%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWC400+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 : n003.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 10:54:10 AM UTC 2026
% Result : Theorem 24.68s 5.14s
% Output : CNFRefutation 24.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 40
% Syntax : Number of formulae : 640 ( 213 unt; 0 typ; 0 def)
% Number of atoms : 6338 (2052 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 9194 (2075 ~;2108 |; 51 &;4619 @)
% ( 18 <=>; 323 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 10 con; 0-2 aty)
% Number of variables : 1530 ( 0 ^;1518 !; 12 ?;1530 :)
% 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_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY140,type,
sK4_SY140: $i ).
thf(tp_sK5_SY163,type,
sK5_SY163: $i ).
thf(tp_sK6_SY139,type,
sK6_SY139: $i ).
thf(tp_sK7_SY142,type,
sK7_SY142: $i ).
thf(tp_sK8_SY152,type,
sK8_SY152: $i > $i > $i ).
thf(tp_sK9_SY168,type,
sK9_SY168: $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(1,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( gt @ U @ V )
& ( gt @ V @ W ) )
=> ( gt @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).
thf(2,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
=> ~ ( gt @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
thf(6,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ~ ( lt @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
thf(7,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( geq @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
thf(8,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ W ) )
=> ( geq @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
thf(9,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
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(30,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
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(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(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(58,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(59,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(60,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( app @ V @ W ) @ U )
<=> ( ( memberP @ V @ U )
| ( memberP @ W @ U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(62,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( lt @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
thf(63,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
=> ~ ( lt @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
thf(65,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ( leq @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(66,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ W ) )
=> ( leq @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(67,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(70,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(77,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssItem @ X )
=> ( ( ( cons @ W @ U )
= ( cons @ X @ V ) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(78,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(79,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(80,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(81,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(89,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( segmentP @ U @ V )
<=> ? [W: $i] :
( ( ssList @ W )
& ? [X: $i] :
( ( ssList @ X )
& ( ( app @ ( app @ W @ V ) @ X )
= U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(94,axiom,
? [U: $i] :
( ( ssItem @ U )
& ? [V: $i] :
( ( ssItem @ V )
& ( U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
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 )
| ~ ( segmentP @ X @ W )
| ~ ( totalorderedP @ W )
| ! [Y: $i] :
( ( ssItem @ Y )
=> ( ~ ( memberP @ U @ Y )
| ( memberP @ V @ Y ) ) ) ) ) ) ) ),
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 )
| ~ ( segmentP @ X @ W )
| ~ ( totalorderedP @ W )
| ! [Y: $i] :
( ( ssItem @ Y )
=> ( ~ ( memberP @ U @ Y )
| ( memberP @ V @ Y ) ) ) ) ) ) ) ) )
= $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 )
| ~ ( segmentP @ X @ W )
| ~ ( totalorderedP @ W )
| ! [Y: $i] :
( ( ssItem @ Y )
=> ( ~ ( memberP @ U @ Y )
| ( memberP @ V @ Y ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( gt @ U @ V )
& ( gt @ V @ W ) )
=> ( gt @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(100,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
=> ~ ( gt @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(101,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( lt @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(102,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( geq @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(103,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ W ) )
=> ( geq @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(104,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(105,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(106,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(107,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(108,plain,
( ( totalorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(109,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(110,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(111,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(112,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(113,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(114,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(115,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(116,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(117,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(118,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(119,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(120,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(121,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(122,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(123,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( app @ V @ W ) @ U )
<=> ( ( memberP @ V @ U )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(124,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( lt @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(125,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
=> ~ ( lt @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(126,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( leq @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(127,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ W ) )
=> ( leq @ U @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(128,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(129,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(130,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssItem @ X )
=> ( ( ( cons @ W @ U )
= ( cons @ X @ V ) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(131,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(132,plain,
( ( ssList @ nil )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(134,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(135,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(136,plain,
( ( ? [U: $i] :
( ( ssItem @ U )
& ? [V: $i] :
( ( ssItem @ V )
& ( U != V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(137,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(138,plain,
( ( ( ssList @ sK1_U )
=> ! [SY88: $i] :
( ( ssList @ SY88 )
=> ! [SY89: $i] :
( ( ssList @ SY89 )
=> ! [SY90: $i] :
( ( ssList @ SY90 )
=> ( ( SY88 != SY90 )
| ( sK1_U != SY89 )
| ~ ( segmentP @ SY90 @ SY89 )
| ~ ( totalorderedP @ SY89 )
| ! [SY91: $i] :
( ( ssItem @ SY91 )
=> ( ~ ( memberP @ sK1_U @ SY91 )
| ( memberP @ SY88 @ SY91 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(139,plain,
( ( ssList @ sK1_U )
= $true ),
inference(standard_cnf,[status(thm)],[138]) ).
thf(140,plain,
( ( ! [SY88: $i] :
( ( ssList @ SY88 )
=> ! [SY89: $i] :
( ( ssList @ SY89 )
=> ! [SY90: $i] :
( ( ssList @ SY90 )
=> ( ( SY88 != SY90 )
| ( sK1_U != SY89 )
| ~ ( segmentP @ SY90 @ SY89 )
| ~ ( totalorderedP @ SY89 )
| ! [SY91: $i] :
( ( ssItem @ SY91 )
=> ( ~ ( memberP @ sK1_U @ SY91 )
| ( memberP @ SY88 @ SY91 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[138]) ).
thf(141,plain,
( ( ~ ! [SY88: $i] :
( ( ssList @ SY88 )
=> ! [SY89: $i] :
( ( ssList @ SY89 )
=> ! [SY90: $i] :
( ( ssList @ SY90 )
=> ( ( SY88 != SY90 )
| ( sK1_U != SY89 )
| ~ ( segmentP @ SY90 @ SY89 )
| ~ ( totalorderedP @ SY89 )
| ! [SY91: $i] :
( ( ssItem @ SY91 )
=> ( ~ ( memberP @ sK1_U @ SY91 )
| ( memberP @ SY88 @ SY91 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[140]) ).
thf(142,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(143,plain,
( ( ? [U: $i] :
( ( ssItem @ U )
& ? [V: $i] :
( ( ssItem @ V )
& ( U != V ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(144,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)],[135]) ).
thf(145,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(146,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ssList @ ( cons @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(147,plain,
( ( ssList @ nil )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(148,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( cons @ V @ U )
!= U ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(149,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ! [X: $i] :
( ( ssItem @ X )
=> ( ( ( cons @ W @ U )
= ( cons @ X @ V ) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(150,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(152,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( leq @ U @ V )
& ( leq @ V @ W ) )
=> ( leq @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(153,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( leq @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(154,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( lt @ U @ V )
=> ~ ( lt @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(155,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( lt @ U @ V )
& ( lt @ V @ W ) )
=> ( lt @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(156,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( app @ V @ W ) @ U )
<=> ( ( memberP @ V @ U )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(157,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( memberP @ ( cons @ V @ W ) @ U )
<=> ( ( U = V )
| ( memberP @ W @ U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(158,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( memberP @ nil @ U ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(159,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)],[120]) ).
thf(160,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(161,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
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)],[117]) ).
thf(163,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(164,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(165,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)],[114]) ).
thf(166,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(167,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(168,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)],[111]) ).
thf(169,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(170,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(171,plain,
( ( totalorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(172,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)],[107]) ).
thf(173,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)],[106]) ).
thf(174,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)],[105]) ).
thf(175,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(176,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( geq @ U @ V )
& ( geq @ V @ W ) )
=> ( geq @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(177,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ( geq @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(178,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ~ ( lt @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(179,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( gt @ U @ V )
=> ~ ( gt @ V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(180,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ! [W: $i] :
( ( ssItem @ W )
=> ( ( ( gt @ U @ V )
& ( gt @ V @ W ) )
=> ( gt @ U @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(181,plain,
( ( ssList @ sK1_U )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(182,plain,
( ( ~ ! [SY88: $i] :
( ( ssList @ SY88 )
=> ! [SY89: $i] :
( ( ssList @ SY89 )
=> ! [SY90: $i] :
( ( ssList @ SY90 )
=> ( ( SY88 != SY90 )
| ( sK1_U != SY89 )
| ~ ( segmentP @ SY90 @ SY89 )
| ~ ( totalorderedP @ SY89 )
| ! [SY91: $i] :
( ( ssItem @ SY91 )
=> ( ~ ( memberP @ sK1_U @ SY91 )
| ( memberP @ SY88 @ SY91 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(183,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( geq @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(184,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ! [SX3: $i] :
( ~ ( ssItem @ SX3 )
| ( ( cons @ SX2 @ SX0 )
!= ( cons @ SX3 @ SX1 ) )
| ~ ( ( SX2 != SX3 )
| ( SX1 != SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(185,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(186,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)],[173]) ).
thf(187,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ~ ( lt @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(188,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( segmentP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(189,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ~ ( memberP @ nil @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(190,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(191,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( lt @ SX0 @ SX1 )
| ~ ( lt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( lt @ SX0 @ SX1 )
| ~ ( lt @ SX1 @ SX2 ) )
| ( lt @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(193,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)],[165]) ).
thf(194,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ssList @ ( cons @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(195,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SX1 @ SX2 ) @ SX0 )
| ( memberP @ SX1 @ SX0 )
| ( memberP @ SX2 @ SX0 ) )
| ~ ( ~ ( ( memberP @ SX1 @ SX0 )
| ( memberP @ SX2 @ SX0 ) )
| ( memberP @ ( app @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(196,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(197,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(198,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ( segmentP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(199,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(200,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)],[174]) ).
thf(201,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ( leq @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(202,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ~ ~ ( ~ ( geq @ SX0 @ SX1 )
| ~ ( geq @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(203,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(204,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ( ( cons @ SX1 @ SX0 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(205,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(206,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = SX1 )
| ( memberP @ SX2 @ SX0 ) )
| ~ ( ~ ( ( SX0 = SX1 )
| ( memberP @ SX2 @ SX0 ) )
| ( memberP @ ( cons @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(207,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)],[144]) ).
thf(208,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)],[142]) ).
thf(209,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(210,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ( ssList @ ( app @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(211,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)],[172]) ).
thf(212,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( ssItem @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(213,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( geq @ SX0 @ SX1 )
| ~ ( geq @ SX1 @ SX2 ) )
| ( geq @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(214,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)],[159]) ).
thf(215,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ( frontsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(216,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(217,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)],[168]) ).
thf(218,plain,
( ( ! [SX0: $i] :
( ~ ( ssItem @ SX0 )
| ! [SX1: $i] :
( ~ ( ssItem @ SX1 )
| ! [SX2: $i] :
( ~ ( ssItem @ SX2 )
| ~ ~ ( ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX2 ) )
