TSTP Solution File: GEO016-3 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GEO016-3 : 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 : n007.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 05:06:06 EDT 2022

% Result   : Unsatisfiable 0.38s 0.59s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  251 ( 132 unt;  14 typ;   0 def)
%            Number of atoms       : 1711 ( 509 equ;   0 cnn)
%            Maximal formula atoms :    8 (   7 avg)
%            Number of connectives : 4459 ( 399   ~; 658   |;   0   &;3402   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   9 con; 0-6 aty)
%            Number of variables   : 1083 (   0   ^1083   !;   0   ?;1083   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_between,type,
    between: $i > $i > $i > $o ).

thf(tp_continuous,type,
    continuous: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_equidistant,type,
    equidistant: $i > $i > $i > $i > $o ).

thf(tp_euclid1,type,
    euclid1: $i > $i > $i > $i > $i > $i ).

thf(tp_euclid2,type,
    euclid2: $i > $i > $i > $i > $i > $i ).

thf(tp_extension,type,
    extension: $i > $i > $i > $i > $i ).

thf(tp_inner_pasch,type,
    inner_pasch: $i > $i > $i > $i > $i > $i ).

thf(tp_lower_dimension_point_1,type,
    lower_dimension_point_1: $i ).

thf(tp_lower_dimension_point_2,type,
    lower_dimension_point_2: $i ).

thf(tp_lower_dimension_point_3,type,
    lower_dimension_point_3: $i ).

thf(tp_u,type,
    u: $i ).

thf(tp_v,type,
    v: $i ).

thf(tp_w,type,
    w: $i ).

thf(tp_x,type,
    x: $i ).

thf(1,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ~ ( equidistant @ U @ V @ W @ X )
      | ( equidistant @ W @ X @ U @ V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).

thf(2,axiom,
    ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).

thf(3,axiom,
    ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
      ( ~ ( equidistant @ U @ V @ U @ V1 )
      | ~ ( equidistant @ U @ X @ U @ X1 )
      | ~ ( between @ U @ V @ X )
      | ~ ( between @ V @ W @ X )
      | ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).

thf(4,axiom,
    ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
      ( ~ ( equidistant @ U @ V @ U @ V1 )
      | ~ ( equidistant @ U @ X @ U @ X1 )
      | ~ ( between @ U @ V @ X )
      | ~ ( between @ V @ W @ X )
      | ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).

thf(5,axiom,
    ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
      ( ~ ( between @ U @ W @ Y )
      | ~ ( between @ V @ W @ X )
      | ( U = W )
      | ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).

thf(6,axiom,
    ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
      ( ~ ( between @ U @ W @ Y )
      | ~ ( between @ V @ W @ X )
      | ( U = W )
      | ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).

thf(7,axiom,
    ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
      ( ~ ( between @ U @ W @ Y )
      | ~ ( between @ V @ W @ X )
      | ( U = W )
      | ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).

thf(8,axiom,
    ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
      ( ~ ( equidistant @ X @ W @ X @ V )
      | ~ ( equidistant @ Y @ W @ Y @ V )
      | ~ ( equidistant @ Z @ W @ Z @ V )
      | ( between @ X @ Y @ Z )
      | ( between @ Y @ Z @ X )
      | ( between @ Z @ X @ Y )
      | ( W = V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).

thf(9,axiom,
    ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).

thf(10,axiom,
    ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).

thf(11,axiom,
    ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).

thf(12,axiom,
    ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
      ( ~ ( between @ U @ V @ W )
      | ~ ( between @ Y @ X @ W )
      | ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).

thf(13,axiom,
    ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
      ( ~ ( between @ U @ V @ W )
      | ~ ( between @ Y @ X @ W )
      | ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).

thf(14,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( between @ X @ Y @ X )
      | ( X = Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).

thf(15,axiom,
    ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
      ( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
      | ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
      | ~ ( equidistant @ X @ V @ X1 @ V1 )
      | ~ ( equidistant @ Y @ V @ Y1 @ V1 )
      | ~ ( between @ X @ Y @ Z )
      | ~ ( between @ X1 @ Y1 @ Z1 )
      | ( X = Y )
      | ( equidistant @ Z @ V @ Z1 @ V1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).

thf(16,axiom,
    ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).

thf(17,axiom,
    ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).

thf(18,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( equidistant @ X @ Y @ Z @ Z )
      | ( X = Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).

thf(19,axiom,
    ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
      ( ~ ( equidistant @ X @ Y @ Z @ V )
      | ~ ( equidistant @ X @ Y @ V2 @ W )
      | ( equidistant @ Z @ V @ V2 @ W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

thf(20,axiom,
    ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

thf(21,axiom,
    equidistant @ u @ v @ w @ x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).

thf(22,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(23,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[22]) ).

thf(24,negated_conjecture,
    ~ ( equidistant @ v @ u @ w @ x ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry) ).

thf(25,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( equidistant @ U @ V @ W @ X )
          | ( equidistant @ W @ X @ U @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(27,plain,
    ( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(28,plain,
    ( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
          ( ~ ( equidistant @ U @ V @ U @ V1 )
          | ~ ( equidistant @ U @ X @ U @ X1 )
          | ~ ( between @ U @ V @ X )
          | ~ ( between @ V @ W @ X )
          | ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(29,plain,
    ( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
          ( ~ ( equidistant @ U @ V @ U @ V1 )
          | ~ ( equidistant @ U @ X @ U @ X1 )
          | ~ ( between @ U @ V @ X )
          | ~ ( between @ V @ W @ X )
          | ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(30,plain,
    ( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ~ ( between @ V @ W @ X )
          | ( U = W )
          | ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(31,plain,
    ( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ~ ( between @ V @ W @ X )
          | ( U = W )
          | ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(32,plain,
    ( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ~ ( between @ V @ W @ X )
          | ( U = W )
          | ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(33,plain,
    ( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
          ( ~ ( equidistant @ X @ W @ X @ V )
          | ~ ( equidistant @ Y @ W @ Y @ V )
          | ~ ( equidistant @ Z @ W @ Z @ V )
          | ( between @ X @ Y @ Z )
          | ( between @ Y @ Z @ X )
          | ( between @ Z @ X @ Y )
          | ( W = V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(34,plain,
    ( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(35,plain,
    ( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(36,plain,
    ( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(37,plain,
    ( ( ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
          ( ~ ( between @ U @ V @ W )
          | ~ ( between @ Y @ X @ W )
          | ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(38,plain,
    ( ( ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
          ( ~ ( between @ U @ V @ W )
          | ~ ( between @ Y @ X @ W )
          | ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(39,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( between @ X @ Y @ X )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(40,plain,
    ( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
          ( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
          | ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
          | ~ ( equidistant @ X @ V @ X1 @ V1 )
          | ~ ( equidistant @ Y @ V @ Y1 @ V1 )
          | ~ ( between @ X @ Y @ Z )
          | ~ ( between @ X1 @ Y1 @ Z1 )
          | ( X = Y )
          | ( equidistant @ Z @ V @ Z1 @ V1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(41,plain,
    ( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(42,plain,
    ( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(43,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( equidistant @ X @ Y @ Z @ Z )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(44,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
          ( ~ ( equidistant @ X @ Y @ Z @ V )
          | ~ ( equidistant @ X @ Y @ V2 @ W )
          | ( equidistant @ Z @ V @ V2 @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(45,plain,
    ( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(46,plain,
    ( ( equidistant @ u @ v @ w @ x )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(47,plain,
    ( ( ~ ( equidistant @ v @ u @ w @ x ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(48,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[25]) ).

thf(49,plain,
    ( ( ! [U: $i,V: $i,V1: $i,X: $i] :
          ( ~ ( equidistant @ U @ V @ U @ V1 )
          | ! [X1: $i] :
              ( ~ ( equidistant @ U @ X @ U @ X1 )
              | ~ ( between @ U @ V @ X )
              | ! [W: $i] :
                  ( ~ ( between @ V @ W @ X )
                  | ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(50,plain,
    ( ( ! [U: $i,V: $i,V1: $i,X: $i] :
          ( ~ ( equidistant @ U @ V @ U @ V1 )
          | ! [X1: $i] :
              ( ~ ( equidistant @ U @ X @ U @ X1 )
              | ~ ( between @ U @ V @ X )
              | ! [W: $i] :
                  ( ~ ( between @ V @ W @ X )
                  | ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(51,plain,
    ( ( ! [U: $i,W: $i,Y: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ! [V: $i,X: $i] :
              ( ~ ( between @ V @ W @ X )
              | ( U = W )
              | ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(52,plain,
    ( ( ! [U: $i,W: $i,Y: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ! [V: $i,X: $i] :
              ( ~ ( between @ V @ W @ X )
              | ( U = W )
              | ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[31]) ).

thf(53,plain,
    ( ( ! [U: $i,W: $i,Y: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ! [V: $i,X: $i] :
              ( ~ ( between @ V @ W @ X )
              | ( U = W )
              | ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[32]) ).

thf(54,plain,
    ( ( ! [X: $i,W: $i,V: $i] :
          ( ~ ( equidistant @ X @ W @ X @ V )
          | ! [Y: $i] :
              ( ~ ( equidistant @ Y @ W @ Y @ V )
              | ! [Z: $i] :
                  ( ~ ( equidistant @ Z @ W @ Z @ V )
                  | ( between @ X @ Y @ Z )
                  | ( between @ Y @ Z @ X )
                  | ( W = V )
                  | ( between @ Z @ X @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[33]) ).

thf(55,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( between @ U @ V @ W )
          | ! [Y: $i,X: $i] :
              ( ~ ( between @ Y @ X @ W )
              | ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(56,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( between @ U @ V @ W )
          | ! [Y: $i,X: $i] :
              ( ~ ( between @ Y @ X @ W )
              | ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[38]) ).

thf(57,plain,
    ( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
          ( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
          | ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
          | ! [V: $i,V1: $i] :
              ( ~ ( equidistant @ X @ V @ X1 @ V1 )
              | ~ ( equidistant @ Y @ V @ Y1 @ V1 )
              | ~ ( between @ X @ Y @ Z )
              | ~ ( between @ X1 @ Y1 @ Z1 )
              | ( X = Y )
              | ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(58,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ! [Z: $i] :
              ~ ( equidistant @ X @ Y @ Z @ Z )
          | ( X = Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(59,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
          ( ~ ( equidistant @ X @ Y @ Z @ V )
          | ! [V2: $i,W: $i] :
              ( ~ ( equidistant @ X @ Y @ V2 @ W )
              | ( equidistant @ Z @ V @ V2 @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[44]) ).

