TSTP Solution File: SET852-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET852-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:39:35 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 13 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 29 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Zorn_OUnion__lemma0_2,plain,
! [A,B,C,D] :
( ~ c_lessequals(A,c_zorn_ounion__lemma0__1(B,A,C,D),tc_set(D))
| c_lessequals(A,c_union(C,D),tc_set(D))
| c_lessequals(c_union(C,D),B,tc_set(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),
[] ).
cnf(146767296,plain,
( ~ c_lessequals(A,c_zorn_ounion__lemma0__1(B,A,C,D),tc_set(D))
| c_lessequals(A,c_union(C,D),tc_set(D))
| c_lessequals(c_union(C,D),B,tc_set(D)) ),
inference(rewrite,[status(thm)],[cls_Zorn_OUnion__lemma0_2]),
[] ).
fof(cls_conjecture_2,plain,
~ c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),
[] ).
cnf(146688344,plain,
~ c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(159889504,plain,
( ~ c_lessequals(A,c_zorn_ounion__lemma0__1(v_m,A,v_y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(A,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[146767296,146688344]),
[] ).
fof(cls_Zorn_OUnion__lemma0_0,plain,
! [A,B,C,D] :
( c_in(c_zorn_ounion__lemma0__1(A,B,C,D),C,tc_set(D))
| c_lessequals(B,c_union(C,D),tc_set(D))
| c_lessequals(c_union(C,D),A,tc_set(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),
[] ).
cnf(146747744,plain,
( c_in(c_zorn_ounion__lemma0__1(A,B,C,D),C,tc_set(D))
| c_lessequals(B,c_union(C,D),tc_set(D))
| c_lessequals(c_union(C,D),A,tc_set(D)) ),
inference(rewrite,[status(thm)],[cls_Zorn_OUnion__lemma0_0]),
[] ).
cnf(159851824,plain,
( c_in(c_zorn_ounion__lemma0__1(v_m,A,v_y,tc_set(t_a)),v_y,tc_set(tc_set(t_a)))
| c_lessequals(A,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[146747744,146688344]),
[] ).
fof(cls_conjecture_3,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),
[] ).
cnf(146692800,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(159914960,plain,
c_in(c_zorn_ounion__lemma0__1(v_m,c_zorn_osucc(v_s,v_m,t_a),v_y,tc_set(t_a)),v_y,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[159851824,146692800]),
[] ).
fof(cls_Zorn_OUnion__lemma0_1,plain,
! [A,B,C,D] :
( ~ c_lessequals(c_zorn_ounion__lemma0__1(A,B,C,D),A,tc_set(D))
| c_lessequals(B,c_union(C,D),tc_set(D))
| c_lessequals(c_union(C,D),A,tc_set(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),
[] ).
cnf(146755520,plain,
( ~ c_lessequals(c_zorn_ounion__lemma0__1(A,B,C,D),A,tc_set(D))
| c_lessequals(B,c_union(C,D),tc_set(D))
| c_lessequals(c_union(C,D),A,tc_set(D)) ),
inference(rewrite,[status(thm)],[cls_Zorn_OUnion__lemma0_1]),
[] ).
cnf(159868976,plain,
( ~ c_lessequals(c_zorn_ounion__lemma0__1(v_m,A,v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(A,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[146755520,146688344]),
[] ).
cnf(159930328,plain,
~ c_lessequals(c_zorn_ounion__lemma0__1(v_m,c_zorn_osucc(v_s,v_m,t_a),v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[159868976,146692800]),
[] ).
fof(cls_conjecture_4,plain,
! [A] :
( c_lessequals(c_zorn_osucc(v_s,v_m,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,v_y,tc_set(tc_set(t_a))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),
[] ).
cnf(146700920,plain,
( c_lessequals(c_zorn_osucc(v_s,v_m,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,v_y,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(160267232,plain,
c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_zorn_ounion__lemma0__1(v_m,c_zorn_osucc(v_s,v_m,t_a),v_y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159914960,159930328,146700920]),
[] ).
cnf(160491600,plain,
c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[159889504,160267232]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[160491600,146692800]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Zorn_OUnion__lemma0_2,plain,(~c_lessequals(A,c_zorn_ounion__lemma0__1(B,A,C,D),tc_set(D))|c_lessequals(A,c_union(C,D),tc_set(D))|c_lessequals(c_union(C,D),B,tc_set(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),[]).
