TSTP Solution File: SEU325+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU325+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:22:10 EST 2010

% Result   : Theorem 0.34s
% Output   : CNFRefutation 0.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   95 (  26 unt;   0 def)
%            Number of atoms       :  297 (  61 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  343 ( 141   ~; 123   |;  60   &)
%                                         (   5 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :  134 (  14 sgn  83   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2] :
      ( X2 = union(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X3,X4)
              & in(X4,X1) ) ) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',d4_tarski) ).

fof(5,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => ! [X2] :
          ( element(X2,powerset(powerset(the_carrier(X1))))
         => ( is_a_cover_of_carrier(X1,X2)
          <=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',d8_pre_topc) ).

fof(18,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',fc1_struct_0) ).

fof(19,axiom,
    ( empty(empty_set)
    & v1_membered(empty_set)
    & v2_membered(empty_set)
    & v3_membered(empty_set)
    & v4_membered(empty_set)
    & v5_membered(empty_set) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',fc6_membered) ).

fof(28,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',t5_subset) ).

fof(31,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',t2_subset) ).

fof(32,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => union_of_subsets(X1,X2) = union(X2) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',redefinition_k5_setfam_1) ).

fof(37,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',existence_m1_subset_1) ).

fof(39,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',t6_boole) ).

fof(43,axiom,
    ! [X1] :
    ? [X2] :
      ( element(X2,powerset(X1))
      & empty(X2) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',rc2_subset_1) ).

fof(44,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => cast_as_carrier_subset(X1) = the_carrier(X1) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',d3_pre_topc) ).

fof(47,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( element(X2,powerset(powerset(the_carrier(X1))))
         => ~ ( is_a_cover_of_carrier(X1,X2)
              & X2 = empty_set ) ) ),
    file('/tmp/tmpvLnoJf/sel_SEU325+1.p_1',t5_tops_2) ).

fof(50,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( element(X2,powerset(powerset(the_carrier(X1))))
           => ~ ( is_a_cover_of_carrier(X1,X2)
                & X2 = empty_set ) ) ),
    inference(assume_negation,[status(cth)],[47]) ).

fof(55,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).

fof(59,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( element(X2,powerset(powerset(the_carrier(X1))))
           => ~ ( is_a_cover_of_carrier(X1,X2)
                & X2 = empty_set ) ) ),
    inference(fof_simplification,[status(thm)],[50,theory(equality)]) ).

fof(61,plain,
    ! [X1,X2] :
      ( ( X2 != union(X1)
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ? [X4] :
                  ( in(X3,X4)
                  & in(X4,X1) ) )
            & ( ! [X4] :
                  ( ~ in(X3,X4)
                  | ~ in(X4,X1) )
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | ! [X4] :
                  ( ~ in(X3,X4)
                  | ~ in(X4,X1) ) )
            & ( in(X3,X2)
              | ? [X4] :
                  ( in(X3,X4)
                  & in(X4,X1) ) ) )
        | X2 = union(X1) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(62,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ? [X8] :
                  ( in(X7,X8)
                  & in(X8,X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ? [X10] :
            ( ( ~ in(X10,X6)
              | ! [X11] :
                  ( ~ in(X10,X11)
                  | ~ in(X11,X5) ) )
            & ( in(X10,X6)
              | ? [X12] :
                  ( in(X10,X12)
                  & in(X12,X5) ) ) )
        | X6 = union(X5) ) ),
    inference(variable_rename,[status(thm)],[61]) ).

fof(63,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ( in(X7,esk1_3(X5,X6,X7))
                & in(esk1_3(X5,X6,X7),X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ( ( ~ in(esk2_2(X5,X6),X6)
            | ! [X11] :
                ( ~ in(esk2_2(X5,X6),X11)
                | ~ in(X11,X5) ) )
          & ( in(esk2_2(X5,X6),X6)
            | ( in(esk2_2(X5,X6),esk3_2(X5,X6))
              & in(esk3_2(X5,X6),X5) ) ) )
        | X6 = union(X5) ) ),
    inference(skolemize,[status(esa)],[62]) ).

fof(64,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ~ in(esk2_2(X5,X6),X11)
            | ~ in(X11,X5)
            | ~ in(esk2_2(X5,X6),X6) )
          & ( in(esk2_2(X5,X6),X6)
            | ( in(esk2_2(X5,X6),esk3_2(X5,X6))
              & in(esk3_2(X5,X6),X5) ) ) )
        | X6 = union(X5) )
      & ( ( ( ~ in(X7,X9)
            | ~ in(X9,X5)
            | in(X7,X6) )
          & ( ~ in(X7,X6)
            | ( in(X7,esk1_3(X5,X6,X7))
              & in(esk1_3(X5,X6,X7),X5) ) ) )
        | X6 != union(X5) ) ),
    inference(shift_quantors,[status(thm)],[63]) ).

