%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 10:51:53 AM UTC 2026
% Result : Theorem 26.75s 5.60s
% Output : CNFRefutation 26.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 44
% Syntax : Number of formulae : 646 ( 219 unt; 0 typ; 0 def)
% Number of atoms : 6027 (2198 equ; 0 cnn)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 8966 (2313 ~;1975 |; 57 &;4322 @)
% ( 27 <=>; 272 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 10 con; 0-2 aty)
% Number of variables : 1425 ( 0 ^;1403 !; 22 ?;1425 :)
% 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_SY135,type,
sK10_SY135: $i > $i > $i ).
thf(tp_sK11_SY146,type,
sK11_SY146: $i > $i > $i ).
thf(tp_sK12_SY162,type,
sK12_SY162: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY125,type,
sK3_SY125: $i ).
thf(tp_sK4_SY139,type,
sK4_SY139: $i ).
thf(tp_sK5_SY155,type,
sK5_SY155: $i ).
thf(tp_sK6_SY117,type,
sK6_SY117: $i > $i ).
thf(tp_sK7_SY159,type,
sK7_SY159: $i ).
thf(tp_sK8_SY161,type,
sK8_SY161: $i ).
thf(tp_sK9_SY131,type,
sK9_SY131: $i > $i > $i ).
thf(tp_segmentP,type,
segmentP: $i > $i > $o ).
thf(tp_singletonP,type,
singletonP: $i > $o ).
thf(tp_ssItem,type,
ssItem: $i > $o ).
thf(tp_ssList,type,
ssList: $i > $o ).
thf(tp_strictorderP,type,
strictorderP: $i > $o ).
thf(tp_strictorderedP,type,
strictorderedP: $i > $o ).
thf(tp_tl,type,
tl: $i > $i ).
thf(tp_totalorderP,type,
totalorderP: $i > $o ).
thf(tp_totalorderedP,type,
totalorderedP: $i > $o ).
thf(10,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
thf(11,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
thf(12,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(13,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
thf(14,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
thf(16,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
thf(17,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ W @ V )
= ( app @ U @ V ) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
thf(20,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
thf(22,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(24,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(27,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(30,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(32,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(34,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(36,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(38,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(39,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(40,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( segmentP @ U @ V )
=> ( segmentP @ ( app @ ( app @ W @ U ) @ X ) @ V ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
thf(41,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(42,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(43,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ W ) )
=> ( segmentP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(44,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(45,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(46,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( rearsegP @ U @ V )
=> ( rearsegP @ ( app @ W @ U ) @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(47,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(48,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
thf(49,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ W ) )
=> ( rearsegP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
thf(50,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(51,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(53,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( frontsegP @ U @ V )
=> ( frontsegP @ ( app @ U @ W ) @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(54,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(55,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(56,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ W ) )
=> ( frontsegP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(57,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(68,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(70,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(72,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(79,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(81,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(89,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( segmentP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ ( app @ W @ V ) @ X )
= U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(90,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( rearsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ W @ V )
= U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(91,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( frontsegP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ( ( app @ V @ W )
= U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(95,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(96,conjecture,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ~ ( ssList @ X )
| ( V != X )
| ( U != W )
| ~ ( neq @ V @ nil )
| ? [Y: $i] :
( ( ssList @ Y )
& ( neq @ Y @ nil )
& ( segmentP @ V @ Y )
& ( segmentP @ U @ Y ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= W )
| ( ( app @ Z @ X2 )
!= X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(97,negated_conjecture,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ~ ( ssList @ X )
| ( V != X )
| ( U != W )
| ~ ( neq @ V @ nil )
| ? [Y: $i] :
( ( ssList @ Y )
& ( neq @ Y @ nil )
& ( segmentP @ V @ Y )
& ( segmentP @ U @ Y ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= W )
| ( ( app @ Z @ X2 )
!= X ) ) ) ) ) ) ) ) )
= $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 )
| ~ ( neq @ V @ nil )
| ? [Y: $i] :
( ( ssList @ Y )
& ( neq @ Y @ nil )
& ( segmentP @ V @ Y )
& ( segmentP @ U @ Y ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= W )
| ( ( app @ Z @ X2 )
!= X ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(100,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(101,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(102,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(103,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(104,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(105,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(106,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(107,plain,
( ( equalelemsP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(108,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(109,plain,
( ( strictorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(110,plain,
( ( totalorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(111,plain,
( ( strictorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(112,plain,
( ( totalorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(113,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(114,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(115,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(116,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(117,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(118,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(119,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(120,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(121,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(122,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(123,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(124,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(125,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(126,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(127,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(128,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(129,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(130,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(131,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(132,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(134,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(135,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(136,plain,
( ( ssList @ nil )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(137,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(138,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(139,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(140,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(141,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(142,plain,
( ( ( ssList @ sK1_U )
=> ! [SY78: $i] :
( ( ssList @ SY78 )
=> ! [SY79: $i] :
( ( ssList @ SY79 )
=> ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( SY78 != SY80 )
| ( sK1_U != SY79 )
| ~ ( neq @ SY78 @ nil )
| ? [SY81: $i] :
( ( ssList @ SY81 )
& ( neq @ SY81 @ nil )
& ( segmentP @ SY78 @ SY81 )
& ( segmentP @ sK1_U @ SY81 ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= SY79 )
| ( ( app @ Z @ X2 )
!= SY80 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(143,plain,
( ( ssList @ sK1_U )
= $true ),
inference(standard_cnf,[status(thm)],[142]) ).
thf(144,plain,
( ( ! [SY78: $i] :
( ( ssList @ SY78 )
=> ! [SY79: $i] :
( ( ssList @ SY79 )
=> ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( SY78 != SY80 )
| ( sK1_U != SY79 )
| ~ ( neq @ SY78 @ nil )
| ? [SY81: $i] :
( ( ssList @ SY81 )
& ( neq @ SY81 @ nil )
& ( segmentP @ SY78 @ SY81 )
& ( segmentP @ sK1_U @ SY81 ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= SY79 )
| ( ( app @ Z @ X2 )
!= SY80 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[142]) ).
thf(145,plain,
( ( ~ ! [SY78: $i] :
( ( ssList @ SY78 )
=> ! [SY79: $i] :
( ( ssList @ SY79 )
=> ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( SY78 != SY80 )
| ( sK1_U != SY79 )
| ~ ( neq @ SY78 @ nil )
| ? [SY81: $i] :
( ( ssList @ SY81 )
& ( neq @ SY81 @ nil )
& ( segmentP @ SY78 @ SY81 )
& ( segmentP @ sK1_U @ SY81 ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= SY79 )
| ( ( app @ Z @ X2 )
!= SY80 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[144]) ).
thf(146,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(147,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)],[140]) ).
thf(148,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)],[139]) ).
thf(149,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)],[138]) ).
thf(150,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(151,plain,
( ( ssList @ nil )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(152,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(153,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(154,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(155,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(156,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)],[131]) ).
thf(157,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(158,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(159,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)],[128]) ).
thf(160,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(161,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(162,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)],[125]) ).
thf(163,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(164,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(165,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)],[122]) ).
thf(166,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(167,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(168,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)],[119]) ).
thf(169,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(170,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(171,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)],[116]) ).
thf(172,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(173,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(174,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(175,plain,
( ( totalorderP @ nil )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(176,plain,
( ( strictorderP @ nil )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(177,plain,
( ( totalorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(178,plain,
( ( strictorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(179,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(180,plain,
( ( equalelemsP @ nil )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(181,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(182,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)],[105]) ).
thf(183,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)],[104]) ).
thf(184,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(185,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(186,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(187,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( hd @ ( app @ U @ V ) )
= ( hd @ U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(188,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil != U )
=> ( ( tl @ ( app @ U @ V ) )
= ( app @ ( tl @ U ) @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(189,plain,
( ( ssList @ sK1_U )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(190,plain,
( ( ~ ! [SY78: $i] :
( ( ssList @ SY78 )
=> ! [SY79: $i] :
( ( ssList @ SY79 )
=> ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( SY78 != SY80 )
| ( sK1_U != SY79 )
| ~ ( neq @ SY78 @ nil )
| ? [SY81: $i] :
( ( ssList @ SY81 )
& ( neq @ SY81 @ nil )
& ( segmentP @ SY78 @ SY81 )
& ( segmentP @ sK1_U @ SY81 ) )
| ! [Z: $i] :
( ( ssList @ Z )
=> ! [X1: $i] :
( ( ssList @ X1 )
=> ! [X2: $i] :
( ~ ( ssList @ X2 )
| ( ( app @ ( app @ Z @ X1 ) @ X2 )
!= SY79 )
| ( ( app @ Z @ X2 )
!= SY80 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(191,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)],[149]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( rearsegP @ SX0 @ SX1 )
| ~ ( rearsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(193,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( segmentP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(194,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)],[147]) ).
thf(195,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(196,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(197,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ nil @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(198,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)],[165]) ).
thf(199,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)],[146]) ).
thf(200,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)],[156]) ).
thf(201,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( rearsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(202,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( neq @ SX0 @ nil )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX3 @ nil ) )
| ~ ( segmentP @ SX0 @ SX3 ) )
| ~ ( segmentP @ sK1_U @ SX3 ) )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ SX4 ) @ SX5 )
!= SX1 )
| ( ( app @ SX3 @ SX5 )
!= SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(203,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(204,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)],[185]) ).
thf(205,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(206,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ( ssList @ ( app @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(207,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)],[162]) ).
thf(208,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)],[184]) ).
thf(209,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)],[148]) ).
thf(210,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ( segmentP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(211,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)],[171]) ).
thf(212,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)],[183]) ).
thf(213,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ( frontsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(214,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( frontsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(215,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ( nil != SX0 ) )
| ( ( hd @ ( app @ SX0 @ SX1 ) )
= ( hd @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(216,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)],[150]) ).
thf(217,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(218,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ SX0 @ nil )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(219,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssList @ SX1 )
| ( ( tl @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(220,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)],[159]) ).
thf(221,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(222,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ssList @ ( tl @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(223,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)],[168]) ).
thf(224,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)],[188]) ).
thf(225,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)],[182]) ).
