TSTP Solution File: SET851-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET851-2 : 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 15:39:32 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 14 ( 2 sgn 7 !; 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/SET851-2.tptp',unknown),
[] ).
cnf(152783880,plain,
c_lessequals(A,A,tc_set(B)),
inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),
[] ).
fof(cls_conjecture_1,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/SET851-2.tptp',unknown),
[] ).
cnf(152816944,plain,
c_in(v_x,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
fof(cls_Zorn_Osucc__trans_0,plain,
! [A,B,C,D] :
( ~ c_lessequals(A,B,tc_set(tc_set(C)))
| c_lessequals(A,c_zorn_osucc(D,B,C),tc_set(tc_set(C))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),
[] ).
cnf(152811968,plain,
( ~ c_lessequals(A,B,tc_set(tc_set(C)))
| c_lessequals(A,c_zorn_osucc(D,B,C),tc_set(tc_set(C))) ),
inference(rewrite,[status(thm)],[cls_Zorn_Osucc__trans_0]),
[] ).
fof(cls_conjecture_3,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_zorn_osucc(v_s,v_x,t_a),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),
[] ).
cnf(152829528,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_zorn_osucc(v_s,v_x,t_a),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(171194272,plain,
~ c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[152811968,152829528]),
[] ).
fof(cls_conjecture_4,plain,
( c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),
[] ).
cnf(152839096,plain,
( c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(171300072,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[171194272,152839096]),
[] ).
fof(cls_conjecture_5,plain,
! [A] :
( c_lessequals(c_zorn_osucc(v_s,A,t_a),v_m,tc_set(tc_set(t_a)))
| $equal(v_m,A)
| ~ c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),
[] ).
cnf(152852496,plain,
( c_lessequals(c_zorn_osucc(v_s,A,t_a),v_m,tc_set(tc_set(t_a)))
| $equal(v_m,A)
| ~ c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[cls_conjecture_5]),
[] ).
fof(cls_conjecture_2,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/SET851-2.tptp',unknown),
[] ).
cnf(152825424,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_2]),
[] ).
cnf(172206200,plain,
$equal(v_m,v_x),
inference(forward_subsumption_resolution__resolution,[status(thm)],[152816944,171300072,152852496,152825424]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152783880,172206200,152829528,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/SET851-2.tptp',unknown),[]).
%
% cnf(152783880,plain,(c_lessequals(A,A,tc_set(B))),inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),[]).
%
% fof(cls_conjecture_1,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/SET851-2.tptp',unknown),[]).
%
% cnf(152816944,plain,(c_in(v_x,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Zorn_Osucc__trans_0,plain,(~c_lessequals(A,B,tc_set(tc_set(C)))|c_lessequals(A,c_zorn_osucc(D,B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),[]).
%
% cnf(152811968,plain,(~c_lessequals(A,B,tc_set(tc_set(C)))|c_lessequals(A,c_zorn_osucc(D,B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_Osucc__trans_0]),[]).
%
% fof(cls_conjecture_3,plain,(~c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_zorn_osucc(v_s,v_x,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),[]).
%
% cnf(152829528,plain,(~c_lessequals(c_zorn_osucc(v_s,v_m,t_a),c_zorn_osucc(v_s,v_x,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(171194272,plain,(~c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_x,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[152811968,152829528]),[]).
%
% fof(cls_conjecture_4,plain,(c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_x,tc_set(tc_set(t_a)))|c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),[]).
%
% cnf(152839096,plain,(c_lessequals(c_zorn_osucc(v_s,v_m,t_a),v_x,tc_set(tc_set(t_a)))|c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(171300072,plain,(c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[171194272,152839096]),[]).
%
% fof(cls_conjecture_5,plain,(c_lessequals(c_zorn_osucc(v_s,A,t_a),v_m,tc_set(tc_set(t_a)))|$equal(v_m,A)|~c_lessequals(A,v_m,tc_set(tc_set(t_a)))|~c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),[]).
%
% cnf(152852496,plain,(c_lessequals(c_zorn_osucc(v_s,A,t_a),v_m,tc_set(tc_set(t_a)))|$equal(v_m,A)|~c_lessequals(A,v_m,tc_set(tc_set(t_a)))|~c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_5]),[]).
%
% fof(cls_conjecture_2,plain,(~c_lessequals(c_zorn_osucc(v_s,v_x,t_a),v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET851-2.tptp',unknown),[]).
%
% cnf(152825424,plain,(~c_lessequals(c_zorn_osucc(v_s,v_x,t_a),v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(172206200,plain,($equal(v_m,v_x)),inference(forward_subsumption_resolution__resolution,[status(thm)],[152816944,171300072,152852496,152825424]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152783880,172206200,152829528,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------