%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:18:14 AM UTC 2026
% Result : Theorem 1.48s 0.48s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 462 ( 234 unt; 0 typ; 0 def)
% Number of atoms : 3081 ( 824 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 5095 (1160 ~; 866 |; 46 &;2964 @)
% ( 12 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-2 aty)
% Number of variables : 1102 ( 0 ^;1102 !; 0 ?;1102 :)
% 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_SY45,type,
sK2_SY45: $i ).
thf(tp_sK3_SY48,type,
sK3_SY48: $i ).
thf(tp_sK4_SY50,type,
sK4_SY50: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(10,axiom,
! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cotno1) ).
thf(12,axiom,
! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coipo1) ).
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/sandbox/benchmark/theBenchmark.p',oac1) ).
thf(17,axiom,
! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
thf(20,axiom,
! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ceq3) ).
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/sandbox/benchmark/theBenchmark.p',ceq1) ).
thf(26,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ci3) ).
thf(30,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(32,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
thf(33,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(35,axiom,
! [X: $i] :
~ ( distinct_points @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(36,conjecture,
! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( convergent_lines @ U @ V )
& ( equal_points @ X @ ( intersection_point @ U @ V ) ) )
=> ( ( incident_point_and_line @ X @ U )
& ( incident_point_and_line @ X @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(37,negated_conjecture,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( convergent_lines @ U @ V )
& ( equal_points @ X @ ( intersection_point @ U @ V ) ) )
=> ( ( incident_point_and_line @ X @ U )
& ( incident_point_and_line @ X @ V ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( convergent_lines @ U @ V )
& ( equal_points @ X @ ( intersection_point @ U @ V ) ) )
=> ( ( incident_point_and_line @ X @ U )
& ( incident_point_and_line @ X @ V ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,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(40,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(42,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(43,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(44,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(45,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(46,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,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(50,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(51,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(52,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(53,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(54,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(55,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(56,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(57,plain,
( ( ! [SY45: $i,SY46: $i,SY47: $i] :
( ( ( distinct_points @ sK1_X @ SY45 )
& ( convergent_lines @ SY46 @ SY47 )
& ( equal_points @ sK1_X @ ( intersection_point @ SY46 @ SY47 ) ) )
=> ( ( incident_point_and_line @ sK1_X @ SY46 )
& ( incident_point_and_line @ sK1_X @ SY47 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(58,plain,
( ( ! [SY48: $i,SY49: $i] :
( ( ( distinct_points @ sK1_X @ sK2_SY45 )
& ( convergent_lines @ SY48 @ SY49 )
& ( equal_points @ sK1_X @ ( intersection_point @ SY48 @ SY49 ) ) )
=> ( ( incident_point_and_line @ sK1_X @ SY48 )
& ( incident_point_and_line @ sK1_X @ SY49 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(59,plain,
( ( ! [SY50: $i] :
( ( ( distinct_points @ sK1_X @ sK2_SY45 )
& ( convergent_lines @ sK3_SY48 @ SY50 )
& ( equal_points @ sK1_X @ ( intersection_point @ sK3_SY48 @ SY50 ) ) )
=> ( ( incident_point_and_line @ sK1_X @ sK3_SY48 )
& ( incident_point_and_line @ sK1_X @ SY50 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(60,plain,
( ( ( ( distinct_points @ sK1_X @ sK2_SY45 )
& ( convergent_lines @ sK3_SY48 @ sK4_SY50 )
& ( equal_points @ sK1_X @ ( intersection_point @ sK3_SY48 @ sK4_SY50 ) ) )
=> ( ( incident_point_and_line @ sK1_X @ sK3_SY48 )
& ( incident_point_and_line @ sK1_X @ sK4_SY50 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(61,plain,
( ( distinct_points @ sK1_X @ sK2_SY45 )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(62,plain,
( ( convergent_lines @ sK3_SY48 @ sK4_SY50 )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(63,plain,
( ( equal_points @ sK1_X @ ( intersection_point @ sK3_SY48 @ sK4_SY50 ) )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(64,plain,
( ( ( incident_point_and_line @ sK1_X @ sK3_SY48 )
& ( incident_point_and_line @ sK1_X @ sK4_SY50 ) )
= $false ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(65,plain,
( ( incident_point_and_line @ sK1_X @ sK3_SY48 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[64]) ).
thf(66,plain,
( ( incident_point_and_line @ sK1_X @ sK4_SY50 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[64]) ).
thf(67,plain,
( ( ~ ( incident_point_and_line @ sK1_X @ sK3_SY48 ) )
= $true ),
inference(polarity_switch,[status(thm)],[65]) ).
thf(68,plain,
( ( ~ ( incident_point_and_line @ sK1_X @ sK4_SY50 ) )
= $true ),
inference(polarity_switch,[status(thm)],[66]) ).
thf(69,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(70,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(75,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(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(79,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(80,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(copy,[status(thm)],[45]) ).
thf(81,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(82,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(copy,[status(thm)],[43]) ).
thf(83,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(87,plain,
( ( equal_points @ sK1_X @ ( intersection_point @ sK3_SY48 @ sK4_SY50 ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(88,plain,
( ( convergent_lines @ sK3_SY48 @ sK4_SY50 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(89,plain,
( ( distinct_points @ sK1_X @ sK2_SY45 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(90,plain,
( ( ~ ( incident_point_and_line @ sK1_X @ sK3_SY48 ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( apart_point_and_line @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX1 @ SX2 )
| ( convergent_lines @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) ) )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(105,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(106,plain,
! [SV2: $i] :
( ( ~ ( convergent_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(107,plain,
! [SV3: $i] :
( ( ! [SY51: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY51 @ SV3 ) @ SY51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(108,plain,
! [SV4: $i] :
( ( ! [SY52: $i] :
( ( convergent_lines @ SV4 @ SY52 )
| ( unorthogonal_lines @ SV4 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(109,plain,
( ( incident_point_and_line @ sK1_X @ sK3_SY48 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(110,plain,
! [SV5: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( incident_point_and_line @ SV5 @ SY53 )
| ~ ( apart_point_and_line @ SV5 @ SY53 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV5 @ SY53 )
| ( incident_point_and_line @ SV5 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV6: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV6 @ SY54 )
| ~ ~ ( unorthogonal_lines @ SV6 @ SY55 ) )
| ~ ( convergent_lines @ SY54 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV7: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( convergent_lines @ SV7 @ SY56 )
| ( convergent_lines @ SV7 @ SY57 )
| ( convergent_lines @ SY56 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV8: $i] :
( ( ! [SY58: $i] :
( ~ ( convergent_lines @ SV8 @ SY58 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV8 @ SY58 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV9: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( distinct_points @ SV9 @ SY59 )
| ( distinct_points @ SV9 @ SY60 )
| ( distinct_points @ SY59 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV10: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( apart_point_and_line @ SV10 @ SY61 )
| ( distinct_points @ SV10 @ SY62 )
| ( apart_point_and_line @ SY62 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV11: $i] :
( ( ! [SY63: $i] :
( ~ ( convergent_lines @ SV11 @ SY63 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV11 @ SY63 ) @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
