%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD034-3 : 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 02:28:25 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('FLD034-3.p',unknown),
    [] ).

cnf(3,axiom,
    product(multiplicative_identity,m,multiplicative_identity),
    file('FLD034-3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ product(m,a,a),
    file('FLD034-3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('FLD034-3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ defined(u)
    | product(multiplicative_identity,u,u) ),
    file('FLD034-3.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ product(u,v,w)
    | product(v,u,w) ),
    file('FLD034-3.p',unknown),
    [] ).

cnf(34,plain,
    product(m,multiplicative_identity,multiplicative_identity),
    inference(res,[status(thm),theory(equality)],[3,14]),
    [iquote('0:Res:3.0,14.0')] ).

cnf(45,plain,
    ( ~ product(u,v,a)
    | ~ product(w,v,a)
    | ~ product(m,w,u) ),
    inference(res,[status(thm),theory(equality)],[10,4]),
    [iquote('0:Res:10.3,4.0')] ).

cnf(672,plain,
    ( ~ defined(a)
    | ~ product(u,a,a)
    | ~ product(m,u,multiplicative_identity) ),
    inference(res,[status(thm),theory(equality)],[12,45]),
    [iquote('0:Res:12.1,45.0')] ).

cnf(674,plain,
    ( ~ product(u,a,a)
    | ~ product(m,u,multiplicative_identity) ),
    inference(ssi,[status(thm)],[672,1]),
    [iquote('0:SSi:672.0,1.0')] ).

cnf(4904,plain,
    ( ~ defined(a)
    | ~ product(m,multiplicative_identity,multiplicative_identity) ),
    inference(res,[status(thm),theory(equality)],[12,674]),
    [iquote('0:Res:12.1,674.0')] ).

cnf(4905,plain,
    ~ product(m,multiplicative_identity,multiplicative_identity),
    inference(ssi,[status(thm)],[4904,1]),
    [iquote('0:SSi:4904.0,1.0')] ).

cnf(4906,plain,
    $false,
    inference(mrr,[status(thm)],[4905,34]),
    [iquote('0:MRR:4905.0,34.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : FLD034-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n019.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 04:23:55 EDT 2022
% 0.13/0.34  % 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 3510 clauses, backtracked 0 clauses, performed 4 splits and kept 2373 clauses.
% 1.60/1.79  SPASS allocated 79326 KBytes.
% 1.60/1.79  SPASS spent	0:00:01.42 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  		0:00:00.06 for the backtracking.
% 1.60/1.79  		0:00:01.24 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 product_3 not_product_4 associativity_multiplication_1 existence_of_identity_multiplication commutativity_multiplication
% 1.60/1.79  
%------------------------------------------------------------------------------