TSTP Solution File: GEO196+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO196+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 : n032.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 05:08:17 EDT 2022
% Result : Theorem 0.55s 0.98s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 56
% Syntax : Number of formulae : 828 ( 491 unt; 20 typ; 0 def)
% Number of atoms : 5317 (1269 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 9069 (1334 ~;1824 |; 88 &;5764 @)
% ( 10 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-2 aty)
% Number of variables : 2202 ( 0 ^2202 !; 0 ?;2202 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $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_equal_lines,type,
equal_lines: $i > $i > $o ).
thf(tp_equal_points,type,
equal_points: $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_line,type,
line: $i > $o ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_orthogonal_lines,type,
orthogonal_lines: $i > $i > $o ).
thf(tp_orthogonal_through_point,type,
orthogonal_through_point: $i > $i > $i ).
thf(tp_parallel_lines,type,
parallel_lines: $i > $i > $o ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY85,type,
sK2_SY85: $i ).
thf(tp_sK3_SY88,type,
sK3_SY88: $i ).
thf(tp_sK4_SY90,type,
sK4_SY90: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( orthogonal_lines @ X @ Y )
<=> ~ ( unorthogonal_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(6,axiom,
! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orth1) ).
thf(7,axiom,
! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',par1) ).
thf(8,axiom,
! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
thf(10,axiom,
! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
thf(11,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).
thf(12,axiom,
! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
thf(13,axiom,
! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ouo1) ).
thf(14,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
thf(15,axiom,
! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
thf(16,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
thf(17,axiom,
! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
thf(18,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
thf(19,axiom,
! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
thf(20,axiom,
! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(23,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(24,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
thf(25,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
thf(26,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
thf(27,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
thf(28,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
thf(29,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
thf(30,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(31,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
thf(32,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
thf(33,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(34,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(35,axiom,
! [X: $i] :
~ ( distinct_points @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
thf(36,conjecture,
! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( convergent_lines @ X @ Y )
& ( convergent_lines @ U @ V )
& ( incident_point_and_line @ ( intersection_point @ X @ Y ) @ U )
& ( incident_point_and_line @ ( intersection_point @ X @ Y ) @ V ) )
=> ( ( incident_point_and_line @ ( intersection_point @ U @ V ) @ X )
& ( incident_point_and_line @ ( intersection_point @ U @ V ) @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(37,negated_conjecture,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( convergent_lines @ X @ Y )
& ( convergent_lines @ U @ V )
& ( incident_point_and_line @ ( intersection_point @ X @ Y ) @ U )
& ( incident_point_and_line @ ( intersection_point @ X @ Y ) @ V ) )
=> ( ( incident_point_and_line @ ( intersection_point @ U @ V ) @ X )
& ( incident_point_and_line @ ( intersection_point @ U @ V ) @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( convergent_lines @ X @ Y )
& ( convergent_lines @ U @ V )
& ( incident_point_and_line @ ( intersection_point @ X @ Y ) @ U )
& ( incident_point_and_line @ ( intersection_point @ X @ Y ) @ V ) )
=> ( ( incident_point_and_line @ ( intersection_point @ U @ V ) @ X )
& ( incident_point_and_line @ ( intersection_point @ U @ V ) @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( orthogonal_lines @ X @ Y )
<=> ~ ( unorthogonal_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(45,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(46,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(48,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(49,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(50,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,plain,
( ( ! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(52,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(53,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(54,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(55,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(71,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(72,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(73,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(74,plain,
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ( ( convergent_lines @ sK1_X @ SY85 )
& ( convergent_lines @ SY86 @ SY87 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ SY85 ) @ SY86 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ SY85 ) @ SY87 ) )
=> ( ( incident_point_and_line @ ( intersection_point @ SY86 @ SY87 ) @ sK1_X )
& ( incident_point_and_line @ ( intersection_point @ SY86 @ SY87 ) @ SY85 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(75,plain,
( ( ! [SY88: $i,SY89: $i] :
( ( ( convergent_lines @ sK1_X @ sK2_SY85 )
& ( convergent_lines @ SY88 @ SY89 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ SY88 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ SY89 ) )
=> ( ( incident_point_and_line @ ( intersection_point @ SY88 @ SY89 ) @ sK1_X )
& ( incident_point_and_line @ ( intersection_point @ SY88 @ SY89 ) @ sK2_SY85 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(76,plain,
( ( ! [SY90: $i] :
( ( ( convergent_lines @ sK1_X @ sK2_SY85 )
& ( convergent_lines @ sK3_SY88 @ SY90 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK3_SY88 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ SY90 ) )
=> ( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ SY90 ) @ sK1_X )
& ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ SY90 ) @ sK2_SY85 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(77,plain,
( ( ( ( convergent_lines @ sK1_X @ sK2_SY85 )
& ( convergent_lines @ sK3_SY88 @ sK4_SY90 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK3_SY88 )
& ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK4_SY90 ) )
=> ( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK1_X )
& ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK2_SY85 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(78,plain,
( ( convergent_lines @ sK1_X @ sK2_SY85 )
= $true ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(79,plain,
( ( convergent_lines @ sK3_SY88 @ sK4_SY90 )
= $true ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(80,plain,
( ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK3_SY88 )
= $true ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(81,plain,
( ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK4_SY90 )
= $true ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(82,plain,
( ( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK1_X )
& ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK2_SY85 ) )
= $false ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(83,plain,
( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK1_X )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[82]) ).
thf(84,plain,
( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK2_SY85 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[82]) ).
thf(85,plain,
( ( ~ ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK1_X ) )
= $true ),
inference(polarity_switch,[status(thm)],[83]) ).
thf(86,plain,
( ( ~ ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK2_SY85 ) )
= $true ),
inference(polarity_switch,[status(thm)],[84]) ).
thf(87,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( orthogonal_lines @ X @ Y )
| ~ ( unorthogonal_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unorthogonal_lines @ X @ Y )
| ( orthogonal_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(88,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( incident_point_and_line @ X @ Y )
| ~ ( apart_point_and_line @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( apart_point_and_line @ X @ Y )
| ( incident_point_and_line @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( parallel_lines @ X @ Y )
| ~ ( convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
| ( parallel_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(90,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_lines @ X @ Y )
| ~ ( distinct_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
| ( equal_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_points @ X @ Y )
| ~ ( distinct_points @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
| ( equal_points @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(92,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(93,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(94,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( convergent_lines @ L @ M )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(96,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(97,plain,
( ( ! [L: $i] :
( ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(98,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(99,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ M @ N )
| ( unorthogonal_lines @ L @ N )
| ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(100,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( distinct_lines @ Y @ Z )
| ( convergent_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(106,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(109,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(114,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(115,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(116,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(126,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(127,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( distinct_lines @ Y @ Z )
| ( convergent_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(132,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(133,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(134,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(135,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(136,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ M @ N )
| ( unorthogonal_lines @ L @ N )
| ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(137,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(138,plain,
( ( ! [L: $i] :
( ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(139,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(141,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( convergent_lines @ L @ M )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(142,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(143,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(144,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_points @ X @ Y )
| ~ ( distinct_points @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
| ( equal_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(145,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_lines @ X @ Y )
| ~ ( distinct_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
| ( equal_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(146,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( parallel_lines @ X @ Y )
| ~ ( convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
| ( parallel_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(147,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( incident_point_and_line @ X @ Y )
| ~ ( apart_point_and_line @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( apart_point_and_line @ X @ Y )
| ( incident_point_and_line @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(148,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( orthogonal_lines @ X @ Y )
| ~ ( unorthogonal_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unorthogonal_lines @ X @ Y )
| ( orthogonal_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(149,plain,
( ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK4_SY90 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(150,plain,
( ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK3_SY88 )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(151,plain,
( ( convergent_lines @ sK3_SY88 @ sK4_SY90 )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(152,plain,
( ( convergent_lines @ sK1_X @ sK2_SY85 )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(153,plain,
( ( ~ ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(154,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(155,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( unorthogonal_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( unorthogonal_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(156,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(157,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( convergent_lines @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(158,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(159,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(160,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(161,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(162,plain,
! [SV2: $i] :
( ( ~ ( distinct_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(163,plain,
! [SV3: $i] :
( ( ~ ( convergent_lines @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(164,plain,
! [SV4: $i] :
( ( ! [SY91: $i] :
( ~ ( distinct_points @ SV4 @ SY91 )
| ! [SY92: $i] :
( ( distinct_points @ SV4 @ SY92 )
| ( distinct_points @ SY91 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(165,plain,
! [SV5: $i] :
( ( ! [SY93: $i] :
( ~ ( distinct_lines @ SV5 @ SY93 )
| ! [SY94: $i] :
( ( distinct_lines @ SV5 @ SY94 )
| ( distinct_lines @ SY93 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(166,plain,
! [SV6: $i] :
( ( ! [SY95: $i] :
( ~ ( convergent_lines @ SV6 @ SY95 )
| ! [SY96: $i] :
( ( convergent_lines @ SV6 @ SY96 )
| ( convergent_lines @ SY95 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(167,plain,
! [SV7: $i] :
( ( ! [SY97: $i] :
( ~ ( distinct_points @ SV7 @ SY97 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(168,plain,
! [SV8: $i] :
( ( ! [SY98: $i] :
( ~ ( distinct_points @ SV8 @ SY98 )
| ~ ( apart_point_and_line @ SY98 @ ( line_connecting @ SV8 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(169,plain,
! [SV9: $i] :
( ( ! [SY99: $i] :
( ~ ( convergent_lines @ SV9 @ SY99 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SY99 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(170,plain,
! [SV10: $i] :
( ( ! [SY100: $i] :
( ~ ( convergent_lines @ SV10 @ SY100 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SY100 ) @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(171,plain,
! [SV11: $i] :
( ( ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ( distinct_lines @ SY102 @ SY103 )
| ~ ( distinct_points @ SV11 @ SY101 )
| ( apart_point_and_line @ SY101 @ SY103 )
| ( apart_point_and_line @ SY101 @ SY102 )
| ( apart_point_and_line @ SV11 @ SY102 )
| ( apart_point_and_line @ SV11 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(172,plain,
! [SV12: $i] :
( ( ! [SY104: $i] :
( ~ ( apart_point_and_line @ SV12 @ SY104 )
| ! [SY105: $i] :
( ( apart_point_and_line @ SY105 @ SY104 )
| ( distinct_points @ SV12 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(173,plain,
! [SV13: $i] :
( ( ! [SY106: $i] :
( ~ ( apart_point_and_line @ SV13 @ SY106 )
| ! [SY107: $i] :
( ( apart_point_and_line @ SV13 @ SY107 )
| ( distinct_lines @ SY106 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(174,plain,
! [SV14: $i] :
( ( ! [SY108: $i] :
( ~ ( convergent_lines @ SV14 @ SY108 )
| ! [SY109: $i] :
( ( convergent_lines @ SV14 @ SY109 )
| ( distinct_lines @ SY108 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(175,plain,
! [SV15: $i] :
( ( ! [SY110: $i] :
( ~ ( distinct_lines @ SV15 @ SY110 )
| ( convergent_lines @ SV15 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(176,plain,
! [SV16: $i] :
