%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO244+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 : n016.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 10:18:38 AM UTC 2026
% Result : Theorem 0.53s 0.28s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 153 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 967 ( 235 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1856 ( 337 ~; 299 |; 12 &;1175 @)
% ( 9 <=>; 24 =>; 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 : 357 ( 0 ^; 357 !; 0 ?; 357 :)
% 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_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: $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(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(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,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( right_apart_point @ C @ ( line_connecting @ A @ B ) )
=> ( left_apart_point @ C @ ( line_connecting @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( right_apart_point @ C @ ( line_connecting @ A @ B ) )
=> ( left_apart_point @ C @ ( line_connecting @ B @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( right_apart_point @ C @ ( line_connecting @ A @ B ) )
=> ( left_apart_point @ C @ ( line_connecting @ B @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,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(41,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(42,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(43,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(44,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(45,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(46,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(47,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(48,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(49,plain,
( ( ! [SY24: $i,SY25: $i] :
( ( distinct_points @ sK1_A @ SY24 )
=> ( ( right_apart_point @ SY25 @ ( line_connecting @ sK1_A @ SY24 ) )
=> ( left_apart_point @ SY25 @ ( line_connecting @ SY24 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(50,plain,
( ( ! [SY26: $i] :
( ( distinct_points @ sK1_A @ sK2_SY24 )
=> ( ( right_apart_point @ SY26 @ ( line_connecting @ sK1_A @ sK2_SY24 ) )
=> ( left_apart_point @ SY26 @ ( line_connecting @ sK2_SY24 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(51,plain,
( ( ( distinct_points @ sK1_A @ sK2_SY24 )
=> ( ( right_apart_point @ sK3_SY26 @ ( line_connecting @ sK1_A @ sK2_SY24 ) )
=> ( left_apart_point @ sK3_SY26 @ ( line_connecting @ sK2_SY24 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(52,plain,
( ( distinct_points @ sK1_A @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[51]) ).
thf(53,plain,
( ( right_apart_point @ sK3_SY26 @ ( line_connecting @ sK1_A @ sK2_SY24 ) )
= $true ),
inference(standard_cnf,[status(thm)],[51]) ).
thf(54,plain,
( ( left_apart_point @ sK3_SY26 @ ( line_connecting @ sK2_SY24 @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[51]) ).
thf(55,plain,
( ( ~ ( left_apart_point @ sK3_SY26 @ ( line_connecting @ sK2_SY24 @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ( right_apart_point @ X @ Y )
<=> ( left_apart_point @ X @ ( reverse_line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(57,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)],[47]) ).
thf(58,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)],[46]) ).
thf(59,plain,
( ( ! [A: $i] :
~ ( distinct_points @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(60,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(61,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(62,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)],[42]) ).
thf(63,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)],[41]) ).
thf(64,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)],[40]) ).
thf(65,plain,
( ( right_apart_point @ sK3_SY26 @ ( line_connecting @ sK1_A @ sK2_SY24 ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(66,plain,
( ( distinct_points @ sK1_A @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(67,plain,
( ( ~ ( left_apart_point @ sK3_SY26 @ ( line_connecting @ sK2_SY24 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(68,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)],[64]) ).
thf(69,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)],[58]) ).
thf(70,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)],[60]) ).
thf(71,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)],[63]) ).
thf(72,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)],[57]) ).
thf(73,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)],[56]) ).
thf(74,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)],[62]) ).
