TSTP Solution File: ANA009-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA009-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 11:24:00 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_Ring__and__Field_Oordered__idom_37,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_opordered__ab__semigroup__add__imp__le(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156444184,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_opordered__ab__semigroup__add__imp__le(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_37]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156462176,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(169537160,plain,
class_orderedgroup_opordered__ab__semigroup__add__imp__le(t_b),
inference(resolution,[status(thm)],[156444184,156462176]),
[] ).
fof(cls_OrderedGroup_Oadd__le__cancel__right_1,plain,
! [A,B,C,D] :
( ~ class_orderedgroup_opordered__ab__semigroup__add__imp__le(A)
| ~ c_lessequals(B,C,A)
| c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156399968,plain,
( ~ class_orderedgroup_opordered__ab__semigroup__add__imp__le(A)
| ~ c_lessequals(B,C,A)
| c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_1]),
[] ).
fof(cls_conjecture_0,plain,
! [A] : c_lessequals(v_lb(A),v_f(A),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156432424,plain,
c_lessequals(v_lb(A),v_f(A),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(169631408,plain,
c_lessequals(c_plus(v_lb(B),A,t_b),c_plus(v_f(B),A,t_b),t_b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169537160,156399968,156432424]),
[] ).
fof(cls_OrderedGroup_Oright__minus_0,plain,
! [A,B] :
( ~ class_orderedgroup_oab__group__add(A)
| $equal(c_plus(B,c_uminus(B,A),A),c_0) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156423216,plain,
( ~ class_orderedgroup_oab__group__add(A)
| $equal(c_plus(B,c_uminus(B,A),A),c_0) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Oright__minus_0]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_4,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_oab__group__add(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156453264,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_oab__group__add(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]),
[] ).
cnf(169546008,plain,
class_orderedgroup_oab__group__add(t_b),
inference(resolution,[status(thm)],[156453264,156462176]),
[] ).
cnf(169605032,plain,
$equal(c_plus(A,c_uminus(A,t_b),t_b),c_0),
inference(resolution,[status(thm)],[156423216,169546008]),
[] ).
cnf(169979616,plain,
c_lessequals(c_0,c_plus(v_f(A),c_uminus(v_lb(A),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[169631408,169605032,theory(equality)]),
[] ).
fof(cls_conjecture_2,plain,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),
[] ).
cnf(156437664,plain,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[169979616,156437664]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_Ring__and__Field_Oordered__idom_37,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_opordered__ab__semigroup__add__imp__le(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156444184,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_opordered__ab__semigroup__add__imp__le(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_37]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156462176,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(169537160,plain,(class_orderedgroup_opordered__ab__semigroup__add__imp__le(t_b)),inference(resolution,[status(thm)],[156444184,156462176]),[]).
%
% fof(cls_OrderedGroup_Oadd__le__cancel__right_1,plain,(~class_orderedgroup_opordered__ab__semigroup__add__imp__le(A)|~c_lessequals(B,C,A)|c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156399968,plain,(~class_orderedgroup_opordered__ab__semigroup__add__imp__le(A)|~c_lessequals(B,C,A)|c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_1]),[]).
%
% fof(cls_conjecture_0,plain,(c_lessequals(v_lb(A),v_f(A),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156432424,plain,(c_lessequals(v_lb(A),v_f(A),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(169631408,plain,(c_lessequals(c_plus(v_lb(B),A,t_b),c_plus(v_f(B),A,t_b),t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169537160,156399968,156432424]),[]).
%
% fof(cls_OrderedGroup_Oright__minus_0,plain,(~class_orderedgroup_oab__group__add(A)|$equal(c_plus(B,c_uminus(B,A),A),c_0)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156423216,plain,(~class_orderedgroup_oab__group__add(A)|$equal(c_plus(B,c_uminus(B,A),A),c_0)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oright__minus_0]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_4,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_oab__group__add(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156453264,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_oab__group__add(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]),[]).
%
% cnf(169546008,plain,(class_orderedgroup_oab__group__add(t_b)),inference(resolution,[status(thm)],[156453264,156462176]),[]).
%
% cnf(169605032,plain,($equal(c_plus(A,c_uminus(A,t_b),t_b),c_0)),inference(resolution,[status(thm)],[156423216,169546008]),[]).
%
% cnf(169979616,plain,(c_lessequals(c_0,c_plus(v_f(A),c_uminus(v_lb(A),t_b),t_b),t_b)),inference(paramodulation,[status(thm)],[169631408,169605032,theory(equality)]),[]).
%
% fof(cls_conjecture_2,plain,(~c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA009-2.tptp',unknown),[]).
%
% cnf(156437664,plain,(~c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[169979616,156437664]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------