%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:18:44 AM UTC 2026
% Result : Theorem 1.11s 0.52s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 37
% Syntax : Number of formulae : 566 ( 272 unt; 0 typ; 0 def)
% Number of atoms : 4119 (1004 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 8376 (1574 ~;1338 |; 117 &;5257 @)
% ( 30 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 8 con; 0-4 aty)
% Number of variables : 1405 ( 0 ^;1405 !; 0 ?;1405 :)
% 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_L,type,
sK1_L: $i ).
thf(tp_sK2_SY87,type,
sK2_SY87: $i ).
thf(tp_sK3_SY92,type,
sK3_SY92: $i ).
thf(tp_sK4_SY96,type,
sK4_SY96: $i ).
thf(tp_sK5_SY99,type,
sK5_SY99: $i ).
thf(tp_sK6_SY101,type,
sK6_SY101: $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,
! [L: $i,M: $i,N: $i,A: $i,B: $i,C: $i] :
( ( ( between_on_line @ L @ A @ B @ C )
& ( convergent_lines @ L @ M )
& ( incident_point_and_line @ B @ M )
& ( convergent_lines @ L @ N )
& ( convergent_lines @ M @ N )
& ( incident_point_and_line @ B @ N ) )
=> ( between_on_line @ M @ ( intersection_point @ M @ ( parallel_through_point @ N @ A ) ) @ B @ ( intersection_point @ M @ ( parallel_through_point @ N @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [L: $i,M: $i,N: $i,A: $i,B: $i,C: $i] :
( ( ( between_on_line @ L @ A @ B @ C )
& ( convergent_lines @ L @ M )
& ( incident_point_and_line @ B @ M )
& ( convergent_lines @ L @ N )
& ( convergent_lines @ M @ N )
& ( incident_point_and_line @ B @ N ) )
=> ( between_on_line @ M @ ( intersection_point @ M @ ( parallel_through_point @ N @ A ) ) @ B @ ( intersection_point @ M @ ( parallel_through_point @ N @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [L: $i,M: $i,N: $i,A: $i,B: $i,C: $i] :
( ( ( between_on_line @ L @ A @ B @ C )
& ( convergent_lines @ L @ M )
& ( incident_point_and_line @ B @ M )
& ( convergent_lines @ L @ N )
& ( convergent_lines @ M @ N )
& ( incident_point_and_line @ B @ N ) )
=> ( between_on_line @ M @ ( intersection_point @ M @ ( parallel_through_point @ N @ A ) ) @ B @ ( intersection_point @ M @ ( parallel_through_point @ N @ C ) ) ) ) )
= $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,
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i,SY91: $i] :
( ( ( between_on_line @ sK1_L @ SY89 @ SY90 @ SY91 )
& ( convergent_lines @ sK1_L @ SY87 )
& ( incident_point_and_line @ SY90 @ SY87 )
& ( convergent_lines @ sK1_L @ SY88 )
& ( convergent_lines @ SY87 @ SY88 )
& ( incident_point_and_line @ SY90 @ SY88 ) )
=> ( between_on_line @ SY87 @ ( intersection_point @ SY87 @ ( parallel_through_point @ SY88 @ SY89 ) ) @ SY90 @ ( intersection_point @ SY87 @ ( parallel_through_point @ SY88 @ SY91 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(77,plain,
( ( ! [SY92: $i,SY93: $i,SY94: $i,SY95: $i] :
( ( ( between_on_line @ sK1_L @ SY93 @ SY94 @ SY95 )
& ( convergent_lines @ sK1_L @ sK2_SY87 )
& ( incident_point_and_line @ SY94 @ sK2_SY87 )
& ( convergent_lines @ sK1_L @ SY92 )
& ( convergent_lines @ sK2_SY87 @ SY92 )
& ( incident_point_and_line @ SY94 @ SY92 ) )
=> ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ SY92 @ SY93 ) ) @ SY94 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ SY92 @ SY95 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(78,plain,
( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ( ( between_on_line @ sK1_L @ SY96 @ SY97 @ SY98 )
& ( convergent_lines @ sK1_L @ sK2_SY87 )
& ( incident_point_and_line @ SY97 @ sK2_SY87 )
& ( convergent_lines @ sK1_L @ sK3_SY92 )
& ( convergent_lines @ sK2_SY87 @ sK3_SY92 )
& ( incident_point_and_line @ SY97 @ sK3_SY92 ) )
=> ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ SY96 ) ) @ SY97 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ SY98 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(79,plain,
( ( ! [SY99: $i,SY100: $i] :
( ( ( between_on_line @ sK1_L @ sK4_SY96 @ SY99 @ SY100 )
& ( convergent_lines @ sK1_L @ sK2_SY87 )
& ( incident_point_and_line @ SY99 @ sK2_SY87 )
& ( convergent_lines @ sK1_L @ sK3_SY92 )
& ( convergent_lines @ sK2_SY87 @ sK3_SY92 )
& ( incident_point_and_line @ SY99 @ sK3_SY92 ) )
=> ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ SY100 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( ! [SY101: $i] :
( ( ( between_on_line @ sK1_L @ sK4_SY96 @ sK5_SY99 @ SY101 )
& ( convergent_lines @ sK1_L @ sK2_SY87 )
& ( incident_point_and_line @ sK5_SY99 @ sK2_SY87 )
& ( convergent_lines @ sK1_L @ sK3_SY92 )
& ( convergent_lines @ sK2_SY87 @ sK3_SY92 )
& ( incident_point_and_line @ sK5_SY99 @ sK3_SY92 ) )
=> ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ sK5_SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ SY101 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(81,plain,
( ( ( ( between_on_line @ sK1_L @ sK4_SY96 @ sK5_SY99 @ sK6_SY101 )
& ( convergent_lines @ sK1_L @ sK2_SY87 )
& ( incident_point_and_line @ sK5_SY99 @ sK2_SY87 )
& ( convergent_lines @ sK1_L @ sK3_SY92 )
& ( convergent_lines @ sK2_SY87 @ sK3_SY92 )
& ( incident_point_and_line @ sK5_SY99 @ sK3_SY92 ) )
=> ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ sK5_SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK6_SY101 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[80]) ).
thf(82,plain,
( ( between_on_line @ sK1_L @ sK4_SY96 @ sK5_SY99 @ sK6_SY101 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(83,plain,
( ( convergent_lines @ sK1_L @ sK2_SY87 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(84,plain,
( ( incident_point_and_line @ sK5_SY99 @ sK2_SY87 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(85,plain,
( ( convergent_lines @ sK1_L @ sK3_SY92 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(86,plain,
( ( convergent_lines @ sK2_SY87 @ sK3_SY92 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(87,plain,
( ( incident_point_and_line @ sK5_SY99 @ sK3_SY92 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(88,plain,
( ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ sK5_SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK6_SY101 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(89,plain,
( ( ~ ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ sK5_SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK6_SY101 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[88]) ).
thf(90,plain,
( ( ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
<=> ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i] :
( ( right_convergent_lines @ X @ Y )
<=> ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(93,plain,
( ( ! [X: $i,Y: $i] :
( ( equally_directed_lines @ X @ Y )
<=> ~ ( unequally_directed_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(94,plain,
( ( ! [X: $i,Y: $i] :
( ( equally_directed_opposite_lines @ X @ Y )
<=> ~ ( unequally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(95,plain,
( ( ! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(96,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
<=> ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_opposite_lines @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(97,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(copy,[status(thm)],[68]) ).
thf(98,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(copy,[status(thm)],[67]) ).
thf(99,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(copy,[status(thm)],[66]) ).
thf(100,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(101,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(102,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(103,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(104,plain,
( ( ! [L: $i] : ( equally_directed_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(105,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(106,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(copy,[status(thm)],[59]) ).
thf(107,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(108,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)],[57]) ).
thf(109,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(110,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(112,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)],[53]) ).
thf(113,plain,
( ( ! [L: $i,A: $i] :
( ( ( point @ A )
& ( line @ L ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(114,plain,
( ( ! [L: $i] :
( ( line @ L )
=> ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(115,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(copy,[status(thm)],[50]) ).
thf(116,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(copy,[status(thm)],[49]) ).
thf(117,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(118,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(119,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)],[46]) ).
thf(120,plain,
( ( ! [A: $i,L: $i] : ( equally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(121,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(copy,[status(thm)],[44]) ).
thf(122,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)],[43]) ).
thf(123,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)],[42]) ).
thf(124,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)],[41]) ).