fof(65,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(esk2_2(X5,X6),X11)
        | ~ in(X11,X5)
        | ~ in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk2_2(X5,X6),esk3_2(X5,X6))
        | in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk3_2(X5,X6),X5)
        | in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( ~ in(X7,X9)
        | ~ in(X9,X5)
        | in(X7,X6)
        | X6 != union(X5) )
      & ( in(X7,esk1_3(X5,X6,X7))
        | ~ in(X7,X6)
        | X6 != union(X5) )
      & ( in(esk1_3(X5,X6,X7),X5)
        | ~ in(X7,X6)
        | X6 != union(X5) ) ),
    inference(distribute,[status(thm)],[64]) ).

cnf(66,plain,
    ( in(esk1_3(X2,X1,X3),X2)
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[65]) ).

fof(78,plain,
    ! [X1] :
      ( ~ one_sorted_str(X1)
      | ! [X2] :
          ( ~ element(X2,powerset(powerset(the_carrier(X1))))
          | ( ( ~ is_a_cover_of_carrier(X1,X2)
              | cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) )
            & ( cast_as_carrier_subset(X1) != union_of_subsets(the_carrier(X1),X2)
              | is_a_cover_of_carrier(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(79,plain,
    ! [X3] :
      ( ~ one_sorted_str(X3)
      | ! [X4] :
          ( ~ element(X4,powerset(powerset(the_carrier(X3))))
          | ( ( ~ is_a_cover_of_carrier(X3,X4)
              | cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4) )
            & ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
              | is_a_cover_of_carrier(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[78]) ).

fof(80,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(the_carrier(X3))))
      | ( ( ~ is_a_cover_of_carrier(X3,X4)
          | cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4) )
        & ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
          | is_a_cover_of_carrier(X3,X4) ) )
      | ~ one_sorted_str(X3) ),
    inference(shift_quantors,[status(thm)],[79]) ).

fof(81,plain,
    ! [X3,X4] :
      ( ( ~ is_a_cover_of_carrier(X3,X4)
        | cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4)
        | ~ element(X4,powerset(powerset(the_carrier(X3))))
        | ~ one_sorted_str(X3) )
      & ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
        | is_a_cover_of_carrier(X3,X4)
        | ~ element(X4,powerset(powerset(the_carrier(X3))))
        | ~ one_sorted_str(X3) ) ),
    inference(distribute,[status(thm)],[80]) ).

cnf(83,plain,
    ( cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2)
    | ~ one_sorted_str(X1)
    | ~ element(X2,powerset(powerset(the_carrier(X1))))
    | ~ is_a_cover_of_carrier(X1,X2) ),
    inference(split_conjunct,[status(thm)],[81]) ).

fof(135,plain,
    ! [X1] :
      ( empty_carrier(X1)
      | ~ one_sorted_str(X1)
      | ~ empty(the_carrier(X1)) ),
    inference(fof_nnf,[status(thm)],[55]) ).

fof(136,plain,
    ! [X2] :
      ( empty_carrier(X2)
      | ~ one_sorted_str(X2)
      | ~ empty(the_carrier(X2)) ),
    inference(variable_rename,[status(thm)],[135]) ).

cnf(137,plain,
    ( empty_carrier(X1)
    | ~ empty(the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[136]) ).

cnf(143,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(177,plain,
    ! [X1,X2,X3] :
      ( ~ in(X1,X2)
      | ~ element(X2,powerset(X3))
      | ~ empty(X3) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(178,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | ~ empty(X6) ),
    inference(variable_rename,[status(thm)],[177]) ).

cnf(179,plain,
    ( ~ empty(X1)
    | ~ element(X2,powerset(X1))
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[178]) ).

fof(188,plain,
    ! [X1,X2] :
      ( ~ element(X1,X2)
      | empty(X2)
      | in(X1,X2) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(189,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[188]) ).

cnf(190,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[189]) ).

fof(191,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(powerset(X1)))
      | union_of_subsets(X1,X2) = union(X2) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(192,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(X3)))
      | union_of_subsets(X3,X4) = union(X4) ),
    inference(variable_rename,[status(thm)],[191]) ).

cnf(193,plain,
    ( union_of_subsets(X1,X2) = union(X2)
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(split_conjunct,[status(thm)],[192]) ).

fof(210,plain,
    ! [X3] :
    ? [X4] : element(X4,X3),
    inference(variable_rename,[status(thm)],[37]) ).

fof(211,plain,
    ! [X3] : element(esk8_1(X3),X3),
    inference(skolemize,[status(esa)],[210]) ).

