%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO210+2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 10:18:25 AM UTC 2026
% Result : Theorem 0.52s 0.31s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 154 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 1033 ( 250 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1720 ( 225 ~; 331 |; 18 &;1116 @)
% ( 0 <=>; 30 =>; 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 : 411 ( 0 ^; 411 !; 0 ?; 411 :)
% 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_SY37,type,
sK2_SY37: $i ).
thf(tp_sK3_SY39,type,
sK3_SY39: $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/sandbox/benchmark/theBenchmark.p',ouo1) ).
thf(2,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(3,axiom,
! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',oac1) ).
thf(5,axiom,
! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
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/sandbox/benchmark/theBenchmark.p',cup1) ).
thf(7,axiom,
! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cu1) ).
thf(16,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
thf(19,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(21,conjecture,
! [A: $i,L: $i,M: $i] :
( ( ~ ( apart_point_and_line @ A @ L )
& ~ ( unorthogonal_lines @ L @ M ) )
=> ~ ( distinct_lines @ L @ ( orthogonal_through_point @ M @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(22,negated_conjecture,
( ( ! [A: $i,L: $i,M: $i] :
( ( ~ ( apart_point_and_line @ A @ L )
& ~ ( unorthogonal_lines @ L @ M ) )
=> ~ ( distinct_lines @ L @ ( orthogonal_through_point @ M @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ! [A: $i,L: $i,M: $i] :
( ( ~ ( apart_point_and_line @ A @ L )
& ~ ( unorthogonal_lines @ L @ M ) )
=> ~ ( distinct_lines @ L @ ( orthogonal_through_point @ M @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,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(25,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,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)],[4]) ).
thf(28,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
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] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $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,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(36,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(37,plain,
( ( ! [SY37: $i,SY38: $i] :
( ( ~ ( apart_point_and_line @ sK1_A @ SY37 )
& ~ ( unorthogonal_lines @ SY37 @ SY38 ) )
=> ~ ( distinct_lines @ SY37 @ ( orthogonal_through_point @ SY38 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(38,plain,
( ( ! [SY39: $i] :
( ( ~ ( apart_point_and_line @ sK1_A @ sK2_SY37 )
& ~ ( unorthogonal_lines @ sK2_SY37 @ SY39 ) )
=> ~ ( distinct_lines @ sK2_SY37 @ ( orthogonal_through_point @ SY39 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(39,plain,
( ( ( ~ ( apart_point_and_line @ sK1_A @ sK2_SY37 )
& ~ ( unorthogonal_lines @ sK2_SY37 @ sK3_SY39 ) )
=> ~ ( distinct_lines @ sK2_SY37 @ ( orthogonal_through_point @ sK3_SY39 @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ~ ( apart_point_and_line @ sK1_A @ sK2_SY37 ) )
= $true ),
inference(standard_cnf,[status(thm)],[39]) ).
thf(41,plain,
( ( ~ ( unorthogonal_lines @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(standard_cnf,[status(thm)],[39]) ).
thf(42,plain,
( ( ~ ( distinct_lines @ sK2_SY37 @ ( orthogonal_through_point @ sK3_SY39 @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[39]) ).
thf(43,plain,
( ( distinct_lines @ sK2_SY37 @ ( orthogonal_through_point @ sK3_SY39 @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(44,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(47,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(48,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(49,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
~ ( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(51,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(52,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
| ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(53,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)],[27]) ).
thf(54,plain,
( ( ! [A: $i,L: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(55,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(56,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)],[24]) ).
thf(57,plain,
( ( ~ ( unorthogonal_lines @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(58,plain,
( ( ~ ( apart_point_and_line @ sK1_A @ sK2_SY37 ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(59,plain,
( ( distinct_lines @ sK2_SY37 @ ( orthogonal_through_point @ sK3_SY39 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(60,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)],[51]) ).
thf(61,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)],[46]) ).
thf(62,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)],[47]) ).
thf(63,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)],[53]) ).
thf(64,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)],[45]) ).
thf(65,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)],[48]) ).
