TSTP Solution File: SET130-6 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET130-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 12:34:05 EDT 2023

% Result   : Unsatisfiable 9.75s 1.59s
% Output   : CNFRefutation 9.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   81 (  21 unt;   0 def)
%            Number of atoms       :  156 (  32 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  137 (  62   ~;  70   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   95 (;  95   !;   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(f4,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | U = X
      | U = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X] : unordered_pair(X,X) = singleton(X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    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(f66,axiom,
    ! [X] :
      ( X = null_class
      | member(regular(X),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f92,axiom,
    ! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    member(u,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f94,negated_conjecture,
    ~ member(u,set_builder(u,set_builder(y,set_builder(z,null_class)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f95,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f95]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f99,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f103,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f103]) ).

fof(f105,plain,
    ! [X] :
      ( ~ member(X,universal_class)
      | ! [Y] : member(X,unordered_pair(X,Y)) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f105]) ).

fof(f110,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f122,plain,
    ! [Z,X] :
      ( ! [Y] : ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    inference(miniscoping,[status(esa)],[f21]) ).

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

fof(f127,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,complement(X1))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f129,plain,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f169,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f200,plain,
    ! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f201,plain,
    member(u,universal_class),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f202,plain,
    ~ member(u,set_builder(u,set_builder(y,set_builder(z,null_class)))),
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( X0 = null_class
      | ~ subclass(X0,X1)
      | member(regular(X0),X1) ),
    inference(resolution,[status(thm)],[f169,f96]) ).

fof(f234,plain,
    ! [X0] :
      ( ~ member(regular(complement(X0)),X0)
      | complement(X0) = null_class ),
    inference(resolution,[status(thm)],[f127,f169]) ).

fof(f236,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | ~ subclass(X2,complement(X1))
      | ~ member(X0,X2) ),
    inference(resolution,[status(thm)],[f127,f96]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f110,f104]) ).

fof(f249,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f248]) ).

fof(f251,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(X0,singleton(X0)) ),
    inference(paramodulation,[status(thm)],[f110,f106]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( not_subclass_element(singleton(X0),X1) = X0
      | subclass(singleton(X0),X1) ),
    inference(resolution,[status(thm)],[f249,f97]) ).

fof(f562,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f96,f99]) ).

fof(f990,plain,
    ( spl0_78
  <=> singleton(u) = null_class ),
    introduced(split_symbol_definition) ).

fof(f991,plain,
    ( singleton(u) = null_class
    | ~ spl0_78 ),
    inference(component_clause,[status(thm)],[f990]) ).

fof(f995,plain,
    ( spl0_79
  <=> member(u,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f997,plain,
    ( ~ member(u,universal_class)
    | spl0_79 ),
    inference(component_clause,[status(thm)],[f995]) ).

fof(f1000,plain,
    ( $false
    | spl0_79 ),
    inference(forward_subsumption_resolution,[status(thm)],[f997,f201]) ).

fof(f1001,plain,
    spl0_79,
    inference(contradiction_clause,[status(thm)],[f1000]) ).

fof(f1068,plain,
    ! [X0] :
      ( complement(X0) = null_class
      | ~ subclass(complement(X0),X0)
      | complement(X0) = null_class ),
    inference(resolution,[status(thm)],[f224,f234]) ).

fof(f1069,plain,
    ! [X0] :
      ( complement(X0) = null_class
      | ~ subclass(complement(X0),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f1068]) ).

fof(f1081,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[f1069,f99]) ).

fof(f1103,plain,
    ! [X0] :
      ( ~ member(X0,null_class)
      | ~ member(X0,universal_class) ),
    inference(paramodulation,[status(thm)],[f1081,f127]) ).

fof(f1104,plain,
    ! [X0] : ~ member(X0,null_class),
    inference(forward_subsumption_resolution,[status(thm)],[f1103,f562]) ).

fof(f1105,plain,
    ! [X0] :
      ( X0 = null_class
      | ~ subclass(X0,null_class) ),
    inference(resolution,[status(thm)],[f1104,f224]) ).

fof(f1184,plain,
    ( spl0_97
  <=> member(u,null_class) ),
    introduced(split_symbol_definition) ).

fof(f1185,plain,
    ( member(u,null_class)
    | ~ spl0_97 ),
    inference(component_clause,[status(thm)],[f1184]) ).

fof(f1203,plain,
    ( ~ member(u,universal_class)
    | member(u,null_class)
    | ~ spl0_78 ),
    inference(paramodulation,[status(thm)],[f991,f251]) ).

