%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP028-1 : 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 11:44:51 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   14 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP028-1.p',unknown),
    [] ).

cnf(2,axiom,
    product(left_solution(u,v),u,v),
    file('GRP028-1.p',unknown),
    [] ).

cnf(3,axiom,
    product(u,right_solution(u,v),v),
    file('GRP028-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ product(not_identity(u),u,not_identity(u)),
    file('GRP028-1.p',unknown),
    [] ).

cnf(5,plain,
    ( ~ product(u,v,w)
    | ~ product(x,w,not_identity(v))
    | ~ product(x,u,not_identity(v)) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.3,4.0')] ).

cnf(6,plain,
    ( ~ product(u,v,w)
    | ~ product(left_solution(w,not_identity(v)),u,not_identity(v)) ),
    inference(res,[status(thm),theory(equality)],[2,5]),
    [iquote('0:Res:2.0,5.1')] ).

cnf(10,plain,
    ~ product(u,v,u),
    inference(res,[status(thm),theory(equality)],[2,6]),
    [iquote('0:Res:2.0,6.1')] ).

cnf(12,plain,
    $false,
    inference(unc,[status(thm)],[10,3]),
    [iquote('0:UnC:10.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP028-1 : 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 : Tue Jun 14 11:54:49 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 7 clauses, backtracked 0 clauses, performed 0 splits and kept 11 clauses.
% 0.19/0.40  SPASS allocated 63090 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.40  		0:00:00.03 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 3, length 8 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : associativity left_soln right_soln prove_there_is_a_right_identity
% 0.19/0.40  
%------------------------------------------------------------------------------