TSTP Solution File: GEO011-5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GEO011-5 : 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 05:06:02 EDT 2022

% Result   : Unsatisfiable 0.36s 0.53s
% Output   : CNFRefutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  166 (  99 unt;   9 typ;   0 def)
%            Number of atoms       :  948 ( 274 equ;   0 cnn)
%            Maximal formula atoms :    8 (   6 avg)
%            Number of connectives : 2593 ( 219   ~; 325   |;   0   &;2049   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   5 con; 0-5 aty)
%            Number of variables   :  623 (   0   ^ 623   !;   0   ?; 623   :)

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

thf(tp_colinear,type,
    colinear: $i > $i > $i > $o ).

thf(tp_distance,type,
    distance: $i > $i > $i ).

thf(tp_equal_distance,type,
    equal_distance: $i > $i > $o ).

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

thf(2,axiom,
    ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).

thf(3,axiom,
    ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).

thf(4,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/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).

thf(5,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/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).

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

thf(7,axiom,
    ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
      ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
      | ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
      | ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
      | ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
      | ~ ( between @ X @ Y @ Z )
      | ~ ( between @ X1 @ Y1 @ Z1 )
      | ( X = Y )
      | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).

thf(8,axiom,
    ! [Y: $i,X: $i,W: $i,V: $i] : ( equal_distance @ ( distance @ Y @ ( extension @ X @ Y @ W @ V ) ) @ ( distance @ W @ V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).

thf(9,axiom,
    ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).

thf(10,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
      | ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).

thf(11,axiom,
    ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
      ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
      | ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
      | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

thf(12,axiom,
    ! [X: $i,Y: $i] : ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

thf(13,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( colinear @ X @ Y @ Z )
      | ( between @ X @ Y @ Z )
      | ( between @ Y @ Z @ X )
      | ( between @ Z @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity4) ).

thf(14,axiom,
    ! [Z: $i,X: $i,Y: $i] :
      ( ~ ( between @ Z @ X @ Y )
      | ( colinear @ X @ Y @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).

thf(15,axiom,
    ! [Y: $i,Z: $i,X: $i] :
      ( ~ ( between @ Y @ Z @ X )
      | ( colinear @ X @ Y @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).

thf(16,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( between @ X @ Y @ Z )
      | ( colinear @ X @ Y @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).

thf(17,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(18,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[17]) ).

thf(19,negated_conjecture,
    colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).

thf(20,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(22,plain,
    ( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(23,plain,
    ( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(24,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)],[4]) ).

thf(25,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)],[5]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( between @ X @ Y @ X )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
          | ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
          | ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
          | ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
          | ~ ( between @ X @ Y @ Z )
          | ~ ( between @ X1 @ Y1 @ Z1 )
          | ( X = Y )
          | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(28,plain,
    ( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equal_distance @ ( distance @ Y @ ( extension @ X @ Y @ W @ V ) ) @ ( distance @ W @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
          | ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
          | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i] : ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( colinear @ X @ Y @ Z )
          | ( between @ X @ Y @ Z )
          | ( between @ Y @ Z @ X )
          | ( between @ Z @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(34,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ~ ( between @ Z @ X @ Y )
          | ( colinear @ X @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(35,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ~ ( between @ Y @ Z @ X )
          | ( colinear @ X @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(36,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( between @ X @ Y @ Z )
          | ( colinear @ X @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(37,plain,
    ( ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[20]) ).

thf(39,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)],[24]) ).

thf(40,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)],[25]) ).

thf(41,plain,
    ( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
          | ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
          | ! [V: $i,V1: $i] :
              ( ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
              | ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
              | ~ ( between @ X @ Y @ Z )
              | ~ ( between @ X1 @ Y1 @ Z1 )
              | ( X = Y )
              | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(42,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ! [Z: $i] :
              ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
          | ( X = Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(43,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
          | ! [V2: $i,W: $i] :
              ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
              | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[31]) ).

thf(44,plain,
    ( ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(45,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( between @ X @ Y @ Z )
          | ( colinear @ X @ Y @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(46,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ~ ( between @ Y @ Z @ X )
          | ( colinear @ X @ Y @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(47,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ~ ( between @ Z @ X @ Y )
          | ( colinear @ X @ Y @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(48,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( colinear @ X @ Y @ Z )
          | ( between @ X @ Y @ Z )
          | ( between @ Y @ Z @ X )
          | ( between @ Z @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(49,plain,
    ( ( ! [X: $i,Y: $i] : ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(50,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
          | ! [V2: $i,W: $i] :
              ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
              | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ! [Z: $i] :
              ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(53,plain,
    ( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equal_distance @ ( distance @ Y @ ( extension @ X @ Y @ W @ V ) ) @ ( distance @ W @ V ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(54,plain,
    ( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
          ( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
          | ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
          | ! [V: $i,V1: $i] :
              ( ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
              | ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
              | ~ ( between @ X @ Y @ Z )
              | ~ ( between @ X1 @ Y1 @ Z1 )
              | ( X = Y )
              | ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(55,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( between @ X @ Y @ X )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