( ( ! [SY111: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY111 @ SV16 ) @ SY111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(177,plain,
! [SV17: $i] :
( ( ! [SY112: $i] :
~ ( apart_point_and_line @ SV17 @ ( parallel_through_point @ SY112 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(178,plain,
! [SV18: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( distinct_lines @ SY113 @ SY114 )
| ( convergent_lines @ SY113 @ SY114 )
| ( apart_point_and_line @ SV18 @ SY113 )
| ( apart_point_and_line @ SV18 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(179,plain,
! [SV19: $i] :
( ( ! [SY115: $i] :
( ( convergent_lines @ SV19 @ SY115 )
| ( unorthogonal_lines @ SV19 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(180,plain,
! [SV20: $i] :
( ( ! [SY116: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ SY116 @ SV20 ) @ SY116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(181,plain,
! [SV21: $i] :
( ( ! [SY117: $i] :
~ ( apart_point_and_line @ SV21 @ ( orthogonal_through_point @ SY117 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(182,plain,
! [SV22: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( distinct_lines @ SY118 @ SY119 )
| ! [SY120: $i] :
( ( unorthogonal_lines @ SY119 @ SY120 )
| ( unorthogonal_lines @ SY118 @ SY120 )
| ( apart_point_and_line @ SV22 @ SY118 )
| ( apart_point_and_line @ SV22 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(183,plain,
! [SV23: $i] :
( ( ! [SY121: $i] :
( ( convergent_lines @ SV23 @ SY121 )
| ( unorthogonal_lines @ SV23 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(184,plain,
! [SV24: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ( unorthogonal_lines @ SV24 @ SY122 )
| ( unorthogonal_lines @ SV24 @ SY123 )
| ~ ( convergent_lines @ SY122 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(185,plain,
! [SV25: $i] :
( ( ! [SY124: $i] :
( ~ ( point @ SV25 )
| ~ ( point @ SY124 )
| ~ ( distinct_points @ SV25 @ SY124 )
| ( line @ ( line_connecting @ SV25 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(186,plain,
! [SV26: $i] :
( ( ! [SY125: $i] :
( ~ ( line @ SV26 )
| ~ ( line @ SY125 )
| ~ ( convergent_lines @ SV26 @ SY125 )
| ( point @ ( intersection_point @ SV26 @ SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(187,plain,
! [SV27: $i] :
( ( ! [SY126: $i] :
( ~ ( line @ SV27 )
| ~ ( point @ SY126 )
| ( line @ ( parallel_through_point @ SV27 @ SY126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(188,plain,
! [SV28: $i] :
( ( ! [SY127: $i] :
( ~ ( line @ SV28 )
| ~ ( point @ SY127 )
| ( line @ ( orthogonal_through_point @ SV28 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(189,plain,
( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(190,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(191,plain,
! [SV29: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
| ~ ~ ( ~ ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) )
| ~ ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(192,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(193,plain,
! [SV30: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
| ~ ~ ( ~ ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) )
| ~ ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(195,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(196,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(197,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(198,plain,
! [SV2: $i] :
( ( distinct_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(199,plain,
! [SV3: $i] :
( ( convergent_lines @ SV3 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(200,plain,
! [SV31: $i,SV4: $i] :
( ( ~ ( distinct_points @ SV4 @ SV31 )
| ! [SY144: $i] :
( ( distinct_points @ SV4 @ SY144 )
| ( distinct_points @ SV31 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(201,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( distinct_lines @ SV5 @ SV32 )
| ! [SY145: $i] :
( ( distinct_lines @ SV5 @ SY145 )
| ( distinct_lines @ SV32 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(202,plain,
! [SV33: $i,SV6: $i] :
( ( ~ ( convergent_lines @ SV6 @ SV33 )
| ! [SY146: $i] :
( ( convergent_lines @ SV6 @ SY146 )
| ( convergent_lines @ SV33 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(203,plain,
! [SV34: $i,SV7: $i] :
( ( ~ ( distinct_points @ SV7 @ SV34 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(204,plain,
! [SV35: $i,SV8: $i] :
( ( ~ ( distinct_points @ SV8 @ SV35 )
| ~ ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(205,plain,
! [SV36: $i,SV9: $i] :
( ( ~ ( convergent_lines @ SV9 @ SV36 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(206,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( convergent_lines @ SV10 @ SV37 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(207,plain,
! [SV38: $i,SV11: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ~ ( distinct_lines @ SY147 @ SY148 )
| ~ ( distinct_points @ SV11 @ SV38 )
| ( apart_point_and_line @ SV38 @ SY148 )
| ( apart_point_and_line @ SV38 @ SY147 )
| ( apart_point_and_line @ SV11 @ SY147 )
| ( apart_point_and_line @ SV11 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(208,plain,
! [SV39: $i,SV12: $i] :
( ( ~ ( apart_point_and_line @ SV12 @ SV39 )
| ! [SY149: $i] :
( ( apart_point_and_line @ SY149 @ SV39 )
| ( distinct_points @ SV12 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(209,plain,
! [SV40: $i,SV13: $i] :
( ( ~ ( apart_point_and_line @ SV13 @ SV40 )
| ! [SY150: $i] :
( ( apart_point_and_line @ SV13 @ SY150 )
| ( distinct_lines @ SV40 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(210,plain,
! [SV41: $i,SV14: $i] :
( ( ~ ( convergent_lines @ SV14 @ SV41 )
| ! [SY151: $i] :
( ( convergent_lines @ SV14 @ SY151 )
| ( distinct_lines @ SV41 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(211,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( distinct_lines @ SV15 @ SV42 )
| ( convergent_lines @ SV15 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(212,plain,
! [SV16: $i,SV43: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV43 @ SV16 ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(213,plain,
! [SV44: $i,SV17: $i] :
( ( ~ ( apart_point_and_line @ SV17 @ ( parallel_through_point @ SV44 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(214,plain,
! [SV18: $i,SV45: $i] :
( ( ! [SY152: $i] :
( ~ ( distinct_lines @ SV45 @ SY152 )
| ( convergent_lines @ SV45 @ SY152 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(215,plain,
! [SV46: $i,SV19: $i] :
( ( ( convergent_lines @ SV19 @ SV46 )
| ( unorthogonal_lines @ SV19 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(216,plain,
! [SV20: $i,SV47: $i] :
( ( ~ ( unorthogonal_lines @ ( orthogonal_through_point @ SV47 @ SV20 ) @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(217,plain,
! [SV48: $i,SV21: $i] :
( ( ~ ( apart_point_and_line @ SV21 @ ( orthogonal_through_point @ SV48 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(218,plain,
! [SV22: $i,SV49: $i] :
( ( ! [SY153: $i] :
( ~ ( distinct_lines @ SV49 @ SY153 )
| ! [SY154: $i] :
( ( unorthogonal_lines @ SY153 @ SY154 )
| ( unorthogonal_lines @ SV49 @ SY154 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(219,plain,
! [SV50: $i,SV23: $i] :
( ( ( convergent_lines @ SV23 @ SV50 )
| ( unorthogonal_lines @ SV23 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(220,plain,
! [SV51: $i,SV24: $i] :
( ( ! [SY155: $i] :
( ( unorthogonal_lines @ SV24 @ SV51 )
| ( unorthogonal_lines @ SV24 @ SY155 )
| ~ ( convergent_lines @ SV51 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(221,plain,
! [SV52: $i,SV25: $i] :
( ( ~ ( point @ SV25 )
| ~ ( point @ SV52 )
| ~ ( distinct_points @ SV25 @ SV52 )
| ( line @ ( line_connecting @ SV25 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(222,plain,
! [SV53: $i,SV26: $i] :
( ( ~ ( line @ SV26 )
| ~ ( line @ SV53 )
| ~ ( convergent_lines @ SV26 @ SV53 )
| ( point @ ( intersection_point @ SV26 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(223,plain,
! [SV54: $i,SV27: $i] :
( ( ~ ( line @ SV27 )
| ~ ( point @ SV54 )
| ( line @ ( parallel_through_point @ SV27 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV55: $i,SV28: $i] :
( ( ~ ( line @ SV28 )
| ~ ( point @ SV55 )
| ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(227,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
| ~ ~ ( ~ ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) )
| ~ ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(228,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(229,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(230,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
| ~ ~ ( ~ ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) )
| ~ ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(231,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(232,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(233,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(234,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(236,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(237,plain,
! [SV31: $i,SV4: $i] :
( ( ( ~ ( distinct_points @ SV4 @ SV31 ) )
= $true )
| ( ( ! [SY144: $i] :
( ( distinct_points @ SV4 @ SY144 )
| ( distinct_points @ SV31 @ SY144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(238,plain,
! [SV32: $i,SV5: $i] :
( ( ( ~ ( distinct_lines @ SV5 @ SV32 ) )
= $true )
| ( ( ! [SY145: $i] :
( ( distinct_lines @ SV5 @ SY145 )
| ( distinct_lines @ SV32 @ SY145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(239,plain,
! [SV33: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV33 ) )
= $true )
| ( ( ! [SY146: $i] :
( ( convergent_lines @ SV6 @ SY146 )
| ( convergent_lines @ SV33 @ SY146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(240,plain,
! [SV34: $i,SV7: $i] :
( ( ( ~ ( distinct_points @ SV7 @ SV34 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV35: $i,SV8: $i] :
( ( ( ~ ( distinct_points @ SV8 @ SV35 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV36: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV36 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV37: $i,SV10: $i] :
( ( ( ~ ( convergent_lines @ SV10 @ SV37 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV38: $i,SV11: $i,SV56: $i] :
( ( ! [SY156: $i] :
( ~ ( distinct_lines @ SV56 @ SY156 )
| ~ ( distinct_points @ SV11 @ SV38 )
| ( apart_point_and_line @ SV38 @ SY156 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV39: $i,SV12: $i] :
( ( ( ~ ( apart_point_and_line @ SV12 @ SV39 ) )
= $true )
| ( ( ! [SY149: $i] :
( ( apart_point_and_line @ SY149 @ SV39 )
| ( distinct_points @ SV12 @ SY149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV40: $i,SV13: $i] :
( ( ( ~ ( apart_point_and_line @ SV13 @ SV40 ) )
= $true )
| ( ( ! [SY150: $i] :
( ( apart_point_and_line @ SV13 @ SY150 )
| ( distinct_lines @ SV40 @ SY150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV41: $i,SV14: $i] :
( ( ( ~ ( convergent_lines @ SV14 @ SV41 ) )
= $true )
| ( ( ! [SY151: $i] :
( ( convergent_lines @ SV14 @ SY151 )
| ( distinct_lines @ SV41 @ SY151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(248,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( distinct_lines @ SV15 @ SV42 ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(249,plain,
! [SV16: $i,SV43: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV43 @ SV16 ) @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(250,plain,
! [SV44: $i,SV17: $i] :
( ( apart_point_and_line @ SV17 @ ( parallel_through_point @ SV44 @ SV17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(251,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ~ ( distinct_lines @ SV45 @ SV57 )
| ( convergent_lines @ SV45 @ SV57 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(252,plain,
! [SV46: $i,SV19: $i] :
( ( ( convergent_lines @ SV19 @ SV46 )
= $true )
| ( ( unorthogonal_lines @ SV19 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(253,plain,
! [SV20: $i,SV47: $i] :
( ( unorthogonal_lines @ ( orthogonal_through_point @ SV47 @ SV20 ) @ SV47 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(254,plain,
! [SV48: $i,SV21: $i] :
( ( apart_point_and_line @ SV21 @ ( orthogonal_through_point @ SV48 @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(255,plain,
! [SV22: $i,SV58: $i,SV49: $i] :
( ( ~ ( distinct_lines @ SV49 @ SV58 )
| ! [SY157: $i] :
( ( unorthogonal_lines @ SV58 @ SY157 )
| ( unorthogonal_lines @ SV49 @ SY157 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(256,plain,
! [SV50: $i,SV23: $i] :
( ( ( convergent_lines @ SV23 @ SV50 )
= $true )
| ( ( unorthogonal_lines @ SV23 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(257,plain,
! [SV59: $i,SV51: $i,SV24: $i] :
( ( ( unorthogonal_lines @ SV24 @ SV51 )
| ( unorthogonal_lines @ SV24 @ SV59 )
| ~ ( convergent_lines @ SV51 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(258,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 )
| ~ ( point @ SV52 )
| ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(259,plain,
! [SV53: $i,SV26: $i] :
( ( ( ~ ( line @ SV26 )
| ~ ( line @ SV53 )
| ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(260,plain,
! [SV54: $i,SV27: $i] :
( ( ( ~ ( line @ SV27 )
| ~ ( point @ SV54 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(261,plain,
! [SV55: $i,SV28: $i] :
( ( ( ~ ( line @ SV28 )
| ~ ( point @ SV55 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(262,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(263,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(264,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(265,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) )
| ~ ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(266,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(267,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(268,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(269,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) )
| ~ ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(270,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(271,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(272,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(274,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(276,plain,
! [SV31: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV31 )
= $false )
| ( ( ! [SY144: $i] :
( ( distinct_points @ SV4 @ SY144 )
| ( distinct_points @ SV31 @ SY144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(277,plain,
! [SV32: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV32 )
= $false )
| ( ( ! [SY145: $i] :
( ( distinct_lines @ SV5 @ SY145 )
| ( distinct_lines @ SV32 @ SY145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(278,plain,
! [SV33: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV33 )
= $false )
| ( ( ! [SY146: $i] :
( ( convergent_lines @ SV6 @ SY146 )
| ( convergent_lines @ SV33 @ SY146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(279,plain,
! [SV34: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV34 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(280,plain,
! [SV35: $i,SV8: $i] :
( ( ( distinct_points @ SV8 @ SV35 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(281,plain,
! [SV36: $i,SV9: $i] :
( ( ( convergent_lines @ SV9 @ SV36 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(282,plain,
! [SV37: $i,SV10: $i] :
( ( ( convergent_lines @ SV10 @ SV37 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(283,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ~ ( distinct_lines @ SV56 @ SV60 )
| ~ ( distinct_points @ SV11 @ SV38 )
| ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(284,plain,
! [SV39: $i,SV12: $i] :
( ( ( apart_point_and_line @ SV12 @ SV39 )
= $false )
| ( ( ! [SY149: $i] :
( ( apart_point_and_line @ SY149 @ SV39 )
| ( distinct_points @ SV12 @ SY149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(285,plain,
! [SV40: $i,SV13: $i] :
( ( ( apart_point_and_line @ SV13 @ SV40 )
= $false )
| ( ( ! [SY150: $i] :
( ( apart_point_and_line @ SV13 @ SY150 )
| ( distinct_lines @ SV40 @ SY150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(286,plain,
! [SV41: $i,SV14: $i] :
( ( ( convergent_lines @ SV14 @ SV41 )
= $false )
| ( ( ! [SY151: $i] :
( ( convergent_lines @ SV14 @ SY151 )
| ( distinct_lines @ SV41 @ SY151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(287,plain,
! [SV42: $i,SV15: $i] :
( ( ( distinct_lines @ SV15 @ SV42 )
= $false )
| ( ( convergent_lines @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(288,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ( ~ ( distinct_lines @ SV45 @ SV57 ) )
= $true )
| ( ( ( convergent_lines @ SV45 @ SV57 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(289,plain,
! [SV22: $i,SV58: $i,SV49: $i] :
( ( ( ~ ( distinct_lines @ SV49 @ SV58 ) )
= $true )
| ( ( ! [SY157: $i] :
( ( unorthogonal_lines @ SV58 @ SY157 )