thf(125,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(126,plain,
( ( incident_point_and_line @ sK5_SY99 @ sK3_SY92 )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(127,plain,
( ( convergent_lines @ sK2_SY87 @ sK3_SY92 )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(128,plain,
( ( convergent_lines @ sK1_L @ sK3_SY92 )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(129,plain,
( ( incident_point_and_line @ sK5_SY99 @ sK2_SY87 )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(130,plain,
( ( convergent_lines @ sK1_L @ sK2_SY87 )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(131,plain,
( ( between_on_line @ sK1_L @ sK4_SY96 @ sK5_SY99 @ sK6_SY101 )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(132,plain,
( ( ~ ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ sK5_SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK6_SY101 ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( ~ ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) )
| ~ ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ( ~ ( ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(135,plain,
( ( ! [SX0: $i] :
( ~ ( line @ SX0 )
| ( line @ ( reverse_line @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(136,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 @ SX2 @ SX3 ) )
| ~ ( ~ ( before_on_line @ SX0 @ SX3 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX1 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX3 ) )
| ~ ( ~ ( 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)],[99]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 ) )
| ~ ( ~ ( right_apart_point @ SX0 @ SX2 )
| ~ ( left_apart_point @ SX1 @ SX2 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 ) )
| ~ ( ~ ( right_apart_point @ SX0 @ SX2 )
| ~ ( left_apart_point @ SX1 @ SX2 ) ) )
| ( divides_points @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX0 @ SX2 )
| ( distinct_points @ SX0 @ SX1 )
| ( left_apart_point @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( line @ SX0 )
| ~ ( line @ SX1 ) )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ( point @ ( intersection_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( point @ SX1 )
| ~ ( line @ SX0 ) )
| ( line @ ( parallel_through_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(142,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 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SX1 @ SX2 )
| ~ ( incident_point_and_line @ SX1 @ SX0 ) )
| ~ ( incident_point_and_line @ SX2 @ SX0 ) )
| ~ ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ( convergent_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SX0 )
| ~ ( point @ SX1 ) )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ( line @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX0 @ SX2 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX1 @ SX2 )
| ~ ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ( left_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( equally_directed_lines @ ( line_connecting @ SX0 @ SX1 ) @ ( reverse_line @ ( line_connecting @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( left_convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX1 @ SX2 )
| ( left_convergent_lines @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( left_apart_point @ SX0 @ SX2 ) )
| ( left_apart_point @ SX1 @ SX2 )
| ( left_convergent_lines @ ( line_connecting @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( left_apart_point @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX1 @ SX2 ) )
| ( distinct_lines @ SX1 @ SX2 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX2 @ SX3 ) )
| ( left_apart_point @ SX0 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 )
| ( left_apart_point @ SX0 @ SX3 )
| ( left_apart_point @ SX1 @ SX3 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX2 ) )
| ( left_apart_point @ SX1 @ ( reverse_line @ SX2 ) )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX3 ) )
| ( left_apart_point @ SX1 @ ( reverse_line @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX2 )
| ( distinct_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(160,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(161,plain,
! [SV2: $i] :
( ( ~ ( distinct_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(162,plain,
! [SV3: $i] :
( ( equally_directed_lines @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(163,plain,
! [SV4: $i] :
( ( ! [SY102: $i] :
( ( unequally_directed_lines @ SV4 @ SY102 )
| ( unequally_directed_lines @ SV4 @ ( reverse_line @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(164,plain,
! [SV5: $i] :
( ( ! [SY103: $i] :
~ ( ( left_apart_point @ SV5 @ SY103 )
| ( left_apart_point @ SV5 @ ( reverse_line @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(165,plain,
! [SV6: $i] :
( ( ! [SY104: $i] :
~ ( ( left_convergent_lines @ SV6 @ SY104 )
| ( left_convergent_lines @ SV6 @ ( reverse_line @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(166,plain,
! [SV7: $i] :
( ( ! [SY105: $i] :
~ ( apart_point_and_line @ SV7 @ ( parallel_through_point @ SY105 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(167,plain,
! [SV8: $i] :
( ( ~ ( distinct_lines @ SV8 @ ( reverse_line @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(168,plain,
! [SV9: $i] :
( ( ! [SY106: $i] : ( equally_directed_lines @ ( parallel_through_point @ SY106 @ SV9 ) @ SY106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(169,plain,
( ( between_on_line @ sK2_SY87 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK4_SY96 ) ) @ sK5_SY99 @ ( intersection_point @ sK2_SY87 @ ( parallel_through_point @ sK3_SY92 @ sK6_SY101 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(170,plain,
! [SV10: $i] :
( ( ! [SY107: $i] :
( ~ ( distinct_points @ SV10 @ SY107 )
| ~ ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SY107 ) )
| ~ ~ ( apart_point_and_line @ SY107 @ ( line_connecting @ SV10 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(171,plain,
! [SV11: $i] :
( ( ! [SY108: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SV11 @ SY108 )
| ( left_apart_point @ SV11 @ SY108 )
| ( right_apart_point @ SV11 @ SY108 ) )
| ~ ( ~ ( ( left_apart_point @ SV11 @ SY108 )
| ( right_apart_point @ SV11 @ SY108 ) )
| ( apart_point_and_line @ SV11 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(172,plain,
! [SV12: $i] :
( ( ~ ( line @ SV12 )
| ( line @ ( reverse_line @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(173,plain,
! [SV13: $i] :
( ( ! [SY109: $i,SY110: $i,SY111: $i] :
~ ( ~ ( ~ ( between_on_line @ SV13 @ SY109 @ SY110 @ SY111 )
| ~ ( ~ ( before_on_line @ SV13 @ SY109 @ SY110 )
| ~ ( before_on_line @ SV13 @ SY110 @ SY111 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SY111 @ SY110 )
| ~ ( before_on_line @ SV13 @ SY110 @ SY109 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SY109 @ SY110 )
| ~ ( before_on_line @ SV13 @ SY110 @ SY111 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SY111 @ SY110 )
| ~ ( before_on_line @ SV13 @ SY110 @ SY109 ) ) )
| ( between_on_line @ SV13 @ SY109 @ SY110 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(174,plain,
! [SV14: $i] :
( ( ! [SY112: $i,SY113: $i] :
~ ( ~ ( ~ ( divides_points @ SY113 @ SV14 @ SY112 )
| ~ ( ~ ( left_apart_point @ SV14 @ SY113 )
| ~ ( right_apart_point @ SY112 @ SY113 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SY113 )
| ~ ( left_apart_point @ SY112 @ SY113 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SY113 )
| ~ ( right_apart_point @ SY112 @ SY113 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SY113 )
| ~ ( left_apart_point @ SY112 @ SY113 ) ) )
| ( divides_points @ SY113 @ SV14 @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(175,plain,
! [SV15: $i] :
( ( ! [SY114: $i] :
~ ( ~ ( ~ ( right_apart_point @ SV15 @ SY114 )
| ( left_apart_point @ SV15 @ ( reverse_line @ SY114 ) ) )
| ~ ( ~ ( left_apart_point @ SV15 @ ( reverse_line @ SY114 ) )
| ( right_apart_point @ SV15 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(176,plain,
! [SV16: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( left_apart_point @ SV16 @ SY116 )
| ( distinct_points @ SV16 @ SY115 )
| ( left_apart_point @ SY115 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(177,plain,
! [SV17: $i] :
( ( ! [SY117: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SY117 ) )
| ~ ( unequally_directed_lines @ SV17 @ SY117 ) )
| ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SY117 ) ) )
| ( point @ ( intersection_point @ SV17 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(178,plain,
! [SV18: $i] :
( ( ! [SY118: $i] :
( ~ ~ ( ~ ( point @ SY118 )
| ~ ( line @ SV18 ) )
| ( line @ ( parallel_through_point @ SV18 @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(179,plain,
! [SV19: $i] :
( ( ! [SY119: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV19 @ SY119 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SY119 ) ) )
| ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SY119 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SY119 ) @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(180,plain,
! [SV20: $i] :
( ( ! [SY120: $i] :
~ ( ~ ( ~ ( unequally_directed_opposite_lines @ SV20 @ SY120 )
| ( unequally_directed_lines @ SV20 @ ( reverse_line @ SY120 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV20 @ ( reverse_line @ SY120 ) )
| ( unequally_directed_opposite_lines @ SV20 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(181,plain,
! [SV21: $i] :
( ( ! [SY121: $i,SY122: $i] :
~ ( ~ ( ~ ( before_on_line @ SV21 @ SY121 @ SY122 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SY121 @ SY122 )
| ~ ( incident_point_and_line @ SY121 @ SV21 ) )
| ~ ( incident_point_and_line @ SY122 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SY121 @ SY122 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SY121 @ SY122 )
| ~ ( incident_point_and_line @ SY121 @ SV21 ) )
| ~ ( incident_point_and_line @ SY122 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SY121 @ SY122 ) ) )
| ( before_on_line @ SV21 @ SY121 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(182,plain,
! [SV22: $i] :
( ( ! [SY123: $i] :
~ ( ~ ( ~ ( equally_directed_opposite_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_opposite_lines @ SV22 @ SY123 ) )
| ~ ( ~ ~ ( unequally_directed_opposite_lines @ SV22 @ SY123 )
| ( equally_directed_opposite_lines @ SV22 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(183,plain,
! [SV23: $i] :
( ( ! [SY124: $i] :
~ ( ~ ( ~ ( convergent_lines @ SV23 @ SY124 )
| ~ ( ~ ( unequally_directed_lines @ SV23 @ SY124 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SY124 ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV23 @ SY124 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SY124 ) )
| ( convergent_lines @ SV23 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(184,plain,
! [SV24: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( distinct_points @ SV24 @ SY125 )
| ( distinct_points @ SV24 @ SY126 )
| ( distinct_points @ SY125 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(185,plain,
! [SV25: $i] :
( ( ! [SY127: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SV25 )
| ~ ( point @ SY127 ) )
| ~ ( distinct_points @ SV25 @ SY127 ) )
| ( line @ ( line_connecting @ SV25 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(186,plain,
! [SV26: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV26 @ SY128 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SY128 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV26 @ SY129 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SY129 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SY128 @ SY129 )
