TSTP Solution File: SET790+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET790+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:39:11 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   45 (   9 unt;   0 def)
%            Number of atoms       :  536 (  35 equ)
%            Maximal formula atoms :  256 (  11 avg)
%            Number of connectives :  680 ( 189   ~; 315   |; 157   &)
%                                         (   4 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   75 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :  138 (   1 sgn  94   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( order(X1,X2)
    <=> ( ! [X3] :
            ( member(X3,X2)
           => apply(X1,X3,X3) )
        & ! [X3,X4] :
            ( ( member(X3,X2)
              & member(X4,X2) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X4,X3) )
             => X3 = X4 ) )
        & ! [X3,X4,X5] :
            ( ( member(X3,X2)
              & member(X4,X2)
              & member(X5,X2) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X4,X5) )
             => apply(X1,X3,X5) ) ) ) ),
    file('/tmp/tmpnnmK6x/sel_SET790+4.p_1',order) ).

fof(2,axiom,
    ! [X1,X2,X6] :
      ( least(X6,X1,X2)
    <=> ( member(X6,X2)
        & ! [X3] :
            ( member(X3,X2)
           => apply(X1,X6,X3) ) ) ),
    file('/tmp/tmpnnmK6x/sel_SET790+4.p_1',least) ).

fof(3,conjecture,
    ! [X1,X2,X6] :
      ( ( order(X1,X2)
        & least(X6,X1,X2) )
     => ! [X3] :
          ( least(X3,X1,X2)
         => X6 = X3 ) ),
    file('/tmp/tmpnnmK6x/sel_SET790+4.p_1',thIV2) ).

fof(4,negated_conjecture,
    ~ ! [X1,X2,X6] :
        ( ( order(X1,X2)
          & least(X6,X1,X2) )
       => ! [X3] :
            ( least(X3,X1,X2)
           => X6 = X3 ) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(5,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
    <=> ( ! [X3] :
            ( member(X3,X2)
           => apply(X1,X3,X3) )
        & ! [X3,X4] :
            ( ( member(X3,X2)
              & member(X4,X2) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X4,X3) )
             => X3 = X4 ) )
        & ! [X3,X4,X5] :
            ( ( member(X3,X2)
              & member(X4,X2)
              & member(X5,X2) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X4,X5) )
             => apply(X1,X3,X5) ) ) ) ),
    introduced(definition) ).

fof(6,plain,
    ! [X1,X2] :
      ( order(X1,X2)
    <=> epred1_2(X1,X2) ),
    inference(apply_def,[status(esa)],[1,5,theory(equality)]) ).

fof(7,plain,
    ! [X1,X2] :
      ( ( ~ order(X1,X2)
        | epred1_2(X1,X2) )
      & ( ~ epred1_2(X1,X2)
        | order(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(8,plain,
    ! [X3,X4] :
      ( ( ~ order(X3,X4)
        | epred1_2(X3,X4) )
      & ( ~ epred1_2(X3,X4)
        | order(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(10,plain,
    ( epred1_2(X1,X2)
    | ~ order(X1,X2) ),
    inference(split_conjunct,[status(thm)],[8]) ).

fof(11,plain,
    ! [X1,X2,X6] :
      ( ( ~ least(X6,X1,X2)
        | ( member(X6,X2)
          & ! [X3] :
              ( ~ member(X3,X2)
              | apply(X1,X6,X3) ) ) )
      & ( ~ member(X6,X2)
        | ? [X3] :
            ( member(X3,X2)
            & ~ apply(X1,X6,X3) )
        | least(X6,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(12,plain,
    ! [X7,X8,X9] :
      ( ( ~ least(X9,X7,X8)
        | ( member(X9,X8)
          & ! [X10] :
              ( ~ member(X10,X8)
              | apply(X7,X9,X10) ) ) )
      & ( ~ member(X9,X8)
        | ? [X11] :
            ( member(X11,X8)
            & ~ apply(X7,X9,X11) )
        | least(X9,X7,X8) ) ),
    inference(variable_rename,[status(thm)],[11]) ).