thf(66,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)],[56]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(68,plain,
! [SV1: $i] :
( ( ~ ( distinct_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(69,plain,
! [SV2: $i] :
( ( ! [SY40: $i] :
~ ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SY40 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV3: $i] :
( ( ! [SY41: $i] :
( ( convergent_lines @ SV3 @ SY41 )
| ( unorthogonal_lines @ SV3 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(71,plain,
! [SV4: $i] :
( ( ! [SY42: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ SY42 @ SV4 ) @ SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV5: $i] :
( ( ! [SY43: $i] :
~ ( apart_point_and_line @ SV5 @ ( orthogonal_through_point @ SY43 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(73,plain,
( ( unorthogonal_lines @ sK2_SY37 @ sK3_SY39 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(74,plain,
( ( apart_point_and_line @ sK1_A @ sK2_SY37 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV6: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( distinct_lines @ SY44 @ SY45 )
| ( apart_point_and_line @ SV6 @ SY44 )
| ( apart_point_and_line @ SV6 @ SY45 )
| ( convergent_lines @ SY44 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV7: $i] :
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ~ ~ ( ~ ( distinct_points @ SV7 @ SY46 )
| ~ ( distinct_lines @ SY47 @ SY48 ) )
| ( apart_point_and_line @ SV7 @ SY47 )
| ( apart_point_and_line @ SV7 @ SY48 )
| ( apart_point_and_line @ SY46 @ SY47 )
| ( apart_point_and_line @ SY46 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
! [SV8: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( apart_point_and_line @ SV8 @ SY49 )
| ( distinct_points @ SV8 @ SY50 )
| ( apart_point_and_line @ SY50 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(78,plain,
! [SV9: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV9 @ SY51 )
| ~ ( unorthogonal_lines @ SV9 @ SY51 ) )
| ~ ( ~ ( convergent_lines @ SV9 @ SY52 )
| ~ ( unorthogonal_lines @ SV9 @ SY52 ) )
| ~ ( ~ ( convergent_lines @ SY51 @ SY52 )
| ~ ( unorthogonal_lines @ SY51 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV10: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ( distinct_lines @ SV10 @ SY53 )
| ( distinct_lines @ SV10 @ SY54 )
| ( distinct_lines @ SY53 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV11: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( apart_point_and_line @ SV11 @ SY55 )
| ( distinct_lines @ SY55 @ SY56 )
| ( apart_point_and_line @ SV11 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV12: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i] :
( ~ ( distinct_lines @ SY57 @ SY58 )
| ( apart_point_and_line @ SV12 @ SY57 )
| ( apart_point_and_line @ SV12 @ SY58 )
| ( unorthogonal_lines @ SY57 @ SY59 )
| ( unorthogonal_lines @ SY58 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV13: $i] :
( ( ! [SY60: $i] :
( ~ ( convergent_lines @ SV13 @ SY60 )
| ( distinct_lines @ SV13 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV1: $i] :
( ( distinct_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(84,plain,
! [SV14: $i,SV2: $i] :
( ( ~ ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SV14 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV15: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV15 )
| ( unorthogonal_lines @ SV3 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV4: $i,SV16: $i] :
( ( ~ ( unorthogonal_lines @ ( orthogonal_through_point @ SV16 @ SV4 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV17: $i,SV5: $i] :
( ( ~ ( apart_point_and_line @ SV5 @ ( orthogonal_through_point @ SV17 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV6: $i,SV18: $i] :
( ( ! [SY61: $i] :
( ~ ( distinct_lines @ SV18 @ SY61 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV6 @ SY61 )
| ( convergent_lines @ SV18 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV19: $i,SV7: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ~ ( ~ ( distinct_points @ SV7 @ SV19 )
| ~ ( distinct_lines @ SY62 @ SY63 ) )
| ( apart_point_and_line @ SV7 @ SY62 )
| ( apart_point_and_line @ SV7 @ SY63 )
| ( apart_point_and_line @ SV19 @ SY62 )
| ( apart_point_and_line @ SV19 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(90,plain,
! [SV20: $i,SV8: $i] :
( ( ! [SY64: $i] :
( ~ ( apart_point_and_line @ SV8 @ SV20 )
| ( distinct_points @ SV8 @ SY64 )
| ( apart_point_and_line @ SY64 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(91,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY65: $i] :
( ~ ~ ( ~ ( convergent_lines @ SV9 @ SV21 )
| ~ ( unorthogonal_lines @ SV9 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV9 @ SY65 )
| ~ ( unorthogonal_lines @ SV9 @ SY65 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SY65 )
