%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO236+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:18:35 AM UTC 2026
% Result : Theorem 0.72s 0.36s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 217 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 1455 ( 357 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2649 ( 473 ~; 464 |; 24 &;1652 @)
% ( 12 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 5 con; 0-4 aty)
% Number of variables : 525 ( 0 ^; 525 !; 0 ?; 525 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $i > $i > $o ).
thf(tp_before_on_line,type,
before_on_line: $i > $i > $i > $o ).
thf(tp_between_on_line,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(tp_convergent_lines,type,
convergent_lines: $i > $i > $o ).
thf(tp_distinct_lines,type,
distinct_lines: $i > $i > $o ).
thf(tp_distinct_points,type,
distinct_points: $i > $i > $o ).
thf(tp_divides_points,type,
divides_points: $i > $i > $i > $o ).
thf(tp_equally_directed_lines,type,
equally_directed_lines: $i > $i > $o ).
thf(tp_equally_directed_opposite_lines,type,
equally_directed_opposite_lines: $i > $i > $o ).
thf(tp_incident_point_and_line,type,
incident_point_and_line: $i > $i > $o ).
thf(tp_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_left_apart_point,type,
left_apart_point: $i > $i > $o ).
thf(tp_left_convergent_lines,type,
left_convergent_lines: $i > $i > $o ).
thf(tp_line,type,
line: $i > $o ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_reverse_line,type,
reverse_line: $i > $i ).
thf(tp_right_apart_point,type,
right_apart_point: $i > $i > $o ).
thf(tp_right_convergent_lines,type,
right_convergent_lines: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY36,type,
sK2_SY36: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i ).
thf(tp_unequally_directed_lines,type,
unequally_directed_lines: $i > $i > $o ).
thf(tp_unequally_directed_opposite_lines,type,
unequally_directed_opposite_lines: $i > $i > $o ).
thf(1,axiom,
! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_subs) ).
thf(2,axiom,
! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( unequally_directed_lines @ L @ M ) )
=> ( ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2_subs) ).
thf(3,axiom,
! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_subs) ).
thf(8,axiom,
! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_cons_objs) ).
thf(17,axiom,
! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10_basics) ).
thf(19,axiom,
! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_basics) ).
thf(20,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7_basics) ).
thf(21,axiom,
! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6_basics) ).
thf(23,axiom,
! [L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_basics) ).
thf(24,axiom,
! [L: $i] :
~ ( distinct_lines @ L @ L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_basics) ).
thf(29,axiom,
! [A: $i,B: $i,L: $i] :
( ( divides_points @ L @ A @ B )
<=> ( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
| ( ( right_apart_point @ A @ L )
& ( left_apart_point @ B @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8_defns) ).
thf(31,axiom,
! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_defns) ).
thf(33,axiom,
! [X: $i,Y: $i] :
( ( equally_directed_lines @ X @ Y )
<=> ~ ( unequally_directed_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_defns) ).
thf(35,axiom,
! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_defns) ).
