%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO252+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 10:18:41 AM UTC 2026
% Result : Theorem 0.92s 0.45s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 312 ( 169 unt; 0 typ; 0 def)
% Number of atoms : 1993 ( 493 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3701 ( 684 ~; 628 |; 29 &;2322 @)
% ( 12 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 5 con; 0-4 aty)
% Number of variables : 742 ( 0 ^; 742 !; 0 ?; 742 :)
% 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_SY29,type,
sK2_SY29: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i ).
thf(tp_unequally_directed_lines,type,
unequally_directed_lines: $i > $i > $o ).
thf(tp_unequally_directed_opposite_lines,type,
unequally_directed_opposite_lines: $i > $i > $o ).
thf(1,axiom,
! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_subs) ).
thf(3,axiom,
! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_subs) ).
thf(4,axiom,
! [A: $i,B: $i,L: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ L ) )
=> ( ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_uniq_cons) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_cons_objs) ).
thf(16,axiom,
! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
thf(17,axiom,
! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_basics) ).
thf(26,axiom,
! [A: $i] :
~ ( distinct_points @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_basics) ).
thf(29,axiom,
! [A: $i,B: $i,L: $i] :
( ( divides_points @ L @ A @ B )
<=> ( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
| ( ( right_apart_point @ A @ L )
& ( left_apart_point @ B @ L ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_defns) ).
thf(31,axiom,
! [A: $i,L: $i] :
( ( apart_point_and_line @ A @ L )
<=> ( ( left_apart_point @ A @ L )
| ( right_apart_point @ A @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_defns) ).
thf(35,axiom,
! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_defns) ).
thf(37,conjecture,
! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
=> ( ( distinct_points @ A @ B )
& ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
=> ( ( distinct_points @ A @ B )
& ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( right_apart_point @ B @ L ) )
=> ( ( distinct_points @ A @ B )
& ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $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,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(42,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ L ) )
=> ( ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(44,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,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(46,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(47,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(48,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(49,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(50,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(51,plain,
( ( ! [SY29: $i,SY30: $i] :
( ( ( left_apart_point @ sK1_A @ SY30 )
& ( right_apart_point @ SY29 @ SY30 ) )
=> ( ( distinct_points @ sK1_A @ SY29 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ SY29 ) @ SY30 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(52,plain,
( ( ! [SY31: $i] :
( ( ( left_apart_point @ sK1_A @ SY31 )
& ( right_apart_point @ sK2_SY29 @ SY31 ) )
=> ( ( distinct_points @ sK1_A @ sK2_SY29 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(53,plain,
( ( ( ( left_apart_point @ sK1_A @ sK3_SY31 )
& ( right_apart_point @ sK2_SY29 @ sK3_SY31 ) )
=> ( ( distinct_points @ sK1_A @ sK2_SY29 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ sK3_SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(54,plain,
( ( left_apart_point @ sK1_A @ sK3_SY31 )
= $true ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(55,plain,
( ( right_apart_point @ sK2_SY29 @ sK3_SY31 )
= $true ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(56,plain,
( ( ( distinct_points @ sK1_A @ sK2_SY29 )
& ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ sK3_SY31 ) )
= $false ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(57,plain,
( ( distinct_points @ sK1_A @ sK2_SY29 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[56]) ).
thf(58,plain,
( ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ sK3_SY31 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[56]) ).
thf(59,plain,
( ( ~ ( distinct_points @ sK1_A @ sK2_SY29 ) )
= $true ),
inference(polarity_switch,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ sK3_SY31 ) )
= $true ),
inference(polarity_switch,[status(thm)],[58]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(62,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)],[49]) ).
thf(63,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)],[48]) ).
thf(64,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(65,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(66,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(67,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(69,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ L ) )
=> ( ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(70,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)],[41]) ).
thf(71,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(72,plain,
( ( right_apart_point @ sK2_SY29 @ sK3_SY31 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(73,plain,
( ( left_apart_point @ sK1_A @ sK3_SY31 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(74,plain,
( ( ~ ( distinct_points @ sK1_A @ sK2_SY29 ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(76,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)],[71]) ).
thf(77,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(78,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)],[63]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( ~ ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) )
| ~ ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
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)],[70]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( left_apart_point @ SX0 @ SX2 ) )
| ( left_apart_point @ SX1 @ SX2 )
| ( left_convergent_lines @ ( line_connecting @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(82,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)],[62]) ).
