TSTP Solution File: REL031+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : REL031+2 : 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 : Sun Dec 26 01:24:36 EST 2010

% Result   : Theorem 6.43s
% Output   : CNFRefutation 6.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   59 (  54 unt;   0 def)
%            Number of atoms       :   69 (  67 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (   6   ~;   0   |;   8   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   87 (   0 sgn  38   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',converse_multiplicativity) ).

fof(2,axiom,
    ! [X1] : converse(converse(X1)) = X1,
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',converse_idempotence) ).

fof(3,axiom,
    ! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',converse_additivity) ).

fof(4,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',maddux1_join_commutativity) ).

fof(5,axiom,
    ! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',composition_associativity) ).

fof(6,axiom,
    ! [X1] : composition(X1,one) = X1,
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',composition_identity) ).

fof(7,axiom,
    ! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',composition_distributivity) ).

fof(8,axiom,
    ! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',maddux2_join_associativity) ).

fof(9,conjecture,
    ! [X1,X2] :
      ( ( join(composition(converse(X1),X1),one) = one
        & join(composition(converse(X2),X2),one) = one )
     => join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
    file('/tmp/tmpkoDaYS/sel_REL031+2.p_1',goals) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( join(composition(converse(X1),X1),one) = one
          & join(composition(converse(X2),X2),one) = one )
       => join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(11,plain,
    ! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(12,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(13,plain,
    ! [X2] : converse(converse(X2)) = X2,
    inference(variable_rename,[status(thm)],[2]) ).

cnf(14,plain,
    converse(converse(X1)) = X1,
    inference(split_conjunct,[status(thm)],[13]) ).

fof(15,plain,
    ! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(16,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(17,plain,
    ! [X3,X4] : join(X3,X4) = join(X4,X3),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(18,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(19,plain,
    ! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(20,plain,
    composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(21,plain,
    ! [X2] : composition(X2,one) = X2,
    inference(variable_rename,[status(thm)],[6]) ).

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

fof(23,plain,
    ! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
    inference(variable_rename,[status(thm)],[7]) ).

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

fof(25,plain,
    ! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(26,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(27,negated_conjecture,
    ? [X1,X2] :
      ( join(composition(converse(X1),X1),one) = one
      & join(composition(converse(X2),X2),one) = one
      & join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) != one ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(28,negated_conjecture,
    ? [X3,X4] :
      ( join(composition(converse(X3),X3),one) = one
      & join(composition(converse(X4),X4),one) = one
      & join(composition(converse(composition(X3,X4)),composition(X3,X4)),one) != one ),
    inference(variable_rename,[status(thm)],[27]) ).

fof(29,negated_conjecture,
    ( join(composition(converse(esk1_0),esk1_0),one) = one
    & join(composition(converse(esk2_0),esk2_0),one) = one
    & join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one ),
    inference(skolemize,[status(esa)],[28]) ).

cnf(30,negated_conjecture,
    join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one,
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(31,negated_conjecture,
    join(composition(converse(esk2_0),esk2_0),one) = one,
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(32,negated_conjecture,
    join(composition(converse(esk1_0),esk1_0),one) = one,
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(33,negated_conjecture,
    join(one,composition(converse(esk2_0),esk2_0)) = one,
    inference(rw,[status(thm)],[31,18,theory(equality)]) ).

cnf(34,negated_conjecture,
    join(one,composition(converse(esk1_0),esk1_0)) = one,
    inference(rw,[status(thm)],[32,18,theory(equality)]) ).

cnf(35,negated_conjecture,
    join(one,composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0))) != one,
    inference(rw,[status(thm)],[30,18,theory(equality)]) ).

cnf(36,plain,
    composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
    inference(spm,[status(thm)],[12,14,theory(equality)]) ).

cnf(37,plain,
    composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
    inference(spm,[status(thm)],[12,14,theory(equality)]) ).

cnf(38,plain,
    join(X1,converse(X2)) = converse(join(converse(X1),X2)),
    inference(spm,[status(thm)],[16,14,theory(equality)]) ).