fof(13,plain,
    ! [X7,X8,X9] :
      ( ( ~ least(X9,X7,X8)
        | ( member(X9,X8)
          & ! [X10] :
              ( ~ member(X10,X8)
              | apply(X7,X9,X10) ) ) )
      & ( ~ member(X9,X8)
        | ( member(esk1_3(X7,X8,X9),X8)
          & ~ apply(X7,X9,esk1_3(X7,X8,X9)) )
        | least(X9,X7,X8) ) ),
    inference(skolemize,[status(esa)],[12]) ).

fof(14,plain,
    ! [X7,X8,X9,X10] :
      ( ( ( ( ~ member(X10,X8)
            | apply(X7,X9,X10) )
          & member(X9,X8) )
        | ~ least(X9,X7,X8) )
      & ( ~ member(X9,X8)
        | ( member(esk1_3(X7,X8,X9),X8)
          & ~ apply(X7,X9,esk1_3(X7,X8,X9)) )
        | least(X9,X7,X8) ) ),
    inference(shift_quantors,[status(thm)],[13]) ).

fof(15,plain,
    ! [X7,X8,X9,X10] :
      ( ( ~ member(X10,X8)
        | apply(X7,X9,X10)
        | ~ least(X9,X7,X8) )
      & ( member(X9,X8)
        | ~ least(X9,X7,X8) )
      & ( member(esk1_3(X7,X8,X9),X8)
        | ~ member(X9,X8)
        | least(X9,X7,X8) )
      & ( ~ apply(X7,X9,esk1_3(X7,X8,X9))
        | ~ member(X9,X8)
        | least(X9,X7,X8) ) ),
    inference(distribute,[status(thm)],[14]) ).

cnf(18,plain,
    ( member(X1,X3)
    | ~ least(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(19,plain,
    ( apply(X2,X1,X4)
    | ~ least(X1,X2,X3)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(20,negated_conjecture,
    ? [X1,X2,X6] :
      ( order(X1,X2)
      & least(X6,X1,X2)
      & ? [X3] :
          ( least(X3,X1,X2)
          & X6 != X3 ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(21,negated_conjecture,
    ? [X7,X8,X9] :
      ( order(X7,X8)
      & least(X9,X7,X8)
      & ? [X10] :
          ( least(X10,X7,X8)
          & X9 != X10 ) ),
    inference(variable_rename,[status(thm)],[20]) ).

fof(22,negated_conjecture,
    ( order(esk2_0,esk3_0)
    & least(esk4_0,esk2_0,esk3_0)
    & least(esk5_0,esk2_0,esk3_0)
    & esk4_0 != esk5_0 ),
    inference(skolemize,[status(esa)],[21]) ).

cnf(23,negated_conjecture,
    esk4_0 != esk5_0,
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(24,negated_conjecture,
    least(esk5_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(25,negated_conjecture,
    least(esk4_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(26,negated_conjecture,
    order(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(27,plain,
    ! [X2,X1] :
      ( ( ~ epred1_2(X1,X2)
        | ( ! [X3] :
              ( ~ member(X3,X2)
              | apply(X1,X3,X3) )
          & ! [X3,X4] :
              ( ~ member(X3,X2)
              | ~ member(X4,X2)
              | ~ apply(X1,X3,X4)
              | ~ apply(X1,X4,X3)
              | X3 = X4 )
          & ! [X3,X4,X5] :
              ( ~ member(X3,X2)
              | ~ member(X4,X2)
              | ~ member(X5,X2)
              | ~ apply(X1,X3,X4)
              | ~ apply(X1,X4,X5)
              | apply(X1,X3,X5) ) ) )
      & ( ? [X3] :
            ( member(X3,X2)
            & ~ apply(X1,X3,X3) )
        | ? [X3,X4] :
            ( member(X3,X2)
            & member(X4,X2)
            & apply(X1,X3,X4)
            & apply(X1,X4,X3)
            & X3 != X4 )
        | ? [X3,X4,X5] :
            ( member(X3,X2)
            & member(X4,X2)
            & member(X5,X2)
            & apply(X1,X3,X4)
            & apply(X1,X4,X5)
            & ~ apply(X1,X3,X5) )
        | epred1_2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(28,plain,
    ! [X6,X7] :
      ( ( ~ epred1_2(X7,X6)
        | ( ! [X8] :
              ( ~ member(X8,X6)
              | apply(X7,X8,X8) )
          & ! [X9,X10] :
              ( ~ member(X9,X6)
              | ~ member(X10,X6)
              | ~ apply(X7,X9,X10)
              | ~ apply(X7,X10,X9)
              | X9 = X10 )
          & ! [X11,X12,X13] :
              ( ~ member(X11,X6)
              | ~ member(X12,X6)
              | ~ member(X13,X6)
              | ~ apply(X7,X11,X12)
              | ~ apply(X7,X12,X13)
              | apply(X7,X11,X13) ) ) )
      & ( ? [X14] :
            ( member(X14,X6)
            & ~ apply(X7,X14,X14) )
        | ? [X15,X16] :
            ( member(X15,X6)
            & member(X16,X6)
            & apply(X7,X15,X16)
            & apply(X7,X16,X15)
            & X15 != X16 )
        | ? [X17,X18,X19] :
            ( member(X17,X6)
            & member(X18,X6)
            & member(X19,X6)
            & apply(X7,X17,X18)
            & apply(X7,X18,X19)
            & ~ apply(X7,X17,X19) )
        | epred1_2(X7,X6) ) ),
    inference(variable_rename,[status(thm)],[27]) ).

