TSTP Solution File: ANA018-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA018-2 : 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 11:24:21 EDT 2009
% Result : Unsatisfiable 109.2s
% Output : Refutation 109.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 19 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 33 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_LOrder_Ojoin__semilorder_1,plain,
! [A] :
( ~ class_lorder_ojoin__semilorder(A)
| class_orderings_oorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164764368,plain,
( ~ class_lorder_ojoin__semilorder(A)
| class_orderings_oorder(A) ),
inference(rewrite,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_35,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_lorder_ojoin__semilorder(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164780512,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_lorder_ojoin__semilorder(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_35]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164638056,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(183244072,plain,
class_lorder_ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[164780512,164638056]),
[] ).
cnf(183305136,plain,
class_orderings_oorder(t_b),
inference(resolution,[status(thm)],[164764368,183244072]),
[] ).
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/ANA018-2.tptp',unknown),
[] ).
cnf(164700888,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_3,plain,
! [A] : c_lessequals(c_hol_oabs(v_x(A),t_b),c_times(v_ca,c_hol_oabs(v_f(A),t_b),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164624144,plain,
c_lessequals(c_hol_oabs(v_x(A),t_b),c_times(v_ca,c_hol_oabs(v_f(A),t_b),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(183910792,plain,
( ~ c_lessequals(c_times(v_ca,c_hol_oabs(v_f(B),t_b),t_b),A,t_b)
| c_lessequals(c_hol_oabs(v_x(B),t_b),A,t_b) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[183305136,164700888,164624144]),
[] ).
fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__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(D,B,A),c_times(D,C,A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164753480,plain,
( ~ class_ring__and__field_opordered__semiring(A)
| ~ c_lessequals(B,C,A)
| ~ c_lessequals(c_0,D,A)
| c_lessequals(c_times(D,B,A),c_times(D,C,A),A) ),
inference(rewrite,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__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/ANA018-2.tptp',unknown),
[] ).
cnf(164785640,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(183257224,plain,
class_ring__and__field_opordered__semiring(t_b),
inference(resolution,[status(thm)],[164785640,164638056]),
[] ).
cnf(183347360,plain,
( ~ c_lessequals(A,B,t_b)
| ~ c_lessequals(c_0,C,t_b)
| c_lessequals(c_times(C,A,t_b),c_times(C,B,t_b),t_b) ),
inference(resolution,[status(thm)],[164753480,183257224]),
[] ).
fof(cls_Orderings_Oorder__less__imp__le_0,plain,
! [A,B,C] :
( ~ class_orderings_oorder(A)
| ~ c_less(B,C,A)
| c_lessequals(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164715200,plain,
( ~ class_orderings_oorder(A)
| ~ c_less(B,C,A)
| c_lessequals(B,C,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]),
[] ).
fof(cls_conjecture_2,plain,
c_less(c_0,v_ca,t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164615392,plain,
c_less(c_0,v_ca,t_b),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(183381144,plain,
c_lessequals(c_0,v_ca,t_b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[183305136,164715200,164615392]),
[] ).
cnf(183494472,plain,
( ~ c_lessequals(A,B,t_b)
| c_lessequals(c_times(v_ca,A,t_b),c_times(v_ca,B,t_b),t_b) ),
inference(resolution,[status(thm)],[183347360,183381144]),
[] ).
fof(cls_conjecture_1,plain,
! [A] : c_lessequals(c_hol_oabs(v_f(A),t_b),c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164609968,plain,
c_lessequals(c_hol_oabs(v_f(A),t_b),c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(183545128,plain,
c_lessequals(c_times(v_ca,c_hol_oabs(v_f(A),t_b),t_b),c_times(v_ca,c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b),t_b),
inference(resolution,[status(thm)],[183494472,164609968]),
[] ).
cnf(193110728,plain,
c_lessequals(c_hol_oabs(v_x(A),t_b),c_times(v_ca,c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b),t_b),
inference(resolution,[status(thm)],[183910792,183545128]),
[] ).
fof(clsrel_Ring__and__Field_Oordered__idom_21,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_osemigroup__mult(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164771240,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_osemigroup__mult(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_21]),
[] ).
cnf(183235000,plain,
class_orderedgroup_osemigroup__mult(t_b),
inference(resolution,[status(thm)],[164771240,164638056]),
[] ).
fof(cls_OrderedGroup_Omult__ac__1_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/ANA018-2.tptp',unknown),
[] ).
cnf(164677120,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_Omult__ac__1_0]),
[] ).
fof(cls_conjecture_4,plain,
~ c_lessequals(c_hol_oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_hol_oabs(v_g(v_xa),t_b),t_b),t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),
[] ).
cnf(164629024,plain,
~ c_lessequals(c_hol_oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_hol_oabs(v_g(v_xa),t_b),t_b),t_b),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(185135448,plain,
~ c_lessequals(c_hol_oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_hol_oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[183235000,164677120,164629024,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[193110728,185135448]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 109 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_LOrder_Ojoin__semilorder_1,plain,(~class_lorder_ojoin__semilorder(A)|class_orderings_oorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164764368,plain,(~class_lorder_ojoin__semilorder(A)|class_orderings_oorder(A)),inference(rewrite,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_35,plain,(~class_ring__and__field_oordered__idom(A)|class_lorder_ojoin__semilorder(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164780512,plain,(~class_ring__and__field_oordered__idom(A)|class_lorder_ojoin__semilorder(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_35]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164638056,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(183244072,plain,(class_lorder_ojoin__semilorder(t_b)),inference(resolution,[status(thm)],[164780512,164638056]),[]).
