%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD020-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 02:28:19 EDT 2022

% Result   : Unsatisfiable 0.37s 0.54s
% Output   : Refutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (   6 unt;   0 nHn;  14 RR)
%            Number of literals    :   26 (   0 equ;  14 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD020-3.p',unknown),
    [] ).

cnf(3,axiom,
    sum__dfg(m,a,a),
    file('FLD020-3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ sum__dfg(additive_identity,m,additive_identity),
    file('FLD020-3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,v,y)
    | ~ sum__dfg(z,x,u)
    | sum__dfg(z,y,w) ),
    file('FLD020-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD020-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD020-3.p',unknown),
    [] ).

cnf(33,plain,
    ( ~ sum__dfg(a,u,v)
    | ~ sum__dfg(a,u,w)
    | sum__dfg(m,w,v) ),
    inference(res,[status(thm),theory(equality)],[3,5]),
    [iquote('0:Res:3.0,5.0')] ).

cnf(46,plain,
    ~ sum__dfg(m,additive_identity,additive_identity),
    inference(res,[status(thm),theory(equality)],[9,4]),
    [iquote('0:Res:9.1,4.0')] ).

cnf(79,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_inverse(u),additive_identity) ),
    inference(res,[status(thm),theory(equality)],[8,9]),
    [iquote('0:Res:8.1,9.0')] ).

cnf(222,plain,
    ( ~ defined(a)
    | ~ sum__dfg(a,additive_inverse(a),u)
    | sum__dfg(m,u,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[79,33]),
    [iquote('0:Res:79.1,33.0')] ).

cnf(233,plain,
    ( ~ sum__dfg(a,additive_inverse(a),u)
    | sum__dfg(m,u,additive_identity) ),
    inference(ssi,[status(thm)],[222,1]),
    [iquote('0:SSi:222.0,1.0')] ).

cnf(676,plain,
    ( ~ defined(a)
    | sum__dfg(m,additive_identity,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[79,233]),
    [iquote('0:Res:79.1,233.0')] ).

cnf(683,plain,
    sum__dfg(m,additive_identity,additive_identity),
    inference(ssi,[status(thm)],[676,1]),
    [iquote('0:SSi:676.0,1.0')] ).

cnf(684,plain,
    $false,
    inference(mrr,[status(thm)],[683,46]),
    [iquote('0:MRR:683.0,46.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : FLD020-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n023.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 : Tue Jun  7 04:27:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.37/0.54  
% 0.37/0.54  SPASS V 3.9 
% 0.37/0.54  SPASS beiseite: Proof found.
% 0.37/0.54  % SZS status Theorem
% 0.37/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.37/0.54  SPASS derived 590 clauses, backtracked 0 clauses, performed 1 splits and kept 474 clauses.
% 0.37/0.54  SPASS allocated 76190 KBytes.
% 0.37/0.54  SPASS spent	0:00:00.19 on the problem.
% 0.37/0.54  		0:00:00.03 for the input.
% 0.37/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.54  		0:00:00.01 for inferences.
% 0.37/0.54  		0:00:00.00 for the backtracking.
% 0.37/0.54  		0:00:00.12 for the reduction.
% 0.37/0.54  
% 0.37/0.54  
% 0.37/0.54  Here is a proof with depth 3, length 14 :
% 0.37/0.54  % SZS output start Refutation
% See solution above
% 0.37/0.54  Formulae used in the proof : a_is_defined sum_3 not_sum_4 associativity_addition_1 existence_of_inverse_addition commutativity_addition
% 0.37/0.54  
%------------------------------------------------------------------------------