%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 10:18:22 AM UTC 2026
% Result : Theorem 4.08s 0.98s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 226 ( 131 unt; 0 typ; 0 def)
% Number of atoms : 1397 ( 351 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2363 ( 432 ~; 406 |; 25 &;1462 @)
% ( 8 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-2 aty)
% Number of variables : 508 ( 0 ^; 508 !; 0 ?; 508 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $i > $i > $o ).
thf(tp_convergent_lines,type,
convergent_lines: $i > $i > $o ).
thf(tp_distinct_lines,type,
distinct_lines: $i > $i > $o ).
thf(tp_distinct_points,type,
distinct_points: $i > $i > $o ).
thf(tp_equal_lines,type,
equal_lines: $i > $i > $o ).
thf(tp_equal_points,type,
equal_points: $i > $i > $o ).
thf(tp_incident_point_and_line,type,
incident_point_and_line: $i > $i > $o ).
thf(tp_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_line,type,
line: $i > $o ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_orthogonal_lines,type,
orthogonal_lines: $i > $i > $o ).
thf(tp_orthogonal_through_point,type,
orthogonal_through_point: $i > $i > $i ).
thf(tp_parallel_lines,type,
parallel_lines: $i > $i > $o ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
thf(24,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
thf(25,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
thf(28,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
thf(29,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
thf(32,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
thf(35,axiom,
! [X: $i] :
~ ( distinct_points @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
thf(36,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( ( distinct_points @ X @ Y )
& ( equal_points @ Y @ Z ) )
=> ( ( distinct_points @ X @ Z )
& ( equal_lines @ ( line_connecting @ X @ Y ) @ ( line_connecting @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(37,negated_conjecture,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( distinct_points @ X @ Y )
& ( equal_points @ Y @ Z ) )
=> ( ( distinct_points @ X @ Z )
& ( equal_lines @ ( line_connecting @ X @ Y ) @ ( line_connecting @ X @ Z ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( distinct_points @ X @ Y )
& ( equal_points @ Y @ Z ) )
=> ( ( distinct_points @ X @ Z )
& ( equal_lines @ ( line_connecting @ X @ Y ) @ ( line_connecting @ X @ Z ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(47,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(48,plain,
( ( ! [SY24: $i,SY25: $i] :
( ( ( distinct_points @ sK1_X @ SY24 )
& ( equal_points @ SY24 @ SY25 ) )
=> ( ( distinct_points @ sK1_X @ SY25 )
& ( equal_lines @ ( line_connecting @ sK1_X @ SY24 ) @ ( line_connecting @ sK1_X @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(49,plain,
( ( ! [SY26: $i] :
( ( ( distinct_points @ sK1_X @ sK2_SY24 )
& ( equal_points @ sK2_SY24 @ SY26 ) )
=> ( ( distinct_points @ sK1_X @ SY26 )
& ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ SY26 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(50,plain,
( ( ( ( distinct_points @ sK1_X @ sK2_SY24 )
& ( equal_points @ sK2_SY24 @ sK3_SY26 ) )
=> ( ( distinct_points @ sK1_X @ sK3_SY26 )
& ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ sK3_SY26 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(51,plain,
( ( distinct_points @ sK1_X @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[50]) ).
thf(52,plain,
( ( equal_points @ sK2_SY24 @ sK3_SY26 )
= $true ),
inference(standard_cnf,[status(thm)],[50]) ).
thf(53,plain,
( ( ( distinct_points @ sK1_X @ sK3_SY26 )
& ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ sK3_SY26 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[50]) ).
thf(54,plain,
( ( distinct_points @ sK1_X @ sK3_SY26 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[53]) ).
thf(55,plain,
( ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ sK3_SY26 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[53]) ).
thf(56,plain,
( ( ~ ( distinct_points @ sK1_X @ sK3_SY26 ) )
= $true ),
inference(polarity_switch,[status(thm)],[54]) ).
