TSTP Solution File: SET803+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET803+4 : TPTP v5.0.0. Released v3.2.0.
% 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 03:40:30 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   42 (  11 unt;   0 def)
%            Number of atoms       :  186 (  29 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  226 (  82   ~;  82   |;  54   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   93 (   2 sgn  56   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( max(X3,X1,X2)
    <=> ( member(X3,X2)
        & ! [X4] :
            ( ( member(X4,X2)
              & apply(X1,X3,X4) )
           => X3 = X4 ) ) ),
    file('/tmp/tmpqVfkts/sel_SET803+4.p_1',max) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( greatest(X3,X1,X2)
    <=> ( member(X3,X2)
        & ! [X4] :
            ( member(X4,X2)
           => apply(X1,X4,X3) ) ) ),
    file('/tmp/tmpqVfkts/sel_SET803+4.p_1',greatest) ).

fof(4,conjecture,
    ! [X1,X2] :
      ( order(X1,X2)
     => ! [X7,X8] :
          ( ( max(X7,X1,X2)
            & max(X8,X1,X2)
            & X7 != X8 )
         => ~ ? [X3] : greatest(X3,X1,X2) ) ),
    file('/tmp/tmpqVfkts/sel_SET803+4.p_1',thIV15) ).

fof(5,negated_conjecture,
    ~ ! [X1,X2] :
        ( order(X1,X2)
       => ! [X7,X8] :
            ( ( max(X7,X1,X2)
              & max(X8,X1,X2)
              & X7 != X8 )
           => ~ ? [X3] : greatest(X3,X1,X2) ) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(8,plain,
    ! [X1,X2,X3] :
      ( ( ~ max(X3,X1,X2)
        | ( member(X3,X2)
          & ! [X4] :
              ( ~ member(X4,X2)
              | ~ apply(X1,X3,X4)
              | X3 = X4 ) ) )
      & ( ~ member(X3,X2)
        | ? [X4] :
            ( member(X4,X2)
            & apply(X1,X3,X4)
            & X3 != X4 )
        | max(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(9,plain,
    ! [X5,X6,X7] :
      ( ( ~ max(X7,X5,X6)
        | ( member(X7,X6)
          & ! [X8] :
              ( ~ member(X8,X6)
              | ~ apply(X5,X7,X8)
              | X7 = X8 ) ) )
      & ( ~ member(X7,X6)
        | ? [X9] :
            ( member(X9,X6)
            & apply(X5,X7,X9)
            & X7 != X9 )
        | max(X7,X5,X6) ) ),
    inference(variable_rename,[status(thm)],[8]) ).

fof(10,plain,
    ! [X5,X6,X7] :
      ( ( ~ max(X7,X5,X6)
        | ( member(X7,X6)
          & ! [X8] :
              ( ~ member(X8,X6)
              | ~ apply(X5,X7,X8)
              | X7 = X8 ) ) )
      & ( ~ member(X7,X6)
        | ( member(esk1_3(X5,X6,X7),X6)
          & apply(X5,X7,esk1_3(X5,X6,X7))
          & X7 != esk1_3(X5,X6,X7) )
        | max(X7,X5,X6) ) ),
    inference(skolemize,[status(esa)],[9]) ).

fof(11,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ member(X8,X6)
            | ~ apply(X5,X7,X8)
            | X7 = X8 )
          & member(X7,X6) )
        | ~ max(X7,X5,X6) )
      & ( ~ member(X7,X6)
        | ( member(esk1_3(X5,X6,X7),X6)
          & apply(X5,X7,esk1_3(X5,X6,X7))
          & X7 != esk1_3(X5,X6,X7) )
        | max(X7,X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[10]) ).

fof(12,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ member(X8,X6)
        | ~ apply(X5,X7,X8)
        | X7 = X8
        | ~ max(X7,X5,X6) )
      & ( member(X7,X6)
        | ~ max(X7,X5,X6) )
      & ( member(esk1_3(X5,X6,X7),X6)
        | ~ member(X7,X6)
        | max(X7,X5,X6) )
      & ( apply(X5,X7,esk1_3(X5,X6,X7))
        | ~ member(X7,X6)
        | max(X7,X5,X6) )
      & ( X7 != esk1_3(X5,X6,X7)
        | ~ member(X7,X6)
        | max(X7,X5,X6) ) ),
    inference(distribute,[status(thm)],[11]) ).

cnf(16,plain,
    ( member(X1,X3)
    | ~ max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(17,plain,
    ( X1 = X4
    | ~ max(X1,X2,X3)
    | ~ apply(X2,X1,X4)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(18,plain,
    ! [X1,X2,X3] :
      ( ( ~ greatest(X3,X1,X2)
        | ( member(X3,X2)
          & ! [X4] :
              ( ~ member(X4,X2)
              | apply(X1,X4,X3) ) ) )
      & ( ~ member(X3,X2)
        | ? [X4] :
            ( member(X4,X2)
            & ~ apply(X1,X4,X3) )
        | greatest(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(19,plain,
    ! [X5,X6,X7] :
      ( ( ~ greatest(X7,X5,X6)
        | ( member(X7,X6)
          & ! [X8] :
              ( ~ member(X8,X6)
              | apply(X5,X8,X7) ) ) )
      & ( ~ member(X7,X6)
        | ? [X9] :
            ( member(X9,X6)
            & ~ apply(X5,X9,X7) )
        | greatest(X7,X5,X6) ) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,plain,
    ! [X5,X6,X7] :
      ( ( ~ greatest(X7,X5,X6)
        | ( member(X7,X6)
          & ! [X8] :
              ( ~ member(X8,X6)
              | apply(X5,X8,X7) ) ) )
      & ( ~ member(X7,X6)
        | ( member(esk2_3(X5,X6,X7),X6)
          & ~ apply(X5,esk2_3(X5,X6,X7),X7) )
        | greatest(X7,X5,X6) ) ),
    inference(skolemize,[status(esa)],[19]) ).

