%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : CAT012-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 20:13:20 EDT 2024

% Result   : Unsatisfiable 0.10s 0.33s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   19 (   8 unt;   0 def)
%            Number of atoms       :   36 (   5 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   40 (  23   ~;  17   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   33 (  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X,Y,Z] :
      ( ~ product(X,Y,Z)
      | defined(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X] : identity_map(domain(X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X] : product(codomain(X),X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | ~ identity_map(Y)
      | product(X,Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [X,Y,Z,W] :
      ( ~ product(X,Y,Z)
      | ~ product(X,Y,W)
      | Z = W ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    codomain(domain(a)) != domain(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,plain,
    ! [X,Y] :
      ( ! [Z] : ~ product(X,Y,Z)
      | defined(X,Y) ),
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | defined(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f37,plain,
    ! [X0] : identity_map(domain(X0)),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f42,plain,
    ! [X0] : product(codomain(X0),X0,X0),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ defined(X0,X1)
      | ~ identity_map(X1)
      | product(X0,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f45,plain,
    ! [Z,W] :
      ( ! [X,Y] :
          ( ~ product(X,Y,Z)
          | ~ product(X,Y,W) )
      | Z = W ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f47,plain,
    codomain(domain(a)) != domain(a),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,codomain(domain(a)))
      | ~ product(X0,X1,domain(a)) ),
    inference(resolution,[status(thm)],[f46,f47]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ product(codomain(domain(a)),X0,domain(a))
      | ~ defined(codomain(domain(a)),X0)
      | ~ identity_map(X0) ),
    inference(resolution,[status(thm)],[f48,f44]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ product(codomain(domain(a)),X0,domain(a))
      | ~ identity_map(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f52,f22]) ).

fof(f56,plain,
    ~ identity_map(domain(a)),
    inference(resolution,[status(thm)],[f53,f42]) ).

fof(f57,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f56,f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : CAT012-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n004.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon Apr 29 22:09:33 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.6.0
% 0.10/0.33  % Refutation found
% 0.10/0.33  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.35  % Elapsed time: 0.018258 seconds
% 0.10/0.35  % CPU time: 0.016674 seconds
% 0.10/0.35  % Total memory used: 2.251 MB
% 0.10/0.35  % Net memory used: 2.205 MB
%------------------------------------------------------------------------------