TSTP Solution File: GEO192+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:08:12 EDT 2022
% Result : Theorem 0.40s 0.56s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 268 ( 151 unt; 9 typ; 0 def)
% Number of atoms : 1612 ( 393 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2747 ( 308 ~; 516 |; 17 &;1872 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 719 ( 0 ^ 719 !; 0 ?; 719 :)
% 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_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY33,type,
sK2_SY33: $i ).
thf(tp_sK3_SY35,type,
sK3_SY35: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(2,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(3,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(4,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(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( ( apart_point_and_line @ Z @ X )
| ( apart_point_and_line @ Z @ Y ) )
=> ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
=> ( ( distinct_points @ Z @ X )
& ( distinct_points @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).
thf(8,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(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
thf(10,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(11,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(12,axiom,
! [X: $i] :
~ ( distinct_points @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(13,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Z )
=> ( ( distinct_lines @ X @ Z )
& ( distinct_lines @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(14,negated_conjecture,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Z )
=> ( ( distinct_lines @ X @ Z )
& ( distinct_lines @ Y @ Z ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( apart_point_and_line @ ( intersection_point @ X @ Y ) @ Z )
=> ( ( distinct_lines @ X @ Z )
& ( distinct_lines @ Y @ Z ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,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)],[2]) ).
thf(18,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)],[3]) ).
thf(19,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)],[4]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( ( apart_point_and_line @ Z @ X )
| ( apart_point_and_line @ Z @ Y ) )
=> ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
=> ( ( distinct_points @ Z @ X )
& ( distinct_points @ Z @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,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)],[7]) ).
thf(23,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)],[8]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ! [SY33: $i,SY34: $i] :
( ( convergent_lines @ sK1_X @ SY33 )
=> ( ( apart_point_and_line @ ( intersection_point @ sK1_X @ SY33 ) @ SY34 )
=> ( ( distinct_lines @ sK1_X @ SY34 )
& ( distinct_lines @ SY33 @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(29,plain,
( ( ! [SY35: $i] :
( ( convergent_lines @ sK1_X @ sK2_SY33 )
=> ( ( apart_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY33 ) @ SY35 )
=> ( ( distinct_lines @ sK1_X @ SY35 )
& ( distinct_lines @ sK2_SY33 @ SY35 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( ( convergent_lines @ sK1_X @ sK2_SY33 )
=> ( ( apart_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY33 ) @ sK3_SY35 )
=> ( ( distinct_lines @ sK1_X @ sK3_SY35 )
& ( distinct_lines @ sK2_SY33 @ sK3_SY35 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(31,plain,
( ( convergent_lines @ sK1_X @ sK2_SY33 )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(32,plain,
( ( apart_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY33 ) @ sK3_SY35 )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(33,plain,
( ( ( distinct_lines @ sK1_X @ sK3_SY35 )
& ( distinct_lines @ sK2_SY33 @ sK3_SY35 ) )
= $false ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(34,plain,
( ( distinct_lines @ sK1_X @ sK3_SY35 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[33]) ).
thf(35,plain,
( ( distinct_lines @ sK2_SY33 @ sK3_SY35 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[33]) ).
thf(36,plain,
( ( ~ ( distinct_lines @ sK1_X @ sK3_SY35 ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ( distinct_lines @ sK2_SY33 @ sK3_SY35 ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(42,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ X )
| ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) )
& ! [Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(43,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
| ( distinct_points @ Z @ X ) ) )
& ! [Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
| ( distinct_points @ Z @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(47,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(48,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(49,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
| ( distinct_points @ Z @ X ) ) )
& ! [Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
| ( distinct_points @ Z @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ X )
| ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) )
& ! [Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( apart_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY33 ) @ sK3_SY35 )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(60,plain,
( ( convergent_lines @ sK1_X @ sK2_SY33 )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(61,plain,
( ( ~ ( distinct_lines @ sK1_X @ sK3_SY35 ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(62,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ ( line_connecting @ SX0 @ SX1 ) )
| ( distinct_points @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ ( line_connecting @ SX0 @ SX1 ) )
| ( distinct_points @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ SX0 )
| ( distinct_points @ SX2 @ ( intersection_point @ SX0 @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ SX1 )
| ( distinct_points @ SX2 @ ( intersection_point @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(64,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV2: $i] :
( ( ~ ( distinct_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV3: $i] :
( ( ~ ( convergent_lines @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV4: $i] :
( ( ! [SY36: $i] :
( ~ ( distinct_points @ SV4 @ SY36 )
| ! [SY37: $i] :
( ( distinct_points @ SV4 @ SY37 )
| ( distinct_points @ SY36 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV5: $i] :
( ( ! [SY38: $i] :
( ~ ( distinct_lines @ SV5 @ SY38 )
| ! [SY39: $i] :
( ( distinct_lines @ SV5 @ SY39 )
