%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA035-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 11:24:50 EDT 2009
% Result : Unsatisfiable 294.7s
% Output : Refutation 294.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsrel_Ring__and__Field_Oordered__idom_17,plain,
! [A] :
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_oab__semigroup__mult(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),
[] ).
cnf(174265480,plain,
( ~ class_ring__and__field_oordered__idom(A)
| class_orderedgroup_oab__semigroup__mult(A) ),
inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_17]),
[] ).
fof(tfree_tcs,plain,
class_ring__and__field_oordered__idom(t_b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),
[] ).
cnf(174154416,plain,
class_ring__and__field_oordered__idom(t_b),
inference(rewrite,[status(thm)],[tfree_tcs]),
[] ).
cnf(183502680,plain,
class_orderedgroup_oab__semigroup__mult(t_b),
inference(resolution,[status(thm)],[174265480,174154416]),
[] ).
fof(cls_OrderedGroup_Omult__ac__3_0,plain,
! [A,C,B,D] :
( ~ class_orderedgroup_oab__semigroup__mult(A)
| $equal(c_times(C,c_times(B,D,A),A),c_times(B,c_times(C,D,A),A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),
[] ).
cnf(174218072,plain,
( ~ class_orderedgroup_oab__semigroup__mult(A)
| $equal(c_times(C,c_times(B,D,A),A),c_times(B,c_times(C,D,A),A)) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Omult__ac__3_0]),
[] ).
fof(cls_OrderedGroup_Omult__ac__2_0,plain,
! [A,C,B] :
( ~ class_orderedgroup_oab__semigroup__mult(A)
| $equal(c_times(C,B,A),c_times(B,C,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),
[] ).
cnf(174183992,plain,
( ~ class_orderedgroup_oab__semigroup__mult(A)
| $equal(c_times(C,B,A),c_times(B,C,A)) ),
inference(rewrite,[status(thm)],[cls_OrderedGroup_Omult__ac__2_0]),
[] ).
cnf(184745056,plain,
$equal(c_times(B,A,t_b),c_times(A,B,t_b)),
inference(resolution,[status(thm)],[174183992,183502680]),
[] ).
cnf(184861232,plain,
$equal(c_times(c_times(A,C,t_b),B,t_b),c_times(A,c_times(B,C,t_b),t_b)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[183502680,174218072,184745056,theory(equality)]),
[] ).
cnf(184834632,plain,
$equal(c_times(A,c_times(B,C,t_b),t_b),c_times(c_times(A,C,t_b),B,t_b)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[183502680,174218072,184745056,theory(equality)]),
[] ).
cnf(185379624,plain,
$equal(c_times(D,c_times(A,c_times(B,C,t_b),t_b),t_b),c_times(c_times(D,B,t_b),c_times(A,C,t_b),t_b)),
inference(paramodulation,[status(thm)],[184861232,184834632,theory(equality)]),
[] ).
cnf(185094728,plain,
$equal(c_times(A,c_times(C,B,t_b),t_b),c_times(c_times(A,C,t_b),B,t_b)),
inference(paramodulation,[status(thm)],[184834632,184745056,theory(equality)]),
[] ).
cnf(225834936,plain,
$equal(c_times(c_times(D,B,t_b),c_times(A,C,t_b),t_b),c_times(c_times(D,A,t_b),c_times(B,C,t_b),t_b)),
inference(paramodulation,[status(thm)],[185379624,185094728,theory(equality)]),
[] ).
fof(cls_conjecture_4,plain,
~ $equal(c_times(c_times(v_c,c_hol_oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_hol_oabs(v_g(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_hol_oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),
[] ).
cnf(174145208,plain,
~ $equal(c_times(c_times(v_c,c_hol_oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_hol_oabs(v_g(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_hol_oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
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/ANA035-2.tptp',unknown),
[] ).
cnf(174260560,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(184726232,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)],[174260560,174154416]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[225834936,174145208,184726232,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 295 seconds
% START OF PROOF SEQUENCE
% fof(clsrel_Ring__and__Field_Oordered__idom_17,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_oab__semigroup__mult(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),[]).