thf(83,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(84,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
~ ( ( left_apart_point @ SV2 @ SY32 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY33: $i] :
~ ( ( left_convergent_lines @ SV3 @ SY33 )
| ( left_convergent_lines @ SV3 @ ( reverse_line @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(86,plain,
( ( distinct_points @ sK1_A @ sK2_SY29 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV4: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( distinct_points @ SV4 @ SY34 )
| ( distinct_points @ SV4 @ SY35 )
| ( distinct_points @ SY34 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV5: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( left_convergent_lines @ SV5 @ SY36 )
| ( unequally_directed_lines @ SY36 @ SY37 )
| ( left_convergent_lines @ SV5 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV6: $i] :
( ( ! [SY38: $i] :
~ ( ~ ( ~ ( right_apart_point @ SV6 @ SY38 )
| ( left_apart_point @ SV6 @ ( reverse_line @ SY38 ) ) )
| ~ ( ~ ( left_apart_point @ SV6 @ ( reverse_line @ SY38 ) )
| ( right_apart_point @ SV6 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(90,plain,
! [SV7: $i] :
( ( ! [SY39: $i,SY40: $i] :
~ ( ~ ( ~ ( divides_points @ SY40 @ SV7 @ SY39 )
| ~ ( ~ ( left_apart_point @ SV7 @ SY40 )
| ~ ( right_apart_point @ SY39 @ SY40 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SY40 )
| ~ ( left_apart_point @ SY39 @ SY40 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SY40 )
| ~ ( right_apart_point @ SY39 @ SY40 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SY40 )
| ~ ( left_apart_point @ SY39 @ SY40 ) ) )
| ( divides_points @ SY40 @ SV7 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(91,plain,
! [SV8: $i] :
( ( ! [SY41: $i] :
( ~ ( distinct_points @ SV8 @ SY41 )
| ~ ( ~ ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SY41 ) )
| ~ ~ ( apart_point_and_line @ SY41 @ ( line_connecting @ SV8 @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(92,plain,
! [SV9: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( left_apart_point @ SV9 @ SY43 )
| ( distinct_points @ SV9 @ SY42 )
| ( left_apart_point @ SY42 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(93,plain,
! [SV10: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ~ ( ~ ( distinct_points @ SV10 @ SY44 )
| ~ ( left_apart_point @ SV10 @ SY45 ) )
| ( left_apart_point @ SY44 @ SY45 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SY44 ) @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV11: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SV11 @ SY46 )
| ( left_apart_point @ SV11 @ SY46 )
| ( right_apart_point @ SV11 @ SY46 ) )
| ~ ( ~ ( ( left_apart_point @ SV11 @ SY46 )
| ( right_apart_point @ SV11 @ SY46 ) )
| ( apart_point_and_line @ SV11 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ( ( left_apart_point @ SV2 @ SV12 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV13: $i,SV3: $i] :
( ( ~ ( ( left_convergent_lines @ SV3 @ SV13 )
| ( left_convergent_lines @ SV3 @ ( reverse_line @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV14: $i,SV4: $i] :
( ( ! [SY47: $i] :
( ~ ( distinct_points @ SV4 @ SV14 )
| ( distinct_points @ SV4 @ SY47 )
| ( distinct_points @ SV14 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY48: $i] :
( ~ ( left_convergent_lines @ SV5 @ SV15 )
| ( unequally_directed_lines @ SV15 @ SY48 )
| ( left_convergent_lines @ SV5 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( right_apart_point @ SV6 @ SV16 )
| ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) ) )
| ~ ( ~ ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV6 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV17: $i,SV7: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ~ ( divides_points @ SY49 @ SV7 @ SV17 )
| ~ ( ~ ( left_apart_point @ SV7 @ SY49 )
| ~ ( right_apart_point @ SV17 @ SY49 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SY49 )
| ~ ( left_apart_point @ SV17 @ SY49 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SY49 )
| ~ ( right_apart_point @ SV17 @ SY49 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SY49 )
| ~ ( left_apart_point @ SV17 @ SY49 ) ) )
| ( divides_points @ SY49 @ SV7 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV18: $i,SV8: $i] :
( ( ~ ( distinct_points @ SV8 @ SV18 )
| ~ ( ~ ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) )
| ~ ~ ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY50: $i] :
( ~ ( left_apart_point @ SV9 @ SY50 )
| ( distinct_points @ SV9 @ SV19 )
| ( left_apart_point @ SV19 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV20: $i,SV10: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ( distinct_points @ SV10 @ SV20 )
| ~ ( left_apart_point @ SV10 @ SY51 ) )
| ( left_apart_point @ SV20 @ SY51 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( apart_point_and_line @ SV11 @ SV21 )
| ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
| ~ ( ~ ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
| ( apart_point_and_line @ SV11 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV12: $i,SV2: $i] :
( ( ( left_apart_point @ SV2 @ SV12 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV13: $i,SV3: $i] :
( ( ( left_convergent_lines @ SV3 @ SV13 )
| ( left_convergent_lines @ SV3 @ ( reverse_line @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ~ ( distinct_points @ SV4 @ SV14 )
| ( distinct_points @ SV4 @ SV22 )
| ( distinct_points @ SV14 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ~ ( left_convergent_lines @ SV5 @ SV15 )
| ( unequally_directed_lines @ SV15 @ SV23 )
| ( left_convergent_lines @ SV5 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( ~ ( right_apart_point @ SV6 @ SV16 )
| ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) ) )
| ~ ( ~ ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV6 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV17: $i,SV7: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( divides_points @ SV24 @ SV7 @ SV17 )
| ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
| ( divides_points @ SV24 @ SV7 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( distinct_points @ SV8 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) )
| ~ ~ ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ~ ( left_apart_point @ SV9 @ SV25 )
| ( distinct_points @ SV9 @ SV19 )
| ( left_apart_point @ SV19 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV26: $i,SV20: $i,SV10: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV10 @ SV20 )
| ~ ( left_apart_point @ SV10 @ SV26 ) )
| ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV11 @ SV21 )
| ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
| ~ ( ~ ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
| ( apart_point_and_line @ SV11 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV12: $i,SV2: $i] :
( ( left_apart_point @ SV2 @ SV12 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(117,plain,
