TSTP Solution File: GEO257+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:09:23 EDT 2022
% Result : Theorem 0.47s 0.64s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 64
% Syntax : Number of formulae : 695 ( 436 unt; 27 typ; 0 def)
% Number of atoms : 4528 ( 993 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 9718 (1470 ~;1664 |; 140 &;6374 @)
% ( 20 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 7 con; 0-4 aty)
% Number of variables : 2103 ( 0 ^2103 !; 0 ?;2103 :)
% 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_SY86,type,
sK2_SY86: $i ).
thf(tp_sK3_SY90,type,
sK3_SY90: $i ).
thf(tp_sK4_SY93,type,
sK4_SY93: $i ).
thf(tp_sK5_SY95,type,
sK5_SY95: $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,A: $i,B: $i,C: $i,D: $i] :
( ( ( distinct_points @ A @ C )
& ( distinct_points @ B @ C )
& ( incident_point_and_line @ C @ L )
& ( left_apart_point @ D @ L ) )
=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
=> ( before_on_line @ L @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [L: $i,A: $i,B: $i,C: $i,D: $i] :
( ( ( distinct_points @ A @ C )
& ( distinct_points @ B @ C )
& ( incident_point_and_line @ C @ L )
& ( left_apart_point @ D @ L ) )
=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
=> ( before_on_line @ L @ A @ C ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [L: $i,A: $i,B: $i,C: $i,D: $i] :
( ( ( distinct_points @ A @ C )
& ( distinct_points @ B @ C )
& ( incident_point_and_line @ C @ L )
& ( left_apart_point @ D @ L ) )
=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
=> ( before_on_line @ L @ A @ 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,
( ( ! [SY86: $i,SY87: $i,SY88: $i,SY89: $i] :
( ( ( distinct_points @ SY86 @ SY88 )
& ( distinct_points @ SY87 @ SY88 )
& ( incident_point_and_line @ SY88 @ sK1_L )
& ( left_apart_point @ SY89 @ sK1_L ) )
=> ( ( ( before_on_line @ sK1_L @ SY86 @ SY87 )
& ( before_on_line @ sK1_L @ SY87 @ SY88 ) )
=> ( before_on_line @ sK1_L @ SY86 @ SY88 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(77,plain,
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( ( distinct_points @ sK2_SY86 @ SY91 )
& ( distinct_points @ SY90 @ SY91 )
& ( incident_point_and_line @ SY91 @ sK1_L )
& ( left_apart_point @ SY92 @ sK1_L ) )
=> ( ( ( before_on_line @ sK1_L @ sK2_SY86 @ SY90 )
& ( before_on_line @ sK1_L @ SY90 @ SY91 ) )
=> ( before_on_line @ sK1_L @ sK2_SY86 @ SY91 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(78,plain,
( ( ! [SY93: $i,SY94: $i] :
( ( ( distinct_points @ sK2_SY86 @ SY93 )
& ( distinct_points @ sK3_SY90 @ SY93 )
& ( incident_point_and_line @ SY93 @ sK1_L )
& ( left_apart_point @ SY94 @ sK1_L ) )
=> ( ( ( before_on_line @ sK1_L @ sK2_SY86 @ sK3_SY90 )
& ( before_on_line @ sK1_L @ sK3_SY90 @ SY93 ) )
=> ( before_on_line @ sK1_L @ sK2_SY86 @ SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(79,plain,
( ( ! [SY95: $i] :
( ( ( distinct_points @ sK2_SY86 @ sK4_SY93 )
& ( distinct_points @ sK3_SY90 @ sK4_SY93 )
& ( incident_point_and_line @ sK4_SY93 @ sK1_L )
& ( left_apart_point @ SY95 @ sK1_L ) )
=> ( ( ( before_on_line @ sK1_L @ sK2_SY86 @ sK3_SY90 )
& ( before_on_line @ sK1_L @ sK3_SY90 @ sK4_SY93 ) )
=> ( before_on_line @ sK1_L @ sK2_SY86 @ sK4_SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( ( ( distinct_points @ sK2_SY86 @ sK4_SY93 )
& ( distinct_points @ sK3_SY90 @ sK4_SY93 )
& ( incident_point_and_line @ sK4_SY93 @ sK1_L )
& ( left_apart_point @ sK5_SY95 @ sK1_L ) )
=> ( ( ( before_on_line @ sK1_L @ sK2_SY86 @ sK3_SY90 )
& ( before_on_line @ sK1_L @ sK3_SY90 @ sK4_SY93 ) )
=> ( before_on_line @ sK1_L @ sK2_SY86 @ sK4_SY93 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(81,plain,
( ( distinct_points @ sK2_SY86 @ sK4_SY93 )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(82,plain,
( ( distinct_points @ sK3_SY90 @ sK4_SY93 )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(83,plain,
( ( incident_point_and_line @ sK4_SY93 @ sK1_L )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(84,plain,
( ( left_apart_point @ sK5_SY95 @ sK1_L )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(85,plain,
( ( before_on_line @ sK1_L @ sK2_SY86 @ sK3_SY90 )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(86,plain,
( ( before_on_line @ sK1_L @ sK3_SY90 @ sK4_SY93 )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(87,plain,
( ( before_on_line @ sK1_L @ sK2_SY86 @ sK4_SY93 )
= $false ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(88,plain,
( ( ~ ( before_on_line @ sK1_L @ sK2_SY86 @ sK4_SY93 ) )
= $true ),
inference(polarity_switch,[status(thm)],[87]) ).
thf(89,plain,
( ( ! [L: $i,M: $i] :
( ~ ( left_convergent_lines @ L @ M )
| ! [N: $i] :
( ( left_convergent_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(90,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(91,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(92,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(93,plain,
( ( ! [A: $i,B: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ~ ( distinct_points @ A @ B )
| ( left_apart_point @ B @ ( reverse_line @ M ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(95,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L ) )
& ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(97,plain,
( ( ! [L: $i] :
( ~ ( line @ L )
| ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(98,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(99,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(101,plain,
( ( ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ M )
& ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ ( reverse_line @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(102,plain,
( ( ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ L )
& ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ ( reverse_line @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(103,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(104,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(105,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(106,plain,
( ( ! [L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ! [C: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(108,plain,
( ( ! [L: $i,A: $i] :
( ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i] :
( ! [C: $i] :
~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ~ ( before_on_line @ L @ B @ C )
| ( between_on_line @ L @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ C @ B )
| ~ ( before_on_line @ L @ B @ A )
| ( between_on_line @ L @ A @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(109,plain,
( ( ! [L: $i] :
( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( incident_point_and_line @ A @ L )
| ~ ( incident_point_and_line @ B @ L )
| ~ ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) )
| ( before_on_line @ L @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( distinct_points @ A @ B ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ A @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ B @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(110,plain,
( ( ! [A: $i] :
( ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( right_apart_point @ B @ L )
| ( divides_points @ L @ A @ B ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ B @ L )
| ~ ( right_apart_point @ A @ L )
| ( divides_points @ L @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(111,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_opposite_lines @ L @ M )
| ( convergent_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_opposite_lines @ L @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(112,plain,
( ( ! [A: $i,L: $i] :
( ~ ( apart_point_and_line @ A @ L )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( right_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_opposite_lines @ X @ Y )
| ~ ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
| ( equally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_lines @ X @ Y )
| ~ ( unequally_directed_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_lines @ X @ Y )
| ( equally_directed_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_convergent_lines @ X @ ( reverse_line @ Y ) )
| ( right_convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_convergent_lines @ X @ Y )
| ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_apart_point @ X @ ( reverse_line @ Y ) )
| ( right_apart_point @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_apart_point @ X @ Y )
| ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( unequally_directed_lines @ X @ ( reverse_line @ Y ) )
| ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( unequally_directed_opposite_lines @ X @ Y )
| ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( unequally_directed_lines @ X @ ( reverse_line @ Y ) )
| ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( unequally_directed_opposite_lines @ X @ Y )
| ( unequally_directed_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_apart_point @ X @ ( reverse_line @ Y ) )
| ( right_apart_point @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_apart_point @ X @ Y )
| ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left_convergent_lines @ X @ ( reverse_line @ Y ) )
| ( right_convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( right_convergent_lines @ X @ Y )
| ( left_convergent_lines @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_lines @ X @ Y )
| ~ ( unequally_directed_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_lines @ X @ Y )
| ( equally_directed_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equally_directed_opposite_lines @ X @ Y )
| ~ ( unequally_directed_opposite_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unequally_directed_opposite_lines @ X @ Y )
| ( equally_directed_opposite_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(123,plain,
( ( ! [A: $i,L: $i] :
( ~ ( apart_point_and_line @ A @ L )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) )
& ! [A: $i,L: $i] :
( ~ ( right_apart_point @ A @ L )
| ( apart_point_and_line @ A @ L ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(124,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_opposite_lines @ L @ M )
| ( convergent_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_lines @ L @ M ) )
& ! [L: $i,M: $i] :
( ~ ( convergent_lines @ L @ M )
| ( unequally_directed_opposite_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(125,plain,
( ( ! [A: $i] :
( ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( left_apart_point @ B @ L ) )
& ! [B: $i,L: $i] :
( ~ ( divides_points @ L @ A @ B )
| ( right_apart_point @ B @ L )
| ( right_apart_point @ A @ L ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ A @ L )
| ~ ( right_apart_point @ B @ L )
| ( divides_points @ L @ A @ B ) )
& ! [B: $i,L: $i] :
( ~ ( left_apart_point @ B @ L )
| ~ ( right_apart_point @ A @ L )
| ( divides_points @ L @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(126,plain,
( ( ! [L: $i] :
( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( incident_point_and_line @ A @ L )
| ~ ( incident_point_and_line @ B @ L )
| ~ ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) )
| ( before_on_line @ L @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( distinct_points @ A @ B ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ A @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( incident_point_and_line @ B @ L ) )
& ! [A: $i,B: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ( equally_directed_lines @ L @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(127,plain,
( ( ! [L: $i,A: $i] :
( ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i] :
( ! [C: $i] :
~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ A @ B )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ C @ B ) )
& ! [B: $i,C: $i] :
( ~ ( between_on_line @ L @ A @ B @ C )
| ( before_on_line @ L @ B @ C )
| ( before_on_line @ L @ B @ A ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ A @ B )
| ~ ( before_on_line @ L @ B @ C )
| ( between_on_line @ L @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( before_on_line @ L @ C @ B )
| ~ ( before_on_line @ L @ B @ A )
| ( between_on_line @ L @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(128,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ! [C: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(130,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(131,plain,
( ( ! [L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(132,plain,
( ( ! [L: $i] : ( equally_directed_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(133,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(134,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ! [N: $i] :
( ( unequally_directed_lines @ L @ ( reverse_line @ N ) )
| ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(135,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(136,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)],[103]) ).
thf(137,plain,
( ( ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ L )
& ! [A: $i,L: $i] :
~ ( left_apart_point @ A @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(138,plain,
( ( ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ M )
& ! [L: $i,M: $i] :
~ ( left_convergent_lines @ L @ ( reverse_line @ M ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(140,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)],[99]) ).
thf(141,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(142,plain,
( ( ! [L: $i] :
( ~ ( line @ L )
| ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( distinct_points @ A @ B )
| ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(144,plain,
( ( ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L ) )
& ! [L: $i,M: $i] :
( ~ ( unequally_directed_lines @ L @ M )
| ~ ( unequally_directed_lines @ L @ ( reverse_line @ M ) )
| ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(145,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(146,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(147,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)],[94]) ).
thf(148,plain,
( ( ! [A: $i,L: $i] : ( equally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(149,plain,
( ( ! [A: $i,B: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ~ ( distinct_points @ A @ B )
| ( left_apart_point @ B @ ( reverse_line @ M ) )
| ( left_apart_point @ A @ ( reverse_line @ M ) )
| ( left_apart_point @ B @ ( reverse_line @ L ) )
| ( left_apart_point @ A @ ( reverse_line @ L ) )
| ( left_apart_point @ B @ M )
| ( left_apart_point @ A @ M )
| ( left_apart_point @ A @ L )
| ( left_apart_point @ B @ L ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(150,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)],[92]) ).
thf(151,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)],[91]) ).
thf(152,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)],[90]) ).
