TSTP Solution File: GEO008-3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GEO008-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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  : 300s
% DateTime : Fri May 19 11:08:50 EDT 2023

% Result   : Unsatisfiable 4.71s 2.18s
% Output   : Refutation 5.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  102
% Syntax   : Number of formulae    :  188 (  59 unt;  17 typ;   0 def)
%            Number of atoms       :  461 (  92 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 2140 ( 256   ~; 290   |;   0   &;1594   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   9 con; 0-6 aty)
%            Number of variables   :  594 (   0   ^; 594   !;   0   ?; 594   :)

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

thf(a_type,type,
    a: $i ).

thf(b_type,type,
    b: $i ).

thf(e_type,type,
    e: $i ).

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

thf(reflection_type,type,
    reflection: $i > $i > $i ).

thf(lower_dimension_point_1_type,type,
    lower_dimension_point_1: $i ).

thf(lower_dimension_point_2_type,type,
    lower_dimension_point_2: $i ).

thf(insertion_type,type,
    insertion: $i > $i > $i > $i > $i ).

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

thf(lower_dimension_point_3_type,type,
    lower_dimension_point_3: $i ).

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

thf(d_type,type,
    d: $i ).

thf(euclid1_type,type,
    euclid1: $i > $i > $i > $i > $i > $i ).

thf(euclid2_type,type,
    euclid2: $i > $i > $i > $i > $i > $i ).

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

thf(c_type,type,
    c: $i ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).

thf(153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ D @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).

thf(125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ D @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).

thf(93,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ D @ C )
      | ( between @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).

thf(253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ D @ C )
      | ( between @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ D )
      | ( between @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).

thf(188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ D )
      | ( between @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(42,axiom,
    ! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).

thf(173,plain,
    ! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(55,axiom,
    ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).

thf(204,plain,
    ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(72,axiom,
    ! [B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_3) ).

thf(245,plain,
    ! [B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ B )
      | ( A = B )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_2) ).

thf(250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ B )
      | ( A = B )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(68,axiom,
    between @ a @ c @ e,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_e) ).

thf(234,plain,
    between @ a @ c @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ A @ B @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).

thf(88,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ A @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ C @ A @ D )
      | ~ ( equidistant @ B @ C @ B @ D )
      | ( A = B )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11) ).

thf(170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ C @ A @ D )
      | ~ ( equidistant @ B @ C @ B @ D )
      | ( A = B )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( reflection @ ( reflection @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).

thf(115,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( reflection @ ( reflection @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ C @ D )
      | ( between @ A @ B @ D )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).

thf(217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ C @ D )
      | ( between @ A @ B @ D )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ( reflection @ A @ B )
      = ( extension @ A @ B @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).

thf(120,plain,
    ! [B: $i,A: $i] :
      ( ( reflection @ A @ B )
      = ( extension @ A @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(54,axiom,
    ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).

thf(202,plain,
    ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(43,axiom,
    ! [B: $i,A: $i] : ( between @ A @ B @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).

thf(174,plain,
    ! [B: $i,A: $i] : ( between @ A @ B @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ A @ C )
      | ~ ( equidistant @ D @ B @ D @ C )
      | ~ ( equidistant @ E @ B @ E @ C )
      | ( between @ A @ D @ E )
      | ( between @ D @ E @ A )
      | ( between @ E @ A @ D )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).

thf(185,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ A @ C )
      | ~ ( equidistant @ D @ B @ D @ C )
      | ~ ( equidistant @ E @ B @ E @ C )
      | ( between @ A @ D @ E )
      | ( between @ D @ E @ A )
      | ( between @ E @ A @ D )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ B )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).

thf(257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ B )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ C @ D @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).

thf(147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ C @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(23,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).

thf(133,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(56,axiom,
    between @ c @ b @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_between_c_and_d) ).

thf(206,plain,
    between @ c @ b @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(74,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ C @ D @ E )
      | ( between @ D @ ( insertion @ D @ E @ A @ B ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_2) ).

thf(248,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ C @ D @ E )
      | ( between @ D @ ( insertion @ D @ E @ A @ B ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ C )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).

thf(117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(84,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( equidistant @ A @ E @ C @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).

thf(270,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( equidistant @ A @ E @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(62,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( equidistant @ A @ G @ C @ H )
      | ~ ( equidistant @ E @ G @ F @ H )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( equidistant @ B @ G @ D @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14) ).

