TSTP Solution File: SEU277+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU277+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 06:39:05 EST 2010

% Result   : Theorem 0.69s
% Output   : CNFRefutation 0.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   63
%            Number of leaves      :    2
% Syntax   : Number of formulae    :  146 (  11 unt;   0 def)
%            Number of atoms       : 1108 ( 326 equ)
%            Maximal formula atoms :  231 (   7 avg)
%            Number of connectives : 1593 ( 631   ~; 832   |; 122   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   48 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   3 con; 0-4 aty)
%            Number of variables   :  387 (   0 sgn  65   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X2)
        & relation(X3)
        & function(X3) )
     => ? [X4] :
        ! [X5] :
          ( in(X5,X4)
        <=> ( in(X5,cartesian_product2(X1,X1))
            & ? [X6,X7] :
                ( X5 = ordered_pair(X6,X7)
                & in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ),
    file('/tmp/tmpNtAbcz/sel_SEU277+1.p_1',s1_xboole_0__e6_21__wellord2__1) ).

fof(10,axiom,
    ! [X1,X2,X3] :
      ( ( relation(X2)
        & relation(X3)
        & function(X3) )
     => ( ! [X4,X5,X6] :
            ( ( X4 = X5
              & ? [X7,X8] :
                  ( X5 = ordered_pair(X7,X8)
                  & in(ordered_pair(apply(X3,X7),apply(X3,X8)),X2) )
              & X4 = X6
              & ? [X9,X10] :
                  ( X6 = ordered_pair(X9,X10)
                  & in(ordered_pair(apply(X3,X9),apply(X3,X10)),X2) ) )
           => X5 = X6 )
       => ? [X4] :
          ! [X5] :
            ( in(X5,X4)
          <=> ? [X6] :
                ( in(X6,cartesian_product2(X1,X1))
                & X6 = X5
                & ? [X11,X12] :
                    ( X5 = ordered_pair(X11,X12)
                    & in(ordered_pair(apply(X3,X11),apply(X3,X12)),X2) ) ) ) ) ),
    file('/tmp/tmpNtAbcz/sel_SEU277+1.p_1',s1_tarski__e6_21__wellord2__1) ).

fof(21,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X2)
          & relation(X3)
          & function(X3) )
       => ? [X4] :
          ! [X5] :
            ( in(X5,X4)
          <=> ( in(X5,cartesian_product2(X1,X1))
              & ? [X6,X7] :
                  ( X5 = ordered_pair(X6,X7)
                  & in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ),
    inference(assume_negation,[status(cth)],[6]) ).

fof(48,negated_conjecture,
    ? [X1,X2,X3] :
      ( relation(X2)
      & relation(X3)
      & function(X3)
      & ! [X4] :
        ? [X5] :
          ( ( ~ in(X5,X4)
            | ~ in(X5,cartesian_product2(X1,X1))
            | ! [X6,X7] :
                ( X5 != ordered_pair(X6,X7)
                | ~ in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) )
          & ( in(X5,X4)
            | ( in(X5,cartesian_product2(X1,X1))
              & ? [X6,X7] :
                  ( X5 = ordered_pair(X6,X7)
                  & in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(49,negated_conjecture,
    ? [X8,X9,X10] :
      ( relation(X9)
      & relation(X10)
      & function(X10)
      & ! [X11] :
        ? [X12] :
          ( ( ~ in(X12,X11)
            | ~ in(X12,cartesian_product2(X8,X8))
            | ! [X13,X14] :
                ( X12 != ordered_pair(X13,X14)
                | ~ in(ordered_pair(apply(X10,X13),apply(X10,X14)),X9) ) )
          & ( in(X12,X11)
            | ( in(X12,cartesian_product2(X8,X8))
              & ? [X15,X16] :
                  ( X12 = ordered_pair(X15,X16)
                  & in(ordered_pair(apply(X10,X15),apply(X10,X16)),X9) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[48]) ).

