%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP031-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   24 (   0 equ;  17 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(3,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('GRP031-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP031-2.p',unknown),
    [] ).

cnf(5,axiom,
    product(u,inverse(u),identity),
    file('GRP031-2.p',unknown),
    [] ).

cnf(6,axiom,
    product(u,identity,u),
    file('GRP031-2.p',unknown),
    [] ).

cnf(7,axiom,
    ~ product(u,a,identity),
    file('GRP031-2.p',unknown),
    [] ).

cnf(8,plain,
    ( ~ product(u,v,w)
    | ~ product(w,x,identity)
    | ~ product(v,x,a) ),
    inference(res,[status(thm),theory(equality)],[3,7]),
    [iquote('0:Res:3.3,7.0')] ).

cnf(17,plain,
    ( ~ product(u,v,identity)
    | ~ product(w,u,x)
    | product(x,v,w) ),
    inference(res,[status(thm),theory(equality)],[6,4]),
    [iquote('0:Res:6.0,4.0')] ).

cnf(21,plain,
    ( ~ product(u,v,w)
    | product(w,inverse(v),u) ),
    inference(res,[status(thm),theory(equality)],[5,17]),
    [iquote('0:Res:5.0,17.0')] ).

cnf(58,plain,
    ( ~ product(u,v,identity)
    | ~ product(identity,v,a) ),
    inference(res,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Res:6.0,8.0')] ).

cnf(64,plain,
    ~ product(identity,inverse(u),a),
    inference(res,[status(thm),theory(equality)],[5,58]),
    [iquote('0:Res:5.0,58.0')] ).

cnf(67,plain,
    ~ product(a,u,identity),
    inference(res,[status(thm),theory(equality)],[21,64]),
    [iquote('0:Res:21.1,64.0')] ).

cnf(68,plain,
    $false,
    inference(unc,[status(thm)],[67,5]),
    [iquote('0:UnC:67.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP031-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jun 14 12:12:54 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.42  
% 0.21/0.42  SPASS V 3.9 
% 0.21/0.42  SPASS beiseite: Proof found.
% 0.21/0.42  % SZS status Theorem
% 0.21/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.42  SPASS derived 60 clauses, backtracked 0 clauses, performed 0 splits and kept 53 clauses.
% 0.21/0.42  SPASS allocated 63146 KBytes.
% 0.21/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.21/0.42  		0:00:00.03 for the input.
% 0.21/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42  		0:00:00.00 for inferences.
% 0.21/0.42  		0:00:00.00 for the backtracking.
% 0.21/0.42  		0:00:00.00 for the reduction.
% 0.21/0.42  
% 0.21/0.42  
% 0.21/0.42  Here is a proof with depth 4, length 12 :
% 0.21/0.42  % SZS output start Refutation
% See solution above
% 0.21/0.42  Formulae used in the proof : associativity1 associativity2 right_inverse right_identity prove_a_has_a_left_inverse
% 0.21/0.42  
%------------------------------------------------------------------------------