TSTP Solution File: GEO076-4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO076-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n016.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 05:06:49 EDT 2022
% Result : Unsatisfiable 0.49s 1.00s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 50
% Syntax : Number of formulae : 455 ( 137 unt; 16 typ; 0 def)
% Number of atoms : 6178 (2307 equ; 0 cnn)
% Maximal formula atoms : 16 ( 14 avg)
% Number of connectives : 8479 (1305 ~;2781 |; 0 &;4393 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 1238 ( 0 ^1238 !; 0 ?;1238 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_point,type,
a_point: $i ).
thf(tp_at_least_one_line,type,
at_least_one_line: $i ).
thf(tp_collinear,type,
collinear: $i > $i > $i > $o ).
thf(tp_common_point_on_planes,type,
common_point_on_planes: $i > $i > $i > $i ).
thf(tp_line,type,
line: $i > $o ).
thf(tp_line_from_to,type,
line_from_to: $i > $i > $i ).
thf(tp_line_through_3_points,type,
line_through_3_points: $i > $i > $i > $i ).
thf(tp_on,type,
on: $i > $i > $o ).
thf(tp_plane,type,
plane: $i > $o ).
thf(tp_plane_for_points,type,
plane_for_points: $i > $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_point_1_on_line,type,
point_1_on_line: $i > $i ).
thf(tp_point_2_on_line,type,
point_2_on_line: $i > $i ).
thf(tp_point_not_on_line,type,
point_not_on_line: $i > $i ).
thf(tp_point_not_on_plane,type,
point_not_on_plane: $i > $i ).
thf(tp_point_on_plane,type,
point_on_plane: $i > $i ).
thf(1,axiom,
! [X1: $i,X2: $i,X3: $i,Y: $i] :
( ( collinear @ X1 @ X2 @ X3 )
| ~ ( on @ X1 @ Y )
| ~ ( on @ X2 @ Y )
| ~ ( on @ X3 @ Y )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ~ ( line @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10E) ).
thf(2,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( line @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10D) ).
thf(3,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X3 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10C) ).
thf(4,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X2 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10B) ).
thf(5,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X1 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10A) ).
thf(6,axiom,
! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( X1
!= ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9D) ).
thf(7,axiom,
! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( point @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9C) ).
thf(8,axiom,
! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9B) ).
thf(9,axiom,
! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9A) ).
thf(10,axiom,
! [X1: $i,Y1: $i,X2: $i,Z1: $i] :
( ~ ( on @ X1 @ Y1 )
| ~ ( on @ X2 @ Y1 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( plane @ Z1 )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( line @ Y1 )
| ( X1 = X2 )
| ( on @ Y1 @ Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G8A) ).
thf(11,axiom,
! [X1: $i,X2: $i,X3: $i,Z1: $i,Z2: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( on @ X3 @ Z1 )
| ~ ( plane @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( on @ X2 @ Z2 )
| ~ ( on @ X3 @ Z2 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7E) ).
thf(12,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( plane @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7D) ).
thf(13,axiom,
! [X3: $i,X1: $i,X2: $i] :
( ( on @ X3 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7C) ).
thf(14,axiom,
! [X2: $i,X1: $i,X3: $i] :
( ( on @ X2 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7B) ).
thf(15,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( on @ X1 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7A) ).
thf(16,axiom,
! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( point @ ( point_not_on_plane @ Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G6B) ).
thf(17,axiom,
! [Z1: $i] :
( ~ ( plane @ Z1 )
| ~ ( on @ ( point_not_on_plane @ Z1 ) @ Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G6A) ).
thf(18,axiom,
! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( point @ ( point_on_plane @ Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G5B) ).
thf(19,axiom,
! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( on @ ( point_on_plane @ Z1 ) @ Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G5A) ).
thf(20,axiom,
line @ at_least_one_line,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G4A) ).
thf(21,axiom,
! [Y1: $i] :
( ( point @ ( point_not_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G3B) ).
thf(22,axiom,
! [Y1: $i] :
( ~ ( on @ ( point_not_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G3A) ).
thf(23,axiom,
! [Y1: $i] :
( ( ( point_1_on_line @ Y1 )
!= ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2E) ).
thf(24,axiom,
! [Y1: $i] :
( ( point @ ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2D) ).
thf(25,axiom,
! [Y1: $i] :
( ( point @ ( point_1_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2C) ).
thf(26,axiom,
! [Y1: $i] :
( ( on @ ( point_2_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2B) ).
thf(27,axiom,
! [Y1: $i] :
( ( on @ ( point_1_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2A) ).
thf(28,axiom,
! [Z1: $i,Y3: $i,Z2: $i,Y4: $i] :
( ~ ( on @ Z1 @ Y3 )
| ( Z1 = Z2 )
| ~ ( on @ Z2 @ Y3 )
| ( Y3 = Y4 )
| ~ ( on @ Z1 @ Y4 )
| ~ ( on @ Z2 @ Y4 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 )
| ~ ( line @ Y3 )
| ~ ( line @ Y4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1D) ).
thf(29,axiom,
! [Z1: $i,Z2: $i] :
( ( line @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1C) ).
thf(30,axiom,
! [Z2: $i,Z1: $i] :
( ( on @ Z2 @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1B) ).
thf(31,axiom,
! [Z1: $i,Z2: $i] :
( ( on @ Z1 @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1A) ).
thf(32,axiom,
point @ a_point,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',there_is_a_point) ).
thf(33,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(34,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,negated_conjecture,
! [Line: $i] :
( ~ ( line @ Line )
| ( on @ a_point @ Line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_point_is_not_on_every_line) ).
thf(36,plain,
$false = $false,
inference(unfold_def,[status(thm)],[34]) ).
thf(37,plain,
( ( ! [X1: $i,X2: $i,X3: $i,Y: $i] :
( ( collinear @ X1 @ X2 @ X3 )
| ~ ( on @ X1 @ Y )
| ~ ( on @ X2 @ Y )
| ~ ( on @ X3 @ Y )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ~ ( line @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(38,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( line @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(39,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X3 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X2 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(41,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X1 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(42,plain,
( ( ! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( X1
!= ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(43,plain,
( ( ! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( point @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(44,plain,
( ( ! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(45,plain,
( ( ! [Z1: $i,Z2: $i,X1: $i] :
( ~ ( plane @ Z1 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(46,plain,
( ( ! [X1: $i,Y1: $i,X2: $i,Z1: $i] :
( ~ ( on @ X1 @ Y1 )
| ~ ( on @ X2 @ Y1 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( plane @ Z1 )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( line @ Y1 )
| ( X1 = X2 )
| ( on @ Y1 @ Z1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(47,plain,
( ( ! [X1: $i,X2: $i,X3: $i,Z1: $i,Z2: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( on @ X3 @ Z1 )
| ~ ( plane @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( on @ X2 @ Z2 )
| ~ ( on @ X3 @ Z2 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(48,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plane @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(49,plain,
( ( ! [X3: $i,X1: $i,X2: $i] :
( ( on @ X3 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(50,plain,
( ( ! [X2: $i,X1: $i,X3: $i] :
( ( on @ X2 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( on @ X1 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( point @ ( point_not_on_plane @ Z1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(53,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ~ ( on @ ( point_not_on_plane @ Z1 ) @ Z1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(54,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( point @ ( point_on_plane @ Z1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( on @ ( point_on_plane @ Z1 ) @ Z1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(56,plain,
( ( line @ at_least_one_line )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(57,plain,
( ( ! [Y1: $i] :
( ( point @ ( point_not_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(58,plain,
( ( ! [Y1: $i] :
( ~ ( on @ ( point_not_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(59,plain,
( ( ! [Y1: $i] :
( ( ( point_1_on_line @ Y1 )
!= ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(60,plain,
( ( ! [Y1: $i] :
( ( point @ ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(61,plain,
( ( ! [Y1: $i] :
( ( point @ ( point_1_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(62,plain,
( ( ! [Y1: $i] :
( ( on @ ( point_2_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(63,plain,
( ( ! [Y1: $i] :
( ( on @ ( point_1_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(64,plain,
( ( ! [Z1: $i,Y3: $i,Z2: $i,Y4: $i] :
( ~ ( on @ Z1 @ Y3 )
| ( Z1 = Z2 )
| ~ ( on @ Z2 @ Y3 )
| ( Y3 = Y4 )
| ~ ( on @ Z1 @ Y4 )
| ~ ( on @ Z2 @ Y4 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 )
| ~ ( line @ Y3 )
| ~ ( line @ Y4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(65,plain,
( ( ! [Z1: $i,Z2: $i] :
( ( line @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(66,plain,
( ( ! [Z2: $i,Z1: $i] :
( ( on @ Z2 @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(67,plain,
( ( ! [Z1: $i,Z2: $i] :
( ( on @ Z1 @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(68,plain,
( ( point @ a_point )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(69,plain,
( ( ! [Line: $i] :
( ~ ( line @ Line )
| ( on @ a_point @ Line ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(70,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(71,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( collinear @ X1 @ X2 @ X3 )
| ! [Y: $i] :
( ~ ( on @ X1 @ Y )
| ~ ( on @ X2 @ Y )
| ~ ( on @ X3 @ Y )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ~ ( line @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(72,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( line @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(73,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X3 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(74,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X2 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(75,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X1 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(76,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( X1
!= ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(77,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( point @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(78,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(79,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(80,plain,
( ( ! [X1: $i,Y1: $i] :
( ~ ( on @ X1 @ Y1 )
| ! [X2: $i] :
( ~ ( on @ X2 @ Y1 )
| ! [Z1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( plane @ Z1 )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( line @ Y1 )
| ( X1 = X2 )
| ( on @ Y1 @ Z1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(81,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ! [Z1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( on @ X3 @ Z1 )
| ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( on @ X1 @ Z2 )
| ~ ( on @ X2 @ Z2 )
| ~ ( on @ X3 @ Z2 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(82,plain,
( ( ! [Y1: $i] :
( ( ( point_1_on_line @ Y1 )
!= ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(83,plain,
( ( ! [Z1: $i,Y3: $i] :
( ~ ( on @ Z1 @ Y3 )