| ( distinct_lines @ SY38 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV6: $i] :
( ( ! [SY40: $i] :
( ~ ( convergent_lines @ SV6 @ SY40 )
| ! [SY41: $i] :
( ( convergent_lines @ SV6 @ SY41 )
| ( convergent_lines @ SY40 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV7: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i] :
( ~ ( distinct_lines @ SY43 @ SY44 )
| ~ ( distinct_points @ SV7 @ SY42 )
| ( apart_point_and_line @ SY42 @ SY44 )
| ( apart_point_and_line @ SY42 @ SY43 )
| ( apart_point_and_line @ SV7 @ SY43 )
| ( apart_point_and_line @ SV7 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(71,plain,
! [SV8: $i] :
( ( ! [SY45: $i] :
( ~ ( apart_point_and_line @ SV8 @ SY45 )
| ! [SY46: $i] :
( ( apart_point_and_line @ SY46 @ SY45 )
| ( distinct_points @ SV8 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
! [SV9: $i] :
( ( ! [SY47: $i] :
( ~ ( apart_point_and_line @ SV9 @ SY47 )
| ! [SY48: $i] :
( ( apart_point_and_line @ SV9 @ SY48 )
| ( distinct_lines @ SY47 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV10: $i] :
( ( ! [SY49: $i] :
( ~ ( convergent_lines @ SV10 @ SY49 )
| ( distinct_lines @ SV10 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
( ( distinct_lines @ sK1_X @ sK3_SY35 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY50: $i] :
( ~ ( distinct_points @ SV11 @ SY50 )
| ! [SY51: $i] :
( ~ ( apart_point_and_line @ SY51 @ ( line_connecting @ SV11 @ SY50 ) )
| ( distinct_points @ SY51 @ SV11 ) ) )
| ~ ! [SY52: $i] :
( ~ ( distinct_points @ SV11 @ SY52 )
| ! [SY53: $i] :
( ~ ( apart_point_and_line @ SY53 @ ( line_connecting @ SV11 @ SY52 ) )
| ( distinct_points @ SY53 @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY54: $i] :
( ~ ( convergent_lines @ SV12 @ SY54 )
| ! [SY55: $i] :
( ~ ( apart_point_and_line @ SY55 @ SV12 )
| ( distinct_points @ SY55 @ ( intersection_point @ SV12 @ SY54 ) ) ) )
| ~ ! [SY56: $i] :
( ~ ( convergent_lines @ SV12 @ SY56 )
| ! [SY57: $i] :
( ~ ( apart_point_and_line @ SY57 @ SY56 )
| ( distinct_points @ SY57 @ ( intersection_point @ SV12 @ SY56 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(77,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(78,plain,
! [SV2: $i] :
( ( distinct_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(79,plain,
! [SV3: $i] :
( ( convergent_lines @ SV3 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(80,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ( distinct_points @ SV4 @ SV13 )
| ! [SY58: $i] :
( ( distinct_points @ SV4 @ SY58 )
| ( distinct_points @ SV13 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(81,plain,
! [SV14: $i,SV5: $i] :
( ( ~ ( distinct_lines @ SV5 @ SV14 )
| ! [SY59: $i] :
( ( distinct_lines @ SV5 @ SY59 )
| ( distinct_lines @ SV14 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(82,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( convergent_lines @ SV6 @ SV15 )
| ! [SY60: $i] :
( ( convergent_lines @ SV6 @ SY60 )
| ( convergent_lines @ SV15 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(83,plain,
! [SV16: $i,SV7: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( distinct_lines @ SY61 @ SY62 )
| ~ ( distinct_points @ SV7 @ SV16 )
| ( apart_point_and_line @ SV16 @ SY62 )
| ( apart_point_and_line @ SV16 @ SY61 )
| ( apart_point_and_line @ SV7 @ SY61 )
| ( apart_point_and_line @ SV7 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(84,plain,
! [SV17: $i,SV8: $i] :
( ( ~ ( apart_point_and_line @ SV8 @ SV17 )
| ! [SY63: $i] :
( ( apart_point_and_line @ SY63 @ SV17 )
| ( distinct_points @ SV8 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(85,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ( apart_point_and_line @ SV9 @ SV18 )
| ! [SY64: $i] :
( ( apart_point_and_line @ SV9 @ SY64 )
| ( distinct_lines @ SV18 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( convergent_lines @ SV10 @ SV19 )
| ( distinct_lines @ SV10 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(87,plain,
! [SV11: $i] :
( ( ~ ! [SY50: $i] :
( ~ ( distinct_points @ SV11 @ SY50 )
| ! [SY51: $i] :
( ~ ( apart_point_and_line @ SY51 @ ( line_connecting @ SV11 @ SY50 ) )
| ( distinct_points @ SY51 @ SV11 ) ) )
| ~ ! [SY52: $i] :
( ~ ( distinct_points @ SV11 @ SY52 )
| ! [SY53: $i] :
( ~ ( apart_point_and_line @ SY53 @ ( line_connecting @ SV11 @ SY52 ) )
| ( distinct_points @ SY53 @ SY52 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV12: $i] :
( ( ~ ! [SY54: $i] :
( ~ ( convergent_lines @ SV12 @ SY54 )
| ! [SY55: $i] :
( ~ ( apart_point_and_line @ SY55 @ SV12 )
| ( distinct_points @ SY55 @ ( intersection_point @ SV12 @ SY54 ) ) ) )
| ~ ! [SY56: $i] :
( ~ ( convergent_lines @ SV12 @ SY56 )
| ! [SY57: $i] :
( ~ ( apart_point_and_line @ SY57 @ SY56 )
| ( distinct_points @ SY57 @ ( intersection_point @ SV12 @ SY56 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( distinct_points @ SV4 @ SV13 ) )
= $true )
| ( ( ! [SY58: $i] :
( ( distinct_points @ SV4 @ SY58 )
| ( distinct_points @ SV13 @ SY58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( distinct_lines @ SV5 @ SV14 ) )
= $true )
| ( ( ! [SY59: $i] :
( ( distinct_lines @ SV5 @ SY59 )
| ( distinct_lines @ SV14 @ SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV15 ) )
= $true )
| ( ( ! [SY60: $i] :
( ( convergent_lines @ SV6 @ SY60 )
| ( convergent_lines @ SV15 @ SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV16: $i,SV7: $i,SV20: $i] :
( ( ! [SY65: $i] :
( ~ ( distinct_lines @ SV20 @ SY65 )
| ~ ( distinct_points @ SV7 @ SV16 )
| ( apart_point_and_line @ SV16 @ SY65 )
| ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( apart_point_and_line @ SV8 @ SV17 ) )
= $true )
| ( ( ! [SY63: $i] :
( ( apart_point_and_line @ SY63 @ SV17 )
| ( distinct_points @ SV8 @ SY63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( apart_point_and_line @ SV9 @ SV18 ) )
= $true )
| ( ( ! [SY64: $i] :
( ( apart_point_and_line @ SV9 @ SY64 )
| ( distinct_lines @ SV18 @ SY64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( convergent_lines @ SV10 @ SV19 ) )
= $true )
| ( ( distinct_lines @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV11: $i] :
( ( ~ ! [SY50: $i] :
( ~ ( distinct_points @ SV11 @ SY50 )
| ! [SY51: $i] :
( ~ ( apart_point_and_line @ SY51 @ ( line_connecting @ SV11 @ SY50 ) )
| ( distinct_points @ SY51 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV11: $i] :
( ( ~ ! [SY52: $i] :
( ~ ( distinct_points @ SV11 @ SY52 )
| ! [SY53: $i] :
( ~ ( apart_point_and_line @ SY53 @ ( line_connecting @ SV11 @ SY52 ) )
| ( distinct_points @ SY53 @ SY52 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV12: $i] :
( ( ~ ! [SY54: $i] :