fof(50,negated_conjecture,
    ( relation(esk5_0)
    & relation(esk6_0)
    & function(esk6_0)
    & ! [X11] :
        ( ( ~ in(esk7_1(X11),X11)
          | ~ in(esk7_1(X11),cartesian_product2(esk4_0,esk4_0))
          | ! [X13,X14] :
              ( esk7_1(X11) != ordered_pair(X13,X14)
              | ~ in(ordered_pair(apply(esk6_0,X13),apply(esk6_0,X14)),esk5_0) ) )
        & ( in(esk7_1(X11),X11)
          | ( in(esk7_1(X11),cartesian_product2(esk4_0,esk4_0))
            & esk7_1(X11) = ordered_pair(esk8_1(X11),esk9_1(X11))
            & in(ordered_pair(apply(esk6_0,esk8_1(X11)),apply(esk6_0,esk9_1(X11))),esk5_0) ) ) ) ),
    inference(skolemize,[status(esa)],[49]) ).

fof(51,negated_conjecture,
    ! [X11,X13,X14] :
      ( ( esk7_1(X11) != ordered_pair(X13,X14)
        | ~ in(ordered_pair(apply(esk6_0,X13),apply(esk6_0,X14)),esk5_0)
        | ~ in(esk7_1(X11),cartesian_product2(esk4_0,esk4_0))
        | ~ in(esk7_1(X11),X11) )
      & ( in(esk7_1(X11),X11)
        | ( in(esk7_1(X11),cartesian_product2(esk4_0,esk4_0))
          & esk7_1(X11) = ordered_pair(esk8_1(X11),esk9_1(X11))
          & in(ordered_pair(apply(esk6_0,esk8_1(X11)),apply(esk6_0,esk9_1(X11))),esk5_0) ) )
      & relation(esk5_0)
      & relation(esk6_0)
      & function(esk6_0) ),
    inference(shift_quantors,[status(thm)],[50]) ).

fof(52,negated_conjecture,
    ! [X11,X13,X14] :
      ( ( esk7_1(X11) != ordered_pair(X13,X14)
        | ~ in(ordered_pair(apply(esk6_0,X13),apply(esk6_0,X14)),esk5_0)
        | ~ in(esk7_1(X11),cartesian_product2(esk4_0,esk4_0))
        | ~ in(esk7_1(X11),X11) )
      & ( in(esk7_1(X11),cartesian_product2(esk4_0,esk4_0))
        | in(esk7_1(X11),X11) )
      & ( esk7_1(X11) = ordered_pair(esk8_1(X11),esk9_1(X11))
        | in(esk7_1(X11),X11) )
      & ( in(ordered_pair(apply(esk6_0,esk8_1(X11)),apply(esk6_0,esk9_1(X11))),esk5_0)
        | in(esk7_1(X11),X11) )
      & relation(esk5_0)
      & relation(esk6_0)
      & function(esk6_0) ),
    inference(distribute,[status(thm)],[51]) ).