thf(60,plain,
    ( ( ~ ( equidistant @ v @ u @ w @ x ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(61,plain,
    ( ( equidistant @ u @ v @ w @ x )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(62,plain,
    ( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(63,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
          ( ~ ( equidistant @ X @ Y @ Z @ V )
          | ! [V2: $i,W: $i] :
              ( ~ ( equidistant @ X @ Y @ V2 @ W )
              | ( equidistant @ Z @ V @ V2 @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(64,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ! [Z: $i] :
              ~ ( equidistant @ X @ Y @ Z @ Z )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(65,plain,
    ( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(66,plain,
    ( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(67,plain,
    ( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
          ( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
          | ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
          | ! [V: $i,V1: $i] :
              ( ~ ( equidistant @ X @ V @ X1 @ V1 )
              | ~ ( equidistant @ Y @ V @ Y1 @ V1 )
              | ~ ( between @ X @ Y @ Z )
              | ~ ( between @ X1 @ Y1 @ Z1 )
              | ( X = Y )
              | ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(68,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( between @ X @ Y @ X )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(69,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( between @ U @ V @ W )
          | ! [Y: $i,X: $i] :
              ( ~ ( between @ Y @ X @ W )
              | ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(70,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( between @ U @ V @ W )
          | ! [Y: $i,X: $i] :
              ( ~ ( between @ Y @ X @ W )
              | ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(71,plain,
    ( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(72,plain,
    ( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(73,plain,
    ( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(74,plain,
    ( ( ! [X: $i,W: $i,V: $i] :
          ( ~ ( equidistant @ X @ W @ X @ V )
          | ! [Y: $i] :
              ( ~ ( equidistant @ Y @ W @ Y @ V )
              | ! [Z: $i] :
                  ( ~ ( equidistant @ Z @ W @ Z @ V )
                  | ( between @ X @ Y @ Z )
                  | ( between @ Y @ Z @ X )
                  | ( W = V )
                  | ( between @ Z @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(75,plain,
    ( ( ! [U: $i,W: $i,Y: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ! [V: $i,X: $i] :
              ( ~ ( between @ V @ W @ X )
              | ( U = W )
              | ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(76,plain,
    ( ( ! [U: $i,W: $i,Y: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ! [V: $i,X: $i] :
              ( ~ ( between @ V @ W @ X )
              | ( U = W )
              | ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(77,plain,
    ( ( ! [U: $i,W: $i,Y: $i] :
          ( ~ ( between @ U @ W @ Y )
          | ! [V: $i,X: $i] :
              ( ~ ( between @ V @ W @ X )
              | ( U = W )
              | ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(78,plain,
    ( ( ! [U: $i,V: $i,V1: $i,X: $i] :
          ( ~ ( equidistant @ U @ V @ U @ V1 )
          | ! [X1: $i] :
              ( ~ ( equidistant @ U @ X @ U @ X1 )
              | ~ ( between @ U @ V @ X )
              | ! [W: $i] :
                  ( ~ ( between @ V @ W @ X )
                  | ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(79,plain,
    ( ( ! [U: $i,V: $i,V1: $i,X: $i] :
          ( ~ ( equidistant @ U @ V @ U @ V1 )
          | ! [X1: $i] :
              ( ~ ( equidistant @ U @ X @ U @ X1 )
              | ~ ( between @ U @ V @ X )
              | ! [W: $i] :
                  ( ~ ( between @ V @ W @ X )
                  | ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(80,plain,
    ( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(81,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( equidistant @ U @ V @ W @ X )
          | ( equidistant @ W @ X @ U @ V ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(82,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(83,plain,
    ( ( equidistant @ v @ u @ w @ x )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(84,plain,
    ! [SV1: $i] :
      ( ( ! [SY77: $i] : ( equidistant @ SV1 @ SY77 @ SY77 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(85,plain,
    ! [SV2: $i] :
      ( ( ! [SY78: $i,SY79: $i,SY80: $i] :
            ( ~ ( equidistant @ SV2 @ SY78 @ SY79 @ SY80 )
            | ! [SY81: $i,SY82: $i] :
                ( ~ ( equidistant @ SV2 @ SY78 @ SY81 @ SY82 )
                | ( equidistant @ SY79 @ SY80 @ SY81 @ SY82 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(86,plain,
    ! [SV3: $i] :
      ( ( ! [SY83: $i] :
            ( ! [SY84: $i] :
                ~ ( equidistant @ SV3 @ SY83 @ SY84 @ SY84 )
            | ( SV3 = SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(87,plain,
    ! [SV4: $i] :
      ( ( ! [SY85: $i,SY86: $i,SY87: $i] : ( between @ SV4 @ SY85 @ ( extension @ SV4 @ SY85 @ SY86 @ SY87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(88,plain,
    ! [SV5: $i] :
      ( ( ! [SY88: $i,SY89: $i,SY90: $i] : ( equidistant @ SV5 @ ( extension @ SY88 @ SV5 @ SY89 @ SY90 ) @ SY89 @ SY90 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(89,plain,
    ! [SV6: $i] :
      ( ( ! [SY91: $i,SY92: $i,SY93: $i,SY94: $i,SY95: $i] :
            ( ~ ( equidistant @ SV6 @ SY91 @ SY92 @ SY93 )
            | ~ ( equidistant @ SY91 @ SY94 @ SY93 @ SY95 )
            | ! [SY96: $i,SY97: $i] :
                ( ~ ( equidistant @ SV6 @ SY96 @ SY92 @ SY97 )
                | ~ ( equidistant @ SY91 @ SY96 @ SY93 @ SY97 )
                | ~ ( between @ SV6 @ SY91 @ SY94 )
                | ~ ( between @ SY92 @ SY93 @ SY95 )
                | ( SV6 = SY91 )
                | ( equidistant @ SY94 @ SY96 @ SY95 @ SY97 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(90,plain,
    ! [SV7: $i] :
      ( ( ! [SY98: $i] :
            ( ~ ( between @ SV7 @ SY98 @ SV7 )
            | ( SV7 = SY98 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(91,plain,
    ! [SV8: $i] :
      ( ( ! [SY99: $i,SY100: $i] :
            ( ~ ( between @ SV8 @ SY99 @ SY100 )
            | ! [SY101: $i,SY102: $i] :
                ( ~ ( between @ SY101 @ SY102 @ SY100 )
                | ( between @ SY99 @ ( inner_pasch @ SV8 @ SY99 @ SY100 @ SY102 @ SY101 ) @ SY101 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(92,plain,
    ! [SV9: $i] :
      ( ( ! [SY103: $i,SY104: $i] :
            ( ~ ( between @ SV9 @ SY103 @ SY104 )
            | ! [SY105: $i,SY106: $i] :
                ( ~ ( between @ SY105 @ SY106 @ SY104 )
                | ( between @ SY106 @ ( inner_pasch @ SV9 @ SY103 @ SY104 @ SY106 @ SY105 ) @ SV9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(93,plain,
    ( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(94,plain,
    ( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(95,plain,
    ( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(96,plain,
    ! [SV10: $i] :
      ( ( ! [SY107: $i,SY108: $i] :
            ( ~ ( equidistant @ SV10 @ SY107 @ SV10 @ SY108 )
            | ! [SY109: $i] :
                ( ~ ( equidistant @ SY109 @ SY107 @ SY109 @ SY108 )
                | ! [SY110: $i] :
                    ( ~ ( equidistant @ SY110 @ SY107 @ SY110 @ SY108 )
                    | ( between @ SV10 @ SY109 @ SY110 )
                    | ( between @ SY109 @ SY110 @ SV10 )
                    | ( SY107 = SY108 )
                    | ( between @ SY110 @ SV10 @ SY109 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(97,plain,
    ! [SV11: $i] :
      ( ( ! [SY111: $i,SY112: $i] :
            ( ~ ( between @ SV11 @ SY111 @ SY112 )
            | ! [SY113: $i,SY114: $i] :
                ( ~ ( between @ SY113 @ SY111 @ SY114 )
                | ( SV11 = SY111 )
                | ( between @ SV11 @ SY113 @ ( euclid1 @ SV11 @ SY113 @ SY111 @ SY114 @ SY112 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(98,plain,
    ! [SV12: $i] :
      ( ( ! [SY115: $i,SY116: $i] :
            ( ~ ( between @ SV12 @ SY115 @ SY116 )
            | ! [SY117: $i,SY118: $i] :
                ( ~ ( between @ SY117 @ SY115 @ SY118 )
                | ( SV12 = SY115 )
                | ( between @ SV12 @ SY118 @ ( euclid2 @ SV12 @ SY117 @ SY115 @ SY118 @ SY116 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(99,plain,
    ! [SV13: $i] :
      ( ( ! [SY119: $i,SY120: $i] :
            ( ~ ( between @ SV13 @ SY119 @ SY120 )
            | ! [SY121: $i,SY122: $i] :
                ( ~ ( between @ SY121 @ SY119 @ SY122 )
                | ( SV13 = SY119 )
                | ( between @ ( euclid1 @ SV13 @ SY121 @ SY119 @ SY122 @ SY120 ) @ SY120 @ ( euclid2 @ SV13 @ SY121 @ SY119 @ SY122 @ SY120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(100,plain,
    ! [SV14: $i] :
      ( ( ! [SY123: $i,SY124: $i,SY125: $i] :
            ( ~ ( equidistant @ SV14 @ SY123 @ SV14 @ SY124 )
            | ! [SY126: $i] :
                ( ~ ( equidistant @ SV14 @ SY125 @ SV14 @ SY126 )
                | ~ ( between @ SV14 @ SY123 @ SY125 )
                | ! [SY127: $i] :
                    ( ~ ( between @ SY123 @ SY127 @ SY125 )
                    | ( between @ SY124 @ ( continuous @ SV14 @ SY123 @ SY124 @ SY127 @ SY125 @ SY126 ) @ SY126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(101,plain,
    ! [SV15: $i] :
      ( ( ! [SY128: $i,SY129: $i,SY130: $i] :
            ( ~ ( equidistant @ SV15 @ SY128 @ SV15 @ SY129 )
            | ! [SY131: $i] :
                ( ~ ( equidistant @ SV15 @ SY130 @ SV15 @ SY131 )
                | ~ ( between @ SV15 @ SY128 @ SY130 )
                | ! [SY132: $i] :
                    ( ~ ( between @ SY128 @ SY132 @ SY130 )
                    | ( equidistant @ SV15 @ SY132 @ SV15 @ ( continuous @ SV15 @ SY128 @ SY129 @ SY132 @ SY130 @ SY131 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(102,plain,
    ! [SV16: $i] :
      ( ( ! [SY133: $i] : ( equidistant @ SV16 @ SY133 @ SV16 @ SY133 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(103,plain,
    ! [SV17: $i] :
      ( ( ! [SY134: $i,SY135: $i,SY136: $i] :
            ( ~ ( equidistant @ SV17 @ SY134 @ SY135 @ SY136 )
            | ( equidistant @ SY135 @ SY136 @ SV17 @ SY134 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(104,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(105,plain,
    ! [SV18: $i,SV1: $i] :
      ( ( equidistant @ SV1 @ SV18 @ SV18 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(106,plain,
    ! [SV19: $i,SV2: $i] :
      ( ( ! [SY137: $i,SY138: $i] :
            ( ~ ( equidistant @ SV2 @ SV19 @ SY137 @ SY138 )
            | ! [SY139: $i,SY140: $i] :
                ( ~ ( equidistant @ SV2 @ SV19 @ SY139 @ SY140 )
                | ( equidistant @ SY137 @ SY138 @ SY139 @ SY140 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(107,plain,
    ! [SV20: $i,SV3: $i] :
      ( ( ! [SY141: $i] :
            ~ ( equidistant @ SV3 @ SV20 @ SY141 @ SY141 )
        | ( SV3 = SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(108,plain,
    ! [SV21: $i,SV4: $i] :
      ( ( ! [SY142: $i,SY143: $i] : ( between @ SV4 @ SV21 @ ( extension @ SV4 @ SV21 @ SY142 @ SY143 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(109,plain,
    ! [SV22: $i,SV5: $i] :
      ( ( ! [SY144: $i,SY145: $i] : ( equidistant @ SV5 @ ( extension @ SV22 @ SV5 @ SY144 @ SY145 ) @ SY144 @ SY145 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(110,plain,
    ! [SV23: $i,SV6: $i] :
      ( ( ! [SY146: $i,SY147: $i,SY148: $i,SY149: $i] :
            ( ~ ( equidistant @ SV6 @ SV23 @ SY146 @ SY147 )
            | ~ ( equidistant @ SV23 @ SY148 @ SY147 @ SY149 )
            | ! [SY150: $i,SY151: $i] :
                ( ~ ( equidistant @ SV6 @ SY150 @ SY146 @ SY151 )
                | ~ ( equidistant @ SV23 @ SY150 @ SY147 @ SY151 )
                | ~ ( between @ SV6 @ SV23 @ SY148 )
                | ~ ( between @ SY146 @ SY147 @ SY149 )
                | ( SV6 = SV23 )
                | ( equidistant @ SY148 @ SY150 @ SY149 @ SY151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(111,plain,
    ! [SV24: $i,SV7: $i] :
      ( ( ~ ( between @ SV7 @ SV24 @ SV7 )
        | ( SV7 = SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(112,plain,
    ! [SV25: $i,SV8: $i] :
      ( ( ! [SY152: $i] :
            ( ~ ( between @ SV8 @ SV25 @ SY152 )
            | ! [SY153: $i,SY154: $i] :
                ( ~ ( between @ SY153 @ SY154 @ SY152 )
                | ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SY152 @ SY154 @ SY153 ) @ SY153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(113,plain,
    ! [SV26: $i,SV9: $i] :
      ( ( ! [SY155: $i] :
            ( ~ ( between @ SV9 @ SV26 @ SY155 )
            | ! [SY156: $i,SY157: $i] :
                ( ~ ( between @ SY156 @ SY157 @ SY155 )
                | ( between @ SY157 @ ( inner_pasch @ SV9 @ SV26 @ SY155 @ SY157 @ SY156 ) @ SV9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(114,plain,
    ! [SV27: $i,SV10: $i] :
      ( ( ! [SY158: $i] :
            ( ~ ( equidistant @ SV10 @ SV27 @ SV10 @ SY158 )
            | ! [SY159: $i] :
                ( ~ ( equidistant @ SY159 @ SV27 @ SY159 @ SY158 )
                | ! [SY160: $i] :
                    ( ~ ( equidistant @ SY160 @ SV27 @ SY160 @ SY158 )
                    | ( between @ SV10 @ SY159 @ SY160 )
                    | ( between @ SY159 @ SY160 @ SV10 )
                    | ( SV27 = SY158 )
                    | ( between @ SY160 @ SV10 @ SY159 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(115,plain,
    ! [SV28: $i,SV11: $i] :
      ( ( ! [SY161: $i] :
            ( ~ ( between @ SV11 @ SV28 @ SY161 )
            | ! [SY162: $i,SY163: $i] :
                ( ~ ( between @ SY162 @ SV28 @ SY163 )
                | ( SV11 = SV28 )
                | ( between @ SV11 @ SY162 @ ( euclid1 @ SV11 @ SY162 @ SV28 @ SY163 @ SY161 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(116,plain,
    ! [SV29: $i,SV12: $i] :
      ( ( ! [SY164: $i] :
            ( ~ ( between @ SV12 @ SV29 @ SY164 )
            | ! [SY165: $i,SY166: $i] :
                ( ~ ( between @ SY165 @ SV29 @ SY166 )
                | ( SV12 = SV29 )
                | ( between @ SV12 @ SY166 @ ( euclid2 @ SV12 @ SY165 @ SV29 @ SY166 @ SY164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(117,plain,
    ! [SV30: $i,SV13: $i] :
      ( ( ! [SY167: $i] :
            ( ~ ( between @ SV13 @ SV30 @ SY167 )
            | ! [SY168: $i,SY169: $i] :
                ( ~ ( between @ SY168 @ SV30 @ SY169 )
                | ( SV13 = SV30 )
                | ( between @ ( euclid1 @ SV13 @ SY168 @ SV30 @ SY169 @ SY167 ) @ SY167 @ ( euclid2 @ SV13 @ SY168 @ SV30 @ SY169 @ SY167 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(118,plain,
    ! [SV31: $i,SV14: $i] :
      ( ( ! [SY170: $i,SY171: $i] :
            ( ~ ( equidistant @ SV14 @ SV31 @ SV14 @ SY170 )
            | ! [SY172: $i] :
                ( ~ ( equidistant @ SV14 @ SY171 @ SV14 @ SY172 )
                | ~ ( between @ SV14 @ SV31 @ SY171 )
                | ! [SY173: $i] :
                    ( ~ ( between @ SV31 @ SY173 @ SY171 )
                    | ( between @ SY170 @ ( continuous @ SV14 @ SV31 @ SY170 @ SY173 @ SY171 @ SY172 ) @ SY172 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(119,plain,
    ! [SV32: $i,SV15: $i] :
      ( ( ! [SY174: $i,SY175: $i] :
            ( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SY174 )
            | ! [SY176: $i] :
                ( ~ ( equidistant @ SV15 @ SY175 @ SV15 @ SY176 )
                | ~ ( between @ SV15 @ SV32 @ SY175 )
                | ! [SY177: $i] :
                    ( ~ ( between @ SV32 @ SY177 @ SY175 )
                    | ( equidistant @ SV15 @ SY177 @ SV15 @ ( continuous @ SV15 @ SV32 @ SY174 @ SY177 @ SY175 @ SY176 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(120,plain,
    ! [SV33: $i,SV16: $i] :
      ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV33 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(121,plain,
    ! [SV34: $i,SV17: $i] :
      ( ( ! [SY178: $i,SY179: $i] :
            ( ~ ( equidistant @ SV17 @ SV34 @ SY178 @ SY179 )
            | ( equidistant @ SY178 @ SY179 @ SV17 @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(122,plain,
    ! [SV35: $i,SV19: $i,SV2: $i] :
      ( ( ! [SY180: $i] :
            ( ~ ( equidistant @ SV2 @ SV19 @ SV35 @ SY180 )
            | ! [SY181: $i,SY182: $i] :
                ( ~ ( equidistant @ SV2 @ SV19 @ SY181 @ SY182 )
                | ( equidistant @ SV35 @ SY180 @ SY181 @ SY182 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(123,plain,
    ! [SV20: $i,SV3: $i] :
      ( ( ( ! [SY141: $i] :
              ~ ( equidistant @ SV3 @ SV20 @ SY141 @ SY141 ) )
        = $true )
      | ( ( SV3 = SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(124,plain,
    ! [SV36: $i,SV21: $i,SV4: $i] :
      ( ( ! [SY183: $i] : ( between @ SV4 @ SV21 @ ( extension @ SV4 @ SV21 @ SV36 @ SY183 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(125,plain,
    ! [SV37: $i,SV22: $i,SV5: $i] :
      ( ( ! [SY184: $i] : ( equidistant @ SV5 @ ( extension @ SV22 @ SV5 @ SV37 @ SY184 ) @ SV37 @ SY184 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(126,plain,
    ! [SV38: $i,SV23: $i,SV6: $i] :
      ( ( ! [SY185: $i,SY186: $i,SY187: $i] :
            ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SY185 )
            | ~ ( equidistant @ SV23 @ SY186 @ SY185 @ SY187 )
            | ! [SY188: $i,SY189: $i] :
                ( ~ ( equidistant @ SV6 @ SY188 @ SV38 @ SY189 )
                | ~ ( equidistant @ SV23 @ SY188 @ SY185 @ SY189 )
                | ~ ( between @ SV6 @ SV23 @ SY186 )
                | ~ ( between @ SV38 @ SY185 @ SY187 )
                | ( SV6 = SV23 )
                | ( equidistant @ SY186 @ SY188 @ SY187 @ SY189 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(127,plain,
    ! [SV24: $i,SV7: $i] :
      ( ( ( ~ ( between @ SV7 @ SV24 @ SV7 ) )
        = $true )
      | ( ( SV7 = SV24 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[111]) ).

