TSTP Solution File: SET864-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET864-2 : 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 15:40:01 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 0-2 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
c_in(c_union(v_c,t_a),v_s,tc_set(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),
[] ).
cnf(172925528,plain,
c_in(c_union(v_c,t_a),v_s,tc_set(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
fof(cls_conjecture_4,plain,
! [A] :
( c_lessequals(A,v_x(A),tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),
[] ).
cnf(172937752,plain,
( c_lessequals(A,v_x(A),tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(191296152,plain,
c_lessequals(c_union(v_c,t_a),v_x(c_union(v_c,t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[172937752,172925528]),
[] ).
fof(cls_Zorn_Omaxchain__Zorn_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,tc_set(C))
| ~ c_in(D,c_zorn_omaxchain(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(c_union(D,C),A,tc_set(C))
| $equal(c_union(D,C),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),
[] ).
cnf(172912040,plain,
( ~ c_in(A,B,tc_set(C))
| ~ c_in(D,c_zorn_omaxchain(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(c_union(D,C),A,tc_set(C))
| $equal(c_union(D,C),A) ),
inference(rewrite,[status(thm)],[cls_Zorn_Omaxchain__Zorn_0]),
[] ).
fof(cls_conjecture_0,plain,
c_in(v_c,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),
[] ).
cnf(172917144,plain,
c_in(v_c,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(193056592,plain,
( ~ c_in(A,v_s,tc_set(t_a))
| ~ c_lessequals(c_union(v_c,t_a),A,tc_set(t_a))
| $equal(c_union(v_c,t_a),A) ),
inference(resolution,[status(thm)],[172912040,172917144]),
[] ).
fof(cls_conjecture_3,plain,
! [A] :
( c_in(v_x(A),v_s,tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),
[] ).
cnf(172931144,plain,
( c_in(v_x(A),v_s,tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(191285216,plain,
c_in(v_x(c_union(v_c,t_a)),v_s,tc_set(t_a)),
inference(resolution,[status(thm)],[172931144,172925528]),
[] ).
cnf(194641200,plain,
$equal(c_union(v_c,t_a),v_x(c_union(v_c,t_a))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[191296152,193056592,191285216]),
[] ).
fof(cls_conjecture_5,plain,
! [A] :
( ~ $equal(v_x(A),A)
| ~ c_in(A,v_s,tc_set(t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),
[] ).
cnf(172948312,plain,
( ~ $equal(v_x(A),A)
| ~ c_in(A,v_s,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_5]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[172925528,194641200,172948312,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,(c_in(c_union(v_c,t_a),v_s,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),[]).
%
% cnf(172925528,plain,(c_in(c_union(v_c,t_a),v_s,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% fof(cls_conjecture_4,plain,(c_lessequals(A,v_x(A),tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),[]).
%
% cnf(172937752,plain,(c_lessequals(A,v_x(A),tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(191296152,plain,(c_lessequals(c_union(v_c,t_a),v_x(c_union(v_c,t_a)),tc_set(t_a))),inference(resolution,[status(thm)],[172937752,172925528]),[]).
%
% fof(cls_Zorn_Omaxchain__Zorn_0,plain,(~c_in(A,B,tc_set(C))|~c_in(D,c_zorn_omaxchain(B,C),tc_set(tc_set(C)))|~c_lessequals(c_union(D,C),A,tc_set(C))|$equal(c_union(D,C),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),[]).
%
% cnf(172912040,plain,(~c_in(A,B,tc_set(C))|~c_in(D,c_zorn_omaxchain(B,C),tc_set(tc_set(C)))|~c_lessequals(c_union(D,C),A,tc_set(C))|$equal(c_union(D,C),A)),inference(rewrite,[status(thm)],[cls_Zorn_Omaxchain__Zorn_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(v_c,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),[]).
%
% cnf(172917144,plain,(c_in(v_c,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(193056592,plain,(~c_in(A,v_s,tc_set(t_a))|~c_lessequals(c_union(v_c,t_a),A,tc_set(t_a))|$equal(c_union(v_c,t_a),A)),inference(resolution,[status(thm)],[172912040,172917144]),[]).
%
% fof(cls_conjecture_3,plain,(c_in(v_x(A),v_s,tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),[]).
%
% cnf(172931144,plain,(c_in(v_x(A),v_s,tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(191285216,plain,(c_in(v_x(c_union(v_c,t_a)),v_s,tc_set(t_a))),inference(resolution,[status(thm)],[172931144,172925528]),[]).
%
% cnf(194641200,plain,($equal(c_union(v_c,t_a),v_x(c_union(v_c,t_a)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[191296152,193056592,191285216]),[]).
%
% fof(cls_conjecture_5,plain,(~$equal(v_x(A),A)|~c_in(A,v_s,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET864-2.tptp',unknown),[]).
%
% cnf(172948312,plain,(~$equal(v_x(A),A)|~c_in(A,v_s,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_5]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[172925528,194641200,172948312,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------