thf(226,plain,
( ( singletonP @ nil )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(227,plain,
! [SV1: $i] :
( ( ~ ( ssList @ SV1 )
| ! [SY85: $i] :
( ~ ( ssList @ SY85 )
| ~ ( ~ ( ~ ( segmentP @ SV1 @ SY85 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( ssList @ SY86 )
| ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( ssList @ SY87 )
| ( ( app @ ( app @ SY86 @ SY85 ) @ SY87 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( ssList @ SY88 )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( ssList @ SY89 )
| ( ( app @ ( app @ SY88 @ SY85 ) @ SY89 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(228,plain,
! [SV2: $i] :
( ( ~ ( ssList @ SV2 )
| ! [SY90: $i] :
( ~ ( ssList @ SY90 )
| ~ ~ ( ~ ( rearsegP @ SV2 @ SY90 )
| ~ ( rearsegP @ SY90 @ SV2 ) )
| ( SV2 = SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(229,plain,
! [SV3: $i] :
( ( ~ ( ssList @ SV3 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SV3 )
| ( nil = SV3 ) )
| ~ ( ( nil != SV3 )
| ( segmentP @ nil @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(230,plain,
! [SV4: $i] :
( ( ~ ( ssList @ SV4 )
| ! [SY91: $i] :
( ~ ( ssList @ SY91 )
| ~ ( ~ ( ~ ( frontsegP @ SV4 @ SY91 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( ssList @ SY92 )
| ( ( app @ SY91 @ SY92 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( ssList @ SY93 )
| ( ( app @ SY91 @ SY93 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(231,plain,
! [SV5: $i] :
( ( ~ ( ssList @ SV5 )
| ( segmentP @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(232,plain,
! [SV6: $i] :
( ( ~ ( ssList @ SV6 )
| ( frontsegP @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(233,plain,
! [SV7: $i] :
( ( ~ ( ssList @ SV7 )
| ( ( app @ nil @ SV7 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(234,plain,
! [SV8: $i] :
( ( ~ ( ssList @ SV8 )
| ! [SY94: $i] :
( ~ ( ssList @ SY94 )
| ! [SY95: $i] :
( ~ ( ssList @ SY95 )
| ~ ( rearsegP @ SV8 @ SY94 )
| ( rearsegP @ ( app @ SY95 @ SV8 ) @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(235,plain,
! [SV9: $i] :
( ( ~ ( ssItem @ SV9 )
| ! [SY96: $i] :
( ~ ( ssItem @ SY96 )
| ~ ( ~ ( ~ ( neq @ SV9 @ SY96 )
| ( SV9 != SY96 ) )
| ~ ( ~ ( ( SV9 != SY96 ) )
| ( neq @ SV9 @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(236,plain,
! [SV10: $i] :
( ( ~ ( ssList @ SV10 )
| ! [SY97: $i] :
( ~ ( ssList @ SY97 )
| ! [SY98: $i] :
( ~ ( ssList @ SY98 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SY97 )
| ~ ( frontsegP @ SY97 @ SY98 ) )
| ( frontsegP @ SV10 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(237,plain,
! [SV11: $i] :
( ( ~ ( ssList @ SV11 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( rearsegP @ nil @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(238,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( neq @ SX0 @ nil )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SX3 )
| ~ ( neq @ SX3 @ nil ) )
| ~ ( segmentP @ SX0 @ SX3 ) )
| ~ ( segmentP @ sK1_U @ SX3 ) )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ SX4 ) @ SX5 )
!= SX1 )
| ( ( app @ SX3 @ SX5 )
!= SX2 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(239,plain,
! [SV12: $i] :
( ( ~ ( ssList @ SV12 )
| ( rearsegP @ SV12 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(240,plain,
! [SV13: $i] :
( ( ~ ( ssList @ SV13 )
| ! [SY99: $i] :
( ~ ( ssList @ SY99 )
| ~ ( ~ ( ( nil
!= ( app @ SV13 @ SY99 ) )
| ~ ( ( nil != SY99 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SY99 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SY99 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(241,plain,
! [SV14: $i] :
( ( ~ ( ssList @ SV14 )
| ( rearsegP @ SV14 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(242,plain,
! [SV15: $i] :
( ( ~ ( ssList @ SV15 )
| ! [SY100: $i] :
( ~ ( ssList @ SY100 )
| ( ssList @ ( app @ SV15 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(243,plain,
! [SV16: $i] :
( ( ~ ( ssList @ SV16 )
| ! [SY101: $i] :
( ~ ( ssList @ SY101 )
| ! [SY102: $i] :
( ~ ( ssList @ SY102 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SY101 )
| ~ ( rearsegP @ SY101 @ SY102 ) )
| ( rearsegP @ SV16 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(244,plain,
! [SV17: $i] :
( ( ~ ( ssList @ SV17 )
| ! [SY103: $i] :
( ~ ( ssList @ SY103 )
| ! [SY104: $i] :
( ~ ( ssList @ SY104 )
| ( ( app @ ( app @ SV17 @ SY103 ) @ SY104 )
= ( app @ SV17 @ ( app @ SY103 @ SY104 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(245,plain,
! [SV18: $i] :
( ( ~ ( ssList @ SV18 )
| ! [SY105: $i] :
( ~ ( ssList @ SY105 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SY105 )
| ~ ! [SY106: $i] :
~ ~ ( ~ ( ssList @ SY106 )
| ( ( app @ SY106 @ SY105 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( ssList @ SY107 )
| ( ( app @ SY107 @ SY105 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SY105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(246,plain,
! [SV19: $i] :
( ( ~ ( ssList @ SV19 )
| ! [SY108: $i] :
( ~ ( ssList @ SY108 )
| ~ ~ ( ~ ( segmentP @ SV19 @ SY108 )
| ~ ( segmentP @ SY108 @ SV19 ) )
| ( SV19 = SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(247,plain,
! [SV20: $i] :
( ( ~ ( ssList @ SV20 )
| ! [SY109: $i] :
( ~ ( ssList @ SY109 )
| ! [SY110: $i] :
( ~ ( ssList @ SY110 )
| ! [SY111: $i] :
( ~ ( ssList @ SY111 )
| ~ ( segmentP @ SV20 @ SY109 )
| ( segmentP @ ( app @ ( app @ SY110 @ SV20 ) @ SY111 ) @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(248,plain,
! [SV21: $i] :
( ( ~ ( ssList @ SV21 )
| ! [SY112: $i] :
( ~ ( ssList @ SY112 )
| ! [SY113: $i] :
( ~ ( ssList @ SY113 )
| ( ( app @ SY112 @ SY113 )
!= ( app @ SY112 @ SV21 ) )
| ( SY113 = SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(249,plain,
! [SV22: $i] :
( ( ~ ( ssList @ SV22 )
| ! [SY114: $i] :
( ~ ( ssList @ SY114 )
| ~ ~ ( ~ ( frontsegP @ SV22 @ SY114 )
| ~ ( frontsegP @ SY114 @ SV22 ) )
| ( SV22 = SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(250,plain,
! [SV23: $i] :
( ( ~ ( ssList @ SV23 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(251,plain,
! [SV24: $i] :
( ( ~ ( ssList @ SV24 )
| ! [SY115: $i] :
( ~ ( ssList @ SY115 )
| ~ ( ( nil != SV24 ) )
| ( ( hd @ ( app @ SV24 @ SY115 ) )
= ( hd @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(252,plain,
! [SV25: $i] :
( ( ~ ( ssList @ SV25 )
| ! [SY116: $i] :
( ~ ( ssList @ SY116 )
| ~ ( ~ ( ~ ( neq @ SV25 @ SY116 )
| ( SV25 != SY116 ) )
| ~ ( ~ ( ( SV25 != SY116 ) )
| ( neq @ SV25 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(253,plain,
! [SV26: $i] :
( ( ~ ( ssList @ SV26 )
| ( segmentP @ SV26 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(254,plain,
! [SV27: $i] :
( ( ~ ( ssList @ SV27 )
| ( ( app @ SV27 @ nil )
= SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(255,plain,
! [SV28: $i] :
( ( ~ ( ssList @ SV28 )
| ~ ( ( nil != SV28 ) )
| ~ ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(256,plain,
! [SV29: $i] :
( ( ~ ( ssList @ SV29 )
| ! [SY118: $i] :
( ~ ( ssList @ SY118 )
| ! [SY119: $i] :
( ~ ( ssList @ SY119 )
| ~ ( frontsegP @ SV29 @ SY118 )
| ( frontsegP @ ( app @ SV29 @ SY119 ) @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(257,plain,
! [SV30: $i] :
( ( ~ ( ssList @ SV30 )
| ( frontsegP @ SV30 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(258,plain,
! [SV31: $i] :
( ( ~ ( ssList @ SV31 )
| ~ ( ( nil != SV31 ) )
| ( ssList @ ( tl @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(259,plain,
! [SV32: $i] :
( ( ~ ( ssList @ SV32 )
| ! [SY120: $i] :
( ~ ( ssList @ SY120 )
| ! [SY121: $i] :
( ~ ( ssList @ SY121 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SY120 )
| ~ ( segmentP @ SY120 @ SY121 ) )
| ( segmentP @ SV32 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(260,plain,
! [SV33: $i] :
( ( ~ ( ssList @ SV33 )
| ! [SY122: $i] :
( ~ ( ssList @ SY122 )
| ~ ( ( nil != SV33 ) )
| ( ( tl @ ( app @ SV33 @ SY122 ) )
= ( app @ ( tl @ SV33 ) @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(261,plain,
! [SV34: $i] :
( ( ~ ( ssList @ SV34 )
| ! [SY123: $i] :
( ~ ( ssList @ SY123 )
| ! [SY124: $i] :
( ~ ( ssList @ SY124 )
| ( ( app @ SY124 @ SY123 )
!= ( app @ SV34 @ SY123 ) )
| ( SY124 = SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(262,plain,
! [SV1: $i] :
( ( ( ~ ( ssList @ SV1 ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( ssList @ SY85 )
| ~ ( ~ ( ~ ( segmentP @ SV1 @ SY85 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( ssList @ SY86 )
| ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( ssList @ SY87 )
| ( ( app @ ( app @ SY86 @ SY85 ) @ SY87 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( ssList @ SY88 )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( ssList @ SY89 )
| ( ( app @ ( app @ SY88 @ SY85 ) @ SY89 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SY85 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(263,plain,
! [SV2: $i] :
( ( ( ~ ( ssList @ SV2 ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( ssList @ SY90 )
| ~ ~ ( ~ ( rearsegP @ SV2 @ SY90 )
| ~ ( rearsegP @ SY90 @ SV2 ) )
| ( SV2 = SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(264,plain,
! [SV3: $i] :
( ( ( ~ ( ssList @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV3 )
| ( nil = SV3 ) )
| ~ ( ( nil != SV3 )
| ( segmentP @ nil @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(265,plain,
! [SV4: $i] :
( ( ( ~ ( ssList @ SV4 ) )
= $true )
| ( ( ! [SY91: $i] :
( ~ ( ssList @ SY91 )
| ~ ( ~ ( ~ ( frontsegP @ SV4 @ SY91 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( ssList @ SY92 )
| ( ( app @ SY91 @ SY92 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( ssList @ SY93 )
| ( ( app @ SY91 @ SY93 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SY91 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(266,plain,
! [SV5: $i] :
( ( ( ~ ( ssList @ SV5 ) )
= $true )
| ( ( segmentP @ SV5 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(267,plain,
! [SV6: $i] :
( ( ( ~ ( ssList @ SV6 ) )
= $true )
| ( ( frontsegP @ SV6 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(268,plain,
! [SV7: $i] :
( ( ( ~ ( ssList @ SV7 ) )
= $true )
| ( ( ( app @ nil @ SV7 )
= SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(269,plain,
! [SV8: $i] :
( ( ( ~ ( ssList @ SV8 ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( ssList @ SY94 )
| ! [SY95: $i] :
( ~ ( ssList @ SY95 )
| ~ ( rearsegP @ SV8 @ SY94 )
| ( rearsegP @ ( app @ SY95 @ SV8 ) @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(270,plain,
! [SV9: $i] :
( ( ( ~ ( ssItem @ SV9 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( ssItem @ SY96 )
| ~ ( ~ ( ~ ( neq @ SV9 @ SY96 )
| ( SV9 != SY96 ) )
| ~ ( ~ ( ( SV9 != SY96 ) )
| ( neq @ SV9 @ SY96 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(271,plain,
! [SV10: $i] :
( ( ( ~ ( ssList @ SV10 ) )
= $true )
| ( ( ! [SY97: $i] :
( ~ ( ssList @ SY97 )
| ! [SY98: $i] :
( ~ ( ssList @ SY98 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SY97 )
| ~ ( frontsegP @ SY97 @ SY98 ) )
| ( frontsegP @ SV10 @ SY98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(272,plain,
! [SV11: $i] :
( ( ( ~ ( ssList @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( rearsegP @ nil @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(273,plain,
( ( ~ ( ssList @ sK2_SX0 )
| ! [SY125: $i] :
( ~ ( ssList @ SY125 )
| ! [SY126: $i] :
( ~ ( ssList @ SY126 )
| ( sK2_SX0 != SY126 )
| ( sK1_U != SY125 )
| ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ SX4 ) @ SX5 )
!= SY125 )
| ( ( app @ SX3 @ SX5 )
!= SY126 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(274,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ SV12 ) )
= $true )
| ( ( rearsegP @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(275,plain,
! [SV13: $i] :
( ( ( ~ ( ssList @ SV13 ) )
= $true )
| ( ( ! [SY99: $i] :
( ~ ( ssList @ SY99 )
| ~ ( ~ ( ( nil
!= ( app @ SV13 @ SY99 ) )
| ~ ( ( nil != SY99 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SY99 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SY99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(276,plain,
! [SV14: $i] :
( ( ( ~ ( ssList @ SV14 ) )
= $true )
| ( ( rearsegP @ SV14 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(277,plain,
! [SV15: $i] :
( ( ( ~ ( ssList @ SV15 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( ssList @ SY100 )
| ( ssList @ ( app @ SV15 @ SY100 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(278,plain,
! [SV16: $i] :
( ( ( ~ ( ssList @ SV16 ) )
= $true )
| ( ( ! [SY101: $i] :
( ~ ( ssList @ SY101 )
| ! [SY102: $i] :
( ~ ( ssList @ SY102 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SY101 )
| ~ ( rearsegP @ SY101 @ SY102 ) )
| ( rearsegP @ SV16 @ SY102 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(279,plain,
! [SV17: $i] :
( ( ( ~ ( ssList @ SV17 ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( ssList @ SY103 )
| ! [SY104: $i] :
( ~ ( ssList @ SY104 )
| ( ( app @ ( app @ SV17 @ SY103 ) @ SY104 )
= ( app @ SV17 @ ( app @ SY103 @ SY104 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(280,plain,
! [SV18: $i] :
( ( ( ~ ( ssList @ SV18 ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( ssList @ SY105 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SY105 )
| ~ ! [SY106: $i] :
~ ~ ( ~ ( ssList @ SY106 )
| ( ( app @ SY106 @ SY105 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( ssList @ SY107 )
| ( ( app @ SY107 @ SY105 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SY105 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(281,plain,
! [SV19: $i] :
( ( ( ~ ( ssList @ SV19 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( ssList @ SY108 )
| ~ ~ ( ~ ( segmentP @ SV19 @ SY108 )
| ~ ( segmentP @ SY108 @ SV19 ) )
| ( SV19 = SY108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(282,plain,
! [SV20: $i] :
( ( ( ~ ( ssList @ SV20 ) )
= $true )
| ( ( ! [SY109: $i] :
( ~ ( ssList @ SY109 )
| ! [SY110: $i] :
( ~ ( ssList @ SY110 )
| ! [SY111: $i] :
( ~ ( ssList @ SY111 )
| ~ ( segmentP @ SV20 @ SY109 )
| ( segmentP @ ( app @ ( app @ SY110 @ SV20 ) @ SY111 ) @ SY109 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(283,plain,
! [SV21: $i] :
( ( ( ~ ( ssList @ SV21 ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( ssList @ SY112 )
| ! [SY113: $i] :
