TSTP Solution File: SET766+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET766+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:39:40 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   34 (   9 unt;   0 def)
%            Number of atoms       :  407 (   0 equ)
%            Maximal formula atoms :  207 (  11 avg)
%            Number of connectives :  511 ( 138   ~; 230   |; 127   &)
%                                         (   4 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   63 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-3 aty)
%            Number of variables   :  112 (   0 sgn  84   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( equivalence(X2,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X2,X3,X3) )
        & ! [X3,X4] :
            ( ( member(X3,X1)
              & member(X4,X1) )
           => ( apply(X2,X3,X4)
             => apply(X2,X4,X3) ) )
        & ! [X3,X4,X5] :
            ( ( member(X3,X1)
              & member(X4,X1)
              & member(X5,X1) )
           => ( ( apply(X2,X3,X4)
                & apply(X2,X4,X5) )
             => apply(X2,X3,X5) ) ) ) ),
    file('/tmp/tmpkmlvOB/sel_SET766+4.p_1',equivalence) ).

fof(2,axiom,
    ! [X2,X6,X1,X3] :
      ( member(X3,equivalence_class(X1,X6,X2))
    <=> ( member(X3,X6)
        & apply(X2,X1,X3) ) ),
    file('/tmp/tmpkmlvOB/sel_SET766+4.p_1',equivalence_class) ).

fof(3,conjecture,
    ! [X6,X2,X1] :
      ( ( equivalence(X2,X6)
        & member(X1,X6) )
     => member(X1,equivalence_class(X1,X6,X2)) ),
    file('/tmp/tmpkmlvOB/sel_SET766+4.p_1',thIII02) ).

fof(4,negated_conjecture,
    ~ ! [X6,X2,X1] :
        ( ( equivalence(X2,X6)
          & member(X1,X6) )
       => member(X1,equivalence_class(X1,X6,X2)) ),
    inference(assume_negation,[status(cth)],[3]) ).

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

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

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

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

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

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

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

fof(13,plain,
    ! [X7,X8,X9,X10] :
      ( ( member(X10,X8)
        | ~ member(X10,equivalence_class(X9,X8,X7)) )
      & ( apply(X7,X9,X10)
        | ~ member(X10,equivalence_class(X9,X8,X7)) )
      & ( ~ member(X10,X8)
        | ~ apply(X7,X9,X10)
        | member(X10,equivalence_class(X9,X8,X7)) ) ),
    inference(distribute,[status(thm)],[12]) ).

cnf(14,plain,
    ( member(X1,equivalence_class(X2,X3,X4))
    | ~ apply(X4,X2,X1)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(17,negated_conjecture,
    ? [X6,X2,X1] :
      ( equivalence(X2,X6)
      & member(X1,X6)
      & ~ member(X1,equivalence_class(X1,X6,X2)) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(18,negated_conjecture,
    ? [X7,X8,X9] :
      ( equivalence(X8,X7)
      & member(X9,X7)
      & ~ member(X9,equivalence_class(X9,X7,X8)) ),
    inference(variable_rename,[status(thm)],[17]) ).

fof(19,negated_conjecture,
    ( equivalence(esk2_0,esk1_0)
    & member(esk3_0,esk1_0)
    & ~ member(esk3_0,equivalence_class(esk3_0,esk1_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[18]) ).

cnf(20,negated_conjecture,
    ~ member(esk3_0,equivalence_class(esk3_0,esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(21,negated_conjecture,
    member(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(22,negated_conjecture,
    equivalence(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(23,plain,
    ! [X1,X2] :
      ( ( ~ epred1_2(X2,X1)
        | ( ! [X3] :
              ( ~ member(X3,X1)
              | apply(X2,X3,X3) )
          & ! [X3,X4] :
              ( ~ member(X3,X1)
              | ~ member(X4,X1)
              | ~ apply(X2,X3,X4)
              | apply(X2,X4,X3) )
          & ! [X3,X4,X5] :
              ( ~ member(X3,X1)
              | ~ member(X4,X1)
              | ~ member(X5,X1)
              | ~ apply(X2,X3,X4)
              | ~ apply(X2,X4,X5)
              | apply(X2,X3,X5) ) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ apply(X2,X3,X3) )
        | ? [X3,X4] :
            ( member(X3,X1)
            & member(X4,X1)
            & apply(X2,X3,X4)
            & ~ apply(X2,X4,X3) )
        | ? [X3,X4,X5] :
            ( member(X3,X1)
            & member(X4,X1)
            & member(X5,X1)
            & apply(X2,X3,X4)
            & apply(X2,X4,X5)
            & ~ apply(X2,X3,X5) )
        | epred1_2(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(24,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) )
          & ! [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) )
        | ? [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)],[23]) ).