thf(37,conjecture,
! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ A @ M ) )
=> ( ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ A @ M ) )
=> ( ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ A @ M ) )
=> ( ( unequally_directed_lines @ L @ M )
| ( distinct_lines @ L @ M ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(41,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( unequally_directed_lines @ L @ M ) )
=> ( ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(44,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(49,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( divides_points @ L @ A @ B )
<=> ( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
| ( ( right_apart_point @ A @ L )
& ( left_apart_point @ B @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(51,plain,
( ( ! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ( equally_directed_lines @ X @ Y )
<=> ~ ( unequally_directed_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(54,plain,
( ( ! [SY36: $i,SY37: $i] :
( ( ( left_apart_point @ sK1_A @ SY36 )
& ( right_apart_point @ sK1_A @ SY37 ) )
=> ( ( unequally_directed_lines @ SY36 @ SY37 )
| ( distinct_lines @ SY36 @ SY37 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(55,plain,
( ( ! [SY38: $i] :
( ( ( left_apart_point @ sK1_A @ sK2_SY36 )
& ( right_apart_point @ sK1_A @ SY38 ) )
=> ( ( unequally_directed_lines @ sK2_SY36 @ SY38 )
| ( distinct_lines @ sK2_SY36 @ SY38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(56,plain,
( ( ( ( left_apart_point @ sK1_A @ sK2_SY36 )
& ( right_apart_point @ sK1_A @ sK3_SY38 ) )
=> ( ( unequally_directed_lines @ sK2_SY36 @ sK3_SY38 )
| ( distinct_lines @ sK2_SY36 @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(57,plain,
( ( left_apart_point @ sK1_A @ sK2_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(58,plain,
( ( right_apart_point @ sK1_A @ sK3_SY38 )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(59,plain,
( ( ( unequally_directed_lines @ sK2_SY36 @ sK3_SY38 )
| ( distinct_lines @ sK2_SY36 @ sK3_SY38 ) )
= $false ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(60,plain,
( ( ~ ( ( unequally_directed_lines @ sK2_SY36 @ sK3_SY38 )
| ( distinct_lines @ sK2_SY36 @ sK3_SY38 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] :
( ( equally_directed_lines @ X @ Y )
<=> ~ ( unequally_directed_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(63,plain,
( ( ! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( divides_points @ L @ A @ B )
<=> ( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
| ( ( right_apart_point @ A @ L )
& ( left_apart_point @ B @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(65,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(66,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( distinct_lines @ L @ N )
| ( distinct_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(67,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(68,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(69,plain,
( ( ! [L: $i,M: $i] :
( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(70,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(71,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(72,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(73,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ( ( left_apart_point @ A @ L )
& ( unequally_directed_lines @ L @ M ) )
=> ( ( distinct_lines @ L @ M )
| ( left_apart_point @ A @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(74,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(75,plain,
( ( right_apart_point @ sK1_A @ sK3_SY38 )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(76,plain,
( ( left_apart_point @ sK1_A @ sK2_SY36 )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(77,plain,
( ( ~ ( ( unequally_directed_lines @ sK2_SY36 @ sK3_SY38 )
| ( distinct_lines @ sK2_SY36 @ sK3_SY38 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX2 )
| ( distinct_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( divides_points @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 ) )
| ~ ( ~ ( right_apart_point @ SX0 @ SX2 )
| ~ ( left_apart_point @ SX1 @ SX2 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SX0 @ SX2 )
| ~ ( right_apart_point @ SX1 @ SX2 ) )
| ~ ( ~ ( right_apart_point @ SX0 @ SX2 )
| ~ ( left_apart_point @ SX1 @ SX2 ) ) )
| ( divides_points @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX0 @ SX2 )
| ( distinct_points @ SX0 @ SX1 )
| ( left_apart_point @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( left_apart_point @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX1 @ SX2 ) )
| ( distinct_lines @ SX1 @ SX2 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( left_convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX1 @ SX2 )
| ( left_convergent_lines @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( right_apart_point @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( left_apart_point @ SX0 @ ( reverse_line @ SX1 ) )
| ( right_apart_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ~ ( ~ ( ( left_apart_point @ SX0 @ SX1 )
| ( right_apart_point @ SX0 @ SX1 ) )
