )
| ( ( ( nil = SV55 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( ssList @ SY328 )
| ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( ssItem @ SY329 )
| ( ( cons @ SY329 @ SY328 )
!= SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(612,plain,
! [SV56: $i] :
( ( ( ssItem @ SV56 )
= $false )
| ( ( ! [SY330: $i] :
( ~ ( ssItem @ SY330 )
| ~ ( gt @ SV56 @ SY330 )
| ~ ( gt @ SY330 @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(613,plain,
! [SV57: $i] :
( ( ( ssList @ SV57 )
= $false )
| ( ( ! [SY331: $i] :
( ~ ( ssList @ SY331 )
| ! [SY332: $i] :
( ~ ( ssList @ SY332 )
| ( ( app @ SY331 @ SY332 )
!= ( app @ SY331 @ SV57 ) )
| ( SY332 = SV57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(614,plain,
! [SV58: $i] :
( ( ( ssList @ SV58 )
= $false )
| ( ( ~ ( ~ ( ~ ( totalorderP @ SV58 )
| ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) )
| ( totalorderP @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(615,plain,
! [SV59: $i] :
( ( ( ssList @ SV59 )
= $false )
| ( ( ! [SY343: $i] :
( ~ ( ssList @ SY343 )
| ! [SY344: $i] :
( ~ ( ssList @ SY344 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SY343 )
| ~ ( segmentP @ SY343 @ SY344 ) )
| ( segmentP @ SV59 @ SY344 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(616,plain,
( ( ~ ( ssList @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(617,plain,
( ( ! [SY389: $i] :
( ~ ( ssList @ SY389 )
| ! [SY390: $i] :
( ~ ( ssList @ SY390 )
| ( sK2_SX0 != SY390 )
| ( sK1_U != SY389 )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ( ( app @ ( app @ SX3 @ SY389 ) @ SX4 )
!= SY390 )
| ~ ( strictorderedP @ SY389 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ SX6 @ ( cons @ SX5 @ nil ) )
!= SX3 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ ( cons @ SX7 @ nil ) @ SX8 )
!= SY389 ) )
| ~ ( lt @ SX5 @ SX7 ) ) ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( ssItem @ SX5 )
| ~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX6 )
| ( ( app @ ( cons @ SX5 @ nil ) @ SX6 )
!= SX4 ) )
| ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( ssItem @ SX7 )
| ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SX8 )
| ( ( app @ SX8 @ ( cons @ SX7 @ nil ) )
!= SY389 ) )
| ~ ( lt @ SX7 @ SX5 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != SY390 ) )
| ( nil != SY389 ) )
| ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(618,plain,
! [SV60: $i] :
( ( ( ssList @ SV60 )
= $false )
| ( ( ! [SY345: $i] :
( ~ ( ssList @ SY345 )
| ! [SY346: $i] :
( ~ ( ssItem @ SY346 )
| ( ( cons @ SY346 @ ( app @ SY345 @ SV60 ) )
= ( app @ ( cons @ SY346 @ SY345 ) @ SV60 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(619,plain,
! [SV61: $i] :
( ( ( ssList @ SV61 )
= $false )
| ( ( ! [SY347: $i] :
( ~ ( ssList @ SY347 )
| ! [SY348: $i] :
( ~ ( ssList @ SY348 )
| ( ( app @ SY348 @ SY347 )
!= ( app @ SV61 @ SY347 ) )
| ( SY348 = SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(620,plain,
! [SV62: $i] :
( ( ( ssItem @ SV62 )
= $false )
| ( ( ! [SY349: $i] :
( ~ ( ssItem @ SY349 )
| ! [SY350: $i] :
( ~ ( ssItem @ SY350 )
| ~ ~ ( ~ ( gt @ SV62 @ SY349 )
| ~ ( gt @ SY349 @ SY350 ) )
| ( gt @ SV62 @ SY350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(621,plain,
! [SV63: $i] :
( ( ( ssList @ SV63 )
= $false )
| ( ( ! [SY351: $i] :
( ~ ( ssList @ SY351 )
| ~ ( ~ ( ( nil
!= ( app @ SV63 @ SY351 ) )
| ~ ( ( nil != SY351 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SY351 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SY351 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(622,plain,
! [SV64: $i] :
( ( ( ssItem @ SV64 )
= $false )
| ( ( geq @ SV64 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(623,plain,
! [SV65: $i] :
( ( ( ssList @ SV65 )
= $false )
| ( ( ! [SY352: $i] :
( ~ ( ssItem @ SY352 )
| ( ( tl @ ( cons @ SY352 @ SV65 ) )
= SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(624,plain,
! [SV66: $i] :
( ( ( ssList @ SV66 )
= $false )
| ( ( ! [SY353: $i] :
( ~ ( ssItem @ SY353 )
| ( ( cons @ SY353 @ SV66 )
!= SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(625,plain,
! [SV67: $i] :
( ( ( ssList @ SV67 )
= $false )
| ( ( ! [SY354: $i] :
( ~ ( ssList @ SY354 )
| ~ ~ ( ~ ( segmentP @ SV67 @ SY354 )
| ~ ( segmentP @ SY354 @ SV67 ) )
| ( SV67 = SY354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(626,plain,
! [SV68: $i] :
( ( ( ssItem @ SV68 )
= $false )
| ( ( ! [SY355: $i] :
( ~ ( ssItem @ SY355 )
| ! [SY356: $i] :
( ~ ( ssList @ SY356 )
| ! [SY357: $i] :
( ~ ( ssList @ SY357 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SY356 ) @ ( cons @ SY355 @ SY357 ) )
| ~ ( ( SV68 != SY355 )
| ~ ( frontsegP @ SY356 @ SY357 ) ) )
| ~ ( ~ ~ ( ( SV68 != SY355 )
| ~ ( frontsegP @ SY356 @ SY357 ) )
| ( frontsegP @ ( cons @ SV68 @ SY356 ) @ ( cons @ SY355 @ SY357 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(627,plain,
! [SV69: $i] :
( ( ( ssList @ SV69 )
= $false )
| ( ( ! [SY358: $i] :
( ~ ( ssList @ SY358 )
| ~ ( ~ ( ~ ( neq @ SV69 @ SY358 )
| ( SV69 != SY358 ) )
| ~ ( ~ ( ( SV69 != SY358 ) )
| ( neq @ SV69 @ SY358 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(628,plain,
! [SV70: $i] :
( ( ( ssItem @ SV70 )
= $false )
| ( ( ! [SY359: $i] :
( ~ ( ssItem @ SY359 )
| ~ ( leq @ SV70 @ SY359 )
| ( SV70 = SY359 )
| ( lt @ SV70 @ SY359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(629,plain,
! [SV71: $i] :
( ( ( ssItem @ SV71 )
= $false )
| ( ( totalorderedP @ ( cons @ SV71 @ nil ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(630,plain,
! [SV72: $i] :
( ( ( ssItem @ SV72 )
= $false )
| ( ( ! [SY360: $i] :
( ~ ( ssList @ SY360 )
| ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SY360 ) )
| ( nil = SY360 )
| ~ ( ~ ~ ( ~ ( ( nil != SY360 ) )
| ~ ( totalorderedP @ SY360 ) )
| ~ ( leq @ SV72 @ ( hd @ SY360 ) ) ) )
| ~ ( ~ ( ( nil = SY360 )
| ~ ( ~ ~ ( ~ ( ( nil != SY360 ) )
| ~ ( totalorderedP @ SY360 ) )
| ~ ( leq @ SV72 @ ( hd @ SY360 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SY360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(631,plain,
( ( ~ ( ~ ( ssItem @ sK3_SX0 )
| ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( ssItem @ SY402 )
| ~ ( ( sK3_SX0 != SY402 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(632,plain,
! [SV73: $i] :
( ( ( ssItem @ SV73 )
= $false )
| ( ( ! [SY361: $i] :
( ~ ( ssItem @ SY361 )
| ~ ~ ( ~ ( leq @ SV73 @ SY361 )
| ~ ( leq @ SY361 @ SV73 ) )
| ( SV73 = SY361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(633,plain,
! [SV74: $i] :
( ( ( ssList @ SV74 )
= $false )
| ( ( ~ ( ~ ( ~ ( equalelemsP @ SV74 )
| ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
| ~ ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) )
| ( equalelemsP @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(634,plain,
! [SV75: $i] :
( ( ( ssList @ SV75 )
= $false )
| ( ( ! [SY370: $i] :
( ~ ( ssList @ SY370 )
| ! [SY371: $i] :
( ~ ( ssList @ SY371 )
| ( ( app @ ( app @ SV75 @ SY370 ) @ SY371 )
= ( app @ SV75 @ ( app @ SY370 @ SY371 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(635,plain,
! [SV76: $i] :
( ( ( ssList @ SV76 )
= $false )
| ( ( ! [SY372: $i] :
( ~ ( ssList @ SY372 )
| ! [SY373: $i] :
( ~ ( ssList @ SY373 )
| ~ ( rearsegP @ SV76 @ SY372 )
| ( rearsegP @ ( app @ SY373 @ SV76 ) @ SY372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(636,plain,
! [SV77: $i] :
( ( ( ssList @ SV77 )
= $false )
| ( ( ! [SY374: $i] :
( ~ ( ssList @ SY374 )
| ! [SY375: $i] :
( ~ ( ssList @ SY375 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SY374 )
| ~ ( frontsegP @ SY374 @ SY375 ) )
| ( frontsegP @ SV77 @ SY375 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(637,plain,
! [SV78: $i] :
( ( ( ssItem @ SV78 )
= $false )
| ( ( ! [SY376: $i] :
( ~ ( ssItem @ SY376 )
| ! [SY377: $i] :
( ~ ( ssItem @ SY377 )
| ~ ~ ( ~ ( lt @ SV78 @ SY376 )
| ~ ( lt @ SY376 @ SY377 ) )
| ( lt @ SV78 @ SY377 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(638,plain,
! [SV79: $i] :
( ( ( ssList @ SV79 )
= $false )
| ( ( frontsegP @ SV79 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(639,plain,
! [SV80: $i] :
( ( ( ssList @ SV80 )
= $false )
| ( ( rearsegP @ SV80 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(640,plain,
! [SV81: $i] :
( ( ( ssItem @ SV81 )
= $false )
| ( ( ~ ( memberP @ nil @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(641,plain,
! [SV82: $i] :
( ( ( ssList @ SV82 )
= $false )
| ( ( ~ ( ~ ( ~ ( cyclefreeP @ SV82 )
| ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) )
| ( cyclefreeP @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(642,plain,
! [SV83: $i] :
( ( ( ssList @ SV83 )
= $false )
| ( ( ~ ( ( nil != SV83 ) )
| ( ssList @ ( tl @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(643,plain,
! [SV84: $i] :
( ( ( ssList @ SV84 )
= $false )
| ( ( ~ ( ( nil != SV84 ) )
| ~ ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(644,plain,
! [SV85: $i] :
( ( ( ssList @ SV85 )
= $false )
| ( ( ~ ( ( nil != SV85 ) )
| ( ssItem @ ( hd @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(645,plain,
! [SV1: $i,SV86: $i] :
( ( ( ~ ( ssList @ SV86 )
| ~ ~ ( ~ ( frontsegP @ SV1 @ SV86 )
| ~ ( frontsegP @ SV86 @ SV1 ) )
| ( SV1 = SV86 ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(646,plain,
! [SV2: $i] :
( ( ( lt @ SV2 @ SV2 )
= $false )
| ( ( ssItem @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(647,plain,
! [SV3: $i,SV87: $i] :
( ( ( ~ ( ssItem @ SV87 )
| ~ ( ~ ( ~ ( lt @ SV3 @ SV87 )
| ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
| ( lt @ SV3 @ SV87 ) ) ) )
= $true )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(648,plain,
! [SV4: $i,SV88: $i] :
( ( ( ~ ( ssItem @ SV88 )
| ~ ( ~ ( ~ ( gt @ SV4 @ SV88 )
| ( lt @ SV88 @ SV4 ) )
| ~ ( ~ ( lt @ SV88 @ SV4 )
| ( gt @ SV4 @ SV88 ) ) ) )
= $true )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(649,plain,
! [SV5: $i,SV89: $i] :
( ( ( ~ ( ssItem @ SV89 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SV89 )
| ( SV5 != SV89 ) )
| ~ ( ~ ( ( SV5 != SV89 ) )
| ( neq @ SV5 @ SV89 ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(650,plain,
! [SV8: $i,SV90: $i] :
( ( ( ~ ( ssList @ SV90 )
| ~ ( ( nil != SV8 ) )
| ( ( hd @ ( app @ SV8 @ SV90 ) )
= ( hd @ SV8 ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(651,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ssList @ SV91 )
| ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
| ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ~ ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) ) ) )
= $true )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(652,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( segmentP @ nil @ SV11 ) ) )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(653,plain,
! [SV12: $i,SV92: $i] :
( ( ( ~ ( ssItem @ SV92 )
| ( ( cons @ SV92 @ SV12 )
= ( app @ ( cons @ SV92 @ nil ) @ SV12 ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(654,plain,
! [SV13: $i,SV93: $i] :
( ( ( ~ ( ssList @ SV93 )
| ( ssList @ ( app @ SV13 @ SV93 ) ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(655,plain,
! [SV15: $i,SV94: $i] :
( ( ( ~ ( ssItem @ SV94 )
| ( ( hd @ ( cons @ SV94 @ SV15 ) )
= SV94 ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(656,plain,
! [SV16: $i,SV95: $i] :
( ( ( ~ ( ssList @ SV95 )
| ~ ( ~ ( ~ ( frontsegP @ SV16 @ SV95 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SV95 ) ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(657,plain,
! [SV17: $i,SV96: $i] :
( ( ( ~ ( ssItem @ SV96 )
| ! [SY405: $i] :
( ~ ( ssItem @ SY405 )
| ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SY405 ) )
| ( lt @ SV17 @ SY405 ) ) )
= $true )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(658,plain,
! [SV18: $i,SV97: $i] :
( ( ( ~ ( ssList @ SV97 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SV97 )
| ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV97 ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(659,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( singletonP @ SV19 )
| ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
| ~ ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) )
| ( singletonP @ SV19 ) ) )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(660,plain,
! [SV20: $i,SV98: $i] :
( ( ( ~ ( ssItem @ SV98 )
| ~ ~ ( ~ ( geq @ SV20 @ SV98 )
| ~ ( geq @ SV98 @ SV20 ) )
| ( SV20 = SV98 ) )
= $true )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(661,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ( ssItem @ SV99 )
| ~ ( ~ ( ~ ( memberP @ SV21 @ SV99 )
| ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SV99 ) ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(662,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( strictorderP @ SV22 )
| ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
| ~ ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) )
| ( strictorderP @ SV22 ) ) )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(663,plain,
! [SV24: $i,SV100: $i] :
( ( ( ~ ( ssList @ SV100 )
| ! [SY412: $i] :
( ~ ( ssList @ SY412 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV100 @ SY412 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SY412 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SY412 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SY412 ) @ SV24 ) ) ) ) )
= $true )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(664,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ssList @ SV101 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SV101 )
!= ( tl @ SV26 ) ) )
| ( SV101 = SV26 ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(665,plain,
! [SV27: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV27 )
| ( nil = SV27 ) )
| ~ ( ( nil != SV27 )
| ( frontsegP @ nil @ SV27 ) ) )
= $false )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(666,plain,
! [SV28: $i,SV102: $i] :
( ( ( ~ ( ssList @ SV102 )
| ! [SY413: $i] :
( ~ ( ssList @ SY413 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SY413 ) )
| ( rearsegP @ SV28 @ SY413 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(667,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( totalorderedP @ SV29 )
| ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
| ~ ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) )
| ( totalorderedP @ SV29 ) ) )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(668,plain,
! [SV31: $i,SV103: $i] :
( ( ( ~ ( ssItem @ SV103 )
| ! [SY414: $i] :
( ~ ( ssItem @ SY414 )
| ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SY414 ) )
| ( leq @ SV31 @ SY414 ) ) )
= $true )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(669,plain,
! [SV33: $i,SV104: $i] :
( ( ( ~ ( ssItem @ SV104 )
| ( ssList @ ( cons @ SV104 @ SV33 ) ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(670,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ( ssList @ SV105 )
| ~ ( ~ ( ~ ( segmentP @ SV34 @ SV105 )
| ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SV105 ) ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(671,plain,
! [SV35: $i,SV106: $i] :
( ( ( ~ ( ssList @ SV106 )
| ! [SY419: $i] :
( ~ ( ssItem @ SY419 )
| ! [SY420: $i] :
( ~ ( ssItem @ SY420 )
| ( ( cons @ SY419 @ SV35 )
!= ( cons @ SY420 @ SV106 ) )
| ~ ( ( SY419 != SY420 )
| ( SV106 != SV35 ) ) ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(672,plain,
! [SV36: $i] :
( ( ( ~ ( ( nil != SV36 ) ) )
= $true )
| ( ( ( cons @ ( hd @ SV36 ) @ ( tl @ SV36 ) )
= SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(673,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( ssItem @ SV107 )
| ~ ( ~ ( ~ ( geq @ SV39 @ SV107 )
| ( leq @ SV107 @ SV39 ) )
| ~ ( ~ ( leq @ SV107 @ SV39 )
| ( geq @ SV39 @ SV107 ) ) ) )
= $true )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(674,plain,
! [SV40: $i,SV108: $i] :
( ( ( ~ ( ssList @ SV108 )
| ! [SY421: $i] :
( ~ ( ssList @ SY421 )
| ! [SY422: $i] :
( ~ ( ssList @ SY422 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SY421 @ SV40 ) @ SY422 ) @ SV108 ) ) ) )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(675,plain,
! [SV41: $i,SV109: $i] :
( ( ( ~ ( ssList @ SV109 )
| ~ ( ( nil != SV41 ) )
| ( ( tl @ ( app @ SV41 @ SV109 ) )
= ( app @ ( tl @ SV41 ) @ SV109 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(676,plain,
! [SV43: $i,SV110: $i] :
( ( ( ~ ( ssItem @ SV110 )
| ~ ( lt @ SV43 @ SV110 )
| ~ ( lt @ SV110 @ SV43 ) )
= $true )
| ( ( ssItem @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(677,plain,
! [SV44: $i,SV111: $i] :
( ( ( ~ ( ssItem @ SV111 )
| ( nil
!= ( cons @ SV111 @ SV44 ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(678,plain,
! [SV45: $i,SV112: $i] :
( ( ( ~ ( ssList @ SV112 )
| ! [SY423: $i] :
( ~ ( ssList @ SY423 )
| ~ ( frontsegP @ SV45 @ SV112 )
| ( frontsegP @ ( app @ SV45 @ SY423 ) @ SV112 ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(679,plain,
! [SV46: $i,SV113: $i] :
( ( ( ~ ( ssItem @ SV113 )
| ! [SY424: $i] :
( ~ ( ssList @ SY424 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SY424 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SY424 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SY424 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SY424 ) @ SV46 ) ) ) ) )
= $true )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(680,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( duplicatefreeP @ SV48 )
| ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
| ~ ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) )
| ( duplicatefreeP @ SV48 ) ) )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(681,plain,
! [SV49: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV49 )
| ( nil = SV49 ) )
| ~ ( ( nil != SV49 )
| ( rearsegP @ nil @ SV49 ) ) )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(682,plain,
! [SV50: $i,SV114: $i] :
( ( ( ~ ( ssList @ SV114 )
| ~ ~ ( ~ ( rearsegP @ SV50 @ SV114 )
| ~ ( rearsegP @ SV114 @ SV50 ) )
| ( SV50 = SV114 ) )
= $true )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(683,plain,
! [SV51: $i] :
( ( ( ~ ( ( nil != SV51 ) ) )
= $true )
| ( ( ~ ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(684,plain,
! [SV52: $i,SV115: $i] :
( ( ( ~ ( ssItem @ SV115 )
| ! [SY425: $i] :
( ~ ( ssItem @ SY425 )
| ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SY425 ) )
| ( geq @ SV52 @ SY425 ) ) )
= $true )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(685,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ( strictorderedP @ SV53 )
| ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) )
| ( strictorderedP @ SV53 ) ) )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(686,plain,
! [SV55: $i] :
( ( ( nil = SV55 )
= $true )
| ( ( ~ ! [SY328: $i] :
~ ~ ( ~ ( ssList @ SY328 )
| ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( ssItem @ SY329 )
| ( ( cons @ SY329 @ SY328 )
!= SV55 ) ) ) )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(687,plain,
! [SV56: $i,SV116: $i] :
( ( ( ~ ( ssItem @ SV116 )
| ~ ( gt @ SV56 @ SV116 )
| ~ ( gt @ SV116 @ SV56 ) )
= $true )
| ( ( ssItem @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(688,plain,
! [SV57: $i,SV117: $i] :
( ( ( ~ ( ssList @ SV117 )
| ! [SY426: $i] :
( ~ ( ssList @ SY426 )
| ( ( app @ SV117 @ SY426 )
!= ( app @ SV117 @ SV57 ) )
| ( SY426 = SV57 ) ) )
= $true )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(689,plain,
! [SV58: $i] :
( ( ( ~ ( ~ ( totalorderP @ SV58 )
| ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) )
| ( totalorderP @ SV58 ) ) )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(690,plain,
! [SV59: $i,SV118: $i] :
( ( ( ~ ( ssList @ SV118 )
| ! [SY427: $i] :
( ~ ( ssList @ SY427 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SY427 ) )
| ( segmentP @ SV59 @ SY427 ) ) )
= $true )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(691,plain,
( ( ssList @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(692,plain,
( ( ~ ( ssList @ sK4_SY389 )
| ! [SY428: $i] :
( ~ ( ssList @ SY428 )
| ( sK2_SX0 != SY428 )
| ( sK1_U != sK4_SY389 )
| ! [SY429: $i] :
( ~ ( ssList @ SY429 )
| ! [SY430: $i] :
( ~ ( ssList @ SY430 )
| ( ( app @ ( app @ SY429 @ sK4_SY389 ) @ SY430 )
!= SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY429 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY430 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != SY428 ) )
| ( nil != sK4_SY389 ) )
| ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[617]) ).
thf(693,plain,
! [SV60: $i,SV119: $i] :
( ( ( ~ ( ssList @ SV119 )
| ! [SY440: $i] :
( ~ ( ssItem @ SY440 )
| ( ( cons @ SY440 @ ( app @ SV119 @ SV60 ) )
= ( app @ ( cons @ SY440 @ SV119 ) @ SV60 ) ) ) )
= $true )
| ( ( ssList @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(694,plain,
! [SV61: $i,SV120: $i] :
( ( ( ~ ( ssList @ SV120 )
| ! [SY441: $i] :
( ~ ( ssList @ SY441 )
| ( ( app @ SY441 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
| ( SY441 = SV61 ) ) )
= $true )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(695,plain,
! [SV62: $i,SV121: $i] :
( ( ( ~ ( ssItem @ SV121 )
| ! [SY442: $i] :
( ~ ( ssItem @ SY442 )
| ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SY442 ) )
| ( gt @ SV62 @ SY442 ) ) )
= $true )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(696,plain,
! [SV63: $i,SV122: $i] :
( ( ( ~ ( ssList @ SV122 )
| ~ ( ~ ( ( nil
!= ( app @ SV63 @ SV122 ) )
| ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SV122 ) ) ) ) )
= $true )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(697,plain,
! [SV65: $i,SV123: $i] :
( ( ( ~ ( ssItem @ SV123 )
| ( ( tl @ ( cons @ SV123 @ SV65 ) )
= SV65 ) )
= $true )
| ( ( ssList @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(698,plain,
! [SV66: $i,SV124: $i] :
( ( ( ~ ( ssItem @ SV124 )
| ( ( cons @ SV124 @ SV66 )
!= SV66 ) )
= $true )
| ( ( ssList @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(699,plain,
! [SV67: $i,SV125: $i] :
( ( ( ~ ( ssList @ SV125 )
| ~ ~ ( ~ ( segmentP @ SV67 @ SV125 )
| ~ ( segmentP @ SV125 @ SV67 ) )
| ( SV67 = SV125 ) )
= $true )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(700,plain,
! [SV68: $i,SV126: $i] :
( ( ( ~ ( ssItem @ SV126 )
| ! [SY443: $i] :
( ~ ( ssList @ SY443 )
| ! [SY444: $i] :
( ~ ( ssList @ SY444 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SY443 ) @ ( cons @ SV126 @ SY444 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SY443 @ SY444 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SY443 @ SY444 ) )
| ( frontsegP @ ( cons @ SV68 @ SY443 ) @ ( cons @ SV126 @ SY444 ) ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(701,plain,
! [SV69: $i,SV127: $i] :
( ( ( ~ ( ssList @ SV127 )
| ~ ( ~ ( ~ ( neq @ SV69 @ SV127 )
| ( SV69 != SV127 ) )
| ~ ( ~ ( ( SV69 != SV127 ) )
| ( neq @ SV69 @ SV127 ) ) ) )
= $true )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(702,plain,
! [SV70: $i,SV128: $i] :
( ( ( ~ ( ssItem @ SV128 )
| ~ ( leq @ SV70 @ SV128 )
| ( SV70 = SV128 )
| ( lt @ SV70 @ SV128 ) )
= $true )
| ( ( ssItem @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(703,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ssList @ SV129 )
| ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
| ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ~ ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) ) ) )
= $true )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(704,plain,
( ( ~ ( ssItem @ sK3_SX0 )
| ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( ssItem @ SY402 )
| ~ ( ( sK3_SX0 != SY402 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(705,plain,
! [SV73: $i,SV130: $i] :
( ( ( ~ ( ssItem @ SV130 )
| ~ ~ ( ~ ( leq @ SV73 @ SV130 )
| ~ ( leq @ SV130 @ SV73 ) )
| ( SV73 = SV130 ) )
= $true )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(706,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ( equalelemsP @ SV74 )
| ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
| ~ ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) )
| ( equalelemsP @ SV74 ) ) )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(707,plain,
! [SV75: $i,SV131: $i] :
( ( ( ~ ( ssList @ SV131 )
| ! [SY445: $i] :
( ~ ( ssList @ SY445 )
| ( ( app @ ( app @ SV75 @ SV131 ) @ SY445 )
= ( app @ SV75 @ ( app @ SV131 @ SY445 ) ) ) ) )
= $true )
| ( ( ssList @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(708,plain,
! [SV76: $i,SV132: $i] :
( ( ( ~ ( ssList @ SV132 )
| ! [SY446: $i] :
( ~ ( ssList @ SY446 )
| ~ ( rearsegP @ SV76 @ SV132 )
| ( rearsegP @ ( app @ SY446 @ SV76 ) @ SV132 ) ) )
= $true )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(709,plain,
! [SV77: $i,SV133: $i] :
( ( ( ~ ( ssList @ SV133 )
| ! [SY447: $i] :
( ~ ( ssList @ SY447 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SY447 ) )
| ( frontsegP @ SV77 @ SY447 ) ) )
= $true )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(710,plain,
! [SV78: $i,SV134: $i] :
( ( ( ~ ( ssItem @ SV134 )
| ! [SY448: $i] :
( ~ ( ssItem @ SY448 )
| ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SY448 ) )
| ( lt @ SV78 @ SY448 ) ) )
= $true )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(711,plain,
! [SV81: $i] :
( ( ( memberP @ nil @ SV81 )
= $false )
| ( ( ssItem @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(712,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ( cyclefreeP @ SV82 )
| ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) )
| ( cyclefreeP @ SV82 ) ) )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(713,plain,
! [SV83: $i] :
( ( ( ~ ( ( nil != SV83 ) ) )
= $true )
| ( ( ssList @ ( tl @ SV83 ) )
= $true )
| ( ( ssList @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(714,plain,
! [SV84: $i] :
( ( ( ~ ( ( nil != SV84 ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(715,plain,
! [SV85: $i] :
( ( ( ~ ( ( nil != SV85 ) ) )
= $true )
| ( ( ssItem @ ( hd @ SV85 ) )
= $true )
| ( ( ssList @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(716,plain,
! [SV1: $i,SV86: $i] :
( ( ( ~ ( ssList @ SV86 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV1 @ SV86 )
| ~ ( frontsegP @ SV86 @ SV1 ) )
| ( SV1 = SV86 ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(717,plain,
! [SV3: $i,SV87: $i] :
( ( ( ~ ( ssItem @ SV87 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( lt @ SV3 @ SV87 )
| ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
| ( lt @ SV3 @ SV87 ) ) ) )
= $true )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(718,plain,
! [SV4: $i,SV88: $i] :
( ( ( ~ ( ssItem @ SV88 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( gt @ SV4 @ SV88 )
| ( lt @ SV88 @ SV4 ) )
| ~ ( ~ ( lt @ SV88 @ SV4 )
| ( gt @ SV4 @ SV88 ) ) ) )
= $true )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(719,plain,
! [SV5: $i,SV89: $i] :
( ( ( ~ ( ssItem @ SV89 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV5 @ SV89 )
| ( SV5 != SV89 ) )
| ~ ( ~ ( ( SV5 != SV89 ) )
| ( neq @ SV5 @ SV89 ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(720,plain,
! [SV8: $i,SV90: $i] :
( ( ( ~ ( ssList @ SV90 ) )
= $true )
| ( ( ~ ( ( nil != SV8 ) )
| ( ( hd @ ( app @ SV8 @ SV90 ) )
= ( hd @ SV8 ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(721,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ssList @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
| ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ~ ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) ) ) )
= $true )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(722,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV11 )
| ( nil = SV11 ) ) )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(723,plain,
! [SV11: $i] :
( ( ( ~ ( ( nil != SV11 )
| ( segmentP @ nil @ SV11 ) ) )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(724,plain,
! [SV12: $i,SV92: $i] :
( ( ( ~ ( ssItem @ SV92 ) )
= $true )
| ( ( ( cons @ SV92 @ SV12 )
= ( app @ ( cons @ SV92 @ nil ) @ SV12 ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(725,plain,
! [SV13: $i,SV93: $i] :
( ( ( ~ ( ssList @ SV93 ) )
= $true )
| ( ( ssList @ ( app @ SV13 @ SV93 ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(726,plain,
! [SV15: $i,SV94: $i] :
( ( ( ~ ( ssItem @ SV94 ) )
= $true )
| ( ( ( hd @ ( cons @ SV94 @ SV15 ) )
= SV94 )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(727,plain,
! [SV16: $i,SV95: $i] :
( ( ( ~ ( ssList @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ SV16 @ SV95 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SV95 ) ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(728,plain,
! [SV17: $i,SV96: $i] :
( ( ( ~ ( ssItem @ SV96 ) )
= $true )
| ( ( ! [SY405: $i] :
( ~ ( ssItem @ SY405 )
| ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SY405 ) )
| ( lt @ SV17 @ SY405 ) ) )
= $true )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(729,plain,
! [SV18: $i,SV97: $i] :
( ( ( ~ ( ssList @ SV97 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ SV18 @ SV97 )
| ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV97 ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(730,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( singletonP @ SV19 )
| ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) ) )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(731,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) )
| ( singletonP @ SV19 ) ) )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(732,plain,
! [SV20: $i,SV98: $i] :
( ( ( ~ ( ssItem @ SV98 ) )
= $true )
| ( ( ~ ~ ( ~ ( geq @ SV20 @ SV98 )
| ~ ( geq @ SV98 @ SV20 ) )
| ( SV20 = SV98 ) )
= $true )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(733,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ( ssItem @ SV99 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ SV21 @ SV99 )
| ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SV99 ) ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(734,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( strictorderP @ SV22 )
| ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(735,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) )
| ( strictorderP @ SV22 ) ) )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(736,plain,
! [SV24: $i,SV100: $i] :
( ( ( ~ ( ssList @ SV100 ) )
= $true )
| ( ( ! [SY412: $i] :
( ~ ( ssList @ SY412 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV100 @ SY412 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SY412 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SY412 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SY412 ) @ SV24 ) ) ) ) )
= $true )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(737,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ssList @ SV101 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SV101 )
!= ( tl @ SV26 ) ) )
| ( SV101 = SV26 ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(738,plain,
! [SV27: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV27 )
| ( nil = SV27 ) ) )
= $false )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(739,plain,
! [SV27: $i] :
( ( ( ~ ( ( nil != SV27 )
| ( frontsegP @ nil @ SV27 ) ) )
= $false )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(740,plain,
! [SV28: $i,SV102: $i] :
( ( ( ~ ( ssList @ SV102 ) )
= $true )
| ( ( ! [SY413: $i] :
( ~ ( ssList @ SY413 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SY413 ) )
| ( rearsegP @ SV28 @ SY413 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(741,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( totalorderedP @ SV29 )
| ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(742,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) )
| ( totalorderedP @ SV29 ) ) )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(743,plain,
! [SV31: $i,SV103: $i] :
( ( ( ~ ( ssItem @ SV103 ) )
= $true )
| ( ( ! [SY414: $i] :
( ~ ( ssItem @ SY414 )
| ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SY414 ) )
| ( leq @ SV31 @ SY414 ) ) )
= $true )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(744,plain,
! [SV33: $i,SV104: $i] :
( ( ( ~ ( ssItem @ SV104 ) )
= $true )
| ( ( ssList @ ( cons @ SV104 @ SV33 ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(745,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ( ssList @ SV105 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV34 @ SV105 )
| ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SV105 ) ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(746,plain,
! [SV35: $i,SV106: $i] :
( ( ( ~ ( ssList @ SV106 ) )
= $true )
| ( ( ! [SY419: $i] :
( ~ ( ssItem @ SY419 )
| ! [SY420: $i] :
( ~ ( ssItem @ SY420 )
| ( ( cons @ SY419 @ SV35 )
!= ( cons @ SY420 @ SV106 ) )
| ~ ( ( SY419 != SY420 )
| ( SV106 != SV35 ) ) ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(747,plain,
! [SV36: $i] :
( ( ( nil != SV36 )
= $false )
| ( ( ( cons @ ( hd @ SV36 ) @ ( tl @ SV36 ) )
= SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(748,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( ssItem @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( geq @ SV39 @ SV107 )
| ( leq @ SV107 @ SV39 ) )
| ~ ( ~ ( leq @ SV107 @ SV39 )
| ( geq @ SV39 @ SV107 ) ) ) )
= $true )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(749,plain,
! [SV40: $i,SV108: $i] :
( ( ( ~ ( ssList @ SV108 ) )
= $true )
| ( ( ! [SY421: $i] :
( ~ ( ssList @ SY421 )
| ! [SY422: $i] :
( ~ ( ssList @ SY422 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SY421 @ SV40 ) @ SY422 ) @ SV108 ) ) ) )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(750,plain,
! [SV41: $i,SV109: $i] :
( ( ( ~ ( ssList @ SV109 ) )
= $true )
| ( ( ~ ( ( nil != SV41 ) )
| ( ( tl @ ( app @ SV41 @ SV109 ) )
= ( app @ ( tl @ SV41 ) @ SV109 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(751,plain,
! [SV43: $i,SV110: $i] :
( ( ( ~ ( ssItem @ SV110 ) )
= $true )
| ( ( ~ ( lt @ SV43 @ SV110 )
| ~ ( lt @ SV110 @ SV43 ) )
= $true )
| ( ( ssItem @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(752,plain,
! [SV44: $i,SV111: $i] :
( ( ( ~ ( ssItem @ SV111 ) )
= $true )
| ( ( nil
!= ( cons @ SV111 @ SV44 ) )
= $true )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(753,plain,
! [SV45: $i,SV112: $i] :
( ( ( ~ ( ssList @ SV112 ) )
= $true )
| ( ( ! [SY423: $i] :
( ~ ( ssList @ SY423 )
| ~ ( frontsegP @ SV45 @ SV112 )
| ( frontsegP @ ( app @ SV45 @ SY423 ) @ SV112 ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(754,plain,
! [SV46: $i,SV113: $i] :
( ( ( ~ ( ssItem @ SV113 ) )
= $true )
| ( ( ! [SY424: $i] :
( ~ ( ssList @ SY424 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SY424 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SY424 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SY424 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SY424 ) @ SV46 ) ) ) ) )
= $true )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(755,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( duplicatefreeP @ SV48 )
| ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(756,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) )
| ( duplicatefreeP @ SV48 ) ) )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(757,plain,
! [SV49: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV49 )
| ( nil = SV49 ) ) )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(758,plain,
! [SV49: $i] :
( ( ( ~ ( ( nil != SV49 )
