TSTP Solution File: SET075-6 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 20:38:59 EDT 2024

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   70 (  23 unt;   0 def)
%            Number of atoms       :  122 (  10 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   92 (  40   ~;  45   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   59 (  59   !;   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(f4,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [Y,X] :
      ( ~ member(Y,universal_class)
      | member(Y,unordered_pair(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,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(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f66,axiom,
    ! [X] :
      ( X = null_class
      | member(regular(X),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f92,negated_conjecture,
    member(ordered_pair(x,y),cross_product(u,v)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    unordered_pair(x,y) = null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f94,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f98,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f106,plain,
    ! [Y] :
      ( ~ member(Y,universal_class)
      | ! [X] : member(Y,unordered_pair(X,Y)) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f106]) ).

fof(f108,plain,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f111,plain,
    ! [U,X] :
      ( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f112,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f111]) ).

fof(f113,plain,
    ! [V,Y] :
      ( ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f114,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f152,plain,
    inductive(omega),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f168,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f199,plain,
    member(ordered_pair(x,y),cross_product(u,v)),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f200,plain,
    unordered_pair(x,y) = null_class,
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f204,plain,
    member(null_class,universal_class),
    inference(paramodulation,[status(thm)],[f200,f108]) ).

fof(f209,plain,
    ( spl0_0
  <=> member(x,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f211,plain,
    ( ~ member(x,universal_class)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f209]) ).

fof(f218,plain,
    ( spl0_2
  <=> member(y,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f220,plain,
    ( ~ member(y,universal_class)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f218]) ).

fof(f221,plain,
    ( spl0_3
  <=> member(y,null_class) ),
    introduced(split_symbol_definition) ).

fof(f222,plain,
    ( member(y,null_class)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f221]) ).

fof(f224,plain,
    ( ~ member(y,universal_class)
    | member(y,null_class) ),
    inference(paramodulation,[status(thm)],[f200,f107]) ).

fof(f225,plain,
    ( ~ spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f224,f218,f221]) ).

fof(f227,plain,
    member(x,u),
    inference(resolution,[status(thm)],[f112,f199]) ).

fof(f228,plain,
    member(y,v),
    inference(resolution,[status(thm)],[f114,f199]) ).

fof(f261,plain,
    ! [X0] :
      ( ~ subclass(v,X0)
      | member(y,X0) ),
    inference(resolution,[status(thm)],[f95,f228]) ).

fof(f262,plain,
    ! [X0] :
      ( ~ subclass(u,X0)
      | member(x,X0) ),
    inference(resolution,[status(thm)],[f95,f227]) ).

fof(f281,plain,
    member(y,universal_class),
    inference(resolution,[status(thm)],[f261,f98]) ).

fof(f282,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f281,f220]) ).

fof(f283,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f282]) ).

fof(f285,plain,
    member(x,universal_class),
    inference(resolution,[status(thm)],[f262,f98]) ).

fof(f286,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f285,f211]) ).

fof(f287,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f286]) ).

fof(f336,plain,
    ( spl0_12
  <=> member(unordered_pair(x,null_class),universal_class) ),
    introduced(split_symbol_definition) ).

fof(f338,plain,
    ( ~ member(unordered_pair(x,null_class),universal_class)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f336]) ).

fof(f351,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f338,f108]) ).

fof(f352,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f351]) ).

fof(f405,plain,
    ! [X0] :
      ( ~ member(regular(complement(X0)),X0)
      | complement(X0) = null_class ),
    inference(resolution,[status(thm)],[f126,f168]) ).

fof(f712,plain,
    ( spl0_50
  <=> inductive(omega) ),
    introduced(split_symbol_definition) ).

fof(f714,plain,
    ( ~ inductive(omega)
    | spl0_50 ),
    inference(component_clause,[status(thm)],[f712]) ).

fof(f724,plain,
    ( $false
    | spl0_50 ),
    inference(forward_subsumption_resolution,[status(thm)],[f714,f152]) ).

fof(f725,plain,
    spl0_50,
    inference(contradiction_clause,[status(thm)],[f724]) ).

fof(f787,plain,
    ( spl0_56
  <=> member(null_class,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f789,plain,
    ( ~ member(null_class,universal_class)
    | spl0_56 ),
    inference(component_clause,[status(thm)],[f787]) ).

fof(f796,plain,
    ( $false
    | spl0_56 ),
    inference(forward_subsumption_resolution,[status(thm)],[f789,f204]) ).

fof(f797,plain,
    spl0_56,
    inference(contradiction_clause,[status(thm)],[f796]) ).

fof(f1239,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | member(regular(X0),X1)
      | X0 = null_class ),
    inference(resolution,[status(thm)],[f95,f168]) ).

fof(f1630,plain,
    ! [X0] :
      ( ~ subclass(complement(X0),X0)
      | complement(X0) = null_class
      | complement(X0) = null_class ),
    inference(resolution,[status(thm)],[f1239,f405]) ).

fof(f1631,plain,
    ! [X0] :
      ( ~ subclass(complement(X0),X0)
      | complement(X0) = null_class ),
    inference(duplicate_literals_removal,[status(esa)],[f1630]) ).

fof(f2154,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[f1631,f98]) ).

fof(f2166,plain,
    ! [X0] :
      ( ~ member(X0,null_class)
      | ~ member(X0,universal_class) ),
    inference(paramodulation,[status(thm)],[f2154,f126]) ).

fof(f2167,plain,
    ( spl0_172
  <=> subclass(universal_class,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f2169,plain,
    ( ~ subclass(universal_class,universal_class)
    | spl0_172 ),
    inference(component_clause,[status(thm)],[f2167]) ).

fof(f2174,plain,
    ( $false
    | spl0_172 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2169,f98]) ).

fof(f2175,plain,
    spl0_172,
    inference(contradiction_clause,[status(thm)],[f2174]) ).

fof(f2192,plain,
    ( ~ member(y,universal_class)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f2166,f222]) ).

fof(f2193,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f2192,f218,f221]) ).

fof(f2194,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f225,f283,f287,f352,f725,f797,f2175,f2193]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34  % Computer : n008.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit : 300
% 0.11/0.34  % WCLimit  : 300
% 0.11/0.34  % DateTime : Mon Apr 29 21:41:27 EDT 2024
% 0.11/0.35  % CPUTime  : 
% 0.11/0.36  % Drodi V3.6.0
% 0.18/0.44  % Refutation found
% 0.18/0.44  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.46  % Elapsed time: 0.099346 seconds
% 0.18/0.46  % CPU time: 0.676175 seconds
% 0.18/0.46  % Total memory used: 73.306 MB
% 0.18/0.46  % Net memory used: 72.469 MB
%------------------------------------------------------------------------------