%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWC255+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:53:03 AM UTC 2026
% Result : Theorem 1.13s 0.46s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 36
% Syntax : Number of formulae : 440 ( 163 unt; 0 typ; 0 def)
% Number of atoms : 3659 (1363 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 4772 (1127 ~;1134 |; 31 &;2272 @)
% ( 18 <=>; 190 =>; 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 : 32 ( 29 usr; 7 con; 0-2 aty)
% Number of variables : 735 ( 0 ^; 732 !; 3 ?; 735 :)
% 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_SY73,type,
sK3_SY73: $i ).
thf(tp_sK4_SY77,type,
sK4_SY77: $i ).
thf(tp_sK5_SY62,type,
sK5_SY62: $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(12,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(13,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
thf(14,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( app @ ( app @ U @ V ) @ W )
= ( app @ U @ ( app @ V @ W ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
thf(16,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ V @ W )
= ( app @ V @ U ) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
thf(17,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( app @ W @ V )
= ( app @ U @ V ) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
thf(20,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(22,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(24,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(27,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(30,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(32,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(34,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(36,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(38,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(39,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(41,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(42,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(43,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ W ) )
=> ( segmentP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(44,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(45,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(47,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(48,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(49,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ W ) )
=> ( rearsegP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(50,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(51,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(54,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(55,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(56,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ W ) )
=> ( frontsegP @ U @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(57,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(68,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(70,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(72,axiom,
! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(79,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(81,axiom,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(95,axiom,
! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(96,conjecture,
! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ( ( ~ ( neq @ V @ nil )
| ~ ( singletonP @ W )
| ( singletonP @ U ) )
& ( ~ ( neq @ V @ nil )
| ( neq @ X @ nil ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(97,negated_conjecture,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ( ( ~ ( neq @ V @ nil )
| ~ ( singletonP @ W )
| ( singletonP @ U ) )
& ( ~ ( neq @ V @ nil )
| ( neq @ X @ nil ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[96]) ).
thf(98,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ! [W: $i] :
( ( ssList @ W )
=> ! [X: $i] :
( ( ssList @ X )
=> ( ( V != X )
| ( U != W )
| ( ( ~ ( neq @ V @ nil )
| ~ ( singletonP @ W )
| ( singletonP @ U ) )
& ( ~ ( neq @ V @ nil )
| ( neq @ X @ nil ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(100,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(101,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(102,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(103,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(104,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(105,plain,
( ( equalelemsP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(106,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(107,plain,
( ( strictorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(108,plain,
( ( totalorderedP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(109,plain,
( ( strictorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(110,plain,
( ( totalorderP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(111,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(112,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(113,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(114,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(115,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(116,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(117,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(118,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(119,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(120,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(121,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(122,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(123,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(124,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(125,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(126,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(127,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(128,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
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 )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(131,plain,
( ( ssList @ nil )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(132,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(134,plain,
( ( ( ssList @ sK1_U )
=> ! [SY50: $i] :
( ( ssList @ SY50 )
=> ! [SY51: $i] :
( ( ssList @ SY51 )
=> ! [SY52: $i] :
( ( ssList @ SY52 )
=> ( ( SY50 != SY52 )
| ( sK1_U != SY51 )
| ( ( ~ ( neq @ SY50 @ nil )
| ~ ( singletonP @ SY51 )
| ( singletonP @ sK1_U ) )
& ( ~ ( neq @ SY50 @ nil )
| ( neq @ SY52 @ nil ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(135,plain,
( ( ssList @ sK1_U )
= $true ),
inference(standard_cnf,[status(thm)],[134]) ).
thf(136,plain,
( ( ! [SY50: $i] :
( ( ssList @ SY50 )
=> ! [SY51: $i] :
( ( ssList @ SY51 )
=> ! [SY52: $i] :
( ( ssList @ SY52 )
=> ( ( SY50 != SY52 )
| ( sK1_U != SY51 )
| ( ( ~ ( neq @ SY50 @ nil )
| ~ ( singletonP @ SY51 )
| ( singletonP @ sK1_U ) )
& ( ~ ( neq @ SY50 @ nil )
| ( neq @ SY52 @ nil ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[134]) ).
thf(137,plain,
( ( ~ ! [SY50: $i] :
( ( ssList @ SY50 )
=> ! [SY51: $i] :
( ( ssList @ SY51 )
=> ! [SY52: $i] :
( ( ssList @ SY52 )
=> ( ( SY50 != SY52 )
| ( sK1_U != SY51 )
| ( ( ~ ( neq @ SY50 @ nil )
| ~ ( singletonP @ SY51 )
| ( singletonP @ sK1_U ) )
& ( ~ ( neq @ SY50 @ nil )
| ( neq @ SY52 @ nil ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[136]) ).
thf(138,plain,
( ( ! [U: $i] :
( ( ssItem @ U )
=> ! [V: $i] :
( ( ssItem @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(139,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( neq @ U @ V )
<=> ( U != V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(140,plain,
( ( ssList @ nil )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(141,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ( ssList @ ( tl @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(142,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ssList @ ( app @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(143,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ nil @ U )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(144,plain,
( ( ~ ( singletonP @ nil ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(145,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)],[126]) ).
thf(146,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( frontsegP @ U @ V )
& ( frontsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(147,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(148,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( frontsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(149,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( frontsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(150,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)],[121]) ).
thf(151,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( rearsegP @ U @ V )
& ( rearsegP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(152,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(153,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( rearsegP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(154,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( rearsegP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(155,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)],[116]) ).
thf(156,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( ( segmentP @ U @ V )
& ( segmentP @ V @ U ) )
=> ( U = V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(157,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(158,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( segmentP @ U @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(159,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( segmentP @ nil @ U )
<=> ( nil = U ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(160,plain,
( ( cyclefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(161,plain,
( ( totalorderP @ nil )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(162,plain,
( ( strictorderP @ nil )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(163,plain,
( ( totalorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(164,plain,
( ( strictorderedP @ nil )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(165,plain,
( ( duplicatefreeP @ nil )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(166,plain,
( ( equalelemsP @ nil )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(167,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( nil != U )
=> ? [V: $i] :
( ( ssList @ V )
& ( ( tl @ U )
= V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(168,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)],[103]) ).
thf(169,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)],[102]) ).
thf(170,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)],[101]) ).
thf(171,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ! [V: $i] :
( ( ssList @ V )
=> ( ( nil
= ( app @ U @ V ) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(172,plain,
( ( ! [U: $i] :
( ( ssList @ U )
=> ( ( app @ U @ nil )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(173,plain,
( ( ssList @ sK1_U )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(174,plain,
( ( ~ ! [SY50: $i] :
( ( ssList @ SY50 )
=> ! [SY51: $i] :
( ( ssList @ SY51 )
=> ! [SY52: $i] :
( ( ssList @ SY52 )
=> ( ( SY50 != SY52 )
| ( sK1_U != SY51 )
| ( ( ~ ( neq @ SY50 @ nil )
| ~ ( singletonP @ SY51 )
| ( singletonP @ sK1_U ) )
& ( ~ ( neq @ SY50 @ nil )
| ( neq @ SY52 @ nil ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(175,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( frontsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(176,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(177,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)],[139]) ).
thf(178,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)],[170]) ).
thf(179,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)],[138]) ).
thf(180,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(181,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( rearsegP @ SX0 @ SX1 )
| ~ ( rearsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(182,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( rearsegP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(183,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)],[155]) ).
thf(184,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( frontsegP @ SX0 @ SX1 )
| ~ ( frontsegP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(185,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ~ ( ~ ( segmentP @ SX0 @ SX1 )
| ~ ( segmentP @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(186,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( ssList @ SX1 )
| ( ( tl @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(187,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( ~ ( ~ ( neq @ SX0 @ nil )
| ~ ( singletonP @ SX1 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ SX0 @ nil )
| ( neq @ SX2 @ nil ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(188,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(189,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( frontsegP @ SX0 @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(190,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)],[169]) ).
thf(191,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ~ ( ~ ( ( nil
!= ( app @ SX0 @ SX1 ) )
| ~ ( ( nil != SX1 )
| ( nil != SX0 ) ) )
| ~ ( ~ ~ ( ( nil != SX1 )
| ( nil != SX0 ) )
| ( nil
= ( app @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( segmentP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(193,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ( ssList @ ( app @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(194,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)],[150]) ).
thf(195,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ SX0 @ nil )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(196,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( ( app @ nil @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(197,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SX0 )
| ( nil = SX0 ) )
| ~ ( ( nil != SX0 )
| ( segmentP @ nil @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(198,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ( rearsegP @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(199,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)],[168]) ).
thf(200,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ~ ( ( nil != SX0 ) )
| ( ssList @ ( tl @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(201,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)],[145]) ).
