TSTP Solution File: SEU134+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU134+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:48:07 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   5 unt;   0 def)
%            Number of atoms       :   37 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   38 (  17   ~;  17   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l32_xboole_1,plain,
    ! [A,B] :
      ( ( ~ $equal(empty_set,set_difference(A,B))
        | subset(A,B) )
      & ( $equal(empty_set,set_difference(A,B))
        | ~ subset(A,B) ) ),
    file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),
    [] ).

cnf(173194880,plain,
    ( ~ $equal(empty_set,set_difference(A,B))
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[l32_xboole_1]),
    [] ).

fof(t6_boole,plain,
    ! [A] :
      ( ~ empty(A)
      | $equal(empty_set,A) ),
    file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),
    [] ).

cnf(173101792,plain,
    ( ~ empty(A)
    | $equal(empty_set,A) ),
    inference(rewrite,[status(thm)],[t6_boole]),
    [] ).

cnf(187112472,plain,
    ( subset(A,B)
    | ~ empty(set_difference(A,B)) ),
    inference(resolution,[status(thm)],[173194880,173101792]),
    [] ).

fof(fc1_xboole_0,plain,
    empty(empty_set),
    file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),
    [] ).

cnf(173089144,plain,
    empty(empty_set),
    inference(rewrite,[status(thm)],[fc1_xboole_0]),
    [] ).

cnf(173189320,plain,
    ( $equal(empty_set,set_difference(A,B))
    | ~ subset(A,B) ),
    inference(rewrite,[status(thm)],[l32_xboole_1]),
    [] ).

fof(t37_xboole_1,plain,
    ( ( subset(a,b)
      | $equal(set_difference(a,b),empty_set) )
    & ( ~ $equal(set_difference(a,b),empty_set)
      | $equal(set_difference(a,b),empty_set) )
    & ( subset(a,b)
      | ~ subset(a,b) )
    & ( ~ $equal(set_difference(a,b),empty_set)
      | ~ subset(a,b) ) ),
    file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),
    [] ).

cnf(173183672,plain,
    ( subset(a,b)
    | $equal(set_difference(a,b),empty_set) ),
    inference(rewrite,[status(thm)],[t37_xboole_1]),
    [] ).

cnf(185775264,plain,
    $equal(empty_set,set_difference(a,b)),
    inference(resolution,[status(thm)],[173189320,173183672]),
    [] ).

cnf(186636904,plain,
    empty(set_difference(a,b)),
    inference(paramodulation,[status(thm)],[185775264,173089144,theory(equality)]),
    [] ).

cnf(173173600,plain,
    ( ~ $equal(set_difference(a,b),empty_set)
    | ~ subset(a,b) ),
    inference(rewrite,[status(thm)],[t37_xboole_1]),
    [] ).

fof(t8_boole,plain,
    ! [A,B] :
      ( ~ empty(A)
      | $equal(B,A)
      | ~ empty(B) ),
    file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),
    [] ).

cnf(173071408,plain,
    ( ~ empty(A)
    | $equal(B,A)
    | ~ empty(B) ),
    inference(rewrite,[status(thm)],[t8_boole]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[187112472,173089144,186636904,173173600,173071408]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l32_xboole_1,plain,(((~$equal(empty_set,set_difference(A,B))|subset(A,B))&($equal(empty_set,set_difference(A,B))|~subset(A,B)))),file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),[]).
% 
% cnf(173194880,plain,(~$equal(empty_set,set_difference(A,B))|subset(A,B)),inference(rewrite,[status(thm)],[l32_xboole_1]),[]).
% 
% fof(t6_boole,plain,(~empty(A)|$equal(empty_set,A)),file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),[]).
% 
% cnf(173101792,plain,(~empty(A)|$equal(empty_set,A)),inference(rewrite,[status(thm)],[t6_boole]),[]).
% 
% cnf(187112472,plain,(subset(A,B)|~empty(set_difference(A,B))),inference(resolution,[status(thm)],[173194880,173101792]),[]).
% 
% fof(fc1_xboole_0,plain,(empty(empty_set)),file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),[]).
% 
% cnf(173089144,plain,(empty(empty_set)),inference(rewrite,[status(thm)],[fc1_xboole_0]),[]).
% 
% cnf(173189320,plain,($equal(empty_set,set_difference(A,B))|~subset(A,B)),inference(rewrite,[status(thm)],[l32_xboole_1]),[]).
% 
% fof(t37_xboole_1,plain,(((subset(a,b)|$equal(set_difference(a,b),empty_set))&(~$equal(set_difference(a,b),empty_set)|$equal(set_difference(a,b),empty_set))&(subset(a,b)|~subset(a,b))&(~$equal(set_difference(a,b),empty_set)|~subset(a,b)))),file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),[]).
% 
% cnf(173183672,plain,(subset(a,b)|$equal(set_difference(a,b),empty_set)),inference(rewrite,[status(thm)],[t37_xboole_1]),[]).
% 
% cnf(185775264,plain,($equal(empty_set,set_difference(a,b))),inference(resolution,[status(thm)],[173189320,173183672]),[]).
% 
% cnf(186636904,plain,(empty(set_difference(a,b))),inference(paramodulation,[status(thm)],[185775264,173089144,theory(equality)]),[]).
% 
% cnf(173173600,plain,(~$equal(set_difference(a,b),empty_set)|~subset(a,b)),inference(rewrite,[status(thm)],[t37_xboole_1]),[]).
% 
% fof(t8_boole,plain,(~empty(A)|$equal(B,A)|~empty(B)),file('/tmp/SystemOnTPTP10415/SEU134+1.p',unknown),[]).
% 
% cnf(173071408,plain,(~empty(A)|$equal(B,A)|~empty(B)),inference(rewrite,[status(thm)],[t8_boole]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[187112472,173089144,186636904,173173600,173071408]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------