TSTP Solution File: SEU293+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU293+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 06:54:38 EST 2010

% Result   : Theorem 0.47s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  105 (  14 unt;   0 def)
%            Number of atoms       :  447 (  86 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  558 ( 216   ~; 243   |;  76   &)
%                                         (   7 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :  208 (  10 sgn 121   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2,X3] :
      ( element(X3,powerset(cartesian_product2(X1,X2)))
     => relation(X3) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',cc1_relset_1) ).

fof(8,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( X3 = relation_inverse_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ( in(X4,relation_dom(X1))
                & in(apply(X1,X4),X2) ) ) ) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',d13_funct_1) ).

fof(13,axiom,
    ! [X1,X2,X3] :
      ( relation_of2(X3,X1,X2)
     => relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',redefinition_k4_relset_1) ).

fof(15,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t4_subset) ).

fof(27,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
    <=> relation_of2(X3,X1,X2) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',redefinition_m2_relset_1) ).

fof(28,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t5_subset) ).

fof(32,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => element(X3,powerset(cartesian_product2(X1,X2))) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',dt_m2_relset_1) ).

fof(33,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t2_subset) ).

fof(37,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t1_subset) ).

fof(50,axiom,
    ! [X1,X2,X3] :
      ( relation_of2(X3,X1,X2)
     => element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',dt_k4_relset_1) ).

fof(51,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => ( ( ( X2 = empty_set
           => X1 = empty_set )
         => ( quasi_total(X3,X1,X2)
          <=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
        & ( X2 = empty_set
         => ( X1 = empty_set
            | ( quasi_total(X3,X1,X2)
            <=> X3 = empty_set ) ) ) ) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',d1_funct_2) ).

fof(53,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( function(X4)
        & quasi_total(X4,X1,X2)
        & relation_of2_as_subset(X4,X1,X2) )
     => ( X2 != empty_set
       => ! [X5] :
            ( in(X5,relation_inverse_image(X4,X3))
          <=> ( in(X5,X1)
              & in(apply(X4,X5),X3) ) ) ) ),
    file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t46_funct_2) ).

fof(54,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( function(X4)
          & quasi_total(X4,X1,X2)
          & relation_of2_as_subset(X4,X1,X2) )
       => ( X2 != empty_set
         => ! [X5] :
              ( in(X5,relation_inverse_image(X4,X3))
            <=> ( in(X5,X1)
                & in(apply(X4,X5),X3) ) ) ) ),
    inference(assume_negation,[status(cth)],[53]) ).

fof(76,plain,
    ! [X1,X2,X3] :
      ( ~ element(X3,powerset(cartesian_product2(X1,X2)))
      | relation(X3) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(77,plain,
    ! [X4,X5,X6] :
      ( ~ element(X6,powerset(cartesian_product2(X4,X5)))
      | relation(X6) ),
    inference(variable_rename,[status(thm)],[76]) ).

cnf(78,plain,
    ( relation(X1)
    | ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[77]) ).

fof(90,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ! [X2,X3] :
          ( ( X3 != relation_inverse_image(X1,X2)
            | ! [X4] :
                ( ( ~ in(X4,X3)
                  | ( in(X4,relation_dom(X1))
                    & in(apply(X1,X4),X2) ) )
                & ( ~ in(X4,relation_dom(X1))
                  | ~ in(apply(X1,X4),X2)
                  | in(X4,X3) ) ) )
          & ( ? [X4] :
                ( ( ~ in(X4,X3)
                  | ~ in(X4,relation_dom(X1))
                  | ~ in(apply(X1,X4),X2) )
                & ( in(X4,X3)
                  | ( in(X4,relation_dom(X1))
                    & in(apply(X1,X4),X2) ) ) )
            | X3 = relation_inverse_image(X1,X2) ) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(91,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ~ function(X5)
      | ! [X6,X7] :
          ( ( X7 != relation_inverse_image(X5,X6)
            | ! [X8] :
                ( ( ~ in(X8,X7)
                  | ( in(X8,relation_dom(X5))
                    & in(apply(X5,X8),X6) ) )
                & ( ~ in(X8,relation_dom(X5))
                  | ~ in(apply(X5,X8),X6)
                  | in(X8,X7) ) ) )
          & ( ? [X9] :
                ( ( ~ in(X9,X7)
                  | ~ in(X9,relation_dom(X5))
                  | ~ in(apply(X5,X9),X6) )
                & ( in(X9,X7)
                  | ( in(X9,relation_dom(X5))
                    & in(apply(X5,X9),X6) ) ) )
            | X7 = relation_inverse_image(X5,X6) ) ) ),
    inference(variable_rename,[status(thm)],[90]) ).