thf(202,plain,
( ( singletonP @ nil )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(203,plain,
! [SV1: $i] :
( ( ~ ( ssList @ SV1 )
| ~ ( ~ ( ~ ( frontsegP @ nil @ SV1 )
| ( nil = SV1 ) )
| ~ ( ( nil != SV1 )
| ( frontsegP @ nil @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(204,plain,
! [SV2: $i] :
( ( ~ ( ssList @ SV2 )
| ( frontsegP @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(205,plain,
! [SV3: $i] :
( ( ~ ( ssList @ SV3 )
| ! [SY53: $i] :
( ~ ( ssList @ SY53 )
| ~ ( ~ ( ~ ( neq @ SV3 @ SY53 )
| ( SV3 != SY53 ) )
| ~ ( ~ ( ( SV3 != SY53 ) )
| ( neq @ SV3 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(206,plain,
! [SV4: $i] :
( ( ~ ( ssList @ SV4 )
| ! [SY54: $i] :
( ~ ( ssList @ SY54 )
| ! [SY55: $i] :
( ~ ( ssList @ SY55 )
| ( ( app @ ( app @ SV4 @ SY54 ) @ SY55 )
= ( app @ SV4 @ ( app @ SY54 @ SY55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(207,plain,
! [SV5: $i] :
( ( ~ ( ssItem @ SV5 )
| ! [SY56: $i] :
( ~ ( ssItem @ SY56 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SY56 )
| ( SV5 != SY56 ) )
| ~ ( ~ ( ( SV5 != SY56 ) )
| ( neq @ SV5 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(208,plain,
! [SV6: $i] :
( ( ~ ( ssList @ SV6 )
| ( segmentP @ SV6 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(209,plain,
! [SV7: $i] :
( ( ~ ( ssList @ SV7 )
| ! [SY57: $i] :
( ~ ( ssList @ SY57 )
| ~ ~ ( ~ ( rearsegP @ SV7 @ SY57 )
| ~ ( rearsegP @ SY57 @ SV7 ) )
| ( SV7 = SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(210,plain,
! [SV8: $i] :
( ( ~ ( ssList @ SV8 )
| ~ ( ~ ( ~ ( rearsegP @ nil @ SV8 )
| ( nil = SV8 ) )
| ~ ( ( nil != SV8 )
| ( rearsegP @ nil @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(211,plain,
! [SV9: $i] :
( ( ~ ( ssList @ SV9 )
| ! [SY58: $i] :
( ~ ( ssList @ SY58 )
| ! [SY59: $i] :
( ~ ( ssList @ SY59 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SY58 )
| ~ ( segmentP @ SY58 @ SY59 ) )
| ( segmentP @ SV9 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(212,plain,
! [SV10: $i] :
( ( ~ ( ssList @ SV10 )
| ! [SY60: $i] :
( ~ ( ssList @ SY60 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SY60 )
| ~ ( frontsegP @ SY60 @ SV10 ) )
| ( SV10 = SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(213,plain,
! [SV11: $i] :
( ( ~ ( ssList @ SV11 )
| ! [SY61: $i] :
( ~ ( ssList @ SY61 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SY61 )
| ~ ( segmentP @ SY61 @ SV11 ) )
| ( SV11 = SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(214,plain,
! [SV12: $i] :
( ( ~ ( ssList @ SV12 )
| ~ ( ( nil != SV12 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(215,plain,
( ( ! [SX0: $i] :
( ~ ( ssList @ SX0 )
| ! [SX1: $i] :
( ~ ( ssList @ SX1 )
| ! [SX2: $i] :
( ~ ( ssList @ SX2 )
| ( SX0 != SX2 )
| ( sK1_U != SX1 )
| ~ ( ~ ( ~ ( neq @ SX0 @ nil )
| ~ ( singletonP @ SX1 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ SX0 @ nil )
| ( neq @ SX2 @ nil ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(216,plain,
! [SV13: $i] :
( ( ~ ( ssList @ SV13 )
| ( rearsegP @ SV13 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(217,plain,
! [SV14: $i] :
( ( ~ ( ssList @ SV14 )
| ( frontsegP @ SV14 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(218,plain,
! [SV15: $i] :
( ( ~ ( ssList @ SV15 )
| ! [SY63: $i] :
( ~ ( ssList @ SY63 )
| ! [SY64: $i] :
( ~ ( ssList @ SY64 )
| ( ( app @ SY63 @ SY64 )
!= ( app @ SY63 @ SV15 ) )
| ( SY64 = SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(219,plain,
! [SV16: $i] :
( ( ~ ( ssList @ SV16 )
| ! [SY65: $i] :
( ~ ( ssList @ SY65 )
| ~ ( ~ ( ( nil
!= ( app @ SV16 @ SY65 ) )
| ~ ( ( nil != SY65 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SY65 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SY65 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(220,plain,
! [SV17: $i] :
( ( ~ ( ssList @ SV17 )
| ( segmentP @ SV17 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(221,plain,
! [SV18: $i] :
( ( ~ ( ssList @ SV18 )
| ! [SY66: $i] :
( ~ ( ssList @ SY66 )
| ( ssList @ ( app @ SV18 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(222,plain,
! [SV19: $i] :
( ( ~ ( ssList @ SV19 )
| ! [SY67: $i] :
( ~ ( ssList @ SY67 )
| ! [SY68: $i] :
( ~ ( ssList @ SY68 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SY67 )
| ~ ( rearsegP @ SY67 @ SY68 ) )
| ( rearsegP @ SV19 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(223,plain,
! [SV20: $i] :
( ( ~ ( ssList @ SV20 )
| ( ( app @ SV20 @ nil )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(224,plain,
! [SV21: $i] :
( ( ~ ( ssList @ SV21 )
| ( ( app @ nil @ SV21 )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(225,plain,
! [SV22: $i] :
( ( ~ ( ssList @ SV22 )
| ~ ( ~ ( ~ ( segmentP @ nil @ SV22 )
| ( nil = SV22 ) )
| ~ ( ( nil != SV22 )
| ( segmentP @ nil @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(226,plain,
! [SV23: $i] :
( ( ~ ( ssList @ SV23 )
| ( rearsegP @ SV23 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(227,plain,
! [SV24: $i] :
( ( ~ ( ssList @ SV24 )
| ! [SY69: $i] :
( ~ ( ssList @ SY69 )
| ! [SY70: $i] :
( ~ ( ssList @ SY70 )
| ( ( app @ SY70 @ SY69 )
!= ( app @ SV24 @ SY69 ) )
| ( SY70 = SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(228,plain,
! [SV25: $i] :
( ( ~ ( ssList @ SV25 )
| ~ ( ( nil != SV25 ) )
| ( ssList @ ( tl @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(229,plain,
! [SV26: $i] :
( ( ~ ( ssList @ SV26 )
| ! [SY71: $i] :
( ~ ( ssList @ SY71 )
| ! [SY72: $i] :
( ~ ( ssList @ SY72 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SY71 )
| ~ ( frontsegP @ SY71 @ SY72 ) )
| ( frontsegP @ SV26 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(230,plain,
! [SV1: $i] :
( ( ( ~ ( ssList @ SV1 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV1 )
| ( nil = SV1 ) )
| ~ ( ( nil != SV1 )
| ( frontsegP @ nil @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(231,plain,
! [SV2: $i] :
( ( ( ~ ( ssList @ SV2 ) )
= $true )
| ( ( frontsegP @ SV2 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(232,plain,
! [SV3: $i] :
( ( ( ~ ( ssList @ SV3 ) )
= $true )
| ( ( ! [SY53: $i] :
( ~ ( ssList @ SY53 )
| ~ ( ~ ( ~ ( neq @ SV3 @ SY53 )
| ( SV3 != SY53 ) )
| ~ ( ~ ( ( SV3 != SY53 ) )
| ( neq @ SV3 @ SY53 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(233,plain,
! [SV4: $i] :
( ( ( ~ ( ssList @ SV4 ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( ssList @ SY54 )
| ! [SY55: $i] :
( ~ ( ssList @ SY55 )
| ( ( app @ ( app @ SV4 @ SY54 ) @ SY55 )
= ( app @ SV4 @ ( app @ SY54 @ SY55 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(234,plain,
! [SV5: $i] :
( ( ( ~ ( ssItem @ SV5 ) )
= $true )
| ( ( ! [SY56: $i] :
( ~ ( ssItem @ SY56 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SY56 )
| ( SV5 != SY56 ) )
| ~ ( ~ ( ( SV5 != SY56 ) )
| ( neq @ SV5 @ SY56 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(235,plain,
! [SV6: $i] :
( ( ( ~ ( ssList @ SV6 ) )
= $true )
| ( ( segmentP @ SV6 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(236,plain,
! [SV7: $i] :
( ( ( ~ ( ssList @ SV7 ) )
= $true )
| ( ( ! [SY57: $i] :
( ~ ( ssList @ SY57 )
| ~ ~ ( ~ ( rearsegP @ SV7 @ SY57 )
| ~ ( rearsegP @ SY57 @ SV7 ) )
| ( SV7 = SY57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(237,plain,
! [SV8: $i] :
( ( ( ~ ( ssList @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV8 )
| ( nil = SV8 ) )
| ~ ( ( nil != SV8 )
| ( rearsegP @ nil @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(238,plain,
! [SV9: $i] :
( ( ( ~ ( ssList @ SV9 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( ssList @ SY58 )
| ! [SY59: $i] :
( ~ ( ssList @ SY59 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SY58 )
| ~ ( segmentP @ SY58 @ SY59 ) )
| ( segmentP @ SV9 @ SY59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(239,plain,
! [SV10: $i] :
( ( ( ~ ( ssList @ SV10 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( ssList @ SY60 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SY60 )
| ~ ( frontsegP @ SY60 @ SV10 ) )
| ( SV10 = SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(240,plain,
! [SV11: $i] :
( ( ( ~ ( ssList @ SV11 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( ssList @ SY61 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SY61 )
| ~ ( segmentP @ SY61 @ SV11 ) )
| ( SV11 = SY61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(241,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ SV12 ) )
= $true )
| ( ( ~ ( ( nil != SV12 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(242,plain,
( ( ~ ( ssList @ sK2_SX0 )
| ! [SY73: $i] :
( ~ ( ssList @ SY73 )
| ! [SY74: $i] :
( ~ ( ssList @ SY74 )
| ( sK2_SX0 != SY74 )
| ( sK1_U != SY73 )
| ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ SY74 @ nil ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[215]) ).
