%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO221+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 10:18:30 AM UTC 2026
% Result : Theorem 0.10s 0.29s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 154 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 854 ( 204 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1487 ( 145 ~; 250 |; 3 &;1050 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 398 ( 0 ^; 398 !; 0 ?; 398 :)
% 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_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_orthogonal_through_point,type,
orthogonal_through_point: $i > $i > $i ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY41,type,
sK2_SY41: $i ).
thf(tp_sK3_SY43,type,
sK3_SY43: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(1,axiom,
! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ouo1) ).
thf(2,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
thf(3,axiom,
! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
thf(6,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(7,axiom,
! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
thf(9,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(10,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(11,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(12,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(13,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
thf(14,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
thf(15,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(16,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(18,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(21,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(23,conjecture,
! [A: $i,B: $i,L: $i] :
( ~ ( apart_point_and_line @ B @ ( orthogonal_through_point @ L @ A ) )
=> ~ ( distinct_lines @ ( orthogonal_through_point @ L @ A ) @ ( orthogonal_through_point @ L @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(24,negated_conjecture,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( apart_point_and_line @ B @ ( orthogonal_through_point @ L @ A ) )
=> ~ ( distinct_lines @ ( orthogonal_through_point @ L @ A ) @ ( orthogonal_through_point @ L @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[23]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ~ ( apart_point_and_line @ B @ ( orthogonal_through_point @ L @ A ) )
=> ~ ( distinct_lines @ ( orthogonal_through_point @ L @ A ) @ ( orthogonal_through_point @ L @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[24]) ).
thf(26,plain,
( ( ! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(29,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)],[6]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,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)],[9]) ).
thf(32,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)],[10]) ).
thf(33,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)],[11]) ).
thf(34,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)],[12]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(39,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)],[18]) ).
thf(40,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [SY41: $i,SY42: $i] :
( ~ ( apart_point_and_line @ SY41 @ ( orthogonal_through_point @ SY42 @ sK1_A ) )
=> ~ ( distinct_lines @ ( orthogonal_through_point @ SY42 @ sK1_A ) @ ( orthogonal_through_point @ SY42 @ SY41 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(42,plain,
( ( ! [SY43: $i] :
( ~ ( apart_point_and_line @ sK2_SY41 @ ( orthogonal_through_point @ SY43 @ sK1_A ) )
=> ~ ( distinct_lines @ ( orthogonal_through_point @ SY43 @ sK1_A ) @ ( orthogonal_through_point @ SY43 @ sK2_SY41 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( ~ ( apart_point_and_line @ sK2_SY41 @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) )
=> ~ ( distinct_lines @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) @ ( orthogonal_through_point @ sK3_SY43 @ sK2_SY41 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(44,plain,
( ( ~ ( apart_point_and_line @ sK2_SY41 @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(45,plain,
( ( ~ ( distinct_lines @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) @ ( orthogonal_through_point @ sK3_SY43 @ sK2_SY41 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(46,plain,
( ( distinct_lines @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) @ ( orthogonal_through_point @ sK3_SY43 @ sK2_SY41 ) )
= $true ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ~ ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(53,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)],[34]) ).
thf(54,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)],[33]) ).
thf(55,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)],[32]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( convergent_lines @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(58,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)],[29]) ).
thf(59,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(60,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(61,plain,
( ( ! [A: $i,L: $i,M: $i,N: $i] :
( ( distinct_lines @ L @ M )
=> ( ( apart_point_and_line @ A @ L )
| ( apart_point_and_line @ A @ M )
| ( unorthogonal_lines @ L @ N )
| ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(62,plain,
( ( ~ ( apart_point_and_line @ sK2_SY41 @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(63,plain,
( ( distinct_lines @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) @ ( orthogonal_through_point @ sK3_SY43 @ sK2_SY41 ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(65,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)],[53]) ).
thf(66,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)],[54]) ).
thf(67,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)],[48]) ).
thf(68,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)],[58]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( distinct_lines @ SX1 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX1 )
| ( apart_point_and_line @ SX0 @ SX2 )
| ( unorthogonal_lines @ SX1 @ SX3 )
| ( unorthogonal_lines @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(70,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)],[56]) ).
