TSTP Solution File: GEO252+3 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO252+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:09:18 EDT 2022
% Result : Theorem 0.56s 0.77s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 62
% Syntax : Number of formulae : 1232 ( 774 unt; 25 typ; 0 def)
% Number of atoms : 8385 (1895 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 17783 (2829 ~;3177 |; 151 &;11566 @)
% ( 20 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 5 con; 0-4 aty)
% Number of variables : 3875 ( 0 ^3875 !; 0 ?;3875 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $i > $i > $o ).
thf(tp_before_on_line,type,
before_on_line: $i > $i > $i > $o ).
thf(tp_between_on_line,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(tp_convergent_lines,type,
convergent_lines: $i > $i > $o ).
thf(tp_distinct_lines,type,
distinct_lines: $i > $i > $o ).
thf(tp_distinct_points,type,
distinct_points: $i > $i > $o ).
thf(tp_divides_points,type,
divides_points: $i > $i > $i > $o ).
thf(tp_equally_directed_lines,type,
equally_directed_lines: $i > $i > $o ).
thf(tp_equally_directed_opposite_lines,type,
equally_directed_opposite_lines: $i > $i > $o ).
thf(tp_incident_point_and_line,type,
incident_point_and_line: $i > $i > $o ).
thf(tp_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_left_apart_point,type,
left_apart_point: $i > $i > $o ).
thf(tp_left_convergent_lines,type,
left_convergent_lines: $i > $i > $o ).
thf(tp_line,type,
line: $i > $o ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_reverse_line,type,
reverse_line: $i > $i ).
thf(tp_right_apart_point,type,
right_apart_point: $i > $i > $o ).
thf(tp_right_convergent_lines,type,
right_convergent_lines: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY84,type,
sK2_SY84: $i ).
thf(tp_sK3_SY86,type,
sK3_SY86: $i ).
thf(tp_unequally_directed_lines,type,
unequally_directed_lines: $i > $i > $o ).
thf(tp_unequally_directed_opposite_lines,type,
unequally_directed_opposite_lines: $i > $i > $o ).
thf(1,axiom,
! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_subs) ).
thf(2,axiom,
! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( unequally_directed_lines @ L @ M ) )
=> ( ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_subs) ).
thf(3,axiom,
! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_subs) ).
thf(4,axiom,
! [A: $i,B: $i,L: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ L ) )
=> ( ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_uniq_cons) ).
thf(5,axiom,
! [A: $i,B: $i,L: $i,M: $i] :
( ( ( distinct_points @ A @ B )
& ( distinct_lines @ L @ M ) )
=> ( ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_uniq_cons) ).
thf(6,axiom,
! [A: $i,L: $i] : ( equally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_cons_objs) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_cons_objs) ).
thf(8,axiom,
! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_cons_objs) ).
thf(9,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7_cons_objs) ).
thf(10,axiom,
! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L )
& ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6_cons_objs) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_cons_objs) ).
thf(12,axiom,
! [L: $i] :
( ( line @ L )
=> ( line @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_cons_objs) ).
thf(13,axiom,
! [L: $i,A: $i] :
( ( ( point @ A )
& ( line @ L ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_cons_objs) ).
thf(14,axiom,
! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( point @ ( intersection_point @ L @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_cons_objs) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_cons_objs) ).
thf(16,axiom,
! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
thf(17,axiom,
! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
thf(18,axiom,
! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
thf(19,axiom,
! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
thf(20,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7_basics) ).
thf(21,axiom,
! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6_basics) ).
thf(22,axiom,
! [L: $i] : ( equally_directed_lines @ L @ L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_basics) ).
thf(23,axiom,
! [L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_basics) ).
thf(24,axiom,
! [L: $i] :
~ ( distinct_lines @ L @ L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_basics) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_basics) ).
thf(26,axiom,
! [A: $i] :
~ ( distinct_points @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_basics) ).
thf(27,axiom,
! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
<=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
| ( ( before_on_line @ L @ C @ B )
& ( before_on_line @ L @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9_defns) ).
thf(28,axiom,
! [L: $i,A: $i,B: $i] :
( ( before_on_line @ L @ A @ B )
<=> ( ( distinct_points @ A @ B )
& ( incident_point_and_line @ A @ L )
& ( incident_point_and_line @ B @ L )
& ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_defns) ).
thf(29,axiom,
! [A: $i,B: $i,L: $i] :
( ( divides_points @ L @ A @ B )
<=> ( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
| ( ( right_apart_point @ A @ L )
& ( left_apart_point @ B @ L ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_defns) ).
thf(30,axiom,
! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
<=> ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_opposite_lines @ L @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_defns) ).
thf(31,axiom,
! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_defns) ).
thf(32,axiom,
! [X: $i,Y: $i] :
( ( equally_directed_opposite_lines @ X @ Y )
<=> ~ ( unequally_directed_opposite_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_defns) ).
thf(33,axiom,
! [X: $i,Y: $i] :
( ( equally_directed_lines @ X @ Y )
<=> ~ ( unequally_directed_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
thf(34,axiom,
! [X: $i,Y: $i] :
( ( right_convergent_lines @ X @ Y )
<=> ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_defns) ).
thf(35,axiom,
! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_defns) ).
thf(36,axiom,
! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
<=> ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
thf(37,conjecture,
! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
=> ( ( distinct_points @ A @ B )
& ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
=> ( ( distinct_points @ A @ B )
& ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
=> ( ( distinct_points @ A @ B )
& ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(41,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( unequally_directed_lines @ L @ M ) )
=> ( ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ L ) )
=> ( ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,L: $i,M: $i] :
( ( ( distinct_points @ A @ B )
& ( distinct_lines @ L @ M ) )
=> ( ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(45,plain,
( ( ! [A: $i,L: $i] : ( equally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(47,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(48,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(49,plain,
( ( ! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L )
& ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(51,plain,
( ( ! [L: $i] :
( ( line @ L )
=> ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(52,plain,
( ( ! [L: $i,A: $i] :
( ( ( point @ A )
& ( line @ L ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(53,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(55,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(56,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(57,plain,
( ( ! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(58,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(59,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(60,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(61,plain,
( ( ! [L: $i] : ( equally_directed_lines @ L @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(62,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(63,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(65,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(66,plain,
( ( ! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
<=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
| ( ( before_on_line @ L @ C @ B )
& ( before_on_line @ L @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [L: $i,A: $i,B: $i] :
( ( before_on_line @ L @ A @ B )
<=> ( ( distinct_points @ A @ B )
& ( incident_point_and_line @ A @ L )
& ( incident_point_and_line @ B @ L )
& ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( divides_points @ L @ A @ B )
<=> ( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
| ( ( right_apart_point @ A @ L )
& ( left_apart_point @ B @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(69,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
<=> ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_opposite_lines @ L @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i] :
( ( equally_directed_opposite_lines @ X @ Y )
<=> ~ ( unequally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i] :
( ( equally_directed_lines @ X @ Y )
<=> ~ ( unequally_directed_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( right_convergent_lines @ X @ Y )
<=> ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
<=> ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(76,plain,
( ( ! [SY84: $i,SY85: $i] :
( ( ( left_apart_point @ sK1_A @ SY85 )
& ( right_apart_point @ SY84 @ SY85 ) )
=> ( ( distinct_points @ sK1_A @ SY84 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ SY84 ) @ SY85 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(77,plain,
( ( ! [SY86: $i] :
( ( ( left_apart_point @ sK1_A @ SY86 )
& ( right_apart_point @ sK2_SY84 @ SY86 ) )
=> ( ( distinct_points @ sK1_A @ sK2_SY84 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ SY86 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(78,plain,
( ( ( ( left_apart_point @ sK1_A @ sK3_SY86 )
& ( right_apart_point @ sK2_SY84 @ sK3_SY86 ) )
=> ( ( distinct_points @ sK1_A @ sK2_SY84 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ sK3_SY86 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(79,plain,
( ( left_apart_point @ sK1_A @ sK3_SY86 )
= $true ),
inference(standard_cnf,[status(thm)],[78]) ).
thf(80,plain,
( ( right_apart_point @ sK2_SY84 @ sK3_SY86 )
= $true ),
inference(standard_cnf,[status(thm)],[78]) ).
thf(81,plain,
( ( ( distinct_points @ sK1_A @ sK2_SY84 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ sK3_SY86 ) )
= $false ),
inference(standard_cnf,[status(thm)],[78]) ).
thf(82,plain,
( ( distinct_points @ sK1_A @ sK2_SY84 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[81]) ).
thf(83,plain,
( ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ sK3_SY86 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[81]) ).
thf(84,plain,
( ( ~ ( distinct_points @ sK1_A @ sK2_SY84 ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(85,plain,
( ( ~ ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ sK3_SY86 ) )
= $true ),
inference(polarity_switch,[status(thm)],[83]) ).
thf(86,plain,
( ( ! [L: $i,M: $i] :
( ~ ( left_convergent_lines @ L @ M )
| ! [N: $i] :
( ( left_convergent_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(87,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(89,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ~ ( distinct_points @ A @ B )
| ( left_apart_point @ B @ ( reverse_line @ M ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(92,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L ) )
& ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(94,plain,
( ( ! [L: $i] :
( ~ ( line @ L )
| ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(95,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(96,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(98,plain,
( ( ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ M )
& ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ ( reverse_line @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(99,plain,
( ( ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ L )
& ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ ( reverse_line @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(100,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(101,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(102,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(103,plain,
( ( ! [L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ! [C: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(105,plain,
( ( ! [L: $i,A: $i] :
( ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i] :
( ! [C: $i] :
~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ~ ( before_on_line @ L @ B @ C )
| ( between_on_line @ L @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ C @ B )
| ~ ( before_on_line @ L @ B @ A )
| ( between_on_line @ L @ A @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(106,plain,
( ( ! [L: $i] :
( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( incident_point_and_line @ A @ L )
| ~ ( incident_point_and_line @ B @ L )
| ~ ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) )
| ( before_on_line @ L @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( distinct_points @ A @ B ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ A @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ B @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(107,plain,
( ( ! [A: $i] :
( ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( right_apart_point @ B @ L )
| ( divides_points @ L @ A @ B ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ B @ L )
| ~ ( right_apart_point @ A @ L )
| ( divides_points @ L @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(108,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_opposite_lines @ L @ M )
| ( convergent_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_opposite_lines @ L @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(109,plain,
( ( ! [A: $i,L: $i] :
( ~ ( apart_point_and_line @ A @ L )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( right_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_opposite_lines @ X @ Y )
| ~ ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
| ( equally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_lines @ X @ Y )
| ~ ( unequally_directed_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_lines @ X @ Y )
| ( equally_directed_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_convergent_lines @ X @ ( reverse_line @ Y ) )
| ( right_convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_convergent_lines @ X @ Y )
| ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_apart_point @ X @ ( reverse_line @ Y ) )
| ( right_apart_point @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_apart_point @ X @ Y )
| ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( unequally_directed_lines @ X @ ( reverse_line @ Y ) )
| ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( unequally_directed_opposite_lines @ X @ Y )
| ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( unequally_directed_lines @ X @ ( reverse_line @ Y ) )
| ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( unequally_directed_opposite_lines @ X @ Y )
| ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_apart_point @ X @ ( reverse_line @ Y ) )
| ( right_apart_point @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_apart_point @ X @ Y )
| ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_convergent_lines @ X @ ( reverse_line @ Y ) )
| ( right_convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_convergent_lines @ X @ Y )
| ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_lines @ X @ Y )
| ~ ( unequally_directed_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_lines @ X @ Y )
| ( equally_directed_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_opposite_lines @ X @ Y )
| ~ ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
| ( equally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(120,plain,
( ( ! [A: $i,L: $i] :
( ~ ( apart_point_and_line @ A @ L )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( right_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(121,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_opposite_lines @ L @ M )
| ( convergent_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_opposite_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(122,plain,
( ( ! [A: $i] :
( ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( right_apart_point @ B @ L )
| ( divides_points @ L @ A @ B ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ B @ L )
| ~ ( right_apart_point @ A @ L )
| ( divides_points @ L @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(123,plain,
( ( ! [L: $i] :
( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( incident_point_and_line @ A @ L )
| ~ ( incident_point_and_line @ B @ L )
| ~ ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) )
| ( before_on_line @ L @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( distinct_points @ A @ B ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ A @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ B @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(124,plain,
( ( ! [L: $i,A: $i] :
( ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i] :
( ! [C: $i] :
~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ~ ( before_on_line @ L @ B @ C )
| ( between_on_line @ L @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ C @ B )
| ~ ( before_on_line @ L @ B @ A )
| ( between_on_line @ L @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(125,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ! [C: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(127,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(128,plain,
( ( ! [L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(129,plain,
( ( ! [L: $i] : ( equally_directed_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(130,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(131,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(132,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(133,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(134,plain,
( ( ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ L )
& ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(135,plain,
( ( ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ M )
& ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ ( reverse_line @ M ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(137,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(138,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(139,plain,
( ( ! [L: $i] :
( ~ ( line @ L )
| ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(141,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L ) )
& ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(142,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(143,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(144,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(145,plain,
( ( ! [A: $i,L: $i] : ( equally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ~ ( distinct_points @ A @ B )
| ( left_apart_point @ B @ ( reverse_line @ M ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(147,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(149,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(150,plain,
( ( ! [L: $i,M: $i] :
( ~ ( left_convergent_lines @ L @ M )
| ! [N: $i] :
( ( left_convergent_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(151,plain,
( ( right_apart_point @ sK2_SY84 @ sK3_SY86 )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(152,plain,
( ( left_apart_point @ sK1_A @ sK3_SY86 )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(153,plain,
( ( ~ ( distinct_points @ sK1_A @ sK2_SY84 ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(154,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(155,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX1 @ SX2 )
| ~ ( incident_point_and_line @ SX1 @ SX0 )
| ~ ( incident_point_and_line @ SX2 @ SX0 )
| ~ ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) )
| ( before_on_line @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( incident_point_and_line @ SX1 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( incident_point_and_line @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(156,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(157,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(158,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(159,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(160,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(161,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(162,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(163,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX2 )
| ( right_apart_point @ SX0 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( right_apart_point @ SX1 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( right_apart_point @ SX1 @ SX2 )
| ( right_apart_point @ SX0 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 )
| ( divides_points @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX1 @ SX2 )
| ~ ( right_apart_point @ SX0 @ SX2 )
| ( divides_points @ SX2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(164,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) )
| ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(165,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( before_on_line @ SX0 @ SX3 @ SX2 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( before_on_line @ SX0 @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX3 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( before_on_line @ SX0 @ SX3 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX1 )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(167,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(168,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(169,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(170,plain,
! [SV2: $i] :
( ( ! [SY87: $i] :
( ~ ( distinct_points @ SV2 @ SY87 )
| ! [SY88: $i] :
( ( distinct_points @ SV2 @ SY88 )
| ( distinct_points @ SY87 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(171,plain,
! [SV3: $i] :
( ( ~ ( distinct_lines @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(172,plain,
! [SV4: $i] :
( ( ! [SY89: $i] :
( ~ ( distinct_lines @ SV4 @ SY89 )
| ! [SY90: $i] :
( ( distinct_lines @ SV4 @ SY90 )
| ( distinct_lines @ SY89 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(173,plain,
! [SV5: $i] :
( ( equally_directed_lines @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(174,plain,
! [SV6: $i] :
( ( ! [SY91: $i] :
( ~ ( unequally_directed_lines @ SV6 @ SY91 )
| ! [SY92: $i] :
( ( unequally_directed_lines @ SV6 @ SY92 )
| ( unequally_directed_lines @ SY91 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(175,plain,
! [SV7: $i] :
( ( ! [SY93: $i] :
( ( unequally_directed_lines @ SV7 @ SY93 )
| ( unequally_directed_lines @ SV7 @ ( reverse_line @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(176,plain,
! [SV8: $i] :
( ( ! [SY94: $i] :
( ~ ( unequally_directed_lines @ SV8 @ SY94 )
| ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SY94 ) )
| ( left_convergent_lines @ SV8 @ SY94 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(177,plain,
! [SV9: $i] :
( ( ! [SY95: $i] :
( ~ ( point @ SV9 )
| ~ ( point @ SY95 )
| ~ ( distinct_points @ SV9 @ SY95 )
| ( line @ ( line_connecting @ SV9 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(178,plain,
! [SV10: $i] :
( ( ! [SY96: $i] :
( ~ ( line @ SV10 )
| ~ ( line @ SY96 )
| ~ ( unequally_directed_lines @ SV10 @ SY96 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SY96 ) )
| ( point @ ( intersection_point @ SV10 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(179,plain,
! [SV11: $i] :
( ( ! [SY97: $i] :
( ~ ( line @ SV11 )
| ~ ( point @ SY97 )
| ( line @ ( parallel_through_point @ SV11 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(180,plain,
! [SV12: $i] :
( ( ~ ( line @ SV12 )
| ( line @ ( reverse_line @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(181,plain,
! [SV13: $i] :
( ( ! [SY98: $i] :
~ ( apart_point_and_line @ SV13 @ ( parallel_through_point @ SY98 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(182,plain,
! [SV14: $i] :
( ( ~ ( distinct_lines @ SV14 @ ( reverse_line @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(183,plain,
! [SV15: $i] :
( ( ! [SY99: $i] :
( ~ ( distinct_points @ SV15 @ SY99 )
| ( equally_directed_lines @ ( line_connecting @ SV15 @ SY99 ) @ ( reverse_line @ ( line_connecting @ SY99 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(184,plain,
! [SV16: $i] :
( ( ! [SY100: $i] : ( equally_directed_lines @ ( parallel_through_point @ SY100 @ SV16 ) @ SY100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(185,plain,
! [SV17: $i] :
( ( ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ( distinct_lines @ SY102 @ SY103 )
| ~ ( distinct_points @ SV17 @ SY101 )
| ( left_apart_point @ SY101 @ ( reverse_line @ SY103 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY103 ) )
| ( left_apart_point @ SY101 @ ( reverse_line @ SY102 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY102 ) )
| ( left_apart_point @ SY101 @ SY103 )
| ( left_apart_point @ SV17 @ SY103 )
| ( left_apart_point @ SV17 @ SY102 )
| ( left_apart_point @ SY101 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(186,plain,
! [SV18: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( distinct_points @ SV18 @ SY104 )
| ~ ( left_apart_point @ SV18 @ SY105 )
| ( left_apart_point @ SY104 @ SY105 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SY104 ) @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(187,plain,
! [SV19: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( left_apart_point @ SV19 @ SY107 )
| ( distinct_points @ SV19 @ SY106 )
| ( left_apart_point @ SY106 @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(188,plain,
! [SV20: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( left_apart_point @ SV20 @ SY108 )
| ~ ( unequally_directed_lines @ SY108 @ SY109 )
| ( distinct_lines @ SY108 @ SY109 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(189,plain,
! [SV21: $i] :
( ( ! [SY110: $i] :
( ~ ( left_convergent_lines @ SV21 @ SY110 )
| ! [SY111: $i] :
( ( left_convergent_lines @ SV21 @ SY111 )
| ( unequally_directed_lines @ SY110 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(190,plain,
( ( distinct_points @ sK1_A @ sK2_SY84 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(191,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(192,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( distinct_points @ SY112 @ SY113 )
| ~ ( incident_point_and_line @ SY112 @ SV22 )
| ~ ( incident_point_and_line @ SY113 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SY112 @ SY113 ) )
| ( before_on_line @ SV22 @ SY112 @ SY113 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
| ~ ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(193,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(195,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(196,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(199,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(200,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
| ~ ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(201,plain,
! [SV24: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) )
| ~ ~ ( ~ ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(202,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(203,plain,
! [SV25: $i] :
( ( ! [SY142: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY143: $i,SY144: $i] :
( ~ ( between_on_line @ SV25 @ SY142 @ SY143 @ SY144 )
| ( before_on_line @ SV25 @ SY142 @ SY143 )
| ( before_on_line @ SV25 @ SY144 @ SY143 ) )
| ~ ! [SY145: $i] :
( ! [SY146: $i] :
~ ( between_on_line @ SV25 @ SY142 @ SY145 @ SY146 )
| ( before_on_line @ SV25 @ SY142 @ SY145 )
