%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD021-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 02:28:20 EDT 2022

% Result   : Unsatisfiable 1.60s 1.79s
% Output   : Refutation 1.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   6 unt;   0 nHn;  13 RR)
%            Number of literals    :   24 (   0 equ;  17 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    :    9 (   9 usr;   9 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD021-3.p',unknown),
    [] ).

cnf(3,axiom,
    sum__dfg(additive_identity,m,additive_identity),
    file('FLD021-3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ sum__dfg(m,a,a),
    file('FLD021-3.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('FLD021-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD021-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD021-3.p',unknown),
    [] ).

cnf(35,plain,
    sum__dfg(m,additive_identity,additive_identity),
    inference(res,[status(thm),theory(equality)],[3,9]),
    [iquote('0:Res:3.0,9.0')] ).

cnf(44,plain,
    ( ~ sum__dfg(u,v,a)
    | ~ sum__dfg(w,v,a)
    | ~ sum__dfg(m,w,u) ),
    inference(res,[status(thm),theory(equality)],[5,4]),
    [iquote('0:Res:5.3,4.0')] ).

cnf(626,plain,
    ( ~ defined(a)
    | ~ sum__dfg(u,a,a)
    | ~ sum__dfg(m,u,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[7,44]),
    [iquote('0:Res:7.1,44.0')] ).

cnf(629,plain,
    ( ~ sum__dfg(u,a,a)
    | ~ sum__dfg(m,u,additive_identity) ),
    inference(ssi,[status(thm)],[626,1]),
    [iquote('0:SSi:626.0,1.0')] ).

cnf(4854,plain,
    ( ~ defined(a)
    | ~ sum__dfg(m,additive_identity,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[7,629]),
    [iquote('0:Res:7.1,629.0')] ).

cnf(4856,plain,
    ~ sum__dfg(m,additive_identity,additive_identity),
    inference(ssi,[status(thm)],[4854,1]),
    [iquote('0:SSi:4854.0,1.0')] ).

cnf(4857,plain,
    $false,
    inference(mrr,[status(thm)],[4856,35]),
    [iquote('0:MRR:4856.0,35.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : FLD021-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n026.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 14:24:00 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.60/1.79  
% 1.60/1.79  SPASS V 3.9 
% 1.60/1.79  SPASS beiseite: Proof found.
% 1.60/1.79  % SZS status Theorem
% 1.60/1.79  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.60/1.79  SPASS derived 3844 clauses, backtracked 0 clauses, performed 0 splits and kept 2391 clauses.
% 1.60/1.79  SPASS allocated 78894 KBytes.
% 1.60/1.79  SPASS spent	0:00:01.39 on the problem.
% 1.60/1.79  		0:00:00.04 for the input.
% 1.60/1.79  		0:00:00.00 for the FLOTTER CNF translation.
% 1.60/1.79  		0:00:00.03 for inferences.
% 1.60/1.79  		0:00:00.00 for the backtracking.
% 1.60/1.79  		0:00:01.28 for the reduction.
% 1.60/1.79  
% 1.60/1.79  
% 1.60/1.79  Here is a proof with depth 3, length 13 :
% 1.60/1.79  % SZS output start Refutation
% See solution above
% 1.60/1.79  Formulae used in the proof : a_is_defined sum_3 not_sum_4 associativity_addition_1 existence_of_identity_addition commutativity_addition
% 1.60/1.79  
%------------------------------------------------------------------------------