TSTP Solution File: GEO077-4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GEO077-4 : 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 : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 05:06:49 EDT 2022

% Result   : Unsatisfiable 8.67s 8.88s
% Output   : CNFRefutation 8.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  489 ( 171 unt;  19 typ;   0 def)
%            Number of atoms       : 6243 (2342 equ;   0 cnn)
%            Maximal formula atoms :   16 (  13 avg)
%            Number of connectives : 8503 (1315   ~;2775   |;   0   &;4413   @)
%                                         (   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     :   22 (  19 usr;   7 con; 0-3 aty)
%            Number of variables   : 1232 (   0   ^1232   !;   0   ?;1232   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a_line,type,
    a_line: $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_point1,type,
    point1: $i ).

thf(tp_point2,type,
    point2: $i ).

thf(tp_point3,type,
    point3: $i ).

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,
    point2 != point3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_not_point3) ).

thf(33,axiom,
    point1 != point3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point3) ).

thf(34,axiom,
    point1 != point2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point2) ).

thf(35,axiom,
    ~ ( on @ point3 @ a_line ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3_not_on_line) ).

thf(36,axiom,
    on @ point2 @ a_line,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_on_line) ).

thf(37,axiom,
    on @ point1 @ a_line,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_on_line) ).

thf(38,axiom,
    line @ a_line,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',line) ).

thf(39,axiom,
    point @ point3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3) ).

thf(40,axiom,
    point @ point2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2) ).

thf(41,axiom,
    point @ point1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1) ).

thf(42,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(43,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[42]) ).

thf(44,negated_conjecture,
    collinear @ point1 @ point2 @ point3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_points_noncollinear) ).

thf(45,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[43]) ).

thf(46,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(47,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(48,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(49,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(50,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(51,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(52,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(53,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(54,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(55,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(56,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(57,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(58,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(59,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(60,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(61,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ( point @ ( point_not_on_plane @ Z1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(62,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ~ ( on @ ( point_not_on_plane @ Z1 ) @ Z1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(63,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ( point @ ( point_on_plane @ Z1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(64,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ( on @ ( point_on_plane @ Z1 ) @ Z1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(65,plain,
    ( ( line @ at_least_one_line )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(66,plain,
    ( ( ! [Y1: $i] :
          ( ( point @ ( point_not_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(67,plain,
    ( ( ! [Y1: $i] :
          ( ~ ( on @ ( point_not_on_line @ Y1 ) @ Y1 )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(68,plain,
    ( ( ! [Y1: $i] :
          ( ( ( point_1_on_line @ Y1 )
           != ( point_2_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(69,plain,
    ( ( ! [Y1: $i] :
          ( ( point @ ( point_2_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(70,plain,
    ( ( ! [Y1: $i] :
          ( ( point @ ( point_1_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(71,plain,
    ( ( ! [Y1: $i] :
          ( ( on @ ( point_2_on_line @ Y1 ) @ Y1 )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(72,plain,
    ( ( ! [Y1: $i] :
          ( ( on @ ( point_1_on_line @ Y1 ) @ Y1 )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(73,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(74,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(75,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(76,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(77,plain,
    ( ( ( point2 != point3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(78,plain,
    ( ( ( point1 != point3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(79,plain,
    ( ( ( point1 != point2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(80,plain,
    ( ( ~ ( on @ point3 @ a_line ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(81,plain,
    ( ( on @ point2 @ a_line )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(82,plain,
    ( ( on @ point1 @ a_line )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(83,plain,
    ( ( line @ a_line )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(84,plain,
    ( ( point @ point3 )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(85,plain,
    ( ( point @ point2 )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(86,plain,
    ( ( point @ point1 )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(87,plain,
    ( ( collinear @ point1 @ point2 @ point3 )
    = $true ),
    inference(unfold_def,[status(thm)],[44]) ).

thf(88,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[45]) ).

thf(89,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)],[46]) ).

thf(90,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)],[47]) ).

thf(91,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)],[48]) ).

thf(92,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)],[49]) ).

thf(93,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)],[50]) ).

thf(94,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)],[51]) ).

thf(95,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)],[52]) ).

thf(96,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)],[53]) ).

thf(97,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)],[54]) ).

thf(98,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)],[55]) ).

thf(99,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)],[56]) ).

thf(100,plain,
    ( ( ! [Y1: $i] :
          ( ( ( point_1_on_line @ Y1 )
           != ( point_2_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[68]) ).

thf(101,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)],[73]) ).

thf(102,plain,
    ( ( ( point2 != point3 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[77]) ).

thf(103,plain,
    ( ( ( point1 != point3 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[78]) ).

thf(104,plain,
    ( ( ( point1 != point2 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[79]) ).

thf(105,plain,
    ( ( collinear @ point1 @ point2 @ point3 )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(106,plain,
    ( ( point @ point1 )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(107,plain,
    ( ( point @ point2 )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(108,plain,
    ( ( point @ point3 )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(109,plain,
    ( ( line @ a_line )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(110,plain,
    ( ( on @ point1 @ a_line )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(111,plain,
    ( ( on @ point2 @ a_line )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(112,plain,
    ( ( ~ ( on @ point3 @ a_line ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(113,plain,
    ( ( ( point1 != point2 ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(114,plain,
    ( ( ( point1 != point3 ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(115,plain,
    ( ( ( point2 != point3 ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(116,plain,
    ( ( ! [Z1: $i,Z2: $i] :
          ( ( on @ Z1 @ ( line_from_to @ Z1 @ Z2 ) )
          | ( Z1 = Z2 )
          | ~ ( point @ Z1 )
          | ~ ( point @ Z2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[76]) ).

thf(117,plain,
    ( ( ! [Z2: $i,Z1: $i] :
          ( ( on @ Z2 @ ( line_from_to @ Z1 @ Z2 ) )
          | ( Z1 = Z2 )
          | ~ ( point @ Z1 )
          | ~ ( point @ Z2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(118,plain,
    ( ( ! [Z1: $i,Z2: $i] :
          ( ( line @ ( line_from_to @ Z1 @ Z2 ) )
          | ( Z1 = Z2 )
          | ~ ( point @ Z1 )
          | ~ ( point @ Z2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(119,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)],[101]) ).

thf(120,plain,
    ( ( ! [Y1: $i] :
          ( ( on @ ( point_1_on_line @ Y1 ) @ Y1 )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(121,plain,
    ( ( ! [Y1: $i] :
          ( ( on @ ( point_2_on_line @ Y1 ) @ Y1 )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(122,plain,
    ( ( ! [Y1: $i] :
          ( ( point @ ( point_1_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(123,plain,
    ( ( ! [Y1: $i] :
          ( ( point @ ( point_2_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(124,plain,
    ( ( ! [Y1: $i] :
          ( ( ( point_1_on_line @ Y1 )
           != ( point_2_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(125,plain,
    ( ( ! [Y1: $i] :
          ( ~ ( on @ ( point_not_on_line @ Y1 ) @ Y1 )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(126,plain,
    ( ( ! [Y1: $i] :
          ( ( point @ ( point_not_on_line @ Y1 ) )
          | ~ ( line @ Y1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(127,plain,
    ( ( line @ at_least_one_line )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(128,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ( on @ ( point_on_plane @ Z1 ) @ Z1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(129,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ( point @ ( point_on_plane @ Z1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(130,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ~ ( on @ ( point_not_on_plane @ Z1 ) @ Z1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[62]) ).

thf(131,plain,
    ( ( ! [Z1: $i] :
          ( ~ ( plane @ Z1 )
          | ( point @ ( point_not_on_plane @ Z1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[61]) ).

thf(132,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)],[60]) ).

thf(133,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)],[59]) ).

thf(134,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)],[58]) ).

thf(135,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)],[57]) ).

thf(136,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)],[99]) ).

thf(137,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)],[98]) ).

thf(138,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)],[97]) ).

thf(139,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)],[96]) ).

thf(140,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)],[95]) ).

thf(141,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)],[94]) ).

thf(142,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)],[93]) ).

thf(143,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)],[92]) ).

thf(144,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)],[91]) ).

thf(145,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)],[90]) ).

thf(146,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)],[89]) ).

thf(147,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(148,plain,
    ( ( on @ point3 @ a_line )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(149,plain,
    ( ( point1 = point2 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(150,plain,
    ( ( point1 = point3 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(151,plain,
    ( ( point2 = point3 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(152,plain,
    ! [SV1: $i] :
      ( ( ! [SY70: $i] :
            ( ( on @ SV1 @ ( line_from_to @ SV1 @ SY70 ) )
            | ( SV1 = SY70 )
            | ~ ( point @ SV1 )
            | ~ ( point @ SY70 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(153,plain,
    ! [SV2: $i] :
      ( ( ! [SY71: $i] :
            ( ( on @ SV2 @ ( line_from_to @ SY71 @ SV2 ) )
            | ( SY71 = SV2 )
            | ~ ( point @ SY71 )
            | ~ ( point @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(154,plain,
    ! [SV3: $i] :
      ( ( ! [SY72: $i] :
            ( ( line @ ( line_from_to @ SV3 @ SY72 ) )
            | ( SV3 = SY72 )
            | ~ ( point @ SV3 )
            | ~ ( point @ SY72 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(155,plain,
    ! [SV4: $i] :
      ( ( ! [SY73: $i] :
            ( ~ ( on @ SV4 @ SY73 )
            | ! [SY74: $i] :
                ( ( SV4 = SY74 )
                | ~ ( on @ SY74 @ SY73 )
                | ! [SY75: $i] :
                    ( ( SY73 = SY75 )
                    | ~ ( on @ SV4 @ SY75 )
                    | ~ ( on @ SY74 @ SY75 )
                    | ~ ( point @ SV4 )
                    | ~ ( point @ SY74 )
                    | ~ ( line @ SY73 )
                    | ~ ( line @ SY75 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(156,plain,
    ! [SV5: $i] :
      ( ( ( on @ ( point_1_on_line @ SV5 ) @ SV5 )
        | ~ ( line @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(157,plain,
    ! [SV6: $i] :
      ( ( ( on @ ( point_2_on_line @ SV6 ) @ SV6 )
        | ~ ( line @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(158,plain,
    ! [SV7: $i] :
      ( ( ( point @ ( point_1_on_line @ SV7 ) )
        | ~ ( line @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(159,plain,
    ! [SV8: $i] :
      ( ( ( point @ ( point_2_on_line @ SV8 ) )
        | ~ ( line @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(160,plain,
    ! [SV9: $i] :
      ( ( ( ( point_1_on_line @ SV9 )
         != ( point_2_on_line @ SV9 ) )
        | ~ ( line @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(161,plain,
    ! [SV10: $i] :
      ( ( ~ ( on @ ( point_not_on_line @ SV10 ) @ SV10 )
        | ~ ( line @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(162,plain,
    ! [SV11: $i] :
      ( ( ( point @ ( point_not_on_line @ SV11 ) )
        | ~ ( line @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(163,plain,
    ! [SV12: $i] :
      ( ( ~ ( plane @ SV12 )
        | ( on @ ( point_on_plane @ SV12 ) @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(164,plain,
    ! [SV13: $i] :
      ( ( ~ ( plane @ SV13 )
        | ( point @ ( point_on_plane @ SV13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(165,plain,
    ! [SV14: $i] :
      ( ( ~ ( plane @ SV14 )
        | ~ ( on @ ( point_not_on_plane @ SV14 ) @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(166,plain,
    ! [SV15: $i] :
      ( ( ~ ( plane @ SV15 )
        | ( point @ ( point_not_on_plane @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(167,plain,
    ! [SV16: $i] :
      ( ( ! [SY76: $i,SY77: $i] :
            ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SY76 @ SY77 ) )
            | ~ ( point @ SV16 )
            | ~ ( point @ SY76 )
            | ~ ( point @ SY77 )
            | ( collinear @ SV16 @ SY76 @ SY77 )
            | ( SV16 = SY76 )
            | ( SV16 = SY77 )
            | ( SY76 = SY77 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(168,plain,
    ! [SV17: $i] :
      ( ( ! [SY78: $i,SY79: $i] :
            ( ( on @ SV17 @ ( plane_for_points @ SY78 @ SV17 @ SY79 ) )
            | ~ ( point @ SY78 )
            | ~ ( point @ SV17 )
            | ~ ( point @ SY79 )
            | ( collinear @ SY78 @ SV17 @ SY79 )
            | ( SY78 = SV17 )
            | ( SY78 = SY79 )
            | ( SV17 = SY79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(169,plain,
    ! [SV18: $i] :
      ( ( ! [SY80: $i,SY81: $i] :
            ( ( on @ SV18 @ ( plane_for_points @ SY80 @ SY81 @ SV18 ) )
            | ~ ( point @ SY80 )
            | ~ ( point @ SY81 )
            | ~ ( point @ SV18 )
            | ( collinear @ SY80 @ SY81 @ SV18 )
            | ( SY80 = SY81 )
            | ( SY80 = SV18 )
            | ( SY81 = SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(170,plain,
    ! [SV19: $i] :
      ( ( ! [SY82: $i,SY83: $i] :
            ( ( plane @ ( plane_for_points @ SV19 @ SY82 @ SY83 ) )
            | ~ ( point @ SV19 )
            | ~ ( point @ SY82 )
            | ~ ( point @ SY83 )
            | ( collinear @ SV19 @ SY82 @ SY83 )
            | ( SV19 = SY82 )
            | ( SV19 = SY83 )
            | ( SY82 = SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(171,plain,
    ! [SV20: $i] :
      ( ( ! [SY84: $i,SY85: $i] :
            ( ~ ( point @ SV20 )
            | ~ ( point @ SY84 )
            | ~ ( point @ SY85 )
            | ( collinear @ SV20 @ SY84 @ SY85 )
            | ( SV20 = SY84 )
            | ( SV20 = SY85 )
            | ( SY84 = SY85 )
            | ! [SY86: $i] :
                ( ~ ( on @ SV20 @ SY86 )
                | ~ ( on @ SY84 @ SY86 )
                | ~ ( on @ SY85 @ SY86 )
                | ~ ( plane @ SY86 )
                | ! [SY87: $i] :
                    ( ~ ( on @ SV20 @ SY87 )
                    | ~ ( on @ SY84 @ SY87 )
                    | ~ ( on @ SY85 @ SY87 )
                    | ~ ( plane @ SY87 )
                    | ( SY86 = SY87 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(172,plain,
    ! [SV21: $i] :
      ( ( ! [SY88: $i] :
            ( ~ ( on @ SV21 @ SY88 )
            | ! [SY89: $i] :
                ( ~ ( on @ SY89 @ SY88 )
                | ! [SY90: $i] :
                    ( ~ ( on @ SV21 @ SY90 )
                    | ~ ( on @ SY89 @ SY90 )
                    | ~ ( plane @ SY90 )
                    | ~ ( point @ SV21 )
                    | ~ ( point @ SY89 )
                    | ~ ( line @ SY88 )
                    | ( SV21 = SY89 )
                    | ( on @ SY88 @ SY90 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(173,plain,
    ! [SV22: $i] :
      ( ( ~ ( plane @ SV22 )
        | ! [SY91: $i] :
            ( ~ ( plane @ SY91 )
            | ( SV22 = SY91 )
            | ! [SY92: $i] :
                ( ~ ( on @ SY92 @ SV22 )
                | ~ ( on @ SY92 @ SY91 )
                | ~ ( point @ SY92 )
                | ( on @ ( common_point_on_planes @ SV22 @ SY91 @ SY92 ) @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(174,plain,
    ! [SV23: $i] :
      ( ( ~ ( plane @ SV23 )
        | ! [SY93: $i] :
            ( ~ ( plane @ SY93 )
            | ( SV23 = SY93 )
            | ! [SY94: $i] :
                ( ~ ( on @ SY94 @ SV23 )
                | ~ ( on @ SY94 @ SY93 )
                | ~ ( point @ SY94 )
                | ( on @ ( common_point_on_planes @ SV23 @ SY93 @ SY94 ) @ SY93 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(175,plain,
    ! [SV24: $i] :
      ( ( ~ ( plane @ SV24 )
        | ! [SY95: $i] :
            ( ~ ( plane @ SY95 )
            | ( SV24 = SY95 )
            | ! [SY96: $i] :
                ( ~ ( on @ SY96 @ SV24 )
                | ~ ( on @ SY96 @ SY95 )
                | ~ ( point @ SY96 )
                | ( point @ ( common_point_on_planes @ SV24 @ SY95 @ SY96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(176,plain,
    ! [SV25: $i] :
      ( ( ~ ( plane @ SV25 )
        | ! [SY97: $i] :
            ( ~ ( plane @ SY97 )
            | ( SV25 = SY97 )
            | ! [SY98: $i] :
                ( ~ ( on @ SY98 @ SV25 )
                | ~ ( on @ SY98 @ SY97 )
                | ~ ( point @ SY98 )
                | ( SY98
                 != ( common_point_on_planes @ SV25 @ SY97 @ SY98 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(177,plain,
    ! [SV26: $i] :
      ( ( ~ ( point @ SV26 )
        | ! [SY99: $i] :
            ( ~ ( point @ SY99 )
            | ! [SY100: $i] :
                ( ~ ( point @ SY100 )
                | ( SV26 = SY99 )
                | ( SV26 = SY100 )
                | ( SY99 = SY100 )
                | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SY99 @ SY100 ) )
                | ~ ( collinear @ SV26 @ SY99 @ SY100 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(178,plain,
    ! [SV27: $i] :
      ( ( ~ ( point @ SV27 )
        | ! [SY101: $i] :
            ( ~ ( point @ SY101 )
            | ! [SY102: $i] :
                ( ~ ( point @ SY102 )
                | ( SV27 = SY101 )
                | ( SV27 = SY102 )
                | ( SY101 = SY102 )
                | ( on @ SY101 @ ( line_through_3_points @ SV27 @ SY101 @ SY102 ) )
                | ~ ( collinear @ SV27 @ SY101 @ SY102 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(179,plain,
    ! [SV28: $i] :
      ( ( ~ ( point @ SV28 )
        | ! [SY103: $i] :
            ( ~ ( point @ SY103 )
            | ! [SY104: $i] :
                ( ~ ( point @ SY104 )
                | ( SV28 = SY103 )
                | ( SV28 = SY104 )
                | ( SY103 = SY104 )
                | ( on @ SY104 @ ( line_through_3_points @ SV28 @ SY103 @ SY104 ) )
                | ~ ( collinear @ SV28 @ SY103 @ SY104 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(180,plain,
    ! [SV29: $i] :
      ( ( ~ ( point @ SV29 )
        | ! [SY105: $i] :
            ( ~ ( point @ SY105 )
            | ! [SY106: $i] :
                ( ~ ( point @ SY106 )
                | ( SV29 = SY105 )
                | ( SV29 = SY106 )
                | ( SY105 = SY106 )
                | ( line @ ( line_through_3_points @ SV29 @ SY105 @ SY106 ) )
                | ~ ( collinear @ SV29 @ SY105 @ SY106 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(181,plain,
    ! [SV30: $i] :
      ( ( ! [SY107: $i,SY108: $i] :
            ( ( collinear @ SV30 @ SY107 @ SY108 )
            | ! [SY109: $i] :
                ( ~ ( on @ SV30 @ SY109 )
                | ~ ( on @ SY107 @ SY109 )
                | ~ ( on @ SY108 @ SY109 )
                | ~ ( point @ SV30 )
                | ~ ( point @ SY107 )
                | ~ ( point @ SY108 )
                | ( SV30 = SY107 )
                | ( SV30 = SY108 )
                | ( SY107 = SY108 )
                | ~ ( line @ SY109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[146]) ).