cnf(53,negated_conjecture,
    function(esk6_0),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(54,negated_conjecture,
    relation(esk6_0),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(55,negated_conjecture,
    relation(esk5_0),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(56,negated_conjecture,
    ( in(esk7_1(X1),X1)
    | in(ordered_pair(apply(esk6_0,esk8_1(X1)),apply(esk6_0,esk9_1(X1))),esk5_0) ),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(57,negated_conjecture,
    ( in(esk7_1(X1),X1)
    | esk7_1(X1) = ordered_pair(esk8_1(X1),esk9_1(X1)) ),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(58,negated_conjecture,
    ( in(esk7_1(X1),X1)
    | in(esk7_1(X1),cartesian_product2(esk4_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(59,negated_conjecture,
    ( ~ in(esk7_1(X1),X1)
    | ~ in(esk7_1(X1),cartesian_product2(esk4_0,esk4_0))
    | ~ in(ordered_pair(apply(esk6_0,X2),apply(esk6_0,X3)),esk5_0)
    | esk7_1(X1) != ordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(67,plain,
    ! [X1,X2,X3] :
      ( ~ relation(X2)
      | ~ relation(X3)
      | ~ function(X3)
      | ? [X4,X5,X6] :
          ( X4 = X5
          & ? [X7,X8] :
              ( X5 = ordered_pair(X7,X8)
              & in(ordered_pair(apply(X3,X7),apply(X3,X8)),X2) )
          & X4 = X6
          & ? [X9,X10] :
              ( X6 = ordered_pair(X9,X10)
              & in(ordered_pair(apply(X3,X9),apply(X3,X10)),X2) )
          & X5 != X6 )
      | ? [X4] :
        ! [X5] :
          ( ( ~ in(X5,X4)
            | ? [X6] :
                ( in(X6,cartesian_product2(X1,X1))
                & X6 = X5
                & ? [X11,X12] :
                    ( X5 = ordered_pair(X11,X12)
                    & in(ordered_pair(apply(X3,X11),apply(X3,X12)),X2) ) ) )
          & ( ! [X6] :
                ( ~ in(X6,cartesian_product2(X1,X1))
                | X6 != X5
                | ! [X11,X12] :
                    ( X5 != ordered_pair(X11,X12)
                    | ~ in(ordered_pair(apply(X3,X11),apply(X3,X12)),X2) ) )
            | in(X5,X4) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(68,plain,
    ! [X13,X14,X15] :
      ( ~ relation(X14)
      | ~ relation(X15)
      | ~ function(X15)
      | ? [X16,X17,X18] :
          ( X16 = X17
          & ? [X19,X20] :
              ( X17 = ordered_pair(X19,X20)
              & in(ordered_pair(apply(X15,X19),apply(X15,X20)),X14) )
          & X16 = X18
          & ? [X21,X22] :
              ( X18 = ordered_pair(X21,X22)
              & in(ordered_pair(apply(X15,X21),apply(X15,X22)),X14) )
          & X17 != X18 )
      | ? [X23] :
        ! [X24] :
          ( ( ~ in(X24,X23)
            | ? [X25] :
                ( in(X25,cartesian_product2(X13,X13))
                & X25 = X24
                & ? [X26,X27] :
                    ( X24 = ordered_pair(X26,X27)
                    & in(ordered_pair(apply(X15,X26),apply(X15,X27)),X14) ) ) )
          & ( ! [X28] :
                ( ~ in(X28,cartesian_product2(X13,X13))
                | X28 != X24
                | ! [X29,X30] :
                    ( X24 != ordered_pair(X29,X30)
                    | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14) ) )
            | in(X24,X23) ) ) ),
    inference(variable_rename,[status(thm)],[67]) ).

fof(69,plain,
    ! [X13,X14,X15] :
      ( ~ relation(X14)
      | ~ relation(X15)
      | ~ function(X15)
      | ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        & esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        & in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        & esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        & esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        & in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        & esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15) )
      | ! [X24] :
          ( ( ~ in(X24,esk18_3(X13,X14,X15))
            | ( in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
              & esk19_4(X13,X14,X15,X24) = X24
              & X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
              & in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14) ) )
          & ( ! [X28] :
                ( ~ in(X28,cartesian_product2(X13,X13))
                | X28 != X24
                | ! [X29,X30] :
                    ( X24 != ordered_pair(X29,X30)
                    | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14) ) )
            | in(X24,esk18_3(X13,X14,X15)) ) ) ),
    inference(skolemize,[status(esa)],[68]) ).

fof(70,plain,
    ! [X13,X14,X15,X24,X28,X29,X30] :
      ( ( ( X24 != ordered_pair(X29,X30)
          | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
          | ~ in(X28,cartesian_product2(X13,X13))
          | X28 != X24
          | in(X24,esk18_3(X13,X14,X15)) )
        & ( ~ in(X24,esk18_3(X13,X14,X15))
          | ( in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
            & esk19_4(X13,X14,X15,X24) = X24
            & X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
            & in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14) ) ) )
      | ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        & esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        & in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        & esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        & esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        & in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        & esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15) )
      | ~ relation(X14)
      | ~ relation(X15)
      | ~ function(X15) ),
    inference(shift_quantors,[status(thm)],[69]) ).