| ~ ( unorthogonal_lines @ SV21 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV22: $i,SV10: $i] :
( ( ! [SY66: $i] :
( ~ ( distinct_lines @ SV10 @ SV22 )
| ( distinct_lines @ SV10 @ SY66 )
| ( distinct_lines @ SV22 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV23: $i,SV11: $i] :
( ( ! [SY67: $i] :
( ~ ( apart_point_and_line @ SV11 @ SV23 )
| ( distinct_lines @ SV23 @ SY67 )
| ( apart_point_and_line @ SV11 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV12: $i,SV24: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ~ ( distinct_lines @ SV24 @ SY68 )
| ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SY68 )
| ( unorthogonal_lines @ SV24 @ SY69 )
| ( unorthogonal_lines @ SY68 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV25: $i,SV13: $i] :
( ( ~ ( convergent_lines @ SV13 @ SV25 )
| ( distinct_lines @ SV13 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV14: $i,SV2: $i] :
( ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SV14 @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV15: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV15 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV4: $i,SV16: $i] :
( ( unorthogonal_lines @ ( orthogonal_through_point @ SV16 @ SV4 ) @ SV16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV17: $i,SV5: $i] :
( ( apart_point_and_line @ SV5 @ ( orthogonal_through_point @ SV17 @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV6: $i,SV26: $i,SV18: $i] :
( ( ~ ( distinct_lines @ SV18 @ SV26 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV6 @ SV26 )
| ( convergent_lines @ SV18 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV27: $i,SV19: $i,SV7: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ( distinct_points @ SV7 @ SV19 )
| ~ ( distinct_lines @ SV27 @ SY70 ) )
| ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SY70 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV28: $i,SV20: $i,SV8: $i] :
( ( ~ ( apart_point_and_line @ SV8 @ SV20 )
| ( distinct_points @ SV8 @ SV28 )
| ( apart_point_and_line @ SV28 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ~ ~ ( ~ ( convergent_lines @ SV9 @ SV21 )
| ~ ( unorthogonal_lines @ SV9 @ SV21 ) )
| ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV30: $i,SV22: $i,SV10: $i] :
( ( ~ ( distinct_lines @ SV10 @ SV22 )
| ( distinct_lines @ SV10 @ SV30 )
| ( distinct_lines @ SV22 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV31: $i,SV23: $i,SV11: $i] :
( ( ~ ( apart_point_and_line @ SV11 @ SV23 )
| ( distinct_lines @ SV23 @ SV31 )
| ( apart_point_and_line @ SV11 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV12: $i,SV32: $i,SV24: $i] :
( ( ! [SY71: $i] :
( ~ ( distinct_lines @ SV24 @ SV32 )
| ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SV32 )
| ( unorthogonal_lines @ SV24 @ SY71 )
| ( unorthogonal_lines @ SV32 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV25: $i,SV13: $i] :
( ( ( ~ ( convergent_lines @ SV13 @ SV25 ) )
= $true )
| ( ( distinct_lines @ SV13 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV6: $i,SV26: $i,SV18: $i] :
( ( ( ~ ( distinct_lines @ SV18 @ SV26 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV6 @ SV26 )
| ( convergent_lines @ SV18 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV33: $i,SV27: $i,SV19: $i,SV7: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV7 @ SV19 )
| ~ ( distinct_lines @ SV27 @ SV33 ) )
| ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV28: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( apart_point_and_line @ SV8 @ SV20 ) )
= $true )
| ( ( ( distinct_points @ SV8 @ SV28 )
| ( apart_point_and_line @ SV28 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( convergent_lines @ SV9 @ SV21 )
| ~ ( unorthogonal_lines @ SV9 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV30: $i,SV22: $i,SV10: $i] :
( ( ( ~ ( distinct_lines @ SV10 @ SV22 ) )
= $true )
| ( ( ( distinct_lines @ SV10 @ SV30 )
| ( distinct_lines @ SV22 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV31: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( apart_point_and_line @ SV11 @ SV23 ) )
= $true )
| ( ( ( distinct_lines @ SV23 @ SV31 )
| ( apart_point_and_line @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV34: $i,SV12: $i,SV32: $i,SV24: $i] :
( ( ~ ( distinct_lines @ SV24 @ SV32 )
| ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SV32 )
| ( unorthogonal_lines @ SV24 @ SV34 )
| ( unorthogonal_lines @ SV32 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV25: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV25 )
= $false )
| ( ( distinct_lines @ SV13 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(116,plain,
! [SV6: $i,SV26: $i,SV18: $i] :
( ( ( distinct_lines @ SV18 @ SV26 )
= $false )
| ( ( ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV6 @ SV26 )
