TSTP Solution File: SET859-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET859-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:39:54 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Set_Osubset__trans_0,plain,
! [A,B,C,D] :
( ~ c_lessequals(A,B,tc_set(C))
| ~ c_lessequals(D,A,tc_set(C))
| c_lessequals(D,B,tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),
[] ).
cnf(148429960,plain,
( ~ c_lessequals(A,B,tc_set(C))
| ~ c_lessequals(D,A,tc_set(C))
| c_lessequals(D,B,tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_Osubset__trans_0]),
[] ).
fof(cls_conjecture_2,plain,
c_lessequals(c_zorn_osucc(v_s,v_n,t_a),v_m,tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),
[] ).
cnf(148438832,plain,
c_lessequals(c_zorn_osucc(v_s,v_n,t_a),v_m,tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(158901608,plain,
( ~ c_lessequals(A,c_zorn_osucc(v_s,v_n,t_a),tc_set(tc_set(t_a)))
| c_lessequals(A,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[148429960,148438832]),
[] ).
fof(cls_conjecture_3,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),
[] ).
cnf(148442776,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(158945136,plain,
~ c_lessequals(v_n,c_zorn_osucc(v_s,v_n,t_a),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[158901608,148442776]),
[] ).
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/SET859-2.tptp',unknown),
[] ).
cnf(148434728,plain,
c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C))),
inference(rewrite,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[158945136,148434728]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Set_Osubset__trans_0,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(D,A,tc_set(C))|c_lessequals(D,B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),[]).
%
% cnf(148429960,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(D,A,tc_set(C))|c_lessequals(D,B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_Osubset__trans_0]),[]).
%
% fof(cls_conjecture_2,plain,(c_lessequals(c_zorn_osucc(v_s,v_n,t_a),v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),[]).
%
% cnf(148438832,plain,(c_lessequals(c_zorn_osucc(v_s,v_n,t_a),v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(158901608,plain,(~c_lessequals(A,c_zorn_osucc(v_s,v_n,t_a),tc_set(tc_set(t_a)))|c_lessequals(A,v_m,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[148429960,148438832]),[]).
%
% fof(cls_conjecture_3,plain,(~c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),[]).
%
% cnf(148442776,plain,(~c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(158945136,plain,(~c_lessequals(v_n,c_zorn_osucc(v_s,v_n,t_a),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[158901608,148442776]),[]).
%
% fof(cls_Zorn_OAbrial__axiom1_0,plain,(c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET859-2.tptp',unknown),[]).
%
% cnf(148434728,plain,(c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[158945136,148434728]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------