%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU115+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 20:41:02 EDT 2024

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   20 (  12 unt;   0 def)
%            Number of atoms       :   44 (  13 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   32 (   8   ~;   4   |;  18   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :   12 (  11   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f22,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B)
      & relation(B)
      & function(B)
      & one_to_one(B)
      & epsilon_transitive(B)
      & epsilon_connected(B)
      & ordinal(B)
      & natural(B)
      & finite(B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [A] :
      ( empty(A)
     => A = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,conjecture,
    finite_subsets(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,negated_conjecture,
    finite_subsets(empty_set) != singleton(empty_set),
    inference(negated_conjecture,[status(cth)],[f33]) ).

fof(f35,axiom,
    ! [A] :
      ( finite(A)
     => finite_subsets(A) = powerset(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    powerset(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f98,plain,
    ! [A] :
      ( element(sk0_3(A),powerset(A))
      & empty(sk0_3(A))
      & relation(sk0_3(A))
      & function(sk0_3(A))
      & one_to_one(sk0_3(A))
      & epsilon_transitive(sk0_3(A))
      & epsilon_connected(sk0_3(A))
      & ordinal(sk0_3(A))
      & natural(sk0_3(A))
      & finite(sk0_3(A)) ),
    inference(skolemization,[status(esa)],[f22]) ).

fof(f100,plain,
    ! [X0] : empty(sk0_3(X0)),
    inference(cnf_transformation,[status(esa)],[f98]) ).

fof(f108,plain,
    ! [X0] : finite(sk0_3(X0)),
    inference(cnf_transformation,[status(esa)],[f98]) ).

fof(f133,plain,
    ! [A] :
      ( ~ empty(A)
      | A = empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f32]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ empty(X0)
      | X0 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f133]) ).

fof(f135,plain,
    finite_subsets(empty_set) != singleton(empty_set),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f136,plain,
    ! [A] :
      ( ~ finite(A)
      | finite_subsets(A) = powerset(A) ),
    inference(pre_NNF_transformation,[status(esa)],[f35]) ).

fof(f137,plain,
    ! [X0] :
      ( ~ finite(X0)
      | finite_subsets(X0) = powerset(X0) ),
    inference(cnf_transformation,[status(esa)],[f136]) ).

fof(f138,plain,
    powerset(empty_set) = singleton(empty_set),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f139,plain,
    finite_subsets(empty_set) != powerset(empty_set),
    inference(backward_demodulation,[status(thm)],[f138,f135]) ).

fof(f142,plain,
    ~ finite(empty_set),
    inference(resolution,[status(thm)],[f137,f139]) ).

fof(f148,plain,
    ! [X0] : sk0_3(X0) = empty_set,
    inference(resolution,[status(thm)],[f100,f134]) ).

fof(f160,plain,
    finite(empty_set),
    inference(forward_demodulation,[status(thm)],[f148,f108]) ).

fof(f161,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f160,f142]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU115+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n024.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 19:42:51 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.36  % Elapsed time: 0.019322 seconds
% 0.12/0.36  % CPU time: 0.029048 seconds
% 0.12/0.36  % Total memory used: 12.983 MB
% 0.12/0.36  % Net memory used: 12.950 MB
%------------------------------------------------------------------------------