| ( convergent_lines @ SV18 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV33: $i,SV27: $i,SV19: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV7 @ SV19 )
| ~ ( distinct_lines @ SV27 @ SV33 ) ) )
= $true )
| ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV28: $i,SV20: $i,SV8: $i] :
( ( ( apart_point_and_line @ SV8 @ SV20 )
= $false )
| ( ( ( distinct_points @ SV8 @ SV28 )
| ( apart_point_and_line @ SV28 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV21 )
| ~ ( unorthogonal_lines @ SV9 @ SV21 ) ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV30: $i,SV22: $i,SV10: $i] :
( ( ( distinct_lines @ SV10 @ SV22 )
= $false )
| ( ( ( distinct_lines @ SV10 @ SV30 )
| ( distinct_lines @ SV22 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(121,plain,
! [SV31: $i,SV23: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ SV23 )
= $false )
| ( ( ( distinct_lines @ SV23 @ SV31 )
| ( apart_point_and_line @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV34: $i,SV12: $i,SV32: $i,SV24: $i] :
( ( ( ~ ( distinct_lines @ SV24 @ SV32 ) )
= $true )
| ( ( ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SV32 )
| ( unorthogonal_lines @ SV24 @ SV34 )
| ( unorthogonal_lines @ SV32 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV26: $i,SV18: $i,SV6: $i] :
( ( ( ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV6 @ SV26 ) )
= $true )
| ( ( convergent_lines @ SV18 @ SV26 )
= $true )
| ( ( distinct_lines @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV33: $i,SV27: $i,SV19: $i,SV7: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV7 @ SV19 )
| ~ ( distinct_lines @ SV27 @ SV33 ) ) )
= $false )
| ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV20: $i,SV28: $i,SV8: $i] :
( ( ( distinct_points @ SV8 @ SV28 )
= $true )
| ( ( apart_point_and_line @ SV28 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV8 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV21 )
| ~ ( unorthogonal_lines @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(127,plain,
! [SV22: $i,SV30: $i,SV10: $i] :
( ( ( distinct_lines @ SV10 @ SV30 )
= $true )
| ( ( distinct_lines @ SV22 @ SV30 )
= $true )
| ( ( distinct_lines @ SV10 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(128,plain,
! [SV11: $i,SV31: $i,SV23: $i] :
( ( ( distinct_lines @ SV23 @ SV31 )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV31 )
= $true )
| ( ( apart_point_and_line @ SV11 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV34: $i,SV12: $i,SV32: $i,SV24: $i] :
( ( ( distinct_lines @ SV24 @ SV32 )
= $false )
| ( ( ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SV32 )
| ( unorthogonal_lines @ SV24 @ SV34 )
| ( unorthogonal_lines @ SV32 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV26: $i,SV18: $i,SV6: $i] :
( ( ( apart_point_and_line @ SV6 @ SV18 )
= $true )
| ( ( apart_point_and_line @ SV6 @ SV26 )
= $true )
| ( ( convergent_lines @ SV18 @ SV26 )
= $true )
| ( ( distinct_lines @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV33: $i,SV27: $i,SV19: $i,SV7: $i] :
( ( ( ~ ( distinct_points @ SV7 @ SV19 )
| ~ ( distinct_lines @ SV27 @ SV33 ) )
= $true )
| ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(132,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV34: $i,SV32: $i,SV24: $i,SV12: $i] :
( ( ( ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SV32 )
| ( unorthogonal_lines @ SV24 @ SV34 ) )
= $true )
| ( ( unorthogonal_lines @ SV32 @ SV34 )
= $true )
| ( ( distinct_lines @ SV24 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV33: $i,SV27: $i,SV19: $i,SV7: $i] :
( ( ( ~ ( distinct_points @ SV7 @ SV19 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV27 @ SV33 ) )
= $true )
| ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(135,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(136,plain,
! [SV34: $i,SV32: $i,SV24: $i,SV12: $i] :
( ( ( ( apart_point_and_line @ SV12 @ SV24 )
| ( apart_point_and_line @ SV12 @ SV32 ) )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV34 )
= $true )
| ( ( unorthogonal_lines @ SV32 @ SV34 )
= $true )
| ( ( distinct_lines @ SV24 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(137,plain,
! [SV33: $i,SV27: $i,SV19: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV19 )
= $false )
| ( ( ~ ( distinct_lines @ SV27 @ SV33 ) )
= $true )
| ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
| ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV34: $i,SV32: $i,SV24: $i,SV12: $i] :
( ( ( apart_point_and_line @ SV12 @ SV24 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV32 )
= $true )
| ( ( unorthogonal_lines @ SV24 @ SV34 )
= $true )
| ( ( unorthogonal_lines @ SV32 @ SV34 )
= $true )
| ( ( distinct_lines @ SV24 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV19: $i,SV7: $i,SV33: $i,SV27: $i] :
( ( ( distinct_lines @ SV27 @ SV33 )
= $false )
| ( ( distinct_points @ SV7 @ SV19 )