fof(29,plain,
    ! [X6,X7] :
      ( ( ~ epred1_2(X7,X6)
        | ( ! [X8] :
              ( ~ member(X8,X6)
              | apply(X7,X8,X8) )
          & ! [X9,X10] :
              ( ~ member(X9,X6)
              | ~ member(X10,X6)
              | ~ apply(X7,X9,X10)
              | ~ apply(X7,X10,X9)
              | X9 = X10 )
          & ! [X11,X12,X13] :
              ( ~ member(X11,X6)
              | ~ member(X12,X6)
              | ~ member(X13,X6)
              | ~ apply(X7,X11,X12)
              | ~ apply(X7,X12,X13)
              | apply(X7,X11,X13) ) ) )
      & ( ( member(esk6_2(X6,X7),X6)
          & ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7)) )
        | ( member(esk7_2(X6,X7),X6)
          & member(esk8_2(X6,X7),X6)
          & apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
          & apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
          & esk7_2(X6,X7) != esk8_2(X6,X7) )
        | ( member(esk9_2(X6,X7),X6)
          & member(esk10_2(X6,X7),X6)
          & member(esk11_2(X6,X7),X6)
          & apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
          & apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
          & ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7)) )
        | epred1_2(X7,X6) ) ),
    inference(skolemize,[status(esa)],[28]) ).

fof(30,plain,
    ! [X6,X7,X8,X9,X10,X11,X12,X13] :
      ( ( ( ( ~ member(X11,X6)
            | ~ member(X12,X6)
            | ~ member(X13,X6)
            | ~ apply(X7,X11,X12)
            | ~ apply(X7,X12,X13)
            | apply(X7,X11,X13) )
          & ( ~ member(X9,X6)
            | ~ member(X10,X6)
            | ~ apply(X7,X9,X10)
            | ~ apply(X7,X10,X9)
            | X9 = X10 )
          & ( ~ member(X8,X6)
            | apply(X7,X8,X8) ) )
        | ~ epred1_2(X7,X6) )
      & ( ( member(esk6_2(X6,X7),X6)
          & ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7)) )
        | ( member(esk7_2(X6,X7),X6)
          & member(esk8_2(X6,X7),X6)
          & apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
          & apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
          & esk7_2(X6,X7) != esk8_2(X6,X7) )
        | ( member(esk9_2(X6,X7),X6)
          & member(esk10_2(X6,X7),X6)
          & member(esk11_2(X6,X7),X6)
          & apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
          & apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
          & ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7)) )
        | epred1_2(X7,X6) ) ),
    inference(shift_quantors,[status(thm)],[29]) ).