%
% cnf(183305136,plain,(class_orderings_oorder(t_b)),inference(resolution,[status(thm)],[164764368,183244072]),[]).
%
% 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/ANA018-2.tptp',unknown),[]).
%
% cnf(164700888,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_3,plain,(c_lessequals(c_hol_oabs(v_x(A),t_b),c_times(v_ca,c_hol_oabs(v_f(A),t_b),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164624144,plain,(c_lessequals(c_hol_oabs(v_x(A),t_b),c_times(v_ca,c_hol_oabs(v_f(A),t_b),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(183910792,plain,(~c_lessequals(c_times(v_ca,c_hol_oabs(v_f(B),t_b),t_b),A,t_b)|c_lessequals(c_hol_oabs(v_x(B),t_b),A,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[183305136,164700888,164624144]),[]).
%
% fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__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(D,B,A),c_times(D,C,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164753480,plain,(~class_ring__and__field_opordered__semiring(A)|~c_lessequals(B,C,A)|~c_lessequals(c_0,D,A)|c_lessequals(c_times(D,B,A),c_times(D,C,A),A)),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__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/ANA018-2.tptp',unknown),[]).
%
% cnf(164785640,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(183257224,plain,(class_ring__and__field_opordered__semiring(t_b)),inference(resolution,[status(thm)],[164785640,164638056]),[]).
%
% cnf(183347360,plain,(~c_lessequals(A,B,t_b)|~c_lessequals(c_0,C,t_b)|c_lessequals(c_times(C,A,t_b),c_times(C,B,t_b),t_b)),inference(resolution,[status(thm)],[164753480,183257224]),[]).
%
% fof(cls_Orderings_Oorder__less__imp__le_0,plain,(~class_orderings_oorder(A)|~c_less(B,C,A)|c_lessequals(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164715200,plain,(~class_orderings_oorder(A)|~c_less(B,C,A)|c_lessequals(B,C,A)),inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]),[]).
%
% fof(cls_conjecture_2,plain,(c_less(c_0,v_ca,t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164615392,plain,(c_less(c_0,v_ca,t_b)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(183381144,plain,(c_lessequals(c_0,v_ca,t_b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[183305136,164715200,164615392]),[]).
%
% cnf(183494472,plain,(~c_lessequals(A,B,t_b)|c_lessequals(c_times(v_ca,A,t_b),c_times(v_ca,B,t_b),t_b)),inference(resolution,[status(thm)],[183347360,183381144]),[]).
%
% fof(cls_conjecture_1,plain,(c_lessequals(c_hol_oabs(v_f(A),t_b),c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164609968,plain,(c_lessequals(c_hol_oabs(v_f(A),t_b),c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(183545128,plain,(c_lessequals(c_times(v_ca,c_hol_oabs(v_f(A),t_b),t_b),c_times(v_ca,c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b),t_b)),inference(resolution,[status(thm)],[183494472,164609968]),[]).
%
% cnf(193110728,plain,(c_lessequals(c_hol_oabs(v_x(A),t_b),c_times(v_ca,c_times(v_c,c_hol_oabs(v_g(A),t_b),t_b),t_b),t_b)),inference(resolution,[status(thm)],[183910792,183545128]),[]).
%
% fof(clsrel_Ring__and__Field_Oordered__idom_21,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_osemigroup__mult(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164771240,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_osemigroup__mult(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_21]),[]).
%
% cnf(183235000,plain,(class_orderedgroup_osemigroup__mult(t_b)),inference(resolution,[status(thm)],[164771240,164638056]),[]).
%
% fof(cls_OrderedGroup_Omult__ac__1_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/ANA018-2.tptp',unknown),[]).
%
% cnf(164677120,plain,(~class_orderedgroup_osemigroup__mult(A)|$equal(c_times(B,c_times(C,D,A),A),c_times(c_times(B,C,A),D,A))),inference(rewrite,[status(thm)],[cls_OrderedGroup_Omult__ac__1_0]),[]).
%
% fof(cls_conjecture_4,plain,(~c_lessequals(c_hol_oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_hol_oabs(v_g(v_xa),t_b),t_b),t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA018-2.tptp',unknown),[]).
%
% cnf(164629024,plain,(~c_lessequals(c_hol_oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_hol_oabs(v_g(v_xa),t_b),t_b),t_b)),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(185135448,plain,(~c_lessequals(c_hol_oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_hol_oabs(v_g(v_xa),t_b),t_b),t_b),t_b)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[183235000,164677120,164629024,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[193110728,185135448]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------