%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO225+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 : n002.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 10:18:32 AM UTC 2026
% Result : Theorem 0.57s 0.29s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 178 ( 98 unt; 0 typ; 0 def)
% Number of atoms : 1109 ( 274 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1814 ( 362 ~; 298 |; 39 &;1069 @)
% ( 6 <=>; 40 =>; 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 : 21 ( 18 usr; 4 con; 0-2 aty)
% Number of variables : 376 ( 0 ^; 368 !; 8 ?; 376 :)
% 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_A,type,
sK1_A: $i ).
thf(tp_sK2_SY30,type,
sK2_SY30: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(6,axiom,
! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orth1) ).
thf(7,axiom,
! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',par1) ).
thf(8,axiom,
! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int1) ).
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,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ? [X: $i] :
( ( line @ X )
=> ( ( incident_point_and_line @ A @ X )
& ( incident_point_and_line @ B @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(37,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ? [X: $i] :
( ( line @ X )
=> ( ( incident_point_and_line @ A @ X )
& ( incident_point_and_line @ B @ X ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ? [X: $i] :
( ( line @ X )
=> ( ( incident_point_and_line @ A @ X )
& ( incident_point_and_line @ B @ X ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
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,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(42,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(43,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(44,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(45,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(46,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(47,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(48,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(49,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(50,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(51,plain,
( ( ! [SY30: $i] :
( ( ( point @ sK1_A )
& ( point @ SY30 )
& ( distinct_points @ sK1_A @ SY30 ) )
=> ? [SY31: $i] :
( ( line @ SY31 )
=> ( ( incident_point_and_line @ sK1_A @ SY31 )
& ( incident_point_and_line @ SY30 @ SY31 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(52,plain,
( ( ( ( point @ sK1_A )
& ( point @ sK2_SY30 )
& ( distinct_points @ sK1_A @ sK2_SY30 ) )
=> ? [SY32: $i] :
( ( line @ SY32 )
=> ( ( incident_point_and_line @ sK1_A @ SY32 )
& ( incident_point_and_line @ sK2_SY30 @ SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(53,plain,
( ( point @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[52]) ).
thf(54,plain,
( ( point @ sK2_SY30 )
= $true ),
inference(standard_cnf,[status(thm)],[52]) ).
thf(55,plain,
( ( distinct_points @ sK1_A @ sK2_SY30 )
= $true ),
inference(standard_cnf,[status(thm)],[52]) ).
thf(56,plain,
( ( ? [SY32: $i] :
( ( line @ SY32 )
=> ( ( incident_point_and_line @ sK1_A @ SY32 )
& ( incident_point_and_line @ sK2_SY30 @ SY32 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[52]) ).
thf(57,plain,
( ( ~ ? [SY32: $i] :
( ( line @ SY32 )
=> ( ( incident_point_and_line @ sK1_A @ SY32 )
& ( incident_point_and_line @ sK2_SY30 @ SY32 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[56]) ).
thf(58,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
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)],[49]) ).
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)],[48]) ).
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)],[47]) ).
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)],[46]) ).
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)],[45]) ).
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)],[44]) ).