( ~ ( convergent_lines @ SV12 @ SY54 )
| ! [SY55: $i] :
( ~ ( apart_point_and_line @ SY55 @ SV12 )
| ( distinct_points @ SY55 @ ( intersection_point @ SV12 @ SY54 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(99,plain,
! [SV12: $i] :
( ( ~ ! [SY56: $i] :
( ~ ( convergent_lines @ SV12 @ SY56 )
| ! [SY57: $i] :
( ~ ( apart_point_and_line @ SY57 @ SY56 )
| ( distinct_points @ SY57 @ ( intersection_point @ SV12 @ SY56 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(100,plain,
! [SV13: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV13 )
= $false )
| ( ( ! [SY58: $i] :
( ( distinct_points @ SV4 @ SY58 )
| ( distinct_points @ SV13 @ SY58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV14: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV14 )
= $false )
| ( ( ! [SY59: $i] :
( ( distinct_lines @ SV5 @ SY59 )
| ( distinct_lines @ SV14 @ SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV15: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV15 )
= $false )
| ( ( ! [SY60: $i] :
( ( convergent_lines @ SV6 @ SY60 )
| ( convergent_lines @ SV15 @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV16: $i,SV7: $i,SV21: $i,SV20: $i] :
( ( ~ ( distinct_lines @ SV20 @ SV21 )
| ~ ( distinct_points @ SV7 @ SV16 )
| ( apart_point_and_line @ SV16 @ SV21 )
| ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV17: $i,SV8: $i] :
( ( ( apart_point_and_line @ SV8 @ SV17 )
= $false )
| ( ( ! [SY63: $i] :
( ( apart_point_and_line @ SY63 @ SV17 )
| ( distinct_points @ SV8 @ SY63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV18: $i,SV9: $i] :
( ( ( apart_point_and_line @ SV9 @ SV18 )
= $false )
| ( ( ! [SY64: $i] :
( ( apart_point_and_line @ SV9 @ SY64 )
| ( distinct_lines @ SV18 @ SY64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV19: $i,SV10: $i] :
( ( ( convergent_lines @ SV10 @ SV19 )
= $false )
| ( ( distinct_lines @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV11: $i] :
( ( ! [SY50: $i] :
( ~ ( distinct_points @ SV11 @ SY50 )
| ! [SY51: $i] :
( ~ ( apart_point_and_line @ SY51 @ ( line_connecting @ SV11 @ SY50 ) )
| ( distinct_points @ SY51 @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(108,plain,
! [SV11: $i] :
( ( ! [SY52: $i] :
( ~ ( distinct_points @ SV11 @ SY52 )
| ! [SY53: $i] :
( ~ ( apart_point_and_line @ SY53 @ ( line_connecting @ SV11 @ SY52 ) )
| ( distinct_points @ SY53 @ SY52 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(109,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
( ~ ( convergent_lines @ SV12 @ SY54 )
| ! [SY55: $i] :
( ~ ( apart_point_and_line @ SY55 @ SV12 )
| ( distinct_points @ SY55 @ ( intersection_point @ SV12 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(110,plain,
! [SV12: $i] :
( ( ! [SY56: $i] :
( ~ ( convergent_lines @ SV12 @ SY56 )
| ! [SY57: $i] :
( ~ ( apart_point_and_line @ SY57 @ SY56 )
| ( distinct_points @ SY57 @ ( intersection_point @ SV12 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(111,plain,
! [SV13: $i,SV22: $i,SV4: $i] :
( ( ( ( distinct_points @ SV4 @ SV22 )
| ( distinct_points @ SV13 @ SV22 ) )
= $true )
| ( ( distinct_points @ SV4 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV14: $i,SV23: $i,SV5: $i] :
( ( ( ( distinct_lines @ SV5 @ SV23 )
| ( distinct_lines @ SV14 @ SV23 ) )
= $true )
| ( ( distinct_lines @ SV5 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV15: $i,SV24: $i,SV6: $i] :
( ( ( ( convergent_lines @ SV6 @ SV24 )
| ( convergent_lines @ SV15 @ SV24 ) )
= $true )
| ( ( convergent_lines @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV16: $i,SV7: $i,SV21: $i,SV20: $i] :
( ( ( ~ ( distinct_lines @ SV20 @ SV21 )
| ~ ( distinct_points @ SV7 @ SV16 ) )
= $true )
| ( ( ( apart_point_and_line @ SV16 @ SV21 )
| ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV8: $i,SV17: $i,SV25: $i] :
( ( ( ( apart_point_and_line @ SV25 @ SV17 )
| ( distinct_points @ SV8 @ SV25 ) )
= $true )
| ( ( apart_point_and_line @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV18: $i,SV26: $i,SV9: $i] :
( ( ( ( apart_point_and_line @ SV9 @ SV26 )
| ( distinct_lines @ SV18 @ SV26 ) )
= $true )
| ( ( apart_point_and_line @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV27: $i,SV11: $i] :
( ( ~ ( distinct_points @ SV11 @ SV27 )
| ! [SY66: $i] :
( ~ ( apart_point_and_line @ SY66 @ ( line_connecting @ SV11 @ SV27 ) )
| ( distinct_points @ SY66 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV28: $i,SV11: $i] :
( ( ~ ( distinct_points @ SV11 @ SV28 )
| ! [SY67: $i] :
( ~ ( apart_point_and_line @ SY67 @ ( line_connecting @ SV11 @ SV28 ) )
| ( distinct_points @ SY67 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( convergent_lines @ SV12 @ SV29 )
| ! [SY68: $i] :
( ~ ( apart_point_and_line @ SY68 @ SV12 )
| ( distinct_points @ SY68 @ ( intersection_point @ SV12 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV30: $i,SV12: $i] :
( ( ~ ( convergent_lines @ SV12 @ SV30 )
| ! [SY69: $i] :
( ~ ( apart_point_and_line @ SY69 @ SV30 )
| ( distinct_points @ SY69 @ ( intersection_point @ SV12 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV13: $i,SV22: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV22 )
= $true )
| ( ( distinct_points @ SV13 @ SV22 )
= $true )
| ( ( distinct_points @ SV4 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV14: $i,SV23: $i,SV5: $i] :
( ( ( distinct_lines @ SV5 @ SV23 )
= $true )
| ( ( distinct_lines @ SV14 @ SV23 )
= $true )
| ( ( distinct_lines @ SV5 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV15: $i,SV24: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV24 )
= $true )
| ( ( convergent_lines @ SV15 @ SV24 )
= $true )
| ( ( convergent_lines @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV16: $i,SV7: $i,SV21: $i,SV20: $i] :
( ( ( ~ ( distinct_lines @ SV20 @ SV21 ) )
= $true )
| ( ( ~ ( distinct_points @ SV7 @ SV16 ) )
= $true )
| ( ( ( apart_point_and_line @ SV16 @ SV21 )
| ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV8: $i,SV17: $i,SV25: $i] :
( ( ( apart_point_and_line @ SV25 @ SV17 )
= $true )
| ( ( distinct_points @ SV8 @ SV25 )
= $true )
| ( ( apart_point_and_line @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV18: $i,SV26: $i,SV9: $i] :
( ( ( apart_point_and_line @ SV9 @ SV26 )
= $true )
| ( ( distinct_lines @ SV18 @ SV26 )
= $true )
| ( ( apart_point_and_line @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV27: $i,SV11: $i] :
( ( ( ~ ( distinct_points @ SV11 @ SV27 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( apart_point_and_line @ SY66 @ ( line_connecting @ SV11 @ SV27 ) )