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(copy,[status(thm)],[40]) ).

thf(57,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)],[39]) ).

thf(58,plain,
    ( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(59,plain,
    ( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(60,plain,
    ( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(61,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(62,plain,
    ! [SV1: $i] :
      ( ( ! [SY51: $i,SY52: $i] :
            ( ~ ( between @ SV1 @ SY51 @ SY52 )
            | ( colinear @ SV1 @ SY51 @ SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(63,plain,
    ! [SV2: $i] :
      ( ( ! [SY53: $i,SY54: $i] :
            ( ~ ( between @ SV2 @ SY53 @ SY54 )
            | ( colinear @ SY54 @ SV2 @ SY53 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(64,plain,
    ! [SV3: $i] :
      ( ( ! [SY55: $i,SY56: $i] :
            ( ~ ( between @ SV3 @ SY55 @ SY56 )
            | ( colinear @ SY55 @ SY56 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(65,plain,
    ! [SV4: $i] :
      ( ( ! [SY57: $i,SY58: $i] :
            ( ~ ( colinear @ SV4 @ SY57 @ SY58 )
            | ( between @ SV4 @ SY57 @ SY58 )
            | ( between @ SY57 @ SY58 @ SV4 )
            | ( between @ SY58 @ SV4 @ SY57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(66,plain,
    ! [SV5: $i] :
      ( ( ! [SY59: $i] : ( equal_distance @ ( distance @ SV5 @ SY59 ) @ ( distance @ SY59 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(67,plain,
    ! [SV6: $i] :
      ( ( ! [SY60: $i,SY61: $i,SY62: $i] :
            ( ~ ( equal_distance @ ( distance @ SV6 @ SY60 ) @ ( distance @ SY61 @ SY62 ) )
            | ! [SY63: $i,SY64: $i] :
                ( ~ ( equal_distance @ ( distance @ SV6 @ SY60 ) @ ( distance @ SY63 @ SY64 ) )
                | ( equal_distance @ ( distance @ SY61 @ SY62 ) @ ( distance @ SY63 @ SY64 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(68,plain,
    ! [SV7: $i] :
      ( ( ! [SY65: $i] :
            ( ! [SY66: $i] :
                ~ ( equal_distance @ ( distance @ SV7 @ SY65 ) @ ( distance @ SY66 @ SY66 ) )
            | ( SV7 = SY65 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(69,plain,
    ! [SV8: $i] :
      ( ( ! [SY67: $i,SY68: $i,SY69: $i] : ( between @ SV8 @ SY67 @ ( extension @ SV8 @ SY67 @ SY68 @ SY69 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(70,plain,
    ! [SV9: $i] :
      ( ( ! [SY70: $i,SY71: $i,SY72: $i] : ( equal_distance @ ( distance @ SV9 @ ( extension @ SY70 @ SV9 @ SY71 @ SY72 ) ) @ ( distance @ SY71 @ SY72 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(71,plain,
    ! [SV10: $i] :
      ( ( ! [SY73: $i,SY74: $i,SY75: $i,SY76: $i,SY77: $i] :
            ( ~ ( equal_distance @ ( distance @ SV10 @ SY73 ) @ ( distance @ SY74 @ SY75 ) )
            | ~ ( equal_distance @ ( distance @ SY73 @ SY76 ) @ ( distance @ SY75 @ SY77 ) )
            | ! [SY78: $i,SY79: $i] :
                ( ~ ( equal_distance @ ( distance @ SV10 @ SY78 ) @ ( distance @ SY74 @ SY79 ) )
                | ~ ( equal_distance @ ( distance @ SY73 @ SY78 ) @ ( distance @ SY75 @ SY79 ) )
                | ~ ( between @ SV10 @ SY73 @ SY76 )
                | ~ ( between @ SY74 @ SY75 @ SY77 )
                | ( SV10 = SY73 )
                | ( equal_distance @ ( distance @ SY76 @ SY78 ) @ ( distance @ SY77 @ SY79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(72,plain,
    ! [SV11: $i] :
      ( ( ! [SY80: $i] :
            ( ~ ( between @ SV11 @ SY80 @ SV11 )
            | ( SV11 = SY80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(73,plain,
    ! [SV12: $i] :
      ( ( ! [SY81: $i,SY82: $i] :
            ( ~ ( between @ SV12 @ SY81 @ SY82 )
            | ! [SY83: $i,SY84: $i] :
                ( ~ ( between @ SY83 @ SY84 @ SY82 )
                | ( between @ SY81 @ ( inner_pasch @ SV12 @ SY81 @ SY82 @ SY84 @ SY83 ) @ SY83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(74,plain,
    ! [SV13: $i] :
      ( ( ! [SY85: $i,SY86: $i] :
            ( ~ ( between @ SV13 @ SY85 @ SY86 )
            | ! [SY87: $i,SY88: $i] :
                ( ~ ( between @ SY87 @ SY88 @ SY86 )
                | ( between @ SY88 @ ( inner_pasch @ SV13 @ SY85 @ SY86 @ SY88 @ SY87 ) @ SV13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(75,plain,
    ( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(76,plain,
    ( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(77,plain,
    ( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(78,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(79,plain,
    ! [SV14: $i,SV1: $i] :
      ( ( ! [SY89: $i] :
            ( ~ ( between @ SV1 @ SV14 @ SY89 )
            | ( colinear @ SV1 @ SV14 @ SY89 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(80,plain,
    ! [SV15: $i,SV2: $i] :
      ( ( ! [SY90: $i] :
            ( ~ ( between @ SV2 @ SV15 @ SY90 )
            | ( colinear @ SY90 @ SV2 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(81,plain,
    ! [SV16: $i,SV3: $i] :
      ( ( ! [SY91: $i] :
            ( ~ ( between @ SV3 @ SV16 @ SY91 )
            | ( colinear @ SV16 @ SY91 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(82,plain,
