%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LAT281-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 13:37:14 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_1,plain,
c_in(c_pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),
[] ).
cnf(161403872,plain,
c_in(c_pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
fof(cls_Tarski_Ocl_A_58_APartialOrder_0,plain,
c_in(v_cl,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),
[] ).
cnf(161460208,plain,
c_in(v_cl,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit)),
inference(rewrite,[status(thm)],[cls_Tarski_Ocl_A_58_APartialOrder_0]),
[] ).
fof(cls_Tarski_OPartialOrder__iff_2,plain,
! [A,B] :
( ~ c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))
| c_relation_otrans(c_tarski_opotype_oorder(A,B,tc_product__type_ounit),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),
[] ).
cnf(161451840,plain,
( ~ c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))
| c_relation_otrans(c_tarski_opotype_oorder(A,B,tc_product__type_ounit),B) ),
inference(rewrite,[status(thm)],[cls_Tarski_OPartialOrder__iff_2]),
[] ).
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/LAT281-2.tptp',unknown),
[] ).
cnf(161465088,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(174628304,plain,
c_relation_otrans(v_r,t_a),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161460208,161451840,161465088,theory(equality)]),
[] ).
fof(cls_Relation_Otrans__def_0,plain,
! [A,B,C,D,E] :
( ~ c_relation_otrans(A,B)
| ~ c_in(c_pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_pair(E,C,B,B),A,tc_prod(B,B))
| c_in(c_pair(E,D,B,B),A,tc_prod(B,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),
[] ).
cnf(161445968,plain,
( ~ c_relation_otrans(A,B)
| ~ c_in(c_pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_pair(E,C,B,B),A,tc_prod(B,B))
| c_in(c_pair(E,D,B,B),A,tc_prod(B,B)) ),
inference(rewrite,[status(thm)],[cls_Relation_Otrans__def_0]),
[] ).
fof(cls_conjecture_0,plain,
c_in(c_pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),
[] ).
cnf(161399432,plain,
c_in(c_pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(174746544,plain,
( ~ c_in(c_pair(v_b,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_pair(v_a,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174628304,161445968,161399432]),
[] ).
fof(cls_conjecture_2,plain,
~ c_in(c_pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),
[] ).
cnf(161408544,plain,
~ c_in(c_pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[161403872,174746544,161408544]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_1,plain,(c_in(c_pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161403872,plain,(c_in(c_pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Tarski_Ocl_A_58_APartialOrder_0,plain,(c_in(v_cl,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161460208,plain,(c_in(v_cl,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(t_a,tc_product__type_ounit))),inference(rewrite,[status(thm)],[cls_Tarski_Ocl_A_58_APartialOrder_0]),[]).
%
% fof(cls_Tarski_OPartialOrder__iff_2,plain,(~c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))|c_relation_otrans(c_tarski_opotype_oorder(A,B,tc_product__type_ounit),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161451840,plain,(~c_in(A,c_tarski_opartialorder,tc_tarski_opotype_opotype__ext__type(B,tc_product__type_ounit))|c_relation_otrans(c_tarski_opotype_oorder(A,B,tc_product__type_ounit),B)),inference(rewrite,[status(thm)],[cls_Tarski_OPartialOrder__iff_2]),[]).
%
% fof(cls_Tarski_Or_A_61_61_Aorder_Acl_0,plain,($equal(c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),v_r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161465088,plain,($equal(c_tarski_opotype_oorder(v_cl,t_a,tc_product__type_ounit),v_r)),inference(rewrite,[status(thm)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]),[]).
%
% cnf(174628304,plain,(c_relation_otrans(v_r,t_a)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161460208,161451840,161465088,theory(equality)]),[]).
%
% fof(cls_Relation_Otrans__def_0,plain,(~c_relation_otrans(A,B)|~c_in(c_pair(C,D,B,B),A,tc_prod(B,B))|~c_in(c_pair(E,C,B,B),A,tc_prod(B,B))|c_in(c_pair(E,D,B,B),A,tc_prod(B,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161445968,plain,(~c_relation_otrans(A,B)|~c_in(c_pair(C,D,B,B),A,tc_prod(B,B))|~c_in(c_pair(E,C,B,B),A,tc_prod(B,B))|c_in(c_pair(E,D,B,B),A,tc_prod(B,B))),inference(rewrite,[status(thm)],[cls_Relation_Otrans__def_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(c_pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161399432,plain,(c_in(c_pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(174746544,plain,(~c_in(c_pair(v_b,A,t_a,t_a),v_r,tc_prod(t_a,t_a))|c_in(c_pair(v_a,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[174628304,161445968,161399432]),[]).
%
% fof(cls_conjecture_2,plain,(~c_in(c_pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT281-2.tptp',unknown),[]).
%
% cnf(161408544,plain,(~c_in(c_pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[161403872,174746544,161408544]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------