%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 11:44:53 EDT 2022

% Result   : Unsatisfiable 0.14s 0.35s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   24 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   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(identity,u,u),
    file('GRP031-1.p',unknown),
    [] ).

cnf(2,axiom,
    product(inverse(u),u,identity),
    file('GRP031-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ product(a,u,identity),
    file('GRP031-1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('GRP031-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP031-1.p',unknown),
    [] ).

cnf(9,plain,
    ( ~ product(u,v,w)
    | ~ product(x,w,identity)
    | ~ product(x,u,a) ),
    inference(res,[status(thm),theory(equality)],[7,3]),
    [iquote('0:Res:7.3,3.0')] ).

cnf(36,plain,
    ( ~ product(u,v,w)
    | ~ product(x,u,identity)
    | product(x,w,v) ),
    inference(res,[status(thm),theory(equality)],[1,6]),
    [iquote('0:Res:1.0,6.0')] ).

cnf(60,plain,
    ( ~ product(u,inverse(v),identity)
    | product(u,identity,v) ),
    inference(res,[status(thm),theory(equality)],[2,36]),
    [iquote('0:Res:2.0,36.0')] ).

cnf(86,plain,
    product(inverse(inverse(u)),identity,u),
    inference(res,[status(thm),theory(equality)],[2,60]),
    [iquote('0:Res:2.0,60.0')] ).

cnf(127,plain,
    ( ~ product(u,v,identity)
    | ~ product(u,identity,a) ),
    inference(res,[status(thm),theory(equality)],[1,9]),
    [iquote('0:Res:1.0,9.0')] ).

cnf(137,plain,
    ~ product(inverse(u),identity,a),
    inference(res,[status(thm),theory(equality)],[2,127]),
    [iquote('0:Res:2.0,127.0')] ).

cnf(139,plain,
    $false,
    inference(unc,[status(thm)],[137,86]),
    [iquote('0:UnC:137.0,86.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.10  % Command  : run_spass %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Tue Jun 14 05:22:12 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35  SPASS V 3.9 
% 0.14/0.35  SPASS beiseite: Proof found.
% 0.14/0.35  % SZS status Theorem
% 0.14/0.35  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.14/0.35  SPASS derived 117 clauses, backtracked 0 clauses, performed 0 splits and kept 60 clauses.
% 0.14/0.35  SPASS allocated 63193 KBytes.
% 0.14/0.35  SPASS spent	0:00:00.05 on the problem.
% 0.14/0.35  		0:00:00.03 for the input.
% 0.14/0.35  		0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.35  		0:00:00.00 for inferences.
% 0.14/0.35  		0:00:00.00 for the backtracking.
% 0.14/0.35  		0:00:00.01 for the reduction.
% 0.14/0.35  
% 0.14/0.35  
% 0.14/0.35  Here is a proof with depth 3, length 12 :
% 0.14/0.35  % SZS output start Refutation
% See solution above
% 0.14/0.35  Formulae used in the proof : left_identity left_inverse prove_a_has_an_inverse associativity1 associativity2
% 0.14/0.35  
%------------------------------------------------------------------------------