thf(57,plain,
( ( ~ ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ sK3_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(67,plain,
( ( equal_points @ sK2_SY24 @ sK3_SY26 )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(68,plain,
( ( distinct_points @ sK1_X @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(69,plain,
( ( ~ ( distinct_points @ sK1_X @ sK3_SY26 ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SX0 )
| ~ ( point @ SX1 ) )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ( line @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(74,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)],[59]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( apart_point_and_line @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX2 @ SX3 ) )
| ( apart_point_and_line @ SX0 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX3 )
| ( apart_point_and_line @ SX1 @ SX2 )
| ( apart_point_and_line @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(78,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(79,plain,
( ( distinct_points @ sK1_X @ sK3_SY26 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV2: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( equal_lines @ SV2 @ SY27 )
| ~ ( distinct_lines @ SV2 @ SY27 ) )
| ~ ( ~ ~ ( distinct_lines @ SV2 @ SY27 )
| ( equal_lines @ SV2 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV3: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SY28 ) )
| ~ ( distinct_points @ SV3 @ SY28 ) )
| ( line @ ( line_connecting @ SV3 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV4: $i] :
( ( ! [SY29: $i] :
~ ( ~ ( ~ ( equal_points @ SV4 @ SY29 )
| ~ ( distinct_points @ SV4 @ SY29 ) )
| ~ ( ~ ~ ( distinct_points @ SV4 @ SY29 )
| ( equal_points @ SV4 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV5: $i] :
( ( ! [SY30: $i] :
( ~ ( distinct_points @ SV5 @ SY30 )
| ~ ( apart_point_and_line @ SY30 @ ( line_connecting @ SV5 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV6: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( distinct_points @ SV6 @ SY31 )
| ( distinct_points @ SV6 @ SY32 )
| ( distinct_points @ SY31 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV7: $i] :
( ( ! [SY33: $i] :
( ~ ( distinct_points @ SV7 @ SY33 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV8: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( apart_point_and_line @ SV8 @ SY34 )
| ( distinct_points @ SV8 @ SY35 )
| ( apart_point_and_line @ SY35 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV9: $i] :
( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( distinct_points @ SV9 @ SY36 )
| ~ ( distinct_lines @ SY37 @ SY38 ) )
| ( apart_point_and_line @ SV9 @ SY37 )
| ( apart_point_and_line @ SV9 @ SY38 )
| ( apart_point_and_line @ SY36 @ SY37 )
| ( apart_point_and_line @ SY36 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( equal_lines @ SV2 @ SV10 )
| ~ ( distinct_lines @ SV2 @ SV10 ) )
| ~ ( ~ ~ ( distinct_lines @ SV2 @ SV10 )
| ( equal_lines @ SV2 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV11: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) )
| ~ ( distinct_points @ SV3 @ SV11 ) )
| ( line @ ( line_connecting @ SV3 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( equal_points @ SV4 @ SV12 )
| ~ ( distinct_points @ SV4 @ SV12 ) )
| ~ ( ~ ~ ( distinct_points @ SV4 @ SV12 )
| ( equal_points @ SV4 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV13: $i,SV5: $i] :
( ( ~ ( distinct_points @ SV5 @ SV13 )
| ~ ( apart_point_and_line @ SV13 @ ( line_connecting @ SV5 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY39: $i] :
( ~ ( distinct_points @ SV6 @ SV14 )
| ( distinct_points @ SV6 @ SY39 )
| ( distinct_points @ SV14 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( distinct_points @ SV7 @ SV15 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV16: $i,SV8: $i] :
( ( ! [SY40: $i] :
( ~ ( apart_point_and_line @ SV8 @ SV16 )
| ( distinct_points @ SV8 @ SY40 )
| ( apart_point_and_line @ SY40 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV17: $i,SV9: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ~ ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( distinct_lines @ SY41 @ SY42 ) )
| ( apart_point_and_line @ SV9 @ SY41 )
| ( apart_point_and_line @ SV9 @ SY42 )
| ( apart_point_and_line @ SV17 @ SY41 )
| ( apart_point_and_line @ SV17 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( ~ ( equal_lines @ SV2 @ SV10 )
| ~ ( distinct_lines @ SV2 @ SV10 ) )
| ~ ( ~ ~ ( distinct_lines @ SV2 @ SV10 )
| ( equal_lines @ SV2 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) )
| ~ ( distinct_points @ SV3 @ SV11 ) ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( ~ ( equal_points @ SV4 @ SV12 )
| ~ ( distinct_points @ SV4 @ SV12 ) )
| ~ ( ~ ~ ( distinct_points @ SV4 @ SV12 )
| ( equal_points @ SV4 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( distinct_points @ SV5 @ SV13 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV13 @ ( line_connecting @ SV5 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ~ ( distinct_points @ SV6 @ SV14 )