| ( gt @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(219,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)],[145]) ).
thf(220,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( segmentP @ SX2 @ SX1 )
| ~ ( totalorderedP @ SX1 )
| ! [SX3: $i] :
( ~ ( ssItem @ SX3 )
| ~ ( memberP @ sK1_U @ SX3 )
| ( memberP @ SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(221,plain,
! [SV1: $i] :
( ( ~ ( ssItem @ SV1 )
| ( geq @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(222,plain,
! [SV2: $i] :
( ( ~ ( ssList @ SV2 )
| ! [SY92: $i] :
( ~ ( ssList @ SY92 )
| ! [SY93: $i] :
( ~ ( ssItem @ SY93 )
| ! [SY94: $i] :
( ~ ( ssItem @ SY94 )
| ( ( cons @ SY93 @ SV2 )
!= ( cons @ SY94 @ SY92 ) )
| ~ ( ( SY93 != SY94 )
| ( SY92 != SV2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(223,plain,
! [SV3: $i] :
( ( ~ ( ssList @ SV3 )
| ! [SY95: $i] :
( ~ ( ssList @ SY95 )
| ~ ~ ( ~ ( rearsegP @ SV3 @ SY95 )
| ~ ( rearsegP @ SY95 @ SV3 ) )
| ( SV3 = SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(224,plain,
! [SV4: $i] :
( ( ~ ( ssList @ SV4 )
| ! [SY96: $i] :
( ~ ( ssList @ SY96 )
| ! [SY97: $i] :
( ~ ( ssList @ SY97 )
| ( ( app @ SY96 @ SY97 )
!= ( app @ SY96 @ SV4 ) )
| ( SY97 = SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(225,plain,
! [SV5: $i] :
( ( ~ ( ssItem @ SV5 )
| ~ ( lt @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(226,plain,
! [SV6: $i] :
( ( ~ ( ssList @ SV6 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SV6 )
| ( nil = SV6 ) )
| ~ ( ( nil != SV6 )
| ( segmentP @ nil @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(227,plain,
! [SV7: $i] :
( ( ~ ( ssItem @ SV7 )
| ~ ( memberP @ nil @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(228,plain,
! [SV8: $i] :
( ( ~ ( ssItem @ SV8 )
| ! [SY98: $i] :
( ~ ( ssItem @ SY98 )
| ~ ~ ( ~ ( leq @ SV8 @ SY98 )
| ~ ( leq @ SY98 @ SV8 ) )
| ( SV8 = SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(229,plain,
! [SV9: $i] :
( ( ~ ( ssItem @ SV9 )
| ! [SY99: $i] :
( ~ ( ssItem @ SY99 )
| ~ ( lt @ SV9 @ SY99 )
| ~ ( lt @ SY99 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(230,plain,
! [SV10: $i] :
( ( ~ ( ssItem @ SV10 )
| ! [SY100: $i] :
( ~ ( ssItem @ SY100 )
| ! [SY101: $i] :
( ~ ( ssItem @ SY101 )
| ~ ~ ( ~ ( lt @ SV10 @ SY100 )
| ~ ( lt @ SY100 @ SY101 ) )
| ( lt @ SV10 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(231,plain,
! [SV11: $i] :
( ( ~ ( ssList @ SV11 )
| ! [SY102: $i] :
( ~ ( ssList @ SY102 )
| ! [SY103: $i] :
( ~ ( ssList @ SY103 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SY102 )
| ~ ( segmentP @ SY102 @ SY103 ) )
| ( segmentP @ SV11 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(232,plain,
! [SV12: $i] :
( ( ~ ( ssList @ SV12 )
| ! [SY104: $i] :
( ~ ( ssItem @ SY104 )
| ( ssList @ ( cons @ SY104 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(233,plain,
! [SV13: $i] :
( ( ~ ( ssItem @ SV13 )
| ! [SY105: $i] :
( ~ ( ssList @ SY105 )
| ! [SY106: $i] :
( ~ ( ssList @ SY106 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY105 @ SY106 ) @ SV13 )
| ( memberP @ SY105 @ SV13 )
| ( memberP @ SY106 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SY105 @ SV13 )
| ( memberP @ SY106 @ SV13 ) )
| ( memberP @ ( app @ SY105 @ SY106 ) @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(234,plain,
! [SV14: $i] :
( ( ~ ( ssList @ SV14 )
| ( segmentP @ SV14 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(235,plain,
! [SV15: $i] :
( ( ~ ( ssList @ SV15 )
| ( rearsegP @ SV15 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(236,plain,
! [SV16: $i] :
( ( ~ ( ssList @ SV16 )
| ! [SY107: $i] :
( ~ ( ssList @ SY107 )
| ~ ~ ( ~ ( segmentP @ SV16 @ SY107 )
| ~ ( segmentP @ SY107 @ SV16 ) )
| ( SV16 = SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(237,plain,
! [SV17: $i] :
( ( ~ ( ssItem @ SV17 )
| ! [SY108: $i] :
( ~ ( ssItem @ SY108 )
| ~ ( gt @ SV17 @ SY108 )
| ~ ( gt @ SY108 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(238,plain,
! [SV18: $i] :
( ( ~ ( ssList @ SV18 )
| ! [SY109: $i] :
( ~ ( ssList @ SY109 )
| ! [SY110: $i] :
( ~ ( ssList @ SY110 )
| ( ( app @ ( app @ SV18 @ SY109 ) @ SY110 )
= ( app @ SV18 @ ( app @ SY109 @ SY110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(239,plain,
! [SV19: $i] :
( ( ~ ( ssItem @ SV19 )
| ( leq @ SV19 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(240,plain,
! [SV20: $i] :
( ( ~ ( ssItem @ SV20 )
| ! [SY111: $i] :
( ~ ( ssItem @ SY111 )
| ~ ~ ( ~ ( geq @ SV20 @ SY111 )
| ~ ( geq @ SY111 @ SV20 ) )
| ( SV20 = SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(241,plain,
! [SV21: $i] :
( ( ~ ( ssList @ SV21 )
| ! [SY112: $i] :
( ~ ( ssList @ SY112 )
| ! [SY113: $i] :
( ~ ( ssList @ SY113 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SY112 )
| ~ ( rearsegP @ SY112 @ SY113 ) )
| ( rearsegP @ SV21 @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(242,plain,
! [SV22: $i] :
( ( ~ ( ssList @ SV22 )
| ! [SY114: $i] :
( ~ ( ssItem @ SY114 )
| ( ( cons @ SY114 @ SV22 )
!= SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(243,plain,
! [SV23: $i] :
( ( ~ ( ssList @ SV23 )
| ( segmentP @ SV23 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(244,plain,
! [SV24: $i] :
( ( ~ ( ssItem @ SV24 )
| ! [SY115: $i] :
( ~ ( ssItem @ SY115 )
| ! [SY116: $i] :
( ~ ( ssList @ SY116 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY115 @ SY116 ) @ SV24 )
| ( SV24 = SY115 )
| ( memberP @ SY116 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SY115 )
| ( memberP @ SY116 @ SV24 ) )
| ( memberP @ ( cons @ SY115 @ SY116 ) @ SV24 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(245,plain,
! [SV25: $i] :
( ( ~ ( ssList @ SV25 )
| ! [SY117: $i] :
( ~ ( ssList @ SY117 )
| ~ ( ~ ( ~ ( segmentP @ SV25 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( ssList @ SY118 )
| ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( ssList @ SY119 )
| ( ( app @ ( app @ SY118 @ SY117 ) @ SY119 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( ssList @ SY120 )
| ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( ssList @ SY121 )
| ( ( app @ ( app @ SY120 @ SY117 ) @ SY121 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(246,plain,
! [SV26: $i] :
( ( ~ ( ssItem @ SV26 )
| ! [SY122: $i] :
( ~ ( ssItem @ SY122 )
| ~ ( ~ ( ~ ( neq @ SV26 @ SY122 )
| ( SV26 != SY122 ) )
| ~ ( ~ ( ( SV26 != SY122 ) )
| ( neq @ SV26 @ SY122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(247,plain,
! [SV27: $i] :
( ( ~ ( ssList @ SV27 )
| ( frontsegP @ SV27 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(248,plain,
! [SV28: $i] :
( ( ~ ( ssList @ SV28 )
| ! [SY123: $i] :
( ~ ( ssList @ SY123 )
| ( ssList @ ( app @ SV28 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(249,plain,
! [SV29: $i] :
( ( ~ ( ssList @ SV29 )
| ! [SY124: $i] :
( ~ ( ssList @ SY124 )
| ! [SY125: $i] :
( ~ ( ssList @ SY125 )
| ( ( app @ SY125 @ SY124 )
!= ( app @ SV29 @ SY124 ) )
| ( SY125 = SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(250,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( ssItem @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ssItem @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(251,plain,
! [SV30: $i] :
( ( ~ ( ssItem @ SV30 )
| ! [SY126: $i] :
( ~ ( ssItem @ SY126 )
| ! [SY127: $i] :
( ~ ( ssItem @ SY127 )
| ~ ~ ( ~ ( geq @ SV30 @ SY126 )
| ~ ( geq @ SY126 @ SY127 ) )
| ( geq @ SV30 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(252,plain,
! [SV31: $i] :
( ( ~ ( ssList @ SV31 )
| ! [SY128: $i] :
( ~ ( ssList @ SY128 )
| ! [SY129: $i] :
( ~ ( ssList @ SY129 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SY128 )
| ~ ( frontsegP @ SY128 @ SY129 ) )
| ( frontsegP @ SV31 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(253,plain,
! [SV32: $i] :
( ( ~ ( ssList @ SV32 )
| ! [SY130: $i] :
( ~ ( ssList @ SY130 )
| ~ ~ ( ~ ( frontsegP @ SV32 @ SY130 )
| ~ ( frontsegP @ SY130 @ SV32 ) )
| ( SV32 = SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(254,plain,
! [SV33: $i] :
( ( ~ ( ssItem @ SV33 )
| ! [SY131: $i] :
( ~ ( ssItem @ SY131 )
| ! [SY132: $i] :
( ~ ( ssItem @ SY132 )
| ~ ~ ( ~ ( leq @ SV33 @ SY131 )
| ~ ( leq @ SY131 @ SY132 ) )
| ( leq @ SV33 @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(255,plain,
! [SV34: $i] :
( ( ~ ( ssList @ SV34 )
| ! [SY133: $i] :
( ~ ( ssList @ SY133 )
| ! [SY134: $i] :
( ~ ( ssList @ SY134 )
| ! [SY135: $i] :
( ~ ( ssList @ SY135 )
| ~ ( segmentP @ SV34 @ SY133 )
| ( segmentP @ ( app @ ( app @ SY134 @ SV34 ) @ SY135 ) @ SY133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(256,plain,
! [SV35: $i] :
( ( ~ ( ssItem @ SV35 )
| ! [SY136: $i] :
( ~ ( ssItem @ SY136 )
| ! [SY137: $i] :
( ~ ( ssItem @ SY137 )
| ~ ~ ( ~ ( gt @ SV35 @ SY136 )
| ~ ( gt @ SY136 @ SY137 ) )
| ( gt @ SV35 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(257,plain,
! [SV36: $i] :
( ( ~ ( ssList @ SV36 )
| ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ( ~ ( ~ ( neq @ SV36 @ SY138 )
| ( SV36 != SY138 ) )
| ~ ( ~ ( ( SV36 != SY138 ) )
| ( neq @ SV36 @ SY138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(258,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( segmentP @ SX2 @ SX1 )
| ~ ( totalorderedP @ SX1 )
| ! [SX3: $i] :
( ~ ( ssItem @ SX3 )
| ~ ( memberP @ sK1_U @ SX3 )
| ( memberP @ SX0 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(259,plain,
! [SV1: $i] :
( ( ( ~ ( ssItem @ SV1 ) )
= $true )
| ( ( geq @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(260,plain,
! [SV2: $i] :
( ( ( ~ ( ssList @ SV2 ) )
= $true )
| ( ( ! [SY92: $i] :
( ~ ( ssList @ SY92 )
| ! [SY93: $i] :
( ~ ( ssItem @ SY93 )
| ! [SY94: $i] :
( ~ ( ssItem @ SY94 )
| ( ( cons @ SY93 @ SV2 )
!= ( cons @ SY94 @ SY92 ) )
| ~ ( ( SY93 != SY94 )
| ( SY92 != SV2 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(261,plain,
! [SV3: $i] :
( ( ( ~ ( ssList @ SV3 ) )
= $true )
| ( ( ! [SY95: $i] :
( ~ ( ssList @ SY95 )
| ~ ~ ( ~ ( rearsegP @ SV3 @ SY95 )
| ~ ( rearsegP @ SY95 @ SV3 ) )
| ( SV3 = SY95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(262,plain,
! [SV4: $i] :
( ( ( ~ ( ssList @ SV4 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( ssList @ SY96 )
| ! [SY97: $i] :
( ~ ( ssList @ SY97 )
| ( ( app @ SY96 @ SY97 )
!= ( app @ SY96 @ SV4 ) )
| ( SY97 = SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(263,plain,
! [SV5: $i] :
( ( ( ~ ( ssItem @ SV5 ) )
= $true )
| ( ( ~ ( lt @ SV5 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(264,plain,
! [SV6: $i] :
( ( ( ~ ( ssList @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV6 )
| ( nil = SV6 ) )
| ~ ( ( nil != SV6 )
| ( segmentP @ nil @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(265,plain,
! [SV7: $i] :
( ( ( ~ ( ssItem @ SV7 ) )
= $true )
| ( ( ~ ( memberP @ nil @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(266,plain,
! [SV8: $i] :
( ( ( ~ ( ssItem @ SV8 ) )
= $true )
| ( ( ! [SY98: $i] :
( ~ ( ssItem @ SY98 )
| ~ ~ ( ~ ( leq @ SV8 @ SY98 )
| ~ ( leq @ SY98 @ SV8 ) )
| ( SV8 = SY98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(267,plain,
! [SV9: $i] :
( ( ( ~ ( ssItem @ SV9 ) )
= $true )
| ( ( ! [SY99: $i] :
( ~ ( ssItem @ SY99 )
| ~ ( lt @ SV9 @ SY99 )
| ~ ( lt @ SY99 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(268,plain,
! [SV10: $i] :
( ( ( ~ ( ssItem @ SV10 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( ssItem @ SY100 )
| ! [SY101: $i] :
( ~ ( ssItem @ SY101 )
| ~ ~ ( ~ ( lt @ SV10 @ SY100 )
| ~ ( lt @ SY100 @ SY101 ) )
| ( lt @ SV10 @ SY101 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(269,plain,
! [SV11: $i] :
( ( ( ~ ( ssList @ SV11 ) )
= $true )
| ( ( ! [SY102: $i] :
( ~ ( ssList @ SY102 )
| ! [SY103: $i] :
( ~ ( ssList @ SY103 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SY102 )
| ~ ( segmentP @ SY102 @ SY103 ) )
| ( segmentP @ SV11 @ SY103 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(270,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ SV12 ) )
= $true )
| ( ( ! [SY104: $i] :
( ~ ( ssItem @ SY104 )
| ( ssList @ ( cons @ SY104 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(271,plain,
! [SV13: $i] :
( ( ( ~ ( ssItem @ SV13 ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( ssList @ SY105 )
| ! [SY106: $i] :
( ~ ( ssList @ SY106 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY105 @ SY106 ) @ SV13 )
| ( memberP @ SY105 @ SV13 )
| ( memberP @ SY106 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SY105 @ SV13 )
| ( memberP @ SY106 @ SV13 ) )
| ( memberP @ ( app @ SY105 @ SY106 ) @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(272,plain,
! [SV14: $i] :
( ( ( ~ ( ssList @ SV14 ) )
= $true )
| ( ( segmentP @ SV14 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(273,plain,
! [SV15: $i] :
( ( ( ~ ( ssList @ SV15 ) )
= $true )
| ( ( rearsegP @ SV15 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(274,plain,
! [SV16: $i] :
( ( ( ~ ( ssList @ SV16 ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( ssList @ SY107 )
| ~ ~ ( ~ ( segmentP @ SV16 @ SY107 )
| ~ ( segmentP @ SY107 @ SV16 ) )
| ( SV16 = SY107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(275,plain,
! [SV17: $i] :
( ( ( ~ ( ssItem @ SV17 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( ssItem @ SY108 )
| ~ ( gt @ SV17 @ SY108 )
| ~ ( gt @ SY108 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(276,plain,
! [SV18: $i] :
( ( ( ~ ( ssList @ SV18 ) )
= $true )
| ( ( ! [SY109: $i] :
( ~ ( ssList @ SY109 )
| ! [SY110: $i] :
( ~ ( ssList @ SY110 )
| ( ( app @ ( app @ SV18 @ SY109 ) @ SY110 )
= ( app @ SV18 @ ( app @ SY109 @ SY110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(277,plain,
! [SV19: $i] :
( ( ( ~ ( ssItem @ SV19 ) )
= $true )
| ( ( leq @ SV19 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(278,plain,
! [SV20: $i] :
( ( ( ~ ( ssItem @ SV20 ) )
= $true )
| ( ( ! [SY111: $i] :
( ~ ( ssItem @ SY111 )
| ~ ~ ( ~ ( geq @ SV20 @ SY111 )
| ~ ( geq @ SY111 @ SV20 ) )
| ( SV20 = SY111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(279,plain,
! [SV21: $i] :
( ( ( ~ ( ssList @ SV21 ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( ssList @ SY112 )
| ! [SY113: $i] :
( ~ ( ssList @ SY113 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SY112 )
| ~ ( rearsegP @ SY112 @ SY113 ) )
| ( rearsegP @ SV21 @ SY113 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(280,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ SV22 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( ssItem @ SY114 )
| ( ( cons @ SY114 @ SV22 )
!= SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(281,plain,
! [SV23: $i] :
( ( ( ~ ( ssList @ SV23 ) )
= $true )
| ( ( segmentP @ SV23 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(282,plain,
! [SV24: $i] :
( ( ( ~ ( ssItem @ SV24 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( ssItem @ SY115 )
| ! [SY116: $i] :
( ~ ( ssList @ SY116 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY115 @ SY116 ) @ SV24 )
| ( SV24 = SY115 )
| ( memberP @ SY116 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SY115 )
| ( memberP @ SY116 @ SV24 ) )
| ( memberP @ ( cons @ SY115 @ SY116 ) @ SV24 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(283,plain,
! [SV25: $i] :
( ( ( ~ ( ssList @ SV25 ) )
= $true )
| ( ( ! [SY117: $i] :
( ~ ( ssList @ SY117 )
| ~ ( ~ ( ~ ( segmentP @ SV25 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( ssList @ SY118 )
| ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( ssList @ SY119 )
| ( ( app @ ( app @ SY118 @ SY117 ) @ SY119 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( ssList @ SY120 )
| ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( ssList @ SY121 )
| ( ( app @ ( app @ SY120 @ SY117 ) @ SY121 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SY117 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(284,plain,
! [SV26: $i] :
( ( ( ~ ( ssItem @ SV26 ) )
= $true )
| ( ( ! [SY122: $i] :
( ~ ( ssItem @ SY122 )
| ~ ( ~ ( ~ ( neq @ SV26 @ SY122 )
| ( SV26 != SY122 ) )
| ~ ( ~ ( ( SV26 != SY122 ) )
| ( neq @ SV26 @ SY122 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(285,plain,
! [SV27: $i] :
( ( ( ~ ( ssList @ SV27 ) )
= $true )
| ( ( frontsegP @ SV27 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(286,plain,
! [SV28: $i] :
( ( ( ~ ( ssList @ SV28 ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( ssList @ SY123 )
| ( ssList @ ( app @ SV28 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(287,plain,
! [SV29: $i] :
( ( ( ~ ( ssList @ SV29 ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( ssList @ SY124 )
| ! [SY125: $i] :
( ~ ( ssList @ SY125 )
| ( ( app @ SY125 @ SY124 )
!= ( app @ SV29 @ SY124 ) )
| ( SY125 = SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(288,plain,
( ( ~ ~ ( ~ ( ssItem @ sK2_SX0 )
| ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( ssItem @ SY139 )
| ~ ( ( sK2_SX0 != SY139 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[250]) ).