thf(128,plain,
    ! [SV39: $i,SV25: $i,SV8: $i] :
      ( ( ~ ( between @ SV8 @ SV25 @ SV39 )
        | ! [SY190: $i,SY191: $i] :
            ( ~ ( between @ SY190 @ SY191 @ SV39 )
            | ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SY191 @ SY190 ) @ SY190 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(129,plain,
    ! [SV40: $i,SV26: $i,SV9: $i] :
      ( ( ~ ( between @ SV9 @ SV26 @ SV40 )
        | ! [SY192: $i,SY193: $i] :
            ( ~ ( between @ SY192 @ SY193 @ SV40 )
            | ( between @ SY193 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SY193 @ SY192 ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(130,plain,
    ! [SV41: $i,SV27: $i,SV10: $i] :
      ( ( ~ ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        | ! [SY194: $i] :
            ( ~ ( equidistant @ SY194 @ SV27 @ SY194 @ SV41 )
            | ! [SY195: $i] :
                ( ~ ( equidistant @ SY195 @ SV27 @ SY195 @ SV41 )
                | ( between @ SV10 @ SY194 @ SY195 )
                | ( between @ SY194 @ SY195 @ SV10 )
                | ( SV27 = SV41 )
                | ( between @ SY195 @ SV10 @ SY194 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(131,plain,
    ! [SV42: $i,SV28: $i,SV11: $i] :
      ( ( ~ ( between @ SV11 @ SV28 @ SV42 )
        | ! [SY196: $i,SY197: $i] :
            ( ~ ( between @ SY196 @ SV28 @ SY197 )
            | ( SV11 = SV28 )
            | ( between @ SV11 @ SY196 @ ( euclid1 @ SV11 @ SY196 @ SV28 @ SY197 @ SV42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(132,plain,
    ! [SV43: $i,SV29: $i,SV12: $i] :
      ( ( ~ ( between @ SV12 @ SV29 @ SV43 )
        | ! [SY198: $i,SY199: $i] :
            ( ~ ( between @ SY198 @ SV29 @ SY199 )
            | ( SV12 = SV29 )
            | ( between @ SV12 @ SY199 @ ( euclid2 @ SV12 @ SY198 @ SV29 @ SY199 @ SV43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(133,plain,
    ! [SV44: $i,SV30: $i,SV13: $i] :
      ( ( ~ ( between @ SV13 @ SV30 @ SV44 )
        | ! [SY200: $i,SY201: $i] :
            ( ~ ( between @ SY200 @ SV30 @ SY201 )
            | ( SV13 = SV30 )
            | ( between @ ( euclid1 @ SV13 @ SY200 @ SV30 @ SY201 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SY200 @ SV30 @ SY201 @ SV44 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(134,plain,
    ! [SV45: $i,SV31: $i,SV14: $i] :
      ( ( ! [SY202: $i] :
            ( ~ ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
            | ! [SY203: $i] :
                ( ~ ( equidistant @ SV14 @ SY202 @ SV14 @ SY203 )
                | ~ ( between @ SV14 @ SV31 @ SY202 )
                | ! [SY204: $i] :
                    ( ~ ( between @ SV31 @ SY204 @ SY202 )
                    | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY204 @ SY202 @ SY203 ) @ SY203 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(135,plain,
    ! [SV46: $i,SV32: $i,SV15: $i] :
      ( ( ! [SY205: $i] :
            ( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
            | ! [SY206: $i] :
                ( ~ ( equidistant @ SV15 @ SY205 @ SV15 @ SY206 )
                | ~ ( between @ SV15 @ SV32 @ SY205 )
                | ! [SY207: $i] :
                    ( ~ ( between @ SV32 @ SY207 @ SY205 )
                    | ( equidistant @ SV15 @ SY207 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY207 @ SY205 @ SY206 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(136,plain,
    ! [SV47: $i,SV34: $i,SV17: $i] :
      ( ( ! [SY208: $i] :
            ( ~ ( equidistant @ SV17 @ SV34 @ SV47 @ SY208 )
            | ( equidistant @ SV47 @ SY208 @ SV17 @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(137,plain,
    ! [SV48: $i,SV35: $i,SV19: $i,SV2: $i] :
      ( ( ~ ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 )
        | ! [SY209: $i,SY210: $i] :
            ( ~ ( equidistant @ SV2 @ SV19 @ SY209 @ SY210 )
            | ( equidistant @ SV35 @ SV48 @ SY209 @ SY210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(138,plain,
    ! [SV49: $i,SV20: $i,SV3: $i] :
      ( ( ( ~ ( equidistant @ SV3 @ SV20 @ SV49 @ SV49 ) )
        = $true )
      | ( ( SV3 = SV20 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(139,plain,
    ! [SV50: $i,SV36: $i,SV21: $i,SV4: $i] :
      ( ( between @ SV4 @ SV21 @ ( extension @ SV4 @ SV21 @ SV36 @ SV50 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(140,plain,
    ! [SV51: $i,SV37: $i,SV22: $i,SV5: $i] :
      ( ( equidistant @ SV5 @ ( extension @ SV22 @ SV5 @ SV37 @ SV51 ) @ SV37 @ SV51 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(141,plain,
    ! [SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
      ( ( ! [SY211: $i,SY212: $i] :
            ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
            | ~ ( equidistant @ SV23 @ SY211 @ SV52 @ SY212 )
            | ! [SY213: $i,SY214: $i] :
                ( ~ ( equidistant @ SV6 @ SY213 @ SV38 @ SY214 )
                | ~ ( equidistant @ SV23 @ SY213 @ SV52 @ SY214 )
                | ~ ( between @ SV6 @ SV23 @ SY211 )
                | ~ ( between @ SV38 @ SV52 @ SY212 )
                | ( SV6 = SV23 )
                | ( equidistant @ SY211 @ SY213 @ SY212 @ SY214 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(142,plain,
    ! [SV24: $i,SV7: $i] :
      ( ( ( between @ SV7 @ SV24 @ SV7 )
        = $false )
      | ( ( SV7 = SV24 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[127]) ).

