%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA012-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 11:24:04 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 21 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Orderings_Oorder__class_Oaxioms__1_0,plain,
! [A,B] :
( ~ class_orderings_oorder(A)
| c_lessequals(B,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144927968,plain,
( ~ class_orderings_oorder(A)
| c_lessequals(B,B,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__field_58,plain,
! [A] :
( ~ class_ring__and__field_oordered__field(A)
| class_orderings_oorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144977632,plain,
( ~ class_ring__and__field_oordered__field(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_58]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__field(t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144883960,plain,
class_ring__and__field_oordered__field(t_a),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(158090512,plain,
class_orderings_oorder(t_a),
inference(resolution,[status(thm)],[144977632,144883960]),
[] ).
cnf(158148720,plain,
c_lessequals(A,A,t_a),
inference(resolution,[status(thm)],[144927968,158090512]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__field_0,plain,
! [A] :
( ~ class_ring__and__field_oordered__field(A)
| class_ring__and__field_ofield(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144963576,plain,
( ~ class_ring__and__field_oordered__field(A)
| class_ring__and__field_ofield(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_0]),
[] ).
cnf(158072760,plain,
class_ring__and__field_ofield(t_a),
inference(resolution,[status(thm)],[144963576,144883960]),
[] ).
fof(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,plain,
! [A,B] :
( ~ class_ring__and__field_ofield(A)
| $equal(c_0,B)
| $equal(c_times(c_hol_oinverse(B,A),B,A),c_1) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144952816,plain,
( ~ class_ring__and__field_ofield(A)
| $equal(c_0,B)
| $equal(c_times(c_hol_oinverse(B,A),B,A),c_1) ),
inference(rewrite,[status(thm)],[cls_Ring__and__Field_Ofield__class_Oaxioms__1_0]),
[] ).
fof(cls_conjecture_1,plain,
! [A] : ~ c_lessequals(c_1,c_times(A,c_hol_oabs(v_c,t_a),t_a),t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144878816,plain,
~ c_lessequals(c_1,c_times(A,c_hol_oabs(v_c,t_a),t_a),t_a),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(159198024,plain,
$equal(c_0,c_hol_oabs(v_c,t_a)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158148720,158072760,144952816,144878816,theory(equality)]),
[] ).
fof(cls_OrderedGroup_Oabs__eq__0_0,plain,
! [A,B] :
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| ~ $equal(c_0,c_hol_oabs(B,A))
| $equal(c_0,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144914568,plain,
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| ~ $equal(c_0,c_hol_oabs(B,A))
| $equal(c_0,B) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__eq__0_0]),
[] ).
fof(cls_conjecture_0,plain,
~ $equal(c_0,v_c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144873568,plain,
~ $equal(c_0,v_c),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(158166704,plain,
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| ~ $equal(c_0,c_hol_oabs(v_c,A)) ),
inference(resolution,[status(thm)],[144914568,144873568]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__field_47,plain,
! [A] :
( ~ class_ring__and__field_oordered__field(A)
| class_orderedgroup_olordered__ab__group__abs(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),
[] ).
cnf(144968536,plain,
( ~ class_ring__and__field_oordered__field(A)
| class_orderedgroup_olordered__ab__group__abs(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_47]),
[] ).
cnf(158081640,plain,
class_orderedgroup_olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[144968536,144883960]),
[] ).
cnf(158183952,plain,
~ $equal(c_0,c_hol_oabs(v_c,t_a)),
inference(resolution,[status(thm)],[158166704,158081640]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[159198024,158183952]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Orderings_Oorder__class_Oaxioms__1_0,plain,(~class_orderings_oorder(A)|c_lessequals(B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144927968,plain,(~class_orderings_oorder(A)|c_lessequals(B,B,A)),inference(rewrite,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__field_58,plain,(~class_ring__and__field_oordered__field(A)|class_orderings_oorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144977632,plain,(~class_ring__and__field_oordered__field(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_58]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__field(t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144883960,plain,(class_ring__and__field_oordered__field(t_a)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(158090512,plain,(class_orderings_oorder(t_a)),inference(resolution,[status(thm)],[144977632,144883960]),[]).
%
% cnf(158148720,plain,(c_lessequals(A,A,t_a)),inference(resolution,[status(thm)],[144927968,158090512]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__field_0,plain,(~class_ring__and__field_oordered__field(A)|class_ring__and__field_ofield(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144963576,plain,(~class_ring__and__field_oordered__field(A)|class_ring__and__field_ofield(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_0]),[]).
%
% cnf(158072760,plain,(class_ring__and__field_ofield(t_a)),inference(resolution,[status(thm)],[144963576,144883960]),[]).
%
% fof(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,plain,(~class_ring__and__field_ofield(A)|$equal(c_0,B)|$equal(c_times(c_hol_oinverse(B,A),B,A),c_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144952816,plain,(~class_ring__and__field_ofield(A)|$equal(c_0,B)|$equal(c_times(c_hol_oinverse(B,A),B,A),c_1)),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Ofield__class_Oaxioms__1_0]),[]).
%
% fof(cls_conjecture_1,plain,(~c_lessequals(c_1,c_times(A,c_hol_oabs(v_c,t_a),t_a),t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144878816,plain,(~c_lessequals(c_1,c_times(A,c_hol_oabs(v_c,t_a),t_a),t_a)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(159198024,plain,($equal(c_0,c_hol_oabs(v_c,t_a))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158148720,158072760,144952816,144878816,theory(equality)]),[]).
%
% fof(cls_OrderedGroup_Oabs__eq__0_0,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|~$equal(c_0,c_hol_oabs(B,A))|$equal(c_0,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144914568,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|~$equal(c_0,c_hol_oabs(B,A))|$equal(c_0,B)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__eq__0_0]),[]).
%
% fof(cls_conjecture_0,plain,(~$equal(c_0,v_c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144873568,plain,(~$equal(c_0,v_c)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(158166704,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|~$equal(c_0,c_hol_oabs(v_c,A))),inference(resolution,[status(thm)],[144914568,144873568]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__field_47,plain,(~class_ring__and__field_oordered__field(A)|class_orderedgroup_olordered__ab__group__abs(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA012-2.tptp',unknown),[]).
%
% cnf(144968536,plain,(~class_ring__and__field_oordered__field(A)|class_orderedgroup_olordered__ab__group__abs(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_47]),[]).
%
% cnf(158081640,plain,(class_orderedgroup_olordered__ab__group__abs(t_a)),inference(resolution,[status(thm)],[144968536,144883960]),[]).
%
% cnf(158183952,plain,(~$equal(c_0,c_hol_oabs(v_c,t_a))),inference(resolution,[status(thm)],[158166704,158081640]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[159198024,158183952]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------