%
% cnf(174265480,plain,(~class_ring__and__field_oordered__idom(A)|class_orderedgroup_oab__semigroup__mult(A)),inference(rewrite,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_17]),[]).
%
% fof(tfree_tcs,plain,(class_ring__and__field_oordered__idom(t_b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),[]).
%
% cnf(174154416,plain,(class_ring__and__field_oordered__idom(t_b)),inference(rewrite,[status(thm)],[tfree_tcs]),[]).
%
% cnf(183502680,plain,(class_orderedgroup_oab__semigroup__mult(t_b)),inference(resolution,[status(thm)],[174265480,174154416]),[]).
%
% fof(cls_OrderedGroup_Omult__ac__3_0,plain,(~class_orderedgroup_oab__semigroup__mult(A)|$equal(c_times(C,c_times(B,D,A),A),c_times(B,c_times(C,D,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),[]).
%
% cnf(174218072,plain,(~class_orderedgroup_oab__semigroup__mult(A)|$equal(c_times(C,c_times(B,D,A),A),c_times(B,c_times(C,D,A),A))),inference(rewrite,[status(thm)],[cls_OrderedGroup_Omult__ac__3_0]),[]).
%
% fof(cls_OrderedGroup_Omult__ac__2_0,plain,(~class_orderedgroup_oab__semigroup__mult(A)|$equal(c_times(C,B,A),c_times(B,C,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),[]).
%
% cnf(174183992,plain,(~class_orderedgroup_oab__semigroup__mult(A)|$equal(c_times(C,B,A),c_times(B,C,A))),inference(rewrite,[status(thm)],[cls_OrderedGroup_Omult__ac__2_0]),[]).
%
% cnf(184745056,plain,($equal(c_times(B,A,t_b),c_times(A,B,t_b))),inference(resolution,[status(thm)],[174183992,183502680]),[]).
%
% cnf(184861232,plain,($equal(c_times(c_times(A,C,t_b),B,t_b),c_times(A,c_times(B,C,t_b),t_b))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[183502680,174218072,184745056,theory(equality)]),[]).
%
% cnf(184834632,plain,($equal(c_times(A,c_times(B,C,t_b),t_b),c_times(c_times(A,C,t_b),B,t_b))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[183502680,174218072,184745056,theory(equality)]),[]).
%
% cnf(185379624,plain,($equal(c_times(D,c_times(A,c_times(B,C,t_b),t_b),t_b),c_times(c_times(D,B,t_b),c_times(A,C,t_b),t_b))),inference(paramodulation,[status(thm)],[184861232,184834632,theory(equality)]),[]).
%
% cnf(185094728,plain,($equal(c_times(A,c_times(C,B,t_b),t_b),c_times(c_times(A,C,t_b),B,t_b))),inference(paramodulation,[status(thm)],[184834632,184745056,theory(equality)]),[]).
%
% cnf(225834936,plain,($equal(c_times(c_times(D,B,t_b),c_times(A,C,t_b),t_b),c_times(c_times(D,A,t_b),c_times(B,C,t_b),t_b))),inference(paramodulation,[status(thm)],[185379624,185094728,theory(equality)]),[]).
%
% fof(cls_conjecture_4,plain,(~$equal(c_times(c_times(v_c,c_hol_oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_hol_oabs(v_g(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_hol_oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA035-2.tptp',unknown),[]).
%
% cnf(174145208,plain,(~$equal(c_times(c_times(v_c,c_hol_oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_hol_oabs(v_g(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_hol_oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% fof(cls_Ring__and__Field_Oabs__mult_0,plain,(~class_ring__and__field_oordered__idom(A)|$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/ANA035-2.tptp',unknown),[]).
%
% cnf(174260560,plain,(~class_ring__and__field_oordered__idom(A)|$equal(c_times(c_hol_oabs(B,A),c_hol_oabs(C,A),A),c_hol_oabs(c_times(B,C,A),A))),inference(rewrite,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]),[]).
%
% cnf(184726232,plain,($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)],[174260560,174154416]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[225834936,174145208,184726232,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------