| ( distinct_points @ SY66 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( distinct_points @ SV11 @ SV28 ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( apart_point_and_line @ SY67 @ ( line_connecting @ SV11 @ SV28 ) )
| ( distinct_points @ SY67 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV29: $i,SV12: $i] :
( ( ( ~ ( convergent_lines @ SV12 @ SV29 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( apart_point_and_line @ SY68 @ SV12 )
| ( distinct_points @ SY68 @ ( intersection_point @ SV12 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ( convergent_lines @ SV12 @ SV30 ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( apart_point_and_line @ SY69 @ SV30 )
| ( distinct_points @ SY69 @ ( intersection_point @ SV12 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV16: $i,SV7: $i,SV21: $i,SV20: $i] :
( ( ( distinct_lines @ SV20 @ SV21 )
= $false )
| ( ( ~ ( distinct_points @ SV7 @ SV16 ) )
= $true )
| ( ( ( apart_point_and_line @ SV16 @ SV21 )
| ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV27: $i,SV11: $i] :
( ( ( distinct_points @ SV11 @ SV27 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( apart_point_and_line @ SY66 @ ( line_connecting @ SV11 @ SV27 ) )
| ( distinct_points @ SY66 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV28: $i,SV11: $i] :
( ( ( distinct_points @ SV11 @ SV28 )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( apart_point_and_line @ SY67 @ ( line_connecting @ SV11 @ SV28 ) )
| ( distinct_points @ SY67 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV29: $i,SV12: $i] :
( ( ( convergent_lines @ SV12 @ SV29 )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( apart_point_and_line @ SY68 @ SV12 )
| ( distinct_points @ SY68 @ ( intersection_point @ SV12 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV30: $i,SV12: $i] :
( ( ( convergent_lines @ SV12 @ SV30 )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( apart_point_and_line @ SY69 @ SV30 )
| ( distinct_points @ SY69 @ ( intersection_point @ SV12 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV21: $i,SV20: $i,SV16: $i,SV7: $i] :
( ( ( distinct_points @ SV7 @ SV16 )
= $false )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false )
| ( ( ( apart_point_and_line @ SV16 @ SV21 )
| ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(137,plain,
! [SV27: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( apart_point_and_line @ SV31 @ ( line_connecting @ SV11 @ SV27 ) )
| ( distinct_points @ SV31 @ SV11 ) )
= $true )
| ( ( distinct_points @ SV11 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(138,plain,
! [SV28: $i,SV11: $i,SV32: $i] :
( ( ( ~ ( apart_point_and_line @ SV32 @ ( line_connecting @ SV11 @ SV28 ) )
| ( distinct_points @ SV32 @ SV28 ) )
= $true )
| ( ( distinct_points @ SV11 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV29: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( apart_point_and_line @ SV33 @ SV12 )
| ( distinct_points @ SV33 @ ( intersection_point @ SV12 @ SV29 ) ) )
= $true )
| ( ( convergent_lines @ SV12 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(140,plain,
! [SV12: $i,SV30: $i,SV34: $i] :
( ( ( ~ ( apart_point_and_line @ SV34 @ SV30 )
| ( distinct_points @ SV34 @ ( intersection_point @ SV12 @ SV30 ) ) )
= $true )
| ( ( convergent_lines @ SV12 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(141,plain,
! [SV7: $i,SV20: $i,SV21: $i,SV16: $i] :
( ( ( apart_point_and_line @ SV16 @ SV21 )
= $true )
| ( ( ( apart_point_and_line @ SV16 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false )
| ( ( distinct_points @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(142,plain,
! [SV27: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( apart_point_and_line @ SV31 @ ( line_connecting @ SV11 @ SV27 ) ) )
= $true )
| ( ( distinct_points @ SV31 @ SV11 )
= $true )
| ( ( distinct_points @ SV11 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(143,plain,
! [SV28: $i,SV11: $i,SV32: $i] :
( ( ( ~ ( apart_point_and_line @ SV32 @ ( line_connecting @ SV11 @ SV28 ) ) )
= $true )
| ( ( distinct_points @ SV32 @ SV28 )
= $true )
| ( ( distinct_points @ SV11 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(144,plain,
! [SV29: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( apart_point_and_line @ SV33 @ SV12 ) )
= $true )
| ( ( distinct_points @ SV33 @ ( intersection_point @ SV12 @ SV29 ) )
= $true )
| ( ( convergent_lines @ SV12 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(145,plain,
! [SV12: $i,SV30: $i,SV34: $i] :
( ( ( ~ ( apart_point_and_line @ SV34 @ SV30 ) )
= $true )
| ( ( distinct_points @ SV34 @ ( intersection_point @ SV12 @ SV30 ) )
= $true )
| ( ( convergent_lines @ SV12 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(146,plain,
! [SV21: $i,SV7: $i,SV20: $i,SV16: $i] :
( ( ( apart_point_and_line @ SV16 @ SV20 )
= $true )
| ( ( ( apart_point_and_line @ SV7 @ SV20 )
| ( apart_point_and_line @ SV7 @ SV21 ) )
= $true )
| ( ( apart_point_and_line @ SV16 @ SV21 )
= $true )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false )
| ( ( distinct_points @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(147,plain,
! [SV27: $i,SV11: $i,SV31: $i] :
( ( ( apart_point_and_line @ SV31 @ ( line_connecting @ SV11 @ SV27 ) )
= $false )
| ( ( distinct_points @ SV31 @ SV11 )
= $true )
| ( ( distinct_points @ SV11 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV28: $i,SV11: $i,SV32: $i] :
( ( ( apart_point_and_line @ SV32 @ ( line_connecting @ SV11 @ SV28 ) )
= $false )
| ( ( distinct_points @ SV32 @ SV28 )
= $true )
| ( ( distinct_points @ SV11 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV29: $i,SV12: $i,SV33: $i] :
( ( ( apart_point_and_line @ SV33 @ SV12 )
= $false )
| ( ( distinct_points @ SV33 @ ( intersection_point @ SV12 @ SV29 ) )
= $true )
| ( ( convergent_lines @ SV12 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(150,plain,
! [SV12: $i,SV30: $i,SV34: $i] :
( ( ( apart_point_and_line @ SV34 @ SV30 )
= $false )
| ( ( distinct_points @ SV34 @ ( intersection_point @ SV12 @ SV30 ) )
= $true )
| ( ( convergent_lines @ SV12 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV16: $i,SV21: $i,SV20: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV21 )
= $true )
| ( ( apart_point_and_line @ SV16 @ SV20 )
= $true )
| ( ( apart_point_and_line @ SV16 @ SV21 )
= $true )
| ( ( distinct_lines @ SV20 @ SV21 )
= $false )
| ( ( distinct_points @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(152,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,151,150,149,148,147,126,125,123,122,121,106,79,78,77,74,60]) ).
