%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO171+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 : n012.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 10:18:07 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 224 ( 112 unt; 0 typ; 0 def)
% Number of atoms : 1502 ( 392 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2473 ( 535 ~; 438 |; 18 &;1444 @)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 4 con; 0-2 aty)
% Number of variables : 553 ( 0 ^; 553 !; 0 ?; 553 :)
% 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_SY40,type,
sK2_SY40: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(10,axiom,
! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
thf(11,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).
thf(12,axiom,
! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
thf(16,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
thf(17,axiom,
! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
thf(18,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
thf(20,axiom,
! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(23,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(30,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(31,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
thf(33,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(34,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(36,conjecture,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(37,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(41,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(44,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(53,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(54,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(55,plain,
( ( ! [SY40: $i] :
( ( convergent_lines @ sK1_X @ SY40 )
=> ( distinct_lines @ sK1_X @ SY40 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(56,plain,
( ( ( convergent_lines @ sK1_X @ sK2_SY40 )
=> ( distinct_lines @ sK1_X @ sK2_SY40 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(57,plain,
( ( convergent_lines @ sK1_X @ sK2_SY40 )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(58,plain,
( ( distinct_lines @ sK1_X @ sK2_SY40 )
= $false ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(59,plain,
( ( ~ ( distinct_lines @ sK1_X @ sK2_SY40 ) )
= $true ),
inference(polarity_switch,[status(thm)],[58]) ).
thf(60,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(61,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_lines @ X @ Y )
=> ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ Y @ Z )
=> ( ( apart_point_and_line @ X @ Y )
| ( apart_point_and_line @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(69,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(70,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( convergent_lines @ L @ M )
& ( unorthogonal_lines @ L @ M ) )
=> ( ( ( convergent_lines @ L @ N )
& ( unorthogonal_lines @ L @ N ) )
| ( ( convergent_lines @ M @ N )
& ( unorthogonal_lines @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(71,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(72,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(73,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i] :
( ( equal_lines @ X @ Y )
<=> ~ ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i] :
( ( parallel_lines @ X @ Y )
<=> ~ ( convergent_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(76,plain,
( ( convergent_lines @ sK1_X @ sK2_SY40 )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(77,plain,
( ( ~ ( distinct_lines @ sK1_X @ sK2_SY40 ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_lines @ SX1 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) ) )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX1 @ SX2 )
| ( convergent_lines @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( parallel_lines @ SX0 @ SX1 )
| ~ ( convergent_lines @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ( parallel_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(85,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)],[74]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_lines @ SX1 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX2 )
| ( distinct_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(90,plain,
! [SV1: $i] :
( ( ~ ( distinct_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(91,plain,
! [SV2: $i] :
( ( ~ ( convergent_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(92,plain,
! [SV3: $i] :
( ( ! [SY41: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY41 @ SV3 ) @ SY41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV4: $i] :
( ( ! [SY42: $i] :
( ( convergent_lines @ SV4 @ SY42 )
