TSTP Solution File: SET097-7 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET097-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : Tue Apr 30 20:39:07 EDT 2024

% Result   : Unsatisfiable 0.20s 0.52s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   80 (  16 unt;   0 def)
%            Number of atoms       :  167 (  40 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  159 (  72   ~;  80   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   58 (  58   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,X)
      | ~ member(Z,Y)
      | member(Z,intersection(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [Z,X] :
      ( ~ member(Z,universal_class)
      | member(Z,complement(X))
      | member(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f103,axiom,
    ! [Z] : ~ member(Z,null_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f105,axiom,
    ! [X] :
      ( ~ subclass(X,null_class)
      | X = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f106,axiom,
    ! [Z] :
      ( Z = null_class
      | member(not_subclass_element(Z,null_class),Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f123,axiom,
    ! [X] :
      ( ~ member(X,universal_class)
      | singleton(X) != null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f125,axiom,
    ! [Y,X] :
      ( ~ member(Y,singleton(X))
      | Y = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f126,axiom,
    ! [X] :
      ( member(X,universal_class)
      | singleton(X) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f140,axiom,
    ! [X,Y] :
      ( ~ subclass(X,singleton(Y))
      | X = null_class
      | singleton(Y) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f141,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f142,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f143,negated_conjecture,
    x != null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f144,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f145,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f144]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f148,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f175,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,complement(X1))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f265,plain,
    ! [X0] : ~ member(X0,null_class),
    inference(cnf_transformation,[status(esa)],[f103]) ).

fof(f267,plain,
    ! [X0] :
      ( ~ subclass(X0,null_class)
      | X0 = null_class ),
    inference(cnf_transformation,[status(esa)],[f105]) ).

fof(f268,plain,
    ! [X0] :
      ( X0 = null_class
      | member(not_subclass_element(X0,null_class),X0) ),
    inference(cnf_transformation,[status(esa)],[f106]) ).

fof(f293,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | singleton(X0) != null_class ),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f295,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f125]) ).

fof(f296,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class ),
    inference(cnf_transformation,[status(esa)],[f126]) ).

fof(f311,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,singleton(X1))
      | X0 = null_class
      | singleton(X1) = X0 ),
    inference(cnf_transformation,[status(esa)],[f140]) ).

fof(f312,plain,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    inference(cnf_transformation,[status(esa)],[f141]) ).

fof(f313,plain,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(cnf_transformation,[status(esa)],[f142]) ).

fof(f314,plain,
    x != null_class,
    inference(cnf_transformation,[status(esa)],[f143]) ).

fof(f317,plain,
    subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
    inference(resolution,[status(thm)],[f146,f312]) ).

fof(f319,plain,
    intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
    inference(resolution,[status(thm)],[f317,f267]) ).

fof(f367,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | not_subclass_element(singleton(X0),null_class) = X0 ),
    inference(resolution,[status(thm)],[f268,f295]) ).

fof(f368,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | member(X0,singleton(X0))
      | singleton(X0) = null_class ),
    inference(paramodulation,[status(thm)],[f367,f268]) ).

fof(f369,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | member(X0,singleton(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f368]) ).

fof(f374,plain,
    ! [X0] :
      ( ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
      | ~ member(X0,x)
      | member(X0,null_class) ),
    inference(paramodulation,[status(thm)],[f319,f175]) ).

fof(f375,plain,
    ! [X0] :
      ( ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
      | ~ member(X0,x) ),
    inference(forward_subsumption_resolution,[status(thm)],[f374,f265]) ).

fof(f386,plain,
    ! [X0] :
      ( ~ member(X0,x)
      | ~ member(X0,universal_class)
      | member(X0,singleton(not_subclass_element(x,null_class))) ),
    inference(resolution,[status(thm)],[f375,f177]) ).

fof(f387,plain,
    ! [X0] :
      ( ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x)
      | ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),universal_class)
      | subclass(X0,singleton(not_subclass_element(x,null_class))) ),
    inference(resolution,[status(thm)],[f386,f147]) ).

fof(f389,plain,
    ( spl0_7
  <=> member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class) ),
    introduced(split_symbol_definition) ).

fof(f391,plain,
    ( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f389]) ).

fof(f392,plain,
    ( spl0_8
  <=> subclass(x,singleton(not_subclass_element(x,null_class))) ),
    introduced(split_symbol_definition) ).

fof(f393,plain,
    ( subclass(x,singleton(not_subclass_element(x,null_class)))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f392]) ).

fof(f395,plain,
    ( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class)
    | subclass(x,singleton(not_subclass_element(x,null_class)))
    | subclass(x,singleton(not_subclass_element(x,null_class))) ),
    inference(resolution,[status(thm)],[f387,f146]) ).

