TSTP Solution File: RNG120+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : RNG120+1 : 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 02:33:52 EST 2010

% Result   : Theorem 0.31s
% Output   : CNFRefutation 0.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   63 (  14 unt;   0 def)
%            Number of atoms       :  244 (  22 equ)
%            Maximal formula atoms :   29 (   3 avg)
%            Number of connectives :  305 ( 124   ~; 116   |;  54   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   8 con; 0-2 aty)
%            Number of variables   :   68 (   0 sgn  50   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mEOfElem) ).

fof(12,axiom,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',m__2273) ).

fof(13,axiom,
    ( aElement0(xq)
    & aElement0(xr)
    & xb = sdtpldt0(sdtasdt0(xq,xu),xr)
    & ( xr = sz00
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',m__2666) ).

fof(27,axiom,
    aElement0(sz10),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mSortsC_01) ).

fof(28,axiom,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',m__2174) ).

fof(29,axiom,
    ! [X1] :
      ( aIdeal0(X1)
    <=> ( aSet0(X1)
        & ! [X2] :
            ( aElementOf0(X2,X1)
           => ( ! [X3] :
                  ( aElementOf0(X3,X1)
                 => aElementOf0(sdtpldt0(X2,X3),X1) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mDefIdeal) ).

fof(34,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mSortsB_02) ).

fof(48,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
        & smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mMulMnOne) ).

fof(49,axiom,
    ! [X1] :
      ( aElement0(X1)
     => aElement0(smndt0(X1)) ),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mSortsU) ).

fof(52,conjecture,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',m__) ).

fof(53,negated_conjecture,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(assume_negation,[status(cth)],[52]) ).

fof(55,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(57,negated_conjecture,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(fof_simplification,[status(thm)],[53,theory(equality)]) ).

fof(58,plain,
    ! [X1] :
      ( ~ aSet0(X1)
      | ! [X2] :
          ( ~ aElementOf0(X2,X1)
          | aElement0(X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(59,plain,
    ! [X3] :
      ( ~ aSet0(X3)
      | ! [X4] :
          ( ~ aElementOf0(X4,X3)
          | aElement0(X4) ) ),
    inference(variable_rename,[status(thm)],[58]) ).

fof(60,plain,
    ! [X3,X4] :
      ( ~ aElementOf0(X4,X3)
      | aElement0(X4)
      | ~ aSet0(X3) ),
    inference(shift_quantors,[status(thm)],[59]) ).

cnf(61,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[60]) ).

fof(109,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ~ aElementOf0(X1,xI)
        | X1 = sz00
        | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_nnf,[status(thm)],[55]) ).

fof(110,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X2] :
        ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
    inference(variable_rename,[status(thm)],[109]) ).

fof(111,plain,
    ! [X2] :
      ( ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
      & aElementOf0(xu,xI)
      & xu != sz00 ),
    inference(shift_quantors,[status(thm)],[110]) ).

cnf(113,plain,
    aElementOf0(xu,xI),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(118,plain,
    aElement0(xq),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(173,plain,
    aElement0(sz10),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(175,plain,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(176,plain,
    ! [X1] :
      ( ( ~ aIdeal0(X1)
        | ( aSet0(X1)
          & ! [X2] :
              ( ~ aElementOf0(X2,X1)
              | ( ! [X3] :
                    ( ~ aElementOf0(X3,X1)
                    | aElementOf0(sdtpldt0(X2,X3),X1) )
                & ! [X3] :
                    ( ~ aElement0(X3)
                    | aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) )
      & ( ~ aSet0(X1)
        | ? [X2] :
            ( aElementOf0(X2,X1)
            & ( ? [X3] :
                  ( aElementOf0(X3,X1)
                  & ~ aElementOf0(sdtpldt0(X2,X3),X1) )
              | ? [X3] :
                  ( aElement0(X3)
                  & ~ aElementOf0(sdtasdt0(X3,X2),X1) ) ) )
        | aIdeal0(X1) ) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(177,plain,
    ! [X4] :
      ( ( ~ aIdeal0(X4)
        | ( aSet0(X4)
          & ! [X5] :
              ( ~ aElementOf0(X5,X4)
              | ( ! [X6] :
                    ( ~ aElementOf0(X6,X4)
                    | aElementOf0(sdtpldt0(X5,X6),X4) )
                & ! [X7] :
                    ( ~ aElement0(X7)
                    | aElementOf0(sdtasdt0(X7,X5),X4) ) ) ) ) )
      & ( ~ aSet0(X4)
        | ? [X8] :
            ( aElementOf0(X8,X4)
            & ( ? [X9] :
                  ( aElementOf0(X9,X4)
                  & ~ aElementOf0(sdtpldt0(X8,X9),X4) )
              | ? [X10] :
                  ( aElement0(X10)
                  & ~ aElementOf0(sdtasdt0(X10,X8),X4) ) ) )
        | aIdeal0(X4) ) ),
    inference(variable_rename,[status(thm)],[176]) ).

