TSTP Solution File: KLE007+4 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE007+4 : 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 : Sat Dec 25 11:38:27 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   51 (  19 unt;   0 def)
%            Number of atoms       :  136 (  53 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  152 (  67   ~;  53   |;  26   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   61 (   0 sgn  40   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',multiplicative_left_identity) ).

fof(6,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',additive_commutativity) ).

fof(7,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',additive_idempotence) ).

fof(10,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',order) ).

fof(12,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',test_3) ).

fof(13,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',test_2) ).

fof(18,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',right_distributivity) ).

fof(19,conjecture,
    ! [X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => ( leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
        & leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
    file('/tmp/tmpz--QhW/sel_KLE007+4.p_1',goals) ).

fof(20,negated_conjecture,
    ~ ! [X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => ( leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
          & leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
    inference(assume_negation,[status(cth)],[19]) ).

fof(24,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[2]) ).

cnf(25,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[24]) ).

fof(32,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

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

fof(34,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[7]) ).

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

fof(40,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(41,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[40]) ).

cnf(42,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(47,plain,
    ! [X4,X5] :
      ( ~ test(X4)
      | ( ( c(X4) != X5
          | complement(X4,X5) )
        & ( ~ complement(X4,X5)
          | c(X4) = X5 ) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(48,plain,
    ! [X6,X7] :
      ( ~ test(X6)
      | ( ( c(X6) != X7
          | complement(X6,X7) )
        & ( ~ complement(X6,X7)
          | c(X6) = X7 ) ) ),
    inference(variable_rename,[status(thm)],[47]) ).

fof(49,plain,
    ! [X6,X7] :
      ( ( c(X6) != X7
        | complement(X6,X7)
        | ~ test(X6) )
      & ( ~ complement(X6,X7)
        | c(X6) = X7
        | ~ test(X6) ) ),
    inference(distribute,[status(thm)],[48]) ).

cnf(51,plain,
    ( complement(X1,X2)
    | ~ test(X1)
    | c(X1) != X2 ),
    inference(split_conjunct,[status(thm)],[49]) ).

fof(52,plain,
    ! [X4,X5] :
      ( ( ~ complement(X5,X4)
        | ( multiplication(X4,X5) = zero
          & multiplication(X5,X4) = zero
          & addition(X4,X5) = one ) )
      & ( multiplication(X4,X5) != zero
        | multiplication(X5,X4) != zero
        | addition(X4,X5) != one
        | complement(X5,X4) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(53,plain,
    ! [X6,X7] :
      ( ( ~ complement(X7,X6)
        | ( multiplication(X6,X7) = zero
          & multiplication(X7,X6) = zero
          & addition(X6,X7) = one ) )
      & ( multiplication(X6,X7) != zero
        | multiplication(X7,X6) != zero
        | addition(X6,X7) != one
        | complement(X7,X6) ) ),
    inference(variable_rename,[status(thm)],[52]) ).

fof(54,plain,
    ! [X6,X7] :
      ( ( multiplication(X6,X7) = zero
        | ~ complement(X7,X6) )
      & ( multiplication(X7,X6) = zero
        | ~ complement(X7,X6) )
      & ( addition(X6,X7) = one
        | ~ complement(X7,X6) )
      & ( multiplication(X6,X7) != zero
        | multiplication(X7,X6) != zero
        | addition(X6,X7) != one
        | complement(X7,X6) ) ),
    inference(distribute,[status(thm)],[53]) ).

cnf(56,plain,
    ( addition(X2,X1) = one
    | ~ complement(X1,X2) ),
    inference(split_conjunct,[status(thm)],[54]) ).

fof(73,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(74,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[73]) ).

fof(75,negated_conjecture,
    ? [X4,X5] :
      ( test(X5)
      & test(X4)
      & ( ~ leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
        | ~ leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(76,negated_conjecture,
    ? [X6,X7] :
      ( test(X7)
      & test(X6)
      & ( ~ leq(one,addition(multiplication(addition(X6,c(X6)),X7),multiplication(addition(X6,c(X6)),c(X7))))
        | ~ leq(addition(multiplication(addition(X6,c(X6)),X7),multiplication(addition(X6,c(X6)),c(X7))),one) ) ),
    inference(variable_rename,[status(thm)],[75]) ).