! [SV12: $i,SV2: $i] :
( ( left_apart_point @ SV2 @ ( reverse_line @ SV12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(118,plain,
! [SV13: $i,SV3: $i] :
( ( left_convergent_lines @ SV3 @ SV13 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV13: $i,SV3: $i] :
( ( left_convergent_lines @ SV3 @ ( reverse_line @ SV13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(120,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( distinct_points @ SV4 @ SV14 ) )
= $true )
| ( ( ( distinct_points @ SV4 @ SV22 )
| ( distinct_points @ SV14 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( left_convergent_lines @ SV5 @ SV15 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV15 @ SV23 )
| ( left_convergent_lines @ SV5 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( ~ ( right_apart_point @ SV6 @ SV16 )
| ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(123,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( ~ ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV6 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(124,plain,
! [SV17: $i,SV7: $i,SV24: $i] :
( ( ~ ( ~ ( divides_points @ SV24 @ SV7 @ SV17 )
| ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
| ( divides_points @ SV24 @ SV7 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV18: $i,SV8: $i] :
( ( ( distinct_points @ SV8 @ SV18 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) )
| ~ ~ ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( left_apart_point @ SV9 @ SV25 ) )
= $true )
| ( ( ( distinct_points @ SV9 @ SV19 )
| ( left_apart_point @ SV19 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV26: $i,SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV10 @ SV20 )
| ~ ( left_apart_point @ SV10 @ SV26 ) ) )
= $true )
| ( ( ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV11 @ SV21 )
| ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(129,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ~ ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
| ( apart_point_and_line @ SV11 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(130,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV14 )
= $false )
| ( ( ( distinct_points @ SV4 @ SV22 )
| ( distinct_points @ SV14 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( left_convergent_lines @ SV5 @ SV15 )
= $false )
| ( ( ( unequally_directed_lines @ SV15 @ SV23 )
| ( left_convergent_lines @ SV5 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( right_apart_point @ SV6 @ SV16 )
| ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(133,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV6 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(134,plain,
! [SV17: $i,SV7: $i,SV24: $i] :
( ( ~ ( ~ ( divides_points @ SV24 @ SV7 @ SV17 )
| ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(135,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
| ( divides_points @ SV24 @ SV7 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) )
| ~ ~ ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) ) )
= $false )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( left_apart_point @ SV9 @ SV25 )
= $false )
| ( ( ( distinct_points @ SV9 @ SV19 )
| ( left_apart_point @ SV19 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV26: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV10 @ SV20 )
| ~ ( left_apart_point @ SV10 @ SV26 ) ) )
= $false )
| ( ( ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( apart_point_and_line @ SV11 @ SV21 )
| ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
| ( apart_point_and_line @ SV11 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(141,plain,
! [SV14: $i,SV22: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV22 )
= $true )
| ( ( distinct_points @ SV14 @ SV22 )
= $true )
| ( ( distinct_points @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV5: $i,SV23: $i,SV15: $i] :
( ( ( unequally_directed_lines @ SV15 @ SV23 )
= $true )
| ( ( left_convergent_lines @ SV5 @ SV23 )
= $true )
| ( ( left_convergent_lines @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( right_apart_point @ SV6 @ SV16 ) )
= $true )
| ( ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) ) )
= $true )
| ( ( right_apart_point @ SV6 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV17: $i,SV7: $i,SV24: $i] :
( ( ~ ( divides_points @ SV24 @ SV7 @ SV17 )
| ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(146,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
| ( divides_points @ SV24 @ SV7 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(147,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) ) )
= $false )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(148,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) ) )
= $false )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(149,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV19 )
= $true )
| ( ( left_apart_point @ SV19 @ SV25 )
= $true )
| ( ( left_apart_point @ SV9 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV26: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( distinct_points @ SV10 @ SV20 )
| ~ ( left_apart_point @ SV10 @ SV26 ) )
= $true )
| ( ( ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(151,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( apart_point_and_line @ SV11 @ SV21 ) )
= $true )
| ( ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) ) )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV16: $i,SV6: $i] :
( ( ( right_apart_point @ SV6 @ SV16 )
= $false )
| ( ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV16: $i,SV6: $i] :
( ( ( left_apart_point @ SV6 @ ( reverse_line @ SV16 ) )
= $false )
| ( ( right_apart_point @ SV6 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV17: $i,SV7: $i,SV24: $i] :
( ( ( ~ ( divides_points @ SV24 @ SV7 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) ) )
= $true )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(158,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) ) )
= $true )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(159,plain,
! [SV26: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( distinct_points @ SV10 @ SV20 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV10 @ SV26 ) )
= $true )
| ( ( ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV21: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV21 )
= $false )
| ( ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV21: $i,SV11: $i] :
( ( ( ( left_apart_point @ SV11 @ SV21 )
| ( right_apart_point @ SV11 @ SV21 ) )
= $false )
| ( ( apart_point_and_line @ SV11 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV17: $i,SV7: $i,SV24: $i] :
( ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false )
| ( ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
| ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $false )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(164,plain,
! [SV18: $i,SV8: $i] :
( ( ( apart_point_and_line @ SV8 @ ( line_connecting @ SV8 @ SV18 ) )