thf(182,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(183,plain,
    ! [SV31: $i,SV1: $i] :
      ( ( ( on @ SV1 @ ( line_from_to @ SV1 @ SV31 ) )
        | ( SV1 = SV31 )
        | ~ ( point @ SV1 )
        | ~ ( point @ SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[152]) ).

thf(184,plain,
    ! [SV32: $i,SV2: $i] :
      ( ( ( on @ SV2 @ ( line_from_to @ SV32 @ SV2 ) )
        | ( SV32 = SV2 )
        | ~ ( point @ SV32 )
        | ~ ( point @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[153]) ).

thf(185,plain,
    ! [SV33: $i,SV3: $i] :
      ( ( ( line @ ( line_from_to @ SV3 @ SV33 ) )
        | ( SV3 = SV33 )
        | ~ ( point @ SV3 )
        | ~ ( point @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(186,plain,
    ! [SV34: $i,SV4: $i] :
      ( ( ~ ( on @ SV4 @ SV34 )
        | ! [SY110: $i] :
            ( ( SV4 = SY110 )
            | ~ ( on @ SY110 @ SV34 )
            | ! [SY111: $i] :
                ( ( SV34 = SY111 )
                | ~ ( on @ SV4 @ SY111 )
                | ~ ( on @ SY110 @ SY111 )
                | ~ ( point @ SV4 )
                | ~ ( point @ SY110 )
                | ~ ( line @ SV34 )
                | ~ ( line @ SY111 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(187,plain,
    ! [SV5: $i] :
      ( ( ( on @ ( point_1_on_line @ SV5 ) @ SV5 )
        = $true )
      | ( ( ~ ( line @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(188,plain,
    ! [SV6: $i] :
      ( ( ( on @ ( point_2_on_line @ SV6 ) @ SV6 )
        = $true )
      | ( ( ~ ( line @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[157]) ).

thf(189,plain,
    ! [SV7: $i] :
      ( ( ( point @ ( point_1_on_line @ SV7 ) )
        = $true )
      | ( ( ~ ( line @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(190,plain,
    ! [SV8: $i] :
      ( ( ( point @ ( point_2_on_line @ SV8 ) )
        = $true )
      | ( ( ~ ( line @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[159]) ).

thf(191,plain,
    ! [SV9: $i] :
      ( ( ( ( ( point_1_on_line @ SV9 )
           != ( point_2_on_line @ SV9 ) ) )
        = $true )
      | ( ( ~ ( line @ SV9 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[160]) ).

thf(192,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( on @ ( point_not_on_line @ SV10 ) @ SV10 ) )
        = $true )
      | ( ( ~ ( line @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[161]) ).

thf(193,plain,
    ! [SV11: $i] :
      ( ( ( point @ ( point_not_on_line @ SV11 ) )
        = $true )
      | ( ( ~ ( line @ SV11 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[162]) ).

thf(194,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( plane @ SV12 ) )
        = $true )
      | ( ( on @ ( point_on_plane @ SV12 ) @ SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[163]) ).

thf(195,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( plane @ SV13 ) )
        = $true )
      | ( ( point @ ( point_on_plane @ SV13 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[164]) ).

thf(196,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( plane @ SV14 ) )
        = $true )
      | ( ( ~ ( on @ ( point_not_on_plane @ SV14 ) @ SV14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[165]) ).

thf(197,plain,
    ! [SV15: $i] :
      ( ( ( ~ ( plane @ SV15 ) )
        = $true )
      | ( ( point @ ( point_not_on_plane @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[166]) ).

thf(198,plain,
    ! [SV35: $i,SV16: $i] :
      ( ( ! [SY112: $i] :
            ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SY112 ) )
            | ~ ( point @ SV16 )
            | ~ ( point @ SV35 )
            | ~ ( point @ SY112 )
            | ( collinear @ SV16 @ SV35 @ SY112 )
            | ( SV16 = SV35 )
            | ( SV16 = SY112 )
            | ( SV35 = SY112 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[167]) ).

thf(199,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ! [SY113: $i] :
            ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SY113 ) )
            | ~ ( point @ SV36 )
            | ~ ( point @ SV17 )
            | ~ ( point @ SY113 )
            | ( collinear @ SV36 @ SV17 @ SY113 )
            | ( SV36 = SV17 )
            | ( SV36 = SY113 )
            | ( SV17 = SY113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[168]) ).

thf(200,plain,
    ! [SV37: $i,SV18: $i] :
      ( ( ! [SY114: $i] :
            ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SY114 @ SV18 ) )
            | ~ ( point @ SV37 )
            | ~ ( point @ SY114 )
            | ~ ( point @ SV18 )
            | ( collinear @ SV37 @ SY114 @ SV18 )
            | ( SV37 = SY114 )
            | ( SV37 = SV18 )
            | ( SY114 = SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(201,plain,
    ! [SV38: $i,SV19: $i] :
      ( ( ! [SY115: $i] :
            ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SY115 ) )
            | ~ ( point @ SV19 )
            | ~ ( point @ SV38 )
            | ~ ( point @ SY115 )
            | ( collinear @ SV19 @ SV38 @ SY115 )
            | ( SV19 = SV38 )
            | ( SV19 = SY115 )
            | ( SV38 = SY115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[170]) ).

thf(202,plain,
    ! [SV39: $i,SV20: $i] :
      ( ( ! [SY116: $i] :
            ( ~ ( point @ SV20 )
            | ~ ( point @ SV39 )
            | ~ ( point @ SY116 )
            | ( collinear @ SV20 @ SV39 @ SY116 )
            | ( SV20 = SV39 )
            | ( SV20 = SY116 )
            | ( SV39 = SY116 )
            | ! [SY117: $i] :
                ( ~ ( on @ SV20 @ SY117 )
                | ~ ( on @ SV39 @ SY117 )
                | ~ ( on @ SY116 @ SY117 )
                | ~ ( plane @ SY117 )
                | ! [SY118: $i] :
                    ( ~ ( on @ SV20 @ SY118 )
                    | ~ ( on @ SV39 @ SY118 )
                    | ~ ( on @ SY116 @ SY118 )
                    | ~ ( plane @ SY118 )
                    | ( SY117 = SY118 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(203,plain,
    ! [SV40: $i,SV21: $i] :
      ( ( ~ ( on @ SV21 @ SV40 )
        | ! [SY119: $i] :
            ( ~ ( on @ SY119 @ SV40 )
            | ! [SY120: $i] :
                ( ~ ( on @ SV21 @ SY120 )
                | ~ ( on @ SY119 @ SY120 )
                | ~ ( plane @ SY120 )
                | ~ ( point @ SV21 )
                | ~ ( point @ SY119 )
                | ~ ( line @ SV40 )
                | ( SV21 = SY119 )
                | ( on @ SV40 @ SY120 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(204,plain,
    ! [SV22: $i] :
      ( ( ( ~ ( plane @ SV22 ) )
        = $true )
      | ( ( ! [SY91: $i] :
              ( ~ ( plane @ SY91 )
              | ( SV22 = SY91 )
              | ! [SY92: $i] :
                  ( ~ ( on @ SY92 @ SV22 )
                  | ~ ( on @ SY92 @ SY91 )
                  | ~ ( point @ SY92 )
                  | ( on @ ( common_point_on_planes @ SV22 @ SY91 @ SY92 ) @ SV22 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[173]) ).

thf(205,plain,
    ! [SV23: $i] :
      ( ( ( ~ ( plane @ SV23 ) )
        = $true )
      | ( ( ! [SY93: $i] :
              ( ~ ( plane @ SY93 )
              | ( SV23 = SY93 )
              | ! [SY94: $i] :
                  ( ~ ( on @ SY94 @ SV23 )
                  | ~ ( on @ SY94 @ SY93 )
                  | ~ ( point @ SY94 )
                  | ( on @ ( common_point_on_planes @ SV23 @ SY93 @ SY94 ) @ SY93 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[174]) ).

thf(206,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( plane @ SV24 ) )
        = $true )
      | ( ( ! [SY95: $i] :
              ( ~ ( plane @ SY95 )
              | ( SV24 = SY95 )
              | ! [SY96: $i] :
                  ( ~ ( on @ SY96 @ SV24 )
                  | ~ ( on @ SY96 @ SY95 )
                  | ~ ( point @ SY96 )
                  | ( point @ ( common_point_on_planes @ SV24 @ SY95 @ SY96 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[175]) ).

thf(207,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( plane @ SV25 ) )
        = $true )
      | ( ( ! [SY97: $i] :
              ( ~ ( plane @ SY97 )
              | ( SV25 = SY97 )
              | ! [SY98: $i] :
                  ( ~ ( on @ SY98 @ SV25 )
                  | ~ ( on @ SY98 @ SY97 )
                  | ~ ( point @ SY98 )
                  | ( SY98
                   != ( common_point_on_planes @ SV25 @ SY97 @ SY98 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[176]) ).

thf(208,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( point @ SV26 ) )
        = $true )
      | ( ( ! [SY99: $i] :
              ( ~ ( point @ SY99 )
              | ! [SY100: $i] :
                  ( ~ ( point @ SY100 )
                  | ( SV26 = SY99 )
                  | ( SV26 = SY100 )
                  | ( SY99 = SY100 )
                  | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SY99 @ SY100 ) )
                  | ~ ( collinear @ SV26 @ SY99 @ SY100 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[177]) ).

thf(209,plain,
    ! [SV27: $i] :
      ( ( ( ~ ( point @ SV27 ) )
        = $true )
      | ( ( ! [SY101: $i] :
              ( ~ ( point @ SY101 )
              | ! [SY102: $i] :
                  ( ~ ( point @ SY102 )
                  | ( SV27 = SY101 )
                  | ( SV27 = SY102 )
                  | ( SY101 = SY102 )
                  | ( on @ SY101 @ ( line_through_3_points @ SV27 @ SY101 @ SY102 ) )
                  | ~ ( collinear @ SV27 @ SY101 @ SY102 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(210,plain,
    ! [SV28: $i] :
      ( ( ( ~ ( point @ SV28 ) )
        = $true )
      | ( ( ! [SY103: $i] :
              ( ~ ( point @ SY103 )
              | ! [SY104: $i] :
                  ( ~ ( point @ SY104 )
                  | ( SV28 = SY103 )
                  | ( SV28 = SY104 )
                  | ( SY103 = SY104 )
                  | ( on @ SY104 @ ( line_through_3_points @ SV28 @ SY103 @ SY104 ) )
                  | ~ ( collinear @ SV28 @ SY103 @ SY104 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(211,plain,
    ! [SV29: $i] :
      ( ( ( ~ ( point @ SV29 ) )
        = $true )
      | ( ( ! [SY105: $i] :
              ( ~ ( point @ SY105 )
              | ! [SY106: $i] :
                  ( ~ ( point @ SY106 )
                  | ( SV29 = SY105 )
                  | ( SV29 = SY106 )
                  | ( SY105 = SY106 )
                  | ( line @ ( line_through_3_points @ SV29 @ SY105 @ SY106 ) )
                  | ~ ( collinear @ SV29 @ SY105 @ SY106 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(212,plain,
    ! [SV41: $i,SV30: $i] :
      ( ( ! [SY121: $i] :
            ( ( collinear @ SV30 @ SV41 @ SY121 )
            | ! [SY122: $i] :
                ( ~ ( on @ SV30 @ SY122 )
                | ~ ( on @ SV41 @ SY122 )
                | ~ ( on @ SY121 @ SY122 )
                | ~ ( point @ SV30 )
                | ~ ( point @ SV41 )
                | ~ ( point @ SY121 )
                | ( SV30 = SV41 )
                | ( SV30 = SY121 )
                | ( SV41 = SY121 )
                | ~ ( line @ SY122 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[181]) ).