( ~ ( ssList @ SY113 )
| ( ( app @ SY112 @ SY113 )
!= ( app @ SY112 @ SV21 ) )
| ( SY113 = SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(284,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ SV22 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( ssList @ SY114 )
| ~ ~ ( ~ ( frontsegP @ SV22 @ SY114 )
| ~ ( frontsegP @ SY114 @ SV22 ) )
| ( SV22 = SY114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(285,plain,
! [SV23: $i] :
( ( ( ~ ( ssList @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(286,plain,
! [SV24: $i] :
( ( ( ~ ( ssList @ SV24 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( ssList @ SY115 )
| ~ ( ( nil != SV24 ) )
| ( ( hd @ ( app @ SV24 @ SY115 ) )
= ( hd @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(287,plain,
! [SV25: $i] :
( ( ( ~ ( ssList @ SV25 ) )
= $true )
| ( ( ! [SY116: $i] :
( ~ ( ssList @ SY116 )
| ~ ( ~ ( ~ ( neq @ SV25 @ SY116 )
| ( SV25 != SY116 ) )
| ~ ( ~ ( ( SV25 != SY116 ) )
| ( neq @ SV25 @ SY116 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(288,plain,
! [SV26: $i] :
( ( ( ~ ( ssList @ SV26 ) )
= $true )
| ( ( segmentP @ SV26 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(289,plain,
! [SV27: $i] :
( ( ( ~ ( ssList @ SV27 ) )
= $true )
| ( ( ( app @ SV27 @ nil )
= SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(290,plain,
! [SV28: $i] :
( ( ( ~ ( ssList @ SV28 ) )
= $true )
| ( ( ~ ( ( nil != SV28 ) )
| ~ ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(291,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ SV29 ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( ssList @ SY118 )
| ! [SY119: $i] :
( ~ ( ssList @ SY119 )
| ~ ( frontsegP @ SV29 @ SY118 )
| ( frontsegP @ ( app @ SV29 @ SY119 ) @ SY118 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(292,plain,
! [SV30: $i] :
( ( ( ~ ( ssList @ SV30 ) )
= $true )
| ( ( frontsegP @ SV30 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(293,plain,
! [SV31: $i] :
( ( ( ~ ( ssList @ SV31 ) )
= $true )
| ( ( ~ ( ( nil != SV31 ) )
| ( ssList @ ( tl @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(294,plain,
! [SV32: $i] :
( ( ( ~ ( ssList @ SV32 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( ssList @ SY120 )
| ! [SY121: $i] :
( ~ ( ssList @ SY121 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SY120 )
| ~ ( segmentP @ SY120 @ SY121 ) )
| ( segmentP @ SV32 @ SY121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(295,plain,
! [SV33: $i] :
( ( ( ~ ( ssList @ SV33 ) )
= $true )
| ( ( ! [SY122: $i] :
( ~ ( ssList @ SY122 )
| ~ ( ( nil != SV33 ) )
| ( ( tl @ ( app @ SV33 @ SY122 ) )
= ( app @ ( tl @ SV33 ) @ SY122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(296,plain,
! [SV34: $i] :
( ( ( ~ ( ssList @ SV34 ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( ssList @ SY123 )
| ! [SY124: $i] :
( ~ ( ssList @ SY124 )
| ( ( app @ SY124 @ SY123 )
!= ( app @ SV34 @ SY123 ) )
| ( SY124 = SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(297,plain,
! [SV1: $i] :
( ( ( ssList @ SV1 )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( ssList @ SY85 )
| ~ ( ~ ( ~ ( segmentP @ SV1 @ SY85 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( ssList @ SY86 )
| ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( ssList @ SY87 )
| ( ( app @ ( app @ SY86 @ SY85 ) @ SY87 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( ssList @ SY88 )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( ssList @ SY89 )
| ( ( app @ ( app @ SY88 @ SY85 ) @ SY89 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SY85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(298,plain,
! [SV2: $i] :
( ( ( ssList @ SV2 )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( ssList @ SY90 )
| ~ ~ ( ~ ( rearsegP @ SV2 @ SY90 )
| ~ ( rearsegP @ SY90 @ SV2 ) )
| ( SV2 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(299,plain,
! [SV3: $i] :
( ( ( ssList @ SV3 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV3 )
| ( nil = SV3 ) )
| ~ ( ( nil != SV3 )
| ( segmentP @ nil @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(300,plain,
! [SV4: $i] :
( ( ( ssList @ SV4 )
= $false )
| ( ( ! [SY91: $i] :
( ~ ( ssList @ SY91 )
| ~ ( ~ ( ~ ( frontsegP @ SV4 @ SY91 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( ssList @ SY92 )
| ( ( app @ SY91 @ SY92 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( ssList @ SY93 )
| ( ( app @ SY91 @ SY93 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SY91 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(301,plain,
! [SV5: $i] :
( ( ( ssList @ SV5 )
= $false )
| ( ( segmentP @ SV5 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(302,plain,
! [SV6: $i] :
( ( ( ssList @ SV6 )
= $false )
| ( ( frontsegP @ SV6 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(303,plain,
! [SV7: $i] :
( ( ( ssList @ SV7 )
= $false )
| ( ( ( app @ nil @ SV7 )
= SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(304,plain,
! [SV8: $i] :
( ( ( ssList @ SV8 )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( ssList @ SY94 )
| ! [SY95: $i] :
( ~ ( ssList @ SY95 )
| ~ ( rearsegP @ SV8 @ SY94 )
| ( rearsegP @ ( app @ SY95 @ SV8 ) @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(305,plain,
! [SV9: $i] :
( ( ( ssItem @ SV9 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( ssItem @ SY96 )
| ~ ( ~ ( ~ ( neq @ SV9 @ SY96 )
| ( SV9 != SY96 ) )
| ~ ( ~ ( ( SV9 != SY96 ) )
| ( neq @ SV9 @ SY96 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(306,plain,
! [SV10: $i] :
( ( ( ssList @ SV10 )
= $false )
| ( ( ! [SY97: $i] :
( ~ ( ssList @ SY97 )
| ! [SY98: $i] :
( ~ ( ssList @ SY98 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SY97 )
| ~ ( frontsegP @ SY97 @ SY98 ) )
| ( frontsegP @ SV10 @ SY98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(307,plain,
! [SV11: $i] :
( ( ( ssList @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( rearsegP @ nil @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(308,plain,
( ( ~ ( ssList @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(309,plain,
( ( ! [SY125: $i] :
( ~ ( ssList @ SY125 )
| ! [SY126: $i] :
( ~ ( ssList @ SY126 )
| ( sK2_SX0 != SY126 )
| ( sK1_U != SY125 )
| ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) )
| ! [SX3: $i] :
( ~ ( ssList @ SX3 )
| ! [SX4: $i] :
( ~ ( ssList @ SX4 )
| ! [SX5: $i] :
( ~ ( ssList @ SX5 )
| ( ( app @ ( app @ SX3 @ SX4 ) @ SX5 )
!= SY125 )
| ( ( app @ SX3 @ SX5 )
!= SY126 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(310,plain,
! [SV12: $i] :
( ( ( ssList @ SV12 )
= $false )
| ( ( rearsegP @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(311,plain,
! [SV13: $i] :
( ( ( ssList @ SV13 )
= $false )
| ( ( ! [SY99: $i] :
( ~ ( ssList @ SY99 )
| ~ ( ~ ( ( nil
!= ( app @ SV13 @ SY99 ) )
| ~ ( ( nil != SY99 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SY99 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SY99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(312,plain,
! [SV14: $i] :
( ( ( ssList @ SV14 )
= $false )
| ( ( rearsegP @ SV14 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(313,plain,
! [SV15: $i] :
( ( ( ssList @ SV15 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( ssList @ SY100 )
| ( ssList @ ( app @ SV15 @ SY100 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(314,plain,
! [SV16: $i] :
( ( ( ssList @ SV16 )
= $false )
| ( ( ! [SY101: $i] :
( ~ ( ssList @ SY101 )
| ! [SY102: $i] :
( ~ ( ssList @ SY102 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SY101 )
| ~ ( rearsegP @ SY101 @ SY102 ) )
| ( rearsegP @ SV16 @ SY102 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(315,plain,
! [SV17: $i] :
( ( ( ssList @ SV17 )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( ssList @ SY103 )
| ! [SY104: $i] :
( ~ ( ssList @ SY104 )
| ( ( app @ ( app @ SV17 @ SY103 ) @ SY104 )
= ( app @ SV17 @ ( app @ SY103 @ SY104 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(316,plain,
! [SV18: $i] :
( ( ( ssList @ SV18 )
= $false )
| ( ( ! [SY105: $i] :
( ~ ( ssList @ SY105 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SY105 )
| ~ ! [SY106: $i] :
~ ~ ( ~ ( ssList @ SY106 )
| ( ( app @ SY106 @ SY105 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( ssList @ SY107 )
| ( ( app @ SY107 @ SY105 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SY105 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(317,plain,
! [SV19: $i] :
( ( ( ssList @ SV19 )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( ssList @ SY108 )
| ~ ~ ( ~ ( segmentP @ SV19 @ SY108 )
| ~ ( segmentP @ SY108 @ SV19 ) )
| ( SV19 = SY108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(318,plain,
! [SV20: $i] :
( ( ( ssList @ SV20 )
= $false )
| ( ( ! [SY109: $i] :
( ~ ( ssList @ SY109 )
| ! [SY110: $i] :
( ~ ( ssList @ SY110 )
| ! [SY111: $i] :
( ~ ( ssList @ SY111 )
| ~ ( segmentP @ SV20 @ SY109 )
| ( segmentP @ ( app @ ( app @ SY110 @ SV20 ) @ SY111 ) @ SY109 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(319,plain,
! [SV21: $i] :
( ( ( ssList @ SV21 )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( ssList @ SY112 )
| ! [SY113: $i] :
( ~ ( ssList @ SY113 )
| ( ( app @ SY112 @ SY113 )
!= ( app @ SY112 @ SV21 ) )
| ( SY113 = SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(320,plain,
! [SV22: $i] :
( ( ( ssList @ SV22 )
= $false )
| ( ( ! [SY114: $i] :
( ~ ( ssList @ SY114 )
| ~ ~ ( ~ ( frontsegP @ SV22 @ SY114 )
| ~ ( frontsegP @ SY114 @ SV22 ) )
| ( SV22 = SY114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(321,plain,
! [SV23: $i] :
( ( ( ssList @ SV23 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(322,plain,
! [SV24: $i] :
( ( ( ssList @ SV24 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( ssList @ SY115 )
| ~ ( ( nil != SV24 ) )
| ( ( hd @ ( app @ SV24 @ SY115 ) )
= ( hd @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(323,plain,
! [SV25: $i] :
( ( ( ssList @ SV25 )
= $false )
| ( ( ! [SY116: $i] :
( ~ ( ssList @ SY116 )
| ~ ( ~ ( ~ ( neq @ SV25 @ SY116 )
| ( SV25 != SY116 ) )
| ~ ( ~ ( ( SV25 != SY116 ) )
| ( neq @ SV25 @ SY116 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(324,plain,
! [SV26: $i] :
( ( ( ssList @ SV26 )
= $false )
| ( ( segmentP @ SV26 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(325,plain,
! [SV27: $i] :
( ( ( ssList @ SV27 )
= $false )
| ( ( ( app @ SV27 @ nil )
= SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(326,plain,
! [SV28: $i] :
( ( ( ssList @ SV28 )
= $false )
| ( ( ~ ( ( nil != SV28 ) )
| ~ ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(327,plain,
! [SV29: $i] :
( ( ( ssList @ SV29 )
= $false )
| ( ( ! [SY118: $i] :
( ~ ( ssList @ SY118 )
| ! [SY119: $i] :
( ~ ( ssList @ SY119 )
| ~ ( frontsegP @ SV29 @ SY118 )
| ( frontsegP @ ( app @ SV29 @ SY119 ) @ SY118 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(328,plain,
! [SV30: $i] :
( ( ( ssList @ SV30 )
= $false )
| ( ( frontsegP @ SV30 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(329,plain,
! [SV31: $i] :
( ( ( ssList @ SV31 )
= $false )
| ( ( ~ ( ( nil != SV31 ) )
| ( ssList @ ( tl @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(330,plain,
! [SV32: $i] :
( ( ( ssList @ SV32 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( ssList @ SY120 )
| ! [SY121: $i] :
( ~ ( ssList @ SY121 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SY120 )
| ~ ( segmentP @ SY120 @ SY121 ) )
| ( segmentP @ SV32 @ SY121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(331,plain,
! [SV33: $i] :
( ( ( ssList @ SV33 )
= $false )
| ( ( ! [SY122: $i] :
( ~ ( ssList @ SY122 )
| ~ ( ( nil != SV33 ) )
| ( ( tl @ ( app @ SV33 @ SY122 ) )
= ( app @ ( tl @ SV33 ) @ SY122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(332,plain,
! [SV34: $i] :
( ( ( ssList @ SV34 )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( ssList @ SY123 )
| ! [SY124: $i] :
( ~ ( ssList @ SY124 )
| ( ( app @ SY124 @ SY123 )
!= ( app @ SV34 @ SY123 ) )
| ( SY124 = SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(333,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ( ssList @ SV35 )
| ~ ( ~ ( ~ ( segmentP @ SV1 @ SV35 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SV35 ) ) ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(334,plain,
! [SV2: $i,SV36: $i] :
( ( ( ~ ( ssList @ SV36 )
| ~ ~ ( ~ ( rearsegP @ SV2 @ SV36 )
| ~ ( rearsegP @ SV36 @ SV2 ) )
| ( SV2 = SV36 ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(335,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV3 )
| ( nil = SV3 ) )
| ~ ( ( nil != SV3 )
| ( segmentP @ nil @ SV3 ) ) )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(336,plain,
! [SV4: $i,SV37: $i] :
( ( ( ~ ( ssList @ SV37 )
| ~ ( ~ ( ~ ( frontsegP @ SV4 @ SV37 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SV37 ) ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(337,plain,
! [SV8: $i,SV38: $i] :
( ( ( ~ ( ssList @ SV38 )
| ! [SY137: $i] :
( ~ ( ssList @ SY137 )
| ~ ( rearsegP @ SV8 @ SV38 )
| ( rearsegP @ ( app @ SY137 @ SV8 ) @ SV38 ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(338,plain,
! [SV9: $i,SV39: $i] :
( ( ( ~ ( ssItem @ SV39 )
| ~ ( ~ ( ~ ( neq @ SV9 @ SV39 )
| ( SV9 != SV39 ) )
| ~ ( ~ ( ( SV9 != SV39 ) )
| ( neq @ SV9 @ SV39 ) ) ) )
= $true )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(339,plain,
! [SV10: $i,SV40: $i] :
( ( ( ~ ( ssList @ SV40 )
| ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SY138 ) )
| ( frontsegP @ SV10 @ SY138 ) ) )
= $true )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(340,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV11 )
| ( nil = SV11 ) )
| ~ ( ( nil != SV11 )
| ( rearsegP @ nil @ SV11 ) ) )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(341,plain,
( ( ssList @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(342,plain,
( ( ~ ( ssList @ sK3_SY125 )
| ! [SY139: $i] :
( ~ ( ssList @ SY139 )
| ( sK2_SX0 != SY139 )
| ( sK1_U != sK3_SY125 )
| ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) )
| ! [SY141: $i] :
( ~ ( ssList @ SY141 )
| ! [SY142: $i] :
( ~ ( ssList @ SY142 )
| ! [SY143: $i] :
( ~ ( ssList @ SY143 )
| ( ( app @ ( app @ SY141 @ SY142 ) @ SY143 )
!= sK3_SY125 )
| ( ( app @ SY141 @ SY143 )
!= SY139 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[309]) ).