    ! [SV17: $i,SV4: $i] :
      ( ( ! [SY92: $i] :
            ( ~ ( colinear @ SV4 @ SV17 @ SY92 )
            | ( between @ SV4 @ SV17 @ SY92 )
            | ( between @ SV17 @ SY92 @ SV4 )
            | ( between @ SY92 @ SV4 @ SV17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(83,plain,
    ! [SV18: $i,SV5: $i] :
      ( ( equal_distance @ ( distance @ SV5 @ SV18 ) @ ( distance @ SV18 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(84,plain,
    ! [SV19: $i,SV6: $i] :
      ( ( ! [SY93: $i,SY94: $i] :
            ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SY93 @ SY94 ) )
            | ! [SY95: $i,SY96: $i] :
                ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SY95 @ SY96 ) )
                | ( equal_distance @ ( distance @ SY93 @ SY94 ) @ ( distance @ SY95 @ SY96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(85,plain,
    ! [SV20: $i,SV7: $i] :
      ( ( ! [SY97: $i] :
            ~ ( equal_distance @ ( distance @ SV7 @ SV20 ) @ ( distance @ SY97 @ SY97 ) )
        | ( SV7 = SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(86,plain,
    ! [SV21: $i,SV8: $i] :
      ( ( ! [SY98: $i,SY99: $i] : ( between @ SV8 @ SV21 @ ( extension @ SV8 @ SV21 @ SY98 @ SY99 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(87,plain,
    ! [SV22: $i,SV9: $i] :
      ( ( ! [SY100: $i,SY101: $i] : ( equal_distance @ ( distance @ SV9 @ ( extension @ SV22 @ SV9 @ SY100 @ SY101 ) ) @ ( distance @ SY100 @ SY101 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(88,plain,
    ! [SV23: $i,SV10: $i] :
      ( ( ! [SY102: $i,SY103: $i,SY104: $i,SY105: $i] :
            ( ~ ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SY102 @ SY103 ) )
            | ~ ( equal_distance @ ( distance @ SV23 @ SY104 ) @ ( distance @ SY103 @ SY105 ) )
            | ! [SY106: $i,SY107: $i] :
                ( ~ ( equal_distance @ ( distance @ SV10 @ SY106 ) @ ( distance @ SY102 @ SY107 ) )
                | ~ ( equal_distance @ ( distance @ SV23 @ SY106 ) @ ( distance @ SY103 @ SY107 ) )
                | ~ ( between @ SV10 @ SV23 @ SY104 )
                | ~ ( between @ SY102 @ SY103 @ SY105 )
                | ( SV10 = SV23 )
                | ( equal_distance @ ( distance @ SY104 @ SY106 ) @ ( distance @ SY105 @ SY107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(89,plain,
    ! [SV24: $i,SV11: $i] :
      ( ( ~ ( between @ SV11 @ SV24 @ SV11 )
        | ( SV11 = SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(90,plain,
    ! [SV25: $i,SV12: $i] :
      ( ( ! [SY108: $i] :
            ( ~ ( between @ SV12 @ SV25 @ SY108 )
            | ! [SY109: $i,SY110: $i] :
                ( ~ ( between @ SY109 @ SY110 @ SY108 )
                | ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SY108 @ SY110 @ SY109 ) @ SY109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(91,plain,
    ! [SV26: $i,SV13: $i] :
      ( ( ! [SY111: $i] :
            ( ~ ( between @ SV13 @ SV26 @ SY111 )
            | ! [SY112: $i,SY113: $i] :
                ( ~ ( between @ SY112 @ SY113 @ SY111 )
                | ( between @ SY113 @ ( inner_pasch @ SV13 @ SV26 @ SY111 @ SY113 @ SY112 ) @ SV13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(92,plain,
    ! [SV27: $i,SV14: $i,SV1: $i] :
      ( ( ~ ( between @ SV1 @ SV14 @ SV27 )
        | ( colinear @ SV1 @ SV14 @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(93,plain,
    ! [SV28: $i,SV15: $i,SV2: $i] :
      ( ( ~ ( between @ SV2 @ SV15 @ SV28 )
        | ( colinear @ SV28 @ SV2 @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(94,plain,
    ! [SV29: $i,SV16: $i,SV3: $i] :
      ( ( ~ ( between @ SV3 @ SV16 @ SV29 )
        | ( colinear @ SV16 @ SV29 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(95,plain,
    ! [SV30: $i,SV17: $i,SV4: $i] :
      ( ( ~ ( colinear @ SV4 @ SV17 @ SV30 )
        | ( between @ SV4 @ SV17 @ SV30 )
        | ( between @ SV17 @ SV30 @ SV4 )
        | ( between @ SV30 @ SV4 @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(96,plain,
    ! [SV31: $i,SV19: $i,SV6: $i] :
      ( ( ! [SY114: $i] :
            ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SY114 ) )
            | ! [SY115: $i,SY116: $i] :
                ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SY115 @ SY116 ) )
                | ( equal_distance @ ( distance @ SV31 @ SY114 ) @ ( distance @ SY115 @ SY116 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(97,plain,
    ! [SV20: $i,SV7: $i] :
      ( ( ( ! [SY97: $i] :
              ~ ( equal_distance @ ( distance @ SV7 @ SV20 ) @ ( distance @ SY97 @ SY97 ) ) )
        = $true )
      | ( ( SV7 = SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(98,plain,
    ! [SV32: $i,SV21: $i,SV8: $i] :
      ( ( ! [SY117: $i] : ( between @ SV8 @ SV21 @ ( extension @ SV8 @ SV21 @ SV32 @ SY117 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(99,plain,
    ! [SV33: $i,SV22: $i,SV9: $i] :
      ( ( ! [SY118: $i] : ( equal_distance @ ( distance @ SV9 @ ( extension @ SV22 @ SV9 @ SV33 @ SY118 ) ) @ ( distance @ SV33 @ SY118 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(100,plain,
    ! [SV34: $i,SV23: $i,SV10: $i] :
      ( ( ! [SY119: $i,SY120: $i,SY121: $i] :
