TSTP Solution File: GEO182+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO182+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:08:01 EDT 2022
% Result : Theorem 0.37s 0.56s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 55
% Syntax : Number of formulae : 472 ( 280 unt; 19 typ; 0 def)
% Number of atoms : 2864 ( 665 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 4980 ( 723 ~; 969 |; 48 &;3176 @)
% ( 10 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-2 aty)
% Number of variables : 1230 ( 0 ^1230 !; 0 ?;1230 :)
% 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_SY84,type,
sK2_SY84: $i ).
thf(tp_sK3_SY86,type,
sK3_SY86: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( orthogonal_lines @ X @ Y )
<=> ~ ( unorthogonal_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ),
file('/export/starexec/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(4,axiom,
! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(6,axiom,
! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',orth1) ).
thf(7,axiom,
! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',par1) ).
thf(8,axiom,
! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
thf(10,axiom,
! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ),
file('/export/starexec/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(13,axiom,
! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
thf(14,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(15,axiom,
! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(16,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ),
file('/export/starexec/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(18,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
thf(19,axiom,
! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
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(23,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
thf(24,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
thf(25,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
thf(26,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ),
file('/export/starexec/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(28,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
thf(29,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
thf(30,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(31,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
thf(32,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
thf(33,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(34,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(35,axiom,
! [X: $i] :
~ ( distinct_points @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(36,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
=> ( apart_point_and_line @ Z @ ( line_connecting @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(37,negated_conjecture,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
=> ( apart_point_and_line @ Z @ ( line_connecting @ Y @ X ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
=> ( apart_point_and_line @ Z @ ( line_connecting @ Y @ X ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( orthogonal_lines @ X @ Y )
<=> ~ ( unorthogonal_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(45,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(46,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(48,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(49,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(50,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,plain,
( ( ! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(52,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(53,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(54,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(55,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(71,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(72,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(73,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(74,plain,
( ( ! [SY84: $i,SY85: $i] :
( ( distinct_points @ sK1_X @ SY84 )
=> ( ( apart_point_and_line @ SY85 @ ( line_connecting @ sK1_X @ SY84 ) )
=> ( apart_point_and_line @ SY85 @ ( line_connecting @ SY84 @ sK1_X ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(75,plain,
( ( ! [SY86: $i] :
( ( distinct_points @ sK1_X @ sK2_SY84 )
=> ( ( apart_point_and_line @ SY86 @ ( line_connecting @ sK1_X @ sK2_SY84 ) )
=> ( apart_point_and_line @ SY86 @ ( line_connecting @ sK2_SY84 @ sK1_X ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(76,plain,
( ( ( distinct_points @ sK1_X @ sK2_SY84 )
=> ( ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK1_X @ sK2_SY84 ) )
=> ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK2_SY84 @ sK1_X ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(77,plain,
( ( distinct_points @ sK1_X @ sK2_SY84 )
= $true ),
inference(standard_cnf,[status(thm)],[76]) ).
thf(78,plain,
( ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK1_X @ sK2_SY84 ) )
= $true ),
inference(standard_cnf,[status(thm)],[76]) ).
thf(79,plain,
( ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK2_SY84 @ sK1_X ) )
= $false ),
inference(standard_cnf,[status(thm)],[76]) ).
thf(80,plain,
( ( ~ ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK2_SY84 @ sK1_X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[79]) ).
thf(81,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( orthogonal_lines @ X @ Y )
| ~ ( unorthogonal_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unorthogonal_lines @ X @ Y )
| ( orthogonal_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(82,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( incident_point_and_line @ X @ Y )
| ~ ( apart_point_and_line @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( apart_point_and_line @ X @ Y )
| ( incident_point_and_line @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(83,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( parallel_lines @ X @ Y )
| ~ ( convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
| ( parallel_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_lines @ X @ Y )
| ~ ( distinct_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
| ( equal_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_points @ X @ Y )
| ~ ( distinct_points @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
| ( equal_points @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(86,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(87,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(88,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( convergent_lines @ L @ M )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(90,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(91,plain,
( ( ! [L: $i] :
( ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(92,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(93,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ M @ N )
| ( unorthogonal_lines @ L @ N )
| ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(94,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(95,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( distinct_lines @ Y @ Z )
| ( convergent_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(96,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(98,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(99,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(106,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(108,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(109,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(110,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( distinct_lines @ Y @ Z )
| ( convergent_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(126,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(127,plain,
( ( ! [L: $i] :
( ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( convergent_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( convergent_lines @ M @ N ) ) )
& ! [M: $i] :
( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(128,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(129,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(130,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ~ ( distinct_lines @ L @ M )
| ! [N: $i] :
( ( unorthogonal_lines @ M @ N )
| ( unorthogonal_lines @ L @ N )
| ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(131,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(132,plain,
