TSTP Solution File: SET848-2 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET848-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:39:23 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 : 19 ( 10 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 35 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Zorn_OTFin__chain__lemma4_0,plain,
! [A,B,C] :
( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),
[] ).
cnf(153347040,plain,
( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C))) ),
inference(rewrite,[status(thm)],[cls_Zorn_OTFin__chain__lemma4_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/SET848-2.tptp',unknown),
[] ).
cnf(153336872,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/SET848-2.tptp',unknown),
[] ).
cnf(153308672,plain,
c_lessequals(A,A,tc_set(B)),
inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),
[] ).
cnf(163837984,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)],[153336872,153308672]),
[] ).
cnf(163882840,plain,
c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_ochain(A,B),tc_set(tc_set(B))),
inference(resolution,[status(thm)],[153347040,163837984]),
[] ).
fof(cls_Set_ODiffI_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| c_in(A,D,C)
| c_in(A,c_minus(B,D,tc_set(C)),C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),
[] ).
cnf(153303656,plain,
( ~ c_in(A,B,C)
| c_in(A,D,C)
| c_in(A,c_minus(B,D,tc_set(C)),C) ),
inference(rewrite,[status(thm)],[cls_Set_ODiffI_0]),
[] ).
fof(cls_conjecture_0,plain,
~ c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),
[] ).
cnf(153374456,plain,
~ c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(163925488,plain,
( ~ c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),A,tc_set(tc_set(t_a)))
| c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_minus(A,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[153303656,153374456]),
[] ).
fof(cls_Zorn_Osucc__not__equals_0,plain,
! [A,B,C] :
( ~ c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))
| ~ $equal(c_zorn_osucc(B,A,C),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),
[] ).
cnf(153366120,plain,
( ~ c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))
| ~ $equal(c_zorn_osucc(B,A,C),A) ),
inference(rewrite,[status(thm)],[cls_Zorn_Osucc__not__equals_0]),
[] ).
fof(cls_conjecture_1,plain,
$equal(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))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),
[] ).
cnf(153383672,plain,
$equal(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))),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(163974432,plain,
~ c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_minus(c_zorn_ochain(v_s,t_a),c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[153366120,153383672]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[163882840,163925488,163974432]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Zorn_OTFin__chain__lemma4_0,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),[]).
%
% cnf(153347040,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OTFin__chain__lemma4_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/SET848-2.tptp',unknown),[]).
%
% cnf(153336872,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/SET848-2.tptp',unknown),[]).
%
% cnf(153308672,plain,(c_lessequals(A,A,tc_set(B))),inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),[]).
%
% cnf(163837984,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)],[153336872,153308672]),[]).
%
% cnf(163882840,plain,(c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_ochain(A,B),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[153347040,163837984]),[]).
%
% fof(cls_Set_ODiffI_0,plain,(~c_in(A,B,C)|c_in(A,D,C)|c_in(A,c_minus(B,D,tc_set(C)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),[]).
%
% cnf(153303656,plain,(~c_in(A,B,C)|c_in(A,D,C)|c_in(A,c_minus(B,D,tc_set(C)),C)),inference(rewrite,[status(thm)],[cls_Set_ODiffI_0]),[]).
%
% fof(cls_conjecture_0,plain,(~c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),[]).
%
% cnf(153374456,plain,(~c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(163925488,plain,(~c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),A,tc_set(tc_set(t_a)))|c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_minus(A,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[153303656,153374456]),[]).
%
% fof(cls_Zorn_Osucc__not__equals_0,plain,(~c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))|~$equal(c_zorn_osucc(B,A,C),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),[]).
%
% cnf(153366120,plain,(~c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))|~$equal(c_zorn_osucc(B,A,C),A)),inference(rewrite,[status(thm)],[cls_Zorn_Osucc__not__equals_0]),[]).
%
% fof(cls_conjecture_1,plain,($equal(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)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET848-2.tptp',unknown),[]).
%
% cnf(153383672,plain,($equal(c_zorn_osucc(v_s,c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),t_a),c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(163974432,plain,(~c_in(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),c_minus(c_zorn_ochain(v_s,t_a),c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[153366120,153383672]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163882840,163925488,163974432]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------