thf(243,plain,
! [SV13: $i] :
( ( ( ~ ( ssList @ SV13 ) )
= $true )
| ( ( rearsegP @ SV13 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(244,plain,
! [SV14: $i] :
( ( ( ~ ( ssList @ SV14 ) )
= $true )
| ( ( frontsegP @ SV14 @ nil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(245,plain,
! [SV15: $i] :
( ( ( ~ ( ssList @ SV15 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( ssList @ SY63 )
| ! [SY64: $i] :
( ~ ( ssList @ SY64 )
| ( ( app @ SY63 @ SY64 )
!= ( app @ SY63 @ SV15 ) )
| ( SY64 = SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(246,plain,
! [SV16: $i] :
( ( ( ~ ( ssList @ SV16 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( ssList @ SY65 )
| ~ ( ~ ( ( nil
!= ( app @ SV16 @ SY65 ) )
| ~ ( ( nil != SY65 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SY65 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SY65 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(247,plain,
! [SV17: $i] :
( ( ( ~ ( ssList @ SV17 ) )
= $true )
| ( ( segmentP @ SV17 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(248,plain,
! [SV18: $i] :
( ( ( ~ ( ssList @ SV18 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( ssList @ SY66 )
| ( ssList @ ( app @ SV18 @ SY66 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(249,plain,
! [SV19: $i] :
( ( ( ~ ( ssList @ SV19 ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( ssList @ SY67 )
| ! [SY68: $i] :
( ~ ( ssList @ SY68 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SY67 )
| ~ ( rearsegP @ SY67 @ SY68 ) )
| ( rearsegP @ SV19 @ SY68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(250,plain,
! [SV20: $i] :
( ( ( ~ ( ssList @ SV20 ) )
= $true )
| ( ( ( app @ SV20 @ nil )
= SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(251,plain,
! [SV21: $i] :
( ( ( ~ ( ssList @ SV21 ) )
= $true )
| ( ( ( app @ nil @ SV21 )
= SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(252,plain,
! [SV22: $i] :
( ( ( ~ ( ssList @ SV22 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV22 )
| ( nil = SV22 ) )
| ~ ( ( nil != SV22 )
| ( segmentP @ nil @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(253,plain,
! [SV23: $i] :
( ( ( ~ ( ssList @ SV23 ) )
= $true )
| ( ( rearsegP @ SV23 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(254,plain,
! [SV24: $i] :
( ( ( ~ ( ssList @ SV24 ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( ssList @ SY69 )
| ! [SY70: $i] :
( ~ ( ssList @ SY70 )
| ( ( app @ SY70 @ SY69 )
!= ( app @ SV24 @ SY69 ) )
| ( SY70 = SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(255,plain,
! [SV25: $i] :
( ( ( ~ ( ssList @ SV25 ) )
= $true )
| ( ( ~ ( ( nil != SV25 ) )
| ( ssList @ ( tl @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(256,plain,
! [SV26: $i] :
( ( ( ~ ( ssList @ SV26 ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( ssList @ SY71 )
| ! [SY72: $i] :
( ~ ( ssList @ SY72 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SY71 )
| ~ ( frontsegP @ SY71 @ SY72 ) )
| ( frontsegP @ SV26 @ SY72 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(257,plain,
! [SV1: $i] :
( ( ( ssList @ SV1 )
= $false )
| ( ( ~ ( ~ ( ~ ( frontsegP @ nil @ SV1 )
| ( nil = SV1 ) )
| ~ ( ( nil != SV1 )
| ( frontsegP @ nil @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(258,plain,
! [SV2: $i] :
( ( ( ssList @ SV2 )
= $false )
| ( ( frontsegP @ SV2 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(259,plain,
! [SV3: $i] :
( ( ( ssList @ SV3 )
= $false )
| ( ( ! [SY53: $i] :
( ~ ( ssList @ SY53 )
| ~ ( ~ ( ~ ( neq @ SV3 @ SY53 )
| ( SV3 != SY53 ) )
| ~ ( ~ ( ( SV3 != SY53 ) )
| ( neq @ SV3 @ SY53 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(260,plain,
! [SV4: $i] :
( ( ( ssList @ SV4 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( ssList @ SY54 )
| ! [SY55: $i] :
( ~ ( ssList @ SY55 )
| ( ( app @ ( app @ SV4 @ SY54 ) @ SY55 )
= ( app @ SV4 @ ( app @ SY54 @ SY55 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(261,plain,
! [SV5: $i] :
( ( ( ssItem @ SV5 )
= $false )
| ( ( ! [SY56: $i] :
( ~ ( ssItem @ SY56 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SY56 )
| ( SV5 != SY56 ) )
| ~ ( ~ ( ( SV5 != SY56 ) )
| ( neq @ SV5 @ SY56 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(262,plain,
! [SV6: $i] :
( ( ( ssList @ SV6 )
= $false )
| ( ( segmentP @ SV6 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(263,plain,
! [SV7: $i] :
( ( ( ssList @ SV7 )
= $false )
| ( ( ! [SY57: $i] :
( ~ ( ssList @ SY57 )
| ~ ~ ( ~ ( rearsegP @ SV7 @ SY57 )
| ~ ( rearsegP @ SY57 @ SV7 ) )
| ( SV7 = SY57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(264,plain,
! [SV8: $i] :
( ( ( ssList @ SV8 )
= $false )
| ( ( ~ ( ~ ( ~ ( rearsegP @ nil @ SV8 )
| ( nil = SV8 ) )
| ~ ( ( nil != SV8 )
| ( rearsegP @ nil @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(265,plain,
! [SV9: $i] :
( ( ( ssList @ SV9 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( ssList @ SY58 )
| ! [SY59: $i] :
( ~ ( ssList @ SY59 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SY58 )
| ~ ( segmentP @ SY58 @ SY59 ) )
| ( segmentP @ SV9 @ SY59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(266,plain,
! [SV10: $i] :
( ( ( ssList @ SV10 )
= $false )
| ( ( ! [SY60: $i] :
( ~ ( ssList @ SY60 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SY60 )
| ~ ( frontsegP @ SY60 @ SV10 ) )
| ( SV10 = SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(267,plain,
! [SV11: $i] :
( ( ( ssList @ SV11 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( ssList @ SY61 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SY61 )
| ~ ( segmentP @ SY61 @ SV11 ) )
| ( SV11 = SY61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(268,plain,
! [SV12: $i] :
( ( ( ssList @ SV12 )
= $false )
| ( ( ~ ( ( nil != SV12 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(269,plain,
( ( ~ ( ssList @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(270,plain,
( ( ! [SY73: $i] :
( ~ ( ssList @ SY73 )
| ! [SY74: $i] :
( ~ ( ssList @ SY74 )
| ( sK2_SX0 != SY74 )
| ( sK1_U != SY73 )
| ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ SY74 @ nil ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(271,plain,
! [SV13: $i] :
( ( ( ssList @ SV13 )
= $false )
| ( ( rearsegP @ SV13 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(272,plain,
! [SV14: $i] :
( ( ( ssList @ SV14 )
= $false )
| ( ( frontsegP @ SV14 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(273,plain,
! [SV15: $i] :
( ( ( ssList @ SV15 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( ssList @ SY63 )
| ! [SY64: $i] :
( ~ ( ssList @ SY64 )
| ( ( app @ SY63 @ SY64 )
!= ( app @ SY63 @ SV15 ) )
| ( SY64 = SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(274,plain,
! [SV16: $i] :
( ( ( ssList @ SV16 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( ssList @ SY65 )
| ~ ( ~ ( ( nil
!= ( app @ SV16 @ SY65 ) )
| ~ ( ( nil != SY65 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SY65 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SY65 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(275,plain,
! [SV17: $i] :
( ( ( ssList @ SV17 )
= $false )
| ( ( segmentP @ SV17 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(276,plain,
! [SV18: $i] :
( ( ( ssList @ SV18 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( ssList @ SY66 )
| ( ssList @ ( app @ SV18 @ SY66 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(277,plain,
! [SV19: $i] :
( ( ( ssList @ SV19 )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( ssList @ SY67 )
| ! [SY68: $i] :
( ~ ( ssList @ SY68 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SY67 )
| ~ ( rearsegP @ SY67 @ SY68 ) )
| ( rearsegP @ SV19 @ SY68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(278,plain,
! [SV20: $i] :
( ( ( ssList @ SV20 )
= $false )
| ( ( ( app @ SV20 @ nil )
= SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(279,plain,
! [SV21: $i] :
( ( ( ssList @ SV21 )
= $false )
| ( ( ( app @ nil @ SV21 )
= SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(280,plain,
! [SV22: $i] :
( ( ( ssList @ SV22 )
= $false )
| ( ( ~ ( ~ ( ~ ( segmentP @ nil @ SV22 )
| ( nil = SV22 ) )
| ~ ( ( nil != SV22 )
| ( segmentP @ nil @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(281,plain,
! [SV23: $i] :
( ( ( ssList @ SV23 )
= $false )
| ( ( rearsegP @ SV23 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(282,plain,