fof(92,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ~ function(X5)
      | ! [X6,X7] :
          ( ( X7 != relation_inverse_image(X5,X6)
            | ! [X8] :
                ( ( ~ in(X8,X7)
                  | ( in(X8,relation_dom(X5))
                    & in(apply(X5,X8),X6) ) )
                & ( ~ in(X8,relation_dom(X5))
                  | ~ in(apply(X5,X8),X6)
                  | in(X8,X7) ) ) )
          & ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
                | ~ in(esk5_3(X5,X6,X7),relation_dom(X5))
                | ~ in(apply(X5,esk5_3(X5,X6,X7)),X6) )
              & ( in(esk5_3(X5,X6,X7),X7)
                | ( in(esk5_3(X5,X6,X7),relation_dom(X5))
                  & in(apply(X5,esk5_3(X5,X6,X7)),X6) ) ) )
            | X7 = relation_inverse_image(X5,X6) ) ) ),
    inference(skolemize,[status(esa)],[91]) ).

fof(93,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ( ~ in(X8,X7)
              | ( in(X8,relation_dom(X5))
                & in(apply(X5,X8),X6) ) )
            & ( ~ in(X8,relation_dom(X5))
              | ~ in(apply(X5,X8),X6)
              | in(X8,X7) ) )
          | X7 != relation_inverse_image(X5,X6) )
        & ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
              | ~ in(esk5_3(X5,X6,X7),relation_dom(X5))
              | ~ in(apply(X5,esk5_3(X5,X6,X7)),X6) )
            & ( in(esk5_3(X5,X6,X7),X7)
              | ( in(esk5_3(X5,X6,X7),relation_dom(X5))
                & in(apply(X5,esk5_3(X5,X6,X7)),X6) ) ) )
          | X7 = relation_inverse_image(X5,X6) ) )
      | ~ relation(X5)
      | ~ function(X5) ),
    inference(shift_quantors,[status(thm)],[92]) ).

fof(94,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,relation_dom(X5))
        | ~ in(X8,X7)
        | X7 != relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(apply(X5,X8),X6)
        | ~ in(X8,X7)
        | X7 != relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( ~ in(X8,relation_dom(X5))
        | ~ in(apply(X5,X8),X6)
        | in(X8,X7)
        | X7 != relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( ~ in(esk5_3(X5,X6,X7),X7)
        | ~ in(esk5_3(X5,X6,X7),relation_dom(X5))
        | ~ in(apply(X5,esk5_3(X5,X6,X7)),X6)
        | X7 = relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(esk5_3(X5,X6,X7),relation_dom(X5))
        | in(esk5_3(X5,X6,X7),X7)
        | X7 = relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(apply(X5,esk5_3(X5,X6,X7)),X6)
        | in(esk5_3(X5,X6,X7),X7)
        | X7 = relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) ) ),
    inference(distribute,[status(thm)],[93]) ).

cnf(98,plain,
    ( in(X4,X2)
    | ~ function(X1)
    | ~ relation(X1)
    | X2 != relation_inverse_image(X1,X3)
    | ~ in(apply(X1,X4),X3)
    | ~ in(X4,relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[94]) ).

cnf(99,plain,
    ( in(apply(X1,X4),X3)
    | ~ function(X1)
    | ~ relation(X1)
    | X2 != relation_inverse_image(X1,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[94]) ).

cnf(100,plain,
    ( in(X4,relation_dom(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | X2 != relation_inverse_image(X1,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[94]) ).

fof(119,plain,
    ! [X1,X2,X3] :
      ( ~ relation_of2(X3,X1,X2)
      | relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(120,plain,
    ! [X4,X5,X6] :
      ( ~ relation_of2(X6,X4,X5)
      | relation_dom_as_subset(X4,X5,X6) = relation_dom(X6) ),
    inference(variable_rename,[status(thm)],[119]) ).

cnf(121,plain,
    ( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
    | ~ relation_of2(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[120]) ).

fof(124,plain,
    ! [X1,X2,X3] :
      ( ~ in(X1,X2)
      | ~ element(X2,powerset(X3))
      | element(X1,X3) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(125,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | element(X4,X6) ),
    inference(variable_rename,[status(thm)],[124]) ).

cnf(126,plain,
    ( element(X1,X2)
    | ~ element(X3,powerset(X2))
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[125]) ).

