TSTP Solution File: SET865-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET865-2 : 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 15:40:04 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 23 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Set_OsubsetD_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| ~ c_lessequals(B,D,tc_set(C))
| c_in(A,D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),
[] ).
cnf(140956616,plain,
( ~ c_in(A,B,C)
| ~ c_lessequals(B,D,tc_set(C))
| c_in(A,D,C) ),
inference(rewrite,[status(thm)],[cls_Set_OsubsetD_0]),
[] ).
fof(cls_Zorn_OHausdorff_0,plain,
! [A,B] : c_in(c_zorn_ohausdorff__1(A,B),c_zorn_omaxchain(A,B),tc_set(tc_set(B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),
[] ).
cnf(140960864,plain,
c_in(c_zorn_ohausdorff__1(A,B),c_zorn_omaxchain(A,B),tc_set(tc_set(B))),
inference(rewrite,[status(thm)],[cls_Zorn_OHausdorff_0]),
[] ).
cnf(156727728,plain,
( ~ c_lessequals(c_zorn_omaxchain(B,C),A,tc_set(tc_set(tc_set(C))))
| c_in(c_zorn_ohausdorff__1(B,C),A,tc_set(tc_set(C))) ),
inference(resolution,[status(thm)],[140956616,140960864]),
[] ).
fof(cls_Zorn_Omaxchain__subset__chain_0,plain,
! [A,B] : c_lessequals(c_zorn_omaxchain(A,B),c_zorn_ochain(A,B),tc_set(tc_set(tc_set(B)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),
[] ).
cnf(141012240,plain,
c_lessequals(c_zorn_omaxchain(A,B),c_zorn_ochain(A,B),tc_set(tc_set(tc_set(B)))),
inference(rewrite,[status(thm)],[cls_Zorn_Omaxchain__subset__chain_0]),
[] ).
cnf(156825184,plain,
c_in(c_zorn_ohausdorff__1(A,B),c_zorn_ochain(A,B),tc_set(tc_set(B))),
inference(resolution,[status(thm)],[156727728,141012240]),
[] ).
fof(cls_conjecture_0,plain,
! [A] :
( c_in(c_union(A,t_a),v_s,tc_set(t_a))
| ~ c_in(A,c_zorn_ochain(v_s,t_a),tc_set(tc_set(t_a))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),
[] ).
cnf(140917728,plain,
( c_in(c_union(A,t_a),v_s,tc_set(t_a))
| ~ c_in(A,c_zorn_ochain(v_s,t_a),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(157722568,plain,
c_in(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a),v_s,tc_set(t_a)),
inference(resolution,[status(thm)],[156825184,140917728]),
[] ).
fof(cls_conjecture_2,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/SET865-2.tptp',unknown),
[] ).
cnf(140930256,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_2]),
[] ).
cnf(157772360,plain,
c_lessequals(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a),v_x(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[157722568,140930256]),
[] ).
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/SET865-2.tptp',unknown),
[] ).
cnf(141004000,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]),
[] ).
cnf(156814256,plain,
( ~ c_in(A,B,tc_set(C))
| ~ c_lessequals(c_union(c_zorn_ohausdorff__1(B,C),C),A,tc_set(C))
| $equal(c_union(c_zorn_ohausdorff__1(B,C),C),A) ),
inference(resolution,[status(thm)],[141004000,140960864]),
[] ).
fof(cls_conjecture_1,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/SET865-2.tptp',unknown),
[] ).
cnf(140923784,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_1]),
[] ).
cnf(157761424,plain,
c_in(v_x(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a)),v_s,tc_set(t_a)),
inference(resolution,[status(thm)],[157722568,140923784]),
[] ).
cnf(165440776,plain,
$equal(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a),v_x(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[157772360,156814256,157761424]),
[] ).
fof(cls_conjecture_3,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/SET865-2.tptp',unknown),
[] ).
cnf(140940880,plain,
( ~ $equal(v_x(A),A)
| ~ c_in(A,v_s,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157722568,165440776,140940880,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Set_OsubsetD_0,plain,(~c_in(A,B,C)|~c_lessequals(B,D,tc_set(C))|c_in(A,D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),[]).