fof(178,plain,
    ! [X4] :
      ( ( ~ aIdeal0(X4)
        | ( aSet0(X4)
          & ! [X5] :
              ( ~ aElementOf0(X5,X4)
              | ( ! [X6] :
                    ( ~ aElementOf0(X6,X4)
                    | aElementOf0(sdtpldt0(X5,X6),X4) )
                & ! [X7] :
                    ( ~ aElement0(X7)
                    | aElementOf0(sdtasdt0(X7,X5),X4) ) ) ) ) )
      & ( ~ aSet0(X4)
        | ( aElementOf0(esk11_1(X4),X4)
          & ( ( aElementOf0(esk12_1(X4),X4)
              & ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4) )
            | ( aElement0(esk13_1(X4))
              & ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4) ) ) )
        | aIdeal0(X4) ) ),
    inference(skolemize,[status(esa)],[177]) ).

fof(179,plain,
    ! [X4,X5,X6,X7] :
      ( ( ( ( ( ( ~ aElement0(X7)
                | aElementOf0(sdtasdt0(X7,X5),X4) )
              & ( ~ aElementOf0(X6,X4)
                | aElementOf0(sdtpldt0(X5,X6),X4) ) )
            | ~ aElementOf0(X5,X4) )
          & aSet0(X4) )
        | ~ aIdeal0(X4) )
      & ( ~ aSet0(X4)
        | ( aElementOf0(esk11_1(X4),X4)
          & ( ( aElementOf0(esk12_1(X4),X4)
              & ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4) )
            | ( aElement0(esk13_1(X4))
              & ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4) ) ) )
        | aIdeal0(X4) ) ),
    inference(shift_quantors,[status(thm)],[178]) ).

fof(180,plain,
    ! [X4,X5,X6,X7] :
      ( ( ~ aElement0(X7)
        | aElementOf0(sdtasdt0(X7,X5),X4)
        | ~ aElementOf0(X5,X4)
        | ~ aIdeal0(X4) )
      & ( ~ aElementOf0(X6,X4)
        | aElementOf0(sdtpldt0(X5,X6),X4)
        | ~ aElementOf0(X5,X4)
        | ~ aIdeal0(X4) )
      & ( aSet0(X4)
        | ~ aIdeal0(X4) )
      & ( aElementOf0(esk11_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( aElement0(esk13_1(X4))
        | aElementOf0(esk12_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4)
        | aElementOf0(esk12_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( aElement0(esk13_1(X4))
        | ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4)
        | ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) ) ),
    inference(distribute,[status(thm)],[179]) ).

cnf(186,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[180]) ).

cnf(188,plain,
    ( aElementOf0(sdtasdt0(X3,X2),X1)
    | ~ aIdeal0(X1)
    | ~ aElementOf0(X2,X1)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[180]) ).

fof(215,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | aElement0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(216,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | aElement0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[215]) ).

cnf(217,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[216]) ).

fof(266,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
        & smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
    inference(fof_nnf,[status(thm)],[48]) ).

fof(267,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
        & smndt0(X2) = sdtasdt0(X2,smndt0(sz10)) ) ),
    inference(variable_rename,[status(thm)],[266]) ).