thf(289,plain,
! [SV30: $i] :
( ( ( ~ ( ssItem @ SV30 ) )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( ssItem @ SY126 )
| ! [SY127: $i] :
( ~ ( ssItem @ SY127 )
| ~ ~ ( ~ ( geq @ SV30 @ SY126 )
| ~ ( geq @ SY126 @ SY127 ) )
| ( geq @ SV30 @ SY127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(290,plain,
! [SV31: $i] :
( ( ( ~ ( ssList @ SV31 ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( ssList @ SY128 )
| ! [SY129: $i] :
( ~ ( ssList @ SY129 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SY128 )
| ~ ( frontsegP @ SY128 @ SY129 ) )
| ( frontsegP @ SV31 @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(291,plain,
! [SV32: $i] :
( ( ( ~ ( ssList @ SV32 ) )
= $true )
| ( ( ! [SY130: $i] :
( ~ ( ssList @ SY130 )
| ~ ~ ( ~ ( frontsegP @ SV32 @ SY130 )
| ~ ( frontsegP @ SY130 @ SV32 ) )
| ( SV32 = SY130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(292,plain,
! [SV33: $i] :
( ( ( ~ ( ssItem @ SV33 ) )
= $true )
| ( ( ! [SY131: $i] :
( ~ ( ssItem @ SY131 )
| ! [SY132: $i] :
( ~ ( ssItem @ SY132 )
| ~ ~ ( ~ ( leq @ SV33 @ SY131 )
| ~ ( leq @ SY131 @ SY132 ) )
| ( leq @ SV33 @ SY132 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(293,plain,
! [SV34: $i] :
( ( ( ~ ( ssList @ SV34 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( ssList @ SY133 )
| ! [SY134: $i] :
( ~ ( ssList @ SY134 )
| ! [SY135: $i] :
( ~ ( ssList @ SY135 )
| ~ ( segmentP @ SV34 @ SY133 )
| ( segmentP @ ( app @ ( app @ SY134 @ SV34 ) @ SY135 ) @ SY133 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(294,plain,
! [SV35: $i] :
( ( ( ~ ( ssItem @ SV35 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( ssItem @ SY136 )
| ! [SY137: $i] :
( ~ ( ssItem @ SY137 )
| ~ ~ ( ~ ( gt @ SV35 @ SY136 )
| ~ ( gt @ SY136 @ SY137 ) )
| ( gt @ SV35 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(295,plain,
! [SV36: $i] :
( ( ( ~ ( ssList @ SV36 ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ( ~ ( ~ ( neq @ SV36 @ SY138 )
| ( SV36 != SY138 ) )
| ~ ( ~ ( ( SV36 != SY138 ) )
| ( neq @ SV36 @ SY138 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(296,plain,
( ( ~ ( ssList @ sK3_SX0 )
| ! [SY140: $i] :
( ~ ( ssList @ SY140 )
| ! [SY141: $i] :
( ~ ( ssList @ SY141 )
| ( sK3_SX0 != SY141 )
| ( sK1_U != SY140 )
| ~ ( segmentP @ SY141 @ SY140 )
| ~ ( totalorderedP @ SY140 )
| ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[258]) ).
thf(297,plain,
! [SV1: $i] :
( ( ( ssItem @ SV1 )
= $false )
| ( ( geq @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(298,plain,
! [SV2: $i] :
( ( ( ssList @ SV2 )
= $false )
| ( ( ! [SY92: $i] :
( ~ ( ssList @ SY92 )
| ! [SY93: $i] :
( ~ ( ssItem @ SY93 )
| ! [SY94: $i] :
( ~ ( ssItem @ SY94 )
| ( ( cons @ SY93 @ SV2 )
!= ( cons @ SY94 @ SY92 ) )
| ~ ( ( SY93 != SY94 )
| ( SY92 != SV2 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(299,plain,
! [SV3: $i] :
( ( ( ssList @ SV3 )
= $false )
| ( ( ! [SY95: $i] :
( ~ ( ssList @ SY95 )
| ~ ~ ( ~ ( rearsegP @ SV3 @ SY95 )
| ~ ( rearsegP @ SY95 @ SV3 ) )
| ( SV3 = SY95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(300,plain,
! [SV4: $i] :
( ( ( ssList @ SV4 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( ssList @ SY96 )
| ! [SY97: $i] :
( ~ ( ssList @ SY97 )
| ( ( app @ SY96 @ SY97 )
!= ( app @ SY96 @ SV4 ) )
| ( SY97 = SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(301,plain,
! [SV5: $i] :
( ( ( ssItem @ SV5 )
= $false )
| ( ( ~ ( lt @ SV5 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(302,plain,
! [SV6: $i] :
( ( ( ssList @ SV6 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV6 )
| ( nil = SV6 ) )
| ~ ( ( nil != SV6 )
| ( segmentP @ nil @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(303,plain,
! [SV7: $i] :
( ( ( ssItem @ SV7 )
= $false )
| ( ( ~ ( memberP @ nil @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(304,plain,
! [SV8: $i] :
( ( ( ssItem @ SV8 )
= $false )
| ( ( ! [SY98: $i] :
( ~ ( ssItem @ SY98 )
| ~ ~ ( ~ ( leq @ SV8 @ SY98 )
| ~ ( leq @ SY98 @ SV8 ) )
| ( SV8 = SY98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(305,plain,
! [SV9: $i] :
( ( ( ssItem @ SV9 )
= $false )
| ( ( ! [SY99: $i] :
( ~ ( ssItem @ SY99 )
| ~ ( lt @ SV9 @ SY99 )
| ~ ( lt @ SY99 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(306,plain,
! [SV10: $i] :
( ( ( ssItem @ SV10 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( ssItem @ SY100 )
| ! [SY101: $i] :
( ~ ( ssItem @ SY101 )
| ~ ~ ( ~ ( lt @ SV10 @ SY100 )
| ~ ( lt @ SY100 @ SY101 ) )
| ( lt @ SV10 @ SY101 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(307,plain,
! [SV11: $i] :
( ( ( ssList @ SV11 )
= $false )
| ( ( ! [SY102: $i] :
( ~ ( ssList @ SY102 )
| ! [SY103: $i] :
( ~ ( ssList @ SY103 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SY102 )
| ~ ( segmentP @ SY102 @ SY103 ) )
| ( segmentP @ SV11 @ SY103 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(308,plain,
! [SV12: $i] :
( ( ( ssList @ SV12 )
= $false )
| ( ( ! [SY104: $i] :
( ~ ( ssItem @ SY104 )
| ( ssList @ ( cons @ SY104 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(309,plain,
! [SV13: $i] :
( ( ( ssItem @ SV13 )
= $false )
| ( ( ! [SY105: $i] :
( ~ ( ssList @ SY105 )
| ! [SY106: $i] :
( ~ ( ssList @ SY106 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SY105 @ SY106 ) @ SV13 )
| ( memberP @ SY105 @ SV13 )
| ( memberP @ SY106 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SY105 @ SV13 )
| ( memberP @ SY106 @ SV13 ) )
| ( memberP @ ( app @ SY105 @ SY106 ) @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(310,plain,
! [SV14: $i] :
( ( ( ssList @ SV14 )
= $false )
| ( ( segmentP @ SV14 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(311,plain,
! [SV15: $i] :
( ( ( ssList @ SV15 )
= $false )
| ( ( rearsegP @ SV15 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(312,plain,
! [SV16: $i] :
( ( ( ssList @ SV16 )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( ssList @ SY107 )
| ~ ~ ( ~ ( segmentP @ SV16 @ SY107 )
| ~ ( segmentP @ SY107 @ SV16 ) )
| ( SV16 = SY107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(313,plain,
! [SV17: $i] :
( ( ( ssItem @ SV17 )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( ssItem @ SY108 )
| ~ ( gt @ SV17 @ SY108 )
| ~ ( gt @ SY108 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(314,plain,
! [SV18: $i] :
( ( ( ssList @ SV18 )
= $false )
| ( ( ! [SY109: $i] :
( ~ ( ssList @ SY109 )
| ! [SY110: $i] :
( ~ ( ssList @ SY110 )
| ( ( app @ ( app @ SV18 @ SY109 ) @ SY110 )
= ( app @ SV18 @ ( app @ SY109 @ SY110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(315,plain,
! [SV19: $i] :
( ( ( ssItem @ SV19 )
= $false )
| ( ( leq @ SV19 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(316,plain,
! [SV20: $i] :
( ( ( ssItem @ SV20 )
= $false )
| ( ( ! [SY111: $i] :
( ~ ( ssItem @ SY111 )
| ~ ~ ( ~ ( geq @ SV20 @ SY111 )
| ~ ( geq @ SY111 @ SV20 ) )
| ( SV20 = SY111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(317,plain,
! [SV21: $i] :
( ( ( ssList @ SV21 )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( ssList @ SY112 )
| ! [SY113: $i] :
( ~ ( ssList @ SY113 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SY112 )
| ~ ( rearsegP @ SY112 @ SY113 ) )
| ( rearsegP @ SV21 @ SY113 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(318,plain,
! [SV22: $i] :
( ( ( ssList @ SV22 )
= $false )
| ( ( ! [SY114: $i] :
( ~ ( ssItem @ SY114 )
| ( ( cons @ SY114 @ SV22 )
!= SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(319,plain,
! [SV23: $i] :
( ( ( ssList @ SV23 )
= $false )
| ( ( segmentP @ SV23 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(320,plain,
! [SV24: $i] :
( ( ( ssItem @ SV24 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( ssItem @ SY115 )
| ! [SY116: $i] :
( ~ ( ssList @ SY116 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SY115 @ SY116 ) @ SV24 )
| ( SV24 = SY115 )
| ( memberP @ SY116 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SY115 )
| ( memberP @ SY116 @ SV24 ) )
| ( memberP @ ( cons @ SY115 @ SY116 ) @ SV24 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(321,plain,
! [SV25: $i] :
( ( ( ssList @ SV25 )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( ssList @ SY117 )
| ~ ( ~ ( ~ ( segmentP @ SV25 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( ssList @ SY118 )
| ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( ssList @ SY119 )
| ( ( app @ ( app @ SY118 @ SY117 ) @ SY119 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( ssList @ SY120 )
| ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( ssList @ SY121 )
| ( ( app @ ( app @ SY120 @ SY117 ) @ SY121 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SY117 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(322,plain,
! [SV26: $i] :
( ( ( ssItem @ SV26 )
= $false )
| ( ( ! [SY122: $i] :
( ~ ( ssItem @ SY122 )
| ~ ( ~ ( ~ ( neq @ SV26 @ SY122 )
| ( SV26 != SY122 ) )
| ~ ( ~ ( ( SV26 != SY122 ) )
| ( neq @ SV26 @ SY122 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(323,plain,
! [SV27: $i] :
( ( ( ssList @ SV27 )
= $false )
| ( ( frontsegP @ SV27 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(324,plain,
! [SV28: $i] :
( ( ( ssList @ SV28 )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( ssList @ SY123 )
| ( ssList @ ( app @ SV28 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(325,plain,
! [SV29: $i] :
( ( ( ssList @ SV29 )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( ssList @ SY124 )
| ! [SY125: $i] :
( ~ ( ssList @ SY125 )
| ( ( app @ SY125 @ SY124 )
!= ( app @ SV29 @ SY124 ) )
| ( SY125 = SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(326,plain,
( ( ~ ( ~ ( ssItem @ sK2_SX0 )
| ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( ssItem @ SY139 )
| ~ ( ( sK2_SX0 != SY139 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(327,plain,
! [SV30: $i] :
( ( ( ssItem @ SV30 )
= $false )
| ( ( ! [SY126: $i] :
( ~ ( ssItem @ SY126 )
| ! [SY127: $i] :
( ~ ( ssItem @ SY127 )
| ~ ~ ( ~ ( geq @ SV30 @ SY126 )
| ~ ( geq @ SY126 @ SY127 ) )
| ( geq @ SV30 @ SY127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(328,plain,
! [SV31: $i] :
( ( ( ssList @ SV31 )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( ssList @ SY128 )
| ! [SY129: $i] :
( ~ ( ssList @ SY129 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SY128 )
| ~ ( frontsegP @ SY128 @ SY129 ) )
| ( frontsegP @ SV31 @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(329,plain,
! [SV32: $i] :
( ( ( ssList @ SV32 )
= $false )
| ( ( ! [SY130: $i] :
( ~ ( ssList @ SY130 )
| ~ ~ ( ~ ( frontsegP @ SV32 @ SY130 )
| ~ ( frontsegP @ SY130 @ SV32 ) )
| ( SV32 = SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(330,plain,
! [SV33: $i] :
( ( ( ssItem @ SV33 )
= $false )
| ( ( ! [SY131: $i] :
( ~ ( ssItem @ SY131 )
| ! [SY132: $i] :
( ~ ( ssItem @ SY132 )
| ~ ~ ( ~ ( leq @ SV33 @ SY131 )
| ~ ( leq @ SY131 @ SY132 ) )
| ( leq @ SV33 @ SY132 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(331,plain,
! [SV34: $i] :
( ( ( ssList @ SV34 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( ssList @ SY133 )
| ! [SY134: $i] :
( ~ ( ssList @ SY134 )
| ! [SY135: $i] :
( ~ ( ssList @ SY135 )
| ~ ( segmentP @ SV34 @ SY133 )
| ( segmentP @ ( app @ ( app @ SY134 @ SV34 ) @ SY135 ) @ SY133 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(332,plain,
! [SV35: $i] :
( ( ( ssItem @ SV35 )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( ssItem @ SY136 )
| ! [SY137: $i] :
( ~ ( ssItem @ SY137 )
| ~ ~ ( ~ ( gt @ SV35 @ SY136 )
| ~ ( gt @ SY136 @ SY137 ) )
| ( gt @ SV35 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(333,plain,
! [SV36: $i] :
( ( ( ssList @ SV36 )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( ssList @ SY138 )
| ~ ( ~ ( ~ ( neq @ SV36 @ SY138 )
| ( SV36 != SY138 ) )
| ~ ( ~ ( ( SV36 != SY138 ) )
| ( neq @ SV36 @ SY138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(334,plain,
( ( ~ ( ssList @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(335,plain,
( ( ! [SY140: $i] :
( ~ ( ssList @ SY140 )
| ! [SY141: $i] :
( ~ ( ssList @ SY141 )
| ( sK3_SX0 != SY141 )
| ( sK1_U != SY140 )
| ~ ( segmentP @ SY141 @ SY140 )
| ~ ( totalorderedP @ SY140 )
| ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(336,plain,
! [SV2: $i,SV37: $i] :
( ( ( ~ ( ssList @ SV37 )
| ! [SY143: $i] :
( ~ ( ssItem @ SY143 )
| ! [SY144: $i] :
( ~ ( ssItem @ SY144 )
| ( ( cons @ SY143 @ SV2 )
!= ( cons @ SY144 @ SV37 ) )
| ~ ( ( SY143 != SY144 )
| ( SV37 != SV2 ) ) ) ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(337,plain,
! [SV3: $i,SV38: $i] :
( ( ( ~ ( ssList @ SV38 )
| ~ ~ ( ~ ( rearsegP @ SV3 @ SV38 )
| ~ ( rearsegP @ SV38 @ SV3 ) )
| ( SV3 = SV38 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(338,plain,
! [SV4: $i,SV39: $i] :
( ( ( ~ ( ssList @ SV39 )
| ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ( ( app @ SV39 @ SY145 )
!= ( app @ SV39 @ SV4 ) )
| ( SY145 = SV4 ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(339,plain,
! [SV5: $i] :
( ( ( lt @ SV5 @ SV5 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(340,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV6 )
| ( nil = SV6 ) )
| ~ ( ( nil != SV6 )
| ( segmentP @ nil @ SV6 ) ) )
= $false )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(341,plain,
! [SV7: $i] :
( ( ( memberP @ nil @ SV7 )
= $false )
| ( ( ssItem @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(342,plain,
! [SV8: $i,SV40: $i] :
( ( ( ~ ( ssItem @ SV40 )
| ~ ~ ( ~ ( leq @ SV8 @ SV40 )
| ~ ( leq @ SV40 @ SV8 ) )
| ( SV8 = SV40 ) )
= $true )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(343,plain,
! [SV9: $i,SV41: $i] :
( ( ( ~ ( ssItem @ SV41 )
| ~ ( lt @ SV9 @ SV41 )
| ~ ( lt @ SV41 @ SV9 ) )
= $true )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(344,plain,
! [SV10: $i,SV42: $i] :
( ( ( ~ ( ssItem @ SV42 )
| ! [SY146: $i] :
( ~ ( ssItem @ SY146 )
| ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SY146 ) )
| ( lt @ SV10 @ SY146 ) ) )
= $true )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(345,plain,
! [SV11: $i,SV43: $i] :
( ( ( ~ ( ssList @ SV43 )
| ! [SY147: $i] :
( ~ ( ssList @ SY147 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SY147 ) )
| ( segmentP @ SV11 @ SY147 ) ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(346,plain,
! [SV12: $i,SV44: $i] :
( ( ( ~ ( ssItem @ SV44 )
| ( ssList @ ( cons @ SV44 @ SV12 ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(347,plain,
! [SV13: $i,SV45: $i] :
( ( ( ~ ( ssList @ SV45 )
| ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV45 @ SY148 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SY148 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SY148 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SY148 ) @ SV13 ) ) ) ) )
= $true )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(348,plain,
! [SV16: $i,SV46: $i] :
( ( ( ~ ( ssList @ SV46 )
| ~ ~ ( ~ ( segmentP @ SV16 @ SV46 )
| ~ ( segmentP @ SV46 @ SV16 ) )
| ( SV16 = SV46 ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(349,plain,
! [SV17: $i,SV47: $i] :
( ( ( ~ ( ssItem @ SV47 )