thf(343,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ( ssList @ SV41 )
| ~ ( ~ ( ( nil
!= ( app @ SV13 @ SV41 ) )
| ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SV41 ) ) ) ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(344,plain,
! [SV15: $i,SV42: $i] :
( ( ( ~ ( ssList @ SV42 )
| ( ssList @ ( app @ SV15 @ SV42 ) ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(345,plain,
! [SV16: $i,SV43: $i] :
( ( ( ~ ( ssList @ SV43 )
| ! [SY144: $i] :
( ~ ( ssList @ SY144 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SY144 ) )
| ( rearsegP @ SV16 @ SY144 ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(346,plain,
! [SV17: $i,SV44: $i] :
( ( ( ~ ( ssList @ SV44 )
| ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ( ( app @ ( app @ SV17 @ SV44 ) @ SY145 )
= ( app @ SV17 @ ( app @ SV44 @ SY145 ) ) ) ) )
= $true )
| ( ( ssList @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(347,plain,
! [SV18: $i,SV45: $i] :
( ( ( ~ ( ssList @ SV45 )
| ~ ( ~ ( ~ ( rearsegP @ SV18 @ SV45 )
| ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV45 ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(348,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ( ssList @ SV46 )
| ~ ~ ( ~ ( segmentP @ SV19 @ SV46 )
| ~ ( segmentP @ SV46 @ SV19 ) )
| ( SV19 = SV46 ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(349,plain,
! [SV20: $i,SV47: $i] :
( ( ( ~ ( ssList @ SV47 )
| ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SY148 @ SV20 ) @ SY149 ) @ SV47 ) ) ) )
= $true )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(350,plain,
! [SV21: $i,SV48: $i] :
( ( ( ~ ( ssList @ SV48 )
| ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ( ( app @ SV48 @ SY150 )
!= ( app @ SV48 @ SV21 ) )
| ( SY150 = SV21 ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(351,plain,
! [SV22: $i,SV49: $i] :
( ( ( ~ ( ssList @ SV49 )
| ~ ~ ( ~ ( frontsegP @ SV22 @ SV49 )
| ~ ( frontsegP @ SV49 @ SV22 ) )
| ( SV22 = SV49 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(352,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
| ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) )
= $false )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(353,plain,
! [SV24: $i,SV50: $i] :
( ( ( ~ ( ssList @ SV50 )
| ~ ( ( nil != SV24 ) )
| ( ( hd @ ( app @ SV24 @ SV50 ) )
= ( hd @ SV24 ) ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(354,plain,
! [SV25: $i,SV51: $i] :
( ( ( ~ ( ssList @ SV51 )
| ~ ( ~ ( ~ ( neq @ SV25 @ SV51 )
| ( SV25 != SV51 ) )
| ~ ( ~ ( ( SV25 != SV51 ) )
| ( neq @ SV25 @ SV51 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(355,plain,
! [SV28: $i] :
( ( ( ~ ( ( nil != SV28 ) ) )
= $true )
| ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(356,plain,
! [SV29: $i,SV52: $i] :
( ( ( ~ ( ssList @ SV52 )
| ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( frontsegP @ SV29 @ SV52 )
| ( frontsegP @ ( app @ SV29 @ SY151 ) @ SV52 ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(357,plain,
! [SV31: $i] :
( ( ( ~ ( ( nil != SV31 ) ) )
= $true )
| ( ( ssList @ ( tl @ SV31 ) )
= $true )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(358,plain,
! [SV32: $i,SV53: $i] :
( ( ( ~ ( ssList @ SV53 )
| ! [SY152: $i] :
( ~ ( ssList @ SY152 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SY152 ) )
| ( segmentP @ SV32 @ SY152 ) ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(359,plain,
! [SV33: $i,SV54: $i] :
( ( ( ~ ( ssList @ SV54 )
| ~ ( ( nil != SV33 ) )
| ( ( tl @ ( app @ SV33 @ SV54 ) )
= ( app @ ( tl @ SV33 ) @ SV54 ) ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(360,plain,
! [SV34: $i,SV55: $i] :
( ( ( ~ ( ssList @ SV55 )
| ! [SY153: $i] :
( ~ ( ssList @ SY153 )
| ( ( app @ SY153 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
| ( SY153 = SV34 ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(361,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ( ssList @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV1 @ SV35 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SV35 ) ) ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(362,plain,
! [SV2: $i,SV36: $i] :
( ( ( ~ ( ssList @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV2 @ SV36 )
| ~ ( rearsegP @ SV36 @ SV2 ) )
| ( SV2 = SV36 ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(363,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV3 )
| ( nil = SV3 ) ) )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(364,plain,
! [SV3: $i] :
( ( ( ~ ( ( nil != SV3 )
| ( segmentP @ nil @ SV3 ) ) )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(365,plain,
! [SV4: $i,SV37: $i] :
( ( ( ~ ( ssList @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ SV4 @ SV37 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SV37 ) ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(366,plain,
! [SV8: $i,SV38: $i] :
( ( ( ~ ( ssList @ SV38 ) )
= $true )
| ( ( ! [SY137: $i] :
( ~ ( ssList @ SY137 )
| ~ ( rearsegP @ SV8 @ SV38 )
| ( rearsegP @ ( app @ SY137 @ SV8 ) @ SV38 ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(367,plain,
! [SV9: $i,SV39: $i] :
( ( ( ~ ( ssItem @ SV39 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV9 @ SV39 )
| ( SV9 != SV39 ) )
| ~ ( ~ ( ( SV9 != SV39 ) )
| ( neq @ SV9 @ SV39 ) ) ) )
= $true )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(368,plain,
! [SV10: $i,SV40: $i] :
( ( ( ~ ( ssList @ SV40 ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SY138 ) )
| ( frontsegP @ SV10 @ SY138 ) ) )
= $true )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(369,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV11 )
| ( nil = SV11 ) ) )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(370,plain,
! [SV11: $i] :
( ( ( ~ ( ( nil != SV11 )
| ( rearsegP @ nil @ SV11 ) ) )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(371,plain,
( ( ~ ( ssList @ sK3_SY125 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(372,plain,
( ( ! [SY139: $i] :
( ~ ( ssList @ SY139 )
| ( sK2_SX0 != SY139 )
| ( sK1_U != sK3_SY125 )
| ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) )
| ! [SY141: $i] :
( ~ ( ssList @ SY141 )
| ! [SY142: $i] :
( ~ ( ssList @ SY142 )
| ! [SY143: $i] :
( ~ ( ssList @ SY143 )
| ( ( app @ ( app @ SY141 @ SY142 ) @ SY143 )
!= sK3_SY125 )
| ( ( app @ SY141 @ SY143 )
!= SY139 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(373,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ( ssList @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV13 @ SV41 ) )
| ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SV41 ) ) ) ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(374,plain,
! [SV15: $i,SV42: $i] :
( ( ( ~ ( ssList @ SV42 ) )
= $true )
| ( ( ssList @ ( app @ SV15 @ SV42 ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(375,plain,
! [SV16: $i,SV43: $i] :
( ( ( ~ ( ssList @ SV43 ) )
= $true )
| ( ( ! [SY144: $i] :
( ~ ( ssList @ SY144 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SY144 ) )
| ( rearsegP @ SV16 @ SY144 ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(376,plain,
! [SV17: $i,SV44: $i] :
( ( ( ~ ( ssList @ SV44 ) )
= $true )
| ( ( ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ( ( app @ ( app @ SV17 @ SV44 ) @ SY145 )
= ( app @ SV17 @ ( app @ SV44 @ SY145 ) ) ) ) )
= $true )
| ( ( ssList @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(377,plain,
! [SV18: $i,SV45: $i] :
( ( ( ~ ( ssList @ SV45 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ SV18 @ SV45 )
| ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV45 ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(378,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ( ssList @ SV46 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV19 @ SV46 )
| ~ ( segmentP @ SV46 @ SV19 ) )
| ( SV19 = SV46 ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(379,plain,
! [SV20: $i,SV47: $i] :
( ( ( ~ ( ssList @ SV47 ) )
= $true )
| ( ( ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SY148 @ SV20 ) @ SY149 ) @ SV47 ) ) ) )
= $true )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(380,plain,
! [SV21: $i,SV48: $i] :
( ( ( ~ ( ssList @ SV48 ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ( ( app @ SV48 @ SY150 )
!= ( app @ SV48 @ SV21 ) )
| ( SY150 = SV21 ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(381,plain,
! [SV22: $i,SV49: $i] :
( ( ( ~ ( ssList @ SV49 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV22 @ SV49 )
| ~ ( frontsegP @ SV49 @ SV22 ) )
| ( SV22 = SV49 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(382,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) ) )
= $false )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(383,plain,
! [SV23: $i] :
( ( ( ~ ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) ) )
= $false )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(384,plain,
! [SV24: $i,SV50: $i] :
( ( ( ~ ( ssList @ SV50 ) )
= $true )
| ( ( ~ ( ( nil != SV24 ) )
| ( ( hd @ ( app @ SV24 @ SV50 ) )
= ( hd @ SV24 ) ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(385,plain,
! [SV25: $i,SV51: $i] :
( ( ( ~ ( ssList @ SV51 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV25 @ SV51 )
| ( SV25 != SV51 ) )
| ~ ( ~ ( ( SV25 != SV51 ) )
| ( neq @ SV25 @ SV51 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(386,plain,
! [SV28: $i] :
( ( ( nil != SV28 )
= $false )
| ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(387,plain,
! [SV29: $i,SV52: $i] :
( ( ( ~ ( ssList @ SV52 ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( frontsegP @ SV29 @ SV52 )
| ( frontsegP @ ( app @ SV29 @ SY151 ) @ SV52 ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(388,plain,
! [SV31: $i] :
( ( ( nil != SV31 )
= $false )
| ( ( ssList @ ( tl @ SV31 ) )
= $true )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(389,plain,
! [SV32: $i,SV53: $i] :
( ( ( ~ ( ssList @ SV53 ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( ssList @ SY152 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SY152 ) )
| ( segmentP @ SV32 @ SY152 ) ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(390,plain,
! [SV33: $i,SV54: $i] :
( ( ( ~ ( ssList @ SV54 ) )
= $true )
| ( ( ~ ( ( nil != SV33 ) )
| ( ( tl @ ( app @ SV33 @ SV54 ) )
= ( app @ ( tl @ SV33 ) @ SV54 ) ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(391,plain,
! [SV34: $i,SV55: $i] :
( ( ( ~ ( ssList @ SV55 ) )
= $true )
| ( ( ! [SY153: $i] :
( ~ ( ssList @ SY153 )
| ( ( app @ SY153 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
| ( SY153 = SV34 ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(392,plain,
! [SV1: $i,SV35: $i] :
( ( ( ssList @ SV35 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV1 @ SV35 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SV35 ) ) ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(393,plain,
! [SV2: $i,SV36: $i] :
( ( ( ssList @ SV36 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV2 @ SV36 )
| ~ ( rearsegP @ SV36 @ SV2 ) )
| ( SV2 = SV36 ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(394,plain,
! [SV3: $i] :
( ( ( ~ ( segmentP @ nil @ SV3 )
| ( nil = SV3 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(395,plain,
! [SV3: $i] :
( ( ( ( nil != SV3 )
| ( segmentP @ nil @ SV3 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(396,plain,
! [SV4: $i,SV37: $i] :
( ( ( ssList @ SV37 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ SV4 @ SV37 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SV37 ) ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(397,plain,
! [SV8: $i,SV38: $i] :
( ( ( ssList @ SV38 )
= $false )
| ( ( ! [SY137: $i] :
( ~ ( ssList @ SY137 )
| ~ ( rearsegP @ SV8 @ SV38 )
| ( rearsegP @ ( app @ SY137 @ SV8 ) @ SV38 ) ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(398,plain,
! [SV9: $i,SV39: $i] :
( ( ( ssItem @ SV39 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV9 @ SV39 )
| ( SV9 != SV39 ) )
| ~ ( ~ ( ( SV9 != SV39 ) )
| ( neq @ SV9 @ SV39 ) ) ) )
= $true )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(399,plain,
! [SV10: $i,SV40: $i] :
( ( ( ssList @ SV40 )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SY138 ) )
| ( frontsegP @ SV10 @ SY138 ) ) )
= $true )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(400,plain,
! [SV11: $i] :
( ( ( ~ ( rearsegP @ nil @ SV11 )
| ( nil = SV11 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(401,plain,
! [SV11: $i] :
( ( ( ( nil != SV11 )
| ( rearsegP @ nil @ SV11 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(402,plain,
( ( ssList @ sK3_SY125 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(403,plain,
( ( ~ ( ssList @ sK4_SY139 )
| ( sK2_SX0 != sK4_SY139 )
| ( sK1_U != sK3_SY125 )
| ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) )
| ! [SY155: $i] :
( ~ ( ssList @ SY155 )
| ! [SY156: $i] :
( ~ ( ssList @ SY156 )
| ! [SY157: $i] :
( ~ ( ssList @ SY157 )
| ( ( app @ ( app @ SY155 @ SY156 ) @ SY157 )
!= sK3_SY125 )
| ( ( app @ SY155 @ SY157 )
!= sK4_SY139 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[372]) ).