= $false )
| ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 )
| ( apart_point_and_line @ SV19 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV19: $i,SV33: $i,SV27: $i,SV7: $i] :
( ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 )
| ( apart_point_and_line @ SV19 @ SV27 ) )
= $true )
| ( ( apart_point_and_line @ SV19 @ SV33 )
= $true )
| ( ( distinct_points @ SV7 @ SV19 )
= $false )
| ( ( distinct_lines @ SV27 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(143,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV29 )
| ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(144,plain,
! [SV19: $i,SV33: $i,SV27: $i,SV7: $i] :
( ( ( ( apart_point_and_line @ SV7 @ SV27 )
| ( apart_point_and_line @ SV7 @ SV33 ) )
= $true )
| ( ( apart_point_and_line @ SV19 @ SV27 )
= $true )
| ( ( apart_point_and_line @ SV19 @ SV33 )
= $true )
| ( ( distinct_points @ SV7 @ SV19 )
= $false )
| ( ( distinct_lines @ SV27 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(145,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( ~ ( convergent_lines @ SV9 @ SV29 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(146,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( ~ ( unorthogonal_lines @ SV9 @ SV29 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(147,plain,
! [SV19: $i,SV33: $i,SV27: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ SV27 )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV33 )
= $true )
| ( ( apart_point_and_line @ SV19 @ SV27 )
= $true )
| ( ( apart_point_and_line @ SV19 @ SV33 )
= $true )
| ( ( distinct_points @ SV7 @ SV19 )
= $false )
| ( ( distinct_lines @ SV27 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(148,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( convergent_lines @ SV9 @ SV29 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(149,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( unorthogonal_lines @ SV9 @ SV29 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(150,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) )
= $false )
| ( ( convergent_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(151,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV29 )
| ~ ( unorthogonal_lines @ SV21 @ SV29 ) )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(152,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV29 ) )
= $false )
| ( ( convergent_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(153,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( unorthogonal_lines @ SV21 @ SV29 ) )
= $false )
| ( ( convergent_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(154,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( convergent_lines @ SV21 @ SV29 ) )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(155,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( unorthogonal_lines @ SV21 @ SV29 ) )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(156,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( convergent_lines @ SV21 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(157,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( unorthogonal_lines @ SV21 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(158,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( convergent_lines @ SV21 @ SV29 )
= $true )
| ( ( unorthogonal_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(159,plain,
! [SV9: $i,SV29: $i,SV21: $i] :
( ( ( unorthogonal_lines @ SV21 @ SV29 )
= $true )
| ( ( unorthogonal_lines @ SV9 @ SV29 )
= $true )
| ( ( convergent_lines @ SV9 @ SV21 )
= $false )
| ( ( unorthogonal_lines @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(160,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,159,158,157,156,147,139,130,128,127,125,115,99,98,97,96,83,74,73]) ).
thf(161,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO210+2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n001.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 10:17:01 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.31
% 0.52/0.31 No.of.Axioms: 13
% 0.52/0.31
% 0.52/0.31 Length.of.Defs: 0
% 0.52/0.31
% 0.52/0.31 Contains.Choice.Funs: false
% 0.52/0.31 ....
% 0.52/0.31
% 0.52/0.31 ********************************
% 0.52/0.31 * All subproblems solved! *
% 0.52/0.31 ********************************
% 0.52/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:160,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.52/0.31
% 0.52/0.31 %**** Beginning of derivation protocol ****
% 0.52/0.31 % SZS output start CNFRefutation
% See solution above
% 0.52/0.31
% 0.52/0.31 %**** End of derivation protocol ****
% 0.52/0.31 %**** no. of clauses in derivation: 154 ****
% 0.52/0.31 %**** clause counter: 160 ****
% 0.52/0.31
% 0.52/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:160,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------