! [SV12: $i] :
( ( ! [SY64: $i] :
~ ( ~ ( ~ ( equal_points @ SV12 @ SY64 )
| ~ ( distinct_points @ SV12 @ SY64 ) )
| ~ ( ~ ~ ( distinct_points @ SV12 @ SY64 )
| ( equal_points @ SV12 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV13: $i] :
( ( ! [SY65: $i] :
~ ( ~ ( ~ ( parallel_lines @ SV13 @ SY65 )
| ~ ( convergent_lines @ SV13 @ SY65 ) )
| ~ ( ~ ~ ( convergent_lines @ SV13 @ SY65 )
| ( parallel_lines @ SV13 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(119,plain,
! [SV14: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( convergent_lines @ SV14 @ SY66 )
| ( distinct_lines @ SY66 @ SY67 )
| ( convergent_lines @ SV14 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(120,plain,
! [SV15: $i] :
( ( ! [SY68: $i] :
( ~ ( distinct_lines @ SV15 @ SY68 )
| ( convergent_lines @ SV15 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(121,plain,
! [SV16: $i] :
( ( ! [SY69: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SV16 @ SY69 )
| ~ ~ ( unorthogonal_lines @ SV16 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(122,plain,
! [SV17: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV17 @ SY70 )
| ~ ( unorthogonal_lines @ SV17 @ SY70 ) )
| ~ ( ~ ( convergent_lines @ SV17 @ SY71 )
| ~ ( unorthogonal_lines @ SV17 @ SY71 ) ) )
| ~ ( convergent_lines @ SY70 @ SY71 )
| ~ ( unorthogonal_lines @ SY70 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(123,plain,
! [SV18: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV18 @ SY72 )
| ~ ( unorthogonal_lines @ SV18 @ SY72 ) )
| ~ ( ~ ( convergent_lines @ SV18 @ SY73 )
| ~ ( unorthogonal_lines @ SV18 @ SY73 ) )
| ~ ( ~ ( convergent_lines @ SY72 @ SY73 )
| ~ ( unorthogonal_lines @ SY72 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(124,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(125,plain,
! [SV2: $i] :
( ( convergent_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(126,plain,
! [SV3: $i,SV19: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV19 @ SV3 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(127,plain,
! [SV20: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV20 )
| ( unorthogonal_lines @ SV4 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(128,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( incident_point_and_line @ SV5 @ SV21 )
| ~ ( apart_point_and_line @ SV5 @ SV21 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV5 @ SV21 )
| ( incident_point_and_line @ SV5 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY74: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV6 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV6 @ SY74 ) )
| ~ ( convergent_lines @ SV22 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY75: $i] :
( ~ ( convergent_lines @ SV7 @ SV23 )
| ( convergent_lines @ SV7 @ SY75 )
| ( convergent_lines @ SV23 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV24: $i,SV8: $i] :
( ( ~ ( convergent_lines @ SV8 @ SV24 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV8 @ SV24 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV25: $i,SV9: $i] :
( ( ! [SY76: $i] :
( ~ ( distinct_points @ SV9 @ SV25 )
| ( distinct_points @ SV9 @ SY76 )
| ( distinct_points @ SV25 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY77: $i] :
( ~ ( apart_point_and_line @ SV10 @ SV26 )
| ( distinct_points @ SV10 @ SY77 )
| ( apart_point_and_line @ SY77 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV27: $i,SV11: $i] :
( ( ~ ( convergent_lines @ SV11 @ SV27 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV11 @ SV27 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( equal_points @ SV12 @ SV28 )
| ~ ( distinct_points @ SV12 @ SV28 ) )
| ~ ( ~ ~ ( distinct_points @ SV12 @ SV28 )
| ( equal_points @ SV12 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( parallel_lines @ SV13 @ SV29 )
| ~ ( convergent_lines @ SV13 @ SV29 ) )
| ~ ( ~ ~ ( convergent_lines @ SV13 @ SV29 )
| ( parallel_lines @ SV13 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV30: $i,SV14: $i] :
( ( ! [SY78: $i] :
( ~ ( convergent_lines @ SV14 @ SV30 )
| ( distinct_lines @ SV30 @ SY78 )
| ( convergent_lines @ SV14 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(138,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( distinct_lines @ SV15 @ SV31 )
| ( convergent_lines @ SV15 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(139,plain,
! [SV32: $i,SV16: $i] :
( ( ~ ~ ( ~ ~ ( convergent_lines @ SV16 @ SV32 )
| ~ ~ ( unorthogonal_lines @ SV16 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(140,plain,
! [SV33: $i,SV17: $i] :
( ( ! [SY79: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
| ~ ( ~ ( convergent_lines @ SV17 @ SY79 )
| ~ ( unorthogonal_lines @ SV17 @ SY79 ) ) )
| ~ ( convergent_lines @ SV33 @ SY79 )
| ~ ( unorthogonal_lines @ SV33 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV34: $i,SV18: $i] :
( ( ! [SY80: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV18 @ SV34 )
| ~ ( unorthogonal_lines @ SV18 @ SV34 ) )
| ~ ( ~ ( convergent_lines @ SV18 @ SY80 )
| ~ ( unorthogonal_lines @ SV18 @ SY80 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SY80 )
| ~ ( unorthogonal_lines @ SV34 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV3: $i,SV19: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV19 @ SV3 ) @ SV19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV20: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV20 )
= $true )
| ( ( unorthogonal_lines @ SV4 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ( ~ ( incident_point_and_line @ SV5 @ SV21 )
| ~ ( apart_point_and_line @ SV5 @ SV21 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV5 @ SV21 )
| ( incident_point_and_line @ SV5 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV6 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) )
| ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ~ ( convergent_lines @ SV7 @ SV23 )
| ( convergent_lines @ SV7 @ SV36 )
| ( convergent_lines @ SV23 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(147,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( convergent_lines @ SV8 @ SV24 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV8 @ SV24 ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ~ ( distinct_points @ SV9 @ SV25 )
| ( distinct_points @ SV9 @ SV37 )
| ( distinct_points @ SV25 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(149,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ~ ( apart_point_and_line @ SV10 @ SV26 )
| ( distinct_points @ SV10 @ SV38 )
| ( apart_point_and_line @ SV38 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV27: $i,SV11: $i] :
( ( ( ~ ( convergent_lines @ SV11 @ SV27 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV11 @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( equal_points @ SV12 @ SV28 )
| ~ ( distinct_points @ SV12 @ SV28 ) )
| ~ ( ~ ~ ( distinct_points @ SV12 @ SV28 )
| ( equal_points @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ( ~ ( parallel_lines @ SV13 @ SV29 )
| ~ ( convergent_lines @ SV13 @ SV29 ) )
| ~ ( ~ ~ ( convergent_lines @ SV13 @ SV29 )
| ( parallel_lines @ SV13 @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ~ ( convergent_lines @ SV14 @ SV30 )
| ( distinct_lines @ SV30 @ SV39 )
| ( convergent_lines @ SV14 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( distinct_lines @ SV15 @ SV31 ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV32: $i,SV16: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV16 @ SV32 )
| ~ ~ ( unorthogonal_lines @ SV16 @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
| ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
| ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ~ ~ ( ~ ( convergent_lines @ SV18 @ SV34 )
| ~ ( unorthogonal_lines @ SV18 @ SV34 ) )
| ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ( ~ ( incident_point_and_line @ SV5 @ SV21 )
| ~ ( apart_point_and_line @ SV5 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(159,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ( ~ ~ ( apart_point_and_line @ SV5 @ SV21 )
| ( incident_point_and_line @ SV5 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(160,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV6 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV23 ) )
= $true )
| ( ( ( convergent_lines @ SV7 @ SV36 )
| ( convergent_lines @ SV23 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV24: $i,SV8: $i] :
( ( ( convergent_lines @ SV8 @ SV24 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV8 @ SV24 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( distinct_points @ SV9 @ SV25 ) )
= $true )
| ( ( ( distinct_points @ SV9 @ SV37 )
| ( distinct_points @ SV25 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( apart_point_and_line @ SV10 @ SV26 ) )
= $true )
| ( ( ( distinct_points @ SV10 @ SV38 )
