TSTP Solution File: TOP005-2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 12:49:54 EDT 2023

% Result   : Unsatisfiable 0.16s 0.33s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   56 (  11 unt;   0 def)
%            Number of atoms       :  128 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  141 (  69   ~;  68   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   68 (;  68   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [U,Vf] :
      ( ~ element_of_set(U,union_of_members(Vf))
      | element_of_set(U,f1(Vf,U)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [U,Vf] :
      ( ~ element_of_set(U,union_of_members(Vf))
      | element_of_collection(f1(Vf,U),Vf) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [U,Vf,X] :
      ( ~ element_of_collection(U,top_of_basis(Vf))
      | ~ element_of_set(X,U)
      | element_of_set(X,f10(Vf,U,X)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [U,Vf,X] :
      ( ~ element_of_collection(U,top_of_basis(Vf))
      | ~ element_of_set(X,U)
      | element_of_collection(f10(Vf,U,X),Vf) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [U,Vf,X] :
      ( ~ element_of_collection(U,top_of_basis(Vf))
      | ~ element_of_set(X,U)
      | subset_sets(f10(Vf,U,X),U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [U,Vf] :
      ( element_of_collection(U,top_of_basis(Vf))
      | element_of_set(f11(Vf,U),U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [U,Vf,Uu11] :
      ( element_of_collection(U,top_of_basis(Vf))
      | ~ element_of_set(f11(Vf,U),Uu11)
      | ~ element_of_collection(Uu11,Vf)
      | ~ subset_sets(Uu11,U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,Z] :
      ( ~ subset_sets(X,Y)
      | ~ element_of_collection(Y,Z)
      | subset_sets(X,union_of_members(Z)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y,U] :
      ( ~ subset_collections(X,Y)
      | ~ element_of_collection(U,X)
      | element_of_collection(U,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,negated_conjecture,
    subset_collections(g,top_of_basis(f)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ element_of_collection(union_of_members(g),top_of_basis(f)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ element_of_set(X0,union_of_members(X1))
      | element_of_set(X0,f1(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ~ element_of_set(X0,union_of_members(X1))
      | element_of_collection(f1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ~ element_of_collection(X0,top_of_basis(X1))
      | ~ element_of_set(X2,X0)
      | element_of_set(X2,f10(X1,X0,X2)) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ~ element_of_collection(X0,top_of_basis(X1))
      | ~ element_of_set(X2,X0)
      | element_of_collection(f10(X1,X0,X2),X1) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ element_of_collection(X0,top_of_basis(X1))
      | ~ element_of_set(X2,X0)
      | subset_sets(f10(X1,X0,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( element_of_collection(X0,top_of_basis(X1))
      | element_of_set(f11(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f19,plain,
    ! [U,Uu11] :
      ( ! [Vf] :
          ( element_of_collection(U,top_of_basis(Vf))
          | ~ element_of_set(f11(Vf,U),Uu11)
          | ~ element_of_collection(Uu11,Vf) )
      | ~ subset_sets(Uu11,U) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( element_of_collection(X0,top_of_basis(X1))
      | ~ element_of_set(f11(X1,X0),X2)
      | ~ element_of_collection(X2,X1)
      | ~ subset_sets(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f23,plain,
    ! [X,Z] :
      ( ! [Y] :
          ( ~ subset_sets(X,Y)
          | ~ element_of_collection(Y,Z) )
      | subset_sets(X,union_of_members(Z)) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ~ subset_sets(X0,X1)
      | ~ element_of_collection(X1,X2)
      | subset_sets(X0,union_of_members(X2)) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subset_collections(X,Y)
          | ~ element_of_collection(U,X) )
      | element_of_collection(U,Y) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ subset_collections(X0,X1)
      | ~ element_of_collection(X2,X0)
      | element_of_collection(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    subset_collections(g,top_of_basis(f)),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f28,plain,
    ~ element_of_collection(union_of_members(g),top_of_basis(f)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ element_of_collection(X0,g)
      | element_of_collection(X0,top_of_basis(f)) ),
    inference(resolution,[status(thm)],[f26,f27]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ element_of_set(X0,X1)
      | element_of_set(X0,f10(f,X1,X0))
      | ~ element_of_collection(X1,g) ),
    inference(resolution,[status(thm)],[f15,f29]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ element_of_set(X0,X1)
      | element_of_collection(f10(f,X1,X0),f)
      | ~ element_of_collection(X1,g) ),
    inference(resolution,[status(thm)],[f16,f29]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ element_of_set(X0,X1)
      | subset_sets(f10(f,X1,X0),X1)
      | ~ element_of_collection(X1,g) ),
    inference(resolution,[status(thm)],[f17,f29]) ).