thf(143,plain,
    ! [SV39: $i,SV25: $i,SV8: $i] :
      ( ( ( ~ ( between @ SV8 @ SV25 @ SV39 ) )
        = $true )
      | ( ( ! [SY190: $i,SY191: $i] :
              ( ~ ( between @ SY190 @ SY191 @ SV39 )
              | ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SY191 @ SY190 ) @ SY190 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[128]) ).

thf(144,plain,
    ! [SV40: $i,SV26: $i,SV9: $i] :
      ( ( ( ~ ( between @ SV9 @ SV26 @ SV40 ) )
        = $true )
      | ( ( ! [SY192: $i,SY193: $i] :
              ( ~ ( between @ SY192 @ SY193 @ SV40 )
              | ( between @ SY193 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SY193 @ SY192 ) @ SV9 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[129]) ).

thf(145,plain,
    ! [SV41: $i,SV27: $i,SV10: $i] :
      ( ( ( ~ ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 ) )
        = $true )
      | ( ( ! [SY194: $i] :
              ( ~ ( equidistant @ SY194 @ SV27 @ SY194 @ SV41 )
              | ! [SY195: $i] :
                  ( ~ ( equidistant @ SY195 @ SV27 @ SY195 @ SV41 )
                  | ( between @ SV10 @ SY194 @ SY195 )
                  | ( between @ SY194 @ SY195 @ SV10 )
                  | ( SV27 = SV41 )
                  | ( between @ SY195 @ SV10 @ SY194 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(146,plain,
    ! [SV42: $i,SV28: $i,SV11: $i] :
      ( ( ( ~ ( between @ SV11 @ SV28 @ SV42 ) )
        = $true )
      | ( ( ! [SY196: $i,SY197: $i] :
              ( ~ ( between @ SY196 @ SV28 @ SY197 )
              | ( SV11 = SV28 )
              | ( between @ SV11 @ SY196 @ ( euclid1 @ SV11 @ SY196 @ SV28 @ SY197 @ SV42 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[131]) ).

thf(147,plain,
    ! [SV43: $i,SV29: $i,SV12: $i] :
      ( ( ( ~ ( between @ SV12 @ SV29 @ SV43 ) )
        = $true )
      | ( ( ! [SY198: $i,SY199: $i] :
              ( ~ ( between @ SY198 @ SV29 @ SY199 )
              | ( SV12 = SV29 )
              | ( between @ SV12 @ SY199 @ ( euclid2 @ SV12 @ SY198 @ SV29 @ SY199 @ SV43 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(148,plain,
    ! [SV44: $i,SV30: $i,SV13: $i] :
      ( ( ( ~ ( between @ SV13 @ SV30 @ SV44 ) )
        = $true )
      | ( ( ! [SY200: $i,SY201: $i] :
              ( ~ ( between @ SY200 @ SV30 @ SY201 )
              | ( SV13 = SV30 )
              | ( between @ ( euclid1 @ SV13 @ SY200 @ SV30 @ SY201 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SY200 @ SV30 @ SY201 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[133]) ).