| ( unorthogonal_lines @ SV49 @ SY157 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(290,plain,
! [SV59: $i,SV51: $i,SV24: $i] :
( ( ( ( unorthogonal_lines @ SV24 @ SV51 )
| ( unorthogonal_lines @ SV24 @ SV59 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV51 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(291,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 )
| ~ ( point @ SV52 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(292,plain,
! [SV53: $i,SV26: $i] :
( ( ( ~ ( line @ SV26 )
| ~ ( line @ SV53 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(293,plain,
! [SV54: $i,SV27: $i] :
( ( ( ~ ( line @ SV27 ) )
= $true )
| ( ( ~ ( point @ SV54 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(294,plain,
! [SV55: $i,SV28: $i] :
( ( ( ~ ( line @ SV28 ) )
= $true )
| ( ( ~ ( point @ SV55 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(295,plain,
! [SV61: $i] :
( ( ! [SY158: $i] :
( ~ ( incident_point_and_line @ SV61 @ SY158 )
| ~ ( apart_point_and_line @ SV61 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(296,plain,
! [SV62: $i] :
( ( ! [SY159: $i] :
( ( apart_point_and_line @ SV62 @ SY159 )
| ( incident_point_and_line @ SV62 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(297,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(298,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) )
| ~ ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(299,plain,
! [SV63: $i] :
( ( ! [SY160: $i] :
( ~ ( parallel_lines @ SV63 @ SY160 )
| ~ ( convergent_lines @ SV63 @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(300,plain,
! [SV64: $i] :
( ( ! [SY161: $i] :
( ( convergent_lines @ SV64 @ SY161 )
| ( parallel_lines @ SV64 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(301,plain,
! [SV30: $i] :
( ( ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(302,plain,
! [SV30: $i] :
( ( ~ ( ~ ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) )
| ~ ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(303,plain,
! [SV65: $i] :
( ( ! [SY162: $i] :
( ~ ( orthogonal_lines @ SV65 @ SY162 )
| ~ ( unorthogonal_lines @ SV65 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(304,plain,
! [SV66: $i] :
( ( ! [SY163: $i] :
( ( unorthogonal_lines @ SV66 @ SY163 )
| ( orthogonal_lines @ SV66 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(305,plain,
! [SV67: $i] :
( ( ! [SY164: $i] :
( ~ ( equal_points @ SV67 @ SY164 )
| ~ ( distinct_points @ SV67 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(306,plain,
! [SV68: $i] :
( ( ! [SY165: $i] :
( ( distinct_points @ SV68 @ SY165 )
| ( equal_points @ SV68 @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(307,plain,
! [SV69: $i] :
( ( ! [SY166: $i] :
( ~ ( equal_lines @ SV69 @ SY166 )
| ~ ( distinct_lines @ SV69 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(308,plain,
! [SV70: $i] :
( ( ! [SY167: $i] :
( ( distinct_lines @ SV70 @ SY167 )
| ( equal_lines @ SV70 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(309,plain,
! [SV31: $i,SV71: $i,SV4: $i] :
( ( ( ( distinct_points @ SV4 @ SV71 )
| ( distinct_points @ SV31 @ SV71 ) )
= $true )
| ( ( distinct_points @ SV4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(310,plain,
! [SV32: $i,SV72: $i,SV5: $i] :
( ( ( ( distinct_lines @ SV5 @ SV72 )
| ( distinct_lines @ SV32 @ SV72 ) )
= $true )
| ( ( distinct_lines @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(311,plain,
! [SV33: $i,SV73: $i,SV6: $i] :
( ( ( ( convergent_lines @ SV6 @ SV73 )
| ( convergent_lines @ SV33 @ SV73 ) )
= $true )
| ( ( convergent_lines @ SV6 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(312,plain,
! [SV34: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) )
= $false )
| ( ( distinct_points @ SV7 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(313,plain,
! [SV8: $i,SV35: $i] :
( ( ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) )
= $false )
| ( ( distinct_points @ SV8 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(314,plain,
! [SV36: $i,SV9: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 )
= $false )
| ( ( convergent_lines @ SV9 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(315,plain,
! [SV37: $i,SV10: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 )
= $false )
| ( ( convergent_lines @ SV10 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(316,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ( ~ ( distinct_lines @ SV56 @ SV60 )
| ~ ( distinct_points @ SV11 @ SV38 ) )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(317,plain,
! [SV12: $i,SV39: $i,SV74: $i] :
( ( ( ( apart_point_and_line @ SV74 @ SV39 )
| ( distinct_points @ SV12 @ SV74 ) )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(318,plain,
! [SV40: $i,SV75: $i,SV13: $i] :
( ( ( ( apart_point_and_line @ SV13 @ SV75 )
| ( distinct_lines @ SV40 @ SV75 ) )
= $true )
| ( ( apart_point_and_line @ SV13 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(319,plain,
! [SV41: $i,SV76: $i,SV14: $i] :
( ( ( ( convergent_lines @ SV14 @ SV76 )
| ( distinct_lines @ SV41 @ SV76 ) )
= $true )
| ( ( convergent_lines @ SV14 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(320,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ( distinct_lines @ SV45 @ SV57 )
= $false )
| ( ( ( convergent_lines @ SV45 @ SV57 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV22: $i,SV58: $i,SV49: $i] :
( ( ( distinct_lines @ SV49 @ SV58 )
= $false )
| ( ( ! [SY157: $i] :
( ( unorthogonal_lines @ SV58 @ SY157 )
| ( unorthogonal_lines @ SV49 @ SY157 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV59: $i,SV51: $i,SV24: $i] :
( ( ( unorthogonal_lines @ SV24 @ SV51 )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV59 )
= $true )
| ( ( ~ ( convergent_lines @ SV51 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(323,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 ) )
= $true )
| ( ( ~ ( point @ SV52 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(324,plain,
! [SV53: $i,SV26: $i] :
( ( ( ~ ( line @ SV26 ) )
= $true )
| ( ( ~ ( line @ SV53 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(325,plain,
! [SV54: $i,SV27: $i] :
( ( ( line @ SV27 )
= $false )
| ( ( ~ ( point @ SV54 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(326,plain,
! [SV55: $i,SV28: $i] :
( ( ( line @ SV28 )
= $false )
| ( ( ~ ( point @ SV55 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(327,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ( incident_point_and_line @ SV61 @ SV77 )
| ~ ( apart_point_and_line @ SV61 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(328,plain,
! [SV78: $i,SV62: $i] :
( ( ( apart_point_and_line @ SV62 @ SV78 )
| ( incident_point_and_line @ SV62 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(329,plain,
! [SV29: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(330,plain,
! [SV29: $i] :
( ( ~ ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) )
| ~ ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(331,plain,
! [SV79: $i,SV63: $i] :
( ( ~ ( parallel_lines @ SV63 @ SV79 )
| ~ ( convergent_lines @ SV63 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(332,plain,
! [SV80: $i,SV64: $i] :
( ( ( convergent_lines @ SV64 @ SV80 )
| ( parallel_lines @ SV64 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(333,plain,
! [SV30: $i] :
( ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(334,plain,
! [SV30: $i] :
( ( ~ ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) )
| ~ ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(335,plain,
! [SV81: $i,SV65: $i] :
( ( ~ ( orthogonal_lines @ SV65 @ SV81 )
| ~ ( unorthogonal_lines @ SV65 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(336,plain,
! [SV82: $i,SV66: $i] :
( ( ( unorthogonal_lines @ SV66 @ SV82 )
| ( orthogonal_lines @ SV66 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(337,plain,
! [SV83: $i,SV67: $i] :
( ( ~ ( equal_points @ SV67 @ SV83 )
| ~ ( distinct_points @ SV67 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(338,plain,
! [SV84: $i,SV68: $i] :
( ( ( distinct_points @ SV68 @ SV84 )
| ( equal_points @ SV68 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(339,plain,
! [SV85: $i,SV69: $i] :
( ( ~ ( equal_lines @ SV69 @ SV85 )
| ~ ( distinct_lines @ SV69 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(340,plain,
! [SV86: $i,SV70: $i] :
( ( ( distinct_lines @ SV70 @ SV86 )
| ( equal_lines @ SV70 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(341,plain,
! [SV31: $i,SV71: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV71 )
= $true )
| ( ( distinct_points @ SV31 @ SV71 )
= $true )
| ( ( distinct_points @ SV4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(342,plain,
! [SV32: $i,SV72: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV72 )
= $true )
| ( ( distinct_lines @ SV32 @ SV72 )
= $true )
| ( ( distinct_lines @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(343,plain,
! [SV33: $i,SV73: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV73 )
= $true )
| ( ( convergent_lines @ SV33 @ SV73 )
= $true )
| ( ( convergent_lines @ SV6 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(344,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ( ~ ( distinct_lines @ SV56 @ SV60 ) )
= $true )
| ( ( ~ ( distinct_points @ SV11 @ SV38 ) )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(345,plain,
! [SV12: $i,SV39: $i,SV74: $i] :
( ( ( apart_point_and_line @ SV74 @ SV39 )
= $true )
| ( ( distinct_points @ SV12 @ SV74 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(346,plain,
! [SV40: $i,SV75: $i,SV13: $i] :
( ( ( apart_point_and_line @ SV13 @ SV75 )
= $true )
| ( ( distinct_lines @ SV40 @ SV75 )
= $true )
| ( ( apart_point_and_line @ SV13 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(347,plain,
! [SV41: $i,SV76: $i,SV14: $i] :
( ( ( convergent_lines @ SV14 @ SV76 )
= $true )
| ( ( distinct_lines @ SV41 @ SV76 )
= $true )
| ( ( convergent_lines @ SV14 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(348,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ( convergent_lines @ SV45 @ SV57 )
= $true )
| ( ( ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true )
| ( ( distinct_lines @ SV45 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(349,plain,
! [SV22: $i,SV49: $i,SV87: $i,SV58: $i] :
( ( ( ( unorthogonal_lines @ SV58 @ SV87 )
| ( unorthogonal_lines @ SV49 @ SV87 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(350,plain,
! [SV24: $i,SV59: $i,SV51: $i] :
( ( ( convergent_lines @ SV51 @ SV59 )
= $false )
| ( ( unorthogonal_lines @ SV24 @ SV59 )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(351,plain,
! [SV52: $i,SV25: $i] :
( ( ( point @ SV25 )
= $false )
| ( ( ~ ( point @ SV52 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(352,plain,
! [SV53: $i,SV26: $i] :
( ( ( line @ SV26 )
= $false )
| ( ( ~ ( line @ SV53 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(353,plain,
! [SV27: $i,SV54: $i] :
( ( ( point @ SV54 )
= $false )
| ( ( line @ SV27 )
= $false )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(354,plain,
! [SV28: $i,SV55: $i] :
( ( ( point @ SV55 )
= $false )
| ( ( line @ SV28 )
= $false )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(355,plain,
! [SV77: $i,SV61: $i] :
( ( ( ~ ( incident_point_and_line @ SV61 @ SV77 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(356,plain,
! [SV78: $i,SV62: $i] :
( ( ( apart_point_and_line @ SV62 @ SV78 )
= $true )
| ( ( incident_point_and_line @ SV62 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(357,plain,
! [SV29: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(358,plain,
! [SV29: $i] :
( ( ~ ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(359,plain,
! [SV29: $i] :
( ( ~ ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(360,plain,
! [SV29: $i] :
( ( ~ ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(361,plain,
! [SV79: $i,SV63: $i] :
( ( ( ~ ( parallel_lines @ SV63 @ SV79 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV63 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(362,plain,
! [SV80: $i,SV64: $i] :
( ( ( convergent_lines @ SV64 @ SV80 )
= $true )
| ( ( parallel_lines @ SV64 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(363,plain,
! [SV30: $i] :
( ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(364,plain,
! [SV30: $i] :
( ( ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(365,plain,
! [SV30: $i] :
( ( ~ ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(366,plain,
! [SV30: $i] :
( ( ~ ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(367,plain,
! [SV81: $i,SV65: $i] :
( ( ( ~ ( orthogonal_lines @ SV65 @ SV81 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV65 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(368,plain,
! [SV82: $i,SV66: $i] :
( ( ( unorthogonal_lines @ SV66 @ SV82 )
= $true )
| ( ( orthogonal_lines @ SV66 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(369,plain,
! [SV83: $i,SV67: $i] :
( ( ( ~ ( equal_points @ SV67 @ SV83 ) )
= $true )
| ( ( ~ ( distinct_points @ SV67 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(370,plain,
! [SV84: $i,SV68: $i] :
( ( ( distinct_points @ SV68 @ SV84 )
= $true )
| ( ( equal_points @ SV68 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(371,plain,
! [SV85: $i,SV69: $i] :
( ( ( ~ ( equal_lines @ SV69 @ SV85 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV69 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(372,plain,
! [SV86: $i,SV70: $i] :
( ( ( distinct_lines @ SV70 @ SV86 )
= $true )
| ( ( equal_lines @ SV70 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(373,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( ~ ( distinct_points @ SV11 @ SV38 ) )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(374,plain,
! [SV57: $i,SV45: $i,SV18: $i] :
( ( ( apart_point_and_line @ SV18 @ SV45 )
= $true )
| ( ( apart_point_and_line @ SV18 @ SV57 )
= $true )
| ( ( convergent_lines @ SV45 @ SV57 )
= $true )
| ( ( distinct_lines @ SV45 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(375,plain,
! [SV22: $i,SV49: $i,SV87: $i,SV58: $i] :
( ( ( unorthogonal_lines @ SV58 @ SV87 )
= $true )
| ( ( ( unorthogonal_lines @ SV49 @ SV87 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(376,plain,
! [SV25: $i,SV52: $i] :
( ( ( point @ SV52 )
= $false )
| ( ( point @ SV25 )
= $false )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(377,plain,
! [SV26: $i,SV53: $i] :
( ( ( line @ SV53 )
= $false )
| ( ( line @ SV26 )
= $false )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(378,plain,
! [SV77: $i,SV61: $i] :
( ( ( incident_point_and_line @ SV61 @ SV77 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(379,plain,
! [SV29: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ( convergent_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(380,plain,
! [SV29: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ( convergent_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(381,plain,
! [SV29: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( unorthogonal_lines @ SV29 @ SY132 )
| ( convergent_lines @ SV29 @ SY133 )
| ~ ( convergent_lines @ SY132 @ SY133 )
| ~ ( unorthogonal_lines @ SY132 @ SY133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(382,plain,
! [SV29: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ( unorthogonal_lines @ SV29 @ SY134 )
| ( unorthogonal_lines @ SV29 @ SY135 )
| ~ ( convergent_lines @ SY134 @ SY135 )
| ~ ( unorthogonal_lines @ SY134 @ SY135 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(383,plain,
! [SV79: $i,SV63: $i] :
( ( ( parallel_lines @ SV63 @ SV79 )
= $false )
| ( ( ~ ( convergent_lines @ SV63 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(384,plain,
! [SV30: $i] :
( ( ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( convergent_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(385,plain,
! [SV30: $i] :
( ( ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( convergent_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(386,plain,
! [SV30: $i] :
( ( ! [SY140: $i] :
( ~ ( convergent_lines @ SV30 @ SY140 )
| ~ ( unorthogonal_lines @ SV30 @ SY140 )
| ! [SY141: $i] :
( ( unorthogonal_lines @ SV30 @ SY141 )
| ( convergent_lines @ SY140 @ SY141 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(387,plain,
! [SV30: $i] :
( ( ! [SY142: $i] :
( ~ ( convergent_lines @ SV30 @ SY142 )
| ~ ( unorthogonal_lines @ SV30 @ SY142 )
| ! [SY143: $i] :
( ( unorthogonal_lines @ SV30 @ SY143 )
| ( unorthogonal_lines @ SY142 @ SY143 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(388,plain,
! [SV81: $i,SV65: $i] :
( ( ( orthogonal_lines @ SV65 @ SV81 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV65 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(389,plain,
! [SV83: $i,SV67: $i] :
( ( ( equal_points @ SV67 @ SV83 )
= $false )
| ( ( ~ ( distinct_points @ SV67 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(390,plain,
! [SV85: $i,SV69: $i] :