thf(404,plain,
! [SV13: $i,SV41: $i] :
( ( ( ssList @ SV41 )
= $false )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV13 @ SV41 ) )
| ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SV41 ) ) ) ) )
= $true )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(405,plain,
! [SV15: $i,SV42: $i] :
( ( ( ssList @ SV42 )
= $false )
| ( ( ssList @ ( app @ SV15 @ SV42 ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(406,plain,
! [SV16: $i,SV43: $i] :
( ( ( ssList @ SV43 )
= $false )
| ( ( ! [SY144: $i] :
( ~ ( ssList @ SY144 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SY144 ) )
| ( rearsegP @ SV16 @ SY144 ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(407,plain,
! [SV17: $i,SV44: $i] :
( ( ( ssList @ SV44 )
= $false )
| ( ( ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ( ( app @ ( app @ SV17 @ SV44 ) @ SY145 )
= ( app @ SV17 @ ( app @ SV44 @ SY145 ) ) ) ) )
= $true )
| ( ( ssList @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(408,plain,
! [SV18: $i,SV45: $i] :
( ( ( ssList @ SV45 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ SV18 @ SV45 )
| ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV45 ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(409,plain,
! [SV19: $i,SV46: $i] :
( ( ( ssList @ SV46 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV19 @ SV46 )
| ~ ( segmentP @ SV46 @ SV19 ) )
| ( SV19 = SV46 ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(410,plain,
! [SV20: $i,SV47: $i] :
( ( ( ssList @ SV47 )
= $false )
| ( ( ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SY148 @ SV20 ) @ SY149 ) @ SV47 ) ) ) )
= $true )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(411,plain,
! [SV21: $i,SV48: $i] :
( ( ( ssList @ SV48 )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ( ( app @ SV48 @ SY150 )
!= ( app @ SV48 @ SV21 ) )
| ( SY150 = SV21 ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(412,plain,
! [SV22: $i,SV49: $i] :
( ( ( ssList @ SV49 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV22 @ SV49 )
| ~ ( frontsegP @ SV49 @ SV22 ) )
| ( SV22 = SV49 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(413,plain,
! [SV23: $i] :
( ( ( ~ ( frontsegP @ nil @ SV23 )
| ( nil = SV23 ) )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(414,plain,
! [SV23: $i] :
( ( ( ( nil != SV23 )
| ( frontsegP @ nil @ SV23 ) )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(415,plain,
! [SV24: $i,SV50: $i] :
( ( ( ssList @ SV50 )
= $false )
| ( ( ~ ( ( nil != SV24 ) )
| ( ( hd @ ( app @ SV24 @ SV50 ) )
= ( hd @ SV24 ) ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(416,plain,
! [SV25: $i,SV51: $i] :
( ( ( ssList @ SV51 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV25 @ SV51 )
| ( SV25 != SV51 ) )
| ~ ( ~ ( ( SV25 != SV51 ) )
| ( neq @ SV25 @ SV51 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(417,plain,
! [SV28: $i] :
( ( ( nil = SV28 )
= $true )
| ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(418,plain,
! [SV29: $i,SV52: $i] :
( ( ( ssList @ SV52 )
= $false )
| ( ( ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( frontsegP @ SV29 @ SV52 )
| ( frontsegP @ ( app @ SV29 @ SY151 ) @ SV52 ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(419,plain,
! [SV31: $i] :
( ( ( nil = SV31 )
= $true )
| ( ( ssList @ ( tl @ SV31 ) )
= $true )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(420,plain,
! [SV32: $i,SV53: $i] :
( ( ( ssList @ SV53 )
= $false )
| ( ( ! [SY152: $i] :
( ~ ( ssList @ SY152 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SY152 ) )
| ( segmentP @ SV32 @ SY152 ) ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(421,plain,
! [SV33: $i,SV54: $i] :
( ( ( ssList @ SV54 )
= $false )
| ( ( ~ ( ( nil != SV33 ) )
| ( ( tl @ ( app @ SV33 @ SV54 ) )
= ( app @ ( tl @ SV33 ) @ SV54 ) ) )
= $true )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(422,plain,
! [SV34: $i,SV55: $i] :
( ( ( ssList @ SV55 )
= $false )
| ( ( ! [SY153: $i] :
( ~ ( ssList @ SY153 )
| ( ( app @ SY153 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
| ( SY153 = SV34 ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(423,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( ~ ( segmentP @ SV1 @ SV35 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SV35 ) ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(424,plain,
! [SV36: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV2 @ SV36 )
| ~ ( rearsegP @ SV36 @ SV2 ) ) )
= $true )
| ( ( SV2 = SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(425,plain,
! [SV3: $i] :
( ( ( ~ ( segmentP @ nil @ SV3 ) )
= $true )
| ( ( nil = SV3 )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(426,plain,
! [SV3: $i] :
( ( ( nil != SV3 )
= $true )
| ( ( segmentP @ nil @ SV3 )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(427,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV4 @ SV37 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
| ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SV37 ) ) )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(428,plain,
! [SV38: $i,SV8: $i,SV56: $i] :
( ( ( ~ ( ssList @ SV56 )
| ~ ( rearsegP @ SV8 @ SV38 )
| ( rearsegP @ ( app @ SV56 @ SV8 ) @ SV38 ) )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(429,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( ~ ( neq @ SV9 @ SV39 )
| ( SV9 != SV39 ) )
| ~ ( ~ ( ( SV9 != SV39 ) )
| ( neq @ SV9 @ SV39 ) ) )
= $false )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(430,plain,
! [SV40: $i,SV10: $i,SV57: $i] :
( ( ( ~ ( ssList @ SV57 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SV57 ) )
| ( frontsegP @ SV10 @ SV57 ) )
= $true )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(431,plain,
! [SV11: $i] :
( ( ( ~ ( rearsegP @ nil @ SV11 ) )
= $true )
| ( ( nil = SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(432,plain,
! [SV11: $i] :
( ( ( nil != SV11 )
= $true )
| ( ( rearsegP @ nil @ SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(433,plain,
( ( ~ ( ssList @ sK4_SY139 )
| ( sK2_SX0 != sK4_SY139 )
| ( sK1_U != sK3_SY125 )
| ~ ( neq @ sK2_SX0 @ nil )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(434,plain,
( ( ! [SY155: $i] :
( ~ ( ssList @ SY155 )
| ! [SY156: $i] :
( ~ ( ssList @ SY156 )
| ! [SY157: $i] :
( ~ ( ssList @ SY157 )
| ( ( app @ ( app @ SY155 @ SY156 ) @ SY157 )
!= sK3_SY125 )
| ( ( app @ SY155 @ SY157 )
!= sK4_SY139 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(435,plain,
! [SV41: $i,SV13: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV13 @ SV41 ) )
| ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
| ~ ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SV41 ) ) ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(436,plain,
! [SV43: $i,SV16: $i,SV58: $i] :
( ( ( ~ ( ssList @ SV58 )
| ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SV58 ) )
| ( rearsegP @ SV16 @ SV58 ) )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(437,plain,
! [SV44: $i,SV17: $i,SV59: $i] :
( ( ( ~ ( ssList @ SV59 )
| ( ( app @ ( app @ SV17 @ SV44 ) @ SV59 )
= ( app @ SV17 @ ( app @ SV44 @ SV59 ) ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false )
| ( ( ssList @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(438,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV18 @ SV45 )
| ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
| ~ ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV45 ) ) )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(439,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV19 @ SV46 )
| ~ ( segmentP @ SV46 @ SV19 ) ) )
= $true )
| ( ( SV19 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(440,plain,
! [SV47: $i,SV20: $i,SV60: $i] :
( ( ( ~ ( ssList @ SV60 )
| ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SY158 ) @ SV47 ) ) )
= $true )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(441,plain,
! [SV21: $i,SV48: $i,SV61: $i] :
( ( ( ~ ( ssList @ SV61 )
| ( ( app @ SV48 @ SV61 )
!= ( app @ SV48 @ SV21 ) )
| ( SV61 = SV21 ) )
= $true )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(442,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV22 @ SV49 )
| ~ ( frontsegP @ SV49 @ SV22 ) ) )
= $true )
| ( ( SV22 = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(443,plain,
! [SV23: $i] :
( ( ( ~ ( frontsegP @ nil @ SV23 ) )
= $true )
| ( ( nil = SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(444,plain,
! [SV23: $i] :
( ( ( nil != SV23 )
= $true )
| ( ( frontsegP @ nil @ SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(445,plain,
! [SV50: $i,SV24: $i] :
( ( ( ~ ( ( nil != SV24 ) ) )
= $true )
| ( ( ( hd @ ( app @ SV24 @ SV50 ) )
= ( hd @ SV24 ) )
= $true )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(446,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( ~ ( neq @ SV25 @ SV51 )
| ( SV25 != SV51 ) )
| ~ ( ~ ( ( SV25 != SV51 ) )
| ( neq @ SV25 @ SV51 ) ) )
= $false )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(447,plain,
! [SV28: $i] :
( ( ( ! [SY117: $i] :
~ ~ ( ~ ( ssList @ SY117 )
| ( ( tl @ SV28 )
!= SY117 ) ) )
= $false )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(448,plain,
! [SV52: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( ssList @ SV62 )
| ~ ( frontsegP @ SV29 @ SV52 )
| ( frontsegP @ ( app @ SV29 @ SV62 ) @ SV52 ) )
= $true )
| ( ( ssList @ SV52 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(449,plain,
! [SV53: $i,SV32: $i,SV63: $i] :
( ( ( ~ ( ssList @ SV63 )
| ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SV63 ) )
| ( segmentP @ SV32 @ SV63 ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(450,plain,
! [SV54: $i,SV33: $i] :
( ( ( ~ ( ( nil != SV33 ) ) )
= $true )
| ( ( ( tl @ ( app @ SV33 @ SV54 ) )
= ( app @ ( tl @ SV33 ) @ SV54 ) )
= $true )
| ( ( ssList @ SV54 )
= $false )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(451,plain,
! [SV34: $i,SV55: $i,SV64: $i] :
( ( ( ~ ( ssList @ SV64 )
| ( ( app @ SV64 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
| ( SV64 = SV34 ) )
= $true )
| ( ( ssList @ SV55 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(452,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( ~ ( segmentP @ SV1 @ SV35 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(453,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SV35 ) ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(454,plain,
! [SV36: $i,SV2: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV2 @ SV36 )
| ~ ( rearsegP @ SV36 @ SV2 ) ) )
= $false )
| ( ( SV2 = SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(455,plain,
! [SV3: $i] :
( ( ( segmentP @ nil @ SV3 )
= $false )
| ( ( nil = SV3 )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(456,plain,
! [SV3: $i] :
( ( ( nil = SV3 )
= $false )
| ( ( segmentP @ nil @ SV3 )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(457,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV4 @ SV37 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) ) )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(458,plain,
! [SV4: $i,SV37: $i] :
( ( ( ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SV37 ) ) )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(459,plain,
! [SV38: $i,SV8: $i,SV56: $i] :
( ( ( ~ ( ssList @ SV56 ) )
= $true )
| ( ( ~ ( rearsegP @ SV8 @ SV38 )
| ( rearsegP @ ( app @ SV56 @ SV8 ) @ SV38 ) )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(460,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( ~ ( neq @ SV9 @ SV39 )
| ( SV9 != SV39 ) ) )
= $false )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(461,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( ~ ( ( SV9 != SV39 ) )
| ( neq @ SV9 @ SV39 ) ) )
= $false )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(462,plain,
! [SV40: $i,SV10: $i,SV57: $i] :
( ( ( ~ ( ssList @ SV57 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SV57 ) )
| ( frontsegP @ SV10 @ SV57 ) )
= $true )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(463,plain,
! [SV11: $i] :
( ( ( rearsegP @ nil @ SV11 )
= $false )
| ( ( nil = SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(464,plain,
! [SV11: $i] :
( ( ( nil = SV11 )
= $false )
| ( ( rearsegP @ nil @ SV11 )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(465,plain,
( ( ~ ( ssList @ sK4_SY139 )
| ( sK2_SX0 != sK4_SY139 )
| ( sK1_U != sK3_SY125 )
| ~ ( neq @ sK2_SX0 @ nil ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(466,plain,
( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(467,plain,
( ( ~ ( ssList @ sK5_SY155 )
| ! [SY159: $i] :
( ~ ( ssList @ SY159 )
| ! [SY160: $i] :
( ~ ( ssList @ SY160 )
| ( ( app @ ( app @ sK5_SY155 @ SY159 ) @ SY160 )
!= sK3_SY125 )
| ( ( app @ sK5_SY155 @ SY160 )
!= sK4_SY139 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[434]) ).
