%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO036-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 06:21:46 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   17 (  15 unt;   2 nHn;  17 RR)
%            Number of literals    :   20 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(25,axiom,
    between(u,v,v),
    file('GEO036-3.p',unknown),
    [] ).

cnf(28,axiom,
    between(u,u,v),
    file('GEO036-3.p',unknown),
    [] ).

cnf(39,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('GEO036-3.p',unknown),
    [] ).

cnf(49,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('GEO036-3.p',unknown),
    [] ).

cnf(50,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('GEO036-3.p',unknown),
    [] ).

cnf(61,plain,
    equal(lower_dimension_point_3,lower_dimension_point_1),
    inference(spt,[spt(split,[position(s1)])],[39]),
    [iquote('1:Spt:39.0')] ).

cnf(63,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1),
    inference(rew,[status(thm),theory(equality)],[61,50]),
    [iquote('1:Rew:61.0,50.0')] ).

cnf(66,plain,
    $false,
    inference(mrr,[status(thm)],[63,25]),
    [iquote('1:MRR:63.0,25.0')] ).

cnf(67,plain,
    ~ equal(lower_dimension_point_3,lower_dimension_point_1),
    inference(spt,[spt(split,[position(sa)])],[66,61]),
    [iquote('1:Spt:66.0,39.0,61.0')] ).

cnf(68,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)])],[39]),
    [iquote('1:Spt:66.0,39.1,39.2')] ).

cnf(69,plain,
    equal(lower_dimension_point_3,lower_dimension_point_2),
    inference(spt,[spt(split,[position(s2s1)])],[68]),
    [iquote('2:Spt:68.0')] ).

cnf(72,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1),
    inference(rew,[status(thm),theory(equality)],[69,50]),
    [iquote('2:Rew:69.0,50.0')] ).

cnf(75,plain,
    $false,
    inference(mrr,[status(thm)],[72,28]),
    [iquote('2:MRR:72.0,28.0')] ).

cnf(76,plain,
    ~ equal(lower_dimension_point_3,lower_dimension_point_2),
    inference(spt,[spt(split,[position(s2sa)])],[75,69]),
    [iquote('2:Spt:75.0,68.0,69.0')] ).

cnf(77,plain,
    equal(lower_dimension_point_2,lower_dimension_point_1),
    inference(spt,[spt(split,[position(s2s2)])],[68]),
    [iquote('2:Spt:75.0,68.1')] ).

cnf(82,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3),
    inference(rew,[status(thm),theory(equality)],[77,49]),
    [iquote('2:Rew:77.0,49.0')] ).

cnf(83,plain,
    $false,
    inference(mrr,[status(thm)],[82,28]),
    [iquote('2:MRR:82.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO036-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n003.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 : Sat Jun 18 01:21:28 EDT 2022
% 0.13/0.34  % 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 9 clauses, backtracked 11 clauses, performed 2 splits and kept 73 clauses.
% 0.19/0.42  SPASS allocated 63166 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 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  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 17 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : t3 t2 prove_axioms_points_are_distinct lower_dimension1 lower_dimension2
% 0.19/0.42  
%------------------------------------------------------------------------------