TSTP Solution File: RNG061+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : RNG061+2 : TPTP v5.0.0. Released v4.0.0.
% 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 01:56:30 EST 2010

% Result   : Theorem 0.68s
% Output   : CNFRefutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   64 (  21 unt;   0 def)
%            Number of atoms       :  165 (  52 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  163 (  62   ~;  70   |;  27   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :   39 (   1 sgn  29   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(16,axiom,
    ! [X1,X2,X3] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3) )
     => ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
        & sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
        & sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
        & sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',mArith) ).

fof(21,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => aScalar0(smndt0(X1)) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',mNegSc) ).

fof(23,axiom,
    ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
    & sdtasdt0(smndt0(xS),xR) = smndt0(xN)
    & sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__2144) ).

fof(25,axiom,
    ( aScalar0(xF)
    & xF = sdtasdt0(xA,xA) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__1837) ).

fof(31,axiom,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__2180) ).

fof(36,axiom,
    ( aScalar0(xR)
    & xR = sdtasdt0(xC,xG) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__1892) ).

fof(38,axiom,
    ( aScalar0(xS)
    & xS = sdtasdt0(xF,xD) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__1930) ).

fof(44,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => aScalar0(sdtasdt0(X1,X2)) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',mMulSc) ).

fof(45,conjecture,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__) ).

fof(46,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
        & sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',mMNeg) ).

fof(49,axiom,
    ( aScalar0(xD)
    & xD = sdtasasdt0(xq,xq) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__1800) ).

fof(55,axiom,
    ( aScalar0(xN)
    & xN = sdtasdt0(xR,xS) ),
    file('/tmp/tmpWS2hru/sel_RNG061+2.p_1',m__1949) ).

fof(61,negated_conjecture,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
    inference(assume_negation,[status(cth)],[45]) ).

fof(62,negated_conjecture,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
    inference(fof_simplification,[status(thm)],[61,theory(equality)]) ).

fof(109,plain,
    ! [X1,X2,X3] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X2)
      | ~ aScalar0(X3)
      | ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
        & sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
        & sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
        & sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(110,plain,
    ! [X4,X5,X6] :
      ( ~ aScalar0(X4)
      | ~ aScalar0(X5)
      | ~ aScalar0(X6)
      | ( sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6))
        & sdtpldt0(X4,X5) = sdtpldt0(X5,X4)
        & sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6))
        & sdtasdt0(X4,X5) = sdtasdt0(X5,X4) ) ),
    inference(variable_rename,[status(thm)],[109]) ).

fof(111,plain,
    ! [X4,X5,X6] :
      ( ( sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6))
        | ~ aScalar0(X4)
        | ~ aScalar0(X5)
        | ~ aScalar0(X6) )
      & ( sdtpldt0(X4,X5) = sdtpldt0(X5,X4)
        | ~ aScalar0(X4)
        | ~ aScalar0(X5)
        | ~ aScalar0(X6) )
      & ( sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6))
        | ~ aScalar0(X4)
        | ~ aScalar0(X5)
        | ~ aScalar0(X6) )
      & ( sdtasdt0(X4,X5) = sdtasdt0(X5,X4)
        | ~ aScalar0(X4)
        | ~ aScalar0(X5)
        | ~ aScalar0(X6) ) ),
    inference(distribute,[status(thm)],[110]) ).

cnf(114,plain,
    ( sdtpldt0(X3,X2) = sdtpldt0(X2,X3)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[111]) ).

fof(127,plain,
    ! [X1] :
      ( ~ aScalar0(X1)
      | aScalar0(smndt0(X1)) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(128,plain,
    ! [X2] :
      ( ~ aScalar0(X2)
      | aScalar0(smndt0(X2)) ),
    inference(variable_rename,[status(thm)],[127]) ).

cnf(129,plain,
    ( aScalar0(smndt0(X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[128]) ).

cnf(133,plain,
    sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(135,plain,
    sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(139,plain,
    aScalar0(xF),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(156,plain,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(180,plain,
    aScalar0(xR),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(184,plain,
    xS = sdtasdt0(xF,xD),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(185,plain,
    aScalar0(xS),
    inference(split_conjunct,[status(thm)],[38]) ).

fof(202,plain,
    ! [X1,X2] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X2)
      | aScalar0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[44]) ).

fof(203,plain,
    ! [X3,X4] :
      ( ~ aScalar0(X3)
      | ~ aScalar0(X4)
      | aScalar0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[202]) ).

cnf(204,plain,
    ( aScalar0(sdtasdt0(X1,X2))
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[203]) ).

cnf(205,negated_conjecture,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(206,plain,
    ! [X1,X2] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X2)
      | ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
        & sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[46]) ).

fof(207,plain,
    ! [X3,X4] :
      ( ~ aScalar0(X3)
      | ~ aScalar0(X4)
      | ( sdtasdt0(X3,smndt0(X4)) = smndt0(sdtasdt0(X3,X4))
        & sdtasdt0(smndt0(X3),X4) = smndt0(sdtasdt0(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[206]) ).