fof(25,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) )
          & ! [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(esk4_2(X6,X7),X6)
          & ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7)) )
        | ( member(esk5_2(X6,X7),X6)
          & member(esk6_2(X6,X7),X6)
          & apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
          & ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7)) )
        | ( member(esk7_2(X6,X7),X6)
          & member(esk8_2(X6,X7),X6)
          & member(esk9_2(X6,X7),X6)
          & apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
          & apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
          & ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7)) )
        | epred1_2(X7,X6) ) ),
    inference(skolemize,[status(esa)],[24]) ).

fof(26,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) )
          & ( ~ member(X8,X6)
            | apply(X7,X8,X8) ) )
        | ~ epred1_2(X7,X6) )
      & ( ( member(esk4_2(X6,X7),X6)
          & ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7)) )
        | ( member(esk5_2(X6,X7),X6)
          & member(esk6_2(X6,X7),X6)
          & apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
          & ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7)) )
        | ( member(esk7_2(X6,X7),X6)
          & member(esk8_2(X6,X7),X6)
          & member(esk9_2(X6,X7),X6)
          & apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
          & apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
          & ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7)) )
        | epred1_2(X7,X6) ) ),
    inference(shift_quantors,[status(thm)],[25]) ).

fof(27,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)
        | ~ epred1_2(X7,X6) )
      & ( ~ member(X8,X6)
        | apply(X7,X8,X8)
        | ~ epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | member(esk5_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | member(esk5_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk5_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk5_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | member(esk5_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | member(esk5_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | member(esk4_2(X6,X7),X6)
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | member(esk5_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | member(esk5_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk5_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk5_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | member(esk5_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | member(esk5_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | member(esk6_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | member(esk6_2(X6,X7),X6)
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | apply(X7,esk5_2(X6,X7),esk6_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk7_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk8_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( member(esk9_2(X6,X7),X6)
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( apply(X7,esk8_2(X6,X7),esk9_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) )
      & ( ~ apply(X7,esk7_2(X6,X7),esk9_2(X6,X7))
        | ~ apply(X7,esk6_2(X6,X7),esk5_2(X6,X7))
        | ~ apply(X7,esk4_2(X6,X7),esk4_2(X6,X7))
        | epred1_2(X7,X6) ) ),
    inference(distribute,[status(thm)],[26]) ).

cnf(76,plain,
    ( apply(X1,X3,X3)
    | ~ epred1_2(X1,X2)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(79,negated_conjecture,
    epred1_2(esk2_0,esk1_0),
    inference(spm,[status(thm)],[10,22,theory(equality)]) ).

cnf(83,negated_conjecture,
    ( ~ apply(esk2_0,esk3_0,esk3_0)
    | ~ member(esk3_0,esk1_0) ),
    inference(spm,[status(thm)],[20,14,theory(equality)]) ).

cnf(86,negated_conjecture,
    ( ~ apply(esk2_0,esk3_0,esk3_0)
    | $false ),
    inference(rw,[status(thm)],[83,21,theory(equality)]) ).

cnf(87,negated_conjecture,
    ~ apply(esk2_0,esk3_0,esk3_0),
    inference(cn,[status(thm)],[86,theory(equality)]) ).

cnf(142,negated_conjecture,
    ( apply(esk2_0,X1,X1)
    | ~ member(X1,esk1_0) ),
    inference(spm,[status(thm)],[76,79,theory(equality)]) ).

cnf(151,negated_conjecture,
    ~ member(esk3_0,esk1_0),
    inference(spm,[status(thm)],[87,142,theory(equality)]) ).

cnf(152,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[151,21,theory(equality)]) ).

cnf(153,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[152,theory(equality)]) ).

cnf(154,negated_conjecture,
    $false,
    153,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET766+4.p
% --creating new selector for [SET006+0.ax, SET006+2.ax]
% -running prover on /tmp/tmpkmlvOB/sel_SET766+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET766+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET766+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET766+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
% 
%------------------------------------------------------------------------------