TSTP Solution File: SEU030+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU030+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:12:23 EST 2010

% Result   : Theorem 1.07s
% Output   : CNFRefutation 1.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   64 (  12 unt;   0 def)
%            Number of atoms       :  311 (  86 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  421 ( 174   ~; 183   |;  49   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   55 (   0 sgn  32   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(5,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
          & relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
    file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',t61_funct_1) ).

fof(15,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',dt_k2_funct_1) ).

fof(23,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( one_to_one(X1)
              & relation_rng(X1) = relation_dom(X2)
              & relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
           => X2 = function_inverse(X1) ) ) ),
    file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',t63_funct_1) ).

fof(38,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_rng(X1) = relation_dom(function_inverse(X1))
          & relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
    file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',t55_funct_1) ).

fof(43,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ! [X4] :
              ( ( relation(X4)
                & function(X4) )
             => ( ( relation_rng(X2) = X1
                  & relation_composition(X2,X3) = identity_relation(relation_dom(X4))
                  & relation_composition(X3,X4) = identity_relation(X1) )
               => X4 = X2 ) ) ) ),
    file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',l72_funct_1) ).

fof(44,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ! [X2] :
            ( ( relation(X2)
              & function(X2) )
           => ( ( one_to_one(X1)
                & relation_rng(X1) = relation_dom(X2)
                & relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
             => X2 = function_inverse(X1) ) ) ),
    inference(assume_negation,[status(cth)],[23]) ).

fof(65,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ~ one_to_one(X1)
      | ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
        & relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(66,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ~ one_to_one(X2)
      | ( relation_composition(X2,function_inverse(X2)) = identity_relation(relation_dom(X2))
        & relation_composition(function_inverse(X2),X2) = identity_relation(relation_rng(X2)) ) ),
    inference(variable_rename,[status(thm)],[65]) ).

fof(67,plain,
    ! [X2] :
      ( ( relation_composition(X2,function_inverse(X2)) = identity_relation(relation_dom(X2))
        | ~ one_to_one(X2)
        | ~ relation(X2)
        | ~ function(X2) )
      & ( relation_composition(function_inverse(X2),X2) = identity_relation(relation_rng(X2))
        | ~ one_to_one(X2)
        | ~ relation(X2)
        | ~ function(X2) ) ),
    inference(distribute,[status(thm)],[66]) ).

cnf(68,plain,
    ( relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(103,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(104,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ( relation(function_inverse(X2))
        & function(function_inverse(X2)) ) ),
    inference(variable_rename,[status(thm)],[103]) ).

fof(105,plain,
    ! [X2] :
      ( ( relation(function_inverse(X2))
        | ~ relation(X2)
        | ~ function(X2) )
      & ( function(function_inverse(X2))
        | ~ relation(X2)
        | ~ function(X2) ) ),
    inference(distribute,[status(thm)],[104]) ).

cnf(106,plain,
    ( function(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(107,plain,
    ( relation(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

fof(129,negated_conjecture,
    ? [X1] :
      ( relation(X1)
      & function(X1)
      & ? [X2] :
          ( relation(X2)
          & function(X2)
          & one_to_one(X1)
          & relation_rng(X1) = relation_dom(X2)
          & relation_composition(X1,X2) = identity_relation(relation_dom(X1))
          & X2 != function_inverse(X1) ) ),
    inference(fof_nnf,[status(thm)],[44]) ).

fof(130,negated_conjecture,
    ? [X3] :
      ( relation(X3)
      & function(X3)
      & ? [X4] :
          ( relation(X4)
          & function(X4)
          & one_to_one(X3)
          & relation_rng(X3) = relation_dom(X4)
          & relation_composition(X3,X4) = identity_relation(relation_dom(X3))
          & X4 != function_inverse(X3) ) ),
    inference(variable_rename,[status(thm)],[129]) ).

fof(131,negated_conjecture,
    ( relation(esk5_0)
    & function(esk5_0)
    & relation(esk6_0)
    & function(esk6_0)
    & one_to_one(esk5_0)
    & relation_rng(esk5_0) = relation_dom(esk6_0)
    & relation_composition(esk5_0,esk6_0) = identity_relation(relation_dom(esk5_0))
    & esk6_0 != function_inverse(esk5_0) ),
    inference(skolemize,[status(esa)],[130]) ).