fof(71,plain,
    ! [X13,X14,X15,X24,X28,X29,X30] :
      ( ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15)
        | X24 != ordered_pair(X29,X30)
        | ~ in(ordered_pair(apply(X15,X29),apply(X15,X30)),X14)
        | ~ in(X28,cartesian_product2(X13,X13))
        | X28 != X24
        | in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15)
        | in(esk19_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15)
        | esk19_4(X13,X14,X15,X24) = X24
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15)
        | X24 = ordered_pair(esk20_4(X13,X14,X15,X24),esk21_4(X13,X14,X15,X24))
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk12_3(X13,X14,X15)
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) = ordered_pair(esk14_3(X13,X14,X15),esk15_3(X13,X14,X15))
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk14_3(X13,X14,X15)),apply(X15,esk15_3(X13,X14,X15))),X14)
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk11_3(X13,X14,X15) = esk13_3(X13,X14,X15)
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk13_3(X13,X14,X15) = ordered_pair(esk16_3(X13,X14,X15),esk17_3(X13,X14,X15))
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(ordered_pair(apply(X15,esk16_3(X13,X14,X15)),apply(X15,esk17_3(X13,X14,X15))),X14)
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk12_3(X13,X14,X15) != esk13_3(X13,X14,X15)
        | in(ordered_pair(apply(X15,esk20_4(X13,X14,X15,X24)),apply(X15,esk21_4(X13,X14,X15,X24))),X14)
        | ~ in(X24,esk18_3(X13,X14,X15))
        | ~ relation(X14)
        | ~ relation(X15)
        | ~ function(X15) ) ),
    inference(distribute,[status(thm)],[70]) ).

cnf(72,plain,
    ( in(ordered_pair(apply(X1,esk20_4(X4,X2,X1,X3)),apply(X1,esk21_4(X4,X2,X1,X3))),X2)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1))
    | esk12_3(X4,X2,X1) != esk13_3(X4,X2,X1) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(75,plain,
    ( in(ordered_pair(apply(X1,esk20_4(X4,X2,X1,X3)),apply(X1,esk21_4(X4,X2,X1,X3))),X2)
    | esk11_3(X4,X2,X1) = esk13_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(78,plain,
    ( in(ordered_pair(apply(X1,esk20_4(X4,X2,X1,X3)),apply(X1,esk21_4(X4,X2,X1,X3))),X2)
    | esk11_3(X4,X2,X1) = esk12_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(79,plain,
    ( X3 = ordered_pair(esk20_4(X4,X2,X1,X3),esk21_4(X4,X2,X1,X3))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1))
    | esk12_3(X4,X2,X1) != esk13_3(X4,X2,X1) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(82,plain,
    ( X3 = ordered_pair(esk20_4(X4,X2,X1,X3),esk21_4(X4,X2,X1,X3))
    | esk11_3(X4,X2,X1) = esk13_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(85,plain,
    ( X3 = ordered_pair(esk20_4(X4,X2,X1,X3),esk21_4(X4,X2,X1,X3))
    | esk11_3(X4,X2,X1) = esk12_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(86,plain,
    ( esk19_4(X4,X2,X1,X3) = X3
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1))
    | esk12_3(X4,X2,X1) != esk13_3(X4,X2,X1) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(89,plain,
    ( esk19_4(X4,X2,X1,X3) = X3
    | esk11_3(X4,X2,X1) = esk13_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(92,plain,
    ( esk19_4(X4,X2,X1,X3) = X3
    | esk11_3(X4,X2,X1) = esk12_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(93,plain,
    ( in(esk19_4(X4,X2,X1,X3),cartesian_product2(X4,X4))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1))
    | esk12_3(X4,X2,X1) != esk13_3(X4,X2,X1) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(96,plain,
    ( in(esk19_4(X4,X2,X1,X3),cartesian_product2(X4,X4))
    | esk11_3(X4,X2,X1) = esk13_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(99,plain,
    ( in(esk19_4(X4,X2,X1,X3),cartesian_product2(X4,X4))
    | esk11_3(X4,X2,X1) = esk12_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ in(X3,esk18_3(X4,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(100,plain,
    ( in(X3,esk18_3(X4,X2,X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | X5 != X3
    | ~ in(X5,cartesian_product2(X4,X4))
    | ~ in(ordered_pair(apply(X1,X6),apply(X1,X7)),X2)
    | X3 != ordered_pair(X6,X7)
    | esk12_3(X4,X2,X1) != esk13_3(X4,X2,X1) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(103,plain,
    ( in(X3,esk18_3(X4,X2,X1))
    | esk11_3(X4,X2,X1) = esk13_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | X5 != X3
    | ~ in(X5,cartesian_product2(X4,X4))
    | ~ in(ordered_pair(apply(X1,X6),apply(X1,X7)),X2)
    | X3 != ordered_pair(X6,X7) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(106,plain,
    ( in(X3,esk18_3(X4,X2,X1))
    | esk11_3(X4,X2,X1) = esk12_3(X4,X2,X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | X5 != X3
    | ~ in(X5,cartesian_product2(X4,X4))
    | ~ in(ordered_pair(apply(X1,X6),apply(X1,X7)),X2)
    | X3 != ordered_pair(X6,X7) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(178,plain,
    ( esk11_3(X1,X2,X3) = esk12_3(X1,X2,X3)
    | in(X4,esk18_3(X1,X2,X3))
    | ordered_pair(X5,X6) != X4
    | ~ in(ordered_pair(apply(X3,X5),apply(X3,X6)),X2)
    | ~ in(X4,cartesian_product2(X1,X1))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(er,[status(thm)],[106,theory(equality)]) ).

