TSTP Solution File: HEN012-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN012-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:16:30 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 17 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 5 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(quotient_less_equal1,plain,
! [A,B] :
( ~ less_equal(A,B)
| $equal(zero,divide(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156139936,plain,
( ~ less_equal(A,B)
| $equal(zero,divide(A,B)) ),
inference(rewrite,[status(thm)],[quotient_less_equal1]),
[] ).
fof(quotient_smaller_than_numerator,plain,
! [A,B] : less_equal(divide(A,B),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156151224,plain,
less_equal(divide(A,B),A),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(164065760,plain,
$equal(zero,divide(divide(A,B),A)),
inference(resolution,[status(thm)],[156139936,156151224]),
[] ).
fof(quotient_property,plain,
! [A,B,C] : less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156155280,plain,
less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(164578760,plain,
less_equal(divide(divide(A,A),divide(B,A)),zero),
inference(paramodulation,[status(thm)],[164065760,156155280,theory(equality)]),
[] ).
fof(zero_is_smallest,plain,
! [A] : less_equal(zero,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156163128,plain,
less_equal(zero,A),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(163946952,plain,
$equal(zero,divide(zero,A)),
inference(resolution,[status(thm)],[156139936,156163128]),
[] ).
cnf(167324504,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(paramodulation,[status(thm)],[164578760,163946952,theory(equality)]),
[] ).
fof(less_equal_and_equal,plain,
! [A,B] :
( ~ less_equal(A,B)
| ~ less_equal(B,A)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156172696,plain,
( ~ less_equal(A,B)
| ~ less_equal(B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[less_equal_and_equal]),
[] ).
cnf(163965568,plain,
( ~ less_equal(A,zero)
| $equal(A,zero) ),
inference(resolution,[status(thm)],[156172696,156163128]),
[] ).
cnf(167444056,plain,
$equal(divide(divide(A,A),zero),zero),
inference(resolution,[status(thm)],[167324504,163965568]),
[] ).
fof(quotient_less_equal2,plain,
! [A,B] :
( ~ $equal(zero,divide(A,B))
| less_equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156146504,plain,
( ~ $equal(zero,divide(A,B))
| less_equal(A,B) ),
inference(rewrite,[status(thm)],[quotient_less_equal2]),
[] ).
cnf(167813168,plain,
less_equal(divide(A,A),zero),
inference(paramodulation,[status(thm)],[167444056,156146504,theory(equality)]),
[] ).
fof(prove_a_LE_a,plain,
~ less_equal(a,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),
[] ).
cnf(156180144,plain,
~ less_equal(a,a),
inference(rewrite,[status(thm)],[prove_a_LE_a]),
[] ).
cnf(164035464,plain,
~ $equal(zero,divide(a,a)),
inference(resolution,[status(thm)],[156146504,156180144]),
[] ).
cnf(165586904,plain,
~ less_equal(divide(a,a),zero),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156163128,156172696,164035464]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[167813168,165586904]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(quotient_less_equal1,plain,(~less_equal(A,B)|$equal(zero,divide(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156139936,plain,(~less_equal(A,B)|$equal(zero,divide(A,B))),inference(rewrite,[status(thm)],[quotient_less_equal1]),[]).
%
% fof(quotient_smaller_than_numerator,plain,(less_equal(divide(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156151224,plain,(less_equal(divide(A,B),A)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(164065760,plain,($equal(zero,divide(divide(A,B),A))),inference(resolution,[status(thm)],[156139936,156151224]),[]).
%
% fof(quotient_property,plain,(less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156155280,plain,(less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B))),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(164578760,plain,(less_equal(divide(divide(A,A),divide(B,A)),zero)),inference(paramodulation,[status(thm)],[164065760,156155280,theory(equality)]),[]).
%
% fof(zero_is_smallest,plain,(less_equal(zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156163128,plain,(less_equal(zero,A)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(163946952,plain,($equal(zero,divide(zero,A))),inference(resolution,[status(thm)],[156139936,156163128]),[]).
%
% cnf(167324504,plain,(less_equal(divide(divide(A,A),zero),zero)),inference(paramodulation,[status(thm)],[164578760,163946952,theory(equality)]),[]).
%
% fof(less_equal_and_equal,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156172696,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[less_equal_and_equal]),[]).
%
% cnf(163965568,plain,(~less_equal(A,zero)|$equal(A,zero)),inference(resolution,[status(thm)],[156172696,156163128]),[]).
%
% cnf(167444056,plain,($equal(divide(divide(A,A),zero),zero)),inference(resolution,[status(thm)],[167324504,163965568]),[]).
%
% fof(quotient_less_equal2,plain,(~$equal(zero,divide(A,B))|less_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156146504,plain,(~$equal(zero,divide(A,B))|less_equal(A,B)),inference(rewrite,[status(thm)],[quotient_less_equal2]),[]).
%
% cnf(167813168,plain,(less_equal(divide(A,A),zero)),inference(paramodulation,[status(thm)],[167444056,156146504,theory(equality)]),[]).
%
% fof(prove_a_LE_a,plain,(~less_equal(a,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-3.tptp',unknown),[]).
%
% cnf(156180144,plain,(~less_equal(a,a)),inference(rewrite,[status(thm)],[prove_a_LE_a]),[]).
%
% cnf(164035464,plain,(~$equal(zero,divide(a,a))),inference(resolution,[status(thm)],[156146504,156180144]),[]).
%
% cnf(165586904,plain,(~less_equal(divide(a,a),zero)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156163128,156172696,164035464]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[167813168,165586904]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------