TSTP Solution File: RNG125+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : RNG125+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 02:35:21 EST 2010

% Result   : Theorem 0.29s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   56 (  17 unt;   0 def)
%            Number of atoms       :  226 (  11 equ)
%            Maximal formula atoms :   29 (   4 avg)
%            Number of connectives :  280 ( 110   ~; 103   |;  57   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   58 (   0 sgn  47   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',mEOfElem) ).

fof(5,axiom,
    ~ ~ doDivides0(xu,xb),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2612) ).

fof(10,axiom,
    ~ ( aDivisorOf0(xu,xa)
      & aDivisorOf0(xu,xb) ),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2383) ).

fof(12,axiom,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2273) ).

fof(21,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aElement0(X2)
            & doDivides0(X2,X1) ) ) ),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',mDefDvs) ).

fof(27,axiom,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2174) ).

fof(28,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/tmpQPTtUR/sel_RNG125+1.p_1',mDefIdeal) ).

fof(38,axiom,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2091) ).

fof(45,axiom,
    ~ ~ doDivides0(xu,xa),
    file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2479) ).

fof(52,plain,
    doDivides0(xu,xb),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(53,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(54,plain,
    doDivides0(xu,xa),
    inference(fof_simplification,[status(thm)],[45,theory(equality)]) ).

fof(56,plain,
    ! [X1] :
      ( ~ aSet0(X1)
      | ! [X2] :
          ( ~ aElementOf0(X2,X1)
          | aElement0(X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(57,plain,
    ! [X3] :
      ( ~ aSet0(X3)
      | ! [X4] :
          ( ~ aElementOf0(X4,X3)
          | aElement0(X4) ) ),
    inference(variable_rename,[status(thm)],[56]) ).

fof(58,plain,
    ! [X3,X4] :
      ( ~ aElementOf0(X4,X3)
      | aElement0(X4)
      | ~ aSet0(X3) ),
    inference(shift_quantors,[status(thm)],[57]) ).

cnf(59,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(71,plain,
    doDivides0(xu,xb),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(97,plain,
    ( ~ aDivisorOf0(xu,xa)
    | ~ aDivisorOf0(xu,xb) ),
    inference(fof_nnf,[status(thm)],[10]) ).

cnf(98,plain,
    ( ~ aDivisorOf0(xu,xb)
    | ~ aDivisorOf0(xu,xa) ),
    inference(split_conjunct,[status(thm)],[97]) ).

fof(107,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ~ aElementOf0(X1,xI)
        | X1 = sz00
        | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_nnf,[status(thm)],[53]) ).

fof(108,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X2] :
        ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
    inference(variable_rename,[status(thm)],[107]) ).

fof(109,plain,
    ! [X2] :
      ( ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
      & aElementOf0(xu,xI)
      & xu != sz00 ),
    inference(shift_quantors,[status(thm)],[108]) ).

cnf(111,plain,
    aElementOf0(xu,xI),
    inference(split_conjunct,[status(thm)],[109]) ).

fof(141,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | ! [X2] :
          ( ( ~ aDivisorOf0(X2,X1)
            | ( aElement0(X2)
              & doDivides0(X2,X1) ) )
          & ( ~ aElement0(X2)
            | ~ doDivides0(X2,X1)
            | aDivisorOf0(X2,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(142,plain,
    ! [X3] :
      ( ~ aElement0(X3)
      | ! [X4] :
          ( ( ~ aDivisorOf0(X4,X3)
            | ( aElement0(X4)
              & doDivides0(X4,X3) ) )
          & ( ~ aElement0(X4)
            | ~ doDivides0(X4,X3)
            | aDivisorOf0(X4,X3) ) ) ),
    inference(variable_rename,[status(thm)],[141]) ).

fof(143,plain,
    ! [X3,X4] :
      ( ( ( ~ aDivisorOf0(X4,X3)
          | ( aElement0(X4)
            & doDivides0(X4,X3) ) )
        & ( ~ aElement0(X4)
          | ~ doDivides0(X4,X3)
          | aDivisorOf0(X4,X3) ) )
      | ~ aElement0(X3) ),
    inference(shift_quantors,[status(thm)],[142]) ).

