%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO225+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 06:23:40 EDT 2022

% Result   : Theorem 0.18s 0.43s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   1 nHn;   8 RR)
%            Number of literals    :   11 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    distinct_points(skc3,skc2),
    file('GEO225+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( apart_point_and_line(skc2,u)
    | apart_point_and_line(skc3,u) ),
    file('GEO225+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ distinct_points(u,v)
    | ~ apart_point_and_line(u,line_connecting(u,v)) ),
    file('GEO225+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ distinct_points(u,v)
    | ~ apart_point_and_line(v,line_connecting(u,v)) ),
    file('GEO225+1.p',unknown),
    [] ).

cnf(27,plain,
    ~ apart_point_and_line(skc3,line_connecting(skc3,skc2)),
    inference(res,[status(thm),theory(equality)],[4,12]),
    [iquote('0:Res:4.0,12.0')] ).

cnf(28,plain,
    ~ apart_point_and_line(skc2,line_connecting(skc3,skc2)),
    inference(res,[status(thm),theory(equality)],[4,13]),
    [iquote('0:Res:4.0,13.0')] ).

cnf(29,plain,
    apart_point_and_line(skc2,line_connecting(skc3,skc2)),
    inference(res,[status(thm),theory(equality)],[8,27]),
    [iquote('0:Res:8.0,27.0')] ).

cnf(31,plain,
    $false,
    inference(mrr,[status(thm)],[29,28]),
    [iquote('0:MRR:29.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GEO225+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 04:54:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.43  
% 0.18/0.43  SPASS V 3.9 
% 0.18/0.43  SPASS beiseite: Proof found.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.43  SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.18/0.43  SPASS allocated 97670 KBytes.
% 0.18/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.18/0.43  		0:00:00.04 for the input.
% 0.18/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43  		0:00:00.00 for inferences.
% 0.18/0.43  		0:00:00.00 for the backtracking.
% 0.18/0.43  		0:00:00.00 for the reduction.
% 0.18/0.43  
% 0.18/0.43  
% 0.18/0.43  Here is a proof with depth 2, length 8 :
% 0.18/0.43  % SZS output start Refutation
% See solution above
% 0.18/0.43  Formulae used in the proof : con ci1 ci2
% 0.18/0.43  
%------------------------------------------------------------------------------