! [SV24: $i] :
( ( ( ssList @ SV24 )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( ssList @ SY69 )
| ! [SY70: $i] :
( ~ ( ssList @ SY70 )
| ( ( app @ SY70 @ SY69 )
!= ( app @ SV24 @ SY69 ) )
| ( SY70 = SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(283,plain,
! [SV25: $i] :
( ( ( ssList @ SV25 )
= $false )
| ( ( ~ ( ( nil != SV25 ) )
| ( ssList @ ( tl @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(284,plain,
! [SV26: $i] :
( ( ( ssList @ SV26 )
= $false )
| ( ( ! [SY71: $i] :
( ~ ( ssList @ SY71 )
| ! [SY72: $i] :
( ~ ( ssList @ SY72 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SY71 )
| ~ ( frontsegP @ SY71 @ SY72 ) )
| ( frontsegP @ SV26 @ SY72 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(285,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV1 )
| ( nil = SV1 ) )
| ~ ( ( nil != SV1 )
| ( frontsegP @ nil @ SV1 ) ) )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(286,plain,
! [SV3: $i,SV27: $i] :
( ( ( ~ ( ssList @ SV27 )
| ~ ( ~ ( ~ ( neq @ SV3 @ SV27 )
| ( SV3 != SV27 ) )
| ~ ( ~ ( ( SV3 != SV27 ) )
| ( neq @ SV3 @ SV27 ) ) ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(287,plain,
! [SV4: $i,SV28: $i] :
( ( ( ~ ( ssList @ SV28 )
| ! [SY75: $i] :
( ~ ( ssList @ SY75 )
| ( ( app @ ( app @ SV4 @ SV28 ) @ SY75 )
= ( app @ SV4 @ ( app @ SV28 @ SY75 ) ) ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV5: $i,SV29: $i] :
( ( ( ~ ( ssItem @ SV29 )
| ~ ( ~ ( ~ ( neq @ SV5 @ SV29 )
| ( SV5 != SV29 ) )
| ~ ( ~ ( ( SV5 != SV29 ) )
| ( neq @ SV5 @ SV29 ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(289,plain,
! [SV7: $i,SV30: $i] :
( ( ( ~ ( ssList @ SV30 )
| ~ ~ ( ~ ( rearsegP @ SV7 @ SV30 )
| ~ ( rearsegP @ SV30 @ SV7 ) )
| ( SV7 = SV30 ) )
= $true )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(290,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV8 )
| ( nil = SV8 ) )
| ~ ( ( nil != SV8 )
| ( rearsegP @ nil @ SV8 ) ) )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(291,plain,
! [SV9: $i,SV31: $i] :
( ( ( ~ ( ssList @ SV31 )
| ! [SY76: $i] :
( ~ ( ssList @ SY76 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SY76 ) )
| ( segmentP @ SV9 @ SY76 ) ) )
= $true )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(292,plain,
! [SV10: $i,SV32: $i] :
( ( ( ~ ( ssList @ SV32 )
| ~ ~ ( ~ ( frontsegP @ SV10 @ SV32 )
| ~ ( frontsegP @ SV32 @ SV10 ) )
| ( SV10 = SV32 ) )
= $true )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(293,plain,
! [SV11: $i,SV33: $i] :
( ( ( ~ ( ssList @ SV33 )
| ~ ~ ( ~ ( segmentP @ SV11 @ SV33 )
| ~ ( segmentP @ SV33 @ SV11 ) )
| ( SV11 = SV33 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(294,plain,
! [SV12: $i] :
( ( ( ~ ( ( nil != SV12 ) ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(295,plain,
( ( ssList @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(296,plain,
( ( ~ ( ssList @ sK3_SY73 )
| ! [SY77: $i] :
( ~ ( ssList @ SY77 )
| ( sK2_SX0 != SY77 )
| ( sK1_U != sK3_SY73 )
| ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ SY77 @ nil ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(297,plain,
! [SV15: $i,SV34: $i] :
( ( ( ~ ( ssList @ SV34 )
| ! [SY78: $i] :
( ~ ( ssList @ SY78 )
| ( ( app @ SV34 @ SY78 )
!= ( app @ SV34 @ SV15 ) )
| ( SY78 = SV15 ) ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(298,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( ssList @ SV35 )
| ~ ( ~ ( ( nil
!= ( app @ SV16 @ SV35 ) )
| ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SV35 ) ) ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(299,plain,
! [SV18: $i,SV36: $i] :
( ( ( ~ ( ssList @ SV36 )
| ( ssList @ ( app @ SV18 @ SV36 ) ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(300,plain,
! [SV19: $i,SV37: $i] :
( ( ( ~ ( ssList @ SV37 )
| ! [SY79: $i] :
( ~ ( ssList @ SY79 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SY79 ) )
| ( rearsegP @ SV19 @ SY79 ) ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(301,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV22 )
| ( nil = SV22 ) )
| ~ ( ( nil != SV22 )
| ( segmentP @ nil @ SV22 ) ) )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(302,plain,
! [SV24: $i,SV38: $i] :
( ( ( ~ ( ssList @ SV38 )
| ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( ( app @ SY80 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
| ( SY80 = SV24 ) ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(303,plain,
! [SV25: $i] :
( ( ( ~ ( ( nil != SV25 ) ) )
= $true )
| ( ( ssList @ ( tl @ SV25 ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(304,plain,
! [SV26: $i,SV39: $i] :
( ( ( ~ ( ssList @ SV39 )
| ! [SY81: $i] :
( ~ ( ssList @ SY81 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SY81 ) )
| ( frontsegP @ SV26 @ SY81 ) ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(305,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( frontsegP @ nil @ SV1 )
| ( nil = SV1 ) ) )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(306,plain,
! [SV1: $i] :
( ( ( ~ ( ( nil != SV1 )
| ( frontsegP @ nil @ SV1 ) ) )
= $false )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(307,plain,
! [SV3: $i,SV27: $i] :
( ( ( ~ ( ssList @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV3 @ SV27 )
| ( SV3 != SV27 ) )
| ~ ( ~ ( ( SV3 != SV27 ) )
| ( neq @ SV3 @ SV27 ) ) ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(308,plain,
! [SV4: $i,SV28: $i] :
( ( ( ~ ( ssList @ SV28 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( ssList @ SY75 )
| ( ( app @ ( app @ SV4 @ SV28 ) @ SY75 )
= ( app @ SV4 @ ( app @ SV28 @ SY75 ) ) ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(309,plain,
! [SV5: $i,SV29: $i] :
( ( ( ~ ( ssItem @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( neq @ SV5 @ SV29 )
| ( SV5 != SV29 ) )
| ~ ( ~ ( ( SV5 != SV29 ) )
| ( neq @ SV5 @ SV29 ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(310,plain,
! [SV7: $i,SV30: $i] :
( ( ( ~ ( ssList @ SV30 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV7 @ SV30 )
| ~ ( rearsegP @ SV30 @ SV7 ) )
| ( SV7 = SV30 ) )
= $true )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(311,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( rearsegP @ nil @ SV8 )
| ( nil = SV8 ) ) )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(312,plain,
! [SV8: $i] :
( ( ( ~ ( ( nil != SV8 )
| ( rearsegP @ nil @ SV8 ) ) )
= $false )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(313,plain,
! [SV9: $i,SV31: $i] :
( ( ( ~ ( ssList @ SV31 ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( ssList @ SY76 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SY76 ) )
| ( segmentP @ SV9 @ SY76 ) ) )
= $true )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(314,plain,
! [SV10: $i,SV32: $i] :
( ( ( ~ ( ssList @ SV32 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV10 @ SV32 )
| ~ ( frontsegP @ SV32 @ SV10 ) )
| ( SV10 = SV32 ) )
= $true )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(315,plain,
! [SV11: $i,SV33: $i] :
( ( ( ~ ( ssList @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV11 @ SV33 )
| ~ ( segmentP @ SV33 @ SV11 ) )
| ( SV11 = SV33 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(316,plain,
! [SV12: $i] :
( ( ( nil != SV12 )
= $false )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(317,plain,
( ( ~ ( ssList @ sK3_SY73 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(318,plain,
( ( ! [SY77: $i] :
( ~ ( ssList @ SY77 )
| ( sK2_SX0 != SY77 )
| ( sK1_U != sK3_SY73 )
| ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ SY77 @ nil ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(319,plain,
! [SV15: $i,SV34: $i] :
( ( ( ~ ( ssList @ SV34 ) )
= $true )
| ( ( ! [SY78: $i] :
( ~ ( ssList @ SY78 )
| ( ( app @ SV34 @ SY78 )
!= ( app @ SV34 @ SV15 ) )
| ( SY78 = SV15 ) ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(320,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( ssList @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV16 @ SV35 ) )
| ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SV35 ) ) ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(321,plain,
! [SV18: $i,SV36: $i] :
( ( ( ~ ( ssList @ SV36 ) )
= $true )
| ( ( ssList @ ( app @ SV18 @ SV36 ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(322,plain,
! [SV19: $i,SV37: $i] :