| ( unorthogonal_lines @ SV4 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(94,plain,
( ( distinct_lines @ sK1_X @ sK2_SY40 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(95,plain,
! [SV5: $i] :
( ( ! [SY43: $i] :
( ~ ( distinct_lines @ SV5 @ SY43 )
| ( convergent_lines @ SV5 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( apart_point_and_line @ SV6 @ SY44 )
| ( distinct_lines @ SY44 @ SY45 )
| ( apart_point_and_line @ SV6 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV7 @ SY46 )
| ~ ( unorthogonal_lines @ SV7 @ SY46 ) )
| ~ ( ~ ( convergent_lines @ SV7 @ SY47 )
| ~ ( unorthogonal_lines @ SV7 @ SY47 ) ) )
| ~ ( convergent_lines @ SY46 @ SY47 )
| ~ ( unorthogonal_lines @ SY46 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV8 @ SY48 )
| ~ ~ ( unorthogonal_lines @ SV8 @ SY49 ) )
| ~ ( convergent_lines @ SY48 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( convergent_lines @ SV9 @ SY50 )
| ( distinct_lines @ SY50 @ SY51 )
| ( convergent_lines @ SV9 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(100,plain,
! [SV10: $i] :
( ( ! [SY52: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SV10 @ SY52 )
| ~ ~ ( unorthogonal_lines @ SV10 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(101,plain,
! [SV11: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( parallel_lines @ SV11 @ SY53 )
| ~ ( convergent_lines @ SV11 @ SY53 ) )
| ~ ( ~ ~ ( convergent_lines @ SV11 @ SY53 )
| ( parallel_lines @ SV11 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( equal_lines @ SV12 @ SY54 )
| ~ ( distinct_lines @ SV12 @ SY54 ) )
| ~ ( ~ ~ ( distinct_lines @ SV12 @ SY54 )
| ( equal_lines @ SV12 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV13: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( convergent_lines @ SV13 @ SY55 )
| ( convergent_lines @ SV13 @ SY56 )
| ( convergent_lines @ SY55 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV14: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( distinct_lines @ SY57 @ SY58 )
| ( apart_point_and_line @ SV14 @ SY57 )
| ( apart_point_and_line @ SV14 @ SY58 )
| ( convergent_lines @ SY57 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV15: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV15 @ SY59 )
| ~ ( unorthogonal_lines @ SV15 @ SY59 ) )
| ~ ( ~ ( convergent_lines @ SV15 @ SY60 )
| ~ ( unorthogonal_lines @ SV15 @ SY60 ) )
| ~ ( ~ ( convergent_lines @ SY59 @ SY60 )
| ~ ( unorthogonal_lines @ SY59 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV16: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( distinct_lines @ SV16 @ SY61 )
| ( distinct_lines @ SV16 @ SY62 )
| ( distinct_lines @ SY61 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
! [SV1: $i] :
( ( distinct_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(108,plain,
! [SV2: $i] :
( ( convergent_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV3: $i,SV17: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV17 @ SV3 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV18: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV18 )
| ( unorthogonal_lines @ SV4 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( distinct_lines @ SV5 @ SV19 )
| ( convergent_lines @ SV5 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY63: $i] :
( ~ ( apart_point_and_line @ SV6 @ SV20 )
| ( distinct_lines @ SV20 @ SY63 )
| ( apart_point_and_line @ SV6 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV7 @ SY64 )
| ~ ( unorthogonal_lines @ SV7 @ SY64 ) ) )
| ~ ( convergent_lines @ SV21 @ SY64 )
| ~ ( unorthogonal_lines @ SV21 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV22: $i,SV8: $i] :
( ( ! [SY65: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV8 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV8 @ SY65 ) )
| ~ ( convergent_lines @ SV22 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY66: $i] :
( ~ ( convergent_lines @ SV9 @ SV23 )
| ( distinct_lines @ SV23 @ SY66 )
| ( convergent_lines @ SV9 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( convergent_lines @ SV10 @ SV24 )
| ~ ~ ( unorthogonal_lines @ SV10 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( parallel_lines @ SV11 @ SV25 )
| ~ ( convergent_lines @ SV11 @ SV25 ) )
| ~ ( ~ ~ ( convergent_lines @ SV11 @ SV25 )
| ( parallel_lines @ SV11 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( equal_lines @ SV12 @ SV26 )
| ~ ( distinct_lines @ SV12 @ SV26 ) )
| ~ ( ~ ~ ( distinct_lines @ SV12 @ SV26 )
| ( equal_lines @ SV12 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV27: $i,SV13: $i] :
( ( ! [SY67: $i] :
( ~ ( convergent_lines @ SV13 @ SV27 )
| ( convergent_lines @ SV13 @ SY67 )
| ( convergent_lines @ SV27 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV14: $i,SV28: $i] :
