TSTP Solution File: SET120-7 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 20:39:12 EDT 2024

% Result   : Unsatisfiable 18.05s 2.72s
% Output   : CNFRefutation 18.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   32 (   9 unt;   0 def)
%            Number of atoms       :   55 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   44 (  21   ~;  20   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f14,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f153,axiom,
    ! [Y,Z] :
      ( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
      | 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(f155,axiom,
    ! [X] :
      ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
      | second(X) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f157,axiom,
    ! [X] :
      ( ordered_pair(first(X),second(X)) = X
      | second(X) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f166,negated_conjecture,
    ~ member(x,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f167,negated_conjecture,
    second(ordered_pair(x,y)) != ordered_pair(x,y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f185,plain,
    ! [U,X] :
      ( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f186,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f185]) ).

fof(f353,plain,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | member(ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1))),cross_product(universal_class,universal_class)) ),
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f355,plain,
    ! [X0] :
      ( member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class))
      | second(X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f155]) ).

fof(f357,plain,
    ! [X0] :
      ( ordered_pair(first(X0),second(X0)) = X0
      | second(X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f157]) ).

fof(f366,plain,
    ~ member(x,universal_class),
    inference(cnf_transformation,[status(esa)],[f166]) ).

fof(f367,plain,
    second(ordered_pair(x,y)) != ordered_pair(x,y),
    inference(cnf_transformation,[status(esa)],[f167]) ).

fof(f1110,plain,
    ! [X0,X1] : ~ member(ordered_pair(x,X0),cross_product(universal_class,X1)),
    inference(resolution,[status(thm)],[f186,f366]) ).

fof(f11854,plain,
    ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y),
    inference(resolution,[status(thm)],[f357,f367]) ).

fof(f12765,plain,
    ( spl0_558
  <=> member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
    introduced(split_symbol_definition) ).

fof(f12768,plain,
    ( spl0_559
  <=> second(ordered_pair(x,y)) = ordered_pair(x,y) ),
    introduced(split_symbol_definition) ).

fof(f12769,plain,
    ( second(ordered_pair(x,y)) = ordered_pair(x,y)
    | ~ spl0_559 ),
    inference(component_clause,[status(thm)],[f12768]) ).

fof(f12771,plain,
    ( member(ordered_pair(x,y),cross_product(universal_class,universal_class))
    | second(ordered_pair(x,y)) = ordered_pair(x,y) ),
    inference(paramodulation,[status(thm)],[f11854,f355]) ).

fof(f12772,plain,
    ( spl0_558
    | spl0_559 ),
    inference(split_clause,[status(thm)],[f12771,f12765,f12768]) ).

fof(f12783,plain,
    ( spl0_562
  <=> member(ordered_pair(first(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y)))),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class)) ),
    introduced(split_symbol_definition) ).

fof(f12784,plain,
    ( member(ordered_pair(first(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y)))),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class))
    | ~ spl0_562 ),
    inference(component_clause,[status(thm)],[f12783]) ).

fof(f12786,plain,
    ( ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
    | member(ordered_pair(first(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y)))),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class)) ),
    inference(paramodulation,[status(thm)],[f11854,f353]) ).

fof(f12787,plain,
    ( ~ spl0_558
    | spl0_562 ),
    inference(split_clause,[status(thm)],[f12786,f12765,f12783]) ).

fof(f12817,plain,
    ( $false
    | ~ spl0_559 ),
    inference(forward_subsumption_resolution,[status(thm)],[f12769,f367]) ).

fof(f12818,plain,
    ~ spl0_559,
    inference(contradiction_clause,[status(thm)],[f12817]) ).

fof(f12819,plain,
    ( member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class))
    | ~ spl0_562 ),
    inference(forward_demodulation,[status(thm)],[f11854,f12784]) ).

fof(f12820,plain,
    ( member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
    | ~ spl0_562 ),
    inference(forward_demodulation,[status(thm)],[f11854,f12819]) ).

fof(f12821,plain,
    ( member(ordered_pair(x,y),cross_product(universal_class,universal_class))
    | ~ spl0_562 ),
    inference(forward_demodulation,[status(thm)],[f11854,f12820]) ).

fof(f12822,plain,
    ( $false
    | ~ spl0_562 ),
    inference(forward_subsumption_resolution,[status(thm)],[f12821,f1110]) ).

fof(f12823,plain,
    ~ spl0_562,
    inference(contradiction_clause,[status(thm)],[f12822]) ).

fof(f12824,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f12772,f12787,f12818,f12823]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.08/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 22:05:41 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.37  % Drodi V3.6.0
% 18.05/2.72  % Refutation found
% 18.05/2.72  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 18.05/2.72  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.65/2.76  % Elapsed time: 2.393670 seconds
% 18.65/2.76  % CPU time: 18.835971 seconds
% 18.65/2.76  % Total memory used: 216.262 MB
% 18.65/2.76  % Net memory used: 210.884 MB
%------------------------------------------------------------------------------