cnf(46,plain,
    composition(converse(composition(X2,X1)),X3) = composition(converse(X1),composition(converse(X2),X3)),
    inference(spm,[status(thm)],[20,12,theory(equality)]) ).

cnf(106,plain,
    converse(converse(X1)) = composition(converse(one),X1),
    inference(spm,[status(thm)],[37,22,theory(equality)]) ).

cnf(119,plain,
    X1 = composition(converse(one),X1),
    inference(rw,[status(thm)],[106,14,theory(equality)]) ).

cnf(130,plain,
    one = converse(one),
    inference(spm,[status(thm)],[22,119,theory(equality)]) ).

cnf(148,plain,
    join(one,converse(X1)) = converse(join(one,X1)),
    inference(spm,[status(thm)],[16,130,theory(equality)]) ).

cnf(152,plain,
    composition(one,X1) = X1,
    inference(rw,[status(thm)],[119,130,theory(equality)]) ).

cnf(159,negated_conjecture,
    join(one,X1) = join(one,join(composition(converse(esk2_0),esk2_0),X1)),
    inference(spm,[status(thm)],[26,33,theory(equality)]) ).

cnf(161,plain,
    join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
    inference(spm,[status(thm)],[24,152,theory(equality)]) ).

cnf(286,plain,
    converse(composition(join(one,X2),converse(X1))) = join(X1,converse(composition(X2,converse(X1)))),
    inference(spm,[status(thm)],[38,161,theory(equality)]) ).

cnf(289,plain,
    composition(X1,join(one,converse(X2))) = join(X1,converse(composition(X2,converse(X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[286,36,theory(equality)]),148,theory(equality)]) ).

cnf(290,plain,
    composition(X1,join(one,converse(X2))) = join(X1,composition(X1,converse(X2))),
    inference(rw,[status(thm)],[289,36,theory(equality)]) ).

cnf(330,negated_conjecture,
    join(one,composition(join(converse(esk2_0),X1),esk2_0)) = join(one,composition(X1,esk2_0)),
    inference(spm,[status(thm)],[159,24,theory(equality)]) ).

cnf(1383,plain,
    join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
    inference(spm,[status(thm)],[290,14,theory(equality)]) ).

cnf(1460,negated_conjecture,
    join(one,composition(composition(converse(esk2_0),join(one,X1)),esk2_0)) = join(one,composition(composition(converse(esk2_0),X1),esk2_0)),
    inference(spm,[status(thm)],[330,1383,theory(equality)]) ).

cnf(1495,negated_conjecture,
    join(one,composition(converse(esk2_0),composition(join(one,X1),esk2_0))) = join(one,composition(composition(converse(esk2_0),X1),esk2_0)),
    inference(rw,[status(thm)],[1460,20,theory(equality)]) ).

cnf(1496,negated_conjecture,
    join(one,composition(converse(esk2_0),composition(join(one,X1),esk2_0))) = join(one,composition(converse(esk2_0),composition(X1,esk2_0))),
    inference(rw,[status(thm)],[1495,20,theory(equality)]) ).

cnf(171145,negated_conjecture,
    join(one,composition(converse(esk2_0),composition(one,esk2_0))) = join(one,composition(converse(esk2_0),composition(composition(converse(esk1_0),esk1_0),esk2_0))),
    inference(spm,[status(thm)],[1496,34,theory(equality)]) ).

cnf(171432,negated_conjecture,
    one = join(one,composition(converse(esk2_0),composition(composition(converse(esk1_0),esk1_0),esk2_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[171145,152,theory(equality)]),33,theory(equality)]) ).

cnf(171433,negated_conjecture,
    one = join(one,composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[171432,20,theory(equality)]),46,theory(equality)]) ).

cnf(171434,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[171433,35,theory(equality)]) ).

cnf(171435,negated_conjecture,
    $false,
    171434,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL031+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpkoDaYS/sel_REL031+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL031+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL031+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL031+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
% 
%------------------------------------------------------------------------------