| ( apart_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX0 @ SX2 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX1 @ SX2 )
| ~ ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ( equally_directed_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(88,plain,
! [SV1: $i] :
( ( ~ ( distinct_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(89,plain,
! [SV2: $i] :
( ( ! [SY39: $i] :
( ( unequally_directed_lines @ SV2 @ SY39 )
| ( unequally_directed_lines @ SV2 @ ( reverse_line @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(90,plain,
! [SV3: $i] :
( ( ! [SY40: $i] :
~ ( ( left_apart_point @ SV3 @ SY40 )
| ( left_apart_point @ SV3 @ ( reverse_line @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(91,plain,
! [SV4: $i] :
( ( ~ ( distinct_lines @ SV4 @ ( reverse_line @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(92,plain,
( ( ( unequally_directed_lines @ sK2_SY36 @ sK3_SY38 )
| ( distinct_lines @ sK2_SY36 @ sK3_SY38 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV5: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ( distinct_lines @ SV5 @ SY41 )
| ( distinct_lines @ SV5 @ SY42 )
| ( distinct_lines @ SY41 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV6: $i] :
( ( ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( divides_points @ SY44 @ SV6 @ SY43 )
| ~ ( ~ ( left_apart_point @ SV6 @ SY44 )
| ~ ( right_apart_point @ SY43 @ SY44 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SY44 )
| ~ ( left_apart_point @ SY43 @ SY44 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SY44 )
| ~ ( right_apart_point @ SY43 @ SY44 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SY44 )
| ~ ( left_apart_point @ SY43 @ SY44 ) ) )
| ( divides_points @ SY44 @ SV6 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV7: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ( left_apart_point @ SV7 @ SY46 )
| ( distinct_points @ SV7 @ SY45 )
| ( left_apart_point @ SY45 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV8: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ~ ( ~ ( left_apart_point @ SV8 @ SY47 )
| ~ ( unequally_directed_lines @ SY47 @ SY48 ) )
| ( distinct_lines @ SY47 @ SY48 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV9: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( left_convergent_lines @ SV9 @ SY49 )
| ( unequally_directed_lines @ SY49 @ SY50 )
| ( left_convergent_lines @ SV9 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV10: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ~ ( right_apart_point @ SV10 @ SY51 )
| ( left_apart_point @ SV10 @ ( reverse_line @ SY51 ) ) )
| ~ ( ~ ( left_apart_point @ SV10 @ ( reverse_line @ SY51 ) )
| ( right_apart_point @ SV10 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV11: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( unequally_directed_lines @ SV11 @ SY52 )
| ( unequally_directed_lines @ SV11 @ SY53 )
| ( unequally_directed_lines @ SY52 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SV12 @ SY54 )
| ( left_apart_point @ SV12 @ SY54 )
| ( right_apart_point @ SV12 @ SY54 ) )
| ~ ( ~ ( ( left_apart_point @ SV12 @ SY54 )
| ( right_apart_point @ SV12 @ SY54 ) )
| ( apart_point_and_line @ SV12 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV13: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SY55 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SY55 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SY56 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SY56 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SY55 @ SY56 )
| ~ ( unequally_directed_lines @ SY55 @ ( reverse_line @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV14: $i] :
( ( ! [SY57: $i] :
~ ( ~ ( ~ ( equally_directed_lines @ SV14 @ SY57 )
| ~ ( unequally_directed_lines @ SV14 @ SY57 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SV14 @ SY57 )
| ( equally_directed_lines @ SV14 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV1: $i] :
( ( distinct_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV15: $i,SV2: $i] :
( ( ( unequally_directed_lines @ SV2 @ SV15 )
| ( unequally_directed_lines @ SV2 @ ( reverse_line @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV16: $i,SV3: $i] :
( ( ~ ( ( left_apart_point @ SV3 @ SV16 )
| ( left_apart_point @ SV3 @ ( reverse_line @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV4: $i] :
( ( distinct_lines @ SV4 @ ( reverse_line @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(107,plain,
( ( unequally_directed_lines @ sK2_SY36 @ sK3_SY38 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(108,plain,
( ( distinct_lines @ sK2_SY36 @ sK3_SY38 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(109,plain,
! [SV17: $i,SV5: $i] :
( ( ! [SY58: $i] :
( ~ ( distinct_lines @ SV5 @ SV17 )
| ( distinct_lines @ SV5 @ SY58 )
| ( distinct_lines @ SV17 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(110,plain,
! [SV18: $i,SV6: $i] :
( ( ! [SY59: $i] :
~ ( ~ ( ~ ( divides_points @ SY59 @ SV6 @ SV18 )
| ~ ( ~ ( left_apart_point @ SV6 @ SY59 )
| ~ ( right_apart_point @ SV18 @ SY59 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SY59 )
| ~ ( left_apart_point @ SV18 @ SY59 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SY59 )