( ( ! [L: $i] :
( ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( convergent_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) )
& ! [M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(133,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unorthogonal_lines @ L @ M )
| ( unorthogonal_lines @ L @ N )
| ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ~ ( point @ A )
| ~ ( point @ B )
| ~ ( distinct_points @ A @ B )
| ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(135,plain,
( ( ! [L: $i,M: $i] :
( ~ ( line @ L )
| ~ ( line @ M )
| ~ ( convergent_lines @ L @ M )
| ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(136,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(137,plain,
( ( ! [L: $i,A: $i] :
( ~ ( line @ L )
| ~ ( point @ A )
| ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(138,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_points @ X @ Y )
| ~ ( distinct_points @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
| ( equal_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(139,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_lines @ X @ Y )
| ~ ( distinct_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
| ( equal_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(140,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( parallel_lines @ X @ Y )
| ~ ( convergent_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
| ( parallel_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( incident_point_and_line @ X @ Y )
| ~ ( apart_point_and_line @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( apart_point_and_line @ X @ Y )
| ( incident_point_and_line @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(142,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( orthogonal_lines @ X @ Y )
| ~ ( unorthogonal_lines @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( unorthogonal_lines @ X @ Y )
| ( orthogonal_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(143,plain,
( ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK1_X @ sK2_SY84 ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(144,plain,
( ( distinct_points @ sK1_X @ sK2_SY84 )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(145,plain,
( ( ~ ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK2_SY84 @ sK1_X ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(146,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(147,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(148,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( unorthogonal_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( unorthogonal_lines @ SX0 @ SX2 )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(149,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( convergent_lines @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ( unorthogonal_lines @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(150,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(151,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(152,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(153,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(154,plain,
! [SV2: $i] :
( ( ~ ( distinct_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(155,plain,
! [SV3: $i] :
( ( ~ ( convergent_lines @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(156,plain,
! [SV4: $i] :
( ( ! [SY87: $i] :
( ~ ( distinct_points @ SV4 @ SY87 )
| ! [SY88: $i] :
( ( distinct_points @ SV4 @ SY88 )
| ( distinct_points @ SY87 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(157,plain,
! [SV5: $i] :
( ( ! [SY89: $i] :
( ~ ( distinct_lines @ SV5 @ SY89 )
| ! [SY90: $i] :
( ( distinct_lines @ SV5 @ SY90 )
| ( distinct_lines @ SY89 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(158,plain,
! [SV6: $i] :
( ( ! [SY91: $i] :
( ~ ( convergent_lines @ SV6 @ SY91 )
| ! [SY92: $i] :
( ( convergent_lines @ SV6 @ SY92 )
| ( convergent_lines @ SY91 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(159,plain,
! [SV7: $i] :
( ( ! [SY93: $i] :
( ~ ( distinct_points @ SV7 @ SY93 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(160,plain,
! [SV8: $i] :
( ( ! [SY94: $i] :
( ~ ( distinct_points @ SV8 @ SY94 )
| ~ ( apart_point_and_line @ SY94 @ ( line_connecting @ SV8 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(161,plain,
! [SV9: $i] :
( ( ! [SY95: $i] :
( ~ ( convergent_lines @ SV9 @ SY95 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SY95 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(162,plain,
! [SV10: $i] :
( ( ! [SY96: $i] :
( ~ ( convergent_lines @ SV10 @ SY96 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SY96 ) @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(163,plain,
! [SV11: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i] :
( ~ ( distinct_lines @ SY98 @ SY99 )
| ~ ( distinct_points @ SV11 @ SY97 )
| ( apart_point_and_line @ SY97 @ SY99 )
| ( apart_point_and_line @ SY97 @ SY98 )
| ( apart_point_and_line @ SV11 @ SY98 )
| ( apart_point_and_line @ SV11 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(164,plain,
! [SV12: $i] :
( ( ! [SY100: $i] :
( ~ ( apart_point_and_line @ SV12 @ SY100 )
| ! [SY101: $i] :
( ( apart_point_and_line @ SY101 @ SY100 )
| ( distinct_points @ SV12 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(165,plain,
! [SV13: $i] :
( ( ! [SY102: $i] :
( ~ ( apart_point_and_line @ SV13 @ SY102 )
| ! [SY103: $i] :
( ( apart_point_and_line @ SV13 @ SY103 )
| ( distinct_lines @ SY102 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(166,plain,
! [SV14: $i] :
( ( ! [SY104: $i] :
( ~ ( convergent_lines @ SV14 @ SY104 )
| ! [SY105: $i] :
( ( convergent_lines @ SV14 @ SY105 )
| ( distinct_lines @ SY104 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(167,plain,
! [SV15: $i] :
( ( ! [SY106: $i] :
( ~ ( distinct_lines @ SV15 @ SY106 )
| ( convergent_lines @ SV15 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(168,plain,
! [SV16: $i] :
( ( ! [SY107: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY107 @ SV16 ) @ SY107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(169,plain,
! [SV17: $i] :
( ( ! [SY108: $i] :
~ ( apart_point_and_line @ SV17 @ ( parallel_through_point @ SY108 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(170,plain,
! [SV18: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( distinct_lines @ SY109 @ SY110 )
| ( convergent_lines @ SY109 @ SY110 )
| ( apart_point_and_line @ SV18 @ SY109 )
| ( apart_point_and_line @ SV18 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(171,plain,
! [SV19: $i] :
( ( ! [SY111: $i] :
( ( convergent_lines @ SV19 @ SY111 )
| ( unorthogonal_lines @ SV19 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(172,plain,
! [SV20: $i] :
( ( ! [SY112: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ SY112 @ SV20 ) @ SY112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(173,plain,
! [SV21: $i] :
( ( ! [SY113: $i] :
~ ( apart_point_and_line @ SV21 @ ( orthogonal_through_point @ SY113 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(174,plain,
! [SV22: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( distinct_lines @ SY114 @ SY115 )
| ! [SY116: $i] :
( ( unorthogonal_lines @ SY115 @ SY116 )
| ( unorthogonal_lines @ SY114 @ SY116 )
| ( apart_point_and_line @ SV22 @ SY114 )
| ( apart_point_and_line @ SV22 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(175,plain,
! [SV23: $i] :
( ( ! [SY117: $i] :
( ( convergent_lines @ SV23 @ SY117 )
| ( unorthogonal_lines @ SV23 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(176,plain,
! [SV24: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ( unorthogonal_lines @ SV24 @ SY118 )
| ( unorthogonal_lines @ SV24 @ SY119 )
| ~ ( convergent_lines @ SY118 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(177,plain,
! [SV25: $i] :
( ( ! [SY120: $i] :
( ~ ( point @ SV25 )
| ~ ( point @ SY120 )
| ~ ( distinct_points @ SV25 @ SY120 )
| ( line @ ( line_connecting @ SV25 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(178,plain,
! [SV26: $i] :
( ( ! [SY121: $i] :
( ~ ( line @ SV26 )
| ~ ( line @ SY121 )
| ~ ( convergent_lines @ SV26 @ SY121 )
| ( point @ ( intersection_point @ SV26 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(179,plain,
! [SV27: $i] :
( ( ! [SY122: $i] :
( ~ ( line @ SV27 )
| ~ ( point @ SY122 )
| ( line @ ( parallel_through_point @ SV27 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(180,plain,