| ( apart_point_and_line @ SV38 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV27: $i,SV11: $i] :
( ( ( convergent_lines @ SV11 @ SV27 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV11 @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( equal_points @ SV12 @ SV28 )
| ~ ( distinct_points @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(167,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ~ ( distinct_points @ SV12 @ SV28 )
| ( equal_points @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(168,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ( ~ ( parallel_lines @ SV13 @ SV29 )
| ~ ( convergent_lines @ SV13 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(169,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV13 @ SV29 )
| ( parallel_lines @ SV13 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(170,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ( ~ ( convergent_lines @ SV14 @ SV30 ) )
= $true )
| ( ( ( distinct_lines @ SV30 @ SV39 )
| ( convergent_lines @ SV14 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(171,plain,
! [SV31: $i,SV15: $i] :
( ( ( distinct_lines @ SV15 @ SV31 )
= $false )
| ( ( convergent_lines @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(172,plain,
! [SV32: $i,SV16: $i] :
( ( ~ ~ ( convergent_lines @ SV16 @ SV32 )
| ~ ~ ( unorthogonal_lines @ SV16 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(173,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
| ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(174,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( convergent_lines @ SV18 @ SV34 )
| ~ ( unorthogonal_lines @ SV18 @ SV34 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(175,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ( incident_point_and_line @ SV5 @ SV21 )
| ~ ( apart_point_and_line @ SV5 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(176,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ~ ( apart_point_and_line @ SV5 @ SV21 )
| ( incident_point_and_line @ SV5 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(177,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( unorthogonal_lines @ SV6 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( convergent_lines @ SV7 @ SV23 )
= $false )
| ( ( ( convergent_lines @ SV7 @ SV36 )
| ( convergent_lines @ SV23 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV24: $i,SV8: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV8 @ SV24 ) @ SV8 )
= $false )
| ( ( convergent_lines @ SV8 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV25 )
= $false )
| ( ( ( distinct_points @ SV9 @ SV37 )
| ( distinct_points @ SV25 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ( apart_point_and_line @ SV10 @ SV26 )
= $false )
| ( ( ( distinct_points @ SV10 @ SV38 )
| ( apart_point_and_line @ SV38 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(182,plain,
! [SV27: $i,SV11: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV11 @ SV27 ) @ SV27 )
= $false )
| ( ( convergent_lines @ SV11 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(183,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( equal_points @ SV12 @ SV28 )
| ~ ( distinct_points @ SV12 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(184,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ~ ( distinct_points @ SV12 @ SV28 )
| ( equal_points @ SV12 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(185,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ( parallel_lines @ SV13 @ SV29 )
| ~ ( convergent_lines @ SV13 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(186,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ~ ( convergent_lines @ SV13 @ SV29 )
| ( parallel_lines @ SV13 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(187,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ( convergent_lines @ SV14 @ SV30 )
= $false )
| ( ( ( distinct_lines @ SV30 @ SV39 )
| ( convergent_lines @ SV14 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV32: $i,SV16: $i] :
( ( ( ~ ~ ( convergent_lines @ SV16 @ SV32 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
| ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV34 )
| ~ ( unorthogonal_lines @ SV18 @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ( incident_point_and_line @ SV5 @ SV21 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV5 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV5 @ SV21 ) )
= $true )
| ( ( incident_point_and_line @ SV5 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV6 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(194,plain,
! [SV23: $i,SV36: $i,SV7: $i] :
( ( ( convergent_lines @ SV7 @ SV36 )
= $true )
| ( ( convergent_lines @ SV23 @ SV36 )
= $true )
| ( ( convergent_lines @ SV7 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV25: $i,SV37: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV37 )
= $true )
| ( ( distinct_points @ SV25 @ SV37 )
= $true )
| ( ( distinct_points @ SV9 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(196,plain,
! [SV26: $i,SV38: $i,SV10: $i] :
( ( ( distinct_points @ SV10 @ SV38 )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV26 )
= $true )
| ( ( apart_point_and_line @ SV10 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(197,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( equal_points @ SV12 @ SV28 ) )
= $true )
| ( ( ~ ( distinct_points @ SV12 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ~ ( distinct_points @ SV12 @ SV28 ) )
= $true )
| ( ( equal_points @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV29: $i,SV13: $i] :
( ( ( ~ ( parallel_lines @ SV13 @ SV29 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV13 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(200,plain,
! [SV29: $i,SV13: $i] :
( ( ( ~ ~ ( convergent_lines @ SV13 @ SV29 ) )
= $true )
| ( ( parallel_lines @ SV13 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(201,plain,
! [SV14: $i,SV39: $i,SV30: $i] :
( ( ( distinct_lines @ SV30 @ SV39 )
= $true )
| ( ( convergent_lines @ SV14 @ SV39 )
= $true )
| ( ( convergent_lines @ SV14 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(202,plain,
! [SV32: $i,SV16: $i] :
( ( ( ~ ( convergent_lines @ SV16 @ SV32 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(203,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
| ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(204,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ( ~ ( convergent_lines @ SV18 @ SV34 )
| ~ ( unorthogonal_lines @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(205,plain,
! [SV21: $i,SV5: $i] :
( ( ( incident_point_and_line @ SV5 @ SV21 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV5 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(206,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ( apart_point_and_line @ SV5 @ SV21 ) )
= $false )
| ( ( incident_point_and_line @ SV5 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(207,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV6 @ SV22 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(208,plain,
! [SV28: $i,SV12: $i] :
( ( ( equal_points @ SV12 @ SV28 )
= $false )
| ( ( ~ ( distinct_points @ SV12 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( distinct_points @ SV12 @ SV28 ) )
= $false )
| ( ( equal_points @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV29: $i,SV13: $i] :
( ( ( parallel_lines @ SV13 @ SV29 )
= $false )
| ( ( ~ ( convergent_lines @ SV13 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV29: $i,SV13: $i] :
( ( ( ~ ( convergent_lines @ SV13 @ SV29 ) )
= $false )
| ( ( parallel_lines @ SV13 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV32: $i,SV16: $i] :
( ( ( convergent_lines @ SV16 @ SV32 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(213,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ( ~ ( convergent_lines @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV21: $i,SV5: $i] :
( ( ( apart_point_and_line @ SV5 @ SV21 )
= $false )
| ( ( incident_point_and_line @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV21: $i,SV5: $i] :
( ( ( apart_point_and_line @ SV5 @ SV21 )
= $true )
| ( ( incident_point_and_line @ SV5 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(217,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( unorthogonal_lines @ SV6 @ SV22 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(218,plain,
! [SV28: $i,SV12: $i] :
( ( ( distinct_points @ SV12 @ SV28 )
= $false )
| ( ( equal_points @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(219,plain,
! [SV28: $i,SV12: $i] :
( ( ( distinct_points @ SV12 @ SV28 )
= $true )
| ( ( equal_points @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(220,plain,
! [SV29: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV29 )
= $false )
| ( ( parallel_lines @ SV13 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(221,plain,