| ( rearsegP @ nil @ SV49 ) ) )
= $false )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(759,plain,
! [SV50: $i,SV114: $i] :
( ( ( ~ ( ssList @ SV114 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV50 @ SV114 )
| ~ ( rearsegP @ SV114 @ SV50 ) )
| ( SV50 = SV114 ) )
= $true )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(760,plain,
! [SV51: $i] :
( ( ( nil != SV51 )
= $false )
| ( ( ~ ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(761,plain,
! [SV52: $i,SV115: $i] :
( ( ( ~ ( ssItem @ SV115 ) )
= $true )
| ( ( ! [SY425: $i] :
( ~ ( ssItem @ SY425 )
| ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SY425 ) )
| ( geq @ SV52 @ SY425 ) ) )
= $true )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(762,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ( strictorderedP @ SV53 )
| ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(763,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) )
| ( strictorderedP @ SV53 ) ) )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(764,plain,
! [SV55: $i] :
( ( ( ! [SY328: $i] :
~ ~ ( ~ ( ssList @ SY328 )
| ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( ssItem @ SY329 )
| ( ( cons @ SY329 @ SY328 )
!= SV55 ) ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(765,plain,
! [SV56: $i,SV116: $i] :
( ( ( ~ ( ssItem @ SV116 ) )
= $true )
| ( ( ~ ( gt @ SV56 @ SV116 )
| ~ ( gt @ SV116 @ SV56 ) )
= $true )
| ( ( ssItem @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(766,plain,
! [SV57: $i,SV117: $i] :
( ( ( ~ ( ssList @ SV117 ) )
= $true )
| ( ( ! [SY426: $i] :
( ~ ( ssList @ SY426 )
| ( ( app @ SV117 @ SY426 )
!= ( app @ SV117 @ SV57 ) )
| ( SY426 = SV57 ) ) )
= $true )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(767,plain,
! [SV58: $i] :
( ( ( ~ ( ~ ( totalorderP @ SV58 )
| ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(768,plain,
! [SV58: $i] :
( ( ( ~ ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) )
| ( totalorderP @ SV58 ) ) )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(769,plain,
! [SV59: $i,SV118: $i] :
( ( ( ~ ( ssList @ SV118 ) )
= $true )
| ( ( ! [SY427: $i] :
( ~ ( ssList @ SY427 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SY427 ) )
| ( segmentP @ SV59 @ SY427 ) ) )
= $true )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(770,plain,
( ( ~ ( ssList @ sK4_SY389 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(771,plain,
( ( ! [SY428: $i] :
( ~ ( ssList @ SY428 )
| ( sK2_SX0 != SY428 )
| ( sK1_U != sK4_SY389 )
| ! [SY429: $i] :
( ~ ( ssList @ SY429 )
| ! [SY430: $i] :
( ~ ( ssList @ SY430 )
| ( ( app @ ( app @ SY429 @ sK4_SY389 ) @ SY430 )
!= SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY429 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY430 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != SY428 ) )
| ( nil != sK4_SY389 ) )
| ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(772,plain,
! [SV60: $i,SV119: $i] :
( ( ( ~ ( ssList @ SV119 ) )
= $true )
| ( ( ! [SY440: $i] :
( ~ ( ssItem @ SY440 )
| ( ( cons @ SY440 @ ( app @ SV119 @ SV60 ) )
= ( app @ ( cons @ SY440 @ SV119 ) @ SV60 ) ) ) )
= $true )
| ( ( ssList @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(773,plain,
! [SV61: $i,SV120: $i] :
( ( ( ~ ( ssList @ SV120 ) )
= $true )
| ( ( ! [SY441: $i] :
( ~ ( ssList @ SY441 )
| ( ( app @ SY441 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
| ( SY441 = SV61 ) ) )
= $true )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(774,plain,
! [SV62: $i,SV121: $i] :
( ( ( ~ ( ssItem @ SV121 ) )
= $true )
| ( ( ! [SY442: $i] :
( ~ ( ssItem @ SY442 )
| ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SY442 ) )
| ( gt @ SV62 @ SY442 ) ) )
= $true )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(775,plain,
! [SV63: $i,SV122: $i] :
( ( ( ~ ( ssList @ SV122 ) )
= $true )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV63 @ SV122 ) )
| ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SV122 ) ) ) ) )
= $true )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(776,plain,
! [SV65: $i,SV123: $i] :
( ( ( ~ ( ssItem @ SV123 ) )
= $true )
| ( ( ( tl @ ( cons @ SV123 @ SV65 ) )
= SV65 )
= $true )
| ( ( ssList @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(777,plain,
! [SV66: $i,SV124: $i] :
( ( ( ~ ( ssItem @ SV124 ) )
= $true )
| ( ( ( cons @ SV124 @ SV66 )
!= SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(778,plain,
! [SV67: $i,SV125: $i] :
( ( ( ~ ( ssList @ SV125 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV67 @ SV125 )
| ~ ( segmentP @ SV125 @ SV67 ) )
| ( SV67 = SV125 ) )
= $true )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(779,plain,
! [SV68: $i,SV126: $i] :
( ( ( ~ ( ssItem @ SV126 ) )
= $true )
| ( ( ! [SY443: $i] :
( ~ ( ssList @ SY443 )
| ! [SY444: $i] :
( ~ ( ssList @ SY444 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SY443 ) @ ( cons @ SV126 @ SY444 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SY443 @ SY444 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SY443 @ SY444 ) )
| ( frontsegP @ ( cons @ SV68 @ SY443 ) @ ( cons @ SV126 @ SY444 ) ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(780,plain,
! [SV69: $i,SV127: $i] :
( ( ( ~ ( ssList @ SV127 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV69 @ SV127 )
| ( SV69 != SV127 ) )
| ~ ( ~ ( ( SV69 != SV127 ) )
| ( neq @ SV69 @ SV127 ) ) ) )
= $true )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(781,plain,
! [SV70: $i,SV128: $i] :
( ( ( ~ ( ssItem @ SV128 ) )
= $true )
| ( ( ~ ( leq @ SV70 @ SV128 )
| ( SV70 = SV128 )
| ( lt @ SV70 @ SV128 ) )
= $true )
| ( ( ssItem @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(782,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ssList @ SV129 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
| ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ~ ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) ) ) )
= $true )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(783,plain,
( ( ~ ( ssItem @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(784,plain,
( ( ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( ssItem @ SY402 )
| ~ ( ( sK3_SX0 != SY402 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(785,plain,
! [SV73: $i,SV130: $i] :
( ( ( ~ ( ssItem @ SV130 ) )
= $true )
| ( ( ~ ~ ( ~ ( leq @ SV73 @ SV130 )
| ~ ( leq @ SV130 @ SV73 ) )
| ( SV73 = SV130 ) )
= $true )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(786,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ( equalelemsP @ SV74 )
| ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(787,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) )
| ( equalelemsP @ SV74 ) ) )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(788,plain,
! [SV75: $i,SV131: $i] :
( ( ( ~ ( ssList @ SV131 ) )
= $true )
| ( ( ! [SY445: $i] :
( ~ ( ssList @ SY445 )
| ( ( app @ ( app @ SV75 @ SV131 ) @ SY445 )
= ( app @ SV75 @ ( app @ SV131 @ SY445 ) ) ) ) )
= $true )
| ( ( ssList @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(789,plain,
! [SV76: $i,SV132: $i] :
( ( ( ~ ( ssList @ SV132 ) )
= $true )
| ( ( ! [SY446: $i] :
( ~ ( ssList @ SY446 )
| ~ ( rearsegP @ SV76 @ SV132 )
| ( rearsegP @ ( app @ SY446 @ SV76 ) @ SV132 ) ) )
= $true )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(790,plain,
! [SV77: $i,SV133: $i] :
( ( ( ~ ( ssList @ SV133 ) )
= $true )
| ( ( ! [SY447: $i] :
( ~ ( ssList @ SY447 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SY447 ) )
| ( frontsegP @ SV77 @ SY447 ) ) )
= $true )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(791,plain,
! [SV78: $i,SV134: $i] :
( ( ( ~ ( ssItem @ SV134 ) )
= $true )
| ( ( ! [SY448: $i] :
( ~ ( ssItem @ SY448 )
| ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SY448 ) )
| ( lt @ SV78 @ SY448 ) ) )
= $true )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(792,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ( cyclefreeP @ SV82 )
| ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(793,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) )
| ( cyclefreeP @ SV82 ) ) )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(794,plain,
! [SV83: $i] :
( ( ( nil != SV83 )
= $false )
| ( ( ssList @ ( tl @ SV83 ) )
= $true )
| ( ( ssList @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(795,plain,
! [SV84: $i] :
( ( ( nil != SV84 )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(796,plain,
! [SV85: $i] :
( ( ( nil != SV85 )
= $false )
| ( ( ssItem @ ( hd @ SV85 ) )
= $true )
| ( ( ssList @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(797,plain,
! [SV1: $i,SV86: $i] :
( ( ( ssList @ SV86 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV1 @ SV86 )
| ~ ( frontsegP @ SV86 @ SV1 ) )
| ( SV1 = SV86 ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(798,plain,
! [SV3: $i,SV87: $i] :
( ( ( ssItem @ SV87 )
= $false )
| ( ( ~ ( ~ ( ~ ( lt @ SV3 @ SV87 )
| ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
| ( lt @ SV3 @ SV87 ) ) ) )
= $true )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(799,plain,
! [SV4: $i,SV88: $i] :
( ( ( ssItem @ SV88 )
= $false )
| ( ( ~ ( ~ ( ~ ( gt @ SV4 @ SV88 )
| ( lt @ SV88 @ SV4 ) )
| ~ ( ~ ( lt @ SV88 @ SV4 )
| ( gt @ SV4 @ SV88 ) ) ) )
= $true )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(800,plain,
! [SV5: $i,SV89: $i] :
( ( ( ssItem @ SV89 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV5 @ SV89 )
| ( SV5 != SV89 ) )
| ~ ( ~ ( ( SV5 != SV89 ) )
| ( neq @ SV5 @ SV89 ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(801,plain,
! [SV8: $i,SV90: $i] :
( ( ( ssList @ SV90 )
= $false )
| ( ( ~ ( ( nil != SV8 ) )
| ( ( hd @ ( app @ SV8 @ SV90 ) )
= ( hd @ SV8 ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(802,plain,
! [SV10: $i,SV91: $i] :
( ( ( ssList @ SV91 )
= $false )
| ( ( ~ ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
| ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ~ ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) ) ) )
= $true )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(803,plain,
! [SV11: $i] :
( ( ( ~ ( segmentP @ nil @ SV11 )
| ( nil = SV11 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(804,plain,
! [SV11: $i] :
( ( ( ( nil != SV11 )
| ( segmentP @ nil @ SV11 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(805,plain,
! [SV12: $i,SV92: $i] :
( ( ( ssItem @ SV92 )
= $false )
| ( ( ( cons @ SV92 @ SV12 )
= ( app @ ( cons @ SV92 @ nil ) @ SV12 ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(806,plain,
! [SV13: $i,SV93: $i] :
( ( ( ssList @ SV93 )
= $false )
| ( ( ssList @ ( app @ SV13 @ SV93 ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(807,plain,
! [SV15: $i,SV94: $i] :
( ( ( ssItem @ SV94 )
= $false )
| ( ( ( hd @ ( cons @ SV94 @ SV15 ) )
= SV94 )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(808,plain,
! [SV16: $i,SV95: $i] :
( ( ( ssList @ SV95 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ SV16 @ SV95 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SV95 ) ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(809,plain,
! [SV17: $i,SV96: $i] :
( ( ( ssItem @ SV96 )
= $false )
| ( ( ! [SY405: $i] :
( ~ ( ssItem @ SY405 )
| ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SY405 ) )
| ( lt @ SV17 @ SY405 ) ) )
= $true )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(810,plain,
! [SV18: $i,SV97: $i] :
( ( ( ssList @ SV97 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ SV18 @ SV97 )
| ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV97 ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(811,plain,
! [SV19: $i] :
( ( ( ~ ( singletonP @ SV19 )
| ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(812,plain,
! [SV19: $i] :
( ( ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) )
| ( singletonP @ SV19 ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(813,plain,
! [SV20: $i,SV98: $i] :
( ( ( ssItem @ SV98 )
= $false )
| ( ( ~ ~ ( ~ ( geq @ SV20 @ SV98 )
| ~ ( geq @ SV98 @ SV20 ) )
| ( SV20 = SV98 ) )
= $true )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(814,plain,
! [SV21: $i,SV99: $i] :
( ( ( ssItem @ SV99 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ SV21 @ SV99 )
| ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SV99 ) ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(815,plain,
! [SV22: $i] :
( ( ( ~ ( strictorderP @ SV22 )
| ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(816,plain,
! [SV22: $i] :
( ( ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) )
| ( strictorderP @ SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(817,plain,
! [SV24: $i,SV100: $i] :
( ( ( ssList @ SV100 )
= $false )
| ( ( ! [SY412: $i] :
( ~ ( ssList @ SY412 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV100 @ SY412 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SY412 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SY412 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SY412 ) @ SV24 ) ) ) ) )
= $true )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(818,plain,
! [SV26: $i,SV101: $i] :
( ( ( ssList @ SV101 )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SV101 )
!= ( tl @ SV26 ) ) )
| ( SV101 = SV26 ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(819,plain,
! [SV27: $i] :
( ( ( ~ ( frontsegP @ nil @ SV27 )
| ( nil = SV27 ) )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(820,plain,
! [SV27: $i] :
( ( ( ( nil != SV27 )
| ( frontsegP @ nil @ SV27 ) )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(821,plain,
! [SV28: $i,SV102: $i] :
( ( ( ssList @ SV102 )
= $false )
| ( ( ! [SY413: $i] :
( ~ ( ssList @ SY413 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SY413 ) )
| ( rearsegP @ SV28 @ SY413 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(822,plain,
! [SV29: $i] :
( ( ( ~ ( totalorderedP @ SV29 )
| ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(823,plain,
! [SV29: $i] :
( ( ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) )
| ( totalorderedP @ SV29 ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(824,plain,
! [SV31: $i,SV103: $i] :
( ( ( ssItem @ SV103 )
= $false )
| ( ( ! [SY414: $i] :
( ~ ( ssItem @ SY414 )
| ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SY414 ) )
| ( leq @ SV31 @ SY414 ) ) )
= $true )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(825,plain,
! [SV33: $i,SV104: $i] :
( ( ( ssItem @ SV104 )
= $false )
| ( ( ssList @ ( cons @ SV104 @ SV33 ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(826,plain,
! [SV34: $i,SV105: $i] :
( ( ( ssList @ SV105 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV34 @ SV105 )
| ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SV105 ) ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(827,plain,
! [SV35: $i,SV106: $i] :
( ( ( ssList @ SV106 )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( ssItem @ SY419 )
| ! [SY420: $i] :
( ~ ( ssItem @ SY420 )
| ( ( cons @ SY419 @ SV35 )
!= ( cons @ SY420 @ SV106 ) )
| ~ ( ( SY419 != SY420 )
| ( SV106 != SV35 ) ) ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(828,plain,
! [SV36: $i] :
( ( ( nil = SV36 )
= $true )
| ( ( ( cons @ ( hd @ SV36 ) @ ( tl @ SV36 ) )
= SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(829,plain,
! [SV39: $i,SV107: $i] :
( ( ( ssItem @ SV107 )
= $false )
| ( ( ~ ( ~ ( ~ ( geq @ SV39 @ SV107 )
| ( leq @ SV107 @ SV39 ) )
| ~ ( ~ ( leq @ SV107 @ SV39 )
| ( geq @ SV39 @ SV107 ) ) ) )
= $true )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(830,plain,
! [SV40: $i,SV108: $i] :
( ( ( ssList @ SV108 )
= $false )
| ( ( ! [SY421: $i] :
( ~ ( ssList @ SY421 )
| ! [SY422: $i] :
( ~ ( ssList @ SY422 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SY421 @ SV40 ) @ SY422 ) @ SV108 ) ) ) )
= $true )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(831,plain,
! [SV41: $i,SV109: $i] :
( ( ( ssList @ SV109 )
= $false )
| ( ( ~ ( ( nil != SV41 ) )
| ( ( tl @ ( app @ SV41 @ SV109 ) )
= ( app @ ( tl @ SV41 ) @ SV109 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(832,plain,
! [SV43: $i,SV110: $i] :
( ( ( ssItem @ SV110 )
= $false )
| ( ( ~ ( lt @ SV43 @ SV110 )
| ~ ( lt @ SV110 @ SV43 ) )
= $true )
| ( ( ssItem @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(833,plain,
! [SV44: $i,SV111: $i] :
( ( ( ssItem @ SV111 )
= $false )
| ( ( nil
!= ( cons @ SV111 @ SV44 ) )
= $true )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(834,plain,
! [SV45: $i,SV112: $i] :
( ( ( ssList @ SV112 )
= $false )
| ( ( ! [SY423: $i] :
( ~ ( ssList @ SY423 )
| ~ ( frontsegP @ SV45 @ SV112 )
| ( frontsegP @ ( app @ SV45 @ SY423 ) @ SV112 ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(835,plain,
! [SV46: $i,SV113: $i] :
( ( ( ssItem @ SV113 )
= $false )
| ( ( ! [SY424: $i] :
( ~ ( ssList @ SY424 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SY424 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SY424 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SY424 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SY424 ) @ SV46 ) ) ) ) )
= $true )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(836,plain,
! [SV48: $i] :
( ( ( ~ ( duplicatefreeP @ SV48 )
| ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(837,plain,
! [SV48: $i] :
( ( ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) )
| ( duplicatefreeP @ SV48 ) )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(838,plain,
! [SV49: $i] :
( ( ( ~ ( rearsegP @ nil @ SV49 )
| ( nil = SV49 ) )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(839,plain,
! [SV49: $i] :
( ( ( ( nil != SV49 )
| ( rearsegP @ nil @ SV49 ) )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(840,plain,
! [SV50: $i,SV114: $i] :
( ( ( ssList @ SV114 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV50 @ SV114 )
| ~ ( rearsegP @ SV114 @ SV50 ) )
| ( SV50 = SV114 ) )
= $true )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(841,plain,
! [SV51: $i] :
( ( ( nil = SV51 )
= $true )
| ( ( ~ ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(842,plain,
! [SV52: $i,SV115: $i] :
( ( ( ssItem @ SV115 )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( ssItem @ SY425 )
| ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SY425 ) )
| ( geq @ SV52 @ SY425 ) ) )
= $true )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(843,plain,
! [SV53: $i] :
( ( ( ~ ( strictorderedP @ SV53 )
| ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(844,plain,
! [SV53: $i] :
( ( ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) )
| ( strictorderedP @ SV53 ) )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(845,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK5_SY328 @ SV55 ) )
| ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( ssItem @ SY449 )
| ( ( cons @ SY449 @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[764]) ).
thf(846,plain,
! [SV56: $i,SV116: $i] :
( ( ( ssItem @ SV116 )
= $false )
| ( ( ~ ( gt @ SV56 @ SV116 )
| ~ ( gt @ SV116 @ SV56 ) )
= $true )
| ( ( ssItem @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(847,plain,
! [SV57: $i,SV117: $i] :
( ( ( ssList @ SV117 )
= $false )
| ( ( ! [SY426: $i] :
( ~ ( ssList @ SY426 )
| ( ( app @ SV117 @ SY426 )
!= ( app @ SV117 @ SV57 ) )
| ( SY426 = SV57 ) ) )
= $true )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(848,plain,
! [SV58: $i] :
( ( ( ~ ( totalorderP @ SV58 )
| ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(849,plain,
! [SV58: $i] :
( ( ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) )
| ( totalorderP @ SV58 ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(850,plain,
! [SV59: $i,SV118: $i] :
( ( ( ssList @ SV118 )
= $false )
| ( ( ! [SY427: $i] :
( ~ ( ssList @ SY427 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SY427 ) )
| ( segmentP @ SV59 @ SY427 ) ) )
= $true )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(851,plain,
( ( ssList @ sK4_SY389 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(852,plain,
( ( ~ ( ssList @ sK6_SY428 )
| ( sK2_SX0 != sK6_SY428 )
| ( sK1_U != sK4_SY389 )
| ! [SY450: $i] :
( ~ ( ssList @ SY450 )
| ! [SY451: $i] :
( ~ ( ssList @ SY451 )
| ( ( app @ ( app @ SY450 @ sK4_SY389 ) @ SY451 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY451 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != sK6_SY428 ) )
| ( nil != sK4_SY389 ) )
| ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[771]) ).
thf(853,plain,
! [SV60: $i,SV119: $i] :
( ( ( ssList @ SV119 )
= $false )
| ( ( ! [SY440: $i] :
( ~ ( ssItem @ SY440 )
| ( ( cons @ SY440 @ ( app @ SV119 @ SV60 ) )
= ( app @ ( cons @ SY440 @ SV119 ) @ SV60 ) ) ) )
= $true )
| ( ( ssList @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(854,plain,
! [SV61: $i,SV120: $i] :
( ( ( ssList @ SV120 )
= $false )
| ( ( ! [SY441: $i] :
( ~ ( ssList @ SY441 )
| ( ( app @ SY441 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
| ( SY441 = SV61 ) ) )
= $true )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(855,plain,
! [SV62: $i,SV121: $i] :
( ( ( ssItem @ SV121 )
= $false )
| ( ( ! [SY442: $i] :
( ~ ( ssItem @ SY442 )
| ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SY442 ) )
| ( gt @ SV62 @ SY442 ) ) )
= $true )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(856,plain,
! [SV63: $i,SV122: $i] :
( ( ( ssList @ SV122 )
= $false )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV63 @ SV122 ) )
| ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SV122 ) ) ) ) )
= $true )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(857,plain,
! [SV65: $i,SV123: $i] :
( ( ( ssItem @ SV123 )
= $false )
| ( ( ( tl @ ( cons @ SV123 @ SV65 ) )
= SV65 )
= $true )
| ( ( ssList @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(858,plain,
! [SV66: $i,SV124: $i] :
( ( ( ssItem @ SV124 )
= $false )
| ( ( ( cons @ SV124 @ SV66 )
!= SV66 )
= $true )
| ( ( ssList @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(859,plain,
! [SV67: $i,SV125: $i] :
( ( ( ssList @ SV125 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV67 @ SV125 )
| ~ ( segmentP @ SV125 @ SV67 ) )
| ( SV67 = SV125 ) )
= $true )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(860,plain,
! [SV68: $i,SV126: $i] :
( ( ( ssItem @ SV126 )
= $false )
| ( ( ! [SY443: $i] :
( ~ ( ssList @ SY443 )
| ! [SY444: $i] :
( ~ ( ssList @ SY444 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SY443 ) @ ( cons @ SV126 @ SY444 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SY443 @ SY444 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SY443 @ SY444 ) )
| ( frontsegP @ ( cons @ SV68 @ SY443 ) @ ( cons @ SV126 @ SY444 ) ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(861,plain,
! [SV69: $i,SV127: $i] :
( ( ( ssList @ SV127 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV69 @ SV127 )
| ( SV69 != SV127 ) )
| ~ ( ~ ( ( SV69 != SV127 ) )
| ( neq @ SV69 @ SV127 ) ) ) )
= $true )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(862,plain,
! [SV70: $i,SV128: $i] :
( ( ( ssItem @ SV128 )
= $false )
| ( ( ~ ( leq @ SV70 @ SV128 )
| ( SV70 = SV128 )
| ( lt @ SV70 @ SV128 ) )
= $true )
| ( ( ssItem @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(863,plain,
! [SV72: $i,SV129: $i] :
( ( ( ssList @ SV129 )
= $false )
| ( ( ~ ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
| ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ~ ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) ) ) )
= $true )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(864,plain,
( ( ssItem @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(865,plain,
( ( ~ ! [SY402: $i] :
~ ~ ( ~ ( ssItem @ SY402 )
| ~ ( ( sK3_SX0 != SY402 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(866,plain,
! [SV73: $i,SV130: $i] :
( ( ( ssItem @ SV130 )
= $false )
| ( ( ~ ~ ( ~ ( leq @ SV73 @ SV130 )
| ~ ( leq @ SV130 @ SV73 ) )
| ( SV73 = SV130 ) )
= $true )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(867,plain,
! [SV74: $i] :
( ( ( ~ ( equalelemsP @ SV74 )
| ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(868,plain,
! [SV74: $i] :
( ( ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) )
| ( equalelemsP @ SV74 ) )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(869,plain,
! [SV75: $i,SV131: $i] :
( ( ( ssList @ SV131 )
= $false )
| ( ( ! [SY445: $i] :
( ~ ( ssList @ SY445 )
| ( ( app @ ( app @ SV75 @ SV131 ) @ SY445 )
= ( app @ SV75 @ ( app @ SV131 @ SY445 ) ) ) ) )
= $true )
| ( ( ssList @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(870,plain,
! [SV76: $i,SV132: $i] :
( ( ( ssList @ SV132 )
= $false )
| ( ( ! [SY446: $i] :
( ~ ( ssList @ SY446 )
| ~ ( rearsegP @ SV76 @ SV132 )
| ( rearsegP @ ( app @ SY446 @ SV76 ) @ SV132 ) ) )
= $true )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(871,plain,
! [SV77: $i,SV133: $i] :
( ( ( ssList @ SV133 )
= $false )
| ( ( ! [SY447: $i] :
( ~ ( ssList @ SY447 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SY447 ) )
| ( frontsegP @ SV77 @ SY447 ) ) )
= $true )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(872,plain,
! [SV78: $i,SV134: $i] :
( ( ( ssItem @ SV134 )
= $false )
| ( ( ! [SY448: $i] :
( ~ ( ssItem @ SY448 )
| ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SY448 ) )
| ( lt @ SV78 @ SY448 ) ) )
= $true )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(873,plain,
! [SV82: $i] :
( ( ( ~ ( cyclefreeP @ SV82 )
| ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(874,plain,
! [SV82: $i] :
( ( ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) )
| ( cyclefreeP @ SV82 ) )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(875,plain,
! [SV83: $i] :
( ( ( nil = SV83 )
= $true )
| ( ( ssList @ ( tl @ SV83 ) )
= $true )
| ( ( ssList @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(876,plain,
! [SV84: $i] :
( ( ( nil = SV84 )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(877,plain,
! [SV85: $i] :
( ( ( nil = SV85 )
= $true )
| ( ( ssItem @ ( hd @ SV85 ) )
= $true )
| ( ( ssList @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(878,plain,
! [SV86: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV1 @ SV86 )
| ~ ( frontsegP @ SV86 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV86 )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(879,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ~ ( lt @ SV3 @ SV87 )
| ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
| ( lt @ SV3 @ SV87 ) ) )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(880,plain,
! [SV88: $i,SV4: $i] :
( ( ( ~ ( ~ ( gt @ SV4 @ SV88 )
| ( lt @ SV88 @ SV4 ) )
| ~ ( ~ ( lt @ SV88 @ SV4 )
| ( gt @ SV4 @ SV88 ) ) )
= $false )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(881,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( ~ ( neq @ SV5 @ SV89 )
| ( SV5 != SV89 ) )
| ~ ( ~ ( ( SV5 != SV89 ) )
| ( neq @ SV5 @ SV89 ) ) )
= $false )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(882,plain,
! [SV90: $i,SV8: $i] :
( ( ( ~ ( ( nil != SV8 ) ) )
= $true )
| ( ( ( hd @ ( app @ SV8 @ SV90 ) )
= ( hd @ SV8 ) )
= $true )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(883,plain,
! [SV91: $i,SV10: $i] :
( ( ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
| ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ~ ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(884,plain,
! [SV11: $i] :
( ( ( ~ ( segmentP @ nil @ SV11 ) )
= $true )
| ( ( nil = SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(885,plain,
! [SV11: $i] :
( ( ( nil != SV11 )
= $true )
| ( ( segmentP @ nil @ SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(886,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV16 @ SV95 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
| ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SV95 ) ) )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(887,plain,
! [SV96: $i,SV17: $i,SV135: $i] :
( ( ( ~ ( ssItem @ SV135 )
| ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SV135 ) )
| ( lt @ SV17 @ SV135 ) )
= $true )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(888,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV18 @ SV97 )
| ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV97 ) ) )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(889,plain,
! [SV19: $i] :
( ( ( ~ ( singletonP @ SV19 ) )
= $true )
| ( ( ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(890,plain,
! [SV19: $i] :
( ( ( ~ ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) ) )
= $true )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(891,plain,
! [SV98: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( geq @ SV20 @ SV98 )
| ~ ( geq @ SV98 @ SV20 ) ) )
= $true )
| ( ( SV20 = SV98 )
= $true )
| ( ( ssItem @ SV98 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(892,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( ~ ( memberP @ SV21 @ SV99 )
| ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
| ~ ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SV99 ) ) )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(893,plain,
! [SV22: $i] :
( ( ( ~ ( strictorderP @ SV22 ) )
= $true )
| ( ( ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(894,plain,
! [SV22: $i] :
( ( ( ~ ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) ) )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(895,plain,
! [SV24: $i,SV100: $i,SV136: $i] :
( ( ( ~ ( ssList @ SV136 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) ) ) )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(896,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SV101 )
!= ( tl @ SV26 ) ) ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(897,plain,
! [SV27: $i] :
( ( ( ~ ( frontsegP @ nil @ SV27 ) )
= $true )
| ( ( nil = SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(898,plain,
! [SV27: $i] :
( ( ( nil != SV27 )
= $true )
| ( ( frontsegP @ nil @ SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(899,plain,
! [SV102: $i,SV28: $i,SV137: $i] :
( ( ( ~ ( ssList @ SV137 )
| ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SV137 ) )
| ( rearsegP @ SV28 @ SV137 ) )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(900,plain,
! [SV29: $i] :
( ( ( ~ ( totalorderedP @ SV29 ) )
= $true )
| ( ( ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(901,plain,
! [SV29: $i] :
( ( ( ~ ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(902,plain,
! [SV103: $i,SV31: $i,SV138: $i] :
( ( ( ~ ( ssItem @ SV138 )
| ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SV138 ) )
| ( leq @ SV31 @ SV138 ) )
= $true )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(903,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( ~ ( segmentP @ SV34 @ SV105 )
| ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
| ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SV105 ) ) )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(904,plain,
! [SV106: $i,SV35: $i,SV139: $i] :
( ( ( ~ ( ssItem @ SV139 )
| ! [SY461: $i] :
( ~ ( ssItem @ SY461 )
| ( ( cons @ SV139 @ SV35 )
!= ( cons @ SY461 @ SV106 ) )
| ~ ( ( SV139 != SY461 )
| ( SV106 != SV35 ) ) ) )
= $true )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(905,plain,
! [SV107: $i,SV39: $i] :
( ( ( ~ ( ~ ( geq @ SV39 @ SV107 )
| ( leq @ SV107 @ SV39 ) )
| ~ ( ~ ( leq @ SV107 @ SV39 )
| ( geq @ SV39 @ SV107 ) ) )
= $false )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(906,plain,
! [SV108: $i,SV40: $i,SV140: $i] :
( ( ( ~ ( ssList @ SV140 )
| ! [SY462: $i] :
( ~ ( ssList @ SY462 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SY462 ) @ SV108 ) ) )
= $true )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(907,plain,
! [SV109: $i,SV41: $i] :
( ( ( ~ ( ( nil != SV41 ) ) )
= $true )
| ( ( ( tl @ ( app @ SV41 @ SV109 ) )
= ( app @ ( tl @ SV41 ) @ SV109 ) )
= $true )
| ( ( ssList @ SV109 )
= $false )
| ( ( ssList @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(908,plain,
! [SV110: $i,SV43: $i] :
( ( ( ~ ( lt @ SV43 @ SV110 ) )
= $true )
| ( ( ~ ( lt @ SV110 @ SV43 ) )
= $true )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(909,plain,
! [SV44: $i,SV111: $i] :
( ( ( nil
= ( cons @ SV111 @ SV44 ) )
= $false )
| ( ( ssItem @ SV111 )
= $false )
| ( ( ssList @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(910,plain,
! [SV112: $i,SV45: $i,SV141: $i] :
( ( ( ~ ( ssList @ SV141 )
| ~ ( frontsegP @ SV45 @ SV112 )
| ( frontsegP @ ( app @ SV45 @ SV141 ) @ SV112 ) )
= $true )
| ( ( ssList @ SV112 )
= $false )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(911,plain,
! [SV46: $i,SV113: $i,SV142: $i] :
( ( ( ~ ( ssList @ SV142 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) ) ) )
= $true )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(912,plain,
! [SV48: $i] :
( ( ( ~ ( duplicatefreeP @ SV48 ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(913,plain,
! [SV48: $i] :
( ( ( ~ ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(914,plain,
! [SV49: $i] :
( ( ( ~ ( rearsegP @ nil @ SV49 ) )
= $true )
| ( ( nil = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(915,plain,
! [SV49: $i] :
( ( ( nil != SV49 )
= $true )
| ( ( rearsegP @ nil @ SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(916,plain,
! [SV114: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV50 @ SV114 )
| ~ ( rearsegP @ SV114 @ SV50 ) ) )
= $true )
| ( ( SV50 = SV114 )
= $true )
| ( ( ssList @ SV114 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(917,plain,
! [SV51: $i] :
( ( ( ! [SY315: $i] :
~ ~ ( ~ ( ssList @ SY315 )
| ( ( tl @ SV51 )
!= SY315 ) ) )
= $false )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(918,plain,
! [SV115: $i,SV52: $i,SV143: $i] :
( ( ( ~ ( ssItem @ SV143 )
| ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SV143 ) )
| ( geq @ SV52 @ SV143 ) )
= $true )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(919,plain,
! [SV53: $i] :
( ( ( ~ ( strictorderedP @ SV53 ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(920,plain,
! [SV53: $i] :
( ( ( ~ ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(921,plain,
! [SV55: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK5_SY328 @ SV55 ) )
| ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( ssItem @ SY449 )
| ( ( cons @ SY449 @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) ) )
= $true )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(922,plain,
! [SV116: $i,SV56: $i] :
( ( ( ~ ( gt @ SV56 @ SV116 ) )
= $true )
| ( ( ~ ( gt @ SV116 @ SV56 ) )
= $true )
| ( ( ssItem @ SV116 )
= $false )
| ( ( ssItem @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(923,plain,
! [SV57: $i,SV117: $i,SV144: $i] :
( ( ( ~ ( ssList @ SV144 )
| ( ( app @ SV117 @ SV144 )
!= ( app @ SV117 @ SV57 ) )
| ( SV144 = SV57 ) )
= $true )
| ( ( ssList @ SV117 )
= $false )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(924,plain,
! [SV58: $i] :
( ( ( ~ ( totalorderP @ SV58 ) )
= $true )
| ( ( ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(925,plain,
! [SV58: $i] :
( ( ( ~ ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) ) )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(926,plain,
! [SV118: $i,SV59: $i,SV145: $i] :
( ( ( ~ ( ssList @ SV145 )
| ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SV145 ) )
| ( segmentP @ SV59 @ SV145 ) )
