%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN002-3 : 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 13:14:56 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 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 : 12 ( 3 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/HEN002-3.tptp',unknown),
[] ).
cnf(173494760,plain,
( ~ less_equal(A,B)
| ~ less_equal(B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[less_equal_and_equal]),
[] ).
fof(zero_is_smallest,plain,
! [A] : less_equal(zero,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),
[] ).
cnf(173485192,plain,
less_equal(zero,A),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(181287728,plain,
( ~ less_equal(A,zero)
| $equal(A,zero) ),
inference(resolution,[status(thm)],[173494760,173485192]),
[] ).
fof(quotient_smaller_than_numerator,plain,
! [A,B] : less_equal(divide(A,B),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),
[] ).
cnf(173473288,plain,
less_equal(divide(A,B),A),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(181313096,plain,
$equal(divide(zero,A),zero),
inference(resolution,[status(thm)],[181287728,173473288]),
[] ).
fof(prove_zero_over_a_is_zero,plain,
~ $equal(divide(zero,a),zero),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),
[] ).
cnf(173502264,plain,
~ $equal(divide(zero,a),zero),
inference(rewrite,[status(thm)],[prove_zero_over_a_is_zero]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[181313096,173502264]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(less_equal_and_equal,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),[]).
%
% cnf(173494760,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[less_equal_and_equal]),[]).
%
% fof(zero_is_smallest,plain,(less_equal(zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),[]).
%
% cnf(173485192,plain,(less_equal(zero,A)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(181287728,plain,(~less_equal(A,zero)|$equal(A,zero)),inference(resolution,[status(thm)],[173494760,173485192]),[]).
%
% fof(quotient_smaller_than_numerator,plain,(less_equal(divide(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),[]).
%
% cnf(173473288,plain,(less_equal(divide(A,B),A)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(181313096,plain,($equal(divide(zero,A),zero)),inference(resolution,[status(thm)],[181287728,173473288]),[]).
%
% fof(prove_zero_over_a_is_zero,plain,(~$equal(divide(zero,a),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-3.tptp',unknown),[]).
%
% cnf(173502264,plain,(~$equal(divide(zero,a),zero)),inference(rewrite,[status(thm)],[prove_zero_over_a_is_zero]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[181313096,173502264]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------