( ( ! [SY68: $i] :
( ~ ( distinct_lines @ SV28 @ SY68 )
| ( apart_point_and_line @ SV14 @ SV28 )
| ( apart_point_and_line @ SV14 @ SY68 )
| ( convergent_lines @ SV28 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV29: $i,SV15: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV15 @ SV29 )
| ~ ( unorthogonal_lines @ SV15 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV15 @ SY69 )
| ~ ( unorthogonal_lines @ SV15 @ SY69 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SY69 )
| ~ ( unorthogonal_lines @ SV29 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY70: $i] :
( ~ ( distinct_lines @ SV16 @ SV30 )
| ( distinct_lines @ SV16 @ SY70 )
| ( distinct_lines @ SV30 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV3: $i,SV17: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV17 @ SV3 ) @ SV17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV18: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV18 )
= $true )
| ( ( unorthogonal_lines @ SV4 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( distinct_lines @ SV5 @ SV19 ) )
= $true )
| ( ( convergent_lines @ SV5 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV31: $i,SV20: $i,SV6: $i] :
( ( ~ ( apart_point_and_line @ SV6 @ SV20 )
| ( distinct_lines @ SV20 @ SV31 )
| ( apart_point_and_line @ SV6 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
| ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV8 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) )
| ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ~ ( convergent_lines @ SV9 @ SV23 )
| ( distinct_lines @ SV23 @ SV34 )
| ( convergent_lines @ SV9 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV10 @ SV24 )
| ~ ~ ( unorthogonal_lines @ SV10 @ SV24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ( parallel_lines @ SV11 @ SV25 )
| ~ ( convergent_lines @ SV11 @ SV25 ) )
| ~ ( ~ ~ ( convergent_lines @ SV11 @ SV25 )
| ( parallel_lines @ SV11 @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( equal_lines @ SV12 @ SV26 )
| ~ ( distinct_lines @ SV12 @ SV26 ) )
| ~ ( ~ ~ ( distinct_lines @ SV12 @ SV26 )
| ( equal_lines @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV35: $i,SV27: $i,SV13: $i] :
( ( ~ ( convergent_lines @ SV13 @ SV27 )
| ( convergent_lines @ SV13 @ SV35 )
| ( convergent_lines @ SV27 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV14: $i,SV36: $i,SV28: $i] :
( ( ~ ( distinct_lines @ SV28 @ SV36 )
| ( apart_point_and_line @ SV14 @ SV28 )
| ( apart_point_and_line @ SV14 @ SV36 )
| ( convergent_lines @ SV28 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ~ ~ ( ~ ( convergent_lines @ SV15 @ SV29 )
| ~ ( unorthogonal_lines @ SV15 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ~ ( distinct_lines @ SV16 @ SV30 )
| ( distinct_lines @ SV16 @ SV38 )
| ( distinct_lines @ SV30 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV19: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV19 )
= $false )
| ( ( convergent_lines @ SV5 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV31: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( apart_point_and_line @ SV6 @ SV20 ) )
= $true )
| ( ( ( distinct_lines @ SV20 @ SV31 )
| ( apart_point_and_line @ SV6 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV8 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV23 ) )
= $true )
| ( ( ( distinct_lines @ SV23 @ SV34 )
| ( convergent_lines @ SV9 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ~ ( convergent_lines @ SV10 @ SV24 )
| ~ ~ ( unorthogonal_lines @ SV10 @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(143,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ( parallel_lines @ SV11 @ SV25 )
| ~ ( convergent_lines @ SV11 @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(144,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV11 @ SV25 )
| ( parallel_lines @ SV11 @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(145,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( equal_lines @ SV12 @ SV26 )
| ~ ( distinct_lines @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(146,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ~ ( distinct_lines @ SV12 @ SV26 )
| ( equal_lines @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(147,plain,
! [SV35: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( convergent_lines @ SV13 @ SV27 ) )
= $true )
| ( ( ( convergent_lines @ SV13 @ SV35 )
| ( convergent_lines @ SV27 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV14: $i,SV36: $i,SV28: $i] :
( ( ( ~ ( distinct_lines @ SV28 @ SV36 ) )
= $true )
| ( ( ( apart_point_and_line @ SV14 @ SV28 )
| ( apart_point_and_line @ SV14 @ SV36 )