fof(163,plain,
    ! [X1,X2,X3] :
      ( ( ~ relation_of2_as_subset(X3,X1,X2)
        | relation_of2(X3,X1,X2) )
      & ( ~ relation_of2(X3,X1,X2)
        | relation_of2_as_subset(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(164,plain,
    ! [X4,X5,X6] :
      ( ( ~ relation_of2_as_subset(X6,X4,X5)
        | relation_of2(X6,X4,X5) )
      & ( ~ relation_of2(X6,X4,X5)
        | relation_of2_as_subset(X6,X4,X5) ) ),
    inference(variable_rename,[status(thm)],[163]) ).

cnf(165,plain,
    ( relation_of2_as_subset(X1,X2,X3)
    | ~ relation_of2(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[164]) ).

cnf(166,plain,
    ( relation_of2(X1,X2,X3)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[164]) ).

fof(167,plain,
    ! [X1,X2,X3] :
      ( ~ in(X1,X2)
      | ~ element(X2,powerset(X3))
      | ~ empty(X3) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(168,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | ~ empty(X6) ),
    inference(variable_rename,[status(thm)],[167]) ).

cnf(169,plain,
    ( ~ empty(X1)
    | ~ element(X2,powerset(X1))
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[168]) ).

fof(177,plain,
    ! [X1,X2,X3] :
      ( ~ relation_of2_as_subset(X3,X1,X2)
      | element(X3,powerset(cartesian_product2(X1,X2))) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(178,plain,
    ! [X4,X5,X6] :
      ( ~ relation_of2_as_subset(X6,X4,X5)
      | element(X6,powerset(cartesian_product2(X4,X5))) ),
    inference(variable_rename,[status(thm)],[177]) ).

cnf(179,plain,
    ( element(X1,powerset(cartesian_product2(X2,X3)))
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[178]) ).

fof(180,plain,
    ! [X1,X2] :
      ( ~ element(X1,X2)
      | empty(X2)
      | in(X1,X2) ),
    inference(fof_nnf,[status(thm)],[33]) ).

fof(181,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[180]) ).

cnf(182,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[181]) ).

fof(191,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | element(X1,X2) ),
    inference(fof_nnf,[status(thm)],[37]) ).

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

cnf(193,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[192]) ).

fof(223,plain,
    ! [X1,X2,X3] :
      ( ~ relation_of2(X3,X1,X2)
      | element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
    inference(fof_nnf,[status(thm)],[50]) ).

fof(224,plain,
    ! [X4,X5,X6] :
      ( ~ relation_of2(X6,X4,X5)
      | element(relation_dom_as_subset(X4,X5,X6),powerset(X4)) ),
    inference(variable_rename,[status(thm)],[223]) ).

cnf(225,plain,
    ( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
    | ~ relation_of2(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[224]) ).

fof(226,plain,
    ! [X1,X2,X3] :
      ( ~ relation_of2_as_subset(X3,X1,X2)
      | ( ( ( X2 = empty_set
            & X1 != empty_set )
          | ( ( ~ quasi_total(X3,X1,X2)
              | X1 = relation_dom_as_subset(X1,X2,X3) )
            & ( X1 != relation_dom_as_subset(X1,X2,X3)
              | quasi_total(X3,X1,X2) ) ) )
        & ( X2 != empty_set
          | X1 = empty_set
          | ( ( ~ quasi_total(X3,X1,X2)
              | X3 = empty_set )
            & ( X3 != empty_set
              | quasi_total(X3,X1,X2) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[51]) ).

fof(227,plain,
    ! [X4,X5,X6] :
      ( ~ relation_of2_as_subset(X6,X4,X5)
      | ( ( ( X5 = empty_set
            & X4 != empty_set )
          | ( ( ~ quasi_total(X6,X4,X5)
              | X4 = relation_dom_as_subset(X4,X5,X6) )
            & ( X4 != relation_dom_as_subset(X4,X5,X6)
              | quasi_total(X6,X4,X5) ) ) )
        & ( X5 != empty_set
          | X4 = empty_set
          | ( ( ~ quasi_total(X6,X4,X5)
              | X6 = empty_set )
            & ( X6 != empty_set
              | quasi_total(X6,X4,X5) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[226]) ).

