%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO237+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 : n015.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 10:18:36 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 119 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 824 ( 204 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1701 ( 353 ~; 256 |; 15 &;1051 @)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 6 con; 0-4 aty)
% Number of variables : 260 ( 0 ^; 260 !; 0 ?; 260 :)
% 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_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $i ).
thf(tp_sK4_SY20,type,
sK4_SY20: $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(9,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7_cons_objs) ).
thf(10,axiom,
! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L )
& ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6_cons_objs) ).
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(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(37,conjecture,
! [A: $i,B: $i,C: $i,L: $i] :
( ( apart_point_and_line @ C @ L )
=> ( ( divides_points @ L @ A @ B )
=> ( ( divides_points @ L @ A @ C )
| ( divides_points @ L @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,L: $i] :
( ( apart_point_and_line @ C @ L )
=> ( ( divides_points @ L @ A @ B )
=> ( ( divides_points @ L @ A @ C )
| ( divides_points @ L @ B @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i,L: $i] :
( ( apart_point_and_line @ C @ L )
=> ( ( divides_points @ L @ A @ B )
=> ( ( divides_points @ L @ A @ C )
| ( divides_points @ L @ B @ C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L )
& ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
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,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(44,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(45,plain,
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( apart_point_and_line @ SY16 @ SY17 )
=> ( ( divides_points @ SY17 @ sK1_A @ SY15 )
=> ( ( divides_points @ SY17 @ sK1_A @ SY16 )
| ( divides_points @ SY17 @ SY15 @ SY16 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(46,plain,
( ( ! [SY18: $i,SY19: $i] :
( ( apart_point_and_line @ SY18 @ SY19 )
=> ( ( divides_points @ SY19 @ sK1_A @ sK2_SY15 )
=> ( ( divides_points @ SY19 @ sK1_A @ SY18 )
| ( divides_points @ SY19 @ sK2_SY15 @ SY18 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(47,plain,
( ( ! [SY20: $i] :
( ( apart_point_and_line @ sK3_SY18 @ SY20 )
=> ( ( divides_points @ SY20 @ sK1_A @ sK2_SY15 )
=> ( ( divides_points @ SY20 @ sK1_A @ sK3_SY18 )
| ( divides_points @ SY20 @ sK2_SY15 @ sK3_SY18 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(48,plain,
( ( ( apart_point_and_line @ sK3_SY18 @ sK4_SY20 )
=> ( ( divides_points @ sK4_SY20 @ sK1_A @ sK2_SY15 )
=> ( ( divides_points @ sK4_SY20 @ sK1_A @ sK3_SY18 )
| ( divides_points @ sK4_SY20 @ sK2_SY15 @ sK3_SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(49,plain,
( ( apart_point_and_line @ sK3_SY18 @ sK4_SY20 )
= $true ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(50,plain,
( ( divides_points @ sK4_SY20 @ sK1_A @ sK2_SY15 )
= $true ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(51,plain,
( ( ( divides_points @ sK4_SY20 @ sK1_A @ sK3_SY18 )
| ( divides_points @ sK4_SY20 @ sK2_SY15 @ sK3_SY18 ) )
= $false ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ( ( divides_points @ sK4_SY20 @ sK1_A @ sK3_SY18 )
| ( divides_points @ sK4_SY20 @ sK2_SY15 @ sK3_SY18 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(53,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)],[44]) ).
thf(54,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)],[43]) ).
thf(55,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(56,plain,
( ( ! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ L )
& ~ ( apart_point_and_line @ ( intersection_point @ L @ M ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(57,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(58,plain,
( ( divides_points @ sK4_SY20 @ sK1_A @ sK2_SY15 )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(59,plain,
( ( apart_point_and_line @ sK3_SY18 @ sK4_SY20 )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(60,plain,
( ( ~ ( ( divides_points @ sK4_SY20 @ sK1_A @ sK3_SY18 )
| ( divides_points @ sK4_SY20 @ sK2_SY15 @ sK3_SY18 ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(61,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)],[53]) ).
thf(62,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)],[54]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(64,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)],[55]) ).
