TSTP Solution File: SEU418+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU418+2 : TPTP v5.0.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 08:53:50 EST 2010

% Result   : Theorem 8.78s
% Output   : CNFRefutation 8.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   61 (  28 unt;   0 def)
%            Number of atoms       :  148 (  22 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  156 (  69   ~;  61   |;  12   &)
%                                         (   1 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   93 (   2 sgn  57   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(20,axiom,
    ! [X1,X2] : r1_tarski(k4_xboole_0(X1,X2),X1),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t36_xboole_1) ).

fof(597,axiom,
    ! [X1,X2] :
      ( k4_xboole_0(X1,X2) = k1_xboole_0
    <=> r1_tarski(X1,X2) ),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t37_xboole_1) ).

fof(658,axiom,
    ! [X1] :
      ( v1_relat_1(X1)
     => ! [X2] :
          ( v1_relat_1(X2)
         => ! [X3] :
              ( v1_relat_1(X3)
             => ( r1_tarski(X1,X2)
               => r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ) ) ) ),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t49_relat_1) ).

fof(966,axiom,
    ! [X1] : k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t2_boole) ).

fof(1076,axiom,
    ! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t3_boole) ).

fof(1123,axiom,
    ! [X1,X2,X3] : k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t49_xboole_1) ).

fof(1324,axiom,
    ! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t48_xboole_1) ).

fof(1630,axiom,
    ! [X1,X2] :
      ( v1_relat_1(X2)
     => ( r1_tarski(X1,X2)
       => v1_relat_1(X1) ) ),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t3_relat_1) ).

fof(1824,axiom,
    ! [X1,X2,X3] :
      ( ( r1_tarski(X1,X2)
        & r1_tarski(X1,X3) )
     => r1_tarski(X1,k3_xboole_0(X2,X3)) ),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t19_xboole_1) ).

fof(2028,conjecture,
    ! [X1] :
      ( v1_relat_1(X1)
     => ! [X2] :
          ( v1_relat_1(X2)
         => ! [X3] :
              ( v1_relat_1(X3)
             => r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
    file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t8_relset_2) ).

fof(2045,negated_conjecture,
    ~ ! [X1] :
        ( v1_relat_1(X1)
       => ! [X2] :
            ( v1_relat_1(X2)
           => ! [X3] :
                ( v1_relat_1(X3)
               => r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
    inference(assume_negation,[status(cth)],[2028]) ).

fof(2259,plain,
    ! [X3,X4] : r1_tarski(k4_xboole_0(X3,X4),X3),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(2260,plain,
    r1_tarski(k4_xboole_0(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[2259]) ).

fof(4115,plain,
    ! [X1,X2] :
      ( ( k4_xboole_0(X1,X2) != k1_xboole_0
        | r1_tarski(X1,X2) )
      & ( ~ r1_tarski(X1,X2)
        | k4_xboole_0(X1,X2) = k1_xboole_0 ) ),
    inference(fof_nnf,[status(thm)],[597]) ).

fof(4116,plain,
    ! [X3,X4] :
      ( ( k4_xboole_0(X3,X4) != k1_xboole_0
        | r1_tarski(X3,X4) )
      & ( ~ r1_tarski(X3,X4)
        | k4_xboole_0(X3,X4) = k1_xboole_0 ) ),
    inference(variable_rename,[status(thm)],[4115]) ).

cnf(4118,plain,
    ( r1_tarski(X1,X2)
    | k4_xboole_0(X1,X2) != k1_xboole_0 ),
    inference(split_conjunct,[status(thm)],[4116]) ).

fof(4333,plain,
    ! [X1] :
      ( ~ v1_relat_1(X1)
      | ! [X2] :
          ( ~ v1_relat_1(X2)
          | ! [X3] :
              ( ~ v1_relat_1(X3)
              | ~ r1_tarski(X1,X2)
              | r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ) ) ),
    inference(fof_nnf,[status(thm)],[658]) ).

fof(4334,plain,
    ! [X4] :
      ( ~ v1_relat_1(X4)
      | ! [X5] :
          ( ~ v1_relat_1(X5)
          | ! [X6] :
              ( ~ v1_relat_1(X6)
              | ~ r1_tarski(X4,X5)
              | r1_tarski(k5_relat_1(X4,X6),k5_relat_1(X5,X6)) ) ) ),
    inference(variable_rename,[status(thm)],[4333]) ).

fof(4335,plain,
    ! [X4,X5,X6] :
      ( ~ v1_relat_1(X6)
      | ~ r1_tarski(X4,X5)
      | r1_tarski(k5_relat_1(X4,X6),k5_relat_1(X5,X6))
      | ~ v1_relat_1(X5)
      | ~ v1_relat_1(X4) ),
    inference(shift_quantors,[status(thm)],[4334]) ).

cnf(4336,plain,
    ( r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3))
    | ~ v1_relat_1(X1)
    | ~ v1_relat_1(X2)
    | ~ r1_tarski(X1,X2)
    | ~ v1_relat_1(X3) ),
    inference(split_conjunct,[status(thm)],[4335]) ).

