TSTP Solution File: SEU025+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU025+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 04:11:51 EST 2010

% Result   : Theorem 0.74s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   55 (   9 unt;   0 def)
%            Number of atoms       :  212 (  53 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  279 ( 122   ~; 121   |;  23   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   50 (   2 sgn  30   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(10,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',reflexivity_r1_tarski) ).

fof(14,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',dt_k2_funct_1) ).

fof(16,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ( subset(relation_rng(X1),relation_dom(X2))
           => relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
    file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',t46_relat_1) ).

fof(19,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ( subset(relation_dom(X1),relation_rng(X2))
           => relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
    file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',t47_relat_1) ).

fof(24,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
          & relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
    file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',t58_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/tmp4gLgjK/sel_SEU025+1.p_1',t55_funct_1) ).

fof(42,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( one_to_one(X1)
         => ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
            & relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
    inference(assume_negation,[status(cth)],[24]) ).

fof(85,plain,
    ! [X3,X4] : subset(X3,X3),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(86,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[85]) ).

fof(96,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(97,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ( relation(function_inverse(X2))
        & function(function_inverse(X2)) ) ),
    inference(variable_rename,[status(thm)],[96]) ).

fof(98,plain,
    ! [X2] :
      ( ( relation(function_inverse(X2))
        | ~ relation(X2)
        | ~ function(X2) )
      & ( function(function_inverse(X2))
        | ~ relation(X2)
        | ~ function(X2) ) ),
    inference(distribute,[status(thm)],[97]) ).

cnf(100,plain,
    ( relation(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[98]) ).

fof(104,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ! [X2] :
          ( ~ relation(X2)
          | ~ subset(relation_rng(X1),relation_dom(X2))
          | relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(105,plain,
    ! [X3] :
      ( ~ relation(X3)
      | ! [X4] :
          ( ~ relation(X4)
          | ~ subset(relation_rng(X3),relation_dom(X4))
          | relation_dom(relation_composition(X3,X4)) = relation_dom(X3) ) ),
    inference(variable_rename,[status(thm)],[104]) ).

fof(106,plain,
    ! [X3,X4] :
      ( ~ relation(X4)
      | ~ subset(relation_rng(X3),relation_dom(X4))
      | relation_dom(relation_composition(X3,X4)) = relation_dom(X3)
      | ~ relation(X3) ),
    inference(shift_quantors,[status(thm)],[105]) ).

cnf(107,plain,
    ( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
    | ~ relation(X1)
    | ~ subset(relation_rng(X1),relation_dom(X2))
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[106]) ).

fof(113,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ! [X2] :
          ( ~ relation(X2)
          | ~ subset(relation_dom(X1),relation_rng(X2))
          | relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(114,plain,
    ! [X3] :
      ( ~ relation(X3)
      | ! [X4] :
          ( ~ relation(X4)
          | ~ subset(relation_dom(X3),relation_rng(X4))
          | relation_rng(relation_composition(X4,X3)) = relation_rng(X3) ) ),
    inference(variable_rename,[status(thm)],[113]) ).

fof(115,plain,
    ! [X3,X4] :
      ( ~ relation(X4)
      | ~ subset(relation_dom(X3),relation_rng(X4))
      | relation_rng(relation_composition(X4,X3)) = relation_rng(X3)
      | ~ relation(X3) ),
    inference(shift_quantors,[status(thm)],[114]) ).

cnf(116,plain,
    ( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
    | ~ relation(X1)
    | ~ subset(relation_dom(X1),relation_rng(X2))
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(130,negated_conjecture,
    ? [X1] :
      ( relation(X1)
      & function(X1)
      & one_to_one(X1)
      & ( relation_dom(relation_composition(X1,function_inverse(X1))) != relation_dom(X1)
        | relation_rng(relation_composition(X1,function_inverse(X1))) != relation_dom(X1) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(131,negated_conjecture,
    ? [X2] :
      ( relation(X2)
      & function(X2)
      & one_to_one(X2)
      & ( relation_dom(relation_composition(X2,function_inverse(X2))) != relation_dom(X2)
        | relation_rng(relation_composition(X2,function_inverse(X2))) != relation_dom(X2) ) ),
    inference(variable_rename,[status(thm)],[130]) ).

fof(132,negated_conjecture,
    ( relation(esk5_0)
    & function(esk5_0)
    & one_to_one(esk5_0)
    & ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
      | relation_rng(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0) ) ),
    inference(skolemize,[status(esa)],[131]) ).