( ( ( equal_lines @ SV69 @ SV85 )
= $false )
| ( ( ~ ( distinct_lines @ SV69 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(391,plain,
! [SV60: $i,SV56: $i,SV38: $i,SV11: $i] :
( ( ( distinct_points @ SV11 @ SV38 )
= $false )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(392,plain,
! [SV58: $i,SV22: $i,SV87: $i,SV49: $i] :
( ( ( unorthogonal_lines @ SV49 @ SV87 )
= $true )
| ( ( ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) )
= $true )
| ( ( unorthogonal_lines @ SV58 @ SV87 )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(393,plain,
! [SV52: $i,SV25: $i] :
( ( ( distinct_points @ SV25 @ SV52 )
= $false )
| ( ( point @ SV25 )
= $false )
| ( ( point @ SV52 )
= $false )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(394,plain,
! [SV53: $i,SV26: $i] :
( ( ( convergent_lines @ SV26 @ SV53 )
= $false )
| ( ( line @ SV26 )
= $false )
| ( ( line @ SV53 )
= $false )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(395,plain,
! [SV77: $i,SV61: $i] :
( ( ( apart_point_and_line @ SV61 @ SV77 )
= $false )
| ( ( incident_point_and_line @ SV61 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(396,plain,
! [SV88: $i,SV29: $i] :
( ( ! [SY168: $i] :
( ( convergent_lines @ SV29 @ SV88 )
| ( convergent_lines @ SV29 @ SY168 )
| ~ ( convergent_lines @ SV88 @ SY168 )
| ~ ( unorthogonal_lines @ SV88 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(397,plain,
! [SV89: $i,SV29: $i] :
( ( ! [SY169: $i] :
( ( convergent_lines @ SV29 @ SV89 )
| ( unorthogonal_lines @ SV29 @ SY169 )
| ~ ( convergent_lines @ SV89 @ SY169 )
| ~ ( unorthogonal_lines @ SV89 @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(398,plain,
! [SV90: $i,SV29: $i] :
( ( ! [SY170: $i] :
( ( unorthogonal_lines @ SV29 @ SV90 )
| ( convergent_lines @ SV29 @ SY170 )
| ~ ( convergent_lines @ SV90 @ SY170 )
| ~ ( unorthogonal_lines @ SV90 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(399,plain,
! [SV91: $i,SV29: $i] :
( ( ! [SY171: $i] :
( ( unorthogonal_lines @ SV29 @ SV91 )
| ( unorthogonal_lines @ SV29 @ SY171 )
| ~ ( convergent_lines @ SV91 @ SY171 )
| ~ ( unorthogonal_lines @ SV91 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(400,plain,
! [SV79: $i,SV63: $i] :
( ( ( convergent_lines @ SV63 @ SV79 )
= $false )
| ( ( parallel_lines @ SV63 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(401,plain,
! [SV92: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV92 )
| ~ ( unorthogonal_lines @ SV30 @ SV92 )
| ! [SY172: $i] :
( ( convergent_lines @ SV30 @ SY172 )
| ( convergent_lines @ SV92 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(402,plain,
! [SV93: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV93 )
| ~ ( unorthogonal_lines @ SV30 @ SV93 )
| ! [SY173: $i] :
( ( convergent_lines @ SV30 @ SY173 )
| ( unorthogonal_lines @ SV93 @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(403,plain,
! [SV94: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV94 )
| ~ ( unorthogonal_lines @ SV30 @ SV94 )
| ! [SY174: $i] :
( ( unorthogonal_lines @ SV30 @ SY174 )
| ( convergent_lines @ SV94 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(404,plain,
! [SV95: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV95 )
| ~ ( unorthogonal_lines @ SV30 @ SV95 )
| ! [SY175: $i] :
( ( unorthogonal_lines @ SV30 @ SY175 )
| ( unorthogonal_lines @ SV95 @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(405,plain,
! [SV81: $i,SV65: $i] :
( ( ( unorthogonal_lines @ SV65 @ SV81 )
= $false )
| ( ( orthogonal_lines @ SV65 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(406,plain,
! [SV83: $i,SV67: $i] :
( ( ( distinct_points @ SV67 @ SV83 )
= $false )
| ( ( equal_points @ SV67 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(407,plain,
! [SV85: $i,SV69: $i] :
( ( ( distinct_lines @ SV69 @ SV85 )
= $false )
| ( ( equal_lines @ SV69 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(408,plain,
! [SV11: $i,SV56: $i,SV60: $i,SV38: $i] :
( ( ( apart_point_and_line @ SV38 @ SV60 )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( distinct_points @ SV11 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(409,plain,
! [SV87: $i,SV58: $i,SV49: $i,SV22: $i] :
( ( ( apart_point_and_line @ SV22 @ SV49 )
= $true )
| ( ( apart_point_and_line @ SV22 @ SV58 )
= $true )
| ( ( unorthogonal_lines @ SV49 @ SV87 )
= $true )
| ( ( unorthogonal_lines @ SV58 @ SV87 )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(410,plain,
! [SV96: $i,SV88: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV88 )
| ( convergent_lines @ SV29 @ SV96 )
| ~ ( convergent_lines @ SV88 @ SV96 )
| ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(411,plain,
! [SV97: $i,SV89: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV89 )
| ( unorthogonal_lines @ SV29 @ SV97 )
| ~ ( convergent_lines @ SV89 @ SV97 )
| ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(412,plain,
! [SV98: $i,SV90: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV90 )
| ( convergent_lines @ SV29 @ SV98 )
| ~ ( convergent_lines @ SV90 @ SV98 )
| ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(413,plain,
! [SV99: $i,SV91: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV91 )
| ( unorthogonal_lines @ SV29 @ SV99 )
| ~ ( convergent_lines @ SV91 @ SV99 )
| ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(414,plain,
! [SV92: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV92 )
| ~ ( unorthogonal_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ! [SY172: $i] :
( ( convergent_lines @ SV30 @ SY172 )
| ( convergent_lines @ SV92 @ SY172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(415,plain,
! [SV93: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV93 )
| ~ ( unorthogonal_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ! [SY173: $i] :
( ( convergent_lines @ SV30 @ SY173 )
| ( unorthogonal_lines @ SV93 @ SY173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(416,plain,
! [SV94: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV94 )
| ~ ( unorthogonal_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ! [SY174: $i] :
( ( unorthogonal_lines @ SV30 @ SY174 )
| ( convergent_lines @ SV94 @ SY174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(417,plain,
! [SV95: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV95 )
| ~ ( unorthogonal_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY175: $i] :
( ( unorthogonal_lines @ SV30 @ SY175 )
| ( unorthogonal_lines @ SV95 @ SY175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(418,plain,
! [SV60: $i,SV11: $i,SV56: $i,SV38: $i] :
( ( ( apart_point_and_line @ SV38 @ SV56 )
= $true )
| ( ( ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV60 )
= $true )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( distinct_points @ SV11 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(419,plain,
! [SV96: $i,SV88: $i,SV29: $i] :
( ( ( ( convergent_lines @ SV29 @ SV88 )
| ( convergent_lines @ SV29 @ SV96 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV88 @ SV96 )
| ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(420,plain,
! [SV97: $i,SV89: $i,SV29: $i] :
( ( ( ( convergent_lines @ SV29 @ SV89 )
| ( unorthogonal_lines @ SV29 @ SV97 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV89 @ SV97 )
| ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(421,plain,
! [SV98: $i,SV90: $i,SV29: $i] :
( ( ( ( unorthogonal_lines @ SV29 @ SV90 )
| ( convergent_lines @ SV29 @ SV98 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV90 @ SV98 )
| ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(422,plain,
! [SV99: $i,SV91: $i,SV29: $i] :
( ( ( ( unorthogonal_lines @ SV29 @ SV91 )
| ( unorthogonal_lines @ SV29 @ SV99 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV91 @ SV99 )
| ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(423,plain,
! [SV92: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ! [SY172: $i] :
( ( convergent_lines @ SV30 @ SY172 )
| ( convergent_lines @ SV92 @ SY172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(424,plain,
! [SV93: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ! [SY173: $i] :
( ( convergent_lines @ SV30 @ SY173 )
| ( unorthogonal_lines @ SV93 @ SY173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(425,plain,
! [SV94: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ! [SY174: $i] :
( ( unorthogonal_lines @ SV30 @ SY174 )
| ( convergent_lines @ SV94 @ SY174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(426,plain,
! [SV95: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY175: $i] :
( ( unorthogonal_lines @ SV30 @ SY175 )
| ( unorthogonal_lines @ SV95 @ SY175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(427,plain,
! [SV38: $i,SV60: $i,SV56: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV56 )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV60 )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV56 )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV60 )
= $true )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( distinct_points @ SV11 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(428,plain,
! [SV96: $i,SV88: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV88 )
= $true )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( ~ ( convergent_lines @ SV88 @ SV96 )
| ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(429,plain,
! [SV97: $i,SV89: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV89 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( ~ ( convergent_lines @ SV89 @ SV97 )
| ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(430,plain,
! [SV98: $i,SV90: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( ~ ( convergent_lines @ SV90 @ SV98 )
| ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(431,plain,
! [SV99: $i,SV91: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( ~ ( convergent_lines @ SV91 @ SV99 )
| ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(432,plain,
! [SV92: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ! [SY172: $i] :
( ( convergent_lines @ SV30 @ SY172 )
| ( convergent_lines @ SV92 @ SY172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(433,plain,
! [SV93: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ! [SY173: $i] :
( ( convergent_lines @ SV30 @ SY173 )
| ( unorthogonal_lines @ SV93 @ SY173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(434,plain,
! [SV94: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ! [SY174: $i] :
( ( unorthogonal_lines @ SV30 @ SY174 )
| ( convergent_lines @ SV94 @ SY174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(435,plain,
! [SV95: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY175: $i] :
( ( unorthogonal_lines @ SV30 @ SY175 )
| ( unorthogonal_lines @ SV95 @ SY175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(436,plain,
! [SV29: $i,SV96: $i,SV88: $i] :
( ( ( ~ ( convergent_lines @ SV88 @ SV96 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( convergent_lines @ SV29 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(437,plain,
! [SV29: $i,SV97: $i,SV89: $i] :
( ( ( ~ ( convergent_lines @ SV89 @ SV97 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( convergent_lines @ SV29 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(438,plain,
! [SV29: $i,SV98: $i,SV90: $i] :
( ( ( ~ ( convergent_lines @ SV90 @ SV98 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(439,plain,
! [SV29: $i,SV99: $i,SV91: $i] :
( ( ( ~ ( convergent_lines @ SV91 @ SV99 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(440,plain,
! [SV92: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV92 )
= $false )
| ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( ! [SY172: $i] :
( ( convergent_lines @ SV30 @ SY172 )
| ( convergent_lines @ SV92 @ SY172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(441,plain,
! [SV93: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV93 )
= $false )
| ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( ! [SY173: $i] :
( ( convergent_lines @ SV30 @ SY173 )
| ( unorthogonal_lines @ SV93 @ SY173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(442,plain,
! [SV94: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV94 )
= $false )
| ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( ! [SY174: $i] :
( ( unorthogonal_lines @ SV30 @ SY174 )
| ( convergent_lines @ SV94 @ SY174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(443,plain,
! [SV95: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV95 )
= $false )
| ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( ! [SY175: $i] :
( ( unorthogonal_lines @ SV30 @ SY175 )
| ( unorthogonal_lines @ SV95 @ SY175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(444,plain,
! [SV29: $i,SV96: $i,SV88: $i] :
( ( ( convergent_lines @ SV88 @ SV96 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( convergent_lines @ SV29 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(445,plain,
! [SV29: $i,SV97: $i,SV89: $i] :
( ( ( convergent_lines @ SV89 @ SV97 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( convergent_lines @ SV29 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(446,plain,
! [SV29: $i,SV98: $i,SV90: $i] :
( ( ( convergent_lines @ SV90 @ SV98 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(447,plain,
! [SV29: $i,SV99: $i,SV91: $i] :
( ( ( convergent_lines @ SV91 @ SV99 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(448,plain,
! [SV92: $i,SV100: $i,SV30: $i] :
( ( ( ( convergent_lines @ SV30 @ SV100 )
| ( convergent_lines @ SV92 @ SV100 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(449,plain,
! [SV93: $i,SV101: $i,SV30: $i] :
( ( ( ( convergent_lines @ SV30 @ SV101 )
| ( unorthogonal_lines @ SV93 @ SV101 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(450,plain,
! [SV94: $i,SV102: $i,SV30: $i] :
( ( ( ( unorthogonal_lines @ SV30 @ SV102 )
| ( convergent_lines @ SV94 @ SV102 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(451,plain,
! [SV95: $i,SV103: $i,SV30: $i] :
( ( ( ( unorthogonal_lines @ SV30 @ SV103 )
| ( unorthogonal_lines @ SV95 @ SV103 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(452,plain,
! [SV29: $i,SV96: $i,SV88: $i] :
( ( ( unorthogonal_lines @ SV88 @ SV96 )
= $false )
| ( ( convergent_lines @ SV88 @ SV96 )
= $false )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( convergent_lines @ SV29 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(453,plain,
! [SV29: $i,SV97: $i,SV89: $i] :
( ( ( unorthogonal_lines @ SV89 @ SV97 )
= $false )
| ( ( convergent_lines @ SV89 @ SV97 )
= $false )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( convergent_lines @ SV29 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(454,plain,
! [SV29: $i,SV98: $i,SV90: $i] :
( ( ( unorthogonal_lines @ SV90 @ SV98 )
= $false )
| ( ( convergent_lines @ SV90 @ SV98 )
= $false )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(455,plain,
! [SV29: $i,SV99: $i,SV91: $i] :
( ( ( unorthogonal_lines @ SV91 @ SV99 )
= $false )
| ( ( convergent_lines @ SV91 @ SV99 )
= $false )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(456,plain,
! [SV92: $i,SV100: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV100 )
= $true )
| ( ( convergent_lines @ SV92 @ SV100 )
= $true )
| ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(457,plain,
! [SV93: $i,SV101: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV101 )
= $true )
| ( ( unorthogonal_lines @ SV93 @ SV101 )
= $true )
| ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(458,plain,
! [SV94: $i,SV102: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV102 )
= $true )
| ( ( convergent_lines @ SV94 @ SV102 )
= $true )
| ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(459,plain,
! [SV95: $i,SV103: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV103 )
= $true )
| ( ( unorthogonal_lines @ SV95 @ SV103 )
= $true )
| ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(460,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[149,459,458,457,456,455,454,453,452,427,409,407,406,405,400,395,394,393,374,372,370,368,362,356,354,353,350,347,346,345,343,342,341,315,314,313,312,287,256,254,253,252,250,249,199,198,197,189,152,151,150]) ).
thf(461,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(462,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(463,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(464,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(465,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(466,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(467,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(468,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(469,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(470,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(471,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(472,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(473,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(474,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(475,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(476,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(477,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(478,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( distinct_lines @ Y @ Z )
