%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD006-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 02:28:14 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :    9 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ sum__dfg(additive_identity,additive_inverse(additive_identity),additive_identity),
    file('FLD006-3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD006-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD006-3.p',unknown),
    [] ).

cnf(15,axiom,
    defined(additive_identity),
    file('FLD006-3.p',unknown),
    [] ).

cnf(31,plain,
    ~ sum__dfg(additive_inverse(additive_identity),additive_identity,additive_identity),
    inference(res,[status(thm),theory(equality)],[6,1]),
    [iquote('0:Res:6.1,1.0')] ).

cnf(41,plain,
    ~ defined(additive_identity),
    inference(res,[status(thm),theory(equality)],[5,31]),
    [iquote('0:Res:5.1,31.0')] ).

cnf(42,plain,
    $false,
    inference(ssi,[status(thm)],[41,15]),
    [iquote('0:SSi:41.0,15.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : FLD006-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n019.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 : Mon Jun  6 21:21:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.42  
% 0.20/0.42  SPASS V 3.9 
% 0.20/0.42  SPASS beiseite: Proof found.
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.42  SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.20/0.42  SPASS allocated 75622 KBytes.
% 0.20/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.42  		0:00:00.04 for the input.
% 0.20/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42  		0:00:00.00 for inferences.
% 0.20/0.42  		0:00:00.00 for the backtracking.
% 0.20/0.42  		0:00:00.00 for the reduction.
% 0.20/0.42  
% 0.20/0.42  
% 0.20/0.42  Here is a proof with depth 2, length 7 :
% 0.20/0.42  % SZS output start Refutation
% See solution above
% 0.20/0.42  Formulae used in the proof : not_sum_1 existence_of_inverse_addition commutativity_addition well_definedness_of_additive_identity
% 0.20/0.42  
%------------------------------------------------------------------------------