TSTP Solution File: SEU037+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU037+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 04:13:24 EST 2010

% Result   : Theorem 0.66s
% Output   : CNFRefutation 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   52 (  14 unt;   0 def)
%            Number of atoms       :  218 (  59 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  289 ( 123   ~; 122   |;  34   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   79 (   4 sgn  48   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(relation_dom_restriction(X1,X2))
        & function(relation_dom_restriction(X1,X2)) ) ),
    file('/tmp/tmp1KI8Ov/sel_SEU037+1.p_1',fc4_funct_1) ).

fof(22,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,set_intersection2(relation_dom(X3),X1))
       => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    file('/tmp/tmp1KI8Ov/sel_SEU037+1.p_1',t71_funct_1) ).

fof(26,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( X2 = relation_dom_restriction(X3,X1)
          <=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
              & ! [X4] :
                  ( in(X4,relation_dom(X2))
                 => apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
    file('/tmp/tmp1KI8Ov/sel_SEU037+1.p_1',t68_funct_1) ).

fof(28,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmp1KI8Ov/sel_SEU037+1.p_1',commutativity_k3_xboole_0) ).

fof(34,axiom,
    ! [X1,X2] :
      ( relation(X1)
     => relation(relation_dom_restriction(X1,X2)) ),
    file('/tmp/tmp1KI8Ov/sel_SEU037+1.p_1',dt_k7_relat_1) ).

fof(40,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,set_intersection2(relation_dom(X3),X1))
         => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    inference(assume_negation,[status(cth)],[22]) ).

fof(47,plain,
    ! [X1,X2] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ( relation(relation_dom_restriction(X1,X2))
        & function(relation_dom_restriction(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(48,plain,
    ! [X3,X4] :
      ( ~ relation(X3)
      | ~ function(X3)
      | ( relation(relation_dom_restriction(X3,X4))
        & function(relation_dom_restriction(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[47]) ).

fof(49,plain,
    ! [X3,X4] :
      ( ( relation(relation_dom_restriction(X3,X4))
        | ~ relation(X3)
        | ~ function(X3) )
      & ( function(relation_dom_restriction(X3,X4))
        | ~ relation(X3)
        | ~ function(X3) ) ),
    inference(distribute,[status(thm)],[48]) ).

cnf(50,plain,
    ( function(relation_dom_restriction(X1,X2))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[49]) ).

fof(119,negated_conjecture,
    ? [X1,X2,X3] :
      ( relation(X3)
      & function(X3)
      & in(X2,set_intersection2(relation_dom(X3),X1))
      & apply(relation_dom_restriction(X3,X1),X2) != apply(X3,X2) ),
    inference(fof_nnf,[status(thm)],[40]) ).

fof(120,negated_conjecture,
    ? [X4,X5,X6] :
      ( relation(X6)
      & function(X6)
      & in(X5,set_intersection2(relation_dom(X6),X4))
      & apply(relation_dom_restriction(X6,X4),X5) != apply(X6,X5) ),
    inference(variable_rename,[status(thm)],[119]) ).

fof(121,negated_conjecture,
    ( relation(esk9_0)
    & function(esk9_0)
    & in(esk8_0,set_intersection2(relation_dom(esk9_0),esk7_0))
    & apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) != apply(esk9_0,esk8_0) ),
    inference(skolemize,[status(esa)],[120]) ).

cnf(122,negated_conjecture,
    apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) != apply(esk9_0,esk8_0),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(123,negated_conjecture,
    in(esk8_0,set_intersection2(relation_dom(esk9_0),esk7_0)),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(124,negated_conjecture,
    function(esk9_0),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(125,negated_conjecture,
    relation(esk9_0),
    inference(split_conjunct,[status(thm)],[121]) ).

fof(137,plain,
    ! [X1,X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ! [X3] :
          ( ~ relation(X3)
          | ~ function(X3)
          | ( ( X2 != relation_dom_restriction(X3,X1)
              | ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
                & ! [X4] :
                    ( ~ in(X4,relation_dom(X2))
                    | apply(X2,X4) = apply(X3,X4) ) ) )
            & ( relation_dom(X2) != set_intersection2(relation_dom(X3),X1)
              | ? [X4] :
                  ( in(X4,relation_dom(X2))
                  & apply(X2,X4) != apply(X3,X4) )
              | X2 = relation_dom_restriction(X3,X1) ) ) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(138,plain,
    ! [X5,X6] :
      ( ~ relation(X6)
      | ~ function(X6)
      | ! [X7] :
          ( ~ relation(X7)
          | ~ function(X7)
          | ( ( X6 != relation_dom_restriction(X7,X5)
              | ( relation_dom(X6) = set_intersection2(relation_dom(X7),X5)
                & ! [X8] :
                    ( ~ in(X8,relation_dom(X6))
                    | apply(X6,X8) = apply(X7,X8) ) ) )
            & ( relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
              | ? [X9] :
                  ( in(X9,relation_dom(X6))
                  & apply(X6,X9) != apply(X7,X9) )
              | X6 = relation_dom_restriction(X7,X5) ) ) ) ),
    inference(variable_rename,[status(thm)],[137]) ).