thf(153,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(154,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(155,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(156,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(157,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( distinct_lines @ X @ Y )
| ! [Z: $i] :
( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(158,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(159,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
| ( distinct_points @ Z @ X ) ) )
& ! [Y: $i] :
( ~ ( distinct_points @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) )
| ( distinct_points @ Z @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(160,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ X )
| ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) )
& ! [Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ! [Z: $i] :
( ~ ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(161,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( distinct_lines @ U @ V )
| ~ ( distinct_points @ X @ Y )
| ( apart_point_and_line @ Y @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(162,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ Z @ Y )
| ( distinct_points @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(163,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apart_point_and_line @ X @ Y )
| ! [Z: $i] :
( ( apart_point_and_line @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(164,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( convergent_lines @ X @ Y )
| ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(165,plain,
( ( apart_point_and_line @ ( intersection_point @ sK1_X @ sK2_SY33 ) @ sK3_SY35 )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(166,plain,
( ( convergent_lines @ sK1_X @ sK2_SY33 )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(167,plain,
( ( ~ ( distinct_lines @ sK2_SY33 @ sK3_SY35 ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(168,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ ( line_connecting @ SX0 @ SX1 ) )
| ( distinct_points @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ ( line_connecting @ SX0 @ SX1 ) )
| ( distinct_points @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(169,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ SX0 )
| ( distinct_points @ SX2 @ ( intersection_point @ SX0 @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( apart_point_and_line @ SX2 @ SX1 )
| ( distinct_points @ SX2 @ ( intersection_point @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(170,plain,
! [SV35: $i] :
( ( ~ ( distinct_points @ SV35 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(171,plain,
! [SV36: $i] :
( ( ~ ( distinct_lines @ SV36 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(172,plain,
! [SV37: $i] :
( ( ~ ( convergent_lines @ SV37 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(173,plain,
! [SV38: $i] :
( ( ! [SY70: $i] :
( ~ ( distinct_points @ SV38 @ SY70 )
| ! [SY71: $i] :
( ( distinct_points @ SV38 @ SY71 )
| ( distinct_points @ SY70 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(174,plain,
! [SV39: $i] :
( ( ! [SY72: $i] :
( ~ ( distinct_lines @ SV39 @ SY72 )
| ! [SY73: $i] :
( ( distinct_lines @ SV39 @ SY73 )
| ( distinct_lines @ SY72 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(175,plain,
! [SV40: $i] :
( ( ! [SY74: $i] :
( ~ ( convergent_lines @ SV40 @ SY74 )
| ! [SY75: $i] :
( ( convergent_lines @ SV40 @ SY75 )
| ( convergent_lines @ SY74 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(176,plain,
! [SV41: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ( distinct_lines @ SY77 @ SY78 )
| ~ ( distinct_points @ SV41 @ SY76 )
| ( apart_point_and_line @ SY76 @ SY78 )
| ( apart_point_and_line @ SY76 @ SY77 )
| ( apart_point_and_line @ SV41 @ SY77 )
| ( apart_point_and_line @ SV41 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV42: $i] :
( ( ! [SY79: $i] :
( ~ ( apart_point_and_line @ SV42 @ SY79 )
| ! [SY80: $i] :
( ( apart_point_and_line @ SY80 @ SY79 )
| ( distinct_points @ SV42 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV43: $i] :
( ( ! [SY81: $i] :
( ~ ( apart_point_and_line @ SV43 @ SY81 )
| ! [SY82: $i] :
( ( apart_point_and_line @ SV43 @ SY82 )
| ( distinct_lines @ SY81 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV44: $i] :
( ( ! [SY83: $i] :
( ~ ( convergent_lines @ SV44 @ SY83 )
| ( distinct_lines @ SV44 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(180,plain,
( ( distinct_lines @ sK2_SY33 @ sK3_SY35 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV45: $i] :
( ( ~ ( ~ ! [SY84: $i] :
( ~ ( distinct_points @ SV45 @ SY84 )
| ! [SY85: $i] :
( ~ ( apart_point_and_line @ SY85 @ ( line_connecting @ SV45 @ SY84 ) )
| ( distinct_points @ SY85 @ SV45 ) ) )
| ~ ! [SY86: $i] :
( ~ ( distinct_points @ SV45 @ SY86 )
| ! [SY87: $i] :
( ~ ( apart_point_and_line @ SY87 @ ( line_connecting @ SV45 @ SY86 ) )
| ( distinct_points @ SY87 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV46: $i] :
( ( ~ ( ~ ! [SY88: $i] :
( ~ ( convergent_lines @ SV46 @ SY88 )
| ! [SY89: $i] :
( ~ ( apart_point_and_line @ SY89 @ SV46 )
| ( distinct_points @ SY89 @ ( intersection_point @ SV46 @ SY88 ) ) ) )
| ~ ! [SY90: $i] :
( ~ ( convergent_lines @ SV46 @ SY90 )
| ! [SY91: $i] :
( ~ ( apart_point_and_line @ SY91 @ SY90 )
| ( distinct_points @ SY91 @ ( intersection_point @ SV46 @ SY90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV35: $i] :
( ( distinct_points @ SV35 @ SV35 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(184,plain,
! [SV36: $i] :
( ( distinct_lines @ SV36 @ SV36 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV37: $i] :
( ( convergent_lines @ SV37 @ SV37 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV47: $i,SV38: $i] :
( ( ~ ( distinct_points @ SV38 @ SV47 )
| ! [SY92: $i] :
( ( distinct_points @ SV38 @ SY92 )
| ( distinct_points @ SV47 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(187,plain,
! [SV48: $i,SV39: $i] :
( ( ~ ( distinct_lines @ SV39 @ SV48 )
| ! [SY93: $i] :
( ( distinct_lines @ SV39 @ SY93 )
| ( distinct_lines @ SV48 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV49: $i,SV40: $i] :
( ( ~ ( convergent_lines @ SV40 @ SV49 )
| ! [SY94: $i] :