thf(71,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)],[55]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ ( intersection_point @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(75,plain,
! [SV1: $i] :
( ( ~ ( distinct_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(76,plain,
! [SV2: $i] :
( ( ! [SY44: $i] :
~ ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SY44 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(77,plain,
! [SV3: $i] :
( ( ! [SY45: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ SY45 @ SV3 ) @ SY45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
! [SV4: $i] :
( ( ! [SY46: $i] :
~ ( apart_point_and_line @ SV4 @ ( orthogonal_through_point @ SY46 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(79,plain,
( ( apart_point_and_line @ sK2_SY41 @ ( orthogonal_through_point @ sK3_SY43 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(80,plain,
! [SV5: $i] :
( ( ! [SY47: $i] :
( ~ ( convergent_lines @ SV5 @ SY47 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV5 @ SY47 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(81,plain,
! [SV6: $i] :
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SY48 )
| ~ ( distinct_lines @ SY49 @ SY50 ) )
| ( apart_point_and_line @ SV6 @ SY49 )
| ( apart_point_and_line @ SV6 @ SY50 )
| ( apart_point_and_line @ SY48 @ SY49 )
| ( apart_point_and_line @ SY48 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(82,plain,
! [SV7: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ( apart_point_and_line @ SV7 @ SY51 )
| ( distinct_points @ SV7 @ SY52 )
| ( apart_point_and_line @ SY52 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(83,plain,
! [SV8: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ( distinct_lines @ SV8 @ SY53 )
| ( distinct_lines @ SV8 @ SY54 )
| ( distinct_lines @ SY53 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(84,plain,
! [SV9: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( distinct_lines @ SY55 @ SY56 )
| ( apart_point_and_line @ SV9 @ SY55 )
| ( apart_point_and_line @ SV9 @ SY56 )
| ( convergent_lines @ SY55 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(85,plain,
! [SV10: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i] :
( ~ ( distinct_lines @ SY57 @ SY58 )
| ( apart_point_and_line @ SV10 @ SY57 )
| ( apart_point_and_line @ SV10 @ SY58 )
| ( unorthogonal_lines @ SY57 @ SY59 )
| ( unorthogonal_lines @ SY58 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(86,plain,
! [SV11: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( convergent_lines @ SV11 @ SY60 )
| ( distinct_lines @ SY60 @ SY61 )
| ( convergent_lines @ SV11 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(87,plain,
! [SV12: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( apart_point_and_line @ SV12 @ SY62 )
| ( distinct_lines @ SY62 @ SY63 )
| ( apart_point_and_line @ SV12 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV13: $i] :
( ( ! [SY64: $i] :
( ~ ( convergent_lines @ SV13 @ SY64 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV13 @ SY64 ) @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(89,plain,
! [SV14: $i] :
( ( ! [SY65: $i] :
( ~ ( distinct_points @ SV14 @ SY65 )
| ~ ( apart_point_and_line @ SV14 @ ( line_connecting @ SV14 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(90,plain,
! [SV15: $i] :
( ( ! [SY66: $i] :
( ~ ( distinct_points @ SV15 @ SY66 )
| ~ ( apart_point_and_line @ SY66 @ ( line_connecting @ SV15 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(91,plain,
! [SV1: $i] :
( ( distinct_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(92,plain,
! [SV16: $i,SV2: $i] :
( ( ~ ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SV16 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(93,plain,
! [SV3: $i,SV17: $i] :
( ( ~ ( unorthogonal_lines @ ( orthogonal_through_point @ SV17 @ SV3 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV18: $i,SV4: $i] :
( ( ~ ( apart_point_and_line @ SV4 @ ( orthogonal_through_point @ SV18 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( convergent_lines @ SV5 @ SV19 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV5 @ SV19 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SV20 )
| ~ ( distinct_lines @ SY67 @ SY68 ) )
| ( apart_point_and_line @ SV6 @ SY67 )
| ( apart_point_and_line @ SV6 @ SY68 )
| ( apart_point_and_line @ SV20 @ SY67 )
| ( apart_point_and_line @ SV20 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY69: $i] :
( ~ ( apart_point_and_line @ SV7 @ SV21 )
| ( distinct_points @ SV7 @ SY69 )
| ( apart_point_and_line @ SY69 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV22: $i,SV8: $i] :
( ( ! [SY70: $i] :
( ~ ( distinct_lines @ SV8 @ SV22 )
| ( distinct_lines @ SV8 @ SY70 )
| ( distinct_lines @ SV22 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV9: $i,SV23: $i] :
