%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP003-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 20:18:44 EDT 2024

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   19 (   9 unt;   0 def)
%            Number of atoms       :   43 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   50 (  26   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   56 (  56   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : product(identity,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : product(inverse(X),X,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y,U,Z,V,W] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W)
      | product(U,Z,W) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    ~ product(a,identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,plain,
    ! [X0] : product(identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f10,plain,
    ! [X0] : product(inverse(X0),X0,identity),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f14,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)],[f5]) ).

fof(f15,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)],[f14]) ).

fof(f16,plain,
    ! [U,Z,W] :
      ( ! [X,V] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(X,V,W) )
      | product(U,Z,W) ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X0,X4,X5)
      | product(X2,X3,X5) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f20,plain,
    ~ product(a,identity,a),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,identity)
      | ~ product(X1,X2,X3)
      | product(X0,X3,X2) ),
    inference(resolution,[status(thm)],[f15,f9]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,identity,X1)
      | ~ product(X0,X2,X3)
      | product(X1,X2,X3) ),
    inference(resolution,[status(thm)],[f17,f9]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(inverse(X0),X2,X1) ),
    inference(resolution,[status(thm)],[f10,f23]) ).

fof(f56,plain,
    ! [X0] : product(inverse(inverse(X0)),identity,X0),
    inference(resolution,[status(thm)],[f34,f10]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ~ product(inverse(inverse(X0)),X1,X2)
      | product(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f56,f26]) ).

fof(f552,plain,
    ! [X0] : product(X0,identity,X0),
    inference(resolution,[status(thm)],[f72,f56]) ).

fof(f557,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f20,f552]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP003-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Apr 30 00:45:13 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.19/0.42  % Refutation found
% 0.19/0.42  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.42  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.44  % Elapsed time: 0.078522 seconds
% 0.19/0.44  % CPU time: 0.507312 seconds
% 0.19/0.44  % Total memory used: 33.945 MB
% 0.19/0.44  % Net memory used: 32.934 MB
%------------------------------------------------------------------------------