%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 11:44:42 EDT 2022

% Result   : Unsatisfiable 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   5 unt;   0 nHn;  11 RR)
%            Number of literals    :   23 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ product(a,inverse(a),identity),
    file('GRP004-2.p',unknown),
    [] ).

cnf(2,axiom,
    product(identity,u,u),
    file('GRP004-2.p',unknown),
    [] ).

cnf(3,axiom,
    product(inverse(u),u,identity),
    file('GRP004-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('GRP004-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP004-2.p',unknown),
    [] ).

cnf(11,plain,
    ( ~ product(u,v,identity)
    | ~ product(u,w,a)
    | ~ product(w,inverse(a),v) ),
    inference(res,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Res:7.3,1.0')] ).

cnf(39,plain,
    ( ~ product(u,v,w)
    | ~ product(x,u,identity)
    | product(x,w,v) ),
    inference(res,[status(thm),theory(equality)],[2,6]),
    [iquote('0:Res:2.0,6.0')] ).

cnf(98,plain,
    ( ~ product(u,inverse(v),identity)
    | product(u,identity,v) ),
    inference(res,[status(thm),theory(equality)],[3,39]),
    [iquote('0:Res:3.0,39.0')] ).

cnf(204,plain,
    ( ~ product(u,inverse(a),identity)
    | ~ product(u,identity,a) ),
    inference(res,[status(thm),theory(equality)],[2,11]),
    [iquote('0:Res:2.0,11.2')] ).

cnf(215,plain,
    ~ product(u,inverse(a),identity),
    inference(mrr,[status(thm)],[204,98]),
    [iquote('0:MRR:204.1,98.1')] ).

cnf(216,plain,
    $false,
    inference(unc,[status(thm)],[215,3]),
    [iquote('0:UnC:215.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 06:40:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 206 clauses, backtracked 0 clauses, performed 0 splits and kept 168 clauses.
% 0.19/0.43  SPASS allocated 63273 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.03 for the input.
% 0.19/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.02 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 2, length 11 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : prove_right_inverse left_identity left_inverse associativity1 associativity2
% 0.19/0.43  
%------------------------------------------------------------------------------