= $true )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(927,plain,
( ( ~ ( ssList @ sK6_SY428 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(928,plain,
( ( ( sK2_SX0 != sK6_SY428 )
| ( sK1_U != sK4_SY389 )
| ! [SY450: $i] :
( ~ ( ssList @ SY450 )
| ! [SY451: $i] :
( ~ ( ssList @ SY451 )
| ( ( app @ ( app @ SY450 @ sK4_SY389 ) @ SY451 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY451 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != sK6_SY428 ) )
| ( nil != sK4_SY389 ) )
| ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(929,plain,
! [SV60: $i,SV119: $i,SV146: $i] :
( ( ( ~ ( ssItem @ SV146 )
| ( ( cons @ SV146 @ ( app @ SV119 @ SV60 ) )
= ( app @ ( cons @ SV146 @ SV119 ) @ SV60 ) ) )
= $true )
| ( ( ssList @ SV119 )
= $false )
| ( ( ssList @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(930,plain,
! [SV61: $i,SV120: $i,SV147: $i] :
( ( ( ~ ( ssList @ SV147 )
| ( ( app @ SV147 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
| ( SV147 = SV61 ) )
= $true )
| ( ( ssList @ SV120 )
= $false )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(931,plain,
! [SV121: $i,SV62: $i,SV148: $i] :
( ( ( ~ ( ssItem @ SV148 )
| ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SV148 ) )
| ( gt @ SV62 @ SV148 ) )
= $true )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(932,plain,
! [SV122: $i,SV63: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV63 @ SV122 ) )
| ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
| ~ ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SV122 ) ) ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(933,plain,
! [SV66: $i,SV124: $i] :
( ( ( ( cons @ SV124 @ SV66 )
= SV66 )
= $false )
| ( ( ssItem @ SV124 )
= $false )
| ( ( ssList @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(934,plain,
! [SV125: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV67 @ SV125 )
| ~ ( segmentP @ SV125 @ SV67 ) ) )
= $true )
| ( ( SV67 = SV125 )
= $true )
| ( ( ssList @ SV125 )
= $false )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(935,plain,
! [SV126: $i,SV68: $i,SV149: $i] :
( ( ( ~ ( ssList @ SV149 )
| ! [SY463: $i] :
( ~ ( ssList @ SY463 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SY463 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SY463 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SY463 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SY463 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(936,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( ~ ( neq @ SV69 @ SV127 )
| ( SV69 != SV127 ) )
| ~ ( ~ ( ( SV69 != SV127 ) )
| ( neq @ SV69 @ SV127 ) ) )
= $false )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(937,plain,
! [SV128: $i,SV70: $i] :
( ( ( ~ ( leq @ SV70 @ SV128 ) )
= $true )
| ( ( ( SV70 = SV128 )
| ( lt @ SV70 @ SV128 ) )
= $true )
| ( ( ssItem @ SV128 )
= $false )
| ( ( ssItem @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(938,plain,
! [SV129: $i,SV72: $i] :
( ( ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
| ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ~ ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(939,plain,
( ( ! [SY402: $i] :
~ ~ ( ~ ( ssItem @ SY402 )
| ~ ( ( sK3_SX0 != SY402 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(940,plain,
! [SV130: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV73 @ SV130 )
| ~ ( leq @ SV130 @ SV73 ) ) )
= $true )
| ( ( SV73 = SV130 )
= $true )
| ( ( ssItem @ SV130 )
= $false )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(941,plain,
! [SV74: $i] :
( ( ( ~ ( equalelemsP @ SV74 ) )
= $true )
| ( ( ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(942,plain,
! [SV74: $i] :
( ( ( ~ ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(943,plain,
! [SV131: $i,SV75: $i,SV150: $i] :
( ( ( ~ ( ssList @ SV150 )
| ( ( app @ ( app @ SV75 @ SV131 ) @ SV150 )
= ( app @ SV75 @ ( app @ SV131 @ SV150 ) ) ) )
= $true )
| ( ( ssList @ SV131 )
= $false )
| ( ( ssList @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(944,plain,
! [SV132: $i,SV76: $i,SV151: $i] :
( ( ( ~ ( ssList @ SV151 )
| ~ ( rearsegP @ SV76 @ SV132 )
| ( rearsegP @ ( app @ SV151 @ SV76 ) @ SV132 ) )
= $true )
| ( ( ssList @ SV132 )
= $false )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(945,plain,
! [SV133: $i,SV77: $i,SV152: $i] :
( ( ( ~ ( ssList @ SV152 )
| ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SV152 ) )
| ( frontsegP @ SV77 @ SV152 ) )
= $true )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(946,plain,
! [SV134: $i,SV78: $i,SV153: $i] :
( ( ( ~ ( ssItem @ SV153 )
| ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SV153 ) )
| ( lt @ SV78 @ SV153 ) )
= $true )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(947,plain,
! [SV82: $i] :
( ( ( ~ ( cyclefreeP @ SV82 ) )
= $true )
| ( ( ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(948,plain,
! [SV82: $i] :
( ( ( ~ ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(949,plain,
! [SV84: $i] :
( ( ( ! [SY388: $i] :
~ ~ ( ~ ( ssItem @ SY388 )
| ( ( hd @ SV84 )
!= SY388 ) ) )
= $false )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(950,plain,
! [SV86: $i,SV1: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV1 @ SV86 )
| ~ ( frontsegP @ SV86 @ SV1 ) ) )
= $false )
| ( ( SV1 = SV86 )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(951,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ~ ( lt @ SV3 @ SV87 )
| ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) ) )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(952,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
| ( lt @ SV3 @ SV87 ) ) )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(953,plain,
! [SV88: $i,SV4: $i] :
( ( ( ~ ( ~ ( gt @ SV4 @ SV88 )
| ( lt @ SV88 @ SV4 ) ) )
= $false )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(954,plain,
! [SV4: $i,SV88: $i] :
( ( ( ~ ( ~ ( lt @ SV88 @ SV4 )
| ( gt @ SV4 @ SV88 ) ) )
= $false )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(955,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( ~ ( neq @ SV5 @ SV89 )
| ( SV5 != SV89 ) ) )
= $false )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(956,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( ~ ( ( SV5 != SV89 ) )
| ( neq @ SV5 @ SV89 ) ) )
= $false )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(957,plain,
! [SV90: $i,SV8: $i] :
( ( ( nil != SV8 )
= $false )
| ( ( ( hd @ ( app @ SV8 @ SV90 ) )
= ( hd @ SV8 ) )
= $true )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(958,plain,
! [SV91: $i,SV10: $i] :
( ( ( ~ ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
| ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(959,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(960,plain,
! [SV11: $i] :
( ( ( segmentP @ nil @ SV11 )
= $false )
| ( ( nil = SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(961,plain,
! [SV11: $i] :
( ( ( nil = SV11 )
= $false )
| ( ( segmentP @ nil @ SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(962,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV16 @ SV95 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) ) )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(963,plain,
! [SV16: $i,SV95: $i] :
( ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SV95 ) ) )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(964,plain,
! [SV96: $i,SV17: $i,SV135: $i] :
( ( ( ~ ( ssItem @ SV135 ) )
= $true )
| ( ( ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SV135 ) )
| ( lt @ SV17 @ SV135 ) )
= $true )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(965,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV18 @ SV97 )
| ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) ) )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(966,plain,
! [SV18: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV97 ) ) )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(967,plain,
! [SV19: $i] :
( ( ( singletonP @ SV19 )
= $false )
| ( ( ~ ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(968,plain,
! [SV19: $i] :
( ( ( ~ ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) ) )
= $false )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(969,plain,
! [SV98: $i,SV20: $i] :
( ( ( ~ ( ~ ( geq @ SV20 @ SV98 )
| ~ ( geq @ SV98 @ SV20 ) ) )
= $false )
| ( ( SV20 = SV98 )
= $true )
| ( ( ssItem @ SV98 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(970,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( ~ ( memberP @ SV21 @ SV99 )
| ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) ) )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(971,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SV99 ) ) )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(972,plain,
! [SV22: $i] :
( ( ( strictorderP @ SV22 )
= $false )
| ( ( ! [SY257: $i] :
( ~ ( ssItem @ SY257 )
| ! [SY258: $i] :
( ~ ( ssItem @ SY258 )
| ! [SY259: $i] :
( ~ ( ssList @ SY259 )
| ! [SY260: $i] :
( ~ ( ssList @ SY260 )
| ! [SY261: $i] :
( ~ ( ssList @ SY261 )
| ( ( app @ ( app @ SY259 @ ( cons @ SY257 @ SY260 ) ) @ ( cons @ SY258 @ SY261 ) )
!= SV22 )
| ( lt @ SY257 @ SY258 )
| ( lt @ SY258 @ SY257 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(973,plain,
! [SV22: $i] :
( ( ( ! [SY262: $i] :
( ~ ( ssItem @ SY262 )
| ! [SY263: $i] :
( ~ ( ssItem @ SY263 )
| ! [SY264: $i] :
( ~ ( ssList @ SY264 )
| ! [SY265: $i] :
( ~ ( ssList @ SY265 )
| ! [SY266: $i] :
( ~ ( ssList @ SY266 )
| ( ( app @ ( app @ SY264 @ ( cons @ SY262 @ SY265 ) ) @ ( cons @ SY263 @ SY266 ) )
!= SV22 )
| ( lt @ SY262 @ SY263 )
| ( lt @ SY263 @ SY262 ) ) ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(974,plain,
! [SV24: $i,SV100: $i,SV136: $i] :
( ( ( ~ ( ssList @ SV136 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) ) ) )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(975,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SV101 )
!= ( tl @ SV26 ) ) ) )
= $false )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(976,plain,
! [SV27: $i] :
( ( ( frontsegP @ nil @ SV27 )
= $false )
| ( ( nil = SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(977,plain,
! [SV27: $i] :
( ( ( nil = SV27 )
= $false )
| ( ( frontsegP @ nil @ SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(978,plain,
! [SV102: $i,SV28: $i,SV137: $i] :
( ( ( ~ ( ssList @ SV137 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SV137 ) )
| ( rearsegP @ SV28 @ SV137 ) )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(979,plain,
! [SV29: $i] :
( ( ( totalorderedP @ SV29 )
= $false )
| ( ( ! [SY272: $i] :
( ~ ( ssItem @ SY272 )
| ! [SY273: $i] :
( ~ ( ssItem @ SY273 )
| ! [SY274: $i] :
( ~ ( ssList @ SY274 )
| ! [SY275: $i] :
( ~ ( ssList @ SY275 )
| ! [SY276: $i] :
( ~ ( ssList @ SY276 )
| ( ( app @ ( app @ SY274 @ ( cons @ SY272 @ SY275 ) ) @ ( cons @ SY273 @ SY276 ) )
!= SV29 )
| ( leq @ SY272 @ SY273 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(980,plain,
! [SV29: $i] :
( ( ( ! [SY277: $i] :
( ~ ( ssItem @ SY277 )
| ! [SY278: $i] :
( ~ ( ssItem @ SY278 )
| ! [SY279: $i] :
( ~ ( ssList @ SY279 )
| ! [SY280: $i] :
( ~ ( ssList @ SY280 )
| ! [SY281: $i] :
( ~ ( ssList @ SY281 )
| ( ( app @ ( app @ SY279 @ ( cons @ SY277 @ SY280 ) ) @ ( cons @ SY278 @ SY281 ) )
!= SV29 )
| ( leq @ SY277 @ SY278 ) ) ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(981,plain,
! [SV103: $i,SV31: $i,SV138: $i] :
( ( ( ~ ( ssItem @ SV138 ) )
= $true )
| ( ( ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SV138 ) )
| ( leq @ SV31 @ SV138 ) )
= $true )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(982,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( ~ ( segmentP @ SV34 @ SV105 )
| ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) ) )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(983,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SV105 ) ) )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(984,plain,
! [SV106: $i,SV35: $i,SV139: $i] :
( ( ( ~ ( ssItem @ SV139 ) )
= $true )
| ( ( ! [SY461: $i] :
( ~ ( ssItem @ SY461 )
| ( ( cons @ SV139 @ SV35 )
!= ( cons @ SY461 @ SV106 ) )
| ~ ( ( SV139 != SY461 )
| ( SV106 != SV35 ) ) ) )
= $true )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(985,plain,
! [SV107: $i,SV39: $i] :
( ( ( ~ ( ~ ( geq @ SV39 @ SV107 )
| ( leq @ SV107 @ SV39 ) ) )
= $false )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(986,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( ~ ( leq @ SV107 @ SV39 )
| ( geq @ SV39 @ SV107 ) ) )
= $false )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(987,plain,
! [SV108: $i,SV40: $i,SV140: $i] :
( ( ( ~ ( ssList @ SV140 ) )
= $true )
| ( ( ! [SY462: $i] :
( ~ ( ssList @ SY462 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SY462 ) @ SV108 ) ) )
= $true )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(988,plain,
! [SV109: $i,SV41: $i] :
( ( ( nil != SV41 )
= $false )
| ( ( ( tl @ ( app @ SV41 @ SV109 ) )
= ( app @ ( tl @ SV41 ) @ SV109 ) )
= $true )
| ( ( ssList @ SV109 )
= $false )
| ( ( ssList @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(989,plain,
! [SV110: $i,SV43: $i] :
( ( ( lt @ SV43 @ SV110 )
= $false )
| ( ( ~ ( lt @ SV110 @ SV43 ) )
= $true )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(990,plain,
! [SV112: $i,SV45: $i,SV141: $i] :
( ( ( ~ ( ssList @ SV141 ) )
= $true )
| ( ( ~ ( frontsegP @ SV45 @ SV112 )
| ( frontsegP @ ( app @ SV45 @ SV141 ) @ SV112 ) )
= $true )
| ( ( ssList @ SV112 )
= $false )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(991,plain,
! [SV46: $i,SV113: $i,SV142: $i] :
( ( ( ~ ( ssList @ SV142 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) ) ) )
= $true )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(992,plain,
! [SV48: $i] :
( ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( ssItem @ SY304 )
| ! [SY305: $i] :
( ~ ( ssItem @ SY305 )
| ! [SY306: $i] :
( ~ ( ssList @ SY306 )
| ! [SY307: $i] :
( ~ ( ssList @ SY307 )
| ! [SY308: $i] :
( ~ ( ssList @ SY308 )
| ( ( app @ ( app @ SY306 @ ( cons @ SY304 @ SY307 ) ) @ ( cons @ SY305 @ SY308 ) )
!= SV48 )
| ( SY304 != SY305 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(993,plain,
! [SV48: $i] :
( ( ( ! [SY309: $i] :
( ~ ( ssItem @ SY309 )
| ! [SY310: $i] :
( ~ ( ssItem @ SY310 )
| ! [SY311: $i] :
( ~ ( ssList @ SY311 )
| ! [SY312: $i] :
( ~ ( ssList @ SY312 )
| ! [SY313: $i] :
( ~ ( ssList @ SY313 )
| ( ( app @ ( app @ SY311 @ ( cons @ SY309 @ SY312 ) ) @ ( cons @ SY310 @ SY313 ) )
!= SV48 )
| ( SY309 != SY310 ) ) ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(994,plain,
! [SV49: $i] :
( ( ( rearsegP @ nil @ SV49 )
= $false )
| ( ( nil = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(995,plain,
! [SV49: $i] :
( ( ( nil = SV49 )
= $false )
| ( ( rearsegP @ nil @ SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(996,plain,
! [SV114: $i,SV50: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV50 @ SV114 )
| ~ ( rearsegP @ SV114 @ SV50 ) ) )
= $false )
| ( ( SV50 = SV114 )
= $true )
| ( ( ssList @ SV114 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(997,plain,
! [SV51: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK7_SY315 @ SV51 ) )
| ( ( tl @ SV51 )
!= ( sK7_SY315 @ SV51 ) ) ) )
= $false )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[917]) ).
thf(998,plain,
! [SV115: $i,SV52: $i,SV143: $i] :
( ( ( ~ ( ssItem @ SV143 ) )
= $true )
| ( ( ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SV143 ) )
| ( geq @ SV52 @ SV143 ) )
= $true )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(999,plain,
! [SV53: $i] :
( ( ( strictorderedP @ SV53 )
= $false )
| ( ( ! [SY318: $i] :
( ~ ( ssItem @ SY318 )
| ! [SY319: $i] :
( ~ ( ssItem @ SY319 )
| ! [SY320: $i] :
( ~ ( ssList @ SY320 )
| ! [SY321: $i] :
( ~ ( ssList @ SY321 )
| ! [SY322: $i] :
( ~ ( ssList @ SY322 )
| ( ( app @ ( app @ SY320 @ ( cons @ SY318 @ SY321 ) ) @ ( cons @ SY319 @ SY322 ) )
!= SV53 )
| ( lt @ SY318 @ SY319 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(1000,plain,
! [SV53: $i] :
( ( ( ! [SY323: $i] :
( ~ ( ssItem @ SY323 )
| ! [SY324: $i] :
( ~ ( ssItem @ SY324 )
| ! [SY325: $i] :
( ~ ( ssList @ SY325 )
| ! [SY326: $i] :
( ~ ( ssList @ SY326 )
| ! [SY327: $i] :
( ~ ( ssList @ SY327 )
| ( ( app @ ( app @ SY325 @ ( cons @ SY323 @ SY326 ) ) @ ( cons @ SY324 @ SY327 ) )
!= SV53 )
| ( lt @ SY323 @ SY324 ) ) ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1001,plain,
! [SV55: $i] :
( ( ( ~ ( ssList @ ( sK5_SY328 @ SV55 ) )
| ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( ssItem @ SY449 )
| ( ( cons @ SY449 @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1002,plain,
! [SV116: $i,SV56: $i] :
( ( ( gt @ SV56 @ SV116 )
= $false )
| ( ( ~ ( gt @ SV116 @ SV56 ) )
= $true )
| ( ( ssItem @ SV116 )
= $false )
| ( ( ssItem @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1003,plain,
! [SV57: $i,SV117: $i,SV144: $i] :
( ( ( ~ ( ssList @ SV144 ) )
= $true )
| ( ( ( ( app @ SV117 @ SV144 )
!= ( app @ SV117 @ SV57 ) )
| ( SV144 = SV57 ) )
= $true )
| ( ( ssList @ SV117 )
= $false )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1004,plain,
! [SV58: $i] :
( ( ( totalorderP @ SV58 )
= $false )
| ( ( ! [SY333: $i] :
( ~ ( ssItem @ SY333 )
| ! [SY334: $i] :
( ~ ( ssItem @ SY334 )
| ! [SY335: $i] :
( ~ ( ssList @ SY335 )
| ! [SY336: $i] :
( ~ ( ssList @ SY336 )
| ! [SY337: $i] :
( ~ ( ssList @ SY337 )
| ( ( app @ ( app @ SY335 @ ( cons @ SY333 @ SY336 ) ) @ ( cons @ SY334 @ SY337 ) )
!= SV58 )
| ( leq @ SY333 @ SY334 )
| ( leq @ SY334 @ SY333 ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1005,plain,
! [SV58: $i] :
( ( ( ! [SY338: $i] :
( ~ ( ssItem @ SY338 )
| ! [SY339: $i] :
( ~ ( ssItem @ SY339 )
| ! [SY340: $i] :
( ~ ( ssList @ SY340 )
| ! [SY341: $i] :
( ~ ( ssList @ SY341 )
| ! [SY342: $i] :
( ~ ( ssList @ SY342 )
| ( ( app @ ( app @ SY340 @ ( cons @ SY338 @ SY341 ) ) @ ( cons @ SY339 @ SY342 ) )
!= SV58 )
| ( leq @ SY338 @ SY339 )
| ( leq @ SY339 @ SY338 ) ) ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1006,plain,
! [SV118: $i,SV59: $i,SV145: $i] :
( ( ( ~ ( ssList @ SV145 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SV145 ) )
| ( segmentP @ SV59 @ SV145 ) )
= $true )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1007,plain,
( ( ssList @ sK6_SY428 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(1008,plain,
( ( ( sK2_SX0 != sK6_SY428 )
| ( sK1_U != sK4_SY389 )
| ! [SY450: $i] :
( ~ ( ssList @ SY450 )
| ! [SY451: $i] :
( ~ ( ssList @ SY451 )
| ( ( app @ ( app @ SY450 @ sK4_SY389 ) @ SY451 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY451 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
| ~ ( ~ ( ( nil != sK6_SY428 ) )
| ( nil != sK4_SY389 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1009,plain,
( ( ~ ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1010,plain,
! [SV60: $i,SV119: $i,SV146: $i] :
( ( ( ~ ( ssItem @ SV146 ) )
= $true )
| ( ( ( cons @ SV146 @ ( app @ SV119 @ SV60 ) )
= ( app @ ( cons @ SV146 @ SV119 ) @ SV60 ) )
= $true )
| ( ( ssList @ SV119 )
= $false )
| ( ( ssList @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1011,plain,
! [SV61: $i,SV120: $i,SV147: $i] :
( ( ( ~ ( ssList @ SV147 ) )
= $true )
| ( ( ( ( app @ SV147 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
| ( SV147 = SV61 ) )
= $true )
| ( ( ssList @ SV120 )
= $false )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1012,plain,
! [SV121: $i,SV62: $i,SV148: $i] :
( ( ( ~ ( ssItem @ SV148 ) )
= $true )
| ( ( ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SV148 ) )
| ( gt @ SV62 @ SV148 ) )
= $true )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1013,plain,
! [SV122: $i,SV63: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV63 @ SV122 ) )
| ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[932]) ).
thf(1014,plain,
! [SV63: $i,SV122: $i] :
( ( ( ~ ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SV122 ) ) ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[932]) ).
thf(1015,plain,
! [SV125: $i,SV67: $i] :
( ( ( ~ ( ~ ( segmentP @ SV67 @ SV125 )
| ~ ( segmentP @ SV125 @ SV67 ) ) )
= $false )
| ( ( SV67 = SV125 )
= $true )
| ( ( ssList @ SV125 )
= $false )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1016,plain,
! [SV126: $i,SV68: $i,SV149: $i] :
( ( ( ~ ( ssList @ SV149 ) )
= $true )
| ( ( ! [SY463: $i] :
( ~ ( ssList @ SY463 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SY463 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SY463 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SY463 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SY463 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1017,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( ~ ( neq @ SV69 @ SV127 )
| ( SV69 != SV127 ) ) )
= $false )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1018,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( ~ ( ( SV69 != SV127 ) )
| ( neq @ SV69 @ SV127 ) ) )
= $false )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1019,plain,
! [SV128: $i,SV70: $i] :
( ( ( leq @ SV70 @ SV128 )
= $false )
| ( ( ( SV70 = SV128 )
| ( lt @ SV70 @ SV128 ) )
= $true )
| ( ( ssItem @ SV128 )
= $false )
| ( ( ssItem @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1020,plain,
! [SV129: $i,SV72: $i] :
( ( ( ~ ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
| ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1021,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1022,plain,
( ( ~ ~ ( ~ ( ssItem @ sK8_SY402 )
| ~ ( ( sK3_SX0 != sK8_SY402 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[939]) ).
thf(1023,plain,
! [SV130: $i,SV73: $i] :
( ( ( ~ ( ~ ( leq @ SV73 @ SV130 )
| ~ ( leq @ SV130 @ SV73 ) ) )
= $false )
| ( ( SV73 = SV130 )
= $true )
| ( ( ssItem @ SV130 )
= $false )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1024,plain,
! [SV74: $i] :
( ( ( equalelemsP @ SV74 )
= $false )
| ( ( ! [SY362: $i] :
( ~ ( ssItem @ SY362 )
| ! [SY363: $i] :
( ~ ( ssItem @ SY363 )
| ! [SY364: $i] :
( ~ ( ssList @ SY364 )
| ! [SY365: $i] :
( ~ ( ssList @ SY365 )
| ( ( app @ SY364 @ ( cons @ SY362 @ ( cons @ SY363 @ SY365 ) ) )
!= SV74 )
| ( SY362 = SY363 ) ) ) ) ) )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1025,plain,
! [SV74: $i] :
( ( ( ! [SY366: $i] :
( ~ ( ssItem @ SY366 )
| ! [SY367: $i] :
( ~ ( ssItem @ SY367 )
| ! [SY368: $i] :
( ~ ( ssList @ SY368 )
| ! [SY369: $i] :
( ~ ( ssList @ SY369 )
| ( ( app @ SY368 @ ( cons @ SY366 @ ( cons @ SY367 @ SY369 ) ) )
!= SV74 )
| ( SY366 = SY367 ) ) ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1026,plain,
! [SV131: $i,SV75: $i,SV150: $i] :
( ( ( ~ ( ssList @ SV150 ) )
= $true )
| ( ( ( app @ ( app @ SV75 @ SV131 ) @ SV150 )
= ( app @ SV75 @ ( app @ SV131 @ SV150 ) ) )
= $true )
| ( ( ssList @ SV131 )
= $false )
| ( ( ssList @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1027,plain,
! [SV132: $i,SV76: $i,SV151: $i] :
( ( ( ~ ( ssList @ SV151 ) )
= $true )
| ( ( ~ ( rearsegP @ SV76 @ SV132 )
| ( rearsegP @ ( app @ SV151 @ SV76 ) @ SV132 ) )
= $true )
| ( ( ssList @ SV132 )
= $false )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1028,plain,
! [SV133: $i,SV77: $i,SV152: $i] :
( ( ( ~ ( ssList @ SV152 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SV152 ) )
| ( frontsegP @ SV77 @ SV152 ) )
= $true )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1029,plain,
! [SV134: $i,SV78: $i,SV153: $i] :
( ( ( ~ ( ssItem @ SV153 ) )
= $true )
| ( ( ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SV153 ) )
| ( lt @ SV78 @ SV153 ) )
= $true )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1030,plain,
! [SV82: $i] :
( ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ! [SY378: $i] :
( ~ ( ssItem @ SY378 )
| ! [SY379: $i] :
( ~ ( ssItem @ SY379 )
| ! [SY380: $i] :
( ~ ( ssList @ SY380 )
| ! [SY381: $i] :
( ~ ( ssList @ SY381 )
| ! [SY382: $i] :
( ~ ( ssList @ SY382 )
| ( ( app @ ( app @ SY380 @ ( cons @ SY378 @ SY381 ) ) @ ( cons @ SY379 @ SY382 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY378 @ SY379 )
| ~ ( leq @ SY379 @ SY378 ) ) ) ) ) ) ) )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1031,plain,
! [SV82: $i] :
( ( ( ! [SY383: $i] :
( ~ ( ssItem @ SY383 )
| ! [SY384: $i] :
( ~ ( ssItem @ SY384 )
| ! [SY385: $i] :
( ~ ( ssList @ SY385 )
| ! [SY386: $i] :
( ~ ( ssList @ SY386 )
| ! [SY387: $i] :
( ~ ( ssList @ SY387 )
| ( ( app @ ( app @ SY385 @ ( cons @ SY383 @ SY386 ) ) @ ( cons @ SY384 @ SY387 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SY383 @ SY384 )
| ~ ( leq @ SY384 @ SY383 ) ) ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1032,plain,
! [SV84: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ ( sK9_SY388 @ SV84 ) )
| ( ( hd @ SV84 )
!= ( sK9_SY388 @ SV84 ) ) ) )
= $false )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[949]) ).
thf(1033,plain,
! [SV86: $i,SV1: $i] :
( ( ( ~ ( frontsegP @ SV1 @ SV86 )
| ~ ( frontsegP @ SV86 @ SV1 ) )
= $true )
| ( ( SV1 = SV86 )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1034,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( lt @ SV3 @ SV87 )
| ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(1035,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
| ( lt @ SV3 @ SV87 ) )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(1036,plain,
! [SV88: $i,SV4: $i] :
( ( ( ~ ( gt @ SV4 @ SV88 )
| ( lt @ SV88 @ SV4 ) )
= $true )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1037,plain,
! [SV4: $i,SV88: $i] :
( ( ( ~ ( lt @ SV88 @ SV4 )
| ( gt @ SV4 @ SV88 ) )
= $true )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1038,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( neq @ SV5 @ SV89 )
| ( SV5 != SV89 ) )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1039,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV89 ) )
| ( neq @ SV5 @ SV89 ) )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1040,plain,
! [SV90: $i,SV8: $i] :
( ( ( nil = SV8 )
= $true )
| ( ( ( hd @ ( app @ SV8 @ SV90 ) )
= ( hd @ SV8 ) )
= $true )
| ( ( ssList @ SV90 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(1041,plain,
! [SV91: $i,SV10: $i] :
( ( ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
| ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(1042,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
| ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1043,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( frontsegP @ SV16 @ SV95 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1044,plain,
! [SV16: $i,SV95: $i] :
( ( ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) )
| ( frontsegP @ SV16 @ SV95 ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1045,plain,
! [SV96: $i,SV17: $i,SV135: $i] :
( ( ( ssItem @ SV135 )
= $false )
| ( ( ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SV135 ) )
| ( lt @ SV17 @ SV135 ) )
= $true )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1046,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( rearsegP @ SV18 @ SV97 )
| ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1047,plain,
! [SV18: $i,SV97: $i] :
( ( ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV97 ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1048,plain,
! [SV19: $i] :
( ( ( ! [SY249: $i] :
~ ~ ( ~ ( ssItem @ SY249 )
| ( ( cons @ SY249 @ nil )
!= SV19 ) ) )
= $false )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1049,plain,
! [SV19: $i] :
( ( ( ! [SY250: $i] :
~ ~ ( ~ ( ssItem @ SY250 )
| ( ( cons @ SY250 @ nil )
!= SV19 ) ) )
= $true )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1050,plain,
! [SV98: $i,SV20: $i] :
( ( ( ~ ( geq @ SV20 @ SV98 )
| ~ ( geq @ SV98 @ SV20 ) )
= $true )
| ( ( SV20 = SV98 )
= $true )
| ( ( ssItem @ SV98 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1051,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( memberP @ SV21 @ SV99 )
| ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1052,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) )
| ( memberP @ SV21 @ SV99 ) )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1053,plain,
! [SV22: $i,SV154: $i] :
( ( ( ~ ( ssItem @ SV154 )
| ! [SY464: $i] :
( ~ ( ssItem @ SY464 )
| ! [SY465: $i] :
( ~ ( ssList @ SY465 )
| ! [SY466: $i] :
( ~ ( ssList @ SY466 )
| ! [SY467: $i] :
( ~ ( ssList @ SY467 )
| ( ( app @ ( app @ SY465 @ ( cons @ SV154 @ SY466 ) ) @ ( cons @ SY464 @ SY467 ) )
!= SV22 )
| ( lt @ SV154 @ SY464 )
| ( lt @ SY464 @ SV154 ) ) ) ) ) )
= $true )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1054,plain,
! [SV22: $i] :
( ( ( ~ ( ssItem @ ( sK10_SY262 @ SV22 ) )
| ! [SY468: $i] :
( ~ ( ssItem @ SY468 )
| ! [SY469: $i] :
( ~ ( ssList @ SY469 )
| ! [SY470: $i] :
( ~ ( ssList @ SY470 )
| ! [SY471: $i] :
( ~ ( ssList @ SY471 )
| ( ( app @ ( app @ SY469 @ ( cons @ ( sK10_SY262 @ SV22 ) @ SY470 ) ) @ ( cons @ SY468 @ SY471 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ SY468 )
| ( lt @ SY468 @ ( sK10_SY262 @ SV22 ) ) ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[973]) ).
thf(1055,plain,
! [SV24: $i,SV100: $i,SV136: $i] :
( ( ( ssList @ SV136 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) ) ) )
= $true )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1056,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
| ( ( tl @ SV101 )
!= ( tl @ SV26 ) ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1057,plain,
! [SV102: $i,SV28: $i,SV137: $i] :
( ( ( ssList @ SV137 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SV137 ) )
| ( rearsegP @ SV28 @ SV137 ) )
= $true )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1058,plain,
! [SV29: $i,SV155: $i] :
( ( ( ~ ( ssItem @ SV155 )
| ! [SY472: $i] :
( ~ ( ssItem @ SY472 )
| ! [SY473: $i] :
( ~ ( ssList @ SY473 )
| ! [SY474: $i] :
( ~ ( ssList @ SY474 )
| ! [SY475: $i] :
( ~ ( ssList @ SY475 )
| ( ( app @ ( app @ SY473 @ ( cons @ SV155 @ SY474 ) ) @ ( cons @ SY472 @ SY475 ) )
!= SV29 )
| ( leq @ SV155 @ SY472 ) ) ) ) ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1059,plain,
! [SV29: $i] :
( ( ( ~ ( ssItem @ ( sK11_SY277 @ SV29 ) )
| ! [SY476: $i] :
( ~ ( ssItem @ SY476 )
| ! [SY477: $i] :
( ~ ( ssList @ SY477 )
| ! [SY478: $i] :
( ~ ( ssList @ SY478 )
| ! [SY479: $i] :
( ~ ( ssList @ SY479 )
| ( ( app @ ( app @ SY477 @ ( cons @ ( sK11_SY277 @ SV29 ) @ SY478 ) ) @ ( cons @ SY476 @ SY479 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ SY476 ) ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[980]) ).
thf(1060,plain,
! [SV103: $i,SV31: $i,SV138: $i] :
( ( ( ssItem @ SV138 )
= $false )
| ( ( ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SV138 ) )
| ( leq @ SV31 @ SV138 ) )
= $true )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1061,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( segmentP @ SV34 @ SV105 )
| ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1062,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) )
| ( segmentP @ SV34 @ SV105 ) )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1063,plain,
! [SV106: $i,SV35: $i,SV139: $i] :
( ( ( ssItem @ SV139 )
= $false )
| ( ( ! [SY461: $i] :
( ~ ( ssItem @ SY461 )
| ( ( cons @ SV139 @ SV35 )
!= ( cons @ SY461 @ SV106 ) )
| ~ ( ( SV139 != SY461 )
| ( SV106 != SV35 ) ) ) )
= $true )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1064,plain,
! [SV107: $i,SV39: $i] :
( ( ( ~ ( geq @ SV39 @ SV107 )
| ( leq @ SV107 @ SV39 ) )
= $true )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1065,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( leq @ SV107 @ SV39 )
| ( geq @ SV39 @ SV107 ) )
= $true )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1066,plain,
! [SV108: $i,SV40: $i,SV140: $i] :
( ( ( ssList @ SV140 )
= $false )
| ( ( ! [SY462: $i] :
( ~ ( ssList @ SY462 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SY462 ) @ SV108 ) ) )
= $true )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1067,plain,
! [SV109: $i,SV41: $i] :
( ( ( nil = SV41 )
= $true )
| ( ( ( tl @ ( app @ SV41 @ SV109 ) )
= ( app @ ( tl @ SV41 ) @ SV109 ) )
= $true )
| ( ( ssList @ SV109 )
= $false )
| ( ( ssList @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1068,plain,
! [SV43: $i,SV110: $i] :
( ( ( lt @ SV110 @ SV43 )
= $false )
| ( ( lt @ SV43 @ SV110 )
= $false )
| ( ( ssItem @ SV110 )
= $false )
| ( ( ssItem @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1069,plain,
! [SV112: $i,SV45: $i,SV141: $i] :
( ( ( ssList @ SV141 )
= $false )
| ( ( ~ ( frontsegP @ SV45 @ SV112 )
| ( frontsegP @ ( app @ SV45 @ SV141 ) @ SV112 ) )
= $true )
| ( ( ssList @ SV112 )
= $false )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1070,plain,
! [SV46: $i,SV113: $i,SV142: $i] :
( ( ( ssList @ SV142 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) ) ) )
= $true )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1071,plain,
! [SV48: $i,SV156: $i] :
( ( ( ~ ( ssItem @ SV156 )
| ! [SY480: $i] :
( ~ ( ssItem @ SY480 )
| ! [SY481: $i] :
( ~ ( ssList @ SY481 )
| ! [SY482: $i] :
( ~ ( ssList @ SY482 )
| ! [SY483: $i] :
( ~ ( ssList @ SY483 )
| ( ( app @ ( app @ SY481 @ ( cons @ SV156 @ SY482 ) ) @ ( cons @ SY480 @ SY483 ) )
!= SV48 )
| ( SV156 != SY480 ) ) ) ) ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1072,plain,
! [SV48: $i] :
( ( ( ~ ( ssItem @ ( sK12_SY309 @ SV48 ) )
| ! [SY484: $i] :
( ~ ( ssItem @ SY484 )
| ! [SY485: $i] :
( ~ ( ssList @ SY485 )
| ! [SY486: $i] :
( ~ ( ssList @ SY486 )
| ! [SY487: $i] :
( ~ ( ssList @ SY487 )
| ( ( app @ ( app @ SY485 @ ( cons @ ( sK12_SY309 @ SV48 ) @ SY486 ) ) @ ( cons @ SY484 @ SY487 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= SY484 ) ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[993]) ).
thf(1073,plain,
! [SV114: $i,SV50: $i] :
( ( ( ~ ( rearsegP @ SV50 @ SV114 )
| ~ ( rearsegP @ SV114 @ SV50 ) )
= $true )
| ( ( SV50 = SV114 )
= $true )
| ( ( ssList @ SV114 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1074,plain,
! [SV51: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK7_SY315 @ SV51 ) )
| ( ( tl @ SV51 )
!= ( sK7_SY315 @ SV51 ) ) ) )
= $true )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1075,plain,
! [SV115: $i,SV52: $i,SV143: $i] :
( ( ( ssItem @ SV143 )
= $false )
| ( ( ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SV143 ) )
| ( geq @ SV52 @ SV143 ) )
= $true )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1076,plain,
! [SV53: $i,SV157: $i] :
( ( ( ~ ( ssItem @ SV157 )
| ! [SY488: $i] :
( ~ ( ssItem @ SY488 )
| ! [SY489: $i] :
( ~ ( ssList @ SY489 )
| ! [SY490: $i] :
( ~ ( ssList @ SY490 )
| ! [SY491: $i] :
( ~ ( ssList @ SY491 )
| ( ( app @ ( app @ SY489 @ ( cons @ SV157 @ SY490 ) ) @ ( cons @ SY488 @ SY491 ) )
!= SV53 )
| ( lt @ SV157 @ SY488 ) ) ) ) ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1077,plain,
! [SV53: $i] :
( ( ( ~ ( ssItem @ ( sK13_SY323 @ SV53 ) )
| ! [SY492: $i] :
( ~ ( ssItem @ SY492 )
| ! [SY493: $i] :
( ~ ( ssList @ SY493 )
| ! [SY494: $i] :
( ~ ( ssList @ SY494 )
| ! [SY495: $i] :
( ~ ( ssList @ SY495 )
| ( ( app @ ( app @ SY493 @ ( cons @ ( sK13_SY323 @ SV53 ) @ SY494 ) ) @ ( cons @ SY492 @ SY495 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ SY492 ) ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1000]) ).