| ( distinct_points @ SV6 @ SV18 )
| ( distinct_points @ SV14 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( distinct_points @ SV7 @ SV15 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV19: $i,SV16: $i,SV8: $i] :
( ( ~ ( apart_point_and_line @ SV8 @ SV16 )
| ( distinct_points @ SV8 @ SV19 )
| ( apart_point_and_line @ SV19 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV20: $i,SV17: $i,SV9: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( distinct_lines @ SV20 @ SY43 ) )
| ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SY43 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( ~ ( equal_lines @ SV2 @ SV10 )
| ~ ( distinct_lines @ SV2 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(106,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( ~ ~ ( distinct_lines @ SV2 @ SV10 )
| ( equal_lines @ SV2 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(107,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) )
| ~ ( distinct_points @ SV3 @ SV11 ) ) )
= $false )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( ~ ( equal_points @ SV4 @ SV12 )
| ~ ( distinct_points @ SV4 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(109,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( ~ ~ ( distinct_points @ SV4 @ SV12 )
| ( equal_points @ SV4 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
! [SV13: $i,SV5: $i] :
( ( ( distinct_points @ SV5 @ SV13 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV13 @ ( line_connecting @ SV5 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV14 ) )
= $true )
| ( ( ( distinct_points @ SV6 @ SV18 )
| ( distinct_points @ SV14 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV15: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV15 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV19: $i,SV16: $i,SV8: $i] :
( ( ( ~ ( apart_point_and_line @ SV8 @ SV16 ) )
= $true )
| ( ( ( distinct_points @ SV8 @ SV19 )
| ( apart_point_and_line @ SV19 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV21: $i,SV20: $i,SV17: $i,SV9: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( distinct_lines @ SV20 @ SV21 ) )
| ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( equal_lines @ SV2 @ SV10 )
| ~ ( distinct_lines @ SV2 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(116,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ~ ( distinct_lines @ SV2 @ SV10 )
| ( equal_lines @ SV2 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(117,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) )
| ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( equal_points @ SV4 @ SV12 )
| ~ ( distinct_points @ SV4 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ~ ( distinct_points @ SV4 @ SV12 )
| ( equal_points @ SV4 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(120,plain,
! [SV5: $i,SV13: $i] :
( ( ( apart_point_and_line @ SV13 @ ( line_connecting @ SV5 @ SV13 ) )
= $false )
| ( ( distinct_points @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV14 )
= $false )
| ( ( ( distinct_points @ SV6 @ SV18 )
| ( distinct_points @ SV14 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV15: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV15 ) )
= $false )
| ( ( distinct_points @ SV7 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV19: $i,SV16: $i,SV8: $i] :
( ( ( apart_point_and_line @ SV8 @ SV16 )
= $false )
| ( ( ( distinct_points @ SV8 @ SV19 )
| ( apart_point_and_line @ SV19 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV21: $i,SV20: $i,SV17: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( distinct_lines @ SV20 @ SV21 ) ) )
= $true )
| ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( equal_lines @ SV2 @ SV10 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV2 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ~ ( distinct_lines @ SV2 @ SV10 ) )
= $true )
| ( ( equal_lines @ SV2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( equal_points @ SV4 @ SV12 ) )
= $true )
| ( ( ~ ( distinct_points @ SV4 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ~ ( distinct_points @ SV4 @ SV12 ) )
= $true )
| ( ( equal_points @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV14: $i,SV18: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV18 )
= $true )
| ( ( distinct_points @ SV14 @ SV18 )
= $true )
| ( ( distinct_points @ SV6 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(131,plain,
! [SV16: $i,SV19: $i,SV8: $i] :
( ( ( distinct_points @ SV8 @ SV19 )
= $true )
| ( ( apart_point_and_line @ SV19 @ SV16 )
= $true )
| ( ( apart_point_and_line @ SV8 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(132,plain,
! [SV21: $i,SV20: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( distinct_lines @ SV20 @ SV21 ) ) )
= $false )
| ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV10: $i,SV2: $i] :
( ( ( equal_lines @ SV2 @ SV10 )
= $false )
| ( ( ~ ( distinct_lines @ SV2 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( distinct_lines @ SV2 @ SV10 ) )
