TSTP Solution File: NUM159-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM159-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n012.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 12:24:34 EDT 2023

% Result   : Unsatisfiable 127.02s 16.37s
% Output   : CNFRefutation 127.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   63 (  20 unt;   0 def)
%            Number of atoms       :  128 (  11 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  114 (  49   ~;  65   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  122 (; 122   !;   0   ?)

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

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

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

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

fof(f5,axiom,
    ! [X,Y] :
      ( X != Y
      | subclass(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f22,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f26,axiom,
    ! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f138,axiom,
    union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f159,negated_conjecture,
    ~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f160,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f161,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f160]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f164,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f189,plain,
    ! [Z,Y] :
      ( ! [X] : ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f190,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f189]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,complement(X1))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f194,plain,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f322,plain,
    union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
    inference(cnf_transformation,[status(esa)],[f138]) ).

fof(f347,plain,
    ~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
    inference(cnf_transformation,[status(esa)],[f159]) ).

fof(f348,plain,
    ! [X0] : subclass(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f165]) ).

fof(f773,plain,
    ! [X0,X1,X2] :
      ( member(X0,complement(X1))
      | member(X0,X1)
      | ~ subclass(X2,universal_class)
      | ~ member(X0,X2) ),
    inference(resolution,[status(thm)],[f193,f161]) ).

fof(f774,plain,
    ! [X0,X1,X2] :
      ( member(X0,complement(X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f773,f164]) ).

fof(f904,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),X1)
      | ~ member(not_subclass_element(complement(X0),X1),X0) ),
    inference(resolution,[status(thm)],[f162,f192]) ).

fof(f913,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),complement(X2))
      | member(not_subclass_element(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f162,f774]) ).

fof(f928,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,X1)
      | ~ subclass(X2,X1)
      | ~ member(not_subclass_element(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f163,f161]) ).

fof(f1087,plain,
    ! [X0,X1,X2] :
      ( member(not_subclass_element(intersection(X0,X1),X2),X1)
      | subclass(intersection(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f190,f162]) ).

fof(f2093,plain,
    ! [X0,X1,X2] :
      ( subclass(complement(X0),X1)
      | ~ subclass(X2,X0)
      | ~ member(not_subclass_element(complement(X0),X1),X2) ),
    inference(resolution,[status(thm)],[f904,f161]) ).

fof(f2306,plain,
    ! [X0,X1,X2,X3] :
      ( subclass(complement(X0),X1)
      | ~ subclass(X2,X0)
      | ~ subclass(X3,X2)
      | ~ member(not_subclass_element(complement(X0),X1),X3) ),
    inference(resolution,[status(thm)],[f2093,f161]) ).

fof(f4451,plain,
    ! [X0,X1] :
      ( subclass(complement(complement(X0)),X1)
      | member(not_subclass_element(complement(complement(X0)),X1),X0)
      | subclass(complement(complement(X0)),X1) ),
    inference(resolution,[status(thm)],[f913,f904]) ).

fof(f4452,plain,
    ! [X0,X1] :
      ( subclass(complement(complement(X0)),X1)
      | member(not_subclass_element(complement(complement(X0)),X1),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f4451]) ).

fof(f4455,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(X1))
      | member(not_subclass_element(X0,complement(X1)),X1)
      | subclass(X0,complement(X1)) ),
    inference(resolution,[status(thm)],[f913,f163]) ).

fof(f4456,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(X1))
      | member(not_subclass_element(X0,complement(X1)),X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f4455]) ).

fof(f4668,plain,
    ! [X0,X1,X2] :
      ( subclass(complement(X0),complement(X1))
      | subclass(complement(X0),complement(X1))
      | ~ subclass(X2,X0)
      | ~ subclass(X1,X2) ),
    inference(resolution,[status(thm)],[f4456,f2306]) ).

fof(f4669,plain,
    ! [X0,X1,X2] :
      ( subclass(complement(X0),complement(X1))
      | ~ subclass(X2,X0)
      | ~ subclass(X1,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f4668]) ).

fof(f4670,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),complement(X1))
      | subclass(complement(X0),complement(X1))
      | ~ subclass(X1,X0) ),
    inference(resolution,[status(thm)],[f4456,f2093]) ).