| ( convergent_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(479,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(480,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(481,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(482,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(483,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ M @ N )
| ( unorthogonal_lines @ L @ N )
| ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(484,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(485,plain,
( ( ! [L: $i] :
( ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(486,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(487,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(488,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( convergent_lines @ L @ M )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(489,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(490,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(491,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_points @ X @ Y )
| ~ ( distinct_points @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
| ( equal_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(492,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_lines @ X @ Y )
| ~ ( distinct_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
| ( equal_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(493,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( parallel_lines @ X @ Y )
| ~ ( convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
| ( parallel_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(494,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( incident_point_and_line @ X @ Y )
| ~ ( apart_point_and_line @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( apart_point_and_line @ X @ Y )
| ( incident_point_and_line @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(495,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( orthogonal_lines @ X @ Y )
| ~ ( unorthogonal_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unorthogonal_lines @ X @ Y )
| ( orthogonal_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(496,plain,
( ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK4_SY90 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(497,plain,
( ( incident_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY85 ) @ sK3_SY88 )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(498,plain,
( ( convergent_lines @ sK3_SY88 @ sK4_SY90 )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(499,plain,
( ( convergent_lines @ sK1_X @ sK2_SY85 )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(500,plain,
( ( ~ ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK2_SY85 ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(501,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(502,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(503,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(504,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( unorthogonal_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( unorthogonal_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(505,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(506,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(507,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( convergent_lines @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(508,plain,
! [SV104: $i] :
( ( ~ ( distinct_points @ SV104 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(509,plain,
! [SV105: $i] :
( ( ~ ( distinct_lines @ SV105 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(510,plain,
! [SV106: $i] :
( ( ~ ( convergent_lines @ SV106 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(511,plain,
! [SV107: $i] :
( ( ! [SY176: $i] :
( ~ ( distinct_points @ SV107 @ SY176 )
| ! [SY177: $i] :
( ( distinct_points @ SV107 @ SY177 )
| ( distinct_points @ SY176 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(512,plain,
! [SV108: $i] :
( ( ! [SY178: $i] :
( ~ ( distinct_lines @ SV108 @ SY178 )
| ! [SY179: $i] :
( ( distinct_lines @ SV108 @ SY179 )
| ( distinct_lines @ SY178 @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(513,plain,
! [SV109: $i] :
( ( ! [SY180: $i] :
( ~ ( convergent_lines @ SV109 @ SY180 )
| ! [SY181: $i] :
( ( convergent_lines @ SV109 @ SY181 )
| ( convergent_lines @ SY180 @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(514,plain,
! [SV110: $i] :
( ( ! [SY182: $i] :
( ~ ( distinct_points @ SV110 @ SY182 )
| ~ ( apart_point_and_line @ SV110 @ ( line_connecting @ SV110 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(515,plain,
! [SV111: $i] :
( ( ! [SY183: $i] :
( ~ ( distinct_points @ SV111 @ SY183 )
| ~ ( apart_point_and_line @ SY183 @ ( line_connecting @ SV111 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(516,plain,
! [SV112: $i] :
( ( ! [SY184: $i] :
( ~ ( convergent_lines @ SV112 @ SY184 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV112 @ SY184 ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(517,plain,
! [SV113: $i] :
( ( ! [SY185: $i] :
( ~ ( convergent_lines @ SV113 @ SY185 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV113 @ SY185 ) @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(518,plain,
! [SV114: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i] :
( ~ ( distinct_lines @ SY187 @ SY188 )
| ~ ( distinct_points @ SV114 @ SY186 )
| ( apart_point_and_line @ SY186 @ SY188 )
| ( apart_point_and_line @ SY186 @ SY187 )
| ( apart_point_and_line @ SV114 @ SY187 )
| ( apart_point_and_line @ SV114 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(519,plain,
! [SV115: $i] :
( ( ! [SY189: $i] :
( ~ ( apart_point_and_line @ SV115 @ SY189 )
| ! [SY190: $i] :
( ( apart_point_and_line @ SY190 @ SY189 )
| ( distinct_points @ SV115 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(520,plain,
! [SV116: $i] :
( ( ! [SY191: $i] :
( ~ ( apart_point_and_line @ SV116 @ SY191 )
| ! [SY192: $i] :
( ( apart_point_and_line @ SV116 @ SY192 )
| ( distinct_lines @ SY191 @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(521,plain,
! [SV117: $i] :
( ( ! [SY193: $i] :
( ~ ( convergent_lines @ SV117 @ SY193 )
| ! [SY194: $i] :
( ( convergent_lines @ SV117 @ SY194 )
| ( distinct_lines @ SY193 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(522,plain,
! [SV118: $i] :
( ( ! [SY195: $i] :
( ~ ( distinct_lines @ SV118 @ SY195 )
| ( convergent_lines @ SV118 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(523,plain,
! [SV119: $i] :
( ( ! [SY196: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY196 @ SV119 ) @ SY196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(524,plain,
! [SV120: $i] :
( ( ! [SY197: $i] :
~ ( apart_point_and_line @ SV120 @ ( parallel_through_point @ SY197 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(525,plain,
! [SV121: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ( distinct_lines @ SY198 @ SY199 )
| ( convergent_lines @ SY198 @ SY199 )
| ( apart_point_and_line @ SV121 @ SY198 )
| ( apart_point_and_line @ SV121 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(526,plain,
! [SV122: $i] :
( ( ! [SY200: $i] :
( ( convergent_lines @ SV122 @ SY200 )
| ( unorthogonal_lines @ SV122 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(527,plain,
! [SV123: $i] :
( ( ! [SY201: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ SY201 @ SV123 ) @ SY201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(528,plain,
! [SV124: $i] :
( ( ! [SY202: $i] :
~ ( apart_point_and_line @ SV124 @ ( orthogonal_through_point @ SY202 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(529,plain,
! [SV125: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( distinct_lines @ SY203 @ SY204 )
| ! [SY205: $i] :
( ( unorthogonal_lines @ SY204 @ SY205 )
| ( unorthogonal_lines @ SY203 @ SY205 )
| ( apart_point_and_line @ SV125 @ SY203 )
| ( apart_point_and_line @ SV125 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(530,plain,
! [SV126: $i] :
( ( ! [SY206: $i] :
( ( convergent_lines @ SV126 @ SY206 )
| ( unorthogonal_lines @ SV126 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(531,plain,
! [SV127: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ( unorthogonal_lines @ SV127 @ SY207 )
| ( unorthogonal_lines @ SV127 @ SY208 )
| ~ ( convergent_lines @ SY207 @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(532,plain,
! [SV128: $i] :
( ( ! [SY209: $i] :
( ~ ( point @ SV128 )
| ~ ( point @ SY209 )
| ~ ( distinct_points @ SV128 @ SY209 )
| ( line @ ( line_connecting @ SV128 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(533,plain,
! [SV129: $i] :
( ( ! [SY210: $i] :
( ~ ( line @ SV129 )
| ~ ( line @ SY210 )
| ~ ( convergent_lines @ SV129 @ SY210 )
| ( point @ ( intersection_point @ SV129 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(534,plain,
! [SV130: $i] :
( ( ! [SY211: $i] :
( ~ ( line @ SV130 )
| ~ ( point @ SY211 )
| ( line @ ( parallel_through_point @ SV130 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(535,plain,
! [SV131: $i] :
( ( ! [SY212: $i] :
( ~ ( line @ SV131 )
| ~ ( point @ SY212 )
| ( line @ ( orthogonal_through_point @ SV131 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(536,plain,
( ( incident_point_and_line @ ( intersection_point @ sK3_SY88 @ sK4_SY90 ) @ sK2_SY85 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(538,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(539,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(540,plain,
! [SV132: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) )
| ~ ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) )
| ~ ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(542,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(543,plain,
! [SV133: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) )
| ~ ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) )
| ~ ~ ( ~ ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) )
| ~ ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(544,plain,
! [SV104: $i] :
( ( distinct_points @ SV104 @ SV104 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(545,plain,
! [SV105: $i] :
( ( distinct_lines @ SV105 @ SV105 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(546,plain,
! [SV106: $i] :
( ( convergent_lines @ SV106 @ SV106 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(547,plain,
! [SV134: $i,SV107: $i] :
( ( ~ ( distinct_points @ SV107 @ SV134 )
| ! [SY229: $i] :
( ( distinct_points @ SV107 @ SY229 )
| ( distinct_points @ SV134 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(548,plain,
! [SV135: $i,SV108: $i] :
( ( ~ ( distinct_lines @ SV108 @ SV135 )
| ! [SY230: $i] :
( ( distinct_lines @ SV108 @ SY230 )
| ( distinct_lines @ SV135 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(549,plain,
! [SV136: $i,SV109: $i] :
( ( ~ ( convergent_lines @ SV109 @ SV136 )
| ! [SY231: $i] :
( ( convergent_lines @ SV109 @ SY231 )
| ( convergent_lines @ SV136 @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(550,plain,
! [SV137: $i,SV110: $i] :
( ( ~ ( distinct_points @ SV110 @ SV137 )
| ~ ( apart_point_and_line @ SV110 @ ( line_connecting @ SV110 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(551,plain,
! [SV138: $i,SV111: $i] :
( ( ~ ( distinct_points @ SV111 @ SV138 )
| ~ ( apart_point_and_line @ SV138 @ ( line_connecting @ SV111 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(552,plain,
! [SV139: $i,SV112: $i] :
( ( ~ ( convergent_lines @ SV112 @ SV139 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV112 @ SV139 ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(553,plain,
! [SV140: $i,SV113: $i] :
( ( ~ ( convergent_lines @ SV113 @ SV140 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV113 @ SV140 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(554,plain,
! [SV141: $i,SV114: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ~ ( distinct_lines @ SY232 @ SY233 )
| ~ ( distinct_points @ SV114 @ SV141 )
| ( apart_point_and_line @ SV141 @ SY233 )
| ( apart_point_and_line @ SV141 @ SY232 )
| ( apart_point_and_line @ SV114 @ SY232 )
| ( apart_point_and_line @ SV114 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(555,plain,
! [SV142: $i,SV115: $i] :
( ( ~ ( apart_point_and_line @ SV115 @ SV142 )
| ! [SY234: $i] :
( ( apart_point_and_line @ SY234 @ SV142 )
| ( distinct_points @ SV115 @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(556,plain,
! [SV143: $i,SV116: $i] :
( ( ~ ( apart_point_and_line @ SV116 @ SV143 )
| ! [SY235: $i] :
( ( apart_point_and_line @ SV116 @ SY235 )
| ( distinct_lines @ SV143 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(557,plain,
! [SV144: $i,SV117: $i] :
( ( ~ ( convergent_lines @ SV117 @ SV144 )
| ! [SY236: $i] :
( ( convergent_lines @ SV117 @ SY236 )
| ( distinct_lines @ SV144 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(558,plain,
! [SV145: $i,SV118: $i] :
( ( ~ ( distinct_lines @ SV118 @ SV145 )
| ( convergent_lines @ SV118 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(559,plain,
! [SV119: $i,SV146: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV146 @ SV119 ) @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(560,plain,
! [SV147: $i,SV120: $i] :
( ( ~ ( apart_point_and_line @ SV120 @ ( parallel_through_point @ SV147 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(561,plain,
! [SV121: $i,SV148: $i] :
( ( ! [SY237: $i] :
( ~ ( distinct_lines @ SV148 @ SY237 )
| ( convergent_lines @ SV148 @ SY237 )
| ( apart_point_and_line @ SV121 @ SV148 )
| ( apart_point_and_line @ SV121 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(562,plain,
! [SV149: $i,SV122: $i] :
( ( ( convergent_lines @ SV122 @ SV149 )
| ( unorthogonal_lines @ SV122 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(563,plain,
! [SV123: $i,SV150: $i] :
( ( ~ ( unorthogonal_lines @ ( orthogonal_through_point @ SV150 @ SV123 ) @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(564,plain,
! [SV151: $i,SV124: $i] :
( ( ~ ( apart_point_and_line @ SV124 @ ( orthogonal_through_point @ SV151 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(565,plain,
! [SV125: $i,SV152: $i] :
( ( ! [SY238: $i] :
( ~ ( distinct_lines @ SV152 @ SY238 )
| ! [SY239: $i] :
( ( unorthogonal_lines @ SY238 @ SY239 )
| ( unorthogonal_lines @ SV152 @ SY239 )
| ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(566,plain,
! [SV153: $i,SV126: $i] :
( ( ( convergent_lines @ SV126 @ SV153 )
| ( unorthogonal_lines @ SV126 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(567,plain,
! [SV154: $i,SV127: $i] :
( ( ! [SY240: $i] :
( ( unorthogonal_lines @ SV127 @ SV154 )
| ( unorthogonal_lines @ SV127 @ SY240 )
| ~ ( convergent_lines @ SV154 @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(568,plain,
! [SV155: $i,SV128: $i] :
( ( ~ ( point @ SV128 )
| ~ ( point @ SV155 )
| ~ ( distinct_points @ SV128 @ SV155 )
| ( line @ ( line_connecting @ SV128 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(569,plain,
! [SV156: $i,SV129: $i] :
( ( ~ ( line @ SV129 )
| ~ ( line @ SV156 )
| ~ ( convergent_lines @ SV129 @ SV156 )
| ( point @ ( intersection_point @ SV129 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(570,plain,
! [SV157: $i,SV130: $i] :
( ( ~ ( line @ SV130 )
| ~ ( point @ SV157 )
| ( line @ ( parallel_through_point @ SV130 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(571,plain,
! [SV158: $i,SV131: $i] :
( ( ~ ( line @ SV131 )
| ~ ( point @ SV158 )
| ( line @ ( orthogonal_through_point @ SV131 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(572,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(573,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(574,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(575,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(576,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(577,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(578,plain,
! [SV132: $i] :
( ( ~ ~ ( ~ ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) )
| ~ ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) )
| ~ ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(579,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(580,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(581,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(582,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(583,plain,
! [SV133: $i] :
( ( ~ ~ ( ~ ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) )
| ~ ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) )
| ~ ~ ( ~ ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) )