thf(153,plain,
( ( ! [L: $i,M: $i] :
( ~ ( left_convergent_lines @ L @ M )
| ! [N: $i] :
( ( left_convergent_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(154,plain,
( ( before_on_line @ sK1_L @ sK3_SY90 @ sK4_SY93 )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(155,plain,
( ( before_on_line @ sK1_L @ sK2_SY86 @ sK3_SY90 )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(156,plain,
( ( left_apart_point @ sK5_SY95 @ sK1_L )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(157,plain,
( ( incident_point_and_line @ sK4_SY93 @ sK1_L )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(158,plain,
( ( distinct_points @ sK3_SY90 @ sK4_SY93 )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(159,plain,
( ( distinct_points @ sK2_SY86 @ sK4_SY93 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(160,plain,
( ( ~ ( before_on_line @ sK1_L @ sK2_SY86 @ sK4_SY93 ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(161,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(162,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(163,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ! [SX2: $i] :
( ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) )
| ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(164,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(165,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX1 @ SX2 )
| ~ ( incident_point_and_line @ SX1 @ SX0 )
| ~ ( incident_point_and_line @ SX2 @ SX0 )
| ~ ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) )
| ( before_on_line @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( incident_point_and_line @ SX1 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( incident_point_and_line @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( equally_directed_lines @ SX0 @ ( line_connecting @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(166,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(167,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( before_on_line @ SX0 @ SX3 @ SX2 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX1 @ SX2 )
| ( before_on_line @ SX0 @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX3 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( before_on_line @ SX0 @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX3 )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( before_on_line @ SX0 @ SX3 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX1 )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(169,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(170,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(171,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(172,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX2 )
| ( right_apart_point @ SX0 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( right_apart_point @ SX1 @ SX2 )
| ( left_apart_point @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ( right_apart_point @ SX1 @ SX2 )
| ( right_apart_point @ SX0 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 )
| ( divides_points @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX1 @ SX2 )
| ~ ( right_apart_point @ SX0 @ SX2 )
| ( divides_points @ SX2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(173,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(174,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(175,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(176,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(177,plain,
! [SV2: $i] :
( ( ! [SY96: $i] :
( ~ ( distinct_points @ SV2 @ SY96 )
| ! [SY97: $i] :
( ( distinct_points @ SV2 @ SY97 )
| ( distinct_points @ SY96 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(178,plain,
! [SV3: $i] :
( ( ~ ( distinct_lines @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(179,plain,
! [SV4: $i] :
( ( ! [SY98: $i] :
( ~ ( distinct_lines @ SV4 @ SY98 )
| ! [SY99: $i] :
( ( distinct_lines @ SV4 @ SY99 )
| ( distinct_lines @ SY98 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(180,plain,
! [SV5: $i] :
( ( equally_directed_lines @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(181,plain,
! [SV6: $i] :
( ( ! [SY100: $i] :
( ~ ( unequally_directed_lines @ SV6 @ SY100 )
| ! [SY101: $i] :
( ( unequally_directed_lines @ SV6 @ SY101 )
| ( unequally_directed_lines @ SY100 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(182,plain,
! [SV7: $i] :
( ( ! [SY102: $i] :
( ( unequally_directed_lines @ SV7 @ SY102 )
| ( unequally_directed_lines @ SV7 @ ( reverse_line @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(183,plain,
! [SV8: $i] :
( ( ! [SY103: $i] :
( ~ ( unequally_directed_lines @ SV8 @ SY103 )
| ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SY103 ) )
| ( left_convergent_lines @ SV8 @ SY103 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(184,plain,
! [SV9: $i] :
( ( ! [SY104: $i] :
( ~ ( point @ SV9 )
| ~ ( point @ SY104 )
| ~ ( distinct_points @ SV9 @ SY104 )
| ( line @ ( line_connecting @ SV9 @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(185,plain,
! [SV10: $i] :
( ( ! [SY105: $i] :
( ~ ( line @ SV10 )
| ~ ( line @ SY105 )
| ~ ( unequally_directed_lines @ SV10 @ SY105 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SY105 ) )
| ( point @ ( intersection_point @ SV10 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(186,plain,
! [SV11: $i] :
( ( ! [SY106: $i] :
( ~ ( line @ SV11 )
| ~ ( point @ SY106 )
| ( line @ ( parallel_through_point @ SV11 @ SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(187,plain,
! [SV12: $i] :
( ( ~ ( line @ SV12 )
| ( line @ ( reverse_line @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(188,plain,
! [SV13: $i] :
( ( ! [SY107: $i] :
~ ( apart_point_and_line @ SV13 @ ( parallel_through_point @ SY107 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(189,plain,
! [SV14: $i] :
( ( ~ ( distinct_lines @ SV14 @ ( reverse_line @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(190,plain,
! [SV15: $i] :
( ( ! [SY108: $i] :
( ~ ( distinct_points @ SV15 @ SY108 )
| ( equally_directed_lines @ ( line_connecting @ SV15 @ SY108 ) @ ( reverse_line @ ( line_connecting @ SY108 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(191,plain,
! [SV16: $i] :
( ( ! [SY109: $i] : ( equally_directed_lines @ ( parallel_through_point @ SY109 @ SV16 ) @ SY109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(192,plain,
! [SV17: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i] :
( ~ ( distinct_lines @ SY111 @ SY112 )
| ~ ( distinct_points @ SV17 @ SY110 )
| ( left_apart_point @ SY110 @ ( reverse_line @ SY112 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY112 ) )
| ( left_apart_point @ SY110 @ ( reverse_line @ SY111 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY111 ) )
| ( left_apart_point @ SY110 @ SY112 )
| ( left_apart_point @ SV17 @ SY112 )
| ( left_apart_point @ SV17 @ SY111 )
| ( left_apart_point @ SY110 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(193,plain,
! [SV18: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( distinct_points @ SV18 @ SY113 )
| ~ ( left_apart_point @ SV18 @ SY114 )
| ( left_apart_point @ SY113 @ SY114 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SY113 ) @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(194,plain,
! [SV19: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( left_apart_point @ SV19 @ SY116 )
| ( distinct_points @ SV19 @ SY115 )
| ( left_apart_point @ SY115 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(195,plain,
! [SV20: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( left_apart_point @ SV20 @ SY117 )
| ~ ( unequally_directed_lines @ SY117 @ SY118 )
| ( distinct_lines @ SY117 @ SY118 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(196,plain,
! [SV21: $i] :
( ( ! [SY119: $i] :
( ~ ( left_convergent_lines @ SV21 @ SY119 )
| ! [SY120: $i] :
( ( left_convergent_lines @ SV21 @ SY120 )
| ( unequally_directed_lines @ SY119 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(197,plain,
( ( before_on_line @ sK1_L @ sK2_SY86 @ sK4_SY93 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(199,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(200,plain,
! [SV22: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) )
| ~ ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) )
| ~ ~ ( ~ ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(201,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(202,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY129: $i,SY130: $i] :
( ~ ( distinct_points @ SY129 @ SY130 )
| ~ ( incident_point_and_line @ SY129 @ SV23 )
| ~ ( incident_point_and_line @ SY130 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SY129 @ SY130 ) )
| ( before_on_line @ SV23 @ SY129 @ SY130 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(203,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(204,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(205,plain,
! [SV24: $i] :
( ( ! [SY139: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( between_on_line @ SV24 @ SY139 @ SY140 @ SY141 )
| ( before_on_line @ SV24 @ SY139 @ SY140 )
| ( before_on_line @ SV24 @ SY141 @ SY140 ) )
| ~ ! [SY142: $i] :
( ! [SY143: $i] :
~ ( between_on_line @ SV24 @ SY139 @ SY142 @ SY143 )
| ( before_on_line @ SV24 @ SY139 @ SY142 )
| ( before_on_line @ SV24 @ SY142 @ SY139 ) ) )
| ~ ~ ( ~ ! [SY144: $i,SY145: $i] :
( ~ ( between_on_line @ SV24 @ SY139 @ SY144 @ SY145 )
| ( before_on_line @ SV24 @ SY144 @ SY145 )
| ( before_on_line @ SV24 @ SY145 @ SY144 ) )
| ~ ! [SY146: $i,SY147: $i] :
( ~ ( between_on_line @ SV24 @ SY139 @ SY146 @ SY147 )
| ( before_on_line @ SV24 @ SY146 @ SY147 )
| ( before_on_line @ SV24 @ SY146 @ SY139 ) ) ) )
| ~ ~ ( ~ ! [SY148: $i,SY149: $i] :
( ~ ( before_on_line @ SV24 @ SY139 @ SY148 )
| ~ ( before_on_line @ SV24 @ SY148 @ SY149 )
| ( between_on_line @ SV24 @ SY139 @ SY148 @ SY149 ) )
| ~ ! [SY150: $i,SY151: $i] :
( ~ ( before_on_line @ SV24 @ SY151 @ SY150 )
| ~ ( before_on_line @ SV24 @ SY150 @ SY139 )
| ( between_on_line @ SV24 @ SY139 @ SY150 @ SY151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(206,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 )
| ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(207,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(208,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(209,plain,
! [SV25: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
| ~ ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) )
| ~ ~ ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) )
| ~ ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(211,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(212,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(213,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(214,plain,
! [SV26: $i,SV2: $i] :
( ( ~ ( distinct_points @ SV2 @ SV26 )
| ! [SY164: $i] :
( ( distinct_points @ SV2 @ SY164 )
| ( distinct_points @ SV26 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(215,plain,
! [SV3: $i] :
( ( distinct_lines @ SV3 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(216,plain,
! [SV27: $i,SV4: $i] :
( ( ~ ( distinct_lines @ SV4 @ SV27 )
| ! [SY165: $i] :
( ( distinct_lines @ SV4 @ SY165 )
| ( distinct_lines @ SV27 @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(217,plain,
! [SV28: $i,SV6: $i] :
( ( ~ ( unequally_directed_lines @ SV6 @ SV28 )
| ! [SY166: $i] :
( ( unequally_directed_lines @ SV6 @ SY166 )
| ( unequally_directed_lines @ SV28 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(218,plain,
! [SV29: $i,SV7: $i] :
( ( ( unequally_directed_lines @ SV7 @ SV29 )
| ( unequally_directed_lines @ SV7 @ ( reverse_line @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(219,plain,
! [SV30: $i,SV8: $i] :
( ( ~ ( unequally_directed_lines @ SV8 @ SV30 )
| ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) )
| ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(220,plain,
! [SV31: $i,SV9: $i] :
( ( ~ ( point @ SV9 )
| ~ ( point @ SV31 )
| ~ ( distinct_points @ SV9 @ SV31 )
| ( line @ ( line_connecting @ SV9 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(221,plain,
! [SV32: $i,SV10: $i] :
( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) )
| ( point @ ( intersection_point @ SV10 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(222,plain,
! [SV33: $i,SV11: $i] :
( ( ~ ( line @ SV11 )
| ~ ( point @ SV33 )
| ( line @ ( parallel_through_point @ SV11 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(223,plain,
! [SV12: $i] :
( ( ( ~ ( line @ SV12 ) )
= $true )
| ( ( line @ ( reverse_line @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV34: $i,SV13: $i] :
( ( ~ ( apart_point_and_line @ SV13 @ ( parallel_through_point @ SV34 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
! [SV14: $i] :
( ( distinct_lines @ SV14 @ ( reverse_line @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(226,plain,
! [SV35: $i,SV15: $i] :
( ( ~ ( distinct_points @ SV15 @ SV35 )
| ( equally_directed_lines @ ( line_connecting @ SV15 @ SV35 ) @ ( reverse_line @ ( line_connecting @ SV35 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(227,plain,
! [SV16: $i,SV36: $i] :
( ( equally_directed_lines @ ( parallel_through_point @ SV36 @ SV16 ) @ SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(228,plain,
! [SV37: $i,SV17: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ( distinct_lines @ SY167 @ SY168 )
| ~ ( distinct_points @ SV17 @ SV37 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY168 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY168 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY167 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY167 ) )
| ( left_apart_point @ SV37 @ SY168 )
| ( left_apart_point @ SV17 @ SY168 )
| ( left_apart_point @ SV17 @ SY167 )
| ( left_apart_point @ SV37 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(229,plain,
! [SV38: $i,SV18: $i] :
( ( ! [SY169: $i] :
( ~ ( distinct_points @ SV18 @ SV38 )
| ~ ( left_apart_point @ SV18 @ SY169 )
