TSTP Solution File: SET511-6 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET511-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 20:39:47 EDT 2024

% Result   : Unsatisfiable 95.67s 12.41s
% Output   : CNFRefutation 96.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   66 (  21 unt;   0 def)
%            Number of atoms       :  135 (  56 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  127 (  58   ~;  69   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :  110 ( 110   !;   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(f8,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | U = X
      | U = 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(f13,axiom,
    ! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    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(f28,axiom,
    ! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ! [X,Z] :
      ( restrict(X,singleton(Z),universal_class) != null_class
      | ~ member(Z,domain_of(X)) ),
    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(f67,axiom,
    ! [X] :
      ( X = null_class
      | intersection(X,regular(X)) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f113,negated_conjecture,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
    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(f122,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f129,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f130,plain,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f141,plain,
    ! [Z,X] :
      ( ! [Y] : ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f142,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f141]) ).

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(f150,plain,
    ! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( restrict(X0,singleton(X1),universal_class) != null_class
      | ~ member(X1,domain_of(X0)) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f188,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f189,plain,
    ! [X0] :
      ( X0 = null_class
      | intersection(X0,regular(X0)) = null_class ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f245,plain,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f129,f123]) ).

fof(f252,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f251]) ).

fof(f755,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | regular(singleton(X0)) = X0 ),
    inference(resolution,[status(thm)],[f188,f252]) ).

fof(f757,plain,
    ! [X0,X1] :
      ( X0 = null_class
      | ~ subclass(X0,X1)
      | member(regular(X0),X1) ),
    inference(resolution,[status(thm)],[f188,f115]) ).

fof(f766,plain,
    ! [X0] :
      ( ~ member(regular(complement(X0)),X0)
      | complement(X0) = null_class ),
    inference(resolution,[status(thm)],[f146,f188]) ).

fof(f795,plain,
    ! [X0,X1,X2] :
      ( member(not_subclass_element(intersection(X0,X1),X2),X0)
      | subclass(intersection(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f142,f116]) ).

fof(f1463,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,regular(X1))
      | member(X0,null_class)
      | X1 = null_class ),
    inference(paramodulation,[status(thm)],[f189,f145]) ).

fof(f6106,plain,
    ! [X0,X1] :
      ( X0 = null_class
      | ~ subclass(X0,complement(X1))
      | ~ member(regular(X0),X1) ),
    inference(resolution,[status(thm)],[f757,f146]) ).

fof(f6270,plain,
    ! [X0] :
      ( complement(X0) = null_class
      | complement(X0) = null_class
      | ~ subclass(complement(X0),X0) ),
    inference(resolution,[status(thm)],[f766,f757]) ).

fof(f6271,plain,
    ! [X0] :
      ( complement(X0) = null_class
      | ~ subclass(complement(X0),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f6270]) ).

fof(f6296,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[f6271,f118]) ).

fof(f16145,plain,
    ! [X0,X1] :
      ( X0 = null_class
      | ~ subclass(X0,complement(X1))
      | X0 = null_class
      | ~ subclass(X0,X1) ),
    inference(resolution,[status(thm)],[f6106,f757]) ).

fof(f16146,plain,
    ! [X0,X1] :
      ( X0 = null_class
      | ~ subclass(X0,complement(X1))
      | ~ subclass(X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f16145]) ).

fof(f19020,plain,
    ! [X0] :
      ( X0 = null_class
      | ~ subclass(X0,null_class)
      | ~ subclass(X0,universal_class) ),
    inference(paramodulation,[status(thm)],[f6296,f16146]) ).

fof(f19021,plain,
    ! [X0] :
      ( X0 = null_class
      | ~ subclass(X0,null_class) ),
    inference(forward_subsumption_resolution,[status(thm)],[f19020,f118]) ).

fof(f20777,plain,
    ! [X0,X1] :
      ( subclass(intersection(X0,X1),X0)
      | subclass(intersection(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f795,f117]) ).

fof(f20778,plain,
    ! [X0,X1] : subclass(intersection(X0,X1),X0),
    inference(duplicate_literals_removal,[status(esa)],[f20777]) ).

fof(f21246,plain,
    ! [X0] : intersection(null_class,X0) = null_class,
    inference(resolution,[status(thm)],[f20778,f19021]) ).

fof(f21281,plain,
    ! [X0,X1] : restrict(null_class,X0,X1) = null_class,
    inference(paramodulation,[status(thm)],[f150,f21246]) ).

fof(f21423,plain,
    ! [X0] : ~ member(X0,domain_of(null_class)),
    inference(resolution,[status(thm)],[f21281,f152]) ).

fof(f21453,plain,
    domain_of(null_class) = null_class,
    inference(resolution,[status(thm)],[f21423,f188]) ).

fof(f21607,plain,
    ! [X0] : ~ member(X0,null_class),
    inference(backward_demodulation,[status(thm)],[f21453,f21423]) ).

fof(f26905,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,regular(X1))
      | X1 = null_class ),
    inference(forward_subsumption_resolution,[status(thm)],[f1463,f21607]) ).

fof(f26932,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | ~ member(X0,X1)
      | singleton(X1) = null_class
      | singleton(X1) = null_class ),
    inference(paramodulation,[status(thm)],[f755,f26905]) ).

fof(f26933,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | ~ member(X0,X1)
      | singleton(X1) = null_class ),
    inference(duplicate_literals_removal,[status(esa)],[f26932]) ).

fof(f27709,plain,
    ! [X0] :
      ( ~ member(regular(singleton(X0)),X0)
      | singleton(X0) = null_class
      | singleton(X0) = null_class ),
    inference(resolution,[status(thm)],[f26933,f188]) ).

fof(f27710,plain,
    ! [X0] :
      ( ~ member(regular(singleton(X0)),X0)
      | singleton(X0) = null_class ),
    inference(duplicate_literals_removal,[status(esa)],[f27709]) ).

fof(f27724,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | singleton(X0) = null_class
      | ~ subclass(singleton(X0),X0) ),
    inference(resolution,[status(thm)],[f27710,f757]) ).

fof(f27725,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | ~ subclass(singleton(X0),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f27724]) ).

fof(f27779,plain,
    singleton(universal_class) = null_class,
    inference(resolution,[status(thm)],[f27725,f118]) ).

fof(f27797,plain,
    ! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,universal_class),
    inference(paramodulation,[status(thm)],[f27779,f130]) ).

fof(f44770,plain,
    ordered_pair(x,universal_class) != ordered_pair(x,universal_class),
    inference(backward_demodulation,[status(thm)],[f27797,f245]) ).

fof(f44771,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f44770]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET511-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.17/0.32  % Computer : n002.cluster.edu
% 0.17/0.32  % Model    : x86_64 x86_64
% 0.17/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.32  % Memory   : 8042.1875MB
% 0.17/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.32  % CPULimit : 300
% 0.17/0.32  % WCLimit  : 300
% 0.17/0.32  % DateTime : Mon Apr 29 22:01:24 EDT 2024
% 0.17/0.32  % CPUTime  : 
% 0.17/0.33  % Drodi V3.6.0
% 95.67/12.41  % Refutation found
% 95.67/12.41  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 95.67/12.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 96.47/12.53  % Elapsed time: 12.192750 seconds
% 96.47/12.53  % CPU time: 96.407254 seconds
% 96.47/12.53  % Total memory used: 509.128 MB
% 96.47/12.53  % Net memory used: 491.562 MB
%------------------------------------------------------------------------------