| ~ ( unequally_directed_lines @ SY128 @ ( reverse_line @ SY129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(187,plain,
! [SV27: $i] :
( ( ! [SY130: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV27 @ SY130 )
| ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SY130 ) ) )
| ( left_convergent_lines @ SV27 @ SY130 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(188,plain,
! [SV28: $i] :
( ( ! [SY131: $i] :
~ ( ~ ( ~ ( right_convergent_lines @ SV28 @ SY131 )
| ( left_convergent_lines @ SV28 @ ( reverse_line @ SY131 ) ) )
| ~ ( ~ ( left_convergent_lines @ SV28 @ ( reverse_line @ SY131 ) )
| ( right_convergent_lines @ SV28 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(189,plain,
! [SV29: $i] :
( ( ! [SY132: $i] :
( ~ ( distinct_points @ SV29 @ SY132 )
| ( equally_directed_lines @ ( line_connecting @ SV29 @ SY132 ) @ ( reverse_line @ ( line_connecting @ SY132 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(190,plain,
! [SV30: $i] :
( ( ! [SY133: $i] :
~ ( ~ ( ~ ( equally_directed_lines @ SV30 @ SY133 )
| ~ ( unequally_directed_lines @ SV30 @ SY133 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SV30 @ SY133 )
| ( equally_directed_lines @ SV30 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(191,plain,
! [SV31: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( left_convergent_lines @ SV31 @ SY134 )
| ( unequally_directed_lines @ SY134 @ SY135 )
| ( left_convergent_lines @ SV31 @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(192,plain,
! [SV32: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ~ ( unequally_directed_lines @ SV32 @ SY136 )
| ( unequally_directed_lines @ SV32 @ SY137 )
| ( unequally_directed_lines @ SY136 @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(193,plain,
! [SV33: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ~ ( ~ ( distinct_points @ SV33 @ SY138 )
| ~ ( left_apart_point @ SV33 @ SY139 ) )
| ( left_apart_point @ SY138 @ SY139 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SY138 ) @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(194,plain,
! [SV34: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ~ ( ~ ( left_apart_point @ SV34 @ SY140 )
| ~ ( unequally_directed_lines @ SY140 @ SY141 ) )
| ( distinct_lines @ SY140 @ SY141 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(195,plain,
! [SV35: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i] :
( ~ ~ ( ~ ( distinct_points @ SV35 @ SY142 )
| ~ ( distinct_lines @ SY143 @ SY144 ) )
| ( left_apart_point @ SV35 @ SY143 )
| ( left_apart_point @ SY142 @ SY143 )
| ( left_apart_point @ SV35 @ SY144 )
| ( left_apart_point @ SY142 @ SY144 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SY143 ) )
| ( left_apart_point @ SY142 @ ( reverse_line @ SY143 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SY144 ) )
| ( left_apart_point @ SY142 @ ( reverse_line @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(196,plain,
! [SV36: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( distinct_lines @ SV36 @ SY145 )
| ( distinct_lines @ SV36 @ SY146 )
| ( distinct_lines @ SY145 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(197,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(198,plain,
! [SV2: $i] :
( ( distinct_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(199,plain,
! [SV37: $i,SV4: $i] :
( ( ( unequally_directed_lines @ SV4 @ SV37 )
| ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(200,plain,
! [SV38: $i,SV5: $i] :
( ( ~ ( ( left_apart_point @ SV5 @ SV38 )
| ( left_apart_point @ SV5 @ ( reverse_line @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(201,plain,
! [SV39: $i,SV6: $i] :
( ( ~ ( ( left_convergent_lines @ SV6 @ SV39 )
| ( left_convergent_lines @ SV6 @ ( reverse_line @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(202,plain,
! [SV40: $i,SV7: $i] :
( ( ~ ( apart_point_and_line @ SV7 @ ( parallel_through_point @ SV40 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(203,plain,
! [SV8: $i] :
( ( distinct_lines @ SV8 @ ( reverse_line @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(204,plain,
! [SV9: $i,SV41: $i] :
( ( equally_directed_lines @ ( parallel_through_point @ SV41 @ SV9 ) @ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(205,plain,
! [SV42: $i,SV10: $i] :
( ( ~ ( distinct_points @ SV10 @ SV42 )
| ~ ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) )
| ~ ~ ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(206,plain,
! [SV43: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( apart_point_and_line @ SV11 @ SV43 )
| ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
| ~ ( ~ ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
| ( apart_point_and_line @ SV11 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(207,plain,
! [SV12: $i] :
( ( ( ~ ( line @ SV12 ) )
= $true )
| ( ( line @ ( reverse_line @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(208,plain,
! [SV44: $i,SV13: $i] :
( ( ! [SY147: $i,SY148: $i] :
~ ( ~ ( ~ ( between_on_line @ SV13 @ SV44 @ SY147 @ SY148 )
| ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SY147 )
| ~ ( before_on_line @ SV13 @ SY147 @ SY148 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SY148 @ SY147 )
| ~ ( before_on_line @ SV13 @ SY147 @ SV44 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SY147 )
| ~ ( before_on_line @ SV13 @ SY147 @ SY148 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SY148 @ SY147 )
| ~ ( before_on_line @ SV13 @ SY147 @ SV44 ) ) )
| ( between_on_line @ SV13 @ SV44 @ SY147 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(209,plain,
! [SV45: $i,SV14: $i] :
( ( ! [SY149: $i] :
~ ( ~ ( ~ ( divides_points @ SY149 @ SV14 @ SV45 )
| ~ ( ~ ( left_apart_point @ SV14 @ SY149 )
| ~ ( right_apart_point @ SV45 @ SY149 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SY149 )
| ~ ( left_apart_point @ SV45 @ SY149 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SY149 )
| ~ ( right_apart_point @ SV45 @ SY149 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SY149 )
| ~ ( left_apart_point @ SV45 @ SY149 ) ) )
| ( divides_points @ SY149 @ SV14 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(210,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( right_apart_point @ SV15 @ SV46 )
| ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) ) )
| ~ ( ~ ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
| ( right_apart_point @ SV15 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(211,plain,
! [SV47: $i,SV16: $i] :
( ( ! [SY150: $i] :
( ~ ( left_apart_point @ SV16 @ SY150 )
| ( distinct_points @ SV16 @ SV47 )
| ( left_apart_point @ SV47 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(212,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
| ( point @ ( intersection_point @ SV17 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(213,plain,
! [SV18: $i,SV49: $i] :
( ( ~ ~ ( ~ ( point @ SV49 )
| ~ ( line @ SV18 ) )
| ( line @ ( parallel_through_point @ SV18 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(214,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV19 @ SV50 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) ) )
| ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(215,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( unequally_directed_opposite_lines @ SV20 @ SV51 )
| ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
| ( unequally_directed_opposite_lines @ SV20 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(216,plain,
! [SV52: $i,SV21: $i] :
( ( ! [SY151: $i] :
~ ( ~ ( ~ ( before_on_line @ SV21 @ SV52 @ SY151 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SY151 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SY151 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SY151 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SY151 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SY151 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SY151 ) ) )
| ( before_on_line @ SV21 @ SV52 @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(217,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( equally_directed_opposite_lines @ SV22 @ SV53 )
| ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
| ~ ( ~ ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 )
| ( equally_directed_opposite_lines @ SV22 @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(218,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( convergent_lines @ SV23 @ SV54 )
| ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
| ( convergent_lines @ SV23 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(219,plain,
! [SV55: $i,SV24: $i] :
( ( ! [SY152: $i] :
( ~ ( distinct_points @ SV24 @ SV55 )
| ( distinct_points @ SV24 @ SY152 )
| ( distinct_points @ SV55 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(220,plain,
! [SV56: $i,SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) )
| ~ ( distinct_points @ SV25 @ SV56 ) )
| ( line @ ( line_connecting @ SV25 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(221,plain,
! [SV57: $i,SV26: $i] :
( ( ! [SY153: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV26 @ SV57 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV26 @ SY153 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SY153 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SY153 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SY153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(222,plain,
! [SV58: $i,SV27: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV27 @ SV58 )
| ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
| ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(223,plain,
! [SV59: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( right_convergent_lines @ SV28 @ SV59 )
| ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) ) )
| ~ ( ~ ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
| ( right_convergent_lines @ SV28 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(224,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( distinct_points @ SV29 @ SV60 )
| ( equally_directed_lines @ ( line_connecting @ SV29 @ SV60 ) @ ( reverse_line @ ( line_connecting @ SV60 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(225,plain,
! [SV61: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( equally_directed_lines @ SV30 @ SV61 )
| ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SV30 @ SV61 )
| ( equally_directed_lines @ SV30 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(226,plain,
! [SV62: $i,SV31: $i] :
( ( ! [SY154: $i] :
( ~ ( left_convergent_lines @ SV31 @ SV62 )
| ( unequally_directed_lines @ SV62 @ SY154 )
| ( left_convergent_lines @ SV31 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(227,plain,
! [SV63: $i,SV32: $i] :
( ( ! [SY155: $i] :
( ~ ( unequally_directed_lines @ SV32 @ SV63 )
| ( unequally_directed_lines @ SV32 @ SY155 )
| ( unequally_directed_lines @ SV63 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(228,plain,
! [SV64: $i,SV33: $i] :
( ( ! [SY156: $i] :
( ~ ~ ( ~ ( distinct_points @ SV33 @ SV64 )
| ~ ( left_apart_point @ SV33 @ SY156 ) )
| ( left_apart_point @ SV64 @ SY156 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(229,plain,
! [SV65: $i,SV34: $i] :
( ( ! [SY157: $i] :
( ~ ~ ( ~ ( left_apart_point @ SV34 @ SV65 )
| ~ ( unequally_directed_lines @ SV65 @ SY157 ) )
| ( distinct_lines @ SV65 @ SY157 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(230,plain,
! [SV66: $i,SV35: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ~ ( ~ ( distinct_points @ SV35 @ SV66 )
