TSTP Solution File: SET787-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET787-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:40:20 EDT 2024

% Result   : Unsatisfiable 0.16s 0.38s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   46 (  11 unt;   0 def)
%            Number of atoms       :   88 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   79 (  37   ~;  37   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   39 (  39   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16,axiom,
    ! [U,V,W] :
      ( ~ member(U,V)
      | member(U,un(W,V)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [U,V,W] :
      ( ~ member(U,V)
      | member(U,un(V,W)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f94,axiom,
    ! [U,V] :
      ( ~ member(U,cons(V,eptset))
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f95,axiom,
    ! [U,V,W] :
      ( ~ member(U,cons(V,W))
      | U = V
      | member(U,W) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f102,axiom,
    ! [U,V] :
      ( ~ member(U,union(V))
      | member(U,unionE_sk1(U,V)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f103,axiom,
    ! [U,V] :
      ( ~ member(U,union(V))
      | member(unionE_sk1(U,V),V) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f148,negated_conjecture,
    member(sk2,union(cons(a,cons(b,eptset)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f149,negated_conjecture,
    ~ member(sk2,un(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f170,plain,
    ! [U,V] :
      ( ~ member(U,V)
      | ! [W] : member(U,un(W,V)) ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f171,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | member(X0,un(X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f170]) ).

fof(f172,plain,
    ! [U,V] :
      ( ~ member(U,V)
      | ! [W] : member(U,un(V,W)) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f173,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | member(X0,un(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f172]) ).

fof(f282,plain,
    ! [X0,X1] :
      ( ~ member(X0,cons(X1,eptset))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f283,plain,
    ! [U,W] :
      ( ! [V] :
          ( ~ member(U,cons(V,W))
          | U = V )
      | member(U,W) ),
    inference(miniscoping,[status(esa)],[f95]) ).

fof(f284,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,cons(X1,X2))
      | X0 = X1
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f283]) ).

fof(f297,plain,
    ! [X0,X1] :
      ( ~ member(X0,union(X1))
      | member(X0,unionE_sk1(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f298,plain,
    ! [X0,X1] :
      ( ~ member(X0,union(X1))
      | member(unionE_sk1(X0,X1),X1) ),
    inference(cnf_transformation,[status(esa)],[f103]) ).

fof(f360,plain,
    member(sk2,union(cons(a,cons(b,eptset)))),
    inference(cnf_transformation,[status(esa)],[f148]) ).

fof(f361,plain,
    ~ member(sk2,un(a,b)),
    inference(cnf_transformation,[status(esa)],[f149]) ).

fof(f368,plain,
    ~ member(sk2,b),
    inference(resolution,[status(thm)],[f171,f361]) ).

fof(f369,plain,
    ~ member(sk2,a),
    inference(resolution,[status(thm)],[f173,f361]) ).

fof(f463,plain,
    member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
    inference(resolution,[status(thm)],[f298,f360]) ).

fof(f477,plain,
    ( spl0_6
  <=> member(sk2,a) ),
    introduced(split_symbol_definition) ).

fof(f478,plain,
    ( member(sk2,a)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f477]) ).

fof(f497,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f478,f369]) ).

fof(f498,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f497]) ).

fof(f509,plain,
    ( spl0_9
  <=> unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
    introduced(split_symbol_definition) ).

fof(f510,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f509]) ).

fof(f512,plain,
    ( spl0_10
  <=> member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    introduced(split_symbol_definition) ).

fof(f513,plain,
    ( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f512]) ).

fof(f515,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    inference(resolution,[status(thm)],[f463,f284]) ).

fof(f516,plain,
    ( spl0_9
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f515,f509,f512]) ).

fof(f518,plain,
    ( spl0_11
  <=> member(sk2,union(cons(a,cons(b,eptset)))) ),
    introduced(split_symbol_definition) ).

fof(f520,plain,
    ( ~ member(sk2,union(cons(a,cons(b,eptset))))
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f518]) ).

fof(f521,plain,
    ( ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(sk2,a)
    | ~ spl0_9 ),
    inference(paramodulation,[status(thm)],[f510,f297]) ).

fof(f522,plain,
    ( ~ spl0_11
    | spl0_6
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f521,f518,f477,f509]) ).

fof(f523,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f520,f360]) ).

fof(f524,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f523]) ).

fof(f525,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
    | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f513,f282]) ).

fof(f536,plain,
    ( spl0_14
  <=> member(sk2,b) ),
    introduced(split_symbol_definition) ).

fof(f537,plain,
    ( member(sk2,b)
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f536]) ).

fof(f539,plain,
    ( ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(sk2,b)
    | ~ spl0_10 ),
    inference(paramodulation,[status(thm)],[f525,f297]) ).

fof(f540,plain,
    ( ~ spl0_11
    | spl0_14
    | ~ spl0_10 ),
    inference(split_clause,[status(thm)],[f539,f518,f536,f512]) ).

fof(f541,plain,
    ( $false
    | ~ spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f537,f368]) ).

fof(f542,plain,
    ~ spl0_14,
    inference(contradiction_clause,[status(thm)],[f541]) ).

fof(f543,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f498,f516,f522,f524,f540,f542]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET787-2 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34  % Computer : n021.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 21:45:55 EDT 2024
% 0.11/0.34  % CPUTime  : 
% 0.16/0.36  % Drodi V3.6.0
% 0.16/0.38  % Refutation found
% 0.16/0.38  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.40  % Elapsed time: 0.049460 seconds
% 0.16/0.40  % CPU time: 0.187599 seconds
% 0.16/0.40  % Total memory used: 51.418 MB
% 0.16/0.40  % Net memory used: 51.211 MB
%------------------------------------------------------------------------------