TSTP Solution File: LAT382+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : LAT382+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 : Sat Dec 25 17:18:10 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   68 (  21 unt;   0 def)
%            Number of atoms       :  237 (  12 equ)
%            Maximal formula atoms :   25 (   3 avg)
%            Number of connectives :  285 ( 116   ~; 136   |;  25   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   62 (   0 sgn  38   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    aSubsetOf0(xS,xT),
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__773_01) ).

fof(2,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',mASymm) ).

fof(4,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',mEOfElem) ).

fof(5,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aSubsetOf0(X2,X1)
         => ! [X3] :
              ( aInfimumOfIn0(X3,X2,X1)
            <=> ( aElementOf0(X3,X1)
                & aLowerBoundOfIn0(X3,X2,X1)
                & ! [X4] :
                    ( aLowerBoundOfIn0(X4,X2,X1)
                   => sdtlseqdt0(X4,X3) ) ) ) ) ),
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',mDefInf) ).

fof(12,conjecture,
    xu = xv,
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__) ).

fof(13,axiom,
    aSet0(xT),
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__773) ).

fof(14,axiom,
    ( aInfimumOfIn0(xu,xS,xT)
    & aInfimumOfIn0(xv,xS,xT) ),
    file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__792) ).

fof(19,negated_conjecture,
    xu != xv,
    inference(assume_negation,[status(cth)],[12]) ).

fof(20,negated_conjecture,
    xu != xv,
    inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).

cnf(21,plain,
    aSubsetOf0(xS,xT),
    inference(split_conjunct,[status(thm)],[1]) ).

fof(22,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X2,X1)
      | X1 = X2 ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(23,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | ~ sdtlseqdt0(X3,X4)
      | ~ sdtlseqdt0(X4,X3)
      | X3 = X4 ),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(24,plain,
    ( X1 = X2
    | ~ sdtlseqdt0(X2,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(28,plain,
    ! [X1] :
      ( ~ aSet0(X1)
      | ! [X2] :
          ( ~ aElementOf0(X2,X1)
          | aElement0(X2) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(29,plain,
    ! [X3] :
      ( ~ aSet0(X3)
      | ! [X4] :
          ( ~ aElementOf0(X4,X3)
          | aElement0(X4) ) ),
    inference(variable_rename,[status(thm)],[28]) ).

fof(30,plain,
    ! [X3,X4] :
      ( ~ aElementOf0(X4,X3)
      | aElement0(X4)
      | ~ aSet0(X3) ),
    inference(shift_quantors,[status(thm)],[29]) ).

cnf(31,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(32,plain,
    ! [X1] :
      ( ~ aSet0(X1)
      | ! [X2] :
          ( ~ aSubsetOf0(X2,X1)
          | ! [X3] :
              ( ( ~ aInfimumOfIn0(X3,X2,X1)
                | ( aElementOf0(X3,X1)
                  & aLowerBoundOfIn0(X3,X2,X1)
                  & ! [X4] :
                      ( ~ aLowerBoundOfIn0(X4,X2,X1)
                      | sdtlseqdt0(X4,X3) ) ) )
              & ( ~ aElementOf0(X3,X1)
                | ~ aLowerBoundOfIn0(X3,X2,X1)
                | ? [X4] :
                    ( aLowerBoundOfIn0(X4,X2,X1)
                    & ~ sdtlseqdt0(X4,X3) )
                | aInfimumOfIn0(X3,X2,X1) ) ) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(33,plain,
    ! [X5] :
      ( ~ aSet0(X5)
      | ! [X6] :
          ( ~ aSubsetOf0(X6,X5)
          | ! [X7] :
              ( ( ~ aInfimumOfIn0(X7,X6,X5)
                | ( aElementOf0(X7,X5)
                  & aLowerBoundOfIn0(X7,X6,X5)
                  & ! [X8] :
                      ( ~ aLowerBoundOfIn0(X8,X6,X5)
                      | sdtlseqdt0(X8,X7) ) ) )
              & ( ~ aElementOf0(X7,X5)
                | ~ aLowerBoundOfIn0(X7,X6,X5)
                | ? [X9] :
                    ( aLowerBoundOfIn0(X9,X6,X5)
                    & ~ sdtlseqdt0(X9,X7) )
                | aInfimumOfIn0(X7,X6,X5) ) ) ) ),
    inference(variable_rename,[status(thm)],[32]) ).