( ( ( ~ ( ssList @ SV37 ) )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( ssList @ SY79 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SY79 ) )
| ( rearsegP @ SV19 @ SY79 ) ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(323,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( segmentP @ nil @ SV22 )
| ( nil = SV22 ) ) )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(324,plain,
! [SV22: $i] :
( ( ( ~ ( ( nil != SV22 )
| ( segmentP @ nil @ SV22 ) ) )
= $false )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(325,plain,
! [SV24: $i,SV38: $i] :
( ( ( ~ ( ssList @ SV38 ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( ( app @ SY80 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
| ( SY80 = SV24 ) ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(326,plain,
! [SV25: $i] :
( ( ( nil != SV25 )
= $false )
| ( ( ssList @ ( tl @ SV25 ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(327,plain,
! [SV26: $i,SV39: $i] :
( ( ( ~ ( ssList @ SV39 ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( ssList @ SY81 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SY81 ) )
| ( frontsegP @ SV26 @ SY81 ) ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(328,plain,
! [SV1: $i] :
( ( ( ~ ( frontsegP @ nil @ SV1 )
| ( nil = SV1 ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(329,plain,
! [SV1: $i] :
( ( ( ( nil != SV1 )
| ( frontsegP @ nil @ SV1 ) )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(330,plain,
! [SV3: $i,SV27: $i] :
( ( ( ssList @ SV27 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV3 @ SV27 )
| ( SV3 != SV27 ) )
| ~ ( ~ ( ( SV3 != SV27 ) )
| ( neq @ SV3 @ SV27 ) ) ) )
= $true )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(331,plain,
! [SV4: $i,SV28: $i] :
( ( ( ssList @ SV28 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( ssList @ SY75 )
| ( ( app @ ( app @ SV4 @ SV28 ) @ SY75 )
= ( app @ SV4 @ ( app @ SV28 @ SY75 ) ) ) ) )
= $true )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(332,plain,
! [SV5: $i,SV29: $i] :
( ( ( ssItem @ SV29 )
= $false )
| ( ( ~ ( ~ ( ~ ( neq @ SV5 @ SV29 )
| ( SV5 != SV29 ) )
| ~ ( ~ ( ( SV5 != SV29 ) )
| ( neq @ SV5 @ SV29 ) ) ) )
= $true )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(333,plain,
! [SV7: $i,SV30: $i] :
( ( ( ssList @ SV30 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV7 @ SV30 )
| ~ ( rearsegP @ SV30 @ SV7 ) )
| ( SV7 = SV30 ) )
= $true )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(334,plain,
! [SV8: $i] :
( ( ( ~ ( rearsegP @ nil @ SV8 )
| ( nil = SV8 ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(335,plain,
! [SV8: $i] :
( ( ( ( nil != SV8 )
| ( rearsegP @ nil @ SV8 ) )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(336,plain,
! [SV9: $i,SV31: $i] :
( ( ( ssList @ SV31 )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( ssList @ SY76 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SY76 ) )
| ( segmentP @ SV9 @ SY76 ) ) )
= $true )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(337,plain,
! [SV10: $i,SV32: $i] :
( ( ( ssList @ SV32 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV10 @ SV32 )
| ~ ( frontsegP @ SV32 @ SV10 ) )
| ( SV10 = SV32 ) )
= $true )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(338,plain,
! [SV11: $i,SV33: $i] :
( ( ( ssList @ SV33 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV11 @ SV33 )
| ~ ( segmentP @ SV33 @ SV11 ) )
| ( SV11 = SV33 ) )
= $true )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(339,plain,
! [SV12: $i] :
( ( ( nil = SV12 )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(340,plain,
( ( ssList @ sK3_SY73 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(341,plain,
( ( ~ ( ssList @ sK4_SY77 )
| ( sK2_SX0 != sK4_SY77 )
| ( sK1_U != sK3_SY73 )
| ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[318]) ).
thf(342,plain,
! [SV15: $i,SV34: $i] :
( ( ( ssList @ SV34 )
= $false )
| ( ( ! [SY78: $i] :
( ~ ( ssList @ SY78 )
| ( ( app @ SV34 @ SY78 )
!= ( app @ SV34 @ SV15 ) )
| ( SY78 = SV15 ) ) )
= $true )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(343,plain,
! [SV16: $i,SV35: $i] :
( ( ( ssList @ SV35 )
= $false )
| ( ( ~ ( ~ ( ( nil
!= ( app @ SV16 @ SV35 ) )
| ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SV35 ) ) ) ) )
= $true )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(344,plain,
! [SV18: $i,SV36: $i] :
( ( ( ssList @ SV36 )
= $false )
| ( ( ssList @ ( app @ SV18 @ SV36 ) )
= $true )
| ( ( ssList @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(345,plain,
! [SV19: $i,SV37: $i] :
( ( ( ssList @ SV37 )
= $false )
| ( ( ! [SY79: $i] :
( ~ ( ssList @ SY79 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SY79 ) )
| ( rearsegP @ SV19 @ SY79 ) ) )
= $true )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(346,plain,
! [SV22: $i] :
( ( ( ~ ( segmentP @ nil @ SV22 )
| ( nil = SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(347,plain,
! [SV22: $i] :
( ( ( ( nil != SV22 )
| ( segmentP @ nil @ SV22 ) )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(348,plain,
! [SV24: $i,SV38: $i] :
( ( ( ssList @ SV38 )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( ssList @ SY80 )
| ( ( app @ SY80 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
| ( SY80 = SV24 ) ) )
= $true )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(349,plain,
! [SV25: $i] :
( ( ( nil = SV25 )
= $true )
| ( ( ssList @ ( tl @ SV25 ) )
= $true )
| ( ( ssList @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(350,plain,
! [SV26: $i,SV39: $i] :
( ( ( ssList @ SV39 )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( ssList @ SY81 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SY81 ) )
| ( frontsegP @ SV26 @ SY81 ) ) )
= $true )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(351,plain,
! [SV1: $i] :
( ( ( ~ ( frontsegP @ nil @ SV1 ) )
= $true )
| ( ( nil = SV1 )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(352,plain,
! [SV1: $i] :
( ( ( nil != SV1 )
= $true )
| ( ( frontsegP @ nil @ SV1 )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(353,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( ~ ( neq @ SV3 @ SV27 )
| ( SV3 != SV27 ) )
| ~ ( ~ ( ( SV3 != SV27 ) )
| ( neq @ SV3 @ SV27 ) ) )
= $false )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(354,plain,
! [SV28: $i,SV4: $i,SV40: $i] :
( ( ( ~ ( ssList @ SV40 )
| ( ( app @ ( app @ SV4 @ SV28 ) @ SV40 )
= ( app @ SV4 @ ( app @ SV28 @ SV40 ) ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(355,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( ~ ( neq @ SV5 @ SV29 )
| ( SV5 != SV29 ) )
| ~ ( ~ ( ( SV5 != SV29 ) )
| ( neq @ SV5 @ SV29 ) ) )
= $false )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(356,plain,
! [SV30: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV7 @ SV30 )
| ~ ( rearsegP @ SV30 @ SV7 ) ) )
= $true )
| ( ( SV7 = SV30 )
= $true )
| ( ( ssList @ SV30 )
= $false )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(357,plain,
! [SV8: $i] :
( ( ( ~ ( rearsegP @ nil @ SV8 ) )
= $true )
| ( ( nil = SV8 )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(358,plain,
! [SV8: $i] :
( ( ( nil != SV8 )
= $true )
| ( ( rearsegP @ nil @ SV8 )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(359,plain,
! [SV31: $i,SV9: $i,SV41: $i] :
( ( ( ~ ( ssList @ SV41 )
| ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SV41 ) )
| ( segmentP @ SV9 @ SV41 ) )
= $true )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(360,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV10 @ SV32 )
| ~ ( frontsegP @ SV32 @ SV10 ) ) )
= $true )
| ( ( SV10 = SV32 )
= $true )
| ( ( ssList @ SV32 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(361,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV11 @ SV33 )
| ~ ( segmentP @ SV33 @ SV11 ) ) )
= $true )
| ( ( SV11 = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(362,plain,
! [SV12: $i] :
( ( ( ! [SY62: $i] :
~ ~ ( ~ ( ssList @ SY62 )
| ( ( tl @ SV12 )
!= SY62 ) ) )
= $false )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(363,plain,
( ( ~ ( ssList @ sK4_SY77 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(364,plain,
( ( ( sK2_SX0 != sK4_SY77 )
| ( sK1_U != sK3_SY73 )
| ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(365,plain,
! [SV15: $i,SV34: $i,SV42: $i] :
( ( ( ~ ( ssList @ SV42 )
| ( ( app @ SV34 @ SV42 )
!= ( app @ SV34 @ SV15 ) )
| ( SV42 = SV15 ) )