            ( ~ ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SY119 ) )
            | ~ ( equal_distance @ ( distance @ SV23 @ SY120 ) @ ( distance @ SY119 @ SY121 ) )
            | ! [SY122: $i,SY123: $i] :
                ( ~ ( equal_distance @ ( distance @ SV10 @ SY122 ) @ ( distance @ SV34 @ SY123 ) )
                | ~ ( equal_distance @ ( distance @ SV23 @ SY122 ) @ ( distance @ SY119 @ SY123 ) )
                | ~ ( between @ SV10 @ SV23 @ SY120 )
                | ~ ( between @ SV34 @ SY119 @ SY121 )
                | ( SV10 = SV23 )
                | ( equal_distance @ ( distance @ SY120 @ SY122 ) @ ( distance @ SY121 @ SY123 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(101,plain,
    ! [SV24: $i,SV11: $i] :
      ( ( ( ~ ( between @ SV11 @ SV24 @ SV11 ) )
        = $true )
      | ( ( SV11 = SV24 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(102,plain,
    ! [SV35: $i,SV25: $i,SV12: $i] :
      ( ( ~ ( between @ SV12 @ SV25 @ SV35 )
        | ! [SY124: $i,SY125: $i] :
            ( ~ ( between @ SY124 @ SY125 @ SV35 )
            | ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SY125 @ SY124 ) @ SY124 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(103,plain,
    ! [SV36: $i,SV26: $i,SV13: $i] :
      ( ( ~ ( between @ SV13 @ SV26 @ SV36 )
        | ! [SY126: $i,SY127: $i] :
            ( ~ ( between @ SY126 @ SY127 @ SV36 )
            | ( between @ SY127 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SY127 @ SY126 ) @ SV13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(104,plain,
    ! [SV27: $i,SV14: $i,SV1: $i] :
      ( ( ( ~ ( between @ SV1 @ SV14 @ SV27 ) )
        = $true )
      | ( ( colinear @ SV1 @ SV14 @ SV27 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(105,plain,
    ! [SV28: $i,SV15: $i,SV2: $i] :
      ( ( ( ~ ( between @ SV2 @ SV15 @ SV28 ) )
        = $true )
      | ( ( colinear @ SV28 @ SV2 @ SV15 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(106,plain,
    ! [SV29: $i,SV16: $i,SV3: $i] :
      ( ( ( ~ ( between @ SV3 @ SV16 @ SV29 ) )
        = $true )
      | ( ( colinear @ SV16 @ SV29 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(107,plain,
    ! [SV30: $i,SV17: $i,SV4: $i] :
      ( ( ( ~ ( colinear @ SV4 @ SV17 @ SV30 ) )
        = $true )
      | ( ( ( between @ SV4 @ SV17 @ SV30 )
          | ( between @ SV17 @ SV30 @ SV4 )
          | ( between @ SV30 @ SV4 @ SV17 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(108,plain,
    ! [SV37: $i,SV31: $i,SV19: $i,SV6: $i] :
      ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) )
        | ! [SY128: $i,SY129: $i] :
            ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SY128 @ SY129 ) )
            | ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SY128 @ SY129 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(109,plain,
    ! [SV38: $i,SV20: $i,SV7: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV7 @ SV20 ) @ ( distance @ SV38 @ SV38 ) ) )
        = $true )
      | ( ( SV7 = SV20 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(110,plain,
    ! [SV39: $i,SV32: $i,SV21: $i,SV8: $i] :
      ( ( between @ SV8 @ SV21 @ ( extension @ SV8 @ SV21 @ SV32 @ SV39 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(111,plain,
    ! [SV40: $i,SV33: $i,SV22: $i,SV9: $i] :
      ( ( equal_distance @ ( distance @ SV9 @ ( extension @ SV22 @ SV9 @ SV33 @ SV40 ) ) @ ( distance @ SV33 @ SV40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(112,plain,
    ! [SV41: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ! [SY130: $i,SY131: $i] :
            ( ~ ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
            | ~ ( equal_distance @ ( distance @ SV23 @ SY130 ) @ ( distance @ SV41 @ SY131 ) )
            | ! [SY132: $i,SY133: $i] :
                ( ~ ( equal_distance @ ( distance @ SV10 @ SY132 ) @ ( distance @ SV34 @ SY133 ) )
                | ~ ( equal_distance @ ( distance @ SV23 @ SY132 ) @ ( distance @ SV41 @ SY133 ) )
                | ~ ( between @ SV10 @ SV23 @ SY130 )
                | ~ ( between @ SV34 @ SV41 @ SY131 )
                | ( SV10 = SV23 )
                | ( equal_distance @ ( distance @ SY130 @ SY132 ) @ ( distance @ SY131 @ SY133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(113,plain,
    ! [SV24: $i,SV11: $i] :
      ( ( ( between @ SV11 @ SV24 @ SV11 )
        = $false )
      | ( ( SV11 = SV24 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(114,plain,
    ! [SV35: $i,SV25: $i,SV12: $i] :
      ( ( ( ~ ( between @ SV12 @ SV25 @ SV35 ) )
        = $true )
      | ( ( ! [SY124: $i,SY125: $i] :
              ( ~ ( between @ SY124 @ SY125 @ SV35 )
              | ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SY125 @ SY124 ) @ SY124 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(115,plain,
    ! [SV36: $i,SV26: $i,SV13: $i] :
      ( ( ( ~ ( between @ SV13 @ SV26 @ SV36 ) )
        = $true )
      | ( ( ! [SY126: $i,SY127: $i] :
              ( ~ ( between @ SY126 @ SY127 @ SV36 )
              | ( between @ SY127 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SY127 @ SY126 ) @ SV13 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[103]) ).