fof(268,plain,
    ! [X2] :
      ( ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
        | ~ aElement0(X2) )
      & ( smndt0(X2) = sdtasdt0(X2,smndt0(sz10))
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[267]) ).

cnf(270,plain,
    ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[268]) ).

fof(271,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | aElement0(smndt0(X1)) ),
    inference(fof_nnf,[status(thm)],[49]) ).

fof(272,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | aElement0(smndt0(X2)) ),
    inference(variable_rename,[status(thm)],[271]) ).

cnf(273,plain,
    ( aElement0(smndt0(X1))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[272]) ).

cnf(291,negated_conjecture,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(split_conjunct,[status(thm)],[57]) ).

cnf(292,plain,
    aSet0(xI),
    inference(spm,[status(thm)],[186,175,theory(equality)]) ).

cnf(301,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(spm,[status(thm)],[61,113,theory(equality)]) ).

cnf(449,plain,
    ( aElementOf0(smndt0(X1),X2)
    | ~ aIdeal0(X2)
    | ~ aElement0(smndt0(sz10))
    | ~ aElementOf0(X1,X2)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[188,270,theory(equality)]) ).

cnf(791,plain,
    ( aElement0(xu)
    | $false ),
    inference(rw,[status(thm)],[301,292,theory(equality)]) ).

cnf(792,plain,
    aElement0(xu),
    inference(cn,[status(thm)],[791,theory(equality)]) ).

cnf(1751,negated_conjecture,
    ( ~ aIdeal0(xI)
    | ~ aElement0(smndt0(sz10))
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
    inference(spm,[status(thm)],[291,449,theory(equality)]) ).

cnf(1759,negated_conjecture,
    ( $false
    | ~ aElement0(smndt0(sz10))
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
    inference(rw,[status(thm)],[1751,175,theory(equality)]) ).

cnf(1760,negated_conjecture,
    ( ~ aElement0(smndt0(sz10))
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
    inference(cn,[status(thm)],[1759,theory(equality)]) ).

cnf(2023,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElementOf0(sdtasdt0(xq,xu),xI)
    | ~ aElement0(sz10) ),
    inference(spm,[status(thm)],[1760,273,theory(equality)]) ).

cnf(2025,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElementOf0(sdtasdt0(xq,xu),xI)
    | $false ),
    inference(rw,[status(thm)],[2023,173,theory(equality)]) ).

cnf(2026,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
    inference(cn,[status(thm)],[2025,theory(equality)]) ).

cnf(2029,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | ~ aIdeal0(xI)
    | ~ aElement0(xq)
    | ~ aElementOf0(xu,xI) ),
    inference(spm,[status(thm)],[2026,188,theory(equality)]) ).

cnf(2037,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | $false
    | ~ aElement0(xq)
    | ~ aElementOf0(xu,xI) ),
    inference(rw,[status(thm)],[2029,175,theory(equality)]) ).

cnf(2038,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | $false
    | $false
    | ~ aElementOf0(xu,xI) ),
    inference(rw,[status(thm)],[2037,118,theory(equality)]) ).

cnf(2039,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[2038,113,theory(equality)]) ).

cnf(2040,negated_conjecture,
    ~ aElement0(sdtasdt0(xq,xu)),
    inference(cn,[status(thm)],[2039,theory(equality)]) ).

cnf(2075,negated_conjecture,
    ( ~ aElement0(xu)
    | ~ aElement0(xq) ),
    inference(spm,[status(thm)],[2040,217,theory(equality)]) ).

cnf(2080,negated_conjecture,
    ( $false
    | ~ aElement0(xq) ),
    inference(rw,[status(thm)],[2075,792,theory(equality)]) ).

cnf(2081,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[2080,118,theory(equality)]) ).

cnf(2082,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[2081,theory(equality)]) ).

cnf(2083,negated_conjecture,
    $false,
    2082,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG120+1.p
% --creating new selector for []
% -running prover on /tmp/tmpq3n1mp/sel_RNG120+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG120+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG120+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG120+1.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
% 
%------------------------------------------------------------------------------