fof(5249,plain,
    ! [X2] : k3_xboole_0(X2,k1_xboole_0) = k1_xboole_0,
    inference(variable_rename,[status(thm)],[966]) ).

cnf(5250,plain,
    k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
    inference(split_conjunct,[status(thm)],[5249]) ).

fof(5566,plain,
    ! [X2] : k4_xboole_0(X2,k1_xboole_0) = X2,
    inference(variable_rename,[status(thm)],[1076]) ).

cnf(5567,plain,
    k4_xboole_0(X1,k1_xboole_0) = X1,
    inference(split_conjunct,[status(thm)],[5566]) ).

fof(5679,plain,
    ! [X4,X5,X6] : k3_xboole_0(X4,k4_xboole_0(X5,X6)) = k4_xboole_0(k3_xboole_0(X4,X5),X6),
    inference(variable_rename,[status(thm)],[1123]) ).

cnf(5680,plain,
    k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[5679]) ).

fof(6232,plain,
    ! [X3,X4] : k4_xboole_0(X3,k4_xboole_0(X3,X4)) = k3_xboole_0(X3,X4),
    inference(variable_rename,[status(thm)],[1324]) ).

cnf(6233,plain,
    k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
    inference(split_conjunct,[status(thm)],[6232]) ).

fof(7113,plain,
    ! [X1,X2] :
      ( ~ v1_relat_1(X2)
      | ~ r1_tarski(X1,X2)
      | v1_relat_1(X1) ),
    inference(fof_nnf,[status(thm)],[1630]) ).

fof(7114,plain,
    ! [X3,X4] :
      ( ~ v1_relat_1(X4)
      | ~ r1_tarski(X3,X4)
      | v1_relat_1(X3) ),
    inference(variable_rename,[status(thm)],[7113]) ).

cnf(7115,plain,
    ( v1_relat_1(X1)
    | ~ r1_tarski(X1,X2)
    | ~ v1_relat_1(X2) ),
    inference(split_conjunct,[status(thm)],[7114]) ).

fof(7715,plain,
    ! [X1,X2,X3] :
      ( ~ r1_tarski(X1,X2)
      | ~ r1_tarski(X1,X3)
      | r1_tarski(X1,k3_xboole_0(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[1824]) ).

fof(7716,plain,
    ! [X4,X5,X6] :
      ( ~ r1_tarski(X4,X5)
      | ~ r1_tarski(X4,X6)
      | r1_tarski(X4,k3_xboole_0(X5,X6)) ),
    inference(variable_rename,[status(thm)],[7715]) ).

cnf(7717,plain,
    ( r1_tarski(X1,k3_xboole_0(X2,X3))
    | ~ r1_tarski(X1,X3)
    | ~ r1_tarski(X1,X2) ),
    inference(split_conjunct,[status(thm)],[7716]) ).

fof(8346,negated_conjecture,
    ? [X1] :
      ( v1_relat_1(X1)
      & ? [X2] :
          ( v1_relat_1(X2)
          & ? [X3] :
              ( v1_relat_1(X3)
              & ~ r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
    inference(fof_nnf,[status(thm)],[2045]) ).

fof(8347,negated_conjecture,
    ? [X4] :
      ( v1_relat_1(X4)
      & ? [X5] :
          ( v1_relat_1(X5)
          & ? [X6] :
              ( v1_relat_1(X6)
              & ~ r1_tarski(k5_relat_1(k3_xboole_0(X4,X5),X6),k3_xboole_0(k5_relat_1(X4,X6),k5_relat_1(X5,X6))) ) ) ),
    inference(variable_rename,[status(thm)],[8346]) ).

fof(8348,negated_conjecture,
    ( v1_relat_1(esk322_0)
    & v1_relat_1(esk323_0)
    & v1_relat_1(esk324_0)
    & ~ r1_tarski(k5_relat_1(k3_xboole_0(esk322_0,esk323_0),esk324_0),k3_xboole_0(k5_relat_1(esk322_0,esk324_0),k5_relat_1(esk323_0,esk324_0))) ),
    inference(skolemize,[status(esa)],[8347]) ).

cnf(8349,negated_conjecture,
    ~ r1_tarski(k5_relat_1(k3_xboole_0(esk322_0,esk323_0),esk324_0),k3_xboole_0(k5_relat_1(esk322_0,esk324_0),k5_relat_1(esk323_0,esk324_0))),
    inference(split_conjunct,[status(thm)],[8348]) ).

cnf(8350,negated_conjecture,
    v1_relat_1(esk324_0),
    inference(split_conjunct,[status(thm)],[8348]) ).

cnf(8351,negated_conjecture,
    v1_relat_1(esk323_0),
    inference(split_conjunct,[status(thm)],[8348]) ).

cnf(8352,negated_conjecture,
    v1_relat_1(esk322_0),
    inference(split_conjunct,[status(thm)],[8348]) ).