| ! [Z2: $i] :
( ( Z1 = Z2 )
| ~ ( on @ Z2 @ Y3 )
| ! [Y4: $i] :
( ( Y3 = Y4 )
| ~ ( on @ Z1 @ Y4 )
| ~ ( on @ Z2 @ Y4 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 )
| ~ ( line @ Y3 )
| ~ ( line @ Y4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(84,plain,
( ( ! [Line: $i] :
( ~ ( line @ Line )
| ( on @ a_point @ Line ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(85,plain,
( ( point @ a_point )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(86,plain,
( ( ! [Z1: $i,Z2: $i] :
( ( on @ Z1 @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(87,plain,
( ( ! [Z2: $i,Z1: $i] :
( ( on @ Z2 @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(88,plain,
( ( ! [Z1: $i,Z2: $i] :
( ( line @ ( line_from_to @ Z1 @ Z2 ) )
| ( Z1 = Z2 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(89,plain,
( ( ! [Z1: $i,Y3: $i] :
( ~ ( on @ Z1 @ Y3 )
| ! [Z2: $i] :
( ( Z1 = Z2 )
| ~ ( on @ Z2 @ Y3 )
| ! [Y4: $i] :
( ( Y3 = Y4 )
| ~ ( on @ Z1 @ Y4 )
| ~ ( on @ Z2 @ Y4 )
| ~ ( point @ Z1 )
| ~ ( point @ Z2 )
| ~ ( line @ Y3 )
| ~ ( line @ Y4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(90,plain,
( ( ! [Y1: $i] :
( ( on @ ( point_1_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(91,plain,
( ( ! [Y1: $i] :
( ( on @ ( point_2_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(92,plain,
( ( ! [Y1: $i] :
( ( point @ ( point_1_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(93,plain,
( ( ! [Y1: $i] :
( ( point @ ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(94,plain,
( ( ! [Y1: $i] :
( ( ( point_1_on_line @ Y1 )
!= ( point_2_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(95,plain,
( ( ! [Y1: $i] :
( ~ ( on @ ( point_not_on_line @ Y1 ) @ Y1 )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(96,plain,
( ( ! [Y1: $i] :
( ( point @ ( point_not_on_line @ Y1 ) )
| ~ ( line @ Y1 ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(97,plain,
( ( line @ at_least_one_line )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(98,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( on @ ( point_on_plane @ Z1 ) @ Z1 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(99,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( point @ ( point_on_plane @ Z1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(100,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ~ ( on @ ( point_not_on_plane @ Z1 ) @ Z1 ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(101,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ( point @ ( point_not_on_plane @ Z1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(102,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( on @ X1 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(103,plain,
( ( ! [X2: $i,X1: $i,X3: $i] :
( ( on @ X2 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(104,plain,
( ( ! [X3: $i,X1: $i,X2: $i] :
( ( on @ X3 @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(105,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plane @ ( plane_for_points @ X1 @ X2 @ X3 ) )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(106,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( collinear @ X1 @ X2 @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ! [Z1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( on @ X3 @ Z1 )
| ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( on @ X1 @ Z2 )
| ~ ( on @ X2 @ Z2 )
| ~ ( on @ X3 @ Z2 )
| ~ ( plane @ Z2 )
| ( Z1 = Z2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(107,plain,
( ( ! [X1: $i,Y1: $i] :
( ~ ( on @ X1 @ Y1 )
| ! [X2: $i] :
( ~ ( on @ X2 @ Y1 )
| ! [Z1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X2 @ Z1 )
| ~ ( plane @ Z1 )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( line @ Y1 )
| ( X1 = X2 )
| ( on @ Y1 @ Z1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(108,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(109,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( on @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) @ Z2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(110,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( point @ ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(111,plain,
( ( ! [Z1: $i] :
( ~ ( plane @ Z1 )
| ! [Z2: $i] :
( ~ ( plane @ Z2 )
| ( Z1 = Z2 )
| ! [X1: $i] :
( ~ ( on @ X1 @ Z1 )
| ~ ( on @ X1 @ Z2 )
| ~ ( point @ X1 )
| ( X1
!= ( common_point_on_planes @ Z1 @ Z2 @ X1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(112,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X1 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(113,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X2 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(114,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( on @ X3 @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(115,plain,
( ( ! [X1: $i] :
( ~ ( point @ X1 )
| ! [X2: $i] :
( ~ ( point @ X2 )
| ! [X3: $i] :
( ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ( line @ ( line_through_3_points @ X1 @ X2 @ X3 ) )
| ~ ( collinear @ X1 @ X2 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(116,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( collinear @ X1 @ X2 @ X3 )
| ! [Y: $i] :
( ~ ( on @ X1 @ Y )
| ~ ( on @ X2 @ Y )
| ~ ( on @ X3 @ Y )
| ~ ( point @ X1 )
| ~ ( point @ X2 )
| ~ ( point @ X3 )
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| ~ ( line @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(117,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(118,plain,
! [SV1: $i] :
( ( ~ ( line @ SV1 )
| ( on @ a_point @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(119,plain,
! [SV2: $i] :
( ( ! [SY71: $i] :
( ( on @ SV2 @ ( line_from_to @ SV2 @ SY71 ) )
| ( SV2 = SY71 )
| ~ ( point @ SV2 )
| ~ ( point @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(120,plain,
! [SV3: $i] :
( ( ! [SY72: $i] :
( ( on @ SV3 @ ( line_from_to @ SY72 @ SV3 ) )
| ( SY72 = SV3 )
| ~ ( point @ SY72 )
| ~ ( point @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(121,plain,
! [SV4: $i] :
( ( ! [SY73: $i] :
( ( line @ ( line_from_to @ SV4 @ SY73 ) )
| ( SV4 = SY73 )
| ~ ( point @ SV4 )
| ~ ( point @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(122,plain,
! [SV5: $i] :
( ( ! [SY74: $i] :
( ~ ( on @ SV5 @ SY74 )
| ! [SY75: $i] :
( ( SV5 = SY75 )
| ~ ( on @ SY75 @ SY74 )
| ! [SY76: $i] :
( ( SY74 = SY76 )
| ~ ( on @ SV5 @ SY76 )
| ~ ( on @ SY75 @ SY76 )
| ~ ( point @ SV5 )
| ~ ( point @ SY75 )
| ~ ( line @ SY74 )
| ~ ( line @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(123,plain,
! [SV6: $i] :
( ( ( on @ ( point_1_on_line @ SV6 ) @ SV6 )
| ~ ( line @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(124,plain,
! [SV7: $i] :
( ( ( on @ ( point_2_on_line @ SV7 ) @ SV7 )
| ~ ( line @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(125,plain,
! [SV8: $i] :
( ( ( point @ ( point_1_on_line @ SV8 ) )
| ~ ( line @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(126,plain,
! [SV9: $i] :
( ( ( point @ ( point_2_on_line @ SV9 ) )
| ~ ( line @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(127,plain,
! [SV10: $i] :
( ( ( ( point_1_on_line @ SV10 )
!= ( point_2_on_line @ SV10 ) )
| ~ ( line @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(128,plain,
! [SV11: $i] :
( ( ~ ( on @ ( point_not_on_line @ SV11 ) @ SV11 )
| ~ ( line @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(129,plain,
! [SV12: $i] :
( ( ( point @ ( point_not_on_line @ SV12 ) )
| ~ ( line @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(130,plain,
! [SV13: $i] :
( ( ~ ( plane @ SV13 )
| ( on @ ( point_on_plane @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(131,plain,
! [SV14: $i] :
( ( ~ ( plane @ SV14 )
| ( point @ ( point_on_plane @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(132,plain,
! [SV15: $i] :
( ( ~ ( plane @ SV15 )
| ~ ( on @ ( point_not_on_plane @ SV15 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(133,plain,
! [SV16: $i] :
( ( ~ ( plane @ SV16 )
| ( point @ ( point_not_on_plane @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(134,plain,
! [SV17: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ( on @ SV17 @ ( plane_for_points @ SV17 @ SY77 @ SY78 ) )
| ~ ( point @ SV17 )
| ~ ( point @ SY77 )
| ~ ( point @ SY78 )
| ( collinear @ SV17 @ SY77 @ SY78 )
| ( SV17 = SY77 )
| ( SV17 = SY78 )
| ( SY77 = SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(135,plain,
! [SV18: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ( on @ SV18 @ ( plane_for_points @ SY79 @ SV18 @ SY80 ) )
| ~ ( point @ SY79 )
| ~ ( point @ SV18 )
| ~ ( point @ SY80 )
| ( collinear @ SY79 @ SV18 @ SY80 )
| ( SY79 = SV18 )
| ( SY79 = SY80 )
| ( SV18 = SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(136,plain,
! [SV19: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ( on @ SV19 @ ( plane_for_points @ SY81 @ SY82 @ SV19 ) )
| ~ ( point @ SY81 )
| ~ ( point @ SY82 )
| ~ ( point @ SV19 )
| ( collinear @ SY81 @ SY82 @ SV19 )
| ( SY81 = SY82 )
| ( SY81 = SV19 )
| ( SY82 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(137,plain,
! [SV20: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ( plane @ ( plane_for_points @ SV20 @ SY83 @ SY84 ) )
| ~ ( point @ SV20 )
| ~ ( point @ SY83 )
| ~ ( point @ SY84 )
| ( collinear @ SV20 @ SY83 @ SY84 )
| ( SV20 = SY83 )
| ( SV20 = SY84 )
| ( SY83 = SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(138,plain,
! [SV21: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( point @ SV21 )
| ~ ( point @ SY85 )
| ~ ( point @ SY86 )
| ( collinear @ SV21 @ SY85 @ SY86 )
| ( SV21 = SY85 )
| ( SV21 = SY86 )
| ( SY85 = SY86 )
| ! [SY87: $i] :
( ~ ( on @ SV21 @ SY87 )
| ~ ( on @ SY85 @ SY87 )
| ~ ( on @ SY86 @ SY87 )
| ~ ( plane @ SY87 )
| ! [SY88: $i] :
( ~ ( on @ SV21 @ SY88 )
| ~ ( on @ SY85 @ SY88 )
| ~ ( on @ SY86 @ SY88 )
| ~ ( plane @ SY88 )
| ( SY87 = SY88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(139,plain,
! [SV22: $i] :
( ( ! [SY89: $i] :
( ~ ( on @ SV22 @ SY89 )
| ! [SY90: $i] :
( ~ ( on @ SY90 @ SY89 )
| ! [SY91: $i] :
( ~ ( on @ SV22 @ SY91 )
| ~ ( on @ SY90 @ SY91 )
| ~ ( plane @ SY91 )
| ~ ( point @ SV22 )
| ~ ( point @ SY90 )
| ~ ( line @ SY89 )
| ( SV22 = SY90 )
| ( on @ SY89 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(140,plain,
! [SV23: $i] :
( ( ~ ( plane @ SV23 )
| ! [SY92: $i] :
( ~ ( plane @ SY92 )
| ( SV23 = SY92 )
| ! [SY93: $i] :
( ~ ( on @ SY93 @ SV23 )
| ~ ( on @ SY93 @ SY92 )
| ~ ( point @ SY93 )
| ( on @ ( common_point_on_planes @ SV23 @ SY92 @ SY93 ) @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(141,plain,
! [SV24: $i] :
( ( ~ ( plane @ SV24 )
| ! [SY94: $i] :
( ~ ( plane @ SY94 )
| ( SV24 = SY94 )
| ! [SY95: $i] :
( ~ ( on @ SY95 @ SV24 )
| ~ ( on @ SY95 @ SY94 )
| ~ ( point @ SY95 )
| ( on @ ( common_point_on_planes @ SV24 @ SY94 @ SY95 ) @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(142,plain,
! [SV25: $i] :
( ( ~ ( plane @ SV25 )
| ! [SY96: $i] :
( ~ ( plane @ SY96 )
| ( SV25 = SY96 )
| ! [SY97: $i] :
( ~ ( on @ SY97 @ SV25 )
| ~ ( on @ SY97 @ SY96 )
| ~ ( point @ SY97 )
| ( point @ ( common_point_on_planes @ SV25 @ SY96 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(143,plain,
! [SV26: $i] :
( ( ~ ( plane @ SV26 )
| ! [SY98: $i] :
( ~ ( plane @ SY98 )
| ( SV26 = SY98 )
| ! [SY99: $i] :
( ~ ( on @ SY99 @ SV26 )
| ~ ( on @ SY99 @ SY98 )
| ~ ( point @ SY99 )
| ( SY99
!= ( common_point_on_planes @ SV26 @ SY98 @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(144,plain,
! [SV27: $i] :
( ( ~ ( point @ SV27 )
| ! [SY100: $i] :
( ~ ( point @ SY100 )
| ! [SY101: $i] :
( ~ ( point @ SY101 )
| ( SV27 = SY100 )
| ( SV27 = SY101 )
| ( SY100 = SY101 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SY100 @ SY101 ) )
| ~ ( collinear @ SV27 @ SY100 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(145,plain,
! [SV28: $i] :
( ( ~ ( point @ SV28 )
| ! [SY102: $i] :
( ~ ( point @ SY102 )
| ! [SY103: $i] :
( ~ ( point @ SY103 )
| ( SV28 = SY102 )
| ( SV28 = SY103 )
| ( SY102 = SY103 )
| ( on @ SY102 @ ( line_through_3_points @ SV28 @ SY102 @ SY103 ) )
| ~ ( collinear @ SV28 @ SY102 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(146,plain,
! [SV29: $i] :
( ( ~ ( point @ SV29 )
| ! [SY104: $i] :
( ~ ( point @ SY104 )
| ! [SY105: $i] :
( ~ ( point @ SY105 )
| ( SV29 = SY104 )
| ( SV29 = SY105 )
| ( SY104 = SY105 )
| ( on @ SY105 @ ( line_through_3_points @ SV29 @ SY104 @ SY105 ) )
| ~ ( collinear @ SV29 @ SY104 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(147,plain,