| ( convergent_lines @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( convergent_lines @ SV15 @ SV29 )
| ~ ( unorthogonal_lines @ SV15 @ SV29 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( distinct_lines @ SV16 @ SV30 ) )
= $true )
| ( ( ( distinct_lines @ SV16 @ SV38 )
| ( distinct_lines @ SV30 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV31: $i,SV20: $i,SV6: $i] :
( ( ( apart_point_and_line @ SV6 @ SV20 )
= $false )
| ( ( ( distinct_lines @ SV20 @ SV31 )
| ( apart_point_and_line @ SV6 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( unorthogonal_lines @ SV8 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ( convergent_lines @ SV9 @ SV23 )
= $false )
| ( ( ( distinct_lines @ SV23 @ SV34 )
| ( convergent_lines @ SV9 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ~ ( convergent_lines @ SV10 @ SV24 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV10 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( parallel_lines @ SV11 @ SV25 )
| ~ ( convergent_lines @ SV11 @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(157,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ~ ( convergent_lines @ SV11 @ SV25 )
| ( parallel_lines @ SV11 @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(158,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( equal_lines @ SV12 @ SV26 )
| ~ ( distinct_lines @ SV12 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(159,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ~ ( distinct_lines @ SV12 @ SV26 )
| ( equal_lines @ SV12 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(160,plain,
! [SV35: $i,SV27: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV27 )
= $false )
| ( ( ( convergent_lines @ SV13 @ SV35 )
| ( convergent_lines @ SV27 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV14: $i,SV36: $i,SV28: $i] :
( ( ( distinct_lines @ SV28 @ SV36 )
= $false )
| ( ( ( apart_point_and_line @ SV14 @ SV28 )
| ( apart_point_and_line @ SV14 @ SV36 )
| ( convergent_lines @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV29 )
| ~ ( unorthogonal_lines @ SV15 @ SV29 ) ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( distinct_lines @ SV16 @ SV30 )
= $false )
| ( ( ( distinct_lines @ SV16 @ SV38 )
| ( distinct_lines @ SV30 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV6: $i,SV31: $i,SV20: $i] :
( ( ( distinct_lines @ SV20 @ SV31 )
= $true )
| ( ( apart_point_and_line @ SV6 @ SV31 )
= $true )
| ( ( apart_point_and_line @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(166,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV8 @ SV22 )
| ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(167,plain,
! [SV9: $i,SV34: $i,SV23: $i] :
( ( ( distinct_lines @ SV23 @ SV34 )
= $true )
| ( ( convergent_lines @ SV9 @ SV34 )
= $true )
| ( ( convergent_lines @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( convergent_lines @ SV10 @ SV24 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV10 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( parallel_lines @ SV11 @ SV25 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( convergent_lines @ SV11 @ SV25 ) )
= $true )
| ( ( parallel_lines @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( equal_lines @ SV12 @ SV26 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV12 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ~ ( distinct_lines @ SV12 @ SV26 ) )
= $true )
| ( ( equal_lines @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV27: $i,SV35: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV35 )
= $true )
| ( ( convergent_lines @ SV27 @ SV35 )
= $true )
| ( ( convergent_lines @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV36: $i,SV28: $i,SV14: $i] :
( ( ( ( apart_point_and_line @ SV14 @ SV28 )
| ( apart_point_and_line @ SV14 @ SV36 ) )
= $true )
| ( ( convergent_lines @ SV28 @ SV36 )
= $true )
| ( ( distinct_lines @ SV28 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( convergent_lines @ SV15 @ SV29 )
| ~ ( unorthogonal_lines @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(176,plain,
! [SV30: $i,SV38: $i,SV16: $i] :
( ( ( distinct_lines @ SV16 @ SV38 )
= $true )
| ( ( distinct_lines @ SV30 @ SV38 )
= $true )
| ( ( distinct_lines @ SV16 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV24: $i,SV10: $i] :
( ( ( convergent_lines @ SV10 @ SV24 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV10 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(180,plain,
! [SV25: $i,SV11: $i] :
( ( ( parallel_lines @ SV11 @ SV25 )
= $false )
| ( ( ~ ( convergent_lines @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(181,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( convergent_lines @ SV11 @ SV25 ) )
= $false )