= $true )
| ( ( ssList @ SV34 )
= $false )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(366,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV16 @ SV35 ) )
| ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
| ~ ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SV35 ) ) ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(367,plain,
! [SV37: $i,SV19: $i,SV43: $i] :
( ( ( ~ ( ssList @ SV43 )
| ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SV43 ) )
| ( rearsegP @ SV19 @ SV43 ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(368,plain,
! [SV22: $i] :
( ( ( ~ ( segmentP @ nil @ SV22 ) )
= $true )
| ( ( nil = SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(369,plain,
! [SV22: $i] :
( ( ( nil != SV22 )
= $true )
| ( ( segmentP @ nil @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(370,plain,
! [SV24: $i,SV38: $i,SV44: $i] :
( ( ( ~ ( ssList @ SV44 )
| ( ( app @ SV44 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
| ( SV44 = SV24 ) )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(371,plain,
! [SV39: $i,SV26: $i,SV45: $i] :
( ( ( ~ ( ssList @ SV45 )
| ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SV45 ) )
| ( frontsegP @ SV26 @ SV45 ) )
= $true )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(372,plain,
! [SV1: $i] :
( ( ( frontsegP @ nil @ SV1 )
= $false )
| ( ( nil = SV1 )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(373,plain,
! [SV1: $i] :
( ( ( nil = SV1 )
= $false )
| ( ( frontsegP @ nil @ SV1 )
= $true )
| ( ( ssList @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(374,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( ~ ( neq @ SV3 @ SV27 )
| ( SV3 != SV27 ) ) )
= $false )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(375,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( ~ ( ( SV3 != SV27 ) )
| ( neq @ SV3 @ SV27 ) ) )
= $false )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(376,plain,
! [SV28: $i,SV4: $i,SV40: $i] :
( ( ( ~ ( ssList @ SV40 ) )
= $true )
| ( ( ( app @ ( app @ SV4 @ SV28 ) @ SV40 )
= ( app @ SV4 @ ( app @ SV28 @ SV40 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(377,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( ~ ( neq @ SV5 @ SV29 )
| ( SV5 != SV29 ) ) )
= $false )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(378,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( ~ ( ( SV5 != SV29 ) )
| ( neq @ SV5 @ SV29 ) ) )
= $false )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(379,plain,
! [SV30: $i,SV7: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV7 @ SV30 )
| ~ ( rearsegP @ SV30 @ SV7 ) ) )
= $false )
| ( ( SV7 = SV30 )
= $true )
| ( ( ssList @ SV30 )
= $false )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(380,plain,
! [SV8: $i] :
( ( ( rearsegP @ nil @ SV8 )
= $false )
| ( ( nil = SV8 )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(381,plain,
! [SV8: $i] :
( ( ( nil = SV8 )
= $false )
| ( ( rearsegP @ nil @ SV8 )
= $true )
| ( ( ssList @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(382,plain,
! [SV31: $i,SV9: $i,SV41: $i] :
( ( ( ~ ( ssList @ SV41 ) )
= $true )
| ( ( ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SV41 ) )
| ( segmentP @ SV9 @ SV41 ) )
= $true )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(383,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV10 @ SV32 )
| ~ ( frontsegP @ SV32 @ SV10 ) ) )
= $false )
| ( ( SV10 = SV32 )
= $true )
| ( ( ssList @ SV32 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(384,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( ~ ( segmentP @ SV11 @ SV33 )
| ~ ( segmentP @ SV33 @ SV11 ) ) )
= $false )
| ( ( SV11 = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(385,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ( ssList @ ( sK5_SY62 @ SV12 ) )
| ( ( tl @ SV12 )
!= ( sK5_SY62 @ SV12 ) ) ) )
= $false )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[362]) ).
thf(386,plain,
( ( ssList @ sK4_SY77 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(387,plain,
( ( ( sK2_SX0 != sK4_SY77 )
| ( sK1_U != sK3_SY73 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(388,plain,
( ( ~ ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(389,plain,
! [SV15: $i,SV34: $i,SV42: $i] :
( ( ( ~ ( ssList @ SV42 ) )
= $true )
| ( ( ( ( app @ SV34 @ SV42 )
!= ( app @ SV34 @ SV15 ) )
| ( SV42 = SV15 ) )
= $true )
| ( ( ssList @ SV34 )
= $false )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(390,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( ( nil
!= ( app @ SV16 @ SV35 ) )
| ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(391,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SV35 ) ) ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(392,plain,
! [SV37: $i,SV19: $i,SV43: $i] :
( ( ( ~ ( ssList @ SV43 ) )
= $true )
| ( ( ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SV43 ) )
| ( rearsegP @ SV19 @ SV43 ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(393,plain,
! [SV22: $i] :
( ( ( segmentP @ nil @ SV22 )
= $false )
| ( ( nil = SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(394,plain,
! [SV22: $i] :
( ( ( nil = SV22 )
= $false )
| ( ( segmentP @ nil @ SV22 )
= $true )
| ( ( ssList @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(395,plain,
! [SV24: $i,SV38: $i,SV44: $i] :
( ( ( ~ ( ssList @ SV44 ) )
= $true )
| ( ( ( ( app @ SV44 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
| ( SV44 = SV24 ) )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(396,plain,
! [SV39: $i,SV26: $i,SV45: $i] :
( ( ( ~ ( ssList @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SV45 ) )
| ( frontsegP @ SV26 @ SV45 ) )
= $true )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(397,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( neq @ SV3 @ SV27 )
| ( SV3 != SV27 ) )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(398,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV27 ) )
| ( neq @ SV3 @ SV27 ) )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(399,plain,
! [SV28: $i,SV4: $i,SV40: $i] :
( ( ( ssList @ SV40 )
= $false )
| ( ( ( app @ ( app @ SV4 @ SV28 ) @ SV40 )
= ( app @ SV4 @ ( app @ SV28 @ SV40 ) ) )
= $true )
| ( ( ssList @ SV28 )
= $false )
| ( ( ssList @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(400,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( neq @ SV5 @ SV29 )
| ( SV5 != SV29 ) )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(401,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV29 ) )
| ( neq @ SV5 @ SV29 ) )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(402,plain,
! [SV30: $i,SV7: $i] :
( ( ( ~ ( rearsegP @ SV7 @ SV30 )
| ~ ( rearsegP @ SV30 @ SV7 ) )
= $true )
| ( ( SV7 = SV30 )
= $true )
| ( ( ssList @ SV30 )
= $false )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(403,plain,
! [SV31: $i,SV9: $i,SV41: $i] :
( ( ( ssList @ SV41 )
= $false )
| ( ( ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SV41 ) )
| ( segmentP @ SV9 @ SV41 ) )
= $true )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(404,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( frontsegP @ SV10 @ SV32 )
| ~ ( frontsegP @ SV32 @ SV10 ) )
= $true )
| ( ( SV10 = SV32 )
= $true )
| ( ( ssList @ SV32 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(405,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( segmentP @ SV11 @ SV33 )
| ~ ( segmentP @ SV33 @ SV11 ) )
= $true )
| ( ( SV11 = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(406,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ( ssList @ ( sK5_SY62 @ SV12 ) )
| ( ( tl @ SV12 )
!= ( sK5_SY62 @ SV12 ) ) ) )
= $true )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(407,plain,
( ( sK2_SX0 != sK4_SY77 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(408,plain,
( ( sK1_U != sK3_SY73 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(409,plain,
( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
| ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(410,plain,
! [SV15: $i,SV34: $i,SV42: $i] :
( ( ( ssList @ SV42 )
= $false )
| ( ( ( ( app @ SV34 @ SV42 )
!= ( app @ SV34 @ SV15 ) )
| ( SV42 = SV15 ) )
= $true )
| ( ( ssList @ SV34 )
= $false )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(411,plain,
! [SV35: $i,SV16: $i] :
( ( ( ( nil
!= ( app @ SV16 @ SV35 ) )
| ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(412,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) )
