TSTP Solution File: LAT269-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LAT269-2 : 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 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:36:44 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0,plain,
c_in(c_tarski_otop(v_cl,t_a),v_a,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),
[] ).
cnf(144427768,plain,
c_in(c_tarski_otop(v_cl,t_a),v_a,t_a),
inference(rewrite,[status(thm)],[cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0]),
[] ).
fof(cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0,plain,
! [A,B] :
( ~ c_in(A,v_a,t_a)
| ~ c_in(B,v_a,t_a)
| c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,B,A,t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,B,A,t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))
| $equal(c_tarski_ointerval(v_r,B,A,t_a),c_emptyset) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),
[] ).
cnf(144481824,plain,
( ~ c_in(A,v_a,t_a)
| ~ c_in(B,v_a,t_a)
| c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,B,A,t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,B,A,t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))
| $equal(c_tarski_ointerval(v_r,B,A,t_a),c_emptyset) ),
inference(rewrite,[status(thm)],[cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0]),
[] ).
fof(cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0,plain,
c_in(c_tarski_olub(v_y,v_cl,t_a),v_a,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),
[] ).
cnf(144495272,plain,
c_in(c_tarski_olub(v_y,v_cl,t_a),v_a,t_a),
inference(rewrite,[status(thm)],[cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0]),
[] ).
cnf(152616984,plain,
( ~ c_in(A,v_a,t_a)
| c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),A,t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),A,t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))
| $equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),A,t_a),c_emptyset) ),
inference(resolution,[status(thm)],[144481824,144495272]),
[] ).
fof(cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0,plain,
! [A] :
( ~ c_in(A,v_a,t_a)
| ~ $equal(c_tarski_ointerval(v_r,A,c_tarski_otop(v_cl,t_a),t_a),c_emptyset) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),
[] ).
cnf(144500392,plain,
( ~ c_in(A,v_a,t_a)
| ~ $equal(c_tarski_ointerval(v_r,A,c_tarski_otop(v_cl,t_a),t_a),c_emptyset) ),
inference(rewrite,[status(thm)],[cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0]),
[] ).
cnf(152476808,plain,
~ $equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),c_emptyset),
inference(resolution,[status(thm)],[144500392,144495272]),
[] ).
cnf(152710128,plain,
c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144427768,152616984,152476808]),
[] ).
fof(cls_conjecture_0,plain,
~ c_in(c_tarski_opotype_opotype__ext(v_inty1,c_tarski_oinduced(v_inty1,v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),
[] ).
cnf(144422440,plain,
~ c_in(c_tarski_opotype_opotype__ext(v_inty1,c_tarski_oinduced(v_inty1,v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
fof(cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0,plain,
$equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),v_inty1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),
[] ).
cnf(144490992,plain,
$equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),v_inty1),
inference(rewrite,[status(thm)],[cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0]),
[] ).
cnf(152742248,plain,
~ c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),c_tarski_oinduced(v_inty1,v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
inference(paramodulation,[status(thm)],[144422440,144490992,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152710128,152742248,144490992,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0,plain,(c_in(c_tarski_otop(v_cl,t_a),v_a,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),[]).
%
% cnf(144427768,plain,(c_in(c_tarski_otop(v_cl,t_a),v_a,t_a)),inference(rewrite,[status(thm)],[cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0]),[]).
%
% fof(cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0,plain,(~c_in(A,v_a,t_a)|~c_in(B,v_a,t_a)|c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,B,A,t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,B,A,t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))|$equal(c_tarski_ointerval(v_r,B,A,t_a),c_emptyset)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),[]).
%
% cnf(144481824,plain,(~c_in(A,v_a,t_a)|~c_in(B,v_a,t_a)|c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,B,A,t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,B,A,t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))|$equal(c_tarski_ointerval(v_r,B,A,t_a),c_emptyset)),inference(rewrite,[status(thm)],[cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0]),[]).
%
% fof(cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0,plain,(c_in(c_tarski_olub(v_y,v_cl,t_a),v_a,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),[]).
%
% cnf(144495272,plain,(c_in(c_tarski_olub(v_y,v_cl,t_a),v_a,t_a)),inference(rewrite,[status(thm)],[cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0]),[]).
%
% cnf(152616984,plain,(~c_in(A,v_a,t_a)|c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),A,t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),A,t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))|$equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),A,t_a),c_emptyset)),inference(resolution,[status(thm)],[144481824,144495272]),[]).
%
% fof(cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0,plain,(~c_in(A,v_a,t_a)|~$equal(c_tarski_ointerval(v_r,A,c_tarski_otop(v_cl,t_a),t_a),c_emptyset)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),[]).
%
% cnf(144500392,plain,(~c_in(A,v_a,t_a)|~$equal(c_tarski_ointerval(v_r,A,c_tarski_otop(v_cl,t_a),t_a),c_emptyset)),inference(rewrite,[status(thm)],[cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0]),[]).
%
% cnf(152476808,plain,(~$equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),c_emptyset)),inference(resolution,[status(thm)],[144500392,144495272]),[]).
%
% cnf(152710128,plain,(c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),c_tarski_oinduced(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),inference(forward_subsumption_resolution__resolution,[status(thm)],[144427768,152616984,152476808]),[]).
%
% fof(cls_conjecture_0,plain,(~c_in(c_tarski_opotype_opotype__ext(v_inty1,c_tarski_oinduced(v_inty1,v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),[]).
%
% cnf(144422440,plain,(~c_in(c_tarski_opotype_opotype__ext(v_inty1,c_tarski_oinduced(v_inty1,v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% fof(cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0,plain,($equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),v_inty1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT269-2.tptp',unknown),[]).
%
% cnf(144490992,plain,($equal(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),v_inty1)),inference(rewrite,[status(thm)],[cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0]),[]).
%
% cnf(152742248,plain,(~c_in(c_tarski_opotype_opotype__ext(c_tarski_ointerval(v_r,c_tarski_olub(v_y,v_cl,t_a),c_tarski_otop(v_cl,t_a),t_a),c_tarski_oinduced(v_inty1,v_r,t_a),c_product__type_ounity,t_a,tc_product__type_ounit),c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),inference(paramodulation,[status(thm)],[144422440,144490992,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152710128,152742248,144490992,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------