! [SV28: $i] :
( ( ! [SY123: $i] :
( ~ ( line @ SV28 )
| ~ ( point @ SY123 )
| ( line @ ( orthogonal_through_point @ SV28 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(181,plain,
( ( apart_point_and_line @ sK3_SY86 @ ( line_connecting @ sK2_SY84 @ sK1_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(182,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(183,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(184,plain,
! [SV29: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(185,plain,
! [SV30: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) )
| ~ ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(186,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(187,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(188,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(189,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(190,plain,
! [SV2: $i] :
( ( distinct_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(191,plain,
! [SV3: $i] :
( ( convergent_lines @ SV3 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(192,plain,
! [SV31: $i,SV4: $i] :
( ( ~ ( distinct_points @ SV4 @ SV31 )
| ! [SY140: $i] :
( ( distinct_points @ SV4 @ SY140 )
| ( distinct_points @ SV31 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(193,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( distinct_lines @ SV5 @ SV32 )
| ! [SY141: $i] :
( ( distinct_lines @ SV5 @ SY141 )
| ( distinct_lines @ SV32 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(194,plain,
! [SV33: $i,SV6: $i] :
( ( ~ ( convergent_lines @ SV6 @ SV33 )
| ! [SY142: $i] :
( ( convergent_lines @ SV6 @ SY142 )
| ( convergent_lines @ SV33 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(195,plain,
! [SV34: $i,SV7: $i] :
( ( ~ ( distinct_points @ SV7 @ SV34 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(196,plain,
! [SV35: $i,SV8: $i] :
( ( ~ ( distinct_points @ SV8 @ SV35 )
| ~ ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(197,plain,
! [SV36: $i,SV9: $i] :
( ( ~ ( convergent_lines @ SV9 @ SV36 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(198,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( convergent_lines @ SV10 @ SV37 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(199,plain,
! [SV38: $i,SV11: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ~ ( distinct_lines @ SY143 @ SY144 )
| ~ ( distinct_points @ SV11 @ SV38 )
| ( apart_point_and_line @ SV38 @ SY144 )
| ( apart_point_and_line @ SV38 @ SY143 )
| ( apart_point_and_line @ SV11 @ SY143 )
| ( apart_point_and_line @ SV11 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(200,plain,
! [SV39: $i,SV12: $i] :
( ( ~ ( apart_point_and_line @ SV12 @ SV39 )
| ! [SY145: $i] :
( ( apart_point_and_line @ SY145 @ SV39 )
| ( distinct_points @ SV12 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(201,plain,
! [SV40: $i,SV13: $i] :
( ( ~ ( apart_point_and_line @ SV13 @ SV40 )
| ! [SY146: $i] :
( ( apart_point_and_line @ SV13 @ SY146 )
| ( distinct_lines @ SV40 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(202,plain,
! [SV41: $i,SV14: $i] :
( ( ~ ( convergent_lines @ SV14 @ SV41 )
| ! [SY147: $i] :
( ( convergent_lines @ SV14 @ SY147 )
| ( distinct_lines @ SV41 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(203,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( distinct_lines @ SV15 @ SV42 )
| ( convergent_lines @ SV15 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(204,plain,
! [SV16: $i,SV43: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV43 @ SV16 ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(205,plain,
! [SV44: $i,SV17: $i] :
( ( ~ ( apart_point_and_line @ SV17 @ ( parallel_through_point @ SV44 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(206,plain,
! [SV18: $i,SV45: $i] :
( ( ! [SY148: $i] :
( ~ ( distinct_lines @ SV45 @ SY148 )
| ( convergent_lines @ SV45 @ SY148 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(207,plain,
! [SV46: $i,SV19: $i] :
( ( ( convergent_lines @ SV19 @ SV46 )
| ( unorthogonal_lines @ SV19 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(208,plain,
! [SV20: $i,SV47: $i] :
( ( ~ ( unorthogonal_lines @ ( orthogonal_through_point @ SV47 @ SV20 ) @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(209,plain,
! [SV48: $i,SV21: $i] :
( ( ~ ( apart_point_and_line @ SV21 @ ( orthogonal_through_point @ SV48 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(210,plain,
! [SV22: $i,SV49: $i] :
( ( ! [SY149: $i] :
( ~ ( distinct_lines @ SV49 @ SY149 )
| ! [SY150: $i] :
( ( unorthogonal_lines @ SY149 @ SY150 )
| ( unorthogonal_lines @ SV49 @ SY150 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(211,plain,
! [SV50: $i,SV23: $i] :
( ( ( convergent_lines @ SV23 @ SV50 )
| ( unorthogonal_lines @ SV23 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(212,plain,
! [SV51: $i,SV24: $i] :
( ( ! [SY151: $i] :
( ( unorthogonal_lines @ SV24 @ SV51 )
| ( unorthogonal_lines @ SV24 @ SY151 )
| ~ ( convergent_lines @ SV51 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(213,plain,
! [SV52: $i,SV25: $i] :
( ( ~ ( point @ SV25 )
| ~ ( point @ SV52 )
| ~ ( distinct_points @ SV25 @ SV52 )
| ( line @ ( line_connecting @ SV25 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(214,plain,
! [SV53: $i,SV26: $i] :
( ( ~ ( line @ SV26 )
| ~ ( line @ SV53 )
| ~ ( convergent_lines @ SV26 @ SV53 )
| ( point @ ( intersection_point @ SV26 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(215,plain,
! [SV54: $i,SV27: $i] :
( ( ~ ( line @ SV27 )
| ~ ( point @ SV54 )
| ( line @ ( parallel_through_point @ SV27 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(216,plain,
! [SV55: $i,SV28: $i] :
( ( ~ ( line @ SV28 )
| ~ ( point @ SV55 )
| ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(217,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(218,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(219,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(220,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(221,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(222,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) )
| ~ ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(223,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(224,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(225,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(227,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(228,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(229,plain,
! [SV31: $i,SV4: $i] :
( ( ( ~ ( distinct_points @ SV4 @ SV31 ) )
= $true )
| ( ( ! [SY140: $i] :
( ( distinct_points @ SV4 @ SY140 )
| ( distinct_points @ SV31 @ SY140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV32: $i,SV5: $i] :
( ( ( ~ ( distinct_lines @ SV5 @ SV32 ) )
= $true )
| ( ( ! [SY141: $i] :
( ( distinct_lines @ SV5 @ SY141 )
| ( distinct_lines @ SV32 @ SY141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(231,plain,
! [SV33: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV33 ) )
= $true )
| ( ( ! [SY142: $i] :
( ( convergent_lines @ SV6 @ SY142 )
| ( convergent_lines @ SV33 @ SY142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(232,plain,
! [SV34: $i,SV7: $i] :
( ( ( ~ ( distinct_points @ SV7 @ SV34 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(233,plain,
! [SV35: $i,SV8: $i] :
( ( ( ~ ( distinct_points @ SV8 @ SV35 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(234,plain,
! [SV36: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV36 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(235,plain,
! [SV37: $i,SV10: $i] :
( ( ( ~ ( convergent_lines @ SV10 @ SV37 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(236,plain,
! [SV38: $i,SV11: $i,SV56: $i] :
( ( ! [SY152: $i] :
( ~ ( distinct_lines @ SV56 @ SY152 )
| ~ ( distinct_points @ SV11 @ SV38 )
| ( apart_point_and_line @ SV38 @ SY152 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(237,plain,
! [SV39: $i,SV12: $i] :
( ( ( ~ ( apart_point_and_line @ SV12 @ SV39 ) )
= $true )
| ( ( ! [SY145: $i] :
( ( apart_point_and_line @ SY145 @ SV39 )
| ( distinct_points @ SV12 @ SY145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(238,plain,
! [SV40: $i,SV13: $i] :
( ( ( ~ ( apart_point_and_line @ SV13 @ SV40 ) )
= $true )
| ( ( ! [SY146: $i] :
( ( apart_point_and_line @ SV13 @ SY146 )
| ( distinct_lines @ SV40 @ SY146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(239,plain,
! [SV41: $i,SV14: $i] :
