TSTP Solution File: SET731+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET731+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 03:21:28 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   41 (   5 unt;   0 def)
%            Number of atoms       :  206 (   8 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  266 ( 101   ~;  96   |;  60   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-4 aty)
%            Number of variables   :  136 (   0 sgn  76   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X4,X1,X2] :
      ( surjective(X4,X1,X2)
    <=> ! [X5] :
          ( member(X5,X2)
         => ? [X6] :
              ( member(X6,X1)
              & apply(X4,X6,X5) ) ) ),
    file('/tmp/tmpEyguyM/sel_SET731+4.p_1',surjective) ).

fof(5,axiom,
    ! [X4,X1,X5] :
      ( member(X5,image2(X4,X1))
    <=> ? [X3] :
          ( member(X3,X1)
          & apply(X4,X3,X5) ) ),
    file('/tmp/tmpEyguyM/sel_SET731+4.p_1',image2) ).

fof(7,conjecture,
    ! [X4,X11,X1,X2,X12] :
      ( ( maps(X4,X1,X2)
        & subset(X12,X2)
        & image2(X4,X1) = X12
        & ! [X3,X5] :
            ( ( member(X3,X1)
              & member(X5,X12) )
           => ( apply(X11,X3,X5)
            <=> apply(X4,X3,X5) ) ) )
     => surjective(X11,X1,X12) ),
    file('/tmp/tmpEyguyM/sel_SET731+4.p_1',thII22) ).

fof(8,negated_conjecture,
    ~ ! [X4,X11,X1,X2,X12] :
        ( ( maps(X4,X1,X2)
          & subset(X12,X2)
          & image2(X4,X1) = X12
          & ! [X3,X5] :
              ( ( member(X3,X1)
                & member(X5,X12) )
             => ( apply(X11,X3,X5)
              <=> apply(X4,X3,X5) ) ) )
       => surjective(X11,X1,X12) ),
    inference(assume_negation,[status(cth)],[7]) ).

fof(17,plain,
    ! [X4,X1,X2] :
      ( ( ~ surjective(X4,X1,X2)
        | ! [X5] :
            ( ~ member(X5,X2)
            | ? [X6] :
                ( member(X6,X1)
                & apply(X4,X6,X5) ) ) )
      & ( ? [X5] :
            ( member(X5,X2)
            & ! [X6] :
                ( ~ member(X6,X1)
                | ~ apply(X4,X6,X5) ) )
        | surjective(X4,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(18,plain,
    ! [X7,X8,X9] :
      ( ( ~ surjective(X7,X8,X9)
        | ! [X10] :
            ( ~ member(X10,X9)
            | ? [X11] :
                ( member(X11,X8)
                & apply(X7,X11,X10) ) ) )
      & ( ? [X12] :
            ( member(X12,X9)
            & ! [X13] :
                ( ~ member(X13,X8)
                | ~ apply(X7,X13,X12) ) )
        | surjective(X7,X8,X9) ) ),
    inference(variable_rename,[status(thm)],[17]) ).

fof(19,plain,
    ! [X7,X8,X9] :
      ( ( ~ surjective(X7,X8,X9)
        | ! [X10] :
            ( ~ member(X10,X9)
            | ( member(esk2_4(X7,X8,X9,X10),X8)
              & apply(X7,esk2_4(X7,X8,X9,X10),X10) ) ) )
      & ( ( member(esk3_3(X7,X8,X9),X9)
          & ! [X13] :
              ( ~ member(X13,X8)
              | ~ apply(X7,X13,esk3_3(X7,X8,X9)) ) )
        | surjective(X7,X8,X9) ) ),
    inference(skolemize,[status(esa)],[18]) ).

