TSTP Solution File: SET084-6 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET084-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 20:39:03 EDT 2024

% Result   : Unsatisfiable 0.15s 0.32s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   67 (  14 unt;   0 def)
%            Number of atoms       :  137 (  40 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  122 (  52   ~;  61   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  10 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   36 (  36   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | U = X
      | U = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X] : unordered_pair(X,X) = singleton(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f48,axiom,
    ! [X] :
      ( ~ inductive(X)
      | subclass(image(successor_relation,X),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f51,axiom,
    ! [Y] :
      ( ~ inductive(Y)
      | subclass(omega,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f66,axiom,
    ! [X] :
      ( X = null_class
      | member(regular(X),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f92,negated_conjecture,
    singleton(x) = singleton(y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    member(y,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f94,negated_conjecture,
    x != y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f103,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f103]) ).

fof(f105,plain,
    ! [X] :
      ( ~ member(X,universal_class)
      | ! [Y] : member(X,unordered_pair(X,Y)) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f105]) ).

fof(f110,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f151,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f153,plain,
    inductive(omega),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f154,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(omega,X0) ),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f169,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f200,plain,
    singleton(x) = singleton(y),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f201,plain,
    member(y,universal_class),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f202,plain,
    x != y,
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f220,plain,
    ! [X0] :
      ( ~ subclass(X0,omega)
      | X0 = omega
      | ~ inductive(X0) ),
    inference(resolution,[status(thm)],[f102,f154]) ).

fof(f244,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f110,f104]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f244]) ).

fof(f247,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(X0,singleton(X0)) ),
    inference(paramodulation,[status(thm)],[f110,f106]) ).

fof(f250,plain,
    ! [X0] :
      ( regular(singleton(X0)) = X0
      | singleton(X0) = null_class ),
    inference(resolution,[status(thm)],[f245,f169]) ).

fof(f253,plain,
    ! [X0] :
      ( ~ member(X0,singleton(x))
      | X0 = y ),
    inference(paramodulation,[status(thm)],[f200,f245]) ).

fof(f254,plain,
    ( spl0_4
  <=> regular(singleton(x)) = y ),
    introduced(split_symbol_definition) ).

fof(f255,plain,
    ( regular(singleton(x)) = y
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f254]) ).

fof(f257,plain,
    ( spl0_5
  <=> singleton(x) = null_class ),
    introduced(split_symbol_definition) ).

fof(f258,plain,
    ( singleton(x) = null_class
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f257]) ).

fof(f260,plain,
    ( regular(singleton(x)) = y
    | singleton(x) = null_class ),
    inference(resolution,[status(thm)],[f253,f169]) ).

fof(f261,plain,
    ( spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f260,f254,f257]) ).

fof(f279,plain,
    ( null_class = singleton(y)
    | ~ spl0_5 ),
    inference(backward_demodulation,[status(thm)],[f258,f200]) ).

fof(f280,plain,
    ! [X0] :
      ( ~ member(X0,null_class)
      | X0 = x
      | ~ spl0_5 ),
    inference(paramodulation,[status(thm)],[f258,f245]) ).

fof(f311,plain,
    ( spl0_12
  <=> member(y,null_class) ),
    introduced(split_symbol_definition) ).

fof(f312,plain,
    ( member(y,null_class)
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f311]) ).

fof(f441,plain,
    ( spl0_26
  <=> image(successor_relation,omega) = omega ),
    introduced(split_symbol_definition) ).

fof(f444,plain,
    ( spl0_27
  <=> inductive(image(successor_relation,omega)) ),
    introduced(split_symbol_definition) ).

fof(f447,plain,
    ( spl0_28
  <=> inductive(omega) ),
    introduced(split_symbol_definition) ).

fof(f449,plain,
    ( ~ inductive(omega)
    | spl0_28 ),
    inference(component_clause,[status(thm)],[f447]) ).

fof(f450,plain,
    ( image(successor_relation,omega) = omega
    | ~ inductive(image(successor_relation,omega))
    | ~ inductive(omega) ),
    inference(resolution,[status(thm)],[f220,f151]) ).

fof(f451,plain,
    ( spl0_26
    | ~ spl0_27
    | ~ spl0_28 ),
    inference(split_clause,[status(thm)],[f450,f441,f444,f447]) ).

fof(f452,plain,
    ( spl0_29
  <=> omega = omega ),
    introduced(split_symbol_definition) ).

fof(f455,plain,
    ( omega = omega
    | ~ inductive(omega)
    | ~ inductive(omega) ),
    inference(resolution,[status(thm)],[f220,f154]) ).

fof(f456,plain,
    ( spl0_29
    | ~ spl0_28 ),
    inference(split_clause,[status(thm)],[f455,f452,f447]) ).

fof(f459,plain,
    ( $false
    | spl0_28 ),
    inference(forward_subsumption_resolution,[status(thm)],[f449,f153]) ).

fof(f460,plain,
    spl0_28,
    inference(contradiction_clause,[status(thm)],[f459]) ).

fof(f462,plain,
    ( spl0_30
  <=> member(y,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f464,plain,
    ( ~ member(y,universal_class)
    | spl0_30 ),
    inference(component_clause,[status(thm)],[f462]) ).

fof(f465,plain,
    ( ~ member(y,universal_class)
    | member(y,null_class)
    | ~ spl0_5 ),
    inference(paramodulation,[status(thm)],[f279,f247]) ).

fof(f466,plain,
    ( ~ spl0_30
    | spl0_12
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f465,f462,f311,f257]) ).

fof(f527,plain,
    ( y = x
    | ~ spl0_12
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f312,f280]) ).

fof(f528,plain,
    ( $false
    | ~ spl0_12
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f527,f202]) ).

fof(f529,plain,
    ( ~ spl0_12
    | ~ spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f528]) ).

fof(f530,plain,
    ( $false
    | spl0_30 ),
    inference(forward_subsumption_resolution,[status(thm)],[f464,f201]) ).

fof(f531,plain,
    spl0_30,
    inference(contradiction_clause,[status(thm)],[f530]) ).

fof(f532,plain,
    ( spl0_39
  <=> x = y ),
    introduced(split_symbol_definition) ).

fof(f533,plain,
    ( x = y
    | ~ spl0_39 ),
    inference(component_clause,[status(thm)],[f532]) ).

fof(f535,plain,
    ( x = y
    | singleton(x) = null_class
    | ~ spl0_4 ),
    inference(paramodulation,[status(thm)],[f250,f255]) ).

fof(f536,plain,
    ( spl0_39
    | spl0_5
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f535,f532,f257,f254]) ).

fof(f546,plain,
    ( $false
    | ~ spl0_39 ),
    inference(forward_subsumption_resolution,[status(thm)],[f533,f202]) ).

fof(f547,plain,
    ~ spl0_39,
    inference(contradiction_clause,[status(thm)],[f546]) ).

fof(f548,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f261,f451,f456,f460,f466,f529,f531,f536,f547]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09  % Problem  : SET084-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n026.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Mon Apr 29 22:01:04 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.15/0.31  % Drodi V3.6.0
% 0.15/0.32  % Refutation found
% 0.15/0.32  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.33  % Elapsed time: 0.020758 seconds
% 0.15/0.33  % CPU time: 0.045309 seconds
% 0.15/0.33  % Total memory used: 15.832 MB
% 0.15/0.33  % Net memory used: 15.806 MB
%------------------------------------------------------------------------------