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