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SInE---0.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU394+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 08:14:36 EST 2010

% Result   : Theorem 0.42s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   65 (  15 unt;   0 def)
%            Number of atoms       :  275 (  28 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  345 ( 135   ~; 131   |;  61   &)
%                                         (   2 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   71 (   1 sgn  49   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',t65_zfmisc_1) ).

fof(18,axiom,
    ( empty(empty_set)
    & relation(empty_set)
    & relation_empty_yielding(empty_set) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',fc12_relat_1) ).

fof(62,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
         => set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',t14_yellow19) ).

fof(64,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',t7_boole) ).

fof(66,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(cast_as_carrier_subset(X1)) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',fc2_pre_topc) ).

fof(71,axiom,
    ! [X1] :
      ( ~ empty(X1)
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(X1))
            & upper_relstr_subset(X2,boole_POSet(X1))
            & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
            & element(X2,powerset(the_carrier(boole_POSet(X1)))) )
         => ! [X3] :
              ~ ( in(X3,X2)
                & empty(X3) ) ) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',t2_yellow19) ).

fof(122,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
            & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
         => X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    file('/tmp/tmpm2d8iW/sel_SEU394+1.p_1',t15_yellow19) ).

fof(128,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
              & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
              & proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
              & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
           => X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    inference(assume_negation,[status(cth)],[122]) ).

fof(129,plain,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).

fof(156,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
         => set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    inference(fof_simplification,[status(thm)],[62,theory(equality)]) ).

fof(158,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(cast_as_carrier_subset(X1)) ),
    inference(fof_simplification,[status(thm)],[66,theory(equality)]) ).

fof(162,plain,
    ! [X1] :
      ( ~ empty(X1)
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(X1))
            & upper_relstr_subset(X2,boole_POSet(X1))
            & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
            & element(X2,powerset(the_carrier(boole_POSet(X1)))) )
         => ! [X3] :
              ~ ( in(X3,X2)
                & empty(X3) ) ) ),
    inference(fof_simplification,[status(thm)],[71,theory(equality)]) ).

fof(193,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
              & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
              & proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
              & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
           => X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    inference(fof_simplification,[status(thm)],[128,theory(equality)]) ).

fof(198,plain,
    ! [X1,X2] :
      ( ( set_difference(X1,singleton(X2)) != X1
        | ~ in(X2,X1) )
      & ( in(X2,X1)
        | set_difference(X1,singleton(X2)) = X1 ) ),
    inference(fof_nnf,[status(thm)],[129]) ).

fof(199,plain,
    ! [X3,X4] :
      ( ( set_difference(X3,singleton(X4)) != X3
        | ~ in(X4,X3) )
      & ( in(X4,X3)
        | set_difference(X3,singleton(X4)) = X3 ) ),
    inference(variable_rename,[status(thm)],[198]) ).

cnf(200,plain,
    ( set_difference(X1,singleton(X2)) = X1
    | in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[199]) ).

cnf(285,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(509,plain,
    ! [X1] :
      ( empty_carrier(X1)
      | ~ one_sorted_str(X1)
      | ! [X2] :
          ( empty(X2)
          | ~ filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
          | ~ upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
          | ~ element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
          | set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    inference(fof_nnf,[status(thm)],[156]) ).

fof(510,plain,
    ! [X3] :
      ( empty_carrier(X3)
      | ~ one_sorted_str(X3)
      | ! [X4] :
          ( empty(X4)
          | ~ filtered_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
          | ~ upper_relstr_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
          | ~ element(X4,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
          | set_difference(X4,singleton(empty_set)) = filter_of_net_str(X3,net_of_bool_filter(X3,cast_as_carrier_subset(X3),X4)) ) ),
    inference(variable_rename,[status(thm)],[509]) ).

fof(511,plain,
    ! [X3,X4] :
      ( empty(X4)
      | ~ filtered_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
      | ~ upper_relstr_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
      | ~ element(X4,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
      | set_difference(X4,singleton(empty_set)) = filter_of_net_str(X3,net_of_bool_filter(X3,cast_as_carrier_subset(X3),X4))
      | empty_carrier(X3)
      | ~ one_sorted_str(X3) ),
    inference(shift_quantors,[status(thm)],[510]) ).

cnf(512,plain,
    ( empty_carrier(X1)
    | set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2))
    | empty(X2)
    | ~ one_sorted_str(X1)
    | ~ element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
    | ~ upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
    | ~ filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1))) ),
    inference(split_conjunct,[status(thm)],[511]) ).

fof(514,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | ~ empty(X2) ),
    inference(fof_nnf,[status(thm)],[64]) ).

fof(515,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ empty(X4) ),
    inference(variable_rename,[status(thm)],[514]) ).

