TSTP Solution File: KLE090+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE090+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 12:14:13 EST 2010

% Result   : Theorem 1.89s
% Output   : CNFRefutation 1.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   75 (  70 unt;   0 def)
%            Number of atoms       :   80 (  78 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   6   ~;   0   |;   3   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   90 (   2 sgn  42   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_identity) ).

fof(3,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',left_distributivity) ).

fof(4,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_associativity) ).

fof(5,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_commutativity) ).

fof(6,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_idempotence) ).

fof(12,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',multiplicative_right_identity) ).

fof(13,axiom,
    ! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',domain3) ).

fof(14,axiom,
    ! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',domain2) ).

fof(15,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',right_distributivity) ).

fof(16,axiom,
    ! [X4] : multiplication(antidomain(X4),X4) = zero,
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',domain1) ).

fof(17,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',multiplicative_left_identity) ).

fof(18,conjecture,
    ! [X4,X5] :
      ( addition(X4,X5) = X5
     => addition(antidomain(X5),antidomain(X4)) = antidomain(X4) ),
    file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',goals) ).

fof(19,negated_conjecture,
    ~ ! [X4,X5] :
        ( addition(X4,X5) = X5
       => addition(antidomain(X5),antidomain(X4)) = antidomain(X4) ),
    inference(assume_negation,[status(cth)],[18]) ).

fof(22,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[2]) ).

cnf(23,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[22]) ).

fof(24,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(25,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[24]) ).

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

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

fof(28,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(29,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(30,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[6]) ).

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

fof(42,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[12]) ).

cnf(43,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[42]) ).

fof(44,plain,
    ! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
    inference(variable_rename,[status(thm)],[13]) ).

cnf(45,plain,
    addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[44]) ).

fof(46,plain,
    ! [X6,X7] : addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7))))) = antidomain(multiplication(X6,antidomain(antidomain(X7)))),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(47,plain,
    addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(48,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(49,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(50,plain,
    ! [X5] : multiplication(antidomain(X5),X5) = zero,
    inference(variable_rename,[status(thm)],[16]) ).

cnf(51,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[50]) ).

fof(52,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[17]) ).

cnf(53,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[52]) ).

fof(54,negated_conjecture,
    ? [X4,X5] :
      ( addition(X4,X5) = X5
      & addition(antidomain(X5),antidomain(X4)) != antidomain(X4) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(55,negated_conjecture,
    ? [X6,X7] :
      ( addition(X6,X7) = X7
      & addition(antidomain(X7),antidomain(X6)) != antidomain(X6) ),
    inference(variable_rename,[status(thm)],[54]) ).

fof(56,negated_conjecture,
    ( addition(esk1_0,esk2_0) = esk2_0
    & addition(antidomain(esk2_0),antidomain(esk1_0)) != antidomain(esk1_0) ),
    inference(skolemize,[status(esa)],[55]) ).

cnf(57,negated_conjecture,
    addition(antidomain(esk2_0),antidomain(esk1_0)) != antidomain(esk1_0),
    inference(split_conjunct,[status(thm)],[56]) ).

cnf(58,negated_conjecture,
    addition(esk1_0,esk2_0) = esk2_0,
    inference(split_conjunct,[status(thm)],[56]) ).

cnf(60,plain,
    zero = antidomain(one),
    inference(spm,[status(thm)],[43,51,theory(equality)]) ).

cnf(63,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[23,29,theory(equality)]) ).

cnf(67,negated_conjecture,
    addition(antidomain(esk1_0),antidomain(esk2_0)) != antidomain(esk1_0),
    inference(rw,[status(thm)],[57,29,theory(equality)]) ).

cnf(68,plain,
    addition(antidomain(X1),antidomain(antidomain(X1))) = one,
    inference(rw,[status(thm)],[45,29,theory(equality)]) ).

cnf(71,plain,
    addition(X1,X2) = addition(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[27,31,theory(equality)]) ).

cnf(121,plain,
    addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
    inference(spm,[status(thm)],[49,51,theory(equality)]) ).

cnf(140,plain,
    multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
    inference(rw,[status(thm)],[121,23,theory(equality)]) ).

cnf(154,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
    inference(spm,[status(thm)],[25,53,theory(equality)]) ).

cnf(159,plain,
    addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
    inference(spm,[status(thm)],[25,51,theory(equality)]) ).

cnf(179,plain,
    multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
    inference(rw,[status(thm)],[159,23,theory(equality)]) ).

