%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD010-3 : 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 02:28:15 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   5 unt;   1 nHn;   8 RR)
%            Number of literals    :   12 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ sum__dfg(additive_identity,multiplicative_identity,additive_identity),
    file('FLD010-3.p',unknown),
    [] ).

cnf(2,axiom,
    ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
    file('FLD010-3.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,additive_identity)
    | product(multiplicative_inverse(u),u,multiplicative_identity) ),
    file('FLD010-3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ product(u,v,w)
    | product(v,u,w) ),
    file('FLD010-3.p',unknown),
    [] ).

cnf(19,axiom,
    defined(multiplicative_identity),
    file('FLD010-3.p',unknown),
    [] ).

cnf(29,plain,
    ( ~ defined(multiplicative_identity)
    | product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
    inference(res,[status(thm),theory(equality)],[11,1]),
    [iquote('0:Res:11.2,1.0')] ).

cnf(36,plain,
    ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
    inference(res,[status(thm),theory(equality)],[12,2]),
    [iquote('0:Res:12.1,2.0')] ).

cnf(41,plain,
    $false,
    inference(mrr,[status(thm)],[29,19,36]),
    [iquote('0:MRR:29.0,29.1,19.0,36.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : FLD010-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n019.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 01:56:25 EDT 2022
% 0.12/0.34  % 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/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.19/0.41  SPASS allocated 75629 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 1, length 8 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : not_sum_1 not_product_2 existence_of_inverse_multiplication commutativity_multiplication well_definedness_of_multiplicative_identity
% 0.19/0.41  
%------------------------------------------------------------------------------