( ( convergent_lines @ SV40 @ SY94 )
| ( convergent_lines @ SV49 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV50: $i,SV41: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( distinct_lines @ SY95 @ SY96 )
| ~ ( distinct_points @ SV41 @ SV50 )
| ( apart_point_and_line @ SV50 @ SY96 )
| ( apart_point_and_line @ SV50 @ SY95 )
| ( apart_point_and_line @ SV41 @ SY95 )
| ( apart_point_and_line @ SV41 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV51: $i,SV42: $i] :
( ( ~ ( apart_point_and_line @ SV42 @ SV51 )
| ! [SY97: $i] :
( ( apart_point_and_line @ SY97 @ SV51 )
| ( distinct_points @ SV42 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(191,plain,
! [SV52: $i,SV43: $i] :
( ( ~ ( apart_point_and_line @ SV43 @ SV52 )
| ! [SY98: $i] :
( ( apart_point_and_line @ SV43 @ SY98 )
| ( distinct_lines @ SV52 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV53: $i,SV44: $i] :
( ( ~ ( convergent_lines @ SV44 @ SV53 )
| ( distinct_lines @ SV44 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV45: $i] :
( ( ~ ! [SY84: $i] :
( ~ ( distinct_points @ SV45 @ SY84 )
| ! [SY85: $i] :
( ~ ( apart_point_and_line @ SY85 @ ( line_connecting @ SV45 @ SY84 ) )
| ( distinct_points @ SY85 @ SV45 ) ) )
| ~ ! [SY86: $i] :
( ~ ( distinct_points @ SV45 @ SY86 )
| ! [SY87: $i] :
( ~ ( apart_point_and_line @ SY87 @ ( line_connecting @ SV45 @ SY86 ) )
| ( distinct_points @ SY87 @ SY86 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV46: $i] :
( ( ~ ! [SY88: $i] :
( ~ ( convergent_lines @ SV46 @ SY88 )
| ! [SY89: $i] :
( ~ ( apart_point_and_line @ SY89 @ SV46 )
| ( distinct_points @ SY89 @ ( intersection_point @ SV46 @ SY88 ) ) ) )
| ~ ! [SY90: $i] :
( ~ ( convergent_lines @ SV46 @ SY90 )
| ! [SY91: $i] :
( ~ ( apart_point_and_line @ SY91 @ SY90 )
| ( distinct_points @ SY91 @ ( intersection_point @ SV46 @ SY90 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ( distinct_points @ SV38 @ SV47 ) )
= $true )
| ( ( ! [SY92: $i] :
( ( distinct_points @ SV38 @ SY92 )
| ( distinct_points @ SV47 @ SY92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(196,plain,
! [SV48: $i,SV39: $i] :
( ( ( ~ ( distinct_lines @ SV39 @ SV48 ) )
= $true )
| ( ( ! [SY93: $i] :
( ( distinct_lines @ SV39 @ SY93 )
| ( distinct_lines @ SV48 @ SY93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(197,plain,
! [SV49: $i,SV40: $i] :
( ( ( ~ ( convergent_lines @ SV40 @ SV49 ) )
= $true )
| ( ( ! [SY94: $i] :
( ( convergent_lines @ SV40 @ SY94 )
| ( convergent_lines @ SV49 @ SY94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(198,plain,
! [SV50: $i,SV41: $i,SV54: $i] :
( ( ! [SY99: $i] :
( ~ ( distinct_lines @ SV54 @ SY99 )
| ~ ( distinct_points @ SV41 @ SV50 )
| ( apart_point_and_line @ SV50 @ SY99 )
| ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(199,plain,
! [SV51: $i,SV42: $i] :
( ( ( ~ ( apart_point_and_line @ SV42 @ SV51 ) )
= $true )
| ( ( ! [SY97: $i] :
( ( apart_point_and_line @ SY97 @ SV51 )
| ( distinct_points @ SV42 @ SY97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(200,plain,
! [SV52: $i,SV43: $i] :
( ( ( ~ ( apart_point_and_line @ SV43 @ SV52 ) )
= $true )
| ( ( ! [SY98: $i] :
( ( apart_point_and_line @ SV43 @ SY98 )
| ( distinct_lines @ SV52 @ SY98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(201,plain,
! [SV53: $i,SV44: $i] :
( ( ( ~ ( convergent_lines @ SV44 @ SV53 ) )
= $true )
| ( ( distinct_lines @ SV44 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV45: $i] :
( ( ~ ! [SY84: $i] :
( ~ ( distinct_points @ SV45 @ SY84 )
| ! [SY85: $i] :
( ~ ( apart_point_and_line @ SY85 @ ( line_connecting @ SV45 @ SY84 ) )
| ( distinct_points @ SY85 @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(203,plain,
! [SV45: $i] :
( ( ~ ! [SY86: $i] :
( ~ ( distinct_points @ SV45 @ SY86 )
| ! [SY87: $i] :
( ~ ( apart_point_and_line @ SY87 @ ( line_connecting @ SV45 @ SY86 ) )
| ( distinct_points @ SY87 @ SY86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(204,plain,
! [SV46: $i] :
( ( ~ ! [SY88: $i] :
( ~ ( convergent_lines @ SV46 @ SY88 )
| ! [SY89: $i] :
( ~ ( apart_point_and_line @ SY89 @ SV46 )
| ( distinct_points @ SY89 @ ( intersection_point @ SV46 @ SY88 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(205,plain,
! [SV46: $i] :
( ( ~ ! [SY90: $i] :
( ~ ( convergent_lines @ SV46 @ SY90 )
| ! [SY91: $i] :
( ~ ( apart_point_and_line @ SY91 @ SY90 )
| ( distinct_points @ SY91 @ ( intersection_point @ SV46 @ SY90 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(206,plain,
! [SV47: $i,SV38: $i] :
( ( ( distinct_points @ SV38 @ SV47 )
= $false )
| ( ( ! [SY92: $i] :
( ( distinct_points @ SV38 @ SY92 )
| ( distinct_points @ SV47 @ SY92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(207,plain,
! [SV48: $i,SV39: $i] :
( ( ( distinct_lines @ SV39 @ SV48 )
= $false )
| ( ( ! [SY93: $i] :
( ( distinct_lines @ SV39 @ SY93 )
| ( distinct_lines @ SV48 @ SY93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(208,plain,
! [SV49: $i,SV40: $i] :
( ( ( convergent_lines @ SV40 @ SV49 )
= $false )
| ( ( ! [SY94: $i] :
( ( convergent_lines @ SV40 @ SY94 )
| ( convergent_lines @ SV49 @ SY94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV50: $i,SV41: $i,SV55: $i,SV54: $i] :
( ( ~ ( distinct_lines @ SV54 @ SV55 )
| ~ ( distinct_points @ SV41 @ SV50 )
| ( apart_point_and_line @ SV50 @ SV55 )
| ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV51: $i,SV42: $i] :
( ( ( apart_point_and_line @ SV42 @ SV51 )
= $false )
| ( ( ! [SY97: $i] :
( ( apart_point_and_line @ SY97 @ SV51 )
| ( distinct_points @ SV42 @ SY97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV52: $i,SV43: $i] :
( ( ( apart_point_and_line @ SV43 @ SV52 )
= $false )
| ( ( ! [SY98: $i] :
( ( apart_point_and_line @ SV43 @ SY98 )
| ( distinct_lines @ SV52 @ SY98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV53: $i,SV44: $i] :
( ( ( convergent_lines @ SV44 @ SV53 )
= $false )
| ( ( distinct_lines @ SV44 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV45: $i] :
( ( ! [SY84: $i] :
( ~ ( distinct_points @ SV45 @ SY84 )
| ! [SY85: $i] :
( ~ ( apart_point_and_line @ SY85 @ ( line_connecting @ SV45 @ SY84 ) )
| ( distinct_points @ SY85 @ SV45 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(214,plain,
! [SV45: $i] :