| ~ ( right_apart_point @ SV18 @ SY59 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SY59 )
| ~ ( left_apart_point @ SV18 @ SY59 ) ) )
| ( divides_points @ SY59 @ SV6 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV19: $i,SV7: $i] :
( ( ! [SY60: $i] :
( ~ ( left_apart_point @ SV7 @ SY60 )
| ( distinct_points @ SV7 @ SV19 )
| ( left_apart_point @ SV19 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV20: $i,SV8: $i] :
( ( ! [SY61: $i] :
( ~ ~ ( ~ ( left_apart_point @ SV8 @ SV20 )
| ~ ( unequally_directed_lines @ SV20 @ SY61 ) )
| ( distinct_lines @ SV20 @ SY61 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY62: $i] :
( ~ ( left_convergent_lines @ SV9 @ SV21 )
| ( unequally_directed_lines @ SV21 @ SY62 )
| ( left_convergent_lines @ SV9 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( right_apart_point @ SV10 @ SV22 )
| ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) ) )
| ~ ( ~ ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
| ( right_apart_point @ SV10 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV23: $i,SV11: $i] :
( ( ! [SY63: $i] :
( ~ ( unequally_directed_lines @ SV11 @ SV23 )
| ( unequally_directed_lines @ SV11 @ SY63 )
| ( unequally_directed_lines @ SV23 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( apart_point_and_line @ SV12 @ SV24 )
| ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
| ~ ( ~ ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
| ( apart_point_and_line @ SV12 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV25 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SY64 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SY64 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SY64 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SY64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( equally_directed_lines @ SV14 @ SV26 )
| ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SV14 @ SV26 )
| ( equally_directed_lines @ SV14 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV15: $i,SV2: $i] :
( ( ( unequally_directed_lines @ SV2 @ SV15 )
= $true )
| ( ( unequally_directed_lines @ SV2 @ ( reverse_line @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV16: $i,SV3: $i] :
( ( ( left_apart_point @ SV3 @ SV16 )
| ( left_apart_point @ SV3 @ ( reverse_line @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV27: $i,SV17: $i,SV5: $i] :
( ( ~ ( distinct_lines @ SV5 @ SV17 )
| ( distinct_lines @ SV5 @ SV27 )
| ( distinct_lines @ SV17 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV18: $i,SV6: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( divides_points @ SV28 @ SV6 @ SV18 )
| ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
| ( divides_points @ SV28 @ SV6 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV19: $i,SV29: $i,SV7: $i] :
( ( ~ ( left_apart_point @ SV7 @ SV29 )
| ( distinct_points @ SV7 @ SV19 )
| ( left_apart_point @ SV19 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ~ ~ ( ~ ( left_apart_point @ SV8 @ SV20 )
| ~ ( unequally_directed_lines @ SV20 @ SV30 ) )
| ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ~ ( left_convergent_lines @ SV9 @ SV21 )
| ( unequally_directed_lines @ SV21 @ SV31 )
| ( left_convergent_lines @ SV9 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( right_apart_point @ SV10 @ SV22 )
| ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) ) )
| ~ ( ~ ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
| ( right_apart_point @ SV10 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ~ ( unequally_directed_lines @ SV11 @ SV23 )
| ( unequally_directed_lines @ SV11 @ SV32 )
| ( unequally_directed_lines @ SV23 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV12 @ SV24 )
| ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
| ~ ( ~ ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
| ( apart_point_and_line @ SV12 @ SV24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV25 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ( ~ ( equally_directed_lines @ SV14 @ SV26 )
| ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
| ~ ( ~ ~ ( unequally_directed_lines @ SV14 @ SV26 )
| ( equally_directed_lines @ SV14 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV16: $i,SV3: $i] :
( ( left_apart_point @ SV3 @ SV16 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV16: $i,SV3: $i] :
( ( left_apart_point @ SV3 @ ( reverse_line @ SV16 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(133,plain,
! [SV27: $i,SV17: $i,SV5: $i] :
( ( ( ~ ( distinct_lines @ SV5 @ SV17 ) )
= $true )
| ( ( ( distinct_lines @ SV5 @ SV27 )
| ( distinct_lines @ SV17 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV18: $i,SV6: $i,SV28: $i] :
( ( ~ ( ~ ( divides_points @ SV28 @ SV6 @ SV18 )
| ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
| ( divides_points @ SV28 @ SV6 @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV19: $i,SV29: $i,SV7: $i] :
( ( ( ~ ( left_apart_point @ SV7 @ SV29 ) )
= $true )
| ( ( ( distinct_points @ SV7 @ SV19 )
| ( left_apart_point @ SV19 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( left_apart_point @ SV8 @ SV20 )