thf(213,plain,
    ! [SV31: $i,SV1: $i] :
      ( ( ( on @ SV1 @ ( line_from_to @ SV1 @ SV31 ) )
        = $true )
      | ( ( ( SV1 = SV31 )
          | ~ ( point @ SV1 )
          | ~ ( point @ SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[183]) ).

thf(214,plain,
    ! [SV32: $i,SV2: $i] :
      ( ( ( on @ SV2 @ ( line_from_to @ SV32 @ SV2 ) )
        = $true )
      | ( ( ( SV32 = SV2 )
          | ~ ( point @ SV32 )
          | ~ ( point @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[184]) ).

thf(215,plain,
    ! [SV33: $i,SV3: $i] :
      ( ( ( line @ ( line_from_to @ SV3 @ SV33 ) )
        = $true )
      | ( ( ( SV3 = SV33 )
          | ~ ( point @ SV3 )
          | ~ ( point @ SV33 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[185]) ).

thf(216,plain,
    ! [SV34: $i,SV4: $i] :
      ( ( ( ~ ( on @ SV4 @ SV34 ) )
        = $true )
      | ( ( ! [SY110: $i] :
              ( ( SV4 = SY110 )
              | ~ ( on @ SY110 @ SV34 )
              | ! [SY111: $i] :
                  ( ( SV34 = SY111 )
                  | ~ ( on @ SV4 @ SY111 )
                  | ~ ( on @ SY110 @ SY111 )
                  | ~ ( point @ SV4 )
                  | ~ ( point @ SY110 )
                  | ~ ( line @ SV34 )
                  | ~ ( line @ SY111 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[186]) ).

thf(217,plain,
    ! [SV5: $i] :
      ( ( ( line @ SV5 )
        = $false )
      | ( ( on @ ( point_1_on_line @ SV5 ) @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[187]) ).

thf(218,plain,
    ! [SV6: $i] :
      ( ( ( line @ SV6 )
        = $false )
      | ( ( on @ ( point_2_on_line @ SV6 ) @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(219,plain,
    ! [SV7: $i] :
      ( ( ( line @ SV7 )
        = $false )
      | ( ( point @ ( point_1_on_line @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(220,plain,
    ! [SV8: $i] :
      ( ( ( line @ SV8 )
        = $false )
      | ( ( point @ ( point_2_on_line @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[190]) ).

thf(221,plain,
    ! [SV9: $i] :
      ( ( ( ( point_1_on_line @ SV9 )
          = ( point_2_on_line @ SV9 ) )
        = $false )
      | ( ( ~ ( line @ SV9 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(222,plain,
    ! [SV10: $i] :
      ( ( ( on @ ( point_not_on_line @ SV10 ) @ SV10 )
        = $false )
      | ( ( ~ ( line @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[192]) ).

thf(223,plain,
    ! [SV11: $i] :
      ( ( ( line @ SV11 )
        = $false )
      | ( ( point @ ( point_not_on_line @ SV11 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[193]) ).

thf(224,plain,
    ! [SV12: $i] :
      ( ( ( plane @ SV12 )
        = $false )
      | ( ( on @ ( point_on_plane @ SV12 ) @ SV12 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(225,plain,
    ! [SV13: $i] :
      ( ( ( plane @ SV13 )
        = $false )
      | ( ( point @ ( point_on_plane @ SV13 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[195]) ).

thf(226,plain,
    ! [SV14: $i] :
      ( ( ( plane @ SV14 )
        = $false )
      | ( ( ~ ( on @ ( point_not_on_plane @ SV14 ) @ SV14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[196]) ).

thf(227,plain,
    ! [SV15: $i] :
      ( ( ( plane @ SV15 )
        = $false )
      | ( ( point @ ( point_not_on_plane @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[197]) ).

thf(228,plain,
    ! [SV42: $i,SV35: $i,SV16: $i] :
      ( ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        | ~ ( point @ SV16 )
        | ~ ( point @ SV35 )
        | ~ ( point @ SV42 )
        | ( collinear @ SV16 @ SV35 @ SV42 )
        | ( SV16 = SV35 )
        | ( SV16 = SV42 )
        | ( SV35 = SV42 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[198]) ).

thf(229,plain,
    ! [SV43: $i,SV36: $i,SV17: $i] :
      ( ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        | ~ ( point @ SV36 )
        | ~ ( point @ SV17 )
        | ~ ( point @ SV43 )
        | ( collinear @ SV36 @ SV17 @ SV43 )
        | ( SV36 = SV17 )
        | ( SV36 = SV43 )
        | ( SV17 = SV43 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(230,plain,
    ! [SV44: $i,SV37: $i,SV18: $i] :
      ( ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        | ~ ( point @ SV37 )
        | ~ ( point @ SV44 )
        | ~ ( point @ SV18 )
        | ( collinear @ SV37 @ SV44 @ SV18 )
        | ( SV37 = SV44 )
        | ( SV37 = SV18 )
        | ( SV44 = SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[200]) ).

thf(231,plain,
    ! [SV45: $i,SV38: $i,SV19: $i] :
      ( ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        | ~ ( point @ SV19 )
        | ~ ( point @ SV38 )
        | ~ ( point @ SV45 )
        | ( collinear @ SV19 @ SV38 @ SV45 )
        | ( SV19 = SV38 )
        | ( SV19 = SV45 )
        | ( SV38 = SV45 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(232,plain,
    ! [SV46: $i,SV39: $i,SV20: $i] :
      ( ( ~ ( point @ SV20 )
        | ~ ( point @ SV39 )
        | ~ ( point @ SV46 )
        | ( collinear @ SV20 @ SV39 @ SV46 )
        | ( SV20 = SV39 )
        | ( SV20 = SV46 )
        | ( SV39 = SV46 )
        | ! [SY123: $i] :
            ( ~ ( on @ SV20 @ SY123 )
            | ~ ( on @ SV39 @ SY123 )
            | ~ ( on @ SV46 @ SY123 )
            | ~ ( plane @ SY123 )
            | ! [SY124: $i] :
                ( ~ ( on @ SV20 @ SY124 )
                | ~ ( on @ SV39 @ SY124 )
                | ~ ( on @ SV46 @ SY124 )
                | ~ ( plane @ SY124 )
                | ( SY123 = SY124 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[202]) ).

thf(233,plain,
    ! [SV40: $i,SV21: $i] :
      ( ( ( ~ ( on @ SV21 @ SV40 ) )
        = $true )
      | ( ( ! [SY119: $i] :
              ( ~ ( on @ SY119 @ SV40 )
              | ! [SY120: $i] :
                  ( ~ ( on @ SV21 @ SY120 )
                  | ~ ( on @ SY119 @ SY120 )
                  | ~ ( plane @ SY120 )
                  | ~ ( point @ SV21 )
                  | ~ ( point @ SY119 )
                  | ~ ( line @ SV40 )
                  | ( SV21 = SY119 )
                  | ( on @ SV40 @ SY120 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[203]) ).

thf(234,plain,
    ! [SV22: $i] :
      ( ( ( plane @ SV22 )
        = $false )
      | ( ( ! [SY91: $i] :
              ( ~ ( plane @ SY91 )
              | ( SV22 = SY91 )
              | ! [SY92: $i] :
                  ( ~ ( on @ SY92 @ SV22 )
                  | ~ ( on @ SY92 @ SY91 )
                  | ~ ( point @ SY92 )
                  | ( on @ ( common_point_on_planes @ SV22 @ SY91 @ SY92 ) @ SV22 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[204]) ).

thf(235,plain,
    ! [SV23: $i] :
      ( ( ( plane @ SV23 )
        = $false )
      | ( ( ! [SY93: $i] :
              ( ~ ( plane @ SY93 )
              | ( SV23 = SY93 )
              | ! [SY94: $i] :
                  ( ~ ( on @ SY94 @ SV23 )
                  | ~ ( on @ SY94 @ SY93 )
                  | ~ ( point @ SY94 )
                  | ( on @ ( common_point_on_planes @ SV23 @ SY93 @ SY94 ) @ SY93 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[205]) ).

thf(236,plain,
    ! [SV24: $i] :
      ( ( ( plane @ SV24 )
        = $false )
      | ( ( ! [SY95: $i] :
              ( ~ ( plane @ SY95 )
              | ( SV24 = SY95 )
              | ! [SY96: $i] :
                  ( ~ ( on @ SY96 @ SV24 )
                  | ~ ( on @ SY96 @ SY95 )
                  | ~ ( point @ SY96 )
                  | ( point @ ( common_point_on_planes @ SV24 @ SY95 @ SY96 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[206]) ).

thf(237,plain,
    ! [SV25: $i] :
      ( ( ( plane @ SV25 )
        = $false )
      | ( ( ! [SY97: $i] :
              ( ~ ( plane @ SY97 )
              | ( SV25 = SY97 )
              | ! [SY98: $i] :
                  ( ~ ( on @ SY98 @ SV25 )
                  | ~ ( on @ SY98 @ SY97 )
                  | ~ ( point @ SY98 )
                  | ( SY98
                   != ( common_point_on_planes @ SV25 @ SY97 @ SY98 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[207]) ).

thf(238,plain,
    ! [SV26: $i] :
      ( ( ( point @ SV26 )
        = $false )
      | ( ( ! [SY99: $i] :
              ( ~ ( point @ SY99 )
              | ! [SY100: $i] :
                  ( ~ ( point @ SY100 )
                  | ( SV26 = SY99 )
                  | ( SV26 = SY100 )
                  | ( SY99 = SY100 )
                  | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SY99 @ SY100 ) )
                  | ~ ( collinear @ SV26 @ SY99 @ SY100 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[208]) ).

thf(239,plain,
    ! [SV27: $i] :
      ( ( ( point @ SV27 )
        = $false )
      | ( ( ! [SY101: $i] :
              ( ~ ( point @ SY101 )
              | ! [SY102: $i] :
                  ( ~ ( point @ SY102 )
                  | ( SV27 = SY101 )
                  | ( SV27 = SY102 )
                  | ( SY101 = SY102 )
                  | ( on @ SY101 @ ( line_through_3_points @ SV27 @ SY101 @ SY102 ) )
                  | ~ ( collinear @ SV27 @ SY101 @ SY102 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[209]) ).

thf(240,plain,
    ! [SV28: $i] :
      ( ( ( point @ SV28 )
        = $false )
      | ( ( ! [SY103: $i] :
              ( ~ ( point @ SY103 )
              | ! [SY104: $i] :
                  ( ~ ( point @ SY104 )
                  | ( SV28 = SY103 )
                  | ( SV28 = SY104 )
                  | ( SY103 = SY104 )
                  | ( on @ SY104 @ ( line_through_3_points @ SV28 @ SY103 @ SY104 ) )
                  | ~ ( collinear @ SV28 @ SY103 @ SY104 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[210]) ).

thf(241,plain,
    ! [SV29: $i] :
      ( ( ( point @ SV29 )
        = $false )
      | ( ( ! [SY105: $i] :
              ( ~ ( point @ SY105 )
              | ! [SY106: $i] :
                  ( ~ ( point @ SY106 )
                  | ( SV29 = SY105 )
                  | ( SV29 = SY106 )
                  | ( SY105 = SY106 )
                  | ( line @ ( line_through_3_points @ SV29 @ SY105 @ SY106 ) )
                  | ~ ( collinear @ SV29 @ SY105 @ SY106 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[211]) ).

thf(242,plain,
    ! [SV47: $i,SV41: $i,SV30: $i] :
      ( ( ( collinear @ SV30 @ SV41 @ SV47 )
        | ! [SY125: $i] :
            ( ~ ( on @ SV30 @ SY125 )
            | ~ ( on @ SV41 @ SY125 )
            | ~ ( on @ SV47 @ SY125 )
            | ~ ( point @ SV30 )
            | ~ ( point @ SV41 )
            | ~ ( point @ SV47 )
            | ( SV30 = SV41 )
            | ( SV30 = SV47 )
            | ( SV41 = SV47 )
            | ~ ( line @ SY125 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[212]) ).

thf(243,plain,
    ! [SV31: $i,SV1: $i] :
      ( ( ( SV1 = SV31 )
        = $true )
      | ( ( ~ ( point @ SV1 )
          | ~ ( point @ SV31 ) )
        = $true )
      | ( ( on @ SV1 @ ( line_from_to @ SV1 @ SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[213]) ).

thf(244,plain,
    ! [SV2: $i,SV32: $i] :
      ( ( ( SV32 = SV2 )
        = $true )
      | ( ( ~ ( point @ SV32 )
          | ~ ( point @ SV2 ) )
        = $true )
      | ( ( on @ SV2 @ ( line_from_to @ SV32 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[214]) ).

thf(245,plain,
    ! [SV33: $i,SV3: $i] :
      ( ( ( SV3 = SV33 )
        = $true )
      | ( ( ~ ( point @ SV3 )
          | ~ ( point @ SV33 ) )
        = $true )
      | ( ( line @ ( line_from_to @ SV3 @ SV33 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[215]) ).

thf(246,plain,
    ! [SV34: $i,SV4: $i] :
      ( ( ( on @ SV4 @ SV34 )
        = $false )
      | ( ( ! [SY110: $i] :
              ( ( SV4 = SY110 )
              | ~ ( on @ SY110 @ SV34 )
              | ! [SY111: $i] :
                  ( ( SV34 = SY111 )
                  | ~ ( on @ SV4 @ SY111 )
                  | ~ ( on @ SY110 @ SY111 )
                  | ~ ( point @ SV4 )
                  | ~ ( point @ SY110 )
                  | ~ ( line @ SV34 )
                  | ~ ( line @ SY111 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[216]) ).

thf(247,plain,
    ! [SV9: $i] :
      ( ( ( line @ SV9 )
        = $false )
      | ( ( ( point_1_on_line @ SV9 )
          = ( point_2_on_line @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[221]) ).

thf(248,plain,
    ! [SV10: $i] :
      ( ( ( line @ SV10 )
        = $false )
      | ( ( on @ ( point_not_on_line @ SV10 ) @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[222]) ).

thf(249,plain,
    ! [SV14: $i] :
      ( ( ( on @ ( point_not_on_plane @ SV14 ) @ SV14 )
        = $false )
      | ( ( plane @ SV14 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[226]) ).

thf(250,plain,
    ! [SV42: $i,SV35: $i,SV16: $i] :
      ( ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true )
      | ( ( ~ ( point @ SV16 )
          | ~ ( point @ SV35 )
          | ~ ( point @ SV42 )
          | ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[228]) ).

thf(251,plain,
    ! [SV43: $i,SV36: $i,SV17: $i] :
      ( ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true )
      | ( ( ~ ( point @ SV36 )
          | ~ ( point @ SV17 )
          | ~ ( point @ SV43 )
          | ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[229]) ).