| ( nil
= ( app @ SV16 @ SV35 ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(413,plain,
! [SV37: $i,SV19: $i,SV43: $i] :
( ( ( ssList @ SV43 )
= $false )
| ( ( ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SV43 ) )
| ( rearsegP @ SV19 @ SV43 ) )
= $true )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(414,plain,
! [SV24: $i,SV38: $i,SV44: $i] :
( ( ( ssList @ SV44 )
= $false )
| ( ( ( ( app @ SV44 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
| ( SV44 = SV24 ) )
= $true )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(415,plain,
! [SV39: $i,SV26: $i,SV45: $i] :
( ( ( ssList @ SV45 )
= $false )
| ( ( ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SV45 ) )
| ( frontsegP @ SV26 @ SV45 ) )
= $true )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(416,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( neq @ SV3 @ SV27 ) )
= $true )
| ( ( SV3 != SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(417,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV27 ) ) )
= $true )
| ( ( neq @ SV3 @ SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(418,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( neq @ SV5 @ SV29 ) )
= $true )
| ( ( SV5 != SV29 )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(419,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV29 ) ) )
= $true )
| ( ( neq @ SV5 @ SV29 )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(420,plain,
! [SV30: $i,SV7: $i] :
( ( ( ~ ( rearsegP @ SV7 @ SV30 ) )
= $true )
| ( ( ~ ( rearsegP @ SV30 @ SV7 ) )
= $true )
| ( ( SV7 = SV30 )
= $true )
| ( ( ssList @ SV30 )
= $false )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(421,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SV41 ) ) )
= $true )
| ( ( segmentP @ SV9 @ SV41 )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(422,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( frontsegP @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( frontsegP @ SV32 @ SV10 ) )
= $true )
| ( ( SV10 = SV32 )
= $true )
| ( ( ssList @ SV32 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(423,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( segmentP @ SV11 @ SV33 ) )
= $true )
| ( ( ~ ( segmentP @ SV33 @ SV11 ) )
= $true )
| ( ( SV11 = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(424,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ ( sK5_SY62 @ SV12 ) )
| ( ( tl @ SV12 )
!= ( sK5_SY62 @ SV12 ) ) )
= $false )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(425,plain,
( ( sK2_SX0 = sK4_SY77 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(426,plain,
( ( sK1_U = sK3_SY73 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(427,plain,
( ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) ) )
= $true )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(428,plain,
! [SV15: $i,SV42: $i,SV34: $i] :
( ( ( ( app @ SV34 @ SV42 )
!= ( app @ SV34 @ SV15 ) )
= $true )
| ( ( SV42 = SV15 )
= $true )
| ( ( ssList @ SV42 )
= $false )
| ( ( ssList @ SV34 )
= $false )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(429,plain,
! [SV35: $i,SV16: $i] :
( ( ( nil
!= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(430,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
= $true )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(431,plain,
! [SV43: $i,SV37: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SV43 ) ) )
= $true )
| ( ( rearsegP @ SV19 @ SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(432,plain,
! [SV24: $i,SV38: $i,SV44: $i] :
( ( ( ( app @ SV44 @ SV38 )
!= ( app @ SV24 @ SV38 ) )
= $true )
| ( ( SV44 = SV24 )
= $true )
| ( ( ssList @ SV44 )
= $false )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(433,plain,
! [SV45: $i,SV39: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SV45 ) ) )
= $true )
| ( ( frontsegP @ SV26 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(434,plain,
! [SV27: $i,SV3: $i] :
( ( ( neq @ SV3 @ SV27 )
= $false )
| ( ( SV3 != SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(435,plain,
! [SV27: $i,SV3: $i] :
( ( ( SV3 != SV27 )
= $false )
| ( ( neq @ SV3 @ SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(436,plain,
! [SV29: $i,SV5: $i] :
( ( ( neq @ SV5 @ SV29 )
= $false )
| ( ( SV5 != SV29 )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(437,plain,
! [SV29: $i,SV5: $i] :
( ( ( SV5 != SV29 )
= $false )
| ( ( neq @ SV5 @ SV29 )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(438,plain,
! [SV30: $i,SV7: $i] :
( ( ( rearsegP @ SV7 @ SV30 )
= $false )
| ( ( ~ ( rearsegP @ SV30 @ SV7 ) )
= $true )
| ( ( SV7 = SV30 )
= $true )
| ( ( ssList @ SV30 )
= $false )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(439,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SV41 ) ) )
= $false )
| ( ( segmentP @ SV9 @ SV41 )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(440,plain,
! [SV32: $i,SV10: $i] :
( ( ( frontsegP @ SV10 @ SV32 )
= $false )
| ( ( ~ ( frontsegP @ SV32 @ SV10 ) )
= $true )
| ( ( SV10 = SV32 )
= $true )
| ( ( ssList @ SV32 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(441,plain,
! [SV33: $i,SV11: $i] :
( ( ( segmentP @ SV11 @ SV33 )
= $false )
| ( ( ~ ( segmentP @ SV33 @ SV11 ) )
= $true )
| ( ( SV11 = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(442,plain,
! [SV12: $i] :
( ( ( ~ ( ssList @ ( sK5_SY62 @ SV12 ) ) )
= $false )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(443,plain,
! [SV12: $i] :
( ( ( ( tl @ SV12 )
!= ( sK5_SY62 @ SV12 ) )
= $false )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(444,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 )
| ( singletonP @ sK1_U ) )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(445,plain,
! [SV15: $i,SV42: $i,SV34: $i] :
( ( ( ( app @ SV34 @ SV42 )
= ( app @ SV34 @ SV15 ) )
= $false )
| ( ( SV42 = SV15 )
= $true )
| ( ( ssList @ SV42 )
= $false )
| ( ( ssList @ SV34 )
= $false )
| ( ( ssList @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(446,plain,
! [SV35: $i,SV16: $i] :
( ( ( nil
= ( app @ SV16 @ SV35 ) )
= $false )
| ( ( ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(447,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( ( nil != SV35 )
| ( nil != SV16 ) ) )
= $false )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(448,plain,
! [SV43: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SV43 ) ) )
= $false )
| ( ( rearsegP @ SV19 @ SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(449,plain,
! [SV24: $i,SV38: $i,SV44: $i] :
( ( ( ( app @ SV44 @ SV38 )
= ( app @ SV24 @ SV38 ) )
= $false )
| ( ( SV44 = SV24 )
= $true )
| ( ( ssList @ SV44 )
= $false )
| ( ( ssList @ SV38 )
= $false )
| ( ( ssList @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(450,plain,
! [SV45: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SV45 ) ) )
= $false )
| ( ( frontsegP @ SV26 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(451,plain,
! [SV27: $i,SV3: $i] :
( ( ( SV3 = SV27 )
= $false )
| ( ( neq @ SV3 @ SV27 )
= $false )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(452,plain,
! [SV27: $i,SV3: $i] :
( ( ( SV3 = SV27 )
= $true )
| ( ( neq @ SV3 @ SV27 )
= $true )
| ( ( ssList @ SV27 )
= $false )
| ( ( ssList @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(453,plain,
! [SV29: $i,SV5: $i] :
( ( ( SV5 = SV29 )
= $false )
| ( ( neq @ SV5 @ SV29 )
= $false )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(454,plain,
! [SV29: $i,SV5: $i] :
( ( ( SV5 = SV29 )
= $true )
| ( ( neq @ SV5 @ SV29 )
= $true )
| ( ( ssItem @ SV29 )
= $false )
| ( ( ssItem @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(455,plain,
! [SV7: $i,SV30: $i] :
( ( ( rearsegP @ SV30 @ SV7 )
= $false )
| ( ( rearsegP @ SV7 @ SV30 )
= $false )
| ( ( SV7 = SV30 )
= $true )
| ( ( ssList @ SV30 )
= $false )
| ( ( ssList @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( segmentP @ SV9 @ SV31 )
| ~ ( segmentP @ SV31 @ SV41 ) )
= $true )
| ( ( segmentP @ SV9 @ SV41 )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(457,plain,
! [SV10: $i,SV32: $i] :
( ( ( frontsegP @ SV32 @ SV10 )
= $false )
| ( ( frontsegP @ SV10 @ SV32 )
= $false )
| ( ( SV10 = SV32 )
= $true )
| ( ( ssList @ SV32 )
= $false )
| ( ( ssList @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(458,plain,
! [SV11: $i,SV33: $i] :
( ( ( segmentP @ SV33 @ SV11 )