( ( ! [SY86: $i] :
( ~ ( distinct_points @ SV45 @ SY86 )
| ! [SY87: $i] :
( ~ ( apart_point_and_line @ SY87 @ ( line_connecting @ SV45 @ SY86 ) )
| ( distinct_points @ SY87 @ SY86 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(215,plain,
! [SV46: $i] :
( ( ! [SY88: $i] :
( ~ ( convergent_lines @ SV46 @ SY88 )
| ! [SY89: $i] :
( ~ ( apart_point_and_line @ SY89 @ SV46 )
| ( distinct_points @ SY89 @ ( intersection_point @ SV46 @ SY88 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(216,plain,
! [SV46: $i] :
( ( ! [SY90: $i] :
( ~ ( convergent_lines @ SV46 @ SY90 )
| ! [SY91: $i] :
( ~ ( apart_point_and_line @ SY91 @ SY90 )
| ( distinct_points @ SY91 @ ( intersection_point @ SV46 @ SY90 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(217,plain,
! [SV47: $i,SV56: $i,SV38: $i] :
( ( ( ( distinct_points @ SV38 @ SV56 )
| ( distinct_points @ SV47 @ SV56 ) )
= $true )
| ( ( distinct_points @ SV38 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(218,plain,
! [SV48: $i,SV57: $i,SV39: $i] :
( ( ( ( distinct_lines @ SV39 @ SV57 )
| ( distinct_lines @ SV48 @ SV57 ) )
= $true )
| ( ( distinct_lines @ SV39 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(219,plain,
! [SV49: $i,SV58: $i,SV40: $i] :
( ( ( ( convergent_lines @ SV40 @ SV58 )
| ( convergent_lines @ SV49 @ SV58 ) )
= $true )
| ( ( convergent_lines @ SV40 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(220,plain,
! [SV50: $i,SV41: $i,SV55: $i,SV54: $i] :
( ( ( ~ ( distinct_lines @ SV54 @ SV55 )
| ~ ( distinct_points @ SV41 @ SV50 ) )
= $true )
| ( ( ( apart_point_and_line @ SV50 @ SV55 )
| ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(221,plain,
! [SV42: $i,SV51: $i,SV59: $i] :
( ( ( ( apart_point_and_line @ SV59 @ SV51 )
| ( distinct_points @ SV42 @ SV59 ) )
= $true )
| ( ( apart_point_and_line @ SV42 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV52: $i,SV60: $i,SV43: $i] :
( ( ( ( apart_point_and_line @ SV43 @ SV60 )
| ( distinct_lines @ SV52 @ SV60 ) )
= $true )
| ( ( apart_point_and_line @ SV43 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(223,plain,
! [SV61: $i,SV45: $i] :
( ( ~ ( distinct_points @ SV45 @ SV61 )
| ! [SY100: $i] :
( ~ ( apart_point_and_line @ SY100 @ ( line_connecting @ SV45 @ SV61 ) )
| ( distinct_points @ SY100 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV62: $i,SV45: $i] :
( ( ~ ( distinct_points @ SV45 @ SV62 )
| ! [SY101: $i] :
( ~ ( apart_point_and_line @ SY101 @ ( line_connecting @ SV45 @ SV62 ) )
| ( distinct_points @ SY101 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(225,plain,
! [SV63: $i,SV46: $i] :
( ( ~ ( convergent_lines @ SV46 @ SV63 )
| ! [SY102: $i] :
( ~ ( apart_point_and_line @ SY102 @ SV46 )
| ( distinct_points @ SY102 @ ( intersection_point @ SV46 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(226,plain,
! [SV64: $i,SV46: $i] :
( ( ~ ( convergent_lines @ SV46 @ SV64 )
| ! [SY103: $i] :
( ~ ( apart_point_and_line @ SY103 @ SV64 )
| ( distinct_points @ SY103 @ ( intersection_point @ SV46 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(227,plain,
! [SV47: $i,SV56: $i,SV38: $i] :
( ( ( distinct_points @ SV38 @ SV56 )
= $true )
| ( ( distinct_points @ SV47 @ SV56 )
= $true )
| ( ( distinct_points @ SV38 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(228,plain,
! [SV48: $i,SV57: $i,SV39: $i] :
( ( ( distinct_lines @ SV39 @ SV57 )
= $true )
| ( ( distinct_lines @ SV48 @ SV57 )
= $true )
| ( ( distinct_lines @ SV39 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(229,plain,
! [SV49: $i,SV58: $i,SV40: $i] :
( ( ( convergent_lines @ SV40 @ SV58 )
= $true )
| ( ( convergent_lines @ SV49 @ SV58 )
= $true )
| ( ( convergent_lines @ SV40 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(230,plain,
! [SV50: $i,SV41: $i,SV55: $i,SV54: $i] :
( ( ( ~ ( distinct_lines @ SV54 @ SV55 ) )
= $true )
| ( ( ~ ( distinct_points @ SV41 @ SV50 ) )
= $true )
| ( ( ( apart_point_and_line @ SV50 @ SV55 )
| ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(231,plain,
! [SV42: $i,SV51: $i,SV59: $i] :
( ( ( apart_point_and_line @ SV59 @ SV51 )
= $true )
| ( ( distinct_points @ SV42 @ SV59 )
= $true )
| ( ( apart_point_and_line @ SV42 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(232,plain,
! [SV52: $i,SV60: $i,SV43: $i] :
( ( ( apart_point_and_line @ SV43 @ SV60 )
= $true )
| ( ( distinct_lines @ SV52 @ SV60 )
= $true )
| ( ( apart_point_and_line @ SV43 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(233,plain,
! [SV61: $i,SV45: $i] :
( ( ( ~ ( distinct_points @ SV45 @ SV61 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( apart_point_and_line @ SY100 @ ( line_connecting @ SV45 @ SV61 ) )
| ( distinct_points @ SY100 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(234,plain,
! [SV62: $i,SV45: $i] :
( ( ( ~ ( distinct_points @ SV45 @ SV62 ) )
= $true )
| ( ( ! [SY101: $i] :
( ~ ( apart_point_and_line @ SY101 @ ( line_connecting @ SV45 @ SV62 ) )
| ( distinct_points @ SY101 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(235,plain,
! [SV63: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV63 ) )
= $true )
| ( ( ! [SY102: $i] :
( ~ ( apart_point_and_line @ SY102 @ SV46 )
| ( distinct_points @ SY102 @ ( intersection_point @ SV46 @ SV63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(236,plain,
! [SV64: $i,SV46: $i] :
( ( ( ~ ( convergent_lines @ SV46 @ SV64 ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( apart_point_and_line @ SY103 @ SV64 )
| ( distinct_points @ SY103 @ ( intersection_point @ SV46 @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(237,plain,
! [SV50: $i,SV41: $i,SV55: $i,SV54: $i] :
( ( ( distinct_lines @ SV54 @ SV55 )
= $false )
| ( ( ~ ( distinct_points @ SV41 @ SV50 ) )
= $true )
| ( ( ( apart_point_and_line @ SV50 @ SV55 )
| ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(238,plain,
! [SV61: $i,SV45: $i] :
( ( ( distinct_points @ SV45 @ SV61 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( apart_point_and_line @ SY100 @ ( line_connecting @ SV45 @ SV61 ) )
| ( distinct_points @ SY100 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(239,plain,
! [SV62: $i,SV45: $i] :
( ( ( distinct_points @ SV45 @ SV62 )
= $false )
| ( ( ! [SY101: $i] :
( ~ ( apart_point_and_line @ SY101 @ ( line_connecting @ SV45 @ SV62 ) )
