TSTP Solution File: KLE082+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE082+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 12:12:47 EST 2010

% Result   : Theorem 0.47s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   89 (  83 unt;   0 def)
%            Number of atoms       :  101 (  98 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   19 (   7   ~;   0   |;  10   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  136 (  12 sgn  52   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/tmp/tmpuDXFJu/sel_KLE082+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/tmpuDXFJu/sel_KLE082+1.p_1',left_distributivity) ).

fof(4,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',additive_commutativity) ).

fof(5,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',additive_idempotence) ).

fof(8,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',additive_associativity) ).

fof(9,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',multiplicative_right_identity) ).

fof(10,axiom,
    ! [X4] : addition(domain(X4),one) = one,
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',domain3) ).

fof(11,axiom,
    ! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',domain2) ).

fof(12,axiom,
    ! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',domain1) ).

fof(13,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',multiplicative_left_identity) ).

fof(14,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',right_distributivity) ).

fof(15,axiom,
    ! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',domain5) ).

fof(17,conjecture,
    ! [X4,X5] :
      ( ! [X6] :
          ( addition(domain(X6),antidomain(X6)) = one
          & multiplication(domain(X6),antidomain(X6)) = zero )
     => addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) = antidomain(multiplication(X4,domain(X5))) ),
    file('/tmp/tmpuDXFJu/sel_KLE082+1.p_1',goals) ).

fof(18,negated_conjecture,
    ~ ! [X4,X5] :
        ( ! [X6] :
            ( addition(domain(X6),antidomain(X6)) = one
            & multiplication(domain(X6),antidomain(X6)) = zero )
       => addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) = antidomain(multiplication(X4,domain(X5))) ),
    inference(assume_negation,[status(cth)],[17]) ).

fof(21,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[2]) ).

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

fof(23,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[3]) ).

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)],[4]) ).

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)],[5]) ).

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

fof(33,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[8]) ).

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

fof(35,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[9]) ).

cnf(36,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[35]) ).

fof(37,plain,
    ! [X5] : addition(domain(X5),one) = one,
    inference(variable_rename,[status(thm)],[10]) ).

cnf(38,plain,
    addition(domain(X1),one) = one,
    inference(split_conjunct,[status(thm)],[37]) ).

fof(39,plain,
    ! [X6,X7] : domain(multiplication(X6,X7)) = domain(multiplication(X6,domain(X7))),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(40,plain,
    domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(41,plain,
    ! [X5] : addition(X5,multiplication(domain(X5),X5)) = multiplication(domain(X5),X5),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(42,plain,
    addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(43,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[13]) ).

cnf(44,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[43]) ).

fof(45,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(46,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(47,plain,
    ! [X6,X7] : domain(addition(X6,X7)) = addition(domain(X6),domain(X7)),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(48,plain,
    domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(50,negated_conjecture,
    ? [X4,X5] :
      ( ! [X6] :
          ( addition(domain(X6),antidomain(X6)) = one
          & multiplication(domain(X6),antidomain(X6)) = zero )
      & addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) != antidomain(multiplication(X4,domain(X5))) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(51,negated_conjecture,
    ? [X7,X8] :
      ( ! [X9] :
          ( addition(domain(X9),antidomain(X9)) = one
          & multiplication(domain(X9),antidomain(X9)) = zero )
      & addition(antidomain(multiplication(X7,X8)),antidomain(multiplication(X7,domain(X8)))) != antidomain(multiplication(X7,domain(X8))) ),
    inference(variable_rename,[status(thm)],[50]) ).

fof(52,negated_conjecture,
    ( ! [X9] :
        ( addition(domain(X9),antidomain(X9)) = one
        & multiplication(domain(X9),antidomain(X9)) = zero )
    & addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0))) ),
    inference(skolemize,[status(esa)],[51]) ).

fof(53,negated_conjecture,
    ! [X9] :
      ( addition(domain(X9),antidomain(X9)) = one
      & multiplication(domain(X9),antidomain(X9)) = zero
      & addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0))) ),
    inference(shift_quantors,[status(thm)],[52]) ).