| ~ ( gt @ SV17 @ SV47 )
| ~ ( gt @ SV47 @ SV17 ) )
= $true )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(350,plain,
! [SV18: $i,SV48: $i] :
( ( ( ~ ( ssList @ SV48 )
| ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ( ( app @ ( app @ SV18 @ SV48 ) @ SY149 )
= ( app @ SV18 @ ( app @ SV48 @ SY149 ) ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(351,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( ssItem @ SV49 )
| ~ ~ ( ~ ( geq @ SV20 @ SV49 )
| ~ ( geq @ SV49 @ SV20 ) )
| ( SV20 = SV49 ) )
= $true )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(352,plain,
! [SV21: $i,SV50: $i] :
( ( ( ~ ( ssList @ SV50 )
| ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SY150 ) )
| ( rearsegP @ SV21 @ SY150 ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(353,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ssItem @ SV51 )
| ( ( cons @ SV51 @ SV22 )
!= SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(354,plain,
! [SV24: $i,SV52: $i] :
( ( ( ~ ( ssItem @ SV52 )
| ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SY151 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SY151 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SY151 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SY151 ) @ SV24 ) ) ) ) )
= $true )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(355,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( ssList @ SV53 )
| ~ ( ~ ( ~ ( segmentP @ SV25 @ SV53 )
| ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SV53 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(356,plain,
! [SV26: $i,SV54: $i] :
( ( ( ~ ( ssItem @ SV54 )
| ~ ( ~ ( ~ ( neq @ SV26 @ SV54 )
| ( SV26 != SV54 ) )
| ~ ( ~ ( ( SV26 != SV54 ) )
| ( neq @ SV26 @ SV54 ) ) ) )
= $true )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(357,plain,
! [SV28: $i,SV55: $i] :
( ( ( ~ ( ssList @ SV55 )
| ( ssList @ ( app @ SV28 @ SV55 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(358,plain,
! [SV29: $i,SV56: $i] :
( ( ( ~ ( ssList @ SV56 )
| ! [SY156: $i] :
( ~ ( ssList @ SY156 )
| ( ( app @ SY156 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
| ( SY156 = SV29 ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(359,plain,
( ( ~ ( ssItem @ sK2_SX0 )
| ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( ssItem @ SY139 )
| ~ ( ( sK2_SX0 != SY139 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(360,plain,
! [SV30: $i,SV57: $i] :
( ( ( ~ ( ssItem @ SV57 )
| ! [SY157: $i] :
( ~ ( ssItem @ SY157 )
| ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SY157 ) )
| ( geq @ SV30 @ SY157 ) ) )
= $true )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(361,plain,
! [SV31: $i,SV58: $i] :
( ( ( ~ ( ssList @ SV58 )
| ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SY158 ) )
| ( frontsegP @ SV31 @ SY158 ) ) )
= $true )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(362,plain,
! [SV32: $i,SV59: $i] :
( ( ( ~ ( ssList @ SV59 )
| ~ ~ ( ~ ( frontsegP @ SV32 @ SV59 )
| ~ ( frontsegP @ SV59 @ SV32 ) )
| ( SV32 = SV59 ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(363,plain,
! [SV33: $i,SV60: $i] :
( ( ( ~ ( ssItem @ SV60 )
| ! [SY159: $i] :
( ~ ( ssItem @ SY159 )
| ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SY159 ) )
| ( leq @ SV33 @ SY159 ) ) )
= $true )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(364,plain,
! [SV34: $i,SV61: $i] :
( ( ( ~ ( ssList @ SV61 )
| ! [SY160: $i] :
( ~ ( ssList @ SY160 )
| ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SY160 @ SV34 ) @ SY161 ) @ SV61 ) ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(365,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( ssItem @ SV62 )
| ! [SY162: $i] :
( ~ ( ssItem @ SY162 )
| ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SY162 ) )
| ( gt @ SV35 @ SY162 ) ) )
= $true )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(366,plain,
! [SV36: $i,SV63: $i] :
( ( ( ~ ( ssList @ SV63 )
| ~ ( ~ ( ~ ( neq @ SV36 @ SV63 )
| ( SV36 != SV63 ) )
| ~ ( ~ ( ( SV36 != SV63 ) )
| ( neq @ SV36 @ SV63 ) ) ) )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(367,plain,
( ( ssList @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(368,plain,
( ( ~ ( ssList @ sK4_SY140 )
| ! [SY163: $i] :
( ~ ( ssList @ SY163 )
| ( sK3_SX0 != SY163 )
| ( sK1_U != sK4_SY140 )
| ~ ( segmentP @ SY163 @ sK4_SY140 )
| ~ ( totalorderedP @ sK4_SY140 )
| ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[335]) ).
thf(369,plain,
! [SV2: $i,SV37: $i] :
( ( ( ~ ( ssList @ SV37 ) )
= $true )
| ( ( ! [SY143: $i] :
( ~ ( ssItem @ SY143 )
| ! [SY144: $i] :
( ~ ( ssItem @ SY144 )
| ( ( cons @ SY143 @ SV2 )
!= ( cons @ SY144 @ SV37 ) )
| ~ ( ( SY143 != SY144 )
| ( SV37 != SV2 ) ) ) ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(370,plain,
! [SV3: $i,SV38: $i] :
( ( ( ~ ( ssList @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV3 @ SV38 )
| ~ ( rearsegP @ SV38 @ SV3 ) )
| ( SV3 = SV38 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(371,plain,
! [SV4: $i,SV39: $i] :
( ( ( ~ ( ssList @ SV39 ) )
= $true )
| ( ( ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ( ( app @ SV39 @ SY145 )
!= ( app @ SV39 @ SV4 ) )
| ( SY145 = SV4 ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(372,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV6 )
| ( nil = SV6 ) ) )
= $false )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(373,plain,
! [SV6: $i] :
( ( ( ~ ( ( nil != SV6 )
| ( segmentP @ nil @ SV6 ) ) )
= $false )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(374,plain,
! [SV8: $i,SV40: $i] :
( ( ( ~ ( ssItem @ SV40 ) )
= $true )
| ( ( ~ ~ ( ~ ( leq @ SV8 @ SV40 )
| ~ ( leq @ SV40 @ SV8 ) )
| ( SV8 = SV40 ) )
= $true )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV9: $i,SV41: $i] :
( ( ( ~ ( ssItem @ SV41 ) )
= $true )
| ( ( ~ ( lt @ SV9 @ SV41 )
| ~ ( lt @ SV41 @ SV9 ) )
= $true )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(376,plain,
! [SV10: $i,SV42: $i] :
( ( ( ~ ( ssItem @ SV42 ) )
= $true )
| ( ( ! [SY146: $i] :
( ~ ( ssItem @ SY146 )
| ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SY146 ) )
| ( lt @ SV10 @ SY146 ) ) )
= $true )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(377,plain,
! [SV11: $i,SV43: $i] :
( ( ( ~ ( ssList @ SV43 ) )
= $true )
| ( ( ! [SY147: $i] :
( ~ ( ssList @ SY147 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SY147 ) )
| ( segmentP @ SV11 @ SY147 ) ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(378,plain,
! [SV12: $i,SV44: $i] :
( ( ( ~ ( ssItem @ SV44 ) )
= $true )
| ( ( ssList @ ( cons @ SV44 @ SV12 ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(379,plain,
! [SV13: $i,SV45: $i] :
( ( ( ~ ( ssList @ SV45 ) )
= $true )
| ( ( ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV45 @ SY148 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SY148 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SY148 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SY148 ) @ SV13 ) ) ) ) )
= $true )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(380,plain,
! [SV16: $i,SV46: $i] :
( ( ( ~ ( ssList @ SV46 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV16 @ SV46 )
| ~ ( segmentP @ SV46 @ SV16 ) )
| ( SV16 = SV46 ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(381,plain,
! [SV17: $i,SV47: $i] :
( ( ( ~ ( ssItem @ SV47 ) )
= $true )
| ( ( ~ ( gt @ SV17 @ SV47 )
| ~ ( gt @ SV47 @ SV17 ) )
= $true )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(382,plain,
! [SV18: $i,SV48: $i] :
( ( ( ~ ( ssList @ SV48 ) )
= $true )
| ( ( ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ( ( app @ ( app @ SV18 @ SV48 ) @ SY149 )
= ( app @ SV18 @ ( app @ SV48 @ SY149 ) ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(383,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( ssItem @ SV49 ) )
= $true )
| ( ( ~ ~ ( ~ ( geq @ SV20 @ SV49 )
| ~ ( geq @ SV49 @ SV20 ) )
| ( SV20 = SV49 ) )
= $true )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(384,plain,
! [SV21: $i,SV50: $i] :
( ( ( ~ ( ssList @ SV50 ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SY150 ) )
| ( rearsegP @ SV21 @ SY150 ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(385,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ssItem @ SV51 ) )
= $true )
| ( ( ( cons @ SV51 @ SV22 )
!= SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(386,plain,
! [SV24: $i,SV52: $i] :
( ( ( ~ ( ssItem @ SV52 ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SY151 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SY151 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SY151 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SY151 ) @ SV24 ) ) ) ) )
= $true )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(387,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( ssList @ SV53 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV25 @ SV53 )
| ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SV53 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(388,plain,
! [SV26: $i,SV54: $i] :
( ( ( ~ ( ssItem @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV26 @ SV54 )
| ( SV26 != SV54 ) )
| ~ ( ~ ( ( SV26 != SV54 ) )
| ( neq @ SV26 @ SV54 ) ) ) )
= $true )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(389,plain,
! [SV28: $i,SV55: $i] :
( ( ( ~ ( ssList @ SV55 ) )
= $true )
| ( ( ssList @ ( app @ SV28 @ SV55 ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(390,plain,
! [SV29: $i,SV56: $i] :
( ( ( ~ ( ssList @ SV56 ) )
= $true )
| ( ( ! [SY156: $i] :
( ~ ( ssList @ SY156 )
| ( ( app @ SY156 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
| ( SY156 = SV29 ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(391,plain,
( ( ~ ( ssItem @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(392,plain,
( ( ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( ssItem @ SY139 )
| ~ ( ( sK2_SX0 != SY139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(393,plain,
! [SV30: $i,SV57: $i] :
( ( ( ~ ( ssItem @ SV57 ) )
= $true )
| ( ( ! [SY157: $i] :
( ~ ( ssItem @ SY157 )
| ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SY157 ) )
| ( geq @ SV30 @ SY157 ) ) )
= $true )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(394,plain,
! [SV31: $i,SV58: $i] :
( ( ( ~ ( ssList @ SV58 ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SY158 ) )
| ( frontsegP @ SV31 @ SY158 ) ) )
= $true )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(395,plain,
! [SV32: $i,SV59: $i] :
( ( ( ~ ( ssList @ SV59 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV32 @ SV59 )
| ~ ( frontsegP @ SV59 @ SV32 ) )
| ( SV32 = SV59 ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(396,plain,
! [SV33: $i,SV60: $i] :
( ( ( ~ ( ssItem @ SV60 ) )
= $true )
| ( ( ! [SY159: $i] :
( ~ ( ssItem @ SY159 )
| ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SY159 ) )
| ( leq @ SV33 @ SY159 ) ) )
= $true )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(397,plain,
! [SV34: $i,SV61: $i] :
( ( ( ~ ( ssList @ SV61 ) )
= $true )
| ( ( ! [SY160: $i] :
( ~ ( ssList @ SY160 )
| ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SY160 @ SV34 ) @ SY161 ) @ SV61 ) ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(398,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( ssItem @ SV62 ) )
= $true )
| ( ( ! [SY162: $i] :
( ~ ( ssItem @ SY162 )
| ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SY162 ) )
| ( gt @ SV35 @ SY162 ) ) )
= $true )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(399,plain,
! [SV36: $i,SV63: $i] :
( ( ( ~ ( ssList @ SV63 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV36 @ SV63 )
| ( SV36 != SV63 ) )
| ~ ( ~ ( ( SV36 != SV63 ) )
| ( neq @ SV36 @ SV63 ) ) ) )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(400,plain,
( ( ~ ( ssList @ sK4_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(401,plain,
( ( ! [SY163: $i] :
( ~ ( ssList @ SY163 )
| ( sK3_SX0 != SY163 )
| ( sK1_U != sK4_SY140 )
| ~ ( segmentP @ SY163 @ sK4_SY140 )
| ~ ( totalorderedP @ sK4_SY140 )
| ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(402,plain,
! [SV2: $i,SV37: $i] :
( ( ( ssList @ SV37 )
= $false )
| ( ( ! [SY143: $i] :
( ~ ( ssItem @ SY143 )
| ! [SY144: $i] :
( ~ ( ssItem @ SY144 )
| ( ( cons @ SY143 @ SV2 )
!= ( cons @ SY144 @ SV37 ) )
| ~ ( ( SY143 != SY144 )
| ( SV37 != SV2 ) ) ) ) )
= $true )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(403,plain,
! [SV3: $i,SV38: $i] :
( ( ( ssList @ SV38 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV3 @ SV38 )
| ~ ( rearsegP @ SV38 @ SV3 ) )
| ( SV3 = SV38 ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(404,plain,
! [SV4: $i,SV39: $i] :
( ( ( ssList @ SV39 )
= $false )
| ( ( ! [SY145: $i] :
( ~ ( ssList @ SY145 )
| ( ( app @ SV39 @ SY145 )
!= ( app @ SV39 @ SV4 ) )
| ( SY145 = SV4 ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(405,plain,
! [SV6: $i] :
( ( ( ~ ( segmentP @ nil @ SV6 )
| ( nil = SV6 ) )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(406,plain,
! [SV6: $i] :
( ( ( ( nil != SV6 )
| ( segmentP @ nil @ SV6 ) )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(407,plain,
! [SV8: $i,SV40: $i] :
( ( ( ssItem @ SV40 )
= $false )
| ( ( ~ ~ ( ~ ( leq @ SV8 @ SV40 )
| ~ ( leq @ SV40 @ SV8 ) )
| ( SV8 = SV40 ) )
= $true )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(408,plain,
! [SV9: $i,SV41: $i] :
( ( ( ssItem @ SV41 )
= $false )
| ( ( ~ ( lt @ SV9 @ SV41 )
| ~ ( lt @ SV41 @ SV9 ) )
= $true )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(409,plain,
! [SV10: $i,SV42: $i] :
( ( ( ssItem @ SV42 )
= $false )
| ( ( ! [SY146: $i] :
( ~ ( ssItem @ SY146 )
| ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SY146 ) )
| ( lt @ SV10 @ SY146 ) ) )
= $true )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(410,plain,
! [SV11: $i,SV43: $i] :
( ( ( ssList @ SV43 )
= $false )
| ( ( ! [SY147: $i] :
( ~ ( ssList @ SY147 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SY147 ) )
| ( segmentP @ SV11 @ SY147 ) ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(411,plain,
! [SV12: $i,SV44: $i] :
( ( ( ssItem @ SV44 )
= $false )
| ( ( ssList @ ( cons @ SV44 @ SV12 ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(412,plain,
! [SV13: $i,SV45: $i] :
( ( ( ssList @ SV45 )
= $false )
| ( ( ! [SY148: $i] :
( ~ ( ssList @ SY148 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV45 @ SY148 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SY148 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SY148 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SY148 ) @ SV13 ) ) ) ) )
= $true )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(413,plain,
! [SV16: $i,SV46: $i] :
( ( ( ssList @ SV46 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV16 @ SV46 )
| ~ ( segmentP @ SV46 @ SV16 ) )
| ( SV16 = SV46 ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(414,plain,
! [SV17: $i,SV47: $i] :
( ( ( ssItem @ SV47 )
= $false )
| ( ( ~ ( gt @ SV17 @ SV47 )
| ~ ( gt @ SV47 @ SV17 ) )
= $true )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(415,plain,
! [SV18: $i,SV48: $i] :
( ( ( ssList @ SV48 )