cnf(186,plain,
    ( in(X4,cartesian_product2(X1,X1))
    | esk13_3(X1,X2,X3) != esk12_3(X1,X2,X3)
    | ~ in(X4,esk18_3(X1,X2,X3))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[93,86,theory(equality)]) ).

cnf(191,plain,
    ( esk11_3(X1,X2,X3) = esk13_3(X1,X2,X3)
    | in(X4,esk18_3(X1,X2,X3))
    | ordered_pair(X5,X6) != X4
    | ~ in(ordered_pair(apply(X3,X5),apply(X3,X6)),X2)
    | ~ in(X4,cartesian_product2(X1,X1))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(er,[status(thm)],[103,theory(equality)]) ).

cnf(201,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[59,78,theory(equality)]) ).

cnf(211,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[201,53,theory(equality)]) ).

cnf(212,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[211,55,theory(equality)]) ).

cnf(213,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[212,54,theory(equality)]) ).

cnf(214,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[213,theory(equality)]) ).

cnf(218,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[59,75,theory(equality)]) ).

cnf(228,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[218,53,theory(equality)]) ).

cnf(229,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[228,55,theory(equality)]) ).

cnf(230,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[229,54,theory(equality)]) ).

cnf(231,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[230,theory(equality)]) ).

cnf(235,negated_conjecture,
    ( ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[59,72,theory(equality)]) ).

cnf(245,negated_conjecture,
    ( ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[235,53,theory(equality)]) ).

cnf(246,negated_conjecture,
    ( ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[245,55,theory(equality)]) ).

cnf(247,negated_conjecture,
    ( ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[246,54,theory(equality)]) ).

cnf(248,negated_conjecture,
    ( ordered_pair(esk20_4(X1,esk5_0,esk6_0,X2),esk21_4(X1,esk5_0,esk6_0,X2)) != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(X3),X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[247,theory(equality)]) ).

cnf(253,plain,
    ( in(X1,esk18_3(X2,X3,X4))
    | esk13_3(X2,X3,X4) != esk12_3(X2,X3,X4)
    | ordered_pair(X5,X6) != X1
    | ~ in(ordered_pair(apply(X4,X5),apply(X4,X6)),X3)
    | ~ in(X1,cartesian_product2(X2,X2))
    | ~ function(X4)
    | ~ relation(X3)
    | ~ relation(X4) ),
    inference(er,[status(thm)],[100,theory(equality)]) ).

cnf(349,negated_conjecture,
    ( in(esk7_1(esk18_3(X1,X2,X3)),cartesian_product2(X1,X1))
    | in(esk7_1(esk18_3(X1,X2,X3)),cartesian_product2(esk4_0,esk4_0))
    | esk13_3(X1,X2,X3) != esk12_3(X1,X2,X3)
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[186,58,theory(equality)]) ).

cnf(375,negated_conjecture,
    ( in(esk7_1(esk18_3(X1,X2,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | in(esk7_1(esk18_3(X1,X2,esk6_0)),cartesian_product2(X1,X1))
    | esk13_3(X1,X2,esk6_0) != esk12_3(X1,X2,esk6_0)
    | ~ relation(X2)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[349,53,theory(equality)]) ).