| ( left_apart_point @ SV38 @ SY169 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(230,plain,
! [SV39: $i,SV19: $i] :
( ( ! [SY170: $i] :
( ~ ( left_apart_point @ SV19 @ SY170 )
| ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(231,plain,
! [SV40: $i,SV20: $i] :
( ( ! [SY171: $i] :
( ~ ( left_apart_point @ SV20 @ SV40 )
| ~ ( unequally_directed_lines @ SV40 @ SY171 )
| ( distinct_lines @ SV40 @ SY171 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(232,plain,
! [SV41: $i,SV21: $i] :
( ( ~ ( left_convergent_lines @ SV21 @ SV41 )
| ! [SY172: $i] :
( ( left_convergent_lines @ SV21 @ SY172 )
| ( unequally_directed_lines @ SV41 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(233,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(234,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(236,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(237,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) )
| ~ ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) )
| ~ ~ ( ~ ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(238,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(239,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(240,plain,
! [SV23: $i] :
( ( ~ ! [SY129: $i,SY130: $i] :
( ~ ( distinct_points @ SY129 @ SY130 )
| ~ ( incident_point_and_line @ SY129 @ SV23 )
| ~ ( incident_point_and_line @ SY130 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SY129 @ SY130 ) )
| ( before_on_line @ SV23 @ SY129 @ SY130 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(241,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(242,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(243,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(245,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) )
| ~ ~ ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) )
| ~ ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(246,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(247,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(249,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(250,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(251,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(252,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
| ~ ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) )
| ~ ~ ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) )
| ~ ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(253,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(254,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(255,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(256,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(257,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(258,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(259,plain,
! [SV26: $i,SV2: $i] :
( ( ( ~ ( distinct_points @ SV2 @ SV26 ) )
= $true )
| ( ( ! [SY164: $i] :
( ( distinct_points @ SV2 @ SY164 )
| ( distinct_points @ SV26 @ SY164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(260,plain,
! [SV27: $i,SV4: $i] :
( ( ( ~ ( distinct_lines @ SV4 @ SV27 ) )
= $true )
| ( ( ! [SY165: $i] :
( ( distinct_lines @ SV4 @ SY165 )
| ( distinct_lines @ SV27 @ SY165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(261,plain,
! [SV28: $i,SV6: $i] :
( ( ( ~ ( unequally_directed_lines @ SV6 @ SV28 ) )
= $true )
| ( ( ! [SY166: $i] :
( ( unequally_directed_lines @ SV6 @ SY166 )
| ( unequally_directed_lines @ SV28 @ SY166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(262,plain,
! [SV29: $i,SV7: $i] :
( ( ( unequally_directed_lines @ SV7 @ SV29 )
= $true )
| ( ( unequally_directed_lines @ SV7 @ ( reverse_line @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(263,plain,
! [SV30: $i,SV8: $i] :
( ( ( ~ ( unequally_directed_lines @ SV8 @ SV30 )
| ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(264,plain,
! [SV31: $i,SV9: $i] :
( ( ( ~ ( point @ SV9 )
| ~ ( point @ SV31 )
| ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(265,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(266,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( line @ SV11 )
| ~ ( point @ SV33 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(267,plain,
! [SV12: $i] :
( ( ( line @ SV12 )
= $false )
| ( ( line @ ( reverse_line @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(268,plain,
! [SV34: $i,SV13: $i] :
( ( apart_point_and_line @ SV13 @ ( parallel_through_point @ SV34 @ SV13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(269,plain,
! [SV35: $i,SV15: $i] :
( ( ( ~ ( distinct_points @ SV15 @ SV35 ) )
= $true )
| ( ( equally_directed_lines @ ( line_connecting @ SV15 @ SV35 ) @ ( reverse_line @ ( line_connecting @ SV35 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(270,plain,
! [SV37: $i,SV17: $i,SV43: $i] :
( ( ! [SY185: $i] :
( ~ ( distinct_lines @ SV43 @ SY185 )
| ~ ( distinct_points @ SV17 @ SV37 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY185 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SY185 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SY185 )
| ( left_apart_point @ SV17 @ SY185 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(271,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ~ ( distinct_points @ SV18 @ SV38 )
| ~ ( left_apart_point @ SV18 @ SV44 )
| ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(272,plain,
! [SV39: $i,SV45: $i,SV19: $i] :
( ( ~ ( left_apart_point @ SV19 @ SV45 )
| ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(273,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ~ ( left_apart_point @ SV20 @ SV40 )
| ~ ( unequally_directed_lines @ SV40 @ SV46 )
| ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(274,plain,
! [SV41: $i,SV21: $i] :
( ( ( ~ ( left_convergent_lines @ SV21 @ SV41 ) )
= $true )
| ( ( ! [SY172: $i] :
( ( left_convergent_lines @ SV21 @ SY172 )
| ( unequally_directed_lines @ SV41 @ SY172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(276,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(277,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(278,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(279,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) )
| ~ ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(280,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(281,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(282,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(283,plain,
! [SV23: $i] :
( ( ~ ! [SY129: $i,SY130: $i] :
( ~ ( distinct_points @ SY129 @ SY130 )
| ~ ( incident_point_and_line @ SY129 @ SV23 )
| ~ ( incident_point_and_line @ SY130 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SY129 @ SY130 ) )
| ( before_on_line @ SV23 @ SY129 @ SY130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(284,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(285,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(286,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(287,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(288,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(289,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) )
| ~ ~ ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) )
| ~ ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(290,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(291,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(292,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(293,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(294,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(295,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(296,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
| ~ ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(297,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) )
| ~ ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(298,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_opposite_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(299,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( equally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_opposite_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(301,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(302,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(303,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(304,plain,
! [SV26: $i,SV2: $i] :
( ( ( distinct_points @ SV2 @ SV26 )
= $false )
| ( ( ! [SY164: $i] :
( ( distinct_points @ SV2 @ SY164 )
| ( distinct_points @ SV26 @ SY164 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(305,plain,
! [SV27: $i,SV4: $i] :
( ( ( distinct_lines @ SV4 @ SV27 )
= $false )
| ( ( ! [SY165: $i] :
( ( distinct_lines @ SV4 @ SY165 )
| ( distinct_lines @ SV27 @ SY165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(306,plain,
! [SV28: $i,SV6: $i] :
( ( ( unequally_directed_lines @ SV6 @ SV28 )
= $false )
| ( ( ! [SY166: $i] :
( ( unequally_directed_lines @ SV6 @ SY166 )
| ( unequally_directed_lines @ SV28 @ SY166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(307,plain,
! [SV30: $i,SV8: $i] :
( ( ( ~ ( unequally_directed_lines @ SV8 @ SV30 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(308,plain,
! [SV31: $i,SV9: $i] :
( ( ( ~ ( point @ SV9 )
| ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(309,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 )
| ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(310,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( line @ SV11 ) )
= $true )
| ( ( ~ ( point @ SV33 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(311,plain,
! [SV35: $i,SV15: $i] :
( ( ( distinct_points @ SV15 @ SV35 )
= $false )
| ( ( equally_directed_lines @ ( line_connecting @ SV15 @ SV35 ) @ ( reverse_line @ ( line_connecting @ SV35 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(312,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ~ ( distinct_lines @ SV43 @ SV47 )
| ~ ( distinct_points @ SV17 @ SV37 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(313,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( ~ ( distinct_points @ SV18 @ SV38 )
| ~ ( left_apart_point @ SV18 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(314,plain,
! [SV39: $i,SV45: $i,SV19: $i] :
( ( ( ~ ( left_apart_point @ SV19 @ SV45 ) )
= $true )
| ( ( ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(315,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ( ~ ( left_apart_point @ SV20 @ SV40 )
| ~ ( unequally_directed_lines @ SV40 @ SV46 ) )
= $true )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(316,plain,
! [SV41: $i,SV21: $i] :
( ( ( left_convergent_lines @ SV21 @ SV41 )
= $false )
| ( ( ! [SY172: $i] :
( ( left_convergent_lines @ SV21 @ SY172 )
| ( unequally_directed_lines @ SV41 @ SY172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(317,plain,
! [SV48: $i] :
( ( ! [SY186: $i] :
( ~ ( apart_point_and_line @ SV48 @ SY186 )
| ( left_apart_point @ SV48 @ SY186 )
| ( right_apart_point @ SV48 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(318,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(319,plain,
! [SV49: $i] :
( ( ! [SY187: $i] :
~ ( left_convergent_lines @ SV49 @ SY187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(320,plain,
! [SV50: $i] :
( ( ! [SY188: $i] :
~ ( left_convergent_lines @ SV50 @ ( reverse_line @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(321,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) )
| ~ ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(322,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(323,plain,
! [SV51: $i] :
( ( ! [SY189: $i] :
( ~ ( unequally_directed_lines @ SV51 @ ( reverse_line @ SY189 ) )
| ( unequally_directed_opposite_lines @ SV51 @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(324,plain,
! [SV52: $i] :
( ( ! [SY190: $i] :
( ~ ( unequally_directed_opposite_lines @ SV52 @ SY190 )
| ( unequally_directed_lines @ SV52 @ ( reverse_line @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(325,plain,
! [SV23: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ( distinct_points @ SY129 @ SY130 )
| ~ ( incident_point_and_line @ SY129 @ SV23 )
| ~ ( incident_point_and_line @ SY130 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SY129 @ SY130 ) )
| ( before_on_line @ SV23 @ SY129 @ SY130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(326,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(327,plain,
! [SV53: $i] :
( ( ! [SY191: $i] :
( ~ ( left_apart_point @ SV53 @ ( reverse_line @ SY191 ) )
| ( right_apart_point @ SV53 @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(328,plain,
! [SV54: $i] :
( ( ! [SY192: $i] :
( ~ ( right_apart_point @ SV54 @ SY192 )
| ( left_apart_point @ SV54 @ ( reverse_line @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(329,plain,
! [SV55: $i] :
( ( ! [SY193: $i] :
( ~ ( left_convergent_lines @ SV55 @ ( reverse_line @ SY193 ) )
| ( right_convergent_lines @ SV55 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(330,plain,
! [SV56: $i] :
( ( ! [SY194: $i] :
( ~ ( right_convergent_lines @ SV56 @ SY194 )
| ( left_convergent_lines @ SV56 @ ( reverse_line @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(331,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(332,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ~ ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) )
| ~ ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(333,plain,
! [SV57: $i] :
( ( ! [SY195: $i] :
~ ( left_apart_point @ SV57 @ SY195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(334,plain,
! [SV58: $i] :
( ( ! [SY196: $i] :
~ ( left_apart_point @ SV58 @ ( reverse_line @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(335,plain,
! [SV59: $i] :
( ( ! [SY197: $i] :
( ~ ( unequally_directed_lines @ SV59 @ SY197 )
| ~ ( unequally_directed_lines @ SV59 @ ( reverse_line @ SY197 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SY197 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(336,plain,
! [SV60: $i] :