( ( ( ~ ( convergent_lines @ SV14 @ SV41 ) )
= $true )
| ( ( ! [SY147: $i] :
( ( convergent_lines @ SV14 @ SY147 )
| ( distinct_lines @ SV41 @ SY147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(240,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( distinct_lines @ SV15 @ SV42 ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV16: $i,SV43: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV43 @ SV16 ) @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV44: $i,SV17: $i] :
( ( apart_point_and_line @ SV17 @ ( parallel_through_point @ SV44 @ SV17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ~ ( distinct_lines @ SV45 @ SV57 )
| ( convergent_lines @ SV45 @ SV57 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV46: $i,SV19: $i] :
( ( ( convergent_lines @ SV19 @ SV46 )
= $true )
| ( ( unorthogonal_lines @ SV19 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV20: $i,SV47: $i] :
( ( unorthogonal_lines @ ( orthogonal_through_point @ SV47 @ SV20 ) @ SV47 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV48: $i,SV21: $i] :
( ( apart_point_and_line @ SV21 @ ( orthogonal_through_point @ SV48 @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV22: $i,SV58: $i,SV49: $i] :
( ( ~ ( distinct_lines @ SV49 @ SV58 )
| ! [SY153: $i] :
( ( unorthogonal_lines @ SV58 @ SY153 )
| ( unorthogonal_lines @ SV49 @ SY153 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(248,plain,
! [SV50: $i,SV23: $i] :
( ( ( convergent_lines @ SV23 @ SV50 )
= $true )
| ( ( unorthogonal_lines @ SV23 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(249,plain,
! [SV59: $i,SV51: $i,SV24: $i] :
( ( ( unorthogonal_lines @ SV24 @ SV51 )
| ( unorthogonal_lines @ SV24 @ SV59 )
| ~ ( convergent_lines @ SV51 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(250,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 )
| ~ ( point @ SV52 )
| ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(251,plain,
! [SV53: $i,SV26: $i] :
( ( ( ~ ( line @ SV26 )
| ~ ( line @ SV53 )
| ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(252,plain,
! [SV54: $i,SV27: $i] :
( ( ( ~ ( line @ SV27 )
| ~ ( point @ SV54 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(253,plain,
! [SV55: $i,SV28: $i] :
( ( ( ~ ( line @ SV28 )
| ~ ( point @ SV55 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(254,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(255,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(256,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(257,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(258,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(259,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(260,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) )
| ~ ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(261,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(262,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( orthogonal_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(263,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( unorthogonal_lines @ SX0 @ SX1 )
| ( orthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(264,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(265,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(266,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(267,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(268,plain,
! [SV31: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV31 )
= $false )
| ( ( ! [SY140: $i] :
( ( distinct_points @ SV4 @ SY140 )
| ( distinct_points @ SV31 @ SY140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(269,plain,
! [SV32: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV32 )
= $false )
| ( ( ! [SY141: $i] :
( ( distinct_lines @ SV5 @ SY141 )
| ( distinct_lines @ SV32 @ SY141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(270,plain,
! [SV33: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV33 )
= $false )
| ( ( ! [SY142: $i] :
( ( convergent_lines @ SV6 @ SY142 )
| ( convergent_lines @ SV33 @ SY142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(271,plain,
! [SV34: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV34 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(272,plain,
! [SV35: $i,SV8: $i] :
( ( ( distinct_points @ SV8 @ SV35 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(273,plain,
! [SV36: $i,SV9: $i] :
( ( ( convergent_lines @ SV9 @ SV36 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(274,plain,
! [SV37: $i,SV10: $i] :
( ( ( convergent_lines @ SV10 @ SV37 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(275,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ~ ( distinct_lines @ SV56 @ SV60 )
| ~ ( distinct_points @ SV11 @ SV38 )
| ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(276,plain,
! [SV39: $i,SV12: $i] :
( ( ( apart_point_and_line @ SV12 @ SV39 )
= $false )
| ( ( ! [SY145: $i] :
( ( apart_point_and_line @ SY145 @ SV39 )
| ( distinct_points @ SV12 @ SY145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(277,plain,
! [SV40: $i,SV13: $i] :
( ( ( apart_point_and_line @ SV13 @ SV40 )
= $false )
| ( ( ! [SY146: $i] :
( ( apart_point_and_line @ SV13 @ SY146 )
| ( distinct_lines @ SV40 @ SY146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(278,plain,
! [SV41: $i,SV14: $i] :
( ( ( convergent_lines @ SV14 @ SV41 )
= $false )
| ( ( ! [SY147: $i] :
( ( convergent_lines @ SV14 @ SY147 )
| ( distinct_lines @ SV41 @ SY147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(279,plain,
! [SV42: $i,SV15: $i] :
( ( ( distinct_lines @ SV15 @ SV42 )
= $false )
| ( ( convergent_lines @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(280,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ( ~ ( distinct_lines @ SV45 @ SV57 ) )
= $true )
| ( ( ( convergent_lines @ SV45 @ SV57 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(281,plain,
! [SV22: $i,SV58: $i,SV49: $i] :
( ( ( ~ ( distinct_lines @ SV49 @ SV58 ) )
= $true )
| ( ( ! [SY153: $i] :
( ( unorthogonal_lines @ SV58 @ SY153 )
| ( unorthogonal_lines @ SV49 @ SY153 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(282,plain,
! [SV59: $i,SV51: $i,SV24: $i] :
( ( ( ( unorthogonal_lines @ SV24 @ SV51 )
| ( unorthogonal_lines @ SV24 @ SV59 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV51 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(283,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 )
| ~ ( point @ SV52 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(284,plain,
! [SV53: $i,SV26: $i] :
( ( ( ~ ( line @ SV26 )
| ~ ( line @ SV53 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(285,plain,
! [SV54: $i,SV27: $i] :
( ( ( ~ ( line @ SV27 ) )
= $true )
| ( ( ~ ( point @ SV54 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(286,plain,
! [SV55: $i,SV28: $i] :
( ( ( ~ ( line @ SV28 ) )
= $true )
| ( ( ~ ( point @ SV55 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(287,plain,
! [SV61: $i] :
( ( ! [SY154: $i] :
( ~ ( equal_lines @ SV61 @ SY154 )
| ~ ( distinct_lines @ SV61 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(288,plain,
! [SV62: $i] :
( ( ! [SY155: $i] :
( ( distinct_lines @ SV62 @ SY155 )
| ( equal_lines @ SV62 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(289,plain,
! [SV63: $i] :
( ( ! [SY156: $i] :
( ~ ( equal_points @ SV63 @ SY156 )
| ~ ( distinct_points @ SV63 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(290,plain,
! [SV64: $i] :
( ( ! [SY157: $i] :
( ( distinct_points @ SV64 @ SY157 )
| ( equal_points @ SV64 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(291,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(292,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(293,plain,
! [SV30: $i] :
( ( ~ ( ~ ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) )
| ~ ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(294,plain,
! [SV30: $i] :
( ( ~ ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(295,plain,
! [SV65: $i] :
( ( ! [SY158: $i] :
( ~ ( orthogonal_lines @ SV65 @ SY158 )
| ~ ( unorthogonal_lines @ SV65 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(296,plain,
! [SV66: $i] :
( ( ! [SY159: $i] :
( ( unorthogonal_lines @ SV66 @ SY159 )
| ( orthogonal_lines @ SV66 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(297,plain,
! [SV67: $i] :
( ( ! [SY160: $i] :
( ~ ( parallel_lines @ SV67 @ SY160 )
| ~ ( convergent_lines @ SV67 @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(298,plain,
! [SV68: $i] :