fof(20,plain,
    ! [X7,X8,X9,X10,X13] :
      ( ( ( ( ~ member(X13,X8)
            | ~ apply(X7,X13,esk3_3(X7,X8,X9)) )
          & member(esk3_3(X7,X8,X9),X9) )
        | surjective(X7,X8,X9) )
      & ( ~ member(X10,X9)
        | ( member(esk2_4(X7,X8,X9,X10),X8)
          & apply(X7,esk2_4(X7,X8,X9,X10),X10) )
        | ~ surjective(X7,X8,X9) ) ),
    inference(shift_quantors,[status(thm)],[19]) ).

fof(21,plain,
    ! [X7,X8,X9,X10,X13] :
      ( ( ~ member(X13,X8)
        | ~ apply(X7,X13,esk3_3(X7,X8,X9))
        | surjective(X7,X8,X9) )
      & ( member(esk3_3(X7,X8,X9),X9)
        | surjective(X7,X8,X9) )
      & ( member(esk2_4(X7,X8,X9,X10),X8)
        | ~ member(X10,X9)
        | ~ surjective(X7,X8,X9) )
      & ( apply(X7,esk2_4(X7,X8,X9,X10),X10)
        | ~ member(X10,X9)
        | ~ surjective(X7,X8,X9) ) ),
    inference(distribute,[status(thm)],[20]) ).

cnf(24,plain,
    ( surjective(X1,X2,X3)
    | member(esk3_3(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(25,plain,
    ( surjective(X1,X2,X3)
    | ~ apply(X1,X4,esk3_3(X1,X2,X3))
    | ~ member(X4,X2) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(52,plain,
    ! [X4,X1,X5] :
      ( ( ~ member(X5,image2(X4,X1))
        | ? [X3] :
            ( member(X3,X1)
            & apply(X4,X3,X5) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | ~ apply(X4,X3,X5) )
        | member(X5,image2(X4,X1)) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(53,plain,
    ! [X6,X7,X8] :
      ( ( ~ member(X8,image2(X6,X7))
        | ? [X9] :
            ( member(X9,X7)
            & apply(X6,X9,X8) ) )
      & ( ! [X10] :
            ( ~ member(X10,X7)
            | ~ apply(X6,X10,X8) )
        | member(X8,image2(X6,X7)) ) ),
    inference(variable_rename,[status(thm)],[52]) ).

fof(54,plain,
    ! [X6,X7,X8] :
      ( ( ~ member(X8,image2(X6,X7))
        | ( member(esk9_3(X6,X7,X8),X7)
          & apply(X6,esk9_3(X6,X7,X8),X8) ) )
      & ( ! [X10] :
            ( ~ member(X10,X7)
            | ~ apply(X6,X10,X8) )
        | member(X8,image2(X6,X7)) ) ),
    inference(skolemize,[status(esa)],[53]) ).

fof(55,plain,
    ! [X6,X7,X8,X10] :
      ( ( ~ member(X10,X7)
        | ~ apply(X6,X10,X8)
        | member(X8,image2(X6,X7)) )
      & ( ~ member(X8,image2(X6,X7))
        | ( member(esk9_3(X6,X7,X8),X7)
          & apply(X6,esk9_3(X6,X7,X8),X8) ) ) ),
    inference(shift_quantors,[status(thm)],[54]) ).

fof(56,plain,
    ! [X6,X7,X8,X10] :
      ( ( ~ member(X10,X7)
        | ~ apply(X6,X10,X8)
        | member(X8,image2(X6,X7)) )
      & ( member(esk9_3(X6,X7,X8),X7)
        | ~ member(X8,image2(X6,X7)) )
      & ( apply(X6,esk9_3(X6,X7,X8),X8)
        | ~ member(X8,image2(X6,X7)) ) ),
    inference(distribute,[status(thm)],[55]) ).

cnf(57,plain,
    ( apply(X2,esk9_3(X2,X3,X1),X1)
    | ~ member(X1,image2(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[56]) ).

cnf(58,plain,
    ( member(esk9_3(X2,X3,X1),X3)
    | ~ member(X1,image2(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[56]) ).