fof(34,plain,
    ! [X5] :
      ( ~ aSet0(X5)
      | ! [X6] :
          ( ~ aSubsetOf0(X6,X5)
          | ! [X7] :
              ( ( ~ aInfimumOfIn0(X7,X6,X5)
                | ( aElementOf0(X7,X5)
                  & aLowerBoundOfIn0(X7,X6,X5)
                  & ! [X8] :
                      ( ~ aLowerBoundOfIn0(X8,X6,X5)
                      | sdtlseqdt0(X8,X7) ) ) )
              & ( ~ aElementOf0(X7,X5)
                | ~ aLowerBoundOfIn0(X7,X6,X5)
                | ( aLowerBoundOfIn0(esk1_3(X5,X6,X7),X6,X5)
                  & ~ sdtlseqdt0(esk1_3(X5,X6,X7),X7) )
                | aInfimumOfIn0(X7,X6,X5) ) ) ) ),
    inference(skolemize,[status(esa)],[33]) ).

fof(35,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ( ~ aLowerBoundOfIn0(X8,X6,X5)
              | sdtlseqdt0(X8,X7) )
            & aElementOf0(X7,X5)
            & aLowerBoundOfIn0(X7,X6,X5) )
          | ~ aInfimumOfIn0(X7,X6,X5) )
        & ( ~ aElementOf0(X7,X5)
          | ~ aLowerBoundOfIn0(X7,X6,X5)
          | ( aLowerBoundOfIn0(esk1_3(X5,X6,X7),X6,X5)
            & ~ sdtlseqdt0(esk1_3(X5,X6,X7),X7) )
          | aInfimumOfIn0(X7,X6,X5) ) )
      | ~ aSubsetOf0(X6,X5)
      | ~ aSet0(X5) ),
    inference(shift_quantors,[status(thm)],[34]) ).

fof(36,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ aLowerBoundOfIn0(X8,X6,X5)
        | sdtlseqdt0(X8,X7)
        | ~ aInfimumOfIn0(X7,X6,X5)
        | ~ aSubsetOf0(X6,X5)
        | ~ aSet0(X5) )
      & ( aElementOf0(X7,X5)
        | ~ aInfimumOfIn0(X7,X6,X5)
        | ~ aSubsetOf0(X6,X5)
        | ~ aSet0(X5) )
      & ( aLowerBoundOfIn0(X7,X6,X5)
        | ~ aInfimumOfIn0(X7,X6,X5)
        | ~ aSubsetOf0(X6,X5)
        | ~ aSet0(X5) )
      & ( aLowerBoundOfIn0(esk1_3(X5,X6,X7),X6,X5)
        | ~ aElementOf0(X7,X5)
        | ~ aLowerBoundOfIn0(X7,X6,X5)
        | aInfimumOfIn0(X7,X6,X5)
        | ~ aSubsetOf0(X6,X5)
        | ~ aSet0(X5) )
      & ( ~ sdtlseqdt0(esk1_3(X5,X6,X7),X7)
        | ~ aElementOf0(X7,X5)
        | ~ aLowerBoundOfIn0(X7,X6,X5)
        | aInfimumOfIn0(X7,X6,X5)
        | ~ aSubsetOf0(X6,X5)
        | ~ aSet0(X5) ) ),
    inference(distribute,[status(thm)],[35]) ).

cnf(39,plain,
    ( aLowerBoundOfIn0(X3,X2,X1)
    | ~ aSet0(X1)
    | ~ aSubsetOf0(X2,X1)
    | ~ aInfimumOfIn0(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(40,plain,
    ( aElementOf0(X3,X1)
    | ~ aSet0(X1)
    | ~ aSubsetOf0(X2,X1)
    | ~ aInfimumOfIn0(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(41,plain,
    ( sdtlseqdt0(X4,X3)
    | ~ aSet0(X1)
    | ~ aSubsetOf0(X2,X1)
    | ~ aInfimumOfIn0(X3,X2,X1)
    | ~ aLowerBoundOfIn0(X4,X2,X1) ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(78,negated_conjecture,
    xu != xv,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(79,plain,
    aSet0(xT),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(80,plain,
    aInfimumOfIn0(xv,xS,xT),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(81,plain,
    aInfimumOfIn0(xu,xS,xT),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(114,plain,
    ( aElementOf0(xu,xT)
    | ~ aSet0(xT)
    | ~ aSubsetOf0(xS,xT) ),
    inference(spm,[status(thm)],[40,81,theory(equality)]) ).