fof(139,plain,
    ! [X5,X6] :
      ( ~ relation(X6)
      | ~ function(X6)
      | ! [X7] :
          ( ~ relation(X7)
          | ~ function(X7)
          | ( ( X6 != relation_dom_restriction(X7,X5)
              | ( relation_dom(X6) = set_intersection2(relation_dom(X7),X5)
                & ! [X8] :
                    ( ~ in(X8,relation_dom(X6))
                    | apply(X6,X8) = apply(X7,X8) ) ) )
            & ( relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
              | ( in(esk10_3(X5,X6,X7),relation_dom(X6))
                & apply(X6,esk10_3(X5,X6,X7)) != apply(X7,esk10_3(X5,X6,X7)) )
              | X6 = relation_dom_restriction(X7,X5) ) ) ) ),
    inference(skolemize,[status(esa)],[138]) ).

fof(140,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ( ~ in(X8,relation_dom(X6))
              | apply(X6,X8) = apply(X7,X8) )
            & relation_dom(X6) = set_intersection2(relation_dom(X7),X5) )
          | X6 != relation_dom_restriction(X7,X5) )
        & ( relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
          | ( in(esk10_3(X5,X6,X7),relation_dom(X6))
            & apply(X6,esk10_3(X5,X6,X7)) != apply(X7,esk10_3(X5,X6,X7)) )
          | X6 = relation_dom_restriction(X7,X5) ) )
      | ~ relation(X7)
      | ~ function(X7)
      | ~ relation(X6)
      | ~ function(X6) ),
    inference(shift_quantors,[status(thm)],[139]) ).

fof(141,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,relation_dom(X6))
        | apply(X6,X8) = apply(X7,X8)
        | X6 != relation_dom_restriction(X7,X5)
        | ~ relation(X7)
        | ~ function(X7)
        | ~ relation(X6)
        | ~ function(X6) )
      & ( relation_dom(X6) = set_intersection2(relation_dom(X7),X5)
        | X6 != relation_dom_restriction(X7,X5)
        | ~ relation(X7)
        | ~ function(X7)
        | ~ relation(X6)
        | ~ function(X6) )
      & ( in(esk10_3(X5,X6,X7),relation_dom(X6))
        | relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
        | X6 = relation_dom_restriction(X7,X5)
        | ~ relation(X7)
        | ~ function(X7)
        | ~ relation(X6)
        | ~ function(X6) )
      & ( apply(X6,esk10_3(X5,X6,X7)) != apply(X7,esk10_3(X5,X6,X7))
        | relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
        | X6 = relation_dom_restriction(X7,X5)
        | ~ relation(X7)
        | ~ function(X7)
        | ~ relation(X6)
        | ~ function(X6) ) ),
    inference(distribute,[status(thm)],[140]) ).

cnf(144,plain,
    ( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ function(X2)
    | ~ relation(X2)
    | X1 != relation_dom_restriction(X2,X3) ),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(145,plain,
    ( apply(X1,X4) = apply(X2,X4)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ function(X2)
    | ~ relation(X2)
    | X1 != relation_dom_restriction(X2,X3)
    | ~ in(X4,relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[141]) ).

fof(150,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[28]) ).

cnf(151,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[150]) ).

fof(167,plain,
    ! [X1,X2] :
      ( ~ relation(X1)
      | relation(relation_dom_restriction(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(168,plain,
    ! [X3,X4] :
      ( ~ relation(X3)
      | relation(relation_dom_restriction(X3,X4)) ),
    inference(variable_rename,[status(thm)],[167]) ).

cnf(169,plain,
    ( relation(relation_dom_restriction(X1,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[168]) ).

cnf(217,negated_conjecture,
    in(esk8_0,set_intersection2(esk7_0,relation_dom(esk9_0))),
    inference(rw,[status(thm)],[123,151,theory(equality)]) ).

cnf(247,plain,
    ( set_intersection2(relation_dom(X1),X2) = relation_dom(relation_dom_restriction(X1,X2))
    | ~ function(X1)
    | ~ function(relation_dom_restriction(X1,X2))
    | ~ relation(X1)
    | ~ relation(relation_dom_restriction(X1,X2)) ),
    inference(er,[status(thm)],[144,theory(equality)]) ).

cnf(427,plain,
    ( set_intersection2(relation_dom(X1),X2) = relation_dom(relation_dom_restriction(X1,X2))
    | ~ function(relation_dom_restriction(X1,X2))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[247,169]) ).

cnf(428,plain,
    ( set_intersection2(relation_dom(X1),X2) = relation_dom(relation_dom_restriction(X1,X2))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[427,50]) ).