fof(f34,plain,
    ! [X0] :
      ( ~ element_of_set(f11(f,union_of_members(g)),X0)
      | ~ element_of_collection(X0,f)
      | ~ subset_sets(X0,union_of_members(g)) ),
    inference(resolution,[status(thm)],[f20,f28]) ).

fof(f38,plain,
    element_of_set(f11(f,union_of_members(g)),union_of_members(g)),
    inference(resolution,[status(thm)],[f18,f28]) ).

fof(f50,plain,
    element_of_collection(f1(g,f11(f,union_of_members(g))),g),
    inference(resolution,[status(thm)],[f38,f14]) ).

fof(f51,plain,
    element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))),
    inference(resolution,[status(thm)],[f38,f13]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ element_of_set(X0,f1(g,f11(f,union_of_members(g))))
      | subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),X0),f1(g,f11(f,union_of_members(g)))) ),
    inference(resolution,[status(thm)],[f50,f33]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ element_of_set(X0,f1(g,f11(f,union_of_members(g))))
      | element_of_set(X0,f10(f,f1(g,f11(f,union_of_members(g))),X0)) ),
    inference(resolution,[status(thm)],[f50,f31]) ).

fof(f62,plain,
    element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))),
    inference(resolution,[status(thm)],[f53,f51]) ).

fof(f63,plain,
    ( spl0_4
  <=> element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
    introduced(split_symbol_definition) ).

fof(f65,plain,
    ( ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f63]) ).

fof(f66,plain,
    ( spl0_5
  <=> subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
    introduced(split_symbol_definition) ).

fof(f68,plain,
    ( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f66]) ).

fof(f69,plain,
    ( ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
    | ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
    inference(resolution,[status(thm)],[f62,f34]) ).

fof(f70,plain,
    ( ~ spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f69,f63,f66]) ).

fof(f71,plain,
    ( spl0_6
  <=> element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ),
    introduced(split_symbol_definition) ).

fof(f73,plain,
    ( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f71]) ).

fof(f74,plain,
    ( spl0_7
  <=> element_of_collection(f1(g,f11(f,union_of_members(g))),g) ),
    introduced(split_symbol_definition) ).

fof(f76,plain,
    ( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f74]) ).

fof(f77,plain,
    ( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
    | ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f65,f32]) ).

fof(f78,plain,
    ( ~ spl0_6
    | ~ spl0_7
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f77,f71,f74,f63]) ).

fof(f79,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f76,f50]) ).

fof(f80,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f79]) ).

fof(f81,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f73,f51]) ).

fof(f82,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f81]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),X0)
      | ~ element_of_collection(X0,g)
      | spl0_5 ),
    inference(resolution,[status(thm)],[f68,f24]) ).

fof(f112,plain,
    ( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
    | ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
    | spl0_5 ),
    inference(resolution,[status(thm)],[f52,f83]) ).

fof(f113,plain,
    ( ~ spl0_6
    | ~ spl0_7
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f112,f71,f74,f66]) ).

fof(f114,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f70,f78,f80,f82,f113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n019.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 10:34:10 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.31  % Drodi V3.5.1
% 0.16/0.33  % Refutation found
% 0.16/0.33  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37  % Elapsed time: 0.064451 seconds
% 0.16/0.37  % CPU time: 0.059800 seconds
% 0.16/0.37  % Memory used: 1.548 MB
%------------------------------------------------------------------------------