TSTP Solution File: ANA039-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : ANA039-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.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 11:24:59 EDT 2009

% Result   : Unsatisfiable 0.3s
% Output   : Refutation 0.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   31 (  14 unt;   0 def)
%            Number of atoms       :   57 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   54 (  28   ~;  26   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   46 (   2 sgn  16   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
    ~ c_lessequals(c_hol_oabs(v_h(v_x),t_a),c_times(c_hol_oabs(v_c,t_a),c_hol_oabs(v_f(v_x),t_a),t_a),t_a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),
    [] ).

cnf(151194816,plain,
    ~ c_lessequals(c_hol_oabs(v_h(v_x),t_a),c_times(c_hol_oabs(v_c,t_a),c_hol_oabs(v_f(v_x),t_a),t_a),t_a),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

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/ANA039-2.tptp',unknown),
    [] ).

cnf(151308944,plain,
    ( ~ class_ring__and__field_oordered__idom(A)
    | class_orderings_oorder(A) ),
    inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]),
    [] ).

fof(tfree_tcs,plain,
    class_ring__and__field_oordered__idom(t_a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),
    [] ).

cnf(151203768,plain,
    class_ring__and__field_oordered__idom(t_a),
    inference(rewrite,[status(thm)],[tfree_tcs]),
    [] ).

cnf(164406072,plain,
    class_orderings_oorder(t_a),
    inference(resolution,[status(thm)],[151308944,151203768]),
    [] ).

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/ANA039-2.tptp',unknown),
    [] ).

cnf(151256800,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_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0,plain,
    ! [A,B,C,D] :
      ( ~ class_ring__and__field_opordered__semiring(A)
      | ~ c_lessequals(B,C,A)
      | ~ c_lessequals(c_0,D,A)
      | c_lessequals(c_times(B,D,A),c_times(C,D,A),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),
    [] ).

cnf(151293256,plain,
    ( ~ class_ring__and__field_opordered__semiring(A)
    | ~ c_lessequals(B,C,A)
    | ~ c_lessequals(c_0,D,A)
    | c_lessequals(c_times(B,D,A),c_times(C,D,A),A) ),
    inference(rewrite,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0]),
    [] ).

fof(clsrel_Ring__and__Field_Oordered__idom_42,plain,
    ! [A] :
      ( ~ class_ring__and__field_oordered__idom(A)
      | class_ring__and__field_opordered__semiring(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),
    [] ).

cnf(151299912,plain,
    ( ~ class_ring__and__field_oordered__idom(A)
    | class_ring__and__field_opordered__semiring(A) ),
    inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]),
    [] ).

cnf(164397160,plain,
    class_ring__and__field_opordered__semiring(t_a),
    inference(resolution,[status(thm)],[151299912,151203768]),
    [] ).

cnf(164462744,plain,
    ( ~ c_lessequals(A,B,t_a)
    | ~ c_lessequals(c_0,C,t_a)
    | c_lessequals(c_times(A,C,t_a),c_times(B,C,t_a),t_a) ),
    inference(resolution,[status(thm)],[151293256,164397160]),
    [] ).

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/ANA039-2.tptp',unknown),
    [] ).

cnf(151233032,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/ANA039-2.tptp',unknown),
    [] ).

cnf(151313872,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(164419064,plain,
    class_orderedgroup_olordered__ab__group__abs(t_a),
    inference(resolution,[status(thm)],[151313872,151203768]),
    [] ).

cnf(164499272,plain,
    c_lessequals(c_0,c_hol_oabs(A,t_a),t_a),
    inference(resolution,[status(thm)],[151233032,164419064]),
    [] ).

cnf(164700024,plain,
    ( ~ c_lessequals(A,B,t_a)
    | c_lessequals(c_times(A,c_hol_oabs(C,t_a),t_a),c_times(B,c_hol_oabs(C,t_a),t_a),t_a) ),
    inference(resolution,[status(thm)],[164462744,164499272]),
    [] ).

fof(cls_OrderedGroup_Oabs__ge__self_0,plain,
    ! [A,B] :
      ( ~ class_orderedgroup_olordered__ab__group__abs(A)
      | c_lessequals(B,c_hol_oabs(B,A),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),
    [] ).

cnf(151222832,plain,
    ( ~ class_orderedgroup_olordered__ab__group__abs(A)
    | c_lessequals(B,c_hol_oabs(B,A),A) ),
    inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__ge__self_0]),
    [] ).

cnf(164488880,plain,
    c_lessequals(A,c_hol_oabs(A,t_a),t_a),
    inference(resolution,[status(thm)],[151222832,164419064]),
    [] ).

cnf(164737320,plain,
    c_lessequals(c_times(A,c_hol_oabs(B,t_a),t_a),c_times(c_hol_oabs(A,t_a),c_hol_oabs(B,t_a),t_a),t_a),
    inference(resolution,[status(thm)],[164700024,164488880]),
    [] ).

cnf(164927400,plain,
    ( ~ c_lessequals(A,c_times(B,c_hol_oabs(C,t_a),t_a),t_a)
    | c_lessequals(A,c_times(c_hol_oabs(B,t_a),c_hol_oabs(C,t_a),t_a),t_a) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[164406072,151256800,164737320]),
    [] ).

fof(cls_conjecture_0,plain,
    ! [A] : c_lessequals(c_hol_oabs(v_h(A),t_a),c_times(v_c,c_hol_oabs(v_f(A),t_a),t_a),t_a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),
    [] ).