cnf(212,plain,
    element(esk8_1(X1),X1),
    inference(split_conjunct,[status(thm)],[211]) ).

fof(214,plain,
    ! [X1] :
      ( ~ empty(X1)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(215,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[214]) ).

cnf(216,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[215]) ).

fof(230,plain,
    ! [X3] :
    ? [X4] :
      ( element(X4,powerset(X3))
      & empty(X4) ),
    inference(variable_rename,[status(thm)],[43]) ).

fof(231,plain,
    ! [X3] :
      ( element(esk10_1(X3),powerset(X3))
      & empty(esk10_1(X3)) ),
    inference(skolemize,[status(esa)],[230]) ).

cnf(232,plain,
    empty(esk10_1(X1)),
    inference(split_conjunct,[status(thm)],[231]) ).

cnf(233,plain,
    element(esk10_1(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[231]) ).

fof(234,plain,
    ! [X1] :
      ( ~ one_sorted_str(X1)
      | cast_as_carrier_subset(X1) = the_carrier(X1) ),
    inference(fof_nnf,[status(thm)],[44]) ).

fof(235,plain,
    ! [X2] :
      ( ~ one_sorted_str(X2)
      | cast_as_carrier_subset(X2) = the_carrier(X2) ),
    inference(variable_rename,[status(thm)],[234]) ).

cnf(236,plain,
    ( cast_as_carrier_subset(X1) = the_carrier(X1)
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[235]) ).

fof(250,negated_conjecture,
    ? [X1] :
      ( ~ empty_carrier(X1)
      & one_sorted_str(X1)
      & ? [X2] :
          ( element(X2,powerset(powerset(the_carrier(X1))))
          & is_a_cover_of_carrier(X1,X2)
          & X2 = empty_set ) ),
    inference(fof_nnf,[status(thm)],[59]) ).

fof(251,negated_conjecture,
    ? [X3] :
      ( ~ empty_carrier(X3)
      & one_sorted_str(X3)
      & ? [X4] :
          ( element(X4,powerset(powerset(the_carrier(X3))))
          & is_a_cover_of_carrier(X3,X4)
          & X4 = empty_set ) ),
    inference(variable_rename,[status(thm)],[250]) ).

fof(252,negated_conjecture,
    ( ~ empty_carrier(esk11_0)
    & one_sorted_str(esk11_0)
    & element(esk12_0,powerset(powerset(the_carrier(esk11_0))))
    & is_a_cover_of_carrier(esk11_0,esk12_0)
    & esk12_0 = empty_set ),
    inference(skolemize,[status(esa)],[251]) ).

cnf(253,negated_conjecture,
    esk12_0 = empty_set,
    inference(split_conjunct,[status(thm)],[252]) ).

cnf(254,negated_conjecture,
    is_a_cover_of_carrier(esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[252]) ).

cnf(256,negated_conjecture,
    one_sorted_str(esk11_0),
    inference(split_conjunct,[status(thm)],[252]) ).

cnf(257,negated_conjecture,
    ~ empty_carrier(esk11_0),
    inference(split_conjunct,[status(thm)],[252]) ).

cnf(269,negated_conjecture,
    is_a_cover_of_carrier(esk11_0,empty_set),
    inference(rw,[status(thm)],[254,253,theory(equality)]) ).

cnf(271,plain,
    empty_set = esk10_1(X1),
    inference(spm,[status(thm)],[216,232,theory(equality)]) ).

cnf(272,negated_conjecture,
    ( ~ one_sorted_str(esk11_0)
    | ~ empty(the_carrier(esk11_0)) ),
    inference(spm,[status(thm)],[257,137,theory(equality)]) ).

cnf(274,negated_conjecture,
    ( $false
    | ~ empty(the_carrier(esk11_0)) ),
    inference(rw,[status(thm)],[272,256,theory(equality)]) ).

cnf(275,negated_conjecture,
    ~ empty(the_carrier(esk11_0)),
    inference(cn,[status(thm)],[274,theory(equality)]) ).

cnf(536,plain,
    ( cast_as_carrier_subset(X1) = union(X2)
    | ~ element(X2,powerset(powerset(the_carrier(X1))))
    | ~ is_a_cover_of_carrier(X1,X2)
    | ~ one_sorted_str(X1) ),
    inference(spm,[status(thm)],[193,83,theory(equality)]) ).

cnf(595,plain,
    element(empty_set,powerset(X1)),
    inference(rw,[status(thm)],[233,271,theory(equality)]) ).

cnf(626,plain,
    ( ~ empty(X1)
    | ~ in(X2,empty_set) ),
    inference(spm,[status(thm)],[179,595,theory(equality)]) ).

fof(645,plain,
    ( ~ epred1_0
  <=> ! [X1] : ~ empty(X1) ),
    introduced(definition),
    [split] ).