! [SV29: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV29 )
= $true )
| ( ( parallel_lines @ SV13 @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(222,plain,
! [SV32: $i,SV16: $i] :
( ( ( ~ ( unorthogonal_lines @ SV16 @ SV32 ) )
= $false )
| ( ( convergent_lines @ SV16 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( convergent_lines @ SV17 @ SV33 )
| ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(225,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ( unorthogonal_lines @ SV6 @ SV22 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(226,plain,
! [SV32: $i,SV16: $i] :
( ( ( unorthogonal_lines @ SV16 @ SV32 )
= $true )
| ( ( convergent_lines @ SV16 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(227,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( convergent_lines @ SV17 @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(228,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( unorthogonal_lines @ SV17 @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(229,plain,
! [SV41: $i,SV34: $i,SV18: $i] :
( ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
| ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(230,plain,
! [SV22: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( unorthogonal_lines @ SV6 @ SV35 ) )
= $false )
| ( ( unorthogonal_lines @ SV6 @ SV22 )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(231,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(232,plain,
! [SV40: $i,SV33: $i,SV17: $i] :
( ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(233,plain,
! [SV34: $i,SV41: $i,SV18: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV22: $i,SV35: $i,SV6: $i] :
( ( ( unorthogonal_lines @ SV6 @ SV35 )
= $true )
| ( ( unorthogonal_lines @ SV6 @ SV22 )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(235,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) )
= $false )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( ~ ( convergent_lines @ SV17 @ SV40 )
| ~ ( unorthogonal_lines @ SV17 @ SV40 ) )
= $false )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV34: $i,SV41: $i,SV18: $i] :
( ( ( ~ ( convergent_lines @ SV18 @ SV41 )
| ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV6: $i,SV35: $i,SV22: $i] :
( ( ( convergent_lines @ SV22 @ SV35 )
= $false )
| ( ( unorthogonal_lines @ SV6 @ SV22 )
= $true )
| ( ( unorthogonal_lines @ SV6 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( ~ ( convergent_lines @ SV17 @ SV40 ) )
= $false )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(240,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( ~ ( unorthogonal_lines @ SV17 @ SV40 ) )
= $false )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(241,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( ~ ( convergent_lines @ SV17 @ SV40 ) )
= $false )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(242,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( ~ ( unorthogonal_lines @ SV17 @ SV40 ) )
= $false )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(243,plain,
! [SV34: $i,SV41: $i,SV18: $i] :
( ( ( ~ ( convergent_lines @ SV18 @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(244,plain,
! [SV34: $i,SV41: $i,SV18: $i] :
( ( ( ~ ( unorthogonal_lines @ SV18 @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(245,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( convergent_lines @ SV17 @ SV40 )
= $true )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(246,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(247,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( convergent_lines @ SV17 @ SV40 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(248,plain,
! [SV33: $i,SV40: $i,SV17: $i] :
( ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( ~ ( convergent_lines @ SV33 @ SV40 )
| ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(249,plain,
! [SV34: $i,SV41: $i,SV18: $i] :
( ( ( convergent_lines @ SV18 @ SV41 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(250,plain,
! [SV34: $i,SV41: $i,SV18: $i] :
( ( ( unorthogonal_lines @ SV18 @ SV41 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(251,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( ~ ( convergent_lines @ SV33 @ SV40 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( convergent_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(252,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( ~ ( convergent_lines @ SV33 @ SV40 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(253,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( ~ ( convergent_lines @ SV33 @ SV40 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( convergent_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( ~ ( convergent_lines @ SV33 @ SV40 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(255,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) )
= $false )
| ( ( convergent_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(256,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( ~ ( convergent_lines @ SV34 @ SV41 )
| ~ ( unorthogonal_lines @ SV34 @ SV41 ) )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(257,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( convergent_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(258,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(259,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( convergent_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(260,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV33 @ SV40 ) )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(261,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( ~ ( convergent_lines @ SV34 @ SV41 ) )
= $false )
| ( ( convergent_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(262,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( ~ ( unorthogonal_lines @ SV34 @ SV41 ) )
= $false )
| ( ( convergent_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(263,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( ~ ( convergent_lines @ SV34 @ SV41 ) )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(264,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( ~ ( unorthogonal_lines @ SV34 @ SV41 ) )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(265,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( unorthogonal_lines @ SV33 @ SV40 )
= $false )
| ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( convergent_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( unorthogonal_lines @ SV33 @ SV40 )
= $false )
| ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( convergent_lines @ SV17 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( unorthogonal_lines @ SV33 @ SV40 )
= $false )
| ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( convergent_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV17: $i,SV40: $i,SV33: $i] :
( ( ( unorthogonal_lines @ SV33 @ SV40 )
= $false )
| ( ( convergent_lines @ SV33 @ SV40 )
= $false )
| ( ( unorthogonal_lines @ SV17 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV17 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(269,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( convergent_lines @ SV34 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(270,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( unorthogonal_lines @ SV34 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( convergent_lines @ SV34 @ SV41 )
= $true )
| ( ( unorthogonal_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(272,plain,
! [SV18: $i,SV41: $i,SV34: $i] :
( ( ( unorthogonal_lines @ SV34 @ SV41 )
= $true )
| ( ( unorthogonal_lines @ SV18 @ SV41 )
= $true )
| ( ( convergent_lines @ SV18 @ SV34 )
= $false )
| ( ( unorthogonal_lines @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(273,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[87,272,271,270,269,268,267,266,265,238,226,221,220,219,218,216,215,201,196,195,194,182,179,171,143,142,125,124,109,89,88]) ).
thf(274,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(275,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(276,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(277,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(278,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(279,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(280,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(copy,[status(thm)],[50]) ).
thf(281,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(282,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(283,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(284,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(285,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(copy,[status(thm)],[45]) ).
thf(286,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(287,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(copy,[status(thm)],[43]) ).