| ( before_on_line @ SV25 @ SY145 @ SY142 ) ) )
| ~ ~ ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( between_on_line @ SV25 @ SY142 @ SY147 @ SY148 )
| ( before_on_line @ SV25 @ SY147 @ SY148 )
| ( before_on_line @ SV25 @ SY148 @ SY147 ) )
| ~ ! [SY149: $i,SY150: $i] :
( ~ ( between_on_line @ SV25 @ SY142 @ SY149 @ SY150 )
| ( before_on_line @ SV25 @ SY149 @ SY150 )
| ( before_on_line @ SV25 @ SY149 @ SY142 ) ) ) )
| ~ ~ ( ~ ! [SY151: $i,SY152: $i] :
( ~ ( before_on_line @ SV25 @ SY142 @ SY151 )
| ~ ( before_on_line @ SV25 @ SY151 @ SY152 )
| ( between_on_line @ SV25 @ SY142 @ SY151 @ SY152 ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( before_on_line @ SV25 @ SY154 @ SY153 )
| ~ ( before_on_line @ SV25 @ SY153 @ SY142 )
| ( between_on_line @ SV25 @ SY142 @ SY153 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(204,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(205,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(206,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(207,plain,
! [SV26: $i,SV2: $i] :
( ( ~ ( distinct_points @ SV2 @ SV26 )
| ! [SY155: $i] :
( ( distinct_points @ SV2 @ SY155 )
| ( distinct_points @ SV26 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(208,plain,
! [SV3: $i] :
( ( distinct_lines @ SV3 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(209,plain,
! [SV27: $i,SV4: $i] :
( ( ~ ( distinct_lines @ SV4 @ SV27 )
| ! [SY156: $i] :
( ( distinct_lines @ SV4 @ SY156 )
| ( distinct_lines @ SV27 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(210,plain,
! [SV28: $i,SV6: $i] :
( ( ~ ( unequally_directed_lines @ SV6 @ SV28 )
| ! [SY157: $i] :
( ( unequally_directed_lines @ SV6 @ SY157 )
| ( unequally_directed_lines @ SV28 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(211,plain,
! [SV29: $i,SV7: $i] :
( ( ( unequally_directed_lines @ SV7 @ SV29 )
| ( unequally_directed_lines @ SV7 @ ( reverse_line @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(212,plain,
! [SV30: $i,SV8: $i] :
( ( ~ ( unequally_directed_lines @ SV8 @ SV30 )
| ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) )
| ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(213,plain,
! [SV31: $i,SV9: $i] :
( ( ~ ( point @ SV9 )
| ~ ( point @ SV31 )
| ~ ( distinct_points @ SV9 @ SV31 )
| ( line @ ( line_connecting @ SV9 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(214,plain,
! [SV32: $i,SV10: $i] :
( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) )
| ( point @ ( intersection_point @ SV10 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(215,plain,
! [SV33: $i,SV11: $i] :
( ( ~ ( line @ SV11 )
| ~ ( point @ SV33 )
| ( line @ ( parallel_through_point @ SV11 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(216,plain,
! [SV12: $i] :
( ( ( ~ ( line @ SV12 ) )
= $true )
| ( ( line @ ( reverse_line @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(217,plain,
! [SV34: $i,SV13: $i] :
( ( ~ ( apart_point_and_line @ SV13 @ ( parallel_through_point @ SV34 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(218,plain,
! [SV14: $i] :
( ( distinct_lines @ SV14 @ ( reverse_line @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(219,plain,
! [SV35: $i,SV15: $i] :
( ( ~ ( distinct_points @ SV15 @ SV35 )
| ( equally_directed_lines @ ( line_connecting @ SV15 @ SV35 ) @ ( reverse_line @ ( line_connecting @ SV35 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(220,plain,
! [SV16: $i,SV36: $i] :
( ( equally_directed_lines @ ( parallel_through_point @ SV36 @ SV16 ) @ SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(221,plain,
! [SV37: $i,SV17: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ( distinct_lines @ SY158 @ SY159 )
| ~ ( distinct_points @ SV17 @ SV37 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY159 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY159 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY158 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY158 ) )
| ( left_apart_point @ SV37 @ SY159 )
| ( left_apart_point @ SV17 @ SY159 )
| ( left_apart_point @ SV17 @ SY158 )
| ( left_apart_point @ SV37 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(222,plain,
! [SV38: $i,SV18: $i] :
( ( ! [SY160: $i] :
( ~ ( distinct_points @ SV18 @ SV38 )
| ~ ( left_apart_point @ SV18 @ SY160 )
| ( left_apart_point @ SV38 @ SY160 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(223,plain,
! [SV39: $i,SV19: $i] :
( ( ! [SY161: $i] :
( ~ ( left_apart_point @ SV19 @ SY161 )
| ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV40: $i,SV20: $i] :
( ( ! [SY162: $i] :
( ~ ( left_apart_point @ SV20 @ SV40 )
| ~ ( unequally_directed_lines @ SV40 @ SY162 )
| ( distinct_lines @ SV40 @ SY162 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
! [SV41: $i,SV21: $i] :
( ( ~ ( left_convergent_lines @ SV21 @ SV41 )
| ! [SY163: $i] :
( ( left_convergent_lines @ SV21 @ SY163 )
| ( unequally_directed_lines @ SV41 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(227,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(228,plain,
! [SV22: $i] :
( ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( distinct_points @ SY112 @ SY113 )
| ~ ( incident_point_and_line @ SY112 @ SV22 )
| ~ ( incident_point_and_line @ SY113 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SY112 @ SY113 ) )
| ( before_on_line @ SV22 @ SY112 @ SY113 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
| ~ ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(229,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(230,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(231,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(232,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(233,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(234,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(236,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(237,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(238,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(239,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(240,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(241,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(242,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(243,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
| ~ ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(244,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) )
| ~ ~ ( ~ ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(245,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(246,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(247,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) )
| ~ ~ ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) )
| ~ ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(249,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(250,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(251,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(252,plain,
! [SV26: $i,SV2: $i] :
( ( ( ~ ( distinct_points @ SV2 @ SV26 ) )
= $true )
| ( ( ! [SY155: $i] :
( ( distinct_points @ SV2 @ SY155 )
| ( distinct_points @ SV26 @ SY155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(253,plain,
! [SV27: $i,SV4: $i] :
( ( ( ~ ( distinct_lines @ SV4 @ SV27 ) )
= $true )
| ( ( ! [SY156: $i] :
( ( distinct_lines @ SV4 @ SY156 )
| ( distinct_lines @ SV27 @ SY156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(254,plain,
! [SV28: $i,SV6: $i] :
( ( ( ~ ( unequally_directed_lines @ SV6 @ SV28 ) )
= $true )
| ( ( ! [SY157: $i] :
( ( unequally_directed_lines @ SV6 @ SY157 )
| ( unequally_directed_lines @ SV28 @ SY157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(255,plain,
! [SV29: $i,SV7: $i] :
( ( ( unequally_directed_lines @ SV7 @ SV29 )
= $true )
| ( ( unequally_directed_lines @ SV7 @ ( reverse_line @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(256,plain,
! [SV30: $i,SV8: $i] :
( ( ( ~ ( unequally_directed_lines @ SV8 @ SV30 )
| ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(257,plain,
! [SV31: $i,SV9: $i] :
( ( ( ~ ( point @ SV9 )
| ~ ( point @ SV31 )
| ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(258,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(259,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( line @ SV11 )
| ~ ( point @ SV33 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(260,plain,
! [SV12: $i] :
( ( ( line @ SV12 )
= $false )
| ( ( line @ ( reverse_line @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(261,plain,
! [SV34: $i,SV13: $i] :
( ( apart_point_and_line @ SV13 @ ( parallel_through_point @ SV34 @ SV13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(262,plain,
! [SV35: $i,SV15: $i] :
( ( ( ~ ( distinct_points @ SV15 @ SV35 ) )
= $true )
| ( ( equally_directed_lines @ ( line_connecting @ SV15 @ SV35 ) @ ( reverse_line @ ( line_connecting @ SV35 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(263,plain,
! [SV37: $i,SV17: $i,SV43: $i] :
( ( ! [SY176: $i] :
( ~ ( distinct_lines @ SV43 @ SY176 )
| ~ ( distinct_points @ SV17 @ SV37 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY176 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY176 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SY176 )
| ( left_apart_point @ SV17 @ SY176 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(264,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ~ ( distinct_points @ SV18 @ SV38 )
| ~ ( left_apart_point @ SV18 @ SV44 )
| ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(265,plain,
! [SV39: $i,SV45: $i,SV19: $i] :
( ( ~ ( left_apart_point @ SV19 @ SV45 )
| ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(266,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ~ ( left_apart_point @ SV20 @ SV40 )
| ~ ( unequally_directed_lines @ SV40 @ SV46 )
| ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(267,plain,
! [SV41: $i,SV21: $i] :
( ( ( ~ ( left_convergent_lines @ SV21 @ SV41 ) )
= $true )
| ( ( ! [SY163: $i] :
( ( left_convergent_lines @ SV21 @ SY163 )
| ( unequally_directed_lines @ SV41 @ SY163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(268,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(269,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(270,plain,
! [SV22: $i] :
( ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( distinct_points @ SY112 @ SY113 )
| ~ ( incident_point_and_line @ SY112 @ SV22 )
| ~ ( incident_point_and_line @ SY113 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SY112 @ SY113 ) )
| ( before_on_line @ SV22 @ SY112 @ SY113 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(271,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
| ~ ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(272,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(274,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(276,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(277,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(278,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(279,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(280,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(281,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(282,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(283,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(284,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(285,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(286,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
| ~ ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(287,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(288,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(289,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(290,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(291,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(292,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) )
| ~ ~ ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) )
| ~ ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(293,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(294,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(295,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(296,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(297,plain,
! [SV26: $i,SV2: $i] :
( ( ( distinct_points @ SV2 @ SV26 )
= $false )
| ( ( ! [SY155: $i] :
( ( distinct_points @ SV2 @ SY155 )
| ( distinct_points @ SV26 @ SY155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(298,plain,
! [SV27: $i,SV4: $i] :
( ( ( distinct_lines @ SV4 @ SV27 )
= $false )
| ( ( ! [SY156: $i] :
( ( distinct_lines @ SV4 @ SY156 )
| ( distinct_lines @ SV27 @ SY156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(299,plain,
! [SV28: $i,SV6: $i] :
( ( ( unequally_directed_lines @ SV6 @ SV28 )
= $false )
| ( ( ! [SY157: $i] :
( ( unequally_directed_lines @ SV6 @ SY157 )
| ( unequally_directed_lines @ SV28 @ SY157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(300,plain,
! [SV30: $i,SV8: $i] :
( ( ( ~ ( unequally_directed_lines @ SV8 @ SV30 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(301,plain,
! [SV31: $i,SV9: $i] :
( ( ( ~ ( point @ SV9 )
| ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(302,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(303,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( line @ SV11 ) )
= $true )
| ( ( ~ ( point @ SV33 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(304,plain,
! [SV35: $i,SV15: $i] :
( ( ( distinct_points @ SV15 @ SV35 )
= $false )
| ( ( equally_directed_lines @ ( line_connecting @ SV15 @ SV35 ) @ ( reverse_line @ ( line_connecting @ SV35 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(305,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ~ ( distinct_lines @ SV43 @ SV47 )
| ~ ( distinct_points @ SV17 @ SV37 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(306,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( ~ ( distinct_points @ SV18 @ SV38 )
| ~ ( left_apart_point @ SV18 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(307,plain,
! [SV39: $i,SV45: $i,SV19: $i] :
( ( ( ~ ( left_apart_point @ SV19 @ SV45 ) )
= $true )
| ( ( ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(308,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ( ~ ( left_apart_point @ SV20 @ SV40 )
| ~ ( unequally_directed_lines @ SV40 @ SV46 ) )
= $true )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(309,plain,
! [SV41: $i,SV21: $i] :
( ( ( left_convergent_lines @ SV21 @ SV41 )
= $false )
| ( ( ! [SY163: $i] :
( ( left_convergent_lines @ SV21 @ SY163 )
| ( unequally_directed_lines @ SV41 @ SY163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(310,plain,
! [SV48: $i] :
( ( ! [SY177: $i] :
( ~ ( unequally_directed_lines @ SV48 @ ( reverse_line @ SY177 ) )
| ( unequally_directed_opposite_lines @ SV48 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(311,plain,
! [SV49: $i] :
( ( ! [SY178: $i] :
( ~ ( unequally_directed_opposite_lines @ SV49 @ SY178 )
| ( unequally_directed_lines @ SV49 @ ( reverse_line @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(312,plain,
! [SV22: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ( distinct_points @ SY112 @ SY113 )
| ~ ( incident_point_and_line @ SY112 @ SV22 )
| ~ ( incident_point_and_line @ SY113 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SY112 @ SY113 ) )
| ( before_on_line @ SV22 @ SY112 @ SY113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(313,plain,
! [SV22: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
| ~ ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(314,plain,
! [SV50: $i] :
( ( ! [SY179: $i] :
( ~ ( left_apart_point @ SV50 @ ( reverse_line @ SY179 ) )
| ( right_apart_point @ SV50 @ SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(315,plain,
! [SV51: $i] :
( ( ! [SY180: $i] :
( ~ ( right_apart_point @ SV51 @ SY180 )
| ( left_apart_point @ SV51 @ ( reverse_line @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(316,plain,
! [SV52: $i] :
( ( ! [SY181: $i] :
~ ( left_apart_point @ SV52 @ SY181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(317,plain,
! [SV53: $i] :
( ( ! [SY182: $i] :
~ ( left_apart_point @ SV53 @ ( reverse_line @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(318,plain,
! [SV54: $i] :
( ( ! [SY183: $i] :
( ~ ( equally_directed_lines @ SV54 @ SY183 )
| ~ ( unequally_directed_lines @ SV54 @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(319,plain,
! [SV55: $i] :
( ( ! [SY184: $i] :
( ( unequally_directed_lines @ SV55 @ SY184 )
| ( equally_directed_lines @ SV55 @ SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(320,plain,
! [SV56: $i] :
( ( ! [SY185: $i] :
( ~ ( equally_directed_opposite_lines @ SV56 @ SY185 )
| ~ ( unequally_directed_opposite_lines @ SV56 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(321,plain,
! [SV57: $i] :
( ( ! [SY186: $i] :
( ( unequally_directed_opposite_lines @ SV57 @ SY186 )
| ( equally_directed_opposite_lines @ SV57 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(322,plain,
! [SV58: $i] :
( ( ! [SY187: $i] :
( ~ ( apart_point_and_line @ SV58 @ SY187 )
| ( left_apart_point @ SV58 @ SY187 )
| ( right_apart_point @ SV58 @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(323,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(324,plain,
! [SV59: $i] :
( ( ! [SY188: $i] :
( ~ ( left_convergent_lines @ SV59 @ ( reverse_line @ SY188 ) )
| ( right_convergent_lines @ SV59 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(325,plain,
! [SV60: $i] :
( ( ! [SY189: $i] :
( ~ ( right_convergent_lines @ SV60 @ SY189 )
| ( left_convergent_lines @ SV60 @ ( reverse_line @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(326,plain,
! [SV61: $i] :
( ( ! [SY190: $i] :
~ ( left_convergent_lines @ SV61 @ SY190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(327,plain,
! [SV62: $i] :
( ( ! [SY191: $i] :
~ ( left_convergent_lines @ SV62 @ ( reverse_line @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(328,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
| ~ ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(329,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(330,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(331,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(332,plain,
! [SV63: $i] :
( ( ! [SY192: $i] :
( ~ ( distinct_points @ SV63 @ SY192 )
| ~ ( apart_point_and_line @ SV63 @ ( line_connecting @ SV63 @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(333,plain,
! [SV64: $i] :
( ( ! [SY193: $i] :
( ~ ( distinct_points @ SV64 @ SY193 )
| ~ ( apart_point_and_line @ SY193 @ ( line_connecting @ SV64 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(334,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(335,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ~ ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) )
| ~ ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(336,plain,
! [SV65: $i] :
( ( ! [SY194: $i] :
( ~ ( unequally_directed_lines @ SV65 @ SY194 )
| ~ ( unequally_directed_lines @ SV65 @ ( reverse_line @ SY194 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV65 @ SY194 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(337,plain,
! [SV66: $i] :
( ( ! [SY195: $i] :
( ~ ( unequally_directed_lines @ SV66 @ SY195 )
| ~ ( unequally_directed_lines @ SV66 @ ( reverse_line @ SY195 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV66 @ SY195 ) @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(338,plain,
! [SV67: $i] :
( ( ! [SY196: $i] :
( ~ ( unequally_directed_lines @ SV67 @ SY196 )
| ~ ( unequally_directed_opposite_lines @ SV67 @ SY196 )
| ( convergent_lines @ SV67 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(339,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(340,plain,
! [SV26: $i,SV68: $i,SV2: $i] :
( ( ( ( distinct_points @ SV2 @ SV68 )
| ( distinct_points @ SV26 @ SV68 ) )
= $true )
| ( ( distinct_points @ SV2 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(341,plain,
! [SV27: $i,SV69: $i,SV4: $i] :
( ( ( ( distinct_lines @ SV4 @ SV69 )
| ( distinct_lines @ SV27 @ SV69 ) )
= $true )
| ( ( distinct_lines @ SV4 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(342,plain,
! [SV28: $i,SV70: $i,SV6: $i] :
( ( ( ( unequally_directed_lines @ SV6 @ SV70 )
| ( unequally_directed_lines @ SV28 @ SV70 ) )
= $true )
| ( ( unequally_directed_lines @ SV6 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(343,plain,
! [SV30: $i,SV8: $i] :
( ( ( unequally_directed_lines @ SV8 @ SV30 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(344,plain,
! [SV31: $i,SV9: $i] :
( ( ( ~ ( point @ SV9 ) )
= $true )
| ( ( ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(345,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(346,plain,
! [SV33: $i,SV11: $i] :
( ( ( line @ SV11 )
= $false )
| ( ( ~ ( point @ SV33 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(347,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ( ~ ( distinct_lines @ SV43 @ SV47 )
| ~ ( distinct_points @ SV17 @ SV37 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(348,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( ~ ( distinct_points @ SV18 @ SV38 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV18 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(349,plain,
! [SV39: $i,SV45: $i,SV19: $i] :
( ( ( left_apart_point @ SV19 @ SV45 )
= $false )
| ( ( ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(350,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ( ~ ( left_apart_point @ SV20 @ SV40 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV40 @ SV46 ) )
= $true )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(351,plain,
! [SV41: $i,SV71: $i,SV21: $i] :
( ( ( ( left_convergent_lines @ SV21 @ SV71 )
| ( unequally_directed_lines @ SV41 @ SV71 ) )
= $true )
| ( ( left_convergent_lines @ SV21 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(352,plain,
! [SV72: $i,SV48: $i] :
( ( ~ ( unequally_directed_lines @ SV48 @ ( reverse_line @ SV72 ) )
| ( unequally_directed_opposite_lines @ SV48 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(353,plain,
! [SV73: $i,SV49: $i] :
( ( ~ ( unequally_directed_opposite_lines @ SV49 @ SV73 )
| ( unequally_directed_lines @ SV49 @ ( reverse_line @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(354,plain,
! [SV22: $i,SV74: $i] :
( ( ! [SY197: $i] :
( ~ ( distinct_points @ SV74 @ SY197 )
| ~ ( incident_point_and_line @ SV74 @ SV22 )
| ~ ( incident_point_and_line @ SY197 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SY197 ) )
| ( before_on_line @ SV22 @ SV74 @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(355,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
| ~ ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(356,plain,
! [SV75: $i,SV50: $i] :
( ( ~ ( left_apart_point @ SV50 @ ( reverse_line @ SV75 ) )
| ( right_apart_point @ SV50 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(357,plain,
! [SV76: $i,SV51: $i] :
( ( ~ ( right_apart_point @ SV51 @ SV76 )
| ( left_apart_point @ SV51 @ ( reverse_line @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(358,plain,
! [SV77: $i,SV52: $i] :
( ( ~ ( left_apart_point @ SV52 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(359,plain,
! [SV78: $i,SV53: $i] :
( ( ~ ( left_apart_point @ SV53 @ ( reverse_line @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(360,plain,
! [SV79: $i,SV54: $i] :
( ( ~ ( equally_directed_lines @ SV54 @ SV79 )
| ~ ( unequally_directed_lines @ SV54 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(361,plain,
! [SV80: $i,SV55: $i] :
( ( ( unequally_directed_lines @ SV55 @ SV80 )
| ( equally_directed_lines @ SV55 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(362,plain,
! [SV81: $i,SV56: $i] :
( ( ~ ( equally_directed_opposite_lines @ SV56 @ SV81 )
| ~ ( unequally_directed_opposite_lines @ SV56 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(363,plain,
! [SV82: $i,SV57: $i] :
( ( ( unequally_directed_opposite_lines @ SV57 @ SV82 )
| ( equally_directed_opposite_lines @ SV57 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(364,plain,
! [SV83: $i,SV58: $i] :
( ( ~ ( apart_point_and_line @ SV58 @ SV83 )
| ( left_apart_point @ SV58 @ SV83 )
| ( right_apart_point @ SV58 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(365,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(366,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(367,plain,
! [SV84: $i,SV59: $i] :
( ( ~ ( left_convergent_lines @ SV59 @ ( reverse_line @ SV84 ) )
| ( right_convergent_lines @ SV59 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(368,plain,
! [SV85: $i,SV60: $i] :
( ( ~ ( right_convergent_lines @ SV60 @ SV85 )
| ( left_convergent_lines @ SV60 @ ( reverse_line @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(369,plain,
! [SV86: $i,SV61: $i] :
( ( ~ ( left_convergent_lines @ SV61 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(370,plain,
! [SV87: $i,SV62: $i] :
( ( ~ ( left_convergent_lines @ SV62 @ ( reverse_line @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(371,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
| ~ ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(372,plain,
! [SV23: $i] :
( ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(373,plain,
! [SV24: $i] :
( ( ~ ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(374,plain,
! [SV24: $i] :
( ( ~ ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(375,plain,
! [SV88: $i,SV63: $i] :
( ( ~ ( distinct_points @ SV63 @ SV88 )
| ~ ( apart_point_and_line @ SV63 @ ( line_connecting @ SV63 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(376,plain,
! [SV89: $i,SV64: $i] :
( ( ~ ( distinct_points @ SV64 @ SV89 )
| ~ ( apart_point_and_line @ SV89 @ ( line_connecting @ SV64 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(377,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(378,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) )
| ~ ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(379,plain,
! [SV90: $i,SV65: $i] :
( ( ~ ( unequally_directed_lines @ SV65 @ SV90 )
| ~ ( unequally_directed_lines @ SV65 @ ( reverse_line @ SV90 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV65 @ SV90 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(380,plain,
! [SV91: $i,SV66: $i] :
( ( ~ ( unequally_directed_lines @ SV66 @ SV91 )
| ~ ( unequally_directed_lines @ SV66 @ ( reverse_line @ SV91 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV66 @ SV91 ) @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(381,plain,
! [SV92: $i,SV67: $i] :
( ( ~ ( unequally_directed_lines @ SV67 @ SV92 )
| ~ ( unequally_directed_opposite_lines @ SV67 @ SV92 )
| ( convergent_lines @ SV67 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(382,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(384,plain,
! [SV26: $i,SV68: $i,SV2: $i] :
( ( ( distinct_points @ SV2 @ SV68 )
= $true )
| ( ( distinct_points @ SV26 @ SV68 )
= $true )
| ( ( distinct_points @ SV2 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(385,plain,
! [SV27: $i,SV69: $i,SV4: $i] :
( ( ( distinct_lines @ SV4 @ SV69 )
= $true )
| ( ( distinct_lines @ SV27 @ SV69 )
= $true )
| ( ( distinct_lines @ SV4 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(386,plain,
! [SV28: $i,SV70: $i,SV6: $i] :
( ( ( unequally_directed_lines @ SV6 @ SV70 )
= $true )
| ( ( unequally_directed_lines @ SV28 @ SV70 )
= $true )
| ( ( unequally_directed_lines @ SV6 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(387,plain,
! [SV30: $i,SV8: $i] :
( ( ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) )
= $false )
| ( ( unequally_directed_lines @ SV8 @ SV30 )
= $false )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(388,plain,
! [SV31: $i,SV9: $i] :
( ( ( point @ SV9 )
= $false )
| ( ( ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(389,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 ) )
= $true )
| ( ( ~ ( line @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(390,plain,
! [SV11: $i,SV33: $i] :
( ( ( point @ SV33 )
= $false )
| ( ( line @ SV11 )
= $false )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(391,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ( ~ ( distinct_lines @ SV43 @ SV47 ) )
= $true )