| ~ ( distinct_lines @ SY158 @ SY159 ) )
| ( left_apart_point @ SV35 @ SY158 )
| ( left_apart_point @ SV66 @ SY158 )
| ( left_apart_point @ SV35 @ SY159 )
| ( left_apart_point @ SV66 @ SY159 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SY158 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SY158 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SY159 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(231,plain,
! [SV67: $i,SV36: $i] :
( ( ! [SY160: $i] :
( ~ ( distinct_lines @ SV36 @ SV67 )
| ( distinct_lines @ SV36 @ SY160 )
| ( distinct_lines @ SV67 @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(232,plain,
! [SV37: $i,SV4: $i] :
( ( ( unequally_directed_lines @ SV4 @ SV37 )
= $true )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(233,plain,
! [SV38: $i,SV5: $i] :
( ( ( left_apart_point @ SV5 @ SV38 )
| ( left_apart_point @ SV5 @ ( reverse_line @ SV38 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(234,plain,
! [SV39: $i,SV6: $i] :
( ( ( left_convergent_lines @ SV6 @ SV39 )
| ( left_convergent_lines @ SV6 @ ( reverse_line @ SV39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(235,plain,
! [SV40: $i,SV7: $i] :
( ( apart_point_and_line @ SV7 @ ( parallel_through_point @ SV40 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(236,plain,
! [SV42: $i,SV10: $i] :
( ( ( ~ ( distinct_points @ SV10 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) )
| ~ ~ ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(237,plain,
! [SV43: $i,SV11: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV11 @ SV43 )
| ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
| ~ ( ~ ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
| ( apart_point_and_line @ SV11 @ SV43 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(238,plain,
! [SV12: $i] :
( ( ( line @ SV12 )
= $false )
| ( ( line @ ( reverse_line @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(239,plain,
! [SV68: $i,SV44: $i,SV13: $i] :
( ( ! [SY161: $i] :
~ ( ~ ( ~ ( between_on_line @ SV13 @ SV44 @ SV68 @ SY161 )
| ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SY161 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SY161 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SY161 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SY161 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ( between_on_line @ SV13 @ SV44 @ SV68 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(240,plain,
! [SV45: $i,SV14: $i,SV69: $i] :
( ( ~ ( ~ ( ~ ( divides_points @ SV69 @ SV14 @ SV45 )
| ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
| ( divides_points @ SV69 @ SV14 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(241,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ~ ( right_apart_point @ SV15 @ SV46 )
| ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) ) )
| ~ ( ~ ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
| ( right_apart_point @ SV15 @ SV46 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(242,plain,
! [SV47: $i,SV70: $i,SV16: $i] :
( ( ~ ( left_apart_point @ SV16 @ SV70 )
| ( distinct_points @ SV16 @ SV47 )
| ( left_apart_point @ SV47 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(243,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(244,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( point @ SV49 )
| ~ ( line @ SV18 ) ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV18 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(245,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV19 @ SV50 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(246,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( unequally_directed_opposite_lines @ SV20 @ SV51 )
| ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
| ( unequally_directed_opposite_lines @ SV20 @ SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(247,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ~ ( ~ ( ~ ( before_on_line @ SV21 @ SV52 @ SV71 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
| ( before_on_line @ SV21 @ SV52 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(248,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ( ~ ( equally_directed_opposite_lines @ SV22 @ SV53 )
| ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
| ~ ( ~ ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 )
| ( equally_directed_opposite_lines @ SV22 @ SV53 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(249,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ( convergent_lines @ SV23 @ SV54 )
| ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
| ( convergent_lines @ SV23 @ SV54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(250,plain,
! [SV72: $i,SV55: $i,SV24: $i] :
( ( ~ ( distinct_points @ SV24 @ SV55 )
| ( distinct_points @ SV24 @ SV72 )
| ( distinct_points @ SV55 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(251,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) )
| ~ ( distinct_points @ SV25 @ SV56 ) ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(252,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV26 @ SV57 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(253,plain,
! [SV58: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV27 @ SV58 )
| ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(254,plain,
! [SV59: $i,SV28: $i] :
( ( ~ ( ~ ( right_convergent_lines @ SV28 @ SV59 )
| ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) ) )
| ~ ( ~ ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
| ( right_convergent_lines @ SV28 @ SV59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(255,plain,
! [SV60: $i,SV29: $i] :
( ( ( ~ ( distinct_points @ SV29 @ SV60 ) )
= $true )
| ( ( equally_directed_lines @ ( line_connecting @ SV29 @ SV60 ) @ ( reverse_line @ ( line_connecting @ SV60 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(256,plain,
! [SV61: $i,SV30: $i] :
( ( ~ ( ~ ( equally_directed_lines @ SV30 @ SV61 )
| ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SV30 @ SV61 )
| ( equally_directed_lines @ SV30 @ SV61 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(257,plain,
! [SV74: $i,SV62: $i,SV31: $i] :
( ( ~ ( left_convergent_lines @ SV31 @ SV62 )
| ( unequally_directed_lines @ SV62 @ SV74 )
| ( left_convergent_lines @ SV31 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(258,plain,
! [SV75: $i,SV63: $i,SV32: $i] :
( ( ~ ( unequally_directed_lines @ SV32 @ SV63 )
| ( unequally_directed_lines @ SV32 @ SV75 )
| ( unequally_directed_lines @ SV63 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(259,plain,
! [SV76: $i,SV64: $i,SV33: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV33 @ SV64 )
| ~ ( left_apart_point @ SV33 @ SV76 ) )
| ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(260,plain,
! [SV77: $i,SV65: $i,SV34: $i] :
( ( ~ ~ ( ~ ( left_apart_point @ SV34 @ SV65 )
| ~ ( unequally_directed_lines @ SV65 @ SV77 ) )
| ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(261,plain,
! [SV78: $i,SV66: $i,SV35: $i] :
( ( ! [SY162: $i] :
( ~ ~ ( ~ ( distinct_points @ SV35 @ SV66 )
| ~ ( distinct_lines @ SV78 @ SY162 ) )
| ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SY162 )
| ( left_apart_point @ SV66 @ SY162 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SY162 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(262,plain,
! [SV79: $i,SV67: $i,SV36: $i] :
( ( ~ ( distinct_lines @ SV36 @ SV67 )
| ( distinct_lines @ SV36 @ SV79 )
| ( distinct_lines @ SV67 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(263,plain,
! [SV38: $i,SV5: $i] :
( ( left_apart_point @ SV5 @ SV38 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(264,plain,
! [SV38: $i,SV5: $i] :
( ( left_apart_point @ SV5 @ ( reverse_line @ SV38 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(265,plain,
! [SV39: $i,SV6: $i] :
( ( left_convergent_lines @ SV6 @ SV39 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(266,plain,
! [SV39: $i,SV6: $i] :
( ( left_convergent_lines @ SV6 @ ( reverse_line @ SV39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(267,plain,
! [SV42: $i,SV10: $i] :
( ( ( distinct_points @ SV10 @ SV42 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) )
| ~ ~ ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(268,plain,
! [SV43: $i,SV11: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV11 @ SV43 )
| ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(269,plain,
! [SV43: $i,SV11: $i] :
( ( ~ ( ~ ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
| ( apart_point_and_line @ SV11 @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(270,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
| ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV45: $i,SV14: $i,SV69: $i] :
( ( ~ ( ~ ( divides_points @ SV69 @ SV14 @ SV45 )
| ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
| ( divides_points @ SV69 @ SV14 @ SV45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(272,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ~ ( right_apart_point @ SV15 @ SV46 )
| ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(273,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ~ ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
| ( right_apart_point @ SV15 @ SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(274,plain,
! [SV47: $i,SV70: $i,SV16: $i] :
( ( ( ~ ( left_apart_point @ SV16 @ SV70 ) )
= $true )
| ( ( ( distinct_points @ SV16 @ SV47 )
| ( left_apart_point @ SV47 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(275,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) ) )
= $false )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(276,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( ~ ( point @ SV49 )
| ~ ( line @ SV18 ) ) )
= $false )
| ( ( line @ ( parallel_through_point @ SV18 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(277,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV50 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(278,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( unequally_directed_opposite_lines @ SV20 @ SV51 )
| ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(279,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
| ( unequally_directed_opposite_lines @ SV20 @ SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(280,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ~ ( ~ ( before_on_line @ SV21 @ SV52 @ SV71 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
| ( before_on_line @ SV21 @ SV52 @ SV71 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(281,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ( ~ ( equally_directed_opposite_lines @ SV22 @ SV53 )
| ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(282,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ( ~ ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 )
| ( equally_directed_opposite_lines @ SV22 @ SV53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(283,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ( convergent_lines @ SV23 @ SV54 )
| ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(284,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
| ( convergent_lines @ SV23 @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(285,plain,
! [SV72: $i,SV55: $i,SV24: $i] :
( ( ( ~ ( distinct_points @ SV24 @ SV55 ) )
= $true )
| ( ( ( distinct_points @ SV24 @ SV72 )
| ( distinct_points @ SV55 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(286,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) )
| ~ ( distinct_points @ SV25 @ SV56 ) ) )
