TSTP Solution File: SEU032+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU032+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 04:12:35 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   47 (   6 unt;   0 def)
%            Number of atoms       :  215 (  55 equ)
%            Maximal formula atoms :    9 (   4 avg)
%            Number of connectives :  294 ( 126   ~; 123   |;  31   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   41 (   0 sgn  25   !;   2   ?)

% 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/tmp-S2Baw/sel_SEU032+1.p_1',t61_funct_1) ).

fof(11,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => one_to_one(function_inverse(X1)) ) ),
    file('/tmp/tmp-S2Baw/sel_SEU032+1.p_1',t62_funct_1) ).

fof(16,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    file('/tmp/tmp-S2Baw/sel_SEU032+1.p_1',dt_k2_funct_1) ).

fof(24,axiom,
    ! [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/tmp-S2Baw/sel_SEU032+1.p_1',t63_funct_1) ).

fof(31,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => function_inverse(function_inverse(X1)) = X1 ) ),
    file('/tmp/tmp-S2Baw/sel_SEU032+1.p_1',t65_funct_1) ).

fof(40,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/tmp-S2Baw/sel_SEU032+1.p_1',t55_funct_1) ).

fof(45,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( one_to_one(X1)
         => function_inverse(function_inverse(X1)) = X1 ) ),
    inference(assume_negation,[status(cth)],[31]) ).

fof(66,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(67,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)],[66]) ).

fof(68,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)],[67]) ).

cnf(69,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)],[68]) ).

fof(93,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ~ one_to_one(X1)
      | one_to_one(function_inverse(X1)) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(94,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ~ one_to_one(X2)
      | one_to_one(function_inverse(X2)) ),
    inference(variable_rename,[status(thm)],[93]) ).

cnf(95,plain,
    ( one_to_one(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[94]) ).

fof(107,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(108,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ( relation(function_inverse(X2))
        & function(function_inverse(X2)) ) ),
    inference(variable_rename,[status(thm)],[107]) ).

fof(109,plain,
    ! [X2] :
      ( ( relation(function_inverse(X2))
        | ~ relation(X2)
        | ~ function(X2) )
      & ( function(function_inverse(X2))
        | ~ relation(X2)
        | ~ function(X2) ) ),
    inference(distribute,[status(thm)],[108]) ).

cnf(110,plain,
    ( function(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[109]) ).

cnf(111,plain,
    ( relation(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[109]) ).

fof(133,plain,
    ! [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)],[24]) ).

fof(134,plain,
    ! [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)],[133]) ).

fof(135,plain,
    ! [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)
      | ~ relation(X3)
      | ~ function(X3) ),
    inference(shift_quantors,[status(thm)],[134]) ).

cnf(136,plain,
    ( X2 = function_inverse(X1)
    | ~ function(X1)
    | ~ relation(X1)
    | relation_composition(X1,X2) != identity_relation(relation_dom(X1))
    | relation_rng(X1) != relation_dom(X2)
    | ~ one_to_one(X1)
    | ~ function(X2)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

fof(162,negated_conjecture,
    ? [X1] :
      ( relation(X1)
      & function(X1)
      & one_to_one(X1)
      & function_inverse(function_inverse(X1)) != X1 ),
    inference(fof_nnf,[status(thm)],[45]) ).

fof(163,negated_conjecture,
    ? [X2] :
      ( relation(X2)
      & function(X2)
      & one_to_one(X2)
      & function_inverse(function_inverse(X2)) != X2 ),
    inference(variable_rename,[status(thm)],[162]) ).

fof(164,negated_conjecture,
    ( relation(esk5_0)
    & function(esk5_0)
    & one_to_one(esk5_0)
    & function_inverse(function_inverse(esk5_0)) != esk5_0 ),
    inference(skolemize,[status(esa)],[163]) ).

cnf(165,negated_conjecture,
    function_inverse(function_inverse(esk5_0)) != esk5_0,
    inference(split_conjunct,[status(thm)],[164]) ).

cnf(166,negated_conjecture,
    one_to_one(esk5_0),
    inference(split_conjunct,[status(thm)],[164]) ).

cnf(167,negated_conjecture,
    function(esk5_0),
    inference(split_conjunct,[status(thm)],[164]) ).

cnf(168,negated_conjecture,
    relation(esk5_0),
    inference(split_conjunct,[status(thm)],[164]) ).

fof(195,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)],[40]) ).

fof(196,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)],[195]) ).

fof(197,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)],[196]) ).

cnf(198,plain,
    ( relation_dom(X1) = relation_rng(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[197]) ).

cnf(199,plain,
    ( relation_rng(X1) = relation_dom(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[197]) ).

cnf(303,plain,
    ( function_inverse(function_inverse(X1)) = X1
    | identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
    | relation_rng(function_inverse(X1)) != relation_dom(X1)
    | ~ one_to_one(function_inverse(X1))
    | ~ function(X1)
    | ~ function(function_inverse(X1))
    | ~ relation(X1)
    | ~ relation(function_inverse(X1))
    | ~ one_to_one(X1) ),
    inference(spm,[status(thm)],[136,69,theory(equality)]) ).

cnf(1208,plain,
    ( function_inverse(function_inverse(X1)) = X1
    | identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
    | relation_rng(function_inverse(X1)) != relation_dom(X1)
    | ~ one_to_one(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ function(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[303,111]) ).

cnf(1209,plain,
    ( function_inverse(function_inverse(X1)) = X1
    | identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
    | relation_rng(function_inverse(X1)) != relation_dom(X1)
    | ~ one_to_one(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[1208,110]) ).

cnf(1210,plain,
    ( function_inverse(function_inverse(X1)) = X1
    | identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
    | relation_rng(function_inverse(X1)) != relation_dom(X1)
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[1209,95]) ).

cnf(1211,plain,
    ( function_inverse(function_inverse(X1)) = X1
    | identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[1210,198]) ).

cnf(1212,plain,
    ( function_inverse(function_inverse(X1)) = X1
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[1211,199,theory(equality)]) ).

cnf(1227,negated_conjecture,
    ( ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[165,1212,theory(equality)]) ).

cnf(1261,negated_conjecture,
    ( $false
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[1227,166,theory(equality)]) ).

cnf(1262,negated_conjecture,
    ( $false
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[1261,167,theory(equality)]) ).

cnf(1263,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[1262,168,theory(equality)]) ).

cnf(1264,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[1263,theory(equality)]) ).

cnf(1265,negated_conjecture,
    $false,
    1264,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU032+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-S2Baw/sel_SEU032+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU032+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU032+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU032+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
% 
%------------------------------------------------------------------------------