| ( ( ~ ( distinct_points @ SV17 @ SV37 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(392,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( distinct_points @ SV18 @ SV38 )
= $false )
| ( ( ~ ( left_apart_point @ SV18 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(393,plain,
! [SV45: $i,SV39: $i,SV19: $i] :
( ( ( distinct_points @ SV19 @ SV39 )
= $true )
| ( ( left_apart_point @ SV39 @ SV45 )
= $true )
| ( ( left_apart_point @ SV19 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(394,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ( left_apart_point @ SV20 @ SV40 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV40 @ SV46 ) )
= $true )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(395,plain,
! [SV41: $i,SV71: $i,SV21: $i] :
( ( ( left_convergent_lines @ SV21 @ SV71 )
= $true )
| ( ( unequally_directed_lines @ SV41 @ SV71 )
= $true )
| ( ( left_convergent_lines @ SV21 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(396,plain,
! [SV72: $i,SV48: $i] :
( ( ( ~ ( unequally_directed_lines @ SV48 @ ( reverse_line @ SV72 ) ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV48 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(397,plain,
! [SV73: $i,SV49: $i] :
( ( ( ~ ( unequally_directed_opposite_lines @ SV49 @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV49 @ ( reverse_line @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(398,plain,
! [SV22: $i,SV93: $i,SV74: $i] :
( ( ~ ( distinct_points @ SV74 @ SV93 )
| ~ ( incident_point_and_line @ SV74 @ SV22 )
| ~ ( incident_point_and_line @ SV93 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) )
| ( before_on_line @ SV22 @ SV74 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(399,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(400,plain,
! [SV22: $i] :
( ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(401,plain,
! [SV75: $i,SV50: $i] :
( ( ( ~ ( left_apart_point @ SV50 @ ( reverse_line @ SV75 ) ) )
= $true )
| ( ( right_apart_point @ SV50 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(402,plain,
! [SV76: $i,SV51: $i] :
( ( ( ~ ( right_apart_point @ SV51 @ SV76 ) )
= $true )
| ( ( left_apart_point @ SV51 @ ( reverse_line @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(403,plain,
! [SV77: $i,SV52: $i] :
( ( left_apart_point @ SV52 @ SV77 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(404,plain,
! [SV78: $i,SV53: $i] :
( ( left_apart_point @ SV53 @ ( reverse_line @ SV78 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(405,plain,
! [SV79: $i,SV54: $i] :
( ( ( ~ ( equally_directed_lines @ SV54 @ SV79 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV54 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(406,plain,
! [SV80: $i,SV55: $i] :
( ( ( unequally_directed_lines @ SV55 @ SV80 )
= $true )
| ( ( equally_directed_lines @ SV55 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(407,plain,
! [SV81: $i,SV56: $i] :
( ( ( ~ ( equally_directed_opposite_lines @ SV56 @ SV81 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV56 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(408,plain,
! [SV82: $i,SV57: $i] :
( ( ( unequally_directed_opposite_lines @ SV57 @ SV82 )
= $true )
| ( ( equally_directed_opposite_lines @ SV57 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(409,plain,
! [SV83: $i,SV58: $i] :
( ( ( ~ ( apart_point_and_line @ SV58 @ SV83 ) )
= $true )
| ( ( ( left_apart_point @ SV58 @ SV83 )
| ( right_apart_point @ SV58 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(410,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(411,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(412,plain,
! [SV84: $i,SV59: $i] :
( ( ( ~ ( left_convergent_lines @ SV59 @ ( reverse_line @ SV84 ) ) )
= $true )
| ( ( right_convergent_lines @ SV59 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(413,plain,
! [SV85: $i,SV60: $i] :
( ( ( ~ ( right_convergent_lines @ SV60 @ SV85 ) )
= $true )
| ( ( left_convergent_lines @ SV60 @ ( reverse_line @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(414,plain,
! [SV86: $i,SV61: $i] :
( ( left_convergent_lines @ SV61 @ SV86 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(415,plain,
! [SV87: $i,SV62: $i] :
( ( left_convergent_lines @ SV62 @ ( reverse_line @ SV87 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(416,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(417,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(418,plain,
! [SV23: $i] :
( ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(419,plain,
! [SV23: $i] :
( ( ~ ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(420,plain,
! [SV24: $i] :
( ( ~ ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(421,plain,
! [SV24: $i] :
( ( ~ ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(422,plain,
! [SV24: $i] :
( ( ~ ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(423,plain,
! [SV24: $i] :
( ( ~ ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(424,plain,
! [SV88: $i,SV63: $i] :
( ( ( ~ ( distinct_points @ SV63 @ SV88 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV63 @ ( line_connecting @ SV63 @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(425,plain,
! [SV89: $i,SV64: $i] :
( ( ( ~ ( distinct_points @ SV64 @ SV89 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV89 @ ( line_connecting @ SV64 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(426,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(427,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) )
| ~ ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(428,plain,
! [SV90: $i,SV65: $i] :
( ( ( ~ ( unequally_directed_lines @ SV65 @ SV90 )
| ~ ( unequally_directed_lines @ SV65 @ ( reverse_line @ SV90 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV65 @ SV90 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(429,plain,
! [SV91: $i,SV66: $i] :
( ( ( ~ ( unequally_directed_lines @ SV66 @ SV91 )
| ~ ( unequally_directed_lines @ SV66 @ ( reverse_line @ SV91 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV66 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(430,plain,
! [SV92: $i,SV67: $i] :
( ( ( ~ ( unequally_directed_lines @ SV67 @ SV92 )
| ~ ( unequally_directed_opposite_lines @ SV67 @ SV92 ) )
= $true )
| ( ( convergent_lines @ SV67 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(431,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(432,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(433,plain,
! [SV30: $i,SV8: $i] :
( ( ( left_convergent_lines @ SV8 @ SV30 )
= $true )
| ( ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) )
= $true )
| ( ( unequally_directed_lines @ SV8 @ SV30 )
= $false )
| ( ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(434,plain,
! [SV9: $i,SV31: $i] :
( ( ( point @ SV31 )
= $false )
| ( ( point @ SV9 )
= $false )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(435,plain,
! [SV32: $i,SV10: $i] :
( ( ( line @ SV10 )
= $false )
| ( ( ~ ( line @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(436,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( ~ ( distinct_points @ SV17 @ SV37 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(437,plain,
! [SV38: $i,SV44: $i,SV18: $i] :
( ( ( left_apart_point @ SV18 @ SV44 )
= $false )
| ( ( distinct_points @ SV18 @ SV38 )
= $false )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(438,plain,
! [SV20: $i,SV46: $i,SV40: $i] :
( ( ( unequally_directed_lines @ SV40 @ SV46 )
= $false )
| ( ( left_apart_point @ SV20 @ SV40 )
= $false )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(439,plain,
! [SV72: $i,SV48: $i] :
( ( ( unequally_directed_lines @ SV48 @ ( reverse_line @ SV72 ) )
= $false )
| ( ( unequally_directed_opposite_lines @ SV48 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(440,plain,
! [SV73: $i,SV49: $i] :
( ( ( unequally_directed_opposite_lines @ SV49 @ SV73 )
= $false )
| ( ( unequally_directed_lines @ SV49 @ ( reverse_line @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(441,plain,
! [SV22: $i,SV93: $i,SV74: $i] :
( ( ( ~ ( distinct_points @ SV74 @ SV93 )
| ~ ( incident_point_and_line @ SV74 @ SV22 )
| ~ ( incident_point_and_line @ SV93 @ SV22 )
| ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(442,plain,
! [SV22: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(443,plain,
! [SV22: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ~ ( before_on_line @ SV22 @ SY120 @ SY121 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SY120 @ SY121 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(444,plain,
! [SV75: $i,SV50: $i] :
( ( ( left_apart_point @ SV50 @ ( reverse_line @ SV75 ) )
= $false )
| ( ( right_apart_point @ SV50 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(445,plain,
! [SV76: $i,SV51: $i] :
( ( ( right_apart_point @ SV51 @ SV76 )
= $false )
| ( ( left_apart_point @ SV51 @ ( reverse_line @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(446,plain,
! [SV79: $i,SV54: $i] :
( ( ( equally_directed_lines @ SV54 @ SV79 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV54 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(447,plain,
! [SV81: $i,SV56: $i] :
( ( ( equally_directed_opposite_lines @ SV56 @ SV81 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV56 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(448,plain,
! [SV83: $i,SV58: $i] :
( ( ( apart_point_and_line @ SV58 @ SV83 )
= $false )
| ( ( ( left_apart_point @ SV58 @ SV83 )
| ( right_apart_point @ SV58 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(449,plain,
! [SV94: $i] :
( ( ! [SY198: $i] :
( ~ ( left_apart_point @ SV94 @ SY198 )
| ( apart_point_and_line @ SV94 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(450,plain,
! [SV95: $i] :
( ( ! [SY199: $i] :
( ~ ( right_apart_point @ SV95 @ SY199 )
| ( apart_point_and_line @ SV95 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(451,plain,
! [SV84: $i,SV59: $i] :
( ( ( left_convergent_lines @ SV59 @ ( reverse_line @ SV84 ) )
= $false )
| ( ( right_convergent_lines @ SV59 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(452,plain,
! [SV85: $i,SV60: $i] :
( ( ( right_convergent_lines @ SV60 @ SV85 )
= $false )
| ( ( left_convergent_lines @ SV60 @ ( reverse_line @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(453,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(454,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(455,plain,
! [SV23: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( left_apart_point @ SV23 @ SY131 )
| ~ ( right_apart_point @ SY130 @ SY131 )
| ( divides_points @ SY131 @ SV23 @ SY130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(456,plain,
! [SV23: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ~ ( left_apart_point @ SY132 @ SY133 )
| ~ ( right_apart_point @ SV23 @ SY133 )
| ( divides_points @ SY133 @ SV23 @ SY132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(457,plain,
! [SV24: $i] :
( ( ! [SY134: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY134 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY134 ) )
| ! [SY135: $i] :
( ( unequally_directed_lines @ SV24 @ SY135 )
| ( unequally_directed_lines @ SY134 @ SY135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(458,plain,
! [SV24: $i] :
( ( ! [SY136: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY136 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY136 ) )
| ! [SY137: $i] :
( ( unequally_directed_lines @ SV24 @ SY137 )
| ( unequally_directed_lines @ SY136 @ ( reverse_line @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(459,plain,
! [SV24: $i] :
( ( ! [SY138: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY138 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY138 ) )
| ! [SY139: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY139 ) )
| ( unequally_directed_lines @ SY138 @ SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(460,plain,
! [SV24: $i] :
( ( ! [SY140: $i] :
( ~ ( unequally_directed_lines @ SV24 @ SY140 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY140 ) )
| ! [SY141: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY141 ) )
| ( unequally_directed_lines @ SY140 @ ( reverse_line @ SY141 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(461,plain,
! [SV88: $i,SV63: $i] :
( ( ( distinct_points @ SV63 @ SV88 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV63 @ ( line_connecting @ SV63 @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(462,plain,
! [SV89: $i,SV64: $i] :
( ( ( distinct_points @ SV64 @ SV89 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV89 @ ( line_connecting @ SV64 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(463,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(464,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(465,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(466,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(467,plain,
! [SV90: $i,SV65: $i] :
( ( ( ~ ( unequally_directed_lines @ SV65 @ SV90 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV65 @ ( reverse_line @ SV90 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV65 @ SV90 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(468,plain,
! [SV91: $i,SV66: $i] :
( ( ( ~ ( unequally_directed_lines @ SV66 @ SV91 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV66 @ ( reverse_line @ SV91 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV66 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(469,plain,
! [SV92: $i,SV67: $i] :
( ( ( ~ ( unequally_directed_lines @ SV67 @ SV92 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV67 @ SV92 ) )
= $true )
| ( ( convergent_lines @ SV67 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(470,plain,
! [SV96: $i] :
( ( ! [SY200: $i] :
( ~ ( convergent_lines @ SV96 @ SY200 )
| ( unequally_directed_lines @ SV96 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(471,plain,
! [SV97: $i] :
( ( ! [SY201: $i] :
( ~ ( convergent_lines @ SV97 @ SY201 )
| ( unequally_directed_opposite_lines @ SV97 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(472,plain,
! [SV31: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV31 )
= $false )
| ( ( point @ SV9 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(473,plain,
! [SV10: $i,SV32: $i] :
( ( ( line @ SV32 )
= $false )
| ( ( line @ SV10 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(474,plain,
! [SV47: $i,SV43: $i,SV37: $i,SV17: $i] :
( ( ( distinct_points @ SV17 @ SV37 )
= $false )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(475,plain,
! [SV18: $i,SV44: $i,SV38: $i] :
( ( ( left_apart_point @ SV38 @ SV44 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 )
= $true )
| ( ( distinct_points @ SV18 @ SV38 )
= $false )
| ( ( left_apart_point @ SV18 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(476,plain,
! [SV20: $i,SV46: $i,SV40: $i] :
( ( ( distinct_lines @ SV40 @ SV46 )
= $true )
| ( ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) )
= $true )
| ( ( left_apart_point @ SV20 @ SV40 )
= $false )
| ( ( unequally_directed_lines @ SV40 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(477,plain,
! [SV22: $i,SV93: $i,SV74: $i] :
( ( ( ~ ( distinct_points @ SV74 @ SV93 )
| ~ ( incident_point_and_line @ SV74 @ SV22 )
| ~ ( incident_point_and_line @ SV93 @ SV22 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(478,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(479,plain,
! [SV98: $i,SV22: $i] :
( ( ! [SY202: $i] :
( ~ ( before_on_line @ SV22 @ SV98 @ SY202 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SV98 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(480,plain,
! [SV79: $i,SV54: $i] :
( ( ( unequally_directed_lines @ SV54 @ SV79 )
= $false )
| ( ( equally_directed_lines @ SV54 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(481,plain,
! [SV81: $i,SV56: $i] :
( ( ( unequally_directed_opposite_lines @ SV56 @ SV81 )
= $false )
| ( ( equally_directed_opposite_lines @ SV56 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(482,plain,
! [SV83: $i,SV58: $i] :
( ( ( left_apart_point @ SV58 @ SV83 )
= $true )
| ( ( right_apart_point @ SV58 @ SV83 )
= $true )
| ( ( apart_point_and_line @ SV58 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(483,plain,
! [SV99: $i,SV94: $i] :
( ( ~ ( left_apart_point @ SV94 @ SV99 )
| ( apart_point_and_line @ SV94 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(484,plain,
! [SV100: $i,SV95: $i] :
( ( ~ ( right_apart_point @ SV95 @ SV100 )
| ( apart_point_and_line @ SV95 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(485,plain,
! [SV23: $i] :
( ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(486,plain,
! [SV23: $i] :
( ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(487,plain,
! [SV101: $i,SV23: $i] :
( ( ! [SY203: $i] :
( ~ ( left_apart_point @ SV23 @ SY203 )
| ~ ( right_apart_point @ SV101 @ SY203 )
| ( divides_points @ SY203 @ SV23 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(488,plain,
! [SV23: $i,SV102: $i] :
( ( ! [SY204: $i] :
( ~ ( left_apart_point @ SV102 @ SY204 )
| ~ ( right_apart_point @ SV23 @ SY204 )
| ( divides_points @ SY204 @ SV23 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(489,plain,
! [SV103: $i,SV24: $i] :
( ( ~ ( unequally_directed_lines @ SV24 @ SV103 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) )
| ! [SY205: $i] :
( ( unequally_directed_lines @ SV24 @ SY205 )
| ( unequally_directed_lines @ SV103 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(490,plain,
! [SV104: $i,SV24: $i] :
( ( ~ ( unequally_directed_lines @ SV24 @ SV104 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) )
| ! [SY206: $i] :
( ( unequally_directed_lines @ SV24 @ SY206 )
| ( unequally_directed_lines @ SV104 @ ( reverse_line @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(491,plain,
! [SV105: $i,SV24: $i] :
( ( ~ ( unequally_directed_lines @ SV24 @ SV105 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) )
| ! [SY207: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY207 ) )
| ( unequally_directed_lines @ SV105 @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(492,plain,
! [SV106: $i,SV24: $i] :
( ( ~ ( unequally_directed_lines @ SV24 @ SV106 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) )
| ! [SY208: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY208 ) )
| ( unequally_directed_lines @ SV106 @ ( reverse_line @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(493,plain,
! [SV88: $i,SV63: $i] :
( ( ( apart_point_and_line @ SV63 @ ( line_connecting @ SV63 @ SV88 ) )
= $false )
| ( ( distinct_points @ SV63 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(494,plain,
! [SV64: $i,SV89: $i] :
( ( ( apart_point_and_line @ SV89 @ ( line_connecting @ SV64 @ SV89 ) )
= $false )
| ( ( distinct_points @ SV64 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(495,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(496,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(497,plain,
! [SV42: $i,SV25: $i] :
( ( ! [SY172: $i,SY173: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SY172 )
| ~ ( before_on_line @ SV25 @ SY172 @ SY173 )
| ( between_on_line @ SV25 @ SV42 @ SY172 @ SY173 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(498,plain,
! [SV42: $i,SV25: $i] :
( ( ! [SY174: $i,SY175: $i] :
( ~ ( before_on_line @ SV25 @ SY175 @ SY174 )
| ~ ( before_on_line @ SV25 @ SY174 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SY174 @ SY175 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(499,plain,
! [SV90: $i,SV65: $i] :
( ( ( unequally_directed_lines @ SV65 @ SV90 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV65 @ ( reverse_line @ SV90 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV65 @ SV90 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(500,plain,
! [SV91: $i,SV66: $i] :
( ( ( unequally_directed_lines @ SV66 @ SV91 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV66 @ ( reverse_line @ SV91 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV66 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(501,plain,
! [SV92: $i,SV67: $i] :
( ( ( unequally_directed_lines @ SV67 @ SV92 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV67 @ SV92 ) )
= $true )
| ( ( convergent_lines @ SV67 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(502,plain,
! [SV107: $i,SV96: $i] :
( ( ~ ( convergent_lines @ SV96 @ SV107 )
| ( unequally_directed_lines @ SV96 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(503,plain,
! [SV108: $i,SV97: $i] :
( ( ~ ( convergent_lines @ SV97 @ SV108 )
| ( unequally_directed_opposite_lines @ SV97 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(504,plain,
! [SV32: $i,SV10: $i] :
( ( ( unequally_directed_lines @ SV10 @ SV32 )
= $false )
| ( ( line @ SV10 )
= $false )
| ( ( line @ SV32 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(505,plain,
! [SV43: $i,SV17: $i,SV47: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(506,plain,
! [SV22: $i,SV93: $i,SV74: $i] :
( ( ( ~ ( distinct_points @ SV74 @ SV93 )
| ~ ( incident_point_and_line @ SV74 @ SV22 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV22 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(507,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(508,plain,
! [SV22: $i] :
( ( ~ ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(509,plain,
! [SV109: $i,SV98: $i,SV22: $i] :
( ( ~ ( before_on_line @ SV22 @ SV98 @ SV109 )
| ( equally_directed_lines @ SV22 @ ( line_connecting @ SV98 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(510,plain,
! [SV99: $i,SV94: $i] :
( ( ( ~ ( left_apart_point @ SV94 @ SV99 ) )
= $true )
| ( ( apart_point_and_line @ SV94 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(511,plain,
! [SV100: $i,SV95: $i] :
( ( ( ~ ( right_apart_point @ SV95 @ SV100 ) )
= $true )
| ( ( apart_point_and_line @ SV95 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(512,plain,
! [SV23: $i] :
( ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(513,plain,
! [SV23: $i] :
( ( ~ ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(514,plain,
! [SV23: $i] :
( ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(515,plain,
! [SV23: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(516,plain,
! [SV101: $i,SV110: $i,SV23: $i] :
( ( ~ ( left_apart_point @ SV23 @ SV110 )
| ~ ( right_apart_point @ SV101 @ SV110 )
| ( divides_points @ SV110 @ SV23 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(517,plain,
! [SV23: $i,SV111: $i,SV102: $i] :
( ( ~ ( left_apart_point @ SV102 @ SV111 )
| ~ ( right_apart_point @ SV23 @ SV111 )
| ( divides_points @ SV111 @ SV23 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(518,plain,
! [SV103: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV103 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) ) )
= $true )
| ( ( ! [SY205: $i] :
( ( unequally_directed_lines @ SV24 @ SY205 )
| ( unequally_directed_lines @ SV103 @ SY205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(519,plain,
! [SV104: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV104 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) ) )
= $true )
| ( ( ! [SY206: $i] :
( ( unequally_directed_lines @ SV24 @ SY206 )
| ( unequally_directed_lines @ SV104 @ ( reverse_line @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(520,plain,
! [SV105: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV105 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) ) )
= $true )
| ( ( ! [SY207: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY207 ) )
| ( unequally_directed_lines @ SV105 @ SY207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(521,plain,
! [SV106: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV106 )
| ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) ) )
= $true )
| ( ( ! [SY208: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY208 ) )
| ( unequally_directed_lines @ SV106 @ ( reverse_line @ SY208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(522,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) )
| ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(523,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(524,plain,
! [SV112: $i,SV42: $i,SV25: $i] :
( ( ! [SY209: $i] :
( ~ ( before_on_line @ SV25 @ SV42 @ SV112 )
| ~ ( before_on_line @ SV25 @ SV112 @ SY209 )
| ( between_on_line @ SV25 @ SV42 @ SV112 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(525,plain,
! [SV42: $i,SV113: $i,SV25: $i] :
( ( ! [SY210: $i] :
( ~ ( before_on_line @ SV25 @ SY210 @ SV113 )
| ~ ( before_on_line @ SV25 @ SV113 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SV113 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(526,plain,
! [SV90: $i,SV65: $i] :
( ( ( unequally_directed_lines @ SV65 @ ( reverse_line @ SV90 ) )
= $false )
| ( ( unequally_directed_lines @ SV65 @ SV90 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV65 @ SV90 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(527,plain,
! [SV91: $i,SV66: $i] :
( ( ( unequally_directed_lines @ SV66 @ ( reverse_line @ SV91 ) )
= $false )
| ( ( unequally_directed_lines @ SV66 @ SV91 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV66 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(528,plain,
! [SV92: $i,SV67: $i] :
( ( ( unequally_directed_opposite_lines @ SV67 @ SV92 )
= $false )
| ( ( unequally_directed_lines @ SV67 @ SV92 )
= $false )
| ( ( convergent_lines @ SV67 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(529,plain,
! [SV107: $i,SV96: $i] :
( ( ( ~ ( convergent_lines @ SV96 @ SV107 ) )
= $true )
| ( ( unequally_directed_lines @ SV96 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(530,plain,
! [SV108: $i,SV97: $i] :
( ( ( ~ ( convergent_lines @ SV97 @ SV108 ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV97 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(531,plain,
! [SV32: $i,SV10: $i] :
( ( ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) )
= $false )
| ( ( line @ SV32 )
= $false )
| ( ( line @ SV10 )
= $false )
| ( ( unequally_directed_lines @ SV10 @ SV32 )
= $false )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(532,plain,
! [SV43: $i,SV37: $i,SV47: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(533,plain,
! [SV22: $i,SV93: $i,SV74: $i] :
( ( ( ~ ( distinct_points @ SV74 @ SV93 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV74 @ SV22 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV22 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(534,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(535,plain,
! [SV22: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( before_on_line @ SV22 @ SY118 @ SY119 )
| ( incident_point_and_line @ SY119 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(536,plain,
! [SV109: $i,SV98: $i,SV22: $i] :
( ( ( ~ ( before_on_line @ SV22 @ SV98 @ SV109 ) )
= $true )
| ( ( equally_directed_lines @ SV22 @ ( line_connecting @ SV98 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(537,plain,
! [SV99: $i,SV94: $i] :
( ( ( left_apart_point @ SV94 @ SV99 )
= $false )
| ( ( apart_point_and_line @ SV94 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(538,plain,
! [SV100: $i,SV95: $i] :
( ( ( right_apart_point @ SV95 @ SV100 )
= $false )
| ( ( apart_point_and_line @ SV95 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(539,plain,
! [SV23: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( divides_points @ SY123 @ SV23 @ SY122 )
| ( left_apart_point @ SV23 @ SY123 )
| ( left_apart_point @ SY122 @ SY123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(540,plain,
! [SV23: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ~ ( divides_points @ SY125 @ SV23 @ SY124 )
| ( left_apart_point @ SV23 @ SY125 )
| ( right_apart_point @ SV23 @ SY125 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(541,plain,
! [SV23: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ( divides_points @ SY127 @ SV23 @ SY126 )
| ( right_apart_point @ SY126 @ SY127 )
| ( left_apart_point @ SY126 @ SY127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(542,plain,
! [SV23: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( divides_points @ SY129 @ SV23 @ SY128 )
| ( right_apart_point @ SY128 @ SY129 )
| ( right_apart_point @ SV23 @ SY129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(543,plain,
! [SV101: $i,SV110: $i,SV23: $i] :
( ( ( ~ ( left_apart_point @ SV23 @ SV110 )
| ~ ( right_apart_point @ SV101 @ SV110 ) )