( ( ! [SY198: $i] :
( ~ ( unequally_directed_lines @ SV60 @ SY198 )
| ~ ( unequally_directed_lines @ SV60 @ ( reverse_line @ SY198 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV60 @ SY198 ) @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(337,plain,
! [SV61: $i] :
( ( ! [SY199: $i] :
( ~ ( distinct_points @ SV61 @ SY199 )
| ~ ( apart_point_and_line @ SV61 @ ( line_connecting @ SV61 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(338,plain,
! [SV62: $i] :
( ( ! [SY200: $i] :
( ~ ( distinct_points @ SV62 @ SY200 )
| ~ ( apart_point_and_line @ SY200 @ ( line_connecting @ SV62 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(339,plain,
! [SV25: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
| ~ ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(340,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) )
| ~ ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(341,plain,
! [SV63: $i] :
( ( ! [SY201: $i] :
( ~ ( equally_directed_opposite_lines @ SV63 @ SY201 )
| ~ ( unequally_directed_opposite_lines @ SV63 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(342,plain,
! [SV64: $i] :
( ( ! [SY202: $i] :
( ( unequally_directed_opposite_lines @ SV64 @ SY202 )
| ( equally_directed_opposite_lines @ SV64 @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(343,plain,
! [SV65: $i] :
( ( ! [SY203: $i] :
( ~ ( unequally_directed_lines @ SV65 @ SY203 )
| ~ ( unequally_directed_opposite_lines @ SV65 @ SY203 )
| ( convergent_lines @ SV65 @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(344,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(345,plain,
! [SV66: $i] :
( ( ! [SY204: $i] :
( ~ ( equally_directed_lines @ SV66 @ SY204 )
| ~ ( unequally_directed_lines @ SV66 @ SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(346,plain,
! [SV67: $i] :
( ( ! [SY205: $i] :
( ( unequally_directed_lines @ SV67 @ SY205 )
| ( equally_directed_lines @ SV67 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(347,plain,
! [SV26: $i,SV68: $i,SV2: $i] :
( ( ( ( distinct_points @ SV2 @ SV68 )
| ( distinct_points @ SV26 @ SV68 ) )
= $true )
| ( ( distinct_points @ SV2 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(348,plain,
! [SV27: $i,SV69: $i,SV4: $i] :
( ( ( ( distinct_lines @ SV4 @ SV69 )
| ( distinct_lines @ SV27 @ SV69 ) )
= $true )
| ( ( distinct_lines @ SV4 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(349,plain,
! [SV28: $i,SV70: $i,SV6: $i] :
( ( ( ( unequally_directed_lines @ SV6 @ SV70 )
| ( unequally_directed_lines @ SV28 @ SV70 ) )
= $true )
| ( ( unequally_directed_lines @ SV6 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(350,plain,
! [SV30: $i,SV8: $i] :
( ( ( unequally_directed_lines @ SV8 @ SV30 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(351,plain,
! [SV31: $i,SV9: $i] :
( ( ( ~ ( point @ SV9 ) )
= $true )
| ( ( ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(352,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 )
| ~ ( line @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(353,plain,
! [SV33: $i,SV11: $i] :
( ( ( line @ SV11 )
= $false )
| ( ( ~ ( point @ SV33 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(354,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ( ~ ( distinct_lines @ SV43 @ SV47 )
| ~ ( distinct_points @ SV17 @ SV37 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(355,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( ~ ( distinct_points @ SV18 @ SV38 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV18 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(356,plain,
! [SV39: $i,SV45: $i,SV19: $i] :
( ( ( left_apart_point @ SV19 @ SV45 )
= $false )
| ( ( ( distinct_points @ SV19 @ SV39 )
| ( left_apart_point @ SV39 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(357,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ( ~ ( left_apart_point @ SV20 @ SV40 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV40 @ SV46 ) )
= $true )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(358,plain,
! [SV41: $i,SV71: $i,SV21: $i] :
( ( ( ( left_convergent_lines @ SV21 @ SV71 )
| ( unequally_directed_lines @ SV41 @ SV71 ) )
= $true )
| ( ( left_convergent_lines @ SV21 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(359,plain,
! [SV72: $i,SV48: $i] :
( ( ~ ( apart_point_and_line @ SV48 @ SV72 )
| ( left_apart_point @ SV48 @ SV72 )
| ( right_apart_point @ SV48 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(360,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(361,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(362,plain,
! [SV73: $i,SV49: $i] :
( ( ~ ( left_convergent_lines @ SV49 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(363,plain,
! [SV74: $i,SV50: $i] :
( ( ~ ( left_convergent_lines @ SV50 @ ( reverse_line @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(364,plain,
! [SV22: $i] :
( ( ~ ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) )
| ~ ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(365,plain,
! [SV22: $i] :
( ( ~ ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(366,plain,
! [SV75: $i,SV51: $i] :
( ( ~ ( unequally_directed_lines @ SV51 @ ( reverse_line @ SV75 ) )
| ( unequally_directed_opposite_lines @ SV51 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(367,plain,
! [SV76: $i,SV52: $i] :
( ( ~ ( unequally_directed_opposite_lines @ SV52 @ SV76 )
| ( unequally_directed_lines @ SV52 @ ( reverse_line @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(368,plain,
! [SV23: $i,SV77: $i] :
( ( ! [SY206: $i] :
( ~ ( distinct_points @ SV77 @ SY206 )
| ~ ( incident_point_and_line @ SV77 @ SV23 )
| ~ ( incident_point_and_line @ SY206 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SY206 ) )
| ( before_on_line @ SV23 @ SV77 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(369,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(370,plain,
! [SV78: $i,SV53: $i] :
( ( ~ ( left_apart_point @ SV53 @ ( reverse_line @ SV78 ) )
| ( right_apart_point @ SV53 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(371,plain,
! [SV79: $i,SV54: $i] :
( ( ~ ( right_apart_point @ SV54 @ SV79 )
| ( left_apart_point @ SV54 @ ( reverse_line @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(372,plain,
! [SV80: $i,SV55: $i] :
( ( ~ ( left_convergent_lines @ SV55 @ ( reverse_line @ SV80 ) )
| ( right_convergent_lines @ SV55 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(373,plain,
! [SV81: $i,SV56: $i] :
( ( ~ ( right_convergent_lines @ SV56 @ SV81 )
| ( left_convergent_lines @ SV56 @ ( reverse_line @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(374,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(375,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) )
| ~ ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(376,plain,
! [SV82: $i,SV57: $i] :
( ( ~ ( left_apart_point @ SV57 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(377,plain,
! [SV83: $i,SV58: $i] :
( ( ~ ( left_apart_point @ SV58 @ ( reverse_line @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(378,plain,
! [SV84: $i,SV59: $i] :
( ( ~ ( unequally_directed_lines @ SV59 @ SV84 )
| ~ ( unequally_directed_lines @ SV59 @ ( reverse_line @ SV84 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV84 ) @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(379,plain,
! [SV85: $i,SV60: $i] :
( ( ~ ( unequally_directed_lines @ SV60 @ SV85 )
| ~ ( unequally_directed_lines @ SV60 @ ( reverse_line @ SV85 ) )
| ~ ( apart_point_and_line @ ( intersection_point @ SV60 @ SV85 ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(380,plain,
! [SV86: $i,SV61: $i] :
( ( ~ ( distinct_points @ SV61 @ SV86 )
| ~ ( apart_point_and_line @ SV61 @ ( line_connecting @ SV61 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(381,plain,
! [SV87: $i,SV62: $i] :
( ( ~ ( distinct_points @ SV62 @ SV87 )
| ~ ( apart_point_and_line @ SV87 @ ( line_connecting @ SV62 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(382,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
| ~ ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(383,plain,
! [SV25: $i] :
( ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) )
| ~ ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(384,plain,
! [SV88: $i,SV63: $i] :
( ( ~ ( equally_directed_opposite_lines @ SV63 @ SV88 )
| ~ ( unequally_directed_opposite_lines @ SV63 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(385,plain,
! [SV89: $i,SV64: $i] :
( ( ( unequally_directed_opposite_lines @ SV64 @ SV89 )
| ( equally_directed_opposite_lines @ SV64 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(386,plain,
! [SV90: $i,SV65: $i] :
( ( ~ ( unequally_directed_lines @ SV65 @ SV90 )
| ~ ( unequally_directed_opposite_lines @ SV65 @ SV90 )
| ( convergent_lines @ SV65 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(387,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(388,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(389,plain,
! [SV91: $i,SV66: $i] :
( ( ~ ( equally_directed_lines @ SV66 @ SV91 )
| ~ ( unequally_directed_lines @ SV66 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(390,plain,
! [SV92: $i,SV67: $i] :
( ( ( unequally_directed_lines @ SV67 @ SV92 )
| ( equally_directed_lines @ SV67 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(391,plain,
! [SV26: $i,SV68: $i,SV2: $i] :
( ( ( distinct_points @ SV2 @ SV68 )
= $true )
| ( ( distinct_points @ SV26 @ SV68 )
= $true )
| ( ( distinct_points @ SV2 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(392,plain,
! [SV27: $i,SV69: $i,SV4: $i] :
( ( ( distinct_lines @ SV4 @ SV69 )
= $true )
| ( ( distinct_lines @ SV27 @ SV69 )
= $true )
| ( ( distinct_lines @ SV4 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(393,plain,
! [SV28: $i,SV70: $i,SV6: $i] :
( ( ( unequally_directed_lines @ SV6 @ SV70 )
= $true )
| ( ( unequally_directed_lines @ SV28 @ SV70 )
= $true )
| ( ( unequally_directed_lines @ SV6 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(394,plain,
! [SV30: $i,SV8: $i] :
( ( ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) )
= $false )
| ( ( unequally_directed_lines @ SV8 @ SV30 )
= $false )
| ( ( ( left_convergent_lines @ SV8 @ SV30 )
| ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(395,plain,
! [SV31: $i,SV9: $i] :
( ( ( point @ SV9 )
= $false )
| ( ( ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(396,plain,
! [SV32: $i,SV10: $i] :
( ( ( ~ ( line @ SV10 ) )
= $true )
| ( ( ~ ( line @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(397,plain,
! [SV11: $i,SV33: $i] :
( ( ( point @ SV33 )
= $false )
| ( ( line @ SV11 )
= $false )
| ( ( line @ ( parallel_through_point @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(398,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ( ~ ( distinct_lines @ SV43 @ SV47 ) )
= $true )
| ( ( ~ ( distinct_points @ SV17 @ SV37 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(399,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( distinct_points @ SV18 @ SV38 )
= $false )
| ( ( ~ ( left_apart_point @ SV18 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(400,plain,
! [SV45: $i,SV39: $i,SV19: $i] :
( ( ( distinct_points @ SV19 @ SV39 )
= $true )
| ( ( left_apart_point @ SV39 @ SV45 )
= $true )
| ( ( left_apart_point @ SV19 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(401,plain,
! [SV46: $i,SV40: $i,SV20: $i] :
( ( ( left_apart_point @ SV20 @ SV40 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV40 @ SV46 ) )
= $true )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(402,plain,
! [SV41: $i,SV71: $i,SV21: $i] :
( ( ( left_convergent_lines @ SV21 @ SV71 )
= $true )
| ( ( unequally_directed_lines @ SV41 @ SV71 )
= $true )
| ( ( left_convergent_lines @ SV21 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(403,plain,
! [SV72: $i,SV48: $i] :
( ( ( ~ ( apart_point_and_line @ SV48 @ SV72 ) )
= $true )
| ( ( ( left_apart_point @ SV48 @ SV72 )
| ( right_apart_point @ SV48 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(404,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(405,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( right_apart_point @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(406,plain,
! [SV73: $i,SV49: $i] :
( ( left_convergent_lines @ SV49 @ SV73 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(407,plain,
! [SV74: $i,SV50: $i] :
( ( left_convergent_lines @ SV50 @ ( reverse_line @ SV74 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(408,plain,
! [SV22: $i] :
( ( ~ ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(409,plain,
! [SV22: $i] :
( ( ~ ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(410,plain,
! [SV22: $i] :
( ( ~ ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(411,plain,
! [SV22: $i] :
( ( ~ ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(412,plain,
! [SV75: $i,SV51: $i] :
( ( ( ~ ( unequally_directed_lines @ SV51 @ ( reverse_line @ SV75 ) ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV51 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(413,plain,
! [SV76: $i,SV52: $i] :
( ( ( ~ ( unequally_directed_opposite_lines @ SV52 @ SV76 ) )
= $true )
| ( ( unequally_directed_lines @ SV52 @ ( reverse_line @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(414,plain,
! [SV23: $i,SV93: $i,SV77: $i] :
( ( ~ ( distinct_points @ SV77 @ SV93 )
| ~ ( incident_point_and_line @ SV77 @ SV23 )
| ~ ( incident_point_and_line @ SV93 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) )
| ( before_on_line @ SV23 @ SV77 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(415,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(416,plain,
! [SV23: $i] :
( ( ~ ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(417,plain,
! [SV78: $i,SV53: $i] :
( ( ( ~ ( left_apart_point @ SV53 @ ( reverse_line @ SV78 ) ) )
= $true )
| ( ( right_apart_point @ SV53 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(418,plain,
! [SV79: $i,SV54: $i] :
( ( ( ~ ( right_apart_point @ SV54 @ SV79 ) )
= $true )