| ~ ( unequally_directed_lines @ SV20 @ SV30 ) ) )
= $true )
| ( ( ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( left_convergent_lines @ SV9 @ SV21 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV21 @ SV31 )
| ( left_convergent_lines @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( right_apart_point @ SV10 @ SV22 )
| ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
| ( right_apart_point @ SV10 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(140,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( unequally_directed_lines @ SV11 @ SV23 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV11 @ SV32 )
| ( unequally_directed_lines @ SV23 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(141,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV12 @ SV24 )
| ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(142,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
| ( apart_point_and_line @ SV12 @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(143,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV25 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ( ~ ( equally_directed_lines @ SV14 @ SV26 )
| ~ ( unequally_directed_lines @ SV14 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(145,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ( ~ ~ ( unequally_directed_lines @ SV14 @ SV26 )
| ( equally_directed_lines @ SV14 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(146,plain,
! [SV27: $i,SV17: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV17 )
= $false )
| ( ( ( distinct_lines @ SV5 @ SV27 )
| ( distinct_lines @ SV17 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(147,plain,
! [SV18: $i,SV6: $i,SV28: $i] :
( ( ~ ( ~ ( divides_points @ SV28 @ SV6 @ SV18 )
| ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(148,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
| ( divides_points @ SV28 @ SV6 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(149,plain,
! [SV19: $i,SV29: $i,SV7: $i] :
( ( ( left_apart_point @ SV7 @ SV29 )
= $false )
| ( ( ( distinct_points @ SV7 @ SV19 )
| ( left_apart_point @ SV19 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV8 @ SV20 )
| ~ ( unequally_directed_lines @ SV20 @ SV30 ) ) )
= $false )
| ( ( ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( left_convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( ( unequally_directed_lines @ SV21 @ SV31 )
| ( left_convergent_lines @ SV9 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( right_apart_point @ SV10 @ SV22 )
| ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(153,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
| ( right_apart_point @ SV10 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(154,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( unequally_directed_lines @ SV11 @ SV23 )
= $false )
| ( ( ( unequally_directed_lines @ SV11 @ SV32 )
| ( unequally_directed_lines @ SV23 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( apart_point_and_line @ SV12 @ SV24 )
| ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(156,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
| ( apart_point_and_line @ SV12 @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(157,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV25 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ( equally_directed_lines @ SV14 @ SV26 )
| ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(159,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ~ ( unequally_directed_lines @ SV14 @ SV26 )
| ( equally_directed_lines @ SV14 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(160,plain,
! [SV17: $i,SV27: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV27 )
= $true )
| ( ( distinct_lines @ SV17 @ SV27 )
= $true )
| ( ( distinct_lines @ SV5 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV18: $i,SV6: $i,SV28: $i] :
( ( ~ ( divides_points @ SV28 @ SV6 @ SV18 )
| ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(162,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
| ( divides_points @ SV28 @ SV6 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(163,plain,
! [SV29: $i,SV19: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV19 )
= $true )
| ( ( left_apart_point @ SV19 @ SV29 )
= $true )
| ( ( left_apart_point @ SV7 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( left_apart_point @ SV8 @ SV20 )
| ~ ( unequally_directed_lines @ SV20 @ SV30 ) )
= $true )
| ( ( ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(165,plain,
! [SV9: $i,SV31: $i,SV21: $i] :
( ( ( unequally_directed_lines @ SV21 @ SV31 )
= $true )
| ( ( left_convergent_lines @ SV9 @ SV31 )
= $true )
| ( ( left_convergent_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(166,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( right_apart_point @ SV10 @ SV22 ) )
= $true )
| ( ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) ) )
= $true )
| ( ( right_apart_point @ SV10 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(168,plain,
! [SV23: $i,SV32: $i,SV11: $i] :
( ( ( unequally_directed_lines @ SV11 @ SV32 )
= $true )
| ( ( unequally_directed_lines @ SV23 @ SV32 )
= $true )
