%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 06:21:26 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :    8 (   0 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ between(a,b,b),
    file('GEO003-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO003-2.p',unknown),
    [] ).

cnf(5,axiom,
    between(u,v,extension(u,v,w,x)),
    file('GEO003-2.p',unknown),
    [] ).

cnf(6,axiom,
    equidistant(u,extension(v,u,w,x),w,x),
    file('GEO003-2.p',unknown),
    [] ).

cnf(30,plain,
    equal(extension(u,v,w,w),v),
    inference(res,[status(thm),theory(equality)],[6,4]),
    [iquote('0:Res:6.0,4.0')] ).

cnf(33,plain,
    between(u,v,v),
    inference(spr,[status(thm),theory(equality)],[30,5]),
    [iquote('0:SpR:30.0,5.0')] ).

cnf(36,plain,
    $false,
    inference(unc,[status(thm)],[33,1]),
    [iquote('0:UnC:33.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jun 17 20:38:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 13 clauses, backtracked 0 clauses, performed 1 splits and kept 27 clauses.
% 0.19/0.41  SPASS allocated 63130 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.04 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 2, length 7 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : prove_b_between_a_and_b identity_for_equidistance segment_construction1 segment_construction2
% 0.19/0.41  
%------------------------------------------------------------------------------