| ( distinct_points @ SY101 @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(240,plain,
! [SV63: $i,SV46: $i] :
( ( ( convergent_lines @ SV46 @ SV63 )
= $false )
| ( ( ! [SY102: $i] :
( ~ ( apart_point_and_line @ SY102 @ SV46 )
| ( distinct_points @ SY102 @ ( intersection_point @ SV46 @ SV63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(241,plain,
! [SV64: $i,SV46: $i] :
( ( ( convergent_lines @ SV46 @ SV64 )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( apart_point_and_line @ SY103 @ SV64 )
| ( distinct_points @ SY103 @ ( intersection_point @ SV46 @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(242,plain,
! [SV55: $i,SV54: $i,SV50: $i,SV41: $i] :
( ( ( distinct_points @ SV41 @ SV50 )
= $false )
| ( ( distinct_lines @ SV54 @ SV55 )
= $false )
| ( ( ( apart_point_and_line @ SV50 @ SV55 )
| ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(243,plain,
! [SV61: $i,SV45: $i,SV65: $i] :
( ( ( ~ ( apart_point_and_line @ SV65 @ ( line_connecting @ SV45 @ SV61 ) )
| ( distinct_points @ SV65 @ SV45 ) )
= $true )
| ( ( distinct_points @ SV45 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(244,plain,
! [SV62: $i,SV45: $i,SV66: $i] :
( ( ( ~ ( apart_point_and_line @ SV66 @ ( line_connecting @ SV45 @ SV62 ) )
| ( distinct_points @ SV66 @ SV62 ) )
= $true )
| ( ( distinct_points @ SV45 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV63: $i,SV46: $i,SV67: $i] :
( ( ( ~ ( apart_point_and_line @ SV67 @ SV46 )
| ( distinct_points @ SV67 @ ( intersection_point @ SV46 @ SV63 ) ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV46: $i,SV64: $i,SV68: $i] :
( ( ( ~ ( apart_point_and_line @ SV68 @ SV64 )
| ( distinct_points @ SV68 @ ( intersection_point @ SV46 @ SV64 ) ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(247,plain,
! [SV41: $i,SV54: $i,SV55: $i,SV50: $i] :
( ( ( apart_point_and_line @ SV50 @ SV55 )
= $true )
| ( ( ( apart_point_and_line @ SV50 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true )
| ( ( distinct_lines @ SV54 @ SV55 )
= $false )
| ( ( distinct_points @ SV41 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(248,plain,
! [SV61: $i,SV45: $i,SV65: $i] :
( ( ( ~ ( apart_point_and_line @ SV65 @ ( line_connecting @ SV45 @ SV61 ) ) )
= $true )
| ( ( distinct_points @ SV65 @ SV45 )
= $true )
| ( ( distinct_points @ SV45 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(249,plain,
! [SV62: $i,SV45: $i,SV66: $i] :
( ( ( ~ ( apart_point_and_line @ SV66 @ ( line_connecting @ SV45 @ SV62 ) ) )
= $true )
| ( ( distinct_points @ SV66 @ SV62 )
= $true )
| ( ( distinct_points @ SV45 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(250,plain,
! [SV63: $i,SV46: $i,SV67: $i] :
( ( ( ~ ( apart_point_and_line @ SV67 @ SV46 ) )
= $true )
| ( ( distinct_points @ SV67 @ ( intersection_point @ SV46 @ SV63 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(251,plain,
! [SV46: $i,SV64: $i,SV68: $i] :
( ( ( ~ ( apart_point_and_line @ SV68 @ SV64 ) )
= $true )
| ( ( distinct_points @ SV68 @ ( intersection_point @ SV46 @ SV64 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(252,plain,
! [SV55: $i,SV41: $i,SV54: $i,SV50: $i] :
( ( ( apart_point_and_line @ SV50 @ SV54 )
= $true )
| ( ( ( apart_point_and_line @ SV41 @ SV54 )
| ( apart_point_and_line @ SV41 @ SV55 ) )
= $true )
| ( ( apart_point_and_line @ SV50 @ SV55 )
= $true )
| ( ( distinct_lines @ SV54 @ SV55 )
= $false )
| ( ( distinct_points @ SV41 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(253,plain,
! [SV61: $i,SV45: $i,SV65: $i] :
( ( ( apart_point_and_line @ SV65 @ ( line_connecting @ SV45 @ SV61 ) )
= $false )
| ( ( distinct_points @ SV65 @ SV45 )
= $true )
| ( ( distinct_points @ SV45 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(254,plain,
! [SV62: $i,SV45: $i,SV66: $i] :
( ( ( apart_point_and_line @ SV66 @ ( line_connecting @ SV45 @ SV62 ) )
= $false )
| ( ( distinct_points @ SV66 @ SV62 )
= $true )
| ( ( distinct_points @ SV45 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(255,plain,
! [SV63: $i,SV46: $i,SV67: $i] :
( ( ( apart_point_and_line @ SV67 @ SV46 )
= $false )
| ( ( distinct_points @ SV67 @ ( intersection_point @ SV46 @ SV63 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(256,plain,
! [SV46: $i,SV64: $i,SV68: $i] :
( ( ( apart_point_and_line @ SV68 @ SV64 )
= $false )
| ( ( distinct_points @ SV68 @ ( intersection_point @ SV46 @ SV64 ) )
= $true )
| ( ( convergent_lines @ SV46 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(257,plain,
! [SV50: $i,SV55: $i,SV54: $i,SV41: $i] :
( ( ( apart_point_and_line @ SV41 @ SV54 )
= $true )
| ( ( apart_point_and_line @ SV41 @ SV55 )
= $true )
| ( ( apart_point_and_line @ SV50 @ SV54 )
= $true )
| ( ( apart_point_and_line @ SV50 @ SV55 )
= $true )
| ( ( distinct_lines @ SV54 @ SV55 )
= $false )
| ( ( distinct_points @ SV41 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(258,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[165,257,256,255,254,253,232,231,229,228,227,212,185,184,183,180,166]) ).
thf(259,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[258,152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.37 % Computer : n017.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Fri Jun 17 15:23:11 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.39
% 0.16/0.39 No.of.Axioms: 12
% 0.16/0.39
% 0.16/0.39 Length.of.Defs: 0
% 0.16/0.39
% 0.16/0.39 Contains.Choice.Funs: false
% 0.16/0.40 (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:14,loop_count:0,foatp_calls:0,translation:fof_full)...............
% 0.40/0.56
% 0.40/0.56 ********************************
% 0.40/0.56 * All subproblems solved! *
% 0.40/0.56 ********************************
% 0.40/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:258,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.41/0.58
% 0.41/0.58 %**** Beginning of derivation protocol ****
% 0.41/0.58 % SZS output start CNFRefutation
% See solution above
% 0.41/0.58
% 0.41/0.58 %**** End of derivation protocol ****
% 0.41/0.58 %**** no. of clauses in derivation: 259 ****
% 0.41/0.58 %**** clause counter: 258 ****
% 0.41/0.58
% 0.41/0.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:258,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------