! [SV30: $i] :
( ( ~ ( point @ SV30 )
| ! [SY106: $i] :
( ~ ( point @ SY106 )
| ! [SY107: $i] :
( ~ ( point @ SY107 )
| ( SV30 = SY106 )
| ( SV30 = SY107 )
| ( SY106 = SY107 )
| ( line @ ( line_through_3_points @ SV30 @ SY106 @ SY107 ) )
| ~ ( collinear @ SV30 @ SY106 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(148,plain,
! [SV31: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ( collinear @ SV31 @ SY108 @ SY109 )
| ! [SY110: $i] :
( ~ ( on @ SV31 @ SY110 )
| ~ ( on @ SY108 @ SY110 )
| ~ ( on @ SY109 @ SY110 )
| ~ ( point @ SV31 )
| ~ ( point @ SY108 )
| ~ ( point @ SY109 )
| ( SV31 = SY108 )
| ( SV31 = SY109 )
| ( SY108 = SY109 )
| ~ ( line @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(149,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(150,plain,
! [SV1: $i] :
( ( ( ~ ( line @ SV1 ) )
= $true )
| ( ( on @ a_point @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(151,plain,
! [SV32: $i,SV2: $i] :
( ( ( on @ SV2 @ ( line_from_to @ SV2 @ SV32 ) )
| ( SV2 = SV32 )
| ~ ( point @ SV2 )
| ~ ( point @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(152,plain,
! [SV33: $i,SV3: $i] :
( ( ( on @ SV3 @ ( line_from_to @ SV33 @ SV3 ) )
| ( SV33 = SV3 )
| ~ ( point @ SV33 )
| ~ ( point @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(153,plain,
! [SV34: $i,SV4: $i] :
( ( ( line @ ( line_from_to @ SV4 @ SV34 ) )
| ( SV4 = SV34 )
| ~ ( point @ SV4 )
| ~ ( point @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(154,plain,
! [SV35: $i,SV5: $i] :
( ( ~ ( on @ SV5 @ SV35 )
| ! [SY111: $i] :
( ( SV5 = SY111 )
| ~ ( on @ SY111 @ SV35 )
| ! [SY112: $i] :
( ( SV35 = SY112 )
| ~ ( on @ SV5 @ SY112 )
| ~ ( on @ SY111 @ SY112 )
| ~ ( point @ SV5 )
| ~ ( point @ SY111 )
| ~ ( line @ SV35 )
| ~ ( line @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(155,plain,
! [SV6: $i] :
( ( ( on @ ( point_1_on_line @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( line @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(156,plain,
! [SV7: $i] :
( ( ( on @ ( point_2_on_line @ SV7 ) @ SV7 )
= $true )
| ( ( ~ ( line @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(157,plain,
! [SV8: $i] :
( ( ( point @ ( point_1_on_line @ SV8 ) )
= $true )
| ( ( ~ ( line @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(158,plain,
! [SV9: $i] :
( ( ( point @ ( point_2_on_line @ SV9 ) )
= $true )
| ( ( ~ ( line @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(159,plain,
! [SV10: $i] :
( ( ( ( ( point_1_on_line @ SV10 )
!= ( point_2_on_line @ SV10 ) ) )
= $true )
| ( ( ~ ( line @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(160,plain,
! [SV11: $i] :
( ( ( ~ ( on @ ( point_not_on_line @ SV11 ) @ SV11 ) )
= $true )
| ( ( ~ ( line @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(161,plain,
! [SV12: $i] :
( ( ( point @ ( point_not_on_line @ SV12 ) )
= $true )
| ( ( ~ ( line @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(162,plain,
! [SV13: $i] :
( ( ( ~ ( plane @ SV13 ) )
= $true )
| ( ( on @ ( point_on_plane @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(163,plain,
! [SV14: $i] :
( ( ( ~ ( plane @ SV14 ) )
= $true )
| ( ( point @ ( point_on_plane @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(164,plain,
! [SV15: $i] :
( ( ( ~ ( plane @ SV15 ) )
= $true )
| ( ( ~ ( on @ ( point_not_on_plane @ SV15 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(165,plain,
! [SV16: $i] :
( ( ( ~ ( plane @ SV16 ) )
= $true )
| ( ( point @ ( point_not_on_plane @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(166,plain,
! [SV36: $i,SV17: $i] :
( ( ! [SY113: $i] :
( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SY113 ) )
| ~ ( point @ SV17 )
| ~ ( point @ SV36 )
| ~ ( point @ SY113 )
| ( collinear @ SV17 @ SV36 @ SY113 )
| ( SV17 = SV36 )
| ( SV17 = SY113 )
| ( SV36 = SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(167,plain,
! [SV37: $i,SV18: $i] :
( ( ! [SY114: $i] :
( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SY114 ) )
| ~ ( point @ SV37 )
| ~ ( point @ SV18 )
| ~ ( point @ SY114 )
| ( collinear @ SV37 @ SV18 @ SY114 )
| ( SV37 = SV18 )
| ( SV37 = SY114 )
| ( SV18 = SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(168,plain,
! [SV38: $i,SV19: $i] :
( ( ! [SY115: $i] :
( ( on @ SV19 @ ( plane_for_points @ SV38 @ SY115 @ SV19 ) )
| ~ ( point @ SV38 )
| ~ ( point @ SY115 )
| ~ ( point @ SV19 )
| ( collinear @ SV38 @ SY115 @ SV19 )
| ( SV38 = SY115 )
| ( SV38 = SV19 )
| ( SY115 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(169,plain,
! [SV39: $i,SV20: $i] :
( ( ! [SY116: $i] :
( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SY116 ) )
| ~ ( point @ SV20 )
| ~ ( point @ SV39 )
| ~ ( point @ SY116 )
| ( collinear @ SV20 @ SV39 @ SY116 )
| ( SV20 = SV39 )
| ( SV20 = SY116 )
| ( SV39 = SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(170,plain,
! [SV40: $i,SV21: $i] :
( ( ! [SY117: $i] :
( ~ ( point @ SV21 )
| ~ ( point @ SV40 )
| ~ ( point @ SY117 )
| ( collinear @ SV21 @ SV40 @ SY117 )
| ( SV21 = SV40 )
| ( SV21 = SY117 )
| ( SV40 = SY117 )
| ! [SY118: $i] :
( ~ ( on @ SV21 @ SY118 )
| ~ ( on @ SV40 @ SY118 )
| ~ ( on @ SY117 @ SY118 )
| ~ ( plane @ SY118 )
| ! [SY119: $i] :
( ~ ( on @ SV21 @ SY119 )
| ~ ( on @ SV40 @ SY119 )
| ~ ( on @ SY117 @ SY119 )
| ~ ( plane @ SY119 )
| ( SY118 = SY119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(171,plain,
! [SV41: $i,SV22: $i] :
( ( ~ ( on @ SV22 @ SV41 )
| ! [SY120: $i] :
( ~ ( on @ SY120 @ SV41 )
| ! [SY121: $i] :
( ~ ( on @ SV22 @ SY121 )
| ~ ( on @ SY120 @ SY121 )
| ~ ( plane @ SY121 )
| ~ ( point @ SV22 )
| ~ ( point @ SY120 )
| ~ ( line @ SV41 )
| ( SV22 = SY120 )
| ( on @ SV41 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(172,plain,
! [SV23: $i] :
( ( ( ~ ( plane @ SV23 ) )
= $true )
| ( ( ! [SY92: $i] :
( ~ ( plane @ SY92 )
| ( SV23 = SY92 )
| ! [SY93: $i] :
( ~ ( on @ SY93 @ SV23 )
| ~ ( on @ SY93 @ SY92 )
| ~ ( point @ SY93 )
| ( on @ ( common_point_on_planes @ SV23 @ SY92 @ SY93 ) @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(173,plain,
! [SV24: $i] :
( ( ( ~ ( plane @ SV24 ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( plane @ SY94 )
| ( SV24 = SY94 )
| ! [SY95: $i] :
( ~ ( on @ SY95 @ SV24 )
| ~ ( on @ SY95 @ SY94 )
| ~ ( point @ SY95 )
| ( on @ ( common_point_on_planes @ SV24 @ SY94 @ SY95 ) @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(174,plain,
! [SV25: $i] :
( ( ( ~ ( plane @ SV25 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( plane @ SY96 )
| ( SV25 = SY96 )
| ! [SY97: $i] :
( ~ ( on @ SY97 @ SV25 )
| ~ ( on @ SY97 @ SY96 )
| ~ ( point @ SY97 )
| ( point @ ( common_point_on_planes @ SV25 @ SY96 @ SY97 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(175,plain,
! [SV26: $i] :
( ( ( ~ ( plane @ SV26 ) )
= $true )
| ( ( ! [SY98: $i] :
( ~ ( plane @ SY98 )
| ( SV26 = SY98 )
| ! [SY99: $i] :
( ~ ( on @ SY99 @ SV26 )
| ~ ( on @ SY99 @ SY98 )
| ~ ( point @ SY99 )
| ( SY99
!= ( common_point_on_planes @ SV26 @ SY98 @ SY99 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(176,plain,
! [SV27: $i] :
( ( ( ~ ( point @ SV27 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( point @ SY100 )
| ! [SY101: $i] :
( ~ ( point @ SY101 )
| ( SV27 = SY100 )
| ( SV27 = SY101 )
| ( SY100 = SY101 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SY100 @ SY101 ) )
| ~ ( collinear @ SV27 @ SY100 @ SY101 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(177,plain,
! [SV28: $i] :
( ( ( ~ ( point @ SV28 ) )
= $true )
| ( ( ! [SY102: $i] :
( ~ ( point @ SY102 )
| ! [SY103: $i] :
( ~ ( point @ SY103 )
| ( SV28 = SY102 )
| ( SV28 = SY103 )
| ( SY102 = SY103 )
| ( on @ SY102 @ ( line_through_3_points @ SV28 @ SY102 @ SY103 ) )
| ~ ( collinear @ SV28 @ SY102 @ SY103 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(178,plain,
! [SV29: $i] :
( ( ( ~ ( point @ SV29 ) )
= $true )
| ( ( ! [SY104: $i] :
( ~ ( point @ SY104 )
| ! [SY105: $i] :
( ~ ( point @ SY105 )
| ( SV29 = SY104 )
| ( SV29 = SY105 )
| ( SY104 = SY105 )
| ( on @ SY105 @ ( line_through_3_points @ SV29 @ SY104 @ SY105 ) )
| ~ ( collinear @ SV29 @ SY104 @ SY105 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(179,plain,
! [SV30: $i] :
( ( ( ~ ( point @ SV30 ) )
= $true )
| ( ( ! [SY106: $i] :
( ~ ( point @ SY106 )
| ! [SY107: $i] :
( ~ ( point @ SY107 )
| ( SV30 = SY106 )
| ( SV30 = SY107 )
| ( SY106 = SY107 )
| ( line @ ( line_through_3_points @ SV30 @ SY106 @ SY107 ) )
| ~ ( collinear @ SV30 @ SY106 @ SY107 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(180,plain,
! [SV42: $i,SV31: $i] :
( ( ! [SY122: $i] :
( ( collinear @ SV31 @ SV42 @ SY122 )
| ! [SY123: $i] :
( ~ ( on @ SV31 @ SY123 )
| ~ ( on @ SV42 @ SY123 )
| ~ ( on @ SY122 @ SY123 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SY122 )
| ( SV31 = SV42 )
| ( SV31 = SY122 )
| ( SV42 = SY122 )
| ~ ( line @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(181,plain,
! [SV1: $i] :
( ( ( line @ SV1 )
= $false )
| ( ( on @ a_point @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(182,plain,
! [SV32: $i,SV2: $i] :
( ( ( on @ SV2 @ ( line_from_to @ SV2 @ SV32 ) )
= $true )
| ( ( ( SV2 = SV32 )
| ~ ( point @ SV2 )
| ~ ( point @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(183,plain,
! [SV33: $i,SV3: $i] :
( ( ( on @ SV3 @ ( line_from_to @ SV33 @ SV3 ) )
= $true )
| ( ( ( SV33 = SV3 )
| ~ ( point @ SV33 )
| ~ ( point @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(184,plain,
! [SV34: $i,SV4: $i] :
( ( ( line @ ( line_from_to @ SV4 @ SV34 ) )
= $true )
| ( ( ( SV4 = SV34 )
| ~ ( point @ SV4 )
| ~ ( point @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(185,plain,
! [SV35: $i,SV5: $i] :
( ( ( ~ ( on @ SV5 @ SV35 ) )
= $true )
| ( ( ! [SY111: $i] :
( ( SV5 = SY111 )
| ~ ( on @ SY111 @ SV35 )
| ! [SY112: $i] :
( ( SV35 = SY112 )
| ~ ( on @ SV5 @ SY112 )
| ~ ( on @ SY111 @ SY112 )
| ~ ( point @ SV5 )
| ~ ( point @ SY111 )
| ~ ( line @ SV35 )
| ~ ( line @ SY112 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(186,plain,
! [SV6: $i] :
( ( ( line @ SV6 )
= $false )
| ( ( on @ ( point_1_on_line @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(187,plain,
! [SV7: $i] :
( ( ( line @ SV7 )
= $false )
| ( ( on @ ( point_2_on_line @ SV7 ) @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(188,plain,
! [SV8: $i] :
( ( ( line @ SV8 )
= $false )
| ( ( point @ ( point_1_on_line @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(189,plain,
! [SV9: $i] :
( ( ( line @ SV9 )
= $false )
| ( ( point @ ( point_2_on_line @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(190,plain,
! [SV10: $i] :
( ( ( ( point_1_on_line @ SV10 )
= ( point_2_on_line @ SV10 ) )
= $false )
| ( ( ~ ( line @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(191,plain,
! [SV11: $i] :
( ( ( on @ ( point_not_on_line @ SV11 ) @ SV11 )
= $false )
| ( ( ~ ( line @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(192,plain,
! [SV12: $i] :
( ( ( line @ SV12 )
= $false )
| ( ( point @ ( point_not_on_line @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(193,plain,
! [SV13: $i] :
( ( ( plane @ SV13 )
= $false )
| ( ( on @ ( point_on_plane @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(194,plain,
! [SV14: $i] :
( ( ( plane @ SV14 )
= $false )
| ( ( point @ ( point_on_plane @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(195,plain,
! [SV15: $i] :
( ( ( plane @ SV15 )
= $false )
| ( ( ~ ( on @ ( point_not_on_plane @ SV15 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(196,plain,
! [SV16: $i] :
( ( ( plane @ SV16 )
= $false )
| ( ( point @ ( point_not_on_plane @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(197,plain,
! [SV43: $i,SV36: $i,SV17: $i] :
( ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
| ~ ( point @ SV17 )
| ~ ( point @ SV36 )
| ~ ( point @ SV43 )
| ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(198,plain,
! [SV44: $i,SV37: $i,SV18: $i] :
( ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
| ~ ( point @ SV37 )
| ~ ( point @ SV18 )
| ~ ( point @ SV44 )
| ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(199,plain,
! [SV45: $i,SV38: $i,SV19: $i] :
( ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
| ~ ( point @ SV38 )
| ~ ( point @ SV45 )
| ~ ( point @ SV19 )
| ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(200,plain,
! [SV46: $i,SV39: $i,SV20: $i] :
( ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
| ~ ( point @ SV20 )
| ~ ( point @ SV39 )
