TSTP Solution File: HEN003-5 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN003-5 : 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 13:15:07 EDT 2009
% Result : Unsatisfiable 4.5s
% Output : Refutation 4.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 26 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 5 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(zero_is_smallest,plain,
! [A] : $equal(divide(zero,A),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),
[] ).
cnf(141242608,plain,
$equal(divide(zero,A),zero),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
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/HEN003-5.tptp',unknown),
[] ).
cnf(141253952,plain,
( ~ $equal(zero,divide(A,B))
| ~ $equal(zero,divide(B,A))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[divide_and_equal]),
[] ).
cnf(149708064,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(zero,A) ),
inference(paramodulation,[status(thm)],[141253952,141242608,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/HEN003-5.tptp',unknown),
[] ).
cnf(141234560,plain,
$equal(divide(divide(A,B),A),zero),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(150411432,plain,
$equal(zero,divide(zero,A)),
inference(paramodulation,[status(thm)],[149708064,141234560,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/HEN003-5.tptp',unknown),
[] ).
cnf(141238808,plain,
$equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(150568264,plain,
$equal(divide(divide(divide(B,A),zero),divide(divide(B,zero),A)),zero),
inference(paramodulation,[status(thm)],[150411432,141238808,theory(equality)]),
[] ).
cnf(149700864,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(A,zero) ),
inference(paramodulation,[status(thm)],[141253952,141242608,theory(equality)]),
[] ).
cnf(150118184,plain,
( ~ $equal(zero,divide(A,divide(divide(B,C),B)))
| $equal(A,zero) ),
inference(paramodulation,[status(thm)],[149700864,141234560,theory(equality)]),
[] ).
cnf(185040152,plain,
$equal(divide(divide(A,A),zero),zero),
inference(paramodulation,[status(thm)],[150568264,150118184,theory(equality)]),
[] ).
fof(prove_x_divide_x_is_zero,plain,
~ $equal(divide(a,a),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),
[] ).
cnf(141265608,plain,
~ $equal(divide(a,a),zero),
inference(rewrite,[status(thm)],[prove_x_divide_x_is_zero]),
[] ).
cnf(149932432,plain,
~ $equal(zero,divide(divide(a,a),zero)),
inference(resolution,[status(thm)],[149700864,141265608]),
[] ).
cnf(150260304,plain,
~ $equal(divide(zero,A),divide(divide(a,a),zero)),
inference(paramodulation,[status(thm)],[149932432,141242608,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[141242608,185040152,150260304,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 seconds
% START OF PROOF SEQUENCE
% fof(zero_is_smallest,plain,($equal(divide(zero,A),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),[]).
%
% cnf(141242608,plain,($equal(divide(zero,A),zero)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% fof(divide_and_equal,plain,(~$equal(zero,divide(A,B))|~$equal(zero,divide(B,A))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),[]).
%
% cnf(141253952,plain,(~$equal(zero,divide(A,B))|~$equal(zero,divide(B,A))|$equal(B,A)),inference(rewrite,[status(thm)],[divide_and_equal]),[]).
%
% cnf(149708064,plain,(~$equal(zero,divide(A,zero))|$equal(zero,A)),inference(paramodulation,[status(thm)],[141253952,141242608,theory(equality)]),[]).
%
% fof(quotient_smaller_than_numerator,plain,($equal(divide(divide(A,B),A),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),[]).
%
% cnf(141234560,plain,($equal(divide(divide(A,B),A),zero)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(150411432,plain,($equal(zero,divide(zero,A))),inference(paramodulation,[status(thm)],[149708064,141234560,theory(equality)]),[]).
%
% fof(quotient_property,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),[]).
%
% cnf(141238808,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(150568264,plain,($equal(divide(divide(divide(B,A),zero),divide(divide(B,zero),A)),zero)),inference(paramodulation,[status(thm)],[150411432,141238808,theory(equality)]),[]).
%
% cnf(149700864,plain,(~$equal(zero,divide(A,zero))|$equal(A,zero)),inference(paramodulation,[status(thm)],[141253952,141242608,theory(equality)]),[]).
%
% cnf(150118184,plain,(~$equal(zero,divide(A,divide(divide(B,C),B)))|$equal(A,zero)),inference(paramodulation,[status(thm)],[149700864,141234560,theory(equality)]),[]).
%
% cnf(185040152,plain,($equal(divide(divide(A,A),zero),zero)),inference(paramodulation,[status(thm)],[150568264,150118184,theory(equality)]),[]).
%
% fof(prove_x_divide_x_is_zero,plain,(~$equal(divide(a,a),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-5.tptp',unknown),[]).
%
% cnf(141265608,plain,(~$equal(divide(a,a),zero)),inference(rewrite,[status(thm)],[prove_x_divide_x_is_zero]),[]).
%
% cnf(149932432,plain,(~$equal(zero,divide(divide(a,a),zero))),inference(resolution,[status(thm)],[149700864,141265608]),[]).
%
% cnf(150260304,plain,(~$equal(divide(zero,A),divide(divide(a,a),zero))),inference(paramodulation,[status(thm)],[149932432,141242608,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[141242608,185040152,150260304,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------