cnf(54,negated_conjecture,
    addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0))),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(55,negated_conjecture,
    multiplication(domain(X1),antidomain(X1)) = zero,
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(56,negated_conjecture,
    addition(domain(X1),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(58,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[22,26,theory(equality)]) ).

cnf(62,plain,
    addition(one,domain(X1)) = one,
    inference(rw,[status(thm)],[38,26,theory(equality)]) ).

cnf(90,plain,
    addition(X1,X2) = addition(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[34,28,theory(equality)]) ).

cnf(105,plain,
    addition(domain(addition(X1,X2)),X3) = addition(domain(X1),addition(domain(X2),X3)),
    inference(spm,[status(thm)],[34,48,theory(equality)]) ).

cnf(114,plain,
    domain(domain(X1)) = domain(multiplication(one,X1)),
    inference(spm,[status(thm)],[40,44,theory(equality)]) ).

cnf(123,plain,
    domain(domain(X1)) = domain(X1),
    inference(rw,[status(thm)],[114,44,theory(equality)]) ).

cnf(130,plain,
    addition(one,domain(one)) = domain(one),
    inference(spm,[status(thm)],[42,36,theory(equality)]) ).

cnf(141,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
    inference(spm,[status(thm)],[46,36,theory(equality)]) ).

cnf(178,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
    inference(spm,[status(thm)],[24,44,theory(equality)]) ).

cnf(181,negated_conjecture,
    addition(zero,multiplication(X2,antidomain(X1))) = multiplication(addition(domain(X1),X2),antidomain(X1)),
    inference(spm,[status(thm)],[24,55,theory(equality)]) ).

cnf(223,plain,
    one = domain(one),
    inference(rw,[status(thm)],[130,62,theory(equality)]) ).

cnf(228,plain,
    addition(one,domain(X1)) = domain(addition(one,X1)),
    inference(spm,[status(thm)],[48,223,theory(equality)]) ).

cnf(233,plain,
    one = domain(addition(one,X1)),
    inference(rw,[status(thm)],[228,62,theory(equality)]) ).

cnf(244,negated_conjecture,
    addition(domain(X1),antidomain(domain(X1))) = one,
    inference(spm,[status(thm)],[56,123,theory(equality)]) ).

cnf(265,plain,
    domain(multiplication(X1,one)) = domain(multiplication(X1,addition(one,X2))),
    inference(spm,[status(thm)],[40,233,theory(equality)]) ).

cnf(279,plain,
    domain(X1) = domain(multiplication(X1,addition(one,X2))),
    inference(rw,[status(thm)],[265,36,theory(equality)]) ).

cnf(476,plain,
    addition(X1,addition(X2,X1)) = addition(X2,X1),
    inference(spm,[status(thm)],[90,26,theory(equality)]) ).

cnf(500,negated_conjecture,
    addition(antidomain(X1),one) = one,
    inference(spm,[status(thm)],[476,56,theory(equality)]) ).

cnf(522,negated_conjecture,
    addition(one,antidomain(X1)) = one,
    inference(rw,[status(thm)],[500,26,theory(equality)]) ).

cnf(744,plain,
    multiplication(one,X1) = multiplication(domain(X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[42,178,theory(equality)]),62,theory(equality)]) ).

cnf(745,plain,
    multiplication(domain(X1),X1) = X1,
    inference(rw,[status(thm)],[744,44,theory(equality)]) ).

cnf(2477,negated_conjecture,
    addition(domain(X1),one) = addition(domain(addition(X1,X2)),antidomain(X2)),
    inference(spm,[status(thm)],[105,56,theory(equality)]) ).

cnf(2553,negated_conjecture,
    one = addition(domain(addition(X1,X2)),antidomain(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2477,26,theory(equality)]),62,theory(equality)]) ).

