%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN003-3 : 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 13:15:03 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 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/HEN003-3.tptp',unknown),
[] ).
cnf(151840856,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/HEN003-3.tptp',unknown),
[] ).
cnf(151852144,plain,
less_equal(divide(A,B),A),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(159748408,plain,
$equal(zero,divide(divide(A,B),A)),
inference(resolution,[status(thm)],[151840856,151852144]),
[] ).
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/HEN003-3.tptp',unknown),
[] ).
cnf(151856200,plain,
less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(160334664,plain,
less_equal(divide(divide(A,A),divide(B,A)),zero),
inference(paramodulation,[status(thm)],[159748408,151856200,theory(equality)]),
[] ).
fof(zero_is_smallest,plain,
! [A] : less_equal(zero,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),
[] ).
cnf(151864048,plain,
less_equal(zero,A),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(159648008,plain,
$equal(zero,divide(zero,A)),
inference(resolution,[status(thm)],[151840856,151864048]),
[] ).
cnf(163293544,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(paramodulation,[status(thm)],[160334664,159648008,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/HEN003-3.tptp',unknown),
[] ).
cnf(151873616,plain,
( ~ less_equal(A,B)
| ~ less_equal(B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[less_equal_and_equal]),
[] ).
cnf(159666584,plain,
( ~ less_equal(A,zero)
| $equal(A,zero) ),
inference(resolution,[status(thm)],[151873616,151864048]),
[] ).
cnf(163409008,plain,
$equal(divide(divide(A,A),zero),zero),
inference(resolution,[status(thm)],[163293544,159666584]),
[] ).
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/HEN003-3.tptp',unknown),
[] ).
cnf(151847424,plain,
( ~ $equal(zero,divide(A,B))
| less_equal(A,B) ),
inference(rewrite,[status(thm)],[quotient_less_equal2]),
[] ).
cnf(163788688,plain,
less_equal(divide(A,A),zero),
inference(paramodulation,[status(thm)],[163409008,151847424,theory(equality)]),
[] ).
fof(prove_x_divide_x_is_zero,plain,
~ $equal(divide(a,a),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),
[] ).
cnf(151881120,plain,
~ $equal(divide(a,a),zero),
inference(rewrite,[status(thm)],[prove_x_divide_x_is_zero]),
[] ).
cnf(161424936,plain,
~ less_equal(divide(a,a),zero),
inference(forward_subsumption_resolution__resolution,[status(thm)],[151864048,151873616,151881120]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[163788688,161424936]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(quotient_less_equal1,plain,(~less_equal(A,B)|$equal(zero,divide(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),[]).
%
% cnf(151840856,plain,(~less_equal(A,B)|$equal(zero,divide(A,B))),inference(rewrite,[status(thm)],[quotient_less_equal1]),[]).
%
% fof(quotient_smaller_than_numerator,plain,(less_equal(divide(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),[]).
%
% cnf(151852144,plain,(less_equal(divide(A,B),A)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(159748408,plain,($equal(zero,divide(divide(A,B),A))),inference(resolution,[status(thm)],[151840856,151852144]),[]).
%
% 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/HEN003-3.tptp',unknown),[]).
%
% cnf(151856200,plain,(less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B))),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(160334664,plain,(less_equal(divide(divide(A,A),divide(B,A)),zero)),inference(paramodulation,[status(thm)],[159748408,151856200,theory(equality)]),[]).
%
% fof(zero_is_smallest,plain,(less_equal(zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),[]).
%
% cnf(151864048,plain,(less_equal(zero,A)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(159648008,plain,($equal(zero,divide(zero,A))),inference(resolution,[status(thm)],[151840856,151864048]),[]).
%
% cnf(163293544,plain,(less_equal(divide(divide(A,A),zero),zero)),inference(paramodulation,[status(thm)],[160334664,159648008,theory(equality)]),[]).
%
% fof(less_equal_and_equal,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),[]).
%
% cnf(151873616,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[less_equal_and_equal]),[]).
%
% cnf(159666584,plain,(~less_equal(A,zero)|$equal(A,zero)),inference(resolution,[status(thm)],[151873616,151864048]),[]).
%
% cnf(163409008,plain,($equal(divide(divide(A,A),zero),zero)),inference(resolution,[status(thm)],[163293544,159666584]),[]).
%
% fof(quotient_less_equal2,plain,(~$equal(zero,divide(A,B))|less_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),[]).
%
% cnf(151847424,plain,(~$equal(zero,divide(A,B))|less_equal(A,B)),inference(rewrite,[status(thm)],[quotient_less_equal2]),[]).
%
% cnf(163788688,plain,(less_equal(divide(A,A),zero)),inference(paramodulation,[status(thm)],[163409008,151847424,theory(equality)]),[]).
%
% fof(prove_x_divide_x_is_zero,plain,(~$equal(divide(a,a),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN003-3.tptp',unknown),[]).
%
% cnf(151881120,plain,(~$equal(divide(a,a),zero)),inference(rewrite,[status(thm)],[prove_x_divide_x_is_zero]),[]).
%
% cnf(161424936,plain,(~less_equal(divide(a,a),zero)),inference(forward_subsumption_resolution__resolution,[status(thm)],[151864048,151873616,151881120]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[163788688,161424936]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------