thf(220,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( equidistant @ A @ G @ C @ H )
      | ~ ( equidistant @ E @ G @ F @ H )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( equidistant @ B @ G @ D @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( B
        = ( insertion @ A @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).

thf(260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( B
        = ( insertion @ A @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(36,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ A @ C )
      | ~ ( equidistant @ A @ D @ A @ E )
      | ~ ( between @ A @ B @ D )
      | ~ ( between @ B @ F @ D )
      | ( equidistant @ A @ F @ A @ ( continuous @ A @ B @ C @ F @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).

thf(160,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ A @ C )
      | ~ ( equidistant @ A @ D @ A @ E )
      | ~ ( between @ A @ B @ D )
      | ~ ( between @ B @ F @ D )
      | ( equidistant @ A @ F @ A @ ( continuous @ A @ B @ C @ F @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(50,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ E )
      | ( A = B )
      | ( between @ ( euclid1 @ A @ D @ B @ E @ C ) @ C @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).

thf(192,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ E )
      | ( A = B )
      | ( between @ ( euclid1 @ A @ D @ B @ E @ C ) @ C @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( extension @ B @ A @ C @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).

thf(137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( extension @ B @ A @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(38,axiom,
    between @ a @ d @ e,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_between_a_and_e) ).

thf(165,plain,
    between @ a @ d @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ B @ D )
      | ( A = B )
      | ( between @ A @ C @ D )
      | ( between @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b12) ).

thf(229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ B @ D )
      | ( A = B )
      | ( between @ A @ C @ D )
      | ( between @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(52,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ A @ C )
      | ~ ( equidistant @ A @ D @ A @ E )
      | ~ ( between @ A @ B @ D )
      | ~ ( between @ B @ F @ D )
      | ( between @ C @ ( continuous @ A @ B @ C @ F @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).

thf(197,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ A @ C )
      | ~ ( equidistant @ A @ D @ A @ E )
      | ~ ( between @ A @ B @ D )
      | ~ ( between @ B @ F @ D )
      | ( between @ C @ ( continuous @ A @ B @ C @ F @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( A
       != ( reflection @ B @ A ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).

thf(97,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( reflection @ B @ A ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(64,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ C )
      | ( between @ B @ ( inner_pasch @ A @ B @ C @ E @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).

thf(224,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ C )
      | ( between @ B @ ( inner_pasch @ A @ B @ C @ E @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(12,axiom,
    lower_dimension_point_1 != lower_dimension_point_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).

thf(109,plain,
    lower_dimension_point_1 != lower_dimension_point_3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(59,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ A @ E @ C @ F )
      | ~ ( equidistant @ A @ G @ C @ H )
      | ~ ( equidistant @ E @ G @ F @ H )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( equidistant @ B @ G @ D @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12) ).

thf(212,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ A @ E @ C @ F )
      | ~ ( equidistant @ A @ G @ C @ H )
      | ~ ( equidistant @ E @ G @ F @ H )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( equidistant @ B @ G @ D @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(24,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( ( insertion @ E @ F @ A @ B )
        = ( insertion @ E @ F @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i4) ).

thf(134,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( ( insertion @ E @ F @ A @ B )
        = ( insertion @ E @ F @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(10,axiom,
    ! [A: $i] :
      ( A
      = ( reflection @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).

thf(105,plain,
    ! [A: $i] :
      ( A
      = ( reflection @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).

thf(266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(39,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ C @ D @ E )
      | ( equidistant @ B @ C @ ( insertion @ D @ E @ A @ B ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_3) ).

thf(166,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ C @ D @ E )
      | ( equidistant @ B @ C @ ( insertion @ D @ E @ A @ B ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ D )
      | ( between @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).

thf(264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ C @ D )
      | ( between @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ C @ ( extension @ D @ C @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_2) ).

thf(149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ C @ ( extension @ D @ C @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( ( extension @ A @ B @ A @ B )
        = ( extension @ A @ B @ B @ A ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).

thf(144,plain,
    ! [B: $i,A: $i] :
      ( ( ( extension @ A @ B @ A @ B )
        = ( extension @ A @ B @ B @ A ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( A != C )
      | ( between @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).

thf(181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( A != C )
      | ( between @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(1,negated_conjecture,
    ~ ( between @ a @ b @ e ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_betweenness) ).