= $false )
| ( ( equal_lines @ SV2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) ) )
= $false )
| ( ( ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(136,plain,
! [SV12: $i,SV4: $i] :
( ( ( equal_points @ SV4 @ SV12 )
= $false )
| ( ( ~ ( distinct_points @ SV4 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( distinct_points @ SV4 @ SV12 ) )
= $false )
| ( ( equal_points @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV21: $i,SV20: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( distinct_points @ SV9 @ SV17 )
| ~ ( distinct_lines @ SV20 @ SV21 ) )
= $true )
| ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(139,plain,
! [SV10: $i,SV2: $i] :
( ( ( distinct_lines @ SV2 @ SV10 )
= $false )
| ( ( equal_lines @ SV2 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV10: $i,SV2: $i] :
( ( ( distinct_lines @ SV2 @ SV10 )
= $true )
| ( ( equal_lines @ SV2 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(141,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( point @ SV3 )
| ~ ( point @ SV11 ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV12: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV12 )
= $false )
| ( ( equal_points @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV12: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV12 )
= $true )
| ( ( equal_points @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV21: $i,SV20: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( distinct_points @ SV9 @ SV17 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV20 @ SV21 ) )
= $true )
| ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( point @ SV3 ) )
= $true )
| ( ( ~ ( point @ SV11 ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV21: $i,SV20: $i,SV17: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV17 )
= $false )
| ( ( ~ ( distinct_lines @ SV20 @ SV21 ) )
= $true )
| ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(147,plain,
! [SV11: $i,SV3: $i] :
( ( ( point @ SV3 )
= $false )
| ( ( ~ ( point @ SV11 ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(148,plain,
! [SV17: $i,SV9: $i,SV21: $i,SV20: $i] :
( ( ( distinct_lines @ SV20 @ SV21 )
= $false )
| ( ( distinct_points @ SV9 @ SV17 )
= $false )
| ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 )
| ( apart_point_and_line @ SV17 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(149,plain,
! [SV3: $i,SV11: $i] :
( ( ( point @ SV11 )
= $false )
| ( ( point @ SV3 )
= $false )
| ( ( ~ ( distinct_points @ SV3 @ SV11 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(150,plain,
! [SV17: $i,SV21: $i,SV20: $i,SV9: $i] :
( ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 )
| ( apart_point_and_line @ SV17 @ SV20 ) )
= $true )
| ( ( apart_point_and_line @ SV17 @ SV21 )
= $true )
| ( ( distinct_points @ SV9 @ SV17 )
= $false )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(151,plain,
! [SV11: $i,SV3: $i] :
( ( ( distinct_points @ SV3 @ SV11 )
= $false )
| ( ( point @ SV3 )
= $false )
| ( ( point @ SV11 )
= $false )
| ( ( line @ ( line_connecting @ SV3 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(152,plain,
! [SV17: $i,SV21: $i,SV20: $i,SV9: $i] :
( ( ( ( apart_point_and_line @ SV9 @ SV20 )
| ( apart_point_and_line @ SV9 @ SV21 ) )
= $true )
| ( ( apart_point_and_line @ SV17 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV17 @ SV21 )
= $true )
| ( ( distinct_points @ SV9 @ SV17 )
= $false )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(153,plain,
! [SV17: $i,SV21: $i,SV20: $i,SV9: $i] :
( ( ( apart_point_and_line @ SV9 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV9 @ SV21 )
= $true )
| ( ( apart_point_and_line @ SV17 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV17 @ SV21 )
= $true )
| ( ( distinct_points @ SV9 @ SV17 )
= $false )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(154,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,153,151,143,142,140,139,131,130,122,120,88,79,68]) ).
thf(155,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(156,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(157,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(158,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(159,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(160,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(162,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(163,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(164,plain,
( ( equal_points @ sK2_SY24 @ sK3_SY26 )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(165,plain,
( ( distinct_points @ sK1_X @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(166,plain,
( ( ~ ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ sK3_SY26 ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_lines @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( distinct_lines @ SX0 @ SX1 )
| ( equal_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(169,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)],[156]) ).