( ( ! [SY161: $i] :
( ( convergent_lines @ SV68 @ SY161 )
| ( parallel_lines @ SV68 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(299,plain,
! [SV69: $i] :
( ( ! [SY162: $i] :
( ~ ( incident_point_and_line @ SV69 @ SY162 )
| ~ ( apart_point_and_line @ SV69 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(300,plain,
! [SV70: $i] :
( ( ! [SY163: $i] :
( ( apart_point_and_line @ SV70 @ SY163 )
| ( incident_point_and_line @ SV70 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(301,plain,
! [SV31: $i,SV71: $i,SV4: $i] :
( ( ( ( distinct_points @ SV4 @ SV71 )
| ( distinct_points @ SV31 @ SV71 ) )
= $true )
| ( ( distinct_points @ SV4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(302,plain,
! [SV32: $i,SV72: $i,SV5: $i] :
( ( ( ( distinct_lines @ SV5 @ SV72 )
| ( distinct_lines @ SV32 @ SV72 ) )
= $true )
| ( ( distinct_lines @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(303,plain,
! [SV33: $i,SV73: $i,SV6: $i] :
( ( ( ( convergent_lines @ SV6 @ SV73 )
| ( convergent_lines @ SV33 @ SV73 ) )
= $true )
| ( ( convergent_lines @ SV6 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(304,plain,
! [SV34: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV34 ) )
= $false )
| ( ( distinct_points @ SV7 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(305,plain,
! [SV8: $i,SV35: $i] :
( ( ( apart_point_and_line @ SV35 @ ( line_connecting @ SV8 @ SV35 ) )
= $false )
| ( ( distinct_points @ SV8 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(306,plain,
! [SV36: $i,SV9: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV9 @ SV36 ) @ SV9 )
= $false )
| ( ( convergent_lines @ SV9 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(307,plain,
! [SV37: $i,SV10: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV10 @ SV37 ) @ SV37 )
= $false )
| ( ( convergent_lines @ SV10 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(308,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ( ~ ( distinct_lines @ SV56 @ SV60 )
| ~ ( distinct_points @ SV11 @ SV38 ) )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(309,plain,
! [SV12: $i,SV39: $i,SV74: $i] :
( ( ( ( apart_point_and_line @ SV74 @ SV39 )
| ( distinct_points @ SV12 @ SV74 ) )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(310,plain,
! [SV40: $i,SV75: $i,SV13: $i] :
( ( ( ( apart_point_and_line @ SV13 @ SV75 )
| ( distinct_lines @ SV40 @ SV75 ) )
= $true )
| ( ( apart_point_and_line @ SV13 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(311,plain,
! [SV41: $i,SV76: $i,SV14: $i] :
( ( ( ( convergent_lines @ SV14 @ SV76 )
| ( distinct_lines @ SV41 @ SV76 ) )
= $true )
| ( ( convergent_lines @ SV14 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(312,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ( distinct_lines @ SV45 @ SV57 )
= $false )
| ( ( ( convergent_lines @ SV45 @ SV57 )
| ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(313,plain,
! [SV22: $i,SV58: $i,SV49: $i] :
( ( ( distinct_lines @ SV49 @ SV58 )
= $false )
| ( ( ! [SY153: $i] :
( ( unorthogonal_lines @ SV58 @ SY153 )
| ( unorthogonal_lines @ SV49 @ SY153 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(314,plain,
! [SV59: $i,SV51: $i,SV24: $i] :
( ( ( unorthogonal_lines @ SV24 @ SV51 )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV59 )
= $true )
| ( ( ~ ( convergent_lines @ SV51 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(315,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( point @ SV25 ) )
= $true )
| ( ( ~ ( point @ SV52 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(316,plain,
! [SV53: $i,SV26: $i] :
( ( ( ~ ( line @ SV26 ) )
= $true )
| ( ( ~ ( line @ SV53 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(317,plain,
! [SV54: $i,SV27: $i] :
( ( ( line @ SV27 )
= $false )
| ( ( ~ ( point @ SV54 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(318,plain,
! [SV55: $i,SV28: $i] :
( ( ( line @ SV28 )
= $false )
| ( ( ~ ( point @ SV55 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(319,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ( equal_lines @ SV61 @ SV77 )
| ~ ( distinct_lines @ SV61 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(320,plain,
! [SV78: $i,SV62: $i] :
( ( ( distinct_lines @ SV62 @ SV78 )
| ( equal_lines @ SV62 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV79: $i,SV63: $i] :
( ( ~ ( equal_points @ SV63 @ SV79 )
| ~ ( distinct_points @ SV63 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV80: $i,SV64: $i] :
( ( ( distinct_points @ SV64 @ SV80 )
| ( equal_points @ SV64 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(323,plain,
! [SV29: $i] :
( ( ~ ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(324,plain,
! [SV29: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) )
| ~ ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(325,plain,
! [SV30: $i] :
( ( ~ ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) )
| ~ ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(326,plain,
! [SV30: $i] :
( ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(327,plain,
! [SV81: $i,SV65: $i] :
( ( ~ ( orthogonal_lines @ SV65 @ SV81 )
| ~ ( unorthogonal_lines @ SV65 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(328,plain,
! [SV82: $i,SV66: $i] :
( ( ( unorthogonal_lines @ SV66 @ SV82 )
| ( orthogonal_lines @ SV66 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(329,plain,
! [SV83: $i,SV67: $i] :
( ( ~ ( parallel_lines @ SV67 @ SV83 )
| ~ ( convergent_lines @ SV67 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(330,plain,
! [SV84: $i,SV68: $i] :
( ( ( convergent_lines @ SV68 @ SV84 )
| ( parallel_lines @ SV68 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(331,plain,
! [SV85: $i,SV69: $i] :
( ( ~ ( incident_point_and_line @ SV69 @ SV85 )
| ~ ( apart_point_and_line @ SV69 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(332,plain,
! [SV86: $i,SV70: $i] :
( ( ( apart_point_and_line @ SV70 @ SV86 )
| ( incident_point_and_line @ SV70 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(333,plain,
! [SV31: $i,SV71: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV71 )
= $true )
| ( ( distinct_points @ SV31 @ SV71 )
= $true )
| ( ( distinct_points @ SV4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(334,plain,
! [SV32: $i,SV72: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV72 )
= $true )
| ( ( distinct_lines @ SV32 @ SV72 )
= $true )
| ( ( distinct_lines @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(335,plain,
! [SV33: $i,SV73: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV73 )
= $true )
| ( ( convergent_lines @ SV33 @ SV73 )
= $true )
| ( ( convergent_lines @ SV6 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(336,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ( ~ ( distinct_lines @ SV56 @ SV60 ) )
= $true )
| ( ( ~ ( distinct_points @ SV11 @ SV38 ) )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(337,plain,
! [SV12: $i,SV39: $i,SV74: $i] :
( ( ( apart_point_and_line @ SV74 @ SV39 )
= $true )
| ( ( distinct_points @ SV12 @ SV74 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(338,plain,
! [SV40: $i,SV75: $i,SV13: $i] :
( ( ( apart_point_and_line @ SV13 @ SV75 )
= $true )
| ( ( distinct_lines @ SV40 @ SV75 )
= $true )
| ( ( apart_point_and_line @ SV13 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(339,plain,
! [SV41: $i,SV76: $i,SV14: $i] :
( ( ( convergent_lines @ SV14 @ SV76 )
= $true )
| ( ( distinct_lines @ SV41 @ SV76 )
= $true )
| ( ( convergent_lines @ SV14 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(340,plain,
! [SV18: $i,SV57: $i,SV45: $i] :
( ( ( convergent_lines @ SV45 @ SV57 )
= $true )
| ( ( ( apart_point_and_line @ SV18 @ SV45 )
| ( apart_point_and_line @ SV18 @ SV57 ) )
= $true )
| ( ( distinct_lines @ SV45 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(341,plain,
! [SV22: $i,SV49: $i,SV87: $i,SV58: $i] :
( ( ( ( unorthogonal_lines @ SV58 @ SV87 )
| ( unorthogonal_lines @ SV49 @ SV87 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(342,plain,
! [SV24: $i,SV59: $i,SV51: $i] :
( ( ( convergent_lines @ SV51 @ SV59 )
= $false )
| ( ( unorthogonal_lines @ SV24 @ SV59 )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(343,plain,
! [SV52: $i,SV25: $i] :
( ( ( point @ SV25 )
= $false )
| ( ( ~ ( point @ SV52 ) )
= $true )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(344,plain,
! [SV53: $i,SV26: $i] :
( ( ( line @ SV26 )
= $false )