thf(1078,plain,
! [SV55: $i] :
( ( ( ~ ( ssList @ ( sK5_SY328 @ SV55 ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1079,plain,
! [SV55: $i] :
( ( ( ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( ssItem @ SY449 )
| ( ( cons @ SY449 @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1080,plain,
! [SV56: $i,SV116: $i] :
( ( ( gt @ SV116 @ SV56 )
= $false )
| ( ( gt @ SV56 @ SV116 )
= $false )
| ( ( ssItem @ SV116 )
= $false )
| ( ( ssItem @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1081,plain,
! [SV57: $i,SV117: $i,SV144: $i] :
( ( ( ssList @ SV144 )
= $false )
| ( ( ( ( app @ SV117 @ SV144 )
!= ( app @ SV117 @ SV57 ) )
| ( SV144 = SV57 ) )
= $true )
| ( ( ssList @ SV117 )
= $false )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1082,plain,
! [SV58: $i,SV158: $i] :
( ( ( ~ ( ssItem @ SV158 )
| ! [SY496: $i] :
( ~ ( ssItem @ SY496 )
| ! [SY497: $i] :
( ~ ( ssList @ SY497 )
| ! [SY498: $i] :
( ~ ( ssList @ SY498 )
| ! [SY499: $i] :
( ~ ( ssList @ SY499 )
| ( ( app @ ( app @ SY497 @ ( cons @ SV158 @ SY498 ) ) @ ( cons @ SY496 @ SY499 ) )
!= SV58 )
| ( leq @ SV158 @ SY496 )
| ( leq @ SY496 @ SV158 ) ) ) ) ) )
= $true )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1083,plain,
! [SV58: $i] :
( ( ( ~ ( ssItem @ ( sK14_SY338 @ SV58 ) )
| ! [SY500: $i] :
( ~ ( ssItem @ SY500 )
| ! [SY501: $i] :
( ~ ( ssList @ SY501 )
| ! [SY502: $i] :
( ~ ( ssList @ SY502 )
| ! [SY503: $i] :
( ~ ( ssList @ SY503 )
| ( ( app @ ( app @ SY501 @ ( cons @ ( sK14_SY338 @ SV58 ) @ SY502 ) ) @ ( cons @ SY500 @ SY503 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ SY500 )
| ( leq @ SY500 @ ( sK14_SY338 @ SV58 ) ) ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1005]) ).
thf(1084,plain,
! [SV118: $i,SV59: $i,SV145: $i] :
( ( ( ssList @ SV145 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SV145 ) )
| ( segmentP @ SV59 @ SV145 ) )
= $true )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1085,plain,
( ( ( sK2_SX0 != sK6_SY428 )
| ( sK1_U != sK4_SY389 )
| ! [SY450: $i] :
( ~ ( ssList @ SY450 )
| ! [SY451: $i] :
( ~ ( ssList @ SY451 )
| ( ( app @ ( app @ SY450 @ sK4_SY389 ) @ SY451 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY451 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1086,plain,
( ( ~ ( ~ ( ( nil != sK6_SY428 ) )
| ( nil != sK4_SY389 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1087,plain,
( ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1088,plain,
! [SV60: $i,SV119: $i,SV146: $i] :
( ( ( ssItem @ SV146 )
= $false )
| ( ( ( cons @ SV146 @ ( app @ SV119 @ SV60 ) )
= ( app @ ( cons @ SV146 @ SV119 ) @ SV60 ) )
= $true )
| ( ( ssList @ SV119 )
= $false )
| ( ( ssList @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1089,plain,
! [SV61: $i,SV120: $i,SV147: $i] :
( ( ( ssList @ SV147 )
= $false )
| ( ( ( ( app @ SV147 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
| ( SV147 = SV61 ) )
= $true )
| ( ( ssList @ SV120 )
= $false )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1090,plain,
! [SV121: $i,SV62: $i,SV148: $i] :
( ( ( ssItem @ SV148 )
= $false )
| ( ( ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SV148 ) )
| ( gt @ SV62 @ SV148 ) )
= $true )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1091,plain,
! [SV122: $i,SV63: $i] :
( ( ( ( nil
!= ( app @ SV63 @ SV122 ) )
| ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1092,plain,
! [SV63: $i,SV122: $i] :
( ( ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) )
| ( nil
= ( app @ SV63 @ SV122 ) ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1093,plain,
! [SV125: $i,SV67: $i] :
( ( ( ~ ( segmentP @ SV67 @ SV125 )
| ~ ( segmentP @ SV125 @ SV67 ) )
= $true )
| ( ( SV67 = SV125 )
= $true )
| ( ( ssList @ SV125 )
= $false )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1094,plain,
! [SV126: $i,SV68: $i,SV149: $i] :
( ( ( ssList @ SV149 )
= $false )
| ( ( ! [SY463: $i] :
( ~ ( ssList @ SY463 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SY463 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SY463 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SY463 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SY463 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1095,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( neq @ SV69 @ SV127 )
| ( SV69 != SV127 ) )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1096,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( ( SV69 != SV127 ) )
| ( neq @ SV69 @ SV127 ) )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1097,plain,
! [SV128: $i,SV70: $i] :
( ( ( SV70 = SV128 )
= $true )
| ( ( lt @ SV70 @ SV128 )
= $true )
| ( ( leq @ SV70 @ SV128 )
= $false )
| ( ( ssItem @ SV128 )
= $false )
| ( ( ssItem @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1098,plain,
! [SV129: $i,SV72: $i] :
( ( ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
| ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1099,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
| ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1100,plain,
( ( ~ ( ~ ( ssItem @ sK8_SY402 )
| ~ ( ( sK3_SX0 != sK8_SY402 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1101,plain,
! [SV130: $i,SV73: $i] :
( ( ( ~ ( leq @ SV73 @ SV130 )
| ~ ( leq @ SV130 @ SV73 ) )
= $true )
| ( ( SV73 = SV130 )
= $true )
| ( ( ssItem @ SV130 )
= $false )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1102,plain,
! [SV74: $i,SV159: $i] :
( ( ( ~ ( ssItem @ SV159 )
| ! [SY504: $i] :
( ~ ( ssItem @ SY504 )
| ! [SY505: $i] :
( ~ ( ssList @ SY505 )
| ! [SY506: $i] :
( ~ ( ssList @ SY506 )
| ( ( app @ SY505 @ ( cons @ SV159 @ ( cons @ SY504 @ SY506 ) ) )
!= SV74 )
| ( SV159 = SY504 ) ) ) ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1103,plain,
! [SV74: $i] :
( ( ( ~ ( ssItem @ ( sK15_SY366 @ SV74 ) )
| ! [SY507: $i] :
( ~ ( ssItem @ SY507 )
| ! [SY508: $i] :
( ~ ( ssList @ SY508 )
| ! [SY509: $i] :
( ~ ( ssList @ SY509 )
| ( ( app @ SY508 @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ SY507 @ SY509 ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= SY507 ) ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1025]) ).
thf(1104,plain,
! [SV131: $i,SV75: $i,SV150: $i] :
( ( ( ssList @ SV150 )
= $false )
| ( ( ( app @ ( app @ SV75 @ SV131 ) @ SV150 )
= ( app @ SV75 @ ( app @ SV131 @ SV150 ) ) )
= $true )
| ( ( ssList @ SV131 )
= $false )
| ( ( ssList @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1105,plain,
! [SV132: $i,SV76: $i,SV151: $i] :
( ( ( ssList @ SV151 )
= $false )
| ( ( ~ ( rearsegP @ SV76 @ SV132 )
| ( rearsegP @ ( app @ SV151 @ SV76 ) @ SV132 ) )
= $true )
| ( ( ssList @ SV132 )
= $false )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1106,plain,
! [SV133: $i,SV77: $i,SV152: $i] :
( ( ( ssList @ SV152 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SV152 ) )
| ( frontsegP @ SV77 @ SV152 ) )
= $true )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1107,plain,
! [SV134: $i,SV78: $i,SV153: $i] :
( ( ( ssItem @ SV153 )
= $false )
| ( ( ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SV153 ) )
| ( lt @ SV78 @ SV153 ) )
= $true )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1108,plain,
! [SV82: $i,SV160: $i] :
( ( ( ~ ( ssItem @ SV160 )
| ! [SY510: $i] :
( ~ ( ssItem @ SY510 )
| ! [SY511: $i] :
( ~ ( ssList @ SY511 )
| ! [SY512: $i] :
( ~ ( ssList @ SY512 )
| ! [SY513: $i] :
( ~ ( ssList @ SY513 )
| ( ( app @ ( app @ SY511 @ ( cons @ SV160 @ SY512 ) ) @ ( cons @ SY510 @ SY513 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SY510 )
| ~ ( leq @ SY510 @ SV160 ) ) ) ) ) ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1109,plain,
! [SV82: $i] :
( ( ( ~ ( ssItem @ ( sK16_SY383 @ SV82 ) )
| ! [SY514: $i] :
( ~ ( ssItem @ SY514 )
| ! [SY515: $i] :
( ~ ( ssList @ SY515 )
| ! [SY516: $i] :
( ~ ( ssList @ SY516 )
| ! [SY517: $i] :
( ~ ( ssList @ SY517 )
| ( ( app @ ( app @ SY515 @ ( cons @ ( sK16_SY383 @ SV82 ) @ SY516 ) ) @ ( cons @ SY514 @ SY517 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ SY514 )
| ~ ( leq @ SY514 @ ( sK16_SY383 @ SV82 ) ) ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1031]) ).
thf(1110,plain,
! [SV84: $i] :
( ( ( ~ ( ~ ( ssItem @ ( sK9_SY388 @ SV84 ) )
| ( ( hd @ SV84 )
!= ( sK9_SY388 @ SV84 ) ) ) )
= $true )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1111,plain,
! [SV86: $i,SV1: $i] :
( ( ( ~ ( frontsegP @ SV1 @ SV86 ) )
= $true )
| ( ( ~ ( frontsegP @ SV86 @ SV1 ) )
= $true )
| ( ( SV1 = SV86 )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1112,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( lt @ SV3 @ SV87 ) )
= $true )
| ( ( ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1113,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1114,plain,
! [SV88: $i,SV4: $i] :
( ( ( ~ ( gt @ SV4 @ SV88 ) )
= $true )
| ( ( lt @ SV88 @ SV4 )
= $true )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1115,plain,
! [SV4: $i,SV88: $i] :
( ( ( ~ ( lt @ SV88 @ SV4 ) )
= $true )
| ( ( gt @ SV4 @ SV88 )
= $true )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1116,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( neq @ SV5 @ SV89 ) )
= $true )
| ( ( SV5 != SV89 )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1117,plain,
! [SV89: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV89 ) ) )
= $true )
| ( ( neq @ SV5 @ SV89 )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1118,plain,
! [SV91: $i,SV10: $i] :
( ( ( ~ ( strictorderedP @ ( cons @ SV10 @ SV91 ) ) )
= $true )
| ( ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1119,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1120,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( frontsegP @ SV16 @ SV95 ) )
= $true )
| ( ( ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1121,plain,
! [SV16: $i,SV95: $i] :
( ( ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) ) )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1122,plain,
! [SV135: $i,SV96: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SV135 ) ) )
= $true )
| ( ( lt @ SV17 @ SV135 )
= $true )
| ( ( ssItem @ SV135 )
= $false )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1123,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( rearsegP @ SV18 @ SV97 ) )
= $true )
| ( ( ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1124,plain,
! [SV18: $i,SV97: $i] :
( ( ( ~ ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1125,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ ( sK17_SY249 @ SV19 ) )
| ( ( cons @ ( sK17_SY249 @ SV19 ) @ nil )
!= SV19 ) ) )
= $false )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1048]) ).
thf(1126,plain,
! [SV19: $i,SV161: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ SV161 )
| ( ( cons @ SV161 @ nil )
!= SV19 ) ) )
= $true )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1127,plain,
! [SV98: $i,SV20: $i] :
( ( ( ~ ( geq @ SV20 @ SV98 ) )
= $true )
| ( ( ~ ( geq @ SV98 @ SV20 ) )
= $true )
| ( ( SV20 = SV98 )
= $true )
| ( ( ssItem @ SV98 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1128,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( memberP @ SV21 @ SV99 ) )
= $true )
| ( ( ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1129,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1130,plain,
! [SV22: $i,SV154: $i] :
( ( ( ~ ( ssItem @ SV154 ) )
= $true )
| ( ( ! [SY464: $i] :
( ~ ( ssItem @ SY464 )
| ! [SY465: $i] :
( ~ ( ssList @ SY465 )
| ! [SY466: $i] :
( ~ ( ssList @ SY466 )
| ! [SY467: $i] :
( ~ ( ssList @ SY467 )
| ( ( app @ ( app @ SY465 @ ( cons @ SV154 @ SY466 ) ) @ ( cons @ SY464 @ SY467 ) )
!= SV22 )
| ( lt @ SV154 @ SY464 )
| ( lt @ SY464 @ SV154 ) ) ) ) ) )
= $true )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1131,plain,
! [SV22: $i] :
( ( ( ~ ( ssItem @ ( sK10_SY262 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1132,plain,
! [SV22: $i] :
( ( ( ! [SY468: $i] :
( ~ ( ssItem @ SY468 )
| ! [SY469: $i] :
( ~ ( ssList @ SY469 )
| ! [SY470: $i] :
( ~ ( ssList @ SY470 )
| ! [SY471: $i] :
( ~ ( ssList @ SY471 )
| ( ( app @ ( app @ SY469 @ ( cons @ ( sK10_SY262 @ SV22 ) @ SY470 ) ) @ ( cons @ SY468 @ SY471 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ SY468 )
| ( lt @ SY468 @ ( sK10_SY262 @ SV22 ) ) ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1133,plain,
! [SV24: $i,SV136: $i,SV100: $i] :
( ( ( ~ ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) ) )
= $false )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1134,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1135,plain,
! [SV137: $i,SV102: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SV137 ) ) )
= $true )
| ( ( rearsegP @ SV28 @ SV137 )
= $true )
| ( ( ssList @ SV137 )
= $false )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1136,plain,
! [SV29: $i,SV155: $i] :
( ( ( ~ ( ssItem @ SV155 ) )
= $true )
| ( ( ! [SY472: $i] :
( ~ ( ssItem @ SY472 )
| ! [SY473: $i] :
( ~ ( ssList @ SY473 )
| ! [SY474: $i] :
( ~ ( ssList @ SY474 )
| ! [SY475: $i] :
( ~ ( ssList @ SY475 )
| ( ( app @ ( app @ SY473 @ ( cons @ SV155 @ SY474 ) ) @ ( cons @ SY472 @ SY475 ) )
!= SV29 )
| ( leq @ SV155 @ SY472 ) ) ) ) ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1137,plain,
! [SV29: $i] :
( ( ( ~ ( ssItem @ ( sK11_SY277 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1138,plain,
! [SV29: $i] :
( ( ( ! [SY476: $i] :
( ~ ( ssItem @ SY476 )
| ! [SY477: $i] :
( ~ ( ssList @ SY477 )
| ! [SY478: $i] :
( ~ ( ssList @ SY478 )
| ! [SY479: $i] :
( ~ ( ssList @ SY479 )
| ( ( app @ ( app @ SY477 @ ( cons @ ( sK11_SY277 @ SV29 ) @ SY478 ) ) @ ( cons @ SY476 @ SY479 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ SY476 ) ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1139,plain,
! [SV138: $i,SV103: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SV138 ) ) )
= $true )
| ( ( leq @ SV31 @ SV138 )
= $true )
| ( ( ssItem @ SV138 )
= $false )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1140,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( segmentP @ SV34 @ SV105 ) )
= $true )
| ( ( ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1141,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1142,plain,
! [SV106: $i,SV35: $i,SV139: $i,SV162: $i] :
( ( ( ~ ( ssItem @ SV162 )
| ( ( cons @ SV139 @ SV35 )
!= ( cons @ SV162 @ SV106 ) )
| ~ ( ( SV139 != SV162 )
| ( SV106 != SV35 ) ) )
= $true )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1143,plain,
! [SV107: $i,SV39: $i] :
( ( ( ~ ( geq @ SV39 @ SV107 ) )
= $true )
| ( ( leq @ SV107 @ SV39 )
= $true )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1144,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( leq @ SV107 @ SV39 ) )
= $true )
| ( ( geq @ SV39 @ SV107 )
= $true )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1145,plain,
! [SV140: $i,SV108: $i,SV40: $i,SV163: $i] :
( ( ( ~ ( ssList @ SV163 )
| ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SV163 ) @ SV108 ) )
= $true )
| ( ( ssList @ SV140 )
= $false )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1146,plain,
! [SV141: $i,SV112: $i,SV45: $i] :
( ( ( ~ ( frontsegP @ SV45 @ SV112 ) )
= $true )
| ( ( frontsegP @ ( app @ SV45 @ SV141 ) @ SV112 )
= $true )
| ( ( ssList @ SV141 )
= $false )
| ( ( ssList @ SV112 )
= $false )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1147,plain,
! [SV46: $i,SV142: $i,SV113: $i] :
( ( ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) ) )
= $false )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1148,plain,
! [SV48: $i,SV156: $i] :
( ( ( ~ ( ssItem @ SV156 ) )
= $true )
| ( ( ! [SY480: $i] :
( ~ ( ssItem @ SY480 )
| ! [SY481: $i] :
( ~ ( ssList @ SY481 )
| ! [SY482: $i] :
( ~ ( ssList @ SY482 )
| ! [SY483: $i] :
( ~ ( ssList @ SY483 )
| ( ( app @ ( app @ SY481 @ ( cons @ SV156 @ SY482 ) ) @ ( cons @ SY480 @ SY483 ) )
!= SV48 )
| ( SV156 != SY480 ) ) ) ) ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1149,plain,
! [SV48: $i] :
( ( ( ~ ( ssItem @ ( sK12_SY309 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1150,plain,
! [SV48: $i] :
( ( ( ! [SY484: $i] :
( ~ ( ssItem @ SY484 )
| ! [SY485: $i] :
( ~ ( ssList @ SY485 )
| ! [SY486: $i] :
( ~ ( ssList @ SY486 )
| ! [SY487: $i] :
( ~ ( ssList @ SY487 )
| ( ( app @ ( app @ SY485 @ ( cons @ ( sK12_SY309 @ SV48 ) @ SY486 ) ) @ ( cons @ SY484 @ SY487 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= SY484 ) ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1151,plain,
! [SV114: $i,SV50: $i] :
( ( ( ~ ( rearsegP @ SV50 @ SV114 ) )
= $true )
| ( ( ~ ( rearsegP @ SV114 @ SV50 ) )
= $true )
| ( ( SV50 = SV114 )
= $true )
| ( ( ssList @ SV114 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1152,plain,
! [SV51: $i] :
( ( ( ~ ( ssList @ ( sK7_SY315 @ SV51 ) )
| ( ( tl @ SV51 )
!= ( sK7_SY315 @ SV51 ) ) )
= $false )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1153,plain,
! [SV143: $i,SV115: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SV143 ) ) )
= $true )
| ( ( geq @ SV52 @ SV143 )
= $true )
| ( ( ssItem @ SV143 )
= $false )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1154,plain,
! [SV53: $i,SV157: $i] :
( ( ( ~ ( ssItem @ SV157 ) )
= $true )
| ( ( ! [SY488: $i] :
( ~ ( ssItem @ SY488 )
| ! [SY489: $i] :
( ~ ( ssList @ SY489 )
| ! [SY490: $i] :
( ~ ( ssList @ SY490 )
| ! [SY491: $i] :
( ~ ( ssList @ SY491 )
| ( ( app @ ( app @ SY489 @ ( cons @ SV157 @ SY490 ) ) @ ( cons @ SY488 @ SY491 ) )
!= SV53 )
| ( lt @ SV157 @ SY488 ) ) ) ) ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1155,plain,
! [SV53: $i] :
( ( ( ~ ( ssItem @ ( sK13_SY323 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1156,plain,
! [SV53: $i] :
( ( ( ! [SY492: $i] :
( ~ ( ssItem @ SY492 )
| ! [SY493: $i] :
( ~ ( ssList @ SY493 )
| ! [SY494: $i] :
( ~ ( ssList @ SY494 )
| ! [SY495: $i] :
( ~ ( ssList @ SY495 )
| ( ( app @ ( app @ SY493 @ ( cons @ ( sK13_SY323 @ SV53 ) @ SY494 ) ) @ ( cons @ SY492 @ SY495 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ SY492 ) ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1157,plain,
! [SV55: $i] :
( ( ( ssList @ ( sK5_SY328 @ SV55 ) )
= $true )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1158,plain,
! [SV55: $i] :
( ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( ssItem @ SY449 )
| ( ( cons @ SY449 @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) )
= $true )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1159,plain,
! [SV57: $i,SV144: $i,SV117: $i] :
( ( ( ( app @ SV117 @ SV144 )
!= ( app @ SV117 @ SV57 ) )
= $true )
| ( ( SV144 = SV57 )
= $true )
| ( ( ssList @ SV144 )
= $false )
| ( ( ssList @ SV117 )
= $false )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1160,plain,
! [SV58: $i,SV158: $i] :
( ( ( ~ ( ssItem @ SV158 ) )
= $true )
| ( ( ! [SY496: $i] :
( ~ ( ssItem @ SY496 )
| ! [SY497: $i] :
( ~ ( ssList @ SY497 )
| ! [SY498: $i] :
( ~ ( ssList @ SY498 )
| ! [SY499: $i] :
( ~ ( ssList @ SY499 )
| ( ( app @ ( app @ SY497 @ ( cons @ SV158 @ SY498 ) ) @ ( cons @ SY496 @ SY499 ) )
!= SV58 )
| ( leq @ SV158 @ SY496 )
| ( leq @ SY496 @ SV158 ) ) ) ) ) )
= $true )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1161,plain,
! [SV58: $i] :
( ( ( ~ ( ssItem @ ( sK14_SY338 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1162,plain,
! [SV58: $i] :
( ( ( ! [SY500: $i] :
( ~ ( ssItem @ SY500 )
| ! [SY501: $i] :
( ~ ( ssList @ SY501 )
| ! [SY502: $i] :
( ~ ( ssList @ SY502 )
| ! [SY503: $i] :
( ~ ( ssList @ SY503 )
| ( ( app @ ( app @ SY501 @ ( cons @ ( sK14_SY338 @ SV58 ) @ SY502 ) ) @ ( cons @ SY500 @ SY503 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ SY500 )
| ( leq @ SY500 @ ( sK14_SY338 @ SV58 ) ) ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1163,plain,
! [SV145: $i,SV118: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SV145 ) ) )
= $true )
| ( ( segmentP @ SV59 @ SV145 )
= $true )
| ( ( ssList @ SV145 )
= $false )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1164,plain,
( ( ( sK2_SX0 != sK6_SY428 )
| ( sK1_U != sK4_SY389 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1165,plain,
( ( ! [SY450: $i] :
( ~ ( ssList @ SY450 )
| ! [SY451: $i] :
( ~ ( ssList @ SY451 )
| ( ( app @ ( app @ SY450 @ sK4_SY389 ) @ SY451 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( ssItem @ SY431 )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY432 )
| ( ( app @ SY432 @ ( cons @ SY431 @ nil ) )
!= SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY431 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY451 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1166,plain,
( ( ~ ( ( nil != sK6_SY428 ) )
| ( nil != sK4_SY389 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1167,plain,
( ( ( ~ ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) ) )
= $true )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1168,plain,
! [SV61: $i,SV120: $i,SV147: $i] :
( ( ( ( app @ SV147 @ SV120 )
!= ( app @ SV61 @ SV120 ) )
= $true )
| ( ( SV147 = SV61 )
= $true )
| ( ( ssList @ SV147 )
= $false )
| ( ( ssList @ SV120 )
= $false )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1169,plain,
! [SV148: $i,SV121: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SV148 ) ) )
= $true )
| ( ( gt @ SV62 @ SV148 )
= $true )
| ( ( ssItem @ SV148 )
= $false )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1170,plain,
! [SV122: $i,SV63: $i] :
( ( ( nil
!= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1171,plain,
! [SV63: $i,SV122: $i] :
( ( ( ~ ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
= $true )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1172,plain,
! [SV125: $i,SV67: $i] :
( ( ( ~ ( segmentP @ SV67 @ SV125 ) )
= $true )
| ( ( ~ ( segmentP @ SV125 @ SV67 ) )
= $true )
| ( ( SV67 = SV125 )
= $true )
| ( ( ssList @ SV125 )
= $false )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1173,plain,
! [SV126: $i,SV149: $i,SV68: $i,SV164: $i] :
( ( ( ~ ( ssList @ SV164 )
| ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) ) ) )
= $true )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1174,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( neq @ SV69 @ SV127 ) )
= $true )
| ( ( SV69 != SV127 )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1175,plain,
! [SV127: $i,SV69: $i] :
( ( ( ~ ( ( SV69 != SV127 ) ) )
= $true )
| ( ( neq @ SV69 @ SV127 )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1176,plain,
! [SV129: $i,SV72: $i] :
( ( ( ~ ( totalorderedP @ ( cons @ SV72 @ SV129 ) ) )
= $true )
| ( ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1177,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1178,plain,
( ( ~ ( ssItem @ sK8_SY402 )
| ~ ( ( sK3_SX0 != sK8_SY402 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1179,plain,
! [SV130: $i,SV73: $i] :
( ( ( ~ ( leq @ SV73 @ SV130 ) )
= $true )
| ( ( ~ ( leq @ SV130 @ SV73 ) )
= $true )
| ( ( SV73 = SV130 )
= $true )
| ( ( ssItem @ SV130 )
= $false )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1180,plain,
! [SV74: $i,SV159: $i] :
( ( ( ~ ( ssItem @ SV159 ) )
= $true )
| ( ( ! [SY504: $i] :
( ~ ( ssItem @ SY504 )
| ! [SY505: $i] :
( ~ ( ssList @ SY505 )
| ! [SY506: $i] :
( ~ ( ssList @ SY506 )
| ( ( app @ SY505 @ ( cons @ SV159 @ ( cons @ SY504 @ SY506 ) ) )
!= SV74 )
| ( SV159 = SY504 ) ) ) ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1181,plain,
! [SV74: $i] :
( ( ( ~ ( ssItem @ ( sK15_SY366 @ SV74 ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1182,plain,
! [SV74: $i] :
( ( ( ! [SY507: $i] :
( ~ ( ssItem @ SY507 )
| ! [SY508: $i] :
( ~ ( ssList @ SY508 )
| ! [SY509: $i] :
( ~ ( ssList @ SY509 )
| ( ( app @ SY508 @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ SY507 @ SY509 ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= SY507 ) ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1183,plain,
! [SV151: $i,SV132: $i,SV76: $i] :
( ( ( ~ ( rearsegP @ SV76 @ SV132 ) )
= $true )
| ( ( rearsegP @ ( app @ SV151 @ SV76 ) @ SV132 )
= $true )
| ( ( ssList @ SV151 )
= $false )
| ( ( ssList @ SV132 )
= $false )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1184,plain,
! [SV152: $i,SV133: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SV152 ) ) )
= $true )
| ( ( frontsegP @ SV77 @ SV152 )
= $true )
| ( ( ssList @ SV152 )
= $false )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1185,plain,
! [SV153: $i,SV134: $i,SV78: $i] :
( ( ( ~ ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SV153 ) ) )
= $true )
| ( ( lt @ SV78 @ SV153 )
= $true )
| ( ( ssItem @ SV153 )
= $false )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1186,plain,
! [SV82: $i,SV160: $i] :
( ( ( ~ ( ssItem @ SV160 ) )
= $true )
| ( ( ! [SY510: $i] :
( ~ ( ssItem @ SY510 )
| ! [SY511: $i] :
( ~ ( ssList @ SY511 )
| ! [SY512: $i] :
( ~ ( ssList @ SY512 )
| ! [SY513: $i] :
( ~ ( ssList @ SY513 )
| ( ( app @ ( app @ SY511 @ ( cons @ SV160 @ SY512 ) ) @ ( cons @ SY510 @ SY513 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SY510 )
| ~ ( leq @ SY510 @ SV160 ) ) ) ) ) ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1187,plain,
! [SV82: $i] :
( ( ( ~ ( ssItem @ ( sK16_SY383 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1188,plain,
! [SV82: $i] :
( ( ( ! [SY514: $i] :
( ~ ( ssItem @ SY514 )
| ! [SY515: $i] :
( ~ ( ssList @ SY515 )
| ! [SY516: $i] :
( ~ ( ssList @ SY516 )
| ! [SY517: $i] :
( ~ ( ssList @ SY517 )
| ( ( app @ ( app @ SY515 @ ( cons @ ( sK16_SY383 @ SV82 ) @ SY516 ) ) @ ( cons @ SY514 @ SY517 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ SY514 )
| ~ ( leq @ SY514 @ ( sK16_SY383 @ SV82 ) ) ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1189,plain,
! [SV84: $i] :
( ( ( ~ ( ssItem @ ( sK9_SY388 @ SV84 ) )
| ( ( hd @ SV84 )
!= ( sK9_SY388 @ SV84 ) ) )
= $false )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1190,plain,
! [SV86: $i,SV1: $i] :
( ( ( frontsegP @ SV1 @ SV86 )
= $false )
| ( ( ~ ( frontsegP @ SV86 @ SV1 ) )
= $true )
| ( ( SV1 = SV86 )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1191,plain,
! [SV87: $i,SV3: $i] :
( ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1192,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) ) )
= $false )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1193,plain,
! [SV88: $i,SV4: $i] :
( ( ( gt @ SV4 @ SV88 )
= $false )
| ( ( lt @ SV88 @ SV4 )
= $true )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1194,plain,
! [SV4: $i,SV88: $i] :
( ( ( lt @ SV88 @ SV4 )
= $false )
| ( ( gt @ SV4 @ SV88 )
= $true )
| ( ( ssItem @ SV88 )
= $false )
| ( ( ssItem @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1195,plain,
! [SV89: $i,SV5: $i] :
( ( ( neq @ SV5 @ SV89 )
= $false )
| ( ( SV5 != SV89 )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1196,plain,
! [SV89: $i,SV5: $i] :
( ( ( SV5 != SV89 )
= $false )
| ( ( neq @ SV5 @ SV89 )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1197,plain,
! [SV91: $i,SV10: $i] :
( ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1198,plain,
! [SV10: $i,SV91: $i] :
( ( ( ( nil = SV91 )
| ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
= $false )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1199,plain,
! [SV95: $i,SV16: $i] :
( ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ~ ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1200,plain,
! [SV16: $i,SV95: $i] :
( ( ( ~ ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) ) )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1201,plain,
! [SV135: $i,SV96: $i,SV17: $i] :
( ( ( ~ ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SV135 ) ) )
= $false )
| ( ( lt @ SV17 @ SV135 )
= $true )
| ( ( ssItem @ SV135 )
= $false )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1202,plain,
! [SV97: $i,SV18: $i] :
( ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ~ ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1203,plain,
! [SV18: $i,SV97: $i] :
( ( ( ~ ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1204,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( ssItem @ ( sK17_SY249 @ SV19 ) )
| ( ( cons @ ( sK17_SY249 @ SV19 ) @ nil )
!= SV19 ) ) )
= $true )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1205,plain,
! [SV19: $i,SV161: $i] :
( ( ( ~ ( ~ ( ssItem @ SV161 )
| ( ( cons @ SV161 @ nil )
!= SV19 ) ) )
= $false )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1206,plain,
! [SV98: $i,SV20: $i] :
( ( ( geq @ SV20 @ SV98 )
= $false )
| ( ( ~ ( geq @ SV98 @ SV20 ) )
= $true )
| ( ( SV20 = SV98 )
= $true )
| ( ( ssItem @ SV98 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1207,plain,
! [SV99: $i,SV21: $i] :
( ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ~ ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1208,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1209,plain,
! [SV22: $i,SV154: $i] :
( ( ( ssItem @ SV154 )
= $false )
| ( ( ! [SY464: $i] :
( ~ ( ssItem @ SY464 )
| ! [SY465: $i] :
( ~ ( ssList @ SY465 )
| ! [SY466: $i] :
( ~ ( ssList @ SY466 )
| ! [SY467: $i] :
( ~ ( ssList @ SY467 )
| ( ( app @ ( app @ SY465 @ ( cons @ SV154 @ SY466 ) ) @ ( cons @ SY464 @ SY467 ) )
!= SV22 )
| ( lt @ SV154 @ SY464 )
| ( lt @ SY464 @ SV154 ) ) ) ) ) )
= $true )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1210,plain,
! [SV22: $i] :
( ( ( ssItem @ ( sK10_SY262 @ SV22 ) )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1211,plain,
! [SV22: $i] :
( ( ( ~ ( ssItem @ ( sK18_SY468 @ SV22 ) )
| ! [SY518: $i] :
( ~ ( ssList @ SY518 )
| ! [SY519: $i] :
( ~ ( ssList @ SY519 )
| ! [SY520: $i] :
( ~ ( ssList @ SY520 )
| ( ( app @ ( app @ SY518 @ ( cons @ ( sK10_SY262 @ SV22 ) @ SY519 ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ SY520 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1132]) ).
thf(1212,plain,
! [SV24: $i,SV136: $i,SV100: $i] :
( ( ( ~ ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) ) )
= $false )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1133]) ).
thf(1213,plain,
! [SV136: $i,SV24: $i,SV100: $i] :
( ( ( ~ ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) ) )
= $false )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1133]) ).
thf(1214,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) ) )
= $false )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1215,plain,
! [SV137: $i,SV102: $i,SV28: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SV137 ) ) )
= $false )
| ( ( rearsegP @ SV28 @ SV137 )
= $true )
| ( ( ssList @ SV137 )
= $false )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1216,plain,
! [SV29: $i,SV155: $i] :
( ( ( ssItem @ SV155 )
= $false )
| ( ( ! [SY472: $i] :
( ~ ( ssItem @ SY472 )
| ! [SY473: $i] :
( ~ ( ssList @ SY473 )
| ! [SY474: $i] :
( ~ ( ssList @ SY474 )
| ! [SY475: $i] :
( ~ ( ssList @ SY475 )
| ( ( app @ ( app @ SY473 @ ( cons @ SV155 @ SY474 ) ) @ ( cons @ SY472 @ SY475 ) )
!= SV29 )
| ( leq @ SV155 @ SY472 ) ) ) ) ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1217,plain,
! [SV29: $i] :
( ( ( ssItem @ ( sK11_SY277 @ SV29 ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1218,plain,
! [SV29: $i] :
( ( ( ~ ( ssItem @ ( sK19_SY476 @ SV29 ) )
| ! [SY521: $i] :
( ~ ( ssList @ SY521 )
| ! [SY522: $i] :
( ~ ( ssList @ SY522 )
| ! [SY523: $i] :
( ~ ( ssList @ SY523 )
| ( ( app @ ( app @ SY521 @ ( cons @ ( sK11_SY277 @ SV29 ) @ SY522 ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ SY523 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1138]) ).
thf(1219,plain,
! [SV138: $i,SV103: $i,SV31: $i] :
( ( ( ~ ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SV138 ) ) )
= $false )
| ( ( leq @ SV31 @ SV138 )
= $true )
| ( ( ssItem @ SV138 )
= $false )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1220,plain,
! [SV105: $i,SV34: $i] :
( ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ~ ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1221,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1222,plain,
! [SV106: $i,SV35: $i,SV139: $i,SV162: $i] :
( ( ( ~ ( ssItem @ SV162 ) )
= $true )
| ( ( ( ( cons @ SV139 @ SV35 )
!= ( cons @ SV162 @ SV106 ) )
| ~ ( ( SV139 != SV162 )
| ( SV106 != SV35 ) ) )
= $true )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1223,plain,
! [SV107: $i,SV39: $i] :
( ( ( geq @ SV39 @ SV107 )
= $false )
| ( ( leq @ SV107 @ SV39 )
= $true )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1224,plain,
! [SV39: $i,SV107: $i] :
( ( ( leq @ SV107 @ SV39 )
= $false )
| ( ( geq @ SV39 @ SV107 )
= $true )
| ( ( ssItem @ SV107 )
= $false )
| ( ( ssItem @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1225,plain,
! [SV140: $i,SV108: $i,SV40: $i,SV163: $i] :
( ( ( ~ ( ssList @ SV163 ) )
= $true )
| ( ( ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SV163 ) @ SV108 ) )
= $true )
| ( ( ssList @ SV140 )
= $false )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1226,plain,
! [SV141: $i,SV112: $i,SV45: $i] :
( ( ( frontsegP @ SV45 @ SV112 )
= $false )
| ( ( frontsegP @ ( app @ SV45 @ SV141 ) @ SV112 )
= $true )
| ( ( ssList @ SV141 )
= $false )
| ( ( ssList @ SV112 )
= $false )
| ( ( ssList @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1227,plain,
! [SV46: $i,SV142: $i,SV113: $i] :
( ( ( ~ ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) ) )
= $false )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1228,plain,
! [SV142: $i,SV113: $i,SV46: $i] :
( ( ( ~ ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) ) )
= $false )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1229,plain,
! [SV48: $i,SV156: $i] :
( ( ( ssItem @ SV156 )
= $false )
| ( ( ! [SY480: $i] :
( ~ ( ssItem @ SY480 )
| ! [SY481: $i] :
( ~ ( ssList @ SY481 )
| ! [SY482: $i] :
( ~ ( ssList @ SY482 )
| ! [SY483: $i] :
( ~ ( ssList @ SY483 )
| ( ( app @ ( app @ SY481 @ ( cons @ SV156 @ SY482 ) ) @ ( cons @ SY480 @ SY483 ) )
!= SV48 )
| ( SV156 != SY480 ) ) ) ) ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1230,plain,
! [SV48: $i] :
( ( ( ssItem @ ( sK12_SY309 @ SV48 ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1231,plain,
! [SV48: $i] :
( ( ( ~ ( ssItem @ ( sK20_SY484 @ SV48 ) )
| ! [SY524: $i] :
( ~ ( ssList @ SY524 )
| ! [SY525: $i] :
( ~ ( ssList @ SY525 )
| ! [SY526: $i] :
( ~ ( ssList @ SY526 )
| ( ( app @ ( app @ SY524 @ ( cons @ ( sK12_SY309 @ SV48 ) @ SY525 ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ SY526 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1150]) ).
