TSTP Solution File: SET841-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET841-2 : 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 15:39:07 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 : 18 ( 15 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET841-2.tptp',unknown),
[] ).
cnf(171931248,plain,
c_lessequals(A,A,tc_set(B)),
inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_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/SET841-2.tptp',unknown),
[] ).
cnf(171979536,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]),
[] ).
fof(cls_conjecture_3,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),
[] ).
cnf(171992256,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
fof(cls_Zorn_OTFin__subsetD_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| ~ c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(A,D,tc_set(tc_set(C)))
| c_lessequals(c_zorn_osucc(B,A,C),D,tc_set(tc_set(C)))
| $equal(D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),
[] ).
cnf(171970528,plain,
( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| ~ c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(A,D,tc_set(tc_set(C)))
| c_lessequals(c_zorn_osucc(B,A,C),D,tc_set(tc_set(C)))
| $equal(D,A) ),
inference(rewrite,[status(thm)],[cls_Zorn_OTFin__subsetD_0]),
[] ).
fof(cls_conjecture_2,plain,
c_in(v_x,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),
[] ).
cnf(171988488,plain,
c_in(v_x,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(190350368,plain,
( ~ c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,A,tc_set(tc_set(t_a)))
| c_lessequals(c_zorn_osucc(v_s,v_x,t_a),A,tc_set(tc_set(t_a)))
| $equal(A,v_x) ),
inference(resolution,[status(thm)],[171970528,171988488]),
[] ).
fof(cls_conjecture_4,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),
[] ).
cnf(172005120,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(190403312,plain,
$equal(v_m,v_x),
inference(forward_subsumption_resolution__resolution,[status(thm)],[171979536,171992256,190350368,172005120]),
[] ).
fof(cls_conjecture_1,plain,
$equal(c_zorn_osucc(v_s,v_m,t_a),v_m),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),
[] ).
cnf(171984432,plain,
$equal(c_zorn_osucc(v_s,v_m,t_a),v_m),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(190420312,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_x,t_a),c_zorn_osucc(v_s,v_m,t_a),tc_set(tc_set(t_a))),
inference(paramodulation,[status(thm)],[172005120,171984432,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171931248,190403312,190420312,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Set_Osubset__refl_0,plain,(c_lessequals(A,A,tc_set(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(171931248,plain,(c_lessequals(A,A,tc_set(B))),inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(171979536,plain,(c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% fof(cls_conjecture_3,plain,(c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(171992256,plain,(c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% fof(cls_Zorn_OTFin__subsetD_0,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~c_lessequals(A,D,tc_set(tc_set(C)))|c_lessequals(c_zorn_osucc(B,A,C),D,tc_set(tc_set(C)))|$equal(D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(171970528,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~c_lessequals(A,D,tc_set(tc_set(C)))|c_lessequals(c_zorn_osucc(B,A,C),D,tc_set(tc_set(C)))|$equal(D,A)),inference(rewrite,[status(thm)],[cls_Zorn_OTFin__subsetD_0]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(v_x,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(171988488,plain,(c_in(v_x,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(190350368,plain,(~c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))|~c_lessequals(v_x,A,tc_set(tc_set(t_a)))|c_lessequals(c_zorn_osucc(v_s,v_x,t_a),A,tc_set(tc_set(t_a)))|$equal(A,v_x)),inference(resolution,[status(thm)],[171970528,171988488]),[]).
%
% fof(cls_conjecture_4,plain,(~c_lessequals(c_zorn_osucc(v_s,v_x,t_a),v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(172005120,plain,(~c_lessequals(c_zorn_osucc(v_s,v_x,t_a),v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(190403312,plain,($equal(v_m,v_x)),inference(forward_subsumption_resolution__resolution,[status(thm)],[171979536,171992256,190350368,172005120]),[]).
%
% fof(cls_conjecture_1,plain,($equal(c_zorn_osucc(v_s,v_m,t_a),v_m)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET841-2.tptp',unknown),[]).
%
% cnf(171984432,plain,($equal(c_zorn_osucc(v_s,v_m,t_a),v_m)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(190420312,plain,(~c_lessequals(c_zorn_osucc(v_s,v_x,t_a),c_zorn_osucc(v_s,v_m,t_a),tc_set(tc_set(t_a)))),inference(paramodulation,[status(thm)],[172005120,171984432,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171931248,190403312,190420312,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------