| ( ( ~ ( line @ SV53 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(345,plain,
! [SV27: $i,SV54: $i] :
( ( ( point @ SV54 )
= $false )
| ( ( line @ SV27 )
= $false )
| ( ( line @ ( parallel_through_point @ SV27 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(346,plain,
! [SV28: $i,SV55: $i] :
( ( ( point @ SV55 )
= $false )
| ( ( line @ SV28 )
= $false )
| ( ( line @ ( orthogonal_through_point @ SV28 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(347,plain,
! [SV77: $i,SV61: $i] :
( ( ( ~ ( equal_lines @ SV61 @ SV77 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(348,plain,
! [SV78: $i,SV62: $i] :
( ( ( distinct_lines @ SV62 @ SV78 )
= $true )
| ( ( equal_lines @ SV62 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(349,plain,
! [SV79: $i,SV63: $i] :
( ( ( ~ ( equal_points @ SV63 @ SV79 ) )
= $true )
| ( ( ~ ( distinct_points @ SV63 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(350,plain,
! [SV80: $i,SV64: $i] :
( ( ( distinct_points @ SV64 @ SV80 )
= $true )
| ( ( equal_points @ SV64 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(351,plain,
! [SV29: $i] :
( ( ~ ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(352,plain,
! [SV29: $i] :
( ( ~ ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(353,plain,
! [SV29: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(354,plain,
! [SV29: $i] :
( ( ~ ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(355,plain,
! [SV30: $i] :
( ( ~ ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(356,plain,
! [SV30: $i] :
( ( ~ ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(357,plain,
! [SV30: $i] :
( ( ~ ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(358,plain,
! [SV30: $i] :
( ( ~ ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(359,plain,
! [SV81: $i,SV65: $i] :
( ( ( ~ ( orthogonal_lines @ SV65 @ SV81 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV65 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(360,plain,
! [SV82: $i,SV66: $i] :
( ( ( unorthogonal_lines @ SV66 @ SV82 )
= $true )
| ( ( orthogonal_lines @ SV66 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(361,plain,
! [SV83: $i,SV67: $i] :
( ( ( ~ ( parallel_lines @ SV67 @ SV83 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV67 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(362,plain,
! [SV84: $i,SV68: $i] :
( ( ( convergent_lines @ SV68 @ SV84 )
= $true )
| ( ( parallel_lines @ SV68 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(363,plain,
! [SV85: $i,SV69: $i] :
( ( ( ~ ( incident_point_and_line @ SV69 @ SV85 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV69 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(364,plain,
! [SV86: $i,SV70: $i] :
( ( ( apart_point_and_line @ SV70 @ SV86 )
= $true )
| ( ( incident_point_and_line @ SV70 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(365,plain,
! [SV38: $i,SV11: $i,SV60: $i,SV56: $i] :
( ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( ~ ( distinct_points @ SV11 @ SV38 ) )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(366,plain,
! [SV57: $i,SV45: $i,SV18: $i] :
( ( ( apart_point_and_line @ SV18 @ SV45 )
= $true )
| ( ( apart_point_and_line @ SV18 @ SV57 )
= $true )
| ( ( convergent_lines @ SV45 @ SV57 )
= $true )
| ( ( distinct_lines @ SV45 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(367,plain,
! [SV22: $i,SV49: $i,SV87: $i,SV58: $i] :
( ( ( unorthogonal_lines @ SV58 @ SV87 )
= $true )
| ( ( ( unorthogonal_lines @ SV49 @ SV87 )
| ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(368,plain,
! [SV25: $i,SV52: $i] :
( ( ( point @ SV52 )
= $false )
| ( ( point @ SV25 )
= $false )
| ( ( ~ ( distinct_points @ SV25 @ SV52 ) )
= $true )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(369,plain,
! [SV26: $i,SV53: $i] :
( ( ( line @ SV53 )
= $false )
| ( ( line @ SV26 )
= $false )
| ( ( ~ ( convergent_lines @ SV26 @ SV53 ) )
= $true )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(370,plain,
! [SV77: $i,SV61: $i] :
( ( ( equal_lines @ SV61 @ SV77 )
= $false )
| ( ( ~ ( distinct_lines @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(371,plain,
! [SV79: $i,SV63: $i] :
( ( ( equal_points @ SV63 @ SV79 )
= $false )
| ( ( ~ ( distinct_points @ SV63 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(372,plain,
! [SV29: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ( convergent_lines @ SV29 @ SY124 )
| ( convergent_lines @ SV29 @ SY125 )
| ~ ( convergent_lines @ SY124 @ SY125 )
| ~ ( unorthogonal_lines @ SY124 @ SY125 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(373,plain,
! [SV29: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ( convergent_lines @ SV29 @ SY126 )
| ( unorthogonal_lines @ SV29 @ SY127 )
| ~ ( convergent_lines @ SY126 @ SY127 )
| ~ ( unorthogonal_lines @ SY126 @ SY127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(374,plain,
! [SV29: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ( unorthogonal_lines @ SV29 @ SY128 )
| ( convergent_lines @ SV29 @ SY129 )
| ~ ( convergent_lines @ SY128 @ SY129 )
| ~ ( unorthogonal_lines @ SY128 @ SY129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(375,plain,
! [SV29: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ( unorthogonal_lines @ SV29 @ SY130 )
| ( unorthogonal_lines @ SV29 @ SY131 )
| ~ ( convergent_lines @ SY130 @ SY131 )
| ~ ( unorthogonal_lines @ SY130 @ SY131 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(376,plain,
! [SV30: $i] :
( ( ! [SY132: $i] :
( ~ ( convergent_lines @ SV30 @ SY132 )
| ~ ( unorthogonal_lines @ SV30 @ SY132 )
| ! [SY133: $i] :
( ( convergent_lines @ SV30 @ SY133 )
| ( convergent_lines @ SY132 @ SY133 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(377,plain,
! [SV30: $i] :
( ( ! [SY134: $i] :
( ~ ( convergent_lines @ SV30 @ SY134 )
| ~ ( unorthogonal_lines @ SV30 @ SY134 )
| ! [SY135: $i] :
( ( convergent_lines @ SV30 @ SY135 )
| ( unorthogonal_lines @ SY134 @ SY135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(378,plain,
! [SV30: $i] :
( ( ! [SY136: $i] :
( ~ ( convergent_lines @ SV30 @ SY136 )
| ~ ( unorthogonal_lines @ SV30 @ SY136 )
| ! [SY137: $i] :
( ( unorthogonal_lines @ SV30 @ SY137 )
| ( convergent_lines @ SY136 @ SY137 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(379,plain,
! [SV30: $i] :
( ( ! [SY138: $i] :
( ~ ( convergent_lines @ SV30 @ SY138 )
| ~ ( unorthogonal_lines @ SV30 @ SY138 )
| ! [SY139: $i] :
( ( unorthogonal_lines @ SV30 @ SY139 )
| ( unorthogonal_lines @ SY138 @ SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(380,plain,
! [SV81: $i,SV65: $i] :
( ( ( orthogonal_lines @ SV65 @ SV81 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV65 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(381,plain,
! [SV83: $i,SV67: $i] :
( ( ( parallel_lines @ SV67 @ SV83 )
= $false )
| ( ( ~ ( convergent_lines @ SV67 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(382,plain,
! [SV85: $i,SV69: $i] :
( ( ( incident_point_and_line @ SV69 @ SV85 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV69 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(383,plain,
! [SV60: $i,SV56: $i,SV38: $i,SV11: $i] :
( ( ( distinct_points @ SV11 @ SV38 )
= $false )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( ( apart_point_and_line @ SV38 @ SV60 )
| ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(384,plain,
! [SV58: $i,SV22: $i,SV87: $i,SV49: $i] :
( ( ( unorthogonal_lines @ SV49 @ SV87 )
= $true )
| ( ( ( apart_point_and_line @ SV22 @ SV49 )
| ( apart_point_and_line @ SV22 @ SV58 ) )
= $true )
| ( ( unorthogonal_lines @ SV58 @ SV87 )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(385,plain,
! [SV52: $i,SV25: $i] :
( ( ( distinct_points @ SV25 @ SV52 )
= $false )
| ( ( point @ SV25 )
= $false )
| ( ( point @ SV52 )
= $false )
| ( ( line @ ( line_connecting @ SV25 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(386,plain,
! [SV53: $i,SV26: $i] :
( ( ( convergent_lines @ SV26 @ SV53 )
= $false )
| ( ( line @ SV26 )
= $false )
| ( ( line @ SV53 )
= $false )
| ( ( point @ ( intersection_point @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(387,plain,
! [SV77: $i,SV61: $i] :
( ( ( distinct_lines @ SV61 @ SV77 )
= $false )
| ( ( equal_lines @ SV61 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(388,plain,
! [SV79: $i,SV63: $i] :
( ( ( distinct_points @ SV63 @ SV79 )
= $false )
| ( ( equal_points @ SV63 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(389,plain,
! [SV88: $i,SV29: $i] :
