%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA023-2 : 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 11:24:30 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_Ring__and__Field_Oordered__idom_54,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_opordered__ab__group__add(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144106816,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_opordered__ab__group__add(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144111808,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(159895800,plain,
class_orderedgroup_opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[144106816,144111808]),
[] ).
fof(cls_OrderedGroup_Ocompare__rls__9_0,plain,
! [A,B,C,D] :
( ~ class_orderedgroup_opordered__ab__group__add(A)
| ~ c_lessequals(B,c_minus(C,D,A),A)
| c_lessequals(c_plus(B,D,A),C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144029344,plain,
( ~ class_orderedgroup_opordered__ab__group__add(A)
| ~ c_lessequals(B,c_minus(C,D,A),A)
| c_lessequals(c_plus(B,D,A),C,A) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_0]),
[] ).
fof(cls_conjecture_1,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144065976,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(160446888,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159895800,144029344,144065976]),
[] ).
fof(cls_Orderings_Oorder__class_Oorder__trans_0,plain,
! [A,B,C,D] :
( ~ class_orderings_oorder(A)
| ~ c_lessequals(B,C,A)
| ~ c_lessequals(D,B,A)
| c_lessequals(D,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144060896,plain,
( ~ class_orderings_oorder(A)
| ~ c_lessequals(B,C,A)
| ~ c_lessequals(D,B,A)
| c_lessequals(D,C,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]),
[] ).
fof(clsrel_Orderings_Olinorder_4,plain,
! [A] :
( ~ class_orderings_olinorder(A)
| class_orderings_oorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144085840,plain,
( ~ class_orderings_olinorder(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Orderings_Olinorder_4]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_33,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_olinorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144101856,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_olinorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]),
[] ).
cnf(159886864,plain,
class_orderings_olinorder(t_b),
inference(resolution,[status(thm)],[144101856,144111808]),
[] ).
cnf(159925400,plain,
class_orderings_oorder(t_b),
inference(resolution,[status(thm)],[144085840,159886864]),
[] ).
cnf(159989400,plain,
( ~ c_lessequals(A,B,t_b)
| ~ c_lessequals(C,A,t_b)
| c_lessequals(C,B,t_b) ),
inference(resolution,[status(thm)],[144060896,159925400]),
[] ).
fof(cls_conjecture_2,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144074520,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(160013336,plain,
( ~ c_lessequals(A,v_k(v_x),t_b)
| c_lessequals(A,v_f(v_x),t_b) ),
inference(resolution,[status(thm)],[159989400,144074520]),
[] ).
cnf(160741520,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),
inference(resolution,[status(thm)],[160446888,160013336]),
[] ).
fof(cls_OrderedGroup_Ocompare__rls__9_1,plain,
! [A,B,C,D] :
( ~ class_orderedgroup_opordered__ab__group__add(A)
| ~ c_lessequals(c_plus(B,C,A),D,A)
| c_lessequals(B,c_minus(D,C,A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144044128,plain,
( ~ class_orderedgroup_opordered__ab__group__add(A)
| ~ c_lessequals(c_plus(B,C,A),D,A)
| c_lessequals(B,c_minus(D,C,A),A) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_1]),
[] ).
fof(cls_conjecture_3,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),
[] ).
cnf(144079272,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[160741520,159895800,144044128,144079272]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_Ring__and__Field_Oordered__idom_54,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_opordered__ab__group__add(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144106816,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_opordered__ab__group__add(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144111808,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(159895800,plain,(class_orderedgroup_opordered__ab__group__add(t_b)),inference(resolution,[status(thm)],[144106816,144111808]),[]).
%
% fof(cls_OrderedGroup_Ocompare__rls__9_0,plain,(~class_orderedgroup_opordered__ab__group__add(A)|~c_lessequals(B,c_minus(C,D,A),A)|c_lessequals(c_plus(B,D,A),C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144029344,plain,(~class_orderedgroup_opordered__ab__group__add(A)|~c_lessequals(B,c_minus(C,D,A),A)|c_lessequals(c_plus(B,D,A),C,A)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_0]),[]).
%
% fof(cls_conjecture_1,plain,(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144065976,plain,(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(160446888,plain,(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159895800,144029344,144065976]),[]).
%
% fof(cls_Orderings_Oorder__class_Oorder__trans_0,plain,(~class_orderings_oorder(A)|~c_lessequals(B,C,A)|~c_lessequals(D,B,A)|c_lessequals(D,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144060896,plain,(~class_orderings_oorder(A)|~c_lessequals(B,C,A)|~c_lessequals(D,B,A)|c_lessequals(D,C,A)),inference(rewrite,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]),[]).
%
% fof(clsrel_Orderings_Olinorder_4,plain,(~class_orderings_olinorder(A)|class_orderings_oorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144085840,plain,(~class_orderings_olinorder(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_Orderings_Olinorder_4]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_33,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_olinorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144101856,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_olinorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]),[]).
%
% cnf(159886864,plain,(class_orderings_olinorder(t_b)),inference(resolution,[status(thm)],[144101856,144111808]),[]).
%
% cnf(159925400,plain,(class_orderings_oorder(t_b)),inference(resolution,[status(thm)],[144085840,159886864]),[]).
%
% cnf(159989400,plain,(~c_lessequals(A,B,t_b)|~c_lessequals(C,A,t_b)|c_lessequals(C,B,t_b)),inference(resolution,[status(thm)],[144060896,159925400]),[]).
%
% fof(cls_conjecture_2,plain,(c_lessequals(v_k(v_x),v_f(v_x),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144074520,plain,(c_lessequals(v_k(v_x),v_f(v_x),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(160013336,plain,(~c_lessequals(A,v_k(v_x),t_b)|c_lessequals(A,v_f(v_x),t_b)),inference(resolution,[status(thm)],[159989400,144074520]),[]).
%
% cnf(160741520,plain,(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)),inference(resolution,[status(thm)],[160446888,160013336]),[]).
%
% fof(cls_OrderedGroup_Ocompare__rls__9_1,plain,(~class_orderedgroup_opordered__ab__group__add(A)|~c_lessequals(c_plus(B,C,A),D,A)|c_lessequals(B,c_minus(D,C,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144044128,plain,(~class_orderedgroup_opordered__ab__group__add(A)|~c_lessequals(c_plus(B,C,A),D,A)|c_lessequals(B,c_minus(D,C,A),A)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_1]),[]).
%
% fof(cls_conjecture_3,plain,(~c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA023-2.tptp',unknown),[]).
%
% cnf(144079272,plain,(~c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[160741520,159895800,144044128,144079272]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------