%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN008-5 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 13:15:55 EDT 2009
% Result : Unsatisfiable 4.8s
% Output : Refutation 4.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 21 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 13 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(divide_and_equal,plain,
! [A,B] :
( ~ $equal(zero,divide(A,B))
| ~ $equal(zero,divide(B,A))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(160993200,plain,
( ~ $equal(zero,divide(A,B))
| ~ $equal(zero,divide(B,A))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[divide_and_equal]),
[] ).
fof(zero_is_smallest,plain,
! [A] : $equal(divide(zero,A),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(160981856,plain,
$equal(divide(zero,A),zero),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(169180488,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(zero,A) ),
inference(paramodulation,[status(thm)],[160993200,160981856,theory(equality)]),
[] ).
fof(quotient_smaller_than_numerator,plain,
! [A,B] : $equal(divide(divide(A,B),A),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(160973744,plain,
$equal(divide(divide(A,B),A),zero),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(169863576,plain,
$equal(zero,divide(zero,A)),
inference(paramodulation,[status(thm)],[169180488,160973744,theory(equality)]),
[] ).
fof(a_divide_b_is_zero,plain,
$equal(divide(a,b),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(161004888,plain,
$equal(divide(a,b),zero),
inference(rewrite,[status(thm)],[a_divide_b_is_zero]),
[] ).
cnf(169969040,plain,
$equal(zero,divide(divide(a,b),A)),
inference(paramodulation,[status(thm)],[169863576,161004888,theory(equality)]),
[] ).
fof(quotient_property,plain,
! [A,B,C] : $equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(160978056,plain,
$equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(171783696,plain,
$equal(divide(divide(divide(a,A),divide(b,A)),zero),zero),
inference(paramodulation,[status(thm)],[169969040,160978056,theory(equality)]),
[] ).
cnf(169173224,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(A,zero) ),
inference(paramodulation,[status(thm)],[160993200,160981856,theory(equality)]),
[] ).
cnf(169697080,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(A,divide(divide(B,C),B)) ),
inference(paramodulation,[status(thm)],[169173224,160973744,theory(equality)]),
[] ).
cnf(203873344,plain,
$equal(divide(divide(a,A),divide(b,A)),divide(divide(B,C),B)),
inference(paramodulation,[status(thm)],[171783696,169697080,theory(equality)]),
[] ).
fof(identity_is_largest,plain,
! [A] : $equal(divide(A,identity),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(161001168,plain,
$equal(divide(A,identity),zero),
inference(rewrite,[status(thm)],[identity_is_largest]),
[] ).
cnf(169944952,plain,
$equal(divide(B,identity),divide(zero,A)),
inference(paramodulation,[status(thm)],[169863576,161001168,theory(equality)]),
[] ).
cnf(170728280,plain,
$equal(divide(divide(B,identity),zero),zero),
inference(paramodulation,[status(thm)],[169944952,160973744,theory(equality)]),
[] ).
cnf(171827616,plain,
$equal(divide(divide(B,identity),zero),divide(divide(C,D),C)),
inference(paramodulation,[status(thm)],[170728280,160973744,theory(equality)]),
[] ).
fof(prove_property_of_divide3,plain,
~ $equal(divide(divide(a,c),divide(b,c)),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),
[] ).
cnf(161009056,plain,
~ $equal(divide(divide(a,c),divide(b,c)),zero),
inference(rewrite,[status(thm)],[prove_property_of_divide3]),
[] ).
cnf(168834752,plain,
~ $equal(divide(divide(a,c),divide(b,c)),divide(divide(A,B),A)),
inference(paramodulation,[status(thm)],[161009056,160973744,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[203873344,171827616,168834752,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 5 seconds
% START OF PROOF SEQUENCE
% fof(divide_and_equal,plain,(~$equal(zero,divide(A,B))|~$equal(zero,divide(B,A))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(160993200,plain,(~$equal(zero,divide(A,B))|~$equal(zero,divide(B,A))|$equal(B,A)),inference(rewrite,[status(thm)],[divide_and_equal]),[]).
%
% fof(zero_is_smallest,plain,($equal(divide(zero,A),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(160981856,plain,($equal(divide(zero,A),zero)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(169180488,plain,(~$equal(zero,divide(A,zero))|$equal(zero,A)),inference(paramodulation,[status(thm)],[160993200,160981856,theory(equality)]),[]).
%
% fof(quotient_smaller_than_numerator,plain,($equal(divide(divide(A,B),A),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(160973744,plain,($equal(divide(divide(A,B),A),zero)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(169863576,plain,($equal(zero,divide(zero,A))),inference(paramodulation,[status(thm)],[169180488,160973744,theory(equality)]),[]).
%
% fof(a_divide_b_is_zero,plain,($equal(divide(a,b),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(161004888,plain,($equal(divide(a,b),zero)),inference(rewrite,[status(thm)],[a_divide_b_is_zero]),[]).
%
% cnf(169969040,plain,($equal(zero,divide(divide(a,b),A))),inference(paramodulation,[status(thm)],[169863576,161004888,theory(equality)]),[]).
%
% fof(quotient_property,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(160978056,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(171783696,plain,($equal(divide(divide(divide(a,A),divide(b,A)),zero),zero)),inference(paramodulation,[status(thm)],[169969040,160978056,theory(equality)]),[]).
%
% cnf(169173224,plain,(~$equal(zero,divide(A,zero))|$equal(A,zero)),inference(paramodulation,[status(thm)],[160993200,160981856,theory(equality)]),[]).
%
% cnf(169697080,plain,(~$equal(zero,divide(A,zero))|$equal(A,divide(divide(B,C),B))),inference(paramodulation,[status(thm)],[169173224,160973744,theory(equality)]),[]).
%
% cnf(203873344,plain,($equal(divide(divide(a,A),divide(b,A)),divide(divide(B,C),B))),inference(paramodulation,[status(thm)],[171783696,169697080,theory(equality)]),[]).
%
% fof(identity_is_largest,plain,($equal(divide(A,identity),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(161001168,plain,($equal(divide(A,identity),zero)),inference(rewrite,[status(thm)],[identity_is_largest]),[]).
%
% cnf(169944952,plain,($equal(divide(B,identity),divide(zero,A))),inference(paramodulation,[status(thm)],[169863576,161001168,theory(equality)]),[]).
%
% cnf(170728280,plain,($equal(divide(divide(B,identity),zero),zero)),inference(paramodulation,[status(thm)],[169944952,160973744,theory(equality)]),[]).
%
% cnf(171827616,plain,($equal(divide(divide(B,identity),zero),divide(divide(C,D),C))),inference(paramodulation,[status(thm)],[170728280,160973744,theory(equality)]),[]).
%
% fof(prove_property_of_divide3,plain,(~$equal(divide(divide(a,c),divide(b,c)),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-5.tptp',unknown),[]).
%
% cnf(161009056,plain,(~$equal(divide(divide(a,c),divide(b,c)),zero)),inference(rewrite,[status(thm)],[prove_property_of_divide3]),[]).
%
% cnf(168834752,plain,(~$equal(divide(divide(a,c),divide(b,c)),divide(divide(A,B),A))),inference(paramodulation,[status(thm)],[161009056,160973744,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[203873344,171827616,168834752,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------