thf(65,plain,
! [SV1: $i] :
( ( ! [SY21: $i] :
~ ( apart_point_and_line @ SV1 @ ( parallel_through_point @ SY21 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(66,plain,
( ( ( divides_points @ sK4_SY20 @ sK1_A @ sK3_SY18 )
| ( divides_points @ sK4_SY20 @ sK2_SY15 @ sK3_SY18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV2: $i] :
( ( ! [SY22: $i] :
~ ( ~ ( ~ ( apart_point_and_line @ SV2 @ SY22 )
| ( left_apart_point @ SV2 @ SY22 )
| ( right_apart_point @ SV2 @ SY22 ) )
| ~ ( ~ ( ( left_apart_point @ SV2 @ SY22 )
| ( right_apart_point @ SV2 @ SY22 ) )
| ( apart_point_and_line @ SV2 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV3: $i] :
( ( ! [SY23: $i,SY24: $i] :
~ ( ~ ( ~ ( divides_points @ SY24 @ SV3 @ SY23 )
| ~ ( ~ ( left_apart_point @ SV3 @ SY24 )
| ~ ( right_apart_point @ SY23 @ SY24 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SY24 )
| ~ ( left_apart_point @ SY23 @ SY24 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SY24 )
| ~ ( right_apart_point @ SY23 @ SY24 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SY24 )
| ~ ( left_apart_point @ SY23 @ SY24 ) ) )
| ( divides_points @ SY24 @ SV3 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV4: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV4 @ SY25 )
| ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SY25 ) ) )
| ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SY25 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SY25 ) @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV5: $i] :
( ( ! [SY26: $i] :
( ~ ( distinct_points @ SV5 @ SY26 )
| ~ ( ~ ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SY26 ) )
| ~ ~ ( apart_point_and_line @ SY26 @ ( line_connecting @ SV5 @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( apart_point_and_line @ SV1 @ ( parallel_through_point @ SV6 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
( ( divides_points @ sK4_SY20 @ sK1_A @ sK3_SY18 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
( ( divides_points @ sK4_SY20 @ sK2_SY15 @ sK3_SY18 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( apart_point_and_line @ SV2 @ SV7 )
| ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
| ~ ( ~ ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
| ( apart_point_and_line @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(75,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( divides_points @ SY27 @ SV3 @ SV8 )
| ~ ( ~ ( left_apart_point @ SV3 @ SY27 )
| ~ ( right_apart_point @ SV8 @ SY27 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SY27 )
| ~ ( left_apart_point @ SV8 @ SY27 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SY27 )
| ~ ( right_apart_point @ SV8 @ SY27 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SY27 )
| ~ ( left_apart_point @ SV8 @ SY27 ) ) )
| ( divides_points @ SY27 @ SV3 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV4 @ SV9 )
| ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) ) )
| ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( distinct_points @ SV5 @ SV10 )
| ~ ( ~ ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) )
| ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV6: $i,SV1: $i] :
( ( apart_point_and_line @ SV1 @ ( parallel_through_point @ SV6 @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(79,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV2 @ SV7 )
| ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
| ~ ( ~ ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
| ( apart_point_and_line @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV8: $i,SV3: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( divides_points @ SV11 @ SV3 @ SV8 )
| ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
| ( divides_points @ SV11 @ SV3 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV4 @ SV9 )
| ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( distinct_points @ SV5 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) )
| ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( apart_point_and_line @ SV2 @ SV7 )
| ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
| ( apart_point_and_line @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV8: $i,SV3: $i,SV11: $i] :
( ( ~ ( ~ ( divides_points @ SV11 @ SV3 @ SV8 )
| ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
| ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
| ( divides_points @ SV11 @ SV3 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV4 @ SV9 )
| ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV10: $i,SV5: $i] :
( ( ( distinct_points @ SV5 @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) )
| ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( apart_point_and_line @ SV2 @ SV7 )
| ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
| ( apart_point_and_line @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(90,plain,
! [SV8: $i,SV3: $i,SV11: $i] :
( ( ~ ( ~ ( divides_points @ SV11 @ SV3 @ SV8 )
| ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(91,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
| ( divides_points @ SV11 @ SV3 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(92,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( unequally_directed_lines @ SV4 @ SV9 )
| ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(93,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) )
| ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) ) )
= $false )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( apart_point_and_line @ SV2 @ SV7 ) )
= $true )
| ( ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) ) )
= $true )
| ( ( apart_point_and_line @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV8: $i,SV3: $i,SV11: $i] :
( ( ~ ( divides_points @ SV11 @ SV3 @ SV8 )
| ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(97,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
| ( divides_points @ SV11 @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(98,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( unequally_directed_lines @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) ) )
= $false )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(100,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) ) )
= $false )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV7: $i,SV2: $i] :
( ( ( apart_point_and_line @ SV2 @ SV7 )
= $false )
| ( ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV7: $i,SV2: $i] :
( ( ( ( left_apart_point @ SV2 @ SV7 )
| ( right_apart_point @ SV2 @ SV7 ) )
= $false )
| ( ( apart_point_and_line @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV8: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( divides_points @ SV11 @ SV3 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV9: $i,SV4: $i] :
( ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) ) )
= $true )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) ) )
= $true )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV7: $i,SV2: $i] :
( ( ( left_apart_point @ SV2 @ SV7 )