| ( ( left_apart_point @ SV54 @ ( reverse_line @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(419,plain,
! [SV80: $i,SV55: $i] :
( ( ( ~ ( left_convergent_lines @ SV55 @ ( reverse_line @ SV80 ) ) )
= $true )
| ( ( right_convergent_lines @ SV55 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(420,plain,
! [SV81: $i,SV56: $i] :
( ( ( ~ ( right_convergent_lines @ SV56 @ SV81 ) )
= $true )
| ( ( left_convergent_lines @ SV56 @ ( reverse_line @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(421,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
| ~ ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(422,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) )
| ~ ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(423,plain,
! [SV82: $i,SV57: $i] :
( ( left_apart_point @ SV57 @ SV82 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(424,plain,
! [SV83: $i,SV58: $i] :
( ( left_apart_point @ SV58 @ ( reverse_line @ SV83 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(425,plain,
! [SV84: $i,SV59: $i] :
( ( ( ~ ( unequally_directed_lines @ SV59 @ SV84 )
| ~ ( unequally_directed_lines @ SV59 @ ( reverse_line @ SV84 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV84 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(426,plain,
! [SV85: $i,SV60: $i] :
( ( ( ~ ( unequally_directed_lines @ SV60 @ SV85 )
| ~ ( unequally_directed_lines @ SV60 @ ( reverse_line @ SV85 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV60 @ SV85 ) @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(427,plain,
! [SV86: $i,SV61: $i] :
( ( ( ~ ( distinct_points @ SV61 @ SV86 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV61 @ ( line_connecting @ SV61 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(428,plain,
! [SV87: $i,SV62: $i] :
( ( ( ~ ( distinct_points @ SV62 @ SV87 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV87 @ ( line_connecting @ SV62 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(429,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(430,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(431,plain,
! [SV25: $i] :
( ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(432,plain,
! [SV25: $i] :
( ( ~ ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(433,plain,
! [SV88: $i,SV63: $i] :
( ( ( ~ ( equally_directed_opposite_lines @ SV63 @ SV88 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV63 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(434,plain,
! [SV89: $i,SV64: $i] :
( ( ( unequally_directed_opposite_lines @ SV64 @ SV89 )
= $true )
| ( ( equally_directed_opposite_lines @ SV64 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(435,plain,
! [SV90: $i,SV65: $i] :
( ( ( ~ ( unequally_directed_lines @ SV65 @ SV90 )
| ~ ( unequally_directed_opposite_lines @ SV65 @ SV90 ) )
= $true )
| ( ( convergent_lines @ SV65 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(436,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(437,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_opposite_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(438,plain,
! [SV91: $i,SV66: $i] :
( ( ( ~ ( equally_directed_lines @ SV66 @ SV91 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV66 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(439,plain,
! [SV92: $i,SV67: $i] :
( ( ( unequally_directed_lines @ SV67 @ SV92 )
= $true )
| ( ( equally_directed_lines @ SV67 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(440,plain,
! [SV30: $i,SV8: $i] :
( ( ( left_convergent_lines @ SV8 @ SV30 )
= $true )
| ( ( left_convergent_lines @ SV8 @ ( reverse_line @ SV30 ) )
= $true )
| ( ( unequally_directed_lines @ SV8 @ SV30 )
= $false )
| ( ( unequally_directed_lines @ SV8 @ ( reverse_line @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(441,plain,
! [SV9: $i,SV31: $i] :
( ( ( point @ SV31 )
= $false )
| ( ( point @ SV9 )
= $false )
| ( ( ~ ( distinct_points @ SV9 @ SV31 ) )
= $true )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(442,plain,
! [SV32: $i,SV10: $i] :
( ( ( line @ SV10 )
= $false )
| ( ( ~ ( line @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(443,plain,
! [SV37: $i,SV17: $i,SV47: $i,SV43: $i] :
( ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( ~ ( distinct_points @ SV17 @ SV37 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(444,plain,
! [SV38: $i,SV44: $i,SV18: $i] :
( ( ( left_apart_point @ SV18 @ SV44 )
= $false )
| ( ( distinct_points @ SV18 @ SV38 )
= $false )
| ( ( ( left_apart_point @ SV38 @ SV44 )
| ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(445,plain,
! [SV20: $i,SV46: $i,SV40: $i] :
( ( ( unequally_directed_lines @ SV40 @ SV46 )
= $false )
| ( ( left_apart_point @ SV20 @ SV40 )
= $false )
| ( ( ( distinct_lines @ SV40 @ SV46 )
| ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(446,plain,
! [SV72: $i,SV48: $i] :
( ( ( apart_point_and_line @ SV48 @ SV72 )
= $false )
| ( ( ( left_apart_point @ SV48 @ SV72 )
| ( right_apart_point @ SV48 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(447,plain,
! [SV94: $i] :
( ( ! [SY207: $i] :
( ~ ( left_apart_point @ SV94 @ SY207 )
| ( apart_point_and_line @ SV94 @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(448,plain,
! [SV95: $i] :
( ( ! [SY208: $i] :
( ~ ( right_apart_point @ SV95 @ SY208 )
| ( apart_point_and_line @ SV95 @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(449,plain,
! [SV22: $i] :
( ( ! [SY121: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY121 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY121 ) )
| ! [SY122: $i] :
( ( unequally_directed_lines @ SV22 @ SY122 )
| ( unequally_directed_lines @ SY121 @ SY122 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(450,plain,
! [SV22: $i] :
( ( ! [SY123: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY123 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY123 ) )
| ! [SY124: $i] :
( ( unequally_directed_lines @ SV22 @ SY124 )
| ( unequally_directed_lines @ SY123 @ ( reverse_line @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(451,plain,
! [SV22: $i] :
( ( ! [SY125: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY125 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY125 ) )
| ! [SY126: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY126 ) )
| ( unequally_directed_lines @ SY125 @ SY126 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(452,plain,
! [SV22: $i] :
( ( ! [SY127: $i] :
( ~ ( unequally_directed_lines @ SV22 @ SY127 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY127 ) )
| ! [SY128: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY128 ) )
| ( unequally_directed_lines @ SY127 @ ( reverse_line @ SY128 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(453,plain,
! [SV75: $i,SV51: $i] :
( ( ( unequally_directed_lines @ SV51 @ ( reverse_line @ SV75 ) )
= $false )
| ( ( unequally_directed_opposite_lines @ SV51 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(454,plain,
! [SV76: $i,SV52: $i] :
( ( ( unequally_directed_opposite_lines @ SV52 @ SV76 )
= $false )
| ( ( unequally_directed_lines @ SV52 @ ( reverse_line @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(455,plain,
! [SV23: $i,SV93: $i,SV77: $i] :
( ( ( ~ ( distinct_points @ SV77 @ SV93 )
| ~ ( incident_point_and_line @ SV77 @ SV23 )
| ~ ( incident_point_and_line @ SV93 @ SV23 )
| ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(456,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(457,plain,
! [SV23: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( before_on_line @ SV23 @ SY137 @ SY138 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SY137 @ SY138 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(458,plain,
! [SV78: $i,SV53: $i] :
( ( ( left_apart_point @ SV53 @ ( reverse_line @ SV78 ) )
= $false )
| ( ( right_apart_point @ SV53 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(459,plain,
! [SV79: $i,SV54: $i] :
( ( ( right_apart_point @ SV54 @ SV79 )
= $false )
| ( ( left_apart_point @ SV54 @ ( reverse_line @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(460,plain,
! [SV80: $i,SV55: $i] :
( ( ( left_convergent_lines @ SV55 @ ( reverse_line @ SV80 ) )
= $false )
| ( ( right_convergent_lines @ SV55 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(461,plain,
! [SV81: $i,SV56: $i] :
( ( ( right_convergent_lines @ SV56 @ SV81 )
= $false )
| ( ( left_convergent_lines @ SV56 @ ( reverse_line @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(462,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(463,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(464,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(465,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(466,plain,
! [SV84: $i,SV59: $i] :
( ( ( ~ ( unequally_directed_lines @ SV59 @ SV84 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV59 @ ( reverse_line @ SV84 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV84 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(467,plain,
! [SV85: $i,SV60: $i] :
( ( ( ~ ( unequally_directed_lines @ SV60 @ SV85 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV60 @ ( reverse_line @ SV85 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV60 @ SV85 ) @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(468,plain,
! [SV86: $i,SV61: $i] :
( ( ( distinct_points @ SV61 @ SV86 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV61 @ ( line_connecting @ SV61 @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(469,plain,
! [SV87: $i,SV62: $i] :
( ( ( distinct_points @ SV62 @ SV87 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV87 @ ( line_connecting @ SV62 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(470,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(471,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(472,plain,
! [SV25: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ~ ( left_apart_point @ SV25 @ SY161 )
| ~ ( right_apart_point @ SY160 @ SY161 )
| ( divides_points @ SY161 @ SV25 @ SY160 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(473,plain,
! [SV25: $i] :
( ( ! [SY162: $i,SY163: $i] :
( ~ ( left_apart_point @ SY162 @ SY163 )
| ~ ( right_apart_point @ SV25 @ SY163 )
| ( divides_points @ SY163 @ SV25 @ SY162 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(474,plain,
! [SV88: $i,SV63: $i] :
( ( ( equally_directed_opposite_lines @ SV63 @ SV88 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV63 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(475,plain,
! [SV90: $i,SV65: $i] :
( ( ( ~ ( unequally_directed_lines @ SV65 @ SV90 ) )
= $true )
| ( ( ~ ( unequally_directed_opposite_lines @ SV65 @ SV90 ) )
= $true )
| ( ( convergent_lines @ SV65 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(476,plain,
! [SV96: $i] :
( ( ! [SY209: $i] :
( ~ ( convergent_lines @ SV96 @ SY209 )
| ( unequally_directed_lines @ SV96 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(477,plain,
! [SV97: $i] :
( ( ! [SY210: $i] :
( ~ ( convergent_lines @ SV97 @ SY210 )
| ( unequally_directed_opposite_lines @ SV97 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(478,plain,
! [SV91: $i,SV66: $i] :
( ( ( equally_directed_lines @ SV66 @ SV91 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV66 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(479,plain,
! [SV31: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV31 )
= $false )
| ( ( point @ SV9 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( line @ ( line_connecting @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(480,plain,
! [SV10: $i,SV32: $i] :
( ( ( line @ SV32 )
= $false )
| ( ( line @ SV10 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV10 @ SV32 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(481,plain,
! [SV47: $i,SV43: $i,SV37: $i,SV17: $i] :
( ( ( distinct_points @ SV17 @ SV37 )
= $false )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(482,plain,
! [SV18: $i,SV44: $i,SV38: $i] :
( ( ( left_apart_point @ SV38 @ SV44 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV18 @ SV38 ) @ SV44 )
= $true )
| ( ( distinct_points @ SV18 @ SV38 )
= $false )
| ( ( left_apart_point @ SV18 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(483,plain,
! [SV20: $i,SV46: $i,SV40: $i] :
( ( ( distinct_lines @ SV40 @ SV46 )
= $true )
| ( ( left_apart_point @ SV20 @ ( reverse_line @ SV46 ) )
= $true )
| ( ( left_apart_point @ SV20 @ SV40 )
= $false )
| ( ( unequally_directed_lines @ SV40 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(484,plain,
! [SV72: $i,SV48: $i] :
( ( ( left_apart_point @ SV48 @ SV72 )
= $true )
| ( ( right_apart_point @ SV48 @ SV72 )
= $true )
| ( ( apart_point_and_line @ SV48 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(485,plain,
! [SV98: $i,SV94: $i] :
( ( ~ ( left_apart_point @ SV94 @ SV98 )
| ( apart_point_and_line @ SV94 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(486,plain,
! [SV99: $i,SV95: $i] :
( ( ~ ( right_apart_point @ SV95 @ SV99 )
| ( apart_point_and_line @ SV95 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(487,plain,
! [SV100: $i,SV22: $i] :
( ( ~ ( unequally_directed_lines @ SV22 @ SV100 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) )
| ! [SY211: $i] :
( ( unequally_directed_lines @ SV22 @ SY211 )
| ( unequally_directed_lines @ SV100 @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(488,plain,
! [SV101: $i,SV22: $i] :
( ( ~ ( unequally_directed_lines @ SV22 @ SV101 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) )
| ! [SY212: $i] :
( ( unequally_directed_lines @ SV22 @ SY212 )
| ( unequally_directed_lines @ SV101 @ ( reverse_line @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(489,plain,
! [SV102: $i,SV22: $i] :
( ( ~ ( unequally_directed_lines @ SV22 @ SV102 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) )
| ! [SY213: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY213 ) )
| ( unequally_directed_lines @ SV102 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(490,plain,
! [SV103: $i,SV22: $i] :