thf(65,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M )
& ( convergent_lines @ L @ M ) )
=> ( point @ ( intersection_point @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(66,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( parallel_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(67,plain,
( ( ! [L: $i,A: $i] :
( ( ( line @ L )
& ( point @ A ) )
=> ( line @ ( orthogonal_through_point @ L @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_points @ X @ Y )
<=> ~ ( distinct_points @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ( incident_point_and_line @ X @ Y )
<=> ~ ( apart_point_and_line @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(70,plain,
( ( distinct_points @ sK1_A @ sK2_SY30 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(71,plain,
( ( point @ sK2_SY30 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(72,plain,
( ( point @ sK1_A )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(73,plain,
( ( ~ ? [SY32: $i] :
( ( line @ SY32 )
=> ( ( incident_point_and_line @ sK1_A @ SY32 )
& ( incident_point_and_line @ sK2_SY30 @ SY32 ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( line @ SX0 )
| ~ ( point @ SX1 ) )
| ( line @ ( parallel_through_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(75,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(76,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ ( line @ SX0 )
| ~ ( ~ ( incident_point_and_line @ sK1_A @ SX0 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( line @ SX0 )
| ~ ( line @ SX1 ) )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ( point @ ( intersection_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(78,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(79,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(80,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(81,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( line @ SX0 )
| ~ ( point @ SX1 ) )
| ( line @ ( orthogonal_through_point @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(82,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(83,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)],[68]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( incident_point_and_line @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( incident_point_and_line @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(85,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(86,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(87,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ~ ~ ( ~ ( line @ SV2 )
| ~ ( point @ SY33 ) )
| ( line @ ( parallel_through_point @ SV2 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(88,plain,
! [SV3: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SY34 ) )
| ~ ( distinct_points @ SV3 @ SY34 ) )
| ( line @ ( line_connecting @ SV3 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( line @ SX0 )
| ~ ( ~ ( incident_point_and_line @ sK1_A @ SX0 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(90,plain,
! [SV4: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ~ ( ~ ( line @ SV4 )
| ~ ( line @ SY35 ) )
| ~ ( convergent_lines @ SV4 @ SY35 ) )
| ( point @ ( intersection_point @ SV4 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(91,plain,
! [SV5: $i] :
( ( ! [SY36: $i] :
( ~ ( distinct_points @ SV5 @ SY36 )
| ~ ( apart_point_and_line @ SY36 @ ( line_connecting @ SV5 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV6: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( distinct_points @ SV6 @ SY37 )
| ( distinct_points @ SV6 @ SY38 )
| ( distinct_points @ SY37 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV7: $i] :
( ( ! [SY39: $i] :
( ~ ( distinct_points @ SV7 @ SY39 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV8: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ( line @ SV8 )
| ~ ( point @ SY40 ) )
| ( line @ ( orthogonal_through_point @ SV8 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV9: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ( apart_point_and_line @ SV9 @ SY41 )
| ( distinct_points @ SV9 @ SY42 )
| ( apart_point_and_line @ SY42 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV10: $i] :
( ( ! [SY43: $i] :
~ ( ~ ( ~ ( equal_points @ SV10 @ SY43 )
| ~ ( distinct_points @ SV10 @ SY43 ) )
| ~ ( ~ ~ ( distinct_points @ SV10 @ SY43 )
| ( equal_points @ SV10 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV11: $i] :
( ( ! [SY44: $i] :
~ ( ~ ( ~ ( incident_point_and_line @ SV11 @ SY44 )
| ~ ( apart_point_and_line @ SV11 @ SY44 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV11 @ SY44 )