= $false )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(287,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV26 @ SV57 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(288,plain,
! [SV58: $i,SV27: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV27 @ SV58 )
| ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) ) ) )
= $false )
| ( ( ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(289,plain,
! [SV59: $i,SV28: $i] :
( ( ~ ( ~ ( right_convergent_lines @ SV28 @ SV59 )
| ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(290,plain,
! [SV59: $i,SV28: $i] :
( ( ~ ( ~ ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
| ( right_convergent_lines @ SV28 @ SV59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(291,plain,
! [SV60: $i,SV29: $i] :
( ( ( distinct_points @ SV29 @ SV60 )
= $false )
| ( ( equally_directed_lines @ ( line_connecting @ SV29 @ SV60 ) @ ( reverse_line @ ( line_connecting @ SV60 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(292,plain,
! [SV61: $i,SV30: $i] :
( ( ~ ( ~ ( equally_directed_lines @ SV30 @ SV61 )
| ~ ( unequally_directed_lines @ SV30 @ SV61 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(293,plain,
! [SV61: $i,SV30: $i] :
( ( ~ ( ~ ~ ( unequally_directed_lines @ SV30 @ SV61 )
| ( equally_directed_lines @ SV30 @ SV61 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(294,plain,
! [SV74: $i,SV62: $i,SV31: $i] :
( ( ( ~ ( left_convergent_lines @ SV31 @ SV62 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV62 @ SV74 )
| ( left_convergent_lines @ SV31 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(295,plain,
! [SV75: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( unequally_directed_lines @ SV32 @ SV63 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV32 @ SV75 )
| ( unequally_directed_lines @ SV63 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(296,plain,
! [SV76: $i,SV64: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV33 @ SV64 )
| ~ ( left_apart_point @ SV33 @ SV76 ) ) )
= $true )
| ( ( ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(297,plain,
! [SV77: $i,SV65: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( left_apart_point @ SV34 @ SV65 )
| ~ ( unequally_directed_lines @ SV65 @ SV77 ) ) )
= $true )
| ( ( ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(298,plain,
! [SV81: $i,SV78: $i,SV66: $i,SV35: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV35 @ SV66 )
| ~ ( distinct_lines @ SV78 @ SV81 ) )
| ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(299,plain,
! [SV79: $i,SV67: $i,SV36: $i] :
( ( ( ~ ( distinct_lines @ SV36 @ SV67 ) )
= $true )
| ( ( ( distinct_lines @ SV36 @ SV79 )
| ( distinct_lines @ SV67 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(300,plain,
! [SV42: $i,SV10: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) )
| ~ ~ ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) ) )
= $false )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(301,plain,
! [SV43: $i,SV11: $i] :
( ( ~ ( apart_point_and_line @ SV11 @ SV43 )
| ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(302,plain,
! [SV43: $i,SV11: $i] :
( ( ~ ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
| ( apart_point_and_line @ SV11 @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(303,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ~ ( ~ ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
| ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(304,plain,
! [SV45: $i,SV14: $i,SV69: $i] :
( ( ~ ( ~ ( divides_points @ SV69 @ SV14 @ SV45 )
| ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(305,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
| ( divides_points @ SV69 @ SV14 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(306,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( right_apart_point @ SV15 @ SV46 )
| ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(307,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
| ( right_apart_point @ SV15 @ SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(308,plain,
! [SV47: $i,SV70: $i,SV16: $i] :
( ( ( left_apart_point @ SV16 @ SV70 )
= $false )
| ( ( ( distinct_points @ SV16 @ SV47 )
| ( left_apart_point @ SV47 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(309,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(310,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( point @ SV49 )
| ~ ( line @ SV18 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV18 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(311,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ SV50 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(312,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( unequally_directed_opposite_lines @ SV20 @ SV51 )
| ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(313,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
| ( unequally_directed_opposite_lines @ SV20 @ SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(314,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ~ ( ~ ( before_on_line @ SV21 @ SV52 @ SV71 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(315,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
| ( before_on_line @ SV21 @ SV52 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(316,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ( equally_directed_opposite_lines @ SV22 @ SV53 )
| ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(317,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 )
| ( equally_directed_opposite_lines @ SV22 @ SV53 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(318,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( convergent_lines @ SV23 @ SV54 )
| ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(319,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
| ( convergent_lines @ SV23 @ SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(320,plain,
! [SV72: $i,SV55: $i,SV24: $i] :
( ( ( distinct_points @ SV24 @ SV55 )
= $false )
| ( ( ( distinct_points @ SV24 @ SV72 )
| ( distinct_points @ SV55 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(321,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) )
| ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(322,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV57 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(323,plain,
! [SV58: $i,SV27: $i] :
( ( ( ~ ( unequally_directed_lines @ SV27 @ SV58 )
| ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(324,plain,
! [SV59: $i,SV28: $i] :
( ( ~ ( right_convergent_lines @ SV28 @ SV59 )
| ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(325,plain,
! [SV59: $i,SV28: $i] :
( ( ~ ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
| ( right_convergent_lines @ SV28 @ SV59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(326,plain,
! [SV61: $i,SV30: $i] :
( ( ~ ( equally_directed_lines @ SV30 @ SV61 )
| ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(327,plain,
! [SV61: $i,SV30: $i] :
( ( ~ ~ ( unequally_directed_lines @ SV30 @ SV61 )
| ( equally_directed_lines @ SV30 @ SV61 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(328,plain,
! [SV74: $i,SV62: $i,SV31: $i] :
( ( ( left_convergent_lines @ SV31 @ SV62 )
= $false )
| ( ( ( unequally_directed_lines @ SV62 @ SV74 )
| ( left_convergent_lines @ SV31 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(329,plain,
! [SV75: $i,SV63: $i,SV32: $i] :
( ( ( unequally_directed_lines @ SV32 @ SV63 )
= $false )
| ( ( ( unequally_directed_lines @ SV32 @ SV75 )
| ( unequally_directed_lines @ SV63 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(330,plain,
! [SV76: $i,SV64: $i,SV33: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV33 @ SV64 )
| ~ ( left_apart_point @ SV33 @ SV76 ) ) )
= $false )
| ( ( ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(331,plain,
! [SV77: $i,SV65: $i,SV34: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV34 @ SV65 )
| ~ ( unequally_directed_lines @ SV65 @ SV77 ) ) )
= $false )
| ( ( ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(332,plain,
! [SV81: $i,SV78: $i,SV66: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV35 @ SV66 )
| ~ ( distinct_lines @ SV78 @ SV81 ) ) )
= $true )
| ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(333,plain,
! [SV79: $i,SV67: $i,SV36: $i] :
( ( ( distinct_lines @ SV36 @ SV67 )
= $false )
| ( ( ( distinct_lines @ SV36 @ SV79 )
| ( distinct_lines @ SV67 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(334,plain,
! [SV42: $i,SV10: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) ) )
= $false )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(335,plain,
! [SV10: $i,SV42: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) ) )
= $false )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(336,plain,
! [SV43: $i,SV11: $i] :
( ( ( ~ ( apart_point_and_line @ SV11 @ SV43 ) )
= $true )
| ( ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(337,plain,
! [SV43: $i,SV11: $i] :
( ( ( ~ ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) ) )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(338,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ~ ( ~ ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
| ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(339,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(340,plain,
! [SV45: $i,SV14: $i,SV69: $i] :
( ( ~ ( divides_points @ SV69 @ SV14 @ SV45 )
| ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(341,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
| ( divides_points @ SV69 @ SV14 @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(342,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( right_apart_point @ SV15 @ SV46 ) )
= $true )
| ( ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(343,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) ) )
= $true )
| ( ( right_apart_point @ SV15 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(344,plain,
! [SV70: $i,SV47: $i,SV16: $i] :
( ( ( distinct_points @ SV16 @ SV47 )
= $true )
| ( ( left_apart_point @ SV47 @ SV70 )
= $true )
| ( ( left_apart_point @ SV16 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(345,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(346,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( point @ SV49 ) )
= $true )
| ( ( ~ ( line @ SV18 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV18 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(347,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ SV50 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(348,plain,
! [SV51: $i,SV20: $i] :
( ( ( ~ ( unequally_directed_opposite_lines @ SV20 @ SV51 ) )
= $true )
| ( ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(349,plain,
! [SV51: $i,SV20: $i] :
( ( ( ~ ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(350,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ~ ( before_on_line @ SV21 @ SV52 @ SV71 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(351,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
| ( before_on_line @ SV21 @ SV52 @ SV71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(352,plain,
! [SV53: $i,SV22: $i] :
( ( ( ~ ( equally_directed_opposite_lines @ SV22 @ SV53 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(353,plain,
! [SV53: $i,SV22: $i] :
( ( ( ~ ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
= $true )
| ( ( equally_directed_opposite_lines @ SV22 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(354,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( convergent_lines @ SV23 @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(355,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
= $true )
