TSTP Solution File: LAT268-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LAT268-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 13:36:41 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 24 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 27 ( 17 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 26 ( 0 sgn 13 !; 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/LAT268-2.tptp',unknown),
[] ).
cnf(154136040,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/LAT268-2.tptp',unknown),
[] ).
cnf(154266440,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/LAT268-2.tptp',unknown),
[] ).
cnf(154274712,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_conjecture_1,plain,
c_in(v_x,v_s,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),
[] ).
cnf(154141352,plain,
c_in(v_x,v_s,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
fof(cls_Tarski_OCL_Olub__upper_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| ~ c_in(D,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))
| ~ c_in(D,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))
| ~ c_lessequals(B,c_tarski_opotype_opset(D,C,tc_product__type_ounit),tc_set(C))
| c_in(c_pair(A,c_tarski_olub(B,D,C),C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),
[] ).
cnf(154241440,plain,
( ~ c_in(A,B,C)
| ~ c_in(D,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))
| ~ c_in(D,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))
| ~ c_lessequals(B,c_tarski_opotype_opset(D,C,tc_product__type_ounit),tc_set(C))
| c_in(c_pair(A,c_tarski_olub(B,D,C),C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C)) ),
inference(rewrite,[status(thm)],[cls_Tarski_OCL_Olub__upper_0]),
[] ).
fof(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0,plain,
! [A,B,C,D] :
( ~ c_in(c_pair(A,B,C,C),c_tarski_opotype_oorder(c_tarski_odual(D,C),C,tc_product__type_ounit),tc_prod(C,C))
| c_in(c_pair(B,A,C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),
[] ).
cnf(154261944,plain,
( ~ c_in(c_pair(A,B,C,C),c_tarski_opotype_oorder(c_tarski_odual(D,C),C,tc_product__type_ounit),tc_prod(C,C))
| c_in(c_pair(B,A,C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C)) ),
inference(rewrite,[status(thm)],[cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0]),
[] ).
fof(cls_conjecture_2,plain,
~ c_in(c_pair(c_tarski_oglb(v_s,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),
[] ).
cnf(154146784,plain,
~ c_in(c_pair(c_tarski_oglb(v_s,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
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/LAT268-2.tptp',unknown),
[] ).
cnf(154278928,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(167555432,plain,
~ c_in(c_pair(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(paramodulation,[status(thm)],[154146784,154278928,theory(equality)]),
[] ).
fof(cls_Tarski_Or_A_61_61_Aorder_Acl_0,plain,
$equal(c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),v_r),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),
[] ).
cnf(154291384,plain,
$equal(c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),v_r),
inference(rewrite,[status(thm)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]),
[] ).
cnf(167579256,plain,
~ c_in(c_pair(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),tc_prod(t_a,t_a)),
inference(paramodulation,[status(thm)],[167555432,154291384,theory(equality)]),
[] ).
cnf(167655336,plain,
~ c_in(c_pair(v_x,c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),t_a,t_a),c_tarski_opotype_oorder(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[154261944,167579256]),
[] ).
cnf(169143784,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)],[154266440,154274712,154141352,154241440,167655336]),
[] ).
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/LAT268-2.tptp',unknown),
[] ).
cnf(154287264,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(170306664,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)],[169143784,154287264,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/LAT268-2.tptp',unknown),
[] ).
cnf(154155992,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(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[154136040,170306664,154155992,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 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/LAT268-2.tptp',unknown),[]).
%
% cnf(154136040,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/LAT268-2.tptp',unknown),[]).
%
% cnf(154266440,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/LAT268-2.tptp',unknown),[]).
%
% cnf(154274712,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_conjecture_1,plain,(c_in(v_x,v_s,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),[]).
%
% cnf(154141352,plain,(c_in(v_x,v_s,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Tarski_OCL_Olub__upper_0,plain,(~c_in(A,B,C)|~c_in(D,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))|~c_in(D,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))|~c_lessequals(B,c_tarski_opotype_opset(D,C,tc_product__type_ounit),tc_set(C))|c_in(c_pair(A,c_tarski_olub(B,D,C),C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),[]).