= $false )
| ( ( segmentP @ SV11 @ SV33 )
= $false )
| ( ( SV11 = SV33 )
= $true )
| ( ( ssList @ SV33 )
= $false )
| ( ( ssList @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(459,plain,
! [SV12: $i] :
( ( ( ssList @ ( sK5_SY62 @ SV12 ) )
= $true )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(460,plain,
! [SV12: $i] :
( ( ( ( tl @ SV12 )
= ( sK5_SY62 @ SV12 ) )
= $true )
| ( ( nil = SV12 )
= $true )
| ( ( ssList @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(461,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ~ ( singletonP @ sK3_SY73 ) )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(462,plain,
( ( ( singletonP @ sK1_U )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(463,plain,
! [SV16: $i,SV35: $i] :
( ( ( ( nil != SV35 )
| ( nil != SV16 ) )
= $false )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(464,plain,
! [SV16: $i,SV35: $i] :
( ( ( ( nil != SV35 )
| ( nil != SV16 ) )
= $true )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(465,plain,
! [SV43: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( rearsegP @ SV19 @ SV37 )
| ~ ( rearsegP @ SV37 @ SV43 ) )
= $true )
| ( ( rearsegP @ SV19 @ SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(466,plain,
! [SV45: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( frontsegP @ SV26 @ SV39 )
| ~ ( frontsegP @ SV39 @ SV45 ) )
= $true )
| ( ( frontsegP @ SV26 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(467,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( segmentP @ SV9 @ SV31 ) )
= $true )
| ( ( ~ ( segmentP @ SV31 @ SV41 ) )
= $true )
| ( ( segmentP @ SV9 @ SV41 )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(468,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(469,plain,
( ( ( ~ ( singletonP @ sK3_SY73 ) )
= $false )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(470,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) )
= $false )
| ( ( singletonP @ sK1_U )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(471,plain,
! [SV16: $i,SV35: $i] :
( ( ( nil != SV35 )
= $false )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(472,plain,
! [SV35: $i,SV16: $i] :
( ( ( nil != SV16 )
= $false )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(473,plain,
! [SV16: $i,SV35: $i] :
( ( ( nil != SV35 )
= $true )
| ( ( nil != SV16 )
= $true )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(474,plain,
! [SV43: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( rearsegP @ SV19 @ SV37 ) )
= $true )
| ( ( ~ ( rearsegP @ SV37 @ SV43 ) )
= $true )
| ( ( rearsegP @ SV19 @ SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(475,plain,
! [SV45: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( frontsegP @ SV26 @ SV39 ) )
= $true )
| ( ( ~ ( frontsegP @ SV39 @ SV45 ) )
= $true )
| ( ( frontsegP @ SV26 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(476,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( segmentP @ SV9 @ SV31 )
= $false )
| ( ( ~ ( segmentP @ SV31 @ SV41 ) )
= $true )
| ( ( segmentP @ SV9 @ SV41 )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(477,plain,
( ( ( neq @ sK2_SX0 @ nil )
= $true )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(478,plain,
( ( ( singletonP @ sK3_SY73 )
= $true )
| ( ( ~ ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(479,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false )
| ( ( singletonP @ sK1_U )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(480,plain,
( ( ( neq @ sK4_SY77 @ nil )
= $false )
| ( ( singletonP @ sK1_U )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(481,plain,
! [SV16: $i,SV35: $i] :
( ( ( nil = SV35 )
= $true )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(482,plain,
! [SV35: $i,SV16: $i] :
( ( ( nil = SV16 )
= $true )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $false )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(483,plain,
! [SV16: $i,SV35: $i] :
( ( ( nil = SV35 )
= $false )
| ( ( nil != SV16 )
= $true )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(484,plain,
! [SV43: $i,SV37: $i,SV19: $i] :
( ( ( rearsegP @ SV19 @ SV37 )
= $false )
| ( ( ~ ( rearsegP @ SV37 @ SV43 ) )
= $true )
| ( ( rearsegP @ SV19 @ SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(485,plain,
! [SV45: $i,SV39: $i,SV26: $i] :
( ( ( frontsegP @ SV26 @ SV39 )
= $false )
| ( ( ~ ( frontsegP @ SV39 @ SV45 ) )
= $true )
| ( ( frontsegP @ SV26 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(486,plain,
! [SV9: $i,SV41: $i,SV31: $i] :
( ( ( segmentP @ SV31 @ SV41 )
= $false )
| ( ( segmentP @ SV9 @ SV31 )
= $false )
| ( ( segmentP @ SV9 @ SV41 )
= $true )
| ( ( ssList @ SV41 )
= $false )
| ( ( ssList @ SV31 )
= $false )
| ( ( ssList @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(487,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) )
= $false )
| ( ( neq @ sK2_SX0 @ nil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(488,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil )
| ( neq @ sK4_SY77 @ nil ) )
= $false )
| ( ( singletonP @ sK3_SY73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(489,plain,
( ( ( neq @ sK2_SX0 @ nil )
= $true )
| ( ( singletonP @ sK1_U )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(490,plain,
! [SV35: $i,SV16: $i] :
( ( ( nil = SV16 )
= $false )
| ( ( nil = SV35 )
= $false )
| ( ( nil
= ( app @ SV16 @ SV35 ) )
= $true )
| ( ( ssList @ SV35 )
= $false )
| ( ( ssList @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(491,plain,
! [SV19: $i,SV43: $i,SV37: $i] :
( ( ( rearsegP @ SV37 @ SV43 )
= $false )
| ( ( rearsegP @ SV19 @ SV37 )
= $false )
| ( ( rearsegP @ SV19 @ SV43 )
= $true )
| ( ( ssList @ SV43 )
= $false )
| ( ( ssList @ SV37 )
= $false )
| ( ( ssList @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(492,plain,
! [SV26: $i,SV45: $i,SV39: $i] :
( ( ( frontsegP @ SV39 @ SV45 )
= $false )
| ( ( frontsegP @ SV26 @ SV39 )
= $false )
| ( ( frontsegP @ SV26 @ SV45 )
= $true )
| ( ( ssList @ SV45 )
= $false )
| ( ( ssList @ SV39 )
= $false )
| ( ( ssList @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(493,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false )
| ( ( neq @ sK2_SX0 @ nil )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(494,plain,
( ( ( neq @ sK4_SY77 @ nil )
= $false )
| ( ( neq @ sK2_SX0 @ nil )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(495,plain,
( ( ( ~ ( neq @ sK2_SX0 @ nil ) )
= $false )
| ( ( singletonP @ sK3_SY73 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(496,plain,
( ( ( neq @ sK4_SY77 @ nil )
= $false )
| ( ( singletonP @ sK3_SY73 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(497,plain,
( ( ( neq @ sK2_SX0 @ nil )
= $true )
| ( ( neq @ sK2_SX0 @ nil )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(498,plain,
( ( ( neq @ sK2_SX0 @ nil )
= $true )
| ( ( singletonP @ sK3_SY73 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(499,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[140,498,497,496,494,492,491,490,489,486,482,481,480,460,459,458,457,455,454,453,452,451,449,445,426,425,399,394,393,386,381,380,373,372,349,344,340,295,281,279,278,275,272,271,262,258,202,173,166,165,164,163,162,161,160]) ).
thf(500,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC255+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 16:06:39 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.13/0.46 .
% 1.13/0.46
% 1.13/0.46 No.of.Axioms: 35
% 1.13/0.46
% 1.13/0.46 Length.of.Defs: 0
% 1.13/0.46
% 1.13/0.46 Contains.Choice.Funs: false
% 1.13/0.46 ............
% 1.13/0.46
% 1.13/0.46 ********************************
% 1.13/0.46 * All subproblems solved! *
% 1.13/0.46 ********************************
% 1.13/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:36,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:499,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.13/0.46
% 1.13/0.46 %**** Beginning of derivation protocol ****
% 1.13/0.46 % SZS output start CNFRefutation
% See solution above
% 1.13/0.46
% 1.13/0.46 %**** End of derivation protocol ****
% 1.13/0.46 %**** no. of clauses in derivation: 440 ****
% 1.13/0.46 %**** clause counter: 499 ****
% 1.13/0.46
% 1.13/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:36,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:499,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------