TSTP Solution File: ANA044-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA044-2 : 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 11:25:10 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 7 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/ANA044-2.tptp',unknown),
[] ).
cnf(140818320,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/ANA044-2.tptp',unknown),
[] ).
cnf(140829016,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]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),
[] ).
cnf(140764264,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(156566984,plain,
class_ring__and__field_opordered__cancel__semiring(t_b),
inference(resolution,[status(thm)],[140829016,140764264]),
[] ).
cnf(156604880,plain,
( ~ c_lessequals(c_0,A,t_b)
| ~ c_lessequals(c_0,B,t_b)
| c_lessequals(c_0,c_times(B,A,t_b),t_b) ),
inference(resolution,[status(thm)],[140818320,156566984]),
[] ).
fof(cls_conjecture_1,plain,
! [A] : c_lessequals(c_0,v_h(A),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),
[] ).
cnf(140750264,plain,
c_lessequals(c_0,v_h(A),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(156665600,plain,
( ~ c_lessequals(c_0,A,t_b)
| c_lessequals(c_0,c_times(A,v_h(B),t_b),t_b) ),
inference(resolution,[status(thm)],[156604880,140750264]),
[] ).
fof(cls_conjecture_0,plain,
! [A,B] : c_lessequals(c_0,v_l(A,B),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),
[] ).
cnf(140745840,plain,
c_lessequals(c_0,v_l(A,B),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(159601080,plain,
c_lessequals(c_0,c_times(v_l(B,C),v_h(A),t_b),t_b),
inference(resolution,[status(thm)],[156665600,140745840]),
[] ).
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/ANA044-2.tptp',unknown),
[] ).
cnf(140792424,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]),
[] ).
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/ANA044-2.tptp',unknown),
[] ).
cnf(140833976,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(156575928,plain,
class_orderedgroup_olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[140833976,140764264]),
[] ).
cnf(156621216,plain,
( ~ c_lessequals(c_0,A,t_b)
| $equal(c_hol_oabs(A,t_b),A) ),
inference(resolution,[status(thm)],[140792424,156575928]),
[] ).
fof(cls_conjecture_3,plain,
~ $equal(c_hol_oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),
[] ).
cnf(140755136,plain,
~ $equal(c_hol_oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[159601080,156621216,140755136]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% 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/ANA044-2.tptp',unknown),[]).
%
% cnf(140818320,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/ANA044-2.tptp',unknown),[]).
%
% cnf(140829016,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]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),[]).
%
% cnf(140764264,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(156566984,plain,(class_ring__and__field_opordered__cancel__semiring(t_b)),inference(resolution,[status(thm)],[140829016,140764264]),[]).
%
% cnf(156604880,plain,(~c_lessequals(c_0,A,t_b)|~c_lessequals(c_0,B,t_b)|c_lessequals(c_0,c_times(B,A,t_b),t_b)),inference(resolution,[status(thm)],[140818320,156566984]),[]).
%
% fof(cls_conjecture_1,plain,(c_lessequals(c_0,v_h(A),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),[]).
%
% cnf(140750264,plain,(c_lessequals(c_0,v_h(A),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(156665600,plain,(~c_lessequals(c_0,A,t_b)|c_lessequals(c_0,c_times(A,v_h(B),t_b),t_b)),inference(resolution,[status(thm)],[156604880,140750264]),[]).
%
% fof(cls_conjecture_0,plain,(c_lessequals(c_0,v_l(A,B),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),[]).
%
% cnf(140745840,plain,(c_lessequals(c_0,v_l(A,B),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(159601080,plain,(c_lessequals(c_0,c_times(v_l(B,C),v_h(A),t_b),t_b)),inference(resolution,[status(thm)],[156665600,140745840]),[]).
%
% 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/ANA044-2.tptp',unknown),[]).
%
% cnf(140792424,plain,(~class_orderedgroup_olordered__ab__group__abs(A)|~c_lessequals(c_0,B,A)|$equal(c_hol_oabs(B,A),B)),inference(rewrite,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_50,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_olordered__ab__group__abs(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),[]).
%
% cnf(140833976,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_olordered__ab__group__abs(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]),[]).
%
% cnf(156575928,plain,(class_orderedgroup_olordered__ab__group__abs(t_b)),inference(resolution,[status(thm)],[140833976,140764264]),[]).
%
% cnf(156621216,plain,(~c_lessequals(c_0,A,t_b)|$equal(c_hol_oabs(A,t_b),A)),inference(resolution,[status(thm)],[140792424,156575928]),[]).
%
% fof(cls_conjecture_3,plain,(~$equal(c_hol_oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA044-2.tptp',unknown),[]).
%
% cnf(140755136,plain,(~$equal(c_hol_oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[159601080,156621216,140755136]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------