%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 : Wed May 31 12:09:41 EDT 2023

% Result   : Unsatisfiable 0.18s 0.58s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (  14 unt;   0 def)
%            Number of atoms       :   42 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   40 (  21   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 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,hypothesis,
    product(a,b,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ product(b,a,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,plain,
    ! [X0] : product(identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ! [X0] : product(X0,identity,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ! [X0] : product(inverse(X0),X0,identity),
    inference(cnf_transformation,[status(esa)],[f3]) ).

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

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

fof(f18,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(f19,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)],[f18]) ).

fof(f22,plain,
    product(a,b,identity),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f23,plain,
    ~ product(b,a,identity),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ product(X0,identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f17,f12]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,a,X1)
      | ~ product(X1,b,X2)
      | product(X0,identity,X2) ),
    inference(resolution,[status(thm)],[f19,f22]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ product(X0,a,identity)
      | product(X0,identity,b) ),
    inference(resolution,[status(thm)],[f28,f11]) ).

fof(f59,plain,
    product(inverse(a),identity,b),
    inference(resolution,[status(thm)],[f13,f55]) ).

fof(f150,plain,
    b = inverse(a),
    inference(resolution,[status(thm)],[f59,f26]) ).

fof(f172,plain,
    product(b,a,identity),
    inference(paramodulation,[status(thm)],[f150,f13]) ).

fof(f173,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f172,f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n011.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue May 30 11:34:12 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 0.18/0.58  % Refutation found
% 0.18/0.58  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.58  % Elapsed time: 0.025955 seconds
% 0.18/0.58  % CPU time: 0.025135 seconds
% 0.18/0.58  % Memory used: 1.115 MB
%------------------------------------------------------------------------------