TSTP Solution File: ANA029-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA029-2 : TPTP v3.4.2. Released v3.2.0.
% 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 11:24:40 EDT 2009
% Result : Unsatisfiable 3.5s
% Output : Refutation 3.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 38 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_OrderedGroup_Opordered__ab__group__add_10,plain,
! [A] :
( ~ class_orderedgroup_opordered__ab__group__add(A)
| class_orderings_oorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150912856,plain,
( ~ class_orderedgroup_opordered__ab__group__add(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_OrderedGroup_Opordered__ab__group__add_10]),
[] ).
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/ANA029-2.tptp',unknown),
[] ).
cnf(150929776,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/ANA029-2.tptp',unknown),
[] ).
cnf(150785968,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(164071376,plain,
class_orderedgroup_opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[150929776,150785968]),
[] ).
cnf(164147656,plain,
class_orderings_oorder(t_b),
inference(resolution,[status(thm)],[150912856,164071376]),
[] ).
fof(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,plain,
! [A,B,C,D] :
( ~ class_orderings_olinorder(A)
| ~ c_lessequals(B,C,A)
| ~ c_lessequals(D,C,A)
| c_lessequals(c_orderings_omax(D,B,A),C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150882624,plain,
( ~ class_orderings_olinorder(A)
| ~ c_lessequals(B,C,A)
| ~ c_lessequals(D,C,A)
| c_lessequals(c_orderings_omax(D,B,A),C,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]),
[] ).
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/ANA029-2.tptp',unknown),
[] ).
cnf(150919552,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_olinorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]),
[] ).
cnf(164057312,plain,
class_orderings_olinorder(t_b),
inference(resolution,[status(thm)],[150919552,150785968]),
[] ).
cnf(164122352,plain,
( ~ c_lessequals(A,B,t_b)
| ~ c_lessequals(C,B,t_b)
| c_lessequals(c_orderings_omax(C,A,t_b),B,t_b) ),
inference(resolution,[status(thm)],[150882624,164057312]),
[] ).
fof(cls_Orderings_Oorder__less__imp__le_0,plain,
! [A,B,C] :
( ~ class_orderings_oorder(A)
| ~ c_less(B,C,A)
| c_lessequals(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150903776,plain,
( ~ class_orderings_oorder(A)
| ~ c_less(B,C,A)
| c_lessequals(B,C,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]),
[] ).
cnf(170103312,plain,
( ~ c_lessequals(A,B,t_b)
| c_lessequals(c_orderings_omax(C,A,t_b),B,t_b)
| ~ c_less(C,B,t_b) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164147656,164122352,150903776]),
[] ).
fof(cls_Orderings_Olinorder__not__le_0,plain,
! [A,B,C] :
( ~ class_orderings_olinorder(A)
| c_less(B,C,A)
| c_lessequals(C,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150859088,plain,
( ~ class_orderings_olinorder(A)
| c_less(B,C,A)
| c_lessequals(C,B,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Olinorder__not__le_0]),
[] ).
fof(cls_conjecture_2,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150772400,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(164468896,plain,
c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164057312,150859088,150772400]),
[] ).
cnf(170528024,plain,
( ~ c_lessequals(A,c_0,t_b)
| c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),A,t_b),c_0,t_b) ),
inference(resolution,[status(thm)],[170103312,164468896]),
[] ).
cnf(164095008,plain,
( c_less(A,B,t_b)
| c_lessequals(B,A,t_b) ),
inference(resolution,[status(thm)],[150859088,164057312]),
[] ).
cnf(164599104,plain,
( c_lessequals(A,B,t_b)
| c_lessequals(B,A,t_b) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164147656,150903776,164095008]),
[] ).
cnf(171376920,plain,
c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b),
inference(resolution,[status(thm)],[170528024,164599104]),
[] ).
fof(cls_conjecture_3,plain,
~ c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_hol_oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150777352,plain,
~ c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_hol_oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
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/ANA029-2.tptp',unknown),
[] ).
cnf(150892936,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(cls_OrderedGroup_Oabs__ge__zero_0,plain,
! [A,B] :
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| c_lessequals(c_0,c_hol_oabs(B,A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150804344,plain,
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| c_lessequals(c_0,c_hol_oabs(B,A),A) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_50,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_olordered__ab__group__abs(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),
[] ).
cnf(150769840,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_olordered__ab__group__abs(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]),
[] ).
cnf(164066288,plain,
class_orderedgroup_olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[150769840,150785968]),
[] ).
cnf(164138768,plain,
c_lessequals(c_0,c_hol_oabs(A,t_b),t_b),
inference(resolution,[status(thm)],[150804344,164066288]),
[] ).
cnf(164248128,plain,
( ~ c_lessequals(A,c_0,t_b)
| c_lessequals(A,c_hol_oabs(B,t_b),t_b) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164147656,150892936,164138768]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[171376920,150777352,164248128]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_OrderedGroup_Opordered__ab__group__add_10,plain,(~class_orderedgroup_opordered__ab__group__add(A)|class_orderings_oorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150912856,plain,(~class_orderedgroup_opordered__ab__group__add(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_OrderedGroup_Opordered__ab__group__add_10]),[]).