thf(170,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_points @ SX0 @ SX1 )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( distinct_points @ SX0 @ SX1 )
| ( equal_points @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SX0 )
| ~ ( point @ SX1 ) )
| ~ ( distinct_points @ SX0 @ SX1 ) )
| ( line @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX2 @ SX3 ) )
| ( apart_point_and_line @ SX0 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX3 )
| ( apart_point_and_line @ SX1 @ SX2 )
| ( apart_point_and_line @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( apart_point_and_line @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(175,plain,
! [SV22: $i] :
( ( ~ ( distinct_points @ SV22 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(176,plain,
( ( equal_lines @ ( line_connecting @ sK1_X @ sK2_SY24 ) @ ( line_connecting @ sK1_X @ sK3_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV23: $i] :
( ( ! [SY44: $i] :
~ ( ~ ( ~ ( equal_lines @ SV23 @ SY44 )
| ~ ( distinct_lines @ SV23 @ SY44 ) )
| ~ ( ~ ~ ( distinct_lines @ SV23 @ SY44 )
| ( equal_lines @ SV23 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV24: $i] :
( ( ! [SY45: $i] :
( ~ ( distinct_points @ SV24 @ SY45 )
| ~ ( apart_point_and_line @ SY45 @ ( line_connecting @ SV24 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV25: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( distinct_points @ SV25 @ SY46 )
| ( distinct_points @ SV25 @ SY47 )
| ( distinct_points @ SY46 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV26: $i] :
( ( ! [SY48: $i] :
~ ( ~ ( ~ ( equal_points @ SV26 @ SY48 )
| ~ ( distinct_points @ SV26 @ SY48 ) )
| ~ ( ~ ~ ( distinct_points @ SV26 @ SY48 )
| ( equal_points @ SV26 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV27: $i] :
( ( ! [SY49: $i] :
( ~ ( distinct_points @ SV27 @ SY49 )
| ~ ( apart_point_and_line @ SV27 @ ( line_connecting @ SV27 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV28: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SV28 )
| ~ ( point @ SY50 ) )
| ~ ( distinct_points @ SV28 @ SY50 ) )
| ( line @ ( line_connecting @ SV28 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV29: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( distinct_points @ SV29 @ SY51 )
| ~ ( distinct_lines @ SY52 @ SY53 ) )
| ( apart_point_and_line @ SV29 @ SY52 )
| ( apart_point_and_line @ SV29 @ SY53 )
| ( apart_point_and_line @ SY51 @ SY52 )
| ( apart_point_and_line @ SY51 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV30: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( apart_point_and_line @ SV30 @ SY54 )
| ( distinct_points @ SV30 @ SY55 )
| ( apart_point_and_line @ SY55 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV22: $i] :
( ( distinct_points @ SV22 @ SV22 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( equal_lines @ SV23 @ SV31 )
| ~ ( distinct_lines @ SV23 @ SV31 ) )
| ~ ( ~ ~ ( distinct_lines @ SV23 @ SV31 )
| ( equal_lines @ SV23 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV32: $i,SV24: $i] :
( ( ~ ( distinct_points @ SV24 @ SV32 )
| ~ ( apart_point_and_line @ SV32 @ ( line_connecting @ SV24 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV33: $i,SV25: $i] :
( ( ! [SY56: $i] :
( ~ ( distinct_points @ SV25 @ SV33 )
| ( distinct_points @ SV25 @ SY56 )
| ( distinct_points @ SV33 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( equal_points @ SV26 @ SV34 )
| ~ ( distinct_points @ SV26 @ SV34 ) )
| ~ ( ~ ~ ( distinct_points @ SV26 @ SV34 )
| ( equal_points @ SV26 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(190,plain,
! [SV35: $i,SV27: $i] :
( ( ~ ( distinct_points @ SV27 @ SV35 )
| ~ ( apart_point_and_line @ SV27 @ ( line_connecting @ SV27 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV36: $i,SV28: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) )
| ~ ( distinct_points @ SV28 @ SV36 ) )
| ( line @ ( line_connecting @ SV28 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(192,plain,
! [SV37: $i,SV29: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( distinct_points @ SV29 @ SV37 )
| ~ ( distinct_lines @ SY57 @ SY58 ) )
| ( apart_point_and_line @ SV29 @ SY57 )
| ( apart_point_and_line @ SV29 @ SY58 )