= $true )
| ( ( divides_points @ SV110 @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(544,plain,
! [SV23: $i,SV111: $i,SV102: $i] :
( ( ( ~ ( left_apart_point @ SV102 @ SV111 )
| ~ ( right_apart_point @ SV23 @ SV111 ) )
= $true )
| ( ( divides_points @ SV111 @ SV23 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(545,plain,
! [SV103: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV103 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) ) )
= $true )
| ( ( ! [SY205: $i] :
( ( unequally_directed_lines @ SV24 @ SY205 )
| ( unequally_directed_lines @ SV103 @ SY205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(546,plain,
! [SV104: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) ) )
= $true )
| ( ( ! [SY206: $i] :
( ( unequally_directed_lines @ SV24 @ SY206 )
| ( unequally_directed_lines @ SV104 @ ( reverse_line @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(547,plain,
! [SV105: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV105 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) ) )
= $true )
| ( ( ! [SY207: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY207 ) )
| ( unequally_directed_lines @ SV105 @ SY207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(548,plain,
! [SV106: $i,SV24: $i] :
( ( ( ~ ( unequally_directed_lines @ SV24 @ SV106 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) ) )
= $true )
| ( ( ! [SY208: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY208 ) )
| ( unequally_directed_lines @ SV106 @ ( reverse_line @ SY208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(549,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(550,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(551,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(552,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(553,plain,
! [SV114: $i,SV112: $i,SV42: $i,SV25: $i] :
( ( ~ ( before_on_line @ SV25 @ SV42 @ SV112 )
| ~ ( before_on_line @ SV25 @ SV112 @ SV114 )
| ( between_on_line @ SV25 @ SV42 @ SV112 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(554,plain,
! [SV42: $i,SV113: $i,SV115: $i,SV25: $i] :
( ( ~ ( before_on_line @ SV25 @ SV115 @ SV113 )
| ~ ( before_on_line @ SV25 @ SV113 @ SV42 )
| ( between_on_line @ SV25 @ SV42 @ SV113 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(555,plain,
! [SV90: $i,SV65: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV65 @ SV90 ) @ SV65 )
= $false )
| ( ( unequally_directed_lines @ SV65 @ SV90 )
= $false )
| ( ( unequally_directed_lines @ SV65 @ ( reverse_line @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(556,plain,
! [SV91: $i,SV66: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV66 @ SV91 ) @ SV91 )
= $false )
| ( ( unequally_directed_lines @ SV66 @ SV91 )
= $false )
| ( ( unequally_directed_lines @ SV66 @ ( reverse_line @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(557,plain,
! [SV107: $i,SV96: $i] :
( ( ( convergent_lines @ SV96 @ SV107 )
= $false )
| ( ( unequally_directed_lines @ SV96 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(558,plain,
! [SV108: $i,SV97: $i] :
( ( ( convergent_lines @ SV97 @ SV108 )
= $false )
| ( ( unequally_directed_opposite_lines @ SV97 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(559,plain,
! [SV47: $i,SV17: $i,SV43: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(560,plain,
! [SV22: $i,SV93: $i,SV74: $i] :
( ( ( distinct_points @ SV74 @ SV93 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV74 @ SV22 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV22 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(561,plain,
! [SV22: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(562,plain,
! [SV116: $i,SV22: $i] :
( ( ! [SY211: $i] :
( ~ ( before_on_line @ SV22 @ SV116 @ SY211 )
| ( incident_point_and_line @ SY211 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(563,plain,
! [SV109: $i,SV98: $i,SV22: $i] :
( ( ( before_on_line @ SV22 @ SV98 @ SV109 )
= $false )
| ( ( equally_directed_lines @ SV22 @ ( line_connecting @ SV98 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(564,plain,
! [SV117: $i,SV23: $i] :
( ( ! [SY212: $i] :
( ~ ( divides_points @ SY212 @ SV23 @ SV117 )
| ( left_apart_point @ SV23 @ SY212 )
| ( left_apart_point @ SV117 @ SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(565,plain,
! [SV118: $i,SV23: $i] :
( ( ! [SY213: $i] :
( ~ ( divides_points @ SY213 @ SV23 @ SV118 )
| ( left_apart_point @ SV23 @ SY213 )
| ( right_apart_point @ SV23 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(566,plain,
! [SV119: $i,SV23: $i] :
( ( ! [SY214: $i] :
( ~ ( divides_points @ SY214 @ SV23 @ SV119 )
| ( right_apart_point @ SV119 @ SY214 )
| ( left_apart_point @ SV119 @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(567,plain,
! [SV120: $i,SV23: $i] :
( ( ! [SY215: $i] :
( ~ ( divides_points @ SY215 @ SV23 @ SV120 )
| ( right_apart_point @ SV120 @ SY215 )
| ( right_apart_point @ SV23 @ SY215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(568,plain,
! [SV101: $i,SV110: $i,SV23: $i] :
( ( ( ~ ( left_apart_point @ SV23 @ SV110 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV101 @ SV110 ) )
= $true )
| ( ( divides_points @ SV110 @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(569,plain,
! [SV23: $i,SV111: $i,SV102: $i] :
( ( ( ~ ( left_apart_point @ SV102 @ SV111 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV23 @ SV111 ) )
= $true )
| ( ( divides_points @ SV111 @ SV23 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(570,plain,
! [SV103: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ SV103 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) ) )
= $true )
| ( ( ! [SY205: $i] :
( ( unequally_directed_lines @ SV24 @ SY205 )
| ( unequally_directed_lines @ SV103 @ SY205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(571,plain,
! [SV104: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ SV104 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) ) )
= $true )
| ( ( ! [SY206: $i] :
( ( unequally_directed_lines @ SV24 @ SY206 )
| ( unequally_directed_lines @ SV104 @ ( reverse_line @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(572,plain,
! [SV105: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ SV105 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) ) )
= $true )
| ( ( ! [SY207: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY207 ) )
| ( unequally_directed_lines @ SV105 @ SY207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(573,plain,
! [SV106: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ SV106 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) ) )
= $true )
| ( ( ! [SY208: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY208 ) )
| ( unequally_directed_lines @ SV106 @ ( reverse_line @ SY208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(574,plain,
! [SV42: $i,SV25: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY164 @ SY165 )
| ( before_on_line @ SV25 @ SV42 @ SY164 )
| ( before_on_line @ SV25 @ SY165 @ SY164 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(575,plain,
! [SV42: $i,SV25: $i] :
( ( ! [SY166: $i] :
( ! [SY167: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SY166 @ SY167 )
| ( before_on_line @ SV25 @ SV42 @ SY166 )
| ( before_on_line @ SV25 @ SY166 @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(576,plain,
! [SV42: $i,SV25: $i] :
( ( ! [SY168: $i,SY169: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY168 @ SY169 )
| ( before_on_line @ SV25 @ SY169 @ SY168 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(577,plain,
! [SV42: $i,SV25: $i] :
( ( ! [SY170: $i,SY171: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SY171 )
| ( before_on_line @ SV25 @ SY170 @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(578,plain,
! [SV114: $i,SV112: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( before_on_line @ SV25 @ SV42 @ SV112 )
| ~ ( before_on_line @ SV25 @ SV112 @ SV114 ) )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV112 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(579,plain,
! [SV42: $i,SV113: $i,SV115: $i,SV25: $i] :
( ( ( ~ ( before_on_line @ SV25 @ SV115 @ SV113 )
| ~ ( before_on_line @ SV25 @ SV113 @ SV42 ) )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV113 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(580,plain,
! [SV47: $i,SV37: $i,SV43: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(581,plain,
! [SV93: $i,SV22: $i,SV74: $i] :
( ( ( incident_point_and_line @ SV74 @ SV22 )
= $false )
| ( ( distinct_points @ SV74 @ SV93 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV22 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(582,plain,
! [SV22: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(583,plain,
! [SV22: $i] :
( ( ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(584,plain,
! [SV121: $i,SV116: $i,SV22: $i] :
( ( ~ ( before_on_line @ SV22 @ SV116 @ SV121 )
| ( incident_point_and_line @ SV121 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(585,plain,
! [SV117: $i,SV23: $i,SV122: $i] :
( ( ~ ( divides_points @ SV122 @ SV23 @ SV117 )
| ( left_apart_point @ SV23 @ SV122 )
| ( left_apart_point @ SV117 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(586,plain,
! [SV118: $i,SV23: $i,SV123: $i] :
( ( ~ ( divides_points @ SV123 @ SV23 @ SV118 )
| ( left_apart_point @ SV23 @ SV123 )
| ( right_apart_point @ SV23 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(587,plain,
! [SV119: $i,SV23: $i,SV124: $i] :
( ( ~ ( divides_points @ SV124 @ SV23 @ SV119 )
| ( right_apart_point @ SV119 @ SV124 )
| ( left_apart_point @ SV119 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(588,plain,
! [SV120: $i,SV23: $i,SV125: $i] :
( ( ~ ( divides_points @ SV125 @ SV23 @ SV120 )
| ( right_apart_point @ SV120 @ SV125 )
| ( right_apart_point @ SV23 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(589,plain,
! [SV101: $i,SV110: $i,SV23: $i] :
( ( ( left_apart_point @ SV23 @ SV110 )
= $false )
| ( ( ~ ( right_apart_point @ SV101 @ SV110 ) )
= $true )
| ( ( divides_points @ SV110 @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(590,plain,
! [SV23: $i,SV111: $i,SV102: $i] :
( ( ( left_apart_point @ SV102 @ SV111 )
= $false )
| ( ( ~ ( right_apart_point @ SV23 @ SV111 ) )
= $true )
| ( ( divides_points @ SV111 @ SV23 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(591,plain,
! [SV103: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) )
= $false )
| ( ( unequally_directed_lines @ SV24 @ SV103 )
= $false )
| ( ( ! [SY205: $i] :
( ( unequally_directed_lines @ SV24 @ SY205 )
| ( unequally_directed_lines @ SV103 @ SY205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(592,plain,
! [SV104: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) )
= $false )
| ( ( unequally_directed_lines @ SV24 @ SV104 )
= $false )
| ( ( ! [SY206: $i] :
( ( unequally_directed_lines @ SV24 @ SY206 )
| ( unequally_directed_lines @ SV104 @ ( reverse_line @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(593,plain,
! [SV105: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) )
= $false )
| ( ( unequally_directed_lines @ SV24 @ SV105 )
= $false )
| ( ( ! [SY207: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY207 ) )
| ( unequally_directed_lines @ SV105 @ SY207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(594,plain,
! [SV106: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) )
= $false )
| ( ( unequally_directed_lines @ SV24 @ SV106 )
= $false )
| ( ( ! [SY208: $i] :
( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SY208 ) )
| ( unequally_directed_lines @ SV106 @ ( reverse_line @ SY208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(595,plain,
! [SV126: $i,SV42: $i,SV25: $i] :
( ( ! [SY216: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SV126 @ SY216 )
| ( before_on_line @ SV25 @ SV42 @ SV126 )
| ( before_on_line @ SV25 @ SY216 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(596,plain,
! [SV127: $i,SV42: $i,SV25: $i] :
( ( ! [SY217: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SV127 @ SY217 )
| ( before_on_line @ SV25 @ SV42 @ SV127 )
| ( before_on_line @ SV25 @ SV127 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(597,plain,
! [SV128: $i,SV42: $i,SV25: $i] :
( ( ! [SY218: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SV128 @ SY218 )
| ( before_on_line @ SV25 @ SV128 @ SY218 )
| ( before_on_line @ SV25 @ SY218 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(598,plain,
! [SV129: $i,SV42: $i,SV25: $i] :
( ( ! [SY219: $i] :
( ~ ( between_on_line @ SV25 @ SV42 @ SV129 @ SY219 )
| ( before_on_line @ SV25 @ SV129 @ SY219 )
| ( before_on_line @ SV25 @ SV129 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(599,plain,
! [SV114: $i,SV112: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( before_on_line @ SV25 @ SV42 @ SV112 ) )
= $true )
| ( ( ~ ( before_on_line @ SV25 @ SV112 @ SV114 ) )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV112 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(600,plain,
! [SV42: $i,SV113: $i,SV115: $i,SV25: $i] :
( ( ( ~ ( before_on_line @ SV25 @ SV115 @ SV113 ) )
= $true )
| ( ( ~ ( before_on_line @ SV25 @ SV113 @ SV42 ) )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV113 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(601,plain,
! [SV43: $i,SV17: $i,SV47: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ SV47 )
= $true )
| ( ( ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(602,plain,
! [SV74: $i,SV22: $i,SV93: $i] :
( ( ( incident_point_and_line @ SV93 @ SV22 )
= $false )
| ( ( distinct_points @ SV74 @ SV93 )
= $false )
| ( ( incident_point_and_line @ SV74 @ SV22 )
= $false )
| ( ( ~ ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(603,plain,
! [SV22: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( before_on_line @ SV22 @ SY114 @ SY115 )
| ( distinct_points @ SY114 @ SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(604,plain,
! [SV22: $i] :
( ( ! [SY116: $i] :
( ! [SY117: $i] :
~ ( before_on_line @ SV22 @ SY116 @ SY117 )
| ( incident_point_and_line @ SY116 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(605,plain,
! [SV121: $i,SV116: $i,SV22: $i] :
( ( ( ~ ( before_on_line @ SV22 @ SV116 @ SV121 ) )
= $true )
| ( ( incident_point_and_line @ SV121 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(606,plain,
! [SV117: $i,SV23: $i,SV122: $i] :
( ( ( ~ ( divides_points @ SV122 @ SV23 @ SV117 ) )
= $true )
| ( ( ( left_apart_point @ SV23 @ SV122 )
| ( left_apart_point @ SV117 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(607,plain,
! [SV118: $i,SV23: $i,SV123: $i] :
( ( ( ~ ( divides_points @ SV123 @ SV23 @ SV118 ) )
= $true )
| ( ( ( left_apart_point @ SV23 @ SV123 )
| ( right_apart_point @ SV23 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(608,plain,
! [SV119: $i,SV23: $i,SV124: $i] :
( ( ( ~ ( divides_points @ SV124 @ SV23 @ SV119 ) )
= $true )
| ( ( ( right_apart_point @ SV119 @ SV124 )
| ( left_apart_point @ SV119 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(609,plain,
! [SV120: $i,SV23: $i,SV125: $i] :
( ( ( ~ ( divides_points @ SV125 @ SV23 @ SV120 ) )
= $true )
| ( ( ( right_apart_point @ SV120 @ SV125 )
| ( right_apart_point @ SV23 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(610,plain,
! [SV23: $i,SV110: $i,SV101: $i] :
( ( ( right_apart_point @ SV101 @ SV110 )
= $false )
| ( ( left_apart_point @ SV23 @ SV110 )
= $false )
| ( ( divides_points @ SV110 @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(611,plain,
! [SV102: $i,SV111: $i,SV23: $i] :
( ( ( right_apart_point @ SV23 @ SV111 )
= $false )
| ( ( left_apart_point @ SV102 @ SV111 )
= $false )
| ( ( divides_points @ SV111 @ SV23 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(612,plain,
! [SV103: $i,SV130: $i,SV24: $i] :
( ( ( ( unequally_directed_lines @ SV24 @ SV130 )
| ( unequally_directed_lines @ SV103 @ SV130 ) )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV103 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(613,plain,
! [SV104: $i,SV131: $i,SV24: $i] :
( ( ( ( unequally_directed_lines @ SV24 @ SV131 )
| ( unequally_directed_lines @ SV104 @ ( reverse_line @ SV131 ) ) )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV104 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(614,plain,
! [SV105: $i,SV132: $i,SV24: $i] :
( ( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV132 ) )
| ( unequally_directed_lines @ SV105 @ SV132 ) )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV105 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(615,plain,
! [SV106: $i,SV133: $i,SV24: $i] :
( ( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV133 ) )
| ( unequally_directed_lines @ SV106 @ ( reverse_line @ SV133 ) ) )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV106 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(616,plain,
! [SV134: $i,SV126: $i,SV42: $i,SV25: $i] :
( ( ~ ( between_on_line @ SV25 @ SV42 @ SV126 @ SV134 )
| ( before_on_line @ SV25 @ SV42 @ SV126 )
| ( before_on_line @ SV25 @ SV134 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(617,plain,
! [SV127: $i,SV42: $i,SV25: $i] :
( ( ( ! [SY217: $i] :
~ ( between_on_line @ SV25 @ SV42 @ SV127 @ SY217 ) )
= $true )
| ( ( ( before_on_line @ SV25 @ SV42 @ SV127 )
| ( before_on_line @ SV25 @ SV127 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(618,plain,
! [SV135: $i,SV128: $i,SV42: $i,SV25: $i] :
( ( ~ ( between_on_line @ SV25 @ SV42 @ SV128 @ SV135 )
| ( before_on_line @ SV25 @ SV128 @ SV135 )
| ( before_on_line @ SV25 @ SV135 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(619,plain,
! [SV136: $i,SV129: $i,SV42: $i,SV25: $i] :
( ( ~ ( between_on_line @ SV25 @ SV42 @ SV129 @ SV136 )
| ( before_on_line @ SV25 @ SV129 @ SV136 )
| ( before_on_line @ SV25 @ SV129 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(620,plain,
! [SV114: $i,SV112: $i,SV42: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV42 @ SV112 )
= $false )
| ( ( ~ ( before_on_line @ SV25 @ SV112 @ SV114 ) )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV112 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(621,plain,
! [SV42: $i,SV113: $i,SV115: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV115 @ SV113 )
= $false )
| ( ( ~ ( before_on_line @ SV25 @ SV113 @ SV42 ) )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV113 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(622,plain,
! [SV37: $i,SV43: $i,SV47: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV47 )
= $true )
| ( ( ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ SV47 )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(623,plain,
! [SV93: $i,SV74: $i,SV22: $i] :
( ( ( equally_directed_lines @ SV22 @ ( line_connecting @ SV74 @ SV93 ) )
= $false )
| ( ( incident_point_and_line @ SV74 @ SV22 )
= $false )
| ( ( distinct_points @ SV74 @ SV93 )
= $false )
| ( ( incident_point_and_line @ SV93 @ SV22 )
= $false )
| ( ( before_on_line @ SV22 @ SV74 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(624,plain,
! [SV137: $i,SV22: $i] :
( ( ! [SY220: $i] :
( ~ ( before_on_line @ SV22 @ SV137 @ SY220 )
| ( distinct_points @ SV137 @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(625,plain,
! [SV138: $i,SV22: $i] :
( ( ! [SY221: $i] :
~ ( before_on_line @ SV22 @ SV138 @ SY221 )
| ( incident_point_and_line @ SV138 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(626,plain,
! [SV121: $i,SV116: $i,SV22: $i] :
( ( ( before_on_line @ SV22 @ SV116 @ SV121 )
= $false )
| ( ( incident_point_and_line @ SV121 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(627,plain,
! [SV117: $i,SV23: $i,SV122: $i] :
( ( ( divides_points @ SV122 @ SV23 @ SV117 )
= $false )
| ( ( ( left_apart_point @ SV23 @ SV122 )
| ( left_apart_point @ SV117 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(628,plain,
! [SV118: $i,SV23: $i,SV123: $i] :
( ( ( divides_points @ SV123 @ SV23 @ SV118 )
= $false )
| ( ( ( left_apart_point @ SV23 @ SV123 )
| ( right_apart_point @ SV23 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(629,plain,
! [SV119: $i,SV23: $i,SV124: $i] :
( ( ( divides_points @ SV124 @ SV23 @ SV119 )
= $false )
| ( ( ( right_apart_point @ SV119 @ SV124 )
| ( left_apart_point @ SV119 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(630,plain,
! [SV120: $i,SV23: $i,SV125: $i] :
( ( ( divides_points @ SV125 @ SV23 @ SV120 )
= $false )
| ( ( ( right_apart_point @ SV120 @ SV125 )
| ( right_apart_point @ SV23 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(631,plain,
! [SV103: $i,SV130: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ SV130 )
= $true )
| ( ( unequally_directed_lines @ SV103 @ SV130 )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV103 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV103 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(632,plain,
! [SV104: $i,SV131: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ SV131 )
= $true )
| ( ( unequally_directed_lines @ SV104 @ ( reverse_line @ SV131 ) )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV104 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(633,plain,
! [SV105: $i,SV132: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV132 ) )
= $true )
| ( ( unequally_directed_lines @ SV105 @ SV132 )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV105 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(634,plain,
! [SV106: $i,SV133: $i,SV24: $i] :
( ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV133 ) )
= $true )
| ( ( unequally_directed_lines @ SV106 @ ( reverse_line @ SV133 ) )
= $true )
| ( ( unequally_directed_lines @ SV24 @ SV106 )
= $false )
| ( ( unequally_directed_lines @ SV24 @ ( reverse_line @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(635,plain,
! [SV134: $i,SV126: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( between_on_line @ SV25 @ SV42 @ SV126 @ SV134 ) )
= $true )
| ( ( ( before_on_line @ SV25 @ SV42 @ SV126 )
| ( before_on_line @ SV25 @ SV134 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(636,plain,
! [SV139: $i,SV127: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( between_on_line @ SV25 @ SV42 @ SV127 @ SV139 ) )
= $true )
| ( ( ( before_on_line @ SV25 @ SV42 @ SV127 )
| ( before_on_line @ SV25 @ SV127 @ SV42 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(637,plain,
! [SV135: $i,SV128: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( between_on_line @ SV25 @ SV42 @ SV128 @ SV135 ) )
= $true )
| ( ( ( before_on_line @ SV25 @ SV128 @ SV135 )
| ( before_on_line @ SV25 @ SV135 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(638,plain,
! [SV136: $i,SV129: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( between_on_line @ SV25 @ SV42 @ SV129 @ SV136 ) )
= $true )
| ( ( ( before_on_line @ SV25 @ SV129 @ SV136 )
| ( before_on_line @ SV25 @ SV129 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(639,plain,
! [SV42: $i,SV114: $i,SV112: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV112 @ SV114 )
= $false )
| ( ( before_on_line @ SV25 @ SV42 @ SV112 )
= $false )
| ( ( between_on_line @ SV25 @ SV42 @ SV112 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(640,plain,
! [SV115: $i,SV42: $i,SV113: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV113 @ SV42 )
= $false )
| ( ( before_on_line @ SV25 @ SV115 @ SV113 )
= $false )
| ( ( between_on_line @ SV25 @ SV42 @ SV113 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(641,plain,
! [SV47: $i,SV37: $i,SV43: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV43 )
= $true )
| ( ( left_apart_point @ SV37 @ SV43 )
= $true )
| ( ( left_apart_point @ SV17 @ SV47 )
= $true )
| ( ( left_apart_point @ SV37 @ SV47 )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(642,plain,
! [SV140: $i,SV137: $i,SV22: $i] :
( ( ~ ( before_on_line @ SV22 @ SV137 @ SV140 )
| ( distinct_points @ SV137 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(643,plain,
! [SV138: $i,SV22: $i] :
( ( ( ! [SY221: $i] :
~ ( before_on_line @ SV22 @ SV138 @ SY221 ) )
= $true )
| ( ( incident_point_and_line @ SV138 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(644,plain,
! [SV117: $i,SV122: $i,SV23: $i] :
( ( ( left_apart_point @ SV23 @ SV122 )
= $true )
| ( ( left_apart_point @ SV117 @ SV122 )
= $true )
| ( ( divides_points @ SV122 @ SV23 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(645,plain,
! [SV118: $i,SV123: $i,SV23: $i] :
( ( ( left_apart_point @ SV23 @ SV123 )
= $true )
| ( ( right_apart_point @ SV23 @ SV123 )
= $true )
| ( ( divides_points @ SV123 @ SV23 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(646,plain,
! [SV23: $i,SV124: $i,SV119: $i] :
( ( ( right_apart_point @ SV119 @ SV124 )
= $true )
| ( ( left_apart_point @ SV119 @ SV124 )
= $true )
| ( ( divides_points @ SV124 @ SV23 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(647,plain,
! [SV23: $i,SV125: $i,SV120: $i] :
( ( ( right_apart_point @ SV120 @ SV125 )
= $true )
| ( ( right_apart_point @ SV23 @ SV125 )
= $true )
| ( ( divides_points @ SV125 @ SV23 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(648,plain,
! [SV134: $i,SV126: $i,SV42: $i,SV25: $i] :
( ( ( between_on_line @ SV25 @ SV42 @ SV126 @ SV134 )
= $false )
| ( ( ( before_on_line @ SV25 @ SV42 @ SV126 )
| ( before_on_line @ SV25 @ SV134 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(649,plain,
! [SV139: $i,SV127: $i,SV42: $i,SV25: $i] :
( ( ( between_on_line @ SV25 @ SV42 @ SV127 @ SV139 )
= $false )
| ( ( ( before_on_line @ SV25 @ SV42 @ SV127 )
| ( before_on_line @ SV25 @ SV127 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(650,plain,
! [SV135: $i,SV128: $i,SV42: $i,SV25: $i] :
( ( ( between_on_line @ SV25 @ SV42 @ SV128 @ SV135 )
= $false )
| ( ( ( before_on_line @ SV25 @ SV128 @ SV135 )
| ( before_on_line @ SV25 @ SV135 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(651,plain,
! [SV136: $i,SV129: $i,SV42: $i,SV25: $i] :
( ( ( between_on_line @ SV25 @ SV42 @ SV129 @ SV136 )
= $false )
| ( ( ( before_on_line @ SV25 @ SV129 @ SV136 )
| ( before_on_line @ SV25 @ SV129 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(652,plain,
! [SV140: $i,SV137: $i,SV22: $i] :
( ( ( ~ ( before_on_line @ SV22 @ SV137 @ SV140 ) )
= $true )
| ( ( distinct_points @ SV137 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(653,plain,
! [SV141: $i,SV138: $i,SV22: $i] :
( ( ( ~ ( before_on_line @ SV22 @ SV138 @ SV141 ) )
= $true )
| ( ( incident_point_and_line @ SV138 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(654,plain,
! [SV134: $i,SV126: $i,SV42: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV42 @ SV126 )
= $true )
| ( ( before_on_line @ SV25 @ SV134 @ SV126 )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV126 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(655,plain,
! [SV139: $i,SV127: $i,SV42: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV42 @ SV127 )
= $true )
| ( ( before_on_line @ SV25 @ SV127 @ SV42 )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV127 @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(656,plain,
! [SV42: $i,SV135: $i,SV128: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV128 @ SV135 )
= $true )
| ( ( before_on_line @ SV25 @ SV135 @ SV128 )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV128 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(657,plain,
! [SV42: $i,SV136: $i,SV129: $i,SV25: $i] :
( ( ( before_on_line @ SV25 @ SV129 @ SV136 )
= $true )
| ( ( before_on_line @ SV25 @ SV129 @ SV42 )
= $true )
| ( ( between_on_line @ SV25 @ SV42 @ SV129 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(658,plain,
! [SV140: $i,SV137: $i,SV22: $i] :
( ( ( before_on_line @ SV22 @ SV137 @ SV140 )
= $false )
| ( ( distinct_points @ SV137 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(659,plain,
! [SV141: $i,SV138: $i,SV22: $i] :
( ( ( before_on_line @ SV22 @ SV138 @ SV141 )
= $false )
| ( ( incident_point_and_line @ SV138 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(660,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[151,659,658,657,656,655,654,647,646,645,644,641,640,639,634,633,632,631,626,623,611,610,563,558,557,556,555,538,537,531,528,494,493,482,481,480,476,475,472,452,451,445,444,440,439,433,415,414,408,406,404,403,395,393,390,386,385,384,304,261,260,255,220,218,208,206,190,173,152]) ).