thf(468,plain,
! [SV41: $i,SV13: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV13 @ SV41 ) )
| ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(469,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SV41 ) ) ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(470,plain,
! [SV43: $i,SV16: $i,SV58: $i] :
( ( ( ~ ( ssList @ SV58 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SV58 ) )
| ( rearsegP @ SV16 @ SV58 ) )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(471,plain,
! [SV44: $i,SV17: $i,SV59: $i] :
( ( ( ~ ( ssList @ SV59 ) )
= $true )
| ( ( ( app @ ( app @ SV17 @ SV44 ) @ SV59 )
= ( app @ SV17 @ ( app @ SV44 @ SV59 ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false )
| ( ( ssList @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(472,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV18 @ SV45 )
| ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) ) )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(473,plain,
! [SV18: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV45 ) ) )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(474,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( ~ ( segmentP @ SV19 @ SV46 )
| ~ ( segmentP @ SV46 @ SV19 ) ) )
= $false )
| ( ( SV19 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(475,plain,
! [SV47: $i,SV20: $i,SV60: $i] :
( ( ( ~ ( ssList @ SV60 ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SY158 ) @ SV47 ) ) )
= $true )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(476,plain,
! [SV21: $i,SV48: $i,SV61: $i] :
( ( ( ~ ( ssList @ SV61 ) )
= $true )
| ( ( ( ( app @ SV48 @ SV61 )
!= ( app @ SV48 @ SV21 ) )
| ( SV61 = SV21 ) )
= $true )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(477,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV22 @ SV49 )
| ~ ( frontsegP @ SV49 @ SV22 ) ) )
= $false )
| ( ( SV22 = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(478,plain,
! [SV23: $i] :
( ( ( frontsegP @ nil @ SV23 )
= $false )
| ( ( nil = SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(479,plain,
! [SV23: $i] :
( ( ( nil = SV23 )
= $false )
| ( ( frontsegP @ nil @ SV23 )
= $true )
| ( ( ssList @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(480,plain,
! [SV50: $i,SV24: $i] :
( ( ( nil != SV24 )
= $false )
| ( ( ( hd @ ( app @ SV24 @ SV50 ) )
= ( hd @ SV24 ) )
= $true )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(481,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( ~ ( neq @ SV25 @ SV51 )
| ( SV25 != SV51 ) ) )
= $false )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(482,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( ~ ( ( SV25 != SV51 ) )
| ( neq @ SV25 @ SV51 ) ) )
= $false )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(483,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK6_SY117 @ SV28 ) )
| ( ( tl @ SV28 )
!= ( sK6_SY117 @ SV28 ) ) ) )
= $false )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[447]) ).
thf(484,plain,
! [SV52: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( ssList @ SV62 ) )
= $true )
| ( ( ~ ( frontsegP @ SV29 @ SV52 )
| ( frontsegP @ ( app @ SV29 @ SV62 ) @ SV52 ) )
= $true )
| ( ( ssList @ SV52 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(485,plain,
! [SV53: $i,SV32: $i,SV63: $i] :
( ( ( ~ ( ssList @ SV63 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SV63 ) )
| ( segmentP @ SV32 @ SV63 ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(486,plain,
! [SV54: $i,SV33: $i] :
( ( ( nil != SV33 )
= $false )
| ( ( ( tl @ ( app @ SV33 @ SV54 ) )
= ( app @ ( tl @ SV33 ) @ SV54 ) )
= $true )
| ( ( ssList @ SV54 )
= $false )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(487,plain,
! [SV34: $i,SV55: $i,SV64: $i] :
( ( ( ~ ( ssList @ SV64 ) )
= $true )
| ( ( ( ( app @ SV64 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
| ( SV64 = SV34 ) )
= $true )
| ( ( ssList @ SV55 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(488,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( segmentP @ SV1 @ SV35 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(489,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) )
| ( segmentP @ SV1 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(490,plain,
! [SV36: $i,SV2: $i] :
( ( ( ~ ( rearsegP @ SV2 @ SV36 )
| ~ ( rearsegP @ SV36 @ SV2 ) )
= $true )
| ( ( SV2 = SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(491,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( frontsegP @ SV4 @ SV37 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(492,plain,
! [SV4: $i,SV37: $i] :
( ( ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) )
| ( frontsegP @ SV4 @ SV37 ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(493,plain,
! [SV38: $i,SV8: $i,SV56: $i] :
( ( ( ssList @ SV56 )
= $false )
| ( ( ~ ( rearsegP @ SV8 @ SV38 )
| ( rearsegP @ ( app @ SV56 @ SV8 ) @ SV38 ) )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(494,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( neq @ SV9 @ SV39 )
| ( SV9 != SV39 ) )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(495,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( ( SV9 != SV39 ) )
| ( neq @ SV9 @ SV39 ) )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(496,plain,
! [SV40: $i,SV10: $i,SV57: $i] :
( ( ( ssList @ SV57 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SV57 ) )
| ( frontsegP @ SV10 @ SV57 ) )
= $true )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(497,plain,
( ( ~ ( ssList @ sK4_SY139 )
| ( sK2_SX0 != sK4_SY139 )
| ( sK1_U != sK3_SY125 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(498,plain,
( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(499,plain,
( ( ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SY127 )
| ~ ( neq @ SY127 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SY127 ) )
| ~ ( segmentP @ sK1_U @ SY127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(500,plain,
( ( ~ ( ssList @ sK5_SY155 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(501,plain,
( ( ! [SY159: $i] :
( ~ ( ssList @ SY159 )
| ! [SY160: $i] :
( ~ ( ssList @ SY160 )
| ( ( app @ ( app @ sK5_SY155 @ SY159 ) @ SY160 )
!= sK3_SY125 )
| ( ( app @ sK5_SY155 @ SY160 )
!= sK4_SY139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(502,plain,
! [SV41: $i,SV13: $i] :
( ( ( ( nil
!= ( app @ SV13 @ SV41 ) )
| ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(503,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) )
| ( nil
= ( app @ SV13 @ SV41 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(504,plain,
! [SV43: $i,SV16: $i,SV58: $i] :
( ( ( ssList @ SV58 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SV58 ) )
| ( rearsegP @ SV16 @ SV58 ) )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(505,plain,
! [SV44: $i,SV17: $i,SV59: $i] :
( ( ( ssList @ SV59 )
= $false )
| ( ( ( app @ ( app @ SV17 @ SV44 ) @ SV59 )
= ( app @ SV17 @ ( app @ SV44 @ SV59 ) ) )
= $true )
| ( ( ssList @ SV44 )
= $false )
| ( ( ssList @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(506,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( rearsegP @ SV18 @ SV45 )
| ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(507,plain,
! [SV18: $i,SV45: $i] :
( ( ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) )
| ( rearsegP @ SV18 @ SV45 ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(508,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( segmentP @ SV19 @ SV46 )
| ~ ( segmentP @ SV46 @ SV19 ) )
= $true )
| ( ( SV19 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(509,plain,
! [SV47: $i,SV20: $i,SV60: $i] :
( ( ( ssList @ SV60 )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SY158 ) @ SV47 ) ) )
= $true )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(510,plain,
! [SV21: $i,SV48: $i,SV61: $i] :
( ( ( ssList @ SV61 )
= $false )
| ( ( ( ( app @ SV48 @ SV61 )
!= ( app @ SV48 @ SV21 ) )
| ( SV61 = SV21 ) )
= $true )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(511,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( frontsegP @ SV22 @ SV49 )
| ~ ( frontsegP @ SV49 @ SV22 ) )
= $true )
| ( ( SV22 = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(512,plain,
! [SV50: $i,SV24: $i] :
( ( ( nil = SV24 )
= $true )
| ( ( ( hd @ ( app @ SV24 @ SV50 ) )
= ( hd @ SV24 ) )
= $true )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(513,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( neq @ SV25 @ SV51 )
| ( SV25 != SV51 ) )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(514,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( ( SV25 != SV51 ) )
| ( neq @ SV25 @ SV51 ) )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(515,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK6_SY117 @ SV28 ) )
| ( ( tl @ SV28 )
!= ( sK6_SY117 @ SV28 ) ) ) )
= $true )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(516,plain,
! [SV52: $i,SV29: $i,SV62: $i] :
( ( ( ssList @ SV62 )
= $false )
| ( ( ~ ( frontsegP @ SV29 @ SV52 )
| ( frontsegP @ ( app @ SV29 @ SV62 ) @ SV52 ) )
= $true )
| ( ( ssList @ SV52 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(517,plain,
! [SV53: $i,SV32: $i,SV63: $i] :
( ( ( ssList @ SV63 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SV63 ) )
| ( segmentP @ SV32 @ SV63 ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(518,plain,
! [SV54: $i,SV33: $i] :
( ( ( nil = SV33 )
= $true )
| ( ( ( tl @ ( app @ SV33 @ SV54 ) )
= ( app @ ( tl @ SV33 ) @ SV54 ) )
= $true )
| ( ( ssList @ SV54 )
= $false )
| ( ( ssList @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(519,plain,
! [SV34: $i,SV55: $i,SV64: $i] :
( ( ( ssList @ SV64 )
= $false )
| ( ( ( ( app @ SV64 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
| ( SV64 = SV34 ) )
= $true )
| ( ( ssList @ SV55 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(520,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( segmentP @ SV1 @ SV35 ) )
= $true )
| ( ( ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(521,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(522,plain,
! [SV36: $i,SV2: $i] :
( ( ( ~ ( rearsegP @ SV2 @ SV36 ) )
= $true )
| ( ( ~ ( rearsegP @ SV36 @ SV2 ) )
= $true )
| ( ( SV2 = SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(523,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( frontsegP @ SV4 @ SV37 ) )
= $true )
| ( ( ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(524,plain,
! [SV4: $i,SV37: $i] :
( ( ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) ) )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(525,plain,
! [SV56: $i,SV38: $i,SV8: $i] :
( ( ( ~ ( rearsegP @ SV8 @ SV38 ) )
= $true )
| ( ( rearsegP @ ( app @ SV56 @ SV8 ) @ SV38 )
= $true )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(526,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( neq @ SV9 @ SV39 ) )
= $true )
| ( ( SV9 != SV39 )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(527,plain,
! [SV39: $i,SV9: $i] :
( ( ( ~ ( ( SV9 != SV39 ) ) )
= $true )
| ( ( neq @ SV9 @ SV39 )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(528,plain,
! [SV57: $i,SV40: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SV57 ) ) )
= $true )
| ( ( frontsegP @ SV10 @ SV57 )
= $true )
| ( ( ssList @ SV57 )
= $false )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(529,plain,
( ( ~ ( ssList @ sK4_SY139 )
| ( sK2_SX0 != sK4_SY139 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(530,plain,
( ( sK1_U != sK3_SY125 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(531,plain,
( ( neq @ sK2_SX0 @ nil )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(532,plain,
! [SV65: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV65 ) )
| ~ ( segmentP @ sK1_U @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(533,plain,
( ( ssList @ sK5_SY155 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(534,plain,
( ( ~ ( ssList @ sK7_SY159 )
| ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ( ( app @ ( app @ sK5_SY155 @ sK7_SY159 ) @ SY161 )
!= sK3_SY125 )
| ( ( app @ sK5_SY155 @ SY161 )
!= sK4_SY139 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[501]) ).