| ( incident_point_and_line @ SV11 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV12: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i] :
( ~ ~ ( ~ ( distinct_points @ SV12 @ SY45 )
| ~ ( distinct_lines @ SY46 @ SY47 ) )
| ( apart_point_and_line @ SV12 @ SY46 )
| ( apart_point_and_line @ SV12 @ SY47 )
| ( apart_point_and_line @ SY45 @ SY46 )
| ( apart_point_and_line @ SY45 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV13: $i,SV2: $i] :
( ( ~ ~ ( ~ ( line @ SV2 )
| ~ ( point @ SV13 ) )
| ( line @ ( parallel_through_point @ SV2 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV14: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) )
| ~ ( distinct_points @ SV3 @ SV14 ) )
| ( line @ ( line_connecting @ SV3 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
( ( ! [SX0: $i] :
~ ( ~ ( line @ SX0 )
| ~ ( ~ ( incident_point_and_line @ sK1_A @ SX0 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(103,plain,
! [SV15: $i,SV4: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) )
| ~ ( convergent_lines @ SV4 @ SV15 ) )
| ( point @ ( intersection_point @ SV4 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( distinct_points @ SV5 @ SV16 )
| ~ ( apart_point_and_line @ SV16 @ ( line_connecting @ SV5 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV17: $i,SV6: $i] :
( ( ! [SY48: $i] :
( ~ ( distinct_points @ SV6 @ SV17 )
| ( distinct_points @ SV6 @ SY48 )
| ( distinct_points @ SV17 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( distinct_points @ SV7 @ SV18 )
| ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ~ ( ~ ( line @ SV8 )
| ~ ( point @ SV19 ) )
| ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(108,plain,
! [SV20: $i,SV9: $i] :
( ( ! [SY49: $i] :
( ~ ( apart_point_and_line @ SV9 @ SV20 )
| ( distinct_points @ SV9 @ SY49 )
| ( apart_point_and_line @ SY49 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( equal_points @ SV10 @ SV21 )
| ~ ( distinct_points @ SV10 @ SV21 ) )
| ~ ( ~ ~ ( distinct_points @ SV10 @ SV21 )
| ( equal_points @ SV10 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( incident_point_and_line @ SV11 @ SV22 )
| ~ ( apart_point_and_line @ SV11 @ SV22 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV11 @ SV22 )
| ( incident_point_and_line @ SV11 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV23: $i,SV12: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ~ ( ~ ( distinct_points @ SV12 @ SV23 )
| ~ ( distinct_lines @ SY50 @ SY51 ) )
| ( apart_point_and_line @ SV12 @ SY50 )
| ( apart_point_and_line @ SV12 @ SY51 )
| ( apart_point_and_line @ SV23 @ SY50 )
| ( apart_point_and_line @ SV23 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( line @ SV2 )
| ~ ( point @ SV13 ) ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) )
| ~ ( distinct_points @ SV3 @ SV14 ) ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV24: $i] :
( ( ~ ( ~ ( line @ SV24 )
| ~ ( ~ ( incident_point_and_line @ sK1_A @ SV24 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) )
| ~ ( convergent_lines @ SV4 @ SV15 ) ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( distinct_points @ SV5 @ SV16 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV16 @ ( line_connecting @ SV5 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV25: $i,SV17: $i,SV6: $i] :
( ( ~ ( distinct_points @ SV6 @ SV17 )
| ( distinct_points @ SV6 @ SV25 )
| ( distinct_points @ SV17 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( distinct_points @ SV7 @ SV18 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( line @ SV8 )
| ~ ( point @ SV19 ) ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV26: $i,SV20: $i,SV9: $i] :
( ( ~ ( apart_point_and_line @ SV9 @ SV20 )
| ( distinct_points @ SV9 @ SV26 )
| ( apart_point_and_line @ SV26 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ( ~ ( equal_points @ SV10 @ SV21 )
| ~ ( distinct_points @ SV10 @ SV21 ) )
| ~ ( ~ ~ ( distinct_points @ SV10 @ SV21 )
| ( equal_points @ SV10 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ( ~ ( incident_point_and_line @ SV11 @ SV22 )
| ~ ( apart_point_and_line @ SV11 @ SV22 ) )
| ~ ( ~ ~ ( apart_point_and_line @ SV11 @ SV22 )
| ( incident_point_and_line @ SV11 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV27: $i,SV23: $i,SV12: $i] :
( ( ! [SY52: $i] :
( ~ ~ ( ~ ( distinct_points @ SV12 @ SV23 )
| ~ ( distinct_lines @ SV27 @ SY52 ) )
| ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SY52 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ( ~ ( line @ SV2 )
| ~ ( point @ SV13 ) ) )
= $false )
