TSTP Solution File: KLE009+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE009+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 11:39:29 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   48 (  24 unt;   0 def)
%            Number of atoms       :  112 (  63 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  115 (  51   ~;  37   |;  22   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    6 (   2 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   :   62 (   0 sgn  38   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(5,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',additive_associativity) ).

fof(6,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',additive_commutativity) ).

fof(11,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',test_3) ).

fof(12,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',test_2) ).

fof(14,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',multiplicative_right_identity) ).

fof(17,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',right_distributivity) ).

fof(18,conjecture,
    ! [X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
    file('/tmp/tmpf333T9/sel_KLE009+2.p_1',goals) ).

fof(19,negated_conjecture,
    ~ ! [X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
    inference(assume_negation,[status(cth)],[18]) ).

fof(29,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(30,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(31,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(32,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(42,plain,
    ! [X4,X5] :
      ( ~ test(X4)
      | ( ( c(X4) != X5
          | complement(X4,X5) )
        & ( ~ complement(X4,X5)
          | c(X4) = X5 ) ) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(43,plain,
    ! [X6,X7] :
      ( ~ test(X6)
      | ( ( c(X6) != X7
          | complement(X6,X7) )
        & ( ~ complement(X6,X7)
          | c(X6) = X7 ) ) ),
    inference(variable_rename,[status(thm)],[42]) ).

fof(44,plain,
    ! [X6,X7] :
      ( ( c(X6) != X7
        | complement(X6,X7)
        | ~ test(X6) )
      & ( ~ complement(X6,X7)
        | c(X6) = X7
        | ~ test(X6) ) ),
    inference(distribute,[status(thm)],[43]) ).

cnf(46,plain,
    ( complement(X1,X2)
    | ~ test(X1)
    | c(X1) != X2 ),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(47,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)],[12]) ).

fof(48,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)],[47]) ).

fof(49,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)],[48]) ).

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

fof(60,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[14]) ).

cnf(61,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[60]) ).

fof(68,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[17]) ).

cnf(69,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[68]) ).

fof(70,negated_conjecture,
    ? [X4,X5] :
      ( test(X5)
      & test(X4)
      & one != addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(71,negated_conjecture,
    ? [X6,X7] :
      ( test(X7)
      & test(X6)
      & one != addition(addition(addition(multiplication(X6,X7),multiplication(X6,c(X7))),multiplication(c(X6),X7)),multiplication(c(X6),c(X7))) ),
    inference(variable_rename,[status(thm)],[70]) ).

fof(72,negated_conjecture,
    ( test(esk3_0)
    & test(esk2_0)
    & one != addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))) ),
    inference(skolemize,[status(esa)],[71]) ).

cnf(73,negated_conjecture,
    one != addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
    inference(split_conjunct,[status(thm)],[72]) ).

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

cnf(75,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(87,plain,
    ( addition(X1,X2) = one
    | c(X2) != X1
    | ~ test(X2) ),
    inference(spm,[status(thm)],[51,46,theory(equality)]) ).

cnf(115,plain,
    addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
    inference(spm,[status(thm)],[32,30,theory(equality)]) ).

cnf(200,negated_conjecture,
    addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[73,69,theory(equality)]),32,theory(equality)]),30,theory(equality)]) ).

cnf(298,plain,
    ( addition(c(X1),X1) = one
    | ~ test(X1) ),
    inference(er,[status(thm)],[87,theory(equality)]) ).

cnf(301,plain,
    ( addition(X1,c(X1)) = one
    | ~ test(X1) ),
    inference(rw,[status(thm)],[298,32,theory(equality)]) ).

cnf(305,negated_conjecture,
    ( addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,one),multiplication(c(esk2_0),c(esk3_0)))) != one
    | ~ test(esk3_0) ),
    inference(spm,[status(thm)],[200,301,theory(equality)]) ).

cnf(310,negated_conjecture,
    ( addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))) != one
    | ~ test(esk3_0) ),
    inference(rw,[status(thm)],[305,61,theory(equality)]) ).

cnf(311,negated_conjecture,
    ( addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))) != one
    | $false ),
    inference(rw,[status(thm)],[310,75,theory(equality)]) ).

cnf(312,negated_conjecture,
    addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))) != one,
    inference(cn,[status(thm)],[311,theory(equality)]) ).

cnf(888,negated_conjecture,
    addition(esk2_0,multiplication(c(esk2_0),addition(esk3_0,c(esk3_0)))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[312,115,theory(equality)]),69,theory(equality)]),32,theory(equality)]) ).

cnf(940,negated_conjecture,
    ( addition(esk2_0,multiplication(c(esk2_0),one)) != one
    | ~ test(esk3_0) ),
    inference(spm,[status(thm)],[888,301,theory(equality)]) ).

cnf(943,negated_conjecture,
    ( addition(esk2_0,c(esk2_0)) != one
    | ~ test(esk3_0) ),
    inference(rw,[status(thm)],[940,61,theory(equality)]) ).

cnf(944,negated_conjecture,
    ( addition(esk2_0,c(esk2_0)) != one
    | $false ),
    inference(rw,[status(thm)],[943,75,theory(equality)]) ).

cnf(945,negated_conjecture,
    addition(esk2_0,c(esk2_0)) != one,
    inference(cn,[status(thm)],[944,theory(equality)]) ).

cnf(950,negated_conjecture,
    ~ test(esk2_0),
    inference(spm,[status(thm)],[945,301,theory(equality)]) ).

cnf(952,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[950,74,theory(equality)]) ).

cnf(953,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[952,theory(equality)]) ).

cnf(954,negated_conjecture,
    $false,
    953,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE009+2.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% -running prover on /tmp/tmpf333T9/sel_KLE009+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE009+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE009+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE009+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
% 
%------------------------------------------------------------------------------