( ( ! [SY71: $i] :
( ~ ( distinct_lines @ SV23 @ SY71 )
| ( apart_point_and_line @ SV9 @ SV23 )
| ( apart_point_and_line @ SV9 @ SY71 )
| ( convergent_lines @ SV23 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV10: $i,SV24: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ( distinct_lines @ SV24 @ SY72 )
| ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SY72 )
| ( unorthogonal_lines @ SV24 @ SY73 )
| ( unorthogonal_lines @ SY72 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY74: $i] :
( ~ ( convergent_lines @ SV11 @ SV25 )
| ( distinct_lines @ SV25 @ SY74 )
| ( convergent_lines @ SV11 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV26: $i,SV12: $i] :
( ( ! [SY75: $i] :
( ~ ( apart_point_and_line @ SV12 @ SV26 )
| ( distinct_lines @ SV26 @ SY75 )
| ( apart_point_and_line @ SV12 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( convergent_lines @ SV13 @ SV27 )
| ~ ( apart_point_and_line @ ( intersection_point @ SV13 @ SV27 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( distinct_points @ SV14 @ SV28 )
| ~ ( apart_point_and_line @ SV14 @ ( line_connecting @ SV14 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( distinct_points @ SV15 @ SV29 )
| ~ ( apart_point_and_line @ SV29 @ ( line_connecting @ SV15 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV16: $i,SV2: $i] :
( ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SV16 @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV3: $i,SV17: $i] :
( ( unorthogonal_lines @ ( orthogonal_through_point @ SV17 @ SV3 ) @ SV17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV18: $i,SV4: $i] :
( ( apart_point_and_line @ SV4 @ ( orthogonal_through_point @ SV18 @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( convergent_lines @ SV5 @ SV19 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV5 @ SV19 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV30: $i,SV20: $i,SV6: $i] :
( ( ! [SY76: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SV20 )
| ~ ( distinct_lines @ SV30 @ SY76 ) )
| ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SY76 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV31: $i,SV21: $i,SV7: $i] :
( ( ~ ( apart_point_and_line @ SV7 @ SV21 )
| ( distinct_points @ SV7 @ SV31 )
| ( apart_point_and_line @ SV31 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(112,plain,
! [SV32: $i,SV22: $i,SV8: $i] :
( ( ~ ( distinct_lines @ SV8 @ SV22 )
| ( distinct_lines @ SV8 @ SV32 )
| ( distinct_lines @ SV22 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(113,plain,
! [SV9: $i,SV33: $i,SV23: $i] :
( ( ~ ( distinct_lines @ SV23 @ SV33 )
| ( apart_point_and_line @ SV9 @ SV23 )
| ( apart_point_and_line @ SV9 @ SV33 )
| ( convergent_lines @ SV23 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV10: $i,SV34: $i,SV24: $i] :
( ( ! [SY77: $i] :
( ~ ( distinct_lines @ SV24 @ SV34 )
| ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SV34 )
| ( unorthogonal_lines @ SV24 @ SY77 )
| ( unorthogonal_lines @ SV34 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(115,plain,
! [SV35: $i,SV25: $i,SV11: $i] :
( ( ~ ( convergent_lines @ SV11 @ SV25 )
| ( distinct_lines @ SV25 @ SV35 )
| ( convergent_lines @ SV11 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(116,plain,
! [SV36: $i,SV26: $i,SV12: $i] :
( ( ~ ( apart_point_and_line @ SV12 @ SV26 )
| ( distinct_lines @ SV26 @ SV36 )
| ( apart_point_and_line @ SV12 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(117,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( convergent_lines @ SV13 @ SV27 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV13 @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( distinct_points @ SV14 @ SV28 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV14 @ ( line_connecting @ SV14 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( distinct_points @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV29 @ ( line_connecting @ SV15 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV19: $i,SV5: $i] :
( ( ( convergent_lines @ SV5 @ SV19 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV5 @ SV19 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV37: $i,SV30: $i,SV20: $i,SV6: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV6 @ SV20 )
| ~ ( distinct_lines @ SV30 @ SV37 ) )
| ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV31: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( apart_point_and_line @ SV7 @ SV21 ) )
= $true )
| ( ( ( distinct_points @ SV7 @ SV31 )
| ( apart_point_and_line @ SV31 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV32: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( distinct_lines @ SV8 @ SV22 ) )
= $true )
| ( ( ( distinct_lines @ SV8 @ SV32 )
| ( distinct_lines @ SV22 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV9: $i,SV33: $i,SV23: $i] :