cnf(225,plain,
    addition(zero,antidomain(zero)) = one,
    inference(spm,[status(thm)],[68,60,theory(equality)]) ).

cnf(242,plain,
    antidomain(zero) = one,
    inference(rw,[status(thm)],[225,63,theory(equality)]) ).

cnf(302,plain,
    addition(antidomain(X1),one) = one,
    inference(spm,[status(thm)],[71,68,theory(equality)]) ).

cnf(320,plain,
    addition(one,antidomain(X1)) = one,
    inference(rw,[status(thm)],[302,29,theory(equality)]) ).

cnf(467,plain,
    multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
    inference(spm,[status(thm)],[179,29,theory(equality)]) ).

cnf(673,plain,
    multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
    inference(spm,[status(thm)],[467,68,theory(equality)]) ).

cnf(695,plain,
    X1 = multiplication(antidomain(antidomain(X1)),X1),
    inference(rw,[status(thm)],[673,53,theory(equality)]) ).

cnf(2730,negated_conjecture,
    multiplication(antidomain(esk2_0),esk2_0) = multiplication(antidomain(esk2_0),esk1_0),
    inference(spm,[status(thm)],[140,58,theory(equality)]) ).

cnf(2731,plain,
    multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
    inference(spm,[status(thm)],[140,68,theory(equality)]) ).

cnf(2784,negated_conjecture,
    zero = multiplication(antidomain(esk2_0),esk1_0),
    inference(rw,[status(thm)],[2730,51,theory(equality)]) ).

cnf(2785,plain,
    antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
    inference(rw,[status(thm)],[2731,43,theory(equality)]) ).

cnf(2786,plain,
    antidomain(antidomain(antidomain(X1))) = antidomain(X1),
    inference(rw,[status(thm)],[2785,695,theory(equality)]) ).

cnf(2904,negated_conjecture,
    addition(antidomain(zero),antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0))))) = antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))),
    inference(spm,[status(thm)],[47,2784,theory(equality)]) ).

cnf(2914,negated_conjecture,
    one = antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2904,242,theory(equality)]),320,theory(equality)]) ).

cnf(3281,negated_conjecture,
    multiplication(one,multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))) = zero,
    inference(spm,[status(thm)],[51,2914,theory(equality)]) ).

cnf(3300,negated_conjecture,
    multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0))) = zero,
    inference(rw,[status(thm)],[3281,53,theory(equality)]) ).

cnf(3427,negated_conjecture,
    addition(zero,multiplication(antidomain(esk2_0),X1)) = multiplication(antidomain(esk2_0),addition(antidomain(antidomain(esk1_0)),X1)),
    inference(spm,[status(thm)],[49,3300,theory(equality)]) ).

cnf(3442,negated_conjecture,
    multiplication(antidomain(esk2_0),X1) = multiplication(antidomain(esk2_0),addition(antidomain(antidomain(esk1_0)),X1)),
    inference(rw,[status(thm)],[3427,63,theory(equality)]) ).

cnf(61052,negated_conjecture,
    multiplication(antidomain(esk2_0),one) = multiplication(antidomain(esk2_0),antidomain(antidomain(antidomain(esk1_0)))),
    inference(spm,[status(thm)],[3442,68,theory(equality)]) ).

cnf(61143,negated_conjecture,
    antidomain(esk2_0) = multiplication(antidomain(esk2_0),antidomain(antidomain(antidomain(esk1_0)))),
    inference(rw,[status(thm)],[61052,43,theory(equality)]) ).

cnf(61144,negated_conjecture,
    antidomain(esk2_0) = multiplication(antidomain(esk2_0),antidomain(esk1_0)),
    inference(rw,[status(thm)],[61143,2786,theory(equality)]) ).

cnf(61235,negated_conjecture,
    addition(antidomain(esk1_0),antidomain(esk2_0)) = multiplication(addition(one,antidomain(esk2_0)),antidomain(esk1_0)),
    inference(spm,[status(thm)],[154,61144,theory(equality)]) ).

cnf(61287,negated_conjecture,
    addition(antidomain(esk1_0),antidomain(esk2_0)) = antidomain(esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[61235,320,theory(equality)]),53,theory(equality)]) ).

cnf(61288,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[61287,67,theory(equality)]) ).

cnf(61289,negated_conjecture,
    $false,
    61288,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE090+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmp3lUOL_/sel_KLE090+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE090+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE090+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE090+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
% 
%------------------------------------------------------------------------------