thf(288,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(289,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(290,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(291,plain,
( ( ! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(292,plain,
( ( equal_points @ sK1_X @ ( intersection_point @ sK3_SY48 @ sK4_SY50 ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(293,plain,
( ( convergent_lines @ sK3_SY48 @ sK4_SY50 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(294,plain,
( ( distinct_points @ sK1_X @ sK2_SY45 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(295,plain,
( ( ~ ( incident_point_and_line @ sK1_X @ sK4_SY50 ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(296,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) ) )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(297,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(298,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(299,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX1 @ SX2 )
| ( convergent_lines @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(302,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(303,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(305,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(306,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( apart_point_and_line @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(307,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(309,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(310,plain,
! [SV42: $i] :
( ( ~ ( distinct_points @ SV42 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(311,plain,
! [SV43: $i] :
( ( ~ ( convergent_lines @ SV43 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(312,plain,
! [SV44: $i] :
( ( ! [SY81: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY81 @ SV44 ) @ SY81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(313,plain,
! [SV45: $i] :
( ( ! [SY82: $i] :
( ( convergent_lines @ SV45 @ SY82 )
| ( unorthogonal_lines @ SV45 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(314,plain,
( ( incident_point_and_line @ sK1_X @ sK4_SY50 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(315,plain,
! [SV46: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV46 @ SY83 )
| ~ ( unorthogonal_lines @ SV46 @ SY83 ) )
| ~ ( ~ ( convergent_lines @ SV46 @ SY84 )
| ~ ( unorthogonal_lines @ SV46 @ SY84 ) ) )
| ~ ( convergent_lines @ SY83 @ SY84 )
| ~ ( unorthogonal_lines @ SY83 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(316,plain,
! [SV47: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ~ ( parallel_lines @ SV47 @ SY85 )
| ~ ( convergent_lines @ SV47 @ SY85 ) )
| ~ ( ~ ~ ( convergent_lines @ SV47 @ SY85 )
| ( parallel_lines @ SV47 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(317,plain,
! [SV48: $i] :
( ( ! [SY86: $i] :
( ~ ( distinct_lines @ SV48 @ SY86 )
| ( convergent_lines @ SV48 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(318,plain,
! [SV49: $i] :
( ( ! [SY87: $i] :
( ~ ( convergent_lines @ SV49 @ SY87 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV49 @ SY87 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(319,plain,
! [SV50: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV50 @ SY88 )
| ~ ~ ( unorthogonal_lines @ SV50 @ SY89 ) )
| ~ ( convergent_lines @ SY88 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(320,plain,
! [SV51: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( convergent_lines @ SV51 @ SY90 )
| ( distinct_lines @ SY90 @ SY91 )
| ( convergent_lines @ SV51 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(321,plain,
! [SV52: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV52 @ SY92 )
| ~ ( unorthogonal_lines @ SV52 @ SY92 ) )
| ~ ( ~ ( convergent_lines @ SV52 @ SY93 )
| ~ ( unorthogonal_lines @ SV52 @ SY93 ) )
| ~ ( ~ ( convergent_lines @ SY92 @ SY93 )
| ~ ( unorthogonal_lines @ SY92 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(322,plain,
! [SV53: $i] :
( ( ! [SY94: $i] :
~ ( ~ ( ~ ( incident_point_and_line @ SV53 @ SY94 )
| ~ ( apart_point_and_line @ SV53 @ SY94 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV53 @ SY94 )
| ( incident_point_and_line @ SV53 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(323,plain,
! [SV54: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( convergent_lines @ SV54 @ SY95 )
| ( convergent_lines @ SV54 @ SY96 )
| ( convergent_lines @ SY95 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(324,plain,
! [SV55: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( distinct_points @ SV55 @ SY97 )
| ( distinct_points @ SV55 @ SY98 )
| ( distinct_points @ SY97 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(325,plain,
! [SV56: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( apart_point_and_line @ SV56 @ SY99 )
| ( distinct_points @ SV56 @ SY100 )
| ( apart_point_and_line @ SY100 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(326,plain,
! [SV57: $i] :
( ( ! [SY101: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SV57 @ SY101 )
| ~ ~ ( unorthogonal_lines @ SV57 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(327,plain,
! [SV58: $i] :
( ( ! [SY102: $i] :
~ ( ~ ( ~ ( equal_points @ SV58 @ SY102 )
| ~ ( distinct_points @ SV58 @ SY102 ) )
| ~ ( ~ ~ ( distinct_points @ SV58 @ SY102 )
| ( equal_points @ SV58 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(328,plain,
! [SV59: $i] :
( ( ! [SY103: $i] :
( ~ ( convergent_lines @ SV59 @ SY103 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SY103 ) @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(329,plain,
! [SV42: $i] :
( ( distinct_points @ SV42 @ SV42 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(330,plain,
! [SV43: $i] :
( ( convergent_lines @ SV43 @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(331,plain,
! [SV44: $i,SV60: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV60 @ SV44 ) @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(332,plain,
! [SV61: $i,SV45: $i] :
( ( ( convergent_lines @ SV45 @ SV61 )
| ( unorthogonal_lines @ SV45 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(333,plain,
! [SV62: $i,SV46: $i] :
( ( ! [SY104: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
| ~ ( ~ ( convergent_lines @ SV46 @ SY104 )
| ~ ( unorthogonal_lines @ SV46 @ SY104 ) ) )
| ~ ( convergent_lines @ SV62 @ SY104 )
| ~ ( unorthogonal_lines @ SV62 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(334,plain,
! [SV63: $i,SV47: $i] :
( ( ~ ( ~ ( ~ ( parallel_lines @ SV47 @ SV63 )
| ~ ( convergent_lines @ SV47 @ SV63 ) )
| ~ ( ~ ~ ( convergent_lines @ SV47 @ SV63 )
| ( parallel_lines @ SV47 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(335,plain,
! [SV64: $i,SV48: $i] :
( ( ~ ( distinct_lines @ SV48 @ SV64 )
| ( convergent_lines @ SV48 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(336,plain,
! [SV65: $i,SV49: $i] :
( ( ~ ( convergent_lines @ SV49 @ SV65 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV49 @ SV65 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(337,plain,
! [SV66: $i,SV50: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV50 @ SV66 )
| ~ ~ ( unorthogonal_lines @ SV50 @ SY105 ) )
| ~ ( convergent_lines @ SV66 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(338,plain,
! [SV67: $i,SV51: $i] :
( ( ! [SY106: $i] :
( ~ ( convergent_lines @ SV51 @ SV67 )
| ( distinct_lines @ SV67 @ SY106 )
| ( convergent_lines @ SV51 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(339,plain,
! [SV68: $i,SV52: $i] :
( ( ! [SY107: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV52 @ SV68 )
| ~ ( unorthogonal_lines @ SV52 @ SV68 ) )
| ~ ( ~ ( convergent_lines @ SV52 @ SY107 )
| ~ ( unorthogonal_lines @ SV52 @ SY107 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SY107 )
| ~ ( unorthogonal_lines @ SV68 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(340,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ( ~ ( ~ ( incident_point_and_line @ SV53 @ SV69 )
| ~ ( apart_point_and_line @ SV53 @ SV69 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV53 @ SV69 )
| ( incident_point_and_line @ SV53 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(341,plain,
! [SV70: $i,SV54: $i] :
( ( ! [SY108: $i] :
( ~ ( convergent_lines @ SV54 @ SV70 )
| ( convergent_lines @ SV54 @ SY108 )
| ( convergent_lines @ SV70 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(342,plain,
! [SV71: $i,SV55: $i] :
( ( ! [SY109: $i] :