thf(1232,plain,
! [SV114: $i,SV50: $i] :
( ( ( rearsegP @ SV50 @ SV114 )
= $false )
| ( ( ~ ( rearsegP @ SV114 @ SV50 ) )
= $true )
| ( ( SV50 = SV114 )
= $true )
| ( ( ssList @ SV114 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1233,plain,
! [SV51: $i] :
( ( ( ~ ( ssList @ ( sK7_SY315 @ SV51 ) ) )
= $false )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1234,plain,
! [SV51: $i] :
( ( ( ( tl @ SV51 )
!= ( sK7_SY315 @ SV51 ) )
= $false )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1235,plain,
! [SV143: $i,SV115: $i,SV52: $i] :
( ( ( ~ ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SV143 ) ) )
= $false )
| ( ( geq @ SV52 @ SV143 )
= $true )
| ( ( ssItem @ SV143 )
= $false )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1236,plain,
! [SV53: $i,SV157: $i] :
( ( ( ssItem @ SV157 )
= $false )
| ( ( ! [SY488: $i] :
( ~ ( ssItem @ SY488 )
| ! [SY489: $i] :
( ~ ( ssList @ SY489 )
| ! [SY490: $i] :
( ~ ( ssList @ SY490 )
| ! [SY491: $i] :
( ~ ( ssList @ SY491 )
| ( ( app @ ( app @ SY489 @ ( cons @ SV157 @ SY490 ) ) @ ( cons @ SY488 @ SY491 ) )
!= SV53 )
| ( lt @ SV157 @ SY488 ) ) ) ) ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1237,plain,
! [SV53: $i] :
( ( ( ssItem @ ( sK13_SY323 @ SV53 ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1238,plain,
! [SV53: $i] :
( ( ( ~ ( ssItem @ ( sK21_SY492 @ SV53 ) )
| ! [SY527: $i] :
( ~ ( ssList @ SY527 )
| ! [SY528: $i] :
( ~ ( ssList @ SY528 )
| ! [SY529: $i] :
( ~ ( ssList @ SY529 )
| ( ( app @ ( app @ SY527 @ ( cons @ ( sK13_SY323 @ SV53 ) @ SY528 ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ SY529 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1156]) ).
thf(1239,plain,
! [SV55: $i] :
( ( ( ! [SY449: $i] :
~ ~ ( ~ ( ssItem @ SY449 )
| ( ( cons @ SY449 @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1240,plain,
! [SV57: $i,SV144: $i,SV117: $i] :
( ( ( ( app @ SV117 @ SV144 )
= ( app @ SV117 @ SV57 ) )
= $false )
| ( ( SV144 = SV57 )
= $true )
| ( ( ssList @ SV144 )
= $false )
| ( ( ssList @ SV117 )
= $false )
| ( ( ssList @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1241,plain,
! [SV58: $i,SV158: $i] :
( ( ( ssItem @ SV158 )
= $false )
| ( ( ! [SY496: $i] :
( ~ ( ssItem @ SY496 )
| ! [SY497: $i] :
( ~ ( ssList @ SY497 )
| ! [SY498: $i] :
( ~ ( ssList @ SY498 )
| ! [SY499: $i] :
( ~ ( ssList @ SY499 )
| ( ( app @ ( app @ SY497 @ ( cons @ SV158 @ SY498 ) ) @ ( cons @ SY496 @ SY499 ) )
!= SV58 )
| ( leq @ SV158 @ SY496 )
| ( leq @ SY496 @ SV158 ) ) ) ) ) )
= $true )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1242,plain,
! [SV58: $i] :
( ( ( ssItem @ ( sK14_SY338 @ SV58 ) )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1243,plain,
! [SV58: $i] :
( ( ( ~ ( ssItem @ ( sK22_SY500 @ SV58 ) )
| ! [SY530: $i] :
( ~ ( ssList @ SY530 )
| ! [SY531: $i] :
( ~ ( ssList @ SY531 )
| ! [SY532: $i] :
( ~ ( ssList @ SY532 )
| ( ( app @ ( app @ SY530 @ ( cons @ ( sK14_SY338 @ SV58 ) @ SY531 ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ SY532 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1162]) ).
thf(1244,plain,
! [SV145: $i,SV118: $i,SV59: $i] :
( ( ( ~ ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SV145 ) ) )
= $false )
| ( ( segmentP @ SV59 @ SV145 )
= $true )
| ( ( ssList @ SV145 )
= $false )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1245,plain,
( ( sK2_SX0 != sK6_SY428 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1164]) ).
thf(1246,plain,
( ( sK1_U != sK4_SY389 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1164]) ).
thf(1247,plain,
( ( ~ ( ssList @ sK23_SY450 )
| ! [SY533: $i] :
( ~ ( ssList @ SY533 )
| ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ SY533 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY533 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1165]) ).
thf(1248,plain,
( ( ( ~ ( ( nil != sK6_SY428 ) ) )
= $true )
| ( ( nil != sK4_SY389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1249,plain,
( ( ( ( nil != sK2_SX0 )
| ( nil = sK1_U ) )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1250,plain,
! [SV61: $i,SV120: $i,SV147: $i] :
( ( ( ( app @ SV147 @ SV120 )
= ( app @ SV61 @ SV120 ) )
= $false )
| ( ( SV147 = SV61 )
= $true )
| ( ( ssList @ SV147 )
= $false )
| ( ( ssList @ SV120 )
= $false )
| ( ( ssList @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1251,plain,
! [SV148: $i,SV121: $i,SV62: $i] :
( ( ( ~ ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SV148 ) ) )
= $false )
| ( ( gt @ SV62 @ SV148 )
= $true )
| ( ( ssItem @ SV148 )
= $false )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1252,plain,
! [SV122: $i,SV63: $i] :
( ( ( nil
= ( app @ SV63 @ SV122 ) )
= $false )
| ( ( ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1253,plain,
! [SV63: $i,SV122: $i] :
( ( ( ~ ( ( nil != SV122 )
| ( nil != SV63 ) ) )
= $false )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1254,plain,
! [SV125: $i,SV67: $i] :
( ( ( segmentP @ SV67 @ SV125 )
= $false )
| ( ( ~ ( segmentP @ SV125 @ SV67 ) )
= $true )
| ( ( SV67 = SV125 )
= $true )
| ( ( ssList @ SV125 )
= $false )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1255,plain,
! [SV126: $i,SV149: $i,SV68: $i,SV164: $i] :
( ( ( ~ ( ssList @ SV164 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) ) ) )
= $true )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1256,plain,
! [SV127: $i,SV69: $i] :
( ( ( neq @ SV69 @ SV127 )
= $false )
| ( ( SV69 != SV127 )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1257,plain,
! [SV127: $i,SV69: $i] :
( ( ( SV69 != SV127 )
= $false )
| ( ( neq @ SV69 @ SV127 )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1258,plain,
! [SV129: $i,SV72: $i] :
( ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1259,plain,
! [SV72: $i,SV129: $i] :
( ( ( ( nil = SV129 )
| ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
= $false )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1260,plain,
( ( ~ ( ssItem @ sK8_SY402 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1261,plain,
( ( ~ ( ( sK3_SX0 != sK8_SY402 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1262,plain,
! [SV130: $i,SV73: $i] :
( ( ( leq @ SV73 @ SV130 )
= $false )
| ( ( ~ ( leq @ SV130 @ SV73 ) )
= $true )
| ( ( SV73 = SV130 )
= $true )
| ( ( ssItem @ SV130 )
= $false )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1263,plain,
! [SV74: $i,SV159: $i] :
( ( ( ssItem @ SV159 )
= $false )
| ( ( ! [SY504: $i] :
( ~ ( ssItem @ SY504 )
| ! [SY505: $i] :
( ~ ( ssList @ SY505 )
| ! [SY506: $i] :
( ~ ( ssList @ SY506 )
| ( ( app @ SY505 @ ( cons @ SV159 @ ( cons @ SY504 @ SY506 ) ) )
!= SV74 )
| ( SV159 = SY504 ) ) ) ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1264,plain,
! [SV74: $i] :
( ( ( ssItem @ ( sK15_SY366 @ SV74 ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1265,plain,
! [SV74: $i] :
( ( ( ~ ( ssItem @ ( sK24_SY507 @ SV74 ) )
| ! [SY542: $i] :
( ~ ( ssList @ SY542 )
| ! [SY543: $i] :
( ~ ( ssList @ SY543 )
| ( ( app @ SY542 @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ SY543 ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1182]) ).
thf(1266,plain,
! [SV151: $i,SV132: $i,SV76: $i] :
( ( ( rearsegP @ SV76 @ SV132 )
= $false )
| ( ( rearsegP @ ( app @ SV151 @ SV76 ) @ SV132 )
= $true )
| ( ( ssList @ SV151 )
= $false )
| ( ( ssList @ SV132 )
= $false )
| ( ( ssList @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1267,plain,
! [SV152: $i,SV133: $i,SV77: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SV152 ) ) )
= $false )
| ( ( frontsegP @ SV77 @ SV152 )
= $true )
| ( ( ssList @ SV152 )
= $false )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1268,plain,
! [SV153: $i,SV134: $i,SV78: $i] :
( ( ( ~ ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SV153 ) ) )
= $false )
| ( ( lt @ SV78 @ SV153 )
= $true )
| ( ( ssItem @ SV153 )
= $false )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1269,plain,
! [SV82: $i,SV160: $i] :
( ( ( ssItem @ SV160 )
= $false )
| ( ( ! [SY510: $i] :
( ~ ( ssItem @ SY510 )
| ! [SY511: $i] :
( ~ ( ssList @ SY511 )
| ! [SY512: $i] :
( ~ ( ssList @ SY512 )
| ! [SY513: $i] :
( ~ ( ssList @ SY513 )
| ( ( app @ ( app @ SY511 @ ( cons @ SV160 @ SY512 ) ) @ ( cons @ SY510 @ SY513 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SY510 )
| ~ ( leq @ SY510 @ SV160 ) ) ) ) ) ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1270,plain,
! [SV82: $i] :
( ( ( ssItem @ ( sK16_SY383 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1271,plain,
! [SV82: $i] :
( ( ( ~ ( ssItem @ ( sK25_SY514 @ SV82 ) )
| ! [SY544: $i] :
( ~ ( ssList @ SY544 )
| ! [SY545: $i] :
( ~ ( ssList @ SY545 )
| ! [SY546: $i] :
( ~ ( ssList @ SY546 )
| ( ( app @ ( app @ SY544 @ ( cons @ ( sK16_SY383 @ SV82 ) @ SY545 ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ SY546 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1188]) ).
thf(1272,plain,
! [SV84: $i] :
( ( ( ~ ( ssItem @ ( sK9_SY388 @ SV84 ) ) )
= $false )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1189]) ).
thf(1273,plain,
! [SV84: $i] :
( ( ( ( hd @ SV84 )
!= ( sK9_SY388 @ SV84 ) )
= $false )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1189]) ).
thf(1274,plain,
! [SV1: $i,SV86: $i] :
( ( ( frontsegP @ SV86 @ SV1 )
= $false )
| ( ( frontsegP @ SV1 @ SV86 )
= $false )
| ( ( SV1 = SV86 )
= $true )
| ( ( ssList @ SV86 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1275,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
= $false )
| ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1276,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV87 ) )
| ~ ( leq @ SV3 @ SV87 ) )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1277,plain,
! [SV89: $i,SV5: $i] :
( ( ( SV5 = SV89 )
= $false )
| ( ( neq @ SV5 @ SV89 )
= $false )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1278,plain,
! [SV89: $i,SV5: $i] :
( ( ( SV5 = SV89 )
= $true )
| ( ( neq @ SV5 @ SV89 )
= $true )
| ( ( ssItem @ SV89 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1279,plain,
! [SV10: $i,SV91: $i] :
( ( ( nil = SV91 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1280,plain,
! [SV10: $i,SV91: $i] :
( ( ( nil = SV91 )
= $false )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1281,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) ) )
= $false )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1282,plain,
! [SV16: $i,SV95: $i] :
( ( ( ! [SY403: $i] :
~ ~ ( ~ ( ssList @ SY403 )
| ( ( app @ SV95 @ SY403 )
!= SV16 ) ) )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1283,plain,
! [SV16: $i,SV95: $i] :
( ( ( ! [SY404: $i] :
~ ~ ( ~ ( ssList @ SY404 )
| ( ( app @ SV95 @ SY404 )
!= SV16 ) ) )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1284,plain,
! [SV135: $i,SV96: $i,SV17: $i] :
( ( ( ~ ( leq @ SV17 @ SV96 )
| ~ ( lt @ SV96 @ SV135 ) )
= $true )
| ( ( lt @ SV17 @ SV135 )
= $true )
| ( ( ssItem @ SV135 )
= $false )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1285,plain,
! [SV18: $i,SV97: $i] :
( ( ( ! [SY406: $i] :
~ ~ ( ~ ( ssList @ SY406 )
| ( ( app @ SY406 @ SV97 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1286,plain,
! [SV18: $i,SV97: $i] :
( ( ( ! [SY407: $i] :
~ ~ ( ~ ( ssList @ SY407 )
| ( ( app @ SY407 @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1287,plain,
! [SV19: $i] :
( ( ( ~ ( ssItem @ ( sK17_SY249 @ SV19 ) )
| ( ( cons @ ( sK17_SY249 @ SV19 ) @ nil )
!= SV19 ) )
= $false )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1288,plain,
! [SV19: $i,SV161: $i] :
( ( ( ~ ( ssItem @ SV161 )
| ( ( cons @ SV161 @ nil )
!= SV19 ) )
= $true )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1289,plain,
! [SV20: $i,SV98: $i] :
( ( ( geq @ SV98 @ SV20 )
= $false )
| ( ( geq @ SV20 @ SV98 )
= $false )
| ( ( SV20 = SV98 )
= $true )
| ( ( ssItem @ SV98 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1290,plain,
! [SV21: $i,SV99: $i] :
( ( ( ! [SY408: $i] :
~ ~ ( ~ ( ssList @ SY408 )
| ~ ~ ! [SY409: $i] :
~ ~ ( ~ ( ssList @ SY409 )
| ( ( app @ SY408 @ ( cons @ SV99 @ SY409 ) )
!= SV21 ) ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1291,plain,
! [SV21: $i,SV99: $i] :
( ( ( ! [SY410: $i] :
~ ~ ( ~ ( ssList @ SY410 )
| ~ ~ ! [SY411: $i] :
~ ~ ( ~ ( ssList @ SY411 )
| ( ( app @ SY410 @ ( cons @ SV99 @ SY411 ) )
!= SV21 ) ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1292,plain,
! [SV22: $i,SV154: $i,SV165: $i] :
( ( ( ~ ( ssItem @ SV165 )
| ! [SY547: $i] :
( ~ ( ssList @ SY547 )
| ! [SY548: $i] :
( ~ ( ssList @ SY548 )
| ! [SY549: $i] :
( ~ ( ssList @ SY549 )
| ( ( app @ ( app @ SY547 @ ( cons @ SV154 @ SY548 ) ) @ ( cons @ SV165 @ SY549 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) ) ) )
= $true )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1293,plain,
! [SV22: $i] :
( ( ( ~ ( ssItem @ ( sK18_SY468 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1294,plain,
! [SV22: $i] :
( ( ( ! [SY518: $i] :
( ~ ( ssList @ SY518 )
| ! [SY519: $i] :
( ~ ( ssList @ SY519 )
| ! [SY520: $i] :
( ~ ( ssList @ SY520 )
| ( ( app @ ( app @ SY518 @ ( cons @ ( sK10_SY262 @ SV22 ) @ SY519 ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ SY520 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1295,plain,
! [SV24: $i,SV136: $i,SV100: $i] :
( ( ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
| ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1296,plain,
! [SV136: $i,SV24: $i,SV100: $i] :
( ( ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
| ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1297,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
| ( ( hd @ SV101 )
!= ( hd @ SV26 ) ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1298,plain,
! [SV137: $i,SV102: $i,SV28: $i] :
( ( ( ~ ( rearsegP @ SV28 @ SV102 )
| ~ ( rearsegP @ SV102 @ SV137 ) )
= $true )
| ( ( rearsegP @ SV28 @ SV137 )
= $true )
| ( ( ssList @ SV137 )
= $false )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1299,plain,
! [SV29: $i,SV155: $i,SV166: $i] :
( ( ( ~ ( ssItem @ SV166 )
| ! [SY550: $i] :
( ~ ( ssList @ SY550 )
| ! [SY551: $i] :
( ~ ( ssList @ SY551 )
| ! [SY552: $i] :
( ~ ( ssList @ SY552 )
| ( ( app @ ( app @ SY550 @ ( cons @ SV155 @ SY551 ) ) @ ( cons @ SV166 @ SY552 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) ) ) )
= $true )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1300,plain,
! [SV29: $i] :
( ( ( ~ ( ssItem @ ( sK19_SY476 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1301,plain,
! [SV29: $i] :
( ( ( ! [SY521: $i] :
( ~ ( ssList @ SY521 )
| ! [SY522: $i] :
( ~ ( ssList @ SY522 )
| ! [SY523: $i] :
( ~ ( ssList @ SY523 )
| ( ( app @ ( app @ SY521 @ ( cons @ ( sK11_SY277 @ SV29 ) @ SY522 ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ SY523 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1302,plain,
! [SV138: $i,SV103: $i,SV31: $i] :
( ( ( ~ ( leq @ SV31 @ SV103 )
| ~ ( leq @ SV103 @ SV138 ) )
= $true )
| ( ( leq @ SV31 @ SV138 )
= $true )
| ( ( ssItem @ SV138 )
= $false )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1303,plain,
! [SV34: $i,SV105: $i] :
( ( ( ! [SY415: $i] :
~ ~ ( ~ ( ssList @ SY415 )
| ~ ~ ! [SY416: $i] :
~ ~ ( ~ ( ssList @ SY416 )
| ( ( app @ ( app @ SY415 @ SV105 ) @ SY416 )
!= SV34 ) ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1304,plain,
! [SV34: $i,SV105: $i] :
( ( ( ! [SY417: $i] :
~ ~ ( ~ ( ssList @ SY417 )
| ~ ~ ! [SY418: $i] :
~ ~ ( ~ ( ssList @ SY418 )
| ( ( app @ ( app @ SY417 @ SV105 ) @ SY418 )
!= SV34 ) ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1305,plain,
! [SV106: $i,SV35: $i,SV139: $i,SV162: $i] :
( ( ( ssItem @ SV162 )
= $false )
| ( ( ( ( cons @ SV139 @ SV35 )
!= ( cons @ SV162 @ SV106 ) )
| ~ ( ( SV139 != SV162 )
| ( SV106 != SV35 ) ) )
= $true )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1306,plain,
! [SV140: $i,SV108: $i,SV40: $i,SV163: $i] :
( ( ( ssList @ SV163 )
= $false )
| ( ( ~ ( segmentP @ SV40 @ SV108 )
| ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SV163 ) @ SV108 ) )
= $true )
| ( ( ssList @ SV140 )
= $false )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1307,plain,
! [SV46: $i,SV142: $i,SV113: $i] :
( ( ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
| ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1308,plain,
! [SV142: $i,SV113: $i,SV46: $i] :
( ( ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
| ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1309,plain,
! [SV48: $i,SV156: $i,SV167: $i] :
( ( ( ~ ( ssItem @ SV167 )
| ! [SY553: $i] :
( ~ ( ssList @ SY553 )
| ! [SY554: $i] :
( ~ ( ssList @ SY554 )
| ! [SY555: $i] :
( ~ ( ssList @ SY555 )
| ( ( app @ ( app @ SY553 @ ( cons @ SV156 @ SY554 ) ) @ ( cons @ SV167 @ SY555 ) )
!= SV48 )
| ( SV156 != SV167 ) ) ) ) )
= $true )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1310,plain,
! [SV48: $i] :
( ( ( ~ ( ssItem @ ( sK20_SY484 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1311,plain,
! [SV48: $i] :
( ( ( ! [SY524: $i] :
( ~ ( ssList @ SY524 )
| ! [SY525: $i] :
( ~ ( ssList @ SY525 )
| ! [SY526: $i] :
( ~ ( ssList @ SY526 )
| ( ( app @ ( app @ SY524 @ ( cons @ ( sK12_SY309 @ SV48 ) @ SY525 ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ SY526 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1312,plain,
! [SV50: $i,SV114: $i] :
( ( ( rearsegP @ SV114 @ SV50 )
= $false )
| ( ( rearsegP @ SV50 @ SV114 )
= $false )
| ( ( SV50 = SV114 )
= $true )
| ( ( ssList @ SV114 )
= $false )
| ( ( ssList @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1313,plain,
! [SV51: $i] :
( ( ( ssList @ ( sK7_SY315 @ SV51 ) )
= $true )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1314,plain,
! [SV51: $i] :
( ( ( ( tl @ SV51 )
= ( sK7_SY315 @ SV51 ) )
= $true )
| ( ( nil = SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1315,plain,
! [SV143: $i,SV115: $i,SV52: $i] :
( ( ( ~ ( geq @ SV52 @ SV115 )
| ~ ( geq @ SV115 @ SV143 ) )
= $true )
| ( ( geq @ SV52 @ SV143 )
= $true )
| ( ( ssItem @ SV143 )
= $false )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1316,plain,
! [SV53: $i,SV157: $i,SV168: $i] :
( ( ( ~ ( ssItem @ SV168 )
| ! [SY556: $i] :
( ~ ( ssList @ SY556 )
| ! [SY557: $i] :
( ~ ( ssList @ SY557 )
| ! [SY558: $i] :
( ~ ( ssList @ SY558 )
| ( ( app @ ( app @ SY556 @ ( cons @ SV157 @ SY557 ) ) @ ( cons @ SV168 @ SY558 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) ) ) )
= $true )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1317,plain,
! [SV53: $i] :
( ( ( ~ ( ssItem @ ( sK21_SY492 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1318,plain,
! [SV53: $i] :
( ( ( ! [SY527: $i] :
( ~ ( ssList @ SY527 )
| ! [SY528: $i] :
( ~ ( ssList @ SY528 )
| ! [SY529: $i] :
( ~ ( ssList @ SY529 )
| ( ( app @ ( app @ SY527 @ ( cons @ ( sK13_SY323 @ SV53 ) @ SY528 ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ SY529 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1319,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ ( sK26_SY449 @ SV55 ) )
| ( ( cons @ ( sK26_SY449 @ SV55 ) @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1239]) ).
thf(1320,plain,
! [SV58: $i,SV158: $i,SV169: $i] :
( ( ( ~ ( ssItem @ SV169 )
| ! [SY559: $i] :
( ~ ( ssList @ SY559 )
| ! [SY560: $i] :
( ~ ( ssList @ SY560 )
| ! [SY561: $i] :
( ~ ( ssList @ SY561 )
| ( ( app @ ( app @ SY559 @ ( cons @ SV158 @ SY560 ) ) @ ( cons @ SV169 @ SY561 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) ) ) )
= $true )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1321,plain,
! [SV58: $i] :
( ( ( ~ ( ssItem @ ( sK22_SY500 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1322,plain,
! [SV58: $i] :
( ( ( ! [SY530: $i] :
( ~ ( ssList @ SY530 )
| ! [SY531: $i] :
( ~ ( ssList @ SY531 )
| ! [SY532: $i] :
( ~ ( ssList @ SY532 )
| ( ( app @ ( app @ SY530 @ ( cons @ ( sK14_SY338 @ SV58 ) @ SY531 ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ SY532 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1323,plain,
! [SV145: $i,SV118: $i,SV59: $i] :
( ( ( ~ ( segmentP @ SV59 @ SV118 )
| ~ ( segmentP @ SV118 @ SV145 ) )
= $true )
| ( ( segmentP @ SV59 @ SV145 )
= $true )
| ( ( ssList @ SV145 )
= $false )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1324,plain,
( ( sK2_SX0 = sK6_SY428 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1325,plain,
( ( sK1_U = sK4_SY389 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1326,plain,
( ( ~ ( ssList @ sK23_SY450 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1327,plain,
( ( ! [SY533: $i] :
( ~ ( ssList @ SY533 )
| ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ SY533 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) )
| ~ ! [SY435: $i] :
~ ~ ( ~ ( ssItem @ SY435 )
| ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY436 )
| ( ( app @ ( cons @ SY435 @ nil ) @ SY436 )
!= SY533 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY435 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1328,plain,
( ( ( nil != sK6_SY428 )
= $false )
| ( ( nil != sK4_SY389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1329,plain,
( ( ( nil != sK2_SX0 )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1330,plain,
( ( ( nil = sK1_U )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1331,plain,
! [SV148: $i,SV121: $i,SV62: $i] :
( ( ( ~ ( gt @ SV62 @ SV121 )
| ~ ( gt @ SV121 @ SV148 ) )
= $true )
| ( ( gt @ SV62 @ SV148 )
= $true )
| ( ( ssItem @ SV148 )
= $false )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1332,plain,
! [SV63: $i,SV122: $i] :
( ( ( ( nil != SV122 )
| ( nil != SV63 ) )
= $false )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1333,plain,
! [SV63: $i,SV122: $i] :
( ( ( ( nil != SV122 )
| ( nil != SV63 ) )
= $true )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1334,plain,
! [SV67: $i,SV125: $i] :
( ( ( segmentP @ SV125 @ SV67 )
= $false )
| ( ( segmentP @ SV67 @ SV125 )
= $false )
| ( ( SV67 = SV125 )
= $true )
| ( ( ssList @ SV125 )
= $false )
| ( ( ssList @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1335,plain,
! [SV126: $i,SV149: $i,SV68: $i,SV164: $i] :
( ( ( ssList @ SV164 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) ) ) )
= $true )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1336,plain,
! [SV127: $i,SV69: $i] :
( ( ( SV69 = SV127 )
= $false )
| ( ( neq @ SV69 @ SV127 )
= $false )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1337,plain,
! [SV127: $i,SV69: $i] :
( ( ( SV69 = SV127 )
= $true )
| ( ( neq @ SV69 @ SV127 )
= $true )
| ( ( ssList @ SV127 )
= $false )
| ( ( ssList @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1338,plain,
! [SV72: $i,SV129: $i] :
( ( ( nil = SV129 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1339,plain,
! [SV72: $i,SV129: $i] :
( ( ( nil = SV129 )
= $false )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1340,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) ) )
= $false )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1341,plain,
( ( ssItem @ sK8_SY402 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1342,plain,
( ( sK3_SX0 != sK8_SY402 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1343,plain,
! [SV73: $i,SV130: $i] :
( ( ( leq @ SV130 @ SV73 )
= $false )
| ( ( leq @ SV73 @ SV130 )
= $false )
| ( ( SV73 = SV130 )
= $true )
| ( ( ssItem @ SV130 )
= $false )
| ( ( ssItem @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1344,plain,
! [SV74: $i,SV159: $i,SV170: $i] :
( ( ( ~ ( ssItem @ SV170 )
| ! [SY562: $i] :
( ~ ( ssList @ SY562 )
| ! [SY563: $i] :
( ~ ( ssList @ SY563 )
| ( ( app @ SY562 @ ( cons @ SV159 @ ( cons @ SV170 @ SY563 ) ) )
!= SV74 )
| ( SV159 = SV170 ) ) ) )
= $true )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1345,plain,
! [SV74: $i] :
( ( ( ~ ( ssItem @ ( sK24_SY507 @ SV74 ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1265]) ).
thf(1346,plain,
! [SV74: $i] :
( ( ( ! [SY542: $i] :
( ~ ( ssList @ SY542 )
| ! [SY543: $i] :
( ~ ( ssList @ SY543 )
| ( ( app @ SY542 @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ SY543 ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1265]) ).
thf(1347,plain,
! [SV152: $i,SV133: $i,SV77: $i] :
( ( ( ~ ( frontsegP @ SV77 @ SV133 )
| ~ ( frontsegP @ SV133 @ SV152 ) )
= $true )
| ( ( frontsegP @ SV77 @ SV152 )
= $true )
| ( ( ssList @ SV152 )
= $false )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1348,plain,
! [SV153: $i,SV134: $i,SV78: $i] :
( ( ( ~ ( lt @ SV78 @ SV134 )
| ~ ( lt @ SV134 @ SV153 ) )
= $true )
| ( ( lt @ SV78 @ SV153 )
= $true )
| ( ( ssItem @ SV153 )
= $false )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1349,plain,
! [SV82: $i,SV160: $i,SV171: $i] :
( ( ( ~ ( ssItem @ SV171 )
| ! [SY564: $i] :
( ~ ( ssList @ SY564 )
| ! [SY565: $i] :
( ~ ( ssList @ SY565 )
| ! [SY566: $i] :
( ~ ( ssList @ SY566 )
| ( ( app @ ( app @ SY564 @ ( cons @ SV160 @ SY565 ) ) @ ( cons @ SV171 @ SY566 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1350,plain,
! [SV82: $i] :
( ( ( ~ ( ssItem @ ( sK25_SY514 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1271]) ).
thf(1351,plain,
! [SV82: $i] :
( ( ( ! [SY544: $i] :
( ~ ( ssList @ SY544 )
| ! [SY545: $i] :
( ~ ( ssList @ SY545 )
| ! [SY546: $i] :
( ~ ( ssList @ SY546 )
| ( ( app @ ( app @ SY544 @ ( cons @ ( sK16_SY383 @ SV82 ) @ SY545 ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ SY546 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1271]) ).
thf(1352,plain,
! [SV84: $i] :
( ( ( ssItem @ ( sK9_SY388 @ SV84 ) )
= $true )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1353,plain,
! [SV84: $i] :
( ( ( ( hd @ SV84 )
= ( sK9_SY388 @ SV84 ) )
= $true )
| ( ( nil = SV84 )
= $true )
| ( ( ssList @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1354,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV87 ) ) )
= $false )
| ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1355,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV87 ) )
= $false )
| ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1356,plain,
! [SV87: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV87 ) ) )
= $true )
| ( ( ~ ( leq @ SV3 @ SV87 ) )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1357,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1358,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
| ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1359,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK27_SY403 @ SV16 @ SV95 ) )
| ( ( app @ SV95 @ ( sK27_SY403 @ SV16 @ SV95 ) )
!= SV16 ) ) )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1282]) ).
thf(1360,plain,
! [SV16: $i,SV95: $i,SV172: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV172 )
| ( ( app @ SV95 @ SV172 )
!= SV16 ) ) )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1361,plain,
! [SV135: $i,SV96: $i,SV17: $i] :
( ( ( ~ ( leq @ SV17 @ SV96 ) )
= $true )
| ( ( ~ ( lt @ SV96 @ SV135 ) )
= $true )
| ( ( lt @ SV17 @ SV135 )
= $true )
| ( ( ssItem @ SV135 )
= $false )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1362,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK28_SY406 @ SV18 @ SV97 ) )
| ( ( app @ ( sK28_SY406 @ SV18 @ SV97 ) @ SV97 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1285]) ).
thf(1363,plain,
! [SV18: $i,SV97: $i,SV173: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV173 )
| ( ( app @ SV173 @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1364,plain,
! [SV19: $i] :
( ( ( ~ ( ssItem @ ( sK17_SY249 @ SV19 ) ) )
= $false )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1365,plain,
! [SV19: $i] :
( ( ( ( cons @ ( sK17_SY249 @ SV19 ) @ nil )
!= SV19 )
= $false )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1366,plain,
! [SV19: $i,SV161: $i] :
( ( ( ~ ( ssItem @ SV161 ) )
= $true )
| ( ( ( cons @ SV161 @ nil )
!= SV19 )
= $true )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1367,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK29_SY408 @ SV21 @ SV99 ) )
| ~ ~ ! [SY567: $i] :
~ ~ ( ~ ( ssList @ SY567 )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ SY567 ) )
!= SV21 ) ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1290]) ).
thf(1368,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV174 )
| ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1369,plain,
! [SV22: $i,SV154: $i,SV165: $i] :
( ( ( ~ ( ssItem @ SV165 ) )
= $true )
| ( ( ! [SY547: $i] :
( ~ ( ssList @ SY547 )
| ! [SY548: $i] :
( ~ ( ssList @ SY548 )
| ! [SY549: $i] :
( ~ ( ssList @ SY549 )
| ( ( app @ ( app @ SY547 @ ( cons @ SV154 @ SY548 ) ) @ ( cons @ SV165 @ SY549 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) ) ) )
= $true )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1370,plain,
! [SV22: $i] :
( ( ( ssItem @ ( sK18_SY468 @ SV22 ) )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1371,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ ( sK30_SY518 @ SV22 ) )
| ! [SY569: $i] :
( ~ ( ssList @ SY569 )
| ! [SY570: $i] :
( ~ ( ssList @ SY570 )
| ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ SY569 ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ SY570 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1294]) ).
thf(1372,plain,
! [SV24: $i,SV136: $i,SV100: $i] :
( ( ( ~ ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 ) )
= $true )
| ( ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1373,plain,
! [SV136: $i,SV24: $i,SV100: $i] :
( ( ( ~ ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) ) )
= $true )
| ( ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1374,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) ) )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1375,plain,
! [SV137: $i,SV102: $i,SV28: $i] :
( ( ( ~ ( rearsegP @ SV28 @ SV102 ) )
= $true )
| ( ( ~ ( rearsegP @ SV102 @ SV137 ) )
= $true )
| ( ( rearsegP @ SV28 @ SV137 )
= $true )
| ( ( ssList @ SV137 )
= $false )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1376,plain,
! [SV29: $i,SV155: $i,SV166: $i] :
( ( ( ~ ( ssItem @ SV166 ) )
= $true )
| ( ( ! [SY550: $i] :
( ~ ( ssList @ SY550 )
| ! [SY551: $i] :
( ~ ( ssList @ SY551 )
| ! [SY552: $i] :
( ~ ( ssList @ SY552 )
| ( ( app @ ( app @ SY550 @ ( cons @ SV155 @ SY551 ) ) @ ( cons @ SV166 @ SY552 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) ) ) )
= $true )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1377,plain,
! [SV29: $i] :
( ( ( ssItem @ ( sK19_SY476 @ SV29 ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1378,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ ( sK31_SY521 @ SV29 ) )
| ! [SY571: $i] :
( ~ ( ssList @ SY571 )
| ! [SY572: $i] :
( ~ ( ssList @ SY572 )
| ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ SY571 ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ SY572 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1301]) ).
thf(1379,plain,
! [SV138: $i,SV103: $i,SV31: $i] :
( ( ( ~ ( leq @ SV31 @ SV103 ) )
= $true )
| ( ( ~ ( leq @ SV103 @ SV138 ) )
= $true )
| ( ( leq @ SV31 @ SV138 )
= $true )
| ( ( ssItem @ SV138 )
= $false )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1380,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK32_SY415 @ SV34 @ SV105 ) )
| ~ ~ ! [SY573: $i] :
~ ~ ( ~ ( ssList @ SY573 )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ SY573 )
!= SV34 ) ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1303]) ).
thf(1381,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV175 )
| ~ ~ ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1382,plain,
! [SV106: $i,SV162: $i,SV35: $i,SV139: $i] :
( ( ( ( cons @ SV139 @ SV35 )
!= ( cons @ SV162 @ SV106 ) )
= $true )
| ( ( ~ ( ( SV139 != SV162 )
| ( SV106 != SV35 ) ) )
= $true )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1383,plain,
! [SV163: $i,SV140: $i,SV108: $i,SV40: $i] :
( ( ( ~ ( segmentP @ SV40 @ SV108 ) )
= $true )
| ( ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SV163 ) @ SV108 )
= $true )
| ( ( ssList @ SV163 )
= $false )
| ( ( ssList @ SV140 )
= $false )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1384,plain,
! [SV46: $i,SV142: $i,SV113: $i] :
( ( ( ~ ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 ) )
= $true )
| ( ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1385,plain,
! [SV142: $i,SV113: $i,SV46: $i] :
( ( ( ~ ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) ) )
= $true )
| ( ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1386,plain,
! [SV48: $i,SV156: $i,SV167: $i] :
( ( ( ~ ( ssItem @ SV167 ) )
= $true )
| ( ( ! [SY553: $i] :
( ~ ( ssList @ SY553 )
| ! [SY554: $i] :
( ~ ( ssList @ SY554 )
| ! [SY555: $i] :
( ~ ( ssList @ SY555 )
| ( ( app @ ( app @ SY553 @ ( cons @ SV156 @ SY554 ) ) @ ( cons @ SV167 @ SY555 ) )
!= SV48 )
| ( SV156 != SV167 ) ) ) ) )
= $true )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1387,plain,
! [SV48: $i] :
( ( ( ssItem @ ( sK20_SY484 @ SV48 ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1310]) ).