thf(116,plain,
    ! [SV27: $i,SV14: $i,SV1: $i] :
      ( ( ( between @ SV1 @ SV14 @ SV27 )
        = $false )
      | ( ( colinear @ SV1 @ SV14 @ SV27 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(117,plain,
    ! [SV28: $i,SV15: $i,SV2: $i] :
      ( ( ( between @ SV2 @ SV15 @ SV28 )
        = $false )
      | ( ( colinear @ SV28 @ SV2 @ SV15 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(118,plain,
    ! [SV29: $i,SV16: $i,SV3: $i] :
      ( ( ( between @ SV3 @ SV16 @ SV29 )
        = $false )
      | ( ( colinear @ SV16 @ SV29 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[106]) ).

thf(119,plain,
    ! [SV30: $i,SV17: $i,SV4: $i] :
      ( ( ( colinear @ SV4 @ SV17 @ SV30 )
        = $false )
      | ( ( ( between @ SV4 @ SV17 @ SV30 )
          | ( between @ SV17 @ SV30 @ SV4 )
          | ( between @ SV30 @ SV4 @ SV17 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[107]) ).

thf(120,plain,
    ! [SV37: $i,SV31: $i,SV19: $i,SV6: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) ) )
        = $true )
      | ( ( ! [SY128: $i,SY129: $i] :
              ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SY128 @ SY129 ) )
              | ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SY128 @ SY129 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[108]) ).

thf(121,plain,
    ! [SV38: $i,SV20: $i,SV7: $i] :
      ( ( ( equal_distance @ ( distance @ SV7 @ SV20 ) @ ( distance @ SV38 @ SV38 ) )
        = $false )
      | ( ( SV7 = SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[109]) ).

