%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD039-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 02:28:26 EDT 2022

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Refutation 0.19s
% 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;  15 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    :    8 (   8 usr;   8 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    sum__dfg(additive_identity,multiplicative_identity,additive_identity),
    file('FLD039-3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ sum__dfg(u,x,z)
    | sum__dfg(z,y,w) ),
    file('FLD039-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD039-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD039-3.p',unknown),
    [] ).

cnf(20,axiom,
    defined(multiplicative_identity),
    file('FLD039-3.p',unknown),
    [] ).

cnf(29,axiom,
    ~ sum__dfg(additive_identity,additive_identity,multiplicative_identity),
    file('FLD039-3.p',unknown),
    [] ).

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

cnf(83,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_identity,u) ),
    inference(res,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Res:6.1,8.0')] ).

cnf(167,plain,
    ( ~ defined(u)
    | ~ sum__dfg(multiplicative_identity,v,u)
    | sum__dfg(additive_identity,v,u) ),
    inference(res,[status(thm),theory(equality)],[6,33]),
    [iquote('0:Res:6.1,33.0')] ).

cnf(269,plain,
    ( ~ defined(multiplicative_identity)
    | ~ sum__dfg(multiplicative_identity,additive_identity,multiplicative_identity) ),
    inference(res,[status(thm),theory(equality)],[167,29]),
    [iquote('0:Res:167.2,29.0')] ).

cnf(278,plain,
    ~ sum__dfg(multiplicative_identity,additive_identity,multiplicative_identity),
    inference(ssi,[status(thm)],[269,20]),
    [iquote('0:SSi:269.0,20.0')] ).

cnf(279,plain,
    ~ defined(multiplicative_identity),
    inference(res,[status(thm),theory(equality)],[83,278]),
    [iquote('0:Res:83.1,278.0')] ).

cnf(280,plain,
    $false,
    inference(ssi,[status(thm)],[279,20]),
    [iquote('0:SSi:279.0,20.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : FLD039-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.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 : Mon Jun  6 10:52:48 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 208 clauses, backtracked 0 clauses, performed 0 splits and kept 172 clauses.
% 0.19/0.44  SPASS allocated 75844 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.44  		0:00:00.03 for the input.
% 0.19/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.03 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 4, length 13 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : sum_3 associativity_addition_2 existence_of_identity_addition commutativity_addition well_definedness_of_multiplicative_identity different_identities
% 0.19/0.44  
%------------------------------------------------------------------------------