= $false )
| ( ( ! [SY149: $i] :
( ~ ( ssList @ SY149 )
| ( ( app @ ( app @ SV18 @ SV48 ) @ SY149 )
= ( app @ SV18 @ ( app @ SV48 @ SY149 ) ) ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(416,plain,
! [SV20: $i,SV49: $i] :
( ( ( ssItem @ SV49 )
= $false )
| ( ( ~ ~ ( ~ ( geq @ SV20 @ SV49 )
| ~ ( geq @ SV49 @ SV20 ) )
| ( SV20 = SV49 ) )
= $true )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(417,plain,
! [SV21: $i,SV50: $i] :
( ( ( ssList @ SV50 )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( ssList @ SY150 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SY150 ) )
| ( rearsegP @ SV21 @ SY150 ) ) )
= $true )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(418,plain,
! [SV22: $i,SV51: $i] :
( ( ( ssItem @ SV51 )
= $false )
| ( ( ( cons @ SV51 @ SV22 )
!= SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(419,plain,
! [SV24: $i,SV52: $i] :
( ( ( ssItem @ SV52 )
= $false )
| ( ( ! [SY151: $i] :
( ~ ( ssList @ SY151 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SY151 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SY151 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SY151 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SY151 ) @ SV24 ) ) ) ) )
= $true )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(420,plain,
! [SV25: $i,SV53: $i] :
( ( ( ssList @ SV53 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ SV25 @ SV53 )
| ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SV53 ) ) ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(421,plain,
! [SV26: $i,SV54: $i] :
( ( ( ssItem @ SV54 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV26 @ SV54 )
| ( SV26 != SV54 ) )
| ~ ( ~ ( ( SV26 != SV54 ) )
| ( neq @ SV26 @ SV54 ) ) ) )
= $true )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(422,plain,
! [SV28: $i,SV55: $i] :
( ( ( ssList @ SV55 )
= $false )
| ( ( ssList @ ( app @ SV28 @ SV55 ) )
= $true )
| ( ( ssList @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(423,plain,
! [SV29: $i,SV56: $i] :
( ( ( ssList @ SV56 )
= $false )
| ( ( ! [SY156: $i] :
( ~ ( ssList @ SY156 )
| ( ( app @ SY156 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
| ( SY156 = SV29 ) ) )
= $true )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(424,plain,
( ( ssItem @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(425,plain,
( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( ssItem @ SY139 )
| ~ ( ( sK2_SX0 != SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(426,plain,
! [SV30: $i,SV57: $i] :
( ( ( ssItem @ SV57 )
= $false )
| ( ( ! [SY157: $i] :
( ~ ( ssItem @ SY157 )
| ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SY157 ) )
| ( geq @ SV30 @ SY157 ) ) )
= $true )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(427,plain,
! [SV31: $i,SV58: $i] :
( ( ( ssList @ SV58 )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( ssList @ SY158 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SY158 ) )
| ( frontsegP @ SV31 @ SY158 ) ) )
= $true )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(428,plain,
! [SV32: $i,SV59: $i] :
( ( ( ssList @ SV59 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV32 @ SV59 )
| ~ ( frontsegP @ SV59 @ SV32 ) )
| ( SV32 = SV59 ) )
= $true )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(429,plain,
! [SV33: $i,SV60: $i] :
( ( ( ssItem @ SV60 )
= $false )
| ( ( ! [SY159: $i] :
( ~ ( ssItem @ SY159 )
| ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SY159 ) )
| ( leq @ SV33 @ SY159 ) ) )
= $true )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(430,plain,
! [SV34: $i,SV61: $i] :
( ( ( ssList @ SV61 )
= $false )
| ( ( ! [SY160: $i] :
( ~ ( ssList @ SY160 )
| ! [SY161: $i] :
( ~ ( ssList @ SY161 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SY160 @ SV34 ) @ SY161 ) @ SV61 ) ) ) )
= $true )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(431,plain,
! [SV35: $i,SV62: $i] :
( ( ( ssItem @ SV62 )
= $false )
| ( ( ! [SY162: $i] :
( ~ ( ssItem @ SY162 )
| ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SY162 ) )
| ( gt @ SV35 @ SY162 ) ) )
= $true )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(432,plain,
! [SV36: $i,SV63: $i] :
( ( ( ssList @ SV63 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV36 @ SV63 )
| ( SV36 != SV63 ) )
| ~ ( ~ ( ( SV36 != SV63 ) )
| ( neq @ SV36 @ SV63 ) ) ) )
= $true )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(433,plain,
( ( ssList @ sK4_SY140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(434,plain,
( ( ~ ( ssList @ sK5_SY163 )
| ( sK3_SX0 != sK5_SY163 )
| ( sK1_U != sK4_SY140 )
| ~ ( segmentP @ sK5_SY163 @ sK4_SY140 )
| ~ ( totalorderedP @ sK4_SY140 )
| ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[401]) ).
thf(435,plain,
! [SV37: $i,SV2: $i,SV64: $i] :
( ( ( ~ ( ssItem @ SV64 )
| ! [SY166: $i] :
( ~ ( ssItem @ SY166 )
| ( ( cons @ SV64 @ SV2 )
!= ( cons @ SY166 @ SV37 ) )
| ~ ( ( SV64 != SY166 )
| ( SV37 != SV2 ) ) ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(436,plain,
! [SV38: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV3 @ SV38 )
| ~ ( rearsegP @ SV38 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(437,plain,
! [SV4: $i,SV39: $i,SV65: $i] :
( ( ( ~ ( ssList @ SV65 )
| ( ( app @ SV39 @ SV65 )
!= ( app @ SV39 @ SV4 ) )
| ( SV65 = SV4 ) )
= $true )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(438,plain,
! [SV6: $i] :
( ( ( ~ ( segmentP @ nil @ SV6 ) )
= $true )
| ( ( nil = SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(439,plain,
! [SV6: $i] :
( ( ( nil != SV6 )
= $true )
| ( ( segmentP @ nil @ SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(440,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV8 @ SV40 )
| ~ ( leq @ SV40 @ SV8 ) ) )
= $true )
| ( ( SV8 = SV40 )
= $true )
| ( ( ssItem @ SV40 )
= $false )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(441,plain,
! [SV41: $i,SV9: $i] :
( ( ( ~ ( lt @ SV9 @ SV41 ) )
= $true )
| ( ( ~ ( lt @ SV41 @ SV9 ) )
= $true )
| ( ( ssItem @ SV41 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(442,plain,
! [SV42: $i,SV10: $i,SV66: $i] :
( ( ( ~ ( ssItem @ SV66 )
| ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SV66 ) )
| ( lt @ SV10 @ SV66 ) )
= $true )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(443,plain,
! [SV43: $i,SV11: $i,SV67: $i] :
( ( ( ~ ( ssList @ SV67 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SV67 ) )
| ( segmentP @ SV11 @ SV67 ) )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(444,plain,
! [SV13: $i,SV45: $i,SV68: $i] :
( ( ( ~ ( ssList @ SV68 )
| ~ ( ~ ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(445,plain,
! [SV46: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV16 @ SV46 )
| ~ ( segmentP @ SV46 @ SV16 ) ) )
= $true )
| ( ( SV16 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(446,plain,
! [SV47: $i,SV17: $i] :
( ( ( ~ ( gt @ SV17 @ SV47 ) )
= $true )
| ( ( ~ ( gt @ SV47 @ SV17 ) )
= $true )
| ( ( ssItem @ SV47 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(447,plain,
! [SV48: $i,SV18: $i,SV69: $i] :
( ( ( ~ ( ssList @ SV69 )
| ( ( app @ ( app @ SV18 @ SV48 ) @ SV69 )
= ( app @ SV18 @ ( app @ SV48 @ SV69 ) ) ) )
= $true )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(448,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( geq @ SV20 @ SV49 )
| ~ ( geq @ SV49 @ SV20 ) ) )
= $true )
| ( ( SV20 = SV49 )
= $true )
| ( ( ssItem @ SV49 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(449,plain,
! [SV50: $i,SV21: $i,SV70: $i] :
( ( ( ~ ( ssList @ SV70 )
| ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SV70 ) )
| ( rearsegP @ SV21 @ SV70 ) )
= $true )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(450,plain,
! [SV22: $i,SV51: $i] :
( ( ( ( cons @ SV51 @ SV22 )
= SV22 )
= $false )
| ( ( ssItem @ SV51 )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(451,plain,
! [SV24: $i,SV52: $i,SV71: $i] :
( ( ( ~ ( ssList @ SV71 )
| ~ ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) ) ) )
= $true )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(452,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( ~ ( segmentP @ SV25 @ SV53 )
| ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
| ~ ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SV53 ) ) )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(453,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( ~ ( neq @ SV26 @ SV54 )
| ( SV26 != SV54 ) )
| ~ ( ~ ( ( SV26 != SV54 ) )
| ( neq @ SV26 @ SV54 ) ) )
= $false )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(454,plain,
! [SV29: $i,SV56: $i,SV72: $i] :
( ( ( ~ ( ssList @ SV72 )
| ( ( app @ SV72 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
| ( SV72 = SV29 ) )
= $true )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(455,plain,
( ( ! [SY139: $i] :
~ ~ ( ~ ( ssItem @ SY139 )
| ~ ( ( sK2_SX0 != SY139 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(456,plain,
! [SV57: $i,SV30: $i,SV73: $i] :
( ( ( ~ ( ssItem @ SV73 )
| ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SV73 ) )
| ( geq @ SV30 @ SV73 ) )
= $true )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(457,plain,
! [SV58: $i,SV31: $i,SV74: $i] :
( ( ( ~ ( ssList @ SV74 )
| ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SV74 ) )
| ( frontsegP @ SV31 @ SV74 ) )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(458,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV32 @ SV59 )
| ~ ( frontsegP @ SV59 @ SV32 ) ) )
= $true )
| ( ( SV32 = SV59 )
= $true )
| ( ( ssList @ SV59 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(459,plain,
! [SV60: $i,SV33: $i,SV75: $i] :
( ( ( ~ ( ssItem @ SV75 )
| ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SV75 ) )
| ( leq @ SV33 @ SV75 ) )
= $true )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(460,plain,
! [SV61: $i,SV34: $i,SV76: $i] :
( ( ( ~ ( ssList @ SV76 )
| ! [SY167: $i] :
( ~ ( ssList @ SY167 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SY167 ) @ SV61 ) ) )
= $true )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(461,plain,
! [SV62: $i,SV35: $i,SV77: $i] :
( ( ( ~ ( ssItem @ SV77 )
| ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SV77 ) )
| ( gt @ SV35 @ SV77 ) )
= $true )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(462,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( ~ ( neq @ SV36 @ SV63 )
| ( SV36 != SV63 ) )
| ~ ( ~ ( ( SV36 != SV63 ) )
| ( neq @ SV36 @ SV63 ) ) )
= $false )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(463,plain,
( ( ~ ( ssList @ sK5_SY163 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(464,plain,
( ( ( sK3_SX0 != sK5_SY163 )
| ( sK1_U != sK4_SY140 )
| ~ ( segmentP @ sK5_SY163 @ sK4_SY140 )
| ~ ( totalorderedP @ sK4_SY140 )
| ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(465,plain,
! [SV37: $i,SV2: $i,SV64: $i] :
( ( ( ~ ( ssItem @ SV64 ) )
= $true )
| ( ( ! [SY166: $i] :
( ~ ( ssItem @ SY166 )
| ( ( cons @ SV64 @ SV2 )
!= ( cons @ SY166 @ SV37 ) )
| ~ ( ( SV64 != SY166 )
| ( SV37 != SV2 ) ) ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(466,plain,
! [SV38: $i,SV3: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV3 @ SV38 )
| ~ ( rearsegP @ SV38 @ SV3 ) ) )
= $false )
| ( ( SV3 = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(467,plain,
! [SV4: $i,SV39: $i,SV65: $i] :
( ( ( ~ ( ssList @ SV65 ) )
= $true )
| ( ( ( ( app @ SV39 @ SV65 )
!= ( app @ SV39 @ SV4 ) )
| ( SV65 = SV4 ) )
= $true )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(468,plain,
! [SV6: $i] :
( ( ( segmentP @ nil @ SV6 )
= $false )
| ( ( nil = SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(469,plain,
! [SV6: $i] :
( ( ( nil = SV6 )
= $false )
| ( ( segmentP @ nil @ SV6 )
= $true )
| ( ( ssList @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(470,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( ~ ( leq @ SV8 @ SV40 )
| ~ ( leq @ SV40 @ SV8 ) ) )
= $false )
| ( ( SV8 = SV40 )
= $true )
| ( ( ssItem @ SV40 )
= $false )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(471,plain,
! [SV41: $i,SV9: $i] :
( ( ( lt @ SV9 @ SV41 )
= $false )
| ( ( ~ ( lt @ SV41 @ SV9 ) )
= $true )
| ( ( ssItem @ SV41 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(472,plain,
! [SV42: $i,SV10: $i,SV66: $i] :
( ( ( ~ ( ssItem @ SV66 ) )
= $true )
| ( ( ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SV66 ) )
| ( lt @ SV10 @ SV66 ) )
= $true )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(473,plain,
! [SV43: $i,SV11: $i,SV67: $i] :
( ( ( ~ ( ssList @ SV67 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SV67 ) )
| ( segmentP @ SV11 @ SV67 ) )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(474,plain,
! [SV13: $i,SV45: $i,SV68: $i] :
( ( ( ~ ( ssList @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(475,plain,
! [SV46: $i,SV16: $i] :
( ( ( ~ ( ~ ( segmentP @ SV16 @ SV46 )
| ~ ( segmentP @ SV46 @ SV16 ) ) )
= $false )
| ( ( SV16 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(476,plain,
! [SV47: $i,SV17: $i] :
( ( ( gt @ SV17 @ SV47 )
= $false )
| ( ( ~ ( gt @ SV47 @ SV17 ) )
= $true )
| ( ( ssItem @ SV47 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(477,plain,
! [SV48: $i,SV18: $i,SV69: $i] :
( ( ( ~ ( ssList @ SV69 ) )
= $true )
| ( ( ( app @ ( app @ SV18 @ SV48 ) @ SV69 )
= ( app @ SV18 @ ( app @ SV48 @ SV69 ) ) )
= $true )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(478,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ( geq @ SV20 @ SV49 )
| ~ ( geq @ SV49 @ SV20 ) ) )
= $false )
| ( ( SV20 = SV49 )
= $true )
| ( ( ssItem @ SV49 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(479,plain,
! [SV50: $i,SV21: $i,SV70: $i] :
( ( ( ~ ( ssList @ SV70 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SV70 ) )
| ( rearsegP @ SV21 @ SV70 ) )
= $true )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(480,plain,
! [SV24: $i,SV52: $i,SV71: $i] :
( ( ( ~ ( ssList @ SV71 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) ) ) )
= $true )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(481,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( ~ ( segmentP @ SV25 @ SV53 )
| ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) ) )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(482,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SV53 ) ) )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(483,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( ~ ( neq @ SV26 @ SV54 )
| ( SV26 != SV54 ) ) )
= $false )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(484,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( ~ ( ( SV26 != SV54 ) )
| ( neq @ SV26 @ SV54 ) ) )
= $false )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(485,plain,
! [SV29: $i,SV56: $i,SV72: $i] :
( ( ( ~ ( ssList @ SV72 ) )
= $true )
| ( ( ( ( app @ SV72 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
| ( SV72 = SV29 ) )
= $true )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(486,plain,
( ( ~ ~ ( ~ ( ssItem @ sK6_SY139 )
| ~ ( ( sK2_SX0 != sK6_SY139 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[455]) ).