thf(661,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( unequally_directed_lines @ X @ ( reverse_line @ Y ) )
| ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( unequally_directed_opposite_lines @ X @ Y )
| ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(662,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_apart_point @ X @ ( reverse_line @ Y ) )
| ( right_apart_point @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_apart_point @ X @ Y )
| ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(663,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_convergent_lines @ X @ ( reverse_line @ Y ) )
| ( right_convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_convergent_lines @ X @ Y )
| ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(664,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_lines @ X @ Y )
| ~ ( unequally_directed_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_lines @ X @ Y )
| ( equally_directed_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(665,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_opposite_lines @ X @ Y )
| ~ ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
| ( equally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(666,plain,
( ( ! [A: $i,L: $i] :
( ~ ( apart_point_and_line @ A @ L )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( right_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(667,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_opposite_lines @ L @ M )
| ( convergent_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_opposite_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(668,plain,
( ( ! [A: $i] :
( ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( right_apart_point @ B @ L )
| ( divides_points @ L @ A @ B ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ B @ L )
| ~ ( right_apart_point @ A @ L )
| ( divides_points @ L @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(669,plain,
( ( ! [L: $i] :
( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( incident_point_and_line @ A @ L )
| ~ ( incident_point_and_line @ B @ L )
| ~ ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) )
| ( before_on_line @ L @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( distinct_points @ A @ B ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ A @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ B @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(670,plain,
( ( ! [L: $i,A: $i] :
( ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i] :
( ! [C: $i] :
~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ~ ( before_on_line @ L @ B @ C )
| ( between_on_line @ L @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ C @ B )
| ~ ( before_on_line @ L @ B @ A )
| ( between_on_line @ L @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(671,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ! [C: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(673,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(674,plain,
( ( ! [L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(675,plain,
( ( ! [L: $i] : ( equally_directed_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(676,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(677,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(678,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(679,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(680,plain,
( ( ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ L )
& ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(681,plain,
( ( ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ M )
& ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ ( reverse_line @ M ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(683,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(684,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(685,plain,
( ( ! [L: $i] :
( ~ ( line @ L )
| ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(686,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(687,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L ) )
& ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(688,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(689,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(690,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(691,plain,
( ( ! [A: $i,L: $i] : ( equally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(692,plain,
( ( ! [A: $i,B: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ~ ( distinct_points @ A @ B )
| ( left_apart_point @ B @ ( reverse_line @ M ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(693,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(694,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(695,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(696,plain,
( ( ! [L: $i,M: $i] :
( ~ ( left_convergent_lines @ L @ M )
| ! [N: $i] :
( ( left_convergent_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(697,plain,
( ( right_apart_point @ sK2_SY84 @ sK3_SY86 )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(698,plain,
( ( left_apart_point @ sK1_A @ sK3_SY86 )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(699,plain,
( ( ~ ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ sK3_SY86 ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(700,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( before_on_line @ SX0 @ SX3 @ SX2 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( before_on_line @ SX0 @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX3 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( before_on_line @ SX0 @ SX3 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX1 )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(701,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(702,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(703,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) )
| ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(704,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX1 @ SX2 )
| ~ ( incident_point_and_line @ SX1 @ SX0 )
| ~ ( incident_point_and_line @ SX2 @ SX0 )
| ~ ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) )
| ( before_on_line @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( incident_point_and_line @ SX1 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( incident_point_and_line @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(705,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(706,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(707,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(708,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(709,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(710,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(711,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(712,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(713,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(714,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX2 )
| ( right_apart_point @ SX0 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( right_apart_point @ SX1 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( right_apart_point @ SX1 @ SX2 )
| ( right_apart_point @ SX0 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 )
| ( divides_points @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX1 @ SX2 )
| ~ ( right_apart_point @ SX0 @ SX2 )
| ( divides_points @ SX2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(715,plain,
! [SV142: $i] :
( ( ~ ( distinct_points @ SV142 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(716,plain,
! [SV143: $i] :
( ( ! [SY222: $i] :
( ~ ( distinct_points @ SV143 @ SY222 )
| ! [SY223: $i] :
( ( distinct_points @ SV143 @ SY223 )
| ( distinct_points @ SY222 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(717,plain,
! [SV144: $i] :
( ( ~ ( distinct_lines @ SV144 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(718,plain,
! [SV145: $i] :
( ( ! [SY224: $i] :
( ~ ( distinct_lines @ SV145 @ SY224 )
| ! [SY225: $i] :
( ( distinct_lines @ SV145 @ SY225 )
| ( distinct_lines @ SY224 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(719,plain,
! [SV146: $i] :
( ( equally_directed_lines @ SV146 @ SV146 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(720,plain,
! [SV147: $i] :
( ( ! [SY226: $i] :
( ~ ( unequally_directed_lines @ SV147 @ SY226 )
| ! [SY227: $i] :
( ( unequally_directed_lines @ SV147 @ SY227 )
| ( unequally_directed_lines @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(721,plain,
! [SV148: $i] :
( ( ! [SY228: $i] :
( ( unequally_directed_lines @ SV148 @ SY228 )
| ( unequally_directed_lines @ SV148 @ ( reverse_line @ SY228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(722,plain,
! [SV149: $i] :
( ( ! [SY229: $i] :
( ~ ( unequally_directed_lines @ SV149 @ SY229 )
| ~ ( unequally_directed_lines @ SV149 @ ( reverse_line @ SY229 ) )
| ( left_convergent_lines @ SV149 @ SY229 )
| ( left_convergent_lines @ SV149 @ ( reverse_line @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(723,plain,
! [SV150: $i] :
( ( ! [SY230: $i] :
( ~ ( point @ SV150 )
| ~ ( point @ SY230 )
| ~ ( distinct_points @ SV150 @ SY230 )
| ( line @ ( line_connecting @ SV150 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(724,plain,
! [SV151: $i] :
( ( ! [SY231: $i] :
( ~ ( line @ SV151 )
| ~ ( line @ SY231 )
| ~ ( unequally_directed_lines @ SV151 @ SY231 )
| ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SY231 ) )
| ( point @ ( intersection_point @ SV151 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(725,plain,
! [SV152: $i] :
( ( ! [SY232: $i] :
( ~ ( line @ SV152 )
| ~ ( point @ SY232 )
| ( line @ ( parallel_through_point @ SV152 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(726,plain,
! [SV153: $i] :
( ( ~ ( line @ SV153 )
| ( line @ ( reverse_line @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(727,plain,
! [SV154: $i] :
( ( ! [SY233: $i] :
~ ( apart_point_and_line @ SV154 @ ( parallel_through_point @ SY233 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(728,plain,
! [SV155: $i] :
( ( ~ ( distinct_lines @ SV155 @ ( reverse_line @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(729,plain,
! [SV156: $i] :
( ( ! [SY234: $i] :
( ~ ( distinct_points @ SV156 @ SY234 )
| ( equally_directed_lines @ ( line_connecting @ SV156 @ SY234 ) @ ( reverse_line @ ( line_connecting @ SY234 @ SV156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(730,plain,
! [SV157: $i] :
( ( ! [SY235: $i] : ( equally_directed_lines @ ( parallel_through_point @ SY235 @ SV157 ) @ SY235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(731,plain,
! [SV158: $i] :
( ( ! [SY236: $i,SY237: $i,SY238: $i] :
( ~ ( distinct_lines @ SY237 @ SY238 )
| ~ ( distinct_points @ SV158 @ SY236 )
| ( left_apart_point @ SY236 @ ( reverse_line @ SY238 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SY238 ) )
| ( left_apart_point @ SY236 @ ( reverse_line @ SY237 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SY237 ) )
| ( left_apart_point @ SY236 @ SY238 )
| ( left_apart_point @ SV158 @ SY238 )
| ( left_apart_point @ SV158 @ SY237 )
| ( left_apart_point @ SY236 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(732,plain,
! [SV159: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ~ ( distinct_points @ SV159 @ SY239 )
| ~ ( left_apart_point @ SV159 @ SY240 )
| ( left_apart_point @ SY239 @ SY240 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SY239 ) @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(733,plain,
! [SV160: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ~ ( left_apart_point @ SV160 @ SY242 )
| ( distinct_points @ SV160 @ SY241 )
| ( left_apart_point @ SY241 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(734,plain,
! [SV161: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ~ ( left_apart_point @ SV161 @ SY243 )
| ~ ( unequally_directed_lines @ SY243 @ SY244 )
| ( distinct_lines @ SY243 @ SY244 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SY244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(735,plain,
! [SV162: $i] :
( ( ! [SY245: $i] :
( ~ ( left_convergent_lines @ SV162 @ SY245 )
| ! [SY246: $i] :
( ( left_convergent_lines @ SV162 @ SY246 )
| ( unequally_directed_lines @ SY245 @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(736,plain,
( ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY84 ) @ sK3_SY86 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(737,plain,
! [SV163: $i] :
( ( ! [SY247: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY248: $i,SY249: $i] :
( ~ ( between_on_line @ SV163 @ SY247 @ SY248 @ SY249 )
| ( before_on_line @ SV163 @ SY247 @ SY248 )
| ( before_on_line @ SV163 @ SY249 @ SY248 ) )
| ~ ! [SY250: $i] :
( ! [SY251: $i] :
~ ( between_on_line @ SV163 @ SY247 @ SY250 @ SY251 )
| ( before_on_line @ SV163 @ SY247 @ SY250 )
| ( before_on_line @ SV163 @ SY250 @ SY247 ) ) )
| ~ ~ ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( between_on_line @ SV163 @ SY247 @ SY252 @ SY253 )
| ( before_on_line @ SV163 @ SY252 @ SY253 )
| ( before_on_line @ SV163 @ SY253 @ SY252 ) )
| ~ ! [SY254: $i,SY255: $i] :
( ~ ( between_on_line @ SV163 @ SY247 @ SY254 @ SY255 )
| ( before_on_line @ SV163 @ SY254 @ SY255 )
| ( before_on_line @ SV163 @ SY254 @ SY247 ) ) ) )
| ~ ~ ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( before_on_line @ SV163 @ SY247 @ SY256 )
| ~ ( before_on_line @ SV163 @ SY256 @ SY257 )
| ( between_on_line @ SV163 @ SY247 @ SY256 @ SY257 ) )
| ~ ! [SY258: $i,SY259: $i] :
( ~ ( before_on_line @ SV163 @ SY259 @ SY258 )
| ~ ( before_on_line @ SV163 @ SY258 @ SY247 )
| ( between_on_line @ SV163 @ SY247 @ SY258 @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(738,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(739,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(740,plain,
! [SV164: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) )
| ~ ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) )
| ~ ~ ( ~ ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) )
| ~ ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(741,plain,
! [SV165: $i] :
( ( ~ ( ~ ! [SY268: $i,SY269: $i] :
( ~ ( distinct_points @ SY268 @ SY269 )
| ~ ( incident_point_and_line @ SY268 @ SV165 )
| ~ ( incident_point_and_line @ SY269 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SY268 @ SY269 ) )
| ( before_on_line @ SV165 @ SY268 @ SY269 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(742,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(743,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(744,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(745,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(746,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(747,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(748,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(749,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(750,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(751,plain,
! [SV166: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) )
| ~ ~ ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(752,plain,
! [SV142: $i] :
( ( distinct_points @ SV142 @ SV142 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(753,plain,
! [SV167: $i,SV143: $i] :
( ( ~ ( distinct_points @ SV143 @ SV167 )
| ! [SY290: $i] :
( ( distinct_points @ SV143 @ SY290 )
| ( distinct_points @ SV167 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(754,plain,
! [SV144: $i] :
( ( distinct_lines @ SV144 @ SV144 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(755,plain,
! [SV168: $i,SV145: $i] :
( ( ~ ( distinct_lines @ SV145 @ SV168 )
| ! [SY291: $i] :
( ( distinct_lines @ SV145 @ SY291 )
| ( distinct_lines @ SV168 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(756,plain,
! [SV169: $i,SV147: $i] :
( ( ~ ( unequally_directed_lines @ SV147 @ SV169 )
| ! [SY292: $i] :
( ( unequally_directed_lines @ SV147 @ SY292 )
| ( unequally_directed_lines @ SV169 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(757,plain,
! [SV170: $i,SV148: $i] :
( ( ( unequally_directed_lines @ SV148 @ SV170 )
| ( unequally_directed_lines @ SV148 @ ( reverse_line @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(758,plain,
! [SV171: $i,SV149: $i] :
( ( ~ ( unequally_directed_lines @ SV149 @ SV171 )
| ~ ( unequally_directed_lines @ SV149 @ ( reverse_line @ SV171 ) )
| ( left_convergent_lines @ SV149 @ SV171 )
| ( left_convergent_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(759,plain,
! [SV172: $i,SV150: $i] :
( ( ~ ( point @ SV150 )
| ~ ( point @ SV172 )
| ~ ( distinct_points @ SV150 @ SV172 )
| ( line @ ( line_connecting @ SV150 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(760,plain,
! [SV173: $i,SV151: $i] :
( ( ~ ( line @ SV151 )
| ~ ( line @ SV173 )
| ~ ( unequally_directed_lines @ SV151 @ SV173 )
| ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) )
| ( point @ ( intersection_point @ SV151 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(761,plain,
! [SV174: $i,SV152: $i] :
( ( ~ ( line @ SV152 )
| ~ ( point @ SV174 )
| ( line @ ( parallel_through_point @ SV152 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(762,plain,
! [SV153: $i] :
( ( ( ~ ( line @ SV153 ) )
= $true )
| ( ( line @ ( reverse_line @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(763,plain,
! [SV175: $i,SV154: $i] :
( ( ~ ( apart_point_and_line @ SV154 @ ( parallel_through_point @ SV175 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(764,plain,
! [SV155: $i] :
( ( distinct_lines @ SV155 @ ( reverse_line @ SV155 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(765,plain,
! [SV176: $i,SV156: $i] :
( ( ~ ( distinct_points @ SV156 @ SV176 )
| ( equally_directed_lines @ ( line_connecting @ SV156 @ SV176 ) @ ( reverse_line @ ( line_connecting @ SV176 @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(766,plain,
! [SV157: $i,SV177: $i] :
( ( equally_directed_lines @ ( parallel_through_point @ SV177 @ SV157 ) @ SV177 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(767,plain,
! [SV178: $i,SV158: $i] :
( ( ! [SY293: $i,SY294: $i] :
( ~ ( distinct_lines @ SY293 @ SY294 )
| ~ ( distinct_points @ SV158 @ SV178 )
| ( left_apart_point @ SV178 @ ( reverse_line @ SY294 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SY294 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SY293 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SY293 ) )
| ( left_apart_point @ SV178 @ SY294 )
| ( left_apart_point @ SV158 @ SY294 )
| ( left_apart_point @ SV158 @ SY293 )
| ( left_apart_point @ SV178 @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(768,plain,
! [SV179: $i,SV159: $i] :
( ( ! [SY295: $i] :
( ~ ( distinct_points @ SV159 @ SV179 )
| ~ ( left_apart_point @ SV159 @ SY295 )
| ( left_apart_point @ SV179 @ SY295 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(769,plain,
! [SV180: $i,SV160: $i] :
( ( ! [SY296: $i] :
( ~ ( left_apart_point @ SV160 @ SY296 )
| ( distinct_points @ SV160 @ SV180 )
| ( left_apart_point @ SV180 @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(770,plain,
! [SV181: $i,SV161: $i] :
( ( ! [SY297: $i] :
( ~ ( left_apart_point @ SV161 @ SV181 )
| ~ ( unequally_directed_lines @ SV181 @ SY297 )
| ( distinct_lines @ SV181 @ SY297 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(771,plain,
! [SV182: $i,SV162: $i] :
( ( ~ ( left_convergent_lines @ SV162 @ SV182 )
| ! [SY298: $i] :
( ( left_convergent_lines @ SV162 @ SY298 )
| ( unequally_directed_lines @ SV182 @ SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(772,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
| ~ ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) )
| ~ ~ ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(773,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(774,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(775,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(776,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(777,plain,
! [SV164: $i] :
( ( ~ ~ ( ~ ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) )
| ~ ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) )
| ~ ~ ( ~ ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) )
| ~ ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(778,plain,
! [SV165: $i] :
( ( ~ ! [SY268: $i,SY269: $i] :
( ~ ( distinct_points @ SY268 @ SY269 )
| ~ ( incident_point_and_line @ SY268 @ SV165 )
| ~ ( incident_point_and_line @ SY269 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SY268 @ SY269 ) )
| ( before_on_line @ SV165 @ SY268 @ SY269 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(779,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(780,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(781,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(782,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(783,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(784,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(785,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(786,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(787,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(788,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(789,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(790,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(792,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(793,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(794,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(795,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(796,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(797,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) )
| ~ ~ ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(798,plain,
! [SV167: $i,SV143: $i] :
( ( ( ~ ( distinct_points @ SV143 @ SV167 ) )
= $true )
| ( ( ! [SY290: $i] :
( ( distinct_points @ SV143 @ SY290 )
| ( distinct_points @ SV167 @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(799,plain,
! [SV168: $i,SV145: $i] :
( ( ( ~ ( distinct_lines @ SV145 @ SV168 ) )
= $true )
| ( ( ! [SY291: $i] :
( ( distinct_lines @ SV145 @ SY291 )
| ( distinct_lines @ SV168 @ SY291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(800,plain,
! [SV169: $i,SV147: $i] :
( ( ( ~ ( unequally_directed_lines @ SV147 @ SV169 ) )
= $true )
| ( ( ! [SY292: $i] :
( ( unequally_directed_lines @ SV147 @ SY292 )
| ( unequally_directed_lines @ SV169 @ SY292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(801,plain,
! [SV170: $i,SV148: $i] :
( ( ( unequally_directed_lines @ SV148 @ SV170 )
= $true )
| ( ( unequally_directed_lines @ SV148 @ ( reverse_line @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(802,plain,
! [SV171: $i,SV149: $i] :
( ( ( ~ ( unequally_directed_lines @ SV149 @ SV171 )
| ~ ( unequally_directed_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV149 @ SV171 )
| ( left_convergent_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(803,plain,
! [SV172: $i,SV150: $i] :
( ( ( ~ ( point @ SV150 )
| ~ ( point @ SV172 )
| ~ ( distinct_points @ SV150 @ SV172 ) )
= $true )
| ( ( line @ ( line_connecting @ SV150 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(804,plain,
! [SV173: $i,SV151: $i] :
( ( ( ~ ( line @ SV151 )
| ~ ( line @ SV173 )
| ~ ( unequally_directed_lines @ SV151 @ SV173 )
| ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(805,plain,
! [SV174: $i,SV152: $i] :
( ( ( ~ ( line @ SV152 )
| ~ ( point @ SV174 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV152 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(806,plain,
! [SV153: $i] :
( ( ( line @ SV153 )
= $false )
| ( ( line @ ( reverse_line @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(807,plain,
! [SV175: $i,SV154: $i] :
( ( apart_point_and_line @ SV154 @ ( parallel_through_point @ SV175 @ SV154 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(808,plain,
! [SV176: $i,SV156: $i] :
( ( ( ~ ( distinct_points @ SV156 @ SV176 ) )
= $true )
| ( ( equally_directed_lines @ ( line_connecting @ SV156 @ SV176 ) @ ( reverse_line @ ( line_connecting @ SV176 @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(809,plain,
! [SV178: $i,SV158: $i,SV184: $i] :
( ( ! [SY311: $i] :
( ~ ( distinct_lines @ SV184 @ SY311 )
| ~ ( distinct_points @ SV158 @ SV178 )
| ( left_apart_point @ SV178 @ ( reverse_line @ SY311 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SY311 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SY311 )
| ( left_apart_point @ SV158 @ SY311 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(810,plain,
! [SV185: $i,SV179: $i,SV159: $i] :
( ( ~ ( distinct_points @ SV159 @ SV179 )
| ~ ( left_apart_point @ SV159 @ SV185 )
| ( left_apart_point @ SV179 @ SV185 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(811,plain,
! [SV180: $i,SV186: $i,SV160: $i] :
( ( ~ ( left_apart_point @ SV160 @ SV186 )
| ( distinct_points @ SV160 @ SV180 )
| ( left_apart_point @ SV180 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(812,plain,
! [SV187: $i,SV181: $i,SV161: $i] :
( ( ~ ( left_apart_point @ SV161 @ SV181 )
| ~ ( unequally_directed_lines @ SV181 @ SV187 )
| ( distinct_lines @ SV181 @ SV187 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(813,plain,
! [SV182: $i,SV162: $i] :
( ( ( ~ ( left_convergent_lines @ SV162 @ SV182 ) )
= $true )
| ( ( ! [SY298: $i] :
( ( left_convergent_lines @ SV162 @ SY298 )
| ( unequally_directed_lines @ SV182 @ SY298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(814,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
| ~ ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) )
| ~ ~ ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(815,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(818,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(819,plain,
! [SV164: $i] :
( ( ~ ~ ( ~ ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) )
| ~ ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(820,plain,
! [SV164: $i] :
( ( ~ ~ ( ~ ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) )
| ~ ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(821,plain,
! [SV165: $i] :
( ( ~ ! [SY268: $i,SY269: $i] :
( ~ ( distinct_points @ SY268 @ SY269 )
| ~ ( incident_point_and_line @ SY268 @ SV165 )
| ~ ( incident_point_and_line @ SY269 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SY268 @ SY269 ) )
| ( before_on_line @ SV165 @ SY268 @ SY269 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(822,plain,