thf(122,plain,
    ! [SV42: $i,SV41: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ! [SY134: $i] :
            ( ~ ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
            | ~ ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SY134 ) )
            | ! [SY135: $i,SY136: $i] :
                ( ~ ( equal_distance @ ( distance @ SV10 @ SY135 ) @ ( distance @ SV34 @ SY136 ) )
                | ~ ( equal_distance @ ( distance @ SV23 @ SY135 ) @ ( distance @ SV41 @ SY136 ) )
                | ~ ( between @ SV10 @ SV23 @ SV42 )
                | ~ ( between @ SV34 @ SV41 @ SY134 )
                | ( SV10 = SV23 )
                | ( equal_distance @ ( distance @ SV42 @ SY135 ) @ ( distance @ SY134 @ SY136 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(123,plain,
    ! [SV35: $i,SV25: $i,SV12: $i] :
      ( ( ( between @ SV12 @ SV25 @ SV35 )
        = $false )
      | ( ( ! [SY124: $i,SY125: $i] :
              ( ~ ( between @ SY124 @ SY125 @ SV35 )
              | ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SY125 @ SY124 ) @ SY124 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(124,plain,
    ! [SV36: $i,SV26: $i,SV13: $i] :
      ( ( ( between @ SV13 @ SV26 @ SV36 )
        = $false )
      | ( ( ! [SY126: $i,SY127: $i] :
              ( ~ ( between @ SY126 @ SY127 @ SV36 )
              | ( between @ SY127 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SY127 @ SY126 ) @ SV13 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(125,plain,
    ! [SV30: $i,SV17: $i,SV4: $i] :
      ( ( ( between @ SV4 @ SV17 @ SV30 )
        = $true )
      | ( ( ( between @ SV17 @ SV30 @ SV4 )
          | ( between @ SV30 @ SV4 @ SV17 ) )
        = $true )
      | ( ( colinear @ SV4 @ SV17 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(126,plain,
    ! [SV37: $i,SV31: $i,SV19: $i,SV6: $i] :
      ( ( ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) )
        = $false )
      | ( ( ! [SY128: $i,SY129: $i] :
              ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SY128 @ SY129 ) )
              | ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SY128 @ SY129 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[120]) ).

thf(127,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        | ~ ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        | ! [SY137: $i,SY138: $i] :
            ( ~ ( equal_distance @ ( distance @ SV10 @ SY137 ) @ ( distance @ SV34 @ SY138 ) )
            | ~ ( equal_distance @ ( distance @ SV23 @ SY137 ) @ ( distance @ SV41 @ SY138 ) )
            | ~ ( between @ SV10 @ SV23 @ SV42 )
            | ~ ( between @ SV34 @ SV41 @ SV43 )
            | ( SV10 = SV23 )
            | ( equal_distance @ ( distance @ SV42 @ SY137 ) @ ( distance @ SV43 @ SY138 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(128,plain,
    ! [SV12: $i,SV25: $i,SV35: $i,SV44: $i] :
      ( ( ( ! [SY139: $i] :
              ( ~ ( between @ SV44 @ SY139 @ SV35 )
              | ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SY139 @ SV44 ) @ SV44 ) ) )
        = $true )
      | ( ( between @ SV12 @ SV25 @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(129,plain,
    ! [SV26: $i,SV13: $i,SV36: $i,SV45: $i] :
      ( ( ( ! [SY140: $i] :
              ( ~ ( between @ SV45 @ SY140 @ SV36 )
              | ( between @ SY140 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SY140 @ SV45 ) @ SV13 ) ) )
        = $true )
      | ( ( between @ SV13 @ SV26 @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(130,plain,
    ! [SV4: $i,SV30: $i,SV17: $i] :
      ( ( ( between @ SV17 @ SV30 @ SV4 )
        = $true )
      | ( ( between @ SV30 @ SV4 @ SV17 )
        = $true )
      | ( ( between @ SV4 @ SV17 @ SV30 )
        = $true )
      | ( ( colinear @ SV4 @ SV17 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[125]) ).

thf(131,plain,
    ! [SV37: $i,SV31: $i,SV46: $i,SV19: $i,SV6: $i] :
      ( ( ( ! [SY141: $i] :
              ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV46 @ SY141 ) )
              | ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SV46 @ SY141 ) ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(132,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) ) )
        = $true )
      | ( ( ~ ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
          | ! [SY137: $i,SY138: $i] :
              ( ~ ( equal_distance @ ( distance @ SV10 @ SY137 ) @ ( distance @ SV34 @ SY138 ) )
              | ~ ( equal_distance @ ( distance @ SV23 @ SY137 ) @ ( distance @ SV41 @ SY138 ) )
              | ~ ( between @ SV10 @ SV23 @ SV42 )
              | ~ ( between @ SV34 @ SV41 @ SV43 )
              | ( SV10 = SV23 )
              | ( equal_distance @ ( distance @ SV42 @ SY137 ) @ ( distance @ SV43 @ SY138 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[127]) ).