thf(75,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(76,plain,
! [SV2: $i] :
( ( ! [SY27: $i] :
~ ( ( left_apart_point @ SV2 @ SY27 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
( ( left_apart_point @ sK3_SY26 @ ( line_connecting @ sK2_SY24 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV3: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( left_apart_point @ SV3 @ SY29 )
| ( distinct_points @ SV3 @ SY28 )
| ( left_apart_point @ SY28 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV4: $i] :
( ( ! [SY30: $i,SY31: $i] :
~ ( ~ ( ~ ( divides_points @ SY31 @ SV4 @ SY30 )
| ~ ( ~ ( left_apart_point @ SV4 @ SY31 )
| ~ ( right_apart_point @ SY30 @ SY31 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SY31 )
| ~ ( left_apart_point @ SY30 @ SY31 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SY31 )
| ~ ( right_apart_point @ SY30 @ SY31 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SY31 )
| ~ ( left_apart_point @ SY30 @ SY31 ) ) )
| ( divides_points @ SY31 @ SV4 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV5: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( distinct_points @ SV5 @ SY32 )
| ( distinct_points @ SV5 @ SY33 )
| ( distinct_points @ SY32 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV6: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SY34 )
| ~ ( left_apart_point @ SV6 @ SY35 ) )
| ( left_apart_point @ SY34 @ SY35 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SY34 ) @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV7: $i] :
( ( ! [SY36: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SV7 @ SY36 )
| ( left_apart_point @ SV7 @ SY36 )
| ( right_apart_point @ SV7 @ SY36 ) )
| ~ ( ~ ( ( left_apart_point @ SV7 @ SY36 )
| ( right_apart_point @ SV7 @ SY36 ) )
| ( apart_point_and_line @ SV7 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV8: $i] :
( ( ! [SY37: $i] :
~ ( ~ ( ~ ( right_apart_point @ SV8 @ SY37 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SY37 ) ) )
| ~ ( ~ ( left_apart_point @ SV8 @ ( reverse_line @ SY37 ) )
| ( right_apart_point @ SV8 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV9: $i] :
( ( ! [SY38: $i] :
( ~ ( distinct_points @ SV9 @ SY38 )
| ~ ( ~ ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SY38 ) )
| ~ ~ ( apart_point_and_line @ SY38 @ ( line_connecting @ SV9 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( ( left_apart_point @ SV2 @ SV10 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY39: $i] :
( ~ ( left_apart_point @ SV3 @ SY39 )
| ( distinct_points @ SV3 @ SV11 )
| ( left_apart_point @ SV11 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV12: $i,SV4: $i] :
( ( ! [SY40: $i] :
~ ( ~ ( ~ ( divides_points @ SY40 @ SV4 @ SV12 )
| ~ ( ~ ( left_apart_point @ SV4 @ SY40 )
| ~ ( right_apart_point @ SV12 @ SY40 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SY40 )
| ~ ( left_apart_point @ SV12 @ SY40 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SY40 )
| ~ ( right_apart_point @ SV12 @ SY40 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SY40 )
| ~ ( left_apart_point @ SV12 @ SY40 ) ) )
| ( divides_points @ SY40 @ SV4 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY41: $i] :
( ~ ( distinct_points @ SV5 @ SV13 )
| ( distinct_points @ SV5 @ SY41 )
| ( distinct_points @ SV13 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SV14 )
| ~ ( left_apart_point @ SV6 @ SY42 ) )
| ( left_apart_point @ SV14 @ SY42 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( apart_point_and_line @ SV7 @ SV15 )
| ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
| ~ ( ~ ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
| ( apart_point_and_line @ SV7 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( right_apart_point @ SV8 @ SV16 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) ) )
| ~ ( ~ ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV8 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( ~ ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) )
| ~ ~ ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV10: $i,SV2: $i] :
( ( ( left_apart_point @ SV2 @ SV10 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV11: $i,SV18: $i,SV3: $i] :
( ( ~ ( left_apart_point @ SV3 @ SV18 )
| ( distinct_points @ SV3 @ SV11 )
| ( left_apart_point @ SV11 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV12: $i,SV4: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( divides_points @ SV19 @ SV4 @ SV12 )
| ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
| ( divides_points @ SV19 @ SV4 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV20: $i,SV13: $i,SV5: $i] :
( ( ~ ( distinct_points @ SV5 @ SV13 )
| ( distinct_points @ SV5 @ SV20 )
| ( distinct_points @ SV13 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV21: $i,SV14: $i,SV6: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV6 @ SV14 )
| ~ ( left_apart_point @ SV6 @ SV21 ) )
| ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV7 @ SV15 )
| ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
| ~ ( ~ ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
| ( apart_point_and_line @ SV7 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( ~ ( right_apart_point @ SV8 @ SV16 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) ) )
| ~ ( ~ ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV8 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV17: $i,SV9: $i] :
( ( ( ~ ( distinct_points @ SV9 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) )
| ~ ~ ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV10: $i,SV2: $i] :
( ( left_apart_point @ SV2 @ SV10 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(103,plain,
! [SV10: $i,SV2: $i] :
( ( left_apart_point @ SV2 @ ( reverse_line @ SV10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(104,plain,
! [SV11: $i,SV18: $i,SV3: $i] :
( ( ( ~ ( left_apart_point @ SV3 @ SV18 ) )
= $true )
| ( ( ( distinct_points @ SV3 @ SV11 )
| ( left_apart_point @ SV11 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV12: $i,SV4: $i,SV19: $i] :
( ( ~ ( ~ ( divides_points @ SV19 @ SV4 @ SV12 )
| ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
