TSTP Solution File: KLE048+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE048+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sat Dec 25 12:04:42 EST 2010

% Result   : Theorem 0.37s
% Output   : CNFRefutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   84 (  50 unt;   0 def)
%            Number of atoms       :  152 (  66 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  114 (  46   ~;  42   |;  20   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  111 (  11 sgn  54   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] : multiplication(X1,zero) = zero,
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',right_annihilation) ).

fof(3,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_identity) ).

fof(5,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_commutativity) ).

fof(6,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_idempotence) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( leq(addition(multiplication(X1,X2),X3),X1)
     => leq(multiplication(X3,star(X2)),X1) ),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',star_induction_right) ).

fof(9,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',order) ).

fof(10,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_associativity) ).

fof(11,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',test_2) ).

fof(12,axiom,
    ! [X4] :
      ( test(X4)
    <=> ? [X5] : complement(X5,X4) ),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',test_1) ).

fof(14,axiom,
    ! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',star_unfold_right) ).

fof(18,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',multiplicative_left_identity) ).

fof(19,conjecture,
    ! [X4] :
      ( test(X4)
     => star(X4) = one ),
    file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',goals) ).

fof(20,negated_conjecture,
    ~ ! [X4] :
        ( test(X4)
       => star(X4) = one ),
    inference(assume_negation,[status(cth)],[19]) ).

fof(21,plain,
    ! [X2] : multiplication(X2,zero) = zero,
    inference(variable_rename,[status(thm)],[1]) ).

cnf(22,plain,
    multiplication(X1,zero) = zero,
    inference(split_conjunct,[status(thm)],[21]) ).

fof(25,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[3]) ).

cnf(26,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[25]) ).

fof(29,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(30,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(31,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[6]) ).

cnf(32,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[31]) ).

fof(33,plain,
    ! [X1,X2,X3] :
      ( ~ leq(addition(multiplication(X1,X2),X3),X1)
      | leq(multiplication(X3,star(X2)),X1) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(34,plain,
    ! [X4,X5,X6] :
      ( ~ leq(addition(multiplication(X4,X5),X6),X4)
      | leq(multiplication(X6,star(X5)),X4) ),
    inference(variable_rename,[status(thm)],[33]) ).

cnf(35,plain,
    ( leq(multiplication(X1,star(X2)),X3)
    | ~ leq(addition(multiplication(X3,X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(38,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(39,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[38]) ).

cnf(40,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(41,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(42,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(43,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(44,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)],[11]) ).

fof(45,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)],[44]) ).

fof(46,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)],[45]) ).

cnf(48,plain,
    ( addition(X2,X1) = one
    | ~ complement(X1,X2) ),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(51,plain,
    ! [X4] :
      ( ( ~ test(X4)
        | ? [X5] : complement(X5,X4) )
      & ( ! [X5] : ~ complement(X5,X4)
        | test(X4) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(52,plain,
    ! [X6] :
      ( ( ~ test(X6)
        | ? [X7] : complement(X7,X6) )
      & ( ! [X8] : ~ complement(X8,X6)
        | test(X6) ) ),
    inference(variable_rename,[status(thm)],[51]) ).

fof(53,plain,
    ! [X6] :
      ( ( ~ test(X6)
        | complement(esk1_1(X6),X6) )
      & ( ! [X8] : ~ complement(X8,X6)
        | test(X6) ) ),
    inference(skolemize,[status(esa)],[52]) ).

fof(54,plain,
    ! [X6,X8] :
      ( ( ~ complement(X8,X6)
        | test(X6) )
      & ( ~ test(X6)
        | complement(esk1_1(X6),X6) ) ),
    inference(shift_quantors,[status(thm)],[53]) ).

cnf(55,plain,
    ( complement(esk1_1(X1),X1)
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[54]) ).

fof(59,plain,
    ! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(60,plain,
    leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    inference(split_conjunct,[status(thm)],[59]) ).

fof(68,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[18]) ).

cnf(69,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[68]) ).

fof(70,negated_conjecture,
    ? [X4] :
      ( test(X4)
      & star(X4) != one ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(71,negated_conjecture,
    ? [X5] :
      ( test(X5)
      & star(X5) != one ),
    inference(variable_rename,[status(thm)],[70]) ).

fof(72,negated_conjecture,
    ( test(esk2_0)
    & star(esk2_0) != one ),
    inference(skolemize,[status(esa)],[71]) ).

cnf(73,negated_conjecture,
    star(esk2_0) != one,
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(74,negated_conjecture,
    test(esk2_0),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(76,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[26,30,theory(equality)]) ).

cnf(83,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[40,32,theory(equality)]) ).

cnf(88,plain,
    ( addition(X1,esk1_1(X1)) = one
    | ~ test(X1) ),
    inference(spm,[status(thm)],[48,55,theory(equality)]) ).

cnf(91,plain,
    addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
    inference(spm,[status(thm)],[41,60,theory(equality)]) ).

cnf(93,plain,
    addition(star(X1),addition(one,multiplication(X1,star(X1)))) = star(X1),
    inference(rw,[status(thm)],[91,30,theory(equality)]) ).