%
% cnf(154241440,plain,(~c_in(A,B,C)|~c_in(D,c_tarski_ocompletelattice,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))|~c_in(D,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(C,tc_product__type_ounit))|~c_lessequals(B,c_tarski_opotype_opset(D,C,tc_product__type_ounit),tc_set(C))|c_in(c_pair(A,c_tarski_olub(B,D,C),C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C))),inference(rewrite,[status(thm)],[cls_Tarski_OCL_Olub__upper_0]),[]).
%
% fof(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0,plain,(~c_in(c_pair(A,B,C,C),c_tarski_opotype_oorder(c_tarski_odual(D,C),C,tc_product__type_ounit),tc_prod(C,C))|c_in(c_pair(B,A,C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),[]).
%
% cnf(154261944,plain,(~c_in(c_pair(A,B,C,C),c_tarski_opotype_oorder(c_tarski_odual(D,C),C,tc_product__type_ounit),tc_prod(C,C))|c_in(c_pair(B,A,C,C),c_tarski_opotype_oorder(D,C,tc_product__type_ounit),tc_prod(C,C))),inference(rewrite,[status(thm)],[cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0]),[]).
%
% fof(cls_conjecture_2,plain,(~c_in(c_pair(c_tarski_oglb(v_s,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),[]).
%
% cnf(154146784,plain,(~c_in(c_pair(c_tarski_oglb(v_s,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% 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/LAT268-2.tptp',unknown),[]).
%
% cnf(154278928,plain,($equal(c_tarski_olub(A,c_tarski_odual(B,C),C),c_tarski_oglb(A,B,C))),inference(rewrite,[status(thm)],[cls_Tarski_Oglb__dual__lub_0]),[]).
%
% cnf(167555432,plain,(~c_in(c_pair(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(paramodulation,[status(thm)],[154146784,154278928,theory(equality)]),[]).
%
% fof(cls_Tarski_Or_A_61_61_Aorder_Acl_0,plain,($equal(c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),v_r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),[]).
%
% cnf(154291384,plain,($equal(c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),v_r)),inference(rewrite,[status(thm)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]),[]).
%
% cnf(167579256,plain,(~c_in(c_pair(c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),tc_prod(t_a,t_a))),inference(paramodulation,[status(thm)],[167555432,154291384,theory(equality)]),[]).
%
% cnf(167655336,plain,(~c_in(c_pair(v_x,c_tarski_olub(v_s,c_tarski_odual(v_cl,t_a),t_a),t_a,t_a),c_tarski_opotype_oorder(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[154261944,167579256]),[]).
%
% cnf(169143784,plain,(~c_lessequals(v_s,c_tarski_opotype_opset(c_tarski_odual(v_cl,t_a),t_a,tc_product__type_ounit),tc_set(t_a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[154266440,154274712,154141352,154241440,167655336]),[]).
%
% fof(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,plain,($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/LAT268-2.tptp',unknown),[]).
%
% cnf(154287264,plain,($equal(c_tarski_opotype_opset(c_tarski_odual(A,B),B,tc_product__type_ounit),c_tarski_opotype_opset(A,B,tc_product__type_ounit))),inference(rewrite,[status(thm)],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0]),[]).
%
% cnf(170306664,plain,(~c_lessequals(v_s,c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),tc_set(t_a))),inference(paramodulation,[status(thm)],[169143784,154287264,theory(equality)]),[]).
%
% fof(cls_Tarski_OA_A_61_61_Apset_Acl_0,plain,($equal(c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),v_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT268-2.tptp',unknown),[]).
%
% cnf(154155992,plain,($equal(c_tarski_opotype_opset(v_cl,t_a,tc_product__type_ounit),v_a)),inference(rewrite,[status(thm)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[154136040,170306664,154155992,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------