= $false )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV8: $i,SV18: $i] :
( ( ( apart_point_and_line @ SV18 @ ( line_connecting @ SV8 @ SV18 ) )
= $false )
| ( ( distinct_points @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(166,plain,
! [SV26: $i,SV20: $i,SV10: $i] :
( ( ( distinct_points @ SV10 @ SV20 )
= $false )
| ( ( ~ ( left_apart_point @ SV10 @ SV26 ) )
= $true )
| ( ( ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(167,plain,
! [SV21: $i,SV11: $i] :
( ( ( left_apart_point @ SV11 @ SV21 )
= $true )
| ( ( right_apart_point @ SV11 @ SV21 )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(168,plain,
! [SV21: $i,SV11: $i] :
( ( ( left_apart_point @ SV11 @ SV21 )
= $false )
| ( ( apart_point_and_line @ SV11 @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(169,plain,
! [SV21: $i,SV11: $i] :
( ( ( right_apart_point @ SV11 @ SV21 )
= $false )
| ( ( apart_point_and_line @ SV11 @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(170,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) ) )
= $false )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(172,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $false )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(173,plain,
! [SV20: $i,SV26: $i,SV10: $i] :
( ( ( left_apart_point @ SV10 @ SV26 )
= $false )
| ( ( distinct_points @ SV10 @ SV20 )
= $false )
| ( ( ( left_apart_point @ SV20 @ SV26 )
| ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(174,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(175,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( left_apart_point @ SV7 @ SV24 )
| ~ ( right_apart_point @ SV17 @ SV24 ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(176,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(177,plain,
! [SV10: $i,SV26: $i,SV20: $i] :
( ( ( left_apart_point @ SV20 @ SV26 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV10 @ SV20 ) @ SV26 )
= $true )
| ( ( distinct_points @ SV10 @ SV20 )
= $false )
| ( ( left_apart_point @ SV10 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( left_apart_point @ SV7 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(179,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( right_apart_point @ SV17 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(180,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( left_apart_point @ SV7 @ SV24 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV17 @ SV24 ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(181,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( right_apart_point @ SV7 @ SV24 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV17 @ SV24 ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(182,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( left_apart_point @ SV7 @ SV24 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( right_apart_point @ SV17 @ SV24 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(184,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( left_apart_point @ SV7 @ SV24 )
= $false )
| ( ( ~ ( right_apart_point @ SV17 @ SV24 ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( right_apart_point @ SV7 @ SV24 )
= $false )
| ( ( ~ ( left_apart_point @ SV17 @ SV24 ) )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(186,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) )
= $false )
| ( ( left_apart_point @ SV7 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(187,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( right_apart_point @ SV7 @ SV24 )
| ~ ( left_apart_point @ SV17 @ SV24 ) )
= $false )
| ( ( right_apart_point @ SV17 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(188,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( right_apart_point @ SV17 @ SV24 )
= $false )
| ( ( left_apart_point @ SV7 @ SV24 )
= $false )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV24 )
= $false )
| ( ( right_apart_point @ SV7 @ SV24 )
= $false )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( right_apart_point @ SV7 @ SV24 ) )
= $false )
| ( ( left_apart_point @ SV7 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(191,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( left_apart_point @ SV17 @ SV24 ) )
= $false )
| ( ( left_apart_point @ SV7 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(192,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( right_apart_point @ SV7 @ SV24 ) )
= $false )
| ( ( right_apart_point @ SV17 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(193,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( left_apart_point @ SV17 @ SV24 ) )
= $false )
| ( ( right_apart_point @ SV17 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(194,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( right_apart_point @ SV7 @ SV24 )
= $true )
| ( ( left_apart_point @ SV7 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(195,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV24 )
= $true )
| ( ( left_apart_point @ SV7 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(196,plain,
! [SV17: $i,SV24: $i,SV7: $i] :
( ( ( right_apart_point @ SV7 @ SV24 )
= $true )
| ( ( right_apart_point @ SV17 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(197,plain,
! [SV7: $i,SV24: $i,SV17: $i] :
( ( ( left_apart_point @ SV17 @ SV24 )
= $true )
| ( ( right_apart_point @ SV17 @ SV24 )
= $true )
| ( ( divides_points @ SV24 @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(198,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,197,196,195,194,189,188,177,169,168,167,165,164,154,153,149,142,141,119,118,117,116,95,86,73]) ).
thf(199,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(200,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)],[49]) ).
thf(201,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)],[48]) ).
thf(202,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(203,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(204,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(205,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(206,plain,
( ( ! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(207,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ L ) )
=> ( ( left_apart_point @ B @ L )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(208,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)],[41]) ).
thf(209,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(210,plain,
( ( right_apart_point @ sK2_SY29 @ sK3_SY31 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(211,plain,
( ( left_apart_point @ sK1_A @ sK3_SY31 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(212,plain,
( ( ~ ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ sK3_SY31 ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(213,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(214,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)],[201]) ).
thf(215,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)],[209]) ).
