TSTP Solution File: ANA010-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA010-2 : 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 11:24:02 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 16 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 37 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_OrderedGroup_Olordered__ab__group__abs_17,plain,
! [A] :
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| class_orderings_oorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174242608,plain,
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]),
[] ).
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/ANA010-2.tptp',unknown),
[] ).
cnf(174247568,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_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174256512,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(189972048,plain,
class_orderedgroup_olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[174247568,174256512]),
[] ).
cnf(190028320,plain,
class_orderings_oorder(t_b),
inference(resolution,[status(thm)],[174242608,189972048]),
[] ).
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/ANA010-2.tptp',unknown),
[] ).
cnf(174178912,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_conjecture_0,plain,
! [A] : c_lessequals(c_0,v_f(A),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174224392,plain,
c_lessequals(c_0,v_f(A),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(190129304,plain,
( ~ c_lessequals(v_f(B),A,t_b)
| c_lessequals(c_0,A,t_b) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[190028320,174178912,174224392]),
[] ).
fof(cls_conjecture_1,plain,
! [A] : c_lessequals(v_f(A),c_times(v_c,v_g(A),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174228728,plain,
c_lessequals(v_f(A),c_times(v_c,v_g(A),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(190141800,plain,
c_lessequals(c_0,c_times(v_c,v_g(A),t_b),t_b),
inference(resolution,[status(thm)],[190129304,174228728]),
[] ).
fof(cls_OrderedGroup_Oabs__of__nonneg_0,plain,
! [A,B] :
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| ~ c_lessequals(c_0,B,A)
| $equal(c_hol_oabs(B,A),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174158656,plain,
( ~ class_orderedgroup_olordered__ab__group__abs(A)
| ~ c_lessequals(c_0,B,A)
| $equal(c_hol_oabs(B,A),B) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]),
[] ).
cnf(190048864,plain,
( ~ c_lessequals(c_0,A,t_b)
| $equal(c_hol_oabs(A,t_b),A) ),
inference(resolution,[status(thm)],[174158656,189972048]),
[] ).
cnf(191498400,plain,
$equal(c_hol_oabs(c_times(v_c,v_g(A),t_b),t_b),c_times(v_c,v_g(A),t_b)),
inference(resolution,[status(thm)],[190141800,190048864]),
[] ).
cnf(192614856,plain,
c_lessequals(v_f(A),c_hol_oabs(c_times(v_c,v_g(A),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[191498400,174228728,theory(equality)]),
[] ).
fof(cls_Ring__and__Field_Oabs__mult_0,plain,
! [A,B,C] :
( ~ class_ring__and__field_oordered__idom(A)
| $equal(c_times(c_hol_oabs(B,A),c_hol_oabs(C,A),A),c_hol_oabs(c_times(B,C,A),A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174215288,plain,
( ~ class_ring__and__field_oordered__idom(A)
| $equal(c_times(c_hol_oabs(B,A),c_hol_oabs(C,A),A),c_hol_oabs(c_times(B,C,A),A)) ),
inference(rewrite,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]),
[] ).
cnf(190015280,plain,
$equal(c_times(c_hol_oabs(A,t_b),c_hol_oabs(B,t_b),t_b),c_hol_oabs(c_times(A,B,t_b),t_b)),
inference(resolution,[status(thm)],[174215288,174256512]),
[] ).
cnf(192914784,plain,
c_lessequals(v_f(A),c_times(c_hol_oabs(v_c,t_b),c_hol_oabs(v_g(A),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[192614856,190015280,theory(equality)]),
[] ).
fof(cls_conjecture_2,plain,
! [A] : ~ c_lessequals(v_f(v_x(A)),c_times(A,c_hol_oabs(v_g(v_x(A)),t_b),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),
[] ).
cnf(174237648,plain,
~ c_lessequals(v_f(v_x(A)),c_times(A,c_hol_oabs(v_g(v_x(A)),t_b),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[192914784,174237648]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_OrderedGroup_Olordered__ab__group__abs_17,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|class_orderings_oorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174242608,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]),[]).
%
% 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/ANA010-2.tptp',unknown),[]).
%
% cnf(174247568,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_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174256512,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(189972048,plain,(class_orderedgroup_olordered__ab__group__abs(t_b)),inference(resolution,[status(thm)],[174247568,174256512]),[]).
%
% cnf(190028320,plain,(class_orderings_oorder(t_b)),inference(resolution,[status(thm)],[174242608,189972048]),[]).
%
% 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/ANA010-2.tptp',unknown),[]).
%
% cnf(174178912,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_conjecture_0,plain,(c_lessequals(c_0,v_f(A),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174224392,plain,(c_lessequals(c_0,v_f(A),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(190129304,plain,(~c_lessequals(v_f(B),A,t_b)|c_lessequals(c_0,A,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[190028320,174178912,174224392]),[]).
%
% fof(cls_conjecture_1,plain,(c_lessequals(v_f(A),c_times(v_c,v_g(A),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174228728,plain,(c_lessequals(v_f(A),c_times(v_c,v_g(A),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(190141800,plain,(c_lessequals(c_0,c_times(v_c,v_g(A),t_b),t_b)),inference(resolution,[status(thm)],[190129304,174228728]),[]).
%
% fof(cls_OrderedGroup_Oabs__of__nonneg_0,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|~c_lessequals(c_0,B,A)|$equal(c_hol_oabs(B,A),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174158656,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|~c_lessequals(c_0,B,A)|$equal(c_hol_oabs(B,A),B)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]),[]).
%
% cnf(190048864,plain,(~c_lessequals(c_0,A,t_b)|$equal(c_hol_oabs(A,t_b),A)),inference(resolution,[status(thm)],[174158656,189972048]),[]).
%
% cnf(191498400,plain,($equal(c_hol_oabs(c_times(v_c,v_g(A),t_b),t_b),c_times(v_c,v_g(A),t_b))),inference(resolution,[status(thm)],[190141800,190048864]),[]).
%
% cnf(192614856,plain,(c_lessequals(v_f(A),c_hol_oabs(c_times(v_c,v_g(A),t_b),t_b),t_b)),inference(paramodulation,[status(thm)],[191498400,174228728,theory(equality)]),[]).
%
% fof(cls_Ring__and__Field_Oabs__mult_0,plain,(~class_ring__and__field_oordered__idom(A)|$equal(c_times(c_hol_oabs(B,A),c_hol_oabs(C,A),A),c_hol_oabs(c_times(B,C,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174215288,plain,(~class_ring__and__field_oordered__idom(A)|$equal(c_times(c_hol_oabs(B,A),c_hol_oabs(C,A),A),c_hol_oabs(c_times(B,C,A),A))),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]),[]).
%
% cnf(190015280,plain,($equal(c_times(c_hol_oabs(A,t_b),c_hol_oabs(B,t_b),t_b),c_hol_oabs(c_times(A,B,t_b),t_b))),inference(resolution,[status(thm)],[174215288,174256512]),[]).
%
% cnf(192914784,plain,(c_lessequals(v_f(A),c_times(c_hol_oabs(v_c,t_b),c_hol_oabs(v_g(A),t_b),t_b),t_b)),inference(paramodulation,[status(thm)],[192614856,190015280,theory(equality)]),[]).
%
% fof(cls_conjecture_2,plain,(~c_lessequals(v_f(v_x(A)),c_times(A,c_hol_oabs(v_g(v_x(A)),t_b),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA010-2.tptp',unknown),[]).
%
% cnf(174237648,plain,(~c_lessequals(v_f(v_x(A)),c_times(A,c_hol_oabs(v_g(v_x(A)),t_b),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[192914784,174237648]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------