thf(1388,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ ( sK33_SY524 @ SV48 ) )
| ! [SY575: $i] :
( ~ ( ssList @ SY575 )
| ! [SY576: $i] :
( ~ ( ssList @ SY576 )
| ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ SY575 ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ SY576 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1311]) ).
thf(1389,plain,
! [SV143: $i,SV115: $i,SV52: $i] :
( ( ( ~ ( geq @ SV52 @ SV115 ) )
= $true )
| ( ( ~ ( geq @ SV115 @ SV143 ) )
= $true )
| ( ( geq @ SV52 @ SV143 )
= $true )
| ( ( ssItem @ SV143 )
= $false )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1390,plain,
! [SV53: $i,SV157: $i,SV168: $i] :
( ( ( ~ ( ssItem @ SV168 ) )
= $true )
| ( ( ! [SY556: $i] :
( ~ ( ssList @ SY556 )
| ! [SY557: $i] :
( ~ ( ssList @ SY557 )
| ! [SY558: $i] :
( ~ ( ssList @ SY558 )
| ( ( app @ ( app @ SY556 @ ( cons @ SV157 @ SY557 ) ) @ ( cons @ SV168 @ SY558 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) ) ) )
= $true )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1391,plain,
! [SV53: $i] :
( ( ( ssItem @ ( sK21_SY492 @ SV53 ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1392,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ ( sK34_SY527 @ SV53 ) )
| ! [SY577: $i] :
( ~ ( ssList @ SY577 )
| ! [SY578: $i] :
( ~ ( ssList @ SY578 )
| ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ SY577 ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ SY578 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1318]) ).
thf(1393,plain,
! [SV55: $i] :
( ( ( ~ ( ~ ( ssItem @ ( sK26_SY449 @ SV55 ) )
| ( ( cons @ ( sK26_SY449 @ SV55 ) @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) ) )
= $true )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1394,plain,
! [SV58: $i,SV158: $i,SV169: $i] :
( ( ( ~ ( ssItem @ SV169 ) )
= $true )
| ( ( ! [SY559: $i] :
( ~ ( ssList @ SY559 )
| ! [SY560: $i] :
( ~ ( ssList @ SY560 )
| ! [SY561: $i] :
( ~ ( ssList @ SY561 )
| ( ( app @ ( app @ SY559 @ ( cons @ SV158 @ SY560 ) ) @ ( cons @ SV169 @ SY561 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) ) ) )
= $true )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1395,plain,
! [SV58: $i] :
( ( ( ssItem @ ( sK22_SY500 @ SV58 ) )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1396,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ ( sK35_SY530 @ SV58 ) )
| ! [SY579: $i] :
( ~ ( ssList @ SY579 )
| ! [SY580: $i] :
( ~ ( ssList @ SY580 )
| ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ SY579 ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ SY580 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1322]) ).
thf(1397,plain,
! [SV145: $i,SV118: $i,SV59: $i] :
( ( ( ~ ( segmentP @ SV59 @ SV118 ) )
= $true )
| ( ( ~ ( segmentP @ SV118 @ SV145 ) )
= $true )
| ( ( segmentP @ SV59 @ SV145 )
= $true )
| ( ( ssList @ SV145 )
= $false )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1398,plain,
( ( ssList @ sK23_SY450 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1399,plain,
( ( ~ ( ssList @ sK36_SY533 )
| ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ sK36_SY533 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) )
| ~ ! [SY585: $i] :
~ ~ ( ~ ( ssItem @ SY585 )
| ~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY586 )
| ( ( app @ ( cons @ SY585 @ nil ) @ SY586 )
!= sK36_SY533 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY585 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1327]) ).
thf(1400,plain,
( ( ( nil = sK6_SY428 )
= $true )
| ( ( nil != sK4_SY389 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1401,plain,
( ( ( nil = sK2_SX0 )
= $true )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1402,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) )
= $false )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1403,plain,
! [SV148: $i,SV121: $i,SV62: $i] :
( ( ( ~ ( gt @ SV62 @ SV121 ) )
= $true )
| ( ( ~ ( gt @ SV121 @ SV148 ) )
= $true )
| ( ( gt @ SV62 @ SV148 )
= $true )
| ( ( ssItem @ SV148 )
= $false )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1404,plain,
! [SV63: $i,SV122: $i] :
( ( ( nil != SV122 )
= $false )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1405,plain,
! [SV122: $i,SV63: $i] :
( ( ( nil != SV63 )
= $false )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1406,plain,
! [SV63: $i,SV122: $i] :
( ( ( nil != SV122 )
= $true )
| ( ( nil != SV63 )
= $true )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1407,plain,
! [SV164: $i,SV126: $i,SV149: $i,SV68: $i] :
( ( ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
| ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1408,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1409,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
| ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1410,plain,
( ( sK3_SX0 = sK8_SY402 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1411,plain,
! [SV74: $i,SV159: $i,SV170: $i] :
( ( ( ~ ( ssItem @ SV170 ) )
= $true )
| ( ( ! [SY562: $i] :
( ~ ( ssList @ SY562 )
| ! [SY563: $i] :
( ~ ( ssList @ SY563 )
| ( ( app @ SY562 @ ( cons @ SV159 @ ( cons @ SV170 @ SY563 ) ) )
!= SV74 )
| ( SV159 = SV170 ) ) ) )
= $true )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1412,plain,
! [SV74: $i] :
( ( ( ssItem @ ( sK24_SY507 @ SV74 ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1413,plain,
! [SV74: $i] :
( ( ( ~ ( ssList @ ( sK37_SY542 @ SV74 ) )
| ! [SY589: $i] :
( ~ ( ssList @ SY589 )
| ( ( app @ ( sK37_SY542 @ SV74 ) @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ SY589 ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1346]) ).
thf(1414,plain,
! [SV152: $i,SV133: $i,SV77: $i] :
( ( ( ~ ( frontsegP @ SV77 @ SV133 ) )
= $true )
| ( ( ~ ( frontsegP @ SV133 @ SV152 ) )
= $true )
| ( ( frontsegP @ SV77 @ SV152 )
= $true )
| ( ( ssList @ SV152 )
= $false )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1415,plain,
! [SV153: $i,SV134: $i,SV78: $i] :
( ( ( ~ ( lt @ SV78 @ SV134 ) )
= $true )
| ( ( ~ ( lt @ SV134 @ SV153 ) )
= $true )
| ( ( lt @ SV78 @ SV153 )
= $true )
| ( ( ssItem @ SV153 )
= $false )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1416,plain,
! [SV82: $i,SV160: $i,SV171: $i] :
( ( ( ~ ( ssItem @ SV171 ) )
= $true )
| ( ( ! [SY564: $i] :
( ~ ( ssList @ SY564 )
| ! [SY565: $i] :
( ~ ( ssList @ SY565 )
| ! [SY566: $i] :
( ~ ( ssList @ SY566 )
| ( ( app @ ( app @ SY564 @ ( cons @ SV160 @ SY565 ) ) @ ( cons @ SV171 @ SY566 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1417,plain,
! [SV82: $i] :
( ( ( ssItem @ ( sK25_SY514 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1418,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ ( sK38_SY544 @ SV82 ) )
| ! [SY590: $i] :
( ~ ( ssList @ SY590 )
| ! [SY591: $i] :
( ~ ( ssList @ SY591 )
| ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ SY590 ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ SY591 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1351]) ).
thf(1419,plain,
! [SV87: $i,SV3: $i] :
( ( ( SV3 != SV87 )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1420,plain,
! [SV87: $i,SV3: $i] :
( ( ( leq @ SV3 @ SV87 )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1421,plain,
! [SV87: $i,SV3: $i] :
( ( ( SV3 != SV87 )
= $false )
| ( ( ~ ( leq @ SV3 @ SV87 ) )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1422,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1423,plain,
! [SV91: $i,SV10: $i] :
( ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1424,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) ) )
= $true )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1425,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK27_SY403 @ SV16 @ SV95 ) )
| ( ( app @ SV95 @ ( sK27_SY403 @ SV16 @ SV95 ) )
!= SV16 ) ) )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1426,plain,
! [SV16: $i,SV95: $i,SV172: $i] :
( ( ( ~ ( ~ ( ssList @ SV172 )
| ( ( app @ SV95 @ SV172 )
!= SV16 ) ) )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1427,plain,
! [SV135: $i,SV96: $i,SV17: $i] :
( ( ( leq @ SV17 @ SV96 )
= $false )
| ( ( ~ ( lt @ SV96 @ SV135 ) )
= $true )
| ( ( lt @ SV17 @ SV135 )
= $true )
| ( ( ssItem @ SV135 )
= $false )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1428,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK28_SY406 @ SV18 @ SV97 ) )
| ( ( app @ ( sK28_SY406 @ SV18 @ SV97 ) @ SV97 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1429,plain,
! [SV18: $i,SV97: $i,SV173: $i] :
( ( ( ~ ( ~ ( ssList @ SV173 )
| ( ( app @ SV173 @ SV97 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1430,plain,
! [SV19: $i] :
( ( ( ssItem @ ( sK17_SY249 @ SV19 ) )
= $true )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1431,plain,
! [SV19: $i] :
( ( ( ( cons @ ( sK17_SY249 @ SV19 ) @ nil )
= SV19 )
= $true )
| ( ( singletonP @ SV19 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1432,plain,
! [SV19: $i,SV161: $i] :
( ( ( ssItem @ SV161 )
= $false )
| ( ( ( cons @ SV161 @ nil )
!= SV19 )
= $true )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1433,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK29_SY408 @ SV21 @ SV99 ) )
| ~ ~ ! [SY567: $i] :
~ ~ ( ~ ( ssList @ SY567 )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ SY567 ) )
!= SV21 ) ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1434,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ~ ( ~ ( ssList @ SV174 )
| ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1435,plain,
! [SV22: $i,SV154: $i,SV165: $i] :
( ( ( ssItem @ SV165 )
= $false )
| ( ( ! [SY547: $i] :
( ~ ( ssList @ SY547 )
| ! [SY548: $i] :
( ~ ( ssList @ SY548 )
| ! [SY549: $i] :
( ~ ( ssList @ SY549 )
| ( ( app @ ( app @ SY547 @ ( cons @ SV154 @ SY548 ) ) @ ( cons @ SV165 @ SY549 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) ) ) )
= $true )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1436,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ ( sK30_SY518 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1437,plain,
! [SV22: $i] :
( ( ( ! [SY569: $i] :
( ~ ( ssList @ SY569 )
| ! [SY570: $i] :
( ~ ( ssList @ SY570 )
| ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ SY569 ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ SY570 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1438,plain,
! [SV24: $i,SV136: $i,SV100: $i] :
( ( ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
= $false )
| ( ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1439,plain,
! [SV136: $i,SV24: $i,SV100: $i] :
( ( ( ( memberP @ SV100 @ SV24 )
| ( memberP @ SV136 @ SV24 ) )
= $false )
| ( ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1440,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) ) )
= $false )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1441,plain,
! [SV137: $i,SV102: $i,SV28: $i] :
( ( ( rearsegP @ SV28 @ SV102 )
= $false )
| ( ( ~ ( rearsegP @ SV102 @ SV137 ) )
= $true )
| ( ( rearsegP @ SV28 @ SV137 )
= $true )
| ( ( ssList @ SV137 )
= $false )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1442,plain,
! [SV29: $i,SV155: $i,SV166: $i] :
( ( ( ssItem @ SV166 )
= $false )
| ( ( ! [SY550: $i] :
( ~ ( ssList @ SY550 )
| ! [SY551: $i] :
( ~ ( ssList @ SY551 )
| ! [SY552: $i] :
( ~ ( ssList @ SY552 )
| ( ( app @ ( app @ SY550 @ ( cons @ SV155 @ SY551 ) ) @ ( cons @ SV166 @ SY552 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) ) ) )
= $true )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1443,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ ( sK31_SY521 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1444,plain,
! [SV29: $i] :
( ( ( ! [SY571: $i] :
( ~ ( ssList @ SY571 )
| ! [SY572: $i] :
( ~ ( ssList @ SY572 )
| ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ SY571 ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ SY572 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1445,plain,
! [SV138: $i,SV103: $i,SV31: $i] :
( ( ( leq @ SV31 @ SV103 )
= $false )
| ( ( ~ ( leq @ SV103 @ SV138 ) )
= $true )
| ( ( leq @ SV31 @ SV138 )
= $true )
| ( ( ssItem @ SV138 )
= $false )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1446,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK32_SY415 @ SV34 @ SV105 ) )
| ~ ~ ! [SY573: $i] :
~ ~ ( ~ ( ssList @ SY573 )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ SY573 )
!= SV34 ) ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1447,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ~ ( ~ ( ssList @ SV175 )
| ~ ~ ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1448,plain,
! [SV106: $i,SV162: $i,SV35: $i,SV139: $i] :
( ( ( ( cons @ SV139 @ SV35 )
= ( cons @ SV162 @ SV106 ) )
= $false )
| ( ( ~ ( ( SV139 != SV162 )
| ( SV106 != SV35 ) ) )
= $true )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1449,plain,
! [SV163: $i,SV140: $i,SV108: $i,SV40: $i] :
( ( ( segmentP @ SV40 @ SV108 )
= $false )
| ( ( segmentP @ ( app @ ( app @ SV140 @ SV40 ) @ SV163 ) @ SV108 )
= $true )
| ( ( ssList @ SV163 )
= $false )
| ( ( ssList @ SV140 )
= $false )
| ( ( ssList @ SV108 )
= $false )
| ( ( ssList @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1450,plain,
! [SV46: $i,SV142: $i,SV113: $i] :
( ( ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
= $false )
| ( ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1451,plain,
! [SV142: $i,SV113: $i,SV46: $i] :
( ( ( ( SV46 = SV113 )
| ( memberP @ SV142 @ SV46 ) )
= $false )
| ( ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1452,plain,
! [SV48: $i,SV156: $i,SV167: $i] :
( ( ( ssItem @ SV167 )
= $false )
| ( ( ! [SY553: $i] :
( ~ ( ssList @ SY553 )
| ! [SY554: $i] :
( ~ ( ssList @ SY554 )
| ! [SY555: $i] :
( ~ ( ssList @ SY555 )
| ( ( app @ ( app @ SY553 @ ( cons @ SV156 @ SY554 ) ) @ ( cons @ SV167 @ SY555 ) )
!= SV48 )
| ( SV156 != SV167 ) ) ) ) )
= $true )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1453,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ ( sK33_SY524 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1454,plain,
! [SV48: $i] :
( ( ( ! [SY575: $i] :
( ~ ( ssList @ SY575 )
| ! [SY576: $i] :
( ~ ( ssList @ SY576 )
| ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ SY575 ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ SY576 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1455,plain,
! [SV143: $i,SV115: $i,SV52: $i] :
( ( ( geq @ SV52 @ SV115 )
= $false )
| ( ( ~ ( geq @ SV115 @ SV143 ) )
= $true )
| ( ( geq @ SV52 @ SV143 )
= $true )
| ( ( ssItem @ SV143 )
= $false )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1456,plain,
! [SV53: $i,SV157: $i,SV168: $i] :
( ( ( ssItem @ SV168 )
= $false )
| ( ( ! [SY556: $i] :
( ~ ( ssList @ SY556 )
| ! [SY557: $i] :
( ~ ( ssList @ SY557 )
| ! [SY558: $i] :
( ~ ( ssList @ SY558 )
| ( ( app @ ( app @ SY556 @ ( cons @ SV157 @ SY557 ) ) @ ( cons @ SV168 @ SY558 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) ) ) )
= $true )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1457,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ ( sK34_SY527 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1458,plain,
! [SV53: $i] :
( ( ( ! [SY577: $i] :
( ~ ( ssList @ SY577 )
| ! [SY578: $i] :
( ~ ( ssList @ SY578 )
| ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ SY577 ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ SY578 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1459,plain,
! [SV55: $i] :
( ( ( ~ ( ssItem @ ( sK26_SY449 @ SV55 ) )
| ( ( cons @ ( sK26_SY449 @ SV55 ) @ ( sK5_SY328 @ SV55 ) )
!= SV55 ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1460,plain,
! [SV58: $i,SV158: $i,SV169: $i] :
( ( ( ssItem @ SV169 )
= $false )
| ( ( ! [SY559: $i] :
( ~ ( ssList @ SY559 )
| ! [SY560: $i] :
( ~ ( ssList @ SY560 )
| ! [SY561: $i] :
( ~ ( ssList @ SY561 )
| ( ( app @ ( app @ SY559 @ ( cons @ SV158 @ SY560 ) ) @ ( cons @ SV169 @ SY561 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) ) ) )
= $true )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1461,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ ( sK35_SY530 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1462,plain,
! [SV58: $i] :
( ( ( ! [SY579: $i] :
( ~ ( ssList @ SY579 )
| ! [SY580: $i] :
( ~ ( ssList @ SY580 )
| ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ SY579 ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ SY580 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1463,plain,
! [SV145: $i,SV118: $i,SV59: $i] :
( ( ( segmentP @ SV59 @ SV118 )
= $false )
| ( ( ~ ( segmentP @ SV118 @ SV145 ) )
= $true )
| ( ( segmentP @ SV59 @ SV145 )
= $true )
| ( ( ssList @ SV145 )
= $false )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1464,plain,
( ( ~ ( ssList @ sK36_SY533 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1465,plain,
( ( ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ sK36_SY533 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) )
| ~ ! [SY585: $i] :
~ ~ ( ~ ( ssItem @ SY585 )
| ~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY586 )
| ( ( app @ ( cons @ SY585 @ nil ) @ SY586 )
!= sK36_SY533 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY585 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1466,plain,
( ( ( nil = sK4_SY389 )
= $false )
| ( ( nil = sK6_SY428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1467,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) )
= $false )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1468,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1469,plain,
( ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) )
= $false )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1470,plain,
! [SV148: $i,SV121: $i,SV62: $i] :
( ( ( gt @ SV62 @ SV121 )
= $false )
| ( ( ~ ( gt @ SV121 @ SV148 ) )
= $true )
| ( ( gt @ SV62 @ SV148 )
= $true )
| ( ( ssItem @ SV148 )
= $false )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1471,plain,
! [SV63: $i,SV122: $i] :
( ( ( nil = SV122 )
= $true )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1472,plain,
! [SV122: $i,SV63: $i] :
( ( ( nil = SV63 )
= $true )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $false )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1473,plain,
! [SV63: $i,SV122: $i] :
( ( ( nil = SV122 )
= $false )
| ( ( nil != SV63 )
= $true )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1474,plain,
! [SV164: $i,SV126: $i,SV149: $i,SV68: $i] :
( ( ( ~ ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1475,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( ~ ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1476,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1408]) ).
thf(1477,plain,
! [SV129: $i,SV72: $i] :
( ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1408]) ).
thf(1478,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) ) )
= $true )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1479,plain,
! [SV74: $i,SV159: $i,SV170: $i] :
( ( ( ssItem @ SV170 )
= $false )
| ( ( ! [SY562: $i] :
( ~ ( ssList @ SY562 )
| ! [SY563: $i] :
( ~ ( ssList @ SY563 )
| ( ( app @ SY562 @ ( cons @ SV159 @ ( cons @ SV170 @ SY563 ) ) )
!= SV74 )
| ( SV159 = SV170 ) ) ) )
= $true )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1480,plain,
! [SV74: $i] :
( ( ( ~ ( ssList @ ( sK37_SY542 @ SV74 ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1481,plain,
! [SV74: $i] :
( ( ( ! [SY589: $i] :
( ~ ( ssList @ SY589 )
| ( ( app @ ( sK37_SY542 @ SV74 ) @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ SY589 ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1482,plain,
! [SV152: $i,SV133: $i,SV77: $i] :
( ( ( frontsegP @ SV77 @ SV133 )
= $false )
| ( ( ~ ( frontsegP @ SV133 @ SV152 ) )
= $true )
| ( ( frontsegP @ SV77 @ SV152 )
= $true )
| ( ( ssList @ SV152 )
= $false )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1483,plain,
! [SV153: $i,SV134: $i,SV78: $i] :
( ( ( lt @ SV78 @ SV134 )
= $false )
| ( ( ~ ( lt @ SV134 @ SV153 ) )
= $true )
| ( ( lt @ SV78 @ SV153 )
= $true )
| ( ( ssItem @ SV153 )
= $false )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1484,plain,
! [SV82: $i,SV160: $i,SV171: $i] :
( ( ( ssItem @ SV171 )
= $false )
| ( ( ! [SY564: $i] :
( ~ ( ssList @ SY564 )
| ! [SY565: $i] :
( ~ ( ssList @ SY565 )
| ! [SY566: $i] :
( ~ ( ssList @ SY566 )
| ( ( app @ ( app @ SY564 @ ( cons @ SV160 @ SY565 ) ) @ ( cons @ SV171 @ SY566 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) ) ) )
= $true )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1485,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ ( sK38_SY544 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1486,plain,
! [SV82: $i] :
( ( ( ! [SY590: $i] :
( ~ ( ssList @ SY590 )
| ! [SY591: $i] :
( ~ ( ssList @ SY591 )
| ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ SY590 ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ SY591 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1487,plain,
! [SV87: $i,SV3: $i] :
( ( ( SV3 = SV87 )
= $false )
| ( ( lt @ SV3 @ SV87 )
= $false )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1488,plain,
! [SV87: $i,SV3: $i] :
( ( ( SV3 = SV87 )
= $true )
| ( ( ~ ( leq @ SV3 @ SV87 ) )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1489,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) ) )
= $true )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1490,plain,
! [SV91: $i,SV10: $i] :
( ( ( lt @ SV10 @ ( hd @ SV91 ) )
= $true )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1491,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) ) )
= $false )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1492,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( ssList @ ( sK27_SY403 @ SV16 @ SV95 ) )
| ( ( app @ SV95 @ ( sK27_SY403 @ SV16 @ SV95 ) )
!= SV16 ) )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1493,plain,
! [SV16: $i,SV95: $i,SV172: $i] :
( ( ( ~ ( ssList @ SV172 )
| ( ( app @ SV95 @ SV172 )
!= SV16 ) )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1494,plain,
! [SV17: $i,SV135: $i,SV96: $i] :
( ( ( lt @ SV96 @ SV135 )
= $false )
| ( ( leq @ SV17 @ SV96 )
= $false )
| ( ( lt @ SV17 @ SV135 )
= $true )
| ( ( ssItem @ SV135 )
= $false )
| ( ( ssItem @ SV96 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1495,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( ssList @ ( sK28_SY406 @ SV18 @ SV97 ) )
| ( ( app @ ( sK28_SY406 @ SV18 @ SV97 ) @ SV97 )
!= SV18 ) )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1496,plain,
! [SV18: $i,SV97: $i,SV173: $i] :
( ( ( ~ ( ssList @ SV173 )
| ( ( app @ SV173 @ SV97 )
!= SV18 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1497,plain,
! [SV19: $i,SV161: $i] :
( ( ( ( cons @ SV161 @ nil )
= SV19 )
= $false )
| ( ( ssItem @ SV161 )
= $false )
| ( ( singletonP @ SV19 )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1498,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( ssList @ ( sK29_SY408 @ SV21 @ SV99 ) )
| ~ ~ ! [SY567: $i] :
~ ~ ( ~ ( ssList @ SY567 )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ SY567 ) )
!= SV21 ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1499,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ~ ( ssList @ SV174 )
| ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1500,plain,
! [SV22: $i,SV165: $i,SV154: $i,SV176: $i] :
( ( ( ~ ( ssList @ SV176 )
| ! [SY592: $i] :
( ~ ( ssList @ SY592 )
| ! [SY593: $i] :
( ~ ( ssList @ SY593 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SY592 ) ) @ ( cons @ SV165 @ SY593 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) ) )
= $true )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1501,plain,
! [SV22: $i] :
( ( ( ssList @ ( sK30_SY518 @ SV22 ) )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1502,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ ( sK39_SY569 @ SV22 ) )
| ! [SY594: $i] :
( ~ ( ssList @ SY594 )
| ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ ( sK39_SY569 @ SV22 ) ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ SY594 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1437]) ).
thf(1503,plain,
! [SV136: $i,SV24: $i,SV100: $i] :
( ( ( memberP @ SV100 @ SV24 )
= $true )
| ( ( memberP @ SV136 @ SV24 )
= $true )
| ( ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
= $false )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1504,plain,
! [SV136: $i,SV24: $i,SV100: $i] :
( ( ( memberP @ SV100 @ SV24 )
= $false )
| ( ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1505,plain,
! [SV100: $i,SV24: $i,SV136: $i] :
( ( ( memberP @ SV136 @ SV24 )
= $false )
| ( ( memberP @ ( app @ SV100 @ SV136 ) @ SV24 )
= $true )
| ( ( ssList @ SV136 )
= $false )
| ( ( ssList @ SV100 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1506,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ( nil != SV101 ) )
| ~ ( ( nil != SV26 ) ) )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1507,plain,
! [SV28: $i,SV137: $i,SV102: $i] :
( ( ( rearsegP @ SV102 @ SV137 )
= $false )
| ( ( rearsegP @ SV28 @ SV102 )
= $false )
| ( ( rearsegP @ SV28 @ SV137 )
= $true )
| ( ( ssList @ SV137 )
= $false )
| ( ( ssList @ SV102 )
= $false )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1508,plain,
! [SV29: $i,SV166: $i,SV155: $i,SV177: $i] :
( ( ( ~ ( ssList @ SV177 )
| ! [SY595: $i] :
( ~ ( ssList @ SY595 )
| ! [SY596: $i] :
( ~ ( ssList @ SY596 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SY595 ) ) @ ( cons @ SV166 @ SY596 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) ) )
= $true )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1509,plain,
! [SV29: $i] :
( ( ( ssList @ ( sK31_SY521 @ SV29 ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1510,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ ( sK40_SY571 @ SV29 ) )
| ! [SY597: $i] :
( ~ ( ssList @ SY597 )
| ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ ( sK40_SY571 @ SV29 ) ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ SY597 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1444]) ).
thf(1511,plain,
! [SV31: $i,SV138: $i,SV103: $i] :
( ( ( leq @ SV103 @ SV138 )
= $false )
| ( ( leq @ SV31 @ SV103 )
= $false )
| ( ( leq @ SV31 @ SV138 )
= $true )
| ( ( ssItem @ SV138 )
= $false )
| ( ( ssItem @ SV103 )
= $false )
| ( ( ssItem @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1512,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( ssList @ ( sK32_SY415 @ SV34 @ SV105 ) )
| ~ ~ ! [SY573: $i] :
~ ~ ( ~ ( ssList @ SY573 )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ SY573 )
!= SV34 ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1513,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ~ ( ssList @ SV175 )
| ~ ~ ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1514,plain,
! [SV35: $i,SV106: $i,SV162: $i,SV139: $i] :
( ( ( ( SV139 != SV162 )
| ( SV106 != SV35 ) )
= $false )
| ( ( ( cons @ SV139 @ SV35 )
= ( cons @ SV162 @ SV106 ) )
= $false )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1515,plain,
! [SV142: $i,SV113: $i,SV46: $i] :
( ( ( SV46 = SV113 )
= $true )
| ( ( memberP @ SV142 @ SV46 )
= $true )
| ( ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
= $false )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1516,plain,
! [SV142: $i,SV113: $i,SV46: $i] :
( ( ( SV46 = SV113 )
= $false )
| ( ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1517,plain,
! [SV113: $i,SV46: $i,SV142: $i] :
( ( ( memberP @ SV142 @ SV46 )
= $false )
| ( ( memberP @ ( cons @ SV113 @ SV142 ) @ SV46 )
= $true )
| ( ( ssList @ SV142 )
= $false )
| ( ( ssItem @ SV113 )
= $false )
| ( ( ssItem @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1518,plain,
! [SV48: $i,SV167: $i,SV156: $i,SV178: $i] :
( ( ( ~ ( ssList @ SV178 )
| ! [SY598: $i] :
( ~ ( ssList @ SY598 )
| ! [SY599: $i] :
( ~ ( ssList @ SY599 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SY598 ) ) @ ( cons @ SV167 @ SY599 ) )
!= SV48 )
| ( SV156 != SV167 ) ) ) )
= $true )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1519,plain,
! [SV48: $i] :
( ( ( ssList @ ( sK33_SY524 @ SV48 ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1520,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ ( sK41_SY575 @ SV48 ) )
| ! [SY600: $i] :
( ~ ( ssList @ SY600 )
| ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ ( sK41_SY575 @ SV48 ) ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ SY600 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1454]) ).
thf(1521,plain,
! [SV52: $i,SV143: $i,SV115: $i] :
( ( ( geq @ SV115 @ SV143 )
= $false )
| ( ( geq @ SV52 @ SV115 )
= $false )
| ( ( geq @ SV52 @ SV143 )
= $true )
| ( ( ssItem @ SV143 )
= $false )
| ( ( ssItem @ SV115 )
= $false )
| ( ( ssItem @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1522,plain,
! [SV53: $i,SV168: $i,SV157: $i,SV179: $i] :
( ( ( ~ ( ssList @ SV179 )
| ! [SY601: $i] :
( ~ ( ssList @ SY601 )
| ! [SY602: $i] :
( ~ ( ssList @ SY602 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SY601 ) ) @ ( cons @ SV168 @ SY602 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) ) )
= $true )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1523,plain,
! [SV53: $i] :
( ( ( ssList @ ( sK34_SY527 @ SV53 ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1524,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ ( sK42_SY577 @ SV53 ) )
| ! [SY603: $i] :
( ~ ( ssList @ SY603 )
| ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ ( sK42_SY577 @ SV53 ) ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ SY603 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1458]) ).
thf(1525,plain,
! [SV55: $i] :
( ( ( ~ ( ssItem @ ( sK26_SY449 @ SV55 ) ) )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1526,plain,
! [SV55: $i] :
( ( ( ( cons @ ( sK26_SY449 @ SV55 ) @ ( sK5_SY328 @ SV55 ) )
!= SV55 )
= $false )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1527,plain,
! [SV58: $i,SV169: $i,SV158: $i,SV180: $i] :
( ( ( ~ ( ssList @ SV180 )
| ! [SY604: $i] :
( ~ ( ssList @ SY604 )
| ! [SY605: $i] :
( ~ ( ssList @ SY605 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SY604 ) ) @ ( cons @ SV169 @ SY605 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) ) )
= $true )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1528,plain,
! [SV58: $i] :
( ( ( ssList @ ( sK35_SY530 @ SV58 ) )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1529,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ ( sK43_SY579 @ SV58 ) )
| ! [SY606: $i] :
( ~ ( ssList @ SY606 )
| ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ ( sK43_SY579 @ SV58 ) ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ SY606 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1462]) ).
thf(1530,plain,
! [SV59: $i,SV145: $i,SV118: $i] :
( ( ( segmentP @ SV118 @ SV145 )
= $false )
| ( ( segmentP @ SV59 @ SV118 )
= $false )
| ( ( segmentP @ SV59 @ SV145 )
= $true )
| ( ( ssList @ SV145 )
= $false )
| ( ( ssList @ SV118 )
= $false )
| ( ( ssList @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1531,plain,
( ( ssList @ sK36_SY533 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1532,plain,
( ( ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ sK36_SY533 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 )
| ~ ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1533,plain,
( ( ~ ! [SY585: $i] :
~ ~ ( ~ ( ssItem @ SY585 )
| ~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY586 )
| ( ( app @ ( cons @ SY585 @ nil ) @ SY586 )
!= sK36_SY533 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY585 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1534,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1535,plain,
( ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) )
= $false )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1536,plain,
( ( ( neq @ sK2_SX0 @ nil )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1537,plain,
( ( ( ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1538,plain,
! [SV62: $i,SV148: $i,SV121: $i] :
( ( ( gt @ SV121 @ SV148 )
= $false )
| ( ( gt @ SV62 @ SV121 )
= $false )
| ( ( gt @ SV62 @ SV148 )
= $true )
| ( ( ssItem @ SV148 )
= $false )
| ( ( ssItem @ SV121 )
= $false )
| ( ( ssItem @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1539,plain,
! [SV122: $i,SV63: $i] :
( ( ( nil = SV63 )
= $false )
| ( ( nil = SV122 )
= $false )
| ( ( nil
= ( app @ SV63 @ SV122 ) )
= $true )
| ( ( ssList @ SV122 )
= $false )
| ( ( ssList @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1540,plain,
! [SV164: $i,SV126: $i,SV149: $i,SV68: $i] :
( ( ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
| ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1541,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
| ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1542,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) ) )
= $true )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1543,plain,
! [SV129: $i,SV72: $i] :
( ( ( leq @ SV72 @ ( hd @ SV129 ) )
= $true )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1544,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) ) )
= $false )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1545,plain,
! [SV74: $i,SV170: $i,SV159: $i,SV181: $i] :
( ( ( ~ ( ssList @ SV181 )
| ! [SY607: $i] :
( ~ ( ssList @ SY607 )
| ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SY607 ) ) )
!= SV74 )
| ( SV159 = SV170 ) ) )
= $true )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1546,plain,
! [SV74: $i] :
( ( ( ssList @ ( sK37_SY542 @ SV74 ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1547,plain,
! [SV74: $i] :
( ( ( ~ ( ssList @ ( sK44_SY589 @ SV74 ) )
| ( ( app @ ( sK37_SY542 @ SV74 ) @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ ( sK44_SY589 @ SV74 ) ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1481]) ).
thf(1548,plain,
! [SV77: $i,SV152: $i,SV133: $i] :
( ( ( frontsegP @ SV133 @ SV152 )
= $false )
| ( ( frontsegP @ SV77 @ SV133 )
= $false )
| ( ( frontsegP @ SV77 @ SV152 )
= $true )
| ( ( ssList @ SV152 )
= $false )
| ( ( ssList @ SV133 )
= $false )
| ( ( ssList @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1549,plain,
! [SV78: $i,SV153: $i,SV134: $i] :
( ( ( lt @ SV134 @ SV153 )
= $false )
| ( ( lt @ SV78 @ SV134 )
= $false )
| ( ( lt @ SV78 @ SV153 )
= $true )
| ( ( ssItem @ SV153 )
= $false )
| ( ( ssItem @ SV134 )
= $false )
| ( ( ssItem @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1550,plain,
! [SV82: $i,SV171: $i,SV160: $i,SV182: $i] :
( ( ( ~ ( ssList @ SV182 )
| ! [SY608: $i] :
( ~ ( ssList @ SY608 )
| ! [SY609: $i] :
( ~ ( ssList @ SY609 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SY608 ) ) @ ( cons @ SV171 @ SY609 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) ) )
= $true )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1551,plain,
! [SV82: $i] :
( ( ( ssList @ ( sK38_SY544 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1552,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ ( sK45_SY590 @ SV82 ) )
| ! [SY610: $i] :
( ~ ( ssList @ SY610 )
| ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ ( sK45_SY590 @ SV82 ) ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ SY610 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1486]) ).