! [SV165: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(823,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(824,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(825,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(826,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(827,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(828,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(829,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(831,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(832,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(833,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(834,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(835,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(836,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(837,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(838,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(839,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(840,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(841,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(842,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(843,plain,
! [SV167: $i,SV143: $i] :
( ( ( distinct_points @ SV143 @ SV167 )
= $false )
| ( ( ! [SY290: $i] :
( ( distinct_points @ SV143 @ SY290 )
| ( distinct_points @ SV167 @ SY290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(844,plain,
! [SV168: $i,SV145: $i] :
( ( ( distinct_lines @ SV145 @ SV168 )
= $false )
| ( ( ! [SY291: $i] :
( ( distinct_lines @ SV145 @ SY291 )
| ( distinct_lines @ SV168 @ SY291 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(845,plain,
! [SV169: $i,SV147: $i] :
( ( ( unequally_directed_lines @ SV147 @ SV169 )
= $false )
| ( ( ! [SY292: $i] :
( ( unequally_directed_lines @ SV147 @ SY292 )
| ( unequally_directed_lines @ SV169 @ SY292 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(846,plain,
! [SV171: $i,SV149: $i] :
( ( ( ~ ( unequally_directed_lines @ SV149 @ SV171 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV149 @ SV171 )
| ( left_convergent_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(847,plain,
! [SV172: $i,SV150: $i] :
( ( ( ~ ( point @ SV150 )
| ~ ( point @ SV172 ) )
= $true )
| ( ( ~ ( distinct_points @ SV150 @ SV172 ) )
= $true )
| ( ( line @ ( line_connecting @ SV150 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(848,plain,
! [SV173: $i,SV151: $i] :
( ( ( ~ ( line @ SV151 )
| ~ ( line @ SV173 )
| ~ ( unequally_directed_lines @ SV151 @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(849,plain,
! [SV174: $i,SV152: $i] :
( ( ( ~ ( line @ SV152 ) )
= $true )
| ( ( ~ ( point @ SV174 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV152 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(850,plain,
! [SV176: $i,SV156: $i] :
( ( ( distinct_points @ SV156 @ SV176 )
= $false )
| ( ( equally_directed_lines @ ( line_connecting @ SV156 @ SV176 ) @ ( reverse_line @ ( line_connecting @ SV176 @ SV156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(851,plain,
! [SV178: $i,SV158: $i,SV188: $i,SV184: $i] :
( ( ~ ( distinct_lines @ SV184 @ SV188 )
| ~ ( distinct_points @ SV158 @ SV178 )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(852,plain,
! [SV185: $i,SV179: $i,SV159: $i] :
( ( ( ~ ( distinct_points @ SV159 @ SV179 )
| ~ ( left_apart_point @ SV159 @ SV185 ) )
= $true )
| ( ( ( left_apart_point @ SV179 @ SV185 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(853,plain,
! [SV180: $i,SV186: $i,SV160: $i] :
( ( ( ~ ( left_apart_point @ SV160 @ SV186 ) )
= $true )
| ( ( ( distinct_points @ SV160 @ SV180 )
| ( left_apart_point @ SV180 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(854,plain,
! [SV187: $i,SV181: $i,SV161: $i] :
( ( ( ~ ( left_apart_point @ SV161 @ SV181 )
| ~ ( unequally_directed_lines @ SV181 @ SV187 ) )
= $true )
| ( ( ( distinct_lines @ SV181 @ SV187 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(855,plain,
! [SV182: $i,SV162: $i] :
( ( ( left_convergent_lines @ SV162 @ SV182 )
= $false )
| ( ( ! [SY298: $i] :
( ( left_convergent_lines @ SV162 @ SY298 )
| ( unequally_directed_lines @ SV182 @ SY298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(856,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
| ~ ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(857,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ~ ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(858,plain,
! [SV189: $i] :
( ( ! [SY312: $i] :
( ~ ( left_convergent_lines @ SV189 @ ( reverse_line @ SY312 ) )
| ( right_convergent_lines @ SV189 @ SY312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(859,plain,
! [SV190: $i] :
( ( ! [SY313: $i] :
( ~ ( right_convergent_lines @ SV190 @ SY313 )
| ( left_convergent_lines @ SV190 @ ( reverse_line @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(860,plain,
! [SV191: $i] :
( ( ! [SY314: $i] :
( ~ ( unequally_directed_lines @ SV191 @ ( reverse_line @ SY314 ) )
| ( unequally_directed_opposite_lines @ SV191 @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(861,plain,
! [SV192: $i] :
( ( ! [SY315: $i] :
( ~ ( unequally_directed_opposite_lines @ SV192 @ SY315 )
| ( unequally_directed_lines @ SV192 @ ( reverse_line @ SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(862,plain,
! [SV164: $i] :
( ( ~ ( ~ ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) )
| ~ ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(863,plain,
! [SV164: $i] :
( ( ~ ( ~ ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) )
| ~ ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(864,plain,
! [SV165: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ( distinct_points @ SY268 @ SY269 )
| ~ ( incident_point_and_line @ SY268 @ SV165 )
| ~ ( incident_point_and_line @ SY269 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SY268 @ SY269 ) )
| ( before_on_line @ SV165 @ SY268 @ SY269 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(865,plain,
! [SV165: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(866,plain,
! [SV193: $i] :
( ( ! [SY316: $i] :
( ~ ( equally_directed_opposite_lines @ SV193 @ SY316 )
| ~ ( unequally_directed_opposite_lines @ SV193 @ SY316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(867,plain,
! [SV194: $i] :
( ( ! [SY317: $i] :
( ( unequally_directed_opposite_lines @ SV194 @ SY317 )
| ( equally_directed_opposite_lines @ SV194 @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(868,plain,
! [SV195: $i] :
( ( ! [SY318: $i] :
( ~ ( apart_point_and_line @ SV195 @ SY318 )
| ( left_apart_point @ SV195 @ SY318 )
| ( right_apart_point @ SV195 @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(869,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(870,plain,
! [SV196: $i] :
( ( ! [SY319: $i] :
( ~ ( equally_directed_lines @ SV196 @ SY319 )
| ~ ( unequally_directed_lines @ SV196 @ SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(871,plain,
! [SV197: $i] :
( ( ! [SY320: $i] :
( ( unequally_directed_lines @ SV197 @ SY320 )
| ( equally_directed_lines @ SV197 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(872,plain,
! [SV198: $i] :
( ( ! [SY321: $i] :
( ~ ( unequally_directed_lines @ SV198 @ SY321 )
| ~ ( unequally_directed_lines @ SV198 @ ( reverse_line @ SY321 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV198 @ SY321 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(873,plain,
! [SV199: $i] :
( ( ! [SY322: $i] :
( ~ ( unequally_directed_lines @ SV199 @ SY322 )
| ~ ( unequally_directed_lines @ SV199 @ ( reverse_line @ SY322 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV199 @ SY322 ) @ SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(874,plain,
! [SV200: $i] :
( ( ! [SY323: $i] :
~ ( left_apart_point @ SV200 @ SY323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(875,plain,
! [SV201: $i] :
( ( ! [SY324: $i] :
~ ( left_apart_point @ SV201 @ ( reverse_line @ SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(876,plain,
! [SV202: $i] :
( ( ! [SY325: $i] :
( ~ ( left_apart_point @ SV202 @ ( reverse_line @ SY325 ) )
| ( right_apart_point @ SV202 @ SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(877,plain,
! [SV203: $i] :
( ( ! [SY326: $i] :
( ~ ( right_apart_point @ SV203 @ SY326 )
| ( left_apart_point @ SV203 @ ( reverse_line @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(878,plain,
! [SV204: $i] :
( ( ! [SY327: $i] :
~ ( left_convergent_lines @ SV204 @ SY327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(879,plain,
! [SV205: $i] :
( ( ! [SY328: $i] :
~ ( left_convergent_lines @ SV205 @ ( reverse_line @ SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(880,plain,
! [SV206: $i] :
( ( ! [SY329: $i] :
( ~ ( unequally_directed_lines @ SV206 @ SY329 )
| ~ ( unequally_directed_opposite_lines @ SV206 @ SY329 )
| ( convergent_lines @ SV206 @ SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(881,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(882,plain,
! [SV207: $i] :
( ( ! [SY330: $i] :
( ~ ( distinct_points @ SV207 @ SY330 )
| ~ ( apart_point_and_line @ SV207 @ ( line_connecting @ SV207 @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(883,plain,
! [SV208: $i] :
( ( ! [SY331: $i] :
( ~ ( distinct_points @ SV208 @ SY331 )
| ~ ( apart_point_and_line @ SY331 @ ( line_connecting @ SV208 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(884,plain,
! [SV166: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(885,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(886,plain,
! [SV167: $i,SV209: $i,SV143: $i] :
( ( ( ( distinct_points @ SV143 @ SV209 )
| ( distinct_points @ SV167 @ SV209 ) )
= $true )
| ( ( distinct_points @ SV143 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(887,plain,
! [SV168: $i,SV210: $i,SV145: $i] :
( ( ( ( distinct_lines @ SV145 @ SV210 )
| ( distinct_lines @ SV168 @ SV210 ) )
= $true )
| ( ( distinct_lines @ SV145 @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(888,plain,
! [SV169: $i,SV211: $i,SV147: $i] :
( ( ( ( unequally_directed_lines @ SV147 @ SV211 )
| ( unequally_directed_lines @ SV169 @ SV211 ) )
= $true )
| ( ( unequally_directed_lines @ SV147 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(889,plain,
! [SV171: $i,SV149: $i] :
( ( ( unequally_directed_lines @ SV149 @ SV171 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV149 @ SV171 )
| ( left_convergent_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(890,plain,
! [SV172: $i,SV150: $i] :
( ( ( ~ ( point @ SV150 ) )
= $true )
| ( ( ~ ( point @ SV172 ) )
= $true )
| ( ( ~ ( distinct_points @ SV150 @ SV172 ) )
= $true )
| ( ( line @ ( line_connecting @ SV150 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(891,plain,
! [SV173: $i,SV151: $i] :
( ( ( ~ ( line @ SV151 )
| ~ ( line @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(892,plain,
! [SV174: $i,SV152: $i] :
( ( ( line @ SV152 )
= $false )
| ( ( ~ ( point @ SV174 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV152 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(893,plain,
! [SV178: $i,SV158: $i,SV188: $i,SV184: $i] :
( ( ( ~ ( distinct_lines @ SV184 @ SV188 )
| ~ ( distinct_points @ SV158 @ SV178 ) )
= $true )
| ( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(894,plain,
! [SV185: $i,SV179: $i,SV159: $i] :
( ( ( ~ ( distinct_points @ SV159 @ SV179 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV159 @ SV185 ) )
= $true )
| ( ( ( left_apart_point @ SV179 @ SV185 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(895,plain,
! [SV180: $i,SV186: $i,SV160: $i] :
( ( ( left_apart_point @ SV160 @ SV186 )
= $false )
| ( ( ( distinct_points @ SV160 @ SV180 )
| ( left_apart_point @ SV180 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(896,plain,
! [SV187: $i,SV181: $i,SV161: $i] :
( ( ( ~ ( left_apart_point @ SV161 @ SV181 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV181 @ SV187 ) )
= $true )
| ( ( ( distinct_lines @ SV181 @ SV187 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(897,plain,
! [SV182: $i,SV212: $i,SV162: $i] :
( ( ( ( left_convergent_lines @ SV162 @ SV212 )
| ( unequally_directed_lines @ SV182 @ SV212 ) )
= $true )
| ( ( left_convergent_lines @ SV162 @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(898,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
| ~ ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(899,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(900,plain,
! [SV213: $i,SV189: $i] :
( ( ~ ( left_convergent_lines @ SV189 @ ( reverse_line @ SV213 ) )
| ( right_convergent_lines @ SV189 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(901,plain,
! [SV214: $i,SV190: $i] :
( ( ~ ( right_convergent_lines @ SV190 @ SV214 )
| ( left_convergent_lines @ SV190 @ ( reverse_line @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(902,plain,
! [SV215: $i,SV191: $i] :
( ( ~ ( unequally_directed_lines @ SV191 @ ( reverse_line @ SV215 ) )
| ( unequally_directed_opposite_lines @ SV191 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(903,plain,
! [SV216: $i,SV192: $i] :
( ( ~ ( unequally_directed_opposite_lines @ SV192 @ SV216 )
| ( unequally_directed_lines @ SV192 @ ( reverse_line @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(904,plain,
! [SV164: $i] :
( ( ~ ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) )
| ~ ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(905,plain,
! [SV164: $i] :
( ( ~ ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) )
| ~ ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(906,plain,
! [SV165: $i,SV217: $i] :
( ( ! [SY332: $i] :
( ~ ( distinct_points @ SV217 @ SY332 )
| ~ ( incident_point_and_line @ SV217 @ SV165 )
| ~ ( incident_point_and_line @ SY332 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SY332 ) )
| ( before_on_line @ SV165 @ SV217 @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(907,plain,
! [SV165: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(908,plain,
! [SV218: $i,SV193: $i] :
( ( ~ ( equally_directed_opposite_lines @ SV193 @ SV218 )
| ~ ( unequally_directed_opposite_lines @ SV193 @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(909,plain,
! [SV219: $i,SV194: $i] :
( ( ( unequally_directed_opposite_lines @ SV194 @ SV219 )
| ( equally_directed_opposite_lines @ SV194 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(910,plain,
! [SV220: $i,SV195: $i] :
( ( ~ ( apart_point_and_line @ SV195 @ SV220 )
| ( left_apart_point @ SV195 @ SV220 )
| ( right_apart_point @ SV195 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(911,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(912,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(913,plain,
! [SV221: $i,SV196: $i] :
( ( ~ ( equally_directed_lines @ SV196 @ SV221 )
| ~ ( unequally_directed_lines @ SV196 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(914,plain,
! [SV222: $i,SV197: $i] :
( ( ( unequally_directed_lines @ SV197 @ SV222 )
| ( equally_directed_lines @ SV197 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(915,plain,
! [SV223: $i,SV198: $i] :
( ( ~ ( unequally_directed_lines @ SV198 @ SV223 )
| ~ ( unequally_directed_lines @ SV198 @ ( reverse_line @ SV223 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV198 @ SV223 ) @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(916,plain,
! [SV224: $i,SV199: $i] :
( ( ~ ( unequally_directed_lines @ SV199 @ SV224 )
| ~ ( unequally_directed_lines @ SV199 @ ( reverse_line @ SV224 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV199 @ SV224 ) @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(917,plain,
! [SV225: $i,SV200: $i] :
( ( ~ ( left_apart_point @ SV200 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(918,plain,
! [SV226: $i,SV201: $i] :
( ( ~ ( left_apart_point @ SV201 @ ( reverse_line @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(919,plain,
! [SV227: $i,SV202: $i] :
( ( ~ ( left_apart_point @ SV202 @ ( reverse_line @ SV227 ) )
| ( right_apart_point @ SV202 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(920,plain,
! [SV228: $i,SV203: $i] :
( ( ~ ( right_apart_point @ SV203 @ SV228 )
| ( left_apart_point @ SV203 @ ( reverse_line @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(921,plain,
! [SV229: $i,SV204: $i] :
( ( ~ ( left_convergent_lines @ SV204 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(922,plain,
! [SV230: $i,SV205: $i] :
( ( ~ ( left_convergent_lines @ SV205 @ ( reverse_line @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(923,plain,
! [SV231: $i,SV206: $i] :
( ( ~ ( unequally_directed_lines @ SV206 @ SV231 )
| ~ ( unequally_directed_opposite_lines @ SV206 @ SV231 )
| ( convergent_lines @ SV206 @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(924,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(925,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(926,plain,
! [SV232: $i,SV207: $i] :
( ( ~ ( distinct_points @ SV207 @ SV232 )
| ~ ( apart_point_and_line @ SV207 @ ( line_connecting @ SV207 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(927,plain,
! [SV233: $i,SV208: $i] :
( ( ~ ( distinct_points @ SV208 @ SV233 )
| ~ ( apart_point_and_line @ SV233 @ ( line_connecting @ SV208 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(928,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(929,plain,
! [SV166: $i] :
( ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(930,plain,
! [SV167: $i,SV209: $i,SV143: $i] :
( ( ( distinct_points @ SV143 @ SV209 )
= $true )
| ( ( distinct_points @ SV167 @ SV209 )
= $true )
| ( ( distinct_points @ SV143 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(931,plain,
! [SV168: $i,SV210: $i,SV145: $i] :
( ( ( distinct_lines @ SV145 @ SV210 )
= $true )
| ( ( distinct_lines @ SV168 @ SV210 )
= $true )
| ( ( distinct_lines @ SV145 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(932,plain,
! [SV169: $i,SV211: $i,SV147: $i] :
( ( ( unequally_directed_lines @ SV147 @ SV211 )
= $true )
| ( ( unequally_directed_lines @ SV169 @ SV211 )
= $true )
| ( ( unequally_directed_lines @ SV147 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(933,plain,
! [SV171: $i,SV149: $i] :
( ( ( unequally_directed_lines @ SV149 @ ( reverse_line @ SV171 ) )
= $false )
| ( ( unequally_directed_lines @ SV149 @ SV171 )
= $false )
| ( ( ( left_convergent_lines @ SV149 @ SV171 )
| ( left_convergent_lines @ SV149 @ ( reverse_line @ SV171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(934,plain,
! [SV172: $i,SV150: $i] :
( ( ( point @ SV150 )
= $false )
| ( ( ~ ( point @ SV172 ) )
= $true )
| ( ( ~ ( distinct_points @ SV150 @ SV172 ) )
= $true )
| ( ( line @ ( line_connecting @ SV150 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(935,plain,
! [SV173: $i,SV151: $i] :
( ( ( ~ ( line @ SV151 ) )
= $true )
| ( ( ~ ( line @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(936,plain,
! [SV152: $i,SV174: $i] :
( ( ( point @ SV174 )
= $false )
| ( ( line @ SV152 )
= $false )
| ( ( line @ ( parallel_through_point @ SV152 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(937,plain,
! [SV178: $i,SV158: $i,SV188: $i,SV184: $i] :
( ( ( ~ ( distinct_lines @ SV184 @ SV188 ) )
= $true )
| ( ( ~ ( distinct_points @ SV158 @ SV178 ) )
= $true )
| ( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(938,plain,
! [SV185: $i,SV179: $i,SV159: $i] :
( ( ( distinct_points @ SV159 @ SV179 )
= $false )
| ( ( ~ ( left_apart_point @ SV159 @ SV185 ) )
= $true )
| ( ( ( left_apart_point @ SV179 @ SV185 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(939,plain,
! [SV186: $i,SV180: $i,SV160: $i] :
( ( ( distinct_points @ SV160 @ SV180 )
= $true )
| ( ( left_apart_point @ SV180 @ SV186 )
= $true )
| ( ( left_apart_point @ SV160 @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(940,plain,
! [SV187: $i,SV181: $i,SV161: $i] :
( ( ( left_apart_point @ SV161 @ SV181 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV181 @ SV187 ) )
= $true )
| ( ( ( distinct_lines @ SV181 @ SV187 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(941,plain,
! [SV182: $i,SV212: $i,SV162: $i] :
( ( ( left_convergent_lines @ SV162 @ SV212 )
= $true )
| ( ( unequally_directed_lines @ SV182 @ SV212 )
= $true )
| ( ( left_convergent_lines @ SV162 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(942,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
| ~ ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(943,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(944,plain,
! [SV213: $i,SV189: $i] :
( ( ( ~ ( left_convergent_lines @ SV189 @ ( reverse_line @ SV213 ) ) )
= $true )
| ( ( right_convergent_lines @ SV189 @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(945,plain,
! [SV214: $i,SV190: $i] :
( ( ( ~ ( right_convergent_lines @ SV190 @ SV214 ) )
= $true )
| ( ( left_convergent_lines @ SV190 @ ( reverse_line @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(946,plain,
! [SV215: $i,SV191: $i] :
( ( ( ~ ( unequally_directed_lines @ SV191 @ ( reverse_line @ SV215 ) ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV191 @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(947,plain,
! [SV216: $i,SV192: $i] :
( ( ( ~ ( unequally_directed_opposite_lines @ SV192 @ SV216 ) )
= $true )
| ( ( unequally_directed_lines @ SV192 @ ( reverse_line @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(948,plain,
! [SV164: $i] :
( ( ~ ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(949,plain,
! [SV164: $i] :
( ( ~ ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(950,plain,
! [SV164: $i] :
( ( ~ ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(951,plain,
! [SV164: $i] :
( ( ~ ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(952,plain,
! [SV165: $i,SV234: $i,SV217: $i] :
( ( ~ ( distinct_points @ SV217 @ SV234 )
| ~ ( incident_point_and_line @ SV217 @ SV165 )
| ~ ( incident_point_and_line @ SV234 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) )
| ( before_on_line @ SV165 @ SV217 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(953,plain,
! [SV165: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(954,plain,
! [SV165: $i] :
( ( ~ ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(955,plain,
! [SV218: $i,SV193: $i] :
( ( ( ~ ( equally_directed_opposite_lines @ SV193 @ SV218 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV193 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(956,plain,
! [SV219: $i,SV194: $i] :
( ( ( unequally_directed_opposite_lines @ SV194 @ SV219 )
= $true )
| ( ( equally_directed_opposite_lines @ SV194 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(957,plain,
! [SV220: $i,SV195: $i] :
( ( ( ~ ( apart_point_and_line @ SV195 @ SV220 ) )
= $true )
| ( ( ( left_apart_point @ SV195 @ SV220 )
| ( right_apart_point @ SV195 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(958,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(960,plain,
! [SV221: $i,SV196: $i] :
( ( ( ~ ( equally_directed_lines @ SV196 @ SV221 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV196 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(961,plain,
! [SV222: $i,SV197: $i] :
( ( ( unequally_directed_lines @ SV197 @ SV222 )
= $true )
| ( ( equally_directed_lines @ SV197 @ SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(962,plain,
! [SV223: $i,SV198: $i] :
( ( ( ~ ( unequally_directed_lines @ SV198 @ SV223 )
| ~ ( unequally_directed_lines @ SV198 @ ( reverse_line @ SV223 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV198 @ SV223 ) @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(963,plain,
! [SV224: $i,SV199: $i] :
( ( ( ~ ( unequally_directed_lines @ SV199 @ SV224 )
| ~ ( unequally_directed_lines @ SV199 @ ( reverse_line @ SV224 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV199 @ SV224 ) @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(964,plain,
! [SV225: $i,SV200: $i] :
( ( left_apart_point @ SV200 @ SV225 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(965,plain,
! [SV226: $i,SV201: $i] :
( ( left_apart_point @ SV201 @ ( reverse_line @ SV226 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(966,plain,
! [SV227: $i,SV202: $i] :
( ( ( ~ ( left_apart_point @ SV202 @ ( reverse_line @ SV227 ) ) )
= $true )
| ( ( right_apart_point @ SV202 @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(967,plain,
! [SV228: $i,SV203: $i] :
( ( ( ~ ( right_apart_point @ SV203 @ SV228 ) )
= $true )
| ( ( left_apart_point @ SV203 @ ( reverse_line @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(968,plain,
! [SV229: $i,SV204: $i] :
( ( left_convergent_lines @ SV204 @ SV229 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(969,plain,
! [SV230: $i,SV205: $i] :
( ( left_convergent_lines @ SV205 @ ( reverse_line @ SV230 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(970,plain,
! [SV231: $i,SV206: $i] :
( ( ( ~ ( unequally_directed_lines @ SV206 @ SV231 )
| ~ ( unequally_directed_opposite_lines @ SV206 @ SV231 ) )
= $true )
| ( ( convergent_lines @ SV206 @ SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(971,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(972,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(973,plain,
! [SV232: $i,SV207: $i] :
( ( ( ~ ( distinct_points @ SV207 @ SV232 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV207 @ ( line_connecting @ SV207 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(974,plain,
! [SV233: $i,SV208: $i] :
( ( ( ~ ( distinct_points @ SV208 @ SV233 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV233 @ ( line_connecting @ SV208 @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(975,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(976,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(977,plain,
! [SV166: $i] :
( ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(978,plain,
! [SV166: $i] :
( ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(979,plain,
! [SV171: $i,SV149: $i] :
( ( ( left_convergent_lines @ SV149 @ SV171 )
= $true )
| ( ( left_convergent_lines @ SV149 @ ( reverse_line @ SV171 ) )
= $true )
| ( ( unequally_directed_lines @ SV149 @ SV171 )
= $false )
| ( ( unequally_directed_lines @ SV149 @ ( reverse_line @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(980,plain,
! [SV150: $i,SV172: $i] :
( ( ( point @ SV172 )
= $false )
| ( ( point @ SV150 )
= $false )
| ( ( ~ ( distinct_points @ SV150 @ SV172 ) )
= $true )
| ( ( line @ ( line_connecting @ SV150 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(981,plain,
! [SV173: $i,SV151: $i] :
( ( ( line @ SV151 )
= $false )
| ( ( ~ ( line @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(982,plain,
! [SV178: $i,SV158: $i,SV188: $i,SV184: $i] :
( ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( ~ ( distinct_points @ SV158 @ SV178 ) )
