TSTP Solution File: SET839-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET839-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 15:39:02 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 8 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_1,plain,
! [A,B] :
( c_lessequals(A,B,tc_set(t_a))
| ~ c_in(B,v_s,tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),
[] ).
cnf(157660368,plain,
( c_lessequals(A,B,tc_set(t_a))
| ~ c_in(B,v_s,tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
fof(cls_Set_Osubset__antisym_0,plain,
! [A,B,C] :
( ~ c_lessequals(A,B,tc_set(C))
| ~ c_lessequals(B,A,tc_set(C))
| $equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),
[] ).
cnf(157689024,plain,
( ~ c_lessequals(A,B,tc_set(C))
| ~ c_lessequals(B,A,tc_set(C))
| $equal(A,B) ),
inference(rewrite,[status(thm)],[cls_Set_Osubset__antisym_0]),
[] ).
cnf(168303640,plain,
( ~ c_in(B,v_s,tc_set(t_a))
| ~ c_in(A,v_s,tc_set(t_a))
| $equal(A,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[157660368,157660368,157689024]),
[] ).
fof(cls_Set_OsubsetI_0,plain,
! [A,B,C] :
( c_in(c_main_osubseti__1(A,B,C),A,C)
| c_lessequals(A,B,tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),
[] ).
cnf(157675056,plain,
( c_in(c_main_osubseti__1(A,B,C),A,C)
| c_lessequals(A,B,tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_OsubsetI_0]),
[] ).
fof(cls_conjecture_0,plain,
! [A] : ~ c_lessequals(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),
[] ).
cnf(157651792,plain,
~ c_lessequals(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(168123104,plain,
c_in(c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),v_s,tc_set(t_a)),
inference(resolution,[status(thm)],[157675056,157651792]),
[] ).
cnf(168334776,plain,
( ~ c_in(A,v_s,tc_set(t_a))
| $equal(A,c_main_osubseti__1(v_s,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a))) ),
inference(resolution,[status(thm)],[168303640,168123104]),
[] ).
cnf(168526392,plain,
$equal(c_main_osubseti__1(v_s,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a))),
inference(resolution,[status(thm)],[168334776,168123104]),
[] ).
fof(cls_Set_OsubsetI_1,plain,
! [A,B,C] :
( ~ c_in(c_main_osubseti__1(A,B,C),B,C)
| c_lessequals(A,B,tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),
[] ).
cnf(157681744,plain,
( ~ c_in(c_main_osubseti__1(A,B,C),B,C)
| c_lessequals(A,B,tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_OsubsetI_1]),
[] ).
cnf(168196896,plain,
~ c_in(c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[157681744,157651792]),
[] ).
cnf(169077064,plain,
~ c_in(c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(paramodulation,[status(thm)],[168526392,168196896,theory(equality)]),
[] ).
fof(cls_Set_OinsertCI_1,plain,
! [A,B,C] : c_in(A,c_insert(A,B,C),C),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),
[] ).
cnf(157665104,plain,
c_in(A,c_insert(A,B,C),C),
inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[169077064,157665104]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_1,plain,(c_lessequals(A,B,tc_set(t_a))|~c_in(B,v_s,tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),[]).
%
% cnf(157660368,plain,(c_lessequals(A,B,tc_set(t_a))|~c_in(B,v_s,tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Set_Osubset__antisym_0,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(B,A,tc_set(C))|$equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),[]).
%
% cnf(157689024,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(B,A,tc_set(C))|$equal(A,B)),inference(rewrite,[status(thm)],[cls_Set_Osubset__antisym_0]),[]).
%
% cnf(168303640,plain,(~c_in(B,v_s,tc_set(t_a))|~c_in(A,v_s,tc_set(t_a))|$equal(A,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[157660368,157660368,157689024]),[]).
%
% fof(cls_Set_OsubsetI_0,plain,(c_in(c_main_osubseti__1(A,B,C),A,C)|c_lessequals(A,B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),[]).
%
% cnf(157675056,plain,(c_in(c_main_osubseti__1(A,B,C),A,C)|c_lessequals(A,B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OsubsetI_0]),[]).
%
% fof(cls_conjecture_0,plain,(~c_lessequals(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),[]).
%
% cnf(157651792,plain,(~c_lessequals(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(168123104,plain,(c_in(c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),v_s,tc_set(t_a))),inference(resolution,[status(thm)],[157675056,157651792]),[]).
%
% cnf(168334776,plain,(~c_in(A,v_s,tc_set(t_a))|$equal(A,c_main_osubseti__1(v_s,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)))),inference(resolution,[status(thm)],[168303640,168123104]),[]).
%
% cnf(168526392,plain,($equal(c_main_osubseti__1(v_s,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)))),inference(resolution,[status(thm)],[168334776,168123104]),[]).
%
% fof(cls_Set_OsubsetI_1,plain,(~c_in(c_main_osubseti__1(A,B,C),B,C)|c_lessequals(A,B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),[]).
%
% cnf(157681744,plain,(~c_in(c_main_osubseti__1(A,B,C),B,C)|c_lessequals(A,B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OsubsetI_1]),[]).
%
% cnf(168196896,plain,(~c_in(c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a))),inference(resolution,[status(thm)],[157681744,157651792]),[]).
%
% cnf(169077064,plain,(~c_in(c_main_osubseti__1(v_s,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a))),inference(paramodulation,[status(thm)],[168526392,168196896,theory(equality)]),[]).
%
% fof(cls_Set_OinsertCI_1,plain,(c_in(A,c_insert(A,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET839-2.tptp',unknown),[]).
%
% cnf(157665104,plain,(c_in(A,c_insert(A,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[169077064,157665104]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------