| ~ ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(584,plain,
! [SV134: $i,SV107: $i] :
( ( ( ~ ( distinct_points @ SV107 @ SV134 ) )
= $true )
| ( ( ! [SY229: $i] :
( ( distinct_points @ SV107 @ SY229 )
| ( distinct_points @ SV134 @ SY229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(585,plain,
! [SV135: $i,SV108: $i] :
( ( ( ~ ( distinct_lines @ SV108 @ SV135 ) )
= $true )
| ( ( ! [SY230: $i] :
( ( distinct_lines @ SV108 @ SY230 )
| ( distinct_lines @ SV135 @ SY230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(586,plain,
! [SV136: $i,SV109: $i] :
( ( ( ~ ( convergent_lines @ SV109 @ SV136 ) )
= $true )
| ( ( ! [SY231: $i] :
( ( convergent_lines @ SV109 @ SY231 )
| ( convergent_lines @ SV136 @ SY231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(587,plain,
! [SV137: $i,SV110: $i] :
( ( ( ~ ( distinct_points @ SV110 @ SV137 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV110 @ ( line_connecting @ SV110 @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(588,plain,
! [SV138: $i,SV111: $i] :
( ( ( ~ ( distinct_points @ SV111 @ SV138 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV138 @ ( line_connecting @ SV111 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(589,plain,
! [SV139: $i,SV112: $i] :
( ( ( ~ ( convergent_lines @ SV112 @ SV139 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV112 @ SV139 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(590,plain,
! [SV140: $i,SV113: $i] :
( ( ( ~ ( convergent_lines @ SV113 @ SV140 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV113 @ SV140 ) @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(591,plain,
! [SV141: $i,SV114: $i,SV159: $i] :
( ( ! [SY241: $i] :
( ~ ( distinct_lines @ SV159 @ SY241 )
| ~ ( distinct_points @ SV114 @ SV141 )
| ( apart_point_and_line @ SV141 @ SY241 )
| ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(592,plain,
! [SV142: $i,SV115: $i] :
( ( ( ~ ( apart_point_and_line @ SV115 @ SV142 ) )
= $true )
| ( ( ! [SY234: $i] :
( ( apart_point_and_line @ SY234 @ SV142 )
| ( distinct_points @ SV115 @ SY234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(593,plain,
! [SV143: $i,SV116: $i] :
( ( ( ~ ( apart_point_and_line @ SV116 @ SV143 ) )
= $true )
| ( ( ! [SY235: $i] :
( ( apart_point_and_line @ SV116 @ SY235 )
| ( distinct_lines @ SV143 @ SY235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(594,plain,
! [SV144: $i,SV117: $i] :
( ( ( ~ ( convergent_lines @ SV117 @ SV144 ) )
= $true )
| ( ( ! [SY236: $i] :
( ( convergent_lines @ SV117 @ SY236 )
| ( distinct_lines @ SV144 @ SY236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(595,plain,
! [SV145: $i,SV118: $i] :
( ( ( ~ ( distinct_lines @ SV118 @ SV145 ) )
= $true )
| ( ( convergent_lines @ SV118 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(596,plain,
! [SV119: $i,SV146: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV146 @ SV119 ) @ SV146 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(597,plain,
! [SV147: $i,SV120: $i] :
( ( apart_point_and_line @ SV120 @ ( parallel_through_point @ SV147 @ SV120 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(598,plain,
! [SV121: $i,SV160: $i,SV148: $i] :
( ( ~ ( distinct_lines @ SV148 @ SV160 )
| ( convergent_lines @ SV148 @ SV160 )
| ( apart_point_and_line @ SV121 @ SV148 )
| ( apart_point_and_line @ SV121 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(599,plain,
! [SV149: $i,SV122: $i] :
( ( ( convergent_lines @ SV122 @ SV149 )
= $true )
| ( ( unorthogonal_lines @ SV122 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(600,plain,
! [SV123: $i,SV150: $i] :
( ( unorthogonal_lines @ ( orthogonal_through_point @ SV150 @ SV123 ) @ SV150 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(601,plain,
! [SV151: $i,SV124: $i] :
( ( apart_point_and_line @ SV124 @ ( orthogonal_through_point @ SV151 @ SV124 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(602,plain,
! [SV125: $i,SV161: $i,SV152: $i] :
( ( ~ ( distinct_lines @ SV152 @ SV161 )
| ! [SY242: $i] :
( ( unorthogonal_lines @ SV161 @ SY242 )
| ( unorthogonal_lines @ SV152 @ SY242 )
| ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(603,plain,
! [SV153: $i,SV126: $i] :
( ( ( convergent_lines @ SV126 @ SV153 )
= $true )
| ( ( unorthogonal_lines @ SV126 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(604,plain,
! [SV162: $i,SV154: $i,SV127: $i] :
( ( ( unorthogonal_lines @ SV127 @ SV154 )
| ( unorthogonal_lines @ SV127 @ SV162 )
| ~ ( convergent_lines @ SV154 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(605,plain,
! [SV155: $i,SV128: $i] :
( ( ( ~ ( point @ SV128 )
| ~ ( point @ SV155 )
| ~ ( distinct_points @ SV128 @ SV155 ) )
= $true )
| ( ( line @ ( line_connecting @ SV128 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(606,plain,
! [SV156: $i,SV129: $i] :
( ( ( ~ ( line @ SV129 )
| ~ ( line @ SV156 )
| ~ ( convergent_lines @ SV129 @ SV156 ) )
= $true )
| ( ( point @ ( intersection_point @ SV129 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(607,plain,
! [SV157: $i,SV130: $i] :
( ( ( ~ ( line @ SV130 )
| ~ ( point @ SV157 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV130 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(608,plain,
! [SV158: $i,SV131: $i] :
( ( ( ~ ( line @ SV131 )
| ~ ( point @ SV158 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV131 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(614,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(615,plain,
! [SV132: $i] :
( ( ~ ~ ( ~ ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) )
| ~ ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(616,plain,
! [SV132: $i] :
( ( ~ ~ ( ~ ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) )
| ~ ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(621,plain,
! [SV133: $i] :
( ( ~ ~ ( ~ ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) )
| ~ ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(622,plain,
! [SV133: $i] :
( ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) )
| ~ ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(623,plain,
! [SV134: $i,SV107: $i] :
( ( ( distinct_points @ SV107 @ SV134 )
= $false )
| ( ( ! [SY229: $i] :
( ( distinct_points @ SV107 @ SY229 )
| ( distinct_points @ SV134 @ SY229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(624,plain,
! [SV135: $i,SV108: $i] :
( ( ( distinct_lines @ SV108 @ SV135 )
= $false )
| ( ( ! [SY230: $i] :
( ( distinct_lines @ SV108 @ SY230 )
| ( distinct_lines @ SV135 @ SY230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(625,plain,
! [SV136: $i,SV109: $i] :
( ( ( convergent_lines @ SV109 @ SV136 )
= $false )
| ( ( ! [SY231: $i] :
( ( convergent_lines @ SV109 @ SY231 )
| ( convergent_lines @ SV136 @ SY231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(626,plain,
! [SV137: $i,SV110: $i] :
( ( ( distinct_points @ SV110 @ SV137 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV110 @ ( line_connecting @ SV110 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(627,plain,
! [SV138: $i,SV111: $i] :
( ( ( distinct_points @ SV111 @ SV138 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV138 @ ( line_connecting @ SV111 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(628,plain,
! [SV139: $i,SV112: $i] :
( ( ( convergent_lines @ SV112 @ SV139 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV112 @ SV139 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(629,plain,
! [SV140: $i,SV113: $i] :
( ( ( convergent_lines @ SV113 @ SV140 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV113 @ SV140 ) @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(630,plain,
! [SV141: $i,SV114: $i,SV163: $i,SV159: $i] :
( ( ~ ( distinct_lines @ SV159 @ SV163 )
| ~ ( distinct_points @ SV114 @ SV141 )
| ( apart_point_and_line @ SV141 @ SV163 )
| ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(631,plain,
! [SV142: $i,SV115: $i] :
( ( ( apart_point_and_line @ SV115 @ SV142 )
= $false )
| ( ( ! [SY234: $i] :
( ( apart_point_and_line @ SY234 @ SV142 )
| ( distinct_points @ SV115 @ SY234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(632,plain,
! [SV143: $i,SV116: $i] :
( ( ( apart_point_and_line @ SV116 @ SV143 )
= $false )
| ( ( ! [SY235: $i] :
( ( apart_point_and_line @ SV116 @ SY235 )
| ( distinct_lines @ SV143 @ SY235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(633,plain,
! [SV144: $i,SV117: $i] :
( ( ( convergent_lines @ SV117 @ SV144 )
= $false )
| ( ( ! [SY236: $i] :
( ( convergent_lines @ SV117 @ SY236 )
| ( distinct_lines @ SV144 @ SY236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(634,plain,
! [SV145: $i,SV118: $i] :
( ( ( distinct_lines @ SV118 @ SV145 )
= $false )
| ( ( convergent_lines @ SV118 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(635,plain,
! [SV121: $i,SV160: $i,SV148: $i] :
( ( ( ~ ( distinct_lines @ SV148 @ SV160 ) )
= $true )
| ( ( ( convergent_lines @ SV148 @ SV160 )
| ( apart_point_and_line @ SV121 @ SV148 )
| ( apart_point_and_line @ SV121 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(636,plain,
! [SV125: $i,SV161: $i,SV152: $i] :
( ( ( ~ ( distinct_lines @ SV152 @ SV161 ) )
= $true )
| ( ( ! [SY242: $i] :
( ( unorthogonal_lines @ SV161 @ SY242 )
| ( unorthogonal_lines @ SV152 @ SY242 )
| ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(637,plain,
! [SV162: $i,SV154: $i,SV127: $i] :
( ( ( ( unorthogonal_lines @ SV127 @ SV154 )
| ( unorthogonal_lines @ SV127 @ SV162 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV154 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(638,plain,
! [SV155: $i,SV128: $i] :
( ( ( ~ ( point @ SV128 )
| ~ ( point @ SV155 ) )
= $true )
| ( ( ~ ( distinct_points @ SV128 @ SV155 ) )
= $true )
| ( ( line @ ( line_connecting @ SV128 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(639,plain,
! [SV156: $i,SV129: $i] :
( ( ( ~ ( line @ SV129 )
| ~ ( line @ SV156 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV129 @ SV156 ) )
= $true )
| ( ( point @ ( intersection_point @ SV129 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(640,plain,
! [SV157: $i,SV130: $i] :
( ( ( ~ ( line @ SV130 ) )
= $true )
| ( ( ~ ( point @ SV157 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV130 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(641,plain,
! [SV158: $i,SV131: $i] :
( ( ( ~ ( line @ SV131 ) )
= $true )
| ( ( ~ ( point @ SV158 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV131 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(642,plain,
! [SV164: $i] :
( ( ! [SY243: $i] :
( ~ ( incident_point_and_line @ SV164 @ SY243 )
| ~ ( apart_point_and_line @ SV164 @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(643,plain,
! [SV165: $i] :
( ( ! [SY244: $i] :
( ( apart_point_and_line @ SV165 @ SY244 )
| ( incident_point_and_line @ SV165 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(644,plain,
! [SV166: $i] :
( ( ! [SY245: $i] :
( ~ ( parallel_lines @ SV166 @ SY245 )
| ~ ( convergent_lines @ SV166 @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(645,plain,
! [SV167: $i] :
( ( ! [SY246: $i] :
( ( convergent_lines @ SV167 @ SY246 )
| ( parallel_lines @ SV167 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(646,plain,
! [SV168: $i] :
( ( ! [SY247: $i] :
( ~ ( orthogonal_lines @ SV168 @ SY247 )
| ~ ( unorthogonal_lines @ SV168 @ SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(647,plain,
! [SV169: $i] :
( ( ! [SY248: $i] :
( ( unorthogonal_lines @ SV169 @ SY248 )
| ( orthogonal_lines @ SV169 @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(648,plain,
! [SV132: $i] :
( ( ~ ( ~ ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) )
| ~ ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(649,plain,
! [SV132: $i] :
( ( ~ ( ~ ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) )
| ~ ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(650,plain,
! [SV170: $i] :
( ( ! [SY249: $i] :
( ~ ( equal_points @ SV170 @ SY249 )
| ~ ( distinct_points @ SV170 @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(651,plain,
! [SV171: $i] :
( ( ! [SY250: $i] :
( ( distinct_points @ SV171 @ SY250 )
| ( equal_points @ SV171 @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(652,plain,
! [SV172: $i] :
( ( ! [SY251: $i] :
( ~ ( equal_lines @ SV172 @ SY251 )
| ~ ( distinct_lines @ SV172 @ SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(653,plain,
! [SV173: $i] :
( ( ! [SY252: $i] :
( ( distinct_lines @ SV173 @ SY252 )
| ( equal_lines @ SV173 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(654,plain,
! [SV133: $i] :
( ( ~ ( ~ ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) )
| ~ ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(655,plain,
! [SV133: $i] :
( ( ~ ( ~ ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) )
| ~ ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(656,plain,
! [SV134: $i,SV174: $i,SV107: $i] :
( ( ( ( distinct_points @ SV107 @ SV174 )
| ( distinct_points @ SV134 @ SV174 ) )
= $true )
| ( ( distinct_points @ SV107 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(657,plain,
! [SV135: $i,SV175: $i,SV108: $i] :
( ( ( ( distinct_lines @ SV108 @ SV175 )
| ( distinct_lines @ SV135 @ SV175 ) )
= $true )
| ( ( distinct_lines @ SV108 @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(658,plain,
! [SV136: $i,SV176: $i,SV109: $i] :
( ( ( ( convergent_lines @ SV109 @ SV176 )
| ( convergent_lines @ SV136 @ SV176 ) )
= $true )
| ( ( convergent_lines @ SV109 @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(659,plain,
! [SV137: $i,SV110: $i] :
( ( ( apart_point_and_line @ SV110 @ ( line_connecting @ SV110 @ SV137 ) )
= $false )
| ( ( distinct_points @ SV110 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(660,plain,
! [SV111: $i,SV138: $i] :
( ( ( apart_point_and_line @ SV138 @ ( line_connecting @ SV111 @ SV138 ) )
= $false )
| ( ( distinct_points @ SV111 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(661,plain,
! [SV139: $i,SV112: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV112 @ SV139 ) @ SV112 )
= $false )
| ( ( convergent_lines @ SV112 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(662,plain,
! [SV140: $i,SV113: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV113 @ SV140 ) @ SV140 )
= $false )
| ( ( convergent_lines @ SV113 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(663,plain,
! [SV141: $i,SV114: $i,SV163: $i,SV159: $i] :
( ( ( ~ ( distinct_lines @ SV159 @ SV163 )
| ~ ( distinct_points @ SV114 @ SV141 ) )
= $true )
| ( ( ( apart_point_and_line @ SV141 @ SV163 )
| ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(664,plain,
! [SV115: $i,SV142: $i,SV177: $i] :
( ( ( ( apart_point_and_line @ SV177 @ SV142 )
| ( distinct_points @ SV115 @ SV177 ) )
= $true )
| ( ( apart_point_and_line @ SV115 @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(665,plain,
! [SV143: $i,SV178: $i,SV116: $i] :
( ( ( ( apart_point_and_line @ SV116 @ SV178 )
| ( distinct_lines @ SV143 @ SV178 ) )
= $true )
| ( ( apart_point_and_line @ SV116 @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(666,plain,
! [SV144: $i,SV179: $i,SV117: $i] :
( ( ( ( convergent_lines @ SV117 @ SV179 )
| ( distinct_lines @ SV144 @ SV179 ) )
= $true )
| ( ( convergent_lines @ SV117 @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(667,plain,
! [SV121: $i,SV160: $i,SV148: $i] :
( ( ( distinct_lines @ SV148 @ SV160 )
= $false )
| ( ( ( convergent_lines @ SV148 @ SV160 )
| ( apart_point_and_line @ SV121 @ SV148 )
| ( apart_point_and_line @ SV121 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(668,plain,
! [SV125: $i,SV161: $i,SV152: $i] :
( ( ( distinct_lines @ SV152 @ SV161 )
= $false )
| ( ( ! [SY242: $i] :
( ( unorthogonal_lines @ SV161 @ SY242 )
| ( unorthogonal_lines @ SV152 @ SY242 )
| ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SV161 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(669,plain,
! [SV162: $i,SV154: $i,SV127: $i] :
( ( ( unorthogonal_lines @ SV127 @ SV154 )
= $true )
| ( ( unorthogonal_lines @ SV127 @ SV162 )
= $true )
| ( ( ~ ( convergent_lines @ SV154 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(670,plain,
! [SV155: $i,SV128: $i] :
( ( ( ~ ( point @ SV128 ) )
= $true )
| ( ( ~ ( point @ SV155 ) )
= $true )
| ( ( ~ ( distinct_points @ SV128 @ SV155 ) )
= $true )
| ( ( line @ ( line_connecting @ SV128 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(671,plain,
! [SV156: $i,SV129: $i] :
( ( ( ~ ( line @ SV129 ) )
= $true )
| ( ( ~ ( line @ SV156 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV129 @ SV156 ) )
= $true )
| ( ( point @ ( intersection_point @ SV129 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(672,plain,
! [SV157: $i,SV130: $i] :
( ( ( line @ SV130 )
= $false )
| ( ( ~ ( point @ SV157 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV130 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(673,plain,
! [SV158: $i,SV131: $i] :
( ( ( line @ SV131 )
= $false )