fof(208,plain,
    ! [X3,X4] :
      ( ( sdtasdt0(X3,smndt0(X4)) = smndt0(sdtasdt0(X3,X4))
        | ~ aScalar0(X3)
        | ~ aScalar0(X4) )
      & ( sdtasdt0(smndt0(X3),X4) = smndt0(sdtasdt0(X3,X4))
        | ~ aScalar0(X3)
        | ~ aScalar0(X4) ) ),
    inference(distribute,[status(thm)],[207]) ).

cnf(210,plain,
    ( sdtasdt0(X2,smndt0(X1)) = smndt0(sdtasdt0(X2,X1))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[208]) ).

cnf(215,plain,
    aScalar0(xD),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(238,plain,
    aScalar0(xN),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(333,plain,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS))
    | ~ aScalar0(xR) ),
    inference(spm,[status(thm)],[204,135,theory(equality)]) ).

cnf(339,plain,
    ( aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(smndt0(xS)) ),
    inference(spm,[status(thm)],[204,133,theory(equality)]) ).

cnf(355,plain,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS))
    | $false ),
    inference(rw,[status(thm)],[333,180,theory(equality)]) ).

cnf(356,plain,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[355,theory(equality)]) ).

cnf(406,plain,
    ( smndt0(xS) = sdtasdt0(xF,smndt0(xD))
    | ~ aScalar0(xF)
    | ~ aScalar0(xD) ),
    inference(spm,[status(thm)],[210,184,theory(equality)]) ).

cnf(428,plain,
    ( smndt0(xS) = sdtasdt0(xF,smndt0(xD))
    | $false
    | ~ aScalar0(xD) ),
    inference(rw,[status(thm)],[406,139,theory(equality)]) ).

cnf(429,plain,
    ( smndt0(xS) = sdtasdt0(xF,smndt0(xD))
    | $false
    | $false ),
    inference(rw,[status(thm)],[428,215,theory(equality)]) ).

cnf(430,plain,
    smndt0(xS) = sdtasdt0(xF,smndt0(xD)),
    inference(cn,[status(thm)],[429,theory(equality)]) ).

cnf(527,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(spm,[status(thm)],[114,238,theory(equality)]) ).

cnf(1423,plain,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xD))
    | ~ aScalar0(xF) ),
    inference(spm,[status(thm)],[204,430,theory(equality)]) ).

cnf(1438,plain,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xD))
    | $false ),
    inference(rw,[status(thm)],[1423,139,theory(equality)]) ).

cnf(1439,plain,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xD)) ),
    inference(cn,[status(thm)],[1438,theory(equality)]) ).

cnf(2964,plain,
    ( aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(xS) ),
    inference(spm,[status(thm)],[339,129,theory(equality)]) ).

cnf(2965,plain,
    ( aScalar0(sdtasdt0(xS,xS))
    | $false ),
    inference(rw,[status(thm)],[2964,185,theory(equality)]) ).

cnf(2966,plain,
    aScalar0(sdtasdt0(xS,xS)),
    inference(cn,[status(thm)],[2965,theory(equality)]) ).

cnf(3066,plain,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(xD) ),
    inference(spm,[status(thm)],[1439,129,theory(equality)]) ).

cnf(3067,plain,
    ( aScalar0(smndt0(xS))
    | $false ),
    inference(rw,[status(thm)],[3066,215,theory(equality)]) ).

cnf(3068,plain,
    aScalar0(smndt0(xS)),
    inference(cn,[status(thm)],[3067,theory(equality)]) ).

cnf(3123,plain,
    ( aScalar0(smndt0(xN))
    | $false ),
    inference(rw,[status(thm)],[356,3068,theory(equality)]) ).

cnf(3124,plain,
    aScalar0(smndt0(xN)),
    inference(cn,[status(thm)],[3123,theory(equality)]) ).

cnf(15306,plain,
    ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
    | ~ aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(smndt0(xN)) ),
    inference(spm,[status(thm)],[156,527,theory(equality)]) ).

cnf(15418,plain,
    ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
    | $false
    | ~ aScalar0(smndt0(xN)) ),
    inference(rw,[status(thm)],[15306,2966,theory(equality)]) ).

cnf(15419,plain,
    ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
    | $false
    | $false ),
    inference(rw,[status(thm)],[15418,3124,theory(equality)]) ).

cnf(15420,plain,
    sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
    inference(cn,[status(thm)],[15419,theory(equality)]) ).

cnf(15421,plain,
    $false,
    inference(sr,[status(thm)],[15420,205,theory(equality)]) ).

cnf(15422,plain,
    $false,
    15421,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG061+2.p
% --creating new selector for []
% -running prover on /tmp/tmpWS2hru/sel_RNG061+2.p_1 with time limit 29
% -prover status Theorem
% Problem RNG061+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG061+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG061+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
% 
%------------------------------------------------------------------------------