fof(f1204,plain,
    ( ~ spl0_79
    | spl0_97
    | ~ spl0_78 ),
    inference(split_clause,[status(thm)],[f1203,f995,f1184,f990]) ).

fof(f1329,plain,
    ( $false
    | ~ spl0_97 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1185,f1104]) ).

fof(f1330,plain,
    ~ spl0_97,
    inference(contradiction_clause,[status(thm)],[f1329]) ).

fof(f3126,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | ~ subclass(X1,null_class)
      | ~ member(X0,X1) ),
    inference(paramodulation,[status(thm)],[f1081,f236]) ).

fof(f3127,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,null_class)
      | ~ member(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f3126,f562]) ).

fof(f3130,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | not_subclass_element(singleton(X1),null_class) = X1 ),
    inference(resolution,[status(thm)],[f3127,f255]) ).

fof(f5929,plain,
    ! [X0] :
      ( not_subclass_element(singleton(X0),null_class) = X0
      | ~ member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f3130,f251]) ).

fof(f5971,plain,
    ! [X0,X1] :
      ( not_subclass_element(singleton(X0),null_class) = X0
      | ~ member(X0,X1) ),
    inference(resolution,[status(thm)],[f5929,f562]) ).

fof(f8519,plain,
    not_subclass_element(singleton(u),null_class) = u,
    inference(resolution,[status(thm)],[f201,f5971]) ).

fof(f8526,plain,
    ( spl0_386
  <=> subclass(singleton(u),null_class) ),
    introduced(split_symbol_definition) ).

fof(f8527,plain,
    ( subclass(singleton(u),null_class)
    | ~ spl0_386 ),
    inference(component_clause,[status(thm)],[f8526]) ).

fof(f8536,plain,
    ( spl0_388
  <=> member(u,singleton(u)) ),
    introduced(split_symbol_definition) ).

fof(f8537,plain,
    ( member(u,singleton(u))
    | ~ spl0_388 ),
    inference(component_clause,[status(thm)],[f8536]) ).

fof(f8539,plain,
    ( member(u,singleton(u))
    | subclass(singleton(u),null_class) ),
    inference(paramodulation,[status(thm)],[f8519,f97]) ).

fof(f8540,plain,
    ( spl0_388
    | spl0_386 ),
    inference(split_clause,[status(thm)],[f8539,f8536,f8526]) ).

fof(f11769,plain,
    ! [X0] :
      ( member(u,complement(X0))
      | member(u,X0) ),
    inference(resolution,[status(thm)],[f128,f201]) ).

fof(f11822,plain,
    ( singleton(u) = null_class
    | ~ spl0_386 ),
    inference(resolution,[status(thm)],[f8527,f1105]) ).

fof(f11823,plain,
    ( spl0_78
    | ~ spl0_386 ),
    inference(split_clause,[status(thm)],[f11822,f990,f8526]) ).

fof(f11984,plain,
    ! [X0,X1] :
      ( member(u,union(X0,X1))
      | member(u,intersection(complement(X0),complement(X1))) ),
    inference(paramodulation,[status(thm)],[f129,f11769]) ).

fof(f12056,plain,
    ! [X0,X1] :
      ( member(u,union(X0,X1))
      | member(u,complement(X0)) ),
    inference(resolution,[status(thm)],[f11984,f123]) ).

fof(f12182,plain,
    ! [X0,X1] :
      ( member(u,set_builder(X0,X1))
      | member(u,complement(singleton(X0))) ),
    inference(paramodulation,[status(thm)],[f200,f12056]) ).

fof(f13111,plain,
    member(u,complement(singleton(u))),
    inference(resolution,[status(thm)],[f12182,f202]) ).

fof(f13155,plain,
    ~ member(u,singleton(u)),
    inference(resolution,[status(thm)],[f13111,f127]) ).

fof(f13156,plain,
    ( $false
    | ~ spl0_388 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13155,f8537]) ).

fof(f13157,plain,
    ~ spl0_388,
    inference(contradiction_clause,[status(thm)],[f13156]) ).

fof(f13158,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1001,f1204,f1330,f8540,f11823,f13157]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET130-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33  % Computer : n011.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue May 30 10:21:42 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  % Drodi V3.5.1
% 9.75/1.59  % Refutation found
% 9.75/1.59  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.75/1.59  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.75/1.62  % Elapsed time: 1.278751 seconds
% 9.75/1.62  % CPU time: 10.014845 seconds
% 9.75/1.62  % Memory used: 156.399 MB
%------------------------------------------------------------------------------