thf(487,plain,
! [SV57: $i,SV30: $i,SV73: $i] :
( ( ( ~ ( ssItem @ SV73 ) )
= $true )
| ( ( ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SV73 ) )
| ( geq @ SV30 @ SV73 ) )
= $true )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(488,plain,
! [SV58: $i,SV31: $i,SV74: $i] :
( ( ( ~ ( ssList @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SV74 ) )
| ( frontsegP @ SV31 @ SV74 ) )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(489,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV32 @ SV59 )
| ~ ( frontsegP @ SV59 @ SV32 ) ) )
= $false )
| ( ( SV32 = SV59 )
= $true )
| ( ( ssList @ SV59 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(490,plain,
! [SV60: $i,SV33: $i,SV75: $i] :
( ( ( ~ ( ssItem @ SV75 ) )
= $true )
| ( ( ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SV75 ) )
| ( leq @ SV33 @ SV75 ) )
= $true )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(491,plain,
! [SV61: $i,SV34: $i,SV76: $i] :
( ( ( ~ ( ssList @ SV76 ) )
= $true )
| ( ( ! [SY167: $i] :
( ~ ( ssList @ SY167 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SY167 ) @ SV61 ) ) )
= $true )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(492,plain,
! [SV62: $i,SV35: $i,SV77: $i] :
( ( ( ~ ( ssItem @ SV77 ) )
= $true )
| ( ( ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SV77 ) )
| ( gt @ SV35 @ SV77 ) )
= $true )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(493,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( ~ ( neq @ SV36 @ SV63 )
| ( SV36 != SV63 ) ) )
= $false )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(494,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( ~ ( ( SV36 != SV63 ) )
| ( neq @ SV36 @ SV63 ) ) )
= $false )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(495,plain,
( ( ssList @ sK5_SY163 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(496,plain,
( ( ( sK3_SX0 != sK5_SY163 )
| ( sK1_U != sK4_SY140 )
| ~ ( segmentP @ sK5_SY163 @ sK4_SY140 )
| ~ ( totalorderedP @ sK4_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(497,plain,
( ( ! [SY142: $i] :
( ~ ( ssItem @ SY142 )
| ~ ( memberP @ sK1_U @ SY142 )
| ( memberP @ sK3_SX0 @ SY142 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(498,plain,
! [SV37: $i,SV2: $i,SV64: $i] :
( ( ( ssItem @ SV64 )
= $false )
| ( ( ! [SY166: $i] :
( ~ ( ssItem @ SY166 )
| ( ( cons @ SV64 @ SV2 )
!= ( cons @ SY166 @ SV37 ) )
| ~ ( ( SV64 != SY166 )
| ( SV37 != SV2 ) ) ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(499,plain,
! [SV38: $i,SV3: $i] :
( ( ( ~ ( rearsegP @ SV3 @ SV38 )
| ~ ( rearsegP @ SV38 @ SV3 ) )
= $true )
| ( ( SV3 = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(500,plain,
! [SV4: $i,SV39: $i,SV65: $i] :
( ( ( ssList @ SV65 )
= $false )
| ( ( ( ( app @ SV39 @ SV65 )
!= ( app @ SV39 @ SV4 ) )
| ( SV65 = SV4 ) )
= $true )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(501,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV40 )
| ~ ( leq @ SV40 @ SV8 ) )
= $true )
| ( ( SV8 = SV40 )
= $true )
| ( ( ssItem @ SV40 )
= $false )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(502,plain,
! [SV9: $i,SV41: $i] :
( ( ( lt @ SV41 @ SV9 )
= $false )
| ( ( lt @ SV9 @ SV41 )
= $false )
| ( ( ssItem @ SV41 )
= $false )
| ( ( ssItem @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(503,plain,
! [SV42: $i,SV10: $i,SV66: $i] :
( ( ( ssItem @ SV66 )
= $false )
| ( ( ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SV66 ) )
| ( lt @ SV10 @ SV66 ) )
= $true )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(504,plain,
! [SV43: $i,SV11: $i,SV67: $i] :
( ( ( ssList @ SV67 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SV67 ) )
| ( segmentP @ SV11 @ SV67 ) )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(505,plain,
! [SV13: $i,SV45: $i,SV68: $i] :
( ( ( ssList @ SV68 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) ) ) )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(506,plain,
! [SV46: $i,SV16: $i] :
( ( ( ~ ( segmentP @ SV16 @ SV46 )
| ~ ( segmentP @ SV46 @ SV16 ) )
= $true )
| ( ( SV16 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(507,plain,
! [SV17: $i,SV47: $i] :
( ( ( gt @ SV47 @ SV17 )
= $false )
| ( ( gt @ SV17 @ SV47 )
= $false )
| ( ( ssItem @ SV47 )
= $false )
| ( ( ssItem @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(508,plain,
! [SV48: $i,SV18: $i,SV69: $i] :
( ( ( ssList @ SV69 )
= $false )
| ( ( ( app @ ( app @ SV18 @ SV48 ) @ SV69 )
= ( app @ SV18 @ ( app @ SV48 @ SV69 ) ) )
= $true )
| ( ( ssList @ SV48 )
= $false )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(509,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( geq @ SV20 @ SV49 )
| ~ ( geq @ SV49 @ SV20 ) )
= $true )
| ( ( SV20 = SV49 )
= $true )
| ( ( ssItem @ SV49 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(510,plain,
! [SV50: $i,SV21: $i,SV70: $i] :
( ( ( ssList @ SV70 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SV70 ) )
| ( rearsegP @ SV21 @ SV70 ) )
= $true )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(511,plain,
! [SV24: $i,SV52: $i,SV71: $i] :
( ( ( ssList @ SV71 )
= $false )
| ( ( ~ ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) ) ) )
= $true )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(512,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( segmentP @ SV25 @ SV53 )
| ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(513,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) )
| ( segmentP @ SV25 @ SV53 ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(514,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( neq @ SV26 @ SV54 )
| ( SV26 != SV54 ) )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(515,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( ( SV26 != SV54 ) )
| ( neq @ SV26 @ SV54 ) )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(516,plain,
! [SV29: $i,SV56: $i,SV72: $i] :
( ( ( ssList @ SV72 )
= $false )
| ( ( ( ( app @ SV72 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
| ( SV72 = SV29 ) )
= $true )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(517,plain,
( ( ~ ( ~ ( ssItem @ sK6_SY139 )
| ~ ( ( sK2_SX0 != sK6_SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(518,plain,
! [SV57: $i,SV30: $i,SV73: $i] :
( ( ( ssItem @ SV73 )
= $false )
| ( ( ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SV73 ) )
| ( geq @ SV30 @ SV73 ) )
= $true )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(519,plain,
! [SV58: $i,SV31: $i,SV74: $i] :
( ( ( ssList @ SV74 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SV74 ) )
| ( frontsegP @ SV31 @ SV74 ) )
= $true )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(520,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( frontsegP @ SV32 @ SV59 )
| ~ ( frontsegP @ SV59 @ SV32 ) )
= $true )
| ( ( SV32 = SV59 )
= $true )
| ( ( ssList @ SV59 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(521,plain,
! [SV60: $i,SV33: $i,SV75: $i] :
( ( ( ssItem @ SV75 )
= $false )
| ( ( ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SV75 ) )
| ( leq @ SV33 @ SV75 ) )
= $true )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(522,plain,
! [SV61: $i,SV34: $i,SV76: $i] :
( ( ( ssList @ SV76 )
= $false )
| ( ( ! [SY167: $i] :
( ~ ( ssList @ SY167 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SY167 ) @ SV61 ) ) )
= $true )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(523,plain,
! [SV62: $i,SV35: $i,SV77: $i] :
( ( ( ssItem @ SV77 )
= $false )
| ( ( ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SV77 ) )
| ( gt @ SV35 @ SV77 ) )
= $true )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(524,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( neq @ SV36 @ SV63 )
| ( SV36 != SV63 ) )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(525,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( ( SV36 != SV63 ) )
| ( neq @ SV36 @ SV63 ) )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(526,plain,
( ( ( sK3_SX0 != sK5_SY163 )
| ( sK1_U != sK4_SY140 )
| ~ ( segmentP @ sK5_SY163 @ sK4_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(527,plain,
( ( ~ ( totalorderedP @ sK4_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(528,plain,
( ( ~ ( ssItem @ sK7_SY142 )
| ~ ( memberP @ sK1_U @ sK7_SY142 )
| ( memberP @ sK3_SX0 @ sK7_SY142 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[497]) ).