thf(252,plain,
    ! [SV44: $i,SV37: $i,SV18: $i] :
      ( ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true )
      | ( ( ~ ( point @ SV37 )
          | ~ ( point @ SV44 )
          | ~ ( point @ SV18 )
          | ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[230]) ).

thf(253,plain,
    ! [SV45: $i,SV38: $i,SV19: $i] :
      ( ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true )
      | ( ( ~ ( point @ SV19 )
          | ~ ( point @ SV38 )
          | ~ ( point @ SV45 )
          | ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[231]) ).

thf(254,plain,
    ! [SV46: $i,SV39: $i,SV20: $i] :
      ( ( ( ~ ( point @ SV20 ) )
        = $true )
      | ( ( ~ ( point @ SV39 )
          | ~ ( point @ SV46 )
          | ( collinear @ SV20 @ SV39 @ SV46 )
          | ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[232]) ).

thf(255,plain,
    ! [SV40: $i,SV21: $i] :
      ( ( ( on @ SV21 @ SV40 )
        = $false )
      | ( ( ! [SY119: $i] :
              ( ~ ( on @ SY119 @ SV40 )
              | ! [SY120: $i] :
                  ( ~ ( on @ SV21 @ SY120 )
                  | ~ ( on @ SY119 @ SY120 )
                  | ~ ( plane @ SY120 )
                  | ~ ( point @ SV21 )
                  | ~ ( point @ SY119 )
                  | ~ ( line @ SV40 )
                  | ( SV21 = SY119 )
                  | ( on @ SV40 @ SY120 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[233]) ).

thf(256,plain,
    ! [SV22: $i,SV48: $i] :
      ( ( ( ~ ( plane @ SV48 )
          | ( SV22 = SV48 )
          | ! [SY126: $i] :
              ( ~ ( on @ SY126 @ SV22 )
              | ~ ( on @ SY126 @ SV48 )
              | ~ ( point @ SY126 )
              | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SY126 ) @ SV22 ) ) )
        = $true )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[234]) ).

thf(257,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 ) @ SV49 ) ) )
        = $true )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[235]) ).

thf(258,plain,
    ! [SV24: $i,SV50: $i] :
      ( ( ( ~ ( plane @ SV50 )
          | ( SV24 = SV50 )
          | ! [SY128: $i] :
              ( ~ ( on @ SY128 @ SV24 )
              | ~ ( on @ SY128 @ SV50 )
              | ~ ( point @ SY128 )
              | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) ) ) )
        = $true )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[236]) ).

thf(259,plain,
    ! [SV25: $i,SV51: $i] :
      ( ( ( ~ ( plane @ SV51 )
          | ( SV25 = SV51 )
          | ! [SY129: $i] :
              ( ~ ( on @ SY129 @ SV25 )
              | ~ ( on @ SY129 @ SV51 )
              | ~ ( point @ SY129 )
              | ( SY129
               != ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
        = $true )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(260,plain,
    ! [SV26: $i,SV52: $i] :
      ( ( ( ~ ( point @ SV52 )
          | ! [SY130: $i] :
              ( ~ ( point @ SY130 )
              | ( SV26 = SV52 )
              | ( SV26 = SY130 )
              | ( SV52 = SY130 )
              | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SY130 ) )
              | ~ ( collinear @ SV26 @ SV52 @ SY130 ) ) )
        = $true )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[238]) ).

thf(261,plain,
    ! [SV27: $i,SV53: $i] :
      ( ( ( ~ ( point @ SV53 )
          | ! [SY131: $i] :
              ( ~ ( point @ SY131 )
              | ( SV27 = SV53 )
              | ( SV27 = SY131 )
              | ( SV53 = SY131 )
              | ( on @ SV53 @ ( line_through_3_points @ SV27 @ SV53 @ SY131 ) )
              | ~ ( collinear @ SV27 @ SV53 @ SY131 ) ) )
        = $true )
      | ( ( point @ SV27 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[239]) ).

thf(262,plain,
    ! [SV28: $i,SV54: $i] :
      ( ( ( ~ ( point @ SV54 )
          | ! [SY132: $i] :
              ( ~ ( point @ SY132 )
              | ( SV28 = SV54 )
              | ( SV28 = SY132 )
              | ( SV54 = SY132 )
              | ( on @ SY132 @ ( line_through_3_points @ SV28 @ SV54 @ SY132 ) )
              | ~ ( collinear @ SV28 @ SV54 @ SY132 ) ) )
        = $true )
      | ( ( point @ SV28 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[240]) ).

thf(263,plain,
    ! [SV29: $i,SV55: $i] :
      ( ( ( ~ ( point @ SV55 )
          | ! [SY133: $i] :
              ( ~ ( point @ SY133 )
              | ( SV29 = SV55 )
              | ( SV29 = SY133 )
              | ( SV55 = SY133 )
              | ( line @ ( line_through_3_points @ SV29 @ SV55 @ SY133 ) )
              | ~ ( collinear @ SV29 @ SV55 @ SY133 ) ) )
        = $true )
      | ( ( point @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[241]) ).

thf(264,plain,
    ! [SV47: $i,SV41: $i,SV30: $i] :
      ( ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true )
      | ( ( ! [SY125: $i] :
              ( ~ ( on @ SV30 @ SY125 )
              | ~ ( on @ SV41 @ SY125 )
              | ~ ( on @ SV47 @ SY125 )
              | ~ ( point @ SV30 )
              | ~ ( point @ SV41 )
              | ~ ( point @ SV47 )
              | ( SV30 = SV41 )
              | ( SV30 = SV47 )
              | ( SV41 = SV47 )
              | ~ ( line @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[242]) ).

thf(265,plain,
    ! [SV31: $i,SV1: $i] :
      ( ( ( ~ ( point @ SV1 ) )
        = $true )
      | ( ( ~ ( point @ SV31 ) )
        = $true )
      | ( ( SV1 = SV31 )
        = $true )
      | ( ( on @ SV1 @ ( line_from_to @ SV1 @ SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[243]) ).

thf(266,plain,
    ! [SV2: $i,SV32: $i] :
      ( ( ( ~ ( point @ SV32 ) )
        = $true )
      | ( ( ~ ( point @ SV2 ) )
        = $true )
      | ( ( SV32 = SV2 )
        = $true )
      | ( ( on @ SV2 @ ( line_from_to @ SV32 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[244]) ).

thf(267,plain,
    ! [SV33: $i,SV3: $i] :
      ( ( ( ~ ( point @ SV3 ) )
        = $true )
      | ( ( ~ ( point @ SV33 ) )
        = $true )
      | ( ( SV3 = SV33 )
        = $true )
      | ( ( line @ ( line_from_to @ SV3 @ SV33 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[245]) ).

thf(268,plain,
    ! [SV34: $i,SV56: $i,SV4: $i] :
      ( ( ( ( SV4 = SV56 )
          | ~ ( on @ SV56 @ SV34 )
          | ! [SY134: $i] :
              ( ( SV34 = SY134 )
              | ~ ( on @ SV4 @ SY134 )
              | ~ ( on @ SV56 @ SY134 )
              | ~ ( point @ SV4 )
              | ~ ( point @ SV56 )
              | ~ ( line @ SV34 )
              | ~ ( line @ SY134 ) ) )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[246]) ).

thf(269,plain,
    ! [SV42: $i,SV35: $i,SV16: $i] :
      ( ( ( ~ ( point @ SV16 ) )
        = $true )
      | ( ( ~ ( point @ SV35 )
          | ~ ( point @ SV42 )
          | ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[250]) ).

thf(270,plain,
    ! [SV43: $i,SV17: $i,SV36: $i] :
      ( ( ( ~ ( point @ SV36 ) )
        = $true )
      | ( ( ~ ( point @ SV17 )
          | ~ ( point @ SV43 )
          | ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[251]) ).

thf(271,plain,
    ! [SV18: $i,SV44: $i,SV37: $i] :
      ( ( ( ~ ( point @ SV37 ) )
        = $true )
      | ( ( ~ ( point @ SV44 )
          | ~ ( point @ SV18 )
          | ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[252]) ).

thf(272,plain,
    ! [SV45: $i,SV38: $i,SV19: $i] :
      ( ( ( ~ ( point @ SV19 ) )
        = $true )
      | ( ( ~ ( point @ SV38 )
          | ~ ( point @ SV45 )
          | ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[253]) ).

thf(273,plain,
    ! [SV46: $i,SV39: $i,SV20: $i] :
      ( ( ( point @ SV20 )
        = $false )
      | ( ( ~ ( point @ SV39 )
          | ~ ( point @ SV46 )
          | ( collinear @ SV20 @ SV39 @ SV46 )
          | ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[254]) ).

thf(274,plain,
    ! [SV21: $i,SV40: $i,SV57: $i] :
      ( ( ( ~ ( on @ SV57 @ SV40 )
          | ! [SY135: $i] :
              ( ~ ( on @ SV21 @ SY135 )
              | ~ ( on @ SV57 @ SY135 )
              | ~ ( plane @ SY135 )
              | ~ ( point @ SV21 )
              | ~ ( point @ SV57 )
              | ~ ( line @ SV40 )
              | ( SV21 = SV57 )
              | ( on @ SV40 @ SY135 ) ) )
        = $true )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[255]) ).

thf(275,plain,
    ! [SV22: $i,SV48: $i] :
      ( ( ( ~ ( plane @ SV48 ) )
        = $true )
      | ( ( ( SV22 = SV48 )
          | ! [SY126: $i] :
              ( ~ ( on @ SY126 @ SV22 )
              | ~ ( on @ SY126 @ SV48 )
              | ~ ( point @ SY126 )
              | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SY126 ) @ SV22 ) ) )
        = $true )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[256]) ).

thf(276,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 ) @ SV49 ) ) )
        = $true )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[257]) ).

thf(277,plain,
    ! [SV24: $i,SV50: $i] :
      ( ( ( ~ ( plane @ SV50 ) )
        = $true )
      | ( ( ( SV24 = SV50 )
          | ! [SY128: $i] :
              ( ~ ( on @ SY128 @ SV24 )
              | ~ ( on @ SY128 @ SV50 )
              | ~ ( point @ SY128 )
              | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) ) ) )
        = $true )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[258]) ).

thf(278,plain,
    ! [SV25: $i,SV51: $i] :
      ( ( ( ~ ( plane @ SV51 ) )
        = $true )
      | ( ( ( SV25 = SV51 )
          | ! [SY129: $i] :
              ( ~ ( on @ SY129 @ SV25 )
              | ~ ( on @ SY129 @ SV51 )
              | ~ ( point @ SY129 )
              | ( SY129
               != ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
        = $true )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[259]) ).

thf(279,plain,
    ! [SV26: $i,SV52: $i] :
      ( ( ( ~ ( point @ SV52 ) )
        = $true )
      | ( ( ! [SY130: $i] :
              ( ~ ( point @ SY130 )
              | ( SV26 = SV52 )
              | ( SV26 = SY130 )
              | ( SV52 = SY130 )
              | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SY130 ) )
              | ~ ( collinear @ SV26 @ SV52 @ SY130 ) ) )
        = $true )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[260]) ).

thf(280,plain,
    ! [SV27: $i,SV53: $i] :
      ( ( ( ~ ( point @ SV53 ) )
        = $true )
      | ( ( ! [SY131: $i] :
              ( ~ ( point @ SY131 )
              | ( SV27 = SV53 )
              | ( SV27 = SY131 )
              | ( SV53 = SY131 )
              | ( on @ SV53 @ ( line_through_3_points @ SV27 @ SV53 @ SY131 ) )
              | ~ ( collinear @ SV27 @ SV53 @ SY131 ) ) )
        = $true )
      | ( ( point @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[261]) ).

thf(281,plain,
    ! [SV28: $i,SV54: $i] :
      ( ( ( ~ ( point @ SV54 ) )
        = $true )
      | ( ( ! [SY132: $i] :
              ( ~ ( point @ SY132 )
              | ( SV28 = SV54 )
              | ( SV28 = SY132 )
              | ( SV54 = SY132 )
              | ( on @ SY132 @ ( line_through_3_points @ SV28 @ SV54 @ SY132 ) )
              | ~ ( collinear @ SV28 @ SV54 @ SY132 ) ) )
        = $true )
      | ( ( point @ SV28 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[262]) ).

thf(282,plain,
    ! [SV29: $i,SV55: $i] :
      ( ( ( ~ ( point @ SV55 ) )
        = $true )
      | ( ( ! [SY133: $i] :
              ( ~ ( point @ SY133 )
              | ( SV29 = SV55 )
              | ( SV29 = SY133 )
              | ( SV55 = SY133 )
              | ( line @ ( line_through_3_points @ SV29 @ SV55 @ SY133 ) )
              | ~ ( collinear @ SV29 @ SV55 @ SY133 ) ) )
        = $true )
      | ( ( point @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[263]) ).

thf(283,plain,
    ! [SV47: $i,SV41: $i,SV58: $i,SV30: $i] :
      ( ( ( ~ ( on @ SV30 @ SV58 )
          | ~ ( on @ SV41 @ SV58 )
          | ~ ( on @ SV47 @ SV58 )
          | ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[264]) ).

thf(284,plain,
    ! [SV31: $i,SV1: $i] :
      ( ( ( point @ SV1 )
        = $false )
      | ( ( ~ ( point @ SV31 ) )
        = $true )
      | ( ( SV1 = SV31 )
        = $true )
      | ( ( on @ SV1 @ ( line_from_to @ SV1 @ SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[265]) ).

thf(285,plain,
    ! [SV2: $i,SV32: $i] :
      ( ( ( point @ SV32 )
        = $false )
      | ( ( ~ ( point @ SV2 ) )
        = $true )
      | ( ( SV32 = SV2 )
        = $true )
      | ( ( on @ SV2 @ ( line_from_to @ SV32 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[266]) ).

thf(286,plain,
    ! [SV33: $i,SV3: $i] :
      ( ( ( point @ SV3 )
        = $false )
      | ( ( ~ ( point @ SV33 ) )
        = $true )
      | ( ( SV3 = SV33 )
        = $true )
      | ( ( line @ ( line_from_to @ SV3 @ SV33 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[267]) ).

thf(287,plain,
    ! [SV34: $i,SV56: $i,SV4: $i] :
      ( ( ( SV4 = SV56 )
        = $true )
      | ( ( ~ ( on @ SV56 @ SV34 )
          | ! [SY134: $i] :
              ( ( SV34 = SY134 )
              | ~ ( on @ SV4 @ SY134 )
              | ~ ( on @ SV56 @ SY134 )
              | ~ ( point @ SV4 )
              | ~ ( point @ SV56 )
              | ~ ( line @ SV34 )
              | ~ ( line @ SY134 ) ) )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[268]) ).

thf(288,plain,
    ! [SV42: $i,SV35: $i,SV16: $i] :
      ( ( ( point @ SV16 )
        = $false )
      | ( ( ~ ( point @ SV35 )
          | ~ ( point @ SV42 )
          | ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[269]) ).

thf(289,plain,
    ! [SV43: $i,SV17: $i,SV36: $i] :
      ( ( ( point @ SV36 )
        = $false )
      | ( ( ~ ( point @ SV17 )
          | ~ ( point @ SV43 )
          | ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[270]) ).

thf(290,plain,
    ! [SV18: $i,SV44: $i,SV37: $i] :
      ( ( ( point @ SV37 )
        = $false )
      | ( ( ~ ( point @ SV44 )
          | ~ ( point @ SV18 )
          | ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[271]) ).