cnf(516,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[515]) ).

fof(520,plain,
    ! [X1] :
      ( empty_carrier(X1)
      | ~ one_sorted_str(X1)
      | ~ empty(cast_as_carrier_subset(X1)) ),
    inference(fof_nnf,[status(thm)],[158]) ).

fof(521,plain,
    ! [X2] :
      ( empty_carrier(X2)
      | ~ one_sorted_str(X2)
      | ~ empty(cast_as_carrier_subset(X2)) ),
    inference(variable_rename,[status(thm)],[520]) ).

cnf(522,plain,
    ( empty_carrier(X1)
    | ~ empty(cast_as_carrier_subset(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[521]) ).

fof(542,plain,
    ! [X1] :
      ( empty(X1)
      | ! [X2] :
          ( empty(X2)
          | ~ filtered_subset(X2,boole_POSet(X1))
          | ~ upper_relstr_subset(X2,boole_POSet(X1))
          | ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
          | ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
          | ! [X3] :
              ( ~ in(X3,X2)
              | ~ empty(X3) ) ) ),
    inference(fof_nnf,[status(thm)],[162]) ).

fof(543,plain,
    ! [X4] :
      ( empty(X4)
      | ! [X5] :
          ( empty(X5)
          | ~ filtered_subset(X5,boole_POSet(X4))
          | ~ upper_relstr_subset(X5,boole_POSet(X4))
          | ~ proper_element(X5,powerset(the_carrier(boole_POSet(X4))))
          | ~ element(X5,powerset(the_carrier(boole_POSet(X4))))
          | ! [X6] :
              ( ~ in(X6,X5)
              | ~ empty(X6) ) ) ),
    inference(variable_rename,[status(thm)],[542]) ).

fof(544,plain,
    ! [X4,X5,X6] :
      ( ~ in(X6,X5)
      | ~ empty(X6)
      | empty(X5)
      | ~ filtered_subset(X5,boole_POSet(X4))
      | ~ upper_relstr_subset(X5,boole_POSet(X4))
      | ~ proper_element(X5,powerset(the_carrier(boole_POSet(X4))))
      | ~ element(X5,powerset(the_carrier(boole_POSet(X4))))
      | empty(X4) ),
    inference(shift_quantors,[status(thm)],[543]) ).

cnf(545,plain,
    ( empty(X1)
    | empty(X2)
    | ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
    | ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
    | ~ upper_relstr_subset(X2,boole_POSet(X1))
    | ~ filtered_subset(X2,boole_POSet(X1))
    | ~ empty(X3)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[544]) ).

fof(834,negated_conjecture,
    ? [X1] :
      ( ~ empty_carrier(X1)
      & one_sorted_str(X1)
      & ? [X2] :
          ( ~ empty(X2)
          & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
          & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
          & proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
          & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
          & X2 != filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    inference(fof_nnf,[status(thm)],[193]) ).

fof(835,negated_conjecture,
    ? [X3] :
      ( ~ empty_carrier(X3)
      & one_sorted_str(X3)
      & ? [X4] :
          ( ~ empty(X4)
          & filtered_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
          & upper_relstr_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
          & proper_element(X4,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
          & element(X4,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
          & X4 != filter_of_net_str(X3,net_of_bool_filter(X3,cast_as_carrier_subset(X3),X4)) ) ),
    inference(variable_rename,[status(thm)],[834]) ).

fof(836,negated_conjecture,
    ( ~ empty_carrier(esk39_0)
    & one_sorted_str(esk39_0)
    & ~ empty(esk40_0)
    & filtered_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    & upper_relstr_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    & proper_element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    & element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    & esk40_0 != filter_of_net_str(esk39_0,net_of_bool_filter(esk39_0,cast_as_carrier_subset(esk39_0),esk40_0)) ),
    inference(skolemize,[status(esa)],[835]) ).

cnf(837,negated_conjecture,
    esk40_0 != filter_of_net_str(esk39_0,net_of_bool_filter(esk39_0,cast_as_carrier_subset(esk39_0),esk40_0)),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(838,negated_conjecture,
    element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0))))),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(839,negated_conjecture,
    proper_element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0))))),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(840,negated_conjecture,
    upper_relstr_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0))),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(841,negated_conjecture,
    filtered_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0))),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(842,negated_conjecture,
    ~ empty(esk40_0),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(843,negated_conjecture,
    one_sorted_str(esk39_0),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(844,negated_conjecture,
    ~ empty_carrier(esk39_0),
    inference(split_conjunct,[status(thm)],[836]) ).