cnf(381,negated_conjecture,
    ( in(esk7_1(esk18_3(X1,X2,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | in(esk7_1(esk18_3(X1,X2,esk6_0)),cartesian_product2(X1,X1))
    | esk13_3(X1,X2,esk6_0) != esk12_3(X1,X2,esk6_0)
    | ~ relation(X2)
    | $false ),
    inference(rw,[status(thm)],[375,54,theory(equality)]) ).

cnf(382,negated_conjecture,
    ( in(esk7_1(esk18_3(X1,X2,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | in(esk7_1(esk18_3(X1,X2,esk6_0)),cartesian_product2(X1,X1))
    | esk13_3(X1,X2,esk6_0) != esk12_3(X1,X2,esk6_0)
    | ~ relation(X2) ),
    inference(cn,[status(thm)],[381,theory(equality)]) ).

cnf(391,negated_conjecture,
    ( in(esk7_1(esk18_3(X1,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | in(esk7_1(esk18_3(X1,esk5_0,esk6_0)),cartesian_product2(X1,X1))
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[382,55,theory(equality)]) ).

cnf(397,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[178,56,theory(equality)]) ).

cnf(403,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[397,53,theory(equality)]) ).

cnf(404,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[403,55,theory(equality)]) ).

cnf(405,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[404,54,theory(equality)]) ).

cnf(406,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1)) ),
    inference(cn,[status(thm)],[405,theory(equality)]) ).

cnf(407,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(ordered_pair(esk8_1(X2),esk9_1(X2)),esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X2),X2)
    | ~ in(ordered_pair(esk8_1(X2),esk9_1(X2)),cartesian_product2(X1,X1)) ),
    inference(er,[status(thm)],[406,theory(equality)]) ).

cnf(409,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | in(esk7_1(X2),esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X2),X2)
    | ~ in(esk7_1(X2),cartesian_product2(X1,X1)) ),
    inference(spm,[status(thm)],[407,57,theory(equality)]) ).

cnf(411,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(X1),esk18_3(esk4_0,esk5_0,esk6_0))
    | in(esk7_1(X1),X1) ),
    inference(spm,[status(thm)],[409,58,theory(equality)]) ).

cnf(414,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(ef,[status(thm)],[411,theory(equality)]) ).

cnf(558,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[92,414,theory(equality)]) ).

cnf(579,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[558,53,theory(equality)]) ).

cnf(580,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[579,55,theory(equality)]) ).

cnf(581,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[580,54,theory(equality)]) ).

cnf(582,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[581,theory(equality)]) ).

cnf(663,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[99,582,theory(equality)]) ).

cnf(669,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[663,53,theory(equality)]) ).

cnf(670,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[669,55,theory(equality)]) ).

cnf(671,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[670,54,theory(equality)]) ).

cnf(672,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[671,theory(equality)]) ).

cnf(760,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0)) ),
    inference(csr,[status(thm)],[672,58]) ).

cnf(892,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[214,85,theory(equality)]) ).

cnf(895,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[892,53,theory(equality)]) ).

cnf(896,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[895,55,theory(equality)]) ).

cnf(897,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[896,54,theory(equality)]) ).

cnf(898,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3) ),
    inference(cn,[status(thm)],[897,theory(equality)]) ).

cnf(910,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[898,760,theory(equality)]) ).

cnf(966,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[231,82,theory(equality)]) ).

cnf(972,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[966,53,theory(equality)]) ).

cnf(973,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[972,55,theory(equality)]) ).

cnf(974,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[973,54,theory(equality)]) ).

cnf(975,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(X3)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3) ),
    inference(cn,[status(thm)],[974,theory(equality)]) ).

cnf(1010,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[191,56,theory(equality)]) ).

cnf(1018,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[1010,53,theory(equality)]) ).

cnf(1019,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[1018,55,theory(equality)]) ).

cnf(1020,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[1019,54,theory(equality)]) ).

cnf(1021,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(X2,esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X2
    | ~ in(X2,cartesian_product2(X1,X1)) ),
    inference(cn,[status(thm)],[1020,theory(equality)]) ).

cnf(1026,negated_conjecture,
    ( X2 != esk7_1(X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[248,79,theory(equality)]) ).

cnf(1035,negated_conjecture,
    ( X2 != esk7_1(X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[1026,53,theory(equality)]) ).