thf(291,plain,
    ! [SV45: $i,SV38: $i,SV19: $i] :
      ( ( ( point @ SV19 )
        = $false )
      | ( ( ~ ( point @ SV38 )
          | ~ ( point @ SV45 )
          | ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[272]) ).

thf(292,plain,
    ! [SV20: $i,SV46: $i,SV39: $i] :
      ( ( ( ~ ( point @ SV39 ) )
        = $true )
      | ( ( ~ ( point @ SV46 )
          | ( collinear @ SV20 @ SV39 @ SV46 )
          | ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[273]) ).

thf(293,plain,
    ! [SV21: $i,SV40: $i,SV57: $i] :
      ( ( ( ~ ( on @ SV57 @ SV40 ) )
        = $true )
      | ( ( ! [SY135: $i] :
              ( ~ ( on @ SV21 @ SY135 )
              | ~ ( on @ SV57 @ SY135 )
              | ~ ( plane @ SY135 )
              | ~ ( point @ SV21 )
              | ~ ( point @ SV57 )
              | ~ ( line @ SV40 )
              | ( SV21 = SV57 )
              | ( on @ SV40 @ SY135 ) ) )
        = $true )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[274]) ).

thf(294,plain,
    ! [SV22: $i,SV48: $i] :
      ( ( ( plane @ SV48 )
        = $false )
      | ( ( ( SV22 = SV48 )
          | ! [SY126: $i] :
              ( ~ ( on @ SY126 @ SV22 )
              | ~ ( on @ SY126 @ SV48 )
              | ~ ( point @ SY126 )
              | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SY126 ) @ SV22 ) ) )
        = $true )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[275]) ).

thf(295,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 ) @ SV49 ) ) )
        = $true )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[276]) ).

thf(296,plain,
    ! [SV24: $i,SV50: $i] :
      ( ( ( plane @ SV50 )
        = $false )
      | ( ( ( SV24 = SV50 )
          | ! [SY128: $i] :
              ( ~ ( on @ SY128 @ SV24 )
              | ~ ( on @ SY128 @ SV50 )
              | ~ ( point @ SY128 )
              | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) ) ) )
        = $true )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[277]) ).

thf(297,plain,
    ! [SV25: $i,SV51: $i] :
      ( ( ( plane @ SV51 )
        = $false )
      | ( ( ( SV25 = SV51 )
          | ! [SY129: $i] :
              ( ~ ( on @ SY129 @ SV25 )
              | ~ ( on @ SY129 @ SV51 )
              | ~ ( point @ SY129 )
              | ( SY129
               != ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
        = $true )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[278]) ).

thf(298,plain,
    ! [SV26: $i,SV52: $i] :
      ( ( ( point @ SV52 )
        = $false )
      | ( ( ! [SY130: $i] :
              ( ~ ( point @ SY130 )
              | ( SV26 = SV52 )
              | ( SV26 = SY130 )
              | ( SV52 = SY130 )
              | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SY130 ) )
              | ~ ( collinear @ SV26 @ SV52 @ SY130 ) ) )
        = $true )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[279]) ).

thf(299,plain,
    ! [SV27: $i,SV53: $i] :
      ( ( ( point @ SV53 )
        = $false )
      | ( ( ! [SY131: $i] :
              ( ~ ( point @ SY131 )
              | ( SV27 = SV53 )
              | ( SV27 = SY131 )
              | ( SV53 = SY131 )
              | ( on @ SV53 @ ( line_through_3_points @ SV27 @ SV53 @ SY131 ) )
              | ~ ( collinear @ SV27 @ SV53 @ SY131 ) ) )
        = $true )
      | ( ( point @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[280]) ).

thf(300,plain,
    ! [SV28: $i,SV54: $i] :
      ( ( ( point @ SV54 )
        = $false )
      | ( ( ! [SY132: $i] :
              ( ~ ( point @ SY132 )
              | ( SV28 = SV54 )
              | ( SV28 = SY132 )
              | ( SV54 = SY132 )
              | ( on @ SY132 @ ( line_through_3_points @ SV28 @ SV54 @ SY132 ) )
              | ~ ( collinear @ SV28 @ SV54 @ SY132 ) ) )
        = $true )
      | ( ( point @ SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[281]) ).

thf(301,plain,
    ! [SV29: $i,SV55: $i] :
      ( ( ( point @ SV55 )
        = $false )
      | ( ( ! [SY133: $i] :
              ( ~ ( point @ SY133 )
              | ( SV29 = SV55 )
              | ( SV29 = SY133 )
              | ( SV55 = SY133 )
              | ( line @ ( line_through_3_points @ SV29 @ SV55 @ SY133 ) )
              | ~ ( collinear @ SV29 @ SV55 @ SY133 ) ) )
        = $true )
      | ( ( point @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[282]) ).

thf(302,plain,
    ! [SV47: $i,SV41: $i,SV58: $i,SV30: $i] :
      ( ( ( ~ ( on @ SV30 @ SV58 ) )
        = $true )
      | ( ( ~ ( on @ SV41 @ SV58 )
          | ~ ( on @ SV47 @ SV58 )
          | ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[283]) ).

thf(303,plain,
    ! [SV1: $i,SV31: $i] :
      ( ( ( point @ SV31 )
        = $false )
      | ( ( point @ SV1 )
        = $false )
      | ( ( SV1 = SV31 )
        = $true )
      | ( ( on @ SV1 @ ( line_from_to @ SV1 @ SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[284]) ).

thf(304,plain,
    ! [SV32: $i,SV2: $i] :
      ( ( ( point @ SV2 )
        = $false )
      | ( ( point @ SV32 )
        = $false )
      | ( ( SV32 = SV2 )
        = $true )
      | ( ( on @ SV2 @ ( line_from_to @ SV32 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[285]) ).

thf(305,plain,
    ! [SV3: $i,SV33: $i] :
      ( ( ( point @ SV33 )
        = $false )
      | ( ( point @ SV3 )
        = $false )
      | ( ( SV3 = SV33 )
        = $true )
      | ( ( line @ ( line_from_to @ SV3 @ SV33 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[286]) ).

thf(306,plain,
    ! [SV4: $i,SV34: $i,SV56: $i] :
      ( ( ( ~ ( on @ SV56 @ SV34 ) )
        = $true )
      | ( ( ! [SY134: $i] :
              ( ( SV34 = SY134 )
              | ~ ( on @ SV4 @ SY134 )
              | ~ ( on @ SV56 @ SY134 )
              | ~ ( point @ SV4 )
              | ~ ( point @ SV56 )
              | ~ ( line @ SV34 )
              | ~ ( line @ SY134 ) ) )
        = $true )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[287]) ).

thf(307,plain,
    ! [SV16: $i,SV42: $i,SV35: $i] :
      ( ( ( ~ ( point @ SV35 ) )
        = $true )
      | ( ( ~ ( point @ SV42 )
          | ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[288]) ).

thf(308,plain,
    ! [SV36: $i,SV43: $i,SV17: $i] :
      ( ( ( ~ ( point @ SV17 ) )
        = $true )
      | ( ( ~ ( point @ SV43 )
          | ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[289]) ).

thf(309,plain,
    ! [SV37: $i,SV18: $i,SV44: $i] :
      ( ( ( ~ ( point @ SV44 ) )
        = $true )
      | ( ( ~ ( point @ SV18 )
          | ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[290]) ).

thf(310,plain,
    ! [SV19: $i,SV45: $i,SV38: $i] :
      ( ( ( ~ ( point @ SV38 ) )
        = $true )
      | ( ( ~ ( point @ SV45 )
          | ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[291]) ).

thf(311,plain,
    ! [SV20: $i,SV46: $i,SV39: $i] :
      ( ( ( point @ SV39 )
        = $false )
      | ( ( ~ ( point @ SV46 )
          | ( collinear @ SV20 @ SV39 @ SV46 )
          | ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[292]) ).

thf(312,plain,
    ! [SV21: $i,SV40: $i,SV57: $i] :
      ( ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( ! [SY135: $i] :
              ( ~ ( on @ SV21 @ SY135 )
              | ~ ( on @ SV57 @ SY135 )
              | ~ ( plane @ SY135 )
              | ~ ( point @ SV21 )
              | ~ ( point @ SV57 )
              | ~ ( line @ SV40 )
              | ( SV21 = SV57 )
              | ( on @ SV40 @ SY135 ) ) )
        = $true )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[293]) ).

thf(313,plain,
    ! [SV48: $i,SV22: $i] :
      ( ( ( SV22 = SV48 )
        = $true )
      | ( ( ! [SY126: $i] :
              ( ~ ( on @ SY126 @ SV22 )
              | ~ ( on @ SY126 @ SV48 )
              | ~ ( point @ SY126 )
              | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SY126 ) @ SV22 ) ) )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[294]) ).

thf(314,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 ) @ SV49 ) ) )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[295]) ).

thf(315,plain,
    ! [SV50: $i,SV24: $i] :
      ( ( ( SV24 = SV50 )
        = $true )
      | ( ( ! [SY128: $i] :
              ( ~ ( on @ SY128 @ SV24 )
              | ~ ( on @ SY128 @ SV50 )
              | ~ ( point @ SY128 )
              | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SY128 ) ) ) )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[296]) ).

thf(316,plain,
    ! [SV51: $i,SV25: $i] :
      ( ( ( SV25 = SV51 )
        = $true )
      | ( ( ! [SY129: $i] :
              ( ~ ( on @ SY129 @ SV25 )
              | ~ ( on @ SY129 @ SV51 )
              | ~ ( point @ SY129 )
              | ( SY129
               != ( common_point_on_planes @ SV25 @ SV51 @ SY129 ) ) ) )
        = $true )
      | ( ( plane @ SV51 )
        = $false )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[297]) ).

thf(317,plain,
    ! [SV52: $i,SV26: $i,SV59: $i] :
      ( ( ( ~ ( point @ SV59 )
          | ( SV26 = SV52 )
          | ( SV26 = SV59 )
          | ( SV52 = SV59 )
          | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
          | ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[298]) ).

thf(318,plain,
    ! [SV53: $i,SV27: $i,SV60: $i] :
      ( ( ( ~ ( point @ SV60 )
          | ( SV27 = SV53 )
          | ( SV27 = SV60 )
          | ( SV53 = SV60 )
          | ( on @ SV53 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
          | ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
        = $true )
      | ( ( point @ SV53 )
        = $false )
      | ( ( point @ SV27 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[299]) ).

thf(319,plain,
    ! [SV54: $i,SV28: $i,SV61: $i] :
      ( ( ( ~ ( point @ SV61 )
          | ( SV28 = SV54 )
          | ( SV28 = SV61 )
          | ( SV54 = SV61 )
          | ( on @ SV61 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
          | ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
        = $true )
      | ( ( point @ SV54 )
        = $false )
      | ( ( point @ SV28 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[300]) ).

thf(320,plain,
    ! [SV55: $i,SV29: $i,SV62: $i] :
      ( ( ( ~ ( point @ SV62 )
          | ( SV29 = SV55 )
          | ( SV29 = SV62 )
          | ( SV55 = SV62 )
          | ( line @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
          | ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
        = $true )
      | ( ( point @ SV55 )
        = $false )
      | ( ( point @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[301]) ).

thf(321,plain,
    ! [SV47: $i,SV41: $i,SV58: $i,SV30: $i] :
      ( ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( ~ ( on @ SV41 @ SV58 )
          | ~ ( on @ SV47 @ SV58 )
          | ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[302]) ).

thf(322,plain,
    ! [SV4: $i,SV34: $i,SV56: $i] :
      ( ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( ! [SY134: $i] :
              ( ( SV34 = SY134 )
              | ~ ( on @ SV4 @ SY134 )
              | ~ ( on @ SV56 @ SY134 )
              | ~ ( point @ SV4 )
              | ~ ( point @ SV56 )
              | ~ ( line @ SV34 )
              | ~ ( line @ SY134 ) ) )
        = $true )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[306]) ).

thf(323,plain,
    ! [SV16: $i,SV42: $i,SV35: $i] :
      ( ( ( point @ SV35 )
        = $false )
      | ( ( ~ ( point @ SV42 )
          | ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[307]) ).

thf(324,plain,
    ! [SV36: $i,SV43: $i,SV17: $i] :
      ( ( ( point @ SV17 )
        = $false )
      | ( ( ~ ( point @ SV43 )
          | ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[308]) ).

thf(325,plain,
    ! [SV37: $i,SV18: $i,SV44: $i] :
      ( ( ( point @ SV44 )
        = $false )
      | ( ( ~ ( point @ SV18 )
          | ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[309]) ).

thf(326,plain,
    ! [SV19: $i,SV45: $i,SV38: $i] :
      ( ( ( point @ SV38 )
        = $false )
      | ( ( ~ ( point @ SV45 )
          | ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[310]) ).

thf(327,plain,
    ! [SV39: $i,SV20: $i,SV46: $i] :
      ( ( ( ~ ( point @ SV46 ) )
        = $true )
      | ( ( ( collinear @ SV20 @ SV39 @ SV46 )
          | ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[311]) ).

thf(328,plain,
    ! [SV40: $i,SV57: $i,SV63: $i,SV21: $i] :
      ( ( ( ~ ( on @ SV21 @ SV63 )
          | ~ ( on @ SV57 @ SV63 )
          | ~ ( plane @ SV63 )
          | ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[312]) ).

thf(329,plain,
    ! [SV48: $i,SV22: $i,SV64: $i] :
      ( ( ( ~ ( on @ SV64 @ SV22 )
          | ~ ( on @ SV64 @ SV48 )
          | ~ ( point @ SV64 )
          | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 ) )
        = $true )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[313]) ).

thf(330,plain,
    ! [SV49: $i,SV23: $i,SV65: $i] :
      ( ( ( ~ ( on @ SV65 @ SV23 )
          | ~ ( on @ SV65 @ SV49 )
          | ~ ( point @ SV65 )
          | ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 ) )
        = $true )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[314]) ).

thf(331,plain,
    ! [SV50: $i,SV24: $i,SV66: $i] :
      ( ( ( ~ ( on @ SV66 @ SV24 )
          | ~ ( on @ SV66 @ SV50 )
          | ~ ( point @ SV66 )
          | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) ) )
        = $true )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[315]) ).

thf(332,plain,
    ! [SV51: $i,SV25: $i,SV67: $i] :
      ( ( ( ~ ( on @ SV67 @ SV25 )
          | ~ ( on @ SV67 @ SV51 )
          | ~ ( point @ SV67 )
          | ( SV67
           != ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
        = $true )
      | ( ( SV25 = SV51 )
        = $true )
      | ( ( plane @ SV51 )
        = $false )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[316]) ).

thf(333,plain,
    ! [SV52: $i,SV26: $i,SV59: $i] :
      ( ( ( ~ ( point @ SV59 ) )
        = $true )
      | ( ( ( SV26 = SV52 )
          | ( SV26 = SV59 )
          | ( SV52 = SV59 )
          | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
          | ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[317]) ).

thf(334,plain,
    ! [SV53: $i,SV27: $i,SV60: $i] :
      ( ( ( ~ ( point @ SV60 ) )
        = $true )
      | ( ( ( SV27 = SV53 )
          | ( SV27 = SV60 )
          | ( SV53 = SV60 )
          | ( on @ SV53 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
          | ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
        = $true )
      | ( ( point @ SV53 )
        = $false )
      | ( ( point @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[318]) ).