fof(21,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ member(X8,X6)
            | apply(X5,X8,X7) )
          & member(X7,X6) )
        | ~ greatest(X7,X5,X6) )
      & ( ~ member(X7,X6)
        | ( member(esk2_3(X5,X6,X7),X6)
          & ~ apply(X5,esk2_3(X5,X6,X7),X7) )
        | greatest(X7,X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[20]) ).

fof(22,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ member(X8,X6)
        | apply(X5,X8,X7)
        | ~ greatest(X7,X5,X6) )
      & ( member(X7,X6)
        | ~ greatest(X7,X5,X6) )
      & ( member(esk2_3(X5,X6,X7),X6)
        | ~ member(X7,X6)
        | greatest(X7,X5,X6) )
      & ( ~ apply(X5,esk2_3(X5,X6,X7),X7)
        | ~ member(X7,X6)
        | greatest(X7,X5,X6) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(25,plain,
    ( member(X1,X3)
    | ~ greatest(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(26,plain,
    ( apply(X2,X4,X1)
    | ~ greatest(X1,X2,X3)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(31,negated_conjecture,
    ? [X1,X2] :
      ( order(X1,X2)
      & ? [X7,X8] :
          ( max(X7,X1,X2)
          & max(X8,X1,X2)
          & X7 != X8
          & ? [X3] : greatest(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(32,negated_conjecture,
    ? [X9,X10] :
      ( order(X9,X10)
      & ? [X11,X12] :
          ( max(X11,X9,X10)
          & max(X12,X9,X10)
          & X11 != X12
          & ? [X13] : greatest(X13,X9,X10) ) ),
    inference(variable_rename,[status(thm)],[31]) ).

fof(33,negated_conjecture,
    ( order(esk3_0,esk4_0)
    & max(esk5_0,esk3_0,esk4_0)
    & max(esk6_0,esk3_0,esk4_0)
    & esk5_0 != esk6_0
    & greatest(esk7_0,esk3_0,esk4_0) ),
    inference(skolemize,[status(esa)],[32]) ).

cnf(34,negated_conjecture,
    greatest(esk7_0,esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(35,negated_conjecture,
    esk5_0 != esk6_0,
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(36,negated_conjecture,
    max(esk6_0,esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(37,negated_conjecture,
    max(esk5_0,esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(109,negated_conjecture,
    member(esk5_0,esk4_0),
    inference(spm,[status(thm)],[16,37,theory(equality)]) ).

cnf(110,negated_conjecture,
    member(esk6_0,esk4_0),
    inference(spm,[status(thm)],[16,36,theory(equality)]) ).

cnf(111,negated_conjecture,
    member(esk7_0,esk4_0),
    inference(spm,[status(thm)],[25,34,theory(equality)]) ).

cnf(112,negated_conjecture,
    ( apply(esk3_0,X1,esk7_0)
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[26,34,theory(equality)]) ).

cnf(213,negated_conjecture,
    ( X1 = esk7_0
    | ~ member(esk7_0,X2)
    | ~ max(X1,esk3_0,X2)
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[17,112,theory(equality)]) ).

cnf(227,negated_conjecture,
    ( esk5_0 = esk7_0
    | ~ member(esk7_0,esk4_0)
    | ~ member(esk5_0,esk4_0) ),
    inference(spm,[status(thm)],[213,37,theory(equality)]) ).

cnf(229,negated_conjecture,
    ( esk5_0 = esk7_0
    | $false
    | ~ member(esk5_0,esk4_0) ),
    inference(rw,[status(thm)],[227,111,theory(equality)]) ).

cnf(230,negated_conjecture,
    ( esk5_0 = esk7_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[229,109,theory(equality)]) ).

cnf(231,negated_conjecture,
    esk5_0 = esk7_0,
    inference(cn,[status(thm)],[230,theory(equality)]) ).

cnf(238,negated_conjecture,
    ( X1 = esk5_0
    | ~ member(esk7_0,X2)
    | ~ member(X1,esk4_0)
    | ~ max(X1,esk3_0,X2) ),
    inference(rw,[status(thm)],[213,231,theory(equality)]) ).

cnf(239,negated_conjecture,
    ( X1 = esk5_0
    | ~ member(esk5_0,X2)
    | ~ member(X1,esk4_0)
    | ~ max(X1,esk3_0,X2) ),
    inference(rw,[status(thm)],[238,231,theory(equality)]) ).

cnf(248,negated_conjecture,
    ( esk6_0 = esk5_0
    | ~ member(esk5_0,esk4_0)
    | ~ member(esk6_0,esk4_0) ),
    inference(spm,[status(thm)],[239,36,theory(equality)]) ).

cnf(249,negated_conjecture,
    ( esk6_0 = esk5_0
    | $false
    | ~ member(esk6_0,esk4_0) ),
    inference(rw,[status(thm)],[248,109,theory(equality)]) ).

cnf(250,negated_conjecture,
    ( esk6_0 = esk5_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[249,110,theory(equality)]) ).

cnf(251,negated_conjecture,
    esk6_0 = esk5_0,
    inference(cn,[status(thm)],[250,theory(equality)]) ).

cnf(252,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[251,35,theory(equality)]) ).

cnf(253,negated_conjecture,
    $false,
    252,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET803+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpqVfkts/sel_SET803+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET803+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET803+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET803+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
% 
%------------------------------------------------------------------------------