| ~ ( point @ SV46 )
| ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(201,plain,
! [SV47: $i,SV40: $i,SV21: $i] :
( ( ~ ( point @ SV21 )
| ~ ( point @ SV40 )
| ~ ( point @ SV47 )
| ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(202,plain,
! [SV41: $i,SV22: $i] :
( ( ( ~ ( on @ SV22 @ SV41 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( on @ SY120 @ SV41 )
| ! [SY121: $i] :
( ~ ( on @ SV22 @ SY121 )
| ~ ( on @ SY120 @ SY121 )
| ~ ( plane @ SY121 )
| ~ ( point @ SV22 )
| ~ ( point @ SY120 )
| ~ ( line @ SV41 )
| ( SV22 = SY120 )
| ( on @ SV41 @ SY121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(203,plain,
! [SV23: $i] :
( ( ( plane @ SV23 )
= $false )
| ( ( ! [SY92: $i] :
( ~ ( plane @ SY92 )
| ( SV23 = SY92 )
| ! [SY93: $i] :
( ~ ( on @ SY93 @ SV23 )
| ~ ( on @ SY93 @ SY92 )
| ~ ( point @ SY93 )
| ( on @ ( common_point_on_planes @ SV23 @ SY92 @ SY93 ) @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(204,plain,
! [SV24: $i] :
( ( ( plane @ SV24 )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( plane @ SY94 )
| ( SV24 = SY94 )
| ! [SY95: $i] :
( ~ ( on @ SY95 @ SV24 )
| ~ ( on @ SY95 @ SY94 )
| ~ ( point @ SY95 )
| ( on @ ( common_point_on_planes @ SV24 @ SY94 @ SY95 ) @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(205,plain,
! [SV25: $i] :
( ( ( plane @ SV25 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( plane @ SY96 )
| ( SV25 = SY96 )
| ! [SY97: $i] :
( ~ ( on @ SY97 @ SV25 )
| ~ ( on @ SY97 @ SY96 )
| ~ ( point @ SY97 )
| ( point @ ( common_point_on_planes @ SV25 @ SY96 @ SY97 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(206,plain,
! [SV26: $i] :
( ( ( plane @ SV26 )
= $false )
| ( ( ! [SY98: $i] :
( ~ ( plane @ SY98 )
| ( SV26 = SY98 )
| ! [SY99: $i] :
( ~ ( on @ SY99 @ SV26 )
| ~ ( on @ SY99 @ SY98 )
| ~ ( point @ SY99 )
| ( SY99
!= ( common_point_on_planes @ SV26 @ SY98 @ SY99 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(207,plain,
! [SV27: $i] :
( ( ( point @ SV27 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( point @ SY100 )
| ! [SY101: $i] :
( ~ ( point @ SY101 )
| ( SV27 = SY100 )
| ( SV27 = SY101 )
| ( SY100 = SY101 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SY100 @ SY101 ) )
| ~ ( collinear @ SV27 @ SY100 @ SY101 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(208,plain,
! [SV28: $i] :
( ( ( point @ SV28 )
= $false )
| ( ( ! [SY102: $i] :
( ~ ( point @ SY102 )
| ! [SY103: $i] :
( ~ ( point @ SY103 )
| ( SV28 = SY102 )
| ( SV28 = SY103 )
| ( SY102 = SY103 )
| ( on @ SY102 @ ( line_through_3_points @ SV28 @ SY102 @ SY103 ) )
| ~ ( collinear @ SV28 @ SY102 @ SY103 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(209,plain,
! [SV29: $i] :
( ( ( point @ SV29 )
= $false )
| ( ( ! [SY104: $i] :
( ~ ( point @ SY104 )
| ! [SY105: $i] :
( ~ ( point @ SY105 )
| ( SV29 = SY104 )
| ( SV29 = SY105 )
| ( SY104 = SY105 )
| ( on @ SY105 @ ( line_through_3_points @ SV29 @ SY104 @ SY105 ) )
| ~ ( collinear @ SV29 @ SY104 @ SY105 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(210,plain,
! [SV30: $i] :
( ( ( point @ SV30 )
= $false )
| ( ( ! [SY106: $i] :
( ~ ( point @ SY106 )
| ! [SY107: $i] :
( ~ ( point @ SY107 )
| ( SV30 = SY106 )
| ( SV30 = SY107 )
| ( SY106 = SY107 )
| ( line @ ( line_through_3_points @ SV30 @ SY106 @ SY107 ) )
| ~ ( collinear @ SV30 @ SY106 @ SY107 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(211,plain,
! [SV48: $i,SV42: $i,SV31: $i] :
( ( ( collinear @ SV31 @ SV42 @ SV48 )
| ! [SY126: $i] :
( ~ ( on @ SV31 @ SY126 )
| ~ ( on @ SV42 @ SY126 )
| ~ ( on @ SV48 @ SY126 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(212,plain,
! [SV32: $i,SV2: $i] :
( ( ( SV2 = SV32 )
= $true )
| ( ( ~ ( point @ SV2 )
| ~ ( point @ SV32 ) )
= $true )
| ( ( on @ SV2 @ ( line_from_to @ SV2 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(213,plain,
! [SV3: $i,SV33: $i] :
( ( ( SV33 = SV3 )
= $true )
| ( ( ~ ( point @ SV33 )
| ~ ( point @ SV3 ) )
= $true )
| ( ( on @ SV3 @ ( line_from_to @ SV33 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(214,plain,
! [SV34: $i,SV4: $i] :
( ( ( SV4 = SV34 )
= $true )
| ( ( ~ ( point @ SV4 )
| ~ ( point @ SV34 ) )
= $true )
| ( ( line @ ( line_from_to @ SV4 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(215,plain,
! [SV35: $i,SV5: $i] :
( ( ( on @ SV5 @ SV35 )
= $false )
| ( ( ! [SY111: $i] :
( ( SV5 = SY111 )
| ~ ( on @ SY111 @ SV35 )
| ! [SY112: $i] :
( ( SV35 = SY112 )
| ~ ( on @ SV5 @ SY112 )
| ~ ( on @ SY111 @ SY112 )
| ~ ( point @ SV5 )
| ~ ( point @ SY111 )
| ~ ( line @ SV35 )
| ~ ( line @ SY112 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(216,plain,
! [SV10: $i] :
( ( ( line @ SV10 )
= $false )
| ( ( ( point_1_on_line @ SV10 )
= ( point_2_on_line @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(217,plain,
! [SV11: $i] :
( ( ( line @ SV11 )
= $false )
| ( ( on @ ( point_not_on_line @ SV11 ) @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV15: $i] :
( ( ( on @ ( point_not_on_plane @ SV15 ) @ SV15 )
= $false )
| ( ( plane @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(219,plain,
! [SV43: $i,SV36: $i,SV17: $i] :
( ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( point @ SV17 )
| ~ ( point @ SV36 )
| ~ ( point @ SV43 )
| ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(220,plain,
! [SV44: $i,SV37: $i,SV18: $i] :
( ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true )
| ( ( ~ ( point @ SV37 )
| ~ ( point @ SV18 )
| ~ ( point @ SV44 )
| ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(221,plain,
! [SV45: $i,SV38: $i,SV19: $i] :
( ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true )
| ( ( ~ ( point @ SV38 )
| ~ ( point @ SV45 )
| ~ ( point @ SV19 )
| ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(222,plain,
! [SV46: $i,SV39: $i,SV20: $i] :
( ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true )
| ( ( ~ ( point @ SV20 )
| ~ ( point @ SV39 )
| ~ ( point @ SV46 )
| ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(223,plain,
! [SV47: $i,SV40: $i,SV21: $i] :
( ( ( ~ ( point @ SV21 ) )
= $true )
| ( ( ~ ( point @ SV40 )
| ~ ( point @ SV47 )
| ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(224,plain,
! [SV41: $i,SV22: $i] :
( ( ( on @ SV22 @ SV41 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( on @ SY120 @ SV41 )
| ! [SY121: $i] :
( ~ ( on @ SV22 @ SY121 )
| ~ ( on @ SY120 @ SY121 )
| ~ ( plane @ SY121 )
| ~ ( point @ SV22 )
| ~ ( point @ SY120 )
| ~ ( line @ SV41 )
| ( SV22 = SY120 )
| ( on @ SV41 @ SY121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(225,plain,
! [SV23: $i,SV49: $i] :
( ( ( ~ ( plane @ SV49 )
| ( SV23 = SV49 )
| ! [SY127: $i] :
( ~ ( on @ SY127 @ SV23 )
| ~ ( on @ SY127 @ SV49 )
| ~ ( point @ SY127 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SY127 ) @ SV23 ) ) )
= $true )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(226,plain,
! [SV24: $i,SV50: $i] :
( ( ( ~ ( plane @ SV50 )
| ( SV24 = SV50 )
| ! [SY128: $i] :
( ~ ( on @ SY128 @ SV24 )
| ~ ( on @ SY128 @ SV50 )
| ~ ( point @ SY128 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) @ SV50 ) ) )
= $true )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(227,plain,
! [SV25: $i,SV51: $i] :
( ( ( ~ ( plane @ SV51 )
| ( SV25 = SV51 )
| ! [SY129: $i] :
( ~ ( on @ SY129 @ SV25 )
| ~ ( on @ SY129 @ SV51 )
| ~ ( point @ SY129 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
= $true )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(228,plain,
! [SV26: $i,SV52: $i] :
( ( ( ~ ( plane @ SV52 )
| ( SV26 = SV52 )
| ! [SY130: $i] :
( ~ ( on @ SY130 @ SV26 )
| ~ ( on @ SY130 @ SV52 )
| ~ ( point @ SY130 )
| ( SY130
!= ( common_point_on_planes @ SV26 @ SV52 @ SY130 ) ) ) )
= $true )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(229,plain,
! [SV27: $i,SV53: $i] :
( ( ( ~ ( point @ SV53 )
| ! [SY131: $i] :
( ~ ( point @ SY131 )
| ( SV27 = SV53 )
| ( SV27 = SY131 )
| ( SV53 = SY131 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SY131 ) )
| ~ ( collinear @ SV27 @ SV53 @ SY131 ) ) )
= $true )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(230,plain,
! [SV28: $i,SV54: $i] :
( ( ( ~ ( point @ SV54 )
| ! [SY132: $i] :
( ~ ( point @ SY132 )
| ( SV28 = SV54 )
| ( SV28 = SY132 )
| ( SV54 = SY132 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SY132 ) )
| ~ ( collinear @ SV28 @ SV54 @ SY132 ) ) )
= $true )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(231,plain,
! [SV29: $i,SV55: $i] :
( ( ( ~ ( point @ SV55 )
| ! [SY133: $i] :
( ~ ( point @ SY133 )
| ( SV29 = SV55 )
| ( SV29 = SY133 )
| ( SV55 = SY133 )
| ( on @ SY133 @ ( line_through_3_points @ SV29 @ SV55 @ SY133 ) )
| ~ ( collinear @ SV29 @ SV55 @ SY133 ) ) )
= $true )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(232,plain,
! [SV30: $i,SV56: $i] :
( ( ( ~ ( point @ SV56 )
| ! [SY134: $i] :
( ~ ( point @ SY134 )
| ( SV30 = SV56 )
| ( SV30 = SY134 )
| ( SV56 = SY134 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SY134 ) )
| ~ ( collinear @ SV30 @ SV56 @ SY134 ) ) )
= $true )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(233,plain,
! [SV48: $i,SV42: $i,SV31: $i] :
( ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( on @ SV31 @ SY126 )
| ~ ( on @ SV42 @ SY126 )
| ~ ( on @ SV48 @ SY126 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SY126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(234,plain,
! [SV32: $i,SV2: $i] :
( ( ( ~ ( point @ SV2 ) )
= $true )
| ( ( ~ ( point @ SV32 ) )
= $true )
| ( ( SV2 = SV32 )
= $true )
| ( ( on @ SV2 @ ( line_from_to @ SV2 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(235,plain,
! [SV3: $i,SV33: $i] :
( ( ( ~ ( point @ SV33 ) )
= $true )
| ( ( ~ ( point @ SV3 ) )
= $true )
| ( ( SV33 = SV3 )
= $true )
| ( ( on @ SV3 @ ( line_from_to @ SV33 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(236,plain,
! [SV34: $i,SV4: $i] :
( ( ( ~ ( point @ SV4 ) )
= $true )
| ( ( ~ ( point @ SV34 ) )
= $true )
| ( ( SV4 = SV34 )
= $true )
| ( ( line @ ( line_from_to @ SV4 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(237,plain,
! [SV35: $i,SV57: $i,SV5: $i] :
( ( ( ( SV5 = SV57 )
| ~ ( on @ SV57 @ SV35 )
| ! [SY135: $i] :
( ( SV35 = SY135 )
| ~ ( on @ SV5 @ SY135 )
| ~ ( on @ SV57 @ SY135 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SY135 ) ) )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(238,plain,
! [SV43: $i,SV36: $i,SV17: $i] :
( ( ( ~ ( point @ SV17 ) )
= $true )
| ( ( ~ ( point @ SV36 )
| ~ ( point @ SV43 )
| ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(239,plain,
! [SV44: $i,SV18: $i,SV37: $i] :
( ( ( ~ ( point @ SV37 ) )
= $true )
| ( ( ~ ( point @ SV18 )
| ~ ( point @ SV44 )
| ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(240,plain,
! [SV19: $i,SV45: $i,SV38: $i] :
( ( ( ~ ( point @ SV38 ) )
= $true )
| ( ( ~ ( point @ SV45 )
| ~ ( point @ SV19 )
| ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(241,plain,
! [SV46: $i,SV39: $i,SV20: $i] :
( ( ( ~ ( point @ SV20 ) )
= $true )
| ( ( ~ ( point @ SV39 )
| ~ ( point @ SV46 )
| ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(242,plain,
! [SV47: $i,SV40: $i,SV21: $i] :
( ( ( point @ SV21 )
= $false )
| ( ( ~ ( point @ SV40 )
| ~ ( point @ SV47 )
| ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(243,plain,
! [SV22: $i,SV41: $i,SV58: $i] :
( ( ( ~ ( on @ SV58 @ SV41 )
| ! [SY136: $i] :
( ~ ( on @ SV22 @ SY136 )
| ~ ( on @ SV58 @ SY136 )
| ~ ( plane @ SY136 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SY136 ) ) )
= $true )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(244,plain,
! [SV23: $i,SV49: $i] :
( ( ( ~ ( plane @ SV49 ) )
= $true )
| ( ( ( SV23 = SV49 )
| ! [SY127: $i] :
( ~ ( on @ SY127 @ SV23 )
| ~ ( on @ SY127 @ SV49 )
| ~ ( point @ SY127 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SY127 ) @ SV23 ) ) )
= $true )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(245,plain,
! [SV24: $i,SV50: $i] :
( ( ( ~ ( plane @ SV50 ) )
= $true )
| ( ( ( SV24 = SV50 )
| ! [SY128: $i] :
( ~ ( on @ SY128 @ SV24 )
| ~ ( on @ SY128 @ SV50 )
| ~ ( point @ SY128 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) @ SV50 ) ) )
= $true )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(246,plain,
! [SV25: $i,SV51: $i] :
( ( ( ~ ( plane @ SV51 ) )
= $true )
| ( ( ( SV25 = SV51 )
| ! [SY129: $i] :
( ~ ( on @ SY129 @ SV25 )
| ~ ( on @ SY129 @ SV51 )
| ~ ( point @ SY129 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
= $true )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(247,plain,