= $true )
| ( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(983,plain,
! [SV179: $i,SV185: $i,SV159: $i] :
( ( ( left_apart_point @ SV159 @ SV185 )
= $false )
| ( ( distinct_points @ SV159 @ SV179 )
= $false )
| ( ( ( left_apart_point @ SV179 @ SV185 )
| ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(984,plain,
! [SV161: $i,SV187: $i,SV181: $i] :
( ( ( unequally_directed_lines @ SV181 @ SV187 )
= $false )
| ( ( left_apart_point @ SV161 @ SV181 )
= $false )
| ( ( ( distinct_lines @ SV181 @ SV187 )
| ( left_apart_point @ SV161 @ ( reverse_line @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(985,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(986,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(987,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(988,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(989,plain,
! [SV213: $i,SV189: $i] :
( ( ( left_convergent_lines @ SV189 @ ( reverse_line @ SV213 ) )
= $false )
| ( ( right_convergent_lines @ SV189 @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(990,plain,
! [SV214: $i,SV190: $i] :
( ( ( right_convergent_lines @ SV190 @ SV214 )
= $false )
| ( ( left_convergent_lines @ SV190 @ ( reverse_line @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(991,plain,
! [SV215: $i,SV191: $i] :
( ( ( unequally_directed_lines @ SV191 @ ( reverse_line @ SV215 ) )
= $false )
| ( ( unequally_directed_opposite_lines @ SV191 @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(992,plain,
! [SV216: $i,SV192: $i] :
( ( ( unequally_directed_opposite_lines @ SV192 @ SV216 )
= $false )
| ( ( unequally_directed_lines @ SV192 @ ( reverse_line @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(993,plain,
! [SV164: $i] :
( ( ! [SY260: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY260 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY260 ) )
| ! [SY261: $i] :
( ( unequally_directed_lines @ SV164 @ SY261 )
| ( unequally_directed_lines @ SY260 @ SY261 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(994,plain,
! [SV164: $i] :
( ( ! [SY262: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY262 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY262 ) )
| ! [SY263: $i] :
( ( unequally_directed_lines @ SV164 @ SY263 )
| ( unequally_directed_lines @ SY262 @ ( reverse_line @ SY263 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(995,plain,
! [SV164: $i] :
( ( ! [SY264: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY264 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY264 ) )
| ! [SY265: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY265 ) )
| ( unequally_directed_lines @ SY264 @ SY265 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(996,plain,
! [SV164: $i] :
( ( ! [SY266: $i] :
( ~ ( unequally_directed_lines @ SV164 @ SY266 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY266 ) )
| ! [SY267: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY267 ) )
| ( unequally_directed_lines @ SY266 @ ( reverse_line @ SY267 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(997,plain,
! [SV165: $i,SV234: $i,SV217: $i] :
( ( ( ~ ( distinct_points @ SV217 @ SV234 )
| ~ ( incident_point_and_line @ SV217 @ SV165 )
| ~ ( incident_point_and_line @ SV234 @ SV165 )
| ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(998,plain,
! [SV165: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(999,plain,
! [SV165: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( before_on_line @ SV165 @ SY276 @ SY277 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SY276 @ SY277 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1000,plain,
! [SV218: $i,SV193: $i] :
( ( ( equally_directed_opposite_lines @ SV193 @ SV218 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV193 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1001,plain,
! [SV220: $i,SV195: $i] :
( ( ( apart_point_and_line @ SV195 @ SV220 )
= $false )
| ( ( ( left_apart_point @ SV195 @ SV220 )
| ( right_apart_point @ SV195 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1002,plain,
! [SV235: $i] :
( ( ! [SY333: $i] :
( ~ ( left_apart_point @ SV235 @ SY333 )
| ( apart_point_and_line @ SV235 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1003,plain,
! [SV236: $i] :
( ( ! [SY334: $i] :
( ~ ( right_apart_point @ SV236 @ SY334 )
| ( apart_point_and_line @ SV236 @ SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1004,plain,
! [SV221: $i,SV196: $i] :
( ( ( equally_directed_lines @ SV196 @ SV221 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV196 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1005,plain,
! [SV223: $i,SV198: $i] :
( ( ( ~ ( unequally_directed_lines @ SV198 @ SV223 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV198 @ ( reverse_line @ SV223 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV198 @ SV223 ) @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1006,plain,
! [SV224: $i,SV199: $i] :
( ( ( ~ ( unequally_directed_lines @ SV199 @ SV224 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV199 @ ( reverse_line @ SV224 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV199 @ SV224 ) @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1007,plain,
! [SV227: $i,SV202: $i] :
( ( ( left_apart_point @ SV202 @ ( reverse_line @ SV227 ) )
= $false )
| ( ( right_apart_point @ SV202 @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1008,plain,
! [SV228: $i,SV203: $i] :
( ( ( right_apart_point @ SV203 @ SV228 )
= $false )
| ( ( left_apart_point @ SV203 @ ( reverse_line @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1009,plain,
! [SV231: $i,SV206: $i] :
( ( ( ~ ( unequally_directed_lines @ SV206 @ SV231 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV206 @ SV231 ) )
= $true )
| ( ( convergent_lines @ SV206 @ SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1010,plain,
! [SV237: $i] :
( ( ! [SY335: $i] :
( ~ ( convergent_lines @ SV237 @ SY335 )
| ( unequally_directed_lines @ SV237 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1011,plain,
! [SV238: $i] :
( ( ! [SY336: $i] :
( ~ ( convergent_lines @ SV238 @ SY336 )
| ( unequally_directed_opposite_lines @ SV238 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1012,plain,
! [SV232: $i,SV207: $i] :
( ( ( distinct_points @ SV207 @ SV232 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV207 @ ( line_connecting @ SV207 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1013,plain,
! [SV233: $i,SV208: $i] :
( ( ( distinct_points @ SV208 @ SV233 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV233 @ ( line_connecting @ SV208 @ SV233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1014,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1015,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1016,plain,
! [SV166: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ~ ( left_apart_point @ SV166 @ SY287 )
| ~ ( right_apart_point @ SY286 @ SY287 )
| ( divides_points @ SY287 @ SV166 @ SY286 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(1017,plain,
! [SV166: $i] :
( ( ! [SY288: $i,SY289: $i] :
( ~ ( left_apart_point @ SY288 @ SY289 )
| ~ ( right_apart_point @ SV166 @ SY289 )
| ( divides_points @ SY289 @ SV166 @ SY288 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1018,plain,
! [SV172: $i,SV150: $i] :
( ( ( distinct_points @ SV150 @ SV172 )
= $false )
| ( ( point @ SV150 )
= $false )
| ( ( point @ SV172 )
= $false )
| ( ( line @ ( line_connecting @ SV150 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1019,plain,
! [SV151: $i,SV173: $i] :
( ( ( line @ SV173 )
= $false )
| ( ( line @ SV151 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV151 @ SV173 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1020,plain,
! [SV188: $i,SV184: $i,SV178: $i,SV158: $i] :
( ( ( distinct_points @ SV158 @ SV178 )
= $false )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1021,plain,
! [SV159: $i,SV185: $i,SV179: $i] :
( ( ( left_apart_point @ SV179 @ SV185 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV159 @ SV179 ) @ SV185 )
= $true )
| ( ( distinct_points @ SV159 @ SV179 )
= $false )
| ( ( left_apart_point @ SV159 @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1022,plain,
! [SV161: $i,SV187: $i,SV181: $i] :
( ( ( distinct_lines @ SV181 @ SV187 )
= $true )
| ( ( left_apart_point @ SV161 @ ( reverse_line @ SV187 ) )
= $true )
| ( ( left_apart_point @ SV161 @ SV181 )
= $false )
| ( ( unequally_directed_lines @ SV181 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1023,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1024,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1025,plain,
! [SV183: $i,SV163: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SY307 )
| ~ ( before_on_line @ SV163 @ SY307 @ SY308 )
| ( between_on_line @ SV163 @ SV183 @ SY307 @ SY308 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1026,plain,
! [SV183: $i,SV163: $i] :
( ( ! [SY309: $i,SY310: $i] :
( ~ ( before_on_line @ SV163 @ SY310 @ SY309 )
| ~ ( before_on_line @ SV163 @ SY309 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SY309 @ SY310 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1027,plain,
! [SV239: $i,SV164: $i] :
( ( ~ ( unequally_directed_lines @ SV164 @ SV239 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) )
| ! [SY337: $i] :
( ( unequally_directed_lines @ SV164 @ SY337 )
| ( unequally_directed_lines @ SV239 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1028,plain,
! [SV240: $i,SV164: $i] :
( ( ~ ( unequally_directed_lines @ SV164 @ SV240 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) )
| ! [SY338: $i] :
( ( unequally_directed_lines @ SV164 @ SY338 )
| ( unequally_directed_lines @ SV240 @ ( reverse_line @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1029,plain,
! [SV241: $i,SV164: $i] :
( ( ~ ( unequally_directed_lines @ SV164 @ SV241 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) )
| ! [SY339: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY339 ) )
| ( unequally_directed_lines @ SV241 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1030,plain,
! [SV242: $i,SV164: $i] :
( ( ~ ( unequally_directed_lines @ SV164 @ SV242 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) )
| ! [SY340: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY340 ) )
| ( unequally_directed_lines @ SV242 @ ( reverse_line @ SY340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1031,plain,
! [SV165: $i,SV234: $i,SV217: $i] :
( ( ( ~ ( distinct_points @ SV217 @ SV234 )
| ~ ( incident_point_and_line @ SV217 @ SV165 )
| ~ ( incident_point_and_line @ SV234 @ SV165 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1032,plain,
! [SV165: $i] :
( ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1033,plain,
! [SV243: $i,SV165: $i] :
( ( ! [SY341: $i] :
( ~ ( before_on_line @ SV165 @ SV243 @ SY341 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SV243 @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1034,plain,
! [SV218: $i,SV193: $i] :
( ( ( unequally_directed_opposite_lines @ SV193 @ SV218 )
= $false )
| ( ( equally_directed_opposite_lines @ SV193 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1035,plain,
! [SV220: $i,SV195: $i] :
( ( ( left_apart_point @ SV195 @ SV220 )
= $true )
| ( ( right_apart_point @ SV195 @ SV220 )
= $true )
| ( ( apart_point_and_line @ SV195 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1036,plain,
! [SV244: $i,SV235: $i] :
( ( ~ ( left_apart_point @ SV235 @ SV244 )
| ( apart_point_and_line @ SV235 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1037,plain,
! [SV245: $i,SV236: $i] :
( ( ~ ( right_apart_point @ SV236 @ SV245 )
| ( apart_point_and_line @ SV236 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1038,plain,
! [SV221: $i,SV196: $i] :
( ( ( unequally_directed_lines @ SV196 @ SV221 )
= $false )
| ( ( equally_directed_lines @ SV196 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1039,plain,
! [SV223: $i,SV198: $i] :
( ( ( unequally_directed_lines @ SV198 @ SV223 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV198 @ ( reverse_line @ SV223 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV198 @ SV223 ) @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1040,plain,
! [SV224: $i,SV199: $i] :
( ( ( unequally_directed_lines @ SV199 @ SV224 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV199 @ ( reverse_line @ SV224 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV199 @ SV224 ) @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1041,plain,
! [SV231: $i,SV206: $i] :
( ( ( unequally_directed_lines @ SV206 @ SV231 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV206 @ SV231 ) )
= $true )
| ( ( convergent_lines @ SV206 @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1042,plain,
! [SV246: $i,SV237: $i] :
( ( ~ ( convergent_lines @ SV237 @ SV246 )
| ( unequally_directed_lines @ SV237 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1043,plain,
! [SV247: $i,SV238: $i] :
( ( ~ ( convergent_lines @ SV238 @ SV247 )
| ( unequally_directed_opposite_lines @ SV238 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1044,plain,
! [SV232: $i,SV207: $i] :
( ( ( apart_point_and_line @ SV207 @ ( line_connecting @ SV207 @ SV232 ) )
= $false )
| ( ( distinct_points @ SV207 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1045,plain,
! [SV208: $i,SV233: $i] :
( ( ( apart_point_and_line @ SV233 @ ( line_connecting @ SV208 @ SV233 ) )
= $false )
| ( ( distinct_points @ SV208 @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1046,plain,
! [SV166: $i] :
( ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) )
| ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1047,plain,
! [SV166: $i] :
( ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1048,plain,
! [SV248: $i,SV166: $i] :
( ( ! [SY342: $i] :
( ~ ( left_apart_point @ SV166 @ SY342 )
| ~ ( right_apart_point @ SV248 @ SY342 )
| ( divides_points @ SY342 @ SV166 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1049,plain,
! [SV166: $i,SV249: $i] :
( ( ! [SY343: $i] :
( ~ ( left_apart_point @ SV249 @ SY343 )
| ~ ( right_apart_point @ SV166 @ SY343 )
| ( divides_points @ SY343 @ SV166 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1050,plain,
! [SV173: $i,SV151: $i] :
( ( ( unequally_directed_lines @ SV151 @ SV173 )
= $false )
| ( ( line @ SV151 )
= $false )
| ( ( line @ SV173 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1051,plain,
! [SV184: $i,SV158: $i,SV188: $i,SV178: $i] :
( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
| ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1052,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) )
| ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1053,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1054,plain,
! [SV250: $i,SV183: $i,SV163: $i] :
( ( ! [SY344: $i] :
( ~ ( before_on_line @ SV163 @ SV183 @ SV250 )
| ~ ( before_on_line @ SV163 @ SV250 @ SY344 )
| ( between_on_line @ SV163 @ SV183 @ SV250 @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1055,plain,
! [SV183: $i,SV251: $i,SV163: $i] :
( ( ! [SY345: $i] :
( ~ ( before_on_line @ SV163 @ SY345 @ SV251 )
| ~ ( before_on_line @ SV163 @ SV251 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SV251 @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1056,plain,
! [SV239: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV239 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) ) )
= $true )
| ( ( ! [SY337: $i] :
( ( unequally_directed_lines @ SV164 @ SY337 )
| ( unequally_directed_lines @ SV239 @ SY337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1057,plain,
! [SV240: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV240 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) ) )
= $true )
| ( ( ! [SY338: $i] :
( ( unequally_directed_lines @ SV164 @ SY338 )
| ( unequally_directed_lines @ SV240 @ ( reverse_line @ SY338 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1058,plain,
! [SV241: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV241 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) ) )
= $true )
| ( ( ! [SY339: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY339 ) )
| ( unequally_directed_lines @ SV241 @ SY339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1059,plain,
! [SV242: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV242 )
| ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY340 ) )
| ( unequally_directed_lines @ SV242 @ ( reverse_line @ SY340 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1060,plain,
! [SV165: $i,SV234: $i,SV217: $i] :
( ( ( ~ ( distinct_points @ SV217 @ SV234 )
| ~ ( incident_point_and_line @ SV217 @ SV165 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV234 @ SV165 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1061,plain,
! [SV165: $i] :
( ( ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1062,plain,
! [SV165: $i] :
( ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1063,plain,
! [SV252: $i,SV243: $i,SV165: $i] :
( ( ~ ( before_on_line @ SV165 @ SV243 @ SV252 )
| ( equally_directed_lines @ SV165 @ ( line_connecting @ SV243 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1064,plain,
! [SV244: $i,SV235: $i] :
( ( ( ~ ( left_apart_point @ SV235 @ SV244 ) )
= $true )
| ( ( apart_point_and_line @ SV235 @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1065,plain,
! [SV245: $i,SV236: $i] :
( ( ( ~ ( right_apart_point @ SV236 @ SV245 ) )
= $true )
| ( ( apart_point_and_line @ SV236 @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1066,plain,
! [SV223: $i,SV198: $i] :
( ( ( unequally_directed_lines @ SV198 @ ( reverse_line @ SV223 ) )
= $false )
| ( ( unequally_directed_lines @ SV198 @ SV223 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV198 @ SV223 ) @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1067,plain,
! [SV224: $i,SV199: $i] :
( ( ( unequally_directed_lines @ SV199 @ ( reverse_line @ SV224 ) )
= $false )
| ( ( unequally_directed_lines @ SV199 @ SV224 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV199 @ SV224 ) @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1068,plain,
! [SV231: $i,SV206: $i] :
( ( ( unequally_directed_opposite_lines @ SV206 @ SV231 )
= $false )
| ( ( unequally_directed_lines @ SV206 @ SV231 )
= $false )
| ( ( convergent_lines @ SV206 @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1069,plain,
! [SV246: $i,SV237: $i] :
( ( ( ~ ( convergent_lines @ SV237 @ SV246 ) )
= $true )
| ( ( unequally_directed_lines @ SV237 @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1070,plain,
! [SV247: $i,SV238: $i] :
( ( ( ~ ( convergent_lines @ SV238 @ SV247 ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV238 @ SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1071,plain,
! [SV166: $i] :
( ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1072,plain,
! [SV166: $i] :
( ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1073,plain,
! [SV166: $i] :
( ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1074,plain,
! [SV166: $i] :
( ( ~ ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1075,plain,
! [SV248: $i,SV253: $i,SV166: $i] :
( ( ~ ( left_apart_point @ SV166 @ SV253 )
| ~ ( right_apart_point @ SV248 @ SV253 )
| ( divides_points @ SV253 @ SV166 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1076,plain,
! [SV166: $i,SV254: $i,SV249: $i] :
( ( ~ ( left_apart_point @ SV249 @ SV254 )
| ~ ( right_apart_point @ SV166 @ SV254 )
| ( divides_points @ SV254 @ SV166 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1077,plain,
! [SV173: $i,SV151: $i] :
( ( ( unequally_directed_lines @ SV151 @ ( reverse_line @ SV173 ) )
= $false )
| ( ( line @ SV173 )
= $false )
| ( ( line @ SV151 )
= $false )
| ( ( unequally_directed_lines @ SV151 @ SV173 )
= $false )
| ( ( point @ ( intersection_point @ SV151 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1078,plain,
! [SV184: $i,SV178: $i,SV188: $i,SV158: $i] :
( ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1079,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1080,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1081,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1082,plain,
! [SV183: $i,SV163: $i] :
( ( ~ ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1083,plain,
! [SV255: $i,SV250: $i,SV183: $i,SV163: $i] :
( ( ~ ( before_on_line @ SV163 @ SV183 @ SV250 )
| ~ ( before_on_line @ SV163 @ SV250 @ SV255 )
| ( between_on_line @ SV163 @ SV183 @ SV250 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1084,plain,
! [SV183: $i,SV251: $i,SV256: $i,SV163: $i] :
( ( ~ ( before_on_line @ SV163 @ SV256 @ SV251 )
| ~ ( before_on_line @ SV163 @ SV251 @ SV183 )
| ( between_on_line @ SV163 @ SV183 @ SV251 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1085,plain,
! [SV239: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV239 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) ) )
= $true )
| ( ( ! [SY337: $i] :
( ( unequally_directed_lines @ SV164 @ SY337 )
| ( unequally_directed_lines @ SV239 @ SY337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1086,plain,
! [SV240: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV240 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) ) )
= $true )
| ( ( ! [SY338: $i] :
( ( unequally_directed_lines @ SV164 @ SY338 )
| ( unequally_directed_lines @ SV240 @ ( reverse_line @ SY338 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1087,plain,
! [SV241: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV241 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) ) )
= $true )
| ( ( ! [SY339: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY339 ) )
| ( unequally_directed_lines @ SV241 @ SY339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1088,plain,
! [SV242: $i,SV164: $i] :
( ( ( ~ ( unequally_directed_lines @ SV164 @ SV242 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY340 ) )
| ( unequally_directed_lines @ SV242 @ ( reverse_line @ SY340 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1089,plain,
! [SV165: $i,SV234: $i,SV217: $i] :
( ( ( ~ ( distinct_points @ SV217 @ SV234 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV217 @ SV165 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV234 @ SV165 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1090,plain,
! [SV165: $i] :
( ( ~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1091,plain,
! [SV165: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ( before_on_line @ SV165 @ SY274 @ SY275 )
| ( incident_point_and_line @ SY275 @ SV165 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1092,plain,
! [SV252: $i,SV243: $i,SV165: $i] :
( ( ( ~ ( before_on_line @ SV165 @ SV243 @ SV252 ) )
= $true )
| ( ( equally_directed_lines @ SV165 @ ( line_connecting @ SV243 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1093,plain,
! [SV244: $i,SV235: $i] :
( ( ( left_apart_point @ SV235 @ SV244 )
= $false )
| ( ( apart_point_and_line @ SV235 @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1094,plain,
! [SV245: $i,SV236: $i] :
( ( ( right_apart_point @ SV236 @ SV245 )
= $false )
| ( ( apart_point_and_line @ SV236 @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1095,plain,
! [SV223: $i,SV198: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV198 @ SV223 ) @ SV198 )
= $false )
| ( ( unequally_directed_lines @ SV198 @ SV223 )
= $false )
| ( ( unequally_directed_lines @ SV198 @ ( reverse_line @ SV223 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1096,plain,
! [SV224: $i,SV199: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV199 @ SV224 ) @ SV224 )
= $false )
| ( ( unequally_directed_lines @ SV199 @ SV224 )
= $false )
| ( ( unequally_directed_lines @ SV199 @ ( reverse_line @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1097,plain,
! [SV246: $i,SV237: $i] :
( ( ( convergent_lines @ SV237 @ SV246 )
= $false )
| ( ( unequally_directed_lines @ SV237 @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1098,plain,
! [SV247: $i,SV238: $i] :
( ( ( convergent_lines @ SV238 @ SV247 )
= $false )
| ( ( unequally_directed_opposite_lines @ SV238 @ SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1099,plain,
! [SV166: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ( divides_points @ SY279 @ SV166 @ SY278 )
| ( left_apart_point @ SV166 @ SY279 )
| ( left_apart_point @ SY278 @ SY279 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1100,plain,
! [SV166: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( divides_points @ SY281 @ SV166 @ SY280 )
| ( left_apart_point @ SV166 @ SY281 )
| ( right_apart_point @ SV166 @ SY281 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1101,plain,
! [SV166: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ~ ( divides_points @ SY283 @ SV166 @ SY282 )
| ( right_apart_point @ SY282 @ SY283 )
| ( left_apart_point @ SY282 @ SY283 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1102,plain,
! [SV166: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ( divides_points @ SY285 @ SV166 @ SY284 )
| ( right_apart_point @ SY284 @ SY285 )
| ( right_apart_point @ SV166 @ SY285 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1103,plain,
! [SV248: $i,SV253: $i,SV166: $i] :
( ( ( ~ ( left_apart_point @ SV166 @ SV253 )
| ~ ( right_apart_point @ SV248 @ SV253 ) )
= $true )
| ( ( divides_points @ SV253 @ SV166 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1104,plain,
! [SV166: $i,SV254: $i,SV249: $i] :
( ( ( ~ ( left_apart_point @ SV249 @ SV254 )
| ~ ( right_apart_point @ SV166 @ SV254 ) )
= $true )
| ( ( divides_points @ SV254 @ SV166 @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1105,plain,
! [SV188: $i,SV158: $i,SV184: $i,SV178: $i] :
( ( ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
| ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1106,plain,
! [SV183: $i,SV163: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY299 @ SY300 )
| ( before_on_line @ SV163 @ SV183 @ SY299 )
| ( before_on_line @ SV163 @ SY300 @ SY299 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1107,plain,
! [SV183: $i,SV163: $i] :
( ( ! [SY301: $i] :
( ! [SY302: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SY301 @ SY302 )
| ( before_on_line @ SV163 @ SV183 @ SY301 )
| ( before_on_line @ SV163 @ SY301 @ SV183 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1108,plain,
! [SV183: $i,SV163: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY303 @ SY304 )
| ( before_on_line @ SV163 @ SY304 @ SY303 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1109,plain,
! [SV183: $i,SV163: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SY306 )
