%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD017-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 02:28:18 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;  11 RR)
%            Number of literals    :   18 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;  11 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    defined(c),
    file('FLD017-3.p',unknown),
    [] ).

cnf(5,axiom,
    sum__dfg(additive_identity,a,x__dfg),
    file('FLD017-3.p',unknown),
    [] ).

cnf(6,axiom,
    sum__dfg(a,b,c),
    file('FLD017-3.p',unknown),
    [] ).

cnf(7,axiom,
    ~ sum__dfg(x__dfg,b,c),
    file('FLD017-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ sum__dfg(u,x,z)
    | sum__dfg(z,y,w) ),
    file('FLD017-3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD017-3.p',unknown),
    [] ).

cnf(42,plain,
    ( ~ sum__dfg(u,c,v)
    | ~ sum__dfg(u,a,w)
    | sum__dfg(w,b,v) ),
    inference(res,[status(thm),theory(equality)],[6,9]),
    [iquote('0:Res:6.0,9.1')] ).

cnf(71,plain,
    ( ~ sum__dfg(additive_identity,c,u)
    | sum__dfg(x__dfg,b,u) ),
    inference(res,[status(thm),theory(equality)],[5,42]),
    [iquote('0:Res:5.0,42.0')] ).

cnf(86,plain,
    ~ sum__dfg(additive_identity,c,c),
    inference(res,[status(thm),theory(equality)],[71,7]),
    [iquote('0:Res:71.1,7.0')] ).

cnf(87,plain,
    ~ defined(c),
    inference(res,[status(thm),theory(equality)],[10,86]),
    [iquote('0:Res:10.1,86.0')] ).

cnf(88,plain,
    $false,
    inference(ssi,[status(thm)],[87,3]),
    [iquote('0:SSi:87.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : FLD017-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun  7 01:43:50 EDT 2022
% 0.13/0.34  % 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/sandbox/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 44 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.19/0.41  SPASS allocated 75677 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 4, length 11 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : c_is_defined sum_5 sum_6 not_sum_7 associativity_addition_2 existence_of_identity_addition
% 0.19/0.41  
%------------------------------------------------------------------------------