cnf(115,plain,
    ( aElementOf0(xv,xT)
    | ~ aSet0(xT)
    | ~ aSubsetOf0(xS,xT) ),
    inference(spm,[status(thm)],[40,80,theory(equality)]) ).

cnf(116,plain,
    ( aElementOf0(xu,xT)
    | $false
    | ~ aSubsetOf0(xS,xT) ),
    inference(rw,[status(thm)],[114,79,theory(equality)]) ).

cnf(117,plain,
    ( aElementOf0(xu,xT)
    | $false
    | $false ),
    inference(rw,[status(thm)],[116,21,theory(equality)]) ).

cnf(118,plain,
    aElementOf0(xu,xT),
    inference(cn,[status(thm)],[117,theory(equality)]) ).

cnf(119,plain,
    ( aElementOf0(xv,xT)
    | $false
    | ~ aSubsetOf0(xS,xT) ),
    inference(rw,[status(thm)],[115,79,theory(equality)]) ).

cnf(120,plain,
    ( aElementOf0(xv,xT)
    | $false
    | $false ),
    inference(rw,[status(thm)],[119,21,theory(equality)]) ).

cnf(121,plain,
    aElementOf0(xv,xT),
    inference(cn,[status(thm)],[120,theory(equality)]) ).

cnf(125,plain,
    ( aLowerBoundOfIn0(xu,xS,xT)
    | ~ aSet0(xT)
    | ~ aSubsetOf0(xS,xT) ),
    inference(spm,[status(thm)],[39,81,theory(equality)]) ).

cnf(126,plain,
    ( aLowerBoundOfIn0(xv,xS,xT)
    | ~ aSet0(xT)
    | ~ aSubsetOf0(xS,xT) ),
    inference(spm,[status(thm)],[39,80,theory(equality)]) ).

cnf(127,plain,
    ( aLowerBoundOfIn0(xu,xS,xT)
    | $false
    | ~ aSubsetOf0(xS,xT) ),
    inference(rw,[status(thm)],[125,79,theory(equality)]) ).

cnf(128,plain,
    ( aLowerBoundOfIn0(xu,xS,xT)
    | $false
    | $false ),
    inference(rw,[status(thm)],[127,21,theory(equality)]) ).

cnf(129,plain,
    aLowerBoundOfIn0(xu,xS,xT),
    inference(cn,[status(thm)],[128,theory(equality)]) ).

cnf(130,plain,
    ( aLowerBoundOfIn0(xv,xS,xT)
    | $false
    | ~ aSubsetOf0(xS,xT) ),
    inference(rw,[status(thm)],[126,79,theory(equality)]) ).

cnf(131,plain,
    ( aLowerBoundOfIn0(xv,xS,xT)
    | $false
    | $false ),
    inference(rw,[status(thm)],[130,21,theory(equality)]) ).

cnf(132,plain,
    aLowerBoundOfIn0(xv,xS,xT),
    inference(cn,[status(thm)],[131,theory(equality)]) ).

cnf(150,plain,
    ( aElement0(xu)
    | ~ aSet0(xT) ),
    inference(spm,[status(thm)],[31,118,theory(equality)]) ).

cnf(152,plain,
    ( aElement0(xu)
    | $false ),
    inference(rw,[status(thm)],[150,79,theory(equality)]) ).

cnf(153,plain,
    aElement0(xu),
    inference(cn,[status(thm)],[152,theory(equality)]) ).

cnf(160,plain,
    ( aElement0(xv)
    | ~ aSet0(xT) ),
    inference(spm,[status(thm)],[31,121,theory(equality)]) ).

