TSTP Solution File: ANA020-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA020-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 11:24:25 EDT 2009
% Result : Unsatisfiable 92.8s
% Output : Refutation 92.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/ANA020-2.tptp',unknown),
[] ).
cnf(147920736,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/ANA020-2.tptp',unknown),
[] ).
cnf(147992384,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]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147889056,plain,
class_ring__and__field_oordered__idom(t_a),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(166414952,plain,
class_orderedgroup_olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[147992384,147889056]),
[] ).
cnf(166501016,plain,
c_lessequals(c_0,c_hol_oabs(A,t_a),t_a),
inference(resolution,[status(thm)],[147920736,166414952]),
[] ).
fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0,plain,
! [A,B,C] :
( ~ class_ring__and__field_opordered__cancel__semiring(A)
| ~ c_lessequals(c_0,B,A)
| ~ c_lessequals(c_0,C,A)
| c_lessequals(c_0,c_times(C,B,A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147971560,plain,
( ~ class_ring__and__field_opordered__cancel__semiring(A)
| ~ c_lessequals(c_0,B,A)
| ~ c_lessequals(c_0,C,A)
| c_lessequals(c_0,c_times(C,B,A),A) ),
inference(rewrite,[status(thm)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_40,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_ring__and__field_opordered__cancel__semiring(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147982384,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_ring__and__field_opordered__cancel__semiring(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_40]),
[] ).
cnf(166397008,plain,
class_ring__and__field_opordered__cancel__semiring(t_a),
inference(resolution,[status(thm)],[147982384,147889056]),
[] ).
cnf(166443136,plain,
( ~ c_lessequals(c_0,A,t_a)
| ~ c_lessequals(c_0,B,t_a)
| c_lessequals(c_0,c_times(B,A,t_a),t_a) ),
inference(resolution,[status(thm)],[147971560,166397008]),
[] ).
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/ANA020-2.tptp',unknown),
[] ).
cnf(147942320,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]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_44,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_oorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147987392,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]),
[] ).
cnf(166405984,plain,
class_orderings_oorder(t_a),
inference(resolution,[status(thm)],[147987392,147889056]),
[] ).
cnf(166465216,plain,
( ~ c_less(A,B,t_a)
| c_lessequals(A,B,t_a) ),
inference(resolution,[status(thm)],[147942320,166405984]),
[] ).
fof(cls_conjecture_1,plain,
c_less(c_0,v_c,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147870584,plain,
c_less(c_0,v_c,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(166509144,plain,
c_lessequals(c_0,v_c,t_a),
inference(resolution,[status(thm)],[166465216,147870584]),
[] ).
cnf(166563960,plain,
( ~ c_lessequals(c_0,A,t_a)
| c_lessequals(c_0,c_times(v_c,A,t_a),t_a) ),
inference(resolution,[status(thm)],[166443136,166509144]),
[] ).
cnf(172631624,plain,
c_lessequals(c_0,c_times(v_c,c_hol_oabs(A,t_a),t_a),t_a),
inference(resolution,[status(thm)],[166501016,166563960]),
[] ).
fof(cls_conjecture_4,plain,
~ c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147879816,plain,
~ c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
fof(cls_OrderedGroup_Oabs__eq__0_1,plain,
! [A] :
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| $equal(c_hol_oabs(c_0,A),c_0) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147899952,plain,
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| $equal(c_hol_oabs(c_0,A),c_0) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__eq__0_1]),
[] ).
cnf(166480840,plain,
$equal(c_hol_oabs(c_0,t_a),c_0),
inference(resolution,[status(thm)],[147899952,166414952]),
[] ).
fof(cls_conjecture_3,plain,
$equal(c_0,v_x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147874984,plain,
$equal(c_0,v_x),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(167001592,plain,
$equal(c_hol_oabs(c_0,t_a),v_x),
inference(paramodulation,[status(thm)],[166480840,147874984,theory(equality)]),
[] ).
cnf(167167312,plain,
$equal(v_x,c_0),
inference(paramodulation,[status(thm)],[167001592,166480840,theory(equality)]),
[] ).
fof(cls_conjecture_0,plain,
$equal(v_f(c_0),c_0),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),
[] ).
cnf(147865392,plain,
$equal(v_f(c_0),c_0),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(167208032,plain,
$equal(v_f(v_x),c_0),
inference(paramodulation,[status(thm)],[167167312,147865392,theory(equality)]),
[] ).
cnf(167335512,plain,
$equal(c_hol_oabs(v_f(v_x),t_a),c_0),
inference(paramodulation,[status(thm)],[167208032,166480840,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[172631624,147879816,167335512,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 92 seconds
% START OF PROOF SEQUENCE
% 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/ANA020-2.tptp',unknown),[]).
