%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP022-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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  : 300s
% DateTime : Tue Apr 30 20:18:48 EDT 2024

% Result   : Unsatisfiable 0.09s 0.31s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   20 (  11 unt;   0 def)
%            Number of atoms       :   39 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   45 (  26   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   42 (  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : product(identity,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : product(X,identity,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] : product(inverse(X),X,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y,Z,W] :
      ( ~ product(X,Y,Z)
      | ~ product(X,Y,W)
      | Z = W ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y,U,Z,V,W] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(U,Z,W)
      | product(X,V,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    inverse(inverse(a)) != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,plain,
    ! [X0] : product(identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f11,plain,
    ! [X0] : product(X0,identity,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [X0] : product(inverse(X0),X0,identity),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f15,plain,
    ! [Z,W] :
      ( ! [X,Y] :
          ( ~ product(X,Y,Z)
          | ~ product(X,Y,W) )
      | Z = W ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f16,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X,V,W] :
      ( ! [U,Z] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(U,Z,W) )
      | product(X,V,W) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X2,X3,X5)
      | product(X0,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    inverse(inverse(a)) != a,
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,inverse(inverse(a)))
      | ~ product(X0,X1,a) ),
    inference(resolution,[status(thm)],[f16,f21]) ).

fof(f25,plain,
    ~ product(inverse(inverse(a)),identity,a),
    inference(resolution,[status(thm)],[f22,f11]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ product(inverse(inverse(a)),X0,X1)
      | ~ product(X0,X2,identity)
      | ~ product(X1,X2,a) ),
    inference(resolution,[status(thm)],[f18,f25]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ product(inverse(a),X0,identity)
      | ~ product(identity,X0,a) ),
    inference(resolution,[status(thm)],[f26,f12]) ).

fof(f50,plain,
    ~ product(identity,a,a),
    inference(resolution,[status(thm)],[f29,f12]) ).

fof(f51,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f50,f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem  : GRP022-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n027.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue Apr 30 00:53:32 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Drodi V3.6.0
% 0.09/0.31  % Refutation found
% 0.09/0.31  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.32  % Elapsed time: 0.012947 seconds
% 0.15/0.32  % CPU time: 0.020677 seconds
% 0.15/0.32  % Total memory used: 3.938 MB
% 0.15/0.32  % Net memory used: 3.818 MB
%------------------------------------------------------------------------------