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