( ~ ( distinct_points @ SV55 @ SV71 )
| ( distinct_points @ SV55 @ SY109 )
| ( distinct_points @ SV71 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(343,plain,
! [SV72: $i,SV56: $i] :
( ( ! [SY110: $i] :
( ~ ( apart_point_and_line @ SV56 @ SV72 )
| ( distinct_points @ SV56 @ SY110 )
| ( apart_point_and_line @ SY110 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(344,plain,
! [SV73: $i,SV57: $i] :
( ( ~ ~ ( ~ ~ ( convergent_lines @ SV57 @ SV73 )
| ~ ~ ( unorthogonal_lines @ SV57 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(345,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( equal_points @ SV58 @ SV74 )
| ~ ( distinct_points @ SV58 @ SV74 ) )
| ~ ( ~ ~ ( distinct_points @ SV58 @ SV74 )
| ( equal_points @ SV58 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(346,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( convergent_lines @ SV59 @ SV75 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV75 ) @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(347,plain,
! [SV44: $i,SV60: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV60 @ SV44 ) @ SV60 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV61: $i,SV45: $i] :
( ( ( convergent_lines @ SV45 @ SV61 )
= $true )
| ( ( unorthogonal_lines @ SV45 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(349,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
| ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
| ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(350,plain,
! [SV63: $i,SV47: $i] :
( ( ~ ( ~ ( parallel_lines @ SV47 @ SV63 )
| ~ ( convergent_lines @ SV47 @ SV63 ) )
| ~ ( ~ ~ ( convergent_lines @ SV47 @ SV63 )
| ( parallel_lines @ SV47 @ SV63 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(351,plain,
! [SV64: $i,SV48: $i] :
( ( ( ~ ( distinct_lines @ SV48 @ SV64 ) )
= $true )
| ( ( convergent_lines @ SV48 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(352,plain,
! [SV65: $i,SV49: $i] :
( ( ( ~ ( convergent_lines @ SV49 @ SV65 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV49 @ SV65 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(353,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV50 @ SV66 )
| ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) )
| ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(354,plain,
! [SV78: $i,SV67: $i,SV51: $i] :
( ( ~ ( convergent_lines @ SV51 @ SV67 )
| ( distinct_lines @ SV67 @ SV78 )
| ( convergent_lines @ SV51 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(355,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ~ ~ ( ~ ( convergent_lines @ SV52 @ SV68 )
| ~ ( unorthogonal_lines @ SV52 @ SV68 ) )
| ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(356,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ( ~ ( incident_point_and_line @ SV53 @ SV69 )
| ~ ( apart_point_and_line @ SV53 @ SV69 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV53 @ SV69 )
| ( incident_point_and_line @ SV53 @ SV69 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(357,plain,
! [SV80: $i,SV70: $i,SV54: $i] :
( ( ~ ( convergent_lines @ SV54 @ SV70 )
| ( convergent_lines @ SV54 @ SV80 )
| ( convergent_lines @ SV70 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(358,plain,
! [SV81: $i,SV71: $i,SV55: $i] :
( ( ~ ( distinct_points @ SV55 @ SV71 )
| ( distinct_points @ SV55 @ SV81 )
| ( distinct_points @ SV71 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(359,plain,
! [SV82: $i,SV72: $i,SV56: $i] :
( ( ~ ( apart_point_and_line @ SV56 @ SV72 )
| ( distinct_points @ SV56 @ SV82 )
| ( apart_point_and_line @ SV82 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(360,plain,
! [SV73: $i,SV57: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV57 @ SV73 )
| ~ ~ ( unorthogonal_lines @ SV57 @ SV73 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(361,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ( ~ ( equal_points @ SV58 @ SV74 )
| ~ ( distinct_points @ SV58 @ SV74 ) )
| ~ ( ~ ~ ( distinct_points @ SV58 @ SV74 )
| ( equal_points @ SV58 @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(362,plain,
! [SV75: $i,SV59: $i] :
( ( ( ~ ( convergent_lines @ SV59 @ SV75 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(363,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
| ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(364,plain,
! [SV63: $i,SV47: $i] :
( ( ~ ( ~ ( parallel_lines @ SV47 @ SV63 )
| ~ ( convergent_lines @ SV47 @ SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(365,plain,
! [SV63: $i,SV47: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV47 @ SV63 )
| ( parallel_lines @ SV47 @ SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(366,plain,
! [SV64: $i,SV48: $i] :
( ( ( distinct_lines @ SV48 @ SV64 )
= $false )
| ( ( convergent_lines @ SV48 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(367,plain,
! [SV65: $i,SV49: $i] :
( ( ( convergent_lines @ SV49 @ SV65 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV49 @ SV65 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(368,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV50 @ SV66 )
| ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(369,plain,
! [SV78: $i,SV67: $i,SV51: $i] :
( ( ( ~ ( convergent_lines @ SV51 @ SV67 ) )
= $true )
| ( ( ( distinct_lines @ SV67 @ SV78 )
| ( convergent_lines @ SV51 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(370,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( convergent_lines @ SV52 @ SV68 )
| ~ ( unorthogonal_lines @ SV52 @ SV68 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(371,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ( ~ ( incident_point_and_line @ SV53 @ SV69 )
| ~ ( apart_point_and_line @ SV53 @ SV69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(372,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ( ~ ~ ( apart_point_and_line @ SV53 @ SV69 )
| ( incident_point_and_line @ SV53 @ SV69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(373,plain,
! [SV80: $i,SV70: $i,SV54: $i] :
( ( ( ~ ( convergent_lines @ SV54 @ SV70 ) )
= $true )
| ( ( ( convergent_lines @ SV54 @ SV80 )
| ( convergent_lines @ SV70 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(374,plain,
! [SV81: $i,SV71: $i,SV55: $i] :
( ( ( ~ ( distinct_points @ SV55 @ SV71 ) )
= $true )
| ( ( ( distinct_points @ SV55 @ SV81 )
| ( distinct_points @ SV71 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(375,plain,
! [SV82: $i,SV72: $i,SV56: $i] :
( ( ( ~ ( apart_point_and_line @ SV56 @ SV72 ) )
= $true )
| ( ( ( distinct_points @ SV56 @ SV82 )
| ( apart_point_and_line @ SV82 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(376,plain,
! [SV73: $i,SV57: $i] :
( ( ~ ~ ( convergent_lines @ SV57 @ SV73 )
| ~ ~ ( unorthogonal_lines @ SV57 @ SV73 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(377,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ( ~ ( equal_points @ SV58 @ SV74 )
| ~ ( distinct_points @ SV58 @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(378,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ( ~ ~ ( distinct_points @ SV58 @ SV74 )
| ( equal_points @ SV58 @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(379,plain,
! [SV75: $i,SV59: $i] :
( ( ( convergent_lines @ SV59 @ SV75 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV59 @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(380,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ( ~ ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
| ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(381,plain,
! [SV63: $i,SV47: $i] :
( ( ~ ( parallel_lines @ SV47 @ SV63 )
| ~ ( convergent_lines @ SV47 @ SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(382,plain,
! [SV63: $i,SV47: $i] :
( ( ~ ~ ( convergent_lines @ SV47 @ SV63 )
| ( parallel_lines @ SV47 @ SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(383,plain,
! [SV65: $i,SV49: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV49 @ SV65 ) @ SV49 )
= $false )
| ( ( convergent_lines @ SV49 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(384,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ( ~ ( ~ ~ ( unorthogonal_lines @ SV50 @ SV66 )
| ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(385,plain,
! [SV78: $i,SV67: $i,SV51: $i] :
( ( ( convergent_lines @ SV51 @ SV67 )
= $false )
| ( ( ( distinct_lines @ SV67 @ SV78 )
| ( convergent_lines @ SV51 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(386,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV68 )
