TSTP Solution File: SET845-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET845-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 15:39:16 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET845-2.tptp',unknown),
[] ).
cnf(170286184,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_conjecture_0,plain,
c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),
[] ).
cnf(170291008,plain,
c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(183405224,plain,
c_in(c_zorn_osucc(v_s,v_m,t_a),c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[170286184,170291008]),
[] ).
fof(cls_Zorn_OAbrial__axiom1_0,plain,
! [A,B,C] : c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),
[] ).
cnf(170258960,plain,
c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C))),
inference(rewrite,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]),
[] ).
fof(cls_Set_Osubset__antisym_0,plain,
! [A,B,C] :
( ~ c_lessequals(A,B,tc_set(C))
| ~ c_lessequals(B,A,tc_set(C))
| $equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),
[] ).
cnf(170254040,plain,
( ~ c_lessequals(A,B,tc_set(C))
| ~ c_lessequals(B,A,tc_set(C))
| $equal(A,B) ),
inference(rewrite,[status(thm)],[cls_Set_Osubset__antisym_0]),
[] ).
fof(cls_conjecture_2,plain,
~ $equal(c_zorn_osucc(v_s,v_m,t_a),v_m),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),
[] ).
cnf(170304856,plain,
~ $equal(c_zorn_osucc(v_s,v_m,t_a),v_m),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(183382728,plain,
( ~ c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_m,tc_set(A))
| ~ c_lessequals(v_m,c_zorn_osucc(v_s,v_m,t_a),tc_set(A)) ),
inference(resolution,[status(thm)],[170254040,170304856]),
[] ).
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/SET845-2.tptp',unknown),
[] ).
cnf(170245544,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_conjecture_1,plain,
$equal(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),
[] ).
cnf(170300072,plain,
$equal(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(183544560,plain,
( ~ c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))
| c_lessequals(A,v_m,tc_set(tc_set(t_a))) ),
inference(paramodulation,[status(thm)],[170245544,170300072,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[183405224,170258960,183382728,183544560]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Zorn_OTFin_OsuccI_0,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(c_zorn_osucc(B,A,C),c_zorn_otfin(B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170286184,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(c_zorn_osucc(B,A,C),c_zorn_otfin(B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OTFin_OsuccI_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170291008,plain,(c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(183405224,plain,(c_in(c_zorn_osucc(v_s,v_m,t_a),c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[170286184,170291008]),[]).
%
% fof(cls_Zorn_OAbrial__axiom1_0,plain,(c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170258960,plain,(c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]),[]).
%
% fof(cls_Set_Osubset__antisym_0,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(B,A,tc_set(C))|$equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170254040,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(B,A,tc_set(C))|$equal(A,B)),inference(rewrite,[status(thm)],[cls_Set_Osubset__antisym_0]),[]).
%
% fof(cls_conjecture_2,plain,(~$equal(c_zorn_osucc(v_s,v_m,t_a),v_m)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170304856,plain,(~$equal(c_zorn_osucc(v_s,v_m,t_a),v_m)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(183382728,plain,(~c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_m,tc_set(A))|~c_lessequals(v_m,c_zorn_osucc(v_s,v_m,t_a),tc_set(A))),inference(resolution,[status(thm)],[170254040,170304856]),[]).
%
% fof(cls_Set_OUnion__upper_0,plain,(~c_in(A,B,tc_set(C))|c_lessequals(A,c_union(B,C),tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170245544,plain,(~c_in(A,B,tc_set(C))|c_lessequals(A,c_union(B,C),tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OUnion__upper_0]),[]).
%
% fof(cls_conjecture_1,plain,($equal(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET845-2.tptp',unknown),[]).
%
% cnf(170300072,plain,($equal(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(183544560,plain,(~c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))|c_lessequals(A,v_m,tc_set(tc_set(t_a)))),inference(paramodulation,[status(thm)],[170245544,170300072,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[183405224,170258960,183382728,183544560]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------