| ( divides_points @ SV19 @ SV4 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV20: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( distinct_points @ SV5 @ SV13 ) )
= $true )
| ( ( ( distinct_points @ SV5 @ SV20 )
| ( distinct_points @ SV13 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV21: $i,SV14: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV6 @ SV14 )
| ~ ( left_apart_point @ SV6 @ SV21 ) ) )
= $true )
| ( ( ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV7 @ SV15 )
| ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(109,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( ~ ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
| ( apart_point_and_line @ SV7 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( ~ ( right_apart_point @ SV8 @ SV16 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(111,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( ~ ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV8 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(112,plain,
! [SV17: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV17 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) )
| ~ ~ ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV11: $i,SV18: $i,SV3: $i] :
( ( ( left_apart_point @ SV3 @ SV18 )
= $false )
| ( ( ( distinct_points @ SV3 @ SV11 )
| ( left_apart_point @ SV11 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV12: $i,SV4: $i,SV19: $i] :
( ( ~ ( ~ ( divides_points @ SV19 @ SV4 @ SV12 )
| ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(115,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
| ( divides_points @ SV19 @ SV4 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(116,plain,
! [SV20: $i,SV13: $i,SV5: $i] :
( ( ( distinct_points @ SV5 @ SV13 )
= $false )
| ( ( ( distinct_points @ SV5 @ SV20 )
| ( distinct_points @ SV13 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV21: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV6 @ SV14 )
| ~ ( left_apart_point @ SV6 @ SV21 ) ) )
= $false )
| ( ( ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( apart_point_and_line @ SV7 @ SV15 )
| ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
| ( apart_point_and_line @ SV7 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(120,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( right_apart_point @ SV8 @ SV16 )
| ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(121,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
| ( right_apart_point @ SV8 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV17: $i,SV9: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) )
| ~ ~ ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) ) )
= $false )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV18: $i,SV11: $i,SV3: $i] :
( ( ( distinct_points @ SV3 @ SV11 )
= $true )
| ( ( left_apart_point @ SV11 @ SV18 )
= $true )
| ( ( left_apart_point @ SV3 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV12: $i,SV4: $i,SV19: $i] :
( ( ~ ( divides_points @ SV19 @ SV4 @ SV12 )
| ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
| ( divides_points @ SV19 @ SV4 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(126,plain,
! [SV13: $i,SV20: $i,SV5: $i] :
( ( ( distinct_points @ SV5 @ SV20 )
= $true )
| ( ( distinct_points @ SV13 @ SV20 )
= $true )
| ( ( distinct_points @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV21: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV14 )
| ~ ( left_apart_point @ SV6 @ SV21 ) )
= $true )
| ( ( ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(128,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( apart_point_and_line @ SV7 @ SV15 ) )
= $true )
| ( ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) ) )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV16: $i,SV8: $i] :
( ( ( ~ ( right_apart_point @ SV8 @ SV16 ) )
= $true )
| ( ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV16: $i,SV8: $i] :
( ( ( ~ ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) ) )
= $true )
| ( ( right_apart_point @ SV8 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV17: $i,SV9: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) ) )
= $false )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(133,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) ) )
= $false )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(134,plain,
! [SV12: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( divides_points @ SV19 @ SV4 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV21: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV14 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV6 @ SV21 ) )
= $true )
| ( ( ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV15: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ SV15 )
= $false )
| ( ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV15: $i,SV7: $i] :
( ( ( ( left_apart_point @ SV7 @ SV15 )
| ( right_apart_point @ SV7 @ SV15 ) )
= $false )
| ( ( apart_point_and_line @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV16: $i,SV8: $i] :
( ( ( right_apart_point @ SV8 @ SV16 )
= $false )
| ( ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV16: $i,SV8: $i] :
( ( ( left_apart_point @ SV8 @ ( reverse_line @ SV16 ) )
= $false )
| ( ( right_apart_point @ SV8 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV17: $i,SV9: $i] :
( ( ( ~ ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) ) )
= $true )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(142,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) ) )
= $true )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(143,plain,
! [SV12: $i,SV4: $i,SV19: $i] :
( ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false )
| ( ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
| ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $false )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV21: $i,SV14: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV14 )
= $false )
| ( ( ~ ( left_apart_point @ SV6 @ SV21 ) )
= $true )
| ( ( ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV15: $i,SV7: $i] :
( ( ( left_apart_point @ SV7 @ SV15 )
= $true )
| ( ( right_apart_point @ SV7 @ SV15 )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV15: $i,SV7: $i] :