%
% cnf(146767296,plain,(~c_lessequals(A,c_zorn_ounion__lemma0__1(B,A,C,D),tc_set(D))|c_lessequals(A,c_union(C,D),tc_set(D))|c_lessequals(c_union(C,D),B,tc_set(D))),inference(rewrite,[status(thm)],[cls_Zorn_OUnion__lemma0_2]),[]).
%
% fof(cls_conjecture_2,plain,(~c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),[]).
%
% cnf(146688344,plain,(~c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(159889504,plain,(~c_lessequals(A,c_zorn_ounion__lemma0__1(v_m,A,v_y,tc_set(t_a)),tc_set(tc_set(t_a)))|c_lessequals(A,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[146767296,146688344]),[]).
%
% fof(cls_Zorn_OUnion__lemma0_0,plain,(c_in(c_zorn_ounion__lemma0__1(A,B,C,D),C,tc_set(D))|c_lessequals(B,c_union(C,D),tc_set(D))|c_lessequals(c_union(C,D),A,tc_set(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),[]).
%
% cnf(146747744,plain,(c_in(c_zorn_ounion__lemma0__1(A,B,C,D),C,tc_set(D))|c_lessequals(B,c_union(C,D),tc_set(D))|c_lessequals(c_union(C,D),A,tc_set(D))),inference(rewrite,[status(thm)],[cls_Zorn_OUnion__lemma0_0]),[]).
%
% cnf(159851824,plain,(c_in(c_zorn_ounion__lemma0__1(v_m,A,v_y,tc_set(t_a)),v_y,tc_set(tc_set(t_a)))|c_lessequals(A,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[146747744,146688344]),[]).
%
% fof(cls_conjecture_3,plain,(~c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),[]).
%
% cnf(146692800,plain,(~c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(159914960,plain,(c_in(c_zorn_ounion__lemma0__1(v_m,c_zorn_osucc(v_s,v_m,t_a),v_y,tc_set(t_a)),v_y,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[159851824,146692800]),[]).
%
% fof(cls_Zorn_OUnion__lemma0_1,plain,(~c_lessequals(c_zorn_ounion__lemma0__1(A,B,C,D),A,tc_set(D))|c_lessequals(B,c_union(C,D),tc_set(D))|c_lessequals(c_union(C,D),A,tc_set(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),[]).
%
% cnf(146755520,plain,(~c_lessequals(c_zorn_ounion__lemma0__1(A,B,C,D),A,tc_set(D))|c_lessequals(B,c_union(C,D),tc_set(D))|c_lessequals(c_union(C,D),A,tc_set(D))),inference(rewrite,[status(thm)],[cls_Zorn_OUnion__lemma0_1]),[]).
%
% cnf(159868976,plain,(~c_lessequals(c_zorn_ounion__lemma0__1(v_m,A,v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))|c_lessequals(A,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[146755520,146688344]),[]).
%
% cnf(159930328,plain,(~c_lessequals(c_zorn_ounion__lemma0__1(v_m,c_zorn_osucc(v_s,v_m,t_a),v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[159868976,146692800]),[]).
%
% fof(cls_conjecture_4,plain,(c_lessequals(c_zorn_osucc(v_s,v_m,t_a),A,tc_set(tc_set(t_a)))|c_lessequals(A,v_m,tc_set(tc_set(t_a)))|~c_in(A,v_y,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET852-2.tptp',unknown),[]).
%
% cnf(146700920,plain,(c_lessequals(c_zorn_osucc(v_s,v_m,t_a),A,tc_set(tc_set(t_a)))|c_lessequals(A,v_m,tc_set(tc_set(t_a)))|~c_in(A,v_y,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(160267232,plain,(c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_zorn_ounion__lemma0__1(v_m,c_zorn_osucc(v_s,v_m,t_a),v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[159914960,159930328,146700920]),[]).
%
% cnf(160491600,plain,(c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[159889504,160267232]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[160491600,146692800]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------