TSTP Solution File: ANA016-2 by Faust---1.0

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%------------------------------------------------------------------------------
% 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
% 
%------------------------------------------------------------------------------