cnf(151189320,plain,
    c_lessequals(c_hol_oabs(v_h(A),t_a),c_times(v_c,c_hol_oabs(v_f(A),t_a),t_a),t_a),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

cnf(164972056,plain,
    c_lessequals(c_hol_oabs(v_h(A),t_a),c_times(c_hol_oabs(v_c,t_a),c_hol_oabs(v_f(A),t_a),t_a),t_a),
    inference(resolution,[status(thm)],[164927400,151189320]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[151194816,164972056]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,(~c_lessequals(c_hol_oabs(v_h(v_x),t_a),c_times(c_hol_oabs(v_c,t_a),c_hol_oabs(v_f(v_x),t_a),t_a),t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),[]).
% 
% cnf(151194816,plain,(~c_lessequals(c_hol_oabs(v_h(v_x),t_a),c_times(c_hol_oabs(v_c,t_a),c_hol_oabs(v_f(v_x),t_a),t_a),t_a)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% 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/ANA039-2.tptp',unknown),[]).
% 
% cnf(151308944,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]),[]).
% 
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),[]).
% 
% cnf(151203768,plain,(class_ring__and__field_oordered__idom(t_a)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
% 
% cnf(164406072,plain,(class_orderings_oorder(t_a)),inference(resolution,[status(thm)],[151308944,151203768]),[]).
% 
% 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/ANA039-2.tptp',unknown),[]).
% 
% cnf(151256800,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_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0,plain,(~class_ring__and__field_opordered__semiring(A)|~c_lessequals(B,C,A)|~c_lessequals(c_0,D,A)|c_lessequals(c_times(B,D,A),c_times(C,D,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),[]).
% 
% cnf(151293256,plain,(~class_ring__and__field_opordered__semiring(A)|~c_lessequals(B,C,A)|~c_lessequals(c_0,D,A)|c_lessequals(c_times(B,D,A),c_times(C,D,A),A)),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0]),[]).
% 
% fof(clsrel_Ring__and__Field_Oordered__idom_42,plain,(~class_ring__and__field_oordered__idom(A)|class_ring__and__field_opordered__semiring(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),[]).
% 
% cnf(151299912,plain,(~class_ring__and__field_oordered__idom(A)|class_ring__and__field_opordered__semiring(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]),[]).
% 
% cnf(164397160,plain,(class_ring__and__field_opordered__semiring(t_a)),inference(resolution,[status(thm)],[151299912,151203768]),[]).
% 
% cnf(164462744,plain,(~c_lessequals(A,B,t_a)|~c_lessequals(c_0,C,t_a)|c_lessequals(c_times(A,C,t_a),c_times(B,C,t_a),t_a)),inference(resolution,[status(thm)],[151293256,164397160]),[]).
% 
% 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/ANA039-2.tptp',unknown),[]).
% 
% cnf(151233032,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/ANA039-2.tptp',unknown),[]).
% 
% cnf(151313872,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(164419064,plain,(class_orderedgroup_olordered__ab__group__abs(t_a)),inference(resolution,[status(thm)],[151313872,151203768]),[]).
% 
% cnf(164499272,plain,(c_lessequals(c_0,c_hol_oabs(A,t_a),t_a)),inference(resolution,[status(thm)],[151233032,164419064]),[]).
% 
% cnf(164700024,plain,(~c_lessequals(A,B,t_a)|c_lessequals(c_times(A,c_hol_oabs(C,t_a),t_a),c_times(B,c_hol_oabs(C,t_a),t_a),t_a)),inference(resolution,[status(thm)],[164462744,164499272]),[]).
% 
% fof(cls_OrderedGroup_Oabs__ge__self_0,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|c_lessequals(B,c_hol_oabs(B,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),[]).
% 
% cnf(151222832,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|c_lessequals(B,c_hol_oabs(B,A),A)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__ge__self_0]),[]).
% 
% cnf(164488880,plain,(c_lessequals(A,c_hol_oabs(A,t_a),t_a)),inference(resolution,[status(thm)],[151222832,164419064]),[]).
% 
% cnf(164737320,plain,(c_lessequals(c_times(A,c_hol_oabs(B,t_a),t_a),c_times(c_hol_oabs(A,t_a),c_hol_oabs(B,t_a),t_a),t_a)),inference(resolution,[status(thm)],[164700024,164488880]),[]).
% 
% cnf(164927400,plain,(~c_lessequals(A,c_times(B,c_hol_oabs(C,t_a),t_a),t_a)|c_lessequals(A,c_times(c_hol_oabs(B,t_a),c_hol_oabs(C,t_a),t_a),t_a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164406072,151256800,164737320]),[]).
% 
% fof(cls_conjecture_0,plain,(c_lessequals(c_hol_oabs(v_h(A),t_a),c_times(v_c,c_hol_oabs(v_f(A),t_a),t_a),t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA039-2.tptp',unknown),[]).
% 
% cnf(151189320,plain,(c_lessequals(c_hol_oabs(v_h(A),t_a),c_times(v_c,c_hol_oabs(v_f(A),t_a),t_a),t_a)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% cnf(164972056,plain,(c_lessequals(c_hol_oabs(v_h(A),t_a),c_times(c_hol_oabs(v_c,t_a),c_hol_oabs(v_f(A),t_a),t_a),t_a)),inference(resolution,[status(thm)],[164927400,151189320]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[151194816,164972056]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------