( ( ( ~ ( distinct_lines @ SV23 @ SV33 ) )
= $true )
| ( ( ( apart_point_and_line @ SV9 @ SV23 )
| ( apart_point_and_line @ SV9 @ SV33 )
| ( convergent_lines @ SV23 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV38: $i,SV10: $i,SV34: $i,SV24: $i] :
( ( ~ ( distinct_lines @ SV24 @ SV34 )
| ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SV34 )
| ( unorthogonal_lines @ SV24 @ SV38 )
| ( unorthogonal_lines @ SV34 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV35: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( convergent_lines @ SV11 @ SV25 ) )
= $true )
| ( ( ( distinct_lines @ SV25 @ SV35 )
| ( convergent_lines @ SV11 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV36: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( apart_point_and_line @ SV12 @ SV26 ) )
= $true )
| ( ( ( distinct_lines @ SV26 @ SV36 )
| ( apart_point_and_line @ SV12 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV27: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV27 )
= $false )
| ( ( ~ ( apart_point_and_line @ ( intersection_point @ SV13 @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV28: $i,SV14: $i] :
( ( ( distinct_points @ SV14 @ SV28 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV14 @ ( line_connecting @ SV14 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV29: $i,SV15: $i] :
( ( ( distinct_points @ SV15 @ SV29 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV29 @ ( line_connecting @ SV15 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV19: $i,SV5: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV5 @ SV19 ) @ SV5 )
= $false )
| ( ( convergent_lines @ SV5 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV37: $i,SV30: $i,SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV6 @ SV20 )
| ~ ( distinct_lines @ SV30 @ SV37 ) ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV31: $i,SV21: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ SV21 )
= $false )
| ( ( ( distinct_points @ SV7 @ SV31 )
| ( apart_point_and_line @ SV31 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV32: $i,SV22: $i,SV8: $i] :
( ( ( distinct_lines @ SV8 @ SV22 )
= $false )
| ( ( ( distinct_lines @ SV8 @ SV32 )
| ( distinct_lines @ SV22 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV9: $i,SV33: $i,SV23: $i] :
( ( ( distinct_lines @ SV23 @ SV33 )
= $false )
| ( ( ( apart_point_and_line @ SV9 @ SV23 )
| ( apart_point_and_line @ SV9 @ SV33 )
| ( convergent_lines @ SV23 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(136,plain,
! [SV38: $i,SV10: $i,SV34: $i,SV24: $i] :
( ( ( ~ ( distinct_lines @ SV24 @ SV34 ) )
= $true )
| ( ( ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SV34 )
| ( unorthogonal_lines @ SV24 @ SV38 )
| ( unorthogonal_lines @ SV34 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV35: $i,SV25: $i,SV11: $i] :
( ( ( convergent_lines @ SV11 @ SV25 )
= $false )
| ( ( ( distinct_lines @ SV25 @ SV35 )
| ( convergent_lines @ SV11 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV36: $i,SV26: $i,SV12: $i] :
( ( ( apart_point_and_line @ SV12 @ SV26 )
= $false )
| ( ( ( distinct_lines @ SV26 @ SV36 )
| ( apart_point_and_line @ SV12 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV27: $i,SV13: $i] :
( ( ( apart_point_and_line @ ( intersection_point @ SV13 @ SV27 ) @ SV27 )
= $false )
| ( ( convergent_lines @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV28: $i,SV14: $i] :
( ( ( apart_point_and_line @ SV14 @ ( line_connecting @ SV14 @ SV28 ) )
= $false )
| ( ( distinct_points @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV15: $i,SV29: $i] :
( ( ( apart_point_and_line @ SV29 @ ( line_connecting @ SV15 @ SV29 ) )
= $false )
| ( ( distinct_points @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV37: $i,SV30: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV6 @ SV20 )
| ~ ( distinct_lines @ SV30 @ SV37 ) ) )
= $false )
| ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV21: $i,SV31: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV31 )
= $true )
| ( ( apart_point_and_line @ SV31 @ SV21 )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV22: $i,SV32: $i,SV8: $i] :
( ( ( distinct_lines @ SV8 @ SV32 )
= $true )
| ( ( distinct_lines @ SV22 @ SV32 )
= $true )
| ( ( distinct_lines @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ( apart_point_and_line @ SV9 @ SV23 )
| ( apart_point_and_line @ SV9 @ SV33 ) )
= $true )
| ( ( convergent_lines @ SV23 @ SV33 )
= $true )
| ( ( distinct_lines @ SV23 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV38: $i,SV10: $i,SV34: $i,SV24: $i] :
( ( ( distinct_lines @ SV24 @ SV34 )
= $false )
| ( ( ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SV34 )
| ( unorthogonal_lines @ SV24 @ SV38 )
| ( unorthogonal_lines @ SV34 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV11: $i,SV35: $i,SV25: $i] :