thf(335,plain,
    ! [SV54: $i,SV28: $i,SV61: $i] :
      ( ( ( ~ ( point @ SV61 ) )
        = $true )
      | ( ( ( SV28 = SV54 )
          | ( SV28 = SV61 )
          | ( SV54 = SV61 )
          | ( on @ SV61 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
          | ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
        = $true )
      | ( ( point @ SV54 )
        = $false )
      | ( ( point @ SV28 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[319]) ).

thf(336,plain,
    ! [SV55: $i,SV29: $i,SV62: $i] :
      ( ( ( ~ ( point @ SV62 ) )
        = $true )
      | ( ( ( SV29 = SV55 )
          | ( SV29 = SV62 )
          | ( SV55 = SV62 )
          | ( line @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
          | ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
        = $true )
      | ( ( point @ SV55 )
        = $false )
      | ( ( point @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[320]) ).

thf(337,plain,
    ! [SV30: $i,SV47: $i,SV58: $i,SV41: $i] :
      ( ( ( ~ ( on @ SV41 @ SV58 ) )
        = $true )
      | ( ( ~ ( on @ SV47 @ SV58 )
          | ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[321]) ).

thf(338,plain,
    ! [SV56: $i,SV4: $i,SV68: $i,SV34: $i] :
      ( ( ( ( SV34 = SV68 )
          | ~ ( on @ SV4 @ SV68 )
          | ~ ( on @ SV56 @ SV68 )
          | ~ ( point @ SV4 )
          | ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[322]) ).

thf(339,plain,
    ! [SV35: $i,SV16: $i,SV42: $i] :
      ( ( ( ~ ( point @ SV42 ) )
        = $true )
      | ( ( ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( point @ SV35 )
        = $false )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[323]) ).

thf(340,plain,
    ! [SV17: $i,SV36: $i,SV43: $i] :
      ( ( ( ~ ( point @ SV43 ) )
        = $true )
      | ( ( ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( point @ SV17 )
        = $false )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[324]) ).

thf(341,plain,
    ! [SV44: $i,SV37: $i,SV18: $i] :
      ( ( ( ~ ( point @ SV18 ) )
        = $true )
      | ( ( ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( point @ SV44 )
        = $false )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[325]) ).

thf(342,plain,
    ! [SV38: $i,SV19: $i,SV45: $i] :
      ( ( ( ~ ( point @ SV45 ) )
        = $true )
      | ( ( ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( point @ SV38 )
        = $false )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[326]) ).

thf(343,plain,
    ! [SV39: $i,SV20: $i,SV46: $i] :
      ( ( ( point @ SV46 )
        = $false )
      | ( ( ( collinear @ SV20 @ SV39 @ SV46 )
          | ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[327]) ).

thf(344,plain,
    ! [SV40: $i,SV57: $i,SV63: $i,SV21: $i] :
      ( ( ( ~ ( on @ SV21 @ SV63 ) )
        = $true )
      | ( ( ~ ( on @ SV57 @ SV63 )
          | ~ ( plane @ SV63 )
          | ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[328]) ).

thf(345,plain,
    ! [SV48: $i,SV22: $i,SV64: $i] :
      ( ( ( ~ ( on @ SV64 @ SV22 ) )
        = $true )
      | ( ( ~ ( on @ SV64 @ SV48 )
          | ~ ( point @ SV64 )
          | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 ) )
        = $true )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[329]) ).

thf(346,plain,
    ! [SV49: $i,SV23: $i,SV65: $i] :
      ( ( ( ~ ( on @ SV65 @ SV23 ) )
        = $true )
      | ( ( ~ ( on @ SV65 @ SV49 )
          | ~ ( point @ SV65 )
          | ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 ) )
        = $true )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[330]) ).

thf(347,plain,
    ! [SV50: $i,SV24: $i,SV66: $i] :
      ( ( ( ~ ( on @ SV66 @ SV24 ) )
        = $true )
      | ( ( ~ ( on @ SV66 @ SV50 )
          | ~ ( point @ SV66 )
          | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) ) )
        = $true )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[331]) ).

thf(348,plain,
    ! [SV51: $i,SV25: $i,SV67: $i] :
      ( ( ( ~ ( on @ SV67 @ SV25 ) )
        = $true )
      | ( ( ~ ( on @ SV67 @ SV51 )
          | ~ ( point @ SV67 )
          | ( SV67
           != ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
        = $true )
      | ( ( SV25 = SV51 )
        = $true )
      | ( ( plane @ SV51 )
        = $false )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[332]) ).

thf(349,plain,
    ! [SV52: $i,SV26: $i,SV59: $i] :
      ( ( ( point @ SV59 )
        = $false )
      | ( ( ( SV26 = SV52 )
          | ( SV26 = SV59 )
          | ( SV52 = SV59 )
          | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
          | ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[333]) ).

thf(350,plain,
    ! [SV53: $i,SV27: $i,SV60: $i] :
      ( ( ( point @ SV60 )
        = $false )
      | ( ( ( SV27 = SV53 )
          | ( SV27 = SV60 )
          | ( SV53 = SV60 )
          | ( on @ SV53 @ ( line_through_3_points @ SV27 @ SV53 @ SV60 ) )
          | ~ ( collinear @ SV27 @ SV53 @ SV60 ) )
        = $true )
      | ( ( point @ SV53 )
        = $false )
      | ( ( point @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[334]) ).

thf(351,plain,
    ! [SV54: $i,SV28: $i,SV61: $i] :
      ( ( ( point @ SV61 )
        = $false )
      | ( ( ( SV28 = SV54 )
          | ( SV28 = SV61 )
          | ( SV54 = SV61 )
          | ( on @ SV61 @ ( line_through_3_points @ SV28 @ SV54 @ SV61 ) )
          | ~ ( collinear @ SV28 @ SV54 @ SV61 ) )
        = $true )
      | ( ( point @ SV54 )
        = $false )
      | ( ( point @ SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[335]) ).

thf(352,plain,
    ! [SV55: $i,SV29: $i,SV62: $i] :
      ( ( ( point @ SV62 )
        = $false )
      | ( ( ( SV29 = SV55 )
          | ( SV29 = SV62 )
          | ( SV55 = SV62 )
          | ( line @ ( line_through_3_points @ SV29 @ SV55 @ SV62 ) )
          | ~ ( collinear @ SV29 @ SV55 @ SV62 ) )
        = $true )
      | ( ( point @ SV55 )
        = $false )
      | ( ( point @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[336]) ).

thf(353,plain,
    ! [SV30: $i,SV47: $i,SV58: $i,SV41: $i] :
      ( ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( ~ ( on @ SV47 @ SV58 )
          | ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[337]) ).

thf(354,plain,
    ! [SV56: $i,SV4: $i,SV68: $i,SV34: $i] :
      ( ( ( SV34 = SV68 )
        = $true )
      | ( ( ~ ( on @ SV4 @ SV68 )
          | ~ ( on @ SV56 @ SV68 )
          | ~ ( point @ SV4 )
          | ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[338]) ).

thf(355,plain,
    ! [SV35: $i,SV16: $i,SV42: $i] :
      ( ( ( point @ SV42 )
        = $false )
      | ( ( ( collinear @ SV16 @ SV35 @ SV42 )
          | ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( point @ SV35 )
        = $false )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(356,plain,
    ! [SV17: $i,SV36: $i,SV43: $i] :
      ( ( ( point @ SV43 )
        = $false )
      | ( ( ( collinear @ SV36 @ SV17 @ SV43 )
          | ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( point @ SV17 )
        = $false )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(357,plain,
    ! [SV44: $i,SV37: $i,SV18: $i] :
      ( ( ( point @ SV18 )
        = $false )
      | ( ( ( collinear @ SV37 @ SV44 @ SV18 )
          | ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( point @ SV44 )
        = $false )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[341]) ).

thf(358,plain,
    ! [SV38: $i,SV19: $i,SV45: $i] :
      ( ( ( point @ SV45 )
        = $false )
      | ( ( ( collinear @ SV19 @ SV38 @ SV45 )
          | ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( point @ SV38 )
        = $false )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[342]) ).

thf(359,plain,
    ! [SV46: $i,SV39: $i,SV20: $i] :
      ( ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( ( SV20 = SV39 )
          | ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[343]) ).

thf(360,plain,
    ! [SV40: $i,SV57: $i,SV63: $i,SV21: $i] :
      ( ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( ~ ( on @ SV57 @ SV63 )
          | ~ ( plane @ SV63 )
          | ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[344]) ).

thf(361,plain,
    ! [SV48: $i,SV22: $i,SV64: $i] :
      ( ( ( on @ SV64 @ SV22 )
        = $false )
      | ( ( ~ ( on @ SV64 @ SV48 )
          | ~ ( point @ SV64 )
          | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 ) )
        = $true )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[345]) ).

thf(362,plain,
    ! [SV49: $i,SV23: $i,SV65: $i] :
      ( ( ( on @ SV65 @ SV23 )
        = $false )
      | ( ( ~ ( on @ SV65 @ SV49 )
          | ~ ( point @ SV65 )
          | ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 ) )
        = $true )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[346]) ).

thf(363,plain,
    ! [SV50: $i,SV24: $i,SV66: $i] :
      ( ( ( on @ SV66 @ SV24 )
        = $false )
      | ( ( ~ ( on @ SV66 @ SV50 )
          | ~ ( point @ SV66 )
          | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) ) )
        = $true )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[347]) ).

thf(364,plain,
    ! [SV51: $i,SV25: $i,SV67: $i] :
      ( ( ( on @ SV67 @ SV25 )
        = $false )
      | ( ( ~ ( on @ SV67 @ SV51 )
          | ~ ( point @ SV67 )
          | ( SV67
           != ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) ) )
        = $true )
      | ( ( SV25 = SV51 )
        = $true )
      | ( ( plane @ SV51 )
        = $false )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[348]) ).

thf(365,plain,
    ! [SV59: $i,SV52: $i,SV26: $i] :
      ( ( ( SV26 = SV52 )
        = $true )
      | ( ( ( SV26 = SV59 )
          | ( SV52 = SV59 )
          | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
          | ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( point @ SV59 )
        = $false )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[349]) ).

thf(366,plain,
    ! [SV60: $i,SV53: $i,SV27: $i] :
      ( ( ( SV27 = SV53 )
        = $true )
      | ( ( ( SV27 = SV60 )
          | ( SV53 = SV60 )
          | ( on @ SV53 @ ( 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)],[350]) ).

thf(367,plain,
    ! [SV61: $i,SV54: $i,SV28: $i] :
      ( ( ( SV28 = SV54 )
        = $true )
      | ( ( ( SV28 = SV61 )
          | ( SV54 = SV61 )
          | ( on @ SV61 @ ( 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)],[351]) ).

thf(368,plain,
    ! [SV62: $i,SV55: $i,SV29: $i] :
      ( ( ( SV29 = SV55 )
        = $true )
      | ( ( ( SV29 = SV62 )
          | ( SV55 = SV62 )
          | ( line @ ( 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)],[352]) ).

thf(369,plain,
    ! [SV41: $i,SV30: $i,SV58: $i,SV47: $i] :
      ( ( ( ~ ( on @ SV47 @ SV58 ) )
        = $true )
      | ( ( ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[353]) ).

thf(370,plain,
    ! [SV34: $i,SV56: $i,SV68: $i,SV4: $i] :
      ( ( ( ~ ( on @ SV4 @ SV68 ) )
        = $true )
      | ( ( ~ ( on @ SV56 @ SV68 )
          | ~ ( point @ SV4 )
          | ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[354]) ).

thf(371,plain,
    ! [SV42: $i,SV35: $i,SV16: $i] :
      ( ( ( collinear @ SV16 @ SV35 @ SV42 )
        = $true )
      | ( ( ( SV16 = SV35 )
          | ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( point @ SV42 )
        = $false )
      | ( ( point @ SV35 )
        = $false )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[355]) ).

thf(372,plain,
    ! [SV43: $i,SV17: $i,SV36: $i] :
      ( ( ( collinear @ SV36 @ SV17 @ SV43 )
        = $true )
      | ( ( ( SV36 = SV17 )
          | ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( point @ SV43 )
        = $false )
      | ( ( point @ SV17 )
        = $false )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[356]) ).

thf(373,plain,
    ! [SV18: $i,SV44: $i,SV37: $i] :
      ( ( ( collinear @ SV37 @ SV44 @ SV18 )
        = $true )
      | ( ( ( SV37 = SV44 )
          | ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( point @ SV18 )
        = $false )
      | ( ( point @ SV44 )
        = $false )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[357]) ).

thf(374,plain,
    ! [SV45: $i,SV38: $i,SV19: $i] :
      ( ( ( collinear @ SV19 @ SV38 @ SV45 )
        = $true )
      | ( ( ( SV19 = SV38 )
          | ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( point @ SV45 )
        = $false )
      | ( ( point @ SV38 )
        = $false )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[358]) ).

thf(375,plain,
    ! [SV46: $i,SV39: $i,SV20: $i] :
      ( ( ( SV20 = SV39 )
        = $true )
      | ( ( ( SV20 = SV46 )
          | ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[359]) ).

thf(376,plain,
    ! [SV40: $i,SV21: $i,SV63: $i,SV57: $i] :
      ( ( ( ~ ( on @ SV57 @ SV63 ) )
        = $true )
      | ( ( ~ ( plane @ SV63 )
          | ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[360]) ).

thf(377,plain,
    ! [SV22: $i,SV48: $i,SV64: $i] :
      ( ( ( ~ ( on @ SV64 @ SV48 ) )
        = $true )
      | ( ( ~ ( point @ SV64 )
          | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 ) )
        = $true )
      | ( ( on @ SV64 @ SV22 )
        = $false )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[361]) ).

thf(378,plain,
    ! [SV23: $i,SV49: $i,SV65: $i] :
      ( ( ( ~ ( on @ SV65 @ SV49 ) )
        = $true )
      | ( ( ~ ( point @ SV65 )
          | ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 ) )
        = $true )
      | ( ( on @ SV65 @ SV23 )
        = $false )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[362]) ).

thf(379,plain,
    ! [SV24: $i,SV50: $i,SV66: $i] :
      ( ( ( ~ ( on @ SV66 @ SV50 ) )
        = $true )
      | ( ( ~ ( point @ SV66 )
          | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) ) )
        = $true )
      | ( ( on @ SV66 @ SV24 )
        = $false )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[363]) ).

thf(380,plain,
    ! [SV25: $i,SV51: $i,SV67: $i] :
      ( ( ( ~ ( on @ SV67 @ SV51 ) )
        = $true )
      | ( ( ~ ( point @ SV67 )
          | ( SV67
           != ( 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)],[364]) ).

thf(381,plain,
    ! [SV52: $i,SV59: $i,SV26: $i] :
      ( ( ( SV26 = SV59 )
        = $true )
      | ( ( ( SV52 = SV59 )
          | ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
          | ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( SV26 = SV52 )
        = $true )
      | ( ( point @ SV59 )
        = $false )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[365]) ).

thf(382,plain,
    ! [SV53: $i,SV60: $i,SV27: $i] :
      ( ( ( SV27 = SV60 )
        = $true )
      | ( ( ( SV53 = SV60 )
          | ( on @ SV53 @ ( 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)],[366]) ).