thf(149,plain,
    ! [SV53: $i,SV45: $i,SV31: $i,SV14: $i] :
      ( ( ~ ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        | ! [SY215: $i] :
            ( ~ ( equidistant @ SV14 @ SV53 @ SV14 @ SY215 )
            | ~ ( between @ SV14 @ SV31 @ SV53 )
            | ! [SY216: $i] :
                ( ~ ( between @ SV31 @ SY216 @ SV53 )
                | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY216 @ SV53 @ SY215 ) @ SY215 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(150,plain,
    ! [SV54: $i,SV46: $i,SV32: $i,SV15: $i] :
      ( ( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        | ! [SY217: $i] :
            ( ~ ( equidistant @ SV15 @ SV54 @ SV15 @ SY217 )
            | ~ ( between @ SV15 @ SV32 @ SV54 )
            | ! [SY218: $i] :
                ( ~ ( between @ SV32 @ SY218 @ SV54 )
                | ( equidistant @ SV15 @ SY218 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY218 @ SV54 @ SY217 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(151,plain,
    ! [SV55: $i,SV47: $i,SV34: $i,SV17: $i] :
      ( ( ~ ( equidistant @ SV17 @ SV34 @ SV47 @ SV55 )
        | ( equidistant @ SV47 @ SV55 @ SV17 @ SV34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(152,plain,
    ! [SV48: $i,SV35: $i,SV19: $i,SV2: $i] :
      ( ( ( ~ ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 ) )
        = $true )
      | ( ( ! [SY209: $i,SY210: $i] :
              ( ~ ( equidistant @ SV2 @ SV19 @ SY209 @ SY210 )
              | ( equidistant @ SV35 @ SV48 @ SY209 @ SY210 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(153,plain,
    ! [SV49: $i,SV20: $i,SV3: $i] :
      ( ( ( equidistant @ SV3 @ SV20 @ SV49 @ SV49 )
        = $false )
      | ( ( SV3 = SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(154,plain,
    ! [SV56: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
      ( ( ! [SY219: $i] :
            ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
            | ~ ( equidistant @ SV23 @ SV56 @ SV52 @ SY219 )
            | ! [SY220: $i,SY221: $i] :
                ( ~ ( equidistant @ SV6 @ SY220 @ SV38 @ SY221 )
                | ~ ( equidistant @ SV23 @ SY220 @ SV52 @ SY221 )
                | ~ ( between @ SV6 @ SV23 @ SV56 )
                | ~ ( between @ SV38 @ SV52 @ SY219 )
                | ( SV6 = SV23 )
                | ( equidistant @ SV56 @ SY220 @ SY219 @ SY221 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(155,plain,
    ! [SV39: $i,SV25: $i,SV8: $i] :
      ( ( ( between @ SV8 @ SV25 @ SV39 )
        = $false )
      | ( ( ! [SY190: $i,SY191: $i] :
              ( ~ ( between @ SY190 @ SY191 @ SV39 )
              | ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SY191 @ SY190 ) @ SY190 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[143]) ).

thf(156,plain,
    ! [SV40: $i,SV26: $i,SV9: $i] :
      ( ( ( between @ SV9 @ SV26 @ SV40 )
        = $false )
      | ( ( ! [SY192: $i,SY193: $i] :
              ( ~ ( between @ SY192 @ SY193 @ SV40 )
              | ( between @ SY193 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SY193 @ SY192 ) @ SV9 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(157,plain,
    ! [SV41: $i,SV27: $i,SV10: $i] :
      ( ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false )
      | ( ( ! [SY194: $i] :
              ( ~ ( equidistant @ SY194 @ SV27 @ SY194 @ SV41 )
              | ! [SY195: $i] :
                  ( ~ ( equidistant @ SY195 @ SV27 @ SY195 @ SV41 )
                  | ( between @ SV10 @ SY194 @ SY195 )
                  | ( between @ SY194 @ SY195 @ SV10 )
                  | ( SV27 = SV41 )
                  | ( between @ SY195 @ SV10 @ SY194 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(158,plain,
    ! [SV42: $i,SV28: $i,SV11: $i] :
      ( ( ( between @ SV11 @ SV28 @ SV42 )
        = $false )
      | ( ( ! [SY196: $i,SY197: $i] :
              ( ~ ( between @ SY196 @ SV28 @ SY197 )
              | ( SV11 = SV28 )
              | ( between @ SV11 @ SY196 @ ( euclid1 @ SV11 @ SY196 @ SV28 @ SY197 @ SV42 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(159,plain,
    ! [SV43: $i,SV29: $i,SV12: $i] :
      ( ( ( between @ SV12 @ SV29 @ SV43 )
        = $false )
      | ( ( ! [SY198: $i,SY199: $i] :
              ( ~ ( between @ SY198 @ SV29 @ SY199 )
              | ( SV12 = SV29 )
              | ( between @ SV12 @ SY199 @ ( euclid2 @ SV12 @ SY198 @ SV29 @ SY199 @ SV43 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(160,plain,
    ! [SV44: $i,SV30: $i,SV13: $i] :
      ( ( ( between @ SV13 @ SV30 @ SV44 )
        = $false )
      | ( ( ! [SY200: $i,SY201: $i] :
              ( ~ ( between @ SY200 @ SV30 @ SY201 )
              | ( SV13 = SV30 )
              | ( between @ ( euclid1 @ SV13 @ SY200 @ SV30 @ SY201 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SY200 @ SV30 @ SY201 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(161,plain,
    ! [SV53: $i,SV45: $i,SV31: $i,SV14: $i] :
      ( ( ( ~ ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 ) )
        = $true )
      | ( ( ! [SY215: $i] :
              ( ~ ( equidistant @ SV14 @ SV53 @ SV14 @ SY215 )
              | ~ ( between @ SV14 @ SV31 @ SV53 )
              | ! [SY216: $i] :
                  ( ~ ( between @ SV31 @ SY216 @ SV53 )
                  | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY216 @ SV53 @ SY215 ) @ SY215 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(162,plain,
    ! [SV54: $i,SV46: $i,SV32: $i,SV15: $i] :
      ( ( ( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 ) )
        = $true )
      | ( ( ! [SY217: $i] :
              ( ~ ( equidistant @ SV15 @ SV54 @ SV15 @ SY217 )
              | ~ ( between @ SV15 @ SV32 @ SV54 )
              | ! [SY218: $i] :
                  ( ~ ( between @ SV32 @ SY218 @ SV54 )
                  | ( equidistant @ SV15 @ SY218 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY218 @ SV54 @ SY217 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(163,plain,
    ! [SV55: $i,SV47: $i,SV34: $i,SV17: $i] :
      ( ( ( ~ ( equidistant @ SV17 @ SV34 @ SV47 @ SV55 ) )
        = $true )
      | ( ( equidistant @ SV47 @ SV55 @ SV17 @ SV34 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(164,plain,
    ! [SV48: $i,SV35: $i,SV19: $i,SV2: $i] :
      ( ( ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 )
        = $false )
      | ( ( ! [SY209: $i,SY210: $i] :
              ( ~ ( equidistant @ SV2 @ SV19 @ SY209 @ SY210 )
              | ( equidistant @ SV35 @ SV48 @ SY209 @ SY210 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(165,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
      ( ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        | ~ ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        | ! [SY222: $i,SY223: $i] :
            ( ~ ( equidistant @ SV6 @ SY222 @ SV38 @ SY223 )
            | ~ ( equidistant @ SV23 @ SY222 @ SV52 @ SY223 )
            | ~ ( between @ SV6 @ SV23 @ SV56 )
            | ~ ( between @ SV38 @ SV52 @ SV57 )
            | ( SV6 = SV23 )
            | ( equidistant @ SV56 @ SY222 @ SV57 @ SY223 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(166,plain,
    ! [SV8: $i,SV25: $i,SV39: $i,SV58: $i] :
      ( ( ( ! [SY224: $i] :
              ( ~ ( between @ SV58 @ SY224 @ SV39 )
              | ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SY224 @ SV58 ) @ SV58 ) ) )
        = $true )
      | ( ( between @ SV8 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(167,plain,
    ! [SV26: $i,SV9: $i,SV40: $i,SV59: $i] :
      ( ( ( ! [SY225: $i] :
              ( ~ ( between @ SV59 @ SY225 @ SV40 )
              | ( between @ SY225 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SY225 @ SV59 ) @ SV9 ) ) )
        = $true )
      | ( ( between @ SV9 @ SV26 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[156]) ).

thf(168,plain,
    ! [SV10: $i,SV41: $i,SV27: $i,SV60: $i] :
      ( ( ( ~ ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
          | ! [SY226: $i] :
              ( ~ ( equidistant @ SY226 @ SV27 @ SY226 @ SV41 )
              | ( between @ SV10 @ SV60 @ SY226 )
              | ( between @ SV60 @ SY226 @ SV10 )
              | ( SV27 = SV41 )
              | ( between @ SY226 @ SV10 @ SV60 ) ) )
        = $true )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(169,plain,
    ! [SV42: $i,SV11: $i,SV28: $i,SV61: $i] :
      ( ( ( ! [SY227: $i] :
              ( ~ ( between @ SV61 @ SV28 @ SY227 )
              | ( SV11 = SV28 )
              | ( between @ SV11 @ SV61 @ ( euclid1 @ SV11 @ SV61 @ SV28 @ SY227 @ SV42 ) ) ) )
        = $true )
      | ( ( between @ SV11 @ SV28 @ SV42 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(170,plain,
    ! [SV43: $i,SV12: $i,SV29: $i,SV62: $i] :
      ( ( ( ! [SY228: $i] :
              ( ~ ( between @ SV62 @ SV29 @ SY228 )
              | ( SV12 = SV29 )
              | ( between @ SV12 @ SY228 @ ( euclid2 @ SV12 @ SV62 @ SV29 @ SY228 @ SV43 ) ) ) )
        = $true )
      | ( ( between @ SV12 @ SV29 @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(171,plain,
    ! [SV44: $i,SV13: $i,SV30: $i,SV63: $i] :
      ( ( ( ! [SY229: $i] :
              ( ~ ( between @ SV63 @ SV30 @ SY229 )
              | ( SV13 = SV30 )
              | ( between @ ( euclid1 @ SV13 @ SV63 @ SV30 @ SY229 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SV63 @ SV30 @ SY229 @ SV44 ) ) ) )
        = $true )
      | ( ( between @ SV13 @ SV30 @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(172,plain,
    ! [SV53: $i,SV45: $i,SV31: $i,SV14: $i] :
      ( ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false )
      | ( ( ! [SY215: $i] :
              ( ~ ( equidistant @ SV14 @ SV53 @ SV14 @ SY215 )
              | ~ ( between @ SV14 @ SV31 @ SV53 )
              | ! [SY216: $i] :
                  ( ~ ( between @ SV31 @ SY216 @ SV53 )
                  | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY216 @ SV53 @ SY215 ) @ SY215 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(173,plain,
    ! [SV54: $i,SV46: $i,SV32: $i,SV15: $i] :
      ( ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false )
      | ( ( ! [SY217: $i] :
              ( ~ ( equidistant @ SV15 @ SV54 @ SV15 @ SY217 )
              | ~ ( between @ SV15 @ SV32 @ SV54 )
              | ! [SY218: $i] :
                  ( ~ ( between @ SV32 @ SY218 @ SV54 )
                  | ( equidistant @ SV15 @ SY218 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY218 @ SV54 @ SY217 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(174,plain,
    ! [SV55: $i,SV47: $i,SV34: $i,SV17: $i] :
      ( ( ( equidistant @ SV17 @ SV34 @ SV47 @ SV55 )
        = $false )
      | ( ( equidistant @ SV47 @ SV55 @ SV17 @ SV34 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(175,plain,
    ! [SV48: $i,SV35: $i,SV64: $i,SV19: $i,SV2: $i] :
      ( ( ( ! [SY230: $i] :
              ( ~ ( equidistant @ SV2 @ SV19 @ SV64 @ SY230 )
              | ( equidistant @ SV35 @ SV48 @ SV64 @ SY230 ) ) )
        = $true )
      | ( ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(176,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
      ( ( ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 ) )
        = $true )
      | ( ( ~ ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
          | ! [SY222: $i,SY223: $i] :
              ( ~ ( equidistant @ SV6 @ SY222 @ SV38 @ SY223 )
              | ~ ( equidistant @ SV23 @ SY222 @ SV52 @ SY223 )
              | ~ ( between @ SV6 @ SV23 @ SV56 )
              | ~ ( between @ SV38 @ SV52 @ SV57 )
              | ( SV6 = SV23 )
              | ( equidistant @ SV56 @ SY222 @ SV57 @ SY223 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[165]) ).

