TSTP Solution File: GEO024-3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GEO024-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 11:08:56 EDT 2023

% Result   : Unsatisfiable 3.98s 1.93s
% Output   : Refutation 4.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   86 (  27 unt;  13 typ;   0 def)
%            Number of atoms       :  173 (  30 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  846 (  94   ~; 100   |;   0   &; 652   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   6 con; 0-6 aty)
%            Number of variables   :  252 (   0   ^; 252   !;   0   ?; 252   :)

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

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

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

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

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

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

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

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

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

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

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( extension @ B @ A @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).

thf(69,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( extension @ B @ A @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( between @ A @ B @ A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ~ ( between @ A @ B @ A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(9,axiom,
    ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).

thf(57,plain,
    ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ C )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).

thf(106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ C @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).

thf(109,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)],[33]) ).

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

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ( reflection @ A @ B )
      = ( extension @ A @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( B
        = ( reflection @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).

thf(71,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( B
        = ( reflection @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(19,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/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).

thf(80,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)],[19]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ B @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).

thf(95,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)],[27]) ).

thf(6,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/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).

thf(50,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)],[6]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).

thf(75,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)],[17]) ).

thf(26,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).

thf(94,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( A
       != ( reflection @ B @ A ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( reflection @ B @ A ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ~ ( equidistant @ u @ u @ v @ v ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_congruence) ).

thf(37,plain,
    ~ ( equidistant @ u @ u @ v @ v ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(11,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/sandbox/benchmark/theBenchmark.p',euclid2) ).

thf(61,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)],[11]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).

thf(89,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)],[23]) ).

thf(21,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/sandbox/benchmark/theBenchmark.p',continuity2) ).

thf(85,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)],[21]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ D @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).

thf(102,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)],[30]) ).

thf(25,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/sandbox/benchmark/theBenchmark.p',d5) ).

thf(92,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)],[25]) ).

thf(28,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/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

thf(97,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)],[28]) ).

thf(4,axiom,
    ! [A: $i] :
      ( A
      = ( reflection @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).

thf(45,plain,
    ! [A: $i] :
      ( A
      = ( reflection @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).

thf(64,plain,
    ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).

thf(113,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)],[35]) ).

thf(18,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( extension @ B @ C @ D @ E ) )
      | ( between @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).

thf(76,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)],[18]) ).

thf(2,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/sandbox/benchmark/theBenchmark.p',euclid1) ).

thf(39,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)],[2]) ).

thf(24,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

thf(91,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(13,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/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).

thf(66,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)],[13]) ).

thf(29,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/sandbox/benchmark/theBenchmark.p',upper_dimension) ).

thf(99,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)],[29]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).

thf(87,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)],[22]) ).

thf(31,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/sandbox/benchmark/theBenchmark.p',continuity1) ).

thf(104,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)],[31]) ).

thf(8,axiom,
    ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).

thf(55,plain,
    ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(36,axiom,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).

thf(114,plain,
    ! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(5,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/sandbox/benchmark/theBenchmark.p',euclid3) ).

thf(47,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)],[5]) ).

thf(14,axiom,
    ! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).

thf(68,plain,
    ! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ D @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).

thf(111,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)],[34]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equidistant @ A @ B @ C @ D )
      | ( equidistant @ A @ B @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).

thf(83,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)],[20]) ).

thf(115,plain,
    $false,
    inference(e,[status(thm)],[69,52,57,106,109,59,71,80,95,50,75,94,42,37,61,89,85,102,92,97,45,64,113,76,39,91,66,99,87,104,55,114,47,68,111,83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO024-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n011.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Fri May 19 04:32:49 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.19/1.00  % [INFO] 	 Parsing done (141ms). 
% 1.43/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.85/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.85/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.29  % [INFO] 	 Found a conjecture and 35 axioms. Running axiom selection ... 
% 1.97/1.34  % [INFO] 	 Axiom selection finished. Selected 35 axioms (removed 0 axioms). 
% 2.22/1.38  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.22/1.38  % [INFO] 	 Type checking passed. 
% 2.41/1.39  % [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 ... 
% 3.65/1.92  % External prover 'e' found a proof!
% 3.65/1.92  % [INFO] 	 Killing All external provers ... 
% 3.65/1.92  % Time passed: 1398ms (effective reasoning time: 910ms)
% 3.65/1.92  % 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)>
% 3.65/1.93  % Axioms used in derivation (35): continuity1, inner_pasch2, d3, reflexivity_for_equidistance, lower_dimension2, reflection, r2_2, identity_for_betweeness, outer_five_segment, upper_dimension, d4_2, d1, euclid3, d5, lower_dimension1, d4_4, continuity2, r2_1, d4_5, transitivity_for_equidistance, e1, r3_2, b0, euclid1, r4, segment_construction2, d2, d4_1, lower_dimension3, inner_pasch1, r3_1, segment_construction1, euclid2, identity_for_equidistance, d4_3
% 3.65/1.93  % No. of inferences in proof: 73
% 3.98/1.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1398 ms resp. 910 ms w/o parsing
% 4.14/1.98  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.14/1.98  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------