( ( ( distinct_lines @ SV25 @ SV35 )
= $true )
| ( ( convergent_lines @ SV11 @ SV35 )
= $true )
| ( ( convergent_lines @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV12: $i,SV36: $i,SV26: $i] :
( ( ( distinct_lines @ SV26 @ SV36 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV36 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV37: $i,SV30: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV20 )
| ~ ( distinct_lines @ SV30 @ SV37 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(150,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( apart_point_and_line @ SV9 @ SV23 )
= $true )
| ( ( apart_point_and_line @ SV9 @ SV33 )
= $true )
| ( ( convergent_lines @ SV23 @ SV33 )
= $true )
| ( ( distinct_lines @ SV23 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV38: $i,SV34: $i,SV24: $i,SV10: $i] :
( ( ( ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SV34 )
| ( unorthogonal_lines @ SV24 @ SV38 ) )
= $true )
| ( ( unorthogonal_lines @ SV34 @ SV38 )
= $true )
| ( ( distinct_lines @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV37: $i,SV30: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV20 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV30 @ SV37 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(153,plain,
! [SV38: $i,SV34: $i,SV24: $i,SV10: $i] :
( ( ( ( apart_point_and_line @ SV10 @ SV24 )
| ( apart_point_and_line @ SV10 @ SV34 ) )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV38 )
= $true )
| ( ( unorthogonal_lines @ SV34 @ SV38 )
= $true )
| ( ( distinct_lines @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(154,plain,
! [SV37: $i,SV30: $i,SV20: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV20 )
= $false )
| ( ( ~ ( distinct_lines @ SV30 @ SV37 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(155,plain,
! [SV38: $i,SV34: $i,SV24: $i,SV10: $i] :
( ( ( apart_point_and_line @ SV10 @ SV24 )
= $true )
| ( ( apart_point_and_line @ SV10 @ SV34 )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV38 )
= $true )
| ( ( unorthogonal_lines @ SV34 @ SV38 )
= $true )
| ( ( distinct_lines @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(156,plain,
! [SV20: $i,SV6: $i,SV37: $i,SV30: $i] :
( ( ( distinct_lines @ SV30 @ SV37 )
= $false )
| ( ( distinct_points @ SV6 @ SV20 )
= $false )
| ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 )
| ( apart_point_and_line @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(157,plain,
! [SV20: $i,SV37: $i,SV30: $i,SV6: $i] :
( ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 )
| ( apart_point_and_line @ SV20 @ SV30 ) )
= $true )
| ( ( apart_point_and_line @ SV20 @ SV37 )
= $true )
| ( ( distinct_points @ SV6 @ SV20 )
= $false )
| ( ( distinct_lines @ SV30 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(158,plain,
! [SV20: $i,SV37: $i,SV30: $i,SV6: $i] :
( ( ( ( apart_point_and_line @ SV6 @ SV30 )
| ( apart_point_and_line @ SV6 @ SV37 ) )
= $true )
| ( ( apart_point_and_line @ SV20 @ SV30 )
= $true )
| ( ( apart_point_and_line @ SV20 @ SV37 )
= $true )
| ( ( distinct_points @ SV6 @ SV20 )
= $false )
| ( ( distinct_lines @ SV30 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(159,plain,
! [SV20: $i,SV37: $i,SV30: $i,SV6: $i] :
( ( ( apart_point_and_line @ SV6 @ SV30 )
= $true )
| ( ( apart_point_and_line @ SV6 @ SV37 )
= $true )
| ( ( apart_point_and_line @ SV20 @ SV30 )
= $true )
| ( ( apart_point_and_line @ SV20 @ SV37 )
= $true )
| ( ( distinct_points @ SV6 @ SV20 )
= $false )
| ( ( distinct_lines @ SV30 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(160,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,159,155,150,148,147,144,143,141,140,139,131,108,107,106,91,79]) ).
thf(161,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO221+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.10/0.16 % Computer : n007.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 10:09:00 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.29
% 0.10/0.29 No.of.Axioms: 15
% 0.10/0.29
% 0.10/0.29 Length.of.Defs: 0
% 0.10/0.29
% 0.10/0.29 Contains.Choice.Funs: false
% 0.10/0.29 ....
% 0.10/0.29
% 0.10/0.29 ********************************
% 0.10/0.29 * All subproblems solved! *
% 0.10/0.29 ********************************
% 0.10/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:160,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.29
% 0.10/0.29 %**** Beginning of derivation protocol ****
% 0.10/0.29 % SZS output start CNFRefutation
% See solution above
% 0.10/0.29
% 0.10/0.29 %**** End of derivation protocol ****
% 0.10/0.29 %**** no. of clauses in derivation: 154 ****
% 0.10/0.29 %**** clause counter: 160 ****
% 0.10/0.29
% 0.10/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:160,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------