! [SV26: $i,SV52: $i] :
( ( ( ~ ( plane @ SV52 ) )
= $true )
| ( ( ( SV26 = SV52 )
| ! [SY130: $i] :
( ~ ( on @ SY130 @ SV26 )
| ~ ( on @ SY130 @ SV52 )
| ~ ( point @ SY130 )
| ( SY130
!= ( common_point_on_planes @ SV26 @ SV52 @ SY130 ) ) ) )
= $true )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(248,plain,
! [SV27: $i,SV53: $i] :
( ( ( ~ ( point @ SV53 ) )
= $true )
| ( ( ! [SY131: $i] :
( ~ ( point @ SY131 )
| ( SV27 = SV53 )
| ( SV27 = SY131 )
| ( SV53 = SY131 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SY131 ) )
| ~ ( collinear @ SV27 @ SV53 @ SY131 ) ) )
= $true )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(249,plain,
! [SV28: $i,SV54: $i] :
( ( ( ~ ( point @ SV54 ) )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( point @ SY132 )
| ( SV28 = SV54 )
| ( SV28 = SY132 )
| ( SV54 = SY132 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SY132 ) )
| ~ ( collinear @ SV28 @ SV54 @ SY132 ) ) )
= $true )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(250,plain,
! [SV29: $i,SV55: $i] :
( ( ( ~ ( point @ SV55 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point @ SY133 )
| ( SV29 = SV55 )
| ( SV29 = SY133 )
| ( SV55 = SY133 )
| ( on @ SY133 @ ( line_through_3_points @ SV29 @ SV55 @ SY133 ) )
| ~ ( collinear @ SV29 @ SV55 @ SY133 ) ) )
= $true )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(251,plain,
! [SV30: $i,SV56: $i] :
( ( ( ~ ( point @ SV56 ) )
= $true )
| ( ( ! [SY134: $i] :
( ~ ( point @ SY134 )
| ( SV30 = SV56 )
| ( SV30 = SY134 )
| ( SV56 = SY134 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SY134 ) )
| ~ ( collinear @ SV30 @ SV56 @ SY134 ) ) )
= $true )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(252,plain,
! [SV48: $i,SV42: $i,SV59: $i,SV31: $i] :
( ( ( ~ ( on @ SV31 @ SV59 )
| ~ ( on @ SV42 @ SV59 )
| ~ ( on @ SV48 @ SV59 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(253,plain,
! [SV32: $i,SV2: $i] :
( ( ( point @ SV2 )
= $false )
| ( ( ~ ( point @ SV32 ) )
= $true )
| ( ( SV2 = SV32 )
= $true )
| ( ( on @ SV2 @ ( line_from_to @ SV2 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(254,plain,
! [SV3: $i,SV33: $i] :
( ( ( point @ SV33 )
= $false )
| ( ( ~ ( point @ SV3 ) )
= $true )
| ( ( SV33 = SV3 )
= $true )
| ( ( on @ SV3 @ ( line_from_to @ SV33 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(255,plain,
! [SV34: $i,SV4: $i] :
( ( ( point @ SV4 )
= $false )
| ( ( ~ ( point @ SV34 ) )
= $true )
| ( ( SV4 = SV34 )
= $true )
| ( ( line @ ( line_from_to @ SV4 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(256,plain,
! [SV35: $i,SV57: $i,SV5: $i] :
( ( ( SV5 = SV57 )
= $true )
| ( ( ~ ( on @ SV57 @ SV35 )
| ! [SY135: $i] :
( ( SV35 = SY135 )
| ~ ( on @ SV5 @ SY135 )
| ~ ( on @ SV57 @ SY135 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SY135 ) ) )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(257,plain,
! [SV43: $i,SV36: $i,SV17: $i] :
( ( ( point @ SV17 )
= $false )
| ( ( ~ ( point @ SV36 )
| ~ ( point @ SV43 )
| ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(258,plain,
! [SV44: $i,SV18: $i,SV37: $i] :
( ( ( point @ SV37 )
= $false )
| ( ( ~ ( point @ SV18 )
| ~ ( point @ SV44 )
| ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(259,plain,
! [SV19: $i,SV45: $i,SV38: $i] :
( ( ( point @ SV38 )
= $false )
| ( ( ~ ( point @ SV45 )
| ~ ( point @ SV19 )
| ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(260,plain,
! [SV46: $i,SV39: $i,SV20: $i] :
( ( ( point @ SV20 )
= $false )
| ( ( ~ ( point @ SV39 )
| ~ ( point @ SV46 )
| ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(261,plain,
! [SV21: $i,SV47: $i,SV40: $i] :
( ( ( ~ ( point @ SV40 ) )
= $true )
| ( ( ~ ( point @ SV47 )
| ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(262,plain,
! [SV22: $i,SV41: $i,SV58: $i] :
( ( ( ~ ( on @ SV58 @ SV41 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( on @ SV22 @ SY136 )
| ~ ( on @ SV58 @ SY136 )
| ~ ( plane @ SY136 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SY136 ) ) )
= $true )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(263,plain,
! [SV23: $i,SV49: $i] :
( ( ( plane @ SV49 )
= $false )
| ( ( ( SV23 = SV49 )
| ! [SY127: $i] :
( ~ ( on @ SY127 @ SV23 )
| ~ ( on @ SY127 @ SV49 )
| ~ ( point @ SY127 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SY127 ) @ SV23 ) ) )
= $true )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(264,plain,
! [SV24: $i,SV50: $i] :
( ( ( plane @ SV50 )
= $false )
| ( ( ( SV24 = SV50 )
| ! [SY128: $i] :
( ~ ( on @ SY128 @ SV24 )
| ~ ( on @ SY128 @ SV50 )
| ~ ( point @ SY128 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) @ SV50 ) ) )
= $true )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(265,plain,
! [SV25: $i,SV51: $i] :
( ( ( plane @ SV51 )
= $false )
| ( ( ( SV25 = SV51 )
| ! [SY129: $i] :
( ~ ( on @ SY129 @ SV25 )
| ~ ( on @ SY129 @ SV51 )
| ~ ( point @ SY129 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
= $true )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(266,plain,
! [SV26: $i,SV52: $i] :
( ( ( plane @ SV52 )
= $false )
| ( ( ( SV26 = SV52 )
| ! [SY130: $i] :
( ~ ( on @ SY130 @ SV26 )
| ~ ( on @ SY130 @ SV52 )
| ~ ( point @ SY130 )
| ( SY130
!= ( common_point_on_planes @ SV26 @ SV52 @ SY130 ) ) ) )
= $true )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(267,plain,
! [SV27: $i,SV53: $i] :
( ( ( point @ SV53 )
= $false )
| ( ( ! [SY131: $i] :
( ~ ( point @ SY131 )
| ( SV27 = SV53 )
| ( SV27 = SY131 )
| ( SV53 = SY131 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SY131 ) )
| ~ ( collinear @ SV27 @ SV53 @ SY131 ) ) )
= $true )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(268,plain,
! [SV28: $i,SV54: $i] :
( ( ( point @ SV54 )
= $false )
| ( ( ! [SY132: $i] :
( ~ ( point @ SY132 )
| ( SV28 = SV54 )
| ( SV28 = SY132 )
| ( SV54 = SY132 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SY132 ) )
| ~ ( collinear @ SV28 @ SV54 @ SY132 ) ) )
= $true )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(269,plain,
! [SV29: $i,SV55: $i] :
( ( ( point @ SV55 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( point @ SY133 )
| ( SV29 = SV55 )
| ( SV29 = SY133 )
| ( SV55 = SY133 )
| ( on @ SY133 @ ( line_through_3_points @ SV29 @ SV55 @ SY133 ) )
| ~ ( collinear @ SV29 @ SV55 @ SY133 ) ) )
= $true )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(270,plain,
! [SV30: $i,SV56: $i] :
( ( ( point @ SV56 )
= $false )
| ( ( ! [SY134: $i] :
( ~ ( point @ SY134 )
| ( SV30 = SV56 )
| ( SV30 = SY134 )
| ( SV56 = SY134 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SY134 ) )
| ~ ( collinear @ SV30 @ SV56 @ SY134 ) ) )
= $true )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(271,plain,
! [SV48: $i,SV42: $i,SV59: $i,SV31: $i] :
( ( ( ~ ( on @ SV31 @ SV59 ) )
= $true )
| ( ( ~ ( on @ SV42 @ SV59 )
| ~ ( on @ SV48 @ SV59 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(272,plain,
! [SV2: $i,SV32: $i] :
( ( ( point @ SV32 )
= $false )
| ( ( point @ SV2 )
= $false )
| ( ( SV2 = SV32 )
= $true )
| ( ( on @ SV2 @ ( line_from_to @ SV2 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(273,plain,
! [SV33: $i,SV3: $i] :
( ( ( point @ SV3 )
= $false )
| ( ( point @ SV33 )
= $false )
| ( ( SV33 = SV3 )
= $true )
| ( ( on @ SV3 @ ( line_from_to @ SV33 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(274,plain,
! [SV4: $i,SV34: $i] :
( ( ( point @ SV34 )
= $false )
| ( ( point @ SV4 )
= $false )
| ( ( SV4 = SV34 )
= $true )
| ( ( line @ ( line_from_to @ SV4 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(275,plain,
! [SV5: $i,SV35: $i,SV57: $i] :
( ( ( ~ ( on @ SV57 @ SV35 ) )
= $true )
| ( ( ! [SY135: $i] :
( ( SV35 = SY135 )
| ~ ( on @ SV5 @ SY135 )
| ~ ( on @ SV57 @ SY135 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SY135 ) ) )
= $true )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(276,plain,
! [SV17: $i,SV43: $i,SV36: $i] :
( ( ( ~ ( point @ SV36 ) )
= $true )
| ( ( ~ ( point @ SV43 )
| ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(277,plain,
! [SV37: $i,SV44: $i,SV18: $i] :
( ( ( ~ ( point @ SV18 ) )
= $true )
| ( ( ~ ( point @ SV44 )
| ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(278,plain,
! [SV38: $i,SV19: $i,SV45: $i] :
( ( ( ~ ( point @ SV45 ) )
= $true )
| ( ( ~ ( point @ SV19 )
| ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV20: $i,SV46: $i,SV39: $i] :
( ( ( ~ ( point @ SV39 ) )
= $true )
| ( ( ~ ( point @ SV46 )
| ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(280,plain,
! [SV21: $i,SV47: $i,SV40: $i] :
( ( ( point @ SV40 )
= $false )
| ( ( ~ ( point @ SV47 )
| ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(281,plain,
! [SV22: $i,SV41: $i,SV58: $i] :
( ( ( on @ SV58 @ SV41 )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( on @ SV22 @ SY136 )
| ~ ( on @ SV58 @ SY136 )
| ~ ( plane @ SY136 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SY136 ) ) )
= $true )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(282,plain,
! [SV49: $i,SV23: $i] :
( ( ( SV23 = SV49 )
= $true )
| ( ( ! [SY127: $i] :
( ~ ( on @ SY127 @ SV23 )
| ~ ( on @ SY127 @ SV49 )
| ~ ( point @ SY127 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SY127 ) @ SV23 ) ) )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(283,plain,
! [SV50: $i,SV24: $i] :
( ( ( SV24 = SV50 )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( on @ SY128 @ SV24 )
| ~ ( on @ SY128 @ SV50 )
| ~ ( point @ SY128 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) @ SV50 ) ) )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(284,plain,
! [SV51: $i,SV25: $i] :
( ( ( SV25 = SV51 )
= $true )
| ( ( ! [SY129: $i] :
( ~ ( on @ SY129 @ SV25 )
| ~ ( on @ SY129 @ SV51 )
| ~ ( point @ SY129 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(285,plain,
! [SV52: $i,SV26: $i] :
( ( ( SV26 = SV52 )
= $true )
| ( ( ! [SY130: $i] :
( ~ ( on @ SY130 @ SV26 )
| ~ ( on @ SY130 @ SV52 )
| ~ ( point @ SY130 )
| ( SY130
!= ( common_point_on_planes @ SV26 @ SV52 @ SY130 ) ) ) )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(286,plain,
! [SV53: $i,SV27: $i,SV60: $i] :
( ( ( ~ ( point @ SV60 )
| ( SV27 = SV53 )
| ( SV27 = SV60 )
| ( SV53 = SV60 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
| ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(287,plain,
! [SV54: $i,SV28: $i,SV61: $i] :
( ( ( ~ ( point @ SV61 )
| ( SV28 = SV54 )
| ( SV28 = SV61 )
| ( SV54 = SV61 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
| ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(288,plain,
! [SV55: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( point @ SV62 )
| ( SV29 = SV55 )
| ( SV29 = SV62 )
| ( SV55 = SV62 )
| ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
| ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(289,plain,
! [SV56: $i,SV30: $i,SV63: $i] :
( ( ( ~ ( point @ SV63 )
| ( SV30 = SV56 )
| ( SV30 = SV63 )
| ( SV56 = SV63 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
| ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(290,plain,
! [SV48: $i,SV42: $i,SV59: $i,SV31: $i] :
( ( ( on @ SV31 @ SV59 )
= $false )
| ( ( ~ ( on @ SV42 @ SV59 )
| ~ ( on @ SV48 @ SV59 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(291,plain,
! [SV5: $i,SV35: $i,SV57: $i] :
( ( ( on @ SV57 @ SV35 )
= $false )
| ( ( ! [SY135: $i] :
( ( SV35 = SY135 )
| ~ ( on @ SV5 @ SY135 )
| ~ ( on @ SV57 @ SY135 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SY135 ) ) )
= $true )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(292,plain,
! [SV17: $i,SV43: $i,SV36: $i] :
( ( ( point @ SV36 )
= $false )
| ( ( ~ ( point @ SV43 )
| ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(293,plain,
! [SV37: $i,SV44: $i,SV18: $i] :
( ( ( point @ SV18 )
= $false )
| ( ( ~ ( point @ SV44 )
| ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(294,plain,
! [SV38: $i,SV19: $i,SV45: $i] :
( ( ( point @ SV45 )
= $false )
| ( ( ~ ( point @ SV19 )
| ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(295,plain,
! [SV20: $i,SV46: $i,SV39: $i] :
( ( ( point @ SV39 )
= $false )
| ( ( ~ ( point @ SV46 )
| ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(296,plain,
! [SV40: $i,SV21: $i,SV47: $i] :
( ( ( ~ ( point @ SV47 ) )
= $true )
| ( ( ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(297,plain,
! [SV41: $i,SV58: $i,SV64: $i,SV22: $i] :
( ( ( ~ ( on @ SV22 @ SV64 )
| ~ ( on @ SV58 @ SV64 )
| ~ ( plane @ SV64 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(298,plain,