| ( ( ~ ( point @ SV158 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV131 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(674,plain,
! [SV180: $i,SV164: $i] :
( ( ~ ( incident_point_and_line @ SV164 @ SV180 )
| ~ ( apart_point_and_line @ SV164 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(675,plain,
! [SV181: $i,SV165: $i] :
( ( ( apart_point_and_line @ SV165 @ SV181 )
| ( incident_point_and_line @ SV165 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(676,plain,
! [SV182: $i,SV166: $i] :
( ( ~ ( parallel_lines @ SV166 @ SV182 )
| ~ ( convergent_lines @ SV166 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(677,plain,
! [SV183: $i,SV167: $i] :
( ( ( convergent_lines @ SV167 @ SV183 )
| ( parallel_lines @ SV167 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(678,plain,
! [SV184: $i,SV168: $i] :
( ( ~ ( orthogonal_lines @ SV168 @ SV184 )
| ~ ( unorthogonal_lines @ SV168 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(679,plain,
! [SV185: $i,SV169: $i] :
( ( ( unorthogonal_lines @ SV169 @ SV185 )
| ( orthogonal_lines @ SV169 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(680,plain,
! [SV132: $i] :
( ( ~ ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) )
| ~ ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(681,plain,
! [SV132: $i] :
( ( ~ ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) )
| ~ ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(682,plain,
! [SV186: $i,SV170: $i] :
( ( ~ ( equal_points @ SV170 @ SV186 )
| ~ ( distinct_points @ SV170 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(683,plain,
! [SV187: $i,SV171: $i] :
( ( ( distinct_points @ SV171 @ SV187 )
| ( equal_points @ SV171 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(684,plain,
! [SV188: $i,SV172: $i] :
( ( ~ ( equal_lines @ SV172 @ SV188 )
| ~ ( distinct_lines @ SV172 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(685,plain,
! [SV189: $i,SV173: $i] :
( ( ( distinct_lines @ SV173 @ SV189 )
| ( equal_lines @ SV173 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(686,plain,
! [SV133: $i] :
( ( ~ ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) )
| ~ ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(687,plain,
! [SV133: $i] :
( ( ~ ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) )
| ~ ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(688,plain,
! [SV134: $i,SV174: $i,SV107: $i] :
( ( ( distinct_points @ SV107 @ SV174 )
= $true )
| ( ( distinct_points @ SV134 @ SV174 )
= $true )
| ( ( distinct_points @ SV107 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(689,plain,
! [SV135: $i,SV175: $i,SV108: $i] :
( ( ( distinct_lines @ SV108 @ SV175 )
= $true )
| ( ( distinct_lines @ SV135 @ SV175 )
= $true )
| ( ( distinct_lines @ SV108 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(690,plain,
! [SV136: $i,SV176: $i,SV109: $i] :
( ( ( convergent_lines @ SV109 @ SV176 )
= $true )
| ( ( convergent_lines @ SV136 @ SV176 )
= $true )
| ( ( convergent_lines @ SV109 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(691,plain,
! [SV141: $i,SV114: $i,SV163: $i,SV159: $i] :
( ( ( ~ ( distinct_lines @ SV159 @ SV163 ) )
= $true )
| ( ( ~ ( distinct_points @ SV114 @ SV141 ) )
= $true )
| ( ( ( apart_point_and_line @ SV141 @ SV163 )
| ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(692,plain,
! [SV115: $i,SV142: $i,SV177: $i] :
( ( ( apart_point_and_line @ SV177 @ SV142 )
= $true )
| ( ( distinct_points @ SV115 @ SV177 )
= $true )
| ( ( apart_point_and_line @ SV115 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(693,plain,
! [SV143: $i,SV178: $i,SV116: $i] :
( ( ( apart_point_and_line @ SV116 @ SV178 )
= $true )
| ( ( distinct_lines @ SV143 @ SV178 )
= $true )
| ( ( apart_point_and_line @ SV116 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(694,plain,
! [SV144: $i,SV179: $i,SV117: $i] :
( ( ( convergent_lines @ SV117 @ SV179 )
= $true )
| ( ( distinct_lines @ SV144 @ SV179 )
= $true )
| ( ( convergent_lines @ SV117 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(695,plain,
! [SV121: $i,SV160: $i,SV148: $i] :
( ( ( convergent_lines @ SV148 @ SV160 )
= $true )
| ( ( ( apart_point_and_line @ SV121 @ SV148 )
| ( apart_point_and_line @ SV121 @ SV160 ) )
= $true )
| ( ( distinct_lines @ SV148 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(696,plain,
! [SV125: $i,SV152: $i,SV190: $i,SV161: $i] :
( ( ( ( unorthogonal_lines @ SV161 @ SV190 )
| ( unorthogonal_lines @ SV152 @ SV190 )
| ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SV161 ) )
= $true )
| ( ( distinct_lines @ SV152 @ SV161 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(697,plain,
! [SV127: $i,SV162: $i,SV154: $i] :
( ( ( convergent_lines @ SV154 @ SV162 )
= $false )
| ( ( unorthogonal_lines @ SV127 @ SV162 )
= $true )
| ( ( unorthogonal_lines @ SV127 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(698,plain,
! [SV155: $i,SV128: $i] :
( ( ( point @ SV128 )
= $false )
| ( ( ~ ( point @ SV155 ) )
= $true )
| ( ( ~ ( distinct_points @ SV128 @ SV155 ) )
= $true )
| ( ( line @ ( line_connecting @ SV128 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(699,plain,
! [SV156: $i,SV129: $i] :
( ( ( line @ SV129 )
= $false )
| ( ( ~ ( line @ SV156 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV129 @ SV156 ) )
= $true )
| ( ( point @ ( intersection_point @ SV129 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(700,plain,
! [SV130: $i,SV157: $i] :
( ( ( point @ SV157 )
= $false )
| ( ( line @ SV130 )
= $false )
| ( ( line @ ( parallel_through_point @ SV130 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(701,plain,
! [SV131: $i,SV158: $i] :
( ( ( point @ SV158 )
= $false )
| ( ( line @ SV131 )
= $false )
| ( ( line @ ( orthogonal_through_point @ SV131 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(702,plain,
! [SV180: $i,SV164: $i] :
( ( ( ~ ( incident_point_and_line @ SV164 @ SV180 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV164 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(703,plain,
! [SV181: $i,SV165: $i] :
( ( ( apart_point_and_line @ SV165 @ SV181 )
= $true )
| ( ( incident_point_and_line @ SV165 @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(704,plain,
! [SV182: $i,SV166: $i] :
( ( ( ~ ( parallel_lines @ SV166 @ SV182 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV166 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(705,plain,
! [SV183: $i,SV167: $i] :
( ( ( convergent_lines @ SV167 @ SV183 )
= $true )
| ( ( parallel_lines @ SV167 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(706,plain,
! [SV184: $i,SV168: $i] :
( ( ( ~ ( orthogonal_lines @ SV168 @ SV184 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV168 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(707,plain,
! [SV185: $i,SV169: $i] :
( ( ( unorthogonal_lines @ SV169 @ SV185 )
= $true )
| ( ( orthogonal_lines @ SV169 @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(708,plain,
! [SV132: $i] :
( ( ~ ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(709,plain,
! [SV132: $i] :
( ( ~ ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(710,plain,
! [SV132: $i] :
( ( ~ ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(711,plain,
! [SV132: $i] :
( ( ~ ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(712,plain,
! [SV186: $i,SV170: $i] :
( ( ( ~ ( equal_points @ SV170 @ SV186 ) )
= $true )
| ( ( ~ ( distinct_points @ SV170 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(713,plain,
! [SV187: $i,SV171: $i] :
( ( ( distinct_points @ SV171 @ SV187 )
= $true )
| ( ( equal_points @ SV171 @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(714,plain,
! [SV188: $i,SV172: $i] :
( ( ( ~ ( equal_lines @ SV172 @ SV188 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV172 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(715,plain,
! [SV189: $i,SV173: $i] :
( ( ( distinct_lines @ SV173 @ SV189 )
= $true )
| ( ( equal_lines @ SV173 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(716,plain,
! [SV133: $i] :
( ( ~ ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(717,plain,
! [SV133: $i] :
( ( ~ ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(718,plain,
! [SV133: $i] :
( ( ~ ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(719,plain,
! [SV133: $i] :
( ( ~ ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(720,plain,
! [SV141: $i,SV114: $i,SV163: $i,SV159: $i] :
( ( ( distinct_lines @ SV159 @ SV163 )
= $false )
| ( ( ~ ( distinct_points @ SV114 @ SV141 ) )
= $true )
| ( ( ( apart_point_and_line @ SV141 @ SV163 )
| ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(721,plain,
! [SV160: $i,SV148: $i,SV121: $i] :
( ( ( apart_point_and_line @ SV121 @ SV148 )
= $true )
| ( ( apart_point_and_line @ SV121 @ SV160 )
= $true )
| ( ( convergent_lines @ SV148 @ SV160 )
= $true )
| ( ( distinct_lines @ SV148 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(722,plain,
! [SV125: $i,SV152: $i,SV190: $i,SV161: $i] :
( ( ( unorthogonal_lines @ SV161 @ SV190 )
= $true )
| ( ( ( unorthogonal_lines @ SV152 @ SV190 )
| ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SV161 ) )
= $true )
| ( ( distinct_lines @ SV152 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(723,plain,
! [SV128: $i,SV155: $i] :
( ( ( point @ SV155 )
= $false )
| ( ( point @ SV128 )
= $false )
| ( ( ~ ( distinct_points @ SV128 @ SV155 ) )
= $true )
| ( ( line @ ( line_connecting @ SV128 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(724,plain,
! [SV129: $i,SV156: $i] :
( ( ( line @ SV156 )
= $false )
| ( ( line @ SV129 )
= $false )
| ( ( ~ ( convergent_lines @ SV129 @ SV156 ) )
= $true )
| ( ( point @ ( intersection_point @ SV129 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(725,plain,
! [SV180: $i,SV164: $i] :
( ( ( incident_point_and_line @ SV164 @ SV180 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV164 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(726,plain,
! [SV182: $i,SV166: $i] :
( ( ( parallel_lines @ SV166 @ SV182 )
= $false )
| ( ( ~ ( convergent_lines @ SV166 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(727,plain,
! [SV184: $i,SV168: $i] :
( ( ( orthogonal_lines @ SV168 @ SV184 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV168 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(728,plain,
! [SV132: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ( convergent_lines @ SV132 @ SY213 )
| ( convergent_lines @ SV132 @ SY214 )
| ~ ( convergent_lines @ SY213 @ SY214 )
| ~ ( unorthogonal_lines @ SY213 @ SY214 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(729,plain,
! [SV132: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ( convergent_lines @ SV132 @ SY215 )
| ( unorthogonal_lines @ SV132 @ SY216 )
| ~ ( convergent_lines @ SY215 @ SY216 )
| ~ ( unorthogonal_lines @ SY215 @ SY216 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(730,plain,
! [SV132: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ( unorthogonal_lines @ SV132 @ SY217 )
| ( convergent_lines @ SV132 @ SY218 )
| ~ ( convergent_lines @ SY217 @ SY218 )
| ~ ( unorthogonal_lines @ SY217 @ SY218 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(731,plain,
! [SV132: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ( unorthogonal_lines @ SV132 @ SY219 )
| ( unorthogonal_lines @ SV132 @ SY220 )
| ~ ( convergent_lines @ SY219 @ SY220 )
| ~ ( unorthogonal_lines @ SY219 @ SY220 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(732,plain,
! [SV186: $i,SV170: $i] :
( ( ( equal_points @ SV170 @ SV186 )
= $false )
| ( ( ~ ( distinct_points @ SV170 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(733,plain,
! [SV188: $i,SV172: $i] :
( ( ( equal_lines @ SV172 @ SV188 )
= $false )
| ( ( ~ ( distinct_lines @ SV172 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(734,plain,
! [SV133: $i] :
( ( ! [SY221: $i] :
( ~ ( convergent_lines @ SV133 @ SY221 )
| ~ ( unorthogonal_lines @ SV133 @ SY221 )
| ! [SY222: $i] :
( ( convergent_lines @ SV133 @ SY222 )
| ( convergent_lines @ SY221 @ SY222 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(735,plain,
! [SV133: $i] :
( ( ! [SY223: $i] :
( ~ ( convergent_lines @ SV133 @ SY223 )
| ~ ( unorthogonal_lines @ SV133 @ SY223 )
| ! [SY224: $i] :
( ( convergent_lines @ SV133 @ SY224 )
| ( unorthogonal_lines @ SY223 @ SY224 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(736,plain,
! [SV133: $i] :
( ( ! [SY225: $i] :
( ~ ( convergent_lines @ SV133 @ SY225 )
| ~ ( unorthogonal_lines @ SV133 @ SY225 )
| ! [SY226: $i] :
( ( unorthogonal_lines @ SV133 @ SY226 )
| ( convergent_lines @ SY225 @ SY226 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(737,plain,
! [SV133: $i] :
( ( ! [SY227: $i] :
( ~ ( convergent_lines @ SV133 @ SY227 )
| ~ ( unorthogonal_lines @ SV133 @ SY227 )
| ! [SY228: $i] :
( ( unorthogonal_lines @ SV133 @ SY228 )
| ( unorthogonal_lines @ SY227 @ SY228 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(738,plain,
! [SV163: $i,SV159: $i,SV141: $i,SV114: $i] :
( ( ( distinct_points @ SV114 @ SV141 )
= $false )
| ( ( distinct_lines @ SV159 @ SV163 )
= $false )
| ( ( ( apart_point_and_line @ SV141 @ SV163 )
| ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(739,plain,
! [SV161: $i,SV125: $i,SV190: $i,SV152: $i] :
( ( ( unorthogonal_lines @ SV152 @ SV190 )
= $true )
| ( ( ( apart_point_and_line @ SV125 @ SV152 )
| ( apart_point_and_line @ SV125 @ SV161 ) )
= $true )
| ( ( unorthogonal_lines @ SV161 @ SV190 )
= $true )
| ( ( distinct_lines @ SV152 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(740,plain,
! [SV155: $i,SV128: $i] :
( ( ( distinct_points @ SV128 @ SV155 )
= $false )
| ( ( point @ SV128 )
= $false )
| ( ( point @ SV155 )
= $false )
| ( ( line @ ( line_connecting @ SV128 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(741,plain,
! [SV156: $i,SV129: $i] :
( ( ( convergent_lines @ SV129 @ SV156 )
= $false )
| ( ( line @ SV129 )
= $false )
| ( ( line @ SV156 )
= $false )
| ( ( point @ ( intersection_point @ SV129 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(742,plain,
! [SV180: $i,SV164: $i] :
( ( ( apart_point_and_line @ SV164 @ SV180 )
= $false )
| ( ( incident_point_and_line @ SV164 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(743,plain,
! [SV182: $i,SV166: $i] :
( ( ( convergent_lines @ SV166 @ SV182 )
= $false )
| ( ( parallel_lines @ SV166 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(744,plain,
! [SV184: $i,SV168: $i] :
( ( ( unorthogonal_lines @ SV168 @ SV184 )
= $false )
| ( ( orthogonal_lines @ SV168 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(745,plain,
! [SV191: $i,SV132: $i] :
( ( ! [SY253: $i] :
( ( convergent_lines @ SV132 @ SV191 )
| ( convergent_lines @ SV132 @ SY253 )
| ~ ( convergent_lines @ SV191 @ SY253 )
| ~ ( unorthogonal_lines @ SV191 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(746,plain,
! [SV192: $i,SV132: $i] :
( ( ! [SY254: $i] :
( ( convergent_lines @ SV132 @ SV192 )
| ( unorthogonal_lines @ SV132 @ SY254 )
| ~ ( convergent_lines @ SV192 @ SY254 )
| ~ ( unorthogonal_lines @ SV192 @ SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(747,plain,
! [SV193: $i,SV132: $i] :
( ( ! [SY255: $i] :
( ( unorthogonal_lines @ SV132 @ SV193 )
| ( convergent_lines @ SV132 @ SY255 )
| ~ ( convergent_lines @ SV193 @ SY255 )
| ~ ( unorthogonal_lines @ SV193 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(748,plain,
! [SV194: $i,SV132: $i] :
( ( ! [SY256: $i] :
( ( unorthogonal_lines @ SV132 @ SV194 )
| ( unorthogonal_lines @ SV132 @ SY256 )
| ~ ( convergent_lines @ SV194 @ SY256 )
| ~ ( unorthogonal_lines @ SV194 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(749,plain,
! [SV186: $i,SV170: $i] :
( ( ( distinct_points @ SV170 @ SV186 )
= $false )
| ( ( equal_points @ SV170 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(750,plain,
! [SV188: $i,SV172: $i] :
( ( ( distinct_lines @ SV172 @ SV188 )
= $false )
| ( ( equal_lines @ SV172 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(751,plain,
! [SV195: $i,SV133: $i] :
( ( ~ ( convergent_lines @ SV133 @ SV195 )
| ~ ( unorthogonal_lines @ SV133 @ SV195 )
| ! [SY257: $i] :
( ( convergent_lines @ SV133 @ SY257 )
| ( convergent_lines @ SV195 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(752,plain,
! [SV196: $i,SV133: $i] :
( ( ~ ( convergent_lines @ SV133 @ SV196 )
| ~ ( unorthogonal_lines @ SV133 @ SV196 )
| ! [SY258: $i] :
( ( convergent_lines @ SV133 @ SY258 )
| ( unorthogonal_lines @ SV196 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(753,plain,
! [SV197: $i,SV133: $i] :
( ( ~ ( convergent_lines @ SV133 @ SV197 )
| ~ ( unorthogonal_lines @ SV133 @ SV197 )
| ! [SY259: $i] :
( ( unorthogonal_lines @ SV133 @ SY259 )
| ( convergent_lines @ SV197 @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(754,plain,
! [SV198: $i,SV133: $i] :
( ( ~ ( convergent_lines @ SV133 @ SV198 )
| ~ ( unorthogonal_lines @ SV133 @ SV198 )
