TSTP Solution File: KLE129+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE129+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 : Sat Dec 25 12:31:12 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   31 (  18 unt;   0 def)
%            Number of atoms       :   51 (  48 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   36 (  16   ~;  10   |;   4   &)
%                                         (   0 <=>;   4  =>;   2  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn  20   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(5,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpZDWEHs/sel_KLE129+1.p_1',additive_idempotence) ).

fof(8,axiom,
    ! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
    file('/tmp/tmpZDWEHs/sel_KLE129+1.p_1',forward_diamond) ).

fof(9,axiom,
    ! [X4] : forward_diamond(X4,divergence(X4)) = divergence(X4),
    file('/tmp/tmpZDWEHs/sel_KLE129+1.p_1',divergence1) ).

fof(14,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/tmp/tmpZDWEHs/sel_KLE129+1.p_1',domain4) ).

fof(15,conjecture,
    ! [X4] :
      ( divergence(X4) = zero
     <= ! [X5] :
          ( addition(domain(X5),forward_diamond(X4,domain(X5))) = forward_diamond(X4,domain(X5))
         => domain(X5) = zero ) ),
    file('/tmp/tmpZDWEHs/sel_KLE129+1.p_1',goals) ).

fof(16,negated_conjecture,
    ~ ! [X4] :
        ( divergence(X4) = zero
       <= ! [X5] :
            ( addition(domain(X5),forward_diamond(X4,domain(X5))) = forward_diamond(X4,domain(X5))
           => domain(X5) = zero ) ),
    inference(assume_negation,[status(cth)],[15]) ).

fof(17,negated_conjecture,
    ~ ! [X4] :
        ( ! [X5] :
            ( addition(domain(X5),forward_diamond(X4,domain(X5))) = forward_diamond(X4,domain(X5))
           => domain(X5) = zero )
       => divergence(X4) = zero ),
    inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).

fof(26,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[5]) ).

cnf(27,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[26]) ).

fof(32,plain,
    ! [X6,X7] : forward_diamond(X6,X7) = domain(multiplication(X6,domain(X7))),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(33,plain,
    forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(34,plain,
    ! [X5] : forward_diamond(X5,divergence(X5)) = divergence(X5),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(35,plain,
    forward_diamond(X1,divergence(X1)) = divergence(X1),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(44,plain,
    ! [X5] : domain(X5) = antidomain(antidomain(X5)),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(45,plain,
    domain(X1) = antidomain(antidomain(X1)),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(46,negated_conjecture,
    ? [X4] :
      ( ! [X5] :
          ( addition(domain(X5),forward_diamond(X4,domain(X5))) != forward_diamond(X4,domain(X5))
          | domain(X5) = zero )
      & divergence(X4) != zero ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(47,negated_conjecture,
    ? [X6] :
      ( ! [X7] :
          ( addition(domain(X7),forward_diamond(X6,domain(X7))) != forward_diamond(X6,domain(X7))
          | domain(X7) = zero )
      & divergence(X6) != zero ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ( ! [X7] :
        ( addition(domain(X7),forward_diamond(esk1_0,domain(X7))) != forward_diamond(esk1_0,domain(X7))
        | domain(X7) = zero )
    & divergence(esk1_0) != zero ),
    inference(skolemize,[status(esa)],[47]) ).

fof(49,negated_conjecture,
    ! [X7] :
      ( ( addition(domain(X7),forward_diamond(esk1_0,domain(X7))) != forward_diamond(esk1_0,domain(X7))
        | domain(X7) = zero )
      & divergence(esk1_0) != zero ),
    inference(shift_quantors,[status(thm)],[48]) ).

cnf(50,negated_conjecture,
    divergence(esk1_0) != zero,
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(51,negated_conjecture,
    ( domain(X1) = zero
    | addition(domain(X1),forward_diamond(esk1_0,domain(X1))) != forward_diamond(esk1_0,domain(X1)) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(52,plain,
    antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))) = forward_diamond(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[33,45,theory(equality)]),45,theory(equality)]),
    [unfolding] ).

cnf(53,negated_conjecture,
    ( antidomain(antidomain(X1)) = zero
    | addition(antidomain(antidomain(X1)),forward_diamond(esk1_0,antidomain(antidomain(X1)))) != forward_diamond(esk1_0,antidomain(antidomain(X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[51,45,theory(equality)]),45,theory(equality)]),45,theory(equality)]),45,theory(equality)]),
    [unfolding] ).

cnf(54,plain,
    antidomain(antidomain(multiplication(X1,antidomain(antidomain(divergence(X1)))))) = divergence(X1),
    inference(rw,[status(thm)],[35,52,theory(equality)]),
    [unfolding] ).

cnf(55,negated_conjecture,
    ( antidomain(antidomain(X1)) = zero
    | addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1)))))))) != antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1))))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[53,52,theory(equality)]),52,theory(equality)]),
    [unfolding] ).

cnf(93,negated_conjecture,
    ( divergence(X1) = zero
    | addition(divergence(X1),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(divergence(X1))))))) != antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(divergence(X1)))))) ),
    inference(spm,[status(thm)],[55,54,theory(equality)]) ).

cnf(423,negated_conjecture,
    ( divergence(esk1_0) = zero
    | addition(divergence(esk1_0),divergence(esk1_0)) != divergence(esk1_0) ),
    inference(spm,[status(thm)],[93,54,theory(equality)]) ).

cnf(425,negated_conjecture,
    ( divergence(esk1_0) = zero
    | $false ),
    inference(rw,[status(thm)],[423,27,theory(equality)]) ).

cnf(426,negated_conjecture,
    divergence(esk1_0) = zero,
    inference(cn,[status(thm)],[425,theory(equality)]) ).

cnf(427,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[426,50,theory(equality)]) ).

cnf(428,negated_conjecture,
    $false,
    427,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE129+1.p
% --creating new selector for [KLE001+7.ax, KLE001+0.ax, KLE001+4.ax, KLE001+6.ax]
% -running prover on /tmp/tmpZDWEHs/sel_KLE129+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE129+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE129+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE129+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
% 
%------------------------------------------------------------------------------