| ~ ( unorthogonal_lines @ SV52 @ SV68 ) ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(387,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ( incident_point_and_line @ SV53 @ SV69 )
| ~ ( apart_point_and_line @ SV53 @ SV69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(388,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ~ ( apart_point_and_line @ SV53 @ SV69 )
| ( incident_point_and_line @ SV53 @ SV69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(389,plain,
! [SV80: $i,SV70: $i,SV54: $i] :
( ( ( convergent_lines @ SV54 @ SV70 )
= $false )
| ( ( ( convergent_lines @ SV54 @ SV80 )
| ( convergent_lines @ SV70 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(390,plain,
! [SV81: $i,SV71: $i,SV55: $i] :
( ( ( distinct_points @ SV55 @ SV71 )
= $false )
| ( ( ( distinct_points @ SV55 @ SV81 )
| ( distinct_points @ SV71 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(391,plain,
! [SV82: $i,SV72: $i,SV56: $i] :
( ( ( apart_point_and_line @ SV56 @ SV72 )
= $false )
| ( ( ( distinct_points @ SV56 @ SV82 )
| ( apart_point_and_line @ SV82 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(392,plain,
! [SV73: $i,SV57: $i] :
( ( ( ~ ~ ( convergent_lines @ SV57 @ SV73 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV57 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(393,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ( equal_points @ SV58 @ SV74 )
| ~ ( distinct_points @ SV58 @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(394,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ~ ( distinct_points @ SV58 @ SV74 )
| ( equal_points @ SV58 @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(395,plain,
! [SV75: $i,SV59: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV59 @ SV75 ) @ SV75 )
= $false )
| ( ( convergent_lines @ SV59 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(396,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
| ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(397,plain,
! [SV63: $i,SV47: $i] :
( ( ( ~ ( parallel_lines @ SV47 @ SV63 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV47 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(398,plain,
! [SV63: $i,SV47: $i] :
( ( ( ~ ~ ( convergent_lines @ SV47 @ SV63 ) )
= $true )
| ( ( parallel_lines @ SV47 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(399,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV50 @ SV66 )
| ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(400,plain,
! [SV51: $i,SV78: $i,SV67: $i] :
( ( ( distinct_lines @ SV67 @ SV78 )
= $true )
| ( ( convergent_lines @ SV51 @ SV78 )
= $true )
| ( ( convergent_lines @ SV51 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(401,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ( ~ ( convergent_lines @ SV52 @ SV68 )
| ~ ( unorthogonal_lines @ SV52 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(402,plain,
! [SV69: $i,SV53: $i] :
( ( ( ~ ( incident_point_and_line @ SV53 @ SV69 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV53 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(403,plain,
! [SV69: $i,SV53: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV53 @ SV69 ) )
= $true )
| ( ( incident_point_and_line @ SV53 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(404,plain,
! [SV70: $i,SV80: $i,SV54: $i] :
( ( ( convergent_lines @ SV54 @ SV80 )
= $true )
| ( ( convergent_lines @ SV70 @ SV80 )
= $true )
| ( ( convergent_lines @ SV54 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(405,plain,
! [SV71: $i,SV81: $i,SV55: $i] :
( ( ( distinct_points @ SV55 @ SV81 )
= $true )
| ( ( distinct_points @ SV71 @ SV81 )
= $true )
| ( ( distinct_points @ SV55 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(406,plain,
! [SV72: $i,SV82: $i,SV56: $i] :
( ( ( distinct_points @ SV56 @ SV82 )
= $true )
| ( ( apart_point_and_line @ SV82 @ SV72 )
= $true )
| ( ( apart_point_and_line @ SV56 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(407,plain,
! [SV73: $i,SV57: $i] :
( ( ( ~ ( convergent_lines @ SV57 @ SV73 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV57 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(408,plain,
! [SV74: $i,SV58: $i] :
( ( ( ~ ( equal_points @ SV58 @ SV74 ) )
= $true )
| ( ( ~ ( distinct_points @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(409,plain,
! [SV74: $i,SV58: $i] :
( ( ( ~ ~ ( distinct_points @ SV58 @ SV74 ) )
= $true )
| ( ( equal_points @ SV58 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(410,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(411,plain,
! [SV63: $i,SV47: $i] :
( ( ( parallel_lines @ SV47 @ SV63 )
= $false )
| ( ( ~ ( convergent_lines @ SV47 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(412,plain,
! [SV63: $i,SV47: $i] :
( ( ( ~ ( convergent_lines @ SV47 @ SV63 ) )
= $false )
| ( ( parallel_lines @ SV47 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(413,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV50 @ SV66 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(414,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ( ~ ( convergent_lines @ SV52 @ SV68 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV52 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(415,plain,
! [SV69: $i,SV53: $i] :
( ( ( incident_point_and_line @ SV53 @ SV69 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV53 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(416,plain,
! [SV69: $i,SV53: $i] :
( ( ( ~ ( apart_point_and_line @ SV53 @ SV69 ) )
= $false )
| ( ( incident_point_and_line @ SV53 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(417,plain,
! [SV73: $i,SV57: $i] :
( ( ( convergent_lines @ SV57 @ SV73 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV57 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(418,plain,
! [SV74: $i,SV58: $i] :
( ( ( equal_points @ SV58 @ SV74 )
= $false )
| ( ( ~ ( distinct_points @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(419,plain,
! [SV74: $i,SV58: $i] :
( ( ( ~ ( distinct_points @ SV58 @ SV74 ) )
= $false )
| ( ( equal_points @ SV58 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(420,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV62 )
| ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(421,plain,
! [SV63: $i,SV47: $i] :
( ( ( convergent_lines @ SV47 @ SV63 )
= $false )
| ( ( parallel_lines @ SV47 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(422,plain,
! [SV63: $i,SV47: $i] :
( ( ( convergent_lines @ SV47 @ SV63 )
= $true )
| ( ( parallel_lines @ SV47 @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(423,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ( ~ ( unorthogonal_lines @ SV50 @ SV66 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(424,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV52 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(425,plain,
! [SV69: $i,SV53: $i] :
( ( ( apart_point_and_line @ SV53 @ SV69 )
= $false )
| ( ( incident_point_and_line @ SV53 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(426,plain,
! [SV69: $i,SV53: $i] :
( ( ( apart_point_and_line @ SV53 @ SV69 )
= $true )
| ( ( incident_point_and_line @ SV53 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(427,plain,
! [SV73: $i,SV57: $i] :
( ( ( ~ ( unorthogonal_lines @ SV57 @ SV73 ) )
= $false )
| ( ( convergent_lines @ SV57 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(428,plain,
! [SV74: $i,SV58: $i] :
( ( ( distinct_points @ SV58 @ SV74 )
= $false )
| ( ( equal_points @ SV58 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(429,plain,
! [SV74: $i,SV58: $i] :
( ( ( distinct_points @ SV58 @ SV74 )
= $true )
| ( ( equal_points @ SV58 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(430,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(431,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( ~ ( unorthogonal_lines @ SV46 @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(432,plain,
! [SV77: $i,SV66: $i,SV50: $i] :
( ( ( unorthogonal_lines @ SV50 @ SV66 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV50 @ SV77 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(433,plain,
! [SV79: $i,SV68: $i,SV52: $i] :
( ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
| ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(434,plain,
! [SV73: $i,SV57: $i] :
( ( ( unorthogonal_lines @ SV57 @ SV73 )
= $true )