cnf(8667,plain,
    k4_xboole_0(X1,k4_xboole_0(X1,k1_xboole_0)) = k1_xboole_0,
    inference(rw,[status(thm)],[5250,6233,theory(equality)]),
    [unfolding] ).

cnf(8678,plain,
    k4_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),X3) = k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X2,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[5680,6233,theory(equality)]),6233,theory(equality)]),
    [unfolding] ).

cnf(8754,plain,
    ( r1_tarski(X1,k4_xboole_0(X2,k4_xboole_0(X2,X3)))
    | ~ r1_tarski(X1,X3)
    | ~ r1_tarski(X1,X2) ),
    inference(rw,[status(thm)],[7717,6233,theory(equality)]),
    [unfolding] ).

cnf(8799,negated_conjecture,
    ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k4_xboole_0(k5_relat_1(esk322_0,esk324_0),k4_xboole_0(k5_relat_1(esk322_0,esk324_0),k5_relat_1(esk323_0,esk324_0)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[8349,6233,theory(equality)]),6233,theory(equality)]),
    [unfolding] ).

cnf(9201,plain,
    k4_xboole_0(X1,X1) = k1_xboole_0,
    inference(rw,[status(thm)],[8667,5567,theory(equality)]) ).

cnf(12472,negated_conjecture,
    ( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk323_0,esk324_0))
    | ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0)) ),
    inference(spm,[status(thm)],[8799,8754,theory(equality)]) ).

cnf(14669,plain,
    ( r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3))
    | ~ v1_relat_1(X3)
    | ~ v1_relat_1(X2)
    | ~ r1_tarski(X1,X2) ),
    inference(csr,[status(thm)],[4336,7115]) ).

cnf(73506,negated_conjecture,
    ( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
    | ~ v1_relat_1(esk324_0)
    | ~ v1_relat_1(esk323_0)
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
    inference(spm,[status(thm)],[12472,14669,theory(equality)]) ).

cnf(73513,negated_conjecture,
    ( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
    | $false
    | ~ v1_relat_1(esk323_0)
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
    inference(rw,[status(thm)],[73506,8350,theory(equality)]) ).

cnf(73514,negated_conjecture,
    ( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
    | $false
    | $false
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
    inference(rw,[status(thm)],[73513,8351,theory(equality)]) ).

cnf(73515,negated_conjecture,
    ( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
    inference(cn,[status(thm)],[73514,theory(equality)]) ).

cnf(73522,negated_conjecture,
    ( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
    | ~ v1_relat_1(esk324_0)
    | ~ v1_relat_1(esk322_0)
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk322_0) ),
    inference(spm,[status(thm)],[73515,14669,theory(equality)]) ).

cnf(73529,negated_conjecture,
    ( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
    | $false
    | ~ v1_relat_1(esk322_0)
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk322_0) ),
    inference(rw,[status(thm)],[73522,8350,theory(equality)]) ).

cnf(73530,negated_conjecture,
    ( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
    | $false
    | $false
    | ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk322_0) ),
    inference(rw,[status(thm)],[73529,8352,theory(equality)]) ).

cnf(73531,negated_conjecture,
    ( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[73530,2260,theory(equality)]) ).

cnf(73532,negated_conjecture,
    ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0),
    inference(cn,[status(thm)],[73531,theory(equality)]) ).

cnf(73538,negated_conjecture,
    k4_xboole_0(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) != k1_xboole_0,
    inference(spm,[status(thm)],[73532,4118,theory(equality)]) ).

cnf(73542,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[73538,8678,theory(equality)]),9201,theory(equality)]),5567,theory(equality)]),9201,theory(equality)]) ).

cnf(73543,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[73542,theory(equality)]) ).

cnf(73544,negated_conjecture,
    $false,
    73543,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU418+2.p
% --creating new selector for [SET007+3.ax, SET007+0.ax, SET007+1.ax, SET007+2.ax, SET007+4.ax, SET007+6.ax, SET007+7.ax, SET007+8.ax, SET007+9.ax, SET007+10.ax, SET007+11.ax, SET007+13.ax, SET007+14.ax, SET007+16.ax, SET007+17.ax, SET007+18.ax, SET007+20.ax, SET007+22.ax, SET007+24.ax, SET007+26.ax, SET007+31.ax, SET007+35.ax, SET007+40.ax, SET007+48.ax, SET007+54.ax, SET007+55.ax, SET007+59.ax, SET007+60.ax, SET007+61.ax, SET007+64.ax, SET007+80.ax, SET007+117.ax, SET007+126.ax, SET007+188.ax, SET007+200.ax, SET007+210.ax, SET007+212.ax, SET007+213.ax, SET007+225.ax, SET007+363.ax, SET007+393.ax, SET007+441.ax]
% -running prover on /tmp/tmpCmCfHu/sel_SEU418+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU418+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU418+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU418+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
% 
%------------------------------------------------------------------------------