! [SV49: $i,SV23: $i,SV65: $i] :
( ( ( ~ ( on @ SV65 @ SV23 )
| ~ ( on @ SV65 @ SV49 )
| ~ ( point @ SV65 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 ) )
= $true )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(299,plain,
! [SV50: $i,SV24: $i,SV66: $i] :
( ( ( ~ ( on @ SV66 @ SV24 )
| ~ ( on @ SV66 @ SV50 )
| ~ ( point @ SV66 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 ) )
= $true )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(300,plain,
! [SV51: $i,SV25: $i,SV67: $i] :
( ( ( ~ ( on @ SV67 @ SV25 )
| ~ ( on @ SV67 @ SV51 )
| ~ ( point @ SV67 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
= $true )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(301,plain,
! [SV52: $i,SV26: $i,SV68: $i] :
( ( ( ~ ( on @ SV68 @ SV26 )
| ~ ( on @ SV68 @ SV52 )
| ~ ( point @ SV68 )
| ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(302,plain,
! [SV53: $i,SV27: $i,SV60: $i] :
( ( ( ~ ( point @ SV60 ) )
= $true )
| ( ( ( SV27 = SV53 )
| ( SV27 = SV60 )
| ( SV53 = SV60 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
| ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(303,plain,
! [SV54: $i,SV28: $i,SV61: $i] :
( ( ( ~ ( point @ SV61 ) )
= $true )
| ( ( ( SV28 = SV54 )
| ( SV28 = SV61 )
| ( SV54 = SV61 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
| ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(304,plain,
! [SV55: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( point @ SV62 ) )
= $true )
| ( ( ( SV29 = SV55 )
| ( SV29 = SV62 )
| ( SV55 = SV62 )
| ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
| ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(305,plain,
! [SV56: $i,SV30: $i,SV63: $i] :
( ( ( ~ ( point @ SV63 ) )
= $true )
| ( ( ( SV30 = SV56 )
| ( SV30 = SV63 )
| ( SV56 = SV63 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
| ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(306,plain,
! [SV31: $i,SV48: $i,SV59: $i,SV42: $i] :
( ( ( ~ ( on @ SV42 @ SV59 ) )
= $true )
| ( ( ~ ( on @ SV48 @ SV59 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(307,plain,
! [SV57: $i,SV5: $i,SV69: $i,SV35: $i] :
( ( ( ( SV35 = SV69 )
| ~ ( on @ SV5 @ SV69 )
| ~ ( on @ SV57 @ SV69 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(308,plain,
! [SV36: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( point @ SV43 ) )
= $true )
| ( ( ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( point @ SV36 )
= $false )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(309,plain,
! [SV18: $i,SV37: $i,SV44: $i] :
( ( ( ~ ( point @ SV44 ) )
= $true )
| ( ( ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( point @ SV18 )
= $false )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(310,plain,
! [SV45: $i,SV38: $i,SV19: $i] :
( ( ( ~ ( point @ SV19 ) )
= $true )
| ( ( ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( point @ SV45 )
= $false )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(311,plain,
! [SV39: $i,SV20: $i,SV46: $i] :
( ( ( ~ ( point @ SV46 ) )
= $true )
| ( ( ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( point @ SV39 )
= $false )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(312,plain,
! [SV40: $i,SV21: $i,SV47: $i] :
( ( ( point @ SV47 )
= $false )
| ( ( ( collinear @ SV21 @ SV40 @ SV47 )
| ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(313,plain,
! [SV41: $i,SV58: $i,SV64: $i,SV22: $i] :
( ( ( ~ ( on @ SV22 @ SV64 ) )
= $true )
| ( ( ~ ( on @ SV58 @ SV64 )
| ~ ( plane @ SV64 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(314,plain,
! [SV49: $i,SV23: $i,SV65: $i] :
( ( ( ~ ( on @ SV65 @ SV23 ) )
= $true )
| ( ( ~ ( on @ SV65 @ SV49 )
| ~ ( point @ SV65 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 ) )
= $true )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(315,plain,
! [SV50: $i,SV24: $i,SV66: $i] :
( ( ( ~ ( on @ SV66 @ SV24 ) )
= $true )
| ( ( ~ ( on @ SV66 @ SV50 )
| ~ ( point @ SV66 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 ) )
= $true )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(316,plain,
! [SV51: $i,SV25: $i,SV67: $i] :
( ( ( ~ ( on @ SV67 @ SV25 ) )
= $true )
| ( ( ~ ( on @ SV67 @ SV51 )
| ~ ( point @ SV67 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
= $true )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(317,plain,
! [SV52: $i,SV26: $i,SV68: $i] :
( ( ( ~ ( on @ SV68 @ SV26 ) )
= $true )
| ( ( ~ ( on @ SV68 @ SV52 )
| ~ ( point @ SV68 )
| ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(318,plain,
! [SV53: $i,SV27: $i,SV60: $i] :
( ( ( point @ SV60 )
= $false )
| ( ( ( SV27 = SV53 )
| ( SV27 = SV60 )
| ( SV53 = SV60 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
| ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(319,plain,
! [SV54: $i,SV28: $i,SV61: $i] :
( ( ( point @ SV61 )
= $false )
| ( ( ( SV28 = SV54 )
| ( SV28 = SV61 )
| ( SV54 = SV61 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
| ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(320,plain,
! [SV55: $i,SV29: $i,SV62: $i] :
( ( ( point @ SV62 )
= $false )
| ( ( ( SV29 = SV55 )
| ( SV29 = SV62 )
| ( SV55 = SV62 )
| ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
| ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(321,plain,
! [SV56: $i,SV30: $i,SV63: $i] :
( ( ( point @ SV63 )
= $false )
| ( ( ( SV30 = SV56 )
| ( SV30 = SV63 )
| ( SV56 = SV63 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
| ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(322,plain,
! [SV31: $i,SV48: $i,SV59: $i,SV42: $i] :
( ( ( on @ SV42 @ SV59 )
= $false )
| ( ( ~ ( on @ SV48 @ SV59 )
| ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(323,plain,
! [SV57: $i,SV5: $i,SV69: $i,SV35: $i] :
( ( ( SV35 = SV69 )
= $true )
| ( ( ~ ( on @ SV5 @ SV69 )
| ~ ( on @ SV57 @ SV69 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(324,plain,
! [SV36: $i,SV17: $i,SV43: $i] :
( ( ( point @ SV43 )
= $false )
| ( ( ( collinear @ SV17 @ SV36 @ SV43 )
| ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( point @ SV36 )
= $false )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(325,plain,
! [SV18: $i,SV37: $i,SV44: $i] :
( ( ( point @ SV44 )
= $false )
| ( ( ( collinear @ SV37 @ SV18 @ SV44 )
| ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( point @ SV18 )
= $false )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(326,plain,
! [SV45: $i,SV38: $i,SV19: $i] :
( ( ( point @ SV19 )
= $false )
| ( ( ( collinear @ SV38 @ SV45 @ SV19 )
| ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( point @ SV45 )
= $false )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(327,plain,
! [SV39: $i,SV20: $i,SV46: $i] :
( ( ( point @ SV46 )
= $false )
| ( ( ( collinear @ SV20 @ SV39 @ SV46 )
| ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( point @ SV39 )
= $false )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(328,plain,
! [SV47: $i,SV40: $i,SV21: $i] :
( ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( ( SV21 = SV40 )
| ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(329,plain,
! [SV41: $i,SV58: $i,SV64: $i,SV22: $i] :
( ( ( on @ SV22 @ SV64 )
= $false )
| ( ( ~ ( on @ SV58 @ SV64 )
| ~ ( plane @ SV64 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(330,plain,
! [SV49: $i,SV23: $i,SV65: $i] :
( ( ( on @ SV65 @ SV23 )
= $false )
| ( ( ~ ( on @ SV65 @ SV49 )
| ~ ( point @ SV65 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 ) )
= $true )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(331,plain,
! [SV50: $i,SV24: $i,SV66: $i] :
( ( ( on @ SV66 @ SV24 )
= $false )
| ( ( ~ ( on @ SV66 @ SV50 )
| ~ ( point @ SV66 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 ) )
= $true )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(332,plain,
! [SV51: $i,SV25: $i,SV67: $i] :
( ( ( on @ SV67 @ SV25 )
= $false )
| ( ( ~ ( on @ SV67 @ SV51 )
| ~ ( point @ SV67 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
= $true )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(333,plain,
! [SV52: $i,SV26: $i,SV68: $i] :
( ( ( on @ SV68 @ SV26 )
= $false )
| ( ( ~ ( on @ SV68 @ SV52 )
| ~ ( point @ SV68 )
| ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(334,plain,
! [SV60: $i,SV53: $i,SV27: $i] :
( ( ( SV27 = SV53 )
= $true )
| ( ( ( SV27 = SV60 )
| ( SV53 = SV60 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
| ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( point @ SV60 )
= $false )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(335,plain,
! [SV61: $i,SV54: $i,SV28: $i] :
( ( ( SV28 = SV54 )
= $true )
| ( ( ( SV28 = SV61 )
| ( SV54 = SV61 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
| ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( point @ SV61 )
= $false )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(336,plain,
! [SV62: $i,SV55: $i,SV29: $i] :
( ( ( SV29 = SV55 )
= $true )
| ( ( ( SV29 = SV62 )
| ( SV55 = SV62 )
| ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
| ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( point @ SV62 )
= $false )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(337,plain,
! [SV63: $i,SV56: $i,SV30: $i] :
( ( ( SV30 = SV56 )
= $true )
| ( ( ( SV30 = SV63 )
| ( SV56 = SV63 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
| ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( point @ SV63 )
= $false )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(338,plain,
! [SV42: $i,SV31: $i,SV59: $i,SV48: $i] :
( ( ( ~ ( on @ SV48 @ SV59 ) )
= $true )
| ( ( ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(339,plain,
! [SV35: $i,SV57: $i,SV69: $i,SV5: $i] :
( ( ( ~ ( on @ SV5 @ SV69 ) )
= $true )
| ( ( ~ ( on @ SV57 @ SV69 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(340,plain,
! [SV43: $i,SV36: $i,SV17: $i] :
( ( ( collinear @ SV17 @ SV36 @ SV43 )
= $true )
| ( ( ( SV17 = SV36 )
| ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( point @ SV43 )
= $false )
| ( ( point @ SV36 )
= $false )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(341,plain,
! [SV44: $i,SV18: $i,SV37: $i] :
( ( ( collinear @ SV37 @ SV18 @ SV44 )
= $true )
| ( ( ( SV37 = SV18 )
| ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( point @ SV44 )
= $false )
| ( ( point @ SV18 )
= $false )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(342,plain,
! [SV19: $i,SV45: $i,SV38: $i] :
( ( ( collinear @ SV38 @ SV45 @ SV19 )
= $true )
| ( ( ( SV38 = SV45 )
| ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( point @ SV19 )
= $false )
| ( ( point @ SV45 )
= $false )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(343,plain,
! [SV46: $i,SV39: $i,SV20: $i] :
( ( ( collinear @ SV20 @ SV39 @ SV46 )
= $true )
| ( ( ( SV20 = SV39 )
| ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( point @ SV46 )
= $false )
| ( ( point @ SV39 )
= $false )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(344,plain,
! [SV47: $i,SV40: $i,SV21: $i] :
( ( ( SV21 = SV40 )
= $true )
| ( ( ( SV21 = SV47 )
| ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV41: $i,SV22: $i,SV64: $i,SV58: $i] :
( ( ( ~ ( on @ SV58 @ SV64 ) )
= $true )
| ( ( ~ ( plane @ SV64 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(346,plain,
! [SV23: $i,SV49: $i,SV65: $i] :
( ( ( ~ ( on @ SV65 @ SV49 ) )
= $true )
| ( ( ~ ( point @ SV65 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 ) )
= $true )
| ( ( on @ SV65 @ SV23 )
= $false )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(347,plain,
! [SV24: $i,SV50: $i,SV66: $i] :
( ( ( ~ ( on @ SV66 @ SV50 ) )
= $true )
| ( ( ~ ( point @ SV66 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 ) )
= $true )
| ( ( on @ SV66 @ SV24 )
= $false )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV25: $i,SV51: $i,SV67: $i] :
( ( ( ~ ( on @ SV67 @ SV51 ) )
= $true )
| ( ( ~ ( point @ SV67 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
= $true )
| ( ( on @ SV67 @ SV25 )
= $false )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(349,plain,
! [SV26: $i,SV52: $i,SV68: $i] :
( ( ( ~ ( on @ SV68 @ SV52 ) )
= $true )
| ( ( ~ ( point @ SV68 )
| ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( on @ SV68 @ SV26 )
= $false )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(350,plain,
! [SV53: $i,SV60: $i,SV27: $i] :
( ( ( SV27 = SV60 )
= $true )
| ( ( ( SV53 = SV60 )
| ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
| ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( SV27 = SV53 )
= $true )
| ( ( point @ SV60 )
= $false )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(351,plain,
