TSTP Solution File: SET287-6 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET287-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 12:34:23 EDT 2023

% Result   : Unsatisfiable 3.75s 0.89s
% Output   : CNFRefutation 3.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   87 (  18 unt;   0 def)
%            Number of atoms       :  163 (  47 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  136 (  60   ~;  72   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :  149 (; 149   !;   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(f4,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | 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(f22,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,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(f113,negated_conjecture,
    subclass(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f114,negated_conjecture,
    domain_of(intersection(complement(y),x)) != null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f115,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f116,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f119,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f142,plain,
    ! [Z,X] :
      ( ! [Y] : ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f143,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f142]) ).

fof(f144,plain,
    ! [Z,Y] :
      ( ! [X] : ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    inference(miniscoping,[status(esa)],[f22]) ).

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

fof(f147,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f151,plain,
    ! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( restrict(X0,singleton(X1),universal_class) != null_class
      | ~ member(X1,domain_of(X0)) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f189,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f246,plain,
    subclass(x,y),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f247,plain,
    domain_of(intersection(complement(y),x)) != null_class,
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f252,plain,
    ! [X0] :
      ( ~ member(X0,x)
      | member(X0,y) ),
    inference(resolution,[status(thm)],[f116,f246]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f116,f119]) ).

fof(f264,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(X0,X1),X2)
      | member(not_subclass_element(intersection(X0,X1),X2),X1) ),
    inference(resolution,[status(thm)],[f117,f145]) ).

fof(f265,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(X0,X1),X2)
      | member(not_subclass_element(intersection(X0,X1),X2),X0) ),
    inference(resolution,[status(thm)],[f117,f143]) ).

fof(f266,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),X1)
      | ~ member(not_subclass_element(complement(X0),X1),X0) ),
    inference(resolution,[status(thm)],[f117,f147]) ).

fof(f269,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),universal_class) ),
    inference(resolution,[status(thm)],[f117,f253]) ).

fof(f927,plain,
    ! [X0] :
      ( subclass(complement(universal_class),X0)
      | subclass(complement(universal_class),X0) ),
    inference(resolution,[status(thm)],[f269,f266]) ).

fof(f928,plain,
    ! [X0] : subclass(complement(universal_class),X0),
    inference(duplicate_literals_removal,[status(esa)],[f927]) ).

fof(f946,plain,
    ! [X0] :
      ( ~ subclass(X0,complement(universal_class))
      | complement(universal_class) = X0 ),
    inference(resolution,[status(thm)],[f928,f122]) ).

fof(f955,plain,
    ! [X0,X1] :
      ( subclass(intersection(X0,x),X1)
      | member(not_subclass_element(intersection(X0,x),X1),y) ),
    inference(resolution,[status(thm)],[f264,f252]) ).

fof(f962,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(complement(X0),X1),X2)
      | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ),
    inference(resolution,[status(thm)],[f265,f147]) ).

fof(f1278,plain,
    ! [X0] :
      ( subclass(intersection(complement(y),x),X0)
      | subclass(intersection(complement(y),x),X0) ),
    inference(resolution,[status(thm)],[f962,f955]) ).

fof(f1279,plain,
    ! [X0] : subclass(intersection(complement(y),x),X0),
    inference(duplicate_literals_removal,[status(esa)],[f1278]) ).

fof(f1323,plain,
    complement(universal_class) = intersection(complement(y),x),
    inference(resolution,[status(thm)],[f1279,f946]) ).

fof(f1352,plain,
    domain_of(complement(universal_class)) != null_class,
    inference(backward_demodulation,[status(thm)],[f1323,f247]) ).

fof(f1605,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = null_class
      | member(regular(intersection(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f189,f145]) ).

fof(f1615,plain,
    ! [X0] :
      ( complement(X0) = null_class
      | ~ member(regular(complement(X0)),X0) ),
    inference(resolution,[status(thm)],[f189,f147]) ).

fof(f1895,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,restrict(X1,X2,X3))
      | member(X0,cross_product(X2,X3)) ),
    inference(paramodulation,[status(thm)],[f151,f145]) ).

fof(f1896,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,restrict(X1,X2,X3))
      | member(X0,X1) ),
    inference(paramodulation,[status(thm)],[f151,f143]) ).