| ( apart_point_and_line @ SV37 @ SY57 )
| ( apart_point_and_line @ SV37 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV38: $i,SV30: $i] :
( ( ! [SY59: $i] :
( ~ ( apart_point_and_line @ SV30 @ SV38 )
| ( distinct_points @ SV30 @ SY59 )
| ( apart_point_and_line @ SY59 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(194,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ( ~ ( equal_lines @ SV23 @ SV31 )
| ~ ( distinct_lines @ SV23 @ SV31 ) )
| ~ ( ~ ~ ( distinct_lines @ SV23 @ SV31 )
| ( equal_lines @ SV23 @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV32: $i,SV24: $i] :
( ( ( ~ ( distinct_points @ SV24 @ SV32 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV32 @ ( line_connecting @ SV24 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV39: $i,SV33: $i,SV25: $i] :
( ( ~ ( distinct_points @ SV25 @ SV33 )
| ( distinct_points @ SV25 @ SV39 )
| ( distinct_points @ SV33 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( ~ ( equal_points @ SV26 @ SV34 )
| ~ ( distinct_points @ SV26 @ SV34 ) )
| ~ ( ~ ~ ( distinct_points @ SV26 @ SV34 )
| ( equal_points @ SV26 @ SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV35: $i,SV27: $i] :
( ( ( ~ ( distinct_points @ SV27 @ SV35 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV27 @ ( line_connecting @ SV27 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) )
| ~ ( distinct_points @ SV28 @ SV36 ) ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV40: $i,SV37: $i,SV29: $i] :
( ( ! [SY60: $i] :
( ~ ~ ( ~ ( distinct_points @ SV29 @ SV37 )
| ~ ( distinct_lines @ SV40 @ SY60 ) )
| ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SY60 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV41: $i,SV38: $i,SV30: $i] :
( ( ~ ( apart_point_and_line @ SV30 @ SV38 )
| ( distinct_points @ SV30 @ SV41 )
| ( apart_point_and_line @ SV41 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ( ~ ( equal_lines @ SV23 @ SV31 )
| ~ ( distinct_lines @ SV23 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(203,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ( ~ ~ ( distinct_lines @ SV23 @ SV31 )
| ( equal_lines @ SV23 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(204,plain,
! [SV32: $i,SV24: $i] :
( ( ( distinct_points @ SV24 @ SV32 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV32 @ ( line_connecting @ SV24 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV39: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( distinct_points @ SV25 @ SV33 ) )
= $true )
| ( ( ( distinct_points @ SV25 @ SV39 )
| ( distinct_points @ SV33 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( ~ ( equal_points @ SV26 @ SV34 )
| ~ ( distinct_points @ SV26 @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(207,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( ~ ~ ( distinct_points @ SV26 @ SV34 )
| ( equal_points @ SV26 @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(208,plain,
! [SV35: $i,SV27: $i] :
( ( ( distinct_points @ SV27 @ SV35 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV27 @ ( line_connecting @ SV27 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(209,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) )
| ~ ( distinct_points @ SV28 @ SV36 ) ) )
= $false )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(210,plain,
! [SV42: $i,SV40: $i,SV37: $i,SV29: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV29 @ SV37 )
| ~ ( distinct_lines @ SV40 @ SV42 ) )
| ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(211,plain,
! [SV41: $i,SV38: $i,SV30: $i] :
( ( ( ~ ( apart_point_and_line @ SV30 @ SV38 ) )
= $true )
| ( ( ( distinct_points @ SV30 @ SV41 )
| ( apart_point_and_line @ SV41 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ( equal_lines @ SV23 @ SV31 )
| ~ ( distinct_lines @ SV23 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(213,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ~ ( distinct_lines @ SV23 @ SV31 )
| ( equal_lines @ SV23 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(214,plain,
! [SV24: $i,SV32: $i] :
( ( ( apart_point_and_line @ SV32 @ ( line_connecting @ SV24 @ SV32 ) )
= $false )
| ( ( distinct_points @ SV24 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV39: $i,SV33: $i,SV25: $i] :
