%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU308+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:36:39 EDT 2023

% Result   : Theorem 0.13s 0.46s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (  12 unt;   0 def)
%            Number of atoms       :   53 (  21 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   42 (  18   ~;  11   |;   5   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :   28 (;  26   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f77,axiom,
    ! [A] :
      ( one_sorted_str(A)
     => cast_as_carrier_subset(A) = the_carrier(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f94,axiom,
    ! [A,B] :
      ( element(B,powerset(A))
     => subset_complement(A,B) = set_difference(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f130,axiom,
    ! [A] :
      ( one_sorted_str(A)
     => element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f291,axiom,
    ! [A,B,C] :
      ( ( element(B,powerset(A))
        & element(C,powerset(A)) )
     => subset_difference(A,B,C) = set_difference(B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f361,conjecture,
    ! [A] :
      ( one_sorted_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f362,negated_conjecture,
    ~ ! [A] :
        ( one_sorted_str(A)
       => ! [B] :
            ( element(B,powerset(the_carrier(A)))
           => subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
    inference(negated_conjecture,[status(cth)],[f361]) ).

fof(f890,plain,
    ! [A] :
      ( ~ one_sorted_str(A)
      | cast_as_carrier_subset(A) = the_carrier(A) ),
    inference(pre_NNF_transformation,[status(esa)],[f77]) ).

fof(f891,plain,
    ! [X0] :
      ( ~ one_sorted_str(X0)
      | cast_as_carrier_subset(X0) = the_carrier(X0) ),
    inference(cnf_transformation,[status(esa)],[f890]) ).

fof(f1019,plain,
    ! [A,B] :
      ( ~ element(B,powerset(A))
      | subset_complement(A,B) = set_difference(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f94]) ).

fof(f1020,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset_complement(X1,X0) = set_difference(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f1019]) ).

fof(f1139,plain,
    ! [A] :
      ( ~ one_sorted_str(A)
      | element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
    inference(pre_NNF_transformation,[status(esa)],[f130]) ).

fof(f1140,plain,
    ! [X0] :
      ( ~ one_sorted_str(X0)
      | element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
    inference(cnf_transformation,[status(esa)],[f1139]) ).

fof(f1624,plain,
    ! [A,B,C] :
      ( ~ element(B,powerset(A))
      | ~ element(C,powerset(A))
      | subset_difference(A,B,C) = set_difference(B,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f291]) ).

fof(f1625,plain,
    ! [X0,X1,X2] :
      ( ~ element(X0,powerset(X1))
      | ~ element(X2,powerset(X1))
      | subset_difference(X1,X0,X2) = set_difference(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f1624]) ).

fof(f2065,plain,
    ? [A] :
      ( one_sorted_str(A)
      & ? [B] :
          ( element(B,powerset(the_carrier(A)))
          & subset_complement(the_carrier(A),B) != subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f362]) ).

fof(f2066,plain,
    ( one_sorted_str(sk0_252)
    & element(sk0_253,powerset(the_carrier(sk0_252)))
    & subset_complement(the_carrier(sk0_252),sk0_253) != subset_difference(the_carrier(sk0_252),cast_as_carrier_subset(sk0_252),sk0_253) ),
    inference(skolemization,[status(esa)],[f2065]) ).

fof(f2067,plain,
    one_sorted_str(sk0_252),
    inference(cnf_transformation,[status(esa)],[f2066]) ).

fof(f2068,plain,
    element(sk0_253,powerset(the_carrier(sk0_252))),
    inference(cnf_transformation,[status(esa)],[f2066]) ).

fof(f2069,plain,
    subset_complement(the_carrier(sk0_252),sk0_253) != subset_difference(the_carrier(sk0_252),cast_as_carrier_subset(sk0_252),sk0_253),
    inference(cnf_transformation,[status(esa)],[f2066]) ).

fof(f2960,plain,
    cast_as_carrier_subset(sk0_252) = the_carrier(sk0_252),
    inference(resolution,[status(thm)],[f891,f2067]) ).

fof(f2961,plain,
    subset_complement(the_carrier(sk0_252),sk0_253) != subset_difference(the_carrier(sk0_252),the_carrier(sk0_252),sk0_253),
    inference(backward_demodulation,[status(thm)],[f2960,f2069]) ).

fof(f2962,plain,
    element(cast_as_carrier_subset(sk0_252),powerset(the_carrier(sk0_252))),
    inference(resolution,[status(thm)],[f1140,f2067]) ).

fof(f2963,plain,
    element(the_carrier(sk0_252),powerset(the_carrier(sk0_252))),
    inference(forward_demodulation,[status(thm)],[f2960,f2962]) ).

fof(f2965,plain,
    subset_complement(the_carrier(sk0_252),sk0_253) = set_difference(the_carrier(sk0_252),sk0_253),
    inference(resolution,[status(thm)],[f1020,f2068]) ).

fof(f3261,plain,
    ! [X0] :
      ( ~ element(X0,powerset(the_carrier(sk0_252)))
      | subset_difference(the_carrier(sk0_252),X0,sk0_253) = set_difference(X0,sk0_253) ),
    inference(resolution,[status(thm)],[f1625,f2068]) ).

fof(f3500,plain,
    subset_difference(the_carrier(sk0_252),the_carrier(sk0_252),sk0_253) = set_difference(the_carrier(sk0_252),sk0_253),
    inference(resolution,[status(thm)],[f3261,f2963]) ).

fof(f3564,plain,
    subset_complement(the_carrier(sk0_252),sk0_253) != set_difference(the_carrier(sk0_252),sk0_253),
    inference(backward_demodulation,[status(thm)],[f3500,f2961]) ).

fof(f3565,plain,
    set_difference(the_carrier(sk0_252),sk0_253) != set_difference(the_carrier(sk0_252),sk0_253),
    inference(forward_demodulation,[status(thm)],[f2965,f3564]) ).

fof(f3566,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f3565]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SEU308+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28  % Computer : n010.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Tue May 30 09:04:37 EDT 2023
% 0.09/0.28  % CPUTime  : 
% 0.13/0.33  % Drodi V3.5.1
% 0.13/0.46  % Refutation found
% 0.13/0.46  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.46  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48  % Elapsed time: 0.194274 seconds
% 0.13/0.48  % CPU time: 1.090899 seconds
% 0.13/0.48  % Memory used: 112.616 MB
%------------------------------------------------------------------------------