TSTP Solution File: RNG099+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : RNG099+2 : TPTP v5.0.0. Released v4.0.0.
% 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 02:21:21 EST 2010

% Result   : Theorem 0.30s
% Output   : CNFRefutation 0.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   58 (  18 unt;   0 def)
%            Number of atoms       :  201 (   3 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  235 (  92   ~;  82   |;  51   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   62 (   0 sgn  53   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ( aElement0(xx)
    & aElement0(xy) ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__1217) ).

fof(2,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',mEOfElem) ).

fof(4,axiom,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__1319) ).

fof(7,axiom,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__1332) ).

fof(10,axiom,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__1409) ).

fof(11,axiom,
    ( aElementOf0(xa,xI)
    & aElementOf0(xb,xJ)
    & sdtpldt0(xa,xb) = sz10 ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__1294) ).

fof(24,axiom,
    ( aSet0(xI)
    & ! [X1] :
        ( aElementOf0(X1,xI)
       => ( ! [X2] :
              ( aElementOf0(X2,xI)
             => aElementOf0(sdtpldt0(X1,X2),xI) )
          & ! [X2] :
              ( aElement0(X2)
             => aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
    & aIdeal0(xI)
    & aSet0(xJ)
    & ! [X1] :
        ( aElementOf0(X1,xJ)
       => ( ! [X2] :
              ( aElementOf0(X2,xJ)
             => aElementOf0(sdtpldt0(X1,X2),xJ) )
          & ! [X2] :
              ( aElement0(X2)
             => aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
    & aIdeal0(xJ) ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__1205) ).

fof(25,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',mSortsB_02) ).

fof(27,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtpldt0(X1,X2)) ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',mSortsB) ).

fof(35,conjecture,
    ? [X1] :
      ( aElement0(X1)
      & ( aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
        | sdteqdtlpzmzozddtrp0(X1,xx,xI) )
      & ( aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
        | sdteqdtlpzmzozddtrp0(X1,xy,xJ) ) ),
    file('/tmp/tmptMz4tL/sel_RNG099+2.p_1',m__) ).

fof(36,negated_conjecture,
    ~ ? [X1] :
        ( aElement0(X1)
        & ( aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
          | sdteqdtlpzmzozddtrp0(X1,xx,xI) )
        & ( aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
          | sdteqdtlpzmzozddtrp0(X1,xy,xJ) ) ),
    inference(assume_negation,[status(cth)],[35]) ).

cnf(37,plain,
    aElement0(xy),
    inference(split_conjunct,[status(thm)],[1]) ).

cnf(38,plain,
    aElement0(xx),
    inference(split_conjunct,[status(thm)],[1]) ).

fof(39,plain,
    ! [X1] :
      ( ~ aSet0(X1)
      | ! [X2] :
          ( ~ aElementOf0(X2,X1)
          | aElement0(X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(40,plain,
    ! [X3] :
      ( ~ aSet0(X3)
      | ! [X4] :
          ( ~ aElementOf0(X4,X3)
          | aElement0(X4) ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,plain,
    ! [X3,X4] :
      ( ~ aElementOf0(X4,X3)
      | aElement0(X4)
      | ~ aSet0(X3) ),
    inference(shift_quantors,[status(thm)],[40]) ).

cnf(42,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(46,plain,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    inference(split_conjunct,[status(thm)],[4]) ).

cnf(55,plain,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    inference(split_conjunct,[status(thm)],[7]) ).