( ( ( left_apart_point @ SV7 @ SV15 )
= $false )
| ( ( apart_point_and_line @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(148,plain,
! [SV15: $i,SV7: $i] :
( ( ( right_apart_point @ SV7 @ SV15 )
= $false )
| ( ( apart_point_and_line @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(149,plain,
! [SV17: $i,SV9: $i] :
( ( ( apart_point_and_line @ SV9 @ ( line_connecting @ SV9 @ SV17 ) )
= $false )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(150,plain,
! [SV9: $i,SV17: $i] :
( ( ( apart_point_and_line @ SV17 @ ( line_connecting @ SV9 @ SV17 ) )
= $false )
| ( ( distinct_points @ SV9 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(151,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) ) )
= $false )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(153,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $false )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(154,plain,
! [SV14: $i,SV21: $i,SV6: $i] :
( ( ( left_apart_point @ SV6 @ SV21 )
= $false )
| ( ( distinct_points @ SV6 @ SV14 )
= $false )
| ( ( ( left_apart_point @ SV14 @ SV21 )
| ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(156,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( left_apart_point @ SV4 @ SV19 )
| ~ ( right_apart_point @ SV12 @ SV19 ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(157,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(158,plain,
! [SV6: $i,SV21: $i,SV14: $i] :
( ( ( left_apart_point @ SV14 @ SV21 )
= $true )
| ( ( left_convergent_lines @ ( line_connecting @ SV6 @ SV14 ) @ SV21 )
= $true )
| ( ( distinct_points @ SV6 @ SV14 )
= $false )
| ( ( left_apart_point @ SV6 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( left_apart_point @ SV4 @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(160,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( right_apart_point @ SV12 @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(161,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( left_apart_point @ SV4 @ SV19 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV12 @ SV19 ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( right_apart_point @ SV4 @ SV19 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV12 @ SV19 ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( left_apart_point @ SV4 @ SV19 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( right_apart_point @ SV12 @ SV19 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( left_apart_point @ SV4 @ SV19 )
= $false )
| ( ( ~ ( right_apart_point @ SV12 @ SV19 ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( right_apart_point @ SV4 @ SV19 )
= $false )
| ( ( ~ ( left_apart_point @ SV12 @ SV19 ) )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) )
= $false )
| ( ( left_apart_point @ SV4 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(168,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( right_apart_point @ SV4 @ SV19 )
| ~ ( left_apart_point @ SV12 @ SV19 ) )
= $false )
| ( ( right_apart_point @ SV12 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( right_apart_point @ SV12 @ SV19 )
= $false )
| ( ( left_apart_point @ SV4 @ SV19 )
= $false )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( left_apart_point @ SV12 @ SV19 )
= $false )
| ( ( right_apart_point @ SV4 @ SV19 )
= $false )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( right_apart_point @ SV4 @ SV19 ) )
= $false )
| ( ( left_apart_point @ SV4 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(172,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( left_apart_point @ SV12 @ SV19 ) )
= $false )
| ( ( left_apart_point @ SV4 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( right_apart_point @ SV4 @ SV19 ) )
= $false )
| ( ( right_apart_point @ SV12 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(174,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( left_apart_point @ SV12 @ SV19 ) )
= $false )
| ( ( right_apart_point @ SV12 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(175,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( right_apart_point @ SV4 @ SV19 )
= $true )
| ( ( left_apart_point @ SV4 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(176,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( left_apart_point @ SV12 @ SV19 )
= $true )
| ( ( left_apart_point @ SV4 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(177,plain,
! [SV12: $i,SV19: $i,SV4: $i] :
( ( ( right_apart_point @ SV4 @ SV19 )
= $true )
| ( ( right_apart_point @ SV12 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(178,plain,
! [SV4: $i,SV19: $i,SV12: $i] :
( ( ( left_apart_point @ SV12 @ SV19 )
= $true )
| ( ( right_apart_point @ SV12 @ SV19 )
= $true )
| ( ( divides_points @ SV19 @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(179,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,178,177,176,175,170,169,158,150,149,148,147,146,140,139,126,123,103,102,85,77,66]) ).
thf(180,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO244+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
% 0.06/0.19 % Computer : n016.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 10:17:44 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.28
% 0.53/0.28 No.of.Axioms: 9
% 0.53/0.28
% 0.53/0.28 Length.of.Defs: 0
% 0.53/0.28
% 0.53/0.28 Contains.Choice.Funs: false
% 0.53/0.28 ....
% 0.53/0.28
% 0.53/0.28 ********************************
% 0.53/0.28 * All subproblems solved! *
% 0.53/0.28 ********************************
% 0.53/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:11,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:179,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.53/0.28
% 0.53/0.28 %**** Beginning of derivation protocol ****
% 0.53/0.28 % SZS output start CNFRefutation
% See solution above
% 0.53/0.29
% 0.53/0.29 %**** End of derivation protocol ****
% 0.53/0.29 %**** no. of clauses in derivation: 153 ****
% 0.53/0.29 %**** clause counter: 179 ****
% 0.53/0.29
% 0.53/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:11,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:179,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------