( ( ! [SY164: $i] :
( ( convergent_lines @ SV29 @ SV88 )
| ( convergent_lines @ SV29 @ SY164 )
| ~ ( convergent_lines @ SV88 @ SY164 )
| ~ ( unorthogonal_lines @ SV88 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(390,plain,
! [SV89: $i,SV29: $i] :
( ( ! [SY165: $i] :
( ( convergent_lines @ SV29 @ SV89 )
| ( unorthogonal_lines @ SV29 @ SY165 )
| ~ ( convergent_lines @ SV89 @ SY165 )
| ~ ( unorthogonal_lines @ SV89 @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(391,plain,
! [SV90: $i,SV29: $i] :
( ( ! [SY166: $i] :
( ( unorthogonal_lines @ SV29 @ SV90 )
| ( convergent_lines @ SV29 @ SY166 )
| ~ ( convergent_lines @ SV90 @ SY166 )
| ~ ( unorthogonal_lines @ SV90 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(392,plain,
! [SV91: $i,SV29: $i] :
( ( ! [SY167: $i] :
( ( unorthogonal_lines @ SV29 @ SV91 )
| ( unorthogonal_lines @ SV29 @ SY167 )
| ~ ( convergent_lines @ SV91 @ SY167 )
| ~ ( unorthogonal_lines @ SV91 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(393,plain,
! [SV92: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV92 )
| ~ ( unorthogonal_lines @ SV30 @ SV92 )
| ! [SY168: $i] :
( ( convergent_lines @ SV30 @ SY168 )
| ( convergent_lines @ SV92 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(394,plain,
! [SV93: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV93 )
| ~ ( unorthogonal_lines @ SV30 @ SV93 )
| ! [SY169: $i] :
( ( convergent_lines @ SV30 @ SY169 )
| ( unorthogonal_lines @ SV93 @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(395,plain,
! [SV94: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV94 )
| ~ ( unorthogonal_lines @ SV30 @ SV94 )
| ! [SY170: $i] :
( ( unorthogonal_lines @ SV30 @ SY170 )
| ( convergent_lines @ SV94 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(396,plain,
! [SV95: $i,SV30: $i] :
( ( ~ ( convergent_lines @ SV30 @ SV95 )
| ~ ( unorthogonal_lines @ SV30 @ SV95 )
| ! [SY171: $i] :
( ( unorthogonal_lines @ SV30 @ SY171 )
| ( unorthogonal_lines @ SV95 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(397,plain,
! [SV81: $i,SV65: $i] :
( ( ( unorthogonal_lines @ SV65 @ SV81 )
= $false )
| ( ( orthogonal_lines @ SV65 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(398,plain,
! [SV83: $i,SV67: $i] :
( ( ( convergent_lines @ SV67 @ SV83 )
= $false )
| ( ( parallel_lines @ SV67 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(399,plain,
! [SV85: $i,SV69: $i] :
( ( ( apart_point_and_line @ SV69 @ SV85 )
= $false )
| ( ( incident_point_and_line @ SV69 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(400,plain,
! [SV11: $i,SV56: $i,SV60: $i,SV38: $i] :
( ( ( apart_point_and_line @ SV38 @ SV60 )
= $true )
| ( ( ( apart_point_and_line @ SV38 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( distinct_points @ SV11 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(401,plain,
! [SV87: $i,SV58: $i,SV49: $i,SV22: $i] :
( ( ( apart_point_and_line @ SV22 @ SV49 )
= $true )
| ( ( apart_point_and_line @ SV22 @ SV58 )
= $true )
| ( ( unorthogonal_lines @ SV49 @ SV87 )
= $true )
| ( ( unorthogonal_lines @ SV58 @ SV87 )
= $true )
| ( ( distinct_lines @ SV49 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(402,plain,
! [SV96: $i,SV88: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV88 )
| ( convergent_lines @ SV29 @ SV96 )
| ~ ( convergent_lines @ SV88 @ SV96 )
| ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(403,plain,
! [SV97: $i,SV89: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV89 )
| ( unorthogonal_lines @ SV29 @ SV97 )
| ~ ( convergent_lines @ SV89 @ SV97 )
| ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(404,plain,
! [SV98: $i,SV90: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV90 )
| ( convergent_lines @ SV29 @ SV98 )
| ~ ( convergent_lines @ SV90 @ SV98 )
| ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(405,plain,
! [SV99: $i,SV91: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV91 )
| ( unorthogonal_lines @ SV29 @ SV99 )
| ~ ( convergent_lines @ SV91 @ SV99 )
| ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(406,plain,
! [SV92: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV92 )
| ~ ( unorthogonal_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ! [SY168: $i] :
( ( convergent_lines @ SV30 @ SY168 )
| ( convergent_lines @ SV92 @ SY168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(407,plain,
! [SV93: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV93 )
| ~ ( unorthogonal_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ! [SY169: $i] :
( ( convergent_lines @ SV30 @ SY169 )
| ( unorthogonal_lines @ SV93 @ SY169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(408,plain,
! [SV94: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV94 )
| ~ ( unorthogonal_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ! [SY170: $i] :
( ( unorthogonal_lines @ SV30 @ SY170 )
| ( convergent_lines @ SV94 @ SY170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(409,plain,
! [SV95: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV95 )
| ~ ( unorthogonal_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY171: $i] :
( ( unorthogonal_lines @ SV30 @ SY171 )
| ( unorthogonal_lines @ SV95 @ SY171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(410,plain,
! [SV60: $i,SV11: $i,SV56: $i,SV38: $i] :
( ( ( apart_point_and_line @ SV38 @ SV56 )
= $true )
| ( ( ( apart_point_and_line @ SV11 @ SV56 )
| ( apart_point_and_line @ SV11 @ SV60 ) )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV60 )
= $true )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( distinct_points @ SV11 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(411,plain,
! [SV96: $i,SV88: $i,SV29: $i] :
( ( ( ( convergent_lines @ SV29 @ SV88 )
| ( convergent_lines @ SV29 @ SV96 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV88 @ SV96 )
| ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(412,plain,
! [SV97: $i,SV89: $i,SV29: $i] :
( ( ( ( convergent_lines @ SV29 @ SV89 )
| ( unorthogonal_lines @ SV29 @ SV97 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV89 @ SV97 )
| ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(413,plain,
! [SV98: $i,SV90: $i,SV29: $i] :
( ( ( ( unorthogonal_lines @ SV29 @ SV90 )
| ( convergent_lines @ SV29 @ SV98 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV90 @ SV98 )
| ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(414,plain,
! [SV99: $i,SV91: $i,SV29: $i] :
( ( ( ( unorthogonal_lines @ SV29 @ SV91 )
| ( unorthogonal_lines @ SV29 @ SV99 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV91 @ SV99 )
| ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(415,plain,
! [SV92: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ! [SY168: $i] :
( ( convergent_lines @ SV30 @ SY168 )
| ( convergent_lines @ SV92 @ SY168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(416,plain,
! [SV93: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ! [SY169: $i] :
( ( convergent_lines @ SV30 @ SY169 )
| ( unorthogonal_lines @ SV93 @ SY169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(417,plain,
! [SV94: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ! [SY170: $i] :
( ( unorthogonal_lines @ SV30 @ SY170 )
| ( convergent_lines @ SV94 @ SY170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(418,plain,
! [SV95: $i,SV30: $i] :
( ( ( ~ ( convergent_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY171: $i] :
( ( unorthogonal_lines @ SV30 @ SY171 )
| ( unorthogonal_lines @ SV95 @ SY171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(419,plain,
! [SV38: $i,SV60: $i,SV56: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV56 )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV60 )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV56 )
= $true )
| ( ( apart_point_and_line @ SV38 @ SV60 )
= $true )
| ( ( distinct_lines @ SV56 @ SV60 )
= $false )
| ( ( distinct_points @ SV11 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(420,plain,
! [SV96: $i,SV88: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV88 )
= $true )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( ~ ( convergent_lines @ SV88 @ SV96 )
| ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(421,plain,
! [SV97: $i,SV89: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV89 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( ~ ( convergent_lines @ SV89 @ SV97 )
| ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(422,plain,