thf(133,plain,
    ! [SV12: $i,SV25: $i,SV35: $i,SV47: $i,SV44: $i] :
      ( ( ( ~ ( between @ SV44 @ SV47 @ SV35 )
          | ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SV47 @ SV44 ) @ SV44 ) )
        = $true )
      | ( ( between @ SV12 @ SV25 @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(134,plain,
    ! [SV26: $i,SV13: $i,SV36: $i,SV48: $i,SV45: $i] :
      ( ( ( ~ ( between @ SV45 @ SV48 @ SV36 )
          | ( between @ SV48 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SV48 @ SV45 ) @ SV13 ) )
        = $true )
      | ( ( between @ SV13 @ SV26 @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(135,plain,
    ! [SV37: $i,SV31: $i,SV49: $i,SV46: $i,SV19: $i,SV6: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV46 @ SV49 ) )
          | ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SV46 @ SV49 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(136,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false )
      | ( ( ~ ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
          | ! [SY137: $i,SY138: $i] :
              ( ~ ( equal_distance @ ( distance @ SV10 @ SY137 ) @ ( distance @ SV34 @ SY138 ) )
              | ~ ( equal_distance @ ( distance @ SV23 @ SY137 ) @ ( distance @ SV41 @ SY138 ) )
              | ~ ( between @ SV10 @ SV23 @ SV42 )
              | ~ ( between @ SV34 @ SV41 @ SV43 )
              | ( SV10 = SV23 )
              | ( equal_distance @ ( distance @ SV42 @ SY137 ) @ ( distance @ SV43 @ SY138 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[132]) ).

thf(137,plain,
    ! [SV12: $i,SV25: $i,SV35: $i,SV47: $i,SV44: $i] :
      ( ( ( ~ ( between @ SV44 @ SV47 @ SV35 ) )
        = $true )
      | ( ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SV47 @ SV44 ) @ SV44 )
        = $true )
      | ( ( between @ SV12 @ SV25 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[133]) ).

thf(138,plain,
    ! [SV26: $i,SV13: $i,SV36: $i,SV48: $i,SV45: $i] :
      ( ( ( ~ ( between @ SV45 @ SV48 @ SV36 ) )
        = $true )
      | ( ( between @ SV48 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SV48 @ SV45 ) @ SV13 )
        = $true )
      | ( ( between @ SV13 @ SV26 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(139,plain,
    ! [SV37: $i,SV31: $i,SV49: $i,SV46: $i,SV19: $i,SV6: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV46 @ SV49 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SV46 @ SV49 ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[135]) ).

thf(140,plain,
    ! [SV34: $i,SV10: $i,SV43: $i,SV41: $i,SV42: $i,SV23: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) ) )
        = $true )
      | ( ( ! [SY137: $i,SY138: $i] :
              ( ~ ( equal_distance @ ( distance @ SV10 @ SY137 ) @ ( distance @ SV34 @ SY138 ) )
              | ~ ( equal_distance @ ( distance @ SV23 @ SY137 ) @ ( distance @ SV41 @ SY138 ) )
              | ~ ( between @ SV10 @ SV23 @ SV42 )
              | ~ ( between @ SV34 @ SV41 @ SV43 )
              | ( SV10 = SV23 )
              | ( equal_distance @ ( distance @ SV42 @ SY137 ) @ ( distance @ SV43 @ SY138 ) ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[136]) ).

thf(141,plain,
    ! [SV12: $i,SV25: $i,SV35: $i,SV47: $i,SV44: $i] :
      ( ( ( between @ SV44 @ SV47 @ SV35 )
        = $false )
      | ( ( between @ SV25 @ ( inner_pasch @ SV12 @ SV25 @ SV35 @ SV47 @ SV44 ) @ SV44 )
        = $true )
      | ( ( between @ SV12 @ SV25 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[137]) ).

thf(142,plain,
    ! [SV26: $i,SV13: $i,SV36: $i,SV48: $i,SV45: $i] :
      ( ( ( between @ SV45 @ SV48 @ SV36 )
        = $false )
      | ( ( between @ SV48 @ ( inner_pasch @ SV13 @ SV26 @ SV36 @ SV48 @ SV45 ) @ SV13 )
        = $true )
      | ( ( between @ SV13 @ SV26 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(143,plain,
    ! [SV37: $i,SV31: $i,SV49: $i,SV46: $i,SV19: $i,SV6: $i] :
      ( ( ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV46 @ SV49 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV31 @ SV37 ) @ ( distance @ SV46 @ SV49 ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV6 @ SV19 ) @ ( distance @ SV31 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[139]) ).

thf(144,plain,
    ! [SV34: $i,SV10: $i,SV43: $i,SV41: $i,SV42: $i,SV23: $i] :
      ( ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( ! [SY137: $i,SY138: $i] :
              ( ~ ( equal_distance @ ( distance @ SV10 @ SY137 ) @ ( distance @ SV34 @ SY138 ) )
              | ~ ( equal_distance @ ( distance @ SV23 @ SY137 ) @ ( distance @ SV41 @ SY138 ) )
              | ~ ( between @ SV10 @ SV23 @ SV42 )
              | ~ ( between @ SV34 @ SV41 @ SV43 )
              | ( SV10 = SV23 )
              | ( equal_distance @ ( distance @ SV42 @ SY137 ) @ ( distance @ SV43 @ SY138 ) ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[140]) ).