thf(216,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( ~ ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) )
| ~ ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(217,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)],[200]) ).
thf(218,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( left_apart_point @ SX0 @ SX2 ) )
| ( left_apart_point @ SX1 @ SX2 )
| ( left_convergent_lines @ ( line_connecting @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(219,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)],[208]) ).
thf(220,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)],[199]) ).
thf(221,plain,
! [SV27: $i] :
( ( ~ ( distinct_points @ SV27 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(222,plain,
! [SV28: $i] :
( ( ! [SY52: $i] :
~ ( ( left_apart_point @ SV28 @ SY52 )
| ( left_apart_point @ SV28 @ ( reverse_line @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(223,plain,
! [SV29: $i] :
( ( ! [SY53: $i] :
~ ( ( left_convergent_lines @ SV29 @ SY53 )
| ( left_convergent_lines @ SV29 @ ( reverse_line @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(224,plain,
( ( left_convergent_lines @ ( line_connecting @ sK1_A @ sK2_SY29 ) @ sK3_SY31 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV30: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( distinct_points @ SV30 @ SY54 )
| ( distinct_points @ SV30 @ SY55 )
| ( distinct_points @ SY54 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(226,plain,
! [SV31: $i] :
( ( ! [SY56: $i,SY57: $i] :
~ ( ~ ( ~ ( divides_points @ SY57 @ SV31 @ SY56 )
| ~ ( ~ ( left_apart_point @ SV31 @ SY57 )
| ~ ( right_apart_point @ SY56 @ SY57 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SY57 )
| ~ ( left_apart_point @ SY56 @ SY57 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SY57 )
| ~ ( right_apart_point @ SY56 @ SY57 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SY57 )
| ~ ( left_apart_point @ SY56 @ SY57 ) ) )
| ( divides_points @ SY57 @ SV31 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(227,plain,
! [SV32: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( left_convergent_lines @ SV32 @ SY58 )
| ( unequally_directed_lines @ SY58 @ SY59 )
| ( left_convergent_lines @ SV32 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(228,plain,
! [SV33: $i] :
( ( ! [SY60: $i] :
( ~ ( distinct_points @ SV33 @ SY60 )
| ~ ( ~ ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SY60 ) )
| ~ ~ ( apart_point_and_line @ SY60 @ ( line_connecting @ SV33 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV34: $i] :
( ( ! [SY61: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SV34 @ SY61 )
| ( left_apart_point @ SV34 @ SY61 )
| ( right_apart_point @ SV34 @ SY61 ) )
| ~ ( ~ ( ( left_apart_point @ SV34 @ SY61 )
| ( right_apart_point @ SV34 @ SY61 ) )
| ( apart_point_and_line @ SV34 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV35: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ~ ( ~ ( distinct_points @ SV35 @ SY62 )
| ~ ( left_apart_point @ SV35 @ SY63 ) )
| ( left_apart_point @ SY62 @ SY63 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SY62 ) @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV36: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( left_apart_point @ SV36 @ SY65 )
| ( distinct_points @ SV36 @ SY64 )
| ( left_apart_point @ SY64 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV37: $i] :
( ( ! [SY66: $i] :
~ ( ~ ( ~ ( right_apart_point @ SV37 @ SY66 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SY66 ) ) )
| ~ ( ~ ( left_apart_point @ SV37 @ ( reverse_line @ SY66 ) )
| ( right_apart_point @ SV37 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV27: $i] :
( ( distinct_points @ SV27 @ SV27 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(234,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( ( left_apart_point @ SV28 @ SV38 )
| ( left_apart_point @ SV28 @ ( reverse_line @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(235,plain,
! [SV39: $i,SV29: $i] :
( ( ~ ( ( left_convergent_lines @ SV29 @ SV39 )
| ( left_convergent_lines @ SV29 @ ( reverse_line @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(236,plain,
! [SV40: $i,SV30: $i] :
( ( ! [SY67: $i] :
( ~ ( distinct_points @ SV30 @ SV40 )
| ( distinct_points @ SV30 @ SY67 )
| ( distinct_points @ SV40 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(237,plain,
! [SV41: $i,SV31: $i] :
( ( ! [SY68: $i] :
~ ( ~ ( ~ ( divides_points @ SY68 @ SV31 @ SV41 )
| ~ ( ~ ( left_apart_point @ SV31 @ SY68 )
| ~ ( right_apart_point @ SV41 @ SY68 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SY68 )
| ~ ( left_apart_point @ SV41 @ SY68 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SY68 )
| ~ ( right_apart_point @ SV41 @ SY68 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SY68 )
| ~ ( left_apart_point @ SV41 @ SY68 ) ) )
| ( divides_points @ SY68 @ SV31 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV42: $i,SV32: $i] :
( ( ! [SY69: $i] :
( ~ ( left_convergent_lines @ SV32 @ SV42 )
| ( unequally_directed_lines @ SV42 @ SY69 )
| ( left_convergent_lines @ SV32 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV43: $i,SV33: $i] :
( ( ~ ( distinct_points @ SV33 @ SV43 )
| ~ ( ~ ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) )
| ~ ~ ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( ~ ( ~ ( apart_point_and_line @ SV34 @ SV44 )
| ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
| ~ ( ~ ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
| ( apart_point_and_line @ SV34 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV45: $i,SV35: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ( distinct_points @ SV35 @ SV45 )
| ~ ( left_apart_point @ SV35 @ SY70 ) )
| ( left_apart_point @ SV45 @ SY70 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV46: $i,SV36: $i] :
( ( ! [SY71: $i] :
( ~ ( left_apart_point @ SV36 @ SY71 )
| ( distinct_points @ SV36 @ SV46 )