fof(f4671,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),complement(X1))
      | ~ subclass(X1,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f4670]) ).

fof(f4691,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(complement(X1)))
      | ~ member(not_subclass_element(X0,complement(complement(X1))),X1) ),
    inference(resolution,[status(thm)],[f4456,f192]) ).

fof(f4862,plain,
    ! [X0] :
      ( subclass(complement(complement(X0)),X0)
      | subclass(complement(complement(X0)),X0) ),
    inference(resolution,[status(thm)],[f4452,f163]) ).

fof(f4863,plain,
    ! [X0] : subclass(complement(complement(X0)),X0),
    inference(duplicate_literals_removal,[status(esa)],[f4862]) ).

fof(f4976,plain,
    ! [X0] : subclass(complement(X0),complement(complement(complement(X0)))),
    inference(resolution,[status(thm)],[f4863,f4671]) ).

fof(f4977,plain,
    ! [X0] :
      ( ~ subclass(X0,complement(complement(X0)))
      | X0 = complement(complement(X0)) ),
    inference(resolution,[status(thm)],[f4863,f167]) ).

fof(f5117,plain,
    ! [X0,X1] :
      ( subclass(complement(complement(complement(complement(X0)))),complement(X1))
      | ~ subclass(X1,complement(X0)) ),
    inference(resolution,[status(thm)],[f4976,f4669]) ).

fof(f7862,plain,
    ! [X0] :
      ( subclass(X0,complement(complement(X0)))
      | subclass(X0,complement(complement(X0))) ),
    inference(resolution,[status(thm)],[f4691,f162]) ).

fof(f7863,plain,
    ! [X0] : subclass(X0,complement(complement(X0))),
    inference(duplicate_literals_removal,[status(esa)],[f7862]) ).

fof(f7905,plain,
    ! [X0] : X0 = complement(complement(X0)),
    inference(backward_subsumption_resolution,[status(thm)],[f4977,f7863]) ).

fof(f8207,plain,
    ! [X0,X1] : complement(intersection(X0,complement(X1))) = union(complement(X0),X1),
    inference(paramodulation,[status(thm)],[f7905,f194]) ).

fof(f9737,plain,
    ! [X0,X1] :
      ( subclass(complement(complement(X0)),complement(X1))
      | ~ subclass(X1,complement(X0)) ),
    inference(forward_demodulation,[status(thm)],[f7905,f5117]) ).

fof(f9738,plain,
    ! [X0,X1] :
      ( subclass(X0,complement(X1))
      | ~ subclass(X1,complement(X0)) ),
    inference(forward_demodulation,[status(thm)],[f7905,f9737]) ).

fof(f64283,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(X0,X1),X2)
      | subclass(intersection(X0,X1),X2)
      | ~ subclass(X1,X2) ),
    inference(resolution,[status(thm)],[f1087,f928]) ).

fof(f64284,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(X0,X1),X2)
      | ~ subclass(X1,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f64283]) ).

fof(f66133,plain,
    ! [X0,X1] : subclass(intersection(X0,X1),X1),
    inference(resolution,[status(thm)],[f64284,f348]) ).

fof(f66174,plain,
    ! [X0,X1] : subclass(X0,complement(intersection(X1,complement(X0)))),
    inference(resolution,[status(thm)],[f66133,f9738]) ).

fof(f66175,plain,
    ! [X0,X1] : subclass(X0,union(complement(X1),X0)),
    inference(forward_demodulation,[status(thm)],[f8207,f66174]) ).

fof(f66560,plain,
    ! [X0,X1] : subclass(X0,union(X1,X0)),
    inference(paramodulation,[status(thm)],[f7905,f66175]) ).

fof(f66655,plain,
    subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
    inference(paramodulation,[status(thm)],[f322,f66560]) ).

fof(f66656,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f66655,f347]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM159-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 09:48:25 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.35  % Drodi V3.5.1
% 127.02/16.37  % Refutation found
% 127.02/16.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 127.02/16.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 127.81/16.51  % Elapsed time: 16.149862 seconds
% 127.81/16.51  % CPU time: 127.710855 seconds
% 127.81/16.51  % Memory used: 429.073 MB
%------------------------------------------------------------------------------