( ( ~ ( unequally_directed_lines @ SV22 @ SV103 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) )
| ! [SY214: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY214 ) )
| ( unequally_directed_lines @ SV103 @ ( reverse_line @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(491,plain,
! [SV23: $i,SV93: $i,SV77: $i] :
( ( ( ~ ( distinct_points @ SV77 @ SV93 )
| ~ ( incident_point_and_line @ SV77 @ SV23 )
| ~ ( incident_point_and_line @ SV93 @ SV23 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(492,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(493,plain,
! [SV104: $i,SV23: $i] :
( ( ! [SY215: $i] :
( ~ ( before_on_line @ SV23 @ SV104 @ SY215 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SV104 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(494,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(495,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(496,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SY181 )
| ~ ( before_on_line @ SV24 @ SY181 @ SY182 )
| ( between_on_line @ SV24 @ SV42 @ SY181 @ SY182 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(497,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY183: $i,SY184: $i] :
( ~ ( before_on_line @ SV24 @ SY184 @ SY183 )
| ~ ( before_on_line @ SV24 @ SY183 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SY183 @ SY184 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(498,plain,
! [SV84: $i,SV59: $i] :
( ( ( unequally_directed_lines @ SV59 @ SV84 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV59 @ ( reverse_line @ SV84 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV84 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(499,plain,
! [SV85: $i,SV60: $i] :
( ( ( unequally_directed_lines @ SV60 @ SV85 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV60 @ ( reverse_line @ SV85 ) ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV60 @ SV85 ) @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(500,plain,
! [SV86: $i,SV61: $i] :
( ( ( apart_point_and_line @ SV61 @ ( line_connecting @ SV61 @ SV86 ) )
= $false )
| ( ( distinct_points @ SV61 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(501,plain,
! [SV62: $i,SV87: $i] :
( ( ( apart_point_and_line @ SV87 @ ( line_connecting @ SV62 @ SV87 ) )
= $false )
| ( ( distinct_points @ SV62 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(502,plain,
! [SV25: $i] :
( ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) )
| ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(503,plain,
! [SV25: $i] :
( ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(504,plain,
! [SV105: $i,SV25: $i] :
( ( ! [SY216: $i] :
( ~ ( left_apart_point @ SV25 @ SY216 )
| ~ ( right_apart_point @ SV105 @ SY216 )
| ( divides_points @ SY216 @ SV25 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(505,plain,
! [SV25: $i,SV106: $i] :
( ( ! [SY217: $i] :
( ~ ( left_apart_point @ SV106 @ SY217 )
| ~ ( right_apart_point @ SV25 @ SY217 )
| ( divides_points @ SY217 @ SV25 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(506,plain,
! [SV88: $i,SV63: $i] :
( ( ( unequally_directed_opposite_lines @ SV63 @ SV88 )
= $false )
| ( ( equally_directed_opposite_lines @ SV63 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(507,plain,
! [SV90: $i,SV65: $i] :
( ( ( unequally_directed_lines @ SV65 @ SV90 )
= $false )
| ( ( ~ ( unequally_directed_opposite_lines @ SV65 @ SV90 ) )
= $true )
| ( ( convergent_lines @ SV65 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(508,plain,
! [SV107: $i,SV96: $i] :
( ( ~ ( convergent_lines @ SV96 @ SV107 )
| ( unequally_directed_lines @ SV96 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(509,plain,
! [SV108: $i,SV97: $i] :
( ( ~ ( convergent_lines @ SV97 @ SV108 )
| ( unequally_directed_opposite_lines @ SV97 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(510,plain,
! [SV91: $i,SV66: $i] :
( ( ( unequally_directed_lines @ SV66 @ SV91 )
= $false )
| ( ( equally_directed_lines @ SV66 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(511,plain,
! [SV32: $i,SV10: $i] :
( ( ( unequally_directed_lines @ SV10 @ SV32 )
= $false )
| ( ( line @ SV10 )
= $false )
| ( ( line @ SV32 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(512,plain,
! [SV43: $i,SV17: $i,SV47: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(513,plain,
! [SV98: $i,SV94: $i] :
( ( ( ~ ( left_apart_point @ SV94 @ SV98 ) )
= $true )
| ( ( apart_point_and_line @ SV94 @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(514,plain,
! [SV99: $i,SV95: $i] :
( ( ( ~ ( right_apart_point @ SV95 @ SV99 ) )
= $true )
| ( ( apart_point_and_line @ SV95 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(515,plain,
! [SV100: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV100 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) ) )
= $true )
| ( ( ! [SY211: $i] :
( ( unequally_directed_lines @ SV22 @ SY211 )
| ( unequally_directed_lines @ SV100 @ SY211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(516,plain,
! [SV101: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV101 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) ) )
= $true )
| ( ( ! [SY212: $i] :
( ( unequally_directed_lines @ SV22 @ SY212 )
| ( unequally_directed_lines @ SV101 @ ( reverse_line @ SY212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(517,plain,
! [SV102: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV102 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) ) )
= $true )
| ( ( ! [SY213: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY213 ) )
| ( unequally_directed_lines @ SV102 @ SY213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(518,plain,
! [SV103: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV103 )
| ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) ) )
= $true )
| ( ( ! [SY214: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY214 ) )
| ( unequally_directed_lines @ SV103 @ ( reverse_line @ SY214 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(519,plain,
! [SV23: $i,SV93: $i,SV77: $i] :
( ( ( ~ ( distinct_points @ SV77 @ SV93 )
| ~ ( incident_point_and_line @ SV77 @ SV23 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV23 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(520,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(521,plain,
! [SV23: $i] :
( ( ~ ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(522,plain,
! [SV109: $i,SV104: $i,SV23: $i] :
( ( ~ ( before_on_line @ SV23 @ SV104 @ SV109 )
| ( equally_directed_lines @ SV23 @ ( line_connecting @ SV104 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(523,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) )
| ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(524,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) )
| ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(525,plain,
! [SV110: $i,SV42: $i,SV24: $i] :
( ( ! [SY218: $i] :
( ~ ( before_on_line @ SV24 @ SV42 @ SV110 )
| ~ ( before_on_line @ SV24 @ SV110 @ SY218 )
| ( between_on_line @ SV24 @ SV42 @ SV110 @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(526,plain,
! [SV42: $i,SV111: $i,SV24: $i] :
( ( ! [SY219: $i] :
( ~ ( before_on_line @ SV24 @ SY219 @ SV111 )
| ~ ( before_on_line @ SV24 @ SV111 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SV111 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(527,plain,
! [SV84: $i,SV59: $i] :
( ( ( unequally_directed_lines @ SV59 @ ( reverse_line @ SV84 ) )
= $false )
| ( ( unequally_directed_lines @ SV59 @ SV84 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV84 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(528,plain,
! [SV85: $i,SV60: $i] :
( ( ( unequally_directed_lines @ SV60 @ ( reverse_line @ SV85 ) )
= $false )
| ( ( unequally_directed_lines @ SV60 @ SV85 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV60 @ SV85 ) @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(529,plain,
! [SV25: $i] :
( ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(530,plain,
! [SV25: $i] :
( ( ~ ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(531,plain,
! [SV25: $i] :
( ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(532,plain,
! [SV25: $i] :
( ( ~ ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(533,plain,
! [SV105: $i,SV112: $i,SV25: $i] :
( ( ~ ( left_apart_point @ SV25 @ SV112 )
| ~ ( right_apart_point @ SV105 @ SV112 )
| ( divides_points @ SV112 @ SV25 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(534,plain,
! [SV25: $i,SV113: $i,SV106: $i] :
( ( ~ ( left_apart_point @ SV106 @ SV113 )
| ~ ( right_apart_point @ SV25 @ SV113 )
| ( divides_points @ SV113 @ SV25 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(535,plain,
! [SV90: $i,SV65: $i] :
( ( ( unequally_directed_opposite_lines @ SV65 @ SV90 )
= $false )
| ( ( unequally_directed_lines @ SV65 @ SV90 )
= $false )
| ( ( convergent_lines @ SV65 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(536,plain,
! [SV107: $i,SV96: $i] :
( ( ( ~ ( convergent_lines @ SV96 @ SV107 ) )
= $true )
| ( ( unequally_directed_lines @ SV96 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(537,plain,
! [SV108: $i,SV97: $i] :
( ( ( ~ ( convergent_lines @ SV97 @ SV108 ) )
= $true )
| ( ( unequally_directed_opposite_lines @ SV97 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(538,plain,
! [SV32: $i,SV10: $i] :
( ( ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV32 ) )
= $false )
| ( ( line @ SV32 )
= $false )
| ( ( line @ SV10 )
= $false )
| ( ( unequally_directed_lines @ SV10 @ SV32 )
= $false )
| ( ( point @ ( intersection_point @ SV10 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(539,plain,
! [SV43: $i,SV37: $i,SV47: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(540,plain,
! [SV98: $i,SV94: $i] :
( ( ( left_apart_point @ SV94 @ SV98 )
= $false )
| ( ( apart_point_and_line @ SV94 @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(541,plain,
! [SV99: $i,SV95: $i] :
( ( ( right_apart_point @ SV95 @ SV99 )
= $false )
| ( ( apart_point_and_line @ SV95 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(542,plain,
! [SV100: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV100 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) ) )
= $true )
| ( ( ! [SY211: $i] :
( ( unequally_directed_lines @ SV22 @ SY211 )
| ( unequally_directed_lines @ SV100 @ SY211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(543,plain,
! [SV101: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV101 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) ) )
= $true )
| ( ( ! [SY212: $i] :
( ( unequally_directed_lines @ SV22 @ SY212 )
| ( unequally_directed_lines @ SV101 @ ( reverse_line @ SY212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(544,plain,
! [SV102: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV102 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) ) )
= $true )
| ( ( ! [SY213: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY213 ) )
| ( unequally_directed_lines @ SV102 @ SY213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(545,plain,
! [SV103: $i,SV22: $i] :
( ( ( ~ ( unequally_directed_lines @ SV22 @ SV103 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) ) )
= $true )
| ( ( ! [SY214: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY214 ) )
| ( unequally_directed_lines @ SV103 @ ( reverse_line @ SY214 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(546,plain,
! [SV23: $i,SV93: $i,SV77: $i] :
( ( ( ~ ( distinct_points @ SV77 @ SV93 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV77 @ SV23 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV23 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(547,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(548,plain,
! [SV23: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ~ ( before_on_line @ SV23 @ SY135 @ SY136 )
| ( incident_point_and_line @ SY136 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(549,plain,
! [SV109: $i,SV104: $i,SV23: $i] :
( ( ( ~ ( before_on_line @ SV23 @ SV104 @ SV109 ) )
= $true )
| ( ( equally_directed_lines @ SV23 @ ( line_connecting @ SV104 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(550,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(551,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(552,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(553,plain,
! [SV42: $i,SV24: $i] :
( ( ~ ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(554,plain,
! [SV114: $i,SV110: $i,SV42: $i,SV24: $i] :
( ( ~ ( before_on_line @ SV24 @ SV42 @ SV110 )
| ~ ( before_on_line @ SV24 @ SV110 @ SV114 )
| ( between_on_line @ SV24 @ SV42 @ SV110 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(555,plain,
! [SV42: $i,SV111: $i,SV115: $i,SV24: $i] :
( ( ~ ( before_on_line @ SV24 @ SV115 @ SV111 )
| ~ ( before_on_line @ SV24 @ SV111 @ SV42 )
| ( between_on_line @ SV24 @ SV42 @ SV111 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(556,plain,
! [SV84: $i,SV59: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV59 @ SV84 ) @ SV59 )
= $false )
| ( ( unequally_directed_lines @ SV59 @ SV84 )
= $false )
| ( ( unequally_directed_lines @ SV59 @ ( reverse_line @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(557,plain,
! [SV85: $i,SV60: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV60 @ SV85 ) @ SV85 )
= $false )
| ( ( unequally_directed_lines @ SV60 @ SV85 )
= $false )
| ( ( unequally_directed_lines @ SV60 @ ( reverse_line @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(558,plain,
! [SV25: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ~ ( divides_points @ SY153 @ SV25 @ SY152 )
| ( left_apart_point @ SV25 @ SY153 )
| ( left_apart_point @ SY152 @ SY153 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(559,plain,
! [SV25: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ~ ( divides_points @ SY155 @ SV25 @ SY154 )
| ( left_apart_point @ SV25 @ SY155 )
| ( right_apart_point @ SV25 @ SY155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(560,plain,