| ( ( line @ ( parallel_through_point @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) )
| ~ ( distinct_points @ SV3 @ SV14 ) ) )
= $false )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV24: $i] :
( ( ~ ( line @ SV24 )
| ~ ( ~ ( incident_point_and_line @ sK1_A @ SV24 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SV24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) )
| ~ ( convergent_lines @ SV4 @ SV15 ) ) )
= $false )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV16: $i,SV5: $i] :
( ( ( distinct_points @ SV5 @ SV16 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV16 @ ( line_connecting @ SV5 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV25: $i,SV17: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV17 ) )
= $true )
| ( ( ( distinct_points @ SV6 @ SV25 )
| ( distinct_points @ SV17 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV18: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV18 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( ~ ( line @ SV8 )
| ~ ( point @ SV19 ) ) )
= $false )
| ( ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV26: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( apart_point_and_line @ SV9 @ SV20 ) )
= $true )
| ( ( ( distinct_points @ SV9 @ SV26 )
| ( apart_point_and_line @ SV26 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ( ~ ( equal_points @ SV10 @ SV21 )
| ~ ( distinct_points @ SV10 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(134,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ( ~ ~ ( distinct_points @ SV10 @ SV21 )
| ( equal_points @ SV10 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(135,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ( ~ ( incident_point_and_line @ SV11 @ SV22 )
| ~ ( apart_point_and_line @ SV11 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(136,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ( ~ ~ ( apart_point_and_line @ SV11 @ SV22 )
| ( incident_point_and_line @ SV11 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(137,plain,
! [SV28: $i,SV27: $i,SV23: $i,SV12: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV12 @ SV23 )
| ~ ( distinct_lines @ SV27 @ SV28 ) )
| ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ( line @ SV2 )
| ~ ( point @ SV13 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(139,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) )
| ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(140,plain,
! [SV24: $i] :
( ( ~ ( line @ SV24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(141,plain,
! [SV24: $i] :
( ( ~ ( ~ ( incident_point_and_line @ sK1_A @ SV24 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(142,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) )
| ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(143,plain,
! [SV5: $i,SV16: $i] :
( ( ( apart_point_and_line @ SV16 @ ( line_connecting @ SV5 @ SV16 ) )
= $false )
| ( ( distinct_points @ SV5 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(144,plain,
! [SV25: $i,SV17: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV17 )
= $false )
| ( ( ( distinct_points @ SV6 @ SV25 )
| ( distinct_points @ SV17 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(145,plain,
! [SV18: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ ( line_connecting @ SV7 @ SV18 ) )
= $false )
| ( ( distinct_points @ SV7 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( line @ SV8 )
| ~ ( point @ SV19 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(147,plain,
! [SV26: $i,SV20: $i,SV9: $i] :
( ( ( apart_point_and_line @ SV9 @ SV20 )
= $false )
| ( ( ( distinct_points @ SV9 @ SV26 )
| ( apart_point_and_line @ SV26 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ( equal_points @ SV10 @ SV21 )
| ~ ( distinct_points @ SV10 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(149,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ~ ( distinct_points @ SV10 @ SV21 )
| ( equal_points @ SV10 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(150,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ( incident_point_and_line @ SV11 @ SV22 )
| ~ ( apart_point_and_line @ SV11 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(151,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ~ ( apart_point_and_line @ SV11 @ SV22 )
| ( incident_point_and_line @ SV11 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(152,plain,
! [SV28: $i,SV27: $i,SV23: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV12 @ SV23 )
| ~ ( distinct_lines @ SV27 @ SV28 ) ) )
= $true )
| ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ( line @ SV2 ) )
= $true )
| ( ( ~ ( point @ SV13 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV24: $i] :
( ( line @ SV24 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(156,plain,
! [SV24: $i] :
( ( ~ ( incident_point_and_line @ sK1_A @ SV24 )
| ~ ( incident_point_and_line @ sK2_SY30 @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(157,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV17: $i,SV25: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV25 )
= $true )
| ( ( distinct_points @ SV17 @ SV25 )
= $true )
| ( ( distinct_points @ SV6 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( line @ SV8 ) )
= $true )
| ( ( ~ ( point @ SV19 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV20: $i,SV26: $i,SV9: $i] :
( ( ( distinct_points @ SV9 @ SV26 )
= $true )
| ( ( apart_point_and_line @ SV26 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV9 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( equal_points @ SV10 @ SV21 ) )
= $true )
| ( ( ~ ( distinct_points @ SV10 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ~ ( distinct_points @ SV10 @ SV21 ) )
= $true )
| ( ( equal_points @ SV10 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( incident_point_and_line @ SV11 @ SV22 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV11 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ~ ( apart_point_and_line @ SV11 @ SV22 ) )
= $true )
| ( ( incident_point_and_line @ SV11 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV28: $i,SV27: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV12 @ SV23 )
| ~ ( distinct_lines @ SV27 @ SV28 ) ) )
= $false )
| ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV13: $i,SV2: $i] :
( ( ( line @ SV2 )
= $false )
| ( ( ~ ( point @ SV13 ) )
= $true )
| ( ( line @ ( parallel_through_point @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) ) )
= $false )
| ( ( ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV24: $i] :
( ( ( ~ ( incident_point_and_line @ sK1_A @ SV24 ) )
= $true )
| ( ( ~ ( incident_point_and_line @ sK2_SY30 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV19: $i,SV8: $i] :
( ( ( line @ SV8 )
= $false )
| ( ( ~ ( point @ SV19 ) )
= $true )
| ( ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(171,plain,
! [SV21: $i,SV10: $i] :
( ( ( equal_points @ SV10 @ SV21 )
= $false )
| ( ( ~ ( distinct_points @ SV10 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( distinct_points @ SV10 @ SV21 ) )
= $false )
| ( ( equal_points @ SV10 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV22: $i,SV11: $i] :
( ( ( incident_point_and_line @ SV11 @ SV22 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV11 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( apart_point_and_line @ SV11 @ SV22 ) )
= $false )
| ( ( incident_point_and_line @ SV11 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV28: $i,SV27: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( distinct_points @ SV12 @ SV23 )
| ~ ( distinct_lines @ SV27 @ SV28 ) )
= $true )
| ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(176,plain,
! [SV2: $i,SV13: $i] :
( ( ( point @ SV13 )
= $false )
| ( ( line @ SV2 )
= $false )
| ( ( line @ ( parallel_through_point @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( point @ SV3 )
| ~ ( point @ SV14 ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV24: $i] :
( ( ( incident_point_and_line @ sK1_A @ SV24 )
= $false )
| ( ( ~ ( incident_point_and_line @ sK2_SY30 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( line @ SV4 )
| ~ ( line @ SV15 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV8: $i,SV19: $i] :
( ( ( point @ SV19 )
= $false )
| ( ( line @ SV8 )
= $false )
| ( ( line @ ( orthogonal_through_point @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV21: $i,SV10: $i] :
( ( ( distinct_points @ SV10 @ SV21 )
= $false )
| ( ( equal_points @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV21: $i,SV10: $i] :
( ( ( distinct_points @ SV10 @ SV21 )
= $true )
| ( ( equal_points @ SV10 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV22: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV22 )
= $false )
| ( ( incident_point_and_line @ SV11 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV22: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV22 )
= $true )
| ( ( incident_point_and_line @ SV11 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(185,plain,
! [SV28: $i,SV27: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( distinct_points @ SV12 @ SV23 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV27 @ SV28 ) )
