%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO036-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 06:21:45 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   21 (  18 unt;   2 nHn;  21 RR)
%            Number of literals    :   25 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( equal(lower_dimension_point_3,lower_dimension_point_1)
    | equal(lower_dimension_point_3,lower_dimension_point_2)
    | equal(lower_dimension_point_2,lower_dimension_point_1) ),
    file('GEO036-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO036-2.p',unknown),
    [] ).

cnf(5,axiom,
    between(u,v,extension(u,v,w,x)),
    file('GEO036-2.p',unknown),
    [] ).

cnf(6,axiom,
    equidistant(u,extension(v,u,w,x),w,x),
    file('GEO036-2.p',unknown),
    [] ).

cnf(11,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('GEO036-2.p',unknown),
    [] ).

cnf(12,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('GEO036-2.p',unknown),
    [] ).

cnf(13,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('GEO036-2.p',unknown),
    [] ).

cnf(20,plain,
    equal(lower_dimension_point_3,lower_dimension_point_1),
    inference(spt,[spt(split,[position(s1)])],[1]),
    [iquote('1:Spt:1.0')] ).

cnf(22,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1),
    inference(rew,[status(thm),theory(equality)],[20,12]),
    [iquote('1:Rew:20.0,12.0')] ).

cnf(26,plain,
    equal(extension(u,v,w,w),v),
    inference(res,[status(thm),theory(equality)],[6,4]),
    [iquote('0:Res:6.0,4.0')] ).

cnf(27,plain,
    between(u,v,v),
    inference(spr,[status(thm),theory(equality)],[26,5]),
    [iquote('0:SpR:26.0,5.0')] ).

cnf(30,plain,
    $false,
    inference(unc,[status(thm)],[27,22]),
    [iquote('1:UnC:27.0,22.0')] ).

cnf(31,plain,
    ~ equal(lower_dimension_point_3,lower_dimension_point_1),
    inference(spt,[spt(split,[position(sa)])],[30,20]),
    [iquote('1:Spt:30.0,1.0,20.0')] ).

cnf(32,plain,
    ( equal(lower_dimension_point_3,lower_dimension_point_2)
    | equal(lower_dimension_point_2,lower_dimension_point_1) ),
    inference(spt,[spt(split,[position(s2)])],[1]),
    [iquote('1:Spt:30.0,1.1,1.2')] ).

cnf(33,plain,
    equal(lower_dimension_point_3,lower_dimension_point_2),
    inference(spt,[spt(split,[position(s2s1)])],[32]),
    [iquote('2:Spt:32.0')] ).

cnf(35,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2),
    inference(rew,[status(thm),theory(equality)],[33,11]),
    [iquote('2:Rew:33.0,11.0')] ).

cnf(38,plain,
    $false,
    inference(mrr,[status(thm)],[35,27]),
    [iquote('2:MRR:35.0,27.0')] ).

cnf(39,plain,
    ~ equal(lower_dimension_point_3,lower_dimension_point_2),
    inference(spt,[spt(split,[position(s2sa)])],[38,33]),
    [iquote('2:Spt:38.0,32.0,33.0')] ).

cnf(40,plain,
    equal(lower_dimension_point_2,lower_dimension_point_1),
    inference(spt,[spt(split,[position(s2s2)])],[32]),
    [iquote('2:Spt:38.0,32.1')] ).

cnf(42,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1),
    inference(rew,[status(thm),theory(equality)],[40,13]),
    [iquote('2:Rew:40.0,13.0')] ).

cnf(43,plain,
    $false,
    inference(mrr,[status(thm)],[42,27]),
    [iquote('2:MRR:42.0,27.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO036-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sat Jun 18 05:38:29 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 15 clauses, backtracked 12 clauses, performed 2 splits and kept 42 clauses.
% 0.19/0.42  SPASS allocated 63122 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 21 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : prove_axioms_points_are_distinct identity_for_equidistance segment_construction1 segment_construction2 lower_dimension1 lower_dimension2 lower_dimension3
% 0.19/0.42  
%------------------------------------------------------------------------------