cnf(59,plain,
    ( member(X1,image2(X2,X3))
    | ~ apply(X2,X4,X1)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[56]) ).

fof(72,negated_conjecture,
    ? [X4,X11,X1,X2,X12] :
      ( maps(X4,X1,X2)
      & subset(X12,X2)
      & image2(X4,X1) = X12
      & ! [X3,X5] :
          ( ~ member(X3,X1)
          | ~ member(X5,X12)
          | ( ( ~ apply(X11,X3,X5)
              | apply(X4,X3,X5) )
            & ( ~ apply(X4,X3,X5)
              | apply(X11,X3,X5) ) ) )
      & ~ surjective(X11,X1,X12) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(73,negated_conjecture,
    ? [X13,X14,X15,X16,X17] :
      ( maps(X13,X15,X16)
      & subset(X17,X16)
      & image2(X13,X15) = X17
      & ! [X18,X19] :
          ( ~ member(X18,X15)
          | ~ member(X19,X17)
          | ( ( ~ apply(X14,X18,X19)
              | apply(X13,X18,X19) )
            & ( ~ apply(X13,X18,X19)
              | apply(X14,X18,X19) ) ) )
      & ~ surjective(X14,X15,X17) ),
    inference(variable_rename,[status(thm)],[72]) ).

fof(74,negated_conjecture,
    ( maps(esk13_0,esk15_0,esk16_0)
    & subset(esk17_0,esk16_0)
    & image2(esk13_0,esk15_0) = esk17_0
    & ! [X18,X19] :
        ( ~ member(X18,esk15_0)
        | ~ member(X19,esk17_0)
        | ( ( ~ apply(esk14_0,X18,X19)
            | apply(esk13_0,X18,X19) )
          & ( ~ apply(esk13_0,X18,X19)
            | apply(esk14_0,X18,X19) ) ) )
    & ~ surjective(esk14_0,esk15_0,esk17_0) ),
    inference(skolemize,[status(esa)],[73]) ).

fof(75,negated_conjecture,
    ! [X18,X19] :
      ( ( ~ member(X18,esk15_0)
        | ~ member(X19,esk17_0)
        | ( ( ~ apply(esk14_0,X18,X19)
            | apply(esk13_0,X18,X19) )
          & ( ~ apply(esk13_0,X18,X19)
            | apply(esk14_0,X18,X19) ) ) )
      & maps(esk13_0,esk15_0,esk16_0)
      & subset(esk17_0,esk16_0)
      & image2(esk13_0,esk15_0) = esk17_0
      & ~ surjective(esk14_0,esk15_0,esk17_0) ),
    inference(shift_quantors,[status(thm)],[74]) ).

fof(76,negated_conjecture,
    ! [X18,X19] :
      ( ( ~ apply(esk14_0,X18,X19)
        | apply(esk13_0,X18,X19)
        | ~ member(X18,esk15_0)
        | ~ member(X19,esk17_0) )
      & ( ~ apply(esk13_0,X18,X19)
        | apply(esk14_0,X18,X19)
        | ~ member(X18,esk15_0)
        | ~ member(X19,esk17_0) )
      & maps(esk13_0,esk15_0,esk16_0)
      & subset(esk17_0,esk16_0)
      & image2(esk13_0,esk15_0) = esk17_0
      & ~ surjective(esk14_0,esk15_0,esk17_0) ),
    inference(distribute,[status(thm)],[75]) ).

cnf(77,negated_conjecture,
    ~ surjective(esk14_0,esk15_0,esk17_0),
    inference(split_conjunct,[status(thm)],[76]) ).

cnf(78,negated_conjecture,
    image2(esk13_0,esk15_0) = esk17_0,
    inference(split_conjunct,[status(thm)],[76]) ).

cnf(81,negated_conjecture,
    ( apply(esk14_0,X2,X1)
    | ~ member(X1,esk17_0)
    | ~ member(X2,esk15_0)
    | ~ apply(esk13_0,X2,X1) ),
    inference(split_conjunct,[status(thm)],[76]) ).