%
% cnf(140956616,plain,(~c_in(A,B,C)|~c_lessequals(B,D,tc_set(C))|c_in(A,D,C)),inference(rewrite,[status(thm)],[cls_Set_OsubsetD_0]),[]).
%
% fof(cls_Zorn_OHausdorff_0,plain,(c_in(c_zorn_ohausdorff__1(A,B),c_zorn_omaxchain(A,B),tc_set(tc_set(B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),[]).
%
% cnf(140960864,plain,(c_in(c_zorn_ohausdorff__1(A,B),c_zorn_omaxchain(A,B),tc_set(tc_set(B)))),inference(rewrite,[status(thm)],[cls_Zorn_OHausdorff_0]),[]).
%
% cnf(156727728,plain,(~c_lessequals(c_zorn_omaxchain(B,C),A,tc_set(tc_set(tc_set(C))))|c_in(c_zorn_ohausdorff__1(B,C),A,tc_set(tc_set(C)))),inference(resolution,[status(thm)],[140956616,140960864]),[]).
%
% fof(cls_Zorn_Omaxchain__subset__chain_0,plain,(c_lessequals(c_zorn_omaxchain(A,B),c_zorn_ochain(A,B),tc_set(tc_set(tc_set(B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),[]).
%
% cnf(141012240,plain,(c_lessequals(c_zorn_omaxchain(A,B),c_zorn_ochain(A,B),tc_set(tc_set(tc_set(B))))),inference(rewrite,[status(thm)],[cls_Zorn_Omaxchain__subset__chain_0]),[]).
%
% cnf(156825184,plain,(c_in(c_zorn_ohausdorff__1(A,B),c_zorn_ochain(A,B),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[156727728,141012240]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(c_union(A,t_a),v_s,tc_set(t_a))|~c_in(A,c_zorn_ochain(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),[]).
%
% cnf(140917728,plain,(c_in(c_union(A,t_a),v_s,tc_set(t_a))|~c_in(A,c_zorn_ochain(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(157722568,plain,(c_in(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a),v_s,tc_set(t_a))),inference(resolution,[status(thm)],[156825184,140917728]),[]).
%
% fof(cls_conjecture_2,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/SET865-2.tptp',unknown),[]).
%
% cnf(140930256,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_2]),[]).
%
% cnf(157772360,plain,(c_lessequals(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a),v_x(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a)),tc_set(t_a))),inference(resolution,[status(thm)],[157722568,140930256]),[]).
%
% 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/SET865-2.tptp',unknown),[]).
%
% cnf(141004000,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))|$equal(c_union(D,C),A)),inference(rewrite,[status(thm)],[cls_Zorn_Omaxchain__Zorn_0]),[]).
%
% cnf(156814256,plain,(~c_in(A,B,tc_set(C))|~c_lessequals(c_union(c_zorn_ohausdorff__1(B,C),C),A,tc_set(C))|$equal(c_union(c_zorn_ohausdorff__1(B,C),C),A)),inference(resolution,[status(thm)],[141004000,140960864]),[]).
%
% fof(cls_conjecture_1,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/SET865-2.tptp',unknown),[]).
%
% cnf(140923784,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_1]),[]).
%
% cnf(157761424,plain,(c_in(v_x(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a)),v_s,tc_set(t_a))),inference(resolution,[status(thm)],[157722568,140923784]),[]).
%
% cnf(165440776,plain,($equal(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a),v_x(c_union(c_zorn_ohausdorff__1(v_s,t_a),t_a)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[157772360,156814256,157761424]),[]).
%
% fof(cls_conjecture_3,plain,(~$equal(v_x(A),A)|~c_in(A,v_s,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET865-2.tptp',unknown),[]).
%
% cnf(140940880,plain,(~$equal(v_x(A),A)|~c_in(A,v_s,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157722568,165440776,140940880,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------