fof(228,plain,
    ! [X4,X5,X6] :
      ( ( ~ quasi_total(X6,X4,X5)
        | X4 = relation_dom_as_subset(X4,X5,X6)
        | X5 = empty_set
        | ~ relation_of2_as_subset(X6,X4,X5) )
      & ( X4 != relation_dom_as_subset(X4,X5,X6)
        | quasi_total(X6,X4,X5)
        | X5 = empty_set
        | ~ relation_of2_as_subset(X6,X4,X5) )
      & ( ~ quasi_total(X6,X4,X5)
        | X4 = relation_dom_as_subset(X4,X5,X6)
        | X4 != empty_set
        | ~ relation_of2_as_subset(X6,X4,X5) )
      & ( X4 != relation_dom_as_subset(X4,X5,X6)
        | quasi_total(X6,X4,X5)
        | X4 != empty_set
        | ~ relation_of2_as_subset(X6,X4,X5) )
      & ( ~ quasi_total(X6,X4,X5)
        | X6 = empty_set
        | X4 = empty_set
        | X5 != empty_set
        | ~ relation_of2_as_subset(X6,X4,X5) )
      & ( X6 != empty_set
        | quasi_total(X6,X4,X5)
        | X4 = empty_set
        | X5 != empty_set
        | ~ relation_of2_as_subset(X6,X4,X5) ) ),
    inference(distribute,[status(thm)],[227]) ).

cnf(234,plain,
    ( X3 = empty_set
    | X2 = relation_dom_as_subset(X2,X3,X1)
    | ~ relation_of2_as_subset(X1,X2,X3)
    | ~ quasi_total(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[228]) ).

fof(240,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( function(X4)
      & quasi_total(X4,X1,X2)
      & relation_of2_as_subset(X4,X1,X2)
      & X2 != empty_set
      & ? [X5] :
          ( ( ~ in(X5,relation_inverse_image(X4,X3))
            | ~ in(X5,X1)
            | ~ in(apply(X4,X5),X3) )
          & ( in(X5,relation_inverse_image(X4,X3))
            | ( in(X5,X1)
              & in(apply(X4,X5),X3) ) ) ) ),
    inference(fof_nnf,[status(thm)],[54]) ).

fof(241,negated_conjecture,
    ? [X6,X7,X8,X9] :
      ( function(X9)
      & quasi_total(X9,X6,X7)
      & relation_of2_as_subset(X9,X6,X7)
      & X7 != empty_set
      & ? [X10] :
          ( ( ~ in(X10,relation_inverse_image(X9,X8))
            | ~ in(X10,X6)
            | ~ in(apply(X9,X10),X8) )
          & ( in(X10,relation_inverse_image(X9,X8))
            | ( in(X10,X6)
              & in(apply(X9,X10),X8) ) ) ) ),
    inference(variable_rename,[status(thm)],[240]) ).

fof(242,negated_conjecture,
    ( function(esk22_0)
    & quasi_total(esk22_0,esk19_0,esk20_0)
    & relation_of2_as_subset(esk22_0,esk19_0,esk20_0)
    & esk20_0 != empty_set
    & ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
      | ~ in(esk23_0,esk19_0)
      | ~ in(apply(esk22_0,esk23_0),esk21_0) )
    & ( in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
      | ( in(esk23_0,esk19_0)
        & in(apply(esk22_0,esk23_0),esk21_0) ) ) ),
    inference(skolemize,[status(esa)],[241]) ).

fof(243,negated_conjecture,
    ( function(esk22_0)
    & quasi_total(esk22_0,esk19_0,esk20_0)
    & relation_of2_as_subset(esk22_0,esk19_0,esk20_0)
    & esk20_0 != empty_set
    & ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
      | ~ in(esk23_0,esk19_0)
      | ~ in(apply(esk22_0,esk23_0),esk21_0) )
    & ( in(esk23_0,esk19_0)
      | in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) )
    & ( in(apply(esk22_0,esk23_0),esk21_0)
      | in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ) ),
    inference(distribute,[status(thm)],[242]) ).

cnf(244,negated_conjecture,
    ( in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | in(apply(esk22_0,esk23_0),esk21_0) ),
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(245,negated_conjecture,
    ( in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | in(esk23_0,esk19_0) ),
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(246,negated_conjecture,
    ( ~ in(apply(esk22_0,esk23_0),esk21_0)
    | ~ in(esk23_0,esk19_0)
    | ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ),
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(247,negated_conjecture,
    esk20_0 != empty_set,
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(248,negated_conjecture,
    relation_of2_as_subset(esk22_0,esk19_0,esk20_0),
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(249,negated_conjecture,
    quasi_total(esk22_0,esk19_0,esk20_0),
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(250,negated_conjecture,
    function(esk22_0),
    inference(split_conjunct,[status(thm)],[243]) ).

