TSTP Solution File: SET846-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET846-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:39:19 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Set_OUnion__upper_0,plain,
! [A,B,C] :
( ~ c_in(A,B,tc_set(C))
| c_lessequals(A,c_union(B,C),tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),
[] ).
cnf(158847568,plain,
( ~ c_in(A,B,tc_set(C))
| c_lessequals(A,c_union(B,C),tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_OUnion__upper_0]),
[] ).
fof(cls_Zorn_OTFin_OsuccI_0,plain,
! [A,B,C] :
( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| c_in(c_zorn_osucc(B,A,C),c_zorn_otfin(B,C),tc_set(tc_set(C))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),
[] ).
cnf(158875680,plain,
( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| c_in(c_zorn_osucc(B,A,C),c_zorn_otfin(B,C),tc_set(tc_set(C))) ),
inference(rewrite,[status(thm)],[cls_Zorn_OTFin_OsuccI_0]),
[] ).
fof(cls_Zorn_OTFin__UnionI_0,plain,
! [A,B,C] :
( ~ c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))
| c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),
[] ).
cnf(158907824,plain,
( ~ c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))
| c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C))) ),
inference(rewrite,[status(thm)],[cls_Zorn_OTFin__UnionI_0]),
[] ).
fof(cls_Set_Osubset__refl_0,plain,
! [A,B] : c_lessequals(A,A,tc_set(B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),
[] ).
cnf(158852624,plain,
c_lessequals(A,A,tc_set(B)),
inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),
[] ).
cnf(166714704,plain,
c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B))),
inference(resolution,[status(thm)],[158907824,158852624]),
[] ).
cnf(166743744,plain,
c_in(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_zorn_otfin(A,B),tc_set(tc_set(B))),
inference(resolution,[status(thm)],[158875680,166714704]),
[] ).
cnf(166755912,plain,
c_lessequals(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B)),tc_set(tc_set(B))),
inference(resolution,[status(thm)],[158847568,166743744]),
[] ).
fof(cls_conjecture_1,plain,
~ c_lessequals(c_zorn_osucc(v_s,c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),t_a),c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),
[] ).
cnf(158912016,plain,
~ c_lessequals(c_zorn_osucc(v_s,c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),t_a),c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[166755912,158912016]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Set_OUnion__upper_0,plain,(~c_in(A,B,tc_set(C))|c_lessequals(A,c_union(B,C),tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),[]).
%
% cnf(158847568,plain,(~c_in(A,B,tc_set(C))|c_lessequals(A,c_union(B,C),tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OUnion__upper_0]),[]).
%
% fof(cls_Zorn_OTFin_OsuccI_0,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(c_zorn_osucc(B,A,C),c_zorn_otfin(B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),[]).
%
% cnf(158875680,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(c_zorn_osucc(B,A,C),c_zorn_otfin(B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OTFin_OsuccI_0]),[]).
%
% fof(cls_Zorn_OTFin__UnionI_0,plain,(~c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))|c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),[]).
%
% cnf(158907824,plain,(~c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))|c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OTFin__UnionI_0]),[]).
%
% fof(cls_Set_Osubset__refl_0,plain,(c_lessequals(A,A,tc_set(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),[]).
%
% cnf(158852624,plain,(c_lessequals(A,A,tc_set(B))),inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),[]).
%
% cnf(166714704,plain,(c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[158907824,158852624]),[]).
%
% cnf(166743744,plain,(c_in(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_zorn_otfin(A,B),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[158875680,166714704]),[]).
%
% cnf(166755912,plain,(c_lessequals(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B)),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[158847568,166743744]),[]).
%
% fof(cls_conjecture_1,plain,(~c_lessequals(c_zorn_osucc(v_s,c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),t_a),c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET846-2.tptp',unknown),[]).
%
% cnf(158912016,plain,(~c_lessequals(c_zorn_osucc(v_s,c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),t_a),c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[166755912,158912016]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------