thf(86,plain,
    ~ ( between @ a @ b @ e ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( insertion @ A @ B @ C @ D )
      = ( extension @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insertion) ).

thf(103,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( insertion @ A @ B @ C @ D )
      = ( extension @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( B
        = ( reflection @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).

thf(140,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( B
        = ( reflection @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).

thf(91,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ C @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(34,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( equidistant @ A @ G @ C @ H )
      | ~ ( equidistant @ B @ G @ D @ H )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( A = B )
      | ( equidistant @ E @ G @ F @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).

thf(155,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( equidistant @ A @ G @ C @ H )
      | ~ ( equidistant @ B @ G @ D @ H )
      | ~ ( between @ A @ B @ E )
      | ~ ( between @ C @ D @ F )
      | ( A = B )
      | ( equidistant @ E @ G @ F @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(21,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).

thf(130,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ C @ D )
      | ( between @ A @ C @ D )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).

thf(226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ C @ D )
      | ( between @ A @ C @ D )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( A = B )
      | ( C
        = ( extension @ A @ B @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).

thf(267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( A = B )
      | ( C
        = ( extension @ A @ B @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ A @ C )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).

thf(162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ A @ C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( between @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).

thf(255,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ( between @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ B @ D )
      | ~ ( equidistant @ B @ C @ B @ D )
      | ( A = B )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).

thf(209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ B @ D )
      | ~ ( equidistant @ B @ C @ B @ D )
      | ( A = B )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(13,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( ( extension @ E @ F @ A @ B )
        = ( extension @ E @ F @ C @ D ) )
      | ( E = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).

thf(112,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( ( extension @ E @ F @ A @ B )
        = ( extension @ E @ F @ C @ D ) )
      | ( E = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(18,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ C @ D @ E @ F )
      | ( equidistant @ A @ B @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).

thf(123,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ C @ D @ E @ F )
      | ( equidistant @ A @ B @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(31,axiom,
    lower_dimension_point_2 != lower_dimension_point_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).

thf(150,plain,
    lower_dimension_point_2 != lower_dimension_point_3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(6,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ A @ B @ E @ F )
      | ( equidistant @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

thf(95,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ A @ B @ E @ F )
      | ( equidistant @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(80,axiom,
    ! [B: $i,A: $i] : ( between @ A @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).

thf(263,plain,
    ! [B: $i,A: $i] : ( between @ A @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(53,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( between @ A @ B @ A )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).

thf(199,plain,
    ! [B: $i,A: $i] :
      ( ~ ( between @ A @ B @ A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( A
     != ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).

thf(127,plain,
    ! [B: $i,A: $i] :
      ( A
     != ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(33,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).

thf(154,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(44,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ E )
      | ( A = B )
      | ( between @ A @ D @ ( euclid1 @ A @ D @ B @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).

thf(175,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ E )
      | ( A = B )
      | ( between @ A @ D @ ( euclid1 @ A @ D @ B @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(35,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( equidistant @ A @ E @ C @ F )
      | ~ ( between @ A @ B @ E )
      | ( between @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).

thf(158,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ~ ( equidistant @ B @ E @ D @ F )
      | ~ ( equidistant @ A @ E @ C @ F )
      | ~ ( between @ A @ B @ E )
      | ( between @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ B @ C @ ( insertion @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_1) ).

thf(139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ B @ C @ ( insertion @ C @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(57,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ C )
      | ~ ( between @ A @ F @ D )
      | ( between @ F @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ C )
      | ( between @ B @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b10) ).

thf(207,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ C )
      | ~ ( between @ A @ F @ D )
      | ( between @ F @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ C )
      | ( between @ B @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ B @ D )
      | ( A = B )
      | ( between @ B @ C @ D )
      | ( between @ B @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b13) ).

thf(272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ B @ D )
      | ( A = B )
      | ( between @ B @ C @ D )
      | ( between @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(60,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ E )
      | ( A = B )
      | ( between @ A @ E @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).

thf(214,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ E )
      | ( A = B )
      | ( between @ A @ E @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(69,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( extension @ B @ C @ D @ E ) )
      | ( between @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).

thf(235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( extension @ B @ C @ D @ E ) )
      | ( between @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ D @ C )
      | ( between @ A @ B @ D )
      | ( between @ A @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9) ).

thf(246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ D @ C )
      | ( between @ A @ B @ D )
      | ( between @ A @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ D @ C )
      | ( between @ B @ D @ C )
      | ( between @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b14) ).