| ( before_on_line @ SV163 @ SY305 @ SV183 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1110,plain,
! [SV255: $i,SV250: $i,SV183: $i,SV163: $i] :
( ( ( ~ ( before_on_line @ SV163 @ SV183 @ SV250 )
| ~ ( before_on_line @ SV163 @ SV250 @ SV255 ) )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV250 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1111,plain,
! [SV183: $i,SV251: $i,SV256: $i,SV163: $i] :
( ( ( ~ ( before_on_line @ SV163 @ SV256 @ SV251 )
| ~ ( before_on_line @ SV163 @ SV251 @ SV183 ) )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV251 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1112,plain,
! [SV239: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ SV239 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) ) )
= $true )
| ( ( ! [SY337: $i] :
( ( unequally_directed_lines @ SV164 @ SY337 )
| ( unequally_directed_lines @ SV239 @ SY337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1113,plain,
! [SV240: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ SV240 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) ) )
= $true )
| ( ( ! [SY338: $i] :
( ( unequally_directed_lines @ SV164 @ SY338 )
| ( unequally_directed_lines @ SV240 @ ( reverse_line @ SY338 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1114,plain,
! [SV241: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ SV241 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) ) )
= $true )
| ( ( ! [SY339: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY339 ) )
| ( unequally_directed_lines @ SV241 @ SY339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1115,plain,
! [SV242: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ SV242 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY340 ) )
| ( unequally_directed_lines @ SV242 @ ( reverse_line @ SY340 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1116,plain,
! [SV165: $i,SV234: $i,SV217: $i] :
( ( ( distinct_points @ SV217 @ SV234 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV217 @ SV165 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV234 @ SV165 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1117,plain,
! [SV165: $i] :
( ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) )
| ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1118,plain,
! [SV257: $i,SV165: $i] :
( ( ! [SY346: $i] :
( ~ ( before_on_line @ SV165 @ SV257 @ SY346 )
| ( incident_point_and_line @ SY346 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1119,plain,
! [SV252: $i,SV243: $i,SV165: $i] :
( ( ( before_on_line @ SV165 @ SV243 @ SV252 )
= $false )
| ( ( equally_directed_lines @ SV165 @ ( line_connecting @ SV243 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1120,plain,
! [SV258: $i,SV166: $i] :
( ( ! [SY347: $i] :
( ~ ( divides_points @ SY347 @ SV166 @ SV258 )
| ( left_apart_point @ SV166 @ SY347 )
| ( left_apart_point @ SV258 @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1121,plain,
! [SV259: $i,SV166: $i] :
( ( ! [SY348: $i] :
( ~ ( divides_points @ SY348 @ SV166 @ SV259 )
| ( left_apart_point @ SV166 @ SY348 )
| ( right_apart_point @ SV166 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1122,plain,
! [SV260: $i,SV166: $i] :
( ( ! [SY349: $i] :
( ~ ( divides_points @ SY349 @ SV166 @ SV260 )
| ( right_apart_point @ SV260 @ SY349 )
| ( left_apart_point @ SV260 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1123,plain,
! [SV261: $i,SV166: $i] :
( ( ! [SY350: $i] :
( ~ ( divides_points @ SY350 @ SV166 @ SV261 )
| ( right_apart_point @ SV261 @ SY350 )
| ( right_apart_point @ SV166 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1124,plain,
! [SV248: $i,SV253: $i,SV166: $i] :
( ( ( ~ ( left_apart_point @ SV166 @ SV253 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV248 @ SV253 ) )
= $true )
| ( ( divides_points @ SV253 @ SV166 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1125,plain,
! [SV166: $i,SV254: $i,SV249: $i] :
( ( ( ~ ( left_apart_point @ SV249 @ SV254 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV166 @ SV254 ) )
= $true )
| ( ( divides_points @ SV254 @ SV166 @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1126,plain,
! [SV188: $i,SV178: $i,SV184: $i,SV158: $i] :
( ( ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( ( left_apart_point @ SV178 @ SV188 )
| ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1127,plain,
! [SV262: $i,SV183: $i,SV163: $i] :
( ( ! [SY351: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SV262 @ SY351 )
| ( before_on_line @ SV163 @ SV183 @ SV262 )
| ( before_on_line @ SV163 @ SY351 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1128,plain,
! [SV263: $i,SV183: $i,SV163: $i] :
( ( ! [SY352: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SV263 @ SY352 )
| ( before_on_line @ SV163 @ SV183 @ SV263 )
| ( before_on_line @ SV163 @ SV263 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1129,plain,
! [SV264: $i,SV183: $i,SV163: $i] :
( ( ! [SY353: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SV264 @ SY353 )
| ( before_on_line @ SV163 @ SV264 @ SY353 )
| ( before_on_line @ SV163 @ SY353 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1130,plain,
! [SV265: $i,SV183: $i,SV163: $i] :
( ( ! [SY354: $i] :
( ~ ( between_on_line @ SV163 @ SV183 @ SV265 @ SY354 )
| ( before_on_line @ SV163 @ SV265 @ SY354 )
| ( before_on_line @ SV163 @ SV265 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1131,plain,
! [SV255: $i,SV250: $i,SV183: $i,SV163: $i] :
( ( ( ~ ( before_on_line @ SV163 @ SV183 @ SV250 ) )
= $true )
| ( ( ~ ( before_on_line @ SV163 @ SV250 @ SV255 ) )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV250 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1132,plain,
! [SV183: $i,SV251: $i,SV256: $i,SV163: $i] :
( ( ( ~ ( before_on_line @ SV163 @ SV256 @ SV251 ) )
= $true )
| ( ( ~ ( before_on_line @ SV163 @ SV251 @ SV183 ) )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV251 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1133,plain,
! [SV239: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) )
= $false )
| ( ( unequally_directed_lines @ SV164 @ SV239 )
= $false )
| ( ( ! [SY337: $i] :
( ( unequally_directed_lines @ SV164 @ SY337 )
| ( unequally_directed_lines @ SV239 @ SY337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1134,plain,
! [SV240: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) )
= $false )
| ( ( unequally_directed_lines @ SV164 @ SV240 )
= $false )
| ( ( ! [SY338: $i] :
( ( unequally_directed_lines @ SV164 @ SY338 )
| ( unequally_directed_lines @ SV240 @ ( reverse_line @ SY338 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1135,plain,
! [SV241: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) )
= $false )
| ( ( unequally_directed_lines @ SV164 @ SV241 )
= $false )
| ( ( ! [SY339: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY339 ) )
| ( unequally_directed_lines @ SV241 @ SY339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1136,plain,
! [SV242: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) )
= $false )
| ( ( unequally_directed_lines @ SV164 @ SV242 )
= $false )
| ( ( ! [SY340: $i] :
( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SY340 ) )
| ( unequally_directed_lines @ SV242 @ ( reverse_line @ SY340 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1137,plain,
! [SV234: $i,SV165: $i,SV217: $i] :
( ( ( incident_point_and_line @ SV217 @ SV165 )
= $false )
| ( ( distinct_points @ SV217 @ SV234 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV234 @ SV165 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1138,plain,
! [SV165: $i] :
( ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1139,plain,
! [SV165: $i] :
( ( ~ ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1140,plain,
! [SV266: $i,SV257: $i,SV165: $i] :
( ( ~ ( before_on_line @ SV165 @ SV257 @ SV266 )
| ( incident_point_and_line @ SV266 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1141,plain,
! [SV258: $i,SV166: $i,SV267: $i] :
( ( ~ ( divides_points @ SV267 @ SV166 @ SV258 )
| ( left_apart_point @ SV166 @ SV267 )
| ( left_apart_point @ SV258 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1142,plain,
! [SV259: $i,SV166: $i,SV268: $i] :
( ( ~ ( divides_points @ SV268 @ SV166 @ SV259 )
| ( left_apart_point @ SV166 @ SV268 )
| ( right_apart_point @ SV166 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1143,plain,
! [SV260: $i,SV166: $i,SV269: $i] :
( ( ~ ( divides_points @ SV269 @ SV166 @ SV260 )
| ( right_apart_point @ SV260 @ SV269 )
| ( left_apart_point @ SV260 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1144,plain,
! [SV261: $i,SV166: $i,SV270: $i] :
( ( ~ ( divides_points @ SV270 @ SV166 @ SV261 )
| ( right_apart_point @ SV261 @ SV270 )
| ( right_apart_point @ SV166 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1145,plain,
! [SV248: $i,SV253: $i,SV166: $i] :
( ( ( left_apart_point @ SV166 @ SV253 )
= $false )
| ( ( ~ ( right_apart_point @ SV248 @ SV253 ) )
= $true )
| ( ( divides_points @ SV253 @ SV166 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1146,plain,
! [SV166: $i,SV254: $i,SV249: $i] :
( ( ( left_apart_point @ SV249 @ SV254 )
= $false )
| ( ( ~ ( right_apart_point @ SV166 @ SV254 ) )
= $true )
| ( ( divides_points @ SV254 @ SV166 @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1147,plain,
! [SV184: $i,SV158: $i,SV188: $i,SV178: $i] :
( ( ( left_apart_point @ SV178 @ SV188 )
= $true )
| ( ( ( left_apart_point @ SV158 @ SV188 )
| ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1148,plain,
! [SV271: $i,SV262: $i,SV183: $i,SV163: $i] :
( ( ~ ( between_on_line @ SV163 @ SV183 @ SV262 @ SV271 )
| ( before_on_line @ SV163 @ SV183 @ SV262 )
| ( before_on_line @ SV163 @ SV271 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1149,plain,
! [SV263: $i,SV183: $i,SV163: $i] :
( ( ( ! [SY352: $i] :
~ ( between_on_line @ SV163 @ SV183 @ SV263 @ SY352 ) )
= $true )
| ( ( ( before_on_line @ SV163 @ SV183 @ SV263 )
| ( before_on_line @ SV163 @ SV263 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1150,plain,
! [SV272: $i,SV264: $i,SV183: $i,SV163: $i] :
( ( ~ ( between_on_line @ SV163 @ SV183 @ SV264 @ SV272 )
| ( before_on_line @ SV163 @ SV264 @ SV272 )
| ( before_on_line @ SV163 @ SV272 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1151,plain,
! [SV273: $i,SV265: $i,SV183: $i,SV163: $i] :
( ( ~ ( between_on_line @ SV163 @ SV183 @ SV265 @ SV273 )
| ( before_on_line @ SV163 @ SV265 @ SV273 )
| ( before_on_line @ SV163 @ SV265 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1152,plain,
! [SV255: $i,SV250: $i,SV183: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV183 @ SV250 )
= $false )
| ( ( ~ ( before_on_line @ SV163 @ SV250 @ SV255 ) )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV250 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1153,plain,
! [SV183: $i,SV251: $i,SV256: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV256 @ SV251 )
= $false )
| ( ( ~ ( before_on_line @ SV163 @ SV251 @ SV183 ) )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV251 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1154,plain,
! [SV239: $i,SV274: $i,SV164: $i] :
( ( ( ( unequally_directed_lines @ SV164 @ SV274 )
| ( unequally_directed_lines @ SV239 @ SV274 ) )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV239 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1155,plain,
! [SV240: $i,SV275: $i,SV164: $i] :
( ( ( ( unequally_directed_lines @ SV164 @ SV275 )
| ( unequally_directed_lines @ SV240 @ ( reverse_line @ SV275 ) ) )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV240 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1156,plain,
! [SV241: $i,SV276: $i,SV164: $i] :
( ( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV276 ) )
| ( unequally_directed_lines @ SV241 @ SV276 ) )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV241 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1157,plain,
! [SV242: $i,SV277: $i,SV164: $i] :
( ( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV277 ) )
| ( unequally_directed_lines @ SV242 @ ( reverse_line @ SV277 ) ) )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV242 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1158,plain,
! [SV217: $i,SV165: $i,SV234: $i] :
( ( ( incident_point_and_line @ SV234 @ SV165 )
= $false )
| ( ( distinct_points @ SV217 @ SV234 )
= $false )
| ( ( incident_point_and_line @ SV217 @ SV165 )
= $false )
| ( ( ~ ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) ) )
= $true )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1159,plain,
! [SV165: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( before_on_line @ SV165 @ SY270 @ SY271 )
| ( distinct_points @ SY270 @ SY271 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1160,plain,
! [SV165: $i] :
( ( ! [SY272: $i] :
( ! [SY273: $i] :
~ ( before_on_line @ SV165 @ SY272 @ SY273 )
| ( incident_point_and_line @ SY272 @ SV165 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1161,plain,
! [SV266: $i,SV257: $i,SV165: $i] :
( ( ( ~ ( before_on_line @ SV165 @ SV257 @ SV266 ) )
= $true )
| ( ( incident_point_and_line @ SV266 @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1162,plain,
! [SV258: $i,SV166: $i,SV267: $i] :
( ( ( ~ ( divides_points @ SV267 @ SV166 @ SV258 ) )
= $true )
| ( ( ( left_apart_point @ SV166 @ SV267 )
| ( left_apart_point @ SV258 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1163,plain,
! [SV259: $i,SV166: $i,SV268: $i] :
( ( ( ~ ( divides_points @ SV268 @ SV166 @ SV259 ) )
= $true )
| ( ( ( left_apart_point @ SV166 @ SV268 )
| ( right_apart_point @ SV166 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1164,plain,
! [SV260: $i,SV166: $i,SV269: $i] :
( ( ( ~ ( divides_points @ SV269 @ SV166 @ SV260 ) )
= $true )
| ( ( ( right_apart_point @ SV260 @ SV269 )
| ( left_apart_point @ SV260 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1165,plain,
! [SV261: $i,SV166: $i,SV270: $i] :
( ( ( ~ ( divides_points @ SV270 @ SV166 @ SV261 ) )
= $true )
| ( ( ( right_apart_point @ SV261 @ SV270 )
| ( right_apart_point @ SV166 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1166,plain,
! [SV166: $i,SV253: $i,SV248: $i] :
( ( ( right_apart_point @ SV248 @ SV253 )
= $false )
| ( ( left_apart_point @ SV166 @ SV253 )
= $false )
| ( ( divides_points @ SV253 @ SV166 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1167,plain,
! [SV249: $i,SV254: $i,SV166: $i] :
( ( ( right_apart_point @ SV166 @ SV254 )
= $false )
| ( ( left_apart_point @ SV249 @ SV254 )
= $false )
| ( ( divides_points @ SV254 @ SV166 @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1168,plain,
! [SV178: $i,SV184: $i,SV188: $i,SV158: $i] :
( ( ( left_apart_point @ SV158 @ SV188 )
= $true )
| ( ( ( left_apart_point @ SV158 @ SV184 )
| ( left_apart_point @ SV178 @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV178 @ SV188 )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1169,plain,
! [SV271: $i,SV262: $i,SV183: $i,SV163: $i] :
( ( ( ~ ( between_on_line @ SV163 @ SV183 @ SV262 @ SV271 ) )
= $true )
| ( ( ( before_on_line @ SV163 @ SV183 @ SV262 )
| ( before_on_line @ SV163 @ SV271 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1170,plain,
! [SV278: $i,SV263: $i,SV183: $i,SV163: $i] :
( ( ( ~ ( between_on_line @ SV163 @ SV183 @ SV263 @ SV278 ) )
= $true )
| ( ( ( before_on_line @ SV163 @ SV183 @ SV263 )
| ( before_on_line @ SV163 @ SV263 @ SV183 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1171,plain,
! [SV272: $i,SV264: $i,SV183: $i,SV163: $i] :
( ( ( ~ ( between_on_line @ SV163 @ SV183 @ SV264 @ SV272 ) )
= $true )
| ( ( ( before_on_line @ SV163 @ SV264 @ SV272 )
| ( before_on_line @ SV163 @ SV272 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1172,plain,
! [SV273: $i,SV265: $i,SV183: $i,SV163: $i] :
( ( ( ~ ( between_on_line @ SV163 @ SV183 @ SV265 @ SV273 ) )
= $true )
| ( ( ( before_on_line @ SV163 @ SV265 @ SV273 )
| ( before_on_line @ SV163 @ SV265 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1173,plain,
! [SV183: $i,SV255: $i,SV250: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV250 @ SV255 )
= $false )
| ( ( before_on_line @ SV163 @ SV183 @ SV250 )
= $false )
| ( ( between_on_line @ SV163 @ SV183 @ SV250 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1174,plain,
! [SV256: $i,SV183: $i,SV251: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV251 @ SV183 )
= $false )
| ( ( before_on_line @ SV163 @ SV256 @ SV251 )
= $false )
| ( ( between_on_line @ SV163 @ SV183 @ SV251 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1175,plain,
! [SV239: $i,SV274: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ SV274 )
= $true )
| ( ( unequally_directed_lines @ SV239 @ SV274 )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV239 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV239 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1176,plain,
! [SV240: $i,SV275: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ SV275 )
= $true )
| ( ( unequally_directed_lines @ SV240 @ ( reverse_line @ SV275 ) )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV240 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV240 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1177,plain,
! [SV241: $i,SV276: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV276 ) )
= $true )
| ( ( unequally_directed_lines @ SV241 @ SV276 )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV241 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV241 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1178,plain,
! [SV242: $i,SV277: $i,SV164: $i] :
( ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV277 ) )
= $true )
| ( ( unequally_directed_lines @ SV242 @ ( reverse_line @ SV277 ) )
= $true )
| ( ( unequally_directed_lines @ SV164 @ SV242 )
= $false )
| ( ( unequally_directed_lines @ SV164 @ ( reverse_line @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1179,plain,
! [SV234: $i,SV217: $i,SV165: $i] :
( ( ( equally_directed_lines @ SV165 @ ( line_connecting @ SV217 @ SV234 ) )
= $false )
| ( ( incident_point_and_line @ SV217 @ SV165 )
= $false )
| ( ( distinct_points @ SV217 @ SV234 )
= $false )
| ( ( incident_point_and_line @ SV234 @ SV165 )
= $false )
| ( ( before_on_line @ SV165 @ SV217 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1180,plain,
! [SV279: $i,SV165: $i] :
( ( ! [SY355: $i] :
( ~ ( before_on_line @ SV165 @ SV279 @ SY355 )
| ( distinct_points @ SV279 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1181,plain,
! [SV280: $i,SV165: $i] :
( ( ! [SY356: $i] :
~ ( before_on_line @ SV165 @ SV280 @ SY356 )
| ( incident_point_and_line @ SV280 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1182,plain,
! [SV266: $i,SV257: $i,SV165: $i] :
( ( ( before_on_line @ SV165 @ SV257 @ SV266 )
= $false )
| ( ( incident_point_and_line @ SV266 @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1183,plain,
! [SV258: $i,SV166: $i,SV267: $i] :
( ( ( divides_points @ SV267 @ SV166 @ SV258 )
= $false )
| ( ( ( left_apart_point @ SV166 @ SV267 )
| ( left_apart_point @ SV258 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1184,plain,
! [SV259: $i,SV166: $i,SV268: $i] :
( ( ( divides_points @ SV268 @ SV166 @ SV259 )
= $false )
| ( ( ( left_apart_point @ SV166 @ SV268 )
| ( right_apart_point @ SV166 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1185,plain,
! [SV260: $i,SV166: $i,SV269: $i] :
( ( ( divides_points @ SV269 @ SV166 @ SV260 )
= $false )
| ( ( ( right_apart_point @ SV260 @ SV269 )
| ( left_apart_point @ SV260 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1186,plain,
! [SV261: $i,SV166: $i,SV270: $i] :
( ( ( divides_points @ SV270 @ SV166 @ SV261 )
= $false )
| ( ( ( right_apart_point @ SV261 @ SV270 )
| ( right_apart_point @ SV166 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1187,plain,
! [SV188: $i,SV178: $i,SV184: $i,SV158: $i] :
( ( ( left_apart_point @ SV158 @ SV184 )
= $true )
| ( ( left_apart_point @ SV178 @ SV184 )
= $true )
| ( ( left_apart_point @ SV158 @ SV188 )
= $true )
| ( ( left_apart_point @ SV178 @ SV188 )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV184 ) )
= $true )
| ( ( left_apart_point @ SV158 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( left_apart_point @ SV178 @ ( reverse_line @ SV188 ) )
= $true )
| ( ( distinct_lines @ SV184 @ SV188 )
= $false )
| ( ( distinct_points @ SV158 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1188,plain,
! [SV271: $i,SV262: $i,SV183: $i,SV163: $i] :
( ( ( between_on_line @ SV163 @ SV183 @ SV262 @ SV271 )
= $false )
| ( ( ( before_on_line @ SV163 @ SV183 @ SV262 )
| ( before_on_line @ SV163 @ SV271 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1189,plain,
! [SV278: $i,SV263: $i,SV183: $i,SV163: $i] :
( ( ( between_on_line @ SV163 @ SV183 @ SV263 @ SV278 )
= $false )
| ( ( ( before_on_line @ SV163 @ SV183 @ SV263 )
| ( before_on_line @ SV163 @ SV263 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1190,plain,
! [SV272: $i,SV264: $i,SV183: $i,SV163: $i] :
( ( ( between_on_line @ SV163 @ SV183 @ SV264 @ SV272 )
= $false )
| ( ( ( before_on_line @ SV163 @ SV264 @ SV272 )
| ( before_on_line @ SV163 @ SV272 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1191,plain,
! [SV273: $i,SV265: $i,SV183: $i,SV163: $i] :
( ( ( between_on_line @ SV163 @ SV183 @ SV265 @ SV273 )
= $false )
| ( ( ( before_on_line @ SV163 @ SV265 @ SV273 )
| ( before_on_line @ SV163 @ SV265 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1192,plain,
! [SV281: $i,SV279: $i,SV165: $i] :
( ( ~ ( before_on_line @ SV165 @ SV279 @ SV281 )
| ( distinct_points @ SV279 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1193,plain,
! [SV280: $i,SV165: $i] :
( ( ( ! [SY356: $i] :
~ ( before_on_line @ SV165 @ SV280 @ SY356 ) )
= $true )
| ( ( incident_point_and_line @ SV280 @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1194,plain,
! [SV258: $i,SV267: $i,SV166: $i] :
( ( ( left_apart_point @ SV166 @ SV267 )
= $true )
| ( ( left_apart_point @ SV258 @ SV267 )
= $true )
| ( ( divides_points @ SV267 @ SV166 @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1195,plain,
! [SV259: $i,SV268: $i,SV166: $i] :
( ( ( left_apart_point @ SV166 @ SV268 )
= $true )
| ( ( right_apart_point @ SV166 @ SV268 )
= $true )
| ( ( divides_points @ SV268 @ SV166 @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1196,plain,
! [SV166: $i,SV269: $i,SV260: $i] :
( ( ( right_apart_point @ SV260 @ SV269 )
= $true )
| ( ( left_apart_point @ SV260 @ SV269 )
= $true )
| ( ( divides_points @ SV269 @ SV166 @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1197,plain,
! [SV166: $i,SV270: $i,SV261: $i] :
( ( ( right_apart_point @ SV261 @ SV270 )
= $true )
| ( ( right_apart_point @ SV166 @ SV270 )
= $true )
| ( ( divides_points @ SV270 @ SV166 @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1198,plain,
! [SV271: $i,SV262: $i,SV183: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV183 @ SV262 )
= $true )
| ( ( before_on_line @ SV163 @ SV271 @ SV262 )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV262 @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1199,plain,
! [SV278: $i,SV263: $i,SV183: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV183 @ SV263 )
= $true )
| ( ( before_on_line @ SV163 @ SV263 @ SV183 )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV263 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1200,plain,
! [SV183: $i,SV272: $i,SV264: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV264 @ SV272 )
= $true )
| ( ( before_on_line @ SV163 @ SV272 @ SV264 )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV264 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1201,plain,
! [SV183: $i,SV273: $i,SV265: $i,SV163: $i] :
( ( ( before_on_line @ SV163 @ SV265 @ SV273 )
= $true )
| ( ( before_on_line @ SV163 @ SV265 @ SV183 )
= $true )
| ( ( between_on_line @ SV163 @ SV183 @ SV265 @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1202,plain,
! [SV281: $i,SV279: $i,SV165: $i] :
( ( ( ~ ( before_on_line @ SV165 @ SV279 @ SV281 ) )
= $true )
| ( ( distinct_points @ SV279 @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1203,plain,
! [SV282: $i,SV280: $i,SV165: $i] :
( ( ( ~ ( before_on_line @ SV165 @ SV280 @ SV282 ) )
= $true )
| ( ( incident_point_and_line @ SV280 @ SV165 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1204,plain,
! [SV281: $i,SV279: $i,SV165: $i] :
( ( ( before_on_line @ SV165 @ SV279 @ SV281 )
= $false )
| ( ( distinct_points @ SV279 @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1205,plain,
! [SV282: $i,SV280: $i,SV165: $i] :
( ( ( before_on_line @ SV165 @ SV280 @ SV282 )
= $false )
| ( ( incident_point_and_line @ SV280 @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1206,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[697,1205,1204,1201,1200,1199,1198,1197,1196,1195,1194,1187,1182,1179,1178,1177,1176,1175,1174,1173,1167,1166,1119,1098,1097,1096,1095,1094,1093,1077,1068,1045,1044,1038,1035,1034,1022,1021,1018,1008,1007,992,991,990,989,979,969,968,965,964,961,956,941,939,936,932,931,930,850,807,806,801,766,764,754,752,736,719,698]) ).
thf(1207,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1206,660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO252+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 18:43:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.37
% 0.18/0.37 No.of.Axioms: 36
% 0.18/0.37
% 0.18/0.37 Length.of.Defs: 0
% 0.18/0.37
% 0.18/0.37 Contains.Choice.Funs: false
% 0.18/0.38 .
% 0.18/0.40 (rf:0,axioms:36,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:38,loop_count:0,foatp_calls:0,translation:fof_full)............................................................................
% 0.56/0.77
% 0.56/0.77 ********************************
% 0.56/0.77 * All subproblems solved! *
% 0.56/0.77 ********************************
% 0.56/0.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:38,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1206,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.89/1.12
% 0.89/1.12 %**** Beginning of derivation protocol ****
% 0.89/1.12 % SZS output start CNFRefutation
% See solution above
% 0.89/1.13
% 0.89/1.13 %**** End of derivation protocol ****
% 0.89/1.13 %**** no. of clauses in derivation: 1207 ****
% 0.89/1.13 %**** clause counter: 1206 ****
% 0.89/1.13
% 0.89/1.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:38,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1206,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------