| ( ( convergent_lines @ SV57 @ SV73 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(435,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(436,plain,
! [SV76: $i,SV62: $i,SV46: $i] :
( ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(437,plain,
! [SV66: $i,SV77: $i,SV50: $i] :
( ( ( ~ ( unorthogonal_lines @ SV50 @ SV77 ) )
= $false )
| ( ( unorthogonal_lines @ SV50 @ SV66 )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(438,plain,
! [SV68: $i,SV79: $i,SV52: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(439,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) )
= $false )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(440,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV76 )
| ~ ( unorthogonal_lines @ SV46 @ SV76 ) )
= $false )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(441,plain,
! [SV66: $i,SV77: $i,SV50: $i] :
( ( ( unorthogonal_lines @ SV50 @ SV77 )
= $true )
| ( ( unorthogonal_lines @ SV50 @ SV66 )
= $true )
| ( ( ~ ( convergent_lines @ SV66 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(442,plain,
! [SV68: $i,SV79: $i,SV52: $i] :
( ( ( ~ ( convergent_lines @ SV52 @ SV79 )
| ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(443,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV76 ) )
= $false )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(444,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( ~ ( unorthogonal_lines @ SV46 @ SV76 ) )
= $false )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(445,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV76 ) )
= $false )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(446,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( ~ ( unorthogonal_lines @ SV46 @ SV76 ) )
= $false )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(447,plain,
! [SV50: $i,SV77: $i,SV66: $i] :
( ( ( convergent_lines @ SV66 @ SV77 )
= $false )
| ( ( unorthogonal_lines @ SV50 @ SV66 )
= $true )
| ( ( unorthogonal_lines @ SV50 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(448,plain,
! [SV68: $i,SV79: $i,SV52: $i] :
( ( ( ~ ( convergent_lines @ SV52 @ SV79 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(449,plain,
! [SV68: $i,SV79: $i,SV52: $i] :
( ( ( ~ ( unorthogonal_lines @ SV52 @ SV79 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(450,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( convergent_lines @ SV46 @ SV76 )
= $true )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(451,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(452,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( convergent_lines @ SV46 @ SV76 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(453,plain,
! [SV62: $i,SV76: $i,SV46: $i] :
( ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( ~ ( convergent_lines @ SV62 @ SV76 )
| ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(454,plain,
! [SV68: $i,SV79: $i,SV52: $i] :
( ( ( convergent_lines @ SV52 @ SV79 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(455,plain,
! [SV68: $i,SV79: $i,SV52: $i] :
( ( ( unorthogonal_lines @ SV52 @ SV79 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) ) )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(456,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( convergent_lines @ SV62 @ SV76 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( convergent_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(457,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( convergent_lines @ SV62 @ SV76 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(458,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( convergent_lines @ SV62 @ SV76 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( convergent_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(459,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( convergent_lines @ SV62 @ SV76 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(460,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) )
= $false )
| ( ( convergent_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(461,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( ~ ( convergent_lines @ SV68 @ SV79 )
| ~ ( unorthogonal_lines @ SV68 @ SV79 ) )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(462,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( convergent_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(463,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(464,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( convergent_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(465,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV62 @ SV76 ) )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(466,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( ~ ( convergent_lines @ SV68 @ SV79 ) )
= $false )
| ( ( convergent_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(467,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( ~ ( unorthogonal_lines @ SV68 @ SV79 ) )
= $false )
| ( ( convergent_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(468,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( ~ ( convergent_lines @ SV68 @ SV79 ) )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(469,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( ~ ( unorthogonal_lines @ SV68 @ SV79 ) )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(470,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( unorthogonal_lines @ SV62 @ SV76 )
= $false )
| ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( convergent_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(471,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( unorthogonal_lines @ SV62 @ SV76 )
= $false )
| ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( convergent_lines @ SV46 @ SV62 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(472,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( unorthogonal_lines @ SV62 @ SV76 )
= $false )
| ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( convergent_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(473,plain,
! [SV46: $i,SV76: $i,SV62: $i] :
( ( ( unorthogonal_lines @ SV62 @ SV76 )
= $false )
| ( ( convergent_lines @ SV62 @ SV76 )
= $false )
| ( ( unorthogonal_lines @ SV46 @ SV62 )
= $true )
| ( ( unorthogonal_lines @ SV46 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(474,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( convergent_lines @ SV68 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(475,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( unorthogonal_lines @ SV68 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(476,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( convergent_lines @ SV68 @ SV79 )
= $true )
| ( ( unorthogonal_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(477,plain,
! [SV52: $i,SV79: $i,SV68: $i] :
( ( ( unorthogonal_lines @ SV68 @ SV79 )
= $true )
| ( ( unorthogonal_lines @ SV52 @ SV79 )
= $true )
| ( ( convergent_lines @ SV52 @ SV68 )
= $false )
| ( ( unorthogonal_lines @ SV52 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(478,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[292,477,476,475,474,473,472,471,470,447,434,429,428,426,425,422,421,406,405,404,400,395,383,366,348,347,330,329,314,294,293]) ).
thf(479,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[478,273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n008.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 10:08:09 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.48/0.48
% 1.48/0.48 No.of.Axioms: 18
% 1.48/0.48
% 1.48/0.48 Length.of.Defs: 0
% 1.48/0.48
% 1.48/0.48 Contains.Choice.Funs: false
% 1.48/0.48 ...........
% 1.48/0.48
% 1.48/0.48 ********************************
% 1.48/0.48 * All subproblems solved! *
% 1.48/0.48 ********************************
% 1.48/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:21,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:478,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.48/0.48
% 1.48/0.48 %**** Beginning of derivation protocol ****
% 1.48/0.48 % SZS output start CNFRefutation
% See solution above
% 1.48/0.49
% 1.48/0.49 %**** End of derivation protocol ****
% 1.48/0.49 %**** no. of clauses in derivation: 462 ****
% 1.48/0.49 %**** clause counter: 478 ****
% 1.48/0.49
% 1.48/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:21,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:478,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------