cnf(302,plain,
    ( relation(X1)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(spm,[status(thm)],[78,179,theory(equality)]) ).

cnf(309,plain,
    ( in(apply(X1,X2),X3)
    | ~ in(X2,relation_inverse_image(X1,X3))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(er,[status(thm)],[99,theory(equality)]) ).

cnf(310,plain,
    ( X1 = relation_dom(X3)
    | empty_set = X2
    | ~ relation_of2(X3,X1,X2)
    | ~ relation_of2_as_subset(X3,X1,X2)
    | ~ quasi_total(X3,X1,X2) ),
    inference(spm,[status(thm)],[121,234,theory(equality)]) ).

cnf(317,plain,
    ( element(relation_dom(X3),powerset(X1))
    | ~ relation_of2(X3,X1,X2) ),
    inference(spm,[status(thm)],[225,121,theory(equality)]) ).

cnf(320,plain,
    ( in(X1,relation_dom(X2))
    | ~ in(X1,relation_inverse_image(X2,X3))
    | ~ function(X2)
    | ~ relation(X2) ),
    inference(er,[status(thm)],[100,theory(equality)]) ).

cnf(468,negated_conjecture,
    relation(esk22_0),
    inference(spm,[status(thm)],[302,248,theory(equality)]) ).

cnf(563,negated_conjecture,
    ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | ~ in(esk23_0,esk19_0)
    | ~ function(esk22_0)
    | ~ relation(esk22_0) ),
    inference(spm,[status(thm)],[246,309,theory(equality)]) ).

cnf(576,negated_conjecture,
    ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | ~ in(esk23_0,esk19_0)
    | $false
    | ~ relation(esk22_0) ),
    inference(rw,[status(thm)],[563,250,theory(equality)]) ).

cnf(577,negated_conjecture,
    ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | ~ in(esk23_0,esk19_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[576,468,theory(equality)]) ).

cnf(578,negated_conjecture,
    ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | ~ in(esk23_0,esk19_0) ),
    inference(cn,[status(thm)],[577,theory(equality)]) ).

cnf(658,plain,
    ( element(relation_dom(X1),powerset(X2))
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(spm,[status(thm)],[317,166,theory(equality)]) ).

cnf(713,plain,
    ( X1 = relation_dom(X3)
    | empty_set = X2
    | ~ quasi_total(X3,X1,X2)
    | ~ relation_of2(X3,X1,X2) ),
    inference(csr,[status(thm)],[310,165]) ).

cnf(717,plain,
    ( X1 = relation_dom(X2)
    | empty_set = X3
    | ~ quasi_total(X2,X1,X3)
    | ~ relation_of2_as_subset(X2,X1,X3) ),
    inference(spm,[status(thm)],[713,166,theory(equality)]) ).

cnf(1063,negated_conjecture,
    ( in(esk23_0,relation_dom(esk22_0))
    | in(esk23_0,esk19_0)
    | ~ function(esk22_0)
    | ~ relation(esk22_0) ),
    inference(spm,[status(thm)],[320,245,theory(equality)]) ).

cnf(1068,negated_conjecture,
    ( in(esk23_0,relation_dom(esk22_0))
    | in(esk23_0,esk19_0)
    | $false
    | ~ relation(esk22_0) ),
    inference(rw,[status(thm)],[1063,250,theory(equality)]) ).

cnf(1069,negated_conjecture,
    ( in(esk23_0,relation_dom(esk22_0))
    | in(esk23_0,esk19_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1068,468,theory(equality)]) ).

cnf(1070,negated_conjecture,
    ( in(esk23_0,relation_dom(esk22_0))
    | in(esk23_0,esk19_0) ),
    inference(cn,[status(thm)],[1069,theory(equality)]) ).

cnf(4076,negated_conjecture,
    element(relation_dom(esk22_0),powerset(esk19_0)),
    inference(spm,[status(thm)],[658,248,theory(equality)]) ).

cnf(4091,negated_conjecture,
    ( ~ in(X1,relation_dom(esk22_0))
    | ~ empty(esk19_0) ),
    inference(spm,[status(thm)],[169,4076,theory(equality)]) ).

cnf(4092,negated_conjecture,
    ( element(X1,esk19_0)
    | ~ in(X1,relation_dom(esk22_0)) ),
    inference(spm,[status(thm)],[126,4076,theory(equality)]) ).