( ( ( distinct_points @ SV25 @ SV33 )
= $false )
| ( ( ( distinct_points @ SV25 @ SV39 )
| ( distinct_points @ SV33 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( equal_points @ SV26 @ SV34 )
| ~ ( distinct_points @ SV26 @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(217,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ~ ( distinct_points @ SV26 @ SV34 )
| ( equal_points @ SV26 @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(218,plain,
! [SV35: $i,SV27: $i] :
( ( ( apart_point_and_line @ SV27 @ ( line_connecting @ SV27 @ SV35 ) )
= $false )
| ( ( distinct_points @ SV27 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(219,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) )
| ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(220,plain,
! [SV42: $i,SV40: $i,SV37: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV29 @ SV37 )
| ~ ( distinct_lines @ SV40 @ SV42 ) ) )
= $true )
| ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(221,plain,
! [SV41: $i,SV38: $i,SV30: $i] :
( ( ( apart_point_and_line @ SV30 @ SV38 )
= $false )
| ( ( ( distinct_points @ SV30 @ SV41 )
| ( apart_point_and_line @ SV41 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(222,plain,
! [SV31: $i,SV23: $i] :
( ( ( ~ ( equal_lines @ SV23 @ SV31 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV23 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV31: $i,SV23: $i] :
( ( ( ~ ~ ( distinct_lines @ SV23 @ SV31 ) )
= $true )
| ( ( equal_lines @ SV23 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV33: $i,SV39: $i,SV25: $i] :
( ( ( distinct_points @ SV25 @ SV39 )
= $true )
| ( ( distinct_points @ SV33 @ SV39 )
= $true )
| ( ( distinct_points @ SV25 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(225,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ( equal_points @ SV26 @ SV34 ) )
= $true )
| ( ( ~ ( distinct_points @ SV26 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(226,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ~ ( distinct_points @ SV26 @ SV34 ) )
= $true )
| ( ( equal_points @ SV26 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(227,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) ) )
= $true )
| ( ( ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV42: $i,SV40: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV29 @ SV37 )
| ~ ( distinct_lines @ SV40 @ SV42 ) ) )
= $false )
| ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV38: $i,SV41: $i,SV30: $i] :
( ( ( distinct_points @ SV30 @ SV41 )
= $true )
| ( ( apart_point_and_line @ SV41 @ SV38 )
= $true )
| ( ( apart_point_and_line @ SV30 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV31: $i,SV23: $i] :
( ( ( equal_lines @ SV23 @ SV31 )
= $false )
| ( ( ~ ( distinct_lines @ SV23 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV31: $i,SV23: $i] :
( ( ( ~ ( distinct_lines @ SV23 @ SV31 ) )
= $false )
| ( ( equal_lines @ SV23 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV34: $i,SV26: $i] :
( ( ( equal_points @ SV26 @ SV34 )
= $false )
| ( ( ~ ( distinct_points @ SV26 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(233,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ( distinct_points @ SV26 @ SV34 ) )
= $false )
| ( ( equal_points @ SV26 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(234,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) ) )
= $false )
| ( ( ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(235,plain,
! [SV42: $i,SV40: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( distinct_points @ SV29 @ SV37 )
| ~ ( distinct_lines @ SV40 @ SV42 ) )
= $true )
| ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(236,plain,
! [SV31: $i,SV23: $i] :
( ( ( distinct_lines @ SV23 @ SV31 )
= $false )
| ( ( equal_lines @ SV23 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(237,plain,
! [SV31: $i,SV23: $i] :
( ( ( distinct_lines @ SV23 @ SV31 )
= $true )
| ( ( equal_lines @ SV23 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(238,plain,
! [SV34: $i,SV26: $i] :
( ( ( distinct_points @ SV26 @ SV34 )
= $false )
| ( ( equal_points @ SV26 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(239,plain,
! [SV34: $i,SV26: $i] :