cnf(2554,negated_conjecture,
    one = addition(antidomain(X2),domain(addition(X1,X2))),
    inference(rw,[status(thm)],[2553,26,theory(equality)]) ).

cnf(2839,negated_conjecture,
    addition(antidomain(multiplication(X1,X2)),domain(multiplication(X1,addition(one,X2)))) = one,
    inference(spm,[status(thm)],[2554,141,theory(equality)]) ).

cnf(2898,negated_conjecture,
    addition(domain(X1),antidomain(multiplication(X1,X2))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2839,279,theory(equality)]),26,theory(equality)]) ).

cnf(11815,negated_conjecture,
    multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
    inference(rw,[status(thm)],[181,58,theory(equality)]) ).

cnf(11834,negated_conjecture,
    multiplication(one,antidomain(X1)) = multiplication(antidomain(domain(X1)),antidomain(X1)),
    inference(spm,[status(thm)],[11815,244,theory(equality)]) ).

cnf(11862,negated_conjecture,
    multiplication(one,antidomain(X1)) = multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)),
    inference(spm,[status(thm)],[11815,2898,theory(equality)]) ).

cnf(11925,negated_conjecture,
    antidomain(X1) = multiplication(antidomain(domain(X1)),antidomain(X1)),
    inference(rw,[status(thm)],[11834,44,theory(equality)]) ).

cnf(11964,negated_conjecture,
    antidomain(X1) = multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)),
    inference(rw,[status(thm)],[11862,44,theory(equality)]) ).

cnf(12087,negated_conjecture,
    addition(antidomain(domain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),addition(one,antidomain(X1))),
    inference(spm,[status(thm)],[141,11925,theory(equality)]) ).

cnf(12155,negated_conjecture,
    addition(antidomain(X1),antidomain(domain(X1))) = multiplication(antidomain(domain(X1)),addition(one,antidomain(X1))),
    inference(rw,[status(thm)],[12087,26,theory(equality)]) ).

cnf(12156,negated_conjecture,
    addition(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[12155,522,theory(equality)]),36,theory(equality)]) ).

cnf(12751,negated_conjecture,
    multiplication(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
    inference(spm,[status(thm)],[11964,745,theory(equality)]) ).

cnf(13045,negated_conjecture,
    addition(antidomain(X1),antidomain(domain(X1))) = multiplication(antidomain(X1),addition(one,antidomain(domain(X1)))),
    inference(spm,[status(thm)],[141,12751,theory(equality)]) ).

cnf(13118,negated_conjecture,
    antidomain(domain(X1)) = multiplication(antidomain(X1),addition(one,antidomain(domain(X1)))),
    inference(rw,[status(thm)],[13045,12156,theory(equality)]) ).

cnf(13119,negated_conjecture,
    antidomain(domain(X1)) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[13118,522,theory(equality)]),36,theory(equality)]) ).

cnf(13180,negated_conjecture,
    antidomain(domain(multiplication(X1,X2))) = antidomain(multiplication(X1,domain(X2))),
    inference(spm,[status(thm)],[13119,40,theory(equality)]) ).

cnf(13277,negated_conjecture,
    antidomain(multiplication(X1,X2)) = antidomain(multiplication(X1,domain(X2))),
    inference(rw,[status(thm)],[13180,13119,theory(equality)]) ).

cnf(13428,negated_conjecture,
    antidomain(multiplication(esk1_0,esk2_0)) != antidomain(multiplication(esk1_0,domain(esk2_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[54,13277,theory(equality)]),28,theory(equality)]) ).

cnf(13429,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[13428,13277,theory(equality)]) ).

cnf(13430,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[13429,theory(equality)]) ).

cnf(13431,negated_conjecture,
    $false,
    13430,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE082+1.p
% --creating new selector for [KLE001+0.ax, KLE001+5.ax]
% -running prover on /tmp/tmpuDXFJu/sel_KLE082+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE082+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE082+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE082+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
% 
%------------------------------------------------------------------------------