thf(383,plain,
    ! [SV54: $i,SV61: $i,SV28: $i] :
      ( ( ( SV28 = SV61 )
        = $true )
      | ( ( ( SV54 = SV61 )
          | ( on @ SV61 @ ( 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)],[367]) ).

thf(384,plain,
    ! [SV55: $i,SV62: $i,SV29: $i] :
      ( ( ( SV29 = SV62 )
        = $true )
      | ( ( ( SV55 = SV62 )
          | ( line @ ( 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)],[368]) ).

thf(385,plain,
    ! [SV41: $i,SV30: $i,SV58: $i,SV47: $i] :
      ( ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( ~ ( point @ SV30 )
          | ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[369]) ).

thf(386,plain,
    ! [SV34: $i,SV56: $i,SV68: $i,SV4: $i] :
      ( ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( ~ ( on @ SV56 @ SV68 )
          | ~ ( point @ SV4 )
          | ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[370]) ).

thf(387,plain,
    ! [SV42: $i,SV35: $i,SV16: $i] :
      ( ( ( SV16 = SV35 )
        = $true )
      | ( ( ( SV16 = SV42 )
          | ( SV35 = SV42 ) )
        = $true )
      | ( ( collinear @ SV16 @ SV35 @ SV42 )
        = $true )
      | ( ( point @ SV42 )
        = $false )
      | ( ( point @ SV35 )
        = $false )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[371]) ).

thf(388,plain,
    ! [SV43: $i,SV17: $i,SV36: $i] :
      ( ( ( SV36 = SV17 )
        = $true )
      | ( ( ( SV36 = SV43 )
          | ( SV17 = SV43 ) )
        = $true )
      | ( ( collinear @ SV36 @ SV17 @ SV43 )
        = $true )
      | ( ( point @ SV43 )
        = $false )
      | ( ( point @ SV17 )
        = $false )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[372]) ).

thf(389,plain,
    ! [SV18: $i,SV44: $i,SV37: $i] :
      ( ( ( SV37 = SV44 )
        = $true )
      | ( ( ( SV37 = SV18 )
          | ( SV44 = SV18 ) )
        = $true )
      | ( ( collinear @ SV37 @ SV44 @ SV18 )
        = $true )
      | ( ( point @ SV18 )
        = $false )
      | ( ( point @ SV44 )
        = $false )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[373]) ).

thf(390,plain,
    ! [SV45: $i,SV38: $i,SV19: $i] :
      ( ( ( SV19 = SV38 )
        = $true )
      | ( ( ( SV19 = SV45 )
          | ( SV38 = SV45 ) )
        = $true )
      | ( ( collinear @ SV19 @ SV38 @ SV45 )
        = $true )
      | ( ( point @ SV45 )
        = $false )
      | ( ( point @ SV38 )
        = $false )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[374]) ).

thf(391,plain,
    ! [SV39: $i,SV46: $i,SV20: $i] :
      ( ( ( SV20 = SV46 )
        = $true )
      | ( ( ( SV39 = SV46 )
          | ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[375]) ).

thf(392,plain,
    ! [SV40: $i,SV21: $i,SV63: $i,SV57: $i] :
      ( ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( ~ ( plane @ SV63 )
          | ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[376]) ).

thf(393,plain,
    ! [SV22: $i,SV48: $i,SV64: $i] :
      ( ( ( on @ SV64 @ SV48 )
        = $false )
      | ( ( ~ ( point @ SV64 )
          | ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 ) )
        = $true )
      | ( ( on @ SV64 @ SV22 )
        = $false )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[377]) ).

thf(394,plain,
    ! [SV23: $i,SV49: $i,SV65: $i] :
      ( ( ( on @ SV65 @ SV49 )
        = $false )
      | ( ( ~ ( point @ SV65 )
          | ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 ) )
        = $true )
      | ( ( on @ SV65 @ SV23 )
        = $false )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[378]) ).

thf(395,plain,
    ! [SV24: $i,SV50: $i,SV66: $i] :
      ( ( ( on @ SV66 @ SV50 )
        = $false )
      | ( ( ~ ( point @ SV66 )
          | ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) ) )
        = $true )
      | ( ( on @ SV66 @ SV24 )
        = $false )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[379]) ).

thf(396,plain,
    ! [SV25: $i,SV51: $i,SV67: $i] :
      ( ( ( on @ SV67 @ SV51 )
        = $false )
      | ( ( ~ ( point @ SV67 )
          | ( SV67
           != ( 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)],[380]) ).

thf(397,plain,
    ! [SV26: $i,SV59: $i,SV52: $i] :
      ( ( ( SV52 = SV59 )
        = $true )
      | ( ( ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
          | ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( SV26 = SV59 )
        = $true )
      | ( ( SV26 = SV52 )
        = $true )
      | ( ( point @ SV59 )
        = $false )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[381]) ).

thf(398,plain,
    ! [SV27: $i,SV60: $i,SV53: $i] :
      ( ( ( SV53 = SV60 )
        = $true )
      | ( ( ( on @ SV53 @ ( 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)],[382]) ).

thf(399,plain,
    ! [SV28: $i,SV61: $i,SV54: $i] :
      ( ( ( SV54 = SV61 )
        = $true )
      | ( ( ( on @ SV61 @ ( 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)],[383]) ).

thf(400,plain,
    ! [SV29: $i,SV62: $i,SV55: $i] :
      ( ( ( SV55 = SV62 )
        = $true )
      | ( ( ( line @ ( 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)],[384]) ).

thf(401,plain,
    ! [SV58: $i,SV47: $i,SV41: $i,SV30: $i] :
      ( ( ( ~ ( point @ SV30 ) )
        = $true )
      | ( ( ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[385]) ).

thf(402,plain,
    ! [SV34: $i,SV4: $i,SV68: $i,SV56: $i] :
      ( ( ( ~ ( on @ SV56 @ SV68 ) )
        = $true )
      | ( ( ~ ( point @ SV4 )
          | ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[386]) ).

thf(403,plain,
    ! [SV35: $i,SV42: $i,SV16: $i] :
      ( ( ( SV16 = SV42 )
        = $true )
      | ( ( SV35 = SV42 )
        = $true )
      | ( ( SV16 = SV35 )
        = $true )
      | ( ( collinear @ SV16 @ SV35 @ SV42 )
        = $true )
      | ( ( point @ SV42 )
        = $false )
      | ( ( point @ SV35 )
        = $false )
      | ( ( point @ SV16 )
        = $false )
      | ( ( on @ SV16 @ ( plane_for_points @ SV16 @ SV35 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[387]) ).

thf(404,plain,
    ! [SV17: $i,SV43: $i,SV36: $i] :
      ( ( ( SV36 = SV43 )
        = $true )
      | ( ( SV17 = SV43 )
        = $true )
      | ( ( SV36 = SV17 )
        = $true )
      | ( ( collinear @ SV36 @ SV17 @ SV43 )
        = $true )
      | ( ( point @ SV43 )
        = $false )
      | ( ( point @ SV17 )
        = $false )
      | ( ( point @ SV36 )
        = $false )
      | ( ( on @ SV17 @ ( plane_for_points @ SV36 @ SV17 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[388]) ).

thf(405,plain,
    ! [SV44: $i,SV18: $i,SV37: $i] :
      ( ( ( SV37 = SV18 )
        = $true )
      | ( ( SV44 = SV18 )
        = $true )
      | ( ( SV37 = SV44 )
        = $true )
      | ( ( collinear @ SV37 @ SV44 @ SV18 )
        = $true )
      | ( ( point @ SV18 )
        = $false )
      | ( ( point @ SV44 )
        = $false )
      | ( ( point @ SV37 )
        = $false )
      | ( ( on @ SV18 @ ( plane_for_points @ SV37 @ SV44 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[389]) ).

thf(406,plain,
    ! [SV38: $i,SV45: $i,SV19: $i] :
      ( ( ( SV19 = SV45 )
        = $true )
      | ( ( SV38 = SV45 )
        = $true )
      | ( ( SV19 = SV38 )
        = $true )
      | ( ( collinear @ SV19 @ SV38 @ SV45 )
        = $true )
      | ( ( point @ SV45 )
        = $false )
      | ( ( point @ SV38 )
        = $false )
      | ( ( point @ SV19 )
        = $false )
      | ( ( plane @ ( plane_for_points @ SV19 @ SV38 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[390]) ).

thf(407,plain,
    ! [SV20: $i,SV46: $i,SV39: $i] :
      ( ( ( SV39 = SV46 )
        = $true )
      | ( ( ! [SY123: $i] :
              ( ~ ( on @ SV20 @ SY123 )
              | ~ ( on @ SV39 @ SY123 )
              | ~ ( on @ SV46 @ SY123 )
              | ~ ( plane @ SY123 )
              | ! [SY124: $i] :
                  ( ~ ( on @ SV20 @ SY124 )
                  | ~ ( on @ SV39 @ SY124 )
                  | ~ ( on @ SV46 @ SY124 )
                  | ~ ( plane @ SY124 )
                  | ( SY123 = SY124 ) ) ) )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[391]) ).

thf(408,plain,
    ! [SV40: $i,SV57: $i,SV21: $i,SV63: $i] :
      ( ( ( ~ ( plane @ SV63 ) )
        = $true )
      | ( ( ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[392]) ).

thf(409,plain,
    ! [SV48: $i,SV22: $i,SV64: $i] :
      ( ( ( ~ ( point @ SV64 ) )
        = $true )
      | ( ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 )
        = $true )
      | ( ( on @ SV64 @ SV48 )
        = $false )
      | ( ( on @ SV64 @ SV22 )
        = $false )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[393]) ).

thf(410,plain,
    ! [SV49: $i,SV23: $i,SV65: $i] :
      ( ( ( ~ ( point @ SV65 ) )
        = $true )
      | ( ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 )
        = $true )
      | ( ( on @ SV65 @ SV49 )
        = $false )
      | ( ( on @ SV65 @ SV23 )
        = $false )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[394]) ).

thf(411,plain,
    ! [SV50: $i,SV24: $i,SV66: $i] :
      ( ( ( ~ ( point @ SV66 ) )
        = $true )
      | ( ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) )
        = $true )
      | ( ( on @ SV66 @ SV50 )
        = $false )
      | ( ( on @ SV66 @ SV24 )
        = $false )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[395]) ).

thf(412,plain,
    ! [SV51: $i,SV25: $i,SV67: $i] :
      ( ( ( ~ ( point @ SV67 ) )
        = $true )
      | ( ( ( SV67
           != ( 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)],[396]) ).

thf(413,plain,
    ! [SV59: $i,SV52: $i,SV26: $i] :
      ( ( ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( ~ ( collinear @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( SV52 = SV59 )
        = $true )
      | ( ( SV26 = SV59 )
        = $true )
      | ( ( SV26 = SV52 )
        = $true )
      | ( ( point @ SV59 )
        = $false )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[397]) ).

thf(414,plain,
    ! [SV60: $i,SV27: $i,SV53: $i] :
      ( ( ( on @ SV53 @ ( 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)],[398]) ).

thf(415,plain,
    ! [SV54: $i,SV28: $i,SV61: $i] :
      ( ( ( on @ SV61 @ ( 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)],[399]) ).

thf(416,plain,
    ! [SV62: $i,SV55: $i,SV29: $i] :
      ( ( ( line @ ( 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)],[400]) ).

thf(417,plain,
    ! [SV58: $i,SV47: $i,SV41: $i,SV30: $i] :
      ( ( ( point @ SV30 )
        = $false )
      | ( ( ~ ( point @ SV41 )
          | ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[401]) ).

thf(418,plain,
    ! [SV34: $i,SV4: $i,SV68: $i,SV56: $i] :
      ( ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( ~ ( point @ SV4 )
          | ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[402]) ).

thf(419,plain,
    ! [SV46: $i,SV39: $i,SV69: $i,SV20: $i] :
      ( ( ( ~ ( on @ SV20 @ SV69 )
          | ~ ( on @ SV39 @ SV69 )
          | ~ ( on @ SV46 @ SV69 )
          | ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[407]) ).

thf(420,plain,
    ! [SV40: $i,SV57: $i,SV21: $i,SV63: $i] :
      ( ( ( plane @ SV63 )
        = $false )
      | ( ( ~ ( point @ SV21 )
          | ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[408]) ).

thf(421,plain,
    ! [SV48: $i,SV22: $i,SV64: $i] :
      ( ( ( point @ SV64 )
        = $false )
      | ( ( on @ ( common_point_on_planes @ SV22 @ SV48 @ SV64 ) @ SV22 )
        = $true )
      | ( ( on @ SV64 @ SV48 )
        = $false )
      | ( ( on @ SV64 @ SV22 )
        = $false )
      | ( ( SV22 = SV48 )
        = $true )
      | ( ( plane @ SV48 )
        = $false )
      | ( ( plane @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[409]) ).

thf(422,plain,
    ! [SV49: $i,SV23: $i,SV65: $i] :
      ( ( ( point @ SV65 )
        = $false )
      | ( ( on @ ( common_point_on_planes @ SV23 @ SV49 @ SV65 ) @ SV49 )
        = $true )
      | ( ( on @ SV65 @ SV49 )
        = $false )
      | ( ( on @ SV65 @ SV23 )
        = $false )
      | ( ( SV23 = SV49 )
        = $true )
      | ( ( plane @ SV49 )
        = $false )
      | ( ( plane @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[410]) ).

thf(423,plain,
    ! [SV50: $i,SV24: $i,SV66: $i] :
      ( ( ( point @ SV66 )
        = $false )
      | ( ( point @ ( common_point_on_planes @ SV24 @ SV50 @ SV66 ) )
        = $true )
      | ( ( on @ SV66 @ SV50 )
        = $false )
      | ( ( on @ SV66 @ SV24 )
        = $false )
      | ( ( SV24 = SV50 )
        = $true )
      | ( ( plane @ SV50 )
        = $false )
      | ( ( plane @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[411]) ).

thf(424,plain,
    ! [SV51: $i,SV25: $i,SV67: $i] :
      ( ( ( point @ SV67 )
        = $false )
      | ( ( ( SV67
           != ( 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)],[412]) ).

thf(425,plain,
    ! [SV59: $i,SV52: $i,SV26: $i] :
      ( ( ( collinear @ SV26 @ SV52 @ SV59 )
        = $false )
      | ( ( on @ SV26 @ ( line_through_3_points @ SV26 @ SV52 @ SV59 ) )
        = $true )
      | ( ( SV52 = SV59 )
        = $true )
      | ( ( SV26 = SV59 )
        = $true )
      | ( ( SV26 = SV52 )
        = $true )
      | ( ( point @ SV59 )
        = $false )
      | ( ( point @ SV52 )
        = $false )
      | ( ( point @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[413]) ).

thf(426,plain,
    ! [SV60: $i,SV53: $i,SV27: $i] :
      ( ( ( collinear @ SV27 @ SV53 @ SV60 )
        = $false )
      | ( ( on @ SV53 @ ( 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)],[414]) ).

thf(427,plain,
    ! [SV61: $i,SV54: $i,SV28: $i] :
      ( ( ( collinear @ SV28 @ SV54 @ SV61 )
        = $false )
      | ( ( on @ SV61 @ ( 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)],[415]) ).

thf(428,plain,
    ! [SV62: $i,SV55: $i,SV29: $i] :
      ( ( ( collinear @ SV29 @ SV55 @ SV62 )
        = $false )
      | ( ( line @ ( 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)],[416]) ).