fof(144,plain,
    ! [X3,X4] :
      ( ( aElement0(X4)
        | ~ aDivisorOf0(X4,X3)
        | ~ aElement0(X3) )
      & ( doDivides0(X4,X3)
        | ~ aDivisorOf0(X4,X3)
        | ~ aElement0(X3) )
      & ( ~ aElement0(X4)
        | ~ doDivides0(X4,X3)
        | aDivisorOf0(X4,X3)
        | ~ aElement0(X3) ) ),
    inference(distribute,[status(thm)],[143]) ).

cnf(145,plain,
    ( aDivisorOf0(X2,X1)
    | ~ aElement0(X1)
    | ~ doDivides0(X2,X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(169,plain,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(170,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)],[28]) ).

fof(171,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)],[170]) ).

fof(172,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)],[171]) ).

fof(173,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)],[172]) ).

fof(174,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)],[173]) ).

cnf(180,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[174]) ).

cnf(230,plain,
    aElement0(xb),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(231,plain,
    aElement0(xa),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(258,plain,
    doDivides0(xu,xa),
    inference(split_conjunct,[status(thm)],[54]) ).

cnf(285,plain,
    aSet0(xI),
    inference(spm,[status(thm)],[180,169,theory(equality)]) ).

cnf(300,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(spm,[status(thm)],[59,111,theory(equality)]) ).

cnf(404,plain,
    ( aDivisorOf0(xu,xb)
    | ~ aElement0(xu)
    | ~ aElement0(xb) ),
    inference(spm,[status(thm)],[145,71,theory(equality)]) ).

cnf(405,plain,
    ( aDivisorOf0(xu,xa)
    | ~ aElement0(xu)
    | ~ aElement0(xa) ),
    inference(spm,[status(thm)],[145,258,theory(equality)]) ).

cnf(407,plain,
    ( aDivisorOf0(xu,xb)
    | ~ aElement0(xu)
    | $false ),
    inference(rw,[status(thm)],[404,230,theory(equality)]) ).

cnf(408,plain,
    ( aDivisorOf0(xu,xb)
    | ~ aElement0(xu) ),
    inference(cn,[status(thm)],[407,theory(equality)]) ).

cnf(409,plain,
    ( aDivisorOf0(xu,xa)
    | ~ aElement0(xu)
    | $false ),
    inference(rw,[status(thm)],[405,231,theory(equality)]) ).

cnf(410,plain,
    ( aDivisorOf0(xu,xa)
    | ~ aElement0(xu) ),
    inference(cn,[status(thm)],[409,theory(equality)]) ).

cnf(750,plain,
    ( aElement0(xu)
    | $false ),
    inference(rw,[status(thm)],[300,285,theory(equality)]) ).

cnf(751,plain,
    aElement0(xu),
    inference(cn,[status(thm)],[750,theory(equality)]) ).

cnf(859,plain,
    ( aDivisorOf0(xu,xb)
    | $false ),
    inference(rw,[status(thm)],[408,751,theory(equality)]) ).

cnf(860,plain,
    aDivisorOf0(xu,xb),
    inference(cn,[status(thm)],[859,theory(equality)]) ).

cnf(862,plain,
    ( $false
    | ~ aDivisorOf0(xu,xa) ),
    inference(rw,[status(thm)],[98,860,theory(equality)]) ).

cnf(863,plain,
    ~ aDivisorOf0(xu,xa),
    inference(cn,[status(thm)],[862,theory(equality)]) ).

cnf(888,plain,
    ( aDivisorOf0(xu,xa)
    | $false ),
    inference(rw,[status(thm)],[410,751,theory(equality)]) ).

cnf(889,plain,
    aDivisorOf0(xu,xa),
    inference(cn,[status(thm)],[888,theory(equality)]) ).

cnf(890,plain,
    $false,
    inference(sr,[status(thm)],[889,863,theory(equality)]) ).

cnf(891,plain,
    $false,
    890,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG125+1.p
% --creating new selector for []
% -running prover on /tmp/tmpQPTtUR/sel_RNG125+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG125+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG125+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG125+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
% 
%------------------------------------------------------------------------------