TSTP Solution File: LAT263-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LAT263-2 : 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 @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:36:22 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 20 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_0,plain,
c_lessequals(v_s,v_a,tc_set(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155847640,plain,
c_lessequals(v_s,v_a,tc_set(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
fof(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,plain,
c_in(c_tarski_odual(v_cl,t_a),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155916280,plain,
c_in(c_tarski_odual(v_cl,t_a),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
inference(rewrite,[status(thm)],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0]),
[] ).
fof(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,plain,
c_in(c_tarski_odual(v_cl,t_a),c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155920440,plain,
c_in(c_tarski_odual(v_cl,t_a),c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
inference(rewrite,[status(thm)],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0]),
[] ).
fof(cls_Tarski_OCL_Olub__in__lattice_0,plain,
! [A,B,C] :
( ~ c_in(A,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))
| ~ c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))
| ~ c_lessequals(C,c_tarski_opotype_opset(A,B,tc_product__type_ounit),tc_set(B))
| c_in(c_tarski_olub(C,A,B),c_tarski_opotype_opset(A,B,tc_product__type_ounit),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155906984,plain,
( ~ c_in(A,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))
| ~ c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))
| ~ c_lessequals(C,c_tarski_opotype_opset(A,B,tc_product__type_ounit),tc_set(B))
| c_in(c_tarski_olub(C,A,B),c_tarski_opotype_opset(A,B,tc_product__type_ounit),B) ),
inference(rewrite,[status(thm)],[cls_Tarski_OCL_Olub__in__lattice_0]),
[] ).
fof(cls_conjecture_1,plain,
~ c_in(c_tarski_oglb(v_s,v_cl,t_a),v_a,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155852832,plain,
~ c_in(c_tarski_oglb(v_s,v_cl,t_a),v_a,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
fof(cls_Tarski_Oglb__dual__lub_0,plain,
! [A,B,C] : $equal(c_tarski_olub(A,c_tarski_odual(B,C),C),c_tarski_oglb(A,B,C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155924544,plain,
$equal(c_tarski_olub(A,c_tarski_odual(B,C),C),c_tarski_oglb(A,B,C)),
inference(rewrite,[status(thm)],[cls_Tarski_Oglb__dual__lub_0]),
[] ).
cnf(166474136,plain,
~ c_in(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),v_a,t_a),
inference(paramodulation,[status(thm)],[155852832,155924544,theory(equality)]),
[] ).
fof(cls_Tarski_OA_A_61_61_Apset_Acl_0,plain,
$equal(c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),v_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155857920,plain,
$equal(c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),v_a),
inference(rewrite,[status(thm)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]),
[] ).
cnf(166492048,plain,
~ c_in(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),t_a),
inference(paramodulation,[status(thm)],[166474136,155857920,theory(equality)]),
[] ).
fof(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,plain,
! [A,B] : $equal(c_tarski_opotype_opset(c_tarski_odual(A,B),B,tc_product__type_ounit),c_tarski_opotype_opset(A,B,tc_product__type_ounit)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),
[] ).
cnf(155932784,plain,
$equal(c_tarski_opotype_opset(c_tarski_odual(A,B),B,tc_product__type_ounit),c_tarski_opotype_opset(A,B,tc_product__type_ounit)),
inference(rewrite,[status(thm)],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0]),
[] ).
cnf(166535040,plain,
~ c_in(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),c_tarski_opotype_opset(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),t_a),
inference(paramodulation,[status(thm)],[166492048,155932784,theory(equality)]),
[] ).
cnf(166920088,plain,
~ c_lessequals(v_s,c_tarski_opotype_opset(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),tc_set(t_a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[155916280,155920440,155906984,166535040]),
[] ).
cnf(167133872,plain,
~ c_lessequals(v_s,c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),tc_set(t_a)),
inference(paramodulation,[status(thm)],[166920088,155932784,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[155847640,167133872,155857920,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_0,plain,(c_lessequals(v_s,v_a,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155847640,plain,(c_lessequals(v_s,v_a,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% fof(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,plain,(c_in(c_tarski_odual(v_cl,t_a),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155916280,plain,(c_in(c_tarski_odual(v_cl,t_a),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),inference(rewrite,[status(thm)],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0]),[]).
%
% fof(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,plain,(c_in(c_tarski_odual(v_cl,t_a),c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155920440,plain,(c_in(c_tarski_odual(v_cl,t_a),c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),inference(rewrite,[status(thm)],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0]),[]).
%
% fof(cls_Tarski_OCL_Olub__in__lattice_0,plain,(~c_in(A,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))|~c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))|~c_lessequals(C,c_tarski_opotype_opset(A,B,tc_product__type_ounit),tc_set(B))|c_in(c_tarski_olub(C,A,B),c_tarski_opotype_opset(A,B,tc_product__type_ounit),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155906984,plain,(~c_in(A,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))|~c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))|~c_lessequals(C,c_tarski_opotype_opset(A,B,tc_product__type_ounit),tc_set(B))|c_in(c_tarski_olub(C,A,B),c_tarski_opotype_opset(A,B,tc_product__type_ounit),B)),inference(rewrite,[status(thm)],[cls_Tarski_OCL_Olub__in__lattice_0]),[]).
%
% fof(cls_conjecture_1,plain,(~c_in(c_tarski_oglb(v_s,v_cl,t_a),v_a,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155852832,plain,(~c_in(c_tarski_oglb(v_s,v_cl,t_a),v_a,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Tarski_Oglb__dual__lub_0,plain,($equal(c_tarski_olub(A,c_tarski_odual(B,C),C),c_tarski_oglb(A,B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155924544,plain,($equal(c_tarski_olub(A,c_tarski_odual(B,C),C),c_tarski_oglb(A,B,C))),inference(rewrite,[status(thm)],[cls_Tarski_Oglb__dual__lub_0]),[]).
%
% cnf(166474136,plain,(~c_in(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),v_a,t_a)),inference(paramodulation,[status(thm)],[155852832,155924544,theory(equality)]),[]).
%
% fof(cls_Tarski_OA_A_61_61_Apset_Acl_0,plain,($equal(c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),v_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155857920,plain,($equal(c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),v_a)),inference(rewrite,[status(thm)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]),[]).
%
% cnf(166492048,plain,(~c_in(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),t_a)),inference(paramodulation,[status(thm)],[166474136,155857920,theory(equality)]),[]).
%
% fof(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,plain,($equal(c_tarski_opotype_opset(c_tarski_odual(A,B),B,tc_product__type_ounit),c_tarski_opotype_opset(A,B,tc_product__type_ounit))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT263-2.tptp',unknown),[]).
%
% cnf(155932784,plain,($equal(c_tarski_opotype_opset(c_tarski_odual(A,B),B,tc_product__type_ounit),c_tarski_opotype_opset(A,B,tc_product__type_ounit))),inference(rewrite,[status(thm)],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0]),[]).
%
% cnf(166535040,plain,(~c_in(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),c_tarski_opotype_opset(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),t_a)),inference(paramodulation,[status(thm)],[166492048,155932784,theory(equality)]),[]).
%
% cnf(166920088,plain,(~c_lessequals(v_s,c_tarski_opotype_opset(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),tc_set(t_a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[155916280,155920440,155906984,166535040]),[]).
%
% cnf(167133872,plain,(~c_lessequals(v_s,c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),tc_set(t_a))),inference(paramodulation,[status(thm)],[166920088,155932784,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[155847640,167133872,155857920,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------