fof(31,plain,
    ! [X6,X7,X8,X9,X10,X11,X12,X13] :
      ( ( ~ member(X11,X6)
        | ~ member(X12,X6)
        | ~ member(X13,X6)
        | ~ apply(X7,X11,X12)
        | ~ apply(X7,X12,X13)
        | apply(X7,X11,X13)
        | ~ epred1_2(X7,X6) )
      & ( ~ member(X9,X6)
        | ~ member(X10,X6)
        | ~ apply(X7,X9,X10)
        | ~ apply(X7,X10,X9)
        | X9 = X10
        | ~ epred1_2(X7,X6) )
      & ( ~ member(X8,X6)
        | apply(X7,X8,X8)
        | ~ epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | member(esk6_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk10_2(X6,X7),X6)
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk11_2(X6,X7),X6)
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
        | esk7_2(X6,X7) != esk8_2(X6,X7)
        | ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
        | epred1_2(X7,X6) ) ),
    inference(distribute,[status(thm)],[30]) ).

cnf(93,plain,
    ( X3 = X4
    | ~ epred1_2(X1,X2)
    | ~ apply(X1,X4,X3)
    | ~ apply(X1,X3,X4)
    | ~ member(X4,X2)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(95,negated_conjecture,
    epred1_2(esk2_0,esk3_0),
    inference(spm,[status(thm)],[10,26,theory(equality)]) ).

cnf(97,negated_conjecture,
    member(esk4_0,esk3_0),
    inference(spm,[status(thm)],[18,25,theory(equality)]) ).

cnf(98,negated_conjecture,
    member(esk5_0,esk3_0),
    inference(spm,[status(thm)],[18,24,theory(equality)]) ).

cnf(99,negated_conjecture,
    ( apply(esk2_0,esk4_0,X1)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[19,25,theory(equality)]) ).

cnf(100,negated_conjecture,
    ( apply(esk2_0,esk5_0,X1)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[19,24,theory(equality)]) ).

cnf(167,negated_conjecture,
    ( X1 = esk4_0
    | ~ epred1_2(esk2_0,X2)
    | ~ apply(esk2_0,X1,esk4_0)
    | ~ member(esk4_0,X2)
    | ~ member(X1,X2)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[93,99,theory(equality)]) ).

cnf(190,negated_conjecture,
    ( esk5_0 = esk4_0
    | ~ epred1_2(esk2_0,X1)
    | ~ member(esk4_0,X1)
    | ~ member(esk5_0,esk3_0)
    | ~ member(esk5_0,X1)
    | ~ member(esk4_0,esk3_0) ),
    inference(spm,[status(thm)],[167,100,theory(equality)]) ).

cnf(191,negated_conjecture,
    ( esk5_0 = esk4_0
    | ~ epred1_2(esk2_0,X1)
    | ~ member(esk4_0,X1)
    | $false
    | ~ member(esk5_0,X1)
    | ~ member(esk4_0,esk3_0) ),
    inference(rw,[status(thm)],[190,98,theory(equality)]) ).

cnf(192,negated_conjecture,
    ( esk5_0 = esk4_0
    | ~ epred1_2(esk2_0,X1)
    | ~ member(esk4_0,X1)
    | $false
    | ~ member(esk5_0,X1)
    | $false ),
    inference(rw,[status(thm)],[191,97,theory(equality)]) ).

cnf(193,negated_conjecture,
    ( esk5_0 = esk4_0
    | ~ epred1_2(esk2_0,X1)
    | ~ member(esk4_0,X1)
    | ~ member(esk5_0,X1) ),
    inference(cn,[status(thm)],[192,theory(equality)]) ).

cnf(194,negated_conjecture,
    ( ~ epred1_2(esk2_0,X1)
    | ~ member(esk4_0,X1)
    | ~ member(esk5_0,X1) ),
    inference(sr,[status(thm)],[193,23,theory(equality)]) ).

cnf(195,negated_conjecture,
    ( ~ member(esk4_0,esk3_0)
    | ~ member(esk5_0,esk3_0) ),
    inference(spm,[status(thm)],[194,95,theory(equality)]) ).

cnf(196,negated_conjecture,
    ( $false
    | ~ member(esk5_0,esk3_0) ),
    inference(rw,[status(thm)],[195,97,theory(equality)]) ).

cnf(197,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[196,98,theory(equality)]) ).

cnf(198,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[197,theory(equality)]) ).

cnf(199,negated_conjecture,
    $false,
    198,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET790+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpnnmK6x/sel_SET790+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET790+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET790+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET790+4.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
% 
%------------------------------------------------------------------------------