%
% 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/ANA029-2.tptp',unknown),[]).
%
% cnf(150929776,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/ANA029-2.tptp',unknown),[]).
%
% cnf(150785968,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(164071376,plain,(class_orderedgroup_opordered__ab__group__add(t_b)),inference(resolution,[status(thm)],[150929776,150785968]),[]).
%
% cnf(164147656,plain,(class_orderings_oorder(t_b)),inference(resolution,[status(thm)],[150912856,164071376]),[]).
%
% fof(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,plain,(~class_orderings_olinorder(A)|~c_lessequals(B,C,A)|~c_lessequals(D,C,A)|c_lessequals(c_orderings_omax(D,B,A),C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150882624,plain,(~class_orderings_olinorder(A)|~c_lessequals(B,C,A)|~c_lessequals(D,C,A)|c_lessequals(c_orderings_omax(D,B,A),C,A)),inference(rewrite,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]),[]).
%
% 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/ANA029-2.tptp',unknown),[]).
%
% cnf(150919552,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_olinorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]),[]).
%
% cnf(164057312,plain,(class_orderings_olinorder(t_b)),inference(resolution,[status(thm)],[150919552,150785968]),[]).
%
% cnf(164122352,plain,(~c_lessequals(A,B,t_b)|~c_lessequals(C,B,t_b)|c_lessequals(c_orderings_omax(C,A,t_b),B,t_b)),inference(resolution,[status(thm)],[150882624,164057312]),[]).
%
% fof(cls_Orderings_Oorder__less__imp__le_0,plain,(~class_orderings_oorder(A)|~c_less(B,C,A)|c_lessequals(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150903776,plain,(~class_orderings_oorder(A)|~c_less(B,C,A)|c_lessequals(B,C,A)),inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]),[]).
%
% cnf(170103312,plain,(~c_lessequals(A,B,t_b)|c_lessequals(c_orderings_omax(C,A,t_b),B,t_b)|~c_less(C,B,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164147656,164122352,150903776]),[]).
%
% fof(cls_Orderings_Olinorder__not__le_0,plain,(~class_orderings_olinorder(A)|c_less(B,C,A)|c_lessequals(C,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150859088,plain,(~class_orderings_olinorder(A)|c_less(B,C,A)|c_lessequals(C,B,A)),inference(rewrite,[status(thm)],[cls_Orderings_Olinorder__not__le_0]),[]).
%
% fof(cls_conjecture_2,plain,(~c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150772400,plain,(~c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(164468896,plain,(c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164057312,150859088,150772400]),[]).
%
% cnf(170528024,plain,(~c_lessequals(A,c_0,t_b)|c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),A,t_b),c_0,t_b)),inference(resolution,[status(thm)],[170103312,164468896]),[]).
%
% cnf(164095008,plain,(c_less(A,B,t_b)|c_lessequals(B,A,t_b)),inference(resolution,[status(thm)],[150859088,164057312]),[]).
%
% cnf(164599104,plain,(c_lessequals(A,B,t_b)|c_lessequals(B,A,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164147656,150903776,164095008]),[]).
%
% cnf(171376920,plain,(c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b)),inference(resolution,[status(thm)],[170528024,164599104]),[]).
%
% fof(cls_conjecture_3,plain,(~c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_hol_oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150777352,plain,(~c_lessequals(c_orderings_omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_hol_oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% 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/ANA029-2.tptp',unknown),[]).
%
% cnf(150892936,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(cls_OrderedGroup_Oabs__ge__zero_0,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|c_lessequals(c_0,c_hol_oabs(B,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150804344,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|c_lessequals(c_0,c_hol_oabs(B,A),A)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_50,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_olordered__ab__group__abs(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA029-2.tptp',unknown),[]).
%
% cnf(150769840,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_olordered__ab__group__abs(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]),[]).
%
% cnf(164066288,plain,(class_orderedgroup_olordered__ab__group__abs(t_b)),inference(resolution,[status(thm)],[150769840,150785968]),[]).
%
% cnf(164138768,plain,(c_lessequals(c_0,c_hol_oabs(A,t_b),t_b)),inference(resolution,[status(thm)],[150804344,164066288]),[]).
%
% cnf(164248128,plain,(~c_lessequals(A,c_0,t_b)|c_lessequals(A,c_hol_oabs(B,t_b),t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164147656,150892936,164138768]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171376920,150777352,164248128]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------