thf(535,plain,
! [SV41: $i,SV13: $i] :
( ( ( nil
!= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(536,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
= $true )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(537,plain,
! [SV58: $i,SV43: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SV58 ) ) )
= $true )
| ( ( rearsegP @ SV16 @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(538,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( rearsegP @ SV18 @ SV45 ) )
= $true )
| ( ( ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(539,plain,
! [SV18: $i,SV45: $i] :
( ( ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(540,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( segmentP @ SV19 @ SV46 ) )
= $true )
| ( ( ~ ( segmentP @ SV46 @ SV19 ) )
= $true )
| ( ( SV19 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(541,plain,
! [SV60: $i,SV47: $i,SV20: $i,SV66: $i] :
( ( ( ~ ( ssList @ SV66 )
| ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SV66 ) @ SV47 ) )
= $true )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(542,plain,
! [SV21: $i,SV61: $i,SV48: $i] :
( ( ( ( app @ SV48 @ SV61 )
!= ( app @ SV48 @ SV21 ) )
= $true )
| ( ( SV61 = SV21 )
= $true )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(543,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( frontsegP @ SV22 @ SV49 ) )
= $true )
| ( ( ~ ( frontsegP @ SV49 @ SV22 ) )
= $true )
| ( ( SV22 = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(544,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( neq @ SV25 @ SV51 ) )
= $true )
| ( ( SV25 != SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(545,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( ( SV25 != SV51 ) ) )
= $true )
| ( ( neq @ SV25 @ SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(546,plain,
! [SV28: $i] :
( ( ( ~ ( ssList @ ( sK6_SY117 @ SV28 ) )
| ( ( tl @ SV28 )
!= ( sK6_SY117 @ SV28 ) ) )
= $false )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(547,plain,
! [SV62: $i,SV52: $i,SV29: $i] :
( ( ( ~ ( frontsegP @ SV29 @ SV52 ) )
= $true )
| ( ( frontsegP @ ( app @ SV29 @ SV62 ) @ SV52 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV52 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(548,plain,
! [SV63: $i,SV53: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SV63 ) ) )
= $true )
| ( ( segmentP @ SV32 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(549,plain,
! [SV34: $i,SV55: $i,SV64: $i] :
( ( ( ( app @ SV64 @ SV55 )
!= ( app @ SV34 @ SV55 ) )
= $true )
| ( ( SV64 = SV34 )
= $true )
| ( ( ssList @ SV64 )
= $false )
| ( ( ssList @ SV55 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(550,plain,
! [SV35: $i,SV1: $i] :
( ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ~ ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(551,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(552,plain,
! [SV36: $i,SV2: $i] :
( ( ( rearsegP @ SV2 @ SV36 )
= $false )
| ( ( ~ ( rearsegP @ SV36 @ SV2 ) )
= $true )
| ( ( SV2 = SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(553,plain,
! [SV37: $i,SV4: $i] :
( ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ~ ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(554,plain,
! [SV4: $i,SV37: $i] :
( ( ( ~ ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) ) )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(555,plain,
! [SV56: $i,SV38: $i,SV8: $i] :
( ( ( rearsegP @ SV8 @ SV38 )
= $false )
| ( ( rearsegP @ ( app @ SV56 @ SV8 ) @ SV38 )
= $true )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(556,plain,
! [SV39: $i,SV9: $i] :
( ( ( neq @ SV9 @ SV39 )
= $false )
| ( ( SV9 != SV39 )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(557,plain,
! [SV39: $i,SV9: $i] :
( ( ( SV9 != SV39 )
= $false )
| ( ( neq @ SV9 @ SV39 )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(558,plain,
! [SV57: $i,SV40: $i,SV10: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SV57 ) ) )
= $false )
| ( ( frontsegP @ SV10 @ SV57 )
= $true )
| ( ( ssList @ SV57 )
= $false )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(559,plain,
( ( ~ ( ssList @ sK4_SY139 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(560,plain,
( ( sK2_SX0 != sK4_SY139 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(561,plain,
( ( sK1_U = sK3_SY125 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(562,plain,
! [SV65: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV65 ) )
| ~ ( segmentP @ sK1_U @ SV65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(563,plain,
( ( ~ ( ssList @ sK7_SY159 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(564,plain,
( ( ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ( ( app @ ( app @ sK5_SY155 @ sK7_SY159 ) @ SY161 )
!= sK3_SY125 )
| ( ( app @ sK5_SY155 @ SY161 )
!= sK4_SY139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(565,plain,
! [SV41: $i,SV13: $i] :
( ( ( nil
= ( app @ SV13 @ SV41 ) )
= $false )
| ( ( ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(566,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ( ( nil != SV41 )
| ( nil != SV13 ) ) )
= $false )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(567,plain,
! [SV58: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SV58 ) ) )
= $false )
| ( ( rearsegP @ SV16 @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(568,plain,
! [SV45: $i,SV18: $i] :
( ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ~ ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(569,plain,
! [SV18: $i,SV45: $i] :
( ( ( ~ ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(570,plain,
! [SV46: $i,SV19: $i] :
( ( ( segmentP @ SV19 @ SV46 )
= $false )
| ( ( ~ ( segmentP @ SV46 @ SV19 ) )
= $true )
| ( ( SV19 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(571,plain,
! [SV60: $i,SV47: $i,SV20: $i,SV66: $i] :
( ( ( ~ ( ssList @ SV66 ) )
= $true )
| ( ( ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SV66 ) @ SV47 ) )
= $true )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(572,plain,
! [SV21: $i,SV61: $i,SV48: $i] :
( ( ( ( app @ SV48 @ SV61 )
= ( app @ SV48 @ SV21 ) )
= $false )
| ( ( SV61 = SV21 )
= $true )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(573,plain,
! [SV49: $i,SV22: $i] :
( ( ( frontsegP @ SV22 @ SV49 )
= $false )
| ( ( ~ ( frontsegP @ SV49 @ SV22 ) )
= $true )
| ( ( SV22 = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(574,plain,
! [SV51: $i,SV25: $i] :
( ( ( neq @ SV25 @ SV51 )
= $false )
| ( ( SV25 != SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(575,plain,
! [SV51: $i,SV25: $i] :
( ( ( SV25 != SV51 )
= $false )
| ( ( neq @ SV25 @ SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(576,plain,
! [SV28: $i] :
( ( ( ~ ( ssList @ ( sK6_SY117 @ SV28 ) ) )
= $false )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(577,plain,
! [SV28: $i] :
( ( ( ( tl @ SV28 )
!= ( sK6_SY117 @ SV28 ) )
= $false )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(578,plain,
! [SV62: $i,SV52: $i,SV29: $i] :
( ( ( frontsegP @ SV29 @ SV52 )
= $false )
| ( ( frontsegP @ ( app @ SV29 @ SV62 ) @ SV52 )
= $true )
| ( ( ssList @ SV62 )
= $false )
| ( ( ssList @ SV52 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(579,plain,
! [SV63: $i,SV53: $i,SV32: $i] :
( ( ( ~ ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SV63 ) ) )
= $false )
| ( ( segmentP @ SV32 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(580,plain,
! [SV34: $i,SV55: $i,SV64: $i] :
( ( ( ( app @ SV64 @ SV55 )
= ( app @ SV34 @ SV55 ) )
= $false )
| ( ( SV64 = SV34 )
= $true )
| ( ( ssList @ SV64 )
= $false )
| ( ( ssList @ SV55 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(581,plain,
! [SV1: $i,SV35: $i] :
( ( ( ! [SY131: $i] :
~ ~ ( ~ ( ssList @ SY131 )
| ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( ssList @ SY132 )
| ( ( app @ ( app @ SY131 @ SV35 ) @ SY132 )
!= SV1 ) ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(582,plain,
! [SV1: $i,SV35: $i] :
( ( ( ! [SY133: $i] :
~ ~ ( ~ ( ssList @ SY133 )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ( ssList @ SY134 )
| ( ( app @ ( app @ SY133 @ SV35 ) @ SY134 )
!= SV1 ) ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(583,plain,
! [SV2: $i,SV36: $i] :
( ( ( rearsegP @ SV36 @ SV2 )
= $false )
| ( ( rearsegP @ SV2 @ SV36 )
= $false )
| ( ( SV2 = SV36 )
= $true )
| ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(584,plain,
! [SV4: $i,SV37: $i] :
( ( ( ! [SY135: $i] :
~ ~ ( ~ ( ssList @ SY135 )
| ( ( app @ SV37 @ SY135 )
!= SV4 ) ) )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(585,plain,
! [SV4: $i,SV37: $i] :
( ( ( ! [SY136: $i] :
~ ~ ( ~ ( ssList @ SY136 )
| ( ( app @ SV37 @ SY136 )
!= SV4 ) ) )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(586,plain,
! [SV39: $i,SV9: $i] :
( ( ( SV9 = SV39 )
= $false )
| ( ( neq @ SV9 @ SV39 )
= $false )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(587,plain,
! [SV39: $i,SV9: $i] :
( ( ( SV9 = SV39 )
= $true )
| ( ( neq @ SV9 @ SV39 )
= $true )
| ( ( ssItem @ SV39 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(588,plain,
! [SV57: $i,SV40: $i,SV10: $i] :
( ( ( ~ ( frontsegP @ SV10 @ SV40 )
| ~ ( frontsegP @ SV40 @ SV57 ) )
= $true )
| ( ( frontsegP @ SV10 @ SV57 )
= $true )
| ( ( ssList @ SV57 )
= $false )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(589,plain,
( ( ssList @ sK4_SY139 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(590,plain,
( ( sK2_SX0 = sK4_SY139 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(591,plain,
! [SV65: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV65 ) )
| ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(592,plain,
( ( ssList @ sK7_SY159 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(593,plain,
( ( ~ ( ssList @ sK8_SY161 )
| ( ( app @ ( app @ sK5_SY155 @ sK7_SY159 ) @ sK8_SY161 )
!= sK3_SY125 )
| ( ( app @ sK5_SY155 @ sK8_SY161 )
!= sK4_SY139 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[564]) ).
thf(594,plain,
! [SV13: $i,SV41: $i] :
( ( ( ( nil != SV41 )
| ( nil != SV13 ) )
= $false )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(595,plain,
! [SV13: $i,SV41: $i] :
( ( ( ( nil != SV41 )
| ( nil != SV13 ) )
= $true )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(596,plain,
! [SV58: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( rearsegP @ SV16 @ SV43 )
| ~ ( rearsegP @ SV43 @ SV58 ) )
= $true )
| ( ( rearsegP @ SV16 @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(597,plain,
! [SV18: $i,SV45: $i] :
( ( ( ! [SY146: $i] :
~ ~ ( ~ ( ssList @ SY146 )
| ( ( app @ SY146 @ SV45 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(598,plain,
! [SV18: $i,SV45: $i] :
( ( ( ! [SY147: $i] :
~ ~ ( ~ ( ssList @ SY147 )
| ( ( app @ SY147 @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(599,plain,
! [SV19: $i,SV46: $i] :
( ( ( segmentP @ SV46 @ SV19 )
= $false )
| ( ( segmentP @ SV19 @ SV46 )
= $false )
| ( ( SV19 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(600,plain,
! [SV60: $i,SV47: $i,SV20: $i,SV66: $i] :
( ( ( ssList @ SV66 )
= $false )
| ( ( ~ ( segmentP @ SV20 @ SV47 )
| ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SV66 ) @ SV47 ) )
= $true )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(601,plain,
! [SV22: $i,SV49: $i] :
( ( ( frontsegP @ SV49 @ SV22 )
= $false )
| ( ( frontsegP @ SV22 @ SV49 )
= $false )
| ( ( SV22 = SV49 )
= $true )
| ( ( ssList @ SV49 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(602,plain,
! [SV51: $i,SV25: $i] :
( ( ( SV25 = SV51 )
= $false )
| ( ( neq @ SV25 @ SV51 )
= $false )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(603,plain,
! [SV51: $i,SV25: $i] :
( ( ( SV25 = SV51 )
= $true )
| ( ( neq @ SV25 @ SV51 )
= $true )
| ( ( ssList @ SV51 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(604,plain,
! [SV28: $i] :
( ( ( ssList @ ( sK6_SY117 @ SV28 ) )
= $true )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(605,plain,
! [SV28: $i] :
( ( ( ( tl @ SV28 )
= ( sK6_SY117 @ SV28 ) )
= $true )
| ( ( nil = SV28 )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(606,plain,
! [SV63: $i,SV53: $i,SV32: $i] :
( ( ( ~ ( segmentP @ SV32 @ SV53 )
| ~ ( segmentP @ SV53 @ SV63 ) )
= $true )
| ( ( segmentP @ SV32 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(607,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK9_SY131 @ SV1 @ SV35 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ SY162 )
!= SV1 ) ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[581]) ).
thf(608,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV67 )
| ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(609,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK10_SY135 @ SV4 @ SV37 ) )
| ( ( app @ SV37 @ ( sK10_SY135 @ SV4 @ SV37 ) )
!= SV4 ) ) )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[584]) ).
thf(610,plain,
! [SV4: $i,SV37: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV68 )
| ( ( app @ SV37 @ SV68 )
!= SV4 ) ) )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(611,plain,
! [SV57: $i,SV40: $i,SV10: $i] :
( ( ( ~ ( frontsegP @ SV10 @ SV40 ) )
= $true )
| ( ( ~ ( frontsegP @ SV40 @ SV57 ) )
= $true )
| ( ( frontsegP @ SV10 @ SV57 )
= $true )
| ( ( ssList @ SV57 )
= $false )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(612,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV65 ) ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(613,plain,
( ( ~ ( ssList @ sK8_SY161 )
| ( ( app @ ( app @ sK5_SY155 @ sK7_SY159 ) @ sK8_SY161 )
!= sK3_SY125 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(614,plain,
( ( ( app @ sK5_SY155 @ sK8_SY161 )
!= sK4_SY139 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(615,plain,
! [SV13: $i,SV41: $i] :
( ( ( nil != SV41 )
= $false )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(616,plain,
! [SV41: $i,SV13: $i] :
( ( ( nil != SV13 )
= $false )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(617,plain,
! [SV13: $i,SV41: $i] :
( ( ( nil != SV41 )
= $true )
| ( ( nil != SV13 )
= $true )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(618,plain,
! [SV58: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( rearsegP @ SV16 @ SV43 ) )
= $true )
| ( ( ~ ( rearsegP @ SV43 @ SV58 ) )
= $true )
| ( ( rearsegP @ SV16 @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(619,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK11_SY146 @ SV18 @ SV45 ) )
| ( ( app @ ( sK11_SY146 @ SV18 @ SV45 ) @ SV45 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[597]) ).