thf(177,plain,
    ! [SV8: $i,SV25: $i,SV39: $i,SV65: $i,SV58: $i] :
      ( ( ( ~ ( between @ SV58 @ SV65 @ SV39 )
          | ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SV65 @ SV58 ) @ SV58 ) )
        = $true )
      | ( ( between @ SV8 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[166]) ).

thf(178,plain,
    ! [SV26: $i,SV9: $i,SV40: $i,SV66: $i,SV59: $i] :
      ( ( ( ~ ( between @ SV59 @ SV66 @ SV40 )
          | ( between @ SV66 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SV66 @ SV59 ) @ SV9 ) )
        = $true )
      | ( ( between @ SV9 @ SV26 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[167]) ).

thf(179,plain,
    ! [SV10: $i,SV41: $i,SV27: $i,SV60: $i] :
      ( ( ( ~ ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 ) )
        = $true )
      | ( ( ! [SY226: $i] :
              ( ~ ( equidistant @ SY226 @ SV27 @ SY226 @ SV41 )
              | ( between @ SV10 @ SV60 @ SY226 )
              | ( between @ SV60 @ SY226 @ SV10 )
              | ( SV27 = SV41 )
              | ( between @ SY226 @ SV10 @ SV60 ) ) )
        = $true )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[168]) ).

thf(180,plain,
    ! [SV42: $i,SV11: $i,SV67: $i,SV28: $i,SV61: $i] :
      ( ( ( ~ ( between @ SV61 @ SV28 @ SV67 )
          | ( SV11 = SV28 )
          | ( between @ SV11 @ SV61 @ ( euclid1 @ SV11 @ SV61 @ SV28 @ SV67 @ SV42 ) ) )
        = $true )
      | ( ( between @ SV11 @ SV28 @ SV42 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(181,plain,
    ! [SV43: $i,SV12: $i,SV68: $i,SV29: $i,SV62: $i] :
      ( ( ( ~ ( between @ SV62 @ SV29 @ SV68 )
          | ( SV12 = SV29 )
          | ( between @ SV12 @ SV68 @ ( euclid2 @ SV12 @ SV62 @ SV29 @ SV68 @ SV43 ) ) )
        = $true )
      | ( ( between @ SV12 @ SV29 @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[170]) ).

thf(182,plain,
    ! [SV44: $i,SV13: $i,SV69: $i,SV30: $i,SV63: $i] :
      ( ( ( ~ ( between @ SV63 @ SV30 @ SV69 )
          | ( SV13 = SV30 )
          | ( between @ ( euclid1 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) ) )
        = $true )
      | ( ( between @ SV13 @ SV30 @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(183,plain,
    ! [SV45: $i,SV31: $i,SV70: $i,SV53: $i,SV14: $i] :
      ( ( ( ~ ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
          | ~ ( between @ SV14 @ SV31 @ SV53 )
          | ! [SY231: $i] :
              ( ~ ( between @ SV31 @ SY231 @ SV53 )
              | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY231 @ SV53 @ SV70 ) @ SV70 ) ) )
        = $true )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(184,plain,
    ! [SV46: $i,SV32: $i,SV71: $i,SV54: $i,SV15: $i] :
      ( ( ( ~ ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
          | ~ ( between @ SV15 @ SV32 @ SV54 )
          | ! [SY232: $i] :
              ( ~ ( between @ SV32 @ SY232 @ SV54 )
              | ( equidistant @ SV15 @ SY232 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY232 @ SV54 @ SV71 ) ) ) )
        = $true )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(185,plain,
    ! [SV48: $i,SV35: $i,SV72: $i,SV64: $i,SV19: $i,SV2: $i] :
      ( ( ( ~ ( equidistant @ SV2 @ SV19 @ SV64 @ SV72 )
          | ( equidistant @ SV35 @ SV48 @ SV64 @ SV72 ) )
        = $true )
      | ( ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(186,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
      ( ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false )
      | ( ( ~ ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
          | ! [SY222: $i,SY223: $i] :
              ( ~ ( equidistant @ SV6 @ SY222 @ SV38 @ SY223 )
              | ~ ( equidistant @ SV23 @ SY222 @ SV52 @ SY223 )
              | ~ ( between @ SV6 @ SV23 @ SV56 )
              | ~ ( between @ SV38 @ SV52 @ SV57 )
              | ( SV6 = SV23 )
              | ( equidistant @ SV56 @ SY222 @ SV57 @ SY223 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[176]) ).

thf(187,plain,
    ! [SV8: $i,SV25: $i,SV39: $i,SV65: $i,SV58: $i] :
      ( ( ( ~ ( between @ SV58 @ SV65 @ SV39 ) )
        = $true )
      | ( ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SV65 @ SV58 ) @ SV58 )
        = $true )
      | ( ( between @ SV8 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[177]) ).

thf(188,plain,
    ! [SV26: $i,SV9: $i,SV40: $i,SV66: $i,SV59: $i] :
      ( ( ( ~ ( between @ SV59 @ SV66 @ SV40 ) )
        = $true )
      | ( ( between @ SV66 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SV66 @ SV59 ) @ SV9 )
        = $true )
      | ( ( between @ SV9 @ SV26 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(189,plain,
    ! [SV10: $i,SV41: $i,SV27: $i,SV60: $i] :
      ( ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( ! [SY226: $i] :
              ( ~ ( equidistant @ SY226 @ SV27 @ SY226 @ SV41 )
              | ( between @ SV10 @ SV60 @ SY226 )
              | ( between @ SV60 @ SY226 @ SV10 )
              | ( SV27 = SV41 )
              | ( between @ SY226 @ SV10 @ SV60 ) ) )
        = $true )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[179]) ).

thf(190,plain,
    ! [SV42: $i,SV11: $i,SV67: $i,SV28: $i,SV61: $i] :
      ( ( ( ~ ( between @ SV61 @ SV28 @ SV67 ) )
        = $true )
      | ( ( ( SV11 = SV28 )
          | ( between @ SV11 @ SV61 @ ( euclid1 @ SV11 @ SV61 @ SV28 @ SV67 @ SV42 ) ) )
        = $true )
      | ( ( between @ SV11 @ SV28 @ SV42 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(191,plain,
    ! [SV43: $i,SV12: $i,SV68: $i,SV29: $i,SV62: $i] :
      ( ( ( ~ ( between @ SV62 @ SV29 @ SV68 ) )
        = $true )
      | ( ( ( SV12 = SV29 )
          | ( between @ SV12 @ SV68 @ ( euclid2 @ SV12 @ SV62 @ SV29 @ SV68 @ SV43 ) ) )
        = $true )
      | ( ( between @ SV12 @ SV29 @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[181]) ).

thf(192,plain,
    ! [SV44: $i,SV13: $i,SV69: $i,SV30: $i,SV63: $i] :
      ( ( ( ~ ( between @ SV63 @ SV30 @ SV69 ) )
        = $true )
      | ( ( ( SV13 = SV30 )
          | ( between @ ( euclid1 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) ) )
        = $true )
      | ( ( between @ SV13 @ SV30 @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[182]) ).

thf(193,plain,
    ! [SV45: $i,SV31: $i,SV70: $i,SV53: $i,SV14: $i] :
      ( ( ( ~ ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 ) )
        = $true )
      | ( ( ~ ( between @ SV14 @ SV31 @ SV53 )
          | ! [SY231: $i] :
              ( ~ ( between @ SV31 @ SY231 @ SV53 )
              | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY231 @ SV53 @ SV70 ) @ SV70 ) ) )
        = $true )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[183]) ).

thf(194,plain,
    ! [SV46: $i,SV32: $i,SV71: $i,SV54: $i,SV15: $i] :
      ( ( ( ~ ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 ) )
        = $true )
      | ( ( ~ ( between @ SV15 @ SV32 @ SV54 )
          | ! [SY232: $i] :
              ( ~ ( between @ SV32 @ SY232 @ SV54 )
              | ( equidistant @ SV15 @ SY232 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY232 @ SV54 @ SV71 ) ) ) )
        = $true )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[184]) ).

thf(195,plain,
    ! [SV48: $i,SV35: $i,SV72: $i,SV64: $i,SV19: $i,SV2: $i] :
      ( ( ( ~ ( equidistant @ SV2 @ SV19 @ SV64 @ SV72 ) )
        = $true )
      | ( ( equidistant @ SV35 @ SV48 @ SV64 @ SV72 )
        = $true )
      | ( ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[185]) ).

thf(196,plain,
    ! [SV38: $i,SV6: $i,SV57: $i,SV52: $i,SV56: $i,SV23: $i] :
      ( ( ( ~ ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 ) )
        = $true )
      | ( ( ! [SY222: $i,SY223: $i] :
              ( ~ ( equidistant @ SV6 @ SY222 @ SV38 @ SY223 )
              | ~ ( equidistant @ SV23 @ SY222 @ SV52 @ SY223 )
              | ~ ( between @ SV6 @ SV23 @ SV56 )
              | ~ ( between @ SV38 @ SV52 @ SV57 )
              | ( SV6 = SV23 )
              | ( equidistant @ SV56 @ SY222 @ SV57 @ SY223 ) ) )
        = $true )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[186]) ).