cnf(162,plain,
    ( aElement0(xv)
    | $false ),
    inference(rw,[status(thm)],[160,79,theory(equality)]) ).

cnf(163,plain,
    aElement0(xv),
    inference(cn,[status(thm)],[162,theory(equality)]) ).

cnf(180,plain,
    ( sdtlseqdt0(xu,X1)
    | ~ aInfimumOfIn0(X1,xS,xT)
    | ~ aSet0(xT)
    | ~ aSubsetOf0(xS,xT) ),
    inference(spm,[status(thm)],[41,129,theory(equality)]) ).

cnf(188,plain,
    ( sdtlseqdt0(xu,X1)
    | ~ aInfimumOfIn0(X1,xS,xT)
    | $false
    | ~ aSubsetOf0(xS,xT) ),
    inference(rw,[status(thm)],[180,79,theory(equality)]) ).

cnf(189,plain,
    ( sdtlseqdt0(xu,X1)
    | ~ aInfimumOfIn0(X1,xS,xT)
    | $false
    | $false ),
    inference(rw,[status(thm)],[188,21,theory(equality)]) ).

cnf(190,plain,
    ( sdtlseqdt0(xu,X1)
    | ~ aInfimumOfIn0(X1,xS,xT) ),
    inference(cn,[status(thm)],[189,theory(equality)]) ).

cnf(193,plain,
    ( sdtlseqdt0(xv,X1)
    | ~ aInfimumOfIn0(X1,xS,xT)
    | ~ aSet0(xT)
    | ~ aSubsetOf0(xS,xT) ),
    inference(spm,[status(thm)],[41,132,theory(equality)]) ).

cnf(201,plain,
    ( sdtlseqdt0(xv,X1)
    | ~ aInfimumOfIn0(X1,xS,xT)
    | $false
    | ~ aSubsetOf0(xS,xT) ),
    inference(rw,[status(thm)],[193,79,theory(equality)]) ).

cnf(202,plain,
    ( sdtlseqdt0(xv,X1)
    | ~ aInfimumOfIn0(X1,xS,xT)
    | $false
    | $false ),
    inference(rw,[status(thm)],[201,21,theory(equality)]) ).

cnf(203,plain,
    ( sdtlseqdt0(xv,X1)
    | ~ aInfimumOfIn0(X1,xS,xT) ),
    inference(cn,[status(thm)],[202,theory(equality)]) ).

cnf(232,plain,
    sdtlseqdt0(xu,xv),
    inference(spm,[status(thm)],[190,80,theory(equality)]) ).

cnf(234,plain,
    ( xv = xu
    | ~ sdtlseqdt0(xv,xu)
    | ~ aElement0(xu)
    | ~ aElement0(xv) ),
    inference(spm,[status(thm)],[24,232,theory(equality)]) ).

cnf(236,plain,
    ( xv = xu
    | ~ sdtlseqdt0(xv,xu)
    | $false
    | ~ aElement0(xv) ),
    inference(rw,[status(thm)],[234,153,theory(equality)]) ).

cnf(237,plain,
    ( xv = xu
    | ~ sdtlseqdt0(xv,xu)
    | $false
    | $false ),
    inference(rw,[status(thm)],[236,163,theory(equality)]) ).

cnf(238,plain,
    ( xv = xu
    | ~ sdtlseqdt0(xv,xu) ),
    inference(cn,[status(thm)],[237,theory(equality)]) ).

cnf(239,plain,
    ~ sdtlseqdt0(xv,xu),
    inference(sr,[status(thm)],[238,78,theory(equality)]) ).

cnf(243,plain,
    sdtlseqdt0(xv,xu),
    inference(spm,[status(thm)],[203,81,theory(equality)]) ).

cnf(249,plain,
    $false,
    inference(sr,[status(thm)],[243,239,theory(equality)]) ).

cnf(250,plain,
    $false,
    249,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT382+1.p
% --creating new selector for []
% -running prover on /tmp/tmpgGfJbJ/sel_LAT382+1.p_1 with time limit 29
% -prover status Theorem
% Problem LAT382+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT382+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT382+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
% 
%------------------------------------------------------------------------------