thf(620,plain,
! [SV18: $i,SV45: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV69 )
| ( ( app @ SV69 @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(621,plain,
! [SV66: $i,SV60: $i,SV47: $i,SV20: $i] :
( ( ( ~ ( segmentP @ SV20 @ SV47 ) )
= $true )
| ( ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SV66 ) @ SV47 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(622,plain,
! [SV63: $i,SV53: $i,SV32: $i] :
( ( ( ~ ( segmentP @ SV32 @ SV53 ) )
= $true )
| ( ( ~ ( segmentP @ SV53 @ SV63 ) )
= $true )
| ( ( segmentP @ SV32 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(623,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK9_SY131 @ SV1 @ SV35 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ SY162 )
!= SV1 ) ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(624,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ~ ( ~ ( ssList @ SV67 )
| ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(625,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK10_SY135 @ SV4 @ SV37 ) )
| ( ( app @ SV37 @ ( sK10_SY135 @ SV4 @ SV37 ) )
!= SV4 ) ) )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(626,plain,
! [SV4: $i,SV37: $i,SV68: $i] :
( ( ( ~ ( ~ ( ssList @ SV68 )
| ( ( app @ SV37 @ SV68 )
!= SV4 ) ) )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(627,plain,
! [SV57: $i,SV40: $i,SV10: $i] :
( ( ( frontsegP @ SV10 @ SV40 )
= $false )
| ( ( ~ ( frontsegP @ SV40 @ SV57 ) )
= $true )
| ( ( frontsegP @ SV10 @ SV57 )
= $true )
| ( ( ssList @ SV57 )
= $false )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(628,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV65 ) ) )
= $false )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(629,plain,
( ( ~ ( ssList @ sK8_SY161 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(630,plain,
( ( ( app @ ( app @ sK5_SY155 @ sK7_SY159 ) @ sK8_SY161 )
!= sK3_SY125 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(631,plain,
( ( ( app @ sK5_SY155 @ sK8_SY161 )
= sK4_SY139 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(632,plain,
! [SV13: $i,SV41: $i] :
( ( ( nil = SV41 )
= $true )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(633,plain,
! [SV41: $i,SV13: $i] :
( ( ( nil = SV13 )
= $true )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $false )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(634,plain,
! [SV13: $i,SV41: $i] :
( ( ( nil = SV41 )
= $false )
| ( ( nil != SV13 )
= $true )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(635,plain,
! [SV58: $i,SV43: $i,SV16: $i] :
( ( ( rearsegP @ SV16 @ SV43 )
= $false )
| ( ( ~ ( rearsegP @ SV43 @ SV58 ) )
= $true )
| ( ( rearsegP @ SV16 @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(636,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK11_SY146 @ SV18 @ SV45 ) )
| ( ( app @ ( sK11_SY146 @ SV18 @ SV45 ) @ SV45 )
!= SV18 ) ) )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(637,plain,
! [SV18: $i,SV45: $i,SV69: $i] :
( ( ( ~ ( ~ ( ssList @ SV69 )
| ( ( app @ SV69 @ SV45 )
!= SV18 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(638,plain,
! [SV66: $i,SV60: $i,SV47: $i,SV20: $i] :
( ( ( segmentP @ SV20 @ SV47 )
= $false )
| ( ( segmentP @ ( app @ ( app @ SV60 @ SV20 ) @ SV66 ) @ SV47 )
= $true )
| ( ( ssList @ SV66 )
= $false )
| ( ( ssList @ SV60 )
= $false )
| ( ( ssList @ SV47 )
= $false )
| ( ( ssList @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(639,plain,
! [SV63: $i,SV53: $i,SV32: $i] :
( ( ( segmentP @ SV32 @ SV53 )
= $false )
| ( ( ~ ( segmentP @ SV53 @ SV63 ) )
= $true )
| ( ( segmentP @ SV32 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(640,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( ssList @ ( sK9_SY131 @ SV1 @ SV35 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ SY162 )
!= SV1 ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(641,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ~ ( ssList @ SV67 )
| ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(642,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( ssList @ ( sK10_SY135 @ SV4 @ SV37 ) )
| ( ( app @ SV37 @ ( sK10_SY135 @ SV4 @ SV37 ) )
!= SV4 ) )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(643,plain,
! [SV4: $i,SV37: $i,SV68: $i] :
( ( ( ~ ( ssList @ SV68 )
| ( ( app @ SV37 @ SV68 )
!= SV4 ) )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(644,plain,
! [SV10: $i,SV57: $i,SV40: $i] :
( ( ( frontsegP @ SV40 @ SV57 )
= $false )
| ( ( frontsegP @ SV10 @ SV40 )
= $false )
| ( ( frontsegP @ SV10 @ SV57 )
= $true )
| ( ( ssList @ SV57 )
= $false )
| ( ( ssList @ SV40 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(645,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
| ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(646,plain,
( ( ssList @ sK8_SY161 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(647,plain,
( ( ( app @ ( app @ sK5_SY155 @ sK7_SY159 ) @ sK8_SY161 )
= sK3_SY125 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(648,plain,
! [SV41: $i,SV13: $i] :
( ( ( nil = SV13 )
= $false )
| ( ( nil = SV41 )
= $false )
| ( ( nil
= ( app @ SV13 @ SV41 ) )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(649,plain,
! [SV16: $i,SV58: $i,SV43: $i] :
( ( ( rearsegP @ SV43 @ SV58 )
= $false )
| ( ( rearsegP @ SV16 @ SV43 )
= $false )
| ( ( rearsegP @ SV16 @ SV58 )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(650,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( ssList @ ( sK11_SY146 @ SV18 @ SV45 ) )
| ( ( app @ ( sK11_SY146 @ SV18 @ SV45 ) @ SV45 )
!= SV18 ) )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(651,plain,
! [SV18: $i,SV45: $i,SV69: $i] :
( ( ( ~ ( ssList @ SV69 )
| ( ( app @ SV69 @ SV45 )
!= SV18 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(652,plain,
! [SV32: $i,SV63: $i,SV53: $i] :
( ( ( segmentP @ SV53 @ SV63 )
= $false )
| ( ( segmentP @ SV32 @ SV53 )
= $false )
| ( ( segmentP @ SV32 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(653,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ( ssList @ ( sK9_SY131 @ SV1 @ SV35 ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(654,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ SY162 )
!= SV1 ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(655,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ~ ( ssList @ SV67 ) )
= $true )
| ( ( ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(656,plain,
! [SV37: $i,SV4: $i] :
( ( ( ~ ( ssList @ ( sK10_SY135 @ SV4 @ SV37 ) ) )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(657,plain,
! [SV4: $i,SV37: $i] :
( ( ( ( app @ SV37 @ ( sK10_SY135 @ SV4 @ SV37 ) )
!= SV4 )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(658,plain,
! [SV4: $i,SV37: $i,SV68: $i] :
( ( ( ~ ( ssList @ SV68 ) )
= $true )
| ( ( ( app @ SV37 @ SV68 )
!= SV4 )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(659,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(660,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( ssList @ ( sK11_SY146 @ SV18 @ SV45 ) ) )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(661,plain,
! [SV45: $i,SV18: $i] :
( ( ( ( app @ ( sK11_SY146 @ SV18 @ SV45 ) @ SV45 )
!= SV18 )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(662,plain,
! [SV18: $i,SV45: $i,SV69: $i] :
( ( ( ~ ( ssList @ SV69 ) )
= $true )
| ( ( ( app @ SV69 @ SV45 )
!= SV18 )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(663,plain,
! [SV35: $i,SV1: $i] :
( ( ( ssList @ ( sK9_SY131 @ SV1 @ SV35 ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(664,plain,
! [SV35: $i,SV1: $i] :
( ( ( ~ ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ SY162 )
!= SV1 ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(665,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ssList @ SV67 )
= $false )
| ( ( ~ ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(666,plain,
! [SV37: $i,SV4: $i] :
( ( ( ssList @ ( sK10_SY135 @ SV4 @ SV37 ) )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(667,plain,
! [SV4: $i,SV37: $i] :
( ( ( ( app @ SV37 @ ( sK10_SY135 @ SV4 @ SV37 ) )
= SV4 )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(668,plain,
! [SV4: $i,SV37: $i,SV68: $i] :
( ( ( ssList @ SV68 )
= $false )
| ( ( ( app @ SV37 @ SV68 )
!= SV4 )
= $true )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(669,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) ) )
= $false )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(670,plain,
! [SV45: $i,SV18: $i] :
( ( ( ssList @ ( sK11_SY146 @ SV18 @ SV45 ) )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(671,plain,
! [SV45: $i,SV18: $i] :
( ( ( ( app @ ( sK11_SY146 @ SV18 @ SV45 ) @ SV45 )
= SV18 )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(672,plain,
! [SV18: $i,SV45: $i,SV69: $i] :
( ( ( ssList @ SV69 )
= $false )
| ( ( ( app @ SV69 @ SV45 )
!= SV18 )
= $true )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(673,plain,
! [SV35: $i,SV1: $i] :
( ( ( ! [SY162: $i] :
~ ~ ( ~ ( ssList @ SY162 )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ SY162 )
!= SV1 ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(674,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ~ ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) )
= $false )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(675,plain,
! [SV4: $i,SV68: $i,SV37: $i] :
( ( ( ( app @ SV37 @ SV68 )
= SV4 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( frontsegP @ SV4 @ SV37 )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(676,plain,
! [SV65: $i] :
( ( ( ~ ( ssList @ SV65 )
| ~ ( neq @ SV65 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(677,plain,
! [SV18: $i,SV45: $i,SV69: $i] :
( ( ( ( app @ SV69 @ SV45 )
= SV18 )
= $false )
| ( ( ssList @ SV69 )
= $false )
| ( ( rearsegP @ SV18 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(678,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK12_SY162 @ SV35 @ SV1 ) )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ ( sK12_SY162 @ SV35 @ SV1 ) )
!= SV1 ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[673]) ).
thf(679,plain,
! [SV1: $i,SV35: $i,SV67: $i] :
( ( ( ! [SY163: $i] :
~ ~ ( ~ ( ssList @ SY163 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SY163 )
!= SV1 ) ) )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(680,plain,
! [SV65: $i] :
( ( ( ~ ( ssList @ SV65 ) )
= $true )
| ( ( ~ ( neq @ SV65 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(681,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK12_SY162 @ SV35 @ SV1 ) )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ ( sK12_SY162 @ SV35 @ SV1 ) )
!= SV1 ) ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(682,plain,
! [SV1: $i,SV35: $i,SV67: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV70 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SV70 )
!= SV1 ) ) )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(683,plain,
! [SV65: $i] :
( ( ( ssList @ SV65 )
= $false )
| ( ( ~ ( neq @ SV65 @ nil ) )
= $true )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(684,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ( ssList @ ( sK12_SY162 @ SV35 @ SV1 ) )
| ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ ( sK12_SY162 @ SV35 @ SV1 ) )
!= SV1 ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(685,plain,
! [SV1: $i,SV35: $i,SV67: $i,SV70: $i] :
( ( ( ~ ( ~ ( ssList @ SV70 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SV70 )
!= SV1 ) ) )
= $false )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(686,plain,
! [SV65: $i] :
( ( ( neq @ SV65 @ nil )
= $false )
| ( ( ssList @ SV65 )
= $false )
| ( ( ~ ( segmentP @ sK2_SX0 @ SV65 ) )
= $true )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(687,plain,
! [SV1: $i,SV35: $i] :
( ( ( ~ ( ssList @ ( sK12_SY162 @ SV35 @ SV1 ) ) )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(688,plain,
! [SV35: $i,SV1: $i] :
( ( ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ ( sK12_SY162 @ SV35 @ SV1 ) )
!= SV1 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(689,plain,
! [SV1: $i,SV35: $i,SV67: $i,SV70: $i] :
( ( ( ~ ( ssList @ SV70 )
| ( ( app @ ( app @ SV67 @ SV35 ) @ SV70 )
!= SV1 ) )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(690,plain,
! [SV65: $i] :
( ( ( segmentP @ sK2_SX0 @ SV65 )
= $false )
| ( ( ssList @ SV65 )
= $false )
| ( ( neq @ SV65 @ nil )
= $false )
| ( ( ~ ( segmentP @ sK1_U @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(691,plain,
! [SV1: $i,SV35: $i] :
( ( ( ssList @ ( sK12_SY162 @ SV35 @ SV1 ) )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(692,plain,
! [SV35: $i,SV1: $i] :
( ( ( ( app @ ( app @ ( sK9_SY131 @ SV1 @ SV35 ) @ SV35 ) @ ( sK12_SY162 @ SV35 @ SV1 ) )
= SV1 )
= $true )
| ( ( segmentP @ SV1 @ SV35 )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(693,plain,
! [SV1: $i,SV35: $i,SV67: $i,SV70: $i] :
( ( ( ~ ( ssList @ SV70 ) )
= $true )
| ( ( ( app @ ( app @ SV67 @ SV35 ) @ SV70 )
!= SV1 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(694,plain,
! [SV65: $i] :
( ( ( segmentP @ sK1_U @ SV65 )
= $false )
| ( ( neq @ SV65 @ nil )
= $false )
| ( ( ssList @ SV65 )
= $false )
| ( ( segmentP @ sK2_SX0 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(695,plain,
! [SV1: $i,SV35: $i,SV67: $i,SV70: $i] :
( ( ( ssList @ SV70 )
= $false )
| ( ( ( app @ ( app @ SV67 @ SV35 ) @ SV70 )
!= SV1 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(696,plain,
! [SV1: $i,SV70: $i,SV35: $i,SV67: $i] :
( ( ( ( app @ ( app @ SV67 @ SV35 ) @ SV70 )
= SV1 )
= $false )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV67 )
= $false )
| ( ( segmentP @ SV1 @ SV35 )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(697,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[151,696,694,692,691,677,675,671,670,667,666,663,652,649,648,647,646,644,638,633,632,631,605,604,603,602,601,599,592,590,589,587,586,583,580,578,572,561,555,533,531,518,512,505,479,478,464,463,456,455,419,405,402,341,328,325,324,312,310,303,302,301,226,189,180,179,178,177,176,175,174]) ).
thf(698,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n006.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 15:58:52 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.75/5.60 .
% 26.75/5.60
% 26.75/5.60 No.of.Axioms: 43
% 26.75/5.60
% 26.75/5.60 Length.of.Defs: 0
% 26.75/5.60
% 26.75/5.60 Contains.Choice.Funs: false
% 26.75/5.60 ....................
% 26.75/5.60
% 26.75/5.60 ********************************
% 26.75/5.60 * All subproblems solved! *
% 26.75/5.60 ********************************
% 26.75/5.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:44,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:697,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.75/5.60
% 26.75/5.60 %**** Beginning of derivation protocol ****
% 26.75/5.60 % SZS output start CNFRefutation
% See solution above
% 26.75/5.61
% 26.75/5.61 %**** End of derivation protocol ****
% 26.75/5.61 %**** no. of clauses in derivation: 646 ****
% 26.75/5.61 %**** clause counter: 697 ****
% 26.75/5.61
% 26.75/5.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:44,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:697,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------