cnf(646,plain,
    ( epred1_0
    | ~ empty(X1) ),
    inference(split_equiv,[status(thm)],[645]) ).

fof(647,plain,
    ( ~ epred2_0
  <=> ! [X2] : ~ in(X2,empty_set) ),
    introduced(definition),
    [split] ).

cnf(648,plain,
    ( epred2_0
    | ~ in(X2,empty_set) ),
    inference(split_equiv,[status(thm)],[647]) ).

cnf(649,plain,
    ( ~ epred2_0
    | ~ epred1_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[626,645,theory(equality)]),647,theory(equality)]),
    [split] ).

cnf(650,plain,
    epred1_0,
    inference(spm,[status(thm)],[646,143,theory(equality)]) ).

cnf(652,plain,
    ( ~ epred2_0
    | $false ),
    inference(rw,[status(thm)],[649,650,theory(equality)]) ).

cnf(653,plain,
    ~ epred2_0,
    inference(cn,[status(thm)],[652,theory(equality)]) ).

cnf(654,plain,
    ~ in(X2,empty_set),
    inference(sr,[status(thm)],[648,653,theory(equality)]) ).

cnf(656,plain,
    ( union(empty_set) != X1
    | ~ in(X2,X1) ),
    inference(spm,[status(thm)],[654,66,theory(equality)]) ).

cnf(665,plain,
    ~ in(X1,union(empty_set)),
    inference(er,[status(thm)],[656,theory(equality)]) ).

cnf(666,plain,
    ( empty(union(empty_set))
    | ~ element(X1,union(empty_set)) ),
    inference(spm,[status(thm)],[665,190,theory(equality)]) ).

cnf(675,plain,
    empty(union(empty_set)),
    inference(spm,[status(thm)],[666,212,theory(equality)]) ).

cnf(676,plain,
    empty_set = union(empty_set),
    inference(spm,[status(thm)],[216,675,theory(equality)]) ).

cnf(682,plain,
    ( empty_set != X1
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[656,676,theory(equality)]) ).

cnf(689,plain,
    ( empty(X1)
    | empty_set != X1
    | ~ element(X2,X1) ),
    inference(spm,[status(thm)],[682,190,theory(equality)]) ).

cnf(695,plain,
    ( empty(X1)
    | empty_set != X1 ),
    inference(spm,[status(thm)],[689,212,theory(equality)]) ).

cnf(710,negated_conjecture,
    empty_set != the_carrier(esk11_0),
    inference(spm,[status(thm)],[275,695,theory(equality)]) ).

cnf(1891,negated_conjecture,
    ( cast_as_carrier_subset(esk11_0) = union(empty_set)
    | ~ element(empty_set,powerset(powerset(the_carrier(esk11_0))))
    | ~ one_sorted_str(esk11_0) ),
    inference(spm,[status(thm)],[536,269,theory(equality)]) ).

cnf(1892,negated_conjecture,
    ( cast_as_carrier_subset(esk11_0) = empty_set
    | ~ element(empty_set,powerset(powerset(the_carrier(esk11_0))))
    | ~ one_sorted_str(esk11_0) ),
    inference(rw,[status(thm)],[1891,676,theory(equality)]) ).

cnf(1893,negated_conjecture,
    ( cast_as_carrier_subset(esk11_0) = empty_set
    | $false
    | ~ one_sorted_str(esk11_0) ),
    inference(rw,[status(thm)],[1892,595,theory(equality)]) ).

cnf(1894,negated_conjecture,
    ( cast_as_carrier_subset(esk11_0) = empty_set
    | $false
    | $false ),
    inference(rw,[status(thm)],[1893,256,theory(equality)]) ).

cnf(1895,negated_conjecture,
    cast_as_carrier_subset(esk11_0) = empty_set,
    inference(cn,[status(thm)],[1894,theory(equality)]) ).

cnf(1896,negated_conjecture,
    ( empty_set = the_carrier(esk11_0)
    | ~ one_sorted_str(esk11_0) ),
    inference(spm,[status(thm)],[236,1895,theory(equality)]) ).

cnf(1937,negated_conjecture,
    ( empty_set = the_carrier(esk11_0)
    | $false ),
    inference(rw,[status(thm)],[1896,256,theory(equality)]) ).

cnf(1938,negated_conjecture,
    empty_set = the_carrier(esk11_0),
    inference(cn,[status(thm)],[1937,theory(equality)]) ).

cnf(1939,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1938,710,theory(equality)]) ).

cnf(1940,negated_conjecture,
    $false,
    1939,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU325+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvLnoJf/sel_SEU325+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU325+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU325+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU325+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
% 
%------------------------------------------------------------------------------