| ( ( convergent_lines @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(356,plain,
! [SV55: $i,SV72: $i,SV24: $i] :
( ( ( distinct_points @ SV24 @ SV72 )
= $true )
| ( ( distinct_points @ SV55 @ SV72 )
= $true )
| ( ( distinct_points @ SV24 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(357,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(358,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( unequally_directed_lines @ SV26 @ SV57 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(359,plain,
! [SV58: $i,SV27: $i] :
( ( ( ~ ( unequally_directed_lines @ SV27 @ SV58 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(360,plain,
! [SV59: $i,SV28: $i] :
( ( ( ~ ( right_convergent_lines @ SV28 @ SV59 ) )
= $true )
| ( ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(361,plain,
! [SV59: $i,SV28: $i] :
( ( ( ~ ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) ) )
= $true )
| ( ( right_convergent_lines @ SV28 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(362,plain,
! [SV61: $i,SV30: $i] :
( ( ( ~ ( equally_directed_lines @ SV30 @ SV61 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(363,plain,
! [SV61: $i,SV30: $i] :
( ( ( ~ ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
= $true )
| ( ( equally_directed_lines @ SV30 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(364,plain,
! [SV31: $i,SV74: $i,SV62: $i] :
( ( ( unequally_directed_lines @ SV62 @ SV74 )
= $true )
| ( ( left_convergent_lines @ SV31 @ SV74 )
= $true )
| ( ( left_convergent_lines @ SV31 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(365,plain,
! [SV63: $i,SV75: $i,SV32: $i] :
( ( ( unequally_directed_lines @ SV32 @ SV75 )
= $true )
| ( ( unequally_directed_lines @ SV63 @ SV75 )
= $true )
| ( ( unequally_directed_lines @ SV32 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(366,plain,
! [SV76: $i,SV64: $i,SV33: $i] :
( ( ( ~ ( distinct_points @ SV33 @ SV64 )
| ~ ( left_apart_point @ SV33 @ SV76 ) )
= $true )
| ( ( ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(367,plain,
! [SV77: $i,SV65: $i,SV34: $i] :
( ( ( ~ ( left_apart_point @ SV34 @ SV65 )
| ~ ( unequally_directed_lines @ SV65 @ SV77 ) )
= $true )
| ( ( ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(368,plain,
! [SV81: $i,SV78: $i,SV66: $i,SV35: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV35 @ SV66 )
| ~ ( distinct_lines @ SV78 @ SV81 ) ) )
= $false )
| ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(369,plain,
! [SV67: $i,SV79: $i,SV36: $i] :
( ( ( distinct_lines @ SV36 @ SV79 )
= $true )
| ( ( distinct_lines @ SV67 @ SV79 )
= $true )
| ( ( distinct_lines @ SV36 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(370,plain,
! [SV42: $i,SV10: $i] :
( ( ( ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) ) )
= $true )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(371,plain,
! [SV10: $i,SV42: $i] :
( ( ( ~ ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) ) )
= $true )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(372,plain,
! [SV43: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV43 )
= $false )
| ( ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(373,plain,
! [SV43: $i,SV11: $i] :
( ( ( ( left_apart_point @ SV11 @ SV43 )
| ( right_apart_point @ SV11 @ SV43 ) )
= $false )
| ( ( apart_point_and_line @ SV11 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(374,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ~ ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
| ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(375,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
| ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(376,plain,
! [SV45: $i,SV14: $i,SV69: $i] :
( ( ( ~ ( divides_points @ SV69 @ SV14 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(377,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(378,plain,
! [SV46: $i,SV15: $i] :
( ( ( right_apart_point @ SV15 @ SV46 )
= $false )
| ( ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(379,plain,
! [SV46: $i,SV15: $i] :
( ( ( left_apart_point @ SV15 @ ( reverse_line @ SV46 ) )
= $false )
| ( ( right_apart_point @ SV15 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(380,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) ) )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(381,plain,
! [SV18: $i,SV49: $i] :
( ( ( point @ SV49 )
= $false )
| ( ( ~ ( line @ SV18 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV18 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(382,plain,
! [SV50: $i,SV19: $i] :
( ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(383,plain,
! [SV51: $i,SV20: $i] :
( ( ( unequally_directed_opposite_lines @ SV20 @ SV51 )
= $false )
| ( ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(384,plain,
! [SV51: $i,SV20: $i] :
( ( ( unequally_directed_lines @ SV20 @ ( reverse_line @ SV51 ) )
= $false )
| ( ( unequally_directed_opposite_lines @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(385,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ( ~ ( before_on_line @ SV21 @ SV52 @ SV71 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(386,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(387,plain,
! [SV53: $i,SV22: $i] :
( ( ( equally_directed_opposite_lines @ SV22 @ SV53 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(388,plain,
! [SV53: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_opposite_lines @ SV22 @ SV53 ) )
= $false )
| ( ( equally_directed_opposite_lines @ SV22 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(389,plain,
! [SV54: $i,SV23: $i] :
( ( ( convergent_lines @ SV23 @ SV54 )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(390,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) ) )
= $false )
| ( ( convergent_lines @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(391,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) ) )
= $false )
| ( ( ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(392,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( unequally_directed_lines @ SV26 @ SV57 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(393,plain,
! [SV58: $i,SV27: $i] :
( ( ( unequally_directed_lines @ SV27 @ SV58 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(394,plain,
! [SV59: $i,SV28: $i] :
( ( ( right_convergent_lines @ SV28 @ SV59 )
= $false )
| ( ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(395,plain,
! [SV59: $i,SV28: $i] :
( ( ( left_convergent_lines @ SV28 @ ( reverse_line @ SV59 ) )
= $false )
| ( ( right_convergent_lines @ SV28 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(396,plain,
! [SV61: $i,SV30: $i] :
( ( ( equally_directed_lines @ SV30 @ SV61 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(397,plain,
! [SV61: $i,SV30: $i] :
( ( ( ~ ( unequally_directed_lines @ SV30 @ SV61 ) )
= $false )
| ( ( equally_directed_lines @ SV30 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(398,plain,
! [SV76: $i,SV64: $i,SV33: $i] :
( ( ( ~ ( distinct_points @ SV33 @ SV64 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV33 @ SV76 ) )
= $true )
| ( ( ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(399,plain,
! [SV77: $i,SV65: $i,SV34: $i] :
( ( ( ~ ( left_apart_point @ SV34 @ SV65 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV65 @ SV77 ) )
= $true )
| ( ( ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(400,plain,
! [SV81: $i,SV78: $i,SV66: $i,SV35: $i] :
( ( ( ~ ( distinct_points @ SV35 @ SV66 )
| ~ ( distinct_lines @ SV78 @ SV81 ) )
= $true )
| ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(401,plain,
! [SV42: $i,SV10: $i] :
( ( ( apart_point_and_line @ SV10 @ ( line_connecting @ SV10 @ SV42 ) )
= $false )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(402,plain,
! [SV10: $i,SV42: $i] :
( ( ( apart_point_and_line @ SV42 @ ( line_connecting @ SV10 @ SV42 ) )
= $false )
| ( ( distinct_points @ SV10 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(403,plain,
! [SV43: $i,SV11: $i] :
( ( ( left_apart_point @ SV11 @ SV43 )
= $true )
| ( ( right_apart_point @ SV11 @ SV43 )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(404,plain,
! [SV43: $i,SV11: $i] :
( ( ( left_apart_point @ SV11 @ SV43 )
= $false )
| ( ( apart_point_and_line @ SV11 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(405,plain,
! [SV43: $i,SV11: $i] :
( ( ( right_apart_point @ SV11 @ SV43 )
= $false )
| ( ( apart_point_and_line @ SV11 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(406,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(407,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(408,plain,
! [SV45: $i,SV14: $i,SV69: $i] :
( ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false )
| ( ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(409,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
| ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $false )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(410,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
| ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(411,plain,
! [SV49: $i,SV18: $i] :
( ( ( line @ SV18 )
= $false )
| ( ( point @ SV49 )
= $false )
| ( ( line @ ( parallel_through_point @ SV18 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(412,plain,
! [SV50: $i,SV19: $i] :
( ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(413,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(414,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(415,plain,
! [SV53: $i,SV22: $i] :
( ( ( unequally_directed_opposite_lines @ SV22 @ SV53 )
= $false )
| ( ( equally_directed_opposite_lines @ SV22 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(416,plain,
! [SV53: $i,SV22: $i] :
( ( ( unequally_directed_opposite_lines @ SV22 @ SV53 )
= $true )
| ( ( equally_directed_opposite_lines @ SV22 @ SV53 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(417,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
= $false )
| ( ( convergent_lines @ SV23 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(418,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( unequally_directed_lines @ SV23 @ SV54 )
| ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
= $true )
| ( ( convergent_lines @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(419,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 )
| ~ ( point @ SV56 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(420,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(421,plain,
! [SV58: $i,SV27: $i] :
( ( ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) )
= $false )
| ( ( unequally_directed_lines @ SV27 @ SV58 )
= $false )
| ( ( ( left_convergent_lines @ SV27 @ SV58 )
| ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(422,plain,
! [SV61: $i,SV30: $i] :
( ( ( unequally_directed_lines @ SV30 @ SV61 )
= $false )
| ( ( equally_directed_lines @ SV30 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(423,plain,
! [SV61: $i,SV30: $i] :
( ( ( unequally_directed_lines @ SV30 @ SV61 )
= $true )
| ( ( equally_directed_lines @ SV30 @ SV61 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(424,plain,
! [SV76: $i,SV64: $i,SV33: $i] :
( ( ( distinct_points @ SV33 @ SV64 )
= $false )
| ( ( ~ ( left_apart_point @ SV33 @ SV76 ) )
= $true )
| ( ( ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(425,plain,
! [SV77: $i,SV65: $i,SV34: $i] :
( ( ( left_apart_point @ SV34 @ SV65 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV65 @ SV77 ) )
= $true )
| ( ( ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(426,plain,
! [SV81: $i,SV78: $i,SV66: $i,SV35: $i] :