fof(77,negated_conjecture,
    ( test(esk3_0)
    & test(esk2_0)
    & ( ~ leq(one,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))))
      | ~ leq(addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))),one) ) ),
    inference(skolemize,[status(esa)],[76]) ).

cnf(78,negated_conjecture,
    ( ~ leq(addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))),one)
    | ~ leq(one,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0)))) ),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(79,negated_conjecture,
    test(esk2_0),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(80,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(93,plain,
    ( addition(X1,X2) = one
    | c(X2) != X1
    | ~ test(X2) ),
    inference(spm,[status(thm)],[56,51,theory(equality)]) ).

cnf(206,negated_conjecture,
    ( ~ leq(one,multiplication(addition(esk2_0,c(esk2_0)),addition(esk3_0,c(esk3_0))))
    | ~ leq(addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))),one) ),
    inference(rw,[status(thm)],[78,74,theory(equality)]) ).

cnf(207,negated_conjecture,
    ( ~ leq(one,multiplication(addition(esk2_0,c(esk2_0)),addition(esk3_0,c(esk3_0))))
    | ~ leq(multiplication(addition(esk2_0,c(esk2_0)),addition(esk3_0,c(esk3_0))),one) ),
    inference(rw,[status(thm)],[206,74,theory(equality)]) ).

cnf(321,plain,
    ( addition(c(X1),X1) = one
    | ~ test(X1) ),
    inference(er,[status(thm)],[93,theory(equality)]) ).

cnf(324,plain,
    ( addition(X1,c(X1)) = one
    | ~ test(X1) ),
    inference(rw,[status(thm)],[321,33,theory(equality)]) ).

cnf(329,negated_conjecture,
    ( ~ leq(one,multiplication(one,addition(esk3_0,c(esk3_0))))
    | ~ leq(multiplication(one,addition(esk3_0,c(esk3_0))),one)
    | ~ test(esk2_0) ),
    inference(spm,[status(thm)],[207,324,theory(equality)]) ).

cnf(337,negated_conjecture,
    ( ~ leq(one,addition(esk3_0,c(esk3_0)))
    | ~ leq(multiplication(one,addition(esk3_0,c(esk3_0))),one)
    | ~ test(esk2_0) ),
    inference(rw,[status(thm)],[329,25,theory(equality)]) ).

cnf(338,negated_conjecture,
    ( ~ leq(one,addition(esk3_0,c(esk3_0)))
    | ~ leq(addition(esk3_0,c(esk3_0)),one)
    | ~ test(esk2_0) ),
    inference(rw,[status(thm)],[337,25,theory(equality)]) ).

cnf(339,negated_conjecture,
    ( ~ leq(one,addition(esk3_0,c(esk3_0)))
    | ~ leq(addition(esk3_0,c(esk3_0)),one)
    | $false ),
    inference(rw,[status(thm)],[338,79,theory(equality)]) ).

cnf(340,negated_conjecture,
    ( ~ leq(one,addition(esk3_0,c(esk3_0)))
    | ~ leq(addition(esk3_0,c(esk3_0)),one) ),
    inference(cn,[status(thm)],[339,theory(equality)]) ).

cnf(365,negated_conjecture,
    ( ~ leq(one,one)
    | ~ test(esk3_0) ),
    inference(spm,[status(thm)],[340,324,theory(equality)]) ).

cnf(367,negated_conjecture,
    ( ~ leq(one,one)
    | $false ),
    inference(rw,[status(thm)],[365,80,theory(equality)]) ).

cnf(368,negated_conjecture,
    ~ leq(one,one),
    inference(cn,[status(thm)],[367,theory(equality)]) ).

cnf(369,negated_conjecture,
    addition(one,one) != one,
    inference(spm,[status(thm)],[368,42,theory(equality)]) ).

cnf(370,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[369,35,theory(equality)]) ).

cnf(371,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[370,theory(equality)]) ).

cnf(372,negated_conjecture,
    $false,
    371,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE007+4.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% -running prover on /tmp/tmpz--QhW/sel_KLE007+4.p_1 with time limit 29
% -prover status Theorem
% Problem KLE007+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE007+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE007+4.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
% 
%------------------------------------------------------------------------------