! [SV54: $i,SV61: $i,SV28: $i] :
( ( ( SV28 = SV61 )
= $true )
| ( ( ( SV54 = SV61 )
| ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
| ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( SV28 = SV54 )
= $true )
| ( ( point @ SV61 )
= $false )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(352,plain,
! [SV55: $i,SV62: $i,SV29: $i] :
( ( ( SV29 = SV62 )
= $true )
| ( ( ( SV55 = SV62 )
| ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
| ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( SV29 = SV55 )
= $true )
| ( ( point @ SV62 )
= $false )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(353,plain,
! [SV56: $i,SV63: $i,SV30: $i] :
( ( ( SV30 = SV63 )
= $true )
| ( ( ( SV56 = SV63 )
| ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
| ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( SV30 = SV56 )
= $true )
| ( ( point @ SV63 )
= $false )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(354,plain,
! [SV42: $i,SV31: $i,SV59: $i,SV48: $i] :
( ( ( on @ SV48 @ SV59 )
= $false )
| ( ( ~ ( point @ SV31 )
| ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(355,plain,
! [SV35: $i,SV57: $i,SV69: $i,SV5: $i] :
( ( ( on @ SV5 @ SV69 )
= $false )
| ( ( ~ ( on @ SV57 @ SV69 )
| ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(356,plain,
! [SV43: $i,SV36: $i,SV17: $i] :
( ( ( SV17 = SV36 )
= $true )
| ( ( ( SV17 = SV43 )
| ( SV36 = SV43 ) )
= $true )
| ( ( collinear @ SV17 @ SV36 @ SV43 )
= $true )
| ( ( point @ SV43 )
= $false )
| ( ( point @ SV36 )
= $false )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(357,plain,
! [SV44: $i,SV18: $i,SV37: $i] :
( ( ( SV37 = SV18 )
= $true )
| ( ( ( SV37 = SV44 )
| ( SV18 = SV44 ) )
= $true )
| ( ( collinear @ SV37 @ SV18 @ SV44 )
= $true )
| ( ( point @ SV44 )
= $false )
| ( ( point @ SV18 )
= $false )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(358,plain,
! [SV19: $i,SV45: $i,SV38: $i] :
( ( ( SV38 = SV45 )
= $true )
| ( ( ( SV38 = SV19 )
| ( SV45 = SV19 ) )
= $true )
| ( ( collinear @ SV38 @ SV45 @ SV19 )
= $true )
| ( ( point @ SV19 )
= $false )
| ( ( point @ SV45 )
= $false )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(359,plain,
! [SV46: $i,SV39: $i,SV20: $i] :
( ( ( SV20 = SV39 )
= $true )
| ( ( ( SV20 = SV46 )
| ( SV39 = SV46 ) )
= $true )
| ( ( collinear @ SV20 @ SV39 @ SV46 )
= $true )
| ( ( point @ SV46 )
= $false )
| ( ( point @ SV39 )
= $false )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(360,plain,
! [SV40: $i,SV47: $i,SV21: $i] :
( ( ( SV21 = SV47 )
= $true )
| ( ( ( SV40 = SV47 )
| ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(361,plain,
! [SV41: $i,SV22: $i,SV64: $i,SV58: $i] :
( ( ( on @ SV58 @ SV64 )
= $false )
| ( ( ~ ( plane @ SV64 )
| ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(362,plain,
! [SV23: $i,SV49: $i,SV65: $i] :
( ( ( on @ SV65 @ SV49 )
= $false )
| ( ( ~ ( point @ SV65 )
| ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 ) )
= $true )
| ( ( on @ SV65 @ SV23 )
= $false )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(363,plain,
! [SV24: $i,SV50: $i,SV66: $i] :
( ( ( on @ SV66 @ SV50 )
= $false )
| ( ( ~ ( point @ SV66 )
| ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 ) )
= $true )
| ( ( on @ SV66 @ SV24 )
= $false )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(364,plain,
! [SV25: $i,SV51: $i,SV67: $i] :
( ( ( on @ SV67 @ SV51 )
= $false )
| ( ( ~ ( point @ SV67 )
| ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
= $true )
| ( ( on @ SV67 @ SV25 )
= $false )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(365,plain,
! [SV26: $i,SV52: $i,SV68: $i] :
( ( ( on @ SV68 @ SV52 )
= $false )
| ( ( ~ ( point @ SV68 )
| ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( on @ SV68 @ SV26 )
= $false )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(366,plain,
! [SV27: $i,SV60: $i,SV53: $i] :
( ( ( SV53 = SV60 )
= $true )
| ( ( ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
| ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( SV27 = SV60 )
= $true )
| ( ( SV27 = SV53 )
= $true )
| ( ( point @ SV60 )
= $false )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(367,plain,
! [SV28: $i,SV61: $i,SV54: $i] :
( ( ( SV54 = SV61 )
= $true )
| ( ( ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
| ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( SV28 = SV61 )
= $true )
| ( ( SV28 = SV54 )
= $true )
| ( ( point @ SV61 )
= $false )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(368,plain,
! [SV29: $i,SV62: $i,SV55: $i] :
( ( ( SV55 = SV62 )
= $true )
| ( ( ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
| ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( SV29 = SV62 )
= $true )
| ( ( SV29 = SV55 )
= $true )
| ( ( point @ SV62 )
= $false )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(369,plain,
! [SV30: $i,SV63: $i,SV56: $i] :
( ( ( SV56 = SV63 )
= $true )
| ( ( ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
| ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( SV30 = SV63 )
= $true )
| ( ( SV30 = SV56 )
= $true )
| ( ( point @ SV63 )
= $false )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(370,plain,
! [SV59: $i,SV48: $i,SV42: $i,SV31: $i] :
( ( ( ~ ( point @ SV31 ) )
= $true )
| ( ( ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(371,plain,
! [SV35: $i,SV5: $i,SV69: $i,SV57: $i] :
( ( ( ~ ( on @ SV57 @ SV69 ) )
= $true )
| ( ( ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(372,plain,
! [SV36: $i,SV43: $i,SV17: $i] :
( ( ( SV17 = SV43 )
= $true )
| ( ( SV36 = SV43 )
= $true )
| ( ( SV17 = SV36 )
= $true )
| ( ( collinear @ SV17 @ SV36 @ SV43 )
= $true )
| ( ( point @ SV43 )
= $false )
| ( ( point @ SV36 )
= $false )
| ( ( point @ SV17 )
= $false )
| ( ( on @ SV17 @ ( plane_for_points @ SV17 @ SV36 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(373,plain,
! [SV18: $i,SV44: $i,SV37: $i] :
( ( ( SV37 = SV44 )
= $true )
| ( ( SV18 = SV44 )
= $true )
| ( ( SV37 = SV18 )
= $true )
| ( ( collinear @ SV37 @ SV18 @ SV44 )
= $true )
| ( ( point @ SV44 )
= $false )
| ( ( point @ SV18 )
= $false )
| ( ( point @ SV37 )
= $false )
| ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV18 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(374,plain,
! [SV45: $i,SV19: $i,SV38: $i] :
( ( ( SV38 = SV19 )
= $true )
| ( ( SV45 = SV19 )
= $true )
| ( ( SV38 = SV45 )
= $true )
| ( ( collinear @ SV38 @ SV45 @ SV19 )
= $true )
| ( ( point @ SV19 )
= $false )
| ( ( point @ SV45 )
= $false )
| ( ( point @ SV38 )
= $false )
| ( ( on @ SV19 @ ( plane_for_points @ SV38 @ SV45 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(375,plain,
! [SV39: $i,SV46: $i,SV20: $i] :
( ( ( SV20 = SV46 )
= $true )
| ( ( SV39 = SV46 )
= $true )
| ( ( SV20 = SV39 )
= $true )
| ( ( collinear @ SV20 @ SV39 @ SV46 )
= $true )
| ( ( point @ SV46 )
= $false )
| ( ( point @ SV39 )
= $false )
| ( ( point @ SV20 )
= $false )
| ( ( plane @ ( plane_for_points @ SV20 @ SV39 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(376,plain,
! [SV21: $i,SV47: $i,SV40: $i] :
( ( ( SV40 = SV47 )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( on @ SV21 @ SY124 )
| ~ ( on @ SV40 @ SY124 )
| ~ ( on @ SV47 @ SY124 )
| ~ ( plane @ SY124 )
| ! [SY125: $i] :
( ~ ( on @ SV21 @ SY125 )
| ~ ( on @ SV40 @ SY125 )
| ~ ( on @ SV47 @ SY125 )
| ~ ( plane @ SY125 )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(377,plain,
! [SV41: $i,SV58: $i,SV22: $i,SV64: $i] :
( ( ( ~ ( plane @ SV64 ) )
= $true )
| ( ( ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(378,plain,
! [SV49: $i,SV23: $i,SV65: $i] :
( ( ( ~ ( point @ SV65 ) )
= $true )
| ( ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 )
= $true )
| ( ( on @ SV65 @ SV49 )
= $false )
| ( ( on @ SV65 @ SV23 )
= $false )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(379,plain,
! [SV50: $i,SV24: $i,SV66: $i] :
( ( ( ~ ( point @ SV66 ) )
= $true )
| ( ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 )
= $true )
| ( ( on @ SV66 @ SV50 )
= $false )
| ( ( on @ SV66 @ SV24 )
= $false )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(380,plain,
! [SV51: $i,SV25: $i,SV67: $i] :
( ( ( ~ ( point @ SV67 ) )
= $true )
| ( ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) )
= $true )
| ( ( on @ SV67 @ SV51 )
= $false )
| ( ( on @ SV67 @ SV25 )
= $false )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(381,plain,
! [SV52: $i,SV26: $i,SV68: $i] :
( ( ( ~ ( point @ SV68 ) )
= $true )
| ( ( ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( on @ SV68 @ SV52 )
= $false )
| ( ( on @ SV68 @ SV26 )
= $false )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(382,plain,
! [SV60: $i,SV53: $i,SV27: $i] :
( ( ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( SV53 = SV60 )
= $true )
| ( ( SV27 = SV60 )
= $true )
| ( ( SV27 = SV53 )
= $true )
| ( ( point @ SV60 )
= $false )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(383,plain,
! [SV61: $i,SV28: $i,SV54: $i] :
( ( ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( SV54 = SV61 )
= $true )
| ( ( SV28 = SV61 )
= $true )
| ( ( SV28 = SV54 )
= $true )
| ( ( point @ SV61 )
= $false )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(384,plain,
! [SV55: $i,SV29: $i,SV62: $i] :
( ( ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( SV55 = SV62 )
= $true )
| ( ( SV29 = SV62 )
= $true )
| ( ( SV29 = SV55 )
= $true )
| ( ( point @ SV62 )
= $false )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(385,plain,
! [SV63: $i,SV56: $i,SV30: $i] :
( ( ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( ~ ( collinear @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( SV56 = SV63 )
= $true )
| ( ( SV30 = SV63 )
= $true )
| ( ( SV30 = SV56 )
= $true )
| ( ( point @ SV63 )
= $false )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(386,plain,
! [SV59: $i,SV48: $i,SV42: $i,SV31: $i] :
( ( ( point @ SV31 )
= $false )
| ( ( ~ ( point @ SV42 )
| ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(387,plain,
! [SV35: $i,SV5: $i,SV69: $i,SV57: $i] :
( ( ( on @ SV57 @ SV69 )
= $false )
| ( ( ~ ( point @ SV5 )
| ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(388,plain,
! [SV47: $i,SV40: $i,SV70: $i,SV21: $i] :
( ( ( ~ ( on @ SV21 @ SV70 )
| ~ ( on @ SV40 @ SV70 )
| ~ ( on @ SV47 @ SV70 )
| ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(389,plain,
! [SV41: $i,SV58: $i,SV22: $i,SV64: $i] :
( ( ( plane @ SV64 )
= $false )
| ( ( ~ ( point @ SV22 )
| ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(390,plain,
! [SV49: $i,SV23: $i,SV65: $i] :
( ( ( point @ SV65 )
= $false )
| ( ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV23 )
= $true )
| ( ( on @ SV65 @ SV49 )
= $false )
| ( ( on @ SV65 @ SV23 )
= $false )
| ( ( SV23 = SV49 )
= $true )
| ( ( plane @ SV49 )
= $false )
| ( ( plane @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(391,plain,
! [SV50: $i,SV24: $i,SV66: $i] :
( ( ( point @ SV66 )
= $false )
| ( ( on @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) @ SV50 )
= $true )
| ( ( on @ SV66 @ SV50 )
= $false )
| ( ( on @ SV66 @ SV24 )
= $false )
| ( ( SV24 = SV50 )
= $true )
| ( ( plane @ SV50 )
= $false )
| ( ( plane @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(392,plain,
! [SV51: $i,SV25: $i,SV67: $i] :
( ( ( point @ SV67 )
= $false )
| ( ( point @ ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) )
= $true )
| ( ( on @ SV67 @ SV51 )
= $false )
| ( ( on @ SV67 @ SV25 )
= $false )
| ( ( SV25 = SV51 )
= $true )
| ( ( plane @ SV51 )
= $false )
| ( ( plane @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(393,plain,
! [SV52: $i,SV26: $i,SV68: $i] :
( ( ( point @ SV68 )
= $false )
| ( ( ( SV68
!= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) ) )
= $true )
| ( ( on @ SV68 @ SV52 )
= $false )
| ( ( on @ SV68 @ SV26 )
= $false )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(394,plain,
! [SV60: $i,SV53: $i,SV27: $i] :
( ( ( collinear @ SV27 @ SV53 @ SV60 )
= $false )
| ( ( on @ SV27 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
= $true )
| ( ( SV53 = SV60 )
= $true )
| ( ( SV27 = SV60 )
= $true )
| ( ( SV27 = SV53 )
= $true )
| ( ( point @ SV60 )
= $false )
| ( ( point @ SV53 )
= $false )
| ( ( point @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(395,plain,
! [SV61: $i,SV54: $i,SV28: $i] :
( ( ( collinear @ SV28 @ SV54 @ SV61 )
= $false )
| ( ( on @ SV54 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
= $true )
| ( ( SV54 = SV61 )
= $true )