( ( ( ~ ( distinct_points @ SV35 @ SV66 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV78 @ SV81 ) )
= $true )
| ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(427,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(428,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
| ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $false )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(429,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(430,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) ) )
= $false )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(431,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $false )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(432,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(433,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) )
= $false )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(434,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(435,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
| ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(436,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( unequally_directed_lines @ SV23 @ SV54 ) )
= $false )
| ( ( convergent_lines @ SV23 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(437,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
= $false )
| ( ( convergent_lines @ SV23 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(438,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( unequally_directed_lines @ SV23 @ SV54 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
= $true )
| ( ( convergent_lines @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(439,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 ) )
= $true )
| ( ( ~ ( point @ SV56 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(440,plain,
! [SV73: $i,SV57: $i,SV26: $i] :
( ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(441,plain,
! [SV58: $i,SV27: $i] :
( ( ( left_convergent_lines @ SV27 @ SV58 )
= $true )
| ( ( left_convergent_lines @ SV27 @ ( reverse_line @ SV58 ) )
= $true )
| ( ( unequally_directed_lines @ SV27 @ SV58 )
= $false )
| ( ( unequally_directed_lines @ SV27 @ ( reverse_line @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(442,plain,
! [SV64: $i,SV76: $i,SV33: $i] :
( ( ( left_apart_point @ SV33 @ SV76 )
= $false )
| ( ( distinct_points @ SV33 @ SV64 )
= $false )
| ( ( ( left_apart_point @ SV64 @ SV76 )
| ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(443,plain,
! [SV34: $i,SV77: $i,SV65: $i] :
( ( ( unequally_directed_lines @ SV65 @ SV77 )
= $false )
| ( ( left_apart_point @ SV34 @ SV65 )
= $false )
| ( ( ( distinct_lines @ SV65 @ SV77 )
| ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(444,plain,
! [SV81: $i,SV78: $i,SV66: $i,SV35: $i] :
( ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( ~ ( distinct_lines @ SV78 @ SV81 ) )
= $true )
| ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(445,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) ) )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(446,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) ) )
= $false )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(447,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $false )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(448,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(449,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( left_apart_point @ SV14 @ SV69 )
| ~ ( right_apart_point @ SV45 @ SV69 ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(450,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(451,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) ) )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(452,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 ) )
= $false )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(453,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) )
= $false )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(454,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(455,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(456,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(457,plain,
! [SV54: $i,SV23: $i] :
( ( ( unequally_directed_lines @ SV23 @ SV54 )
= $true )
| ( ( convergent_lines @ SV23 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(458,plain,
! [SV54: $i,SV23: $i] :
( ( ( unequally_directed_opposite_lines @ SV23 @ SV54 )
= $true )
| ( ( convergent_lines @ SV23 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(459,plain,
! [SV54: $i,SV23: $i] :
( ( ( unequally_directed_lines @ SV23 @ SV54 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV23 @ SV54 ) )
= $true )
| ( ( convergent_lines @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(460,plain,
! [SV56: $i,SV25: $i] :
( ( ( point @ SV25 )
= $false )
| ( ( ~ ( point @ SV56 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(461,plain,
! [SV57: $i,SV73: $i,SV26: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(462,plain,
! [SV33: $i,SV76: $i,SV64: $i] :
( ( ( left_apart_point @ SV64 @ SV76 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV33 @ SV64 ) @ SV76 )
= $true )
| ( ( distinct_points @ SV33 @ SV64 )
= $false )
| ( ( left_apart_point @ SV33 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(463,plain,
! [SV34: $i,SV77: $i,SV65: $i] :
( ( ( distinct_lines @ SV65 @ SV77 )
= $true )
| ( ( left_apart_point @ SV34 @ ( reverse_line @ SV77 ) )
= $true )
| ( ( left_apart_point @ SV34 @ SV65 )
= $false )
| ( ( unequally_directed_lines @ SV65 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(464,plain,
! [SV66: $i,SV35: $i,SV81: $i,SV78: $i] :
( ( ( distinct_lines @ SV78 @ SV81 )
= $false )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(465,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(466,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(467,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(468,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( left_apart_point @ SV14 @ SV69 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(469,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( ~ ( right_apart_point @ SV45 @ SV69 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(470,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( left_apart_point @ SV14 @ SV69 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV45 @ SV69 ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(471,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( right_apart_point @ SV14 @ SV69 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV45 @ SV69 ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(472,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( line @ SV17 )
| ~ ( line @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(473,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 ) )
= $true )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(474,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 ) )
= $true )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(475,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(476,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(477,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) ) )
= $false )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(478,plain,
! [SV54: $i,SV23: $i] :
( ( ( unequally_directed_opposite_lines @ SV23 @ SV54 )
= $false )
| ( ( unequally_directed_lines @ SV23 @ SV54 )
= $false )
| ( ( convergent_lines @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(479,plain,
! [SV25: $i,SV56: $i] :
( ( ( point @ SV56 )
= $false )
| ( ( point @ SV25 )
= $false )
| ( ( ~ ( distinct_points @ SV25 @ SV56 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(480,plain,
! [SV57: $i,SV73: $i,SV26: $i] :
( ( ( ~ ( unequally_directed_lines @ SV26 @ SV73 )
| ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(481,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(482,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 ) )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(483,plain,
! [SV44: $i,SV80: $i,SV68: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(484,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV44 @ SV68 ) )
= $true )
| ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(485,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 ) )
= $true )
| ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(486,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( left_apart_point @ SV14 @ SV69 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(487,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( right_apart_point @ SV45 @ SV69 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(488,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( left_apart_point @ SV14 @ SV69 )
= $false )
| ( ( ~ ( right_apart_point @ SV45 @ SV69 ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(489,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( right_apart_point @ SV14 @ SV69 )
= $false )
| ( ( ~ ( left_apart_point @ SV45 @ SV69 ) )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(490,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( line @ SV17 ) )
= $true )
| ( ( ~ ( line @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(491,plain,
! [SV50: $i,SV19: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(492,plain,
! [SV50: $i,SV19: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV19 @ SV50 ) @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ SV50 )
= $false )
| ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(493,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(494,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
| ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(495,plain,
! [SV56: $i,SV25: $i] :
( ( ( distinct_points @ SV25 @ SV56 )
= $false )
| ( ( point @ SV25 )
= $false )
| ( ( point @ SV56 )
= $false )
| ( ( line @ ( line_connecting @ SV25 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(496,plain,
! [SV57: $i,SV73: $i,SV26: $i] :
( ( ( ~ ( unequally_directed_lines @ SV26 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(497,plain,
! [SV57: $i,SV73: $i,SV26: $i] :
( ( ( ~ ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(498,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
| ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(499,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(500,plain,
! [SV44: $i,SV80: $i,SV68: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(501,plain,
! [SV80: $i,SV68: $i,SV44: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $false )
| ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV80 ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(502,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV80 @ SV68 )
= $false )
| ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(503,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) )
= $false )
| ( ( left_apart_point @ SV14 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(504,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( right_apart_point @ SV14 @ SV69 )
| ~ ( left_apart_point @ SV45 @ SV69 ) )
= $false )
| ( ( right_apart_point @ SV45 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(505,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( right_apart_point @ SV45 @ SV69 )
= $false )
| ( ( left_apart_point @ SV14 @ SV69 )
= $false )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(506,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( left_apart_point @ SV45 @ SV69 )
= $false )
| ( ( right_apart_point @ SV14 @ SV69 )
= $false )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(507,plain,