cnf(1036,negated_conjecture,
    ( X2 != esk7_1(X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[1035,55,theory(equality)]) ).

cnf(1037,negated_conjecture,
    ( X2 != esk7_1(X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[1036,54,theory(equality)]) ).

cnf(1038,negated_conjecture,
    ( X2 != esk7_1(X3)
    | esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(X3),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(X3),X3) ),
    inference(cn,[status(thm)],[1037,theory(equality)]) ).

cnf(2136,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(csr,[status(thm)],[910,414]) ).

cnf(2137,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk11_3(X1,esk5_0,esk6_0) = esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(X1,esk5_0,esk6_0)) ),
    inference(er,[status(thm)],[2136,theory(equality)]) ).

cnf(2138,negated_conjecture,
    esk11_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0),
    inference(spm,[status(thm)],[2137,414,theory(equality)]) ).

cnf(2187,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(ordered_pair(esk8_1(X2),esk9_1(X2)),esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X2),X2)
    | ~ in(ordered_pair(esk8_1(X2),esk9_1(X2)),cartesian_product2(X1,X1)) ),
    inference(er,[status(thm)],[1021,theory(equality)]) ).

cnf(2189,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | in(esk7_1(X2),esk18_3(X1,esk5_0,esk6_0))
    | in(esk7_1(X2),X2)
    | ~ in(esk7_1(X2),cartesian_product2(X1,X1)) ),
    inference(spm,[status(thm)],[2187,57,theory(equality)]) ).

cnf(2191,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(X1),esk18_3(esk4_0,esk5_0,esk6_0))
    | in(esk7_1(X1),X1) ),
    inference(spm,[status(thm)],[2189,58,theory(equality)]) ).

cnf(2198,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(X1),esk18_3(esk4_0,esk5_0,esk6_0))
    | in(esk7_1(X1),X1) ),
    inference(rw,[status(thm)],[2191,2138,theory(equality)]) ).

cnf(2202,negated_conjecture,
    ( esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(ef,[status(thm)],[2198,theory(equality)]) ).

cnf(2382,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[89,2202,theory(equality)]) ).

cnf(2410,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[2382,2138,theory(equality)]) ).

cnf(2411,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[2410,53,theory(equality)]) ).

cnf(2412,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[2411,55,theory(equality)]) ).

cnf(2413,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[2412,54,theory(equality)]) ).

cnf(2414,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | esk19_4(esk4_0,esk5_0,esk6_0,esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))) = esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[2413,theory(equality)]) ).

cnf(2497,negated_conjecture,
    ( esk11_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[96,2414,theory(equality)]) ).

cnf(2511,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[2497,2138,theory(equality)]) ).

cnf(2512,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[2511,53,theory(equality)]) ).

cnf(2513,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[2512,55,theory(equality)]) ).

cnf(2514,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[2513,54,theory(equality)]) ).

cnf(2515,negated_conjecture,
    ( esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[2514,theory(equality)]) ).

cnf(2648,negated_conjecture,
    ( esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0)) ),
    inference(csr,[status(thm)],[2515,58]) ).

cnf(2654,negated_conjecture,
    ( esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[975,2648,theory(equality)]) ).

cnf(4197,negated_conjecture,
    ( esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(csr,[status(thm)],[2654,2202]) ).

cnf(4198,negated_conjecture,
    ( esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk11_3(X1,esk5_0,esk6_0) = esk13_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(X1,esk5_0,esk6_0)) ),
    inference(er,[status(thm)],[4197,theory(equality)]) ).

cnf(4199,negated_conjecture,
    ( esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk11_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[4198,2202,theory(equality)]) ).

cnf(4200,negated_conjecture,
    ( esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0)
    | esk12_3(esk4_0,esk5_0,esk6_0) = esk13_3(esk4_0,esk5_0,esk6_0) ),
    inference(rw,[status(thm)],[4199,2138,theory(equality)]) ).

cnf(4201,negated_conjecture,
    esk13_3(esk4_0,esk5_0,esk6_0) = esk12_3(esk4_0,esk5_0,esk6_0),
    inference(cn,[status(thm)],[4200,theory(equality)]) ).