! [SV25: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ~ ( divides_points @ SY157 @ SV25 @ SY156 )
| ( right_apart_point @ SY156 @ SY157 )
| ( left_apart_point @ SY156 @ SY157 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(561,plain,
! [SV25: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ( divides_points @ SY159 @ SV25 @ SY158 )
| ( right_apart_point @ SY158 @ SY159 )
| ( right_apart_point @ SV25 @ SY159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(562,plain,
! [SV105: $i,SV112: $i,SV25: $i] :
( ( ( ~ ( left_apart_point @ SV25 @ SV112 )
| ~ ( right_apart_point @ SV105 @ SV112 ) )
= $true )
| ( ( divides_points @ SV112 @ SV25 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(563,plain,
! [SV25: $i,SV113: $i,SV106: $i] :
( ( ( ~ ( left_apart_point @ SV106 @ SV113 )
| ~ ( right_apart_point @ SV25 @ SV113 ) )
= $true )
| ( ( divides_points @ SV113 @ SV25 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(564,plain,
! [SV107: $i,SV96: $i] :
( ( ( convergent_lines @ SV96 @ SV107 )
= $false )
| ( ( unequally_directed_lines @ SV96 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(565,plain,
! [SV108: $i,SV97: $i] :
( ( ( convergent_lines @ SV97 @ SV108 )
= $false )
| ( ( unequally_directed_opposite_lines @ SV97 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(566,plain,
! [SV47: $i,SV17: $i,SV43: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
| ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(567,plain,
! [SV100: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ SV100 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) ) )
= $true )
| ( ( ! [SY211: $i] :
( ( unequally_directed_lines @ SV22 @ SY211 )
| ( unequally_directed_lines @ SV100 @ SY211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(568,plain,
! [SV101: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ SV101 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) ) )
= $true )
| ( ( ! [SY212: $i] :
( ( unequally_directed_lines @ SV22 @ SY212 )
| ( unequally_directed_lines @ SV101 @ ( reverse_line @ SY212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(569,plain,
! [SV102: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ SV102 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) ) )
= $true )
| ( ( ! [SY213: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY213 ) )
| ( unequally_directed_lines @ SV102 @ SY213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(570,plain,
! [SV103: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ SV103 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) ) )
= $true )
| ( ( ! [SY214: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY214 ) )
| ( unequally_directed_lines @ SV103 @ ( reverse_line @ SY214 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(571,plain,
! [SV23: $i,SV93: $i,SV77: $i] :
( ( ( distinct_points @ SV77 @ SV93 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV77 @ SV23 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV23 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(572,plain,
! [SV23: $i] :
( ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(573,plain,
! [SV116: $i,SV23: $i] :
( ( ! [SY220: $i] :
( ~ ( before_on_line @ SV23 @ SV116 @ SY220 )
| ( incident_point_and_line @ SY220 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(574,plain,
! [SV109: $i,SV104: $i,SV23: $i] :
( ( ( before_on_line @ SV23 @ SV104 @ SV109 )
= $false )
| ( ( equally_directed_lines @ SV23 @ ( line_connecting @ SV104 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(575,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY173 @ SY174 )
| ( before_on_line @ SV24 @ SV42 @ SY173 )
| ( before_on_line @ SV24 @ SY174 @ SY173 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(576,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY175: $i] :
( ! [SY176: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SY175 @ SY176 )
| ( before_on_line @ SV24 @ SV42 @ SY175 )
| ( before_on_line @ SV24 @ SY175 @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(577,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY177 @ SY178 )
| ( before_on_line @ SV24 @ SY178 @ SY177 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(578,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SY180 )
| ( before_on_line @ SV24 @ SY179 @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(579,plain,
! [SV114: $i,SV110: $i,SV42: $i,SV24: $i] :
( ( ( ~ ( before_on_line @ SV24 @ SV42 @ SV110 )
| ~ ( before_on_line @ SV24 @ SV110 @ SV114 ) )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV110 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(580,plain,
! [SV42: $i,SV111: $i,SV115: $i,SV24: $i] :
( ( ( ~ ( before_on_line @ SV24 @ SV115 @ SV111 )
| ~ ( before_on_line @ SV24 @ SV111 @ SV42 ) )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV111 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(581,plain,
! [SV117: $i,SV25: $i] :
( ( ! [SY221: $i] :
( ~ ( divides_points @ SY221 @ SV25 @ SV117 )
| ( left_apart_point @ SV25 @ SY221 )
| ( left_apart_point @ SV117 @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(582,plain,
! [SV118: $i,SV25: $i] :
( ( ! [SY222: $i] :
( ~ ( divides_points @ SY222 @ SV25 @ SV118 )
| ( left_apart_point @ SV25 @ SY222 )
| ( right_apart_point @ SV25 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(583,plain,
! [SV119: $i,SV25: $i] :
( ( ! [SY223: $i] :
( ~ ( divides_points @ SY223 @ SV25 @ SV119 )
| ( right_apart_point @ SV119 @ SY223 )
| ( left_apart_point @ SV119 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(584,plain,
! [SV120: $i,SV25: $i] :
( ( ! [SY224: $i] :
( ~ ( divides_points @ SY224 @ SV25 @ SV120 )
| ( right_apart_point @ SV120 @ SY224 )
| ( right_apart_point @ SV25 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(585,plain,
! [SV105: $i,SV112: $i,SV25: $i] :
( ( ( ~ ( left_apart_point @ SV25 @ SV112 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV105 @ SV112 ) )
= $true )
| ( ( divides_points @ SV112 @ SV25 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(586,plain,
! [SV25: $i,SV113: $i,SV106: $i] :
( ( ( ~ ( left_apart_point @ SV106 @ SV113 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV25 @ SV113 ) )
= $true )
| ( ( divides_points @ SV113 @ SV25 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(587,plain,
! [SV47: $i,SV37: $i,SV43: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( ( left_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(588,plain,
! [SV100: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) )
= $false )
| ( ( unequally_directed_lines @ SV22 @ SV100 )
= $false )
| ( ( ! [SY211: $i] :
( ( unequally_directed_lines @ SV22 @ SY211 )
| ( unequally_directed_lines @ SV100 @ SY211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(589,plain,
! [SV101: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) )
= $false )
| ( ( unequally_directed_lines @ SV22 @ SV101 )
= $false )
| ( ( ! [SY212: $i] :
( ( unequally_directed_lines @ SV22 @ SY212 )
| ( unequally_directed_lines @ SV101 @ ( reverse_line @ SY212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(590,plain,
! [SV102: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) )
= $false )
| ( ( unequally_directed_lines @ SV22 @ SV102 )
= $false )
| ( ( ! [SY213: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY213 ) )
| ( unequally_directed_lines @ SV102 @ SY213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(591,plain,
! [SV103: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) )
= $false )
| ( ( unequally_directed_lines @ SV22 @ SV103 )
= $false )
| ( ( ! [SY214: $i] :
( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SY214 ) )
| ( unequally_directed_lines @ SV103 @ ( reverse_line @ SY214 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(592,plain,
! [SV93: $i,SV23: $i,SV77: $i] :
( ( ( incident_point_and_line @ SV77 @ SV23 )
= $false )
| ( ( distinct_points @ SV77 @ SV93 )
= $false )
| ( ( ~ ( incident_point_and_line @ SV93 @ SV23 ) )
= $true )
| ( ( ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(593,plain,
! [SV23: $i] :
( ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(594,plain,
! [SV23: $i] :
( ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(595,plain,
! [SV121: $i,SV116: $i,SV23: $i] :
( ( ~ ( before_on_line @ SV23 @ SV116 @ SV121 )
| ( incident_point_and_line @ SV121 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(596,plain,
! [SV122: $i,SV42: $i,SV24: $i] :
( ( ! [SY225: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SV122 @ SY225 )
| ( before_on_line @ SV24 @ SV42 @ SV122 )
| ( before_on_line @ SV24 @ SY225 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(597,plain,
! [SV123: $i,SV42: $i,SV24: $i] :
( ( ! [SY226: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SV123 @ SY226 )
| ( before_on_line @ SV24 @ SV42 @ SV123 )
| ( before_on_line @ SV24 @ SV123 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(598,plain,
! [SV124: $i,SV42: $i,SV24: $i] :
( ( ! [SY227: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SV124 @ SY227 )
| ( before_on_line @ SV24 @ SV124 @ SY227 )
| ( before_on_line @ SV24 @ SY227 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(599,plain,
! [SV125: $i,SV42: $i,SV24: $i] :
( ( ! [SY228: $i] :
( ~ ( between_on_line @ SV24 @ SV42 @ SV125 @ SY228 )
| ( before_on_line @ SV24 @ SV125 @ SY228 )
| ( before_on_line @ SV24 @ SV125 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(600,plain,
! [SV114: $i,SV110: $i,SV42: $i,SV24: $i] :
( ( ( ~ ( before_on_line @ SV24 @ SV42 @ SV110 ) )
= $true )
| ( ( ~ ( before_on_line @ SV24 @ SV110 @ SV114 ) )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV110 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(601,plain,
! [SV42: $i,SV111: $i,SV115: $i,SV24: $i] :
( ( ( ~ ( before_on_line @ SV24 @ SV115 @ SV111 ) )
= $true )
| ( ( ~ ( before_on_line @ SV24 @ SV111 @ SV42 ) )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV111 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(602,plain,
! [SV117: $i,SV25: $i,SV126: $i] :
( ( ~ ( divides_points @ SV126 @ SV25 @ SV117 )
| ( left_apart_point @ SV25 @ SV126 )
| ( left_apart_point @ SV117 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(603,plain,
! [SV118: $i,SV25: $i,SV127: $i] :
( ( ~ ( divides_points @ SV127 @ SV25 @ SV118 )
| ( left_apart_point @ SV25 @ SV127 )
| ( right_apart_point @ SV25 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(604,plain,
! [SV119: $i,SV25: $i,SV128: $i] :
( ( ~ ( divides_points @ SV128 @ SV25 @ SV119 )
| ( right_apart_point @ SV119 @ SV128 )
| ( left_apart_point @ SV119 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(605,plain,
! [SV120: $i,SV25: $i,SV129: $i] :
( ( ~ ( divides_points @ SV129 @ SV25 @ SV120 )
| ( right_apart_point @ SV120 @ SV129 )
| ( right_apart_point @ SV25 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(606,plain,
! [SV105: $i,SV112: $i,SV25: $i] :
( ( ( left_apart_point @ SV25 @ SV112 )
= $false )
| ( ( ~ ( right_apart_point @ SV105 @ SV112 ) )
= $true )
| ( ( divides_points @ SV112 @ SV25 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(607,plain,
! [SV25: $i,SV113: $i,SV106: $i] :
( ( ( left_apart_point @ SV106 @ SV113 )
= $false )
| ( ( ~ ( right_apart_point @ SV25 @ SV113 ) )
= $true )
| ( ( divides_points @ SV113 @ SV25 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(608,plain,
! [SV43: $i,SV17: $i,SV47: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ SV47 )
= $true )
| ( ( ( left_apart_point @ SV17 @ SV47 )
| ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(609,plain,
! [SV100: $i,SV130: $i,SV22: $i] :
( ( ( ( unequally_directed_lines @ SV22 @ SV130 )
| ( unequally_directed_lines @ SV100 @ SV130 ) )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV100 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(610,plain,
! [SV101: $i,SV131: $i,SV22: $i] :
( ( ( ( unequally_directed_lines @ SV22 @ SV131 )
| ( unequally_directed_lines @ SV101 @ ( reverse_line @ SV131 ) ) )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV101 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(611,plain,
! [SV102: $i,SV132: $i,SV22: $i] :
( ( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV132 ) )
| ( unequally_directed_lines @ SV102 @ SV132 ) )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV102 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(612,plain,
! [SV103: $i,SV133: $i,SV22: $i] :
( ( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV133 ) )
| ( unequally_directed_lines @ SV103 @ ( reverse_line @ SV133 ) ) )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV103 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(613,plain,
! [SV77: $i,SV23: $i,SV93: $i] :
( ( ( incident_point_and_line @ SV93 @ SV23 )
= $false )
| ( ( distinct_points @ SV77 @ SV93 )
= $false )
| ( ( incident_point_and_line @ SV77 @ SV23 )
= $false )
| ( ( ~ ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) ) )
= $true )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(614,plain,
! [SV23: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ~ ( before_on_line @ SV23 @ SY131 @ SY132 )
| ( distinct_points @ SY131 @ SY132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(615,plain,
! [SV23: $i] :
( ( ! [SY133: $i] :
( ! [SY134: $i] :
~ ( before_on_line @ SV23 @ SY133 @ SY134 )
| ( incident_point_and_line @ SY133 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(616,plain,
! [SV121: $i,SV116: $i,SV23: $i] :
( ( ( ~ ( before_on_line @ SV23 @ SV116 @ SV121 ) )
= $true )
| ( ( incident_point_and_line @ SV121 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(617,plain,
! [SV134: $i,SV122: $i,SV42: $i,SV24: $i] :
( ( ~ ( between_on_line @ SV24 @ SV42 @ SV122 @ SV134 )
| ( before_on_line @ SV24 @ SV42 @ SV122 )
| ( before_on_line @ SV24 @ SV134 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(618,plain,
! [SV123: $i,SV42: $i,SV24: $i] :
( ( ( ! [SY226: $i] :
~ ( between_on_line @ SV24 @ SV42 @ SV123 @ SY226 ) )