cnf(132,negated_conjecture,
    esk6_0 != function_inverse(esk5_0),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(133,negated_conjecture,
    relation_composition(esk5_0,esk6_0) = identity_relation(relation_dom(esk5_0)),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(134,negated_conjecture,
    relation_rng(esk5_0) = relation_dom(esk6_0),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(135,negated_conjecture,
    one_to_one(esk5_0),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(136,negated_conjecture,
    function(esk6_0),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(137,negated_conjecture,
    relation(esk6_0),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(138,negated_conjecture,
    function(esk5_0),
    inference(split_conjunct,[status(thm)],[131]) ).

cnf(139,negated_conjecture,
    relation(esk5_0),
    inference(split_conjunct,[status(thm)],[131]) ).

fof(191,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ~ one_to_one(X1)
      | ( relation_rng(X1) = relation_dom(function_inverse(X1))
        & relation_dom(X1) = relation_rng(function_inverse(X1)) ) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(192,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ~ one_to_one(X2)
      | ( relation_rng(X2) = relation_dom(function_inverse(X2))
        & relation_dom(X2) = relation_rng(function_inverse(X2)) ) ),
    inference(variable_rename,[status(thm)],[191]) ).

fof(193,plain,
    ! [X2] :
      ( ( relation_rng(X2) = relation_dom(function_inverse(X2))
        | ~ one_to_one(X2)
        | ~ relation(X2)
        | ~ function(X2) )
      & ( relation_dom(X2) = relation_rng(function_inverse(X2))
        | ~ one_to_one(X2)
        | ~ relation(X2)
        | ~ function(X2) ) ),
    inference(distribute,[status(thm)],[192]) ).

cnf(194,plain,
    ( relation_dom(X1) = relation_rng(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[193]) ).

fof(212,plain,
    ! [X1,X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ! [X3] :
          ( ~ relation(X3)
          | ~ function(X3)
          | ! [X4] :
              ( ~ relation(X4)
              | ~ function(X4)
              | relation_rng(X2) != X1
              | relation_composition(X2,X3) != identity_relation(relation_dom(X4))
              | relation_composition(X3,X4) != identity_relation(X1)
              | X4 = X2 ) ) ),
    inference(fof_nnf,[status(thm)],[43]) ).

fof(213,plain,
    ! [X5,X6] :
      ( ~ relation(X6)
      | ~ function(X6)
      | ! [X7] :
          ( ~ relation(X7)
          | ~ function(X7)
          | ! [X8] :
              ( ~ relation(X8)
              | ~ function(X8)
              | relation_rng(X6) != X5
              | relation_composition(X6,X7) != identity_relation(relation_dom(X8))
              | relation_composition(X7,X8) != identity_relation(X5)
              | X8 = X6 ) ) ),
    inference(variable_rename,[status(thm)],[212]) ).

fof(214,plain,
    ! [X5,X6,X7,X8] :
      ( ~ relation(X8)
      | ~ function(X8)
      | relation_rng(X6) != X5
      | relation_composition(X6,X7) != identity_relation(relation_dom(X8))
      | relation_composition(X7,X8) != identity_relation(X5)
      | X8 = X6
      | ~ relation(X7)
      | ~ function(X7)
      | ~ relation(X6)
      | ~ function(X6) ),
    inference(shift_quantors,[status(thm)],[213]) ).

cnf(215,plain,
    ( X3 = X1
    | ~ function(X1)
    | ~ relation(X1)
    | ~ function(X2)
    | ~ relation(X2)
    | relation_composition(X2,X3) != identity_relation(X4)
    | relation_composition(X1,X2) != identity_relation(relation_dom(X3))
    | relation_rng(X1) != X4
    | ~ function(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[214]) ).

cnf(291,negated_conjecture,
    ( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
    | ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[68,134,theory(equality)]) ).

cnf(298,negated_conjecture,
    ( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
    | $false
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[291,135,theory(equality)]) ).

cnf(299,negated_conjecture,
    ( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
    | $false
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[298,138,theory(equality)]) ).

cnf(300,negated_conjecture,
    ( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[299,139,theory(equality)]) ).

cnf(301,negated_conjecture,
    relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0)),
    inference(cn,[status(thm)],[300,theory(equality)]) ).

cnf(317,plain,
    ( X1 = X2
    | identity_relation(relation_dom(X2)) != relation_composition(X1,X3)
    | relation_composition(X3,X2) != identity_relation(relation_rng(X1))
    | ~ function(X2)
    | ~ function(X3)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ relation(X1) ),
    inference(er,[status(thm)],[215,theory(equality)]) ).

cnf(1737,negated_conjecture,
    ( X1 = esk6_0
    | relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
    | relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
    | ~ function(esk6_0)
    | ~ function(X2)
    | ~ function(X1)
    | ~ relation(esk6_0)
    | ~ relation(X2)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[317,301,theory(equality)]) ).