cnf(69,plain,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(71,plain,
    aElementOf0(xb,xJ),
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(72,plain,
    aElementOf0(xa,xI),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(135,plain,
    ( aSet0(xI)
    & ! [X1] :
        ( ~ aElementOf0(X1,xI)
        | ( ! [X2] :
              ( ~ aElementOf0(X2,xI)
              | aElementOf0(sdtpldt0(X1,X2),xI) )
          & ! [X2] :
              ( ~ aElement0(X2)
              | aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
    & aIdeal0(xI)
    & aSet0(xJ)
    & ! [X1] :
        ( ~ aElementOf0(X1,xJ)
        | ( ! [X2] :
              ( ~ aElementOf0(X2,xJ)
              | aElementOf0(sdtpldt0(X1,X2),xJ) )
          & ! [X2] :
              ( ~ aElement0(X2)
              | aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
    & aIdeal0(xJ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(136,plain,
    ( aSet0(xI)
    & ! [X3] :
        ( ~ aElementOf0(X3,xI)
        | ( ! [X4] :
              ( ~ aElementOf0(X4,xI)
              | aElementOf0(sdtpldt0(X3,X4),xI) )
          & ! [X5] :
              ( ~ aElement0(X5)
              | aElementOf0(sdtasdt0(X5,X3),xI) ) ) )
    & aIdeal0(xI)
    & aSet0(xJ)
    & ! [X6] :
        ( ~ aElementOf0(X6,xJ)
        | ( ! [X7] :
              ( ~ aElementOf0(X7,xJ)
              | aElementOf0(sdtpldt0(X6,X7),xJ) )
          & ! [X8] :
              ( ~ aElement0(X8)
              | aElementOf0(sdtasdt0(X8,X6),xJ) ) ) )
    & aIdeal0(xJ) ),
    inference(variable_rename,[status(thm)],[135]) ).

fof(137,plain,
    ! [X3,X4,X5,X6,X7,X8] :
      ( ( ( ( ~ aElement0(X8)
            | aElementOf0(sdtasdt0(X8,X6),xJ) )
          & ( ~ aElementOf0(X7,xJ)
            | aElementOf0(sdtpldt0(X6,X7),xJ) ) )
        | ~ aElementOf0(X6,xJ) )
      & ( ( ( ~ aElement0(X5)
            | aElementOf0(sdtasdt0(X5,X3),xI) )
          & ( ~ aElementOf0(X4,xI)
            | aElementOf0(sdtpldt0(X3,X4),xI) ) )
        | ~ aElementOf0(X3,xI) )
      & aSet0(xI)
      & aIdeal0(xI)
      & aSet0(xJ)
      & aIdeal0(xJ) ),
    inference(shift_quantors,[status(thm)],[136]) ).

fof(138,plain,
    ! [X3,X4,X5,X6,X7,X8] :
      ( ( ~ aElement0(X8)
        | aElementOf0(sdtasdt0(X8,X6),xJ)
        | ~ aElementOf0(X6,xJ) )
      & ( ~ aElementOf0(X7,xJ)
        | aElementOf0(sdtpldt0(X6,X7),xJ)
        | ~ aElementOf0(X6,xJ) )
      & ( ~ aElement0(X5)
        | aElementOf0(sdtasdt0(X5,X3),xI)
        | ~ aElementOf0(X3,xI) )
      & ( ~ aElementOf0(X4,xI)
        | aElementOf0(sdtpldt0(X3,X4),xI)
        | ~ aElementOf0(X3,xI) )
      & aSet0(xI)
      & aIdeal0(xI)
      & aSet0(xJ)
      & aIdeal0(xJ) ),
    inference(distribute,[status(thm)],[137]) ).

cnf(140,plain,
    aSet0(xJ),
    inference(split_conjunct,[status(thm)],[138]) ).

cnf(142,plain,
    aSet0(xI),
    inference(split_conjunct,[status(thm)],[138]) ).

fof(147,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | aElement0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(148,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | aElement0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[147]) ).

cnf(149,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[148]) ).

fof(151,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | aElement0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(152,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | aElement0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[151]) ).

cnf(153,plain,
    ( aElement0(sdtpldt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[152]) ).

fof(190,negated_conjecture,
    ! [X1] :
      ( ~ aElement0(X1)
      | ( ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
        & ~ sdteqdtlpzmzozddtrp0(X1,xx,xI) )
      | ( ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
        & ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ) ) ),
    inference(fof_nnf,[status(thm)],[36]) ).

fof(191,negated_conjecture,
    ! [X2] :
      ( ~ aElement0(X2)
      | ( ~ aElementOf0(sdtpldt0(X2,smndt0(xx)),xI)
        & ~ sdteqdtlpzmzozddtrp0(X2,xx,xI) )
      | ( ~ aElementOf0(sdtpldt0(X2,smndt0(xy)),xJ)
        & ~ sdteqdtlpzmzozddtrp0(X2,xy,xJ) ) ),
    inference(variable_rename,[status(thm)],[190]) ).