thf(168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ A @ D @ C )
      | ( between @ B @ D @ C )
      | ( between @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ C @ D )
      | ( between @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).

thf(190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ C @ D )
      | ( between @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ D @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).

thf(107,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ D @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(51,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ C )
      | ( between @ E @ ( inner_pasch @ A @ B @ C @ E @ D ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).

thf(195,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ C )
      | ( between @ E @ ( inner_pasch @ A @ B @ C @ E @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ A @ C )
      | ( A = B )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_1) ).

thf(239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ B @ A @ C )
      | ( A = B )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ B @ A @ D )
      | ~ ( equidistant @ C @ B @ C @ D )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15) ).

thf(242,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( equidistant @ A @ B @ A @ D )
      | ~ ( equidistant @ C @ B @ C @ D )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ B @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).

thf(131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ B @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ C )
      | ( B = C )
      | ( between @ A @ D @ B )
      | ( between @ D @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).

thf(178,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ B @ C )
      | ( B = C )
      | ( between @ A @ D @ B )
      | ( between @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(3,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).

thf(90,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(17,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

thf(122,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(63,axiom,
    ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).

thf(222,plain,
    ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(67,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ F )
      | ~ ( equidistant @ A @ B @ D @ E )
      | ~ ( equidistant @ A @ C @ D @ F )
      | ( equidistant @ B @ C @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13) ).

thf(232,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( between @ A @ B @ C )
      | ~ ( between @ D @ E @ F )
      | ~ ( equidistant @ A @ B @ D @ E )
      | ~ ( equidistant @ A @ C @ D @ F )
      | ( equidistant @ B @ C @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(8,axiom,
    lower_dimension_point_1 != lower_dimension_point_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).

thf(100,plain,
    lower_dimension_point_1 != lower_dimension_point_2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(282,plain,
    $false,
    inference(e,[status(thm)],[153,125,93,253,188,173,204,245,250,234,88,170,115,217,120,202,174,185,257,147,133,206,248,117,270,220,260,160,192,137,165,229,197,97,224,109,212,134,105,266,166,264,149,144,181,86,103,140,91,155,130,226,267,162,255,209,112,123,150,95,263,199,127,154,175,158,139,207,272,214,235,246,168,190,107,195,239,242,131,178,90,122,222,232,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO008-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May 19 04:31:04 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.82/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/1.05  % [INFO] 	 Parsing done (181ms). 
% 1.34/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.90/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.90/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.32  % [INFO] 	 Found a conjecture and 84 axioms. Running axiom selection ... 
% 2.14/1.37  % [INFO] 	 Axiom selection finished. Selected 84 axioms (removed 0 axioms). 
% 2.37/1.43  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.37/1.44  % [INFO] 	 Type checking passed. 
% 2.37/1.45  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.71/2.17  % External prover 'e' found a proof!
% 4.71/2.17  % [INFO] 	 Killing All external provers ... 
% 4.71/2.17  % Time passed: 1662ms (effective reasoning time: 1114ms)
% 4.71/2.17  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.71/2.17  % Axioms used in derivation (84): e3_2, d3, reflexivity_for_equidistance, outer_five_segment, d8, euclid3, d5, i2_3, continuity1, e2_2, lower_dimension1, d4_4, b2, continuity2, b_between_c_and_d, b10, t9, b3, r2_1, d4_5, transitivity_for_equidistance, e1, b14, b7, d9, r6, inner_pasch2, i4, b4, lower_dimension2, t3, b1, d13, reflection, r2_2, b8, d12, identity_for_betweeness, b11, r5, i3, c_between_a_and_e, r3_2, b0, upper_dimension, t2, t7, b5, d15, euclid1, d7, d10_2, r4, e2_3, segment_construction2, d2, d10_3, e3_1, d4_2, i2_1, b12, d4_1, lower_dimension3, d_between_a_and_e, t6_2, b9, b6, inner_pasch1, e3_3, r3_1, b13, segment_construction1, d14, euclid2, d10_1, e2_1, d1, t1, d11, identity_for_equidistance, d4_3, t6_1, insertion, i2_2
% 4.71/2.17  % No. of inferences in proof: 171
% 4.71/2.18  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1662 ms resp. 1114 ms w/o parsing
% 5.09/2.24  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.09/2.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------