| ( ( unequally_directed_lines @ SV11 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( apart_point_and_line @ SV12 @ SV24 ) )
= $true )
| ( ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) ) )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(171,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV25 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(172,plain,
! [SV26: $i,SV14: $i] :
( ( ( ~ ( equally_directed_lines @ SV14 @ SV26 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV26: $i,SV14: $i] :
( ( ( ~ ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
= $true )
| ( ( equally_directed_lines @ SV14 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV18: $i,SV6: $i,SV28: $i] :
( ( ( ~ ( divides_points @ SV28 @ SV6 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( left_apart_point @ SV8 @ SV20 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV20 @ SV30 ) )
= $true )
| ( ( ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV22: $i,SV10: $i] :
( ( ( right_apart_point @ SV10 @ SV22 )
= $false )
| ( ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV22: $i,SV10: $i] :
( ( ( left_apart_point @ SV10 @ ( reverse_line @ SV22 ) )
= $false )
| ( ( right_apart_point @ SV10 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV24: $i,SV12: $i] :
( ( ( apart_point_and_line @ SV12 @ SV24 )
= $false )
| ( ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV24: $i,SV12: $i] :
( ( ( ( left_apart_point @ SV12 @ SV24 )
| ( right_apart_point @ SV12 @ SV24 ) )
= $false )
| ( ( apart_point_and_line @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV25 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV26: $i,SV14: $i] :
( ( ( equally_directed_lines @ SV14 @ SV26 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV26: $i,SV14: $i] :
( ( ( ~ ( unequally_directed_lines @ SV14 @ SV26 ) )
= $false )
| ( ( equally_directed_lines @ SV14 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV18: $i,SV6: $i,SV28: $i] :
( ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false )
| ( ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
| ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $false )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( left_apart_point @ SV8 @ SV20 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV20 @ SV30 ) )
= $true )
| ( ( ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV24: $i,SV12: $i] :
( ( ( left_apart_point @ SV12 @ SV24 )
= $true )
| ( ( right_apart_point @ SV12 @ SV24 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV24: $i,SV12: $i] :
( ( ( left_apart_point @ SV12 @ SV24 )
= $false )
| ( ( apart_point_and_line @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(189,plain,
! [SV24: $i,SV12: $i] :
( ( ( right_apart_point @ SV12 @ SV24 )
= $false )
| ( ( apart_point_and_line @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(190,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV26: $i,SV14: $i] :
( ( ( unequally_directed_lines @ SV14 @ SV26 )
= $false )
| ( ( equally_directed_lines @ SV14 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(192,plain,
! [SV26: $i,SV14: $i] :
( ( ( unequally_directed_lines @ SV14 @ SV26 )
= $true )
| ( ( equally_directed_lines @ SV14 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(194,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) ) )
= $false )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(195,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $false )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(196,plain,
! [SV8: $i,SV30: $i,SV20: $i] :
( ( ( unequally_directed_lines @ SV20 @ SV30 )
= $false )
| ( ( left_apart_point @ SV8 @ SV20 )
= $false )
| ( ( ( distinct_lines @ SV20 @ SV30 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(197,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( left_apart_point @ SV6 @ SV28 )
| ~ ( right_apart_point @ SV18 @ SV28 ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(200,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(201,plain,
! [SV8: $i,SV30: $i,SV20: $i] :
( ( ( distinct_lines @ SV20 @ SV30 )
= $true )
| ( ( left_apart_point @ SV8 @ ( reverse_line @ SV30 ) )
= $true )
| ( ( left_apart_point @ SV8 @ SV20 )
= $false )
| ( ( unequally_directed_lines @ SV20 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(203,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( left_apart_point @ SV6 @ SV28 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(204,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( ~ ( right_apart_point @ SV18 @ SV28 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(205,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( left_apart_point @ SV6 @ SV28 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV18 @ SV28 ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(206,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV28 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV18 @ SV28 ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(207,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV33 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( left_apart_point @ SV6 @ SV28 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( right_apart_point @ SV18 @ SV28 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(210,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( left_apart_point @ SV6 @ SV28 )