| ( left_apart_point @ SV46 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV47: $i,SV37: $i] :
( ( ~ ( ~ ( ~ ( right_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) ) )
| ~ ( ~ ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( right_apart_point @ SV37 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV38: $i,SV28: $i] :
( ( ( left_apart_point @ SV28 @ SV38 )
| ( left_apart_point @ SV28 @ ( reverse_line @ SV38 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV39: $i,SV29: $i] :
( ( ( left_convergent_lines @ SV29 @ SV39 )
| ( left_convergent_lines @ SV29 @ ( reverse_line @ SV39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(246,plain,
! [SV48: $i,SV40: $i,SV30: $i] :
( ( ~ ( distinct_points @ SV30 @ SV40 )
| ( distinct_points @ SV30 @ SV48 )
| ( distinct_points @ SV40 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV41: $i,SV31: $i,SV49: $i] :
( ( ~ ( ~ ( ~ ( divides_points @ SV49 @ SV31 @ SV41 )
| ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
| ( divides_points @ SV49 @ SV31 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV50: $i,SV42: $i,SV32: $i] :
( ( ~ ( left_convergent_lines @ SV32 @ SV42 )
| ( unequally_directed_lines @ SV42 @ SV50 )
| ( left_convergent_lines @ SV32 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( distinct_points @ SV33 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) )
| ~ ~ ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(250,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV34 @ SV44 )
| ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
| ~ ( ~ ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
| ( apart_point_and_line @ SV34 @ SV44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(251,plain,
! [SV51: $i,SV45: $i,SV35: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV35 @ SV45 )
| ~ ( left_apart_point @ SV35 @ SV51 ) )
| ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(252,plain,
! [SV46: $i,SV52: $i,SV36: $i] :
( ( ~ ( left_apart_point @ SV36 @ SV52 )
| ( distinct_points @ SV36 @ SV46 )
| ( left_apart_point @ SV46 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV47: $i,SV37: $i] :
( ( ~ ( ~ ( right_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) ) )
| ~ ( ~ ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( right_apart_point @ SV37 @ SV47 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(254,plain,
! [SV38: $i,SV28: $i] :
( ( left_apart_point @ SV28 @ SV38 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(255,plain,
! [SV38: $i,SV28: $i] :
( ( left_apart_point @ SV28 @ ( reverse_line @ SV38 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(256,plain,
! [SV39: $i,SV29: $i] :
( ( left_convergent_lines @ SV29 @ SV39 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(257,plain,
! [SV39: $i,SV29: $i] :
( ( left_convergent_lines @ SV29 @ ( reverse_line @ SV39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(258,plain,
! [SV48: $i,SV40: $i,SV30: $i] :
( ( ( ~ ( distinct_points @ SV30 @ SV40 ) )
= $true )
| ( ( ( distinct_points @ SV30 @ SV48 )
| ( distinct_points @ SV40 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV41: $i,SV31: $i,SV49: $i] :
( ( ~ ( ~ ( divides_points @ SV49 @ SV31 @ SV41 )
| ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
| ( divides_points @ SV49 @ SV31 @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(260,plain,
! [SV50: $i,SV42: $i,SV32: $i] :
( ( ( ~ ( left_convergent_lines @ SV32 @ SV42 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV42 @ SV50 )
| ( left_convergent_lines @ SV32 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV43: $i,SV33: $i] :
( ( ( distinct_points @ SV33 @ SV43 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) )
| ~ ~ ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(262,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV34 @ SV44 )
| ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(263,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( ~ ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
| ( apart_point_and_line @ SV34 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(264,plain,
! [SV51: $i,SV45: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV35 @ SV45 )
| ~ ( left_apart_point @ SV35 @ SV51 ) ) )
= $true )
| ( ( ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(265,plain,
! [SV46: $i,SV52: $i,SV36: $i] :
( ( ( ~ ( left_apart_point @ SV36 @ SV52 ) )
= $true )
| ( ( ( distinct_points @ SV36 @ SV46 )
| ( left_apart_point @ SV46 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(266,plain,
! [SV47: $i,SV37: $i] :
( ( ~ ( ~ ( right_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(267,plain,
! [SV47: $i,SV37: $i] :
( ( ~ ( ~ ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( right_apart_point @ SV37 @ SV47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(268,plain,
! [SV48: $i,SV40: $i,SV30: $i] :
( ( ( distinct_points @ SV30 @ SV40 )
= $false )
| ( ( ( distinct_points @ SV30 @ SV48 )
| ( distinct_points @ SV40 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(269,plain,
! [SV41: $i,SV31: $i,SV49: $i] :
( ( ~ ( ~ ( divides_points @ SV49 @ SV31 @ SV41 )
| ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(270,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
| ( divides_points @ SV49 @ SV31 @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(271,plain,
! [SV50: $i,SV42: $i,SV32: $i] :
( ( ( left_convergent_lines @ SV32 @ SV42 )
= $false )
| ( ( ( unequally_directed_lines @ SV42 @ SV50 )
| ( left_convergent_lines @ SV32 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) )
| ~ ~ ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) ) )
= $false )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( apart_point_and_line @ SV34 @ SV44 )
| ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(274,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
| ( apart_point_and_line @ SV34 @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(275,plain,