cnf(4112,negated_conjecture,
    ( element(esk23_0,esk19_0)
    | in(esk23_0,esk19_0) ),
    inference(spm,[status(thm)],[4092,1070,theory(equality)]) ).

cnf(4138,negated_conjecture,
    ( in(esk23_0,esk19_0)
    | ~ empty(esk19_0) ),
    inference(spm,[status(thm)],[4091,1070,theory(equality)]) ).

cnf(4156,negated_conjecture,
    element(esk23_0,esk19_0),
    inference(csr,[status(thm)],[4112,193]) ).

cnf(4157,negated_conjecture,
    ( in(esk23_0,esk19_0)
    | empty(esk19_0) ),
    inference(spm,[status(thm)],[182,4156,theory(equality)]) ).

cnf(4163,negated_conjecture,
    in(esk23_0,esk19_0),
    inference(csr,[status(thm)],[4138,4157]) ).

cnf(4178,negated_conjecture,
    ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
    | $false ),
    inference(rw,[status(thm)],[578,4163,theory(equality)]) ).

cnf(4179,negated_conjecture,
    ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0)),
    inference(cn,[status(thm)],[4178,theory(equality)]) ).

cnf(4188,negated_conjecture,
    in(apply(esk22_0,esk23_0),esk21_0),
    inference(sr,[status(thm)],[244,4179,theory(equality)]) ).

cnf(4197,negated_conjecture,
    ( in(esk23_0,X1)
    | relation_inverse_image(esk22_0,esk21_0) != X1
    | ~ in(esk23_0,relation_dom(esk22_0))
    | ~ function(esk22_0)
    | ~ relation(esk22_0) ),
    inference(spm,[status(thm)],[98,4188,theory(equality)]) ).

cnf(4199,negated_conjecture,
    ( in(esk23_0,X1)
    | relation_inverse_image(esk22_0,esk21_0) != X1
    | ~ in(esk23_0,relation_dom(esk22_0))
    | $false
    | ~ relation(esk22_0) ),
    inference(rw,[status(thm)],[4197,250,theory(equality)]) ).

cnf(4200,negated_conjecture,
    ( in(esk23_0,X1)
    | relation_inverse_image(esk22_0,esk21_0) != X1
    | ~ in(esk23_0,relation_dom(esk22_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[4199,468,theory(equality)]) ).

cnf(4201,negated_conjecture,
    ( in(esk23_0,X1)
    | relation_inverse_image(esk22_0,esk21_0) != X1
    | ~ in(esk23_0,relation_dom(esk22_0)) ),
    inference(cn,[status(thm)],[4200,theory(equality)]) ).

cnf(4494,negated_conjecture,
    ( esk19_0 = relation_dom(esk22_0)
    | empty_set = esk20_0
    | ~ relation_of2_as_subset(esk22_0,esk19_0,esk20_0) ),
    inference(spm,[status(thm)],[717,249,theory(equality)]) ).

cnf(4502,negated_conjecture,
    ( esk19_0 = relation_dom(esk22_0)
    | empty_set = esk20_0
    | $false ),
    inference(rw,[status(thm)],[4494,248,theory(equality)]) ).

cnf(4503,negated_conjecture,
    ( esk19_0 = relation_dom(esk22_0)
    | empty_set = esk20_0 ),
    inference(cn,[status(thm)],[4502,theory(equality)]) ).

cnf(4504,negated_conjecture,
    relation_dom(esk22_0) = esk19_0,
    inference(sr,[status(thm)],[4503,247,theory(equality)]) ).

cnf(4557,negated_conjecture,
    ( in(esk23_0,X1)
    | relation_inverse_image(esk22_0,esk21_0) != X1
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[4201,4504,theory(equality)]),4163,theory(equality)]) ).

cnf(4558,negated_conjecture,
    ( in(esk23_0,X1)
    | relation_inverse_image(esk22_0,esk21_0) != X1 ),
    inference(cn,[status(thm)],[4557,theory(equality)]) ).

cnf(4584,negated_conjecture,
    in(esk23_0,relation_inverse_image(esk22_0,esk21_0)),
    inference(er,[status(thm)],[4558,theory(equality)]) ).

cnf(4587,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[4584,4179,theory(equality)]) ).

cnf(4588,negated_conjecture,
    $false,
    4587,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU293+1.p
% --creating new selector for []
% -running prover on /tmp/tmpFx5MoK/sel_SEU293+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU293+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU293+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU293+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
% 
%------------------------------------------------------------------------------