fof(f2238,plain,
    ( spl0_26
  <=> null_class = null_class ),
    introduced(split_symbol_definition) ).

fof(f2240,plain,
    ( null_class != null_class
    | spl0_26 ),
    inference(component_clause,[status(thm)],[f2238]) ).

fof(f2287,plain,
    ! [X0] :
      ( restrict(X0,singleton(regular(domain_of(X0))),universal_class) != null_class
      | domain_of(X0) = null_class ),
    inference(resolution,[status(thm)],[f153,f189]) ).

fof(f2663,plain,
    ! [X0,X1,X2] :
      ( member(regular(restrict(X0,X1,X2)),cross_product(X1,X2))
      | restrict(X0,X1,X2) = null_class ),
    inference(resolution,[status(thm)],[f1895,f189]) ).

fof(f2865,plain,
    ! [X0,X1,X2] :
      ( member(regular(restrict(X0,X1,X2)),X0)
      | restrict(X0,X1,X2) = null_class ),
    inference(resolution,[status(thm)],[f1896,f189]) ).

fof(f3001,plain,
    ! [X0,X1,X2,X3,X4] :
      ( restrict(restrict(X0,X1,X2),X3,X4) = null_class
      | member(regular(restrict(restrict(X0,X1,X2),X3,X4)),X0) ),
    inference(resolution,[status(thm)],[f2865,f1896]) ).

fof(f3002,plain,
    ! [X0,X1,X2,X3,X4] :
      ( restrict(restrict(X0,X1,X2),X3,X4) = null_class
      | member(regular(restrict(restrict(X0,X1,X2),X3,X4)),cross_product(X1,X2)) ),
    inference(resolution,[status(thm)],[f2865,f1895]) ).

fof(f3537,plain,
    ( spl0_74
  <=> intersection(complement(y),x) = null_class ),
    introduced(split_symbol_definition) ).

fof(f3538,plain,
    ( intersection(complement(y),x) = null_class
    | ~ spl0_74 ),
    inference(component_clause,[status(thm)],[f3537]) ).

fof(f3542,plain,
    ( spl0_75
  <=> member(regular(complement(universal_class)),x) ),
    introduced(split_symbol_definition) ).

fof(f3543,plain,
    ( member(regular(complement(universal_class)),x)
    | ~ spl0_75 ),
    inference(component_clause,[status(thm)],[f3542]) ).

fof(f3545,plain,
    ( intersection(complement(y),x) = null_class
    | member(regular(complement(universal_class)),x) ),
    inference(paramodulation,[status(thm)],[f1323,f1605]) ).

fof(f3546,plain,
    ( spl0_74
    | spl0_75 ),
    inference(split_clause,[status(thm)],[f3545,f3537,f3542]) ).

fof(f3550,plain,
    ( complement(universal_class) = null_class
    | ~ spl0_74 ),
    inference(forward_demodulation,[status(thm)],[f1323,f3538]) ).

fof(f3602,plain,
    ( domain_of(null_class) != null_class
    | ~ spl0_74 ),
    inference(backward_demodulation,[status(thm)],[f3550,f1352]) ).

fof(f4538,plain,
    ! [X0,X1,X2,X3,X4] :
      ( restrict(restrict(complement(X0),X1,X2),X3,X4) = null_class
      | ~ member(regular(restrict(restrict(complement(X0),X1,X2),X3,X4)),X0) ),
    inference(resolution,[status(thm)],[f3001,f147]) ).

fof(f5536,plain,
    ! [X0,X1,X2,X3] :
      ( restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1) = null_class
      | restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1) = null_class ),
    inference(resolution,[status(thm)],[f4538,f2663]) ).

fof(f5537,plain,
    ! [X0,X1,X2,X3] : restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1) = null_class,
    inference(duplicate_literals_removal,[status(esa)],[f5536]) ).

fof(f5556,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( restrict(restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1),X4,X5) = null_class
      | member(regular(restrict(null_class,X4,X5)),cross_product(X0,X1)) ),
    inference(paramodulation,[status(thm)],[f5537,f3002]) ).

fof(f5557,plain,
    ! [X0,X1,X2,X3] :
      ( restrict(null_class,X0,X1) = null_class
      | member(regular(restrict(null_class,X0,X1)),cross_product(X2,X3)) ),
    inference(forward_demodulation,[status(thm)],[f5537,f5556]) ).