thf(197,plain,
    ! [SV8: $i,SV25: $i,SV39: $i,SV65: $i,SV58: $i] :
      ( ( ( between @ SV58 @ SV65 @ SV39 )
        = $false )
      | ( ( between @ SV25 @ ( inner_pasch @ SV8 @ SV25 @ SV39 @ SV65 @ SV58 ) @ SV58 )
        = $true )
      | ( ( between @ SV8 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[187]) ).

thf(198,plain,
    ! [SV26: $i,SV9: $i,SV40: $i,SV66: $i,SV59: $i] :
      ( ( ( between @ SV59 @ SV66 @ SV40 )
        = $false )
      | ( ( between @ SV66 @ ( inner_pasch @ SV9 @ SV26 @ SV40 @ SV66 @ SV59 ) @ SV9 )
        = $true )
      | ( ( between @ SV9 @ SV26 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(199,plain,
    ! [SV60: $i,SV10: $i,SV41: $i,SV27: $i,SV73: $i] :
      ( ( ( ~ ( equidistant @ SV73 @ SV27 @ SV73 @ SV41 )
          | ( between @ SV10 @ SV60 @ SV73 )
          | ( between @ SV60 @ SV73 @ SV10 )
          | ( SV27 = SV41 )
          | ( between @ SV73 @ SV10 @ SV60 ) )
        = $true )
      | ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[189]) ).

thf(200,plain,
    ! [SV42: $i,SV11: $i,SV67: $i,SV28: $i,SV61: $i] :
      ( ( ( between @ SV61 @ SV28 @ SV67 )
        = $false )
      | ( ( ( SV11 = SV28 )
          | ( between @ SV11 @ SV61 @ ( euclid1 @ SV11 @ SV61 @ SV28 @ SV67 @ SV42 ) ) )
        = $true )
      | ( ( between @ SV11 @ SV28 @ SV42 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[190]) ).

thf(201,plain,
    ! [SV43: $i,SV12: $i,SV68: $i,SV29: $i,SV62: $i] :
      ( ( ( between @ SV62 @ SV29 @ SV68 )
        = $false )
      | ( ( ( SV12 = SV29 )
          | ( between @ SV12 @ SV68 @ ( euclid2 @ SV12 @ SV62 @ SV29 @ SV68 @ SV43 ) ) )
        = $true )
      | ( ( between @ SV12 @ SV29 @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(202,plain,
    ! [SV44: $i,SV13: $i,SV69: $i,SV30: $i,SV63: $i] :
      ( ( ( between @ SV63 @ SV30 @ SV69 )
        = $false )
      | ( ( ( SV13 = SV30 )
          | ( between @ ( euclid1 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) ) )
        = $true )
      | ( ( between @ SV13 @ SV30 @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[192]) ).

thf(203,plain,
    ! [SV45: $i,SV31: $i,SV70: $i,SV53: $i,SV14: $i] :
      ( ( ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
        = $false )
      | ( ( ~ ( between @ SV14 @ SV31 @ SV53 )
          | ! [SY231: $i] :
              ( ~ ( between @ SV31 @ SY231 @ SV53 )
              | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY231 @ SV53 @ SV70 ) @ SV70 ) ) )
        = $true )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[193]) ).

thf(204,plain,
    ! [SV46: $i,SV32: $i,SV71: $i,SV54: $i,SV15: $i] :
      ( ( ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
        = $false )
      | ( ( ~ ( between @ SV15 @ SV32 @ SV54 )
          | ! [SY232: $i] :
              ( ~ ( between @ SV32 @ SY232 @ SV54 )
              | ( equidistant @ SV15 @ SY232 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY232 @ SV54 @ SV71 ) ) ) )
        = $true )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(205,plain,
    ! [SV48: $i,SV35: $i,SV72: $i,SV64: $i,SV19: $i,SV2: $i] :
      ( ( ( equidistant @ SV2 @ SV19 @ SV64 @ SV72 )
        = $false )
      | ( ( equidistant @ SV35 @ SV48 @ SV64 @ SV72 )
        = $true )
      | ( ( equidistant @ SV2 @ SV19 @ SV35 @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[195]) ).

thf(206,plain,
    ! [SV38: $i,SV6: $i,SV57: $i,SV52: $i,SV56: $i,SV23: $i] :
      ( ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( ! [SY222: $i,SY223: $i] :
              ( ~ ( equidistant @ SV6 @ SY222 @ SV38 @ SY223 )
              | ~ ( equidistant @ SV23 @ SY222 @ SV52 @ SY223 )
              | ~ ( between @ SV6 @ SV23 @ SV56 )
              | ~ ( between @ SV38 @ SV52 @ SV57 )
              | ( SV6 = SV23 )
              | ( equidistant @ SV56 @ SY222 @ SV57 @ SY223 ) ) )
        = $true )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[196]) ).

thf(207,plain,
    ! [SV60: $i,SV10: $i,SV41: $i,SV27: $i,SV73: $i] :
      ( ( ( ~ ( equidistant @ SV73 @ SV27 @ SV73 @ SV41 ) )
        = $true )
      | ( ( ( between @ SV10 @ SV60 @ SV73 )
          | ( between @ SV60 @ SV73 @ SV10 )
          | ( SV27 = SV41 )
          | ( between @ SV73 @ SV10 @ SV60 ) )
        = $true )
      | ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[199]) ).

thf(208,plain,
    ! [SV42: $i,SV67: $i,SV61: $i,SV28: $i,SV11: $i] :
      ( ( ( SV11 = SV28 )
        = $true )
      | ( ( between @ SV11 @ SV61 @ ( euclid1 @ SV11 @ SV61 @ SV28 @ SV67 @ SV42 ) )
        = $true )
      | ( ( between @ SV61 @ SV28 @ SV67 )
        = $false )
      | ( ( between @ SV11 @ SV28 @ SV42 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[200]) ).

thf(209,plain,
    ! [SV43: $i,SV62: $i,SV68: $i,SV29: $i,SV12: $i] :
      ( ( ( SV12 = SV29 )
        = $true )
      | ( ( between @ SV12 @ SV68 @ ( euclid2 @ SV12 @ SV62 @ SV29 @ SV68 @ SV43 ) )
        = $true )
      | ( ( between @ SV62 @ SV29 @ SV68 )
        = $false )
      | ( ( between @ SV12 @ SV29 @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[201]) ).

thf(210,plain,
    ! [SV44: $i,SV69: $i,SV63: $i,SV30: $i,SV13: $i] :
      ( ( ( SV13 = SV30 )
        = $true )
      | ( ( between @ ( euclid1 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) @ SV44 @ ( euclid2 @ SV13 @ SV63 @ SV30 @ SV69 @ SV44 ) )
        = $true )
      | ( ( between @ SV63 @ SV30 @ SV69 )
        = $false )
      | ( ( between @ SV13 @ SV30 @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[202]) ).

thf(211,plain,
    ! [SV70: $i,SV45: $i,SV53: $i,SV31: $i,SV14: $i] :
      ( ( ( ~ ( between @ SV14 @ SV31 @ SV53 ) )
        = $true )
      | ( ( ! [SY231: $i] :
              ( ~ ( between @ SV31 @ SY231 @ SV53 )
              | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY231 @ SV53 @ SV70 ) @ SV70 ) ) )
        = $true )
      | ( ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
        = $false )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[203]) ).

thf(212,plain,
    ! [SV71: $i,SV46: $i,SV54: $i,SV32: $i,SV15: $i] :
      ( ( ( ~ ( between @ SV15 @ SV32 @ SV54 ) )
        = $true )
      | ( ( ! [SY232: $i] :
              ( ~ ( between @ SV32 @ SY232 @ SV54 )
              | ( equidistant @ SV15 @ SY232 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY232 @ SV54 @ SV71 ) ) ) )
        = $true )
      | ( ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
        = $false )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[204]) ).

thf(213,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV23: $i,SV38: $i,SV74: $i,SV6: $i] :
      ( ( ( ! [SY233: $i] :
              ( ~ ( equidistant @ SV6 @ SV74 @ SV38 @ SY233 )
              | ~ ( equidistant @ SV23 @ SV74 @ SV52 @ SY233 )
              | ~ ( between @ SV6 @ SV23 @ SV56 )
              | ~ ( between @ SV38 @ SV52 @ SV57 )
              | ( SV6 = SV23 )
              | ( equidistant @ SV56 @ SV74 @ SV57 @ SY233 ) ) )
        = $true )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[206]) ).

thf(214,plain,
    ! [SV60: $i,SV10: $i,SV41: $i,SV27: $i,SV73: $i] :
      ( ( ( equidistant @ SV73 @ SV27 @ SV73 @ SV41 )
        = $false )
      | ( ( ( between @ SV10 @ SV60 @ SV73 )
          | ( between @ SV60 @ SV73 @ SV10 )
          | ( SV27 = SV41 )
          | ( between @ SV73 @ SV10 @ SV60 ) )
        = $true )
      | ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[207]) ).

thf(215,plain,
    ! [SV70: $i,SV45: $i,SV53: $i,SV31: $i,SV14: $i] :
      ( ( ( between @ SV14 @ SV31 @ SV53 )
        = $false )
      | ( ( ! [SY231: $i] :
              ( ~ ( between @ SV31 @ SY231 @ SV53 )
              | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SY231 @ SV53 @ SV70 ) @ SV70 ) ) )
        = $true )
      | ( ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
        = $false )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[211]) ).

thf(216,plain,
    ! [SV71: $i,SV46: $i,SV54: $i,SV32: $i,SV15: $i] :
      ( ( ( between @ SV15 @ SV32 @ SV54 )
        = $false )
      | ( ( ! [SY232: $i] :
              ( ~ ( between @ SV32 @ SY232 @ SV54 )
              | ( equidistant @ SV15 @ SY232 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SY232 @ SV54 @ SV71 ) ) ) )
        = $true )
      | ( ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
        = $false )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[212]) ).

