TSTP Solution File: ANA037-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA037-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 11:24:53 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/ANA037-2.tptp',unknown),
[] ).
cnf(143871096,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/ANA037-2.tptp',unknown),
[] ).
cnf(143886992,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]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),
[] ).
cnf(143791944,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(159643640,plain,
class_ring__and__field_opordered__semiring(t_b),
inference(resolution,[status(thm)],[143886992,143791944]),
[] ).
cnf(159710096,plain,
( ~ c_lessequals(A,B,t_b)
| ~ c_lessequals(c_0,C,t_b)
| c_lessequals(c_times(A,C,t_b),c_times(B,C,t_b),t_b) ),
inference(resolution,[status(thm)],[143871096,159643640]),
[] ).
fof(cls_conjecture_2,plain,
c_lessequals(c_0,v_f(v_xa),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),
[] ).
cnf(143769408,plain,
c_lessequals(c_0,v_f(v_xa),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(159839944,plain,
( ~ c_lessequals(A,B,t_b)
| c_lessequals(c_times(A,v_f(v_xa),t_b),c_times(B,v_f(v_xa),t_b),t_b) ),
inference(resolution,[status(thm)],[159710096,143769408]),
[] ).
fof(cls_Orderings_Ole__maxI1_0,plain,
! [A,B,C] :
( ~ class_orderings_olinorder(A)
| c_lessequals(B,c_orderings_omax(B,C,A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),
[] ).
cnf(143812712,plain,
( ~ class_orderings_olinorder(A)
| c_lessequals(B,c_orderings_omax(B,C,A),A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Ole__maxI1_0]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_33,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_olinorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),
[] ).
cnf(143881904,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_olinorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]),
[] ).
cnf(159630560,plain,
class_orderings_olinorder(t_b),
inference(resolution,[status(thm)],[143881904,143791944]),
[] ).
cnf(159668320,plain,
c_lessequals(A,c_orderings_omax(A,B,t_b),t_b),
inference(resolution,[status(thm)],[143812712,159630560]),
[] ).
cnf(159891504,plain,
c_lessequals(c_times(A,v_f(v_xa),t_b),c_times(c_orderings_omax(A,B,t_b),v_f(v_xa),t_b),t_b),
inference(resolution,[status(thm)],[159839944,159668320]),
[] ).
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/ANA037-2.tptp',unknown),
[] ).
cnf(143891936,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]),
[] ).
cnf(159652608,plain,
class_orderings_oorder(t_b),
inference(resolution,[status(thm)],[143891936,143791944]),
[] ).
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/ANA037-2.tptp',unknown),
[] ).
cnf(143834608,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_4,plain,
c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(v_c,v_f(v_xa),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),
[] ).
cnf(143773912,plain,
c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(v_c,v_f(v_xa),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(160189376,plain,
( ~ c_lessequals(c_times(v_c,v_f(v_xa),t_b),A,t_b)
| c_lessequals(c_hol_oabs(v_a(v_xa),t_b),A,t_b) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159652608,143834608,143773912]),
[] ).
fof(cls_conjecture_8,plain,
~ c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(c_orderings_omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),
[] ).
cnf(143783040,plain,
~ c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(c_orderings_omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_8]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[159891504,160189376,143783040]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/ANA037-2.tptp',unknown),[]).
%
% cnf(143871096,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/ANA037-2.tptp',unknown),[]).
%
% cnf(143886992,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]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),[]).
%
% cnf(143791944,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(159643640,plain,(class_ring__and__field_opordered__semiring(t_b)),inference(resolution,[status(thm)],[143886992,143791944]),[]).
%
% cnf(159710096,plain,(~c_lessequals(A,B,t_b)|~c_lessequals(c_0,C,t_b)|c_lessequals(c_times(A,C,t_b),c_times(B,C,t_b),t_b)),inference(resolution,[status(thm)],[143871096,159643640]),[]).
%
% fof(cls_conjecture_2,plain,(c_lessequals(c_0,v_f(v_xa),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),[]).
%
% cnf(143769408,plain,(c_lessequals(c_0,v_f(v_xa),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(159839944,plain,(~c_lessequals(A,B,t_b)|c_lessequals(c_times(A,v_f(v_xa),t_b),c_times(B,v_f(v_xa),t_b),t_b)),inference(resolution,[status(thm)],[159710096,143769408]),[]).
%
% fof(cls_Orderings_Ole__maxI1_0,plain,(~class_orderings_olinorder(A)|c_lessequals(B,c_orderings_omax(B,C,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),[]).
%
% cnf(143812712,plain,(~class_orderings_olinorder(A)|c_lessequals(B,c_orderings_omax(B,C,A),A)),inference(rewrite,[status(thm)],[cls_Orderings_Ole__maxI1_0]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_33,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_olinorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),[]).
%
% cnf(143881904,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_olinorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]),[]).
%
% cnf(159630560,plain,(class_orderings_olinorder(t_b)),inference(resolution,[status(thm)],[143881904,143791944]),[]).
%
% cnf(159668320,plain,(c_lessequals(A,c_orderings_omax(A,B,t_b),t_b)),inference(resolution,[status(thm)],[143812712,159630560]),[]).
%
% cnf(159891504,plain,(c_lessequals(c_times(A,v_f(v_xa),t_b),c_times(c_orderings_omax(A,B,t_b),v_f(v_xa),t_b),t_b)),inference(resolution,[status(thm)],[159839944,159668320]),[]).
%
% 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/ANA037-2.tptp',unknown),[]).
%
% cnf(143891936,plain,(~class_ring__and__field_oordered__idom(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]),[]).
%
% cnf(159652608,plain,(class_orderings_oorder(t_b)),inference(resolution,[status(thm)],[143891936,143791944]),[]).
%
% 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/ANA037-2.tptp',unknown),[]).
%
% cnf(143834608,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_4,plain,(c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(v_c,v_f(v_xa),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),[]).
%
% cnf(143773912,plain,(c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(v_c,v_f(v_xa),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(160189376,plain,(~c_lessequals(c_times(v_c,v_f(v_xa),t_b),A,t_b)|c_lessequals(c_hol_oabs(v_a(v_xa),t_b),A,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159652608,143834608,143773912]),[]).
%
% fof(cls_conjecture_8,plain,(~c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(c_orderings_omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA037-2.tptp',unknown),[]).
%
% cnf(143783040,plain,(~c_lessequals(c_hol_oabs(v_a(v_xa),t_b),c_times(c_orderings_omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_8]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[159891504,160189376,143783040]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------