thf(145,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV23: $i,SV34: $i,SV50: $i,SV10: $i] :
      ( ( ( ! [SY142: $i] :
              ( ~ ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SY142 ) )
              | ~ ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SY142 ) )
              | ~ ( between @ SV10 @ SV23 @ SV42 )
              | ~ ( between @ SV34 @ SV41 @ SV43 )
              | ( SV10 = SV23 )
              | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SY142 ) ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(146,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV23: $i,SV51: $i,SV34: $i,SV50: $i,SV10: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
          | ~ ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
          | ~ ( between @ SV10 @ SV23 @ SV42 )
          | ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(147,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV23: $i,SV51: $i,SV34: $i,SV50: $i,SV10: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) ) )
        = $true )
      | ( ( ~ ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
          | ~ ( between @ SV10 @ SV23 @ SV42 )
          | ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[146]) ).

thf(148,plain,
    ! [SV43: $i,SV42: $i,SV41: $i,SV23: $i,SV51: $i,SV34: $i,SV50: $i,SV10: $i] :
      ( ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( ~ ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
          | ~ ( between @ SV10 @ SV23 @ SV42 )
          | ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(149,plain,
    ! [SV43: $i,SV34: $i,SV42: $i,SV10: $i,SV51: $i,SV41: $i,SV50: $i,SV23: $i] :
      ( ( ( ~ ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) ) )
        = $true )
      | ( ( ~ ( between @ SV10 @ SV23 @ SV42 )
          | ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[148]) ).

thf(150,plain,
    ! [SV43: $i,SV34: $i,SV42: $i,SV10: $i,SV51: $i,SV41: $i,SV50: $i,SV23: $i] :
      ( ( ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
        = $false )
      | ( ( ~ ( between @ SV10 @ SV23 @ SV42 )
          | ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(151,plain,
    ! [SV51: $i,SV50: $i,SV43: $i,SV41: $i,SV34: $i,SV42: $i,SV23: $i,SV10: $i] :
      ( ( ( ~ ( between @ SV10 @ SV23 @ SV42 ) )
        = $true )
      | ( ( ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(152,plain,
    ! [SV51: $i,SV50: $i,SV43: $i,SV41: $i,SV34: $i,SV42: $i,SV23: $i,SV10: $i] :
      ( ( ( between @ SV10 @ SV23 @ SV42 )
        = $false )
      | ( ( ~ ( between @ SV34 @ SV41 @ SV43 )
          | ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(153,plain,
    ! [SV51: $i,SV50: $i,SV42: $i,SV23: $i,SV10: $i,SV43: $i,SV41: $i,SV34: $i] :
      ( ( ( ~ ( between @ SV34 @ SV41 @ SV43 ) )
        = $true )
      | ( ( ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( between @ SV10 @ SV23 @ SV42 )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[152]) ).

thf(154,plain,
    ! [SV51: $i,SV50: $i,SV42: $i,SV23: $i,SV10: $i,SV43: $i,SV41: $i,SV34: $i] :
      ( ( ( between @ SV34 @ SV41 @ SV43 )
        = $false )
      | ( ( ( SV10 = SV23 )
          | ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) ) )
        = $true )
      | ( ( between @ SV10 @ SV23 @ SV42 )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(155,plain,
    ! [SV41: $i,SV34: $i,SV51: $i,SV43: $i,SV50: $i,SV42: $i,SV23: $i,SV10: $i] :
      ( ( ( SV10 = SV23 )
        = $true )
      | ( ( equal_distance @ ( distance @ SV42 @ SV50 ) @ ( distance @ SV43 @ SV51 ) )
        = $true )
      | ( ( between @ SV34 @ SV41 @ SV43 )
        = $false )
      | ( ( between @ SV10 @ SV23 @ SV42 )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV50 ) @ ( distance @ SV41 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV50 ) @ ( distance @ SV34 @ SV51 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV23 @ SV42 ) @ ( distance @ SV41 @ SV43 ) )
        = $false )
      | ( ( equal_distance @ ( distance @ SV10 @ SV23 ) @ ( distance @ SV34 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(156,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[44,155,143,142,141,130,121,118,117,116,113,111,110,83,78,77,76,75]) ).

thf(157,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[156]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jun 17 17:16:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.38  
% 0.13/0.38   No.of.Axioms: 17
% 0.13/0.38  
% 0.13/0.38   Length.of.Defs: 0
% 0.13/0.38  
% 0.13/0.38   Contains.Choice.Funs: false
% 0.20/0.41  (rf:0,axioms:17,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:19,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.36/0.53  
% 0.36/0.53  ********************************
% 0.36/0.53  *   All subproblems solved!    *
% 0.36/0.53  ********************************
% 0.36/0.53  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:156,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.36/0.53  
% 0.36/0.53  %**** Beginning of derivation protocol ****
% 0.36/0.53  % SZS output start CNFRefutation
% See solution above
% 0.36/0.53  
% 0.36/0.53  %**** End of derivation protocol ****
% 0.36/0.53  %**** no. of clauses in derivation: 157 ****
% 0.36/0.53  %**** clause counter: 156 ****
% 0.36/0.53  
% 0.36/0.53  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:156,loop_count:0,foatp_calls:1,translation:fof_full)
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