TSTP Solution File: SET195-6 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET195-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 20:39:23 EDT 2024

% Result   : Unsatisfiable 174.13s 22.31s
% Output   : CNFRefutation 175.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   51 (   9 unt;   0 def)
%            Number of atoms       :  118 (   4 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  120 (  53   ~;  67   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  116 ( 116   !;   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(f5,axiom,
    ! [X,Y] :
      ( X != Y
      | subclass(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    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(f24,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    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(f26,axiom,
    ! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f113,negated_conjecture,
    ~ subclass(y,union(x,y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f114,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f118,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f143,plain,
    ! [Z,Y] :
      ( ! [X] : ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f144,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f143]) ).

fof(f145,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,complement(X1))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f148,plain,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f245,plain,
    ~ subclass(y,union(x,y)),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f246,plain,
    ! [X0] : subclass(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f119]) ).

fof(f6959,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,X1)
      | ~ subclass(X0,X2)
      | member(not_subclass_element(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f116,f115]) ).

fof(f6987,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | ~ subclass(intersection(X1,X2),X3)
      | member(X0,X3) ),
    inference(resolution,[status(thm)],[f145,f115]) ).

fof(f7055,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f6987,f118]) ).

fof(f7216,plain,
    ! [X0,X1,X2] :
      ( ~ member(not_subclass_element(X0,X1),X2)
      | subclass(X0,X1)
      | ~ subclass(X0,complement(X2)) ),
    inference(resolution,[status(thm)],[f146,f6959]) ).

fof(f7254,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,universal_class)
      | member(X0,union(X1,X2))
      | member(X0,intersection(complement(X1),complement(X2))) ),
    inference(paramodulation,[status(thm)],[f148,f147]) ).

fof(f8704,plain,
    ! [X0,X1,X2] :
      ( member(X0,complement(X1))
      | ~ member(X0,universal_class)
      | member(X0,union(X2,X1)) ),
    inference(resolution,[status(thm)],[f144,f7254]) ).

fof(f9596,plain,
    ! [X0,X1,X2] :
      ( ~ member(not_subclass_element(X0,X1),X2)
      | member(not_subclass_element(X0,X1),universal_class)
      | subclass(X0,X1) ),
    inference(resolution,[status(thm)],[f7055,f116]) ).

fof(f9671,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),universal_class)
      | subclass(X0,X1)
      | subclass(X0,X1) ),
    inference(resolution,[status(thm)],[f9596,f116]) ).

fof(f9672,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),universal_class)
      | subclass(X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f9671]) ).

fof(f26091,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
      | member(not_subclass_element(X0,complement(X1)),X1)
      | subclass(X0,complement(X1)) ),
    inference(resolution,[status(thm)],[f147,f117]) ).

fof(f26092,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,complement(X1)),X1)
      | subclass(X0,complement(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f26091,f9672]) ).

fof(f26118,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,X2)
      | member(not_subclass_element(X0,complement(X1)),X2) ),
    inference(resolution,[status(thm)],[f26092,f115]) ).

fof(f29430,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,X2)
      | subclass(X0,complement(X1))
      | ~ subclass(X0,complement(X2)) ),
    inference(resolution,[status(thm)],[f26118,f7216]) ).

fof(f29431,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,X2)
      | ~ subclass(X0,complement(X2)) ),
    inference(duplicate_literals_removal,[status(esa)],[f29430]) ).

fof(f29436,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,complement(X2))
      | ~ member(not_subclass_element(X0,complement(X1)),X2) ),
    inference(resolution,[status(thm)],[f26118,f146]) ).

fof(f29560,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),complement(X1))
      | ~ subclass(X1,X0) ),
    inference(resolution,[status(thm)],[f29431,f246]) ).

fof(f57375,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,complement(X0))
      | subclass(X0,complement(X1)) ),
    inference(resolution,[status(thm)],[f29436,f116]) ).

fof(f57376,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,complement(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f57375]) ).

fof(f57421,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(complement(X1)))
      | ~ subclass(X0,X1) ),
    inference(resolution,[status(thm)],[f57376,f29560]) ).

fof(f83955,plain,
    ! [X0,X1,X2] :
      ( member(not_subclass_element(X0,union(X1,X2)),complement(X2))
      | ~ member(not_subclass_element(X0,union(X1,X2)),universal_class)
      | subclass(X0,union(X1,X2)) ),
    inference(resolution,[status(thm)],[f8704,f117]) ).

fof(f83956,plain,
    ! [X0,X1,X2] :
      ( member(not_subclass_element(X0,union(X1,X2)),complement(X2))
      | subclass(X0,union(X1,X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f83955,f9672]) ).

fof(f84236,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,union(X1,X2))
      | subclass(X0,union(X1,X2))
      | ~ subclass(X0,complement(complement(X2))) ),
    inference(resolution,[status(thm)],[f83956,f7216]) ).

fof(f84237,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,union(X1,X2))
      | ~ subclass(X0,complement(complement(X2))) ),
    inference(duplicate_literals_removal,[status(esa)],[f84236]) ).

fof(f84352,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,union(X1,X2))
      | ~ subclass(X0,X2) ),
    inference(resolution,[status(thm)],[f84237,f57421]) ).

fof(f84379,plain,
    ~ subclass(y,y),
    inference(resolution,[status(thm)],[f84352,f245]) ).

fof(f84380,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f84379,f246]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SET195-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n025.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 21:53:26 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.32  % Drodi V3.6.0
% 174.13/22.31  % Refutation found
% 174.13/22.31  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 174.13/22.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 177.12/22.90  % Elapsed time: 22.568604 seconds
% 177.12/22.90  % CPU time: 176.519101 seconds
% 177.12/22.90  % Total memory used: 2.425 GB
% 177.12/22.90  % Net memory used: 2.380 GB
%------------------------------------------------------------------------------