thf(1553,plain,
! [SV87: $i,SV3: $i] :
( ( ( leq @ SV3 @ SV87 )
= $false )
| ( ( SV3 = SV87 )
= $true )
| ( ( lt @ SV3 @ SV87 )
= $true )
| ( ( ssItem @ SV87 )
= $false )
| ( ( ssItem @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1554,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1555,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ( nil != SV91 ) )
| ~ ( strictorderedP @ SV91 ) )
= $true )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1556,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( ssList @ ( sK27_SY403 @ SV16 @ SV95 ) ) )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1557,plain,
! [SV16: $i,SV95: $i] :
( ( ( ( app @ SV95 @ ( sK27_SY403 @ SV16 @ SV95 ) )
!= SV16 )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1558,plain,
! [SV16: $i,SV95: $i,SV172: $i] :
( ( ( ~ ( ssList @ SV172 ) )
= $true )
| ( ( ( app @ SV95 @ SV172 )
!= SV16 )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1559,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( ssList @ ( sK28_SY406 @ SV18 @ SV97 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1560,plain,
! [SV97: $i,SV18: $i] :
( ( ( ( app @ ( sK28_SY406 @ SV18 @ SV97 ) @ SV97 )
!= SV18 )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1561,plain,
! [SV18: $i,SV97: $i,SV173: $i] :
( ( ( ~ ( ssList @ SV173 ) )
= $true )
| ( ( ( app @ SV173 @ SV97 )
!= SV18 )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1562,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ( ssList @ ( sK29_SY408 @ SV21 @ SV99 ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1563,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ~ ! [SY567: $i] :
~ ~ ( ~ ( ssList @ SY567 )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ SY567 ) )
!= SV21 ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1564,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ~ ( ssList @ SV174 ) )
= $true )
| ( ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1565,plain,
! [SV22: $i,SV165: $i,SV154: $i,SV176: $i] :
( ( ( ~ ( ssList @ SV176 ) )
= $true )
| ( ( ! [SY592: $i] :
( ~ ( ssList @ SY592 )
| ! [SY593: $i] :
( ~ ( ssList @ SY593 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SY592 ) ) @ ( cons @ SV165 @ SY593 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) ) )
= $true )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1566,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ ( sK39_SY569 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1567,plain,
! [SV22: $i] :
( ( ( ! [SY594: $i] :
( ~ ( ssList @ SY594 )
| ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ ( sK39_SY569 @ SV22 ) ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ SY594 ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1568,plain,
! [SV26: $i,SV101: $i] :
( ( ( ~ ( ( nil != SV101 ) ) )
= $true )
| ( ( ~ ( ( nil != SV26 ) ) )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1569,plain,
! [SV29: $i,SV166: $i,SV155: $i,SV177: $i] :
( ( ( ~ ( ssList @ SV177 ) )
= $true )
| ( ( ! [SY595: $i] :
( ~ ( ssList @ SY595 )
| ! [SY596: $i] :
( ~ ( ssList @ SY596 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SY595 ) ) @ ( cons @ SV166 @ SY596 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) ) )
= $true )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1570,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ ( sK40_SY571 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1571,plain,
! [SV29: $i] :
( ( ( ! [SY597: $i] :
( ~ ( ssList @ SY597 )
| ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ ( sK40_SY571 @ SV29 ) ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ SY597 ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1572,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ( ssList @ ( sK32_SY415 @ SV34 @ SV105 ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1573,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ~ ! [SY573: $i] :
~ ~ ( ~ ( ssList @ SY573 )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ SY573 )
!= SV34 ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1574,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ~ ( ssList @ SV175 ) )
= $true )
| ( ( ~ ~ ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1575,plain,
! [SV106: $i,SV35: $i,SV162: $i,SV139: $i] :
( ( ( SV139 != SV162 )
= $false )
| ( ( ( cons @ SV139 @ SV35 )
= ( cons @ SV162 @ SV106 ) )
= $false )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1576,plain,
! [SV162: $i,SV139: $i,SV35: $i,SV106: $i] :
( ( ( SV106 != SV35 )
= $false )
| ( ( ( cons @ SV139 @ SV35 )
= ( cons @ SV162 @ SV106 ) )
= $false )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1577,plain,
! [SV48: $i,SV167: $i,SV156: $i,SV178: $i] :
( ( ( ~ ( ssList @ SV178 ) )
= $true )
| ( ( ! [SY598: $i] :
( ~ ( ssList @ SY598 )
| ! [SY599: $i] :
( ~ ( ssList @ SY599 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SY598 ) ) @ ( cons @ SV167 @ SY599 ) )
!= SV48 )
| ( SV156 != SV167 ) ) ) )
= $true )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1578,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ ( sK41_SY575 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1579,plain,
! [SV48: $i] :
( ( ( ! [SY600: $i] :
( ~ ( ssList @ SY600 )
| ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ ( sK41_SY575 @ SV48 ) ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ SY600 ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1580,plain,
! [SV53: $i,SV168: $i,SV157: $i,SV179: $i] :
( ( ( ~ ( ssList @ SV179 ) )
= $true )
| ( ( ! [SY601: $i] :
( ~ ( ssList @ SY601 )
| ! [SY602: $i] :
( ~ ( ssList @ SY602 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SY601 ) ) @ ( cons @ SV168 @ SY602 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) ) )
= $true )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1581,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ ( sK42_SY577 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1582,plain,
! [SV53: $i] :
( ( ( ! [SY603: $i] :
( ~ ( ssList @ SY603 )
| ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ ( sK42_SY577 @ SV53 ) ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ SY603 ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1583,plain,
! [SV55: $i] :
( ( ( ssItem @ ( sK26_SY449 @ SV55 ) )
= $true )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1584,plain,
! [SV55: $i] :
( ( ( ( cons @ ( sK26_SY449 @ SV55 ) @ ( sK5_SY328 @ SV55 ) )
= SV55 )
= $true )
| ( ( nil = SV55 )
= $true )
| ( ( ssList @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1585,plain,
! [SV58: $i,SV169: $i,SV158: $i,SV180: $i] :
( ( ( ~ ( ssList @ SV180 ) )
= $true )
| ( ( ! [SY604: $i] :
( ~ ( ssList @ SY604 )
| ! [SY605: $i] :
( ~ ( ssList @ SY605 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SY604 ) ) @ ( cons @ SV169 @ SY605 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) ) )
= $true )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1586,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ ( sK43_SY579 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1587,plain,
! [SV58: $i] :
( ( ( ! [SY606: $i] :
( ~ ( ssList @ SY606 )
| ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ ( sK43_SY579 @ SV58 ) ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ SY606 ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1588,plain,
( ( ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ sK36_SY533 )
!= sK6_SY428 )
| ~ ( strictorderedP @ sK4_SY389 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1589,plain,
( ( ~ ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1590,plain,
( ( ! [SY585: $i] :
~ ~ ( ~ ( ssItem @ SY585 )
| ~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY586 )
| ( ( app @ ( cons @ SY585 @ nil ) @ SY586 )
!= sK36_SY533 ) )
| ~ ~ ! [SY437: $i] :
~ ~ ( ~ ( ssItem @ SY437 )
| ~ ~ ! [SY438: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY438 )
| ( ( app @ SY438 @ ( cons @ SY437 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY437 @ SY585 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1591,plain,
( ( ( neq @ sK2_SX0 @ nil )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1592,plain,
( ( ( ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY401 )
| ~ ( neq @ SY401 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY401 ) )
| ~ ( segmentP @ sK1_U @ SY401 ) ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1593,plain,
! [SV183: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV183 ) )
| ~ ( segmentP @ sK1_U @ SV183 ) ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1594,plain,
! [SV164: $i,SV126: $i,SV149: $i,SV68: $i] :
( ( ( ~ ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) ) )
= $true )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1595,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( ~ ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
= $true )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1596,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1597,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ( nil != SV129 ) )
| ~ ( totalorderedP @ SV129 ) )
= $true )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1598,plain,
! [SV74: $i,SV170: $i,SV159: $i,SV181: $i] :
( ( ( ~ ( ssList @ SV181 ) )
= $true )
| ( ( ! [SY607: $i] :
( ~ ( ssList @ SY607 )
| ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SY607 ) ) )
!= SV74 )
| ( SV159 = SV170 ) ) )
= $true )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1599,plain,
! [SV74: $i] :
( ( ( ~ ( ssList @ ( sK44_SY589 @ SV74 ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1600,plain,
! [SV74: $i] :
( ( ( ( ( app @ ( sK37_SY542 @ SV74 ) @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ ( sK44_SY589 @ SV74 ) ) ) )
!= SV74 )
| ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1601,plain,
! [SV82: $i,SV171: $i,SV160: $i,SV182: $i] :
( ( ( ~ ( ssList @ SV182 ) )
= $true )
| ( ( ! [SY608: $i] :
( ~ ( ssList @ SY608 )
| ! [SY609: $i] :
( ~ ( ssList @ SY609 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SY608 ) ) @ ( cons @ SV171 @ SY609 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) ) )
= $true )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1602,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ ( sK45_SY590 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1603,plain,
! [SV82: $i] :
( ( ( ! [SY610: $i] :
( ~ ( ssList @ SY610 )
| ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ ( sK45_SY590 @ SV82 ) ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ SY610 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1604,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ( nil != SV91 ) ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1605,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( strictorderedP @ SV91 ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1606,plain,
! [SV10: $i,SV91: $i] :
( ( ( ~ ( ( nil != SV91 ) ) )
= $true )
| ( ( ~ ( strictorderedP @ SV91 ) )
= $true )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1607,plain,
! [SV95: $i,SV16: $i] :
( ( ( ssList @ ( sK27_SY403 @ SV16 @ SV95 ) )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1608,plain,
! [SV16: $i,SV95: $i] :
( ( ( ( app @ SV95 @ ( sK27_SY403 @ SV16 @ SV95 ) )
= SV16 )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $false )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1609,plain,
! [SV16: $i,SV95: $i,SV172: $i] :
( ( ( ssList @ SV172 )
= $false )
| ( ( ( app @ SV95 @ SV172 )
!= SV16 )
= $true )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1610,plain,
! [SV97: $i,SV18: $i] :
( ( ( ssList @ ( sK28_SY406 @ SV18 @ SV97 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1611,plain,
! [SV97: $i,SV18: $i] :
( ( ( ( app @ ( sK28_SY406 @ SV18 @ SV97 ) @ SV97 )
= SV18 )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $false )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1612,plain,
! [SV18: $i,SV97: $i,SV173: $i] :
( ( ( ssList @ SV173 )
= $false )
| ( ( ( app @ SV173 @ SV97 )
!= SV18 )
= $true )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1613,plain,
! [SV99: $i,SV21: $i] :
( ( ( ssList @ ( sK29_SY408 @ SV21 @ SV99 ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1614,plain,
! [SV99: $i,SV21: $i] :
( ( ( ~ ! [SY567: $i] :
~ ~ ( ~ ( ssList @ SY567 )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ SY567 ) )
!= SV21 ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1615,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ssList @ SV174 )
= $false )
| ( ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1616,plain,
! [SV22: $i,SV165: $i,SV154: $i,SV176: $i] :
( ( ( ssList @ SV176 )
= $false )
| ( ( ! [SY592: $i] :
( ~ ( ssList @ SY592 )
| ! [SY593: $i] :
( ~ ( ssList @ SY593 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SY592 ) ) @ ( cons @ SV165 @ SY593 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) ) )
= $true )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1617,plain,
! [SV22: $i] :
( ( ( ssList @ ( sK39_SY569 @ SV22 ) )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1618,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ ( sK46_SY594 @ SV22 ) )
| ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ ( sK39_SY569 @ SV22 ) ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ ( sK46_SY594 @ SV22 ) ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1567]) ).
thf(1619,plain,
! [SV26: $i,SV101: $i] :
( ( ( nil != SV101 )
= $false )
| ( ( ~ ( ( nil != SV26 ) ) )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1620,plain,
! [SV29: $i,SV166: $i,SV155: $i,SV177: $i] :
( ( ( ssList @ SV177 )
= $false )
| ( ( ! [SY595: $i] :
( ~ ( ssList @ SY595 )
| ! [SY596: $i] :
( ~ ( ssList @ SY596 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SY595 ) ) @ ( cons @ SV166 @ SY596 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) ) )
= $true )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1621,plain,
! [SV29: $i] :
( ( ( ssList @ ( sK40_SY571 @ SV29 ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1622,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ ( sK47_SY597 @ SV29 ) )
| ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ ( sK40_SY571 @ SV29 ) ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ ( sK47_SY597 @ SV29 ) ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1571]) ).
thf(1623,plain,
! [SV105: $i,SV34: $i] :
( ( ( ssList @ ( sK32_SY415 @ SV34 @ SV105 ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1624,plain,
! [SV105: $i,SV34: $i] :
( ( ( ~ ! [SY573: $i] :
~ ~ ( ~ ( ssList @ SY573 )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ SY573 )
!= SV34 ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1625,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ssList @ SV175 )
= $false )
| ( ( ~ ~ ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1626,plain,
! [SV106: $i,SV35: $i,SV162: $i,SV139: $i] :
( ( ( SV139 = SV162 )
= $true )
| ( ( ( cons @ SV139 @ SV35 )
= ( cons @ SV162 @ SV106 ) )
= $false )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1627,plain,
! [SV162: $i,SV139: $i,SV35: $i,SV106: $i] :
( ( ( SV106 = SV35 )
= $true )
| ( ( ( cons @ SV139 @ SV35 )
= ( cons @ SV162 @ SV106 ) )
= $false )
| ( ( ssItem @ SV162 )
= $false )
| ( ( ssItem @ SV139 )
= $false )
| ( ( ssList @ SV106 )
= $false )
| ( ( ssList @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1628,plain,
! [SV48: $i,SV167: $i,SV156: $i,SV178: $i] :
( ( ( ssList @ SV178 )
= $false )
| ( ( ! [SY598: $i] :
( ~ ( ssList @ SY598 )
| ! [SY599: $i] :
( ~ ( ssList @ SY599 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SY598 ) ) @ ( cons @ SV167 @ SY599 ) )
!= SV48 )
| ( SV156 != SV167 ) ) ) )
= $true )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1629,plain,
! [SV48: $i] :
( ( ( ssList @ ( sK41_SY575 @ SV48 ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1630,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ ( sK48_SY600 @ SV48 ) )
| ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ ( sK41_SY575 @ SV48 ) ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ ( sK48_SY600 @ SV48 ) ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1579]) ).
thf(1631,plain,
! [SV53: $i,SV168: $i,SV157: $i,SV179: $i] :
( ( ( ssList @ SV179 )
= $false )
| ( ( ! [SY601: $i] :
( ~ ( ssList @ SY601 )
| ! [SY602: $i] :
( ~ ( ssList @ SY602 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SY601 ) ) @ ( cons @ SV168 @ SY602 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) ) )
= $true )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1632,plain,
! [SV53: $i] :
( ( ( ssList @ ( sK42_SY577 @ SV53 ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1633,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ ( sK49_SY603 @ SV53 ) )
| ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ ( sK42_SY577 @ SV53 ) ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ ( sK49_SY603 @ SV53 ) ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1582]) ).
thf(1634,plain,
! [SV58: $i,SV169: $i,SV158: $i,SV180: $i] :
( ( ( ssList @ SV180 )
= $false )
| ( ( ! [SY604: $i] :
( ~ ( ssList @ SY604 )
| ! [SY605: $i] :
( ~ ( ssList @ SY605 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SY604 ) ) @ ( cons @ SV169 @ SY605 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) ) )
= $true )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1635,plain,
! [SV58: $i] :
( ( ( ssList @ ( sK43_SY579 @ SV58 ) )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1636,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ ( sK50_SY606 @ SV58 ) )
| ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ ( sK43_SY579 @ SV58 ) ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ ( sK50_SY606 @ SV58 ) ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1587]) ).
thf(1637,plain,
( ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ sK36_SY533 )
!= sK6_SY428 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1638,plain,
( ( ~ ( strictorderedP @ sK4_SY389 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1639,plain,
( ( ! [SY534: $i] :
~ ~ ( ~ ( ssItem @ SY534 )
| ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY535 )
| ( ( app @ SY535 @ ( cons @ SY534 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( ssItem @ SY433 )
| ~ ~ ! [SY434: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY434 )
| ( ( app @ ( cons @ SY433 @ nil ) @ SY434 )
!= sK4_SY389 ) )
| ~ ( lt @ SY534 @ SY433 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1640,plain,
! [SV184: $i] :
( ( ~ ~ ( ~ ( ssItem @ SV184 )
| ~ ~ ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1641,plain,
! [SV185: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV185 ) )
| ~ ( segmentP @ sK1_U @ SV185 ) ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1642,plain,
! [SV183: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV183 ) )
| ~ ( segmentP @ sK1_U @ SV183 ) ) )
= $false )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1643,plain,
! [SV164: $i,SV126: $i,SV149: $i,SV68: $i] :
( ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $false )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1644,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( ~ ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) ) )
= $false )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1645,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ( nil != SV129 ) ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1646,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( totalorderedP @ SV129 ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1647,plain,
! [SV72: $i,SV129: $i] :
( ( ( ~ ( ( nil != SV129 ) ) )
= $true )
| ( ( ~ ( totalorderedP @ SV129 ) )
= $true )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1648,plain,
! [SV74: $i,SV170: $i,SV159: $i,SV181: $i] :
( ( ( ssList @ SV181 )
= $false )
| ( ( ! [SY607: $i] :
( ~ ( ssList @ SY607 )
| ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SY607 ) ) )
!= SV74 )
| ( SV159 = SV170 ) ) )
= $true )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1649,plain,
! [SV74: $i] :
( ( ( ssList @ ( sK44_SY589 @ SV74 ) )
= $true )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1650,plain,
! [SV74: $i] :
( ( ( ( app @ ( sK37_SY542 @ SV74 ) @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ ( sK44_SY589 @ SV74 ) ) ) )
!= SV74 )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1651,plain,
! [SV74: $i] :
( ( ( ( sK15_SY366 @ SV74 )
= ( sK24_SY507 @ SV74 ) )
= $false )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1652,plain,
! [SV82: $i,SV171: $i,SV160: $i,SV182: $i] :
( ( ( ssList @ SV182 )
= $false )
| ( ( ! [SY608: $i] :
( ~ ( ssList @ SY608 )
| ! [SY609: $i] :
( ~ ( ssList @ SY609 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SY608 ) ) @ ( cons @ SV171 @ SY609 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) ) )
= $true )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1653,plain,
! [SV82: $i] :
( ( ( ssList @ ( sK45_SY590 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1654,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ ( sK51_SY610 @ SV82 ) )
| ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ ( sK45_SY590 @ SV82 ) ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ ( sK51_SY610 @ SV82 ) ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1603]) ).
thf(1655,plain,
! [SV10: $i,SV91: $i] :
( ( ( nil != SV91 )
= $true )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1656,plain,
! [SV10: $i,SV91: $i] :
( ( ( strictorderedP @ SV91 )
= $true )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1657,plain,
! [SV10: $i,SV91: $i] :
( ( ( nil != SV91 )
= $false )
| ( ( ~ ( strictorderedP @ SV91 ) )
= $true )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1658,plain,
! [SV16: $i,SV172: $i,SV95: $i] :
( ( ( ( app @ SV95 @ SV172 )
= SV16 )
= $false )
| ( ( ssList @ SV172 )
= $false )
| ( ( frontsegP @ SV16 @ SV95 )
= $true )
| ( ( ssList @ SV95 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1659,plain,
! [SV18: $i,SV97: $i,SV173: $i] :
( ( ( ( app @ SV173 @ SV97 )
= SV18 )
= $false )
| ( ( ssList @ SV173 )
= $false )
| ( ( rearsegP @ SV18 @ SV97 )
= $true )
| ( ( ssList @ SV97 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1660,plain,
! [SV99: $i,SV21: $i] :
( ( ( ! [SY567: $i] :
~ ~ ( ~ ( ssList @ SY567 )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ SY567 ) )
!= SV21 ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1661,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ~ ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) )
= $false )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1662,plain,
! [SV22: $i,SV165: $i,SV154: $i,SV176: $i,SV186: $i] :
( ( ( ~ ( ssList @ SV186 )
| ! [SY614: $i] :
( ~ ( ssList @ SY614 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SY614 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) )
= $true )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1663,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ ( sK46_SY594 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1664,plain,
! [SV22: $i] :
( ( ( ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ ( sK39_SY569 @ SV22 ) ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ ( sK46_SY594 @ SV22 ) ) )
!= SV22 )
| ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1665,plain,
! [SV26: $i,SV101: $i] :
( ( ( nil = SV101 )
= $true )
| ( ( ~ ( ( nil != SV26 ) ) )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1666,plain,
! [SV29: $i,SV166: $i,SV155: $i,SV177: $i,SV187: $i] :
( ( ( ~ ( ssList @ SV187 )
| ! [SY615: $i] :
( ~ ( ssList @ SY615 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SY615 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) )
= $true )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1667,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ ( sK47_SY597 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1668,plain,
! [SV29: $i] :
( ( ( ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ ( sK40_SY571 @ SV29 ) ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ ( sK47_SY597 @ SV29 ) ) )
!= SV29 )
| ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1669,plain,
! [SV105: $i,SV34: $i] :
( ( ( ! [SY573: $i] :
~ ~ ( ~ ( ssList @ SY573 )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ SY573 )
!= SV34 ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1670,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ~ ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) )
= $false )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1671,plain,
! [SV48: $i,SV167: $i,SV156: $i,SV178: $i,SV188: $i] :
( ( ( ~ ( ssList @ SV188 )
| ! [SY616: $i] :
( ~ ( ssList @ SY616 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SY616 ) )
!= SV48 )
| ( SV156 != SV167 ) ) )
= $true )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1672,plain,
! [SV48: $i] :
( ( ( ~ ( ssList @ ( sK48_SY600 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1673,plain,
! [SV48: $i] :
( ( ( ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ ( sK41_SY575 @ SV48 ) ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ ( sK48_SY600 @ SV48 ) ) )
!= SV48 )
| ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1674,plain,
! [SV53: $i,SV168: $i,SV157: $i,SV179: $i,SV189: $i] :
( ( ( ~ ( ssList @ SV189 )
| ! [SY617: $i] :
( ~ ( ssList @ SY617 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SY617 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) )
= $true )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1675,plain,
! [SV53: $i] :
( ( ( ~ ( ssList @ ( sK49_SY603 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1676,plain,
! [SV53: $i] :
( ( ( ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ ( sK42_SY577 @ SV53 ) ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ ( sK49_SY603 @ SV53 ) ) )
!= SV53 )
| ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1677,plain,
! [SV58: $i,SV169: $i,SV158: $i,SV180: $i,SV190: $i] :
( ( ( ~ ( ssList @ SV190 )
| ! [SY618: $i] :
( ~ ( ssList @ SY618 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SY618 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) )
= $true )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1678,plain,
! [SV58: $i] :
( ( ( ~ ( ssList @ ( sK50_SY606 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1679,plain,
! [SV58: $i] :
( ( ( ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ ( sK43_SY579 @ SV58 ) ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ ( sK50_SY606 @ SV58 ) ) )
!= SV58 )
| ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1680,plain,
( ( ( app @ ( app @ sK23_SY450 @ sK4_SY389 ) @ sK36_SY533 )
= sK6_SY428 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1681,plain,
( ( strictorderedP @ sK4_SY389 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1682,plain,
! [SV191: $i] :
( ( ~ ~ ( ~ ( ssItem @ SV191 )
| ~ ~ ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1683,plain,
! [SV184: $i] :
( ( ~ ( ~ ( ssItem @ SV184 )
| ~ ~ ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1684,plain,
! [SV185: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV185 ) )
| ~ ( segmentP @ sK1_U @ SV185 ) ) )
= $false )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1685,plain,
! [SV183: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV183 ) )
| ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1686,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
= $false )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1687,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( ( SV68 != SV126 )
| ~ ( frontsegP @ SV149 @ SV164 ) )
= $true )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1688,plain,
! [SV72: $i,SV129: $i] :
( ( ( nil != SV129 )
= $true )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1689,plain,
! [SV72: $i,SV129: $i] :
( ( ( totalorderedP @ SV129 )
= $true )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1690,plain,
! [SV72: $i,SV129: $i] :
( ( ( nil != SV129 )
= $false )
| ( ( ~ ( totalorderedP @ SV129 ) )
= $true )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1691,plain,
! [SV74: $i,SV170: $i,SV159: $i,SV181: $i,SV192: $i] :
( ( ( ~ ( ssList @ SV192 )
| ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SV192 ) ) )
!= SV74 )
| ( SV159 = SV170 ) )
= $true )
| ( ( ssList @ SV181 )
= $false )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1692,plain,
! [SV74: $i] :
( ( ( ( app @ ( sK37_SY542 @ SV74 ) @ ( cons @ ( sK15_SY366 @ SV74 ) @ ( cons @ ( sK24_SY507 @ SV74 ) @ ( sK44_SY589 @ SV74 ) ) ) )
= SV74 )
= $true )
| ( ( equalelemsP @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1693,plain,
! [SV82: $i,SV171: $i,SV160: $i,SV182: $i,SV193: $i] :
( ( ( ~ ( ssList @ SV193 )
| ! [SY622: $i] :
( ~ ( ssList @ SY622 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SY622 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) )
= $true )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1694,plain,
! [SV82: $i] :
( ( ( ~ ( ssList @ ( sK51_SY610 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1695,plain,
! [SV82: $i] :
( ( ( ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ ( sK45_SY590 @ SV82 ) ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ ( sK51_SY610 @ SV82 ) ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1696,plain,
! [SV10: $i,SV91: $i] :
( ( ( nil = SV91 )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $false )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1697,plain,
! [SV10: $i,SV91: $i] :
( ( ( nil = SV91 )
= $true )
| ( ( ~ ( strictorderedP @ SV91 ) )
= $true )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1698,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK52_SY567 @ SV99 @ SV21 ) )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ ( sK52_SY567 @ SV99 @ SV21 ) ) )
!= SV21 ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1660]) ).
thf(1699,plain,
! [SV21: $i,SV99: $i,SV174: $i] :
( ( ( ! [SY568: $i] :
~ ~ ( ~ ( ssList @ SY568 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SY568 ) )
!= SV21 ) ) )
= $true )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1700,plain,
! [SV22: $i,SV165: $i,SV154: $i,SV176: $i,SV186: $i] :
( ( ( ~ ( ssList @ SV186 ) )
= $true )
| ( ( ! [SY614: $i] :
( ~ ( ssList @ SY614 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SY614 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) )
= $true )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1701,plain,
! [SV22: $i] :
( ( ( ssList @ ( sK46_SY594 @ SV22 ) )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1702,plain,
! [SV22: $i] :
( ( ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ ( sK39_SY569 @ SV22 ) ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ ( sK46_SY594 @ SV22 ) ) )
!= SV22 )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1664]) ).
thf(1703,plain,
! [SV22: $i] :
( ( ( ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
| ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1664]) ).
thf(1704,plain,
! [SV101: $i,SV26: $i] :
( ( ( nil != SV26 )
= $false )
| ( ( nil = SV101 )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1705,plain,
! [SV29: $i,SV166: $i,SV155: $i,SV177: $i,SV187: $i] :
( ( ( ~ ( ssList @ SV187 ) )
= $true )
| ( ( ! [SY615: $i] :
( ~ ( ssList @ SY615 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SY615 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) )
= $true )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1706,plain,
! [SV29: $i] :
( ( ( ssList @ ( sK47_SY597 @ SV29 ) )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1707,plain,
! [SV29: $i] :
( ( ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ ( sK40_SY571 @ SV29 ) ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ ( sK47_SY597 @ SV29 ) ) )
!= SV29 )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1708,plain,
! [SV29: $i] :
( ( ( leq @ ( sK11_SY277 @ SV29 ) @ ( sK19_SY476 @ SV29 ) )
= $false )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1709,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK53_SY573 @ SV105 @ SV34 ) )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ ( sK53_SY573 @ SV105 @ SV34 ) )
!= SV34 ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1669]) ).
thf(1710,plain,
! [SV34: $i,SV105: $i,SV175: $i] :
( ( ( ! [SY574: $i] :
~ ~ ( ~ ( ssList @ SY574 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SY574 )
!= SV34 ) ) )
= $true )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1711,plain,
! [SV48: $i,SV167: $i,SV156: $i,SV178: $i,SV188: $i] :
( ( ( ~ ( ssList @ SV188 ) )
= $true )
| ( ( ! [SY616: $i] :
( ~ ( ssList @ SY616 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SY616 ) )
!= SV48 )
| ( SV156 != SV167 ) ) )
= $true )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1712,plain,
! [SV48: $i] :
( ( ( ssList @ ( sK48_SY600 @ SV48 ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1713,plain,
! [SV48: $i] :
( ( ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ ( sK41_SY575 @ SV48 ) ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ ( sK48_SY600 @ SV48 ) ) )
!= SV48 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1714,plain,
! [SV48: $i] :
( ( ( ( sK12_SY309 @ SV48 )
!= ( sK20_SY484 @ SV48 ) )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1715,plain,
! [SV53: $i,SV168: $i,SV157: $i,SV179: $i,SV189: $i] :
( ( ( ~ ( ssList @ SV189 ) )
= $true )
| ( ( ! [SY617: $i] :
( ~ ( ssList @ SY617 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SY617 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) )
= $true )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1716,plain,
! [SV53: $i] :
( ( ( ssList @ ( sK49_SY603 @ SV53 ) )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1717,plain,
! [SV53: $i] :
( ( ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ ( sK42_SY577 @ SV53 ) ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ ( sK49_SY603 @ SV53 ) ) )
!= SV53 )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1718,plain,
! [SV53: $i] :
( ( ( lt @ ( sK13_SY323 @ SV53 ) @ ( sK21_SY492 @ SV53 ) )
= $false )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1719,plain,
! [SV58: $i,SV169: $i,SV158: $i,SV180: $i,SV190: $i] :
( ( ( ~ ( ssList @ SV190 ) )
= $true )
| ( ( ! [SY618: $i] :
( ~ ( ssList @ SY618 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SY618 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) )
= $true )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1720,plain,
! [SV58: $i] :
( ( ( ssList @ ( sK50_SY606 @ SV58 ) )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1721,plain,
! [SV58: $i] :
( ( ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ ( sK43_SY579 @ SV58 ) ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ ( sK50_SY606 @ SV58 ) ) )
!= SV58 )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1679]) ).
thf(1722,plain,
! [SV58: $i] :
( ( ( ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
| ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1679]) ).