! [SV51: $i,SV45: $i,SV35: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV35 @ SV45 )
| ~ ( left_apart_point @ SV35 @ SV51 ) ) )
= $false )
| ( ( ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV46: $i,SV52: $i,SV36: $i] :
( ( ( left_apart_point @ SV36 @ SV52 )
= $false )
| ( ( ( distinct_points @ SV36 @ SV46 )
| ( left_apart_point @ SV46 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV47: $i,SV37: $i] :
( ( ~ ( right_apart_point @ SV37 @ SV47 )
| ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(278,plain,
! [SV47: $i,SV37: $i] :
( ( ~ ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
| ( right_apart_point @ SV37 @ SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(279,plain,
! [SV40: $i,SV48: $i,SV30: $i] :
( ( ( distinct_points @ SV30 @ SV48 )
= $true )
| ( ( distinct_points @ SV40 @ SV48 )
= $true )
| ( ( distinct_points @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV41: $i,SV31: $i,SV49: $i] :
( ( ~ ( divides_points @ SV49 @ SV31 @ SV41 )
| ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(281,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
| ( divides_points @ SV49 @ SV31 @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(282,plain,
! [SV32: $i,SV50: $i,SV42: $i] :
( ( ( unequally_directed_lines @ SV42 @ SV50 )
= $true )
| ( ( left_convergent_lines @ SV32 @ SV50 )
= $true )
| ( ( left_convergent_lines @ SV32 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(283,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) ) )
= $false )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(284,plain,
! [SV33: $i,SV43: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) ) )
= $false )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(285,plain,
! [SV44: $i,SV34: $i] :
( ( ( ~ ( apart_point_and_line @ SV34 @ SV44 ) )
= $true )
| ( ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(286,plain,
! [SV44: $i,SV34: $i] :
( ( ( ~ ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) ) )
= $true )
| ( ( apart_point_and_line @ SV34 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(287,plain,
! [SV51: $i,SV45: $i,SV35: $i] :
( ( ( ~ ( distinct_points @ SV35 @ SV45 )
| ~ ( left_apart_point @ SV35 @ SV51 ) )
= $true )
| ( ( ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(288,plain,
! [SV52: $i,SV46: $i,SV36: $i] :
( ( ( distinct_points @ SV36 @ SV46 )
= $true )
| ( ( left_apart_point @ SV46 @ SV52 )
= $true )
| ( ( left_apart_point @ SV36 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(289,plain,
! [SV47: $i,SV37: $i] :
( ( ( ~ ( right_apart_point @ SV37 @ SV47 ) )
= $true )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(290,plain,
! [SV47: $i,SV37: $i] :
( ( ( ~ ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) ) )
= $true )
| ( ( right_apart_point @ SV37 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(291,plain,
! [SV41: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( divides_points @ SV49 @ SV31 @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(292,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(293,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) ) )
= $true )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(294,plain,
! [SV33: $i,SV43: $i] :
( ( ( ~ ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) ) )
= $true )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(295,plain,
! [SV44: $i,SV34: $i] :
( ( ( apart_point_and_line @ SV34 @ SV44 )
= $false )
| ( ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(296,plain,
! [SV44: $i,SV34: $i] :
( ( ( ( left_apart_point @ SV34 @ SV44 )
| ( right_apart_point @ SV34 @ SV44 ) )
= $false )
| ( ( apart_point_and_line @ SV34 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(297,plain,
! [SV51: $i,SV45: $i,SV35: $i] :
( ( ( ~ ( distinct_points @ SV35 @ SV45 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV35 @ SV51 ) )
= $true )
| ( ( ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(298,plain,
! [SV47: $i,SV37: $i] :
( ( ( right_apart_point @ SV37 @ SV47 )
= $false )
| ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(299,plain,
! [SV47: $i,SV37: $i] :
( ( ( left_apart_point @ SV37 @ ( reverse_line @ SV47 ) )
= $false )
| ( ( right_apart_point @ SV37 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(300,plain,
! [SV41: $i,SV31: $i,SV49: $i] :
( ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false )
| ( ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(301,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
| ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $false )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(302,plain,
! [SV43: $i,SV33: $i] :
( ( ( apart_point_and_line @ SV33 @ ( line_connecting @ SV33 @ SV43 ) )
= $false )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(303,plain,
! [SV33: $i,SV43: $i] :
( ( ( apart_point_and_line @ SV43 @ ( line_connecting @ SV33 @ SV43 ) )
= $false )
| ( ( distinct_points @ SV33 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(304,plain,
! [SV44: $i,SV34: $i] :
( ( ( left_apart_point @ SV34 @ SV44 )
= $true )
| ( ( right_apart_point @ SV34 @ SV44 )
= $true )
| ( ( apart_point_and_line @ SV34 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(305,plain,
! [SV44: $i,SV34: $i] :
( ( ( left_apart_point @ SV34 @ SV44 )
= $false )
| ( ( apart_point_and_line @ SV34 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(306,plain,
! [SV44: $i,SV34: $i] :
( ( ( right_apart_point @ SV34 @ SV44 )
= $false )
| ( ( apart_point_and_line @ SV34 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(307,plain,
! [SV51: $i,SV45: $i,SV35: $i] :
( ( ( distinct_points @ SV35 @ SV45 )
= $false )
| ( ( ~ ( left_apart_point @ SV35 @ SV51 ) )
= $true )
| ( ( ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(308,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(309,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) ) )
= $false )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(310,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $false )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(311,plain,