= $true )
| ( ( ( before_on_line @ SV24 @ SV42 @ SV123 )
| ( before_on_line @ SV24 @ SV123 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(619,plain,
! [SV135: $i,SV124: $i,SV42: $i,SV24: $i] :
( ( ~ ( between_on_line @ SV24 @ SV42 @ SV124 @ SV135 )
| ( before_on_line @ SV24 @ SV124 @ SV135 )
| ( before_on_line @ SV24 @ SV135 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(620,plain,
! [SV136: $i,SV125: $i,SV42: $i,SV24: $i] :
( ( ~ ( between_on_line @ SV24 @ SV42 @ SV125 @ SV136 )
| ( before_on_line @ SV24 @ SV125 @ SV136 )
| ( before_on_line @ SV24 @ SV125 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(621,plain,
! [SV114: $i,SV110: $i,SV42: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV42 @ SV110 )
= $false )
| ( ( ~ ( before_on_line @ SV24 @ SV110 @ SV114 ) )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV110 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(622,plain,
! [SV42: $i,SV111: $i,SV115: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV115 @ SV111 )
= $false )
| ( ( ~ ( before_on_line @ SV24 @ SV111 @ SV42 ) )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV111 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(623,plain,
! [SV117: $i,SV25: $i,SV126: $i] :
( ( ( ~ ( divides_points @ SV126 @ SV25 @ SV117 ) )
= $true )
| ( ( ( left_apart_point @ SV25 @ SV126 )
| ( left_apart_point @ SV117 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(624,plain,
! [SV118: $i,SV25: $i,SV127: $i] :
( ( ( ~ ( divides_points @ SV127 @ SV25 @ SV118 ) )
= $true )
| ( ( ( left_apart_point @ SV25 @ SV127 )
| ( right_apart_point @ SV25 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(625,plain,
! [SV119: $i,SV25: $i,SV128: $i] :
( ( ( ~ ( divides_points @ SV128 @ SV25 @ SV119 ) )
= $true )
| ( ( ( right_apart_point @ SV119 @ SV128 )
| ( left_apart_point @ SV119 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(626,plain,
! [SV120: $i,SV25: $i,SV129: $i] :
( ( ( ~ ( divides_points @ SV129 @ SV25 @ SV120 ) )
= $true )
| ( ( ( right_apart_point @ SV120 @ SV129 )
| ( right_apart_point @ SV25 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(627,plain,
! [SV25: $i,SV112: $i,SV105: $i] :
( ( ( right_apart_point @ SV105 @ SV112 )
= $false )
| ( ( left_apart_point @ SV25 @ SV112 )
= $false )
| ( ( divides_points @ SV112 @ SV25 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(628,plain,
! [SV106: $i,SV113: $i,SV25: $i] :
( ( ( right_apart_point @ SV25 @ SV113 )
= $false )
| ( ( left_apart_point @ SV106 @ SV113 )
= $false )
| ( ( divides_points @ SV113 @ SV25 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(629,plain,
! [SV37: $i,SV43: $i,SV47: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV47 )
= $true )
| ( ( ( left_apart_point @ SV17 @ SV43 )
| ( left_apart_point @ SV37 @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ SV47 )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(630,plain,
! [SV100: $i,SV130: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ SV130 )
= $true )
| ( ( unequally_directed_lines @ SV100 @ SV130 )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV100 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(631,plain,
! [SV101: $i,SV131: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ SV131 )
= $true )
| ( ( unequally_directed_lines @ SV101 @ ( reverse_line @ SV131 ) )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV101 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(632,plain,
! [SV102: $i,SV132: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV132 ) )
= $true )
| ( ( unequally_directed_lines @ SV102 @ SV132 )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV102 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(633,plain,
! [SV103: $i,SV133: $i,SV22: $i] :
( ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV133 ) )
= $true )
| ( ( unequally_directed_lines @ SV103 @ ( reverse_line @ SV133 ) )
= $true )
| ( ( unequally_directed_lines @ SV22 @ SV103 )
= $false )
| ( ( unequally_directed_lines @ SV22 @ ( reverse_line @ SV103 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(634,plain,
! [SV93: $i,SV77: $i,SV23: $i] :
( ( ( equally_directed_lines @ SV23 @ ( line_connecting @ SV77 @ SV93 ) )
= $false )
| ( ( incident_point_and_line @ SV77 @ SV23 )
= $false )
| ( ( distinct_points @ SV77 @ SV93 )
= $false )
| ( ( incident_point_and_line @ SV93 @ SV23 )
= $false )
| ( ( before_on_line @ SV23 @ SV77 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(635,plain,
! [SV137: $i,SV23: $i] :
( ( ! [SY229: $i] :
( ~ ( before_on_line @ SV23 @ SV137 @ SY229 )
| ( distinct_points @ SV137 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(636,plain,
! [SV138: $i,SV23: $i] :
( ( ! [SY230: $i] :
~ ( before_on_line @ SV23 @ SV138 @ SY230 )
| ( incident_point_and_line @ SV138 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(637,plain,
! [SV121: $i,SV116: $i,SV23: $i] :
( ( ( before_on_line @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( incident_point_and_line @ SV121 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(638,plain,
! [SV134: $i,SV122: $i,SV42: $i,SV24: $i] :
( ( ( ~ ( between_on_line @ SV24 @ SV42 @ SV122 @ SV134 ) )
= $true )
| ( ( ( before_on_line @ SV24 @ SV42 @ SV122 )
| ( before_on_line @ SV24 @ SV134 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(639,plain,
! [SV139: $i,SV123: $i,SV42: $i,SV24: $i] :
( ( ( ~ ( between_on_line @ SV24 @ SV42 @ SV123 @ SV139 ) )
= $true )
| ( ( ( before_on_line @ SV24 @ SV42 @ SV123 )
| ( before_on_line @ SV24 @ SV123 @ SV42 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(640,plain,
! [SV135: $i,SV124: $i,SV42: $i,SV24: $i] :
( ( ( ~ ( between_on_line @ SV24 @ SV42 @ SV124 @ SV135 ) )
= $true )
| ( ( ( before_on_line @ SV24 @ SV124 @ SV135 )
| ( before_on_line @ SV24 @ SV135 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(641,plain,
! [SV136: $i,SV125: $i,SV42: $i,SV24: $i] :
( ( ( ~ ( between_on_line @ SV24 @ SV42 @ SV125 @ SV136 ) )
= $true )
| ( ( ( before_on_line @ SV24 @ SV125 @ SV136 )
| ( before_on_line @ SV24 @ SV125 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(642,plain,
! [SV42: $i,SV114: $i,SV110: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV110 @ SV114 )
= $false )
| ( ( before_on_line @ SV24 @ SV42 @ SV110 )
= $false )
| ( ( between_on_line @ SV24 @ SV42 @ SV110 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(643,plain,
! [SV115: $i,SV42: $i,SV111: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV111 @ SV42 )
= $false )
| ( ( before_on_line @ SV24 @ SV115 @ SV111 )
= $false )
| ( ( between_on_line @ SV24 @ SV42 @ SV111 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(644,plain,
! [SV117: $i,SV25: $i,SV126: $i] :
( ( ( divides_points @ SV126 @ SV25 @ SV117 )
= $false )
| ( ( ( left_apart_point @ SV25 @ SV126 )
| ( left_apart_point @ SV117 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(645,plain,
! [SV118: $i,SV25: $i,SV127: $i] :
( ( ( divides_points @ SV127 @ SV25 @ SV118 )
= $false )
| ( ( ( left_apart_point @ SV25 @ SV127 )
| ( right_apart_point @ SV25 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(646,plain,
! [SV119: $i,SV25: $i,SV128: $i] :
( ( ( divides_points @ SV128 @ SV25 @ SV119 )
= $false )
| ( ( ( right_apart_point @ SV119 @ SV128 )
| ( left_apart_point @ SV119 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(647,plain,
! [SV120: $i,SV25: $i,SV129: $i] :
( ( ( divides_points @ SV129 @ SV25 @ SV120 )
= $false )
| ( ( ( right_apart_point @ SV120 @ SV129 )
| ( right_apart_point @ SV25 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(648,plain,
! [SV47: $i,SV37: $i,SV43: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV43 )
= $true )
| ( ( left_apart_point @ SV37 @ SV43 )
= $true )
| ( ( left_apart_point @ SV17 @ SV47 )
= $true )
| ( ( left_apart_point @ SV37 @ SV47 )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV43 ) )
= $true )
| ( ( left_apart_point @ SV17 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true )
| ( ( distinct_lines @ SV43 @ SV47 )
= $false )
| ( ( distinct_points @ SV17 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(649,plain,
! [SV140: $i,SV137: $i,SV23: $i] :
( ( ~ ( before_on_line @ SV23 @ SV137 @ SV140 )
| ( distinct_points @ SV137 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(650,plain,
! [SV138: $i,SV23: $i] :
( ( ( ! [SY230: $i] :
~ ( before_on_line @ SV23 @ SV138 @ SY230 ) )
= $true )
| ( ( incident_point_and_line @ SV138 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(651,plain,
! [SV134: $i,SV122: $i,SV42: $i,SV24: $i] :
( ( ( between_on_line @ SV24 @ SV42 @ SV122 @ SV134 )
= $false )
| ( ( ( before_on_line @ SV24 @ SV42 @ SV122 )
| ( before_on_line @ SV24 @ SV134 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(652,plain,
! [SV139: $i,SV123: $i,SV42: $i,SV24: $i] :
( ( ( between_on_line @ SV24 @ SV42 @ SV123 @ SV139 )
= $false )
| ( ( ( before_on_line @ SV24 @ SV42 @ SV123 )
| ( before_on_line @ SV24 @ SV123 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(653,plain,
! [SV135: $i,SV124: $i,SV42: $i,SV24: $i] :
( ( ( between_on_line @ SV24 @ SV42 @ SV124 @ SV135 )
= $false )
| ( ( ( before_on_line @ SV24 @ SV124 @ SV135 )
| ( before_on_line @ SV24 @ SV135 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(654,plain,
! [SV136: $i,SV125: $i,SV42: $i,SV24: $i] :
( ( ( between_on_line @ SV24 @ SV42 @ SV125 @ SV136 )
= $false )
| ( ( ( before_on_line @ SV24 @ SV125 @ SV136 )
| ( before_on_line @ SV24 @ SV125 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(655,plain,
! [SV117: $i,SV126: $i,SV25: $i] :
( ( ( left_apart_point @ SV25 @ SV126 )
= $true )
| ( ( left_apart_point @ SV117 @ SV126 )
= $true )
| ( ( divides_points @ SV126 @ SV25 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(656,plain,
! [SV118: $i,SV127: $i,SV25: $i] :
( ( ( left_apart_point @ SV25 @ SV127 )
= $true )
| ( ( right_apart_point @ SV25 @ SV127 )
= $true )
| ( ( divides_points @ SV127 @ SV25 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(657,plain,
! [SV25: $i,SV128: $i,SV119: $i] :
( ( ( right_apart_point @ SV119 @ SV128 )
= $true )
| ( ( left_apart_point @ SV119 @ SV128 )
= $true )
| ( ( divides_points @ SV128 @ SV25 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(658,plain,
! [SV25: $i,SV129: $i,SV120: $i] :
( ( ( right_apart_point @ SV120 @ SV129 )
= $true )
| ( ( right_apart_point @ SV25 @ SV129 )
= $true )
| ( ( divides_points @ SV129 @ SV25 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(659,plain,
! [SV140: $i,SV137: $i,SV23: $i] :
( ( ( ~ ( before_on_line @ SV23 @ SV137 @ SV140 ) )
= $true )
| ( ( distinct_points @ SV137 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(660,plain,
! [SV141: $i,SV138: $i,SV23: $i] :
( ( ( ~ ( before_on_line @ SV23 @ SV138 @ SV141 ) )
= $true )
| ( ( incident_point_and_line @ SV138 @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(661,plain,
! [SV134: $i,SV122: $i,SV42: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV42 @ SV122 )
= $true )
| ( ( before_on_line @ SV24 @ SV134 @ SV122 )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV122 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(662,plain,
! [SV139: $i,SV123: $i,SV42: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV42 @ SV123 )
= $true )
| ( ( before_on_line @ SV24 @ SV123 @ SV42 )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV123 @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(663,plain,
! [SV42: $i,SV135: $i,SV124: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV124 @ SV135 )
= $true )
| ( ( before_on_line @ SV24 @ SV135 @ SV124 )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV124 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(664,plain,
! [SV42: $i,SV136: $i,SV125: $i,SV24: $i] :
( ( ( before_on_line @ SV24 @ SV125 @ SV136 )
= $true )
| ( ( before_on_line @ SV24 @ SV125 @ SV42 )
= $true )
| ( ( between_on_line @ SV24 @ SV42 @ SV125 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(665,plain,
! [SV140: $i,SV137: $i,SV23: $i] :
( ( ( before_on_line @ SV23 @ SV137 @ SV140 )
= $false )
| ( ( distinct_points @ SV137 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(666,plain,
! [SV141: $i,SV138: $i,SV23: $i] :
( ( ( before_on_line @ SV23 @ SV138 @ SV141 )
= $false )
| ( ( incident_point_and_line @ SV138 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(667,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[154,666,665,664,663,662,661,658,657,656,655,648,643,642,637,634,633,632,631,630,628,627,574,565,564,557,556,541,540,538,535,510,506,501,500,484,483,482,479,461,460,459,458,454,453,440,439,434,424,423,407,406,402,400,397,393,392,391,311,268,267,262,227,225,215,213,197,180,159,158,157,156,155]) ).
thf(668,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 00:49:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.38
% 0.21/0.38 No.of.Axioms: 36
% 0.21/0.38
% 0.21/0.38 Length.of.Defs: 0
% 0.21/0.38
% 0.21/0.38 Contains.Choice.Funs: false
% 0.21/0.39 .
% 0.21/0.41 (rf:0,axioms:36,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:38,loop_count:0,foatp_calls:0,translation:fof_full)..............................................
% 0.47/0.64
% 0.47/0.64 ********************************
% 0.47/0.64 * All subproblems solved! *
% 0.47/0.64 ********************************
% 0.47/0.64 % 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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:667,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.80
% 0.60/0.80 %**** Beginning of derivation protocol ****
% 0.60/0.80 % SZS output start CNFRefutation
% See solution above
% 0.60/0.80
% 0.60/0.80 %**** End of derivation protocol ****
% 0.60/0.80 %**** no. of clauses in derivation: 668 ****
% 0.60/0.80 %**** clause counter: 667 ****
% 0.60/0.80
% 0.60/0.80 % 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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:667,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------