cnf(1756,negated_conjecture,
    ( X1 = esk6_0
    | relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
    | relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
    | $false
    | ~ function(X2)
    | ~ function(X1)
    | ~ relation(esk6_0)
    | ~ relation(X2)
    | ~ relation(X1) ),
    inference(rw,[status(thm)],[1737,136,theory(equality)]) ).

cnf(1757,negated_conjecture,
    ( X1 = esk6_0
    | relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
    | relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
    | $false
    | ~ function(X2)
    | ~ function(X1)
    | $false
    | ~ relation(X2)
    | ~ relation(X1) ),
    inference(rw,[status(thm)],[1756,137,theory(equality)]) ).

cnf(1758,negated_conjecture,
    ( X1 = esk6_0
    | relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
    | relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
    | ~ function(X2)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ relation(X1) ),
    inference(cn,[status(thm)],[1757,theory(equality)]) ).

cnf(21809,negated_conjecture,
    ( function_inverse(esk5_0) = esk6_0
    | relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
    | ~ function(esk5_0)
    | ~ function(function_inverse(esk5_0))
    | ~ relation(esk5_0)
    | ~ relation(function_inverse(esk5_0)) ),
    inference(er,[status(thm)],[1758,theory(equality)]) ).

cnf(21886,negated_conjecture,
    ( function_inverse(esk5_0) = esk6_0
    | relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
    | $false
    | ~ function(function_inverse(esk5_0))
    | ~ relation(esk5_0)
    | ~ relation(function_inverse(esk5_0)) ),
    inference(rw,[status(thm)],[21809,138,theory(equality)]) ).

cnf(21887,negated_conjecture,
    ( function_inverse(esk5_0) = esk6_0
    | relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
    | $false
    | ~ function(function_inverse(esk5_0))
    | $false
    | ~ relation(function_inverse(esk5_0)) ),
    inference(rw,[status(thm)],[21886,139,theory(equality)]) ).

cnf(21888,negated_conjecture,
    ( function_inverse(esk5_0) = esk6_0
    | relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0)) ),
    inference(cn,[status(thm)],[21887,theory(equality)]) ).

cnf(21889,negated_conjecture,
    ( identity_relation(relation_rng(function_inverse(esk5_0))) != relation_composition(esk5_0,esk6_0)
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0)) ),
    inference(sr,[status(thm)],[21888,132,theory(equality)]) ).

cnf(21985,negated_conjecture,
    ( identity_relation(relation_dom(esk5_0)) != relation_composition(esk5_0,esk6_0)
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0))
    | ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[21889,194,theory(equality)]) ).

cnf(22018,negated_conjecture,
    ( $false
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0))
    | ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[21985,133,theory(equality)]) ).

cnf(22019,negated_conjecture,
    ( $false
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0))
    | $false
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[22018,135,theory(equality)]) ).

cnf(22020,negated_conjecture,
    ( $false
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0))
    | $false
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[22019,138,theory(equality)]) ).

cnf(22021,negated_conjecture,
    ( $false
    | ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[22020,139,theory(equality)]) ).

cnf(22022,negated_conjecture,
    ( ~ function(function_inverse(esk5_0))
    | ~ relation(function_inverse(esk5_0)) ),
    inference(cn,[status(thm)],[22021,theory(equality)]) ).

cnf(22056,negated_conjecture,
    ( ~ relation(function_inverse(esk5_0))
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[22022,106,theory(equality)]) ).

cnf(22065,negated_conjecture,
    ( ~ relation(function_inverse(esk5_0))
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[22056,138,theory(equality)]) ).

cnf(22066,negated_conjecture,
    ( ~ relation(function_inverse(esk5_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[22065,139,theory(equality)]) ).

cnf(22067,negated_conjecture,
    ~ relation(function_inverse(esk5_0)),
    inference(cn,[status(thm)],[22066,theory(equality)]) ).

cnf(22325,negated_conjecture,
    ( ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[22067,107,theory(equality)]) ).

cnf(22333,negated_conjecture,
    ( $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[22325,138,theory(equality)]) ).

cnf(22334,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[22333,139,theory(equality)]) ).

cnf(22335,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[22334,theory(equality)]) ).

cnf(22336,negated_conjecture,
    $false,
    22335,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU030+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLWeqLq/sel_SEU030+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU030+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU030+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU030+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
% 
%------------------------------------------------------------------------------