TSTP Solution File: ANA016-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA016-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 11:24:17 EDT 2009
% Result : Unsatisfiable 0.4s
% Output : Refutation 0.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_Ring__and__Field_Ofield_21,plain,
! [A] :
( ~ class_ring__and__field_ofield(A)
| class_orderedgroup_osemigroup__mult(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154230680,plain,
( ~ class_ring__and__field_ofield(A)
| class_orderedgroup_osemigroup__mult(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Ofield_21]),
[] ).
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/ANA016-2.tptp',unknown),
[] ).
cnf(154237280,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]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__field(t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154120504,plain,
class_ring__and__field_oordered__field(t_a),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(167324608,plain,
class_ring__and__field_ofield(t_a),
inference(resolution,[status(thm)],[154237280,154120504]),
[] ).
cnf(167342424,plain,
class_orderedgroup_osemigroup__mult(t_a),
inference(resolution,[status(thm)],[154230680,167324608]),
[] ).
fof(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,plain,
! [A,B,C,D] :
( ~ class_orderedgroup_osemigroup__mult(A)
| $equal(c_times(B,c_times(C,D,A),A),c_times(c_times(B,C,A),D,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154186736,plain,
( ~ class_orderedgroup_osemigroup__mult(A)
| $equal(c_times(B,c_times(C,D,A),A),c_times(c_times(B,C,A),D,A)) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]),
[] ).
fof(cls_Ring__and__Field_Oright__inverse_0,plain,
! [A,B] :
( ~ class_ring__and__field_ofield(A)
| $equal(c_0,B)
| $equal(c_times(B,c_hol_oinverse(B,A),A),c_1) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154220600,plain,
( ~ class_ring__and__field_ofield(A)
| $equal(c_0,B)
| $equal(c_times(B,c_hol_oinverse(B,A),A),c_1) ),
inference(rewrite,[status(thm)],[cls_Ring__and__Field_Oright__inverse_0]),
[] ).
fof(cls_conjecture_0,plain,
~ $equal(c_0,v_c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154111296,plain,
~ $equal(c_0,v_c),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(167442368,plain,
( ~ class_ring__and__field_ofield(A)
| $equal(c_times(v_c,c_hol_oinverse(v_c,A),A),c_1) ),
inference(resolution,[status(thm)],[154220600,154111296]),
[] ).
cnf(167462912,plain,
$equal(c_times(v_c,c_hol_oinverse(v_c,t_a),t_a),c_1),
inference(resolution,[status(thm)],[167442368,167324608]),
[] ).
fof(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,plain,
! [A,B] :
( ~ class_orderedgroup_omonoid__mult(A)
| $equal(c_times(c_1,B,A),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154143696,plain,
( ~ class_orderedgroup_omonoid__mult(A)
| $equal(c_times(c_1,B,A),B) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0]),
[] ).
fof(clsrel_Ring__and__Field_Ofield_12,plain,
! [A] :
( ~ class_ring__and__field_ofield(A)
| class_orderedgroup_omonoid__mult(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154225720,plain,
( ~ class_ring__and__field_ofield(A)
| class_orderedgroup_omonoid__mult(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Ofield_12]),
[] ).
cnf(167333520,plain,
class_orderedgroup_omonoid__mult(t_a),
inference(resolution,[status(thm)],[154225720,167324608]),
[] ).
cnf(167386008,plain,
$equal(c_times(c_1,A,t_a),A),
inference(resolution,[status(thm)],[154143696,167333520]),
[] ).
cnf(168056816,plain,
$equal(c_times(c_times(v_c,c_hol_oinverse(v_c,t_a),t_a),A,t_a),A),
inference(paramodulation,[status(thm)],[167462912,167386008,theory(equality)]),
[] ).
cnf(172970360,plain,
$equal(c_times(v_c,c_times(c_hol_oinverse(v_c,t_a),A,t_a),t_a),A),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[167342424,154186736,168056816,theory(equality)]),
[] ).
fof(cls_conjecture_2,plain,
~ $equal(c_times(v_c,c_times(c_hol_oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),
[] ).