! [SV45: $i,SV51: $i,SV35: $i] :
( ( ( left_apart_point @ SV35 @ SV51 )
= $false )
| ( ( distinct_points @ SV35 @ SV45 )
= $false )
| ( ( ( left_apart_point @ SV45 @ SV51 )
| ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(312,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(313,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( left_apart_point @ SV31 @ SV49 )
| ~ ( right_apart_point @ SV41 @ SV49 ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(314,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(315,plain,
! [SV35: $i,SV51: $i,SV45: $i] :
( ( ( left_apart_point @ SV45 @ SV51 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV35 @ SV45 ) @ SV51 )
= $true )
| ( ( distinct_points @ SV35 @ SV45 )
= $false )
| ( ( left_apart_point @ SV35 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(316,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( left_apart_point @ SV31 @ SV49 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(317,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( ~ ( right_apart_point @ SV41 @ SV49 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(318,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( left_apart_point @ SV31 @ SV49 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV41 @ SV49 ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(319,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( right_apart_point @ SV31 @ SV49 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV41 @ SV49 ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(320,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( left_apart_point @ SV31 @ SV49 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(321,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( right_apart_point @ SV41 @ SV49 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(322,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( left_apart_point @ SV31 @ SV49 )
= $false )
| ( ( ~ ( right_apart_point @ SV41 @ SV49 ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(323,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( right_apart_point @ SV31 @ SV49 )
= $false )
| ( ( ~ ( left_apart_point @ SV41 @ SV49 ) )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(324,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) )
= $false )
| ( ( left_apart_point @ SV31 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(325,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( right_apart_point @ SV31 @ SV49 )
| ~ ( left_apart_point @ SV41 @ SV49 ) )
= $false )
| ( ( right_apart_point @ SV41 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(326,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( right_apart_point @ SV41 @ SV49 )
= $false )
| ( ( left_apart_point @ SV31 @ SV49 )
= $false )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(327,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( left_apart_point @ SV41 @ SV49 )
= $false )
| ( ( right_apart_point @ SV31 @ SV49 )
= $false )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(328,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( right_apart_point @ SV31 @ SV49 ) )
= $false )
| ( ( left_apart_point @ SV31 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(329,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( ~ ( left_apart_point @ SV41 @ SV49 ) )
= $false )
| ( ( left_apart_point @ SV31 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(330,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( ~ ( right_apart_point @ SV31 @ SV49 ) )
= $false )
| ( ( right_apart_point @ SV41 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(331,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( ~ ( left_apart_point @ SV41 @ SV49 ) )
= $false )
| ( ( right_apart_point @ SV41 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(332,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( right_apart_point @ SV31 @ SV49 )
= $true )
| ( ( left_apart_point @ SV31 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(333,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( left_apart_point @ SV41 @ SV49 )
= $true )
| ( ( left_apart_point @ SV31 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(334,plain,
! [SV41: $i,SV49: $i,SV31: $i] :
( ( ( right_apart_point @ SV31 @ SV49 )
= $true )
| ( ( right_apart_point @ SV41 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(335,plain,
! [SV31: $i,SV49: $i,SV41: $i] :
( ( ( left_apart_point @ SV41 @ SV49 )
= $true )
| ( ( right_apart_point @ SV41 @ SV49 )
= $true )
| ( ( divides_points @ SV49 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(336,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[210,335,334,333,332,327,326,315,306,305,304,303,302,299,298,288,282,279,257,256,255,254,233,224,211]) ).
thf(337,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[336,198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO252+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 10:13:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/0.45
% 0.92/0.45 No.of.Axioms: 11
% 0.92/0.45
% 0.92/0.45 Length.of.Defs: 0
% 0.92/0.45
% 0.92/0.45 Contains.Choice.Funs: false
% 0.92/0.45 ........
% 0.92/0.45
% 0.92/0.45 ********************************
% 0.92/0.45 * All subproblems solved! *
% 0.92/0.45 ********************************
% 0.92/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:336,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.92/0.45
% 0.92/0.45 %**** Beginning of derivation protocol ****
% 0.92/0.45 % SZS output start CNFRefutation
% See solution above
% 0.92/0.46
% 0.92/0.46 %**** End of derivation protocol ****
% 0.92/0.46 %**** no. of clauses in derivation: 312 ****
% 0.92/0.46 %**** clause counter: 336 ****
% 0.92/0.46
% 0.92/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:336,loop_count:0,foatp_calls:1,translation:fof_full)
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