%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET108-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 12:34:01 EDT 2023

% Result   : Unsatisfiable 0.07s 0.27s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   28 (   9 unt;   0 def)
%            Number of atoms       :   55 (  21 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   58 (  31   ~;  27   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   73 (;  73   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,cross_product(X,Y))
      | ordered_pair(first(Z),second(Z)) = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f94,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f95,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f151,axiom,
    ! [W,X,Y,Z] :
      ( ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(W,universal_class)
      | W = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f152,axiom,
    ! [W,X,Y,Z] :
      ( ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(X,universal_class)
      | X = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f153,negated_conjecture,
    member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f154,negated_conjecture,
    ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f177,plain,
    ! [Z] :
      ( ! [X,Y] : ~ member(Z,cross_product(X,Y))
      | ordered_pair(first(Z),second(Z)) = Z ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f178,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,cross_product(X1,X2))
      | ordered_pair(first(X0),second(X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f177]) ).

fof(f264,plain,
    ! [U] :
      ( ! [V,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,universal_class) ),
    inference(miniscoping,[status(esa)],[f94]) ).

fof(f265,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,universal_class) ),
    inference(cnf_transformation,[status(esa)],[f264]) ).

fof(f266,plain,
    ! [V] :
      ( ! [U,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,universal_class) ),
    inference(miniscoping,[status(esa)],[f95]) ).

fof(f267,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,universal_class) ),
    inference(cnf_transformation,[status(esa)],[f266]) ).

fof(f336,plain,
    ! [W,Y] :
      ( ! [X,Z] : ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(W,universal_class)
      | W = Y ),
    inference(miniscoping,[status(esa)],[f151]) ).

fof(f337,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | ~ member(X0,universal_class)
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f336]) ).

fof(f338,plain,
    ! [X,Z] :
      ( ! [W,Y] : ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(X,universal_class)
      | X = Z ),
    inference(miniscoping,[status(esa)],[f152]) ).

fof(f339,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | ~ member(X1,universal_class)
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f338]) ).

fof(f340,plain,
    member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f341,plain,
    ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
    inference(cnf_transformation,[status(esa)],[f154]) ).

fof(f351,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,universal_class)
      | X1 = second(ordered_pair(X0,X1)) ),
    inference(resolution,[status(thm)],[f178,f339]) ).

fof(f352,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | X1 = second(ordered_pair(X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f351,f267]) ).

fof(f353,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X0,universal_class)
      | X0 = first(ordered_pair(X0,X1)) ),
    inference(resolution,[status(thm)],[f178,f337]) ).

fof(f354,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | X0 = first(ordered_pair(X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f353,f265]) ).

fof(f355,plain,
    z = second(ordered_pair(y,z)),
    inference(resolution,[status(thm)],[f352,f340]) ).

fof(f356,plain,
    ~ member(ordered_pair(first(ordered_pair(y,z)),z),cross_product(universal_class,universal_class)),
    inference(backward_demodulation,[status(thm)],[f355,f341]) ).

fof(f365,plain,
    y = first(ordered_pair(y,z)),
    inference(resolution,[status(thm)],[f354,f340]) ).

fof(f390,plain,
    ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    inference(forward_demodulation,[status(thm)],[f365,f356]) ).

fof(f391,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f390,f340]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET108-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n031.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Tue May 30 10:40:22 EDT 2023
% 0.07/0.26  % CPUTime  : 
% 0.07/0.26  % Drodi V3.5.1
% 0.07/0.27  % Refutation found
% 0.07/0.27  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28  % Elapsed time: 0.015999 seconds
% 0.07/0.28  % CPU time: 0.025436 seconds
% 0.07/0.28  % Memory used: 15.659 MB
%------------------------------------------------------------------------------