%
% cnf(147920736,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/ANA020-2.tptp',unknown),[]).
%
% cnf(147992384,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]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147889056,plain,(class_ring__and__field_oordered__idom(t_a)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(166414952,plain,(class_orderedgroup_olordered__ab__group__abs(t_a)),inference(resolution,[status(thm)],[147992384,147889056]),[]).
%
% cnf(166501016,plain,(c_lessequals(c_0,c_hol_oabs(A,t_a),t_a)),inference(resolution,[status(thm)],[147920736,166414952]),[]).
%
% fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0,plain,(~class_ring__and__field_opordered__cancel__semiring(A)|~c_lessequals(c_0,B,A)|~c_lessequals(c_0,C,A)|c_lessequals(c_0,c_times(C,B,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147971560,plain,(~class_ring__and__field_opordered__cancel__semiring(A)|~c_lessequals(c_0,B,A)|~c_lessequals(c_0,C,A)|c_lessequals(c_0,c_times(C,B,A),A)),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_40,plain,(~class_ring__and__field_oordered__idom(A)|class_ring__and__field_opordered__cancel__semiring(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147982384,plain,(~class_ring__and__field_oordered__idom(A)|class_ring__and__field_opordered__cancel__semiring(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_40]),[]).
%
% cnf(166397008,plain,(class_ring__and__field_opordered__cancel__semiring(t_a)),inference(resolution,[status(thm)],[147982384,147889056]),[]).
%
% cnf(166443136,plain,(~c_lessequals(c_0,A,t_a)|~c_lessequals(c_0,B,t_a)|c_lessequals(c_0,c_times(B,A,t_a),t_a)),inference(resolution,[status(thm)],[147971560,166397008]),[]).
%
% 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/ANA020-2.tptp',unknown),[]).
%
% cnf(147942320,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]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_44,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_oorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147987392,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]),[]).
%
% cnf(166405984,plain,(class_orderings_oorder(t_a)),inference(resolution,[status(thm)],[147987392,147889056]),[]).
%
% cnf(166465216,plain,(~c_less(A,B,t_a)|c_lessequals(A,B,t_a)),inference(resolution,[status(thm)],[147942320,166405984]),[]).
%
% fof(cls_conjecture_1,plain,(c_less(c_0,v_c,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147870584,plain,(c_less(c_0,v_c,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(166509144,plain,(c_lessequals(c_0,v_c,t_a)),inference(resolution,[status(thm)],[166465216,147870584]),[]).
%
% cnf(166563960,plain,(~c_lessequals(c_0,A,t_a)|c_lessequals(c_0,c_times(v_c,A,t_a),t_a)),inference(resolution,[status(thm)],[166443136,166509144]),[]).
%
% cnf(172631624,plain,(c_lessequals(c_0,c_times(v_c,c_hol_oabs(A,t_a),t_a),t_a)),inference(resolution,[status(thm)],[166501016,166563960]),[]).
%
% fof(cls_conjecture_4,plain,(~c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147879816,plain,(~c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a)),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% fof(cls_OrderedGroup_Oabs__eq__0_1,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|$equal(c_hol_oabs(c_0,A),c_0)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147899952,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|$equal(c_hol_oabs(c_0,A),c_0)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__eq__0_1]),[]).
%
% cnf(166480840,plain,($equal(c_hol_oabs(c_0,t_a),c_0)),inference(resolution,[status(thm)],[147899952,166414952]),[]).
%
% fof(cls_conjecture_3,plain,($equal(c_0,v_x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147874984,plain,($equal(c_0,v_x)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(167001592,plain,($equal(c_hol_oabs(c_0,t_a),v_x)),inference(paramodulation,[status(thm)],[166480840,147874984,theory(equality)]),[]).
%
% cnf(167167312,plain,($equal(v_x,c_0)),inference(paramodulation,[status(thm)],[167001592,166480840,theory(equality)]),[]).
%
% fof(cls_conjecture_0,plain,($equal(v_f(c_0),c_0)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA020-2.tptp',unknown),[]).
%
% cnf(147865392,plain,($equal(v_f(c_0),c_0)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(167208032,plain,($equal(v_f(v_x),c_0)),inference(paramodulation,[status(thm)],[167167312,147865392,theory(equality)]),[]).
%
% cnf(167335512,plain,($equal(c_hol_oabs(v_f(v_x),t_a),c_0)),inference(paramodulation,[status(thm)],[167208032,166480840,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[172631624,147879816,167335512,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------