TSTP Solution File: HEN007-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN007-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 13:15:39 EDT 2009
% Result : Unsatisfiable 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_zQyLEzQx,plain,
~ less_equal(zqy,zqx),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156876296,plain,
~ less_equal(zqy,zqx),
inference(rewrite,[status(thm)],[prove_zQyLEzQx]),
[] ).
fof(xQyLEz_implies_xQzLEy,plain,
! [A,B,C,D,E] :
( ~ quotient(A,B,C)
| ~ less_equal(C,D)
| ~ quotient(A,D,E)
| less_equal(E,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156856856,plain,
( ~ quotient(A,B,C)
| ~ less_equal(C,D)
| ~ quotient(A,D,E)
| less_equal(E,B) ),
inference(rewrite,[status(thm)],[xQyLEz_implies_xQzLEy]),
[] ).
fof(zQy,plain,
quotient(z,y,zqy),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156864488,plain,
quotient(z,y,zqy),
inference(rewrite,[status(thm)],[zQy]),
[] ).
cnf(165717864,plain,
( ~ quotient(z,A,B)
| ~ less_equal(B,y)
| less_equal(zqy,A) ),
inference(resolution,[status(thm)],[156856856,156864488]),
[] ).
fof(closure,plain,
! [A,B] : quotient(A,B,divide(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156819352,plain,
quotient(A,B,divide(A,B)),
inference(rewrite,[status(thm)],[closure]),
[] ).
cnf(166543688,plain,
( ~ less_equal(divide(z,A),y)
| less_equal(zqy,A) ),
inference(resolution,[status(thm)],[165717864,156819352]),
[] ).
fof(transitivity_of_less_equal,plain,
! [A,B,C] :
( ~ less_equal(A,B)
| ~ less_equal(B,C)
| less_equal(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156848472,plain,
( ~ less_equal(A,B)
| ~ less_equal(B,C)
| less_equal(A,C) ),
inference(rewrite,[status(thm)],[transitivity_of_less_equal]),
[] ).
fof(xLEy,plain,
less_equal(x,y),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156860616,plain,
less_equal(x,y),
inference(rewrite,[status(thm)],[xLEy]),
[] ).
cnf(165578952,plain,
( ~ less_equal(A,x)
| less_equal(A,y) ),
inference(resolution,[status(thm)],[156848472,156860616]),
[] ).
fof(zQx,plain,
quotient(z,x,zqx),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156763776,plain,
quotient(z,x,zqx),
inference(rewrite,[status(thm)],[zQx]),
[] ).
cnf(165794368,plain,
( ~ less_equal(zqx,A)
| ~ quotient(z,A,B)
| less_equal(B,x) ),
inference(resolution,[status(thm)],[156856856,156763776]),
[] ).
cnf(166560248,plain,
( ~ less_equal(zqx,A)
| less_equal(divide(z,A),x) ),
inference(resolution,[status(thm)],[165794368,156819352]),
[] ).
fof(divisor_existence,plain,
! [A,B,C] :
( ~ quotient(A,B,C)
| less_equal(C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156780504,plain,
( ~ quotient(A,B,C)
| less_equal(C,A) ),
inference(rewrite,[status(thm)],[divisor_existence]),
[] ).
fof(x_divde_zero_is_x,plain,
! [A] : quotient(A,zero,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),
[] ).
cnf(156843976,plain,
quotient(A,zero,A),
inference(rewrite,[status(thm)],[x_divde_zero_is_x]),
[] ).
cnf(165015824,plain,
less_equal(A,A),
inference(resolution,[status(thm)],[156780504,156843976]),
[] ).
cnf(166588864,plain,
less_equal(divide(z,zqx),x),
inference(resolution,[status(thm)],[166560248,165015824]),
[] ).
cnf(167940464,plain,
less_equal(divide(z,zqx),y),
inference(resolution,[status(thm)],[165578952,166588864]),
[] ).
cnf(180386024,plain,
less_equal(zqy,zqx),
inference(resolution,[status(thm)],[166543688,167940464]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[156876296,180386024]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_zQyLEzQx,plain,(~less_equal(zqy,zqx)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156876296,plain,(~less_equal(zqy,zqx)),inference(rewrite,[status(thm)],[prove_zQyLEzQx]),[]).
%
% fof(xQyLEz_implies_xQzLEy,plain,(~quotient(A,B,C)|~less_equal(C,D)|~quotient(A,D,E)|less_equal(E,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156856856,plain,(~quotient(A,B,C)|~less_equal(C,D)|~quotient(A,D,E)|less_equal(E,B)),inference(rewrite,[status(thm)],[xQyLEz_implies_xQzLEy]),[]).
%
% fof(zQy,plain,(quotient(z,y,zqy)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156864488,plain,(quotient(z,y,zqy)),inference(rewrite,[status(thm)],[zQy]),[]).
%
% cnf(165717864,plain,(~quotient(z,A,B)|~less_equal(B,y)|less_equal(zqy,A)),inference(resolution,[status(thm)],[156856856,156864488]),[]).
%
% fof(closure,plain,(quotient(A,B,divide(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156819352,plain,(quotient(A,B,divide(A,B))),inference(rewrite,[status(thm)],[closure]),[]).
%
% cnf(166543688,plain,(~less_equal(divide(z,A),y)|less_equal(zqy,A)),inference(resolution,[status(thm)],[165717864,156819352]),[]).
%
% fof(transitivity_of_less_equal,plain,(~less_equal(A,B)|~less_equal(B,C)|less_equal(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156848472,plain,(~less_equal(A,B)|~less_equal(B,C)|less_equal(A,C)),inference(rewrite,[status(thm)],[transitivity_of_less_equal]),[]).
%
% fof(xLEy,plain,(less_equal(x,y)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156860616,plain,(less_equal(x,y)),inference(rewrite,[status(thm)],[xLEy]),[]).
%
% cnf(165578952,plain,(~less_equal(A,x)|less_equal(A,y)),inference(resolution,[status(thm)],[156848472,156860616]),[]).
%
% fof(zQx,plain,(quotient(z,x,zqx)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156763776,plain,(quotient(z,x,zqx)),inference(rewrite,[status(thm)],[zQx]),[]).
%
% cnf(165794368,plain,(~less_equal(zqx,A)|~quotient(z,A,B)|less_equal(B,x)),inference(resolution,[status(thm)],[156856856,156763776]),[]).
%
% cnf(166560248,plain,(~less_equal(zqx,A)|less_equal(divide(z,A),x)),inference(resolution,[status(thm)],[165794368,156819352]),[]).
%
% fof(divisor_existence,plain,(~quotient(A,B,C)|less_equal(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156780504,plain,(~quotient(A,B,C)|less_equal(C,A)),inference(rewrite,[status(thm)],[divisor_existence]),[]).
%
% fof(x_divde_zero_is_x,plain,(quotient(A,zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-2.tptp',unknown),[]).
%
% cnf(156843976,plain,(quotient(A,zero,A)),inference(rewrite,[status(thm)],[x_divde_zero_is_x]),[]).
%
% cnf(165015824,plain,(less_equal(A,A)),inference(resolution,[status(thm)],[156780504,156843976]),[]).
%
% cnf(166588864,plain,(less_equal(divide(z,zqx),x)),inference(resolution,[status(thm)],[166560248,165015824]),[]).
%
% cnf(167940464,plain,(less_equal(divide(z,zqx),y)),inference(resolution,[status(thm)],[165578952,166588864]),[]).
%
% cnf(180386024,plain,(less_equal(zqy,zqx)),inference(resolution,[status(thm)],[166543688,167940464]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[156876296,180386024]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------