thf(529,plain,
! [SV37: $i,SV2: $i,SV64: $i,SV78: $i] :
( ( ( ~ ( ssItem @ SV78 )
| ( ( cons @ SV64 @ SV2 )
!= ( cons @ SV78 @ SV37 ) )
| ~ ( ( SV64 != SV78 )
| ( SV37 != SV2 ) ) )
= $true )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(530,plain,
! [SV38: $i,SV3: $i] :
( ( ( ~ ( rearsegP @ SV3 @ SV38 ) )
= $true )
| ( ( ~ ( rearsegP @ SV38 @ SV3 ) )
= $true )
| ( ( SV3 = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(531,plain,
! [SV4: $i,SV65: $i,SV39: $i] :
( ( ( ( app @ SV39 @ SV65 )
!= ( app @ SV39 @ SV4 ) )
= $true )
| ( ( SV65 = SV4 )
= $true )
| ( ( ssList @ SV65 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(532,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV40 ) )
= $true )
| ( ( ~ ( leq @ SV40 @ SV8 ) )
= $true )
| ( ( SV8 = SV40 )
= $true )
| ( ( ssItem @ SV40 )
= $false )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(533,plain,
! [SV66: $i,SV42: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SV66 ) ) )
= $true )
| ( ( lt @ SV10 @ SV66 )
= $true )
| ( ( ssItem @ SV66 )
= $false )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(534,plain,
! [SV67: $i,SV43: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SV67 ) ) )
= $true )
| ( ( segmentP @ SV11 @ SV67 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(535,plain,
! [SV13: $i,SV68: $i,SV45: $i] :
( ( ( ~ ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) ) )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(536,plain,
! [SV46: $i,SV16: $i] :
( ( ( ~ ( segmentP @ SV16 @ SV46 ) )
= $true )
| ( ( ~ ( segmentP @ SV46 @ SV16 ) )
= $true )
| ( ( SV16 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(537,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( geq @ SV20 @ SV49 ) )
= $true )
| ( ( ~ ( geq @ SV49 @ SV20 ) )
= $true )
| ( ( SV20 = SV49 )
= $true )
| ( ( ssItem @ SV49 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(538,plain,
! [SV70: $i,SV50: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SV70 ) ) )
= $true )
| ( ( rearsegP @ SV21 @ SV70 )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(539,plain,
! [SV24: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) ) )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(540,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( segmentP @ SV25 @ SV53 ) )
= $true )
| ( ( ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(541,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(542,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( neq @ SV26 @ SV54 ) )
= $true )
| ( ( SV26 != SV54 )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(543,plain,
! [SV54: $i,SV26: $i] :
( ( ( ~ ( ( SV26 != SV54 ) ) )
= $true )
| ( ( neq @ SV26 @ SV54 )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(544,plain,
! [SV29: $i,SV56: $i,SV72: $i] :
( ( ( ( app @ SV72 @ SV56 )
!= ( app @ SV29 @ SV56 ) )
= $true )
| ( ( SV72 = SV29 )
= $true )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(545,plain,
( ( ~ ( ssItem @ sK6_SY139 )
| ~ ( ( sK2_SX0 != sK6_SY139 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(546,plain,
! [SV73: $i,SV57: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SV73 ) ) )
= $true )
| ( ( geq @ SV30 @ SV73 )
= $true )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(547,plain,
! [SV74: $i,SV58: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SV74 ) ) )
= $true )
| ( ( frontsegP @ SV31 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(548,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( frontsegP @ SV32 @ SV59 ) )
= $true )
| ( ( ~ ( frontsegP @ SV59 @ SV32 ) )
= $true )
| ( ( SV32 = SV59 )
= $true )
| ( ( ssList @ SV59 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(549,plain,
! [SV75: $i,SV60: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SV75 ) ) )
= $true )
| ( ( leq @ SV33 @ SV75 )
= $true )
| ( ( ssItem @ SV75 )
= $false )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(550,plain,
! [SV76: $i,SV61: $i,SV34: $i,SV79: $i] :
( ( ( ~ ( ssList @ SV79 )
| ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SV79 ) @ SV61 ) )
= $true )
| ( ( ssList @ SV76 )
= $false )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(551,plain,
! [SV77: $i,SV62: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SV77 ) ) )
= $true )
| ( ( gt @ SV35 @ SV77 )
= $true )
| ( ( ssItem @ SV77 )
= $false )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(552,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( neq @ SV36 @ SV63 ) )
= $true )
| ( ( SV36 != SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(553,plain,
! [SV63: $i,SV36: $i] :
( ( ( ~ ( ( SV36 != SV63 ) ) )
= $true )
| ( ( neq @ SV36 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(554,plain,
( ( ( sK3_SX0 != sK5_SY163 )
| ( sK1_U != sK4_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(555,plain,
( ( ~ ( segmentP @ sK5_SY163 @ sK4_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(556,plain,
( ( totalorderedP @ sK4_SY140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(557,plain,
( ( ~ ( ssItem @ sK7_SY142 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(558,plain,
( ( ~ ( memberP @ sK1_U @ sK7_SY142 )
| ( memberP @ sK3_SX0 @ sK7_SY142 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(559,plain,
! [SV37: $i,SV2: $i,SV64: $i,SV78: $i] :
( ( ( ~ ( ssItem @ SV78 ) )
= $true )
| ( ( ( ( cons @ SV64 @ SV2 )
!= ( cons @ SV78 @ SV37 ) )
| ~ ( ( SV64 != SV78 )
| ( SV37 != SV2 ) ) )
= $true )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(560,plain,
! [SV38: $i,SV3: $i] :
( ( ( rearsegP @ SV3 @ SV38 )
= $false )
| ( ( ~ ( rearsegP @ SV38 @ SV3 ) )
= $true )
| ( ( SV3 = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(561,plain,
! [SV4: $i,SV65: $i,SV39: $i] :
( ( ( ( app @ SV39 @ SV65 )
= ( app @ SV39 @ SV4 ) )
= $false )
| ( ( SV65 = SV4 )
= $true )
| ( ( ssList @ SV65 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(562,plain,
! [SV40: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV40 )
= $false )
| ( ( ~ ( leq @ SV40 @ SV8 ) )
= $true )
| ( ( SV8 = SV40 )
= $true )
| ( ( ssItem @ SV40 )
= $false )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(563,plain,
! [SV66: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SV66 ) ) )
= $false )
| ( ( lt @ SV10 @ SV66 )
= $true )
| ( ( ssItem @ SV66 )
= $false )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(564,plain,
! [SV67: $i,SV43: $i,SV11: $i] :
( ( ( ~ ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SV67 ) ) )
= $false )
| ( ( segmentP @ SV11 @ SV67 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(565,plain,
! [SV13: $i,SV68: $i,SV45: $i] :
( ( ( ~ ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) ) )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(566,plain,
! [SV68: $i,SV13: $i,SV45: $i] :
( ( ( ~ ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) ) )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(567,plain,
! [SV46: $i,SV16: $i] :
( ( ( segmentP @ SV16 @ SV46 )
= $false )
| ( ( ~ ( segmentP @ SV46 @ SV16 ) )
= $true )
| ( ( SV16 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(568,plain,
! [SV49: $i,SV20: $i] :
( ( ( geq @ SV20 @ SV49 )
= $false )
| ( ( ~ ( geq @ SV49 @ SV20 ) )
= $true )
| ( ( SV20 = SV49 )
= $true )
| ( ( ssItem @ SV49 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(569,plain,
! [SV70: $i,SV50: $i,SV21: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SV70 ) ) )
= $false )
| ( ( rearsegP @ SV21 @ SV70 )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(570,plain,
! [SV24: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) ) )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(571,plain,
! [SV71: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) ) )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(572,plain,
! [SV53: $i,SV25: $i] :
( ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ~ ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(573,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(574,plain,
! [SV54: $i,SV26: $i] :
( ( ( neq @ SV26 @ SV54 )
= $false )
| ( ( SV26 != SV54 )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(575,plain,
! [SV54: $i,SV26: $i] :
( ( ( SV26 != SV54 )
= $false )
| ( ( neq @ SV26 @ SV54 )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(576,plain,
! [SV29: $i,SV56: $i,SV72: $i] :
( ( ( ( app @ SV72 @ SV56 )
= ( app @ SV29 @ SV56 ) )
= $false )
| ( ( SV72 = SV29 )
= $true )
| ( ( ssList @ SV72 )
= $false )
| ( ( ssList @ SV56 )
= $false )
| ( ( ssList @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(577,plain,
( ( ~ ( ssItem @ sK6_SY139 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(578,plain,
( ( ~ ( ( sK2_SX0 != sK6_SY139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(579,plain,
! [SV73: $i,SV57: $i,SV30: $i] :
( ( ( ~ ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SV73 ) ) )
= $false )
| ( ( geq @ SV30 @ SV73 )
= $true )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(580,plain,
! [SV74: $i,SV58: $i,SV31: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SV74 ) ) )
= $false )
| ( ( frontsegP @ SV31 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(581,plain,
! [SV59: $i,SV32: $i] :
( ( ( frontsegP @ SV32 @ SV59 )
= $false )
| ( ( ~ ( frontsegP @ SV59 @ SV32 ) )
= $true )
| ( ( SV32 = SV59 )
= $true )
| ( ( ssList @ SV59 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(582,plain,
! [SV75: $i,SV60: $i,SV33: $i] :
( ( ( ~ ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SV75 ) ) )
= $false )
| ( ( leq @ SV33 @ SV75 )
= $true )
| ( ( ssItem @ SV75 )
= $false )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(583,plain,
! [SV76: $i,SV61: $i,SV34: $i,SV79: $i] :
( ( ( ~ ( ssList @ SV79 ) )
= $true )
| ( ( ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SV79 ) @ SV61 ) )
= $true )
| ( ( ssList @ SV76 )
= $false )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(584,plain,
! [SV77: $i,SV62: $i,SV35: $i] :
( ( ( ~ ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SV77 ) ) )
= $false )
| ( ( gt @ SV35 @ SV77 )
= $true )
| ( ( ssItem @ SV77 )
= $false )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(585,plain,
! [SV63: $i,SV36: $i] :
( ( ( neq @ SV36 @ SV63 )
= $false )
| ( ( SV36 != SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(586,plain,
! [SV63: $i,SV36: $i] :
( ( ( SV36 != SV63 )
= $false )
| ( ( neq @ SV36 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(587,plain,
( ( sK3_SX0 != sK5_SY163 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(588,plain,
( ( sK1_U != sK4_SY140 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(589,plain,
( ( segmentP @ sK5_SY163 @ sK4_SY140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(590,plain,
( ( ssItem @ sK7_SY142 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(591,plain,
( ( ~ ( memberP @ sK1_U @ sK7_SY142 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(592,plain,
( ( memberP @ sK3_SX0 @ sK7_SY142 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(593,plain,
! [SV37: $i,SV2: $i,SV64: $i,SV78: $i] :
( ( ( ssItem @ SV78 )
= $false )
| ( ( ( ( cons @ SV64 @ SV2 )
!= ( cons @ SV78 @ SV37 ) )
| ~ ( ( SV64 != SV78 )
| ( SV37 != SV2 ) ) )
= $true )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(594,plain,
! [SV3: $i,SV38: $i] :
( ( ( rearsegP @ SV38 @ SV3 )
= $false )
| ( ( rearsegP @ SV3 @ SV38 )
= $false )
| ( ( SV3 = SV38 )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(595,plain,
! [SV8: $i,SV40: $i] :
( ( ( leq @ SV40 @ SV8 )
= $false )
| ( ( leq @ SV8 @ SV40 )
= $false )
| ( ( SV8 = SV40 )
= $true )
| ( ( ssItem @ SV40 )
= $false )
| ( ( ssItem @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(596,plain,
! [SV66: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( lt @ SV10 @ SV42 )
| ~ ( lt @ SV42 @ SV66 ) )
= $true )
| ( ( lt @ SV10 @ SV66 )
= $true )
| ( ( ssItem @ SV66 )
= $false )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(597,plain,
! [SV67: $i,SV43: $i,SV11: $i] :
( ( ( ~ ( segmentP @ SV11 @ SV43 )
| ~ ( segmentP @ SV43 @ SV67 ) )
= $true )
| ( ( segmentP @ SV11 @ SV67 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(598,plain,
! [SV13: $i,SV68: $i,SV45: $i] :
( ( ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
| ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(599,plain,
! [SV68: $i,SV13: $i,SV45: $i] :
( ( ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
| ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(600,plain,
! [SV16: $i,SV46: $i] :
( ( ( segmentP @ SV46 @ SV16 )
= $false )
| ( ( segmentP @ SV16 @ SV46 )
= $false )
| ( ( SV16 = SV46 )
= $true )
| ( ( ssList @ SV46 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(601,plain,
! [SV20: $i,SV49: $i] :
( ( ( geq @ SV49 @ SV20 )
= $false )
| ( ( geq @ SV20 @ SV49 )
= $false )
| ( ( SV20 = SV49 )
= $true )
| ( ( ssItem @ SV49 )
= $false )
| ( ( ssItem @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(602,plain,
! [SV70: $i,SV50: $i,SV21: $i] :
( ( ( ~ ( rearsegP @ SV21 @ SV50 )
| ~ ( rearsegP @ SV50 @ SV70 ) )
= $true )
| ( ( rearsegP @ SV21 @ SV70 )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(603,plain,
! [SV24: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
| ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(604,plain,
! [SV71: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
| ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(605,plain,
! [SV25: $i,SV53: $i] :
( ( ( ! [SY152: $i] :
~ ~ ( ~ ( ssList @ SY152 )
| ~ ~ ! [SY153: $i] :
~ ~ ( ~ ( ssList @ SY153 )
| ( ( app @ ( app @ SY152 @ SV53 ) @ SY153 )
!= SV25 ) ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(606,plain,
! [SV25: $i,SV53: $i] :
( ( ( ! [SY154: $i] :
~ ~ ( ~ ( ssList @ SY154 )
| ~ ~ ! [SY155: $i] :
~ ~ ( ~ ( ssList @ SY155 )
| ( ( app @ ( app @ SY154 @ SV53 ) @ SY155 )
!= SV25 ) ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(607,plain,
! [SV54: $i,SV26: $i] :
( ( ( SV26 = SV54 )
= $false )
| ( ( neq @ SV26 @ SV54 )
= $false )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(608,plain,
! [SV54: $i,SV26: $i] :
( ( ( SV26 = SV54 )
= $true )
| ( ( neq @ SV26 @ SV54 )
= $true )
| ( ( ssItem @ SV54 )
= $false )
| ( ( ssItem @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(609,plain,
( ( ssItem @ sK6_SY139 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(610,plain,
( ( sK2_SX0 != sK6_SY139 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(611,plain,
! [SV73: $i,SV57: $i,SV30: $i] :
( ( ( ~ ( geq @ SV30 @ SV57 )
| ~ ( geq @ SV57 @ SV73 ) )
= $true )
| ( ( geq @ SV30 @ SV73 )
= $true )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(612,plain,
! [SV74: $i,SV58: $i,SV31: $i] :
( ( ( ~ ( frontsegP @ SV31 @ SV58 )
| ~ ( frontsegP @ SV58 @ SV74 ) )
= $true )
| ( ( frontsegP @ SV31 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(613,plain,
! [SV32: $i,SV59: $i] :
( ( ( frontsegP @ SV59 @ SV32 )
= $false )
| ( ( frontsegP @ SV32 @ SV59 )
= $false )
| ( ( SV32 = SV59 )
= $true )
| ( ( ssList @ SV59 )
= $false )
| ( ( ssList @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(614,plain,
! [SV75: $i,SV60: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV60 )
| ~ ( leq @ SV60 @ SV75 ) )
= $true )
| ( ( leq @ SV33 @ SV75 )
= $true )
| ( ( ssItem @ SV75 )
= $false )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(615,plain,
! [SV76: $i,SV61: $i,SV34: $i,SV79: $i] :
( ( ( ssList @ SV79 )
= $false )
| ( ( ~ ( segmentP @ SV34 @ SV61 )
| ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SV79 ) @ SV61 ) )
= $true )
| ( ( ssList @ SV76 )
= $false )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(616,plain,
! [SV77: $i,SV62: $i,SV35: $i] :
( ( ( ~ ( gt @ SV35 @ SV62 )
| ~ ( gt @ SV62 @ SV77 ) )
= $true )
| ( ( gt @ SV35 @ SV77 )
= $true )
| ( ( ssItem @ SV77 )
= $false )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(617,plain,
! [SV63: $i,SV36: $i] :
( ( ( SV36 = SV63 )
= $false )
| ( ( neq @ SV36 @ SV63 )
= $false )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(618,plain,
! [SV63: $i,SV36: $i] :
( ( ( SV36 = SV63 )
= $true )
| ( ( neq @ SV36 @ SV63 )
= $true )
| ( ( ssList @ SV63 )
= $false )
| ( ( ssList @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(619,plain,
( ( sK3_SX0 = sK5_SY163 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(620,plain,
( ( sK1_U = sK4_SY140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(621,plain,
( ( memberP @ sK1_U @ sK7_SY142 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(622,plain,
! [SV37: $i,SV78: $i,SV2: $i,SV64: $i] :
( ( ( ( cons @ SV64 @ SV2 )
!= ( cons @ SV78 @ SV37 ) )
= $true )
| ( ( ~ ( ( SV64 != SV78 )
| ( SV37 != SV2 ) ) )
= $true )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(623,plain,
! [SV66: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( lt @ SV10 @ SV42 ) )
= $true )
| ( ( ~ ( lt @ SV42 @ SV66 ) )
= $true )
| ( ( lt @ SV10 @ SV66 )
= $true )
| ( ( ssItem @ SV66 )
= $false )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(624,plain,
! [SV67: $i,SV43: $i,SV11: $i] :
( ( ( ~ ( segmentP @ SV11 @ SV43 ) )
= $true )
| ( ( ~ ( segmentP @ SV43 @ SV67 ) )
= $true )
| ( ( segmentP @ SV11 @ SV67 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(625,plain,
! [SV13: $i,SV68: $i,SV45: $i] :
( ( ( ~ ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 ) )
= $true )
| ( ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(626,plain,
! [SV68: $i,SV13: $i,SV45: $i] :
( ( ( ~ ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) ) )
= $true )
| ( ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(627,plain,
! [SV70: $i,SV50: $i,SV21: $i] :
( ( ( ~ ( rearsegP @ SV21 @ SV50 ) )
= $true )
| ( ( ~ ( rearsegP @ SV50 @ SV70 ) )
= $true )
| ( ( rearsegP @ SV21 @ SV70 )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(628,plain,
! [SV24: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 ) )
= $true )
| ( ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(629,plain,
! [SV71: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) ) )
= $true )
| ( ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(630,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK8_SY152 @ SV25 @ SV53 ) )
| ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( ssList @ SY168 )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ SY168 )
!= SV25 ) ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[605]) ).