fof(f396,plain,
    ( ~ spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f395,f389,f392]) ).

fof(f397,plain,
    ( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class
    | spl0_7 ),
    inference(resolution,[status(thm)],[f391,f296]) ).

fof(f398,plain,
    ( spl0_9
  <=> singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class ),
    introduced(split_symbol_definition) ).

fof(f399,plain,
    ( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f398]) ).

fof(f401,plain,
    ( spl0_10
  <=> member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class) ),
    introduced(split_symbol_definition) ).

fof(f402,plain,
    ( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class)
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f401]) ).

fof(f404,plain,
    ( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class
    | member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class)
    | spl0_7 ),
    inference(paramodulation,[status(thm)],[f397,f369]) ).

fof(f405,plain,
    ( spl0_9
    | spl0_10
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f404,f398,f401,f389]) ).

fof(f437,plain,
    ( spl0_13
  <=> member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x) ),
    introduced(split_symbol_definition) ).

fof(f438,plain,
    ( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f437]) ).

fof(f439,plain,
    ( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f437]) ).

fof(f486,plain,
    ( subclass(x,singleton(not_subclass_element(x,null_class)))
    | spl0_13 ),
    inference(resolution,[status(thm)],[f439,f146]) ).

fof(f487,plain,
    ( spl0_22
  <=> x = null_class ),
    introduced(split_symbol_definition) ).

fof(f488,plain,
    ( x = null_class
    | ~ spl0_22 ),
    inference(component_clause,[status(thm)],[f487]) ).

fof(f490,plain,
    ( spl0_23
  <=> singleton(not_subclass_element(x,null_class)) = x ),
    introduced(split_symbol_definition) ).

fof(f491,plain,
    ( singleton(not_subclass_element(x,null_class)) = x
    | ~ spl0_23 ),
    inference(component_clause,[status(thm)],[f490]) ).

fof(f493,plain,
    ( x = null_class
    | singleton(not_subclass_element(x,null_class)) = x
    | spl0_13 ),
    inference(resolution,[status(thm)],[f486,f311]) ).

fof(f494,plain,
    ( spl0_22
    | spl0_23
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f493,f487,f490,f437]) ).

fof(f495,plain,
    ( $false
    | ~ spl0_23 ),
    inference(forward_subsumption_resolution,[status(thm)],[f491,f313]) ).

fof(f496,plain,
    ~ spl0_23,
    inference(contradiction_clause,[status(thm)],[f495]) ).

fof(f497,plain,
    ( $false
    | ~ spl0_22 ),
    inference(forward_subsumption_resolution,[status(thm)],[f488,f314]) ).

fof(f498,plain,
    ~ spl0_22,
    inference(contradiction_clause,[status(thm)],[f497]) ).

fof(f528,plain,
    ( x = null_class
    | singleton(not_subclass_element(x,null_class)) = x
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f393,f311]) ).

fof(f529,plain,
    ( spl0_22
    | spl0_23
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f528,f487,f490,f392]) ).

fof(f719,plain,
    ( $false
    | ~ spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f402,f265]) ).

fof(f720,plain,
    ~ spl0_10,
    inference(contradiction_clause,[status(thm)],[f719]) ).

fof(f1266,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,universal_class)
      | ~ member(X1,X0)
      | singleton(X1) != null_class ),
    inference(resolution,[status(thm)],[f145,f293]) ).

fof(f1267,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | singleton(X0) != null_class ),
    inference(forward_subsumption_resolution,[status(thm)],[f1266,f148]) ).

fof(f1292,plain,
    ( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) != null_class
    | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f1267,f438]) ).

fof(f1293,plain,
    ( null_class != null_class
    | ~ spl0_9
    | ~ spl0_13 ),
    inference(forward_demodulation,[status(thm)],[f399,f1292]) ).

fof(f1294,plain,
    ( $false
    | ~ spl0_9
    | ~ spl0_13 ),
    inference(trivial_equality_resolution,[status(esa)],[f1293]) ).

fof(f1295,plain,
    ( ~ spl0_9
    | ~ spl0_13 ),
    inference(contradiction_clause,[status(thm)],[f1294]) ).

fof(f1296,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f396,f405,f494,f496,f498,f529,f720,f1295]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET097-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 21:48:16 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.37  % Drodi V3.6.0
% 0.20/0.52  % Refutation found
% 0.20/0.52  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.52  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.54  % Elapsed time: 0.175529 seconds
% 0.20/0.54  % CPU time: 1.261963 seconds
% 0.20/0.54  % Total memory used: 82.423 MB
% 0.20/0.54  % Net memory used: 81.635 MB
%------------------------------------------------------------------------------