( ( ( distinct_points @ SV26 @ SV34 )
= $true )
| ( ( equal_points @ SV26 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(240,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ( point @ SV28 )
| ~ ( point @ SV36 ) )
= $true )
| ( ( ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(241,plain,
! [SV42: $i,SV40: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( distinct_points @ SV29 @ SV37 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV40 @ SV42 ) )
= $true )
| ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(242,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ( point @ SV28 ) )
= $true )
| ( ( ~ ( point @ SV36 ) )
= $true )
| ( ( ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(243,plain,
! [SV42: $i,SV40: $i,SV37: $i,SV29: $i] :
( ( ( distinct_points @ SV29 @ SV37 )
= $false )
| ( ( ~ ( distinct_lines @ SV40 @ SV42 ) )
= $true )
| ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(244,plain,
! [SV36: $i,SV28: $i] :
( ( ( point @ SV28 )
= $false )
| ( ( ~ ( point @ SV36 ) )
= $true )
| ( ( ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(245,plain,
! [SV37: $i,SV29: $i,SV42: $i,SV40: $i] :
( ( ( distinct_lines @ SV40 @ SV42 )
= $false )
| ( ( distinct_points @ SV29 @ SV37 )
= $false )
| ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 )
| ( apart_point_and_line @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(246,plain,
! [SV28: $i,SV36: $i] :
( ( ( point @ SV36 )
= $false )
| ( ( point @ SV28 )
= $false )
| ( ( ~ ( distinct_points @ SV28 @ SV36 ) )
= $true )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(247,plain,
! [SV37: $i,SV42: $i,SV40: $i,SV29: $i] :
( ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 )
| ( apart_point_and_line @ SV37 @ SV40 ) )
= $true )
| ( ( apart_point_and_line @ SV37 @ SV42 )
= $true )
| ( ( distinct_points @ SV29 @ SV37 )
= $false )
| ( ( distinct_lines @ SV40 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(248,plain,
! [SV36: $i,SV28: $i] :
( ( ( distinct_points @ SV28 @ SV36 )
= $false )
| ( ( point @ SV28 )
= $false )
| ( ( point @ SV36 )
= $false )
| ( ( line @ ( line_connecting @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(249,plain,
! [SV37: $i,SV42: $i,SV40: $i,SV29: $i] :
( ( ( ( apart_point_and_line @ SV29 @ SV40 )
| ( apart_point_and_line @ SV29 @ SV42 ) )
= $true )
| ( ( apart_point_and_line @ SV37 @ SV40 )
= $true )
| ( ( apart_point_and_line @ SV37 @ SV42 )
= $true )
| ( ( distinct_points @ SV29 @ SV37 )
= $false )
| ( ( distinct_lines @ SV40 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(250,plain,
! [SV37: $i,SV42: $i,SV40: $i,SV29: $i] :
( ( ( apart_point_and_line @ SV29 @ SV40 )
= $true )
| ( ( apart_point_and_line @ SV29 @ SV42 )
= $true )
| ( ( apart_point_and_line @ SV37 @ SV40 )
= $true )
| ( ( apart_point_and_line @ SV37 @ SV42 )
= $true )
| ( ( distinct_points @ SV29 @ SV37 )
= $false )
| ( ( distinct_lines @ SV40 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(251,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[164,250,248,239,238,237,236,229,224,218,214,185,176,165]) ).
thf(252,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[251,154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 10:12:28 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/0.98
% 4.08/0.98 No.of.Axioms: 9
% 4.08/0.98
% 4.08/0.98 Length.of.Defs: 0
% 4.08/0.98
% 4.08/0.98 Contains.Choice.Funs: false
% 4.08/0.98 ......
% 4.08/0.98
% 4.08/0.98 ********************************
% 4.08/0.98 * All subproblems solved! *
% 4.08/0.98 ********************************
% 4.08/0.98 % SZS status Theorem for /export/starexec/sandbox2/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:251,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.08/0.98
% 4.08/0.98 %**** Beginning of derivation protocol ****
% 4.08/0.98 % SZS output start CNFRefutation
% See solution above
% 4.08/0.98
% 4.08/0.98 %**** End of derivation protocol ****
% 4.08/0.98 %**** no. of clauses in derivation: 226 ****
% 4.08/0.98 %**** clause counter: 251 ****
% 4.08/0.98
% 4.08/0.98 % SZS status Theorem for /export/starexec/sandbox2/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:251,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------