thf(429,plain,
    ! [SV58: $i,SV30: $i,SV47: $i,SV41: $i] :
      ( ( ( ~ ( point @ SV41 ) )
        = $true )
      | ( ( ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[417]) ).

thf(430,plain,
    ! [SV68: $i,SV34: $i,SV56: $i,SV4: $i] :
      ( ( ( ~ ( point @ SV4 ) )
        = $true )
      | ( ( ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[418]) ).

thf(431,plain,
    ! [SV46: $i,SV39: $i,SV69: $i,SV20: $i] :
      ( ( ( ~ ( on @ SV20 @ SV69 ) )
        = $true )
      | ( ( ~ ( on @ SV39 @ SV69 )
          | ~ ( on @ SV46 @ SV69 )
          | ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[419]) ).

thf(432,plain,
    ! [SV63: $i,SV40: $i,SV57: $i,SV21: $i] :
      ( ( ( ~ ( point @ SV21 ) )
        = $true )
      | ( ( ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[420]) ).

thf(433,plain,
    ! [SV51: $i,SV25: $i,SV67: $i] :
      ( ( ( SV67
          = ( common_point_on_planes @ SV25 @ SV51 @ SV67 ) )
        = $false )
      | ( ( point @ SV67 )
        = $false )
      | ( ( on @ SV67 @ SV51 )
        = $false )
      | ( ( on @ SV67 @ SV25 )
        = $false )
      | ( ( SV25 = SV51 )
        = $true )
      | ( ( plane @ SV51 )
        = $false )
      | ( ( plane @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[424]) ).

thf(434,plain,
    ! [SV58: $i,SV30: $i,SV47: $i,SV41: $i] :
      ( ( ( point @ SV41 )
        = $false )
      | ( ( ~ ( point @ SV47 )
          | ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[429]) ).

thf(435,plain,
    ! [SV68: $i,SV34: $i,SV56: $i,SV4: $i] :
      ( ( ( point @ SV4 )
        = $false )
      | ( ( ~ ( point @ SV56 )
          | ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[430]) ).

thf(436,plain,
    ! [SV46: $i,SV39: $i,SV69: $i,SV20: $i] :
      ( ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( ~ ( on @ SV39 @ SV69 )
          | ~ ( on @ SV46 @ SV69 )
          | ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[431]) ).

thf(437,plain,
    ! [SV63: $i,SV40: $i,SV57: $i,SV21: $i] :
      ( ( ( point @ SV21 )
        = $false )
      | ( ( ~ ( point @ SV57 )
          | ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[432]) ).

thf(438,plain,
    ! [SV58: $i,SV41: $i,SV30: $i,SV47: $i] :
      ( ( ( ~ ( point @ SV47 ) )
        = $true )
      | ( ( ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( point @ SV41 )
        = $false )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[434]) ).

thf(439,plain,
    ! [SV4: $i,SV68: $i,SV34: $i,SV56: $i] :
      ( ( ( ~ ( point @ SV56 ) )
        = $true )
      | ( ( ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( point @ SV4 )
        = $false )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[435]) ).

thf(440,plain,
    ! [SV20: $i,SV46: $i,SV69: $i,SV39: $i] :
      ( ( ( ~ ( on @ SV39 @ SV69 ) )
        = $true )
      | ( ( ~ ( on @ SV46 @ SV69 )
          | ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[436]) ).

thf(441,plain,
    ! [SV63: $i,SV21: $i,SV40: $i,SV57: $i] :
      ( ( ( ~ ( point @ SV57 ) )
        = $true )
      | ( ( ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( point @ SV21 )
        = $false )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[437]) ).

thf(442,plain,
    ! [SV58: $i,SV41: $i,SV30: $i,SV47: $i] :
      ( ( ( point @ SV47 )
        = $false )
      | ( ( ( SV30 = SV41 )
          | ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( point @ SV41 )
        = $false )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[438]) ).

thf(443,plain,
    ! [SV4: $i,SV68: $i,SV34: $i,SV56: $i] :
      ( ( ( point @ SV56 )
        = $false )
      | ( ( ~ ( line @ SV34 )
          | ~ ( line @ SV68 ) )
        = $true )
      | ( ( point @ SV4 )
        = $false )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[439]) ).

thf(444,plain,
    ! [SV20: $i,SV46: $i,SV69: $i,SV39: $i] :
      ( ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( ~ ( on @ SV46 @ SV69 )
          | ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[440]) ).

thf(445,plain,
    ! [SV63: $i,SV21: $i,SV40: $i,SV57: $i] :
      ( ( ( point @ SV57 )
        = $false )
      | ( ( ~ ( line @ SV40 )
          | ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( point @ SV21 )
        = $false )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[441]) ).

thf(446,plain,
    ! [SV58: $i,SV47: $i,SV41: $i,SV30: $i] :
      ( ( ( SV30 = SV41 )
        = $true )
      | ( ( ( SV30 = SV47 )
          | ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( point @ SV47 )
        = $false )
      | ( ( point @ SV41 )
        = $false )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[442]) ).

thf(447,plain,
    ! [SV4: $i,SV56: $i,SV68: $i,SV34: $i] :
      ( ( ( ~ ( line @ SV34 ) )
        = $true )
      | ( ( ~ ( line @ SV68 ) )
        = $true )
      | ( ( point @ SV56 )
        = $false )
      | ( ( point @ SV4 )
        = $false )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[443]) ).

thf(448,plain,
    ! [SV39: $i,SV20: $i,SV69: $i,SV46: $i] :
      ( ( ( ~ ( on @ SV46 @ SV69 ) )
        = $true )
      | ( ( ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[444]) ).

thf(449,plain,
    ! [SV63: $i,SV57: $i,SV21: $i,SV40: $i] :
      ( ( ( ~ ( line @ SV40 ) )
        = $true )
      | ( ( ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( point @ SV57 )
        = $false )
      | ( ( point @ SV21 )
        = $false )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[445]) ).

thf(450,plain,
    ! [SV58: $i,SV41: $i,SV47: $i,SV30: $i] :
      ( ( ( SV30 = SV47 )
        = $true )
      | ( ( ( SV41 = SV47 )
          | ~ ( line @ SV58 ) )
        = $true )
      | ( ( SV30 = SV41 )
        = $true )
      | ( ( point @ SV47 )
        = $false )
      | ( ( point @ SV41 )
        = $false )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[446]) ).

thf(451,plain,
    ! [SV4: $i,SV56: $i,SV68: $i,SV34: $i] :
      ( ( ( line @ SV34 )
        = $false )
      | ( ( ~ ( line @ SV68 ) )
        = $true )
      | ( ( point @ SV56 )
        = $false )
      | ( ( point @ SV4 )
        = $false )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[447]) ).

thf(452,plain,
    ! [SV39: $i,SV20: $i,SV69: $i,SV46: $i] :
      ( ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( ~ ( plane @ SV69 )
          | ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[448]) ).

thf(453,plain,
    ! [SV63: $i,SV57: $i,SV21: $i,SV40: $i] :
      ( ( ( line @ SV40 )
        = $false )
      | ( ( ( SV21 = SV57 )
          | ( on @ SV40 @ SV63 ) )
        = $true )
      | ( ( point @ SV57 )
        = $false )
      | ( ( point @ SV21 )
        = $false )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[449]) ).

thf(454,plain,
    ! [SV30: $i,SV58: $i,SV47: $i,SV41: $i] :
      ( ( ( SV41 = SV47 )
        = $true )
      | ( ( ~ ( line @ SV58 ) )
        = $true )
      | ( ( SV30 = SV47 )
        = $true )
      | ( ( SV30 = SV41 )
        = $true )
      | ( ( point @ SV47 )
        = $false )
      | ( ( point @ SV41 )
        = $false )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[450]) ).

thf(455,plain,
    ! [SV4: $i,SV56: $i,SV34: $i,SV68: $i] :
      ( ( ( line @ SV68 )
        = $false )
      | ( ( line @ SV34 )
        = $false )
      | ( ( point @ SV56 )
        = $false )
      | ( ( point @ SV4 )
        = $false )
      | ( ( on @ SV56 @ SV68 )
        = $false )
      | ( ( on @ SV4 @ SV68 )
        = $false )
      | ( ( SV34 = SV68 )
        = $true )
      | ( ( on @ SV56 @ SV34 )
        = $false )
      | ( ( SV4 = SV56 )
        = $true )
      | ( ( on @ SV4 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[451]) ).

thf(456,plain,
    ! [SV46: $i,SV39: $i,SV20: $i,SV69: $i] :
      ( ( ( ~ ( plane @ SV69 ) )
        = $true )
      | ( ( ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[452]) ).

thf(457,plain,
    ! [SV63: $i,SV40: $i,SV57: $i,SV21: $i] :
      ( ( ( SV21 = SV57 )
        = $true )
      | ( ( on @ SV40 @ SV63 )
        = $true )
      | ( ( line @ SV40 )
        = $false )
      | ( ( point @ SV57 )
        = $false )
      | ( ( point @ SV21 )
        = $false )
      | ( ( plane @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV63 )
        = $false )
      | ( ( on @ SV21 @ SV63 )
        = $false )
      | ( ( on @ SV57 @ SV40 )
        = $false )
      | ( ( on @ SV21 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[453]) ).

thf(458,plain,
    ! [SV30: $i,SV47: $i,SV41: $i,SV58: $i] :
      ( ( ( line @ SV58 )
        = $false )
      | ( ( SV41 = SV47 )
        = $true )
      | ( ( SV30 = SV47 )
        = $true )
      | ( ( SV30 = SV41 )
        = $true )
      | ( ( point @ SV47 )
        = $false )
      | ( ( point @ SV41 )
        = $false )
      | ( ( point @ SV30 )
        = $false )
      | ( ( on @ SV47 @ SV58 )
        = $false )
      | ( ( on @ SV41 @ SV58 )
        = $false )
      | ( ( on @ SV30 @ SV58 )
        = $false )
      | ( ( collinear @ SV30 @ SV41 @ SV47 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[454]) ).

thf(459,plain,
    ! [SV46: $i,SV39: $i,SV20: $i,SV69: $i] :
      ( ( ( plane @ SV69 )
        = $false )
      | ( ( ! [SY136: $i] :
              ( ~ ( on @ SV20 @ SY136 )
              | ~ ( on @ SV39 @ SY136 )
              | ~ ( on @ SV46 @ SY136 )
              | ~ ( plane @ SY136 )
              | ( SV69 = SY136 ) ) )
        = $true )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[456]) ).

thf(460,plain,
    ! [SV69: $i,SV46: $i,SV39: $i,SV70: $i,SV20: $i] :
      ( ( ( ~ ( on @ SV20 @ SV70 )
          | ~ ( on @ SV39 @ SV70 )
          | ~ ( on @ SV46 @ SV70 )
          | ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[459]) ).

thf(461,plain,
    ! [SV69: $i,SV46: $i,SV39: $i,SV70: $i,SV20: $i] :
      ( ( ( ~ ( on @ SV20 @ SV70 ) )
        = $true )
      | ( ( ~ ( on @ SV39 @ SV70 )
          | ~ ( on @ SV46 @ SV70 )
          | ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[460]) ).

thf(462,plain,
    ! [SV69: $i,SV46: $i,SV39: $i,SV70: $i,SV20: $i] :
      ( ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( ~ ( on @ SV39 @ SV70 )
          | ~ ( on @ SV46 @ SV70 )
          | ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[461]) ).

thf(463,plain,
    ! [SV20: $i,SV69: $i,SV46: $i,SV70: $i,SV39: $i] :
      ( ( ( ~ ( on @ SV39 @ SV70 ) )
        = $true )
      | ( ( ~ ( on @ SV46 @ SV70 )
          | ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[462]) ).

thf(464,plain,
    ! [SV20: $i,SV69: $i,SV46: $i,SV70: $i,SV39: $i] :
      ( ( ( on @ SV39 @ SV70 )
        = $false )
      | ( ( ~ ( on @ SV46 @ SV70 )
          | ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[463]) ).

thf(465,plain,
    ! [SV20: $i,SV39: $i,SV69: $i,SV70: $i,SV46: $i] :
      ( ( ( ~ ( on @ SV46 @ SV70 ) )
        = $true )
      | ( ( ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( on @ SV39 @ SV70 )
        = $false )
      | ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[464]) ).

thf(466,plain,
    ! [SV20: $i,SV39: $i,SV69: $i,SV70: $i,SV46: $i] :
      ( ( ( on @ SV46 @ SV70 )
        = $false )
      | ( ( ~ ( plane @ SV70 )
          | ( SV69 = SV70 ) )
        = $true )
      | ( ( on @ SV39 @ SV70 )
        = $false )
      | ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[465]) ).

thf(467,plain,
    ! [SV20: $i,SV39: $i,SV46: $i,SV69: $i,SV70: $i] :
      ( ( ( ~ ( plane @ SV70 ) )
        = $true )
      | ( ( SV69 = SV70 )
        = $true )
      | ( ( on @ SV46 @ SV70 )
        = $false )
      | ( ( on @ SV39 @ SV70 )
        = $false )
      | ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[466]) ).

thf(468,plain,
    ! [SV20: $i,SV39: $i,SV46: $i,SV69: $i,SV70: $i] :
      ( ( ( plane @ SV70 )
        = $false )
      | ( ( SV69 = SV70 )
        = $true )
      | ( ( on @ SV46 @ SV70 )
        = $false )
      | ( ( on @ SV39 @ SV70 )
        = $false )
      | ( ( on @ SV20 @ SV70 )
        = $false )
      | ( ( plane @ SV69 )
        = $false )
      | ( ( on @ SV46 @ SV69 )
        = $false )
      | ( ( on @ SV39 @ SV69 )
        = $false )
      | ( ( on @ SV20 @ SV69 )
        = $false )
      | ( ( SV39 = SV46 )
        = $true )
      | ( ( SV20 = SV46 )
        = $true )
      | ( ( SV20 = SV39 )
        = $true )
      | ( ( collinear @ SV20 @ SV39 @ SV46 )
        = $true )
      | ( ( point @ SV46 )
        = $false )
      | ( ( point @ SV39 )
        = $false )
      | ( ( point @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[467]) ).

thf(469,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[105,468,458,457,455,433,428,427,426,425,423,422,421,406,405,404,403,305,304,303,249,248,247,227,225,224,223,220,219,218,217,182,151,150,149,148,127,111,110,109,108,107,106]) ).

thf(470,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[469]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO077-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 12:08:57 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41   No.of.Axioms: 42
% 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  .
% 0.20/0.47  (rf:0,axioms:42,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:44,loop_count:0,foatp_calls:0,translation:fof_full)........................
% 8.67/8.88  
% 8.67/8.88  ********************************
% 8.67/8.88  *   All subproblems solved!    *
% 8.67/8.88  ********************************
% 8.67/8.88  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,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:469,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.83/9.02  
% 8.83/9.02  %**** Beginning of derivation protocol ****
% 8.83/9.02  % SZS output start CNFRefutation
% See solution above
% 8.83/9.02  
% 8.83/9.02  %**** End of derivation protocol ****
% 8.83/9.02  %**** no. of clauses in derivation: 470 ****
% 8.83/9.02  %**** clause counter: 469 ****
% 8.83/9.02  
% 8.83/9.02  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,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:469,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------