! [SV98: $i,SV90: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( ~ ( convergent_lines @ SV90 @ SV98 )
| ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(423,plain,
! [SV99: $i,SV91: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( ~ ( convergent_lines @ SV91 @ SV99 )
| ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(424,plain,
! [SV92: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV92 ) )
= $true )
| ( ( ! [SY168: $i] :
( ( convergent_lines @ SV30 @ SY168 )
| ( convergent_lines @ SV92 @ SY168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(425,plain,
! [SV93: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV93 ) )
= $true )
| ( ( ! [SY169: $i] :
( ( convergent_lines @ SV30 @ SY169 )
| ( unorthogonal_lines @ SV93 @ SY169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(426,plain,
! [SV94: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV94 ) )
= $true )
| ( ( ! [SY170: $i] :
( ( unorthogonal_lines @ SV30 @ SY170 )
| ( convergent_lines @ SV94 @ SY170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(427,plain,
! [SV95: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY171: $i] :
( ( unorthogonal_lines @ SV30 @ SY171 )
| ( unorthogonal_lines @ SV95 @ SY171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(428,plain,
! [SV29: $i,SV96: $i,SV88: $i] :
( ( ( ~ ( convergent_lines @ SV88 @ SV96 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( convergent_lines @ SV29 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(429,plain,
! [SV29: $i,SV97: $i,SV89: $i] :
( ( ( ~ ( convergent_lines @ SV89 @ SV97 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( convergent_lines @ SV29 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV29: $i,SV98: $i,SV90: $i] :
( ( ( ~ ( convergent_lines @ SV90 @ SV98 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(431,plain,
! [SV29: $i,SV99: $i,SV91: $i] :
( ( ( ~ ( convergent_lines @ SV91 @ SV99 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(432,plain,
! [SV92: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV92 )
= $false )
| ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( ! [SY168: $i] :
( ( convergent_lines @ SV30 @ SY168 )
| ( convergent_lines @ SV92 @ SY168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(433,plain,
! [SV93: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV93 )
= $false )
| ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( ! [SY169: $i] :
( ( convergent_lines @ SV30 @ SY169 )
| ( unorthogonal_lines @ SV93 @ SY169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(434,plain,
! [SV94: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV94 )
= $false )
| ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( ! [SY170: $i] :
( ( unorthogonal_lines @ SV30 @ SY170 )
| ( convergent_lines @ SV94 @ SY170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(435,plain,
! [SV95: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV95 )
= $false )
| ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( ! [SY171: $i] :
( ( unorthogonal_lines @ SV30 @ SY171 )
| ( unorthogonal_lines @ SV95 @ SY171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(436,plain,
! [SV29: $i,SV96: $i,SV88: $i] :
( ( ( convergent_lines @ SV88 @ SV96 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV88 @ SV96 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( convergent_lines @ SV29 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(437,plain,
! [SV29: $i,SV97: $i,SV89: $i] :
( ( ( convergent_lines @ SV89 @ SV97 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV89 @ SV97 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( convergent_lines @ SV29 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(438,plain,
! [SV29: $i,SV98: $i,SV90: $i] :
( ( ( convergent_lines @ SV90 @ SV98 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV90 @ SV98 ) )
= $true )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(439,plain,
! [SV29: $i,SV99: $i,SV91: $i] :
( ( ( convergent_lines @ SV91 @ SV99 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV91 @ SV99 ) )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(440,plain,
! [SV92: $i,SV100: $i,SV30: $i] :
( ( ( ( convergent_lines @ SV30 @ SV100 )
| ( convergent_lines @ SV92 @ SV100 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(441,plain,
! [SV93: $i,SV101: $i,SV30: $i] :
( ( ( ( convergent_lines @ SV30 @ SV101 )
| ( unorthogonal_lines @ SV93 @ SV101 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(442,plain,
! [SV94: $i,SV102: $i,SV30: $i] :
( ( ( ( unorthogonal_lines @ SV30 @ SV102 )
| ( convergent_lines @ SV94 @ SV102 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(443,plain,
! [SV95: $i,SV103: $i,SV30: $i] :
( ( ( ( unorthogonal_lines @ SV30 @ SV103 )
| ( unorthogonal_lines @ SV95 @ SV103 ) )
= $true )
| ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(444,plain,
! [SV29: $i,SV96: $i,SV88: $i] :
( ( ( unorthogonal_lines @ SV88 @ SV96 )
= $false )
| ( ( convergent_lines @ SV88 @ SV96 )
= $false )
| ( ( convergent_lines @ SV29 @ SV96 )
= $true )
| ( ( convergent_lines @ SV29 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(445,plain,
! [SV29: $i,SV97: $i,SV89: $i] :
( ( ( unorthogonal_lines @ SV89 @ SV97 )
= $false )
| ( ( convergent_lines @ SV89 @ SV97 )
= $false )
| ( ( unorthogonal_lines @ SV29 @ SV97 )
= $true )
| ( ( convergent_lines @ SV29 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(446,plain,
! [SV29: $i,SV98: $i,SV90: $i] :
( ( ( unorthogonal_lines @ SV90 @ SV98 )
= $false )
| ( ( convergent_lines @ SV90 @ SV98 )
= $false )
| ( ( convergent_lines @ SV29 @ SV98 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(447,plain,
! [SV29: $i,SV99: $i,SV91: $i] :
( ( ( unorthogonal_lines @ SV91 @ SV99 )
= $false )
| ( ( convergent_lines @ SV91 @ SV99 )
= $false )
| ( ( unorthogonal_lines @ SV29 @ SV99 )
= $true )
| ( ( unorthogonal_lines @ SV29 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(448,plain,
! [SV92: $i,SV100: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV100 )
= $true )
| ( ( convergent_lines @ SV92 @ SV100 )
= $true )
| ( ( convergent_lines @ SV30 @ SV92 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(449,plain,
! [SV93: $i,SV101: $i,SV30: $i] :
( ( ( convergent_lines @ SV30 @ SV101 )
= $true )
| ( ( unorthogonal_lines @ SV93 @ SV101 )
= $true )
| ( ( convergent_lines @ SV30 @ SV93 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(450,plain,
! [SV94: $i,SV102: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV102 )
= $true )
| ( ( convergent_lines @ SV94 @ SV102 )
= $true )
| ( ( convergent_lines @ SV30 @ SV94 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(451,plain,
! [SV95: $i,SV103: $i,SV30: $i] :
( ( ( unorthogonal_lines @ SV30 @ SV103 )
= $true )
| ( ( unorthogonal_lines @ SV95 @ SV103 )
= $true )
| ( ( convergent_lines @ SV30 @ SV95 )
= $false )
| ( ( unorthogonal_lines @ SV30 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(452,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[143,451,450,449,448,447,446,445,444,419,401,399,398,397,388,387,386,385,366,364,362,360,350,348,346,345,342,339,338,337,335,334,333,307,306,305,304,279,248,246,245,244,242,241,191,190,189,181,144]) ).
thf(453,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO182+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 03:48:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 35
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 0
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.12/0.38 .
% 0.19/0.39 (rf:0,axioms:35,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:0,translation:fof_full)...........................
% 0.37/0.56
% 0.37/0.56 ********************************
% 0.37/0.56 * All subproblems solved! *
% 0.37/0.56 ********************************
% 0.37/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:37,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:452,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.37/0.61
% 0.37/0.61 %**** Beginning of derivation protocol ****
% 0.37/0.61 % SZS output start CNFRefutation
% See solution above
% 0.37/0.62
% 0.37/0.62 %**** End of derivation protocol ****
% 0.37/0.62 %**** no. of clauses in derivation: 453 ****
% 0.37/0.62 %**** clause counter: 452 ****
% 0.37/0.62
% 0.37/0.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:37,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:452,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------