= $false )
| ( ( ~ ( right_apart_point @ SV18 @ SV28 ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(211,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( right_apart_point @ SV6 @ SV28 )
= $false )
| ( ( ~ ( left_apart_point @ SV18 @ SV28 ) )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(212,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(213,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) )
= $false )
| ( ( left_apart_point @ SV6 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(215,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV28 )
| ~ ( left_apart_point @ SV18 @ SV28 ) )
= $false )
| ( ( right_apart_point @ SV18 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( right_apart_point @ SV18 @ SV28 )
= $false )
| ( ( left_apart_point @ SV6 @ SV28 )
= $false )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( left_apart_point @ SV18 @ SV28 )
= $false )
| ( ( right_apart_point @ SV6 @ SV28 )
= $false )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ SV33 )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(219,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV28 ) )
= $false )
| ( ( left_apart_point @ SV6 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(221,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( ~ ( left_apart_point @ SV18 @ SV28 ) )
= $false )
| ( ( left_apart_point @ SV6 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(222,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV28 ) )
= $false )
| ( ( right_apart_point @ SV18 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(223,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( ~ ( left_apart_point @ SV18 @ SV28 ) )
= $false )
| ( ( right_apart_point @ SV18 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(224,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( unequally_directed_lines @ SV25 @ SV33 )
| ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( right_apart_point @ SV6 @ SV28 )
= $true )
| ( ( left_apart_point @ SV6 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(227,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( left_apart_point @ SV18 @ SV28 )
= $true )
| ( ( left_apart_point @ SV6 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(228,plain,
! [SV18: $i,SV28: $i,SV6: $i] :
( ( ( right_apart_point @ SV6 @ SV28 )
= $true )
| ( ( right_apart_point @ SV18 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(229,plain,
! [SV6: $i,SV28: $i,SV18: $i] :
( ( ( left_apart_point @ SV18 @ SV28 )
= $true )
| ( ( right_apart_point @ SV18 @ SV28 )
= $true )
| ( ( divides_points @ SV28 @ SV6 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(230,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( unequally_directed_lines @ SV25 @ SV33 ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(231,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(232,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( unequally_directed_lines @ SV25 @ SV33 ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(233,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(234,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( unequally_directed_lines @ SV25 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(235,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(236,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( unequally_directed_lines @ SV25 @ SV33 )
= $true )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(237,plain,
! [SV13: $i,SV33: $i,SV25: $i] :
( ( ( unequally_directed_lines @ SV25 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV33 ) )
= $true )
| ( ( unequally_directed_lines @ SV13 @ SV25 )
= $false )
| ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(238,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,237,236,235,234,229,228,227,226,217,216,201,192,191,189,188,187,178,177,168,165,163,160,132,131,119,108,107,106,103,76]) ).
thf(239,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO236+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.19 % Computer : n001.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Oct 6 10:17:38 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.72/0.36
% 0.72/0.36 No.of.Axioms: 14
% 0.72/0.36
% 0.72/0.36 Length.of.Defs: 0
% 0.72/0.36
% 0.72/0.36 Contains.Choice.Funs: false
% 0.72/0.36 ......
% 0.72/0.36
% 0.72/0.36 ********************************
% 0.72/0.36 * All subproblems solved! *
% 0.72/0.36 ********************************
% 0.72/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:238,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.72/0.36
% 0.72/0.36 %**** Beginning of derivation protocol ****
% 0.72/0.36 % SZS output start CNFRefutation
% See solution above
% 0.72/0.36
% 0.72/0.36 %**** End of derivation protocol ****
% 0.72/0.36 %**** no. of clauses in derivation: 217 ****
% 0.72/0.36 %**** clause counter: 238 ****
% 0.72/0.36
% 0.72/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:238,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------