thf(631,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV80 )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(632,plain,
( ( sK2_SX0 = sK6_SY139 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(633,plain,
! [SV73: $i,SV57: $i,SV30: $i] :
( ( ( ~ ( geq @ SV30 @ SV57 ) )
= $true )
| ( ( ~ ( geq @ SV57 @ SV73 ) )
= $true )
| ( ( geq @ SV30 @ SV73 )
= $true )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(634,plain,
! [SV74: $i,SV58: $i,SV31: $i] :
( ( ( ~ ( frontsegP @ SV31 @ SV58 ) )
= $true )
| ( ( ~ ( frontsegP @ SV58 @ SV74 ) )
= $true )
| ( ( frontsegP @ SV31 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(635,plain,
! [SV75: $i,SV60: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV60 ) )
= $true )
| ( ( ~ ( leq @ SV60 @ SV75 ) )
= $true )
| ( ( leq @ SV33 @ SV75 )
= $true )
| ( ( ssItem @ SV75 )
= $false )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(636,plain,
! [SV79: $i,SV76: $i,SV61: $i,SV34: $i] :
( ( ( ~ ( segmentP @ SV34 @ SV61 ) )
= $true )
| ( ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SV79 ) @ SV61 )
= $true )
| ( ( ssList @ SV79 )
= $false )
| ( ( ssList @ SV76 )
= $false )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(637,plain,
! [SV77: $i,SV62: $i,SV35: $i] :
( ( ( ~ ( gt @ SV35 @ SV62 ) )
= $true )
| ( ( ~ ( gt @ SV62 @ SV77 ) )
= $true )
| ( ( gt @ SV35 @ SV77 )
= $true )
| ( ( ssItem @ SV77 )
= $false )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(638,plain,
! [SV37: $i,SV78: $i,SV2: $i,SV64: $i] :
( ( ( ( cons @ SV64 @ SV2 )
= ( cons @ SV78 @ SV37 ) )
= $false )
| ( ( ~ ( ( SV64 != SV78 )
| ( SV37 != SV2 ) ) )
= $true )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(639,plain,
! [SV66: $i,SV42: $i,SV10: $i] :
( ( ( lt @ SV10 @ SV42 )
= $false )
| ( ( ~ ( lt @ SV42 @ SV66 ) )
= $true )
| ( ( lt @ SV10 @ SV66 )
= $true )
| ( ( ssItem @ SV66 )
= $false )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(640,plain,
! [SV67: $i,SV43: $i,SV11: $i] :
( ( ( segmentP @ SV11 @ SV43 )
= $false )
| ( ( ~ ( segmentP @ SV43 @ SV67 ) )
= $true )
| ( ( segmentP @ SV11 @ SV67 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(641,plain,
! [SV13: $i,SV68: $i,SV45: $i] :
( ( ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
= $false )
| ( ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(642,plain,
! [SV68: $i,SV13: $i,SV45: $i] :
( ( ( ( memberP @ SV45 @ SV13 )
| ( memberP @ SV68 @ SV13 ) )
= $false )
| ( ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(643,plain,
! [SV70: $i,SV50: $i,SV21: $i] :
( ( ( rearsegP @ SV21 @ SV50 )
= $false )
| ( ( ~ ( rearsegP @ SV50 @ SV70 ) )
= $true )
| ( ( rearsegP @ SV21 @ SV70 )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(644,plain,
! [SV24: $i,SV71: $i,SV52: $i] :
( ( ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
= $false )
| ( ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(645,plain,
! [SV71: $i,SV52: $i,SV24: $i] :
( ( ( ( SV24 = SV52 )
| ( memberP @ SV71 @ SV24 ) )
= $false )
| ( ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(646,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK8_SY152 @ SV25 @ SV53 ) )
| ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( ssList @ SY168 )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ SY168 )
!= SV25 ) ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(647,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ~ ( ~ ( ssList @ SV80 )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(648,plain,
! [SV73: $i,SV57: $i,SV30: $i] :
( ( ( geq @ SV30 @ SV57 )
= $false )
| ( ( ~ ( geq @ SV57 @ SV73 ) )
= $true )
| ( ( geq @ SV30 @ SV73 )
= $true )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(649,plain,
! [SV74: $i,SV58: $i,SV31: $i] :
( ( ( frontsegP @ SV31 @ SV58 )
= $false )
| ( ( ~ ( frontsegP @ SV58 @ SV74 ) )
= $true )
| ( ( frontsegP @ SV31 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(650,plain,
! [SV75: $i,SV60: $i,SV33: $i] :
( ( ( leq @ SV33 @ SV60 )
= $false )
| ( ( ~ ( leq @ SV60 @ SV75 ) )
= $true )
| ( ( leq @ SV33 @ SV75 )
= $true )
| ( ( ssItem @ SV75 )
= $false )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(651,plain,
! [SV79: $i,SV76: $i,SV61: $i,SV34: $i] :
( ( ( segmentP @ SV34 @ SV61 )
= $false )
| ( ( segmentP @ ( app @ ( app @ SV76 @ SV34 ) @ SV79 ) @ SV61 )
= $true )
| ( ( ssList @ SV79 )
= $false )
| ( ( ssList @ SV76 )
= $false )
| ( ( ssList @ SV61 )
= $false )
| ( ( ssList @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(652,plain,
! [SV77: $i,SV62: $i,SV35: $i] :
( ( ( gt @ SV35 @ SV62 )
= $false )
| ( ( ~ ( gt @ SV62 @ SV77 ) )
= $true )
| ( ( gt @ SV35 @ SV77 )
= $true )
| ( ( ssItem @ SV77 )
= $false )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(653,plain,
! [SV2: $i,SV37: $i,SV78: $i,SV64: $i] :
( ( ( ( SV64 != SV78 )
| ( SV37 != SV2 ) )
= $false )
| ( ( ( cons @ SV64 @ SV2 )
= ( cons @ SV78 @ SV37 ) )
= $false )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(654,plain,
! [SV10: $i,SV66: $i,SV42: $i] :
( ( ( lt @ SV42 @ SV66 )
= $false )
| ( ( lt @ SV10 @ SV42 )
= $false )
| ( ( lt @ SV10 @ SV66 )
= $true )
| ( ( ssItem @ SV66 )
= $false )
| ( ( ssItem @ SV42 )
= $false )
| ( ( ssItem @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(655,plain,
! [SV11: $i,SV67: $i,SV43: $i] :
( ( ( segmentP @ SV43 @ SV67 )
= $false )
| ( ( segmentP @ SV11 @ SV43 )
= $false )
| ( ( segmentP @ SV11 @ SV67 )
= $true )
| ( ( ssList @ SV67 )
= $false )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(656,plain,
! [SV68: $i,SV13: $i,SV45: $i] :
( ( ( memberP @ SV45 @ SV13 )
= $true )
| ( ( memberP @ SV68 @ SV13 )
= $true )
| ( ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
= $false )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(657,plain,
! [SV68: $i,SV13: $i,SV45: $i] :
( ( ( memberP @ SV45 @ SV13 )
= $false )
| ( ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(658,plain,
! [SV45: $i,SV13: $i,SV68: $i] :
( ( ( memberP @ SV68 @ SV13 )
= $false )
| ( ( memberP @ ( app @ SV45 @ SV68 ) @ SV13 )
= $true )
| ( ( ssList @ SV68 )
= $false )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssItem @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(659,plain,
! [SV21: $i,SV70: $i,SV50: $i] :
( ( ( rearsegP @ SV50 @ SV70 )
= $false )
| ( ( rearsegP @ SV21 @ SV50 )
= $false )
| ( ( rearsegP @ SV21 @ SV70 )
= $true )
| ( ( ssList @ SV70 )
= $false )
| ( ( ssList @ SV50 )
= $false )
| ( ( ssList @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(660,plain,
! [SV71: $i,SV52: $i,SV24: $i] :
( ( ( SV24 = SV52 )
= $true )
| ( ( memberP @ SV71 @ SV24 )
= $true )
| ( ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
= $false )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(661,plain,
! [SV71: $i,SV52: $i,SV24: $i] :
( ( ( SV24 = SV52 )
= $false )
| ( ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(662,plain,
! [SV52: $i,SV24: $i,SV71: $i] :
( ( ( memberP @ SV71 @ SV24 )
= $false )
| ( ( memberP @ ( cons @ SV52 @ SV71 ) @ SV24 )
= $true )
| ( ( ssList @ SV71 )
= $false )
| ( ( ssItem @ SV52 )
= $false )
| ( ( ssItem @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(663,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( ssList @ ( sK8_SY152 @ SV25 @ SV53 ) )
| ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( ssList @ SY168 )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ SY168 )
!= SV25 ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(664,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ~ ( ssList @ SV80 )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(665,plain,
! [SV30: $i,SV73: $i,SV57: $i] :
( ( ( geq @ SV57 @ SV73 )
= $false )
| ( ( geq @ SV30 @ SV57 )
= $false )
| ( ( geq @ SV30 @ SV73 )
= $true )
| ( ( ssItem @ SV73 )
= $false )
| ( ( ssItem @ SV57 )
= $false )
| ( ( ssItem @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(666,plain,
! [SV31: $i,SV74: $i,SV58: $i] :
( ( ( frontsegP @ SV58 @ SV74 )
= $false )
| ( ( frontsegP @ SV31 @ SV58 )
= $false )
| ( ( frontsegP @ SV31 @ SV74 )
= $true )
| ( ( ssList @ SV74 )
= $false )
| ( ( ssList @ SV58 )
= $false )
| ( ( ssList @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(667,plain,
! [SV33: $i,SV75: $i,SV60: $i] :
( ( ( leq @ SV60 @ SV75 )
= $false )
| ( ( leq @ SV33 @ SV60 )
= $false )
| ( ( leq @ SV33 @ SV75 )
= $true )
| ( ( ssItem @ SV75 )
= $false )
| ( ( ssItem @ SV60 )
= $false )
| ( ( ssItem @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(668,plain,
! [SV35: $i,SV77: $i,SV62: $i] :
( ( ( gt @ SV62 @ SV77 )
= $false )
| ( ( gt @ SV35 @ SV62 )
= $false )
| ( ( gt @ SV35 @ SV77 )
= $true )
| ( ( ssItem @ SV77 )
= $false )
| ( ( ssItem @ SV62 )
= $false )
| ( ( ssItem @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(669,plain,
! [SV37: $i,SV2: $i,SV78: $i,SV64: $i] :
( ( ( SV64 != SV78 )
= $false )
| ( ( ( cons @ SV64 @ SV2 )
= ( cons @ SV78 @ SV37 ) )
= $false )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(670,plain,
! [SV78: $i,SV64: $i,SV2: $i,SV37: $i] :
( ( ( SV37 != SV2 )
= $false )
| ( ( ( cons @ SV64 @ SV2 )
= ( cons @ SV78 @ SV37 ) )
= $false )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(671,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ( ssList @ ( sK8_SY152 @ SV25 @ SV53 ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(672,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( ssList @ SY168 )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ SY168 )
!= SV25 ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(673,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ~ ( ssList @ SV80 ) )
= $true )
| ( ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(674,plain,
! [SV37: $i,SV2: $i,SV78: $i,SV64: $i] :
( ( ( SV64 = SV78 )
= $true )
| ( ( ( cons @ SV64 @ SV2 )
= ( cons @ SV78 @ SV37 ) )
= $false )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(675,plain,
! [SV78: $i,SV64: $i,SV2: $i,SV37: $i] :
( ( ( SV37 = SV2 )
= $true )
| ( ( ( cons @ SV64 @ SV2 )
= ( cons @ SV78 @ SV37 ) )
= $false )
| ( ( ssItem @ SV78 )
= $false )
| ( ( ssItem @ SV64 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(676,plain,
! [SV53: $i,SV25: $i] :
( ( ( ssList @ ( sK8_SY152 @ SV25 @ SV53 ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(677,plain,
! [SV53: $i,SV25: $i] :
( ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( ssList @ SY168 )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ SY168 )
!= SV25 ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(678,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ssList @ SV80 )
= $false )
| ( ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(679,plain,
! [SV53: $i,SV25: $i] :
( ( ( ! [SY168: $i] :
~ ~ ( ~ ( ssList @ SY168 )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ SY168 )
!= SV25 ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(680,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ~ ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(681,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK9_SY168 @ SV53 @ SV25 ) )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ ( sK9_SY168 @ SV53 @ SV25 ) )
!= SV25 ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[679]) ).
thf(682,plain,
! [SV25: $i,SV53: $i,SV80: $i] :
( ( ( ! [SY169: $i] :
~ ~ ( ~ ( ssList @ SY169 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SY169 )
!= SV25 ) ) )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(683,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK9_SY168 @ SV53 @ SV25 ) )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ ( sK9_SY168 @ SV53 @ SV25 ) )
!= SV25 ) ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(684,plain,
! [SV25: $i,SV53: $i,SV80: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( ssList @ SV81 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SV81 )
!= SV25 ) ) )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(685,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( ssList @ ( sK9_SY168 @ SV53 @ SV25 ) )
| ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ ( sK9_SY168 @ SV53 @ SV25 ) )
!= SV25 ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(686,plain,
! [SV25: $i,SV53: $i,SV80: $i,SV81: $i] :
( ( ( ~ ( ~ ( ssList @ SV81 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SV81 )
!= SV25 ) ) )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(687,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( ssList @ ( sK9_SY168 @ SV53 @ SV25 ) ) )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(688,plain,
! [SV53: $i,SV25: $i] :
( ( ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ ( sK9_SY168 @ SV53 @ SV25 ) )
!= SV25 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(689,plain,
! [SV25: $i,SV53: $i,SV80: $i,SV81: $i] :
( ( ( ~ ( ssList @ SV81 )
| ( ( app @ ( app @ SV80 @ SV53 ) @ SV81 )
!= SV25 ) )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(690,plain,
! [SV25: $i,SV53: $i] :
( ( ( ssList @ ( sK9_SY168 @ SV53 @ SV25 ) )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(691,plain,
! [SV53: $i,SV25: $i] :
( ( ( ( app @ ( app @ ( sK8_SY152 @ SV25 @ SV53 ) @ SV53 ) @ ( sK9_SY168 @ SV53 @ SV25 ) )
= SV25 )
= $true )
| ( ( segmentP @ SV25 @ SV53 )
= $false )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(692,plain,
! [SV25: $i,SV53: $i,SV80: $i,SV81: $i] :
( ( ( ~ ( ssList @ SV81 ) )
= $true )
| ( ( ( app @ ( app @ SV80 @ SV53 ) @ SV81 )
!= SV25 )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(693,plain,
! [SV25: $i,SV53: $i,SV80: $i,SV81: $i] :
( ( ( ssList @ SV81 )
= $false )
| ( ( ( app @ ( app @ SV80 @ SV53 ) @ SV81 )
!= SV25 )
= $true )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(694,plain,
! [SV25: $i,SV81: $i,SV53: $i,SV80: $i] :
( ( ( ( app @ ( app @ SV80 @ SV53 ) @ SV81 )
= SV25 )
= $false )
| ( ( ssList @ SV81 )
= $false )
| ( ( ssList @ SV80 )
= $false )
| ( ( segmentP @ SV25 @ SV53 )
= $true )
| ( ( ssList @ SV53 )
= $false )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(695,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[147,694,691,690,676,675,674,668,667,666,665,662,661,660,659,658,657,656,655,654,651,632,621,620,619,618,617,613,609,608,607,601,600,595,594,592,590,589,576,561,556,508,507,502,495,469,468,450,433,424,422,411,367,341,339,323,319,315,311,310,297,181,171]) ).
thf(696,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC400+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
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 16:13:24 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.68/5.14 .
% 24.68/5.14
% 24.68/5.14 No.of.Axioms: 39
% 24.68/5.14
% 24.68/5.14 Length.of.Defs: 0
% 24.68/5.14
% 24.68/5.14 Contains.Choice.Funs: false
% 24.68/5.14 ....................
% 24.68/5.14
% 24.68/5.14 ********************************
% 24.68/5.14 * All subproblems solved! *
% 24.68/5.14 ********************************
% 24.68/5.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:40,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:695,loop_count:0,foatp_calls:1,translation:fof_full)
% 24.68/5.14
% 24.68/5.14 %**** Beginning of derivation protocol ****
% 24.68/5.14 % SZS output start CNFRefutation
% See solution above
% 24.68/5.15
% 24.68/5.15 %**** End of derivation protocol ****
% 24.68/5.15 %**** no. of clauses in derivation: 640 ****
% 24.68/5.15 %**** clause counter: 695 ****
% 24.68/5.15
% 24.68/5.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:40,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:695,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------