thf(217,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV23: $i,SV75: $i,SV38: $i,SV74: $i,SV6: $i] :
      ( ( ( ~ ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
          | ~ ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
          | ~ ( between @ SV6 @ SV23 @ SV56 )
          | ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[213]) ).

thf(218,plain,
    ! [SV41: $i,SV27: $i,SV73: $i,SV60: $i,SV10: $i] :
      ( ( ( between @ SV10 @ SV60 @ SV73 )
        = $true )
      | ( ( ( between @ SV60 @ SV73 @ SV10 )
          | ( SV27 = SV41 )
          | ( between @ SV73 @ SV10 @ SV60 ) )
        = $true )
      | ( ( equidistant @ SV73 @ SV27 @ SV73 @ SV41 )
        = $false )
      | ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[214]) ).

thf(219,plain,
    ! [SV70: $i,SV14: $i,SV45: $i,SV53: $i,SV76: $i,SV31: $i] :
      ( ( ( ~ ( between @ SV31 @ SV76 @ SV53 )
          | ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SV76 @ SV53 @ SV70 ) @ SV70 ) )
        = $true )
      | ( ( between @ SV14 @ SV31 @ SV53 )
        = $false )
      | ( ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
        = $false )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[215]) ).

thf(220,plain,
    ! [SV71: $i,SV46: $i,SV15: $i,SV54: $i,SV77: $i,SV32: $i] :
      ( ( ( ~ ( between @ SV32 @ SV77 @ SV54 )
          | ( equidistant @ SV15 @ SV77 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SV77 @ SV54 @ SV71 ) ) )
        = $true )
      | ( ( between @ SV15 @ SV32 @ SV54 )
        = $false )
      | ( ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
        = $false )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[216]) ).

thf(221,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV23: $i,SV75: $i,SV38: $i,SV74: $i,SV6: $i] :
      ( ( ( ~ ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 ) )
        = $true )
      | ( ( ~ ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
          | ~ ( between @ SV6 @ SV23 @ SV56 )
          | ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[217]) ).

thf(222,plain,
    ! [SV41: $i,SV27: $i,SV10: $i,SV73: $i,SV60: $i] :
      ( ( ( between @ SV60 @ SV73 @ SV10 )
        = $true )
      | ( ( ( SV27 = SV41 )
          | ( between @ SV73 @ SV10 @ SV60 ) )
        = $true )
      | ( ( between @ SV10 @ SV60 @ SV73 )
        = $true )
      | ( ( equidistant @ SV73 @ SV27 @ SV73 @ SV41 )
        = $false )
      | ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[218]) ).

thf(223,plain,
    ! [SV70: $i,SV14: $i,SV45: $i,SV53: $i,SV76: $i,SV31: $i] :
      ( ( ( ~ ( between @ SV31 @ SV76 @ SV53 ) )
        = $true )
      | ( ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SV76 @ SV53 @ SV70 ) @ SV70 )
        = $true )
      | ( ( between @ SV14 @ SV31 @ SV53 )
        = $false )
      | ( ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
        = $false )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[219]) ).

thf(224,plain,
    ! [SV71: $i,SV46: $i,SV15: $i,SV54: $i,SV77: $i,SV32: $i] :
      ( ( ( ~ ( between @ SV32 @ SV77 @ SV54 ) )
        = $true )
      | ( ( equidistant @ SV15 @ SV77 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SV77 @ SV54 @ SV71 ) )
        = $true )
      | ( ( between @ SV15 @ SV32 @ SV54 )
        = $false )
      | ( ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
        = $false )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[220]) ).

thf(225,plain,
    ! [SV57: $i,SV56: $i,SV52: $i,SV23: $i,SV75: $i,SV38: $i,SV74: $i,SV6: $i] :
      ( ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( ~ ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
          | ~ ( between @ SV6 @ SV23 @ SV56 )
          | ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[221]) ).

thf(226,plain,
    ! [SV60: $i,SV10: $i,SV73: $i,SV41: $i,SV27: $i] :
      ( ( ( SV27 = SV41 )
        = $true )
      | ( ( between @ SV73 @ SV10 @ SV60 )
        = $true )
      | ( ( between @ SV60 @ SV73 @ SV10 )
        = $true )
      | ( ( between @ SV10 @ SV60 @ SV73 )
        = $true )
      | ( ( equidistant @ SV73 @ SV27 @ SV73 @ SV41 )
        = $false )
      | ( ( equidistant @ SV60 @ SV27 @ SV60 @ SV41 )
        = $false )
      | ( ( equidistant @ SV10 @ SV27 @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[222]) ).

thf(227,plain,
    ! [SV70: $i,SV14: $i,SV45: $i,SV53: $i,SV76: $i,SV31: $i] :
      ( ( ( between @ SV31 @ SV76 @ SV53 )
        = $false )
      | ( ( between @ SV45 @ ( continuous @ SV14 @ SV31 @ SV45 @ SV76 @ SV53 @ SV70 ) @ SV70 )
        = $true )
      | ( ( between @ SV14 @ SV31 @ SV53 )
        = $false )
      | ( ( equidistant @ SV14 @ SV53 @ SV14 @ SV70 )
        = $false )
      | ( ( equidistant @ SV14 @ SV31 @ SV14 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[223]) ).

thf(228,plain,
    ! [SV71: $i,SV46: $i,SV15: $i,SV54: $i,SV77: $i,SV32: $i] :
      ( ( ( between @ SV32 @ SV77 @ SV54 )
        = $false )
      | ( ( equidistant @ SV15 @ SV77 @ SV15 @ ( continuous @ SV15 @ SV32 @ SV46 @ SV77 @ SV54 @ SV71 ) )
        = $true )
      | ( ( between @ SV15 @ SV32 @ SV54 )
        = $false )
      | ( ( equidistant @ SV15 @ SV54 @ SV15 @ SV71 )
        = $false )
      | ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[224]) ).

thf(229,plain,
    ! [SV57: $i,SV38: $i,SV56: $i,SV6: $i,SV75: $i,SV52: $i,SV74: $i,SV23: $i] :
      ( ( ( ~ ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 ) )
        = $true )
      | ( ( ~ ( between @ SV6 @ SV23 @ SV56 )
          | ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[225]) ).

thf(230,plain,
    ! [SV57: $i,SV38: $i,SV56: $i,SV6: $i,SV75: $i,SV52: $i,SV74: $i,SV23: $i] :
      ( ( ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
        = $false )
      | ( ( ~ ( between @ SV6 @ SV23 @ SV56 )
          | ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[229]) ).

thf(231,plain,
    ! [SV75: $i,SV74: $i,SV57: $i,SV52: $i,SV38: $i,SV56: $i,SV23: $i,SV6: $i] :
      ( ( ( ~ ( between @ SV6 @ SV23 @ SV56 ) )
        = $true )
      | ( ( ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
        = $false )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[230]) ).

thf(232,plain,
    ! [SV75: $i,SV74: $i,SV57: $i,SV52: $i,SV38: $i,SV56: $i,SV23: $i,SV6: $i] :
      ( ( ( between @ SV6 @ SV23 @ SV56 )
        = $false )
      | ( ( ~ ( between @ SV38 @ SV52 @ SV57 )
          | ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
        = $false )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[231]) ).

thf(233,plain,
    ! [SV75: $i,SV74: $i,SV56: $i,SV23: $i,SV6: $i,SV57: $i,SV52: $i,SV38: $i] :
      ( ( ( ~ ( between @ SV38 @ SV52 @ SV57 ) )
        = $true )
      | ( ( ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( between @ SV6 @ SV23 @ SV56 )
        = $false )
      | ( ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
        = $false )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[232]) ).

thf(234,plain,
    ! [SV75: $i,SV74: $i,SV56: $i,SV23: $i,SV6: $i,SV57: $i,SV52: $i,SV38: $i] :
      ( ( ( between @ SV38 @ SV52 @ SV57 )
        = $false )
      | ( ( ( SV6 = SV23 )
          | ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 ) )
        = $true )
      | ( ( between @ SV6 @ SV23 @ SV56 )
        = $false )
      | ( ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
        = $false )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[233]) ).

thf(235,plain,
    ! [SV52: $i,SV38: $i,SV75: $i,SV57: $i,SV74: $i,SV56: $i,SV23: $i,SV6: $i] :
      ( ( ( SV6 = SV23 )
        = $true )
      | ( ( equidistant @ SV56 @ SV74 @ SV57 @ SV75 )
        = $true )
      | ( ( between @ SV38 @ SV52 @ SV57 )
        = $false )
      | ( ( between @ SV6 @ SV23 @ SV56 )
        = $false )
      | ( ( equidistant @ SV23 @ SV74 @ SV52 @ SV75 )
        = $false )
      | ( ( equidistant @ SV6 @ SV74 @ SV38 @ SV75 )
        = $false )
      | ( ( equidistant @ SV23 @ SV56 @ SV52 @ SV57 )
        = $false )
      | ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[234]) ).

thf(236,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[61,235,228,227,226,210,209,208,205,198,197,174,153,142,140,139,120,105,104,95,94,93,83]) ).

thf(237,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[236]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07  % Problem  : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.07  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.06/0.26  % Computer : n007.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 600
% 0.06/0.26  % DateTime : Sat Jun 18 12:20:13 EDT 2022
% 0.06/0.26  % CPUTime  : 
% 0.06/0.30  
% 0.06/0.30   No.of.Axioms: 22
% 0.06/0.30  
% 0.06/0.30   Length.of.Defs: 0
% 0.06/0.30  
% 0.06/0.30   Contains.Choice.Funs: false
% 0.10/0.34  (rf:0,axioms:22,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:24,loop_count:0,foatp_calls:0,translation:fof_full).................
% 0.38/0.59  
% 0.38/0.59  ********************************
% 0.38/0.59  *   All subproblems solved!    *
% 0.38/0.59  ********************************
% 0.38/0.59  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:22,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:236,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.38/0.61  
% 0.38/0.61  %**** Beginning of derivation protocol ****
% 0.38/0.61  % SZS output start CNFRefutation
% See solution above
% 0.38/0.61  
% 0.38/0.61  %**** End of derivation protocol ****
% 0.38/0.61  %**** no. of clauses in derivation: 237 ****
% 0.38/0.61  %**** clause counter: 236 ****
% 0.38/0.61  
% 0.38/0.61  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:22,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:236,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------