cnf(133,negated_conjecture,
    ( relation_rng(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
    | relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0) ),
    inference(split_conjunct,[status(thm)],[132]) ).

cnf(134,negated_conjecture,
    one_to_one(esk5_0),
    inference(split_conjunct,[status(thm)],[132]) ).

cnf(135,negated_conjecture,
    function(esk5_0),
    inference(split_conjunct,[status(thm)],[132]) ).

cnf(136,negated_conjecture,
    relation(esk5_0),
    inference(split_conjunct,[status(thm)],[132]) ).

fof(186,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(187,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)],[186]) ).

fof(188,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)],[187]) ).

cnf(189,plain,
    ( relation_dom(X1) = relation_rng(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[188]) ).

cnf(190,plain,
    ( relation_rng(X1) = relation_dom(function_inverse(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[188]) ).

cnf(243,plain,
    ( relation_dom(relation_composition(X1,function_inverse(X2))) = relation_dom(X1)
    | ~ subset(relation_rng(X1),relation_rng(X2))
    | ~ relation(function_inverse(X2))
    | ~ relation(X1)
    | ~ one_to_one(X2)
    | ~ function(X2)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[107,190,theory(equality)]) ).

cnf(253,plain,
    ( relation_rng(relation_composition(X1,function_inverse(X2))) = relation_rng(function_inverse(X2))
    | ~ subset(relation_rng(X2),relation_rng(X1))
    | ~ relation(X1)
    | ~ relation(function_inverse(X2))
    | ~ one_to_one(X2)
    | ~ function(X2)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[116,190,theory(equality)]) ).

cnf(580,plain,
    ( relation_dom(relation_composition(X1,function_inverse(X2))) = relation_dom(X1)
    | ~ one_to_one(X2)
    | ~ subset(relation_rng(X1),relation_rng(X2))
    | ~ function(X2)
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(csr,[status(thm)],[243,100]) ).

cnf(581,plain,
    ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[580,86,theory(equality)]) ).

cnf(741,plain,
    ( relation_rng(relation_composition(X1,function_inverse(X2))) = relation_rng(function_inverse(X2))
    | ~ one_to_one(X2)
    | ~ subset(relation_rng(X2),relation_rng(X1))
    | ~ function(X2)
    | ~ relation(X2)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[253,100]) ).

cnf(742,plain,
    ( relation_rng(relation_composition(X1,function_inverse(X1))) = relation_rng(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[741,86,theory(equality)]) ).

cnf(10999,negated_conjecture,
    ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
    | relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[133,742,theory(equality)]) ).

cnf(11063,negated_conjecture,
    ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
    | relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | $false
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[10999,134,theory(equality)]) ).

cnf(11064,negated_conjecture,
    ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
    | relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | $false
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[11063,135,theory(equality)]) ).

cnf(11065,negated_conjecture,
    ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
    | relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[11064,136,theory(equality)]) ).

cnf(11066,negated_conjecture,
    ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
    | relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0) ),
    inference(cn,[status(thm)],[11065,theory(equality)]) ).

cnf(13237,negated_conjecture,
    ( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[11066,581,theory(equality)]) ).

cnf(13273,negated_conjecture,
    ( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | $false
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[13237,134,theory(equality)]) ).

cnf(13274,negated_conjecture,
    ( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | $false
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[13273,135,theory(equality)]) ).

cnf(13275,negated_conjecture,
    ( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[13274,136,theory(equality)]) ).

cnf(13276,negated_conjecture,
    relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0),
    inference(cn,[status(thm)],[13275,theory(equality)]) ).

cnf(13284,negated_conjecture,
    ( ~ one_to_one(esk5_0)
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[13276,189,theory(equality)]) ).

cnf(13305,negated_conjecture,
    ( $false
    | ~ function(esk5_0)
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[13284,134,theory(equality)]) ).

cnf(13306,negated_conjecture,
    ( $false
    | $false
    | ~ relation(esk5_0) ),
    inference(rw,[status(thm)],[13305,135,theory(equality)]) ).

cnf(13307,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[13306,136,theory(equality)]) ).

cnf(13308,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[13307,theory(equality)]) ).

cnf(13309,negated_conjecture,
    $false,
    13308,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU025+1.p
% --creating new selector for []
% -running prover on /tmp/tmp4gLgjK/sel_SEU025+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU025+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU025+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU025+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
% 
%------------------------------------------------------------------------------