| ( ( SV28 = SV61 )
= $true )
| ( ( SV28 = SV54 )
= $true )
| ( ( point @ SV61 )
= $false )
| ( ( point @ SV54 )
= $false )
| ( ( point @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(396,plain,
! [SV62: $i,SV55: $i,SV29: $i] :
( ( ( collinear @ SV29 @ SV55 @ SV62 )
= $false )
| ( ( on @ SV62 @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
= $true )
| ( ( SV55 = SV62 )
= $true )
| ( ( SV29 = SV62 )
= $true )
| ( ( SV29 = SV55 )
= $true )
| ( ( point @ SV62 )
= $false )
| ( ( point @ SV55 )
= $false )
| ( ( point @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(397,plain,
! [SV63: $i,SV56: $i,SV30: $i] :
( ( ( collinear @ SV30 @ SV56 @ SV63 )
= $false )
| ( ( line @ ( line_through_3_points @ SV30 @ SV56 @ SV63 ) )
= $true )
| ( ( SV56 = SV63 )
= $true )
| ( ( SV30 = SV63 )
= $true )
| ( ( SV30 = SV56 )
= $true )
| ( ( point @ SV63 )
= $false )
| ( ( point @ SV56 )
= $false )
| ( ( point @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(398,plain,
! [SV59: $i,SV31: $i,SV48: $i,SV42: $i] :
( ( ( ~ ( point @ SV42 ) )
= $true )
| ( ( ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(399,plain,
! [SV69: $i,SV35: $i,SV57: $i,SV5: $i] :
( ( ( ~ ( point @ SV5 ) )
= $true )
| ( ( ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(400,plain,
! [SV47: $i,SV40: $i,SV70: $i,SV21: $i] :
( ( ( ~ ( on @ SV21 @ SV70 ) )
= $true )
| ( ( ~ ( on @ SV40 @ SV70 )
| ~ ( on @ SV47 @ SV70 )
| ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(401,plain,
! [SV64: $i,SV41: $i,SV58: $i,SV22: $i] :
( ( ( ~ ( point @ SV22 ) )
= $true )
| ( ( ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(402,plain,
! [SV52: $i,SV26: $i,SV68: $i] :
( ( ( SV68
= ( common_point_on_planes @ SV26 @ SV52 @ SV68 ) )
= $false )
| ( ( point @ SV68 )
= $false )
| ( ( on @ SV68 @ SV52 )
= $false )
| ( ( on @ SV68 @ SV26 )
= $false )
| ( ( SV26 = SV52 )
= $true )
| ( ( plane @ SV52 )
= $false )
| ( ( plane @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(403,plain,
! [SV59: $i,SV31: $i,SV48: $i,SV42: $i] :
( ( ( point @ SV42 )
= $false )
| ( ( ~ ( point @ SV48 )
| ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(404,plain,
! [SV69: $i,SV35: $i,SV57: $i,SV5: $i] :
( ( ( point @ SV5 )
= $false )
| ( ( ~ ( point @ SV57 )
| ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(405,plain,
! [SV47: $i,SV40: $i,SV70: $i,SV21: $i] :
( ( ( on @ SV21 @ SV70 )
= $false )
| ( ( ~ ( on @ SV40 @ SV70 )
| ~ ( on @ SV47 @ SV70 )
| ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(406,plain,
! [SV64: $i,SV41: $i,SV58: $i,SV22: $i] :
( ( ( point @ SV22 )
= $false )
| ( ( ~ ( point @ SV58 )
| ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(407,plain,
! [SV59: $i,SV42: $i,SV31: $i,SV48: $i] :
( ( ( ~ ( point @ SV48 ) )
= $true )
| ( ( ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( point @ SV42 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(408,plain,
! [SV5: $i,SV69: $i,SV35: $i,SV57: $i] :
( ( ( ~ ( point @ SV57 ) )
= $true )
| ( ( ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( point @ SV5 )
= $false )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(409,plain,
! [SV21: $i,SV47: $i,SV70: $i,SV40: $i] :
( ( ( ~ ( on @ SV40 @ SV70 ) )
= $true )
| ( ( ~ ( on @ SV47 @ SV70 )
| ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(410,plain,
! [SV64: $i,SV22: $i,SV41: $i,SV58: $i] :
( ( ( ~ ( point @ SV58 ) )
= $true )
| ( ( ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( point @ SV22 )
= $false )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(411,plain,
! [SV59: $i,SV42: $i,SV31: $i,SV48: $i] :
( ( ( point @ SV48 )
= $false )
| ( ( ( SV31 = SV42 )
| ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( point @ SV42 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(412,plain,
! [SV5: $i,SV69: $i,SV35: $i,SV57: $i] :
( ( ( point @ SV57 )
= $false )
| ( ( ~ ( line @ SV35 )
| ~ ( line @ SV69 ) )
= $true )
| ( ( point @ SV5 )
= $false )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(413,plain,
! [SV21: $i,SV47: $i,SV70: $i,SV40: $i] :
( ( ( on @ SV40 @ SV70 )
= $false )
| ( ( ~ ( on @ SV47 @ SV70 )
| ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(414,plain,
! [SV64: $i,SV22: $i,SV41: $i,SV58: $i] :
( ( ( point @ SV58 )
= $false )
| ( ( ~ ( line @ SV41 )
| ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( point @ SV22 )
= $false )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(415,plain,
! [SV59: $i,SV48: $i,SV42: $i,SV31: $i] :
( ( ( SV31 = SV42 )
= $true )
| ( ( ( SV31 = SV48 )
| ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( point @ SV48 )
= $false )
| ( ( point @ SV42 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(416,plain,
! [SV5: $i,SV57: $i,SV69: $i,SV35: $i] :
( ( ( ~ ( line @ SV35 ) )
= $true )
| ( ( ~ ( line @ SV69 ) )
= $true )
| ( ( point @ SV57 )
= $false )
| ( ( point @ SV5 )
= $false )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(417,plain,
! [SV40: $i,SV21: $i,SV70: $i,SV47: $i] :
( ( ( ~ ( on @ SV47 @ SV70 ) )
= $true )
| ( ( ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(418,plain,
! [SV64: $i,SV58: $i,SV22: $i,SV41: $i] :
( ( ( ~ ( line @ SV41 ) )
= $true )
| ( ( ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( point @ SV58 )
= $false )
| ( ( point @ SV22 )
= $false )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(419,plain,
! [SV59: $i,SV42: $i,SV48: $i,SV31: $i] :
( ( ( SV31 = SV48 )
= $true )
| ( ( ( SV42 = SV48 )
| ~ ( line @ SV59 ) )
= $true )
| ( ( SV31 = SV42 )
= $true )
| ( ( point @ SV48 )
= $false )
| ( ( point @ SV42 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(420,plain,
! [SV5: $i,SV57: $i,SV69: $i,SV35: $i] :
( ( ( line @ SV35 )
= $false )
| ( ( ~ ( line @ SV69 ) )
= $true )
| ( ( point @ SV57 )
= $false )
| ( ( point @ SV5 )
= $false )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(421,plain,
! [SV40: $i,SV21: $i,SV70: $i,SV47: $i] :
( ( ( on @ SV47 @ SV70 )
= $false )
| ( ( ~ ( plane @ SV70 )
| ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(422,plain,
! [SV64: $i,SV58: $i,SV22: $i,SV41: $i] :
( ( ( line @ SV41 )
= $false )
| ( ( ( SV22 = SV58 )
| ( on @ SV41 @ SV64 ) )
= $true )
| ( ( point @ SV58 )
= $false )
| ( ( point @ SV22 )
= $false )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(423,plain,
! [SV31: $i,SV59: $i,SV48: $i,SV42: $i] :
( ( ( SV42 = SV48 )
= $true )
| ( ( ~ ( line @ SV59 ) )
= $true )
| ( ( SV31 = SV48 )
= $true )
| ( ( SV31 = SV42 )
= $true )
| ( ( point @ SV48 )
= $false )
| ( ( point @ SV42 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(424,plain,
! [SV5: $i,SV57: $i,SV35: $i,SV69: $i] :
( ( ( line @ SV69 )
= $false )
| ( ( line @ SV35 )
= $false )
| ( ( point @ SV57 )
= $false )
| ( ( point @ SV5 )
= $false )
| ( ( on @ SV57 @ SV69 )
= $false )
| ( ( on @ SV5 @ SV69 )
= $false )
| ( ( SV35 = SV69 )
= $true )
| ( ( on @ SV57 @ SV35 )
= $false )
| ( ( SV5 = SV57 )
= $true )
| ( ( on @ SV5 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(425,plain,
! [SV47: $i,SV40: $i,SV21: $i,SV70: $i] :
( ( ( ~ ( plane @ SV70 ) )
= $true )
| ( ( ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(426,plain,
! [SV64: $i,SV41: $i,SV58: $i,SV22: $i] :
( ( ( SV22 = SV58 )
= $true )
| ( ( on @ SV41 @ SV64 )
= $true )
| ( ( line @ SV41 )
= $false )
| ( ( point @ SV58 )
= $false )
| ( ( point @ SV22 )
= $false )
| ( ( plane @ SV64 )
= $false )
| ( ( on @ SV58 @ SV64 )
= $false )
| ( ( on @ SV22 @ SV64 )
= $false )
| ( ( on @ SV58 @ SV41 )
= $false )
| ( ( on @ SV22 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(427,plain,
! [SV31: $i,SV48: $i,SV42: $i,SV59: $i] :
( ( ( line @ SV59 )
= $false )
| ( ( SV42 = SV48 )
= $true )
| ( ( SV31 = SV48 )
= $true )
| ( ( SV31 = SV42 )
= $true )
| ( ( point @ SV48 )
= $false )
| ( ( point @ SV42 )
= $false )
| ( ( point @ SV31 )
= $false )
| ( ( on @ SV48 @ SV59 )
= $false )
| ( ( on @ SV42 @ SV59 )
= $false )
| ( ( on @ SV31 @ SV59 )
= $false )
| ( ( collinear @ SV31 @ SV42 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(428,plain,
! [SV47: $i,SV40: $i,SV21: $i,SV70: $i] :
( ( ( plane @ SV70 )
= $false )
| ( ( ! [SY137: $i] :
( ~ ( on @ SV21 @ SY137 )
| ~ ( on @ SV40 @ SY137 )
| ~ ( on @ SV47 @ SY137 )
| ~ ( plane @ SY137 )
| ( SV70 = SY137 ) ) )
= $true )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(429,plain,
! [SV70: $i,SV47: $i,SV40: $i,SV71: $i,SV21: $i] :
( ( ( ~ ( on @ SV21 @ SV71 )
| ~ ( on @ SV40 @ SV71 )
| ~ ( on @ SV47 @ SV71 )
| ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(430,plain,
! [SV70: $i,SV47: $i,SV40: $i,SV71: $i,SV21: $i] :
( ( ( ~ ( on @ SV21 @ SV71 ) )
= $true )
| ( ( ~ ( on @ SV40 @ SV71 )
| ~ ( on @ SV47 @ SV71 )
| ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(431,plain,
! [SV70: $i,SV47: $i,SV40: $i,SV71: $i,SV21: $i] :
( ( ( on @ SV21 @ SV71 )
= $false )
| ( ( ~ ( on @ SV40 @ SV71 )
| ~ ( on @ SV47 @ SV71 )
| ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(432,plain,
! [SV21: $i,SV70: $i,SV47: $i,SV71: $i,SV40: $i] :
( ( ( ~ ( on @ SV40 @ SV71 ) )
= $true )
| ( ( ~ ( on @ SV47 @ SV71 )
| ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( on @ SV21 @ SV71 )
= $false )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(433,plain,
! [SV21: $i,SV70: $i,SV47: $i,SV71: $i,SV40: $i] :
( ( ( on @ SV40 @ SV71 )
= $false )
| ( ( ~ ( on @ SV47 @ SV71 )
| ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( on @ SV21 @ SV71 )
= $false )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(434,plain,
! [SV21: $i,SV40: $i,SV70: $i,SV71: $i,SV47: $i] :
( ( ( ~ ( on @ SV47 @ SV71 ) )
= $true )
| ( ( ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( on @ SV40 @ SV71 )
= $false )
| ( ( on @ SV21 @ SV71 )
= $false )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(435,plain,
! [SV21: $i,SV40: $i,SV70: $i,SV71: $i,SV47: $i] :
( ( ( on @ SV47 @ SV71 )
= $false )
| ( ( ~ ( plane @ SV71 )
| ( SV70 = SV71 ) )
= $true )
| ( ( on @ SV40 @ SV71 )
= $false )
| ( ( on @ SV21 @ SV71 )
= $false )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(436,plain,
! [SV21: $i,SV40: $i,SV47: $i,SV70: $i,SV71: $i] :
( ( ( ~ ( plane @ SV71 ) )
= $true )
| ( ( SV70 = SV71 )
= $true )
| ( ( on @ SV47 @ SV71 )
= $false )
| ( ( on @ SV40 @ SV71 )
= $false )
| ( ( on @ SV21 @ SV71 )
= $false )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(437,plain,
! [SV21: $i,SV40: $i,SV47: $i,SV70: $i,SV71: $i] :
( ( ( plane @ SV71 )
= $false )
| ( ( SV70 = SV71 )
= $true )
| ( ( on @ SV47 @ SV71 )
= $false )
| ( ( on @ SV40 @ SV71 )
= $false )
| ( ( on @ SV21 @ SV71 )
= $false )
| ( ( plane @ SV70 )
= $false )
| ( ( on @ SV47 @ SV70 )
= $false )
| ( ( on @ SV40 @ SV70 )
= $false )
| ( ( on @ SV21 @ SV70 )
= $false )
| ( ( SV40 = SV47 )
= $true )
| ( ( SV21 = SV47 )
= $true )
| ( ( SV21 = SV40 )
= $true )
| ( ( collinear @ SV21 @ SV40 @ SV47 )
= $true )
| ( ( point @ SV47 )
= $false )
| ( ( point @ SV40 )
= $false )
| ( ( point @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(438,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[85,437,427,426,424,402,397,396,395,394,392,391,390,375,374,373,372,274,273,272,218,217,216,196,194,193,192,189,188,187,186,181,149,97]) ).
thf(439,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO076-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 09:31:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.41
% 0.20/0.41 No.of.Axioms: 33
% 0.20/0.41
% 0.20/0.41 Length.of.Defs: 0
% 0.20/0.41
% 0.20/0.41 Contains.Choice.Funs: false
% 0.20/0.44 .
% 0.20/0.48 (rf:0,axioms:33,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:35,loop_count:0,foatp_calls:0,translation:fof_full).......................
% 0.49/1.00
% 0.49/1.00 ********************************
% 0.49/1.00 * All subproblems solved! *
% 0.49/1.00 ********************************
% 0.49/1.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:33,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:438,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.91/1.12
% 0.91/1.12 %**** Beginning of derivation protocol ****
% 0.91/1.12 % SZS output start CNFRefutation
% See solution above
% 0.91/1.12
% 0.91/1.12 %**** End of derivation protocol ****
% 0.91/1.12 %**** no. of clauses in derivation: 439 ****
% 0.91/1.12 %**** clause counter: 438 ****
% 0.91/1.12
% 0.91/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:33,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:438,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------