thf(1723,plain,
! [SV191: $i] :
( ( ~ ( ~ ( ssItem @ SV191 )
| ~ ~ ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1724,plain,
! [SV184: $i] :
( ( ~ ( ssItem @ SV184 )
| ~ ~ ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1725,plain,
! [SV185: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV185 ) )
| ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1726,plain,
! [SV183: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV183 ) ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1727,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( SV68 != SV126 )
= $false )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1728,plain,
! [SV126: $i,SV68: $i,SV164: $i,SV149: $i] :
( ( ( ~ ( frontsegP @ SV149 @ SV164 ) )
= $false )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1729,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( SV68 != SV126 )
= $true )
| ( ( ~ ( frontsegP @ SV149 @ SV164 ) )
= $true )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1730,plain,
! [SV72: $i,SV129: $i] :
( ( ( nil = SV129 )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $false )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1731,plain,
! [SV72: $i,SV129: $i] :
( ( ( nil = SV129 )
= $true )
| ( ( ~ ( totalorderedP @ SV129 ) )
= $true )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1732,plain,
! [SV74: $i,SV170: $i,SV159: $i,SV181: $i,SV192: $i] :
( ( ( ~ ( ssList @ SV192 ) )
= $true )
| ( ( ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SV192 ) ) )
!= SV74 )
| ( SV159 = SV170 ) )
= $true )
| ( ( ssList @ SV181 )
= $false )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1733,plain,
! [SV82: $i,SV171: $i,SV160: $i,SV182: $i,SV193: $i] :
( ( ( ~ ( ssList @ SV193 ) )
= $true )
| ( ( ! [SY622: $i] :
( ~ ( ssList @ SY622 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SY622 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) )
= $true )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1734,plain,
! [SV82: $i] :
( ( ( ssList @ ( sK51_SY610 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1735,plain,
! [SV82: $i] :
( ( ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ ( sK45_SY590 @ SV82 ) ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ ( sK51_SY610 @ SV82 ) ) )
!= SV82 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1736,plain,
! [SV82: $i] :
( ( ( ~ ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1737,plain,
! [SV10: $i,SV91: $i] :
( ( ( strictorderedP @ SV91 )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( ~ ( lt @ SV10 @ ( hd @ SV91 ) ) )
= $true )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1738,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK52_SY567 @ SV99 @ SV21 ) )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ ( sK52_SY567 @ SV99 @ SV21 ) ) )
!= SV21 ) ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1739,plain,
! [SV21: $i,SV99: $i,SV174: $i,SV194: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV194 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SV194 ) )
!= SV21 ) ) )
= $true )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1740,plain,
! [SV22: $i,SV165: $i,SV154: $i,SV176: $i,SV186: $i] :
( ( ( ssList @ SV186 )
= $false )
| ( ( ! [SY614: $i] :
( ~ ( ssList @ SY614 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SY614 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) ) )
= $true )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1741,plain,
! [SV22: $i] :
( ( ( ( app @ ( app @ ( sK30_SY518 @ SV22 ) @ ( cons @ ( sK10_SY262 @ SV22 ) @ ( sK39_SY569 @ SV22 ) ) ) @ ( cons @ ( sK18_SY468 @ SV22 ) @ ( sK46_SY594 @ SV22 ) ) )
= SV22 )
= $true )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1742,plain,
! [SV22: $i] :
( ( ( lt @ ( sK10_SY262 @ SV22 ) @ ( sK18_SY468 @ SV22 ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1743,plain,
! [SV22: $i] :
( ( ( lt @ ( sK18_SY468 @ SV22 ) @ ( sK10_SY262 @ SV22 ) )
= $false )
| ( ( strictorderP @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1744,plain,
! [SV101: $i,SV26: $i] :
( ( ( nil = SV26 )
= $true )
| ( ( nil = SV101 )
= $true )
| ( ( ( hd @ SV101 )
!= ( hd @ SV26 ) )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1745,plain,
! [SV29: $i,SV166: $i,SV155: $i,SV177: $i,SV187: $i] :
( ( ( ssList @ SV187 )
= $false )
| ( ( ! [SY615: $i] :
( ~ ( ssList @ SY615 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SY615 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) ) )
= $true )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1746,plain,
! [SV29: $i] :
( ( ( ( app @ ( app @ ( sK31_SY521 @ SV29 ) @ ( cons @ ( sK11_SY277 @ SV29 ) @ ( sK40_SY571 @ SV29 ) ) ) @ ( cons @ ( sK19_SY476 @ SV29 ) @ ( sK47_SY597 @ SV29 ) ) )
= SV29 )
= $true )
| ( ( totalorderedP @ SV29 )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(1747,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK53_SY573 @ SV105 @ SV34 ) )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ ( sK53_SY573 @ SV105 @ SV34 ) )
!= SV34 ) ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1748,plain,
! [SV34: $i,SV105: $i,SV175: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV195 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SV195 )
!= SV34 ) ) )
= $true )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1749,plain,
! [SV48: $i,SV167: $i,SV156: $i,SV178: $i,SV188: $i] :
( ( ( ssList @ SV188 )
= $false )
| ( ( ! [SY616: $i] :
( ~ ( ssList @ SY616 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SY616 ) )
!= SV48 )
| ( SV156 != SV167 ) ) )
= $true )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1750,plain,
! [SV48: $i] :
( ( ( ( app @ ( app @ ( sK33_SY524 @ SV48 ) @ ( cons @ ( sK12_SY309 @ SV48 ) @ ( sK41_SY575 @ SV48 ) ) ) @ ( cons @ ( sK20_SY484 @ SV48 ) @ ( sK48_SY600 @ SV48 ) ) )
= SV48 )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1751,plain,
! [SV48: $i] :
( ( ( ( sK12_SY309 @ SV48 )
= ( sK20_SY484 @ SV48 ) )
= $true )
| ( ( duplicatefreeP @ SV48 )
= $true )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1752,plain,
! [SV53: $i,SV168: $i,SV157: $i,SV179: $i,SV189: $i] :
( ( ( ssList @ SV189 )
= $false )
| ( ( ! [SY617: $i] :
( ~ ( ssList @ SY617 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SY617 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) ) )
= $true )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1753,plain,
! [SV53: $i] :
( ( ( ( app @ ( app @ ( sK34_SY527 @ SV53 ) @ ( cons @ ( sK13_SY323 @ SV53 ) @ ( sK42_SY577 @ SV53 ) ) ) @ ( cons @ ( sK21_SY492 @ SV53 ) @ ( sK49_SY603 @ SV53 ) ) )
= SV53 )
= $true )
| ( ( strictorderedP @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1754,plain,
! [SV58: $i,SV169: $i,SV158: $i,SV180: $i,SV190: $i] :
( ( ( ssList @ SV190 )
= $false )
| ( ( ! [SY618: $i] :
( ~ ( ssList @ SY618 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SY618 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) ) )
= $true )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1755,plain,
! [SV58: $i] :
( ( ( ( app @ ( app @ ( sK35_SY530 @ SV58 ) @ ( cons @ ( sK14_SY338 @ SV58 ) @ ( sK43_SY579 @ SV58 ) ) ) @ ( cons @ ( sK22_SY500 @ SV58 ) @ ( sK50_SY606 @ SV58 ) ) )
= SV58 )
= $true )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1756,plain,
! [SV58: $i] :
( ( ( leq @ ( sK14_SY338 @ SV58 ) @ ( sK22_SY500 @ SV58 ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1757,plain,
! [SV58: $i] :
( ( ( leq @ ( sK22_SY500 @ SV58 ) @ ( sK14_SY338 @ SV58 ) )
= $false )
| ( ( totalorderP @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1758,plain,
! [SV191: $i] :
( ( ~ ( ssItem @ SV191 )
| ~ ~ ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1759,plain,
! [SV184: $i] :
( ( ( ~ ( ssItem @ SV184 ) )
= $true )
| ( ( ~ ~ ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1760,plain,
! [SV185: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV185 ) ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1761,plain,
! [SV183: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV183 ) ) )
= $false )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1762,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( SV68 = SV126 )
= $true )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1763,plain,
! [SV126: $i,SV68: $i,SV164: $i,SV149: $i] :
( ( ( frontsegP @ SV149 @ SV164 )
= $true )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $false )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1764,plain,
! [SV164: $i,SV149: $i,SV126: $i,SV68: $i] :
( ( ( SV68 = SV126 )
= $false )
| ( ( ~ ( frontsegP @ SV149 @ SV164 ) )
= $true )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1765,plain,
! [SV72: $i,SV129: $i] :
( ( ( totalorderedP @ SV129 )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( ~ ( leq @ SV72 @ ( hd @ SV129 ) ) )
= $true )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1766,plain,
! [SV74: $i,SV170: $i,SV159: $i,SV181: $i,SV192: $i] :
( ( ( ssList @ SV192 )
= $false )
| ( ( ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SV192 ) ) )
!= SV74 )
| ( SV159 = SV170 ) )
= $true )
| ( ( ssList @ SV181 )
= $false )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1767,plain,
! [SV82: $i,SV171: $i,SV160: $i,SV182: $i,SV193: $i] :
( ( ( ssList @ SV193 )
= $false )
| ( ( ! [SY622: $i] :
( ~ ( ssList @ SY622 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SY622 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) ) )
= $true )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1768,plain,
! [SV82: $i] :
( ( ( ( app @ ( app @ ( sK38_SY544 @ SV82 ) @ ( cons @ ( sK16_SY383 @ SV82 ) @ ( sK45_SY590 @ SV82 ) ) ) @ ( cons @ ( sK25_SY514 @ SV82 ) @ ( sK51_SY610 @ SV82 ) ) )
= SV82 )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1769,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1770,plain,
! [SV91: $i,SV10: $i] :
( ( ( lt @ SV10 @ ( hd @ SV91 ) )
= $false )
| ( ( nil = SV91 )
= $true )
| ( ( strictorderedP @ SV91 )
= $false )
| ( ( strictorderedP @ ( cons @ SV10 @ SV91 ) )
= $true )
| ( ( ssList @ SV91 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1771,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ( ssList @ ( sK52_SY567 @ SV99 @ SV21 ) )
| ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ ( sK52_SY567 @ SV99 @ SV21 ) ) )
!= SV21 ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1772,plain,
! [SV21: $i,SV99: $i,SV174: $i,SV194: $i] :
( ( ( ~ ( ~ ( ssList @ SV194 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SV194 ) )
!= SV21 ) ) )
= $false )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1773,plain,
! [SV22: $i,SV165: $i,SV186: $i,SV154: $i,SV176: $i,SV196: $i] :
( ( ( ~ ( ssList @ SV196 )
| ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SV196 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) )
= $true )
| ( ( ssList @ SV186 )
= $false )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1774,plain,
! [SV26: $i,SV101: $i] :
( ( ( ( hd @ SV101 )
= ( hd @ SV26 ) )
= $false )
| ( ( nil = SV101 )
= $true )
| ( ( nil = SV26 )
= $true )
| ( ( ( tl @ SV101 )
!= ( tl @ SV26 ) )
= $true )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1775,plain,
! [SV29: $i,SV166: $i,SV187: $i,SV155: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ssList @ SV197 )
| ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SV197 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) )
= $true )
| ( ( ssList @ SV187 )
= $false )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1776,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ( ssList @ ( sK53_SY573 @ SV105 @ SV34 ) )
| ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ ( sK53_SY573 @ SV105 @ SV34 ) )
!= SV34 ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1777,plain,
! [SV34: $i,SV105: $i,SV175: $i,SV195: $i] :
( ( ( ~ ( ~ ( ssList @ SV195 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SV195 )
!= SV34 ) ) )
= $false )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1778,plain,
! [SV48: $i,SV167: $i,SV188: $i,SV156: $i,SV178: $i,SV198: $i] :
( ( ( ~ ( ssList @ SV198 )
| ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SV198 ) )
!= SV48 )
| ( SV156 != SV167 ) )
= $true )
| ( ( ssList @ SV188 )
= $false )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(1779,plain,
! [SV53: $i,SV168: $i,SV189: $i,SV157: $i,SV179: $i,SV199: $i] :
( ( ( ~ ( ssList @ SV199 )
| ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SV199 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) )
= $true )
| ( ( ssList @ SV189 )
= $false )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1780,plain,
! [SV58: $i,SV169: $i,SV190: $i,SV158: $i,SV180: $i,SV200: $i] :
( ( ( ~ ( ssList @ SV200 )
| ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SV200 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) )
= $true )
| ( ( ssList @ SV190 )
= $false )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1781,plain,
! [SV191: $i] :
( ( ( ~ ( ssItem @ SV191 ) )
= $true )
| ( ( ~ ~ ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(1782,plain,
! [SV184: $i] :
( ( ( ssItem @ SV184 )
= $false )
| ( ( ~ ~ ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1783,plain,
! [SV185: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV185 ) ) )
= $false )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1784,plain,
! [SV183: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1785,plain,
! [SV126: $i,SV68: $i,SV164: $i,SV149: $i] :
( ( ( frontsegP @ SV149 @ SV164 )
= $false )
| ( ( SV68 = SV126 )
= $false )
| ( ( frontsegP @ ( cons @ SV68 @ SV149 ) @ ( cons @ SV126 @ SV164 ) )
= $true )
| ( ( ssList @ SV164 )
= $false )
| ( ( ssList @ SV149 )
= $false )
| ( ( ssItem @ SV126 )
= $false )
| ( ( ssItem @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1786,plain,
! [SV129: $i,SV72: $i] :
( ( ( leq @ SV72 @ ( hd @ SV129 ) )
= $false )
| ( ( nil = SV129 )
= $true )
| ( ( totalorderedP @ SV129 )
= $false )
| ( ( totalorderedP @ ( cons @ SV72 @ SV129 ) )
= $true )
| ( ( ssList @ SV129 )
= $false )
| ( ( ssItem @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1787,plain,
! [SV74: $i,SV192: $i,SV170: $i,SV159: $i,SV181: $i] :
( ( ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SV192 ) ) )
!= SV74 )
= $true )
| ( ( SV159 = SV170 )
= $true )
| ( ( ssList @ SV192 )
= $false )
| ( ( ssList @ SV181 )
= $false )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1788,plain,
! [SV82: $i,SV171: $i,SV193: $i,SV160: $i,SV182: $i,SV201: $i] :
( ( ( ~ ( ssList @ SV201 )
| ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) )
= $true )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(1789,plain,
! [SV82: $i] :
( ( ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
| ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1790,plain,
! [SV21: $i,SV99: $i] :
( ( ( ~ ( ssList @ ( sK52_SY567 @ SV99 @ SV21 ) ) )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1791,plain,
! [SV99: $i,SV21: $i] :
( ( ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ ( sK52_SY567 @ SV99 @ SV21 ) ) )
!= SV21 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1792,plain,
! [SV21: $i,SV99: $i,SV174: $i,SV194: $i] :
( ( ( ~ ( ssList @ SV194 )
| ( ( app @ SV174 @ ( cons @ SV99 @ SV194 ) )
!= SV21 ) )
= $true )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1793,plain,
! [SV22: $i,SV165: $i,SV186: $i,SV154: $i,SV176: $i,SV196: $i] :
( ( ( ~ ( ssList @ SV196 ) )
= $true )
| ( ( ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SV196 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) )
= $true )
| ( ( ssList @ SV186 )
= $false )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1794,plain,
! [SV26: $i,SV101: $i] :
( ( ( ( tl @ SV101 )
= ( tl @ SV26 ) )
= $false )
| ( ( nil = SV26 )
= $true )
| ( ( nil = SV101 )
= $true )
| ( ( ( hd @ SV101 )
= ( hd @ SV26 ) )
= $false )
| ( ( SV101 = SV26 )
= $true )
| ( ( ssList @ SV101 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1795,plain,
! [SV29: $i,SV166: $i,SV187: $i,SV155: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ssList @ SV197 ) )
= $true )
| ( ( ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SV197 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) )
= $true )
| ( ( ssList @ SV187 )
= $false )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1796,plain,
! [SV34: $i,SV105: $i] :
( ( ( ~ ( ssList @ ( sK53_SY573 @ SV105 @ SV34 ) ) )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1797,plain,
! [SV105: $i,SV34: $i] :
( ( ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ ( sK53_SY573 @ SV105 @ SV34 ) )
!= SV34 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1798,plain,
! [SV34: $i,SV105: $i,SV175: $i,SV195: $i] :
( ( ( ~ ( ssList @ SV195 )
| ( ( app @ ( app @ SV175 @ SV105 ) @ SV195 )
!= SV34 ) )
= $true )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1799,plain,
! [SV48: $i,SV167: $i,SV188: $i,SV156: $i,SV178: $i,SV198: $i] :
( ( ( ~ ( ssList @ SV198 ) )
= $true )
| ( ( ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SV198 ) )
!= SV48 )
| ( SV156 != SV167 ) )
= $true )
| ( ( ssList @ SV188 )
= $false )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1800,plain,
! [SV53: $i,SV168: $i,SV189: $i,SV157: $i,SV179: $i,SV199: $i] :
( ( ( ~ ( ssList @ SV199 ) )
= $true )
| ( ( ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SV199 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) )
= $true )
| ( ( ssList @ SV189 )
= $false )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1801,plain,
! [SV58: $i,SV169: $i,SV190: $i,SV158: $i,SV180: $i,SV200: $i] :
( ( ( ~ ( ssList @ SV200 ) )
= $true )
| ( ( ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SV200 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) )
= $true )
| ( ( ssList @ SV190 )
= $false )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1802,plain,
! [SV191: $i] :
( ( ( ssItem @ SV191 )
= $false )
| ( ( ~ ~ ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1803,plain,
! [SV184: $i] :
( ( ( ~ ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1804,plain,
! [SV185: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1805,plain,
! [SV183: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1806,plain,
! [SV74: $i,SV192: $i,SV170: $i,SV159: $i,SV181: $i] :
( ( ( ( app @ SV181 @ ( cons @ SV159 @ ( cons @ SV170 @ SV192 ) ) )
= SV74 )
= $false )
| ( ( SV159 = SV170 )
= $true )
| ( ( ssList @ SV192 )
= $false )
| ( ( ssList @ SV181 )
= $false )
| ( ( ssItem @ SV170 )
= $false )
| ( ( ssItem @ SV159 )
= $false )
| ( ( equalelemsP @ SV74 )
= $false )
| ( ( ssList @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1807,plain,
! [SV82: $i,SV171: $i,SV193: $i,SV160: $i,SV182: $i,SV201: $i] :
( ( ( ~ ( ssList @ SV201 ) )
= $true )
| ( ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) )
= $true )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1808,plain,
! [SV82: $i] :
( ( ( ~ ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1809,plain,
! [SV82: $i] :
( ( ( ~ ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) ) )
= $false )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1810,plain,
! [SV21: $i,SV99: $i] :
( ( ( ssList @ ( sK52_SY567 @ SV99 @ SV21 ) )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1811,plain,
! [SV99: $i,SV21: $i] :
( ( ( ( app @ ( sK29_SY408 @ SV21 @ SV99 ) @ ( cons @ SV99 @ ( sK52_SY567 @ SV99 @ SV21 ) ) )
= SV21 )
= $true )
| ( ( memberP @ SV21 @ SV99 )
= $false )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1812,plain,
! [SV21: $i,SV99: $i,SV174: $i,SV194: $i] :
( ( ( ~ ( ssList @ SV194 ) )
= $true )
| ( ( ( app @ SV174 @ ( cons @ SV99 @ SV194 ) )
!= SV21 )
= $true )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(1813,plain,
! [SV22: $i,SV165: $i,SV186: $i,SV154: $i,SV176: $i,SV196: $i] :
( ( ( ssList @ SV196 )
= $false )
| ( ( ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SV196 ) )
!= SV22 )
| ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) )
= $true )
| ( ( ssList @ SV186 )
= $false )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1814,plain,
! [SV29: $i,SV166: $i,SV187: $i,SV155: $i,SV177: $i,SV197: $i] :
( ( ( ssList @ SV197 )
= $false )
| ( ( ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SV197 ) )
!= SV29 )
| ( leq @ SV155 @ SV166 ) )
= $true )
| ( ( ssList @ SV187 )
= $false )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1815,plain,
! [SV34: $i,SV105: $i] :
( ( ( ssList @ ( sK53_SY573 @ SV105 @ SV34 ) )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1816,plain,
! [SV105: $i,SV34: $i] :
( ( ( ( app @ ( app @ ( sK32_SY415 @ SV34 @ SV105 ) @ SV105 ) @ ( sK53_SY573 @ SV105 @ SV34 ) )
= SV34 )
= $true )
| ( ( segmentP @ SV34 @ SV105 )
= $false )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1817,plain,
! [SV34: $i,SV105: $i,SV175: $i,SV195: $i] :
( ( ( ~ ( ssList @ SV195 ) )
= $true )
| ( ( ( app @ ( app @ SV175 @ SV105 ) @ SV195 )
!= SV34 )
= $true )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1818,plain,
! [SV48: $i,SV167: $i,SV188: $i,SV156: $i,SV178: $i,SV198: $i] :
( ( ( ssList @ SV198 )
= $false )
| ( ( ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SV198 ) )
!= SV48 )
| ( SV156 != SV167 ) )
= $true )
| ( ( ssList @ SV188 )
= $false )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1819,plain,
! [SV53: $i,SV168: $i,SV189: $i,SV157: $i,SV179: $i,SV199: $i] :
( ( ( ssList @ SV199 )
= $false )
| ( ( ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SV199 ) )
!= SV53 )
| ( lt @ SV157 @ SV168 ) )
= $true )
| ( ( ssList @ SV189 )
= $false )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1820,plain,
! [SV58: $i,SV169: $i,SV190: $i,SV158: $i,SV180: $i,SV200: $i] :
( ( ( ssList @ SV200 )
= $false )
| ( ( ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SV200 ) )
!= SV58 )
| ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) )
= $true )
| ( ( ssList @ SV190 )
= $false )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1821,plain,
! [SV191: $i] :
( ( ( ~ ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1822,plain,
! [SV184: $i] :
( ( ( ! [SY611: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY611 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SY611 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1823,plain,
! [SV185: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1824,plain,
! [SV183: $i] :
( ( ( ~ ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) ) )
= $false )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1825,plain,
! [SV82: $i,SV171: $i,SV193: $i,SV160: $i,SV182: $i,SV201: $i] :
( ( ( ssList @ SV201 )
= $false )
| ( ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
!= SV82 )
| ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) )
= $true )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1826,plain,
! [SV82: $i] :
( ( ( leq @ ( sK16_SY383 @ SV82 ) @ ( sK25_SY514 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1827,plain,
! [SV82: $i] :
( ( ( leq @ ( sK25_SY514 @ SV82 ) @ ( sK16_SY383 @ SV82 ) )
= $true )
| ( ( cyclefreeP @ SV82 )
= $true )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1828,plain,
! [SV21: $i,SV99: $i,SV174: $i,SV194: $i] :
( ( ( ssList @ SV194 )
= $false )
| ( ( ( app @ SV174 @ ( cons @ SV99 @ SV194 ) )
!= SV21 )
= $true )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1829,plain,
! [SV22: $i,SV196: $i,SV165: $i,SV186: $i,SV154: $i,SV176: $i] :
( ( ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SV196 ) )
!= SV22 )
= $true )
| ( ( ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) )
= $true )
| ( ( ssList @ SV196 )
= $false )
| ( ( ssList @ SV186 )
= $false )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1830,plain,
! [SV29: $i,SV197: $i,SV166: $i,SV187: $i,SV155: $i,SV177: $i] :
( ( ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SV197 ) )
!= SV29 )
= $true )
| ( ( leq @ SV155 @ SV166 )
= $true )
| ( ( ssList @ SV197 )
= $false )
| ( ( ssList @ SV187 )
= $false )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1831,plain,
! [SV34: $i,SV105: $i,SV175: $i,SV195: $i] :
( ( ( ssList @ SV195 )
= $false )
| ( ( ( app @ ( app @ SV175 @ SV105 ) @ SV195 )
!= SV34 )
= $true )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1832,plain,
! [SV48: $i,SV198: $i,SV167: $i,SV188: $i,SV156: $i,SV178: $i] :
( ( ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SV198 ) )
!= SV48 )
= $true )
| ( ( SV156 != SV167 )
= $true )
| ( ( ssList @ SV198 )
= $false )
| ( ( ssList @ SV188 )
= $false )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(1833,plain,
! [SV53: $i,SV199: $i,SV168: $i,SV189: $i,SV157: $i,SV179: $i] :
( ( ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SV199 ) )
!= SV53 )
= $true )
| ( ( lt @ SV157 @ SV168 )
= $true )
| ( ( ssList @ SV199 )
= $false )
| ( ( ssList @ SV189 )
= $false )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1834,plain,
! [SV58: $i,SV200: $i,SV169: $i,SV190: $i,SV158: $i,SV180: $i] :
( ( ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SV200 ) )
!= SV58 )
= $true )
| ( ( ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) )
= $true )
| ( ( ssList @ SV200 )
= $false )
| ( ( ssList @ SV190 )
= $false )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1835,plain,
! [SV191: $i] :
( ( ( ! [SY619: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY619 )
| ( ( app @ SY619 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1836,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV202 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(1837,plain,
! [SV185: $i] :
( ( ( ~ ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) ) )
= $false )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1838,plain,
! [SV183: $i] :
( ( ( ~ ( ssList @ SV183 )
| ~ ( neq @ SV183 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1839,plain,
! [SV82: $i,SV201: $i,SV171: $i,SV193: $i,SV160: $i,SV182: $i] :
( ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
!= SV82 )
= $true )
| ( ( ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) )
= $true )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1840,plain,
! [SV21: $i,SV194: $i,SV99: $i,SV174: $i] :
( ( ( ( app @ SV174 @ ( cons @ SV99 @ SV194 ) )
= SV21 )
= $false )
| ( ( ssList @ SV194 )
= $false )
| ( ( ssList @ SV174 )
= $false )
| ( ( memberP @ SV21 @ SV99 )
= $true )
| ( ( ssItem @ SV99 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1841,plain,
! [SV22: $i,SV196: $i,SV165: $i,SV186: $i,SV154: $i,SV176: $i] :
( ( ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SV196 ) )
= SV22 )
= $false )
| ( ( ( lt @ SV154 @ SV165 )
| ( lt @ SV165 @ SV154 ) )
= $true )
| ( ( ssList @ SV196 )
= $false )
| ( ( ssList @ SV186 )
= $false )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1842,plain,
! [SV29: $i,SV197: $i,SV166: $i,SV187: $i,SV155: $i,SV177: $i] :
( ( ( ( app @ ( app @ SV177 @ ( cons @ SV155 @ SV187 ) ) @ ( cons @ SV166 @ SV197 ) )
= SV29 )
= $false )
| ( ( leq @ SV155 @ SV166 )
= $true )
| ( ( ssList @ SV197 )
= $false )
| ( ( ssList @ SV187 )
= $false )
| ( ( ssList @ SV177 )
= $false )
| ( ( ssItem @ SV166 )
= $false )
| ( ( ssItem @ SV155 )
= $false )
| ( ( totalorderedP @ SV29 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1843,plain,
! [SV34: $i,SV195: $i,SV105: $i,SV175: $i] :
( ( ( ( app @ ( app @ SV175 @ SV105 ) @ SV195 )
= SV34 )
= $false )
| ( ( ssList @ SV195 )
= $false )
| ( ( ssList @ SV175 )
= $false )
| ( ( segmentP @ SV34 @ SV105 )
= $true )
| ( ( ssList @ SV105 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1844,plain,
! [SV48: $i,SV198: $i,SV167: $i,SV188: $i,SV156: $i,SV178: $i] :
( ( ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SV198 ) )
= SV48 )
= $false )
| ( ( SV156 != SV167 )
= $true )
| ( ( ssList @ SV198 )
= $false )
| ( ( ssList @ SV188 )
= $false )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1845,plain,
! [SV53: $i,SV199: $i,SV168: $i,SV189: $i,SV157: $i,SV179: $i] :
( ( ( ( app @ ( app @ SV179 @ ( cons @ SV157 @ SV189 ) ) @ ( cons @ SV168 @ SV199 ) )
= SV53 )
= $false )
| ( ( lt @ SV157 @ SV168 )
= $true )
| ( ( ssList @ SV199 )
= $false )
| ( ( ssList @ SV189 )
= $false )
| ( ( ssList @ SV179 )
= $false )
| ( ( ssItem @ SV168 )
= $false )
| ( ( ssItem @ SV157 )
= $false )
| ( ( strictorderedP @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1846,plain,
! [SV58: $i,SV200: $i,SV169: $i,SV190: $i,SV158: $i,SV180: $i] :
( ( ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SV200 ) )
= SV58 )
= $false )
| ( ( ( leq @ SV158 @ SV169 )
| ( leq @ SV169 @ SV158 ) )
= $true )
| ( ( ssList @ SV200 )
= $false )
| ( ( ssList @ SV190 )
= $false )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1847,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV203 )
| ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(1848,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV202 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) ) )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1849,plain,
! [SV185: $i] :
( ( ( ~ ( ssList @ SV185 )
| ~ ( neq @ SV185 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1850,plain,
! [SV183: $i] :
( ( ( ~ ( ssList @ SV183 ) )
= $true )
| ( ( ~ ( neq @ SV183 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1851,plain,
! [SV82: $i,SV201: $i,SV171: $i,SV193: $i,SV160: $i,SV182: $i] :
( ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
= SV82 )
= $false )
| ( ( ~ ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) )
= $true )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1852,plain,
! [SV22: $i,SV196: $i,SV186: $i,SV176: $i,SV165: $i,SV154: $i] :
( ( ( lt @ SV154 @ SV165 )
= $true )
| ( ( lt @ SV165 @ SV154 )
= $true )
| ( ( ( app @ ( app @ SV176 @ ( cons @ SV154 @ SV186 ) ) @ ( cons @ SV165 @ SV196 ) )
= SV22 )
= $false )
| ( ( ssList @ SV196 )
= $false )
| ( ( ssList @ SV186 )
= $false )
| ( ( ssList @ SV176 )
= $false )
| ( ( ssItem @ SV165 )
= $false )
| ( ( ssItem @ SV154 )
= $false )
| ( ( strictorderP @ SV22 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1853,plain,
! [SV48: $i,SV198: $i,SV188: $i,SV178: $i,SV167: $i,SV156: $i] :
( ( ( SV156 = SV167 )
= $false )
| ( ( ( app @ ( app @ SV178 @ ( cons @ SV156 @ SV188 ) ) @ ( cons @ SV167 @ SV198 ) )
= SV48 )
= $false )
| ( ( ssList @ SV198 )
= $false )
| ( ( ssList @ SV188 )
= $false )
| ( ( ssList @ SV178 )
= $false )
| ( ( ssItem @ SV167 )
= $false )
| ( ( ssItem @ SV156 )
= $false )
| ( ( duplicatefreeP @ SV48 )
= $false )
| ( ( ssList @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1854,plain,
! [SV58: $i,SV200: $i,SV190: $i,SV180: $i,SV169: $i,SV158: $i] :
( ( ( leq @ SV158 @ SV169 )
= $true )
| ( ( leq @ SV169 @ SV158 )
= $true )
| ( ( ( app @ ( app @ SV180 @ ( cons @ SV158 @ SV190 ) ) @ ( cons @ SV169 @ SV200 ) )
= SV58 )
= $false )
| ( ( ssList @ SV200 )
= $false )
| ( ( ssList @ SV190 )
= $false )
| ( ( ssList @ SV180 )
= $false )
| ( ( ssItem @ SV169 )
= $false )
| ( ( ssItem @ SV158 )
= $false )
| ( ( totalorderP @ SV58 )
= $false )
| ( ( ssList @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1855,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV203 )
| ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) ) )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1856,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV202 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 ) )
| ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1857,plain,
! [SV185: $i] :
( ( ( ~ ( ssList @ SV185 ) )
= $true )
| ( ( ~ ( neq @ SV185 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1858,plain,
! [SV183: $i] :
( ( ( ssList @ SV183 )
= $false )
| ( ( ~ ( neq @ SV183 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1859,plain,
! [SV82: $i,SV201: $i,SV193: $i,SV182: $i,SV171: $i,SV160: $i] :
( ( ( ~ ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) ) )
= $false )
| ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
= SV82 )
= $false )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1860,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV203 )
| ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
| ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1861,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV202 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 ) ) )
= $true )
| ( ( ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1862,plain,
! [SV185: $i] :
( ( ( ssList @ SV185 )
= $false )
| ( ( ~ ( neq @ SV185 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1863,plain,
! [SV183: $i] :
( ( ( neq @ SV183 @ nil )
= $false )
| ( ( ssList @ SV183 )
= $false )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV183 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1864,plain,
! [SV82: $i,SV201: $i,SV193: $i,SV182: $i,SV171: $i,SV160: $i] :
( ( ( ~ ( leq @ SV160 @ SV171 )
| ~ ( leq @ SV171 @ SV160 ) )
= $true )
| ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
= SV82 )
= $false )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1865,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV203 )
| ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) ) )
= $true )
| ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1866,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ( ~ ( ssList @ SV202 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 ) ) )
= $false )
| ( ( ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1867,plain,
! [SV185: $i] :
( ( ( neq @ SV185 @ nil )
= $false )
| ( ( ssList @ SV185 )
= $false )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV185 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1868,plain,
! [SV183: $i] :
( ( ( segmentP @ sK2_SX0 @ SV183 )
= $false )
| ( ( ssList @ SV183 )
= $false )
| ( ( neq @ SV183 @ nil )
= $false )
| ( ( ~ ( segmentP @ sK1_U @ SV183 ) )
= $true )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1869,plain,
! [SV82: $i,SV201: $i,SV193: $i,SV182: $i,SV171: $i,SV160: $i] :
( ( ( ~ ( leq @ SV160 @ SV171 ) )
= $true )
| ( ( ~ ( leq @ SV171 @ SV160 ) )
= $true )
| ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
= SV82 )
= $false )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1870,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ( ~ ( ssList @ SV203 )
| ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) ) )
= $false )
| ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1871,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ( ssList @ SV202 )
| ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 ) )
= $true )
| ( ( ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1872,plain,
! [SV185: $i] :
( ( ( segmentP @ sK2_SX0 @ SV185 )
= $false )
| ( ( ssList @ SV185 )
= $false )
| ( ( neq @ SV185 @ nil )
= $false )
| ( ( ~ ( segmentP @ sK1_U @ SV185 ) )
= $true )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1873,plain,
! [SV183: $i] :
( ( ( segmentP @ sK1_U @ SV183 )
= $false )
| ( ( neq @ SV183 @ nil )
= $false )
| ( ( ssList @ SV183 )
= $false )
| ( ( segmentP @ sK2_SX0 @ SV183 )
= $false )
| ( ( nil = sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1874,plain,
! [SV82: $i,SV201: $i,SV193: $i,SV182: $i,SV171: $i,SV160: $i] :
( ( ( leq @ SV160 @ SV171 )
= $false )
| ( ( ~ ( leq @ SV171 @ SV160 ) )
= $true )
| ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
= SV82 )
= $false )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1875,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ( ssList @ SV203 )
| ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 ) )
= $true )
| ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1870]) ).
thf(1876,plain,
! [SV184: $i,SV202: $i] :
( ( ( ~ ( ssList @ SV202 ) )
= $true )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 )
= $true )
| ( ( ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(1877,plain,
! [SV185: $i] :
( ( ( segmentP @ sK1_U @ SV185 )
= $false )
| ( ( neq @ SV185 @ nil )
= $false )
| ( ( ssList @ SV185 )
= $false )
| ( ( segmentP @ sK2_SX0 @ SV185 )
= $false )
| ( ( nil = sK2_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1878,plain,
! [SV82: $i,SV201: $i,SV193: $i,SV182: $i,SV160: $i,SV171: $i] :
( ( ( leq @ SV171 @ SV160 )
= $false )
| ( ( leq @ SV160 @ SV171 )
= $false )
| ( ( ( app @ ( app @ SV182 @ ( cons @ SV160 @ SV193 ) ) @ ( cons @ SV171 @ SV201 ) )
= SV82 )
= $false )
| ( ( ssList @ SV201 )
= $false )
| ( ( ssList @ SV193 )
= $false )
| ( ( ssList @ SV182 )
= $false )
| ( ( ssItem @ SV171 )
= $false )
| ( ( ssItem @ SV160 )
= $false )
| ( ( cyclefreeP @ SV82 )
= $false )
| ( ( ssList @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1879,plain,
! [SV191: $i,SV203: $i] :
( ( ( ~ ( ssList @ SV203 ) )
= $true )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 )
= $true )
| ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1880,plain,
! [SV184: $i,SV202: $i] :
( ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
!= sK36_SY533 )
= $true )
| ( ( ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1881,plain,
! [SV191: $i,SV203: $i] :
( ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
!= sK23_SY450 )
= $true )
| ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1882,plain,
! [SV202: $i,SV184: $i] :
( ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ~ ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1883,plain,
! [SV191: $i,SV203: $i] :
( ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1884,plain,
! [SV202: $i,SV184: $i] :
( ( ( ~ ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1885,plain,
! [SV203: $i,SV191: $i] :
( ( ( ~ ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1886,plain,
! [SV202: $i,SV184: $i] :
( ( ( ! [SY612: $i] :
~ ~ ( ~ ( ssItem @ SY612 )
| ~ ~ ! [SY613: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY613 )
| ( ( app @ SY613 @ ( cons @ SY612 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SY612 @ SV184 ) ) ) )
= $true )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(1887,plain,
! [SV203: $i,SV191: $i] :
( ( ( ! [SY620: $i] :
~ ~ ( ~ ( ssItem @ SY620 )
| ~ ~ ! [SY621: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY621 )
| ( ( app @ ( cons @ SY620 @ nil ) @ SY621 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SY620 ) ) ) )
= $true )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(1888,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ SV204 )
| ~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) ) )
= $true )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(1889,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ~ ~ ( ~ ( ssItem @ SV205 )
| ~ ~ ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) ) )
= $true )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1890,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ~ ( ~ ( ssItem @ SV204 )
| ~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) ) )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1891,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ~ ( ~ ( ssItem @ SV205 )
| ~ ~ ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) ) )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1892,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ~ ( ssItem @ SV204 )
| ~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $true )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1893,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ~ ( ssItem @ SV205 )
| ~ ~ ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $true )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1894,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ~ ( ssItem @ SV204 ) )
= $true )
| ( ( ~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $true )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(1895,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ~ ( ssItem @ SV205 ) )
= $true )
| ( ( ~ ~ ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $true )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1896,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ssItem @ SV204 )
= $false )
| ( ( ~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $true )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1897,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ssItem @ SV205 )
= $false )
| ( ( ~ ~ ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $true )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1898,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $false )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1899,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ~ ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $false )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1900,plain,
! [SV202: $i,SV184: $i,SV204: $i] :
( ( ( ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY627 )
| ( ( app @ SY627 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1901,plain,
! [SV203: $i,SV191: $i,SV205: $i] :
( ( ( ! [SY628: $i] :
~ ~ ( ~ ~ ( ~ ( ssList @ SY628 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SY628 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1902,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV206 )
| ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(1903,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV207 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(1904,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV206 )
| ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) ) )
= $false )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1905,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV207 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) ) )
= $false )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1906,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV206 )
| ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
| ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1907,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV207 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 ) )
| ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(1908,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV206 )
| ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) ) )
= $true )
| ( ( ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(1909,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV207 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 ) ) )
= $true )
| ( ( ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(1910,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ( ~ ( ssList @ SV206 )
| ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) ) )
= $false )
| ( ( ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1911,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ( ~ ( ssList @ SV207 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 ) ) )
= $false )
| ( ( ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1912,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ( ssList @ SV206 )
| ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 ) )
= $true )
| ( ( ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1913,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ( ssList @ SV207 )
| ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 ) )
= $true )
| ( ( ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1914,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ~ ( ssList @ SV206 ) )
= $true )
| ( ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 )
= $true )
| ( ( ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1915,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ~ ( ssList @ SV207 ) )
= $true )
| ( ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 )
= $true )
| ( ( ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(1916,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ssList @ SV206 )
= $false )
| ( ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
!= sK4_SY389 )
= $true )
| ( ( ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1917,plain,
! [SV203: $i,SV191: $i,SV205: $i,SV207: $i] :
( ( ( ssList @ SV207 )
= $false )
| ( ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
!= sK4_SY389 )
= $true )
| ( ( ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1918,plain,
! [SV202: $i,SV184: $i,SV204: $i,SV206: $i] :
( ( ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
= sK4_SY389 )
= $false )
| ( ( ssList @ SV206 )
= $false )
| ( ( ~ ( lt @ SV204 @ SV184 ) )
= $true )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1919,plain,
! [SV203: $i,SV191: $i,SV207: $i,SV205: $i] :
( ( ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
= sK4_SY389 )
= $false )
| ( ( ssList @ SV207 )
= $false )
| ( ( ~ ( lt @ SV191 @ SV205 ) )
= $true )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1920,plain,
! [SV202: $i,SV206: $i,SV184: $i,SV204: $i] :
( ( ( lt @ SV204 @ SV184 )
= $false )
| ( ( ssList @ SV206 )
= $false )
| ( ( ( app @ SV206 @ ( cons @ SV204 @ nil ) )
= sK4_SY389 )
= $false )
| ( ( ssItem @ SV204 )
= $false )
| ( ( ssList @ SV202 )
= $false )
| ( ( ( app @ ( cons @ SV184 @ nil ) @ SV202 )
= sK36_SY533 )
= $false )
| ( ( ssItem @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1921,plain,
! [SV203: $i,SV207: $i,SV205: $i,SV191: $i] :
( ( ( lt @ SV191 @ SV205 )
= $false )
| ( ( ssList @ SV207 )
= $false )
| ( ( ( app @ ( cons @ SV205 @ nil ) @ SV207 )
= sK4_SY389 )
= $false )
| ( ( ssItem @ SV205 )
= $false )
| ( ( ssList @ SV203 )
= $false )
| ( ( ( app @ SV203 @ ( cons @ SV191 @ nil ) )
= sK23_SY450 )
= $false )
| ( ( ssItem @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1922,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[214,1921,1920,1878,1877,1873,1854,1853,1852,1845,1843,1842,1840,1827,1826,1816,1815,1811,1810,1806,1794,1786,1785,1770,1768,1763,1762,1757,1756,1755,1753,1751,1750,1746,1743,1742,1741,1734,1730,1720,1718,1716,1712,1708,1706,1701,1696,1692,1689,1681,1680,1659,1658,1656,1653,1651,1649,1635,1632,1629,1627,1626,1623,1621,1617,1613,1611,1610,1608,1607,1591,1584,1583,1553,1551,1549,1548,1546,1543,1539,1538,1536,1531,1530,1528,1523,1521,1519,1517,1516,1515,1511,1509,1507,1505,1504,1503,1501,1497,1494,1490,1487,1472,1471,1466,1449,1431,1430,1420,1417,1412,1410,1398,1395,1391,1387,1377,1370,1353,1352,1343,1341,1339,1337,1336,1334,1325,1324,1314,1313,1312,1289,1280,1278,1277,1274,1270,1266,1264,1250,1242,1240,1237,1230,1226,1224,1223,1217,1210,1194,1193,1157,1104,1097,1088,1080,1068,1067,1040,1007,995,994,977,976,961,960,933,909,877,875,864,857,851,828,825,807,806,805,711,691,646,639,638,629,622,610,603,598,594,593,588,586,581,579,570,565,563,562,382,293,271,269,266,263,261,259,257]) ).
thf(1923,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC067+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:59:21 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.84/2.95 .
% 15.84/2.95
% 15.84/2.95 No.of.Axioms: 95
% 15.84/2.95
% 15.84/2.95 Length.of.Defs: 0
% 15.84/2.95
% 15.84/2.95 Contains.Choice.Funs: false
% 15.84/2.95 ..............................................................................
% 15.84/2.95
% 15.84/2.95 ********************************
% 15.84/2.95 * All subproblems solved! *
% 15.84/2.95 ********************************
% 15.84/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:96,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:1922,loop_count:0,foatp_calls:1,translation:fof_full)
% 15.84/2.95
% 15.84/2.95 %**** Beginning of derivation protocol ****
% 15.84/2.95 % SZS output start CNFRefutation
% See solution above
% 15.84/2.96
% 15.84/2.96 %**** End of derivation protocol ****
% 15.84/2.96 %**** no. of clauses in derivation: 1923 ****
% 15.84/2.96 %**** clause counter: 1922 ****
% 15.84/2.96
% 15.84/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:96,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:1922,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------