%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD056-3 : 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 0.21s 0.43s
% Output   : Refutation 0.21s
% 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('FLD056-3.p',unknown),
    [] ).

cnf(2,axiom,
    ~ less_or_equal(a,a),
    file('FLD056-3.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ defined(u)
    | ~ defined(v)
    | less_or_equal(u,v)
    | less_or_equal(v,u) ),
    file('FLD056-3.p',unknown),
    [] ).

cnf(29,plain,
    ( ~ defined(a)
    | ~ defined(a)
    | less_or_equal(a,a) ),
    inference(res,[status(thm),theory(equality)],[25,2]),
    [iquote('0:Res:25.2,2.0')] ).

cnf(32,plain,
    ( ~ defined(a)
    | less_or_equal(a,a) ),
    inference(obv,[status(thm),theory(equality)],[29]),
    [iquote('0:Obv:29.0')] ).

cnf(33,plain,
    $false,
    inference(mrr,[status(thm)],[32,1,2]),
    [iquote('0:MRR:32.0,32.1,1.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : FLD056-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n029.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jun  6 22:44:05 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.43  
% 0.21/0.43  SPASS V 3.9 
% 0.21/0.43  SPASS beiseite: Proof found.
% 0.21/0.43  % SZS status Theorem
% 0.21/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.43  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 28 clauses.
% 0.21/0.43  SPASS allocated 75616 KBytes.
% 0.21/0.43  SPASS spent	0:00:00.06 on the problem.
% 0.21/0.43  		0:00:00.04 for the input.
% 0.21/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43  		0:00:00.00 for inferences.
% 0.21/0.43  		0:00:00.00 for the backtracking.
% 0.21/0.43  		0:00:00.00 for the reduction.
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  Here is a proof with depth 1, length 6 :
% 0.21/0.43  % SZS output start Refutation
% See solution above
% 0.21/0.43  Formulae used in the proof : a_is_defined not_less_or_equal_2 totality_of_order_relation
% 0.21/0.43  
%------------------------------------------------------------------------------