cnf(154115752,plain,
~ $equal(c_times(v_c,c_times(c_hol_oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[172970360,154115752]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_Ring__and__Field_Ofield_21,plain,(~class_ring__and__field_ofield(A)|class_orderedgroup_osemigroup__mult(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154230680,plain,(~class_ring__and__field_ofield(A)|class_orderedgroup_osemigroup__mult(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Ofield_21]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__field_0,plain,(~class_ring__and__field_oordered__field(A)|class_ring__and__field_ofield(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154237280,plain,(~class_ring__and__field_oordered__field(A)|class_ring__and__field_ofield(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_0]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__field(t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154120504,plain,(class_ring__and__field_oordered__field(t_a)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(167324608,plain,(class_ring__and__field_ofield(t_a)),inference(resolution,[status(thm)],[154237280,154120504]),[]).
%
% cnf(167342424,plain,(class_orderedgroup_osemigroup__mult(t_a)),inference(resolution,[status(thm)],[154230680,167324608]),[]).
%
% fof(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,plain,(~class_orderedgroup_osemigroup__mult(A)|$equal(c_times(B,c_times(C,D,A),A),c_times(c_times(B,C,A),D,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154186736,plain,(~class_orderedgroup_osemigroup__mult(A)|$equal(c_times(B,c_times(C,D,A),A),c_times(c_times(B,C,A),D,A))),inference(rewrite,[status(thm)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]),[]).
%
% fof(cls_Ring__and__Field_Oright__inverse_0,plain,(~class_ring__and__field_ofield(A)|$equal(c_0,B)|$equal(c_times(B,c_hol_oinverse(B,A),A),c_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154220600,plain,(~class_ring__and__field_ofield(A)|$equal(c_0,B)|$equal(c_times(B,c_hol_oinverse(B,A),A),c_1)),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Oright__inverse_0]),[]).
%
% fof(cls_conjecture_0,plain,(~$equal(c_0,v_c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154111296,plain,(~$equal(c_0,v_c)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(167442368,plain,(~class_ring__and__field_ofield(A)|$equal(c_times(v_c,c_hol_oinverse(v_c,A),A),c_1)),inference(resolution,[status(thm)],[154220600,154111296]),[]).
%
% cnf(167462912,plain,($equal(c_times(v_c,c_hol_oinverse(v_c,t_a),t_a),c_1)),inference(resolution,[status(thm)],[167442368,167324608]),[]).
%
% fof(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,plain,(~class_orderedgroup_omonoid__mult(A)|$equal(c_times(c_1,B,A),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154143696,plain,(~class_orderedgroup_omonoid__mult(A)|$equal(c_times(c_1,B,A),B)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0]),[]).
%
% fof(clsrel_Ring__and__Field_Ofield_12,plain,(~class_ring__and__field_ofield(A)|class_orderedgroup_omonoid__mult(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154225720,plain,(~class_ring__and__field_ofield(A)|class_orderedgroup_omonoid__mult(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Ofield_12]),[]).
%
% cnf(167333520,plain,(class_orderedgroup_omonoid__mult(t_a)),inference(resolution,[status(thm)],[154225720,167324608]),[]).
%
% cnf(167386008,plain,($equal(c_times(c_1,A,t_a),A)),inference(resolution,[status(thm)],[154143696,167333520]),[]).
%
% cnf(168056816,plain,($equal(c_times(c_times(v_c,c_hol_oinverse(v_c,t_a),t_a),A,t_a),A)),inference(paramodulation,[status(thm)],[167462912,167386008,theory(equality)]),[]).
%
% cnf(172970360,plain,($equal(c_times(v_c,c_times(c_hol_oinverse(v_c,t_a),A,t_a),t_a),A)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[167342424,154186736,168056816,theory(equality)]),[]).
%
% fof(cls_conjecture_2,plain,(~$equal(c_times(v_c,c_times(c_hol_oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA016-2.tptp',unknown),[]).
%
% cnf(154115752,plain,(~$equal(c_times(v_c,c_times(c_hol_oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[172970360,154115752]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------