| ! [SY260: $i] :
( ( unorthogonal_lines @ SV133 @ SY260 )
| ( unorthogonal_lines @ SV198 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(755,plain,
! [SV114: $i,SV159: $i,SV163: $i,SV141: $i] :
( ( ( apart_point_and_line @ SV141 @ SV163 )
= $true )
| ( ( ( apart_point_and_line @ SV141 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true )
| ( ( distinct_lines @ SV159 @ SV163 )
= $false )
| ( ( distinct_points @ SV114 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(756,plain,
! [SV190: $i,SV161: $i,SV152: $i,SV125: $i] :
( ( ( apart_point_and_line @ SV125 @ SV152 )
= $true )
| ( ( apart_point_and_line @ SV125 @ SV161 )
= $true )
| ( ( unorthogonal_lines @ SV152 @ SV190 )
= $true )
| ( ( unorthogonal_lines @ SV161 @ SV190 )
= $true )
| ( ( distinct_lines @ SV152 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(757,plain,
! [SV199: $i,SV191: $i,SV132: $i] :
( ( ( convergent_lines @ SV132 @ SV191 )
| ( convergent_lines @ SV132 @ SV199 )
| ~ ( convergent_lines @ SV191 @ SV199 )
| ~ ( unorthogonal_lines @ SV191 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(758,plain,
! [SV200: $i,SV192: $i,SV132: $i] :
( ( ( convergent_lines @ SV132 @ SV192 )
| ( unorthogonal_lines @ SV132 @ SV200 )
| ~ ( convergent_lines @ SV192 @ SV200 )
| ~ ( unorthogonal_lines @ SV192 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(759,plain,
! [SV201: $i,SV193: $i,SV132: $i] :
( ( ( unorthogonal_lines @ SV132 @ SV193 )
| ( convergent_lines @ SV132 @ SV201 )
| ~ ( convergent_lines @ SV193 @ SV201 )
| ~ ( unorthogonal_lines @ SV193 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(760,plain,
! [SV202: $i,SV194: $i,SV132: $i] :
( ( ( unorthogonal_lines @ SV132 @ SV194 )
| ( unorthogonal_lines @ SV132 @ SV202 )
| ~ ( convergent_lines @ SV194 @ SV202 )
| ~ ( unorthogonal_lines @ SV194 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(761,plain,
! [SV195: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV195 )
| ~ ( unorthogonal_lines @ SV133 @ SV195 ) )
= $true )
| ( ( ! [SY257: $i] :
( ( convergent_lines @ SV133 @ SY257 )
| ( convergent_lines @ SV195 @ SY257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(762,plain,
! [SV196: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV196 )
| ~ ( unorthogonal_lines @ SV133 @ SV196 ) )
= $true )
| ( ( ! [SY258: $i] :
( ( convergent_lines @ SV133 @ SY258 )
| ( unorthogonal_lines @ SV196 @ SY258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(763,plain,
! [SV197: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV197 )
| ~ ( unorthogonal_lines @ SV133 @ SV197 ) )
= $true )
| ( ( ! [SY259: $i] :
( ( unorthogonal_lines @ SV133 @ SY259 )
| ( convergent_lines @ SV197 @ SY259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(764,plain,
! [SV198: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV198 )
| ~ ( unorthogonal_lines @ SV133 @ SV198 ) )
= $true )
| ( ( ! [SY260: $i] :
( ( unorthogonal_lines @ SV133 @ SY260 )
| ( unorthogonal_lines @ SV198 @ SY260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(765,plain,
! [SV163: $i,SV114: $i,SV159: $i,SV141: $i] :
( ( ( apart_point_and_line @ SV141 @ SV159 )
= $true )
| ( ( ( apart_point_and_line @ SV114 @ SV159 )
| ( apart_point_and_line @ SV114 @ SV163 ) )
= $true )
| ( ( apart_point_and_line @ SV141 @ SV163 )
= $true )
| ( ( distinct_lines @ SV159 @ SV163 )
= $false )
| ( ( distinct_points @ SV114 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(766,plain,
! [SV199: $i,SV191: $i,SV132: $i] :
( ( ( ( convergent_lines @ SV132 @ SV191 )
| ( convergent_lines @ SV132 @ SV199 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV191 @ SV199 )
| ~ ( unorthogonal_lines @ SV191 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(767,plain,
! [SV200: $i,SV192: $i,SV132: $i] :
( ( ( ( convergent_lines @ SV132 @ SV192 )
| ( unorthogonal_lines @ SV132 @ SV200 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV192 @ SV200 )
| ~ ( unorthogonal_lines @ SV192 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(768,plain,
! [SV201: $i,SV193: $i,SV132: $i] :
( ( ( ( unorthogonal_lines @ SV132 @ SV193 )
| ( convergent_lines @ SV132 @ SV201 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV193 @ SV201 )
| ~ ( unorthogonal_lines @ SV193 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(769,plain,
! [SV202: $i,SV194: $i,SV132: $i] :
( ( ( ( unorthogonal_lines @ SV132 @ SV194 )
| ( unorthogonal_lines @ SV132 @ SV202 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV194 @ SV202 )
| ~ ( unorthogonal_lines @ SV194 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(770,plain,
! [SV195: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV195 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV195 ) )
= $true )
| ( ( ! [SY257: $i] :
( ( convergent_lines @ SV133 @ SY257 )
| ( convergent_lines @ SV195 @ SY257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(771,plain,
! [SV196: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV196 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV196 ) )
= $true )
| ( ( ! [SY258: $i] :
( ( convergent_lines @ SV133 @ SY258 )
| ( unorthogonal_lines @ SV196 @ SY258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(772,plain,
! [SV197: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV197 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV197 ) )
= $true )
| ( ( ! [SY259: $i] :
( ( unorthogonal_lines @ SV133 @ SY259 )
| ( convergent_lines @ SV197 @ SY259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(773,plain,
! [SV198: $i,SV133: $i] :
( ( ( ~ ( convergent_lines @ SV133 @ SV198 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV198 ) )
= $true )
| ( ( ! [SY260: $i] :
( ( unorthogonal_lines @ SV133 @ SY260 )
| ( unorthogonal_lines @ SV198 @ SY260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(774,plain,
! [SV141: $i,SV163: $i,SV159: $i,SV114: $i] :
( ( ( apart_point_and_line @ SV114 @ SV159 )
= $true )
| ( ( apart_point_and_line @ SV114 @ SV163 )
= $true )
| ( ( apart_point_and_line @ SV141 @ SV159 )
= $true )
| ( ( apart_point_and_line @ SV141 @ SV163 )
= $true )
| ( ( distinct_lines @ SV159 @ SV163 )
= $false )
| ( ( distinct_points @ SV114 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(775,plain,
! [SV199: $i,SV191: $i,SV132: $i] :
( ( ( convergent_lines @ SV132 @ SV191 )
= $true )
| ( ( convergent_lines @ SV132 @ SV199 )
= $true )
| ( ( ~ ( convergent_lines @ SV191 @ SV199 )
| ~ ( unorthogonal_lines @ SV191 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(776,plain,
! [SV200: $i,SV192: $i,SV132: $i] :
( ( ( convergent_lines @ SV132 @ SV192 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV200 )
= $true )
| ( ( ~ ( convergent_lines @ SV192 @ SV200 )
| ~ ( unorthogonal_lines @ SV192 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(777,plain,
! [SV201: $i,SV193: $i,SV132: $i] :
( ( ( unorthogonal_lines @ SV132 @ SV193 )
= $true )
| ( ( convergent_lines @ SV132 @ SV201 )
= $true )
| ( ( ~ ( convergent_lines @ SV193 @ SV201 )
| ~ ( unorthogonal_lines @ SV193 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(778,plain,
! [SV202: $i,SV194: $i,SV132: $i] :
( ( ( unorthogonal_lines @ SV132 @ SV194 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV202 )
= $true )
| ( ( ~ ( convergent_lines @ SV194 @ SV202 )
| ~ ( unorthogonal_lines @ SV194 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(779,plain,
! [SV195: $i,SV133: $i] :
( ( ( convergent_lines @ SV133 @ SV195 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV195 ) )
= $true )
| ( ( ! [SY257: $i] :
( ( convergent_lines @ SV133 @ SY257 )
| ( convergent_lines @ SV195 @ SY257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(780,plain,
! [SV196: $i,SV133: $i] :
( ( ( convergent_lines @ SV133 @ SV196 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV196 ) )
= $true )
| ( ( ! [SY258: $i] :
( ( convergent_lines @ SV133 @ SY258 )
| ( unorthogonal_lines @ SV196 @ SY258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(781,plain,
! [SV197: $i,SV133: $i] :
( ( ( convergent_lines @ SV133 @ SV197 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV197 ) )
= $true )
| ( ( ! [SY259: $i] :
( ( unorthogonal_lines @ SV133 @ SY259 )
| ( convergent_lines @ SV197 @ SY259 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(782,plain,
! [SV198: $i,SV133: $i] :
( ( ( convergent_lines @ SV133 @ SV198 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV133 @ SV198 ) )
= $true )
| ( ( ! [SY260: $i] :
( ( unorthogonal_lines @ SV133 @ SY260 )
| ( unorthogonal_lines @ SV198 @ SY260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(783,plain,
! [SV132: $i,SV199: $i,SV191: $i] :
( ( ( ~ ( convergent_lines @ SV191 @ SV199 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV191 @ SV199 ) )
= $true )
| ( ( convergent_lines @ SV132 @ SV199 )
= $true )
| ( ( convergent_lines @ SV132 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(784,plain,
! [SV132: $i,SV200: $i,SV192: $i] :
( ( ( ~ ( convergent_lines @ SV192 @ SV200 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV192 @ SV200 ) )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV200 )
= $true )
| ( ( convergent_lines @ SV132 @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(785,plain,
! [SV132: $i,SV201: $i,SV193: $i] :
( ( ( ~ ( convergent_lines @ SV193 @ SV201 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV193 @ SV201 ) )
= $true )
| ( ( convergent_lines @ SV132 @ SV201 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(786,plain,
! [SV132: $i,SV202: $i,SV194: $i] :
( ( ( ~ ( convergent_lines @ SV194 @ SV202 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV194 @ SV202 ) )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV202 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(787,plain,
! [SV195: $i,SV133: $i] :
( ( ( unorthogonal_lines @ SV133 @ SV195 )
= $false )
| ( ( convergent_lines @ SV133 @ SV195 )
= $false )
| ( ( ! [SY257: $i] :
( ( convergent_lines @ SV133 @ SY257 )
| ( convergent_lines @ SV195 @ SY257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(788,plain,
! [SV196: $i,SV133: $i] :
( ( ( unorthogonal_lines @ SV133 @ SV196 )
= $false )
| ( ( convergent_lines @ SV133 @ SV196 )
= $false )
| ( ( ! [SY258: $i] :
( ( convergent_lines @ SV133 @ SY258 )
| ( unorthogonal_lines @ SV196 @ SY258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(789,plain,
! [SV197: $i,SV133: $i] :
( ( ( unorthogonal_lines @ SV133 @ SV197 )
= $false )
| ( ( convergent_lines @ SV133 @ SV197 )
= $false )
| ( ( ! [SY259: $i] :
( ( unorthogonal_lines @ SV133 @ SY259 )
| ( convergent_lines @ SV197 @ SY259 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(790,plain,
! [SV198: $i,SV133: $i] :
( ( ( unorthogonal_lines @ SV133 @ SV198 )
= $false )
| ( ( convergent_lines @ SV133 @ SV198 )
= $false )
| ( ( ! [SY260: $i] :
( ( unorthogonal_lines @ SV133 @ SY260 )
| ( unorthogonal_lines @ SV198 @ SY260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(791,plain,
! [SV132: $i,SV199: $i,SV191: $i] :
( ( ( convergent_lines @ SV191 @ SV199 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV191 @ SV199 ) )
= $true )
| ( ( convergent_lines @ SV132 @ SV199 )
= $true )
| ( ( convergent_lines @ SV132 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(792,plain,
! [SV132: $i,SV200: $i,SV192: $i] :
( ( ( convergent_lines @ SV192 @ SV200 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV192 @ SV200 ) )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV200 )
= $true )
| ( ( convergent_lines @ SV132 @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(793,plain,
! [SV132: $i,SV201: $i,SV193: $i] :
( ( ( convergent_lines @ SV193 @ SV201 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV193 @ SV201 ) )
= $true )
| ( ( convergent_lines @ SV132 @ SV201 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(794,plain,
! [SV132: $i,SV202: $i,SV194: $i] :
( ( ( convergent_lines @ SV194 @ SV202 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV194 @ SV202 ) )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV202 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(795,plain,
! [SV195: $i,SV203: $i,SV133: $i] :
( ( ( ( convergent_lines @ SV133 @ SV203 )
| ( convergent_lines @ SV195 @ SV203 ) )
= $true )
| ( ( convergent_lines @ SV133 @ SV195 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(796,plain,
! [SV196: $i,SV204: $i,SV133: $i] :
( ( ( ( convergent_lines @ SV133 @ SV204 )
| ( unorthogonal_lines @ SV196 @ SV204 ) )
= $true )
| ( ( convergent_lines @ SV133 @ SV196 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV196 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(797,plain,
! [SV197: $i,SV205: $i,SV133: $i] :
( ( ( ( unorthogonal_lines @ SV133 @ SV205 )
| ( convergent_lines @ SV197 @ SV205 ) )
= $true )
| ( ( convergent_lines @ SV133 @ SV197 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(798,plain,
! [SV198: $i,SV206: $i,SV133: $i] :
( ( ( ( unorthogonal_lines @ SV133 @ SV206 )
| ( unorthogonal_lines @ SV198 @ SV206 ) )
= $true )
| ( ( convergent_lines @ SV133 @ SV198 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(799,plain,
! [SV132: $i,SV199: $i,SV191: $i] :
( ( ( unorthogonal_lines @ SV191 @ SV199 )
= $false )
| ( ( convergent_lines @ SV191 @ SV199 )
= $false )
| ( ( convergent_lines @ SV132 @ SV199 )
= $true )
| ( ( convergent_lines @ SV132 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(800,plain,
! [SV132: $i,SV200: $i,SV192: $i] :
( ( ( unorthogonal_lines @ SV192 @ SV200 )
= $false )
| ( ( convergent_lines @ SV192 @ SV200 )
= $false )
| ( ( unorthogonal_lines @ SV132 @ SV200 )
= $true )
| ( ( convergent_lines @ SV132 @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(801,plain,
! [SV132: $i,SV201: $i,SV193: $i] :
( ( ( unorthogonal_lines @ SV193 @ SV201 )
= $false )
| ( ( convergent_lines @ SV193 @ SV201 )
= $false )
| ( ( convergent_lines @ SV132 @ SV201 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(802,plain,
! [SV132: $i,SV202: $i,SV194: $i] :
( ( ( unorthogonal_lines @ SV194 @ SV202 )
= $false )
| ( ( convergent_lines @ SV194 @ SV202 )
= $false )
| ( ( unorthogonal_lines @ SV132 @ SV202 )
= $true )
| ( ( unorthogonal_lines @ SV132 @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(803,plain,
! [SV195: $i,SV203: $i,SV133: $i] :
( ( ( convergent_lines @ SV133 @ SV203 )
= $true )
| ( ( convergent_lines @ SV195 @ SV203 )
= $true )
| ( ( convergent_lines @ SV133 @ SV195 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(804,plain,
! [SV196: $i,SV204: $i,SV133: $i] :
( ( ( convergent_lines @ SV133 @ SV204 )
= $true )
| ( ( unorthogonal_lines @ SV196 @ SV204 )
= $true )
| ( ( convergent_lines @ SV133 @ SV196 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(805,plain,
! [SV197: $i,SV205: $i,SV133: $i] :
( ( ( unorthogonal_lines @ SV133 @ SV205 )
= $true )
| ( ( convergent_lines @ SV197 @ SV205 )
= $true )
| ( ( convergent_lines @ SV133 @ SV197 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(806,plain,
! [SV198: $i,SV206: $i,SV133: $i] :
( ( ( unorthogonal_lines @ SV133 @ SV206 )
= $true )
| ( ( unorthogonal_lines @ SV198 @ SV206 )
= $true )
| ( ( convergent_lines @ SV133 @ SV198 )
= $false )
| ( ( unorthogonal_lines @ SV133 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(807,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[496,806,805,804,803,802,801,800,799,774,756,750,749,744,743,742,741,740,721,715,713,707,705,703,701,700,697,694,693,692,690,689,688,662,661,660,659,634,603,601,600,599,597,596,546,545,544,536,499,498,497]) ).
thf(808,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[807,460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GEO196+3 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sat Jun 18 10:01:47 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.31
% 0.10/0.31 No.of.Axioms: 35
% 0.10/0.31
% 0.10/0.31 Length.of.Defs: 0
% 0.10/0.31
% 0.10/0.31 Contains.Choice.Funs: false
% 0.14/0.32 .
% 0.14/0.33 (rf:0,axioms:35,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:37,loop_count:0,foatp_calls:0,translation:fof_full)..........................................
% 0.55/0.98
% 0.55/0.98 ********************************
% 0.55/0.98 * All subproblems solved! *
% 0.55/0.98 ********************************
% 0.55/0.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:39,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:807,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.00/1.22
% 1.00/1.22 %**** Beginning of derivation protocol ****
% 1.00/1.22 % SZS output start CNFRefutation
% See solution above
% 1.00/1.22
% 1.00/1.22 %**** End of derivation protocol ****
% 1.00/1.22 %**** no. of clauses in derivation: 808 ****
% 1.00/1.22 %**** clause counter: 807 ****
% 1.00/1.22
% 1.00/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:39,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:807,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------