cnf(85,negated_conjecture,
    ( member(X1,image2(esk14_0,X2))
    | ~ member(X3,X2)
    | ~ apply(esk13_0,X3,X1)
    | ~ member(X3,esk15_0)
    | ~ member(X1,esk17_0) ),
    inference(spm,[status(thm)],[59,81,theory(equality)]) ).

cnf(90,plain,
    ( surjective(X1,X2,X3)
    | ~ member(esk9_3(X1,X4,esk3_3(X1,X2,X3)),X2)
    | ~ member(esk3_3(X1,X2,X3),image2(X1,X4)) ),
    inference(spm,[status(thm)],[25,57,theory(equality)]) ).

cnf(123,negated_conjecture,
    ( member(X1,image2(esk14_0,X2))
    | ~ member(esk9_3(esk13_0,X3,X1),esk15_0)
    | ~ member(X1,esk17_0)
    | ~ member(esk9_3(esk13_0,X3,X1),X2)
    | ~ member(X1,image2(esk13_0,X3)) ),
    inference(spm,[status(thm)],[85,57,theory(equality)]) ).

cnf(165,plain,
    ( surjective(X1,X2,X3)
    | ~ member(esk3_3(X1,X2,X3),image2(X1,X2)) ),
    inference(spm,[status(thm)],[90,58,theory(equality)]) ).

cnf(228,negated_conjecture,
    ( member(X1,image2(esk14_0,X2))
    | ~ member(esk9_3(esk13_0,esk15_0,X1),X2)
    | ~ member(X1,image2(esk13_0,esk15_0))
    | ~ member(X1,esk17_0) ),
    inference(spm,[status(thm)],[123,58,theory(equality)]) ).

cnf(229,negated_conjecture,
    ( member(X1,image2(esk14_0,X2))
    | ~ member(esk9_3(esk13_0,esk15_0,X1),X2)
    | ~ member(X1,esk17_0)
    | ~ member(X1,esk17_0) ),
    inference(rw,[status(thm)],[228,78,theory(equality)]) ).

cnf(230,negated_conjecture,
    ( member(X1,image2(esk14_0,X2))
    | ~ member(esk9_3(esk13_0,esk15_0,X1),X2)
    | ~ member(X1,esk17_0) ),
    inference(cn,[status(thm)],[229,theory(equality)]) ).

cnf(231,negated_conjecture,
    ( member(X1,image2(esk14_0,esk15_0))
    | ~ member(X1,esk17_0)
    | ~ member(X1,image2(esk13_0,esk15_0)) ),
    inference(spm,[status(thm)],[230,58,theory(equality)]) ).

cnf(236,negated_conjecture,
    ( member(X1,image2(esk14_0,esk15_0))
    | ~ member(X1,esk17_0)
    | ~ member(X1,esk17_0) ),
    inference(rw,[status(thm)],[231,78,theory(equality)]) ).

cnf(237,negated_conjecture,
    ( member(X1,image2(esk14_0,esk15_0))
    | ~ member(X1,esk17_0) ),
    inference(cn,[status(thm)],[236,theory(equality)]) ).

cnf(242,negated_conjecture,
    ( surjective(esk14_0,esk15_0,X1)
    | ~ member(esk3_3(esk14_0,esk15_0,X1),esk17_0) ),
    inference(spm,[status(thm)],[165,237,theory(equality)]) ).

cnf(246,negated_conjecture,
    surjective(esk14_0,esk15_0,esk17_0),
    inference(spm,[status(thm)],[242,24,theory(equality)]) ).

cnf(247,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[246,77,theory(equality)]) ).

cnf(248,negated_conjecture,
    $false,
    247,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET731+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpEyguyM/sel_SET731+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET731+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET731+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET731+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
% 
%------------------------------------------------------------------------------