= $true )
| ( ( right_apart_point @ SV2 @ SV7 )
= $true )
| ( ( apart_point_and_line @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV7: $i,SV2: $i] :
( ( ( left_apart_point @ SV2 @ SV7 )
= $false )
| ( ( apart_point_and_line @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(110,plain,
! [SV7: $i,SV2: $i] :
( ( ( right_apart_point @ SV2 @ SV7 )
= $false )
| ( ( apart_point_and_line @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(111,plain,
! [SV8: $i,SV3: $i,SV11: $i] :
( ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false )
| ( ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
| ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $false )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV9: $i,SV4: $i] :
( ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( ~ ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV10: $i,SV5: $i] :
( ( ( apart_point_and_line @ SV5 @ ( line_connecting @ SV5 @ SV10 ) )
= $false )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV5: $i,SV10: $i] :
( ( ( apart_point_and_line @ SV10 @ ( line_connecting @ SV5 @ SV10 ) )
= $false )
| ( ( distinct_points @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(116,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) ) )
= $false )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(118,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $false )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(119,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
| ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) )
= $false )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( left_apart_point @ SV3 @ SV11 )
| ~ ( right_apart_point @ SV8 @ SV11 ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(122,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(123,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 ) )
= $false )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) )
= $false )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(125,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( left_apart_point @ SV3 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(126,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( right_apart_point @ SV8 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(127,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( left_apart_point @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( right_apart_point @ SV8 @ SV11 ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( right_apart_point @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( left_apart_point @ SV8 @ SV11 ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 ) )
= $true )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(130,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 ) )
= $true )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( left_apart_point @ SV3 @ SV11 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(132,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( right_apart_point @ SV8 @ SV11 )
= $true )
| ( ( ~ ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(133,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( left_apart_point @ SV3 @ SV11 )
= $false )
| ( ( ~ ( right_apart_point @ SV8 @ SV11 ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( right_apart_point @ SV3 @ SV11 )
= $false )
| ( ( ~ ( left_apart_point @ SV8 @ SV11 ) )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV9: $i,SV4: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV4 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV9: $i,SV4: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV4 @ SV9 ) @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ SV9 )
= $false )
| ( ( unequally_directed_lines @ SV4 @ ( reverse_line @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) )
= $false )
| ( ( left_apart_point @ SV3 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( right_apart_point @ SV3 @ SV11 )
| ~ ( left_apart_point @ SV8 @ SV11 ) )
= $false )
| ( ( right_apart_point @ SV8 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( right_apart_point @ SV8 @ SV11 )
= $false )
| ( ( left_apart_point @ SV3 @ SV11 )
= $false )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( left_apart_point @ SV8 @ SV11 )
= $false )
| ( ( right_apart_point @ SV3 @ SV11 )
= $false )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( right_apart_point @ SV3 @ SV11 ) )
= $false )
| ( ( left_apart_point @ SV3 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(142,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( left_apart_point @ SV8 @ SV11 ) )
= $false )
| ( ( left_apart_point @ SV3 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(143,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( right_apart_point @ SV3 @ SV11 ) )
= $false )
| ( ( right_apart_point @ SV8 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(144,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( left_apart_point @ SV8 @ SV11 ) )
= $false )
| ( ( right_apart_point @ SV8 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(145,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( right_apart_point @ SV3 @ SV11 )
= $true )
| ( ( left_apart_point @ SV3 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(146,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( left_apart_point @ SV8 @ SV11 )
= $true )
| ( ( left_apart_point @ SV3 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(147,plain,
! [SV8: $i,SV11: $i,SV3: $i] :
( ( ( right_apart_point @ SV3 @ SV11 )
= $true )
| ( ( right_apart_point @ SV8 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(148,plain,
! [SV3: $i,SV11: $i,SV8: $i] :
( ( ( left_apart_point @ SV8 @ SV11 )
= $true )
| ( ( right_apart_point @ SV8 @ SV11 )
= $true )
| ( ( divides_points @ SV11 @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(149,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[58,148,147,146,145,140,139,136,135,115,114,110,109,108,78,73,72,59]) ).
thf(150,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO237+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n015.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 10:14:57 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25
% 0.09/0.25 No.of.Axioms: 5
% 0.09/0.25
% 0.09/0.25 Length.of.Defs: 0
% 0.09/0.25
% 0.09/0.25 Contains.Choice.Funs: false
% 0.09/0.25 ...
% 0.09/0.25
% 0.09/0.25 ********************************
% 0.09/0.25 * All subproblems solved! *
% 0.09/0.25 ********************************
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:149,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.25
% 0.09/0.25 %**** Beginning of derivation protocol ****
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 %**** End of derivation protocol ****
% 0.09/0.25 %**** no. of clauses in derivation: 119 ****
% 0.09/0.25 %**** clause counter: 149 ****
% 0.09/0.25
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:149,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------