TSTP Solution File: KLE035+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE035+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 11:57:06 EST 2010

% Result   : Theorem 22.94s
% Output   : CNFRefutation 22.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   51 (  41 unt;   0 def)
%            Number of atoms       :   80 (  40 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   43 (  14   ~;   6   |;  20   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   72 (   0 sgn  40   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',additive_identity) ).

fof(4,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',left_distributivity) ).

fof(6,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',additive_commutativity) ).

fof(7,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',additive_idempotence) ).

fof(8,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',multiplicative_associativity) ).

fof(15,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',right_distributivity) ).

fof(16,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',order) ).

fof(17,conjecture,
    ! [X4,X5,X6,X7] :
      ( ( test(X7)
        & test(X6)
        & leq(multiplication(multiplication(X6,X4),c(X7)),zero)
        & leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
     => leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
    file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',goals) ).

fof(18,negated_conjecture,
    ~ ! [X4,X5,X6,X7] :
        ( ( test(X7)
          & test(X6)
          & leq(multiplication(multiplication(X6,X4),c(X7)),zero)
          & leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
       => leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
    inference(assume_negation,[status(cth)],[17]) ).

fof(24,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[3]) ).

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

fof(26,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(27,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(30,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(31,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(32,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[7]) ).

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

fof(34,plain,
    ! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(35,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(61,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(62,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[61]) ).

fof(63,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(64,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[63]) ).

cnf(65,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(66,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[64]) ).

fof(67,negated_conjecture,
    ? [X4,X5,X6,X7] :
      ( test(X7)
      & test(X6)
      & leq(multiplication(multiplication(X6,X4),c(X7)),zero)
      & leq(multiplication(multiplication(X6,X5),c(X7)),zero)
      & ~ leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(68,negated_conjecture,
    ? [X8,X9,X10,X11] :
      ( test(X11)
      & test(X10)
      & leq(multiplication(multiplication(X10,X8),c(X11)),zero)
      & leq(multiplication(multiplication(X10,X9),c(X11)),zero)
      & ~ leq(multiplication(multiplication(X10,addition(X8,X9)),c(X11)),zero) ),
    inference(variable_rename,[status(thm)],[67]) ).

fof(69,negated_conjecture,
    ( test(esk5_0)
    & test(esk4_0)
    & leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
    & leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero)
    & ~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero) ),
    inference(skolemize,[status(esa)],[68]) ).

cnf(70,negated_conjecture,
    ~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero),
    inference(split_conjunct,[status(thm)],[69]) ).

cnf(71,negated_conjecture,
    leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero),
    inference(split_conjunct,[status(thm)],[69]) ).

cnf(72,negated_conjecture,
    leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
    inference(split_conjunct,[status(thm)],[69]) ).

cnf(75,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[25,31,theory(equality)]) ).

cnf(111,negated_conjecture,
    leq(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero),
    inference(rw,[status(thm)],[71,35,theory(equality)]) ).

cnf(112,negated_conjecture,
    leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
    inference(rw,[status(thm)],[72,35,theory(equality)]) ).

cnf(113,negated_conjecture,
    ~ leq(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero),
    inference(rw,[status(thm)],[70,35,theory(equality)]) ).

cnf(207,negated_conjecture,
    addition(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero) != zero,
    inference(spm,[status(thm)],[113,65,theory(equality)]) ).

cnf(210,negated_conjecture,
    multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))) != zero,
    inference(rw,[status(thm)],[207,25,theory(equality)]) ).

cnf(223,negated_conjecture,
    addition(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero) = zero,
    inference(spm,[status(thm)],[66,111,theory(equality)]) ).

cnf(226,negated_conjecture,
    multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))) = zero,
    inference(rw,[status(thm)],[223,25,theory(equality)]) ).

cnf(228,negated_conjecture,
    addition(zero,multiplication(esk4_0,X1)) = multiplication(esk4_0,addition(multiplication(esk3_0,c(esk5_0)),X1)),
    inference(spm,[status(thm)],[62,226,theory(equality)]) ).

cnf(236,negated_conjecture,
    multiplication(esk4_0,X1) = multiplication(esk4_0,addition(multiplication(esk3_0,c(esk5_0)),X1)),
    inference(rw,[status(thm)],[228,75,theory(equality)]) ).

cnf(245,negated_conjecture,
    addition(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero) = zero,
    inference(spm,[status(thm)],[66,112,theory(equality)]) ).

cnf(249,negated_conjecture,
    multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
    inference(rw,[status(thm)],[245,25,theory(equality)]) ).

cnf(264,negated_conjecture,
    addition(multiplication(esk4_0,X1),zero) = multiplication(esk4_0,addition(X1,multiplication(esk2_0,c(esk5_0)))),
    inference(spm,[status(thm)],[62,249,theory(equality)]) ).

cnf(273,negated_conjecture,
    multiplication(esk4_0,X1) = multiplication(esk4_0,addition(X1,multiplication(esk2_0,c(esk5_0)))),
    inference(rw,[status(thm)],[264,25,theory(equality)]) ).

cnf(5201,negated_conjecture,
    addition(multiplication(esk4_0,X1),multiplication(X2,addition(multiplication(esk3_0,c(esk5_0)),X1))) = multiplication(addition(esk4_0,X2),addition(multiplication(esk3_0,c(esk5_0)),X1)),
    inference(spm,[status(thm)],[27,236,theory(equality)]) ).

cnf(580719,negated_conjecture,
    addition(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),multiplication(esk4_0,multiplication(esk3_0,c(esk5_0)))) = multiplication(addition(esk4_0,esk4_0),addition(multiplication(esk3_0,c(esk5_0)),multiplication(esk2_0,c(esk5_0)))),
    inference(spm,[status(thm)],[5201,273,theory(equality)]) ).

cnf(581338,negated_conjecture,
    zero = multiplication(addition(esk4_0,esk4_0),addition(multiplication(esk3_0,c(esk5_0)),multiplication(esk2_0,c(esk5_0)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[580719,249,theory(equality)]),226,theory(equality)]),25,theory(equality)]) ).

cnf(581339,negated_conjecture,
    zero = multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[581338,33,theory(equality)]),27,theory(equality)]),31,theory(equality)]) ).

cnf(581340,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[581339,210,theory(equality)]) ).

cnf(581341,negated_conjecture,
    $false,
    581340,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE035+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpTkKqmG/sel_KLE035+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE035+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE035+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE035+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
% 
%------------------------------------------------------------------------------