! [SV48: $i,SV17: $i] :
( ( ( line @ SV17 )
= $false )
| ( ( ~ ( line @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(508,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(509,plain,
! [SV52: $i,SV21: $i,SV71: $i] :
( ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(510,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(511,plain,
! [SV57: $i,SV73: $i,SV26: $i] :
( ( ( unequally_directed_lines @ SV26 @ SV73 )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(512,plain,
! [SV57: $i,SV73: $i,SV26: $i] :
( ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(513,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 )
| ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(514,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $false )
| ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(515,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 )
| ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $false )
| ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(516,plain,
! [SV44: $i,SV80: $i,SV68: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $false )
| ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $false )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(517,plain,
! [SV80: $i,SV44: $i,SV68: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV68 @ SV44 )
= $false )
| ( ( before_on_line @ SV13 @ SV80 @ SV68 )
= $false )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(518,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( right_apart_point @ SV14 @ SV69 ) )
= $false )
| ( ( left_apart_point @ SV14 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(519,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( ~ ( left_apart_point @ SV45 @ SV69 ) )
= $false )
| ( ( left_apart_point @ SV14 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(520,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( ~ ( right_apart_point @ SV14 @ SV69 ) )
= $false )
| ( ( right_apart_point @ SV45 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(521,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( ~ ( left_apart_point @ SV45 @ SV69 ) )
= $false )
| ( ( right_apart_point @ SV45 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(522,plain,
! [SV17: $i,SV48: $i] :
( ( ( line @ SV48 )
= $false )
| ( ( line @ SV17 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV17 @ SV48 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(523,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(524,plain,
! [SV52: $i,SV21: $i,SV71: $i] :
( ( ( incident_point_and_line @ SV71 @ SV21 )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(525,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) ) )
= $false )
| ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(526,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(527,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( ~ ( unequally_directed_lines @ SV57 @ SV73 )
| ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(528,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 )
| ( left_apart_point @ SV66 @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(529,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 ) )
= $false )
| ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(530,plain,
! [SV80: $i,SV44: $i,SV68: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $false )
| ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(531,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV80 @ SV68 ) )
= $false )
| ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(532,plain,
! [SV80: $i,SV44: $i,SV68: $i,SV13: $i] :
( ( ( ~ ( before_on_line @ SV13 @ SV68 @ SV44 ) )
= $false )
| ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(533,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( right_apart_point @ SV14 @ SV69 )
= $true )
| ( ( left_apart_point @ SV14 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(534,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( left_apart_point @ SV45 @ SV69 )
= $true )
| ( ( left_apart_point @ SV14 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(535,plain,
! [SV45: $i,SV69: $i,SV14: $i] :
( ( ( right_apart_point @ SV14 @ SV69 )
= $true )
| ( ( right_apart_point @ SV45 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(536,plain,
! [SV14: $i,SV69: $i,SV45: $i] :
( ( ( left_apart_point @ SV45 @ SV69 )
= $true )
| ( ( right_apart_point @ SV45 @ SV69 )
= $true )
| ( ( divides_points @ SV69 @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(537,plain,
! [SV48: $i,SV17: $i] :
( ( ( unequally_directed_lines @ SV17 @ SV48 )
= $false )
| ( ( line @ SV17 )
= $false )
| ( ( line @ SV48 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(538,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(539,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( distinct_points @ SV52 @ SV71 )
| ~ ( incident_point_and_line @ SV52 @ SV21 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(540,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( ~ ( unequally_directed_lines @ SV57 @ SV73 ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(541,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(542,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( ~ ( unequally_directed_lines @ SV57 @ SV73 ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(543,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( ~ ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(544,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 )
| ( left_apart_point @ SV35 @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ SV81 )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(545,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV80 @ SV68 )
= $true )
| ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(546,plain,
! [SV80: $i,SV44: $i,SV68: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV68 @ SV44 )
= $true )
| ( ( before_on_line @ SV13 @ SV44 @ SV68 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(547,plain,
! [SV44: $i,SV68: $i,SV80: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV80 @ SV68 )
= $true )
| ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(548,plain,
! [SV80: $i,SV44: $i,SV68: $i,SV13: $i] :
( ( ( before_on_line @ SV13 @ SV68 @ SV44 )
= $true )
| ( ( before_on_line @ SV13 @ SV68 @ SV80 )
= $true )
| ( ( between_on_line @ SV13 @ SV44 @ SV68 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(549,plain,
! [SV48: $i,SV17: $i] :
( ( ( unequally_directed_lines @ SV17 @ ( reverse_line @ SV48 ) )
= $false )
| ( ( line @ SV48 )
= $false )
| ( ( line @ SV17 )
= $false )
| ( ( unequally_directed_lines @ SV17 @ SV48 )
= $false )
| ( ( point @ ( intersection_point @ SV17 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(550,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( distinct_points @ SV52 @ SV71 ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(551,plain,
! [SV71: $i,SV21: $i,SV52: $i] :
( ( ( ~ ( incident_point_and_line @ SV52 @ SV21 ) )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(552,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( ~ ( distinct_points @ SV52 @ SV71 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV52 @ SV21 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(553,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( unequally_directed_lines @ SV57 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(554,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(555,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( unequally_directed_lines @ SV57 @ SV73 )
= $true )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(556,plain,
! [SV26: $i,SV73: $i,SV57: $i] :
( ( ( unequally_directed_lines @ SV57 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV73 ) )
= $true )
| ( ( unequally_directed_lines @ SV26 @ SV57 )
= $false )
| ( ( unequally_directed_lines @ SV26 @ ( reverse_line @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(557,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( ( left_apart_point @ SV35 @ SV78 )
| ( left_apart_point @ SV66 @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV35 @ SV81 )
= $true )
| ( ( left_apart_point @ SV66 @ SV81 )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(558,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( distinct_points @ SV52 @ SV71 )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(559,plain,
! [SV71: $i,SV21: $i,SV52: $i] :
( ( ( incident_point_and_line @ SV52 @ SV21 )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(560,plain,
! [SV21: $i,SV71: $i,SV52: $i] :
( ( ( distinct_points @ SV52 @ SV71 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV52 @ SV21 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(561,plain,
! [SV81: $i,SV66: $i,SV78: $i,SV35: $i] :
( ( ( left_apart_point @ SV35 @ SV78 )
= $true )
| ( ( left_apart_point @ SV66 @ SV78 )
= $true )
| ( ( left_apart_point @ SV35 @ SV81 )
= $true )
| ( ( left_apart_point @ SV66 @ SV81 )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV78 ) )
= $true )
| ( ( left_apart_point @ SV35 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( left_apart_point @ SV66 @ ( reverse_line @ SV81 ) )
= $true )
| ( ( distinct_points @ SV35 @ SV66 )
= $false )
| ( ( distinct_lines @ SV78 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(562,plain,
! [SV71: $i,SV21: $i,SV52: $i] :
( ( ( incident_point_and_line @ SV52 @ SV21 )
= $false )
| ( ( distinct_points @ SV52 @ SV71 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(563,plain,
! [SV52: $i,SV21: $i,SV71: $i] :
( ( ( incident_point_and_line @ SV71 @ SV21 )
= $false )
| ( ( distinct_points @ SV52 @ SV71 )
= $false )
| ( ( incident_point_and_line @ SV52 @ SV21 )
= $false )
| ( ( ~ ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) ) )
= $true )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(564,plain,
! [SV71: $i,SV52: $i,SV21: $i] :
( ( ( equally_directed_lines @ SV21 @ ( line_connecting @ SV52 @ SV71 ) )
= $false )
| ( ( incident_point_and_line @ SV52 @ SV21 )
= $false )
| ( ( distinct_points @ SV52 @ SV71 )
= $false )
| ( ( incident_point_and_line @ SV71 @ SV21 )
= $false )
| ( ( before_on_line @ SV21 @ SV52 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(565,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[126,564,561,559,558,556,555,554,553,549,548,547,546,545,536,535,534,533,524,517,516,506,505,495,492,491,478,476,463,462,458,457,441,423,422,416,415,411,405,404,403,402,401,395,394,384,383,379,378,369,365,364,356,344,291,266,265,264,263,238,235,232,204,203,198,197,169,162,131,130,129,128,127]) ).
thf(566,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 10:18:14 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.11/0.52
% 1.11/0.52 No.of.Axioms: 36
% 1.11/0.52
% 1.11/0.52 Length.of.Defs: 0
% 1.11/0.52
% 1.11/0.52 Contains.Choice.Funs: false
% 1.11/0.52 .................
% 1.11/0.52
% 1.11/0.52 ********************************
% 1.11/0.52 * All subproblems solved! *
% 1.11/0.52 ********************************
% 1.11/0.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:565,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.11/0.52
% 1.11/0.52 %**** Beginning of derivation protocol ****
% 1.11/0.52 % SZS output start CNFRefutation
% See solution above
% 0.48/0.52
% 0.48/0.52 %**** End of derivation protocol ****
% 0.48/0.52 %**** no. of clauses in derivation: 566 ****
% 0.48/0.52 %**** clause counter: 565 ****
% 0.48/0.52
% 0.48/0.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:565,loop_count:0,foatp_calls:1,translation:fof_full)
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