%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN005-5 : 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 13:15:23 EDT 2009
% Result : Unsatisfiable 13.6s
% Output : Refutation 13.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 19 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 6 sgn 8 !; 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/HEN005-5.tptp',unknown),
[] ).
cnf(165727624,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/HEN005-5.tptp',unknown),
[] ).
cnf(165716280,plain,
$equal(divide(zero,A),zero),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(174643320,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(zero,A) ),
inference(paramodulation,[status(thm)],[165727624,165716280,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/HEN005-5.tptp',unknown),
[] ).
cnf(165708168,plain,
$equal(divide(divide(A,B),A),zero),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(175459608,plain,
$equal(zero,divide(zero,A)),
inference(paramodulation,[status(thm)],[174643320,165708168,theory(equality)]),
[] ).
fof(a_divide_b_is_zero,plain,
$equal(divide(a,b),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),
[] ).
cnf(165739312,plain,
$equal(divide(a,b),zero),
inference(rewrite,[status(thm)],[a_divide_b_is_zero]),
[] ).
cnf(175572776,plain,
$equal(zero,divide(divide(a,b),A)),
inference(paramodulation,[status(thm)],[175459608,165739312,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/HEN005-5.tptp',unknown),
[] ).
cnf(165712480,plain,
$equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(177640016,plain,
$equal(divide(divide(divide(a,A),divide(b,A)),zero),zero),
inference(paramodulation,[status(thm)],[175572776,165712480,theory(equality)]),
[] ).
cnf(237602336,plain,
$equal(divide(divide(B,C),B),divide(divide(divide(a,A),divide(b,A)),zero)),
inference(paramodulation,[status(thm)],[177640016,165708168,theory(equality)]),
[] ).
cnf(175463272,plain,
( ~ $equal(divide(divide(B,C),B),divide(A,zero))
| $equal(zero,A) ),
inference(paramodulation,[status(thm)],[174643320,165708168,theory(equality)]),
[] ).
cnf(174636056,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(A,zero) ),
inference(paramodulation,[status(thm)],[165727624,165716280,theory(equality)]),
[] ).
fof(prove_transitivity_of_divide_to_zero,plain,
~ $equal(divide(a,c),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),
[] ).
cnf(165747072,plain,
~ $equal(divide(a,c),zero),
inference(rewrite,[status(thm)],[prove_transitivity_of_divide_to_zero]),
[] ).
cnf(174983640,plain,
~ $equal(zero,divide(divide(a,c),zero)),
inference(resolution,[status(thm)],[174636056,165747072]),
[] ).
fof(b_divide_c_is_zero,plain,
$equal(divide(b,c),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),
[] ).
cnf(165743208,plain,
$equal(divide(b,c),zero),
inference(rewrite,[status(thm)],[b_divide_c_is_zero]),
[] ).
cnf(179008792,plain,
~ $equal(zero,divide(divide(a,c),divide(b,c))),
inference(paramodulation,[status(thm)],[174983640,165743208,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[237602336,175463272,179008792]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 13 seconds
% START OF PROOF SEQUENCE
% fof(divide_and_equal,plain,(~$equal(zero,divide(A,B))|~$equal(zero,divide(B,A))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),[]).
%
% cnf(165727624,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/HEN005-5.tptp',unknown),[]).
%
% cnf(165716280,plain,($equal(divide(zero,A),zero)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(174643320,plain,(~$equal(zero,divide(A,zero))|$equal(zero,A)),inference(paramodulation,[status(thm)],[165727624,165716280,theory(equality)]),[]).
%
% fof(quotient_smaller_than_numerator,plain,($equal(divide(divide(A,B),A),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),[]).
%
% cnf(165708168,plain,($equal(divide(divide(A,B),A),zero)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(175459608,plain,($equal(zero,divide(zero,A))),inference(paramodulation,[status(thm)],[174643320,165708168,theory(equality)]),[]).
%
% fof(a_divide_b_is_zero,plain,($equal(divide(a,b),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),[]).
%
% cnf(165739312,plain,($equal(divide(a,b),zero)),inference(rewrite,[status(thm)],[a_divide_b_is_zero]),[]).
%
% cnf(175572776,plain,($equal(zero,divide(divide(a,b),A))),inference(paramodulation,[status(thm)],[175459608,165739312,theory(equality)]),[]).
%
% fof(quotient_property,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),[]).
%
% cnf(165712480,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(177640016,plain,($equal(divide(divide(divide(a,A),divide(b,A)),zero),zero)),inference(paramodulation,[status(thm)],[175572776,165712480,theory(equality)]),[]).
%
% cnf(237602336,plain,($equal(divide(divide(B,C),B),divide(divide(divide(a,A),divide(b,A)),zero))),inference(paramodulation,[status(thm)],[177640016,165708168,theory(equality)]),[]).
%
% cnf(175463272,plain,(~$equal(divide(divide(B,C),B),divide(A,zero))|$equal(zero,A)),inference(paramodulation,[status(thm)],[174643320,165708168,theory(equality)]),[]).
%
% cnf(174636056,plain,(~$equal(zero,divide(A,zero))|$equal(A,zero)),inference(paramodulation,[status(thm)],[165727624,165716280,theory(equality)]),[]).
%
% fof(prove_transitivity_of_divide_to_zero,plain,(~$equal(divide(a,c),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),[]).
%
% cnf(165747072,plain,(~$equal(divide(a,c),zero)),inference(rewrite,[status(thm)],[prove_transitivity_of_divide_to_zero]),[]).
%
% cnf(174983640,plain,(~$equal(zero,divide(divide(a,c),zero))),inference(resolution,[status(thm)],[174636056,165747072]),[]).
%
% fof(b_divide_c_is_zero,plain,($equal(divide(b,c),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN005-5.tptp',unknown),[]).
%
% cnf(165743208,plain,($equal(divide(b,c),zero)),inference(rewrite,[status(thm)],[b_divide_c_is_zero]),[]).
%
% cnf(179008792,plain,(~$equal(zero,divide(divide(a,c),divide(b,c)))),inference(paramodulation,[status(thm)],[174983640,165743208,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[237602336,175463272,179008792]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------