cnf(4202,negated_conjecture,
    in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),cartesian_product2(esk4_0,esk4_0)),
    inference(spm,[status(thm)],[391,4201,theory(equality)]) ).

cnf(4264,negated_conjecture,
    ( esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0))
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[1038,4202,theory(equality)]) ).

cnf(4916,negated_conjecture,
    ( in(X1,esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X1
    | ~ in(X1,cartesian_product2(X2,X2))
    | ~ function(esk6_0)
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(spm,[status(thm)],[253,56,theory(equality)]) ).

cnf(4924,negated_conjecture,
    ( in(X1,esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X1
    | ~ in(X1,cartesian_product2(X2,X2))
    | $false
    | ~ relation(esk5_0)
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[4916,53,theory(equality)]) ).

cnf(4925,negated_conjecture,
    ( in(X1,esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X1
    | ~ in(X1,cartesian_product2(X2,X2))
    | $false
    | $false
    | ~ relation(esk6_0) ),
    inference(rw,[status(thm)],[4924,55,theory(equality)]) ).

cnf(4926,negated_conjecture,
    ( in(X1,esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X1
    | ~ in(X1,cartesian_product2(X2,X2))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[4925,54,theory(equality)]) ).

cnf(4927,negated_conjecture,
    ( in(X1,esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X3),X3)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ordered_pair(esk8_1(X3),esk9_1(X3)) != X1
    | ~ in(X1,cartesian_product2(X2,X2)) ),
    inference(cn,[status(thm)],[4926,theory(equality)]) ).

cnf(4946,negated_conjecture,
    ( in(ordered_pair(esk8_1(X1),esk9_1(X1)),esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X1),X1)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ~ in(ordered_pair(esk8_1(X1),esk9_1(X1)),cartesian_product2(X2,X2)) ),
    inference(er,[status(thm)],[4927,theory(equality)]) ).

cnf(4948,negated_conjecture,
    ( in(esk7_1(X1),esk18_3(X2,esk5_0,esk6_0))
    | in(esk7_1(X1),X1)
    | esk13_3(X2,esk5_0,esk6_0) != esk12_3(X2,esk5_0,esk6_0)
    | ~ in(esk7_1(X1),cartesian_product2(X2,X2)) ),
    inference(spm,[status(thm)],[4946,57,theory(equality)]) ).

cnf(4950,negated_conjecture,
    ( in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | esk13_3(esk4_0,esk5_0,esk6_0) != esk12_3(esk4_0,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[4948,4202,theory(equality)]) ).

cnf(4993,negated_conjecture,
    ( in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0))
    | $false ),
    inference(rw,[status(thm)],[4950,4201,theory(equality)]) ).

cnf(4994,negated_conjecture,
    in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(esk4_0,esk5_0,esk6_0)),
    inference(cn,[status(thm)],[4993,theory(equality)]) ).

cnf(5026,negated_conjecture,
    ( esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | $false
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(rw,[status(thm)],[4264,4994,theory(equality)]) ).

cnf(5027,negated_conjecture,
    ( esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | X2 != esk7_1(esk18_3(esk4_0,esk5_0,esk6_0))
    | ~ in(X2,esk18_3(X1,esk5_0,esk6_0)) ),
    inference(cn,[status(thm)],[5026,theory(equality)]) ).

cnf(5334,negated_conjecture,
    ( esk13_3(X1,esk5_0,esk6_0) != esk12_3(X1,esk5_0,esk6_0)
    | ~ in(esk7_1(esk18_3(esk4_0,esk5_0,esk6_0)),esk18_3(X1,esk5_0,esk6_0)) ),
    inference(er,[status(thm)],[5027,theory(equality)]) ).

cnf(5338,negated_conjecture,
    esk13_3(esk4_0,esk5_0,esk6_0) != esk12_3(esk4_0,esk5_0,esk6_0),
    inference(spm,[status(thm)],[5334,4994,theory(equality)]) ).

cnf(5339,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[5338,4201,theory(equality)]) ).

cnf(5340,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[5339,theory(equality)]) ).

cnf(5341,negated_conjecture,
    $false,
    5340,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU277+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNtAbcz/sel_SEU277+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU277+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU277+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU277+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
% 
%------------------------------------------------------------------------------