cnf(431,plain,
    ( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(X2,relation_dom(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[151,428,theory(equality)]) ).

cnf(547,negated_conjecture,
    ( in(esk8_0,relation_dom(relation_dom_restriction(esk9_0,esk7_0)))
    | ~ function(esk9_0)
    | ~ relation(esk9_0) ),
    inference(spm,[status(thm)],[217,431,theory(equality)]) ).

cnf(564,negated_conjecture,
    ( in(esk8_0,relation_dom(relation_dom_restriction(esk9_0,esk7_0)))
    | $false
    | ~ relation(esk9_0) ),
    inference(rw,[status(thm)],[547,124,theory(equality)]) ).

cnf(565,negated_conjecture,
    ( in(esk8_0,relation_dom(relation_dom_restriction(esk9_0,esk7_0)))
    | $false
    | $false ),
    inference(rw,[status(thm)],[564,125,theory(equality)]) ).

cnf(566,negated_conjecture,
    in(esk8_0,relation_dom(relation_dom_restriction(esk9_0,esk7_0))),
    inference(cn,[status(thm)],[565,theory(equality)]) ).

cnf(601,negated_conjecture,
    ( apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) = apply(X1,esk8_0)
    | relation_dom_restriction(X1,X2) != relation_dom_restriction(esk9_0,esk7_0)
    | ~ function(X1)
    | ~ function(relation_dom_restriction(esk9_0,esk7_0))
    | ~ relation(X1)
    | ~ relation(relation_dom_restriction(esk9_0,esk7_0)) ),
    inference(spm,[status(thm)],[145,566,theory(equality)]) ).

cnf(11956,negated_conjecture,
    ( apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) = apply(esk9_0,esk8_0)
    | ~ function(relation_dom_restriction(esk9_0,esk7_0))
    | ~ function(esk9_0)
    | ~ relation(relation_dom_restriction(esk9_0,esk7_0))
    | ~ relation(esk9_0) ),
    inference(er,[status(thm)],[601,theory(equality)]) ).

cnf(11983,negated_conjecture,
    ( apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) = apply(esk9_0,esk8_0)
    | ~ function(relation_dom_restriction(esk9_0,esk7_0))
    | $false
    | ~ relation(relation_dom_restriction(esk9_0,esk7_0))
    | ~ relation(esk9_0) ),
    inference(rw,[status(thm)],[11956,124,theory(equality)]) ).

cnf(11984,negated_conjecture,
    ( apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) = apply(esk9_0,esk8_0)
    | ~ function(relation_dom_restriction(esk9_0,esk7_0))
    | $false
    | ~ relation(relation_dom_restriction(esk9_0,esk7_0))
    | $false ),
    inference(rw,[status(thm)],[11983,125,theory(equality)]) ).

cnf(11985,negated_conjecture,
    ( apply(relation_dom_restriction(esk9_0,esk7_0),esk8_0) = apply(esk9_0,esk8_0)
    | ~ function(relation_dom_restriction(esk9_0,esk7_0))
    | ~ relation(relation_dom_restriction(esk9_0,esk7_0)) ),
    inference(cn,[status(thm)],[11984,theory(equality)]) ).

cnf(11986,negated_conjecture,
    ( ~ function(relation_dom_restriction(esk9_0,esk7_0))
    | ~ relation(relation_dom_restriction(esk9_0,esk7_0)) ),
    inference(sr,[status(thm)],[11985,122,theory(equality)]) ).

cnf(12028,negated_conjecture,
    ( ~ relation(relation_dom_restriction(esk9_0,esk7_0))
    | ~ function(esk9_0)
    | ~ relation(esk9_0) ),
    inference(spm,[status(thm)],[11986,50,theory(equality)]) ).

cnf(12031,negated_conjecture,
    ( ~ relation(relation_dom_restriction(esk9_0,esk7_0))
    | $false
    | ~ relation(esk9_0) ),
    inference(rw,[status(thm)],[12028,124,theory(equality)]) ).

cnf(12032,negated_conjecture,
    ( ~ relation(relation_dom_restriction(esk9_0,esk7_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[12031,125,theory(equality)]) ).

cnf(12033,negated_conjecture,
    ~ relation(relation_dom_restriction(esk9_0,esk7_0)),
    inference(cn,[status(thm)],[12032,theory(equality)]) ).

cnf(12040,negated_conjecture,
    ~ relation(esk9_0),
    inference(spm,[status(thm)],[12033,169,theory(equality)]) ).

cnf(12043,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[12040,125,theory(equality)]) ).

cnf(12044,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[12043,theory(equality)]) ).

cnf(12045,negated_conjecture,
    $false,
    12044,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU037+1.p
% --creating new selector for []
% -running prover on /tmp/tmp1KI8Ov/sel_SEU037+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU037+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU037+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU037+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
% 
%------------------------------------------------------------------------------