= $true )
| ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( point @ SV3 ) )
= $true )
| ( ( ~ ( point @ SV14 ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV24: $i] :
( ( ( incident_point_and_line @ sK2_SY30 @ SV24 )
= $false )
| ( ( incident_point_and_line @ sK1_A @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( line @ SV4 ) )
= $true )
| ( ( ~ ( line @ SV15 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV28: $i,SV27: $i,SV23: $i,SV12: $i] :
( ( ( distinct_points @ SV12 @ SV23 )
= $false )
| ( ( ~ ( distinct_lines @ SV27 @ SV28 ) )
= $true )
| ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV14: $i,SV3: $i] :
( ( ( point @ SV3 )
= $false )
| ( ( ~ ( point @ SV14 ) )
= $true )
| ( ( ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(191,plain,
! [SV15: $i,SV4: $i] :
( ( ( line @ SV4 )
= $false )
| ( ( ~ ( line @ SV15 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(192,plain,
! [SV23: $i,SV12: $i,SV28: $i,SV27: $i] :
( ( ( distinct_lines @ SV27 @ SV28 )
= $false )
| ( ( distinct_points @ SV12 @ SV23 )
= $false )
| ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 )
| ( apart_point_and_line @ SV23 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(193,plain,
! [SV3: $i,SV14: $i] :
( ( ( point @ SV14 )
= $false )
| ( ( point @ SV3 )
= $false )
| ( ( ~ ( distinct_points @ SV3 @ SV14 ) )
= $true )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(194,plain,
! [SV4: $i,SV15: $i] :
( ( ( line @ SV15 )
= $false )
| ( ( line @ SV4 )
= $false )
| ( ( ~ ( convergent_lines @ SV4 @ SV15 ) )
= $true )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(195,plain,
! [SV23: $i,SV28: $i,SV27: $i,SV12: $i] :
( ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 )
| ( apart_point_and_line @ SV23 @ SV27 ) )
= $true )
| ( ( apart_point_and_line @ SV23 @ SV28 )
= $true )
| ( ( distinct_points @ SV12 @ SV23 )
= $false )
| ( ( distinct_lines @ SV27 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(196,plain,
! [SV14: $i,SV3: $i] :
( ( ( distinct_points @ SV3 @ SV14 )
= $false )
| ( ( point @ SV3 )
= $false )
| ( ( point @ SV14 )
= $false )
| ( ( line @ ( line_connecting @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(197,plain,
! [SV15: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV15 )
= $false )
| ( ( line @ SV4 )
= $false )
| ( ( line @ SV15 )
= $false )
| ( ( point @ ( intersection_point @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(198,plain,
! [SV23: $i,SV28: $i,SV27: $i,SV12: $i] :
( ( ( ( apart_point_and_line @ SV12 @ SV27 )
| ( apart_point_and_line @ SV12 @ SV28 ) )
= $true )
| ( ( apart_point_and_line @ SV23 @ SV27 )
= $true )
| ( ( apart_point_and_line @ SV23 @ SV28 )
= $true )
| ( ( distinct_points @ SV12 @ SV23 )
= $false )
| ( ( distinct_lines @ SV27 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(199,plain,
! [SV23: $i,SV28: $i,SV27: $i,SV12: $i] :
( ( ( apart_point_and_line @ SV12 @ SV27 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV28 )
= $true )
| ( ( apart_point_and_line @ SV23 @ SV27 )
= $true )
| ( ( apart_point_and_line @ SV23 @ SV28 )
= $true )
| ( ( distinct_points @ SV12 @ SV23 )
= $false )
| ( ( distinct_lines @ SV27 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(200,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,199,197,196,187,184,183,182,181,180,176,160,158,155,145,143,99,72,71]) ).
thf(201,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO225+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
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 10:13:57 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.29
% 0.57/0.29 No.of.Axioms: 12
% 0.57/0.29
% 0.57/0.29 Length.of.Defs: 0
% 0.57/0.29
% 0.57/0.29 Contains.Choice.Funs: false
% 0.57/0.29 ....
% 0.57/0.29
% 0.57/0.29 ********************************
% 0.57/0.29 * All subproblems solved! *
% 0.57/0.29 ********************************
% 0.57/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,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:200,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.29
% 0.57/0.29 %**** Beginning of derivation protocol ****
% 0.57/0.29 % SZS output start CNFRefutation
% See solution above
% 0.57/0.29
% 0.57/0.29 %**** End of derivation protocol ****
% 0.57/0.29 %**** no. of clauses in derivation: 178 ****
% 0.57/0.29 %**** clause counter: 200 ****
% 0.57/0.29
% 0.57/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,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:200,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------