TSTP Solution File: SET065+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:38:56 EDT 2024

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (   9 unt;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   68 (  24   ~;  22   |;  17   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   38 (  34   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,axiom,
    ! [X] :
      ( inductive(X)
    <=> ( member(null_class,X)
        & subclass(image(successor_relation,X),X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ? [X] :
      ( member(X,universal_class)
      & inductive(X)
      & ! [Y] :
          ( inductive(Y)
         => subclass(X,Y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    member(null_class,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ member(null_class,universal_class),
    inference(negated_conjecture,[status(cth)],[f44]) ).

fof(f46,plain,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( ~ member(U,X)
          | member(U,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f47,plain,
    ! [X,Y] :
      ( ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
      & ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ( member(sk0_0(Y,X),X)
          & ~ member(sk0_0(Y,X),Y) ) ) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f53,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f130,plain,
    ! [X] :
      ( ( ~ inductive(X)
        | ( member(null_class,X)
          & subclass(image(successor_relation,X),X) ) )
      & ( inductive(X)
        | ~ member(null_class,X)
        | ~ subclass(image(successor_relation,X),X) ) ),
    inference(NNF_transformation,[status(esa)],[f29]) ).

fof(f131,plain,
    ( ! [X] :
        ( ~ inductive(X)
        | ( member(null_class,X)
          & subclass(image(successor_relation,X),X) ) )
    & ! [X] :
        ( inductive(X)
        | ~ member(null_class,X)
        | ~ subclass(image(successor_relation,X),X) ) ),
    inference(miniscoping,[status(esa)],[f130]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    inference(cnf_transformation,[status(esa)],[f131]) ).

fof(f135,plain,
    ? [X] :
      ( member(X,universal_class)
      & inductive(X)
      & ! [Y] :
          ( ~ inductive(Y)
          | subclass(X,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f136,plain,
    ( member(sk0_1,universal_class)
    & inductive(sk0_1)
    & ! [Y] :
        ( ~ inductive(Y)
        | subclass(sk0_1,Y) ) ),
    inference(skolemization,[status(esa)],[f135]) ).

fof(f138,plain,
    inductive(sk0_1),
    inference(cnf_transformation,[status(esa)],[f136]) ).

fof(f191,plain,
    ~ member(null_class,universal_class),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f53,f50]) ).

fof(f200,plain,
    member(null_class,sk0_1),
    inference(resolution,[status(thm)],[f132,f138]) ).

fof(f206,plain,
    member(null_class,universal_class),
    inference(resolution,[status(thm)],[f198,f200]) ).

fof(f207,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f206,f191]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 21:39:35 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37  % Elapsed time: 0.021405 seconds
% 0.12/0.37  % CPU time: 0.028024 seconds
% 0.12/0.37  % Total memory used: 13.369 MB
% 0.12/0.37  % Net memory used: 13.354 MB
%------------------------------------------------------------------------------