fof(f5560,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( restrict(restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1),X4,X5) = null_class
      | member(regular(restrict(null_class,X4,X5)),restrict(complement(cross_product(X0,X1)),X2,X3)) ),
    inference(paramodulation,[status(thm)],[f5537,f3001]) ).

fof(f5561,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( restrict(null_class,X0,X1) = null_class
      | member(regular(restrict(null_class,X0,X1)),restrict(complement(cross_product(X2,X3)),X4,X5)) ),
    inference(forward_demodulation,[status(thm)],[f5537,f5560]) ).

fof(f5653,plain,
    ! [X0,X1,X2,X3] :
      ( restrict(null_class,X0,X1) = null_class
      | member(regular(restrict(null_class,X0,X1)),complement(cross_product(X2,X3))) ),
    inference(resolution,[status(thm)],[f5561,f1896]) ).

fof(f5662,plain,
    ! [X0,X1,X2,X3] :
      ( restrict(null_class,X0,X1) = null_class
      | ~ member(regular(restrict(null_class,X0,X1)),cross_product(X2,X3)) ),
    inference(resolution,[status(thm)],[f5653,f147]) ).

fof(f5663,plain,
    ! [X0,X1] : restrict(null_class,X0,X1) = null_class,
    inference(forward_subsumption_resolution,[status(thm)],[f5662,f5557]) ).

fof(f5697,plain,
    domain_of(null_class) = null_class,
    inference(resolution,[status(thm)],[f5663,f2287]) ).

fof(f5703,plain,
    ( spl0_127
  <=> domain_of(null_class) = null_class ),
    introduced(split_symbol_definition) ).

fof(f5704,plain,
    ( domain_of(null_class) = null_class
    | ~ spl0_127 ),
    inference(component_clause,[status(thm)],[f5703]) ).

fof(f5706,plain,
    ( null_class != null_class
    | domain_of(null_class) = null_class ),
    inference(paramodulation,[status(thm)],[f5663,f2287]) ).

fof(f5707,plain,
    ( ~ spl0_26
    | spl0_127 ),
    inference(split_clause,[status(thm)],[f5706,f2238,f5703]) ).

fof(f5864,plain,
    ( member(regular(complement(universal_class)),universal_class)
    | ~ spl0_75 ),
    inference(resolution,[status(thm)],[f3543,f253]) ).

fof(f6010,plain,
    ( complement(universal_class) = null_class
    | ~ spl0_75 ),
    inference(resolution,[status(thm)],[f5864,f1615]) ).

fof(f6049,plain,
    ( domain_of(null_class) != null_class
    | ~ spl0_75 ),
    inference(backward_demodulation,[status(thm)],[f6010,f1352]) ).

fof(f6690,plain,
    ( $false
    | ~ spl0_74 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5697,f3602]) ).

fof(f6691,plain,
    ~ spl0_74,
    inference(contradiction_clause,[status(thm)],[f6690]) ).

fof(f7229,plain,
    ( null_class != null_class
    | ~ spl0_127
    | ~ spl0_75 ),
    inference(forward_demodulation,[status(thm)],[f5704,f6049]) ).

fof(f7230,plain,
    ( $false
    | ~ spl0_127
    | ~ spl0_75 ),
    inference(trivial_equality_resolution,[status(esa)],[f7229]) ).

fof(f7231,plain,
    ( ~ spl0_127
    | ~ spl0_75 ),
    inference(contradiction_clause,[status(thm)],[f7230]) ).

fof(f7238,plain,
    ( $false
    | spl0_26 ),
    inference(trivial_equality_resolution,[status(esa)],[f2240]) ).

fof(f7239,plain,
    spl0_26,
    inference(contradiction_clause,[status(thm)],[f7238]) ).

fof(f7240,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f3546,f5707,f6691,f7231,f7239]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET287-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n022.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue May 30 10:14:12 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.34  % Drodi V3.5.1
% 3.75/0.89  % Refutation found
% 3.75/0.89  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.75/0.89  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.75/0.92  % Elapsed time: 0.585293 seconds
% 3.75/0.92  % CPU time: 4.133341 seconds
% 3.75/0.92  % Memory used: 92.356 MB
%------------------------------------------------------------------------------