cnf(1282,plain,
    ( empty(X1)
    | ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
    | ~ upper_relstr_subset(X2,boole_POSet(X1))
    | ~ filtered_subset(X2,boole_POSet(X1))
    | ~ empty(X3)
    | ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
    | ~ in(X3,X2) ),
    inference(csr,[status(thm)],[545,516]) ).

cnf(1283,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | ~ upper_relstr_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    | ~ filtered_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    | ~ empty(X1)
    | ~ element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    | ~ in(X1,esk40_0) ),
    inference(spm,[status(thm)],[1282,839,theory(equality)]) ).

cnf(1285,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | $false
    | ~ filtered_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    | ~ empty(X1)
    | ~ element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    | ~ in(X1,esk40_0) ),
    inference(rw,[status(thm)],[1283,840,theory(equality)]) ).

cnf(1286,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | $false
    | $false
    | ~ empty(X1)
    | ~ element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    | ~ in(X1,esk40_0) ),
    inference(rw,[status(thm)],[1285,841,theory(equality)]) ).

cnf(1287,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | $false
    | $false
    | ~ empty(X1)
    | $false
    | ~ in(X1,esk40_0) ),
    inference(rw,[status(thm)],[1286,838,theory(equality)]) ).

cnf(1288,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | ~ empty(X1)
    | ~ in(X1,esk40_0) ),
    inference(cn,[status(thm)],[1287,theory(equality)]) ).

cnf(1384,negated_conjecture,
    ( empty(esk40_0)
    | empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0
    | ~ upper_relstr_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    | ~ filtered_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    | ~ element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    | ~ one_sorted_str(esk39_0) ),
    inference(spm,[status(thm)],[837,512,theory(equality)]) ).

cnf(1390,negated_conjecture,
    ( empty(esk40_0)
    | empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0
    | $false
    | ~ filtered_subset(esk40_0,boole_POSet(cast_as_carrier_subset(esk39_0)))
    | ~ element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    | ~ one_sorted_str(esk39_0) ),
    inference(rw,[status(thm)],[1384,840,theory(equality)]) ).

cnf(1391,negated_conjecture,
    ( empty(esk40_0)
    | empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0
    | $false
    | $false
    | ~ element(esk40_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk39_0)))))
    | ~ one_sorted_str(esk39_0) ),
    inference(rw,[status(thm)],[1390,841,theory(equality)]) ).

cnf(1392,negated_conjecture,
    ( empty(esk40_0)
    | empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0
    | $false
    | $false
    | $false
    | ~ one_sorted_str(esk39_0) ),
    inference(rw,[status(thm)],[1391,838,theory(equality)]) ).

cnf(1393,negated_conjecture,
    ( empty(esk40_0)
    | empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0
    | $false
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[1392,843,theory(equality)]) ).

cnf(1394,negated_conjecture,
    ( empty(esk40_0)
    | empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0 ),
    inference(cn,[status(thm)],[1393,theory(equality)]) ).

cnf(1395,negated_conjecture,
    ( empty_carrier(esk39_0)
    | set_difference(esk40_0,singleton(empty_set)) != esk40_0 ),
    inference(sr,[status(thm)],[1394,842,theory(equality)]) ).

cnf(1396,negated_conjecture,
    set_difference(esk40_0,singleton(empty_set)) != esk40_0,
    inference(sr,[status(thm)],[1395,844,theory(equality)]) ).

cnf(1665,negated_conjecture,
    in(empty_set,esk40_0),
    inference(spm,[status(thm)],[1396,200,theory(equality)]) ).

cnf(1669,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | ~ empty(empty_set) ),
    inference(spm,[status(thm)],[1288,1665,theory(equality)]) ).

cnf(1671,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk39_0))
    | $false ),
    inference(rw,[status(thm)],[1669,285,theory(equality)]) ).

cnf(1672,negated_conjecture,
    empty(cast_as_carrier_subset(esk39_0)),
    inference(cn,[status(thm)],[1671,theory(equality)]) ).

cnf(1675,negated_conjecture,
    ( empty_carrier(esk39_0)
    | ~ one_sorted_str(esk39_0) ),
    inference(spm,[status(thm)],[522,1672,theory(equality)]) ).

cnf(1684,negated_conjecture,
    ( empty_carrier(esk39_0)
    | $false ),
    inference(rw,[status(thm)],[1675,843,theory(equality)]) ).

cnf(1685,negated_conjecture,
    empty_carrier(esk39_0),
    inference(cn,[status(thm)],[1684,theory(equality)]) ).

cnf(1686,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1685,844,theory(equality)]) ).

cnf(1687,negated_conjecture,
    $false,
    1686,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU394+1.p
% --creating new selector for []
% -running prover on /tmp/tmpm2d8iW/sel_SEU394+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU394+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU394+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU394+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------