| ( ( parallel_lines @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV26: $i,SV12: $i] :
( ( ( equal_lines @ SV12 @ SV26 )
= $false )
| ( ( ~ ( distinct_lines @ SV12 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( distinct_lines @ SV12 @ SV26 ) )
= $false )
| ( ( equal_lines @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV36: $i,SV28: $i,SV14: $i] :
( ( ( apart_point_and_line @ SV14 @ SV28 )
= $true )
| ( ( apart_point_and_line @ SV14 @ SV36 )
= $true )
| ( ( convergent_lines @ SV28 @ SV36 )
= $true )
| ( ( distinct_lines @ SV28 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( convergent_lines @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV21 )
| ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( unorthogonal_lines @ SV8 @ SV22 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( unorthogonal_lines @ SV10 @ SV24 ) )
= $false )
| ( ( convergent_lines @ SV10 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV25: $i,SV11: $i] :
( ( ( convergent_lines @ SV11 @ SV25 )
= $false )
| ( ( parallel_lines @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(190,plain,
! [SV25: $i,SV11: $i] :
( ( ( convergent_lines @ SV11 @ SV25 )
= $true )
| ( ( parallel_lines @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(191,plain,
! [SV26: $i,SV12: $i] :
( ( ( distinct_lines @ SV12 @ SV26 )
= $false )
| ( ( equal_lines @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(192,plain,
! [SV26: $i,SV12: $i] :
( ( ( distinct_lines @ SV12 @ SV26 )
= $true )
| ( ( equal_lines @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(195,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( unorthogonal_lines @ SV7 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(196,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( unorthogonal_lines @ SV8 @ SV22 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV8 @ SV33 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(197,plain,
! [SV24: $i,SV10: $i] :
( ( ( unorthogonal_lines @ SV10 @ SV24 )
= $true )
| ( ( convergent_lines @ SV10 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(198,plain,
! [SV37: $i,SV29: $i,SV15: $i] :
( ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
| ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(200,plain,
! [SV32: $i,SV21: $i,SV7: $i] :
( ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(201,plain,
! [SV22: $i,SV33: $i,SV8: $i] :
( ( ( ~ ( unorthogonal_lines @ SV8 @ SV33 ) )
= $false )
| ( ( unorthogonal_lines @ SV8 @ SV22 )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV29: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) )
= $false )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(204,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV32 )
| ~ ( unorthogonal_lines @ SV7 @ SV32 ) )
= $false )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV22: $i,SV33: $i,SV8: $i] :
( ( ( unorthogonal_lines @ SV8 @ SV33 )
= $true )
| ( ( unorthogonal_lines @ SV8 @ SV22 )
= $true )
| ( ( ~ ( convergent_lines @ SV22 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(206,plain,
! [SV29: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( convergent_lines @ SV15 @ SV37 )
| ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV32 ) )
= $false )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(208,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( unorthogonal_lines @ SV7 @ SV32 ) )
= $false )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( convergent_lines @ SV7 @ SV32 ) )
= $false )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(210,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( unorthogonal_lines @ SV7 @ SV32 ) )
= $false )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(211,plain,
! [SV8: $i,SV33: $i,SV22: $i] :
( ( ( convergent_lines @ SV22 @ SV33 )
= $false )
| ( ( unorthogonal_lines @ SV8 @ SV22 )
= $true )
| ( ( unorthogonal_lines @ SV8 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(212,plain,
! [SV29: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( convergent_lines @ SV15 @ SV37 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(213,plain,
! [SV29: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( unorthogonal_lines @ SV15 @ SV37 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(214,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( convergent_lines @ SV7 @ SV32 )
= $true )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(215,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(216,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( convergent_lines @ SV7 @ SV32 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(217,plain,
! [SV21: $i,SV32: $i,SV7: $i] :
( ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( ~ ( convergent_lines @ SV21 @ SV32 )
| ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(218,plain,
! [SV29: $i,SV37: $i,SV15: $i] :
( ( ( convergent_lines @ SV15 @ SV37 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(219,plain,
! [SV29: $i,SV37: $i,SV15: $i] :
( ( ( unorthogonal_lines @ SV15 @ SV37 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) ) )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV32 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( convergent_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV32 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV32 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( convergent_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(223,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV32 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) )
= $false )
| ( ( convergent_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( convergent_lines @ SV29 @ SV37 )
| ~ ( unorthogonal_lines @ SV29 @ SV37 ) )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( convergent_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( convergent_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(229,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV21 @ SV32 ) )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(230,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( convergent_lines @ SV29 @ SV37 ) )
= $false )
| ( ( convergent_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(231,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( unorthogonal_lines @ SV29 @ SV37 ) )
= $false )
| ( ( convergent_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(232,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( convergent_lines @ SV29 @ SV37 ) )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(233,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( unorthogonal_lines @ SV29 @ SV37 ) )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(234,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( unorthogonal_lines @ SV21 @ SV32 )
= $false )
| ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( convergent_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(235,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( unorthogonal_lines @ SV21 @ SV32 )
= $false )
| ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( convergent_lines @ SV7 @ SV21 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(236,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( unorthogonal_lines @ SV21 @ SV32 )
= $false )
| ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( convergent_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(237,plain,
! [SV7: $i,SV32: $i,SV21: $i] :
( ( ( unorthogonal_lines @ SV21 @ SV32 )
= $false )
| ( ( convergent_lines @ SV21 @ SV32 )
= $false )
| ( ( unorthogonal_lines @ SV7 @ SV21 )
= $true )
| ( ( unorthogonal_lines @ SV7 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(238,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(239,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( convergent_lines @ SV29 @ SV37 )
= $true )
| ( ( unorthogonal_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(241,plain,
! [SV15: $i,SV37: $i,SV29: $i] :
( ( ( unorthogonal_lines @ SV29 @ SV37 )
= $true )
| ( ( unorthogonal_lines @ SV15 @ SV37 )
= $true )
| ( ( convergent_lines @ SV15 @ SV29 )
= $false )
| ( ( unorthogonal_lines @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(242,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[76,241,240,239,238,237,236,235,234,211,197,192,191,190,189,184,176,173,167,164,137,124,123,108,107,94]) ).
thf(243,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO171+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Oct 6 10:06:16 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.15
% 0.08/0.15 No.of.Axioms: 16
% 0.08/0.15
% 0.08/0.15 Length.of.Defs: 0
% 0.08/0.15
% 0.08/0.15 Contains.Choice.Funs: false
% 0.08/0.15 .....
% 0.08/0.15
% 0.08/0.15 ********************************
% 0.08/0.15 * All subproblems solved! *
% 0.08/0.15 ********************************
% 0.08/0.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,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:242,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.15
% 0.08/0.15 %**** Beginning of derivation protocol ****
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15
% 0.08/0.15 %**** End of derivation protocol ****
% 0.08/0.15 %**** no. of clauses in derivation: 224 ****
% 0.08/0.15 %**** clause counter: 242 ****
% 0.08/0.15
% 0.08/0.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,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:242,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------