%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SWV255-2 : TPTP v3.4.2. Released v3.2.0.
% 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 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 16:28:50 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 27 ( 7 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_1,plain,
! [A] :
( ~ c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)
| ~ c_lessequals(v_x,A,tc_nat) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),
[] ).
cnf(162753192,plain,
( ~ c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)
| ~ c_lessequals(v_x,A,tc_nat) ),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
fof(cls_Nat_Oadd__leE_0,plain,
! [A,B,C] :
( ~ c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)
| c_lessequals(B,C,tc_nat) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),
[] ).
cnf(162784088,plain,
( ~ c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)
| c_lessequals(B,C,tc_nat) ),
inference(rewrite,[status(thm)],[cls_Nat_Oadd__leE_0]),
[] ).
fof(cls_conjecture_0,plain,
! [A] : c_lessequals(A,v_xb(A),tc_nat),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),
[] ).
cnf(162746352,plain,
c_lessequals(A,v_xb(A),tc_nat),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(178512320,plain,
c_lessequals(B,v_xb(c_plus(A,B,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[162784088,162746352]),
[] ).
cnf(178669128,plain,
~ c_in(c_message_omsg_ononce(v_xb(c_plus(A,v_x,tc_nat))),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg),
inference(resolution,[status(thm)],[162753192,178512320]),
[] ).
fof(cls_conjecture_3,plain,
! [A] :
( c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)
| c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),
[] ).
cnf(162770128,plain,
( c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)
| c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(179798016,plain,
c_in(c_message_omsg_ononce(v_xb(c_plus(A,v_x,tc_nat))),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg),
inference(resolution,[status(thm)],[178669128,162770128]),
[] ).
fof(cls_conjecture_2,plain,
! [A] :
( ~ c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)
| ~ c_lessequals(v_xa,A,tc_nat) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),
[] ).
cnf(162763480,plain,
( ~ c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)
| ~ c_lessequals(v_xa,A,tc_nat) ),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(183825296,plain,
~ c_lessequals(v_xa,v_xb(c_plus(A,v_x,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[179798016,162763480]),
[] ).
fof(cls_Nat_Oadd__leE_1,plain,
! [A,B,C] :
( ~ c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)
| c_lessequals(A,C,tc_nat) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),
[] ).
cnf(162788600,plain,
( ~ c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)
| c_lessequals(A,C,tc_nat) ),
inference(rewrite,[status(thm)],[cls_Nat_Oadd__leE_1]),
[] ).
cnf(178526896,plain,
c_lessequals(A,v_xb(c_plus(A,B,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[162788600,162746352]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[183825296,178526896]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_1,plain,(~c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)|~c_lessequals(v_x,A,tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),[]).
%
% cnf(162753192,plain,(~c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)|~c_lessequals(v_x,A,tc_nat)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Nat_Oadd__leE_0,plain,(~c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)|c_lessequals(B,C,tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),[]).
%
% cnf(162784088,plain,(~c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)|c_lessequals(B,C,tc_nat)),inference(rewrite,[status(thm)],[cls_Nat_Oadd__leE_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_lessequals(A,v_xb(A),tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),[]).
%
% cnf(162746352,plain,(c_lessequals(A,v_xb(A),tc_nat)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(178512320,plain,(c_lessequals(B,v_xb(c_plus(A,B,tc_nat)),tc_nat)),inference(resolution,[status(thm)],[162784088,162746352]),[]).
%
% cnf(178669128,plain,(~c_in(c_message_omsg_ononce(v_xb(c_plus(A,v_x,tc_nat))),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)),inference(resolution,[status(thm)],[162753192,178512320]),[]).
%
% fof(cls_conjecture_3,plain,(c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)|c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),[]).
%
% cnf(162770128,plain,(c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)|c_in(c_message_omsg_ononce(v_xb(A)),c_message_oparts(c_insert(v_msg1,c_emptyset,tc_message_omsg)),tc_message_omsg)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(179798016,plain,(c_in(c_message_omsg_ononce(v_xb(c_plus(A,v_x,tc_nat))),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)),inference(resolution,[status(thm)],[178669128,162770128]),[]).
%
% fof(cls_conjecture_2,plain,(~c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)|~c_lessequals(v_xa,A,tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),[]).
%
% cnf(162763480,plain,(~c_in(c_message_omsg_ononce(A),c_message_oparts(c_insert(v_msg2,c_emptyset,tc_message_omsg)),tc_message_omsg)|~c_lessequals(v_xa,A,tc_nat)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(183825296,plain,(~c_lessequals(v_xa,v_xb(c_plus(A,v_x,tc_nat)),tc_nat)),inference(resolution,[status(thm)],[179798016,162763480]),[]).
%
% fof(cls_Nat_Oadd__leE_1,plain,(~c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)|c_lessequals(A,C,tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV255-2.tptp',unknown),[]).
%
% cnf(162788600,plain,(~c_lessequals(c_plus(A,B,tc_nat),C,tc_nat)|c_lessequals(A,C,tc_nat)),inference(rewrite,[status(thm)],[cls_Nat_Oadd__leE_1]),[]).
%
% cnf(178526896,plain,(c_lessequals(A,v_xb(c_plus(A,B,tc_nat)),tc_nat)),inference(resolution,[status(thm)],[162788600,162746352]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[183825296,178526896]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------