%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO011-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 06:21:33 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    7 (   5 unt;   2 nHn;   7 RR)
%            Number of literals    :   12 (   0 equ;   4 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(10,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('GEO011-5.p',unknown),
    [] ).

cnf(11,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('GEO011-5.p',unknown),
    [] ).

cnf(12,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('GEO011-5.p',unknown),
    [] ).

cnf(13,axiom,
    colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('GEO011-5.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ colinear(u,v,w)
    | between(w,u,v)
    | between(v,w,u)
    | between(u,v,w) ),
    file('GEO011-5.p',unknown),
    [] ).

cnf(18,plain,
    ( between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
    | between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
    | between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
    inference(res,[status(thm),theory(equality)],[13,17]),
    [iquote('0:Res:13.0,17.0')] ).

cnf(19,plain,
    $false,
    inference(mrr,[status(thm)],[18,10,11,12]),
    [iquote('0:MRR:18.0,18.1,18.2,10.0,11.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n023.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 17:54:04 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 1 clauses, backtracked 0 clauses, performed 0 splits and kept 18 clauses.
% 0.20/0.41  SPASS allocated 63103 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.41  		0:00:00.03 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.00 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 1, length 7 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : lower_dimension1 lower_dimension2 lower_dimension3 prove_lower_dimension_points_not_colinear colinearity4
% 0.20/0.41  
%------------------------------------------------------------------------------