TSTP Solution File: KLE026+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE026+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 11:50:07 EST 2010

% Result   : Theorem 0.29s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   56 (  30 unt;   0 def)
%            Number of atoms       :  126 (  62 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  109 (  39   ~;  35   |;  28   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   95 (   0 sgn  55   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',multiplicative_left_identity) ).

fof(4,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',left_distributivity) ).

fof(5,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',additive_commutativity) ).

fof(6,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',additive_idempotence) ).

fof(7,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',multiplicative_associativity) ).

fof(9,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',additive_associativity) ).

fof(10,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',test_2) ).

fof(11,axiom,
    ! [X4] :
      ( test(X4)
    <=> ? [X5] : complement(X5,X4) ),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',test_1) ).

fof(14,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',order) ).

fof(15,conjecture,
    ! [X4,X5,X6] :
      ( ( test(X5)
        & test(X6) )
     => ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
       => leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
    file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',goals) ).

fof(16,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( ( test(X5)
          & test(X6) )
       => ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
         => leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
    inference(assume_negation,[status(cth)],[15]) ).

fof(19,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[2]) ).

cnf(20,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[19]) ).

fof(23,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(24,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(25,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(26,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(27,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[6]) ).

cnf(28,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[27]) ).

fof(29,plain,
    ! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
    inference(variable_rename,[status(thm)],[7]) ).

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

fof(33,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(34,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[33]) ).

fof(35,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)],[10]) ).

fof(36,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)],[35]) ).

fof(37,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)],[36]) ).

cnf(39,plain,
    ( addition(X2,X1) = one
    | ~ complement(X1,X2) ),
    inference(split_conjunct,[status(thm)],[37]) ).

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

fof(43,plain,
    ! [X6] :
      ( ( ~ test(X6)
        | ? [X7] : complement(X7,X6) )
      & ( ! [X8] : ~ complement(X8,X6)
        | test(X6) ) ),
    inference(variable_rename,[status(thm)],[42]) ).

fof(44,plain,
    ! [X6] :
      ( ( ~ test(X6)
        | complement(esk1_1(X6),X6) )
      & ( ! [X8] : ~ complement(X8,X6)
        | test(X6) ) ),
    inference(skolemize,[status(esa)],[43]) ).

fof(45,plain,
    ! [X6,X8] :
      ( ( ~ complement(X8,X6)
        | test(X6) )
      & ( ~ test(X6)
        | complement(esk1_1(X6),X6) ) ),
    inference(shift_quantors,[status(thm)],[44]) ).

cnf(46,plain,
    ( complement(esk1_1(X1),X1)
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(52,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(53,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[52]) ).

cnf(54,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[53]) ).

fof(56,negated_conjecture,
    ? [X4,X5,X6] :
      ( test(X5)
      & test(X6)
      & multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
      & ~ leq(multiplication(X5,X4),multiplication(X4,X6)) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(57,negated_conjecture,
    ? [X7,X8,X9] :
      ( test(X8)
      & test(X9)
      & multiplication(X8,X7) = multiplication(multiplication(X8,X7),X9)
      & ~ leq(multiplication(X8,X7),multiplication(X7,X9)) ),
    inference(variable_rename,[status(thm)],[56]) ).

fof(58,negated_conjecture,
    ( test(esk3_0)
    & test(esk4_0)
    & multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0)
    & ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[57]) ).

cnf(59,negated_conjecture,
    ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(60,negated_conjecture,
    multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(62,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(71,plain,
    ( leq(X1,X2)
    | addition(X2,X1) != X2 ),
    inference(spm,[status(thm)],[54,26,theory(equality)]) ).

cnf(76,plain,
    ( addition(X1,esk1_1(X1)) = one
    | ~ test(X1) ),
    inference(spm,[status(thm)],[39,46,theory(equality)]) ).

cnf(100,negated_conjecture,
    multiplication(esk3_0,multiplication(esk2_0,esk4_0)) = multiplication(esk3_0,esk2_0),
    inference(rw,[status(thm)],[60,30,theory(equality)]) ).

cnf(114,plain,
    addition(X1,X2) = addition(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[34,28,theory(equality)]) ).

cnf(165,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
    inference(spm,[status(thm)],[24,20,theory(equality)]) ).

cnf(479,plain,
    ( addition(X1,one) = one
    | ~ test(X1) ),
    inference(spm,[status(thm)],[114,76,theory(equality)]) ).

cnf(513,negated_conjecture,
    addition(esk3_0,one) = one,
    inference(spm,[status(thm)],[479,62,theory(equality)]) ).

cnf(517,negated_conjecture,
    addition(one,esk3_0) = one,
    inference(rw,[status(thm)],[513,26,theory(equality)]) ).

cnf(1133,plain,
    ( leq(multiplication(X1,X2),X2)
    | multiplication(addition(one,X1),X2) != X2 ),
    inference(spm,[status(thm)],[71,165,theory(equality)]) ).

cnf(1497,negated_conjecture,
    ( leq(multiplication(esk3_0,X1),X1)
    | multiplication(one,X1) != X1 ),
    inference(spm,[status(thm)],[1133,517,theory(equality)]) ).

cnf(1518,negated_conjecture,
    ( leq(multiplication(esk3_0,X1),X1)
    | $false ),
    inference(rw,[status(thm)],[1497,20,theory(equality)]) ).

cnf(1519,negated_conjecture,
    leq(multiplication(esk3_0,X1),X1),
    inference(cn,[status(thm)],[1518,theory(equality)]) ).

cnf(1534,negated_conjecture,
    leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
    inference(spm,[status(thm)],[1519,100,theory(equality)]) ).

cnf(1539,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1534,59,theory(equality)]) ).

cnf(1540,negated_conjecture,
    $false,
    1539,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE026+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmp-8DO3D/sel_KLE026+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE026+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE026+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE026+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
% 
%------------------------------------------------------------------------------