TSTP Solution File: HEN004-5 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN004-5 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:15:14 EDT 2009
% Result : Unsatisfiable 16.3s
% Output : Refutation 16.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 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 : 33 ( 6 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/HEN004-5.tptp',unknown),
[] ).
cnf(159076064,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/HEN004-5.tptp',unknown),
[] ).
cnf(159064720,plain,
$equal(divide(zero,A),zero),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(167649896,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(zero,A) ),
inference(paramodulation,[status(thm)],[159076064,159064720,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/HEN004-5.tptp',unknown),
[] ).
cnf(159056672,plain,
$equal(divide(divide(A,B),A),zero),
inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),
[] ).
cnf(168308976,plain,
$equal(zero,divide(zero,A)),
inference(paramodulation,[status(thm)],[167649896,159056672,theory(equality)]),
[] ).
cnf(168443672,plain,
$equal(divide(divide(B,C),B),divide(zero,A)),
inference(paramodulation,[status(thm)],[168308976,159056672,theory(equality)]),
[] ).
fof(x_divide_x_is_zero,plain,
! [A] : $equal(zero,divide(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),
[] ).
cnf(159087912,plain,
$equal(zero,divide(A,A)),
inference(rewrite,[status(thm)],[x_divide_x_is_zero]),
[] ).
cnf(171319456,plain,
$equal(zero,divide(divide(A,B),A)),
inference(paramodulation,[status(thm)],[168443672,159087912,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/HEN004-5.tptp',unknown),
[] ).
cnf(159060920,plain,
$equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(168492392,plain,
$equal(divide(divide(divide(B,A),zero),divide(divide(B,zero),A)),zero),
inference(paramodulation,[status(thm)],[168308976,159060920,theory(equality)]),
[] ).
cnf(167638600,plain,
( ~ $equal(zero,divide(A,zero))
| $equal(A,zero) ),
inference(paramodulation,[status(thm)],[159076064,159064720,theory(equality)]),
[] ).
cnf(168076128,plain,
( ~ $equal(zero,divide(A,divide(B,B)))
| $equal(A,zero) ),
inference(paramodulation,[status(thm)],[167638600,159087912,theory(equality)]),
[] ).
cnf(213212192,plain,
$equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(paramodulation,[status(thm)],[168492392,168076128,theory(equality)]),
[] ).
cnf(219824504,plain,
$equal(divide(A,divide(A,zero)),zero),
inference(paramodulation,[status(thm)],[213212192,167638600,theory(equality)]),
[] ).
cnf(224373424,plain,
$equal(divide(A,zero),A),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171319456,219824504,159076064,theory(equality)]),
[] ).
fof(prove_x_divide_zero_is_x,plain,
~ $equal(divide(a,zero),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),
[] ).
cnf(159091592,plain,
~ $equal(divide(a,zero),a),
inference(rewrite,[status(thm)],[prove_x_divide_zero_is_x]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[224373424,159091592]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 16 seconds
% START OF PROOF SEQUENCE
% fof(divide_and_equal,plain,(~$equal(zero,divide(A,B))|~$equal(zero,divide(B,A))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),[]).
%
% cnf(159076064,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/HEN004-5.tptp',unknown),[]).
%
% cnf(159064720,plain,($equal(divide(zero,A),zero)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(167649896,plain,(~$equal(zero,divide(A,zero))|$equal(zero,A)),inference(paramodulation,[status(thm)],[159076064,159064720,theory(equality)]),[]).
%
% fof(quotient_smaller_than_numerator,plain,($equal(divide(divide(A,B),A),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),[]).
%
% cnf(159056672,plain,($equal(divide(divide(A,B),A),zero)),inference(rewrite,[status(thm)],[quotient_smaller_than_numerator]),[]).
%
% cnf(168308976,plain,($equal(zero,divide(zero,A))),inference(paramodulation,[status(thm)],[167649896,159056672,theory(equality)]),[]).
%
% cnf(168443672,plain,($equal(divide(divide(B,C),B),divide(zero,A))),inference(paramodulation,[status(thm)],[168308976,159056672,theory(equality)]),[]).
%
% fof(x_divide_x_is_zero,plain,($equal(zero,divide(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),[]).
%
% cnf(159087912,plain,($equal(zero,divide(A,A))),inference(rewrite,[status(thm)],[x_divide_x_is_zero]),[]).
%
% cnf(171319456,plain,($equal(zero,divide(divide(A,B),A))),inference(paramodulation,[status(thm)],[168443672,159087912,theory(equality)]),[]).
%
% fof(quotient_property,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),[]).
%
% cnf(159060920,plain,($equal(divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),zero)),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(168492392,plain,($equal(divide(divide(divide(B,A),zero),divide(divide(B,zero),A)),zero)),inference(paramodulation,[status(thm)],[168308976,159060920,theory(equality)]),[]).
%
% cnf(167638600,plain,(~$equal(zero,divide(A,zero))|$equal(A,zero)),inference(paramodulation,[status(thm)],[159076064,159064720,theory(equality)]),[]).
%
% cnf(168076128,plain,(~$equal(zero,divide(A,divide(B,B)))|$equal(A,zero)),inference(paramodulation,[status(thm)],[167638600,159087912,theory(equality)]),[]).
%
% cnf(213212192,plain,($equal(divide(divide(A,divide(A,zero)),zero),zero)),inference(paramodulation,[status(thm)],[168492392,168076128,theory(equality)]),[]).
%
% cnf(219824504,plain,($equal(divide(A,divide(A,zero)),zero)),inference(paramodulation,[status(thm)],[213212192,167638600,theory(equality)]),[]).
%
% cnf(224373424,plain,($equal(divide(A,zero),A)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171319456,219824504,159076064,theory(equality)]),[]).
%
% fof(prove_x_divide_zero_is_x,plain,(~$equal(divide(a,zero),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN004-5.tptp',unknown),[]).
%
% cnf(159091592,plain,(~$equal(divide(a,zero),a)),inference(rewrite,[status(thm)],[prove_x_divide_zero_is_x]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[224373424,159091592]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------