cnf(134,plain,
    addition(X1,X2) = addition(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[43,32,theory(equality)]) ).

cnf(146,plain,
    ( leq(multiplication(X1,star(zero)),X2)
    | ~ leq(addition(zero,X1),X2) ),
    inference(spm,[status(thm)],[35,22,theory(equality)]) ).

cnf(150,plain,
    ( leq(multiplication(X1,star(X2)),one)
    | ~ leq(addition(X2,X1),one) ),
    inference(spm,[status(thm)],[35,69,theory(equality)]) ).

cnf(265,plain,
    leq(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[40,134,theory(equality)]) ).

cnf(286,plain,
    leq(X1,addition(X2,X1)),
    inference(spm,[status(thm)],[265,30,theory(equality)]) ).

cnf(328,plain,
    leq(X1,addition(X2,addition(X3,X1))),
    inference(spm,[status(thm)],[286,43,theory(equality)]) ).

cnf(391,plain,
    leq(X1,addition(X2,addition(X1,X3))),
    inference(spm,[status(thm)],[328,30,theory(equality)]) ).

cnf(535,plain,
    ( leq(X1,one)
    | ~ test(X1) ),
    inference(spm,[status(thm)],[265,88,theory(equality)]) ).

cnf(567,negated_conjecture,
    leq(esk2_0,one),
    inference(spm,[status(thm)],[535,74,theory(equality)]) ).

cnf(572,negated_conjecture,
    addition(esk2_0,one) = one,
    inference(spm,[status(thm)],[41,567,theory(equality)]) ).

cnf(573,negated_conjecture,
    addition(one,esk2_0) = one,
    inference(rw,[status(thm)],[572,30,theory(equality)]) ).

cnf(585,plain,
    leq(one,star(X1)),
    inference(spm,[status(thm)],[391,93,theory(equality)]) ).

cnf(608,negated_conjecture,
    leq(esk2_0,addition(X1,one)),
    inference(spm,[status(thm)],[328,573,theory(equality)]) ).

cnf(619,plain,
    addition(one,star(X1)) = star(X1),
    inference(spm,[status(thm)],[41,585,theory(equality)]) ).

cnf(639,negated_conjecture,
    leq(esk2_0,addition(one,X1)),
    inference(spm,[status(thm)],[608,30,theory(equality)]) ).

cnf(675,negated_conjecture,
    leq(esk2_0,star(X1)),
    inference(spm,[status(thm)],[639,619,theory(equality)]) ).

cnf(686,negated_conjecture,
    addition(esk2_0,star(X1)) = star(X1),
    inference(spm,[status(thm)],[41,675,theory(equality)]) ).

cnf(1523,plain,
    ( leq(multiplication(X1,star(zero)),X2)
    | ~ leq(X1,X2) ),
    inference(rw,[status(thm)],[146,76,theory(equality)]) ).

cnf(1526,plain,
    leq(multiplication(X1,star(zero)),X1),
    inference(spm,[status(thm)],[1523,83,theory(equality)]) ).

cnf(1599,plain,
    leq(star(zero),one),
    inference(spm,[status(thm)],[1526,69,theory(equality)]) ).

cnf(1612,plain,
    addition(star(zero),one) = one,
    inference(spm,[status(thm)],[41,1599,theory(equality)]) ).

cnf(1614,plain,
    star(zero) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1612,30,theory(equality)]),619,theory(equality)]) ).

cnf(1677,negated_conjecture,
    ( leq(multiplication(star(X1),star(esk2_0)),one)
    | ~ leq(star(X1),one) ),
    inference(spm,[status(thm)],[150,686,theory(equality)]) ).

cnf(6528,negated_conjecture,
    ( leq(multiplication(one,star(esk2_0)),one)
    | ~ leq(one,one) ),
    inference(spm,[status(thm)],[1677,1614,theory(equality)]) ).

cnf(6530,negated_conjecture,
    ( leq(star(esk2_0),one)
    | ~ leq(one,one) ),
    inference(rw,[status(thm)],[6528,69,theory(equality)]) ).

cnf(6531,negated_conjecture,
    ( leq(star(esk2_0),one)
    | $false ),
    inference(rw,[status(thm)],[6530,83,theory(equality)]) ).

cnf(6532,negated_conjecture,
    leq(star(esk2_0),one),
    inference(cn,[status(thm)],[6531,theory(equality)]) ).

cnf(6536,negated_conjecture,
    addition(star(esk2_0),one) = one,
    inference(spm,[status(thm)],[41,6532,theory(equality)]) ).

cnf(6540,negated_conjecture,
    star(esk2_0) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[6536,30,theory(equality)]),619,theory(equality)]) ).

cnf(6541,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[6540,73,theory(equality)]) ).

cnf(6542,negated_conjecture,
    $false,
    6541,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE048+1.p
% --creating new selector for [KLE002+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmps5mfKk/sel_KLE048+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE048+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE048+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE048+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
% 
%------------------------------------------------------------------------------