%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD056-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 02:28:33 EDT 2022

% Result   : Unsatisfiable 0.23s 0.44s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    6 (   3 unt;   1 nHn;   6 RR)
%            Number of literals    :   12 (   0 equ;   6 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD056-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ less_or_equal(a,a),
    file('FLD056-1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ defined(u)
    | ~ defined(v)
    | less_or_equal(u,v)
    | less_or_equal(v,u) ),
    file('FLD056-1.p',unknown),
    [] ).

cnf(30,plain,
    ( ~ defined(a)
    | ~ defined(a)
    | less_or_equal(a,a) ),
    inference(res,[status(thm),theory(equality)],[20,2]),
    [iquote('0:Res:20.2,2.0')] ).

cnf(33,plain,
    ( ~ defined(a)
    | less_or_equal(a,a) ),
    inference(obv,[status(thm),theory(equality)],[30]),
    [iquote('0:Obv:30.0')] ).

cnf(34,plain,
    $false,
    inference(mrr,[status(thm)],[33,1,2]),
    [iquote('0:MRR:33.0,33.1,1.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : FLD056-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.15  % Command  : run_spass %d %s
% 0.14/0.37  % Computer : n029.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 600
% 0.14/0.37  % DateTime : Mon Jun  6 15:39:49 EDT 2022
% 0.14/0.37  % CPUTime  : 
% 0.23/0.44  
% 0.23/0.44  SPASS V 3.9 
% 0.23/0.44  SPASS beiseite: Proof found.
% 0.23/0.44  % SZS status Theorem
% 0.23/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.23/0.44  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 28 clauses.
% 0.23/0.44  SPASS allocated 75619 KBytes.
% 0.23/0.44  SPASS spent	0:00:00.06 on the problem.
% 0.23/0.44  		0:00:00.04 for the input.
% 0.23/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.44  		0:00:00.00 for inferences.
% 0.23/0.44  		0:00:00.00 for the backtracking.
% 0.23/0.44  		0:00:00.00 for the reduction.
% 0.23/0.44  
% 0.23/0.44  
% 0.23/0.44  Here is a proof with depth 1, length 6 :
% 0.23/0.44  % SZS output start Refutation
% See solution above
% 0.23/0.44  Formulae used in the proof : a_is_defined not_less_or_equal_2 totality_of_order_relation
% 0.23/0.44  
%------------------------------------------------------------------------------