fof(192,negated_conjecture,
    ! [X2] :
      ( ( ~ aElementOf0(sdtpldt0(X2,smndt0(xy)),xJ)
        | ~ aElementOf0(sdtpldt0(X2,smndt0(xx)),xI)
        | ~ aElement0(X2) )
      & ( ~ sdteqdtlpzmzozddtrp0(X2,xy,xJ)
        | ~ aElementOf0(sdtpldt0(X2,smndt0(xx)),xI)
        | ~ aElement0(X2) )
      & ( ~ aElementOf0(sdtpldt0(X2,smndt0(xy)),xJ)
        | ~ sdteqdtlpzmzozddtrp0(X2,xx,xI)
        | ~ aElement0(X2) )
      & ( ~ sdteqdtlpzmzozddtrp0(X2,xy,xJ)
        | ~ sdteqdtlpzmzozddtrp0(X2,xx,xI)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[191]) ).

cnf(196,negated_conjecture,
    ( ~ aElement0(X1)
    | ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
    | ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ) ),
    inference(split_conjunct,[status(thm)],[192]) ).

cnf(219,plain,
    ( aElement0(xa)
    | ~ aSet0(xI) ),
    inference(spm,[status(thm)],[42,72,theory(equality)]) ).

cnf(220,plain,
    ( aElement0(xb)
    | ~ aSet0(xJ) ),
    inference(spm,[status(thm)],[42,71,theory(equality)]) ).

cnf(226,plain,
    ( aElement0(xa)
    | $false ),
    inference(rw,[status(thm)],[219,142,theory(equality)]) ).

cnf(227,plain,
    aElement0(xa),
    inference(cn,[status(thm)],[226,theory(equality)]) ).

cnf(228,plain,
    ( aElement0(xb)
    | $false ),
    inference(rw,[status(thm)],[220,140,theory(equality)]) ).

cnf(229,plain,
    aElement0(xb),
    inference(cn,[status(thm)],[228,theory(equality)]) ).

cnf(262,plain,
    ( aElement0(xw)
    | ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa)) ),
    inference(spm,[status(thm)],[153,46,theory(equality)]) ).

cnf(547,plain,
    ( ~ aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
    | ~ aElement0(xw) ),
    inference(spm,[status(thm)],[196,55,theory(equality)]) ).

cnf(556,plain,
    ( $false
    | ~ aElement0(xw) ),
    inference(rw,[status(thm)],[547,69,theory(equality)]) ).

cnf(557,plain,
    ~ aElement0(xw),
    inference(cn,[status(thm)],[556,theory(equality)]) ).

cnf(874,plain,
    ( ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa)) ),
    inference(sr,[status(thm)],[262,557,theory(equality)]) ).

cnf(875,plain,
    ( ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(xb)
    | ~ aElement0(xx) ),
    inference(spm,[status(thm)],[874,149,theory(equality)]) ).

cnf(876,plain,
    ( ~ aElement0(sdtasdt0(xy,xa))
    | $false
    | ~ aElement0(xx) ),
    inference(rw,[status(thm)],[875,229,theory(equality)]) ).

cnf(877,plain,
    ( ~ aElement0(sdtasdt0(xy,xa))
    | $false
    | $false ),
    inference(rw,[status(thm)],[876,38,theory(equality)]) ).

cnf(878,plain,
    ~ aElement0(sdtasdt0(xy,xa)),
    inference(cn,[status(thm)],[877,theory(equality)]) ).

cnf(879,plain,
    ( ~ aElement0(xa)
    | ~ aElement0(xy) ),
    inference(spm,[status(thm)],[878,149,theory(equality)]) ).

cnf(880,plain,
    ( $false
    | ~ aElement0(xy) ),
    inference(rw,[status(thm)],[879,227,theory(equality)]) ).

cnf(881,plain,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[880,37,theory(equality)]) ).

cnf(882,plain,
    $false,
    inference(cn,[status(thm)],[881,theory(equality)]) ).

cnf(883,plain,
    $false,
    882,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG099+2.p
% --creating new selector for []
% -running prover on /tmp/tmptMz4tL/sel_RNG099+2.p_1 with time limit 29
% -prover status Theorem
% Problem RNG099+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG099+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG099+2.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
% 
%------------------------------------------------------------------------------