TSTP Solution File: SET842-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET842-2 : 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 15:39:10 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET842-2.tptp',unknown),
[] ).
cnf(157614400,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_3,plain,
~ c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),
[] ).
cnf(157574784,plain,
~ c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(168045976,plain,
c_in(c_main_osubseti__1(c_union(v_y,tc_set(t_a)),v_m,tc_set(t_a)),c_union(v_y,tc_set(t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[157614400,157574784]),
[] ).
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/SET842-2.tptp',unknown),
[] ).
cnf(157607864,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_Set_OUnionE_1,plain,
! [A,B,C] :
( ~ c_in(A,c_union(B,C),C)
| c_in(A,c_main_ounione__1(A,B,C),C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),
[] ).
cnf(157596672,plain,
( ~ c_in(A,c_union(B,C),C)
| c_in(A,c_main_ounione__1(A,B,C),C) ),
inference(rewrite,[status(thm)],[cls_Set_OUnionE_1]),
[] ).
cnf(168424264,plain,
( ~ c_lessequals(c_main_ounione__1(A,D,B),C,tc_set(B))
| c_in(A,C,B)
| ~ c_in(A,c_union(D,B),B) ),
inference(resolution,[status(thm)],[157607864,157596672]),
[] ).
fof(cls_Set_OUnionE_0,plain,
! [A,B,C] :
( ~ c_in(A,c_union(B,C),C)
| c_in(c_main_ounione__1(A,B,C),B,tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),
[] ).
cnf(157588144,plain,
( ~ c_in(A,c_union(B,C),C)
| c_in(c_main_ounione__1(A,B,C),B,tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_OUnionE_0]),
[] ).
fof(cls_conjecture_4,plain,
! [A] :
( c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,v_y,tc_set(tc_set(t_a))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),
[] ).
cnf(157581512,plain,
( c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,v_y,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(168244136,plain,
( ~ c_in(A,c_union(v_y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_main_ounione__1(A,v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[157588144,157581512]),
[] ).
cnf(170699624,plain,
( c_in(A,v_m,tc_set(t_a))
| ~ c_in(A,c_union(v_y,tc_set(t_a)),tc_set(t_a)) ),
inference(resolution,[status(thm)],[168424264,168244136]),
[] ).
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/SET842-2.tptp',unknown),
[] ).
cnf(157624288,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(168076656,plain,
~ c_in(c_main_osubseti__1(c_union(v_y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a)),
inference(resolution,[status(thm)],[157624288,157574784]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[168045976,170699624,168076656]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/SET842-2.tptp',unknown),[]).
%
% cnf(157614400,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_3,plain,(~c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),[]).
%
% cnf(157574784,plain,(~c_lessequals(c_union(v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(168045976,plain,(c_in(c_main_osubseti__1(c_union(v_y,tc_set(t_a)),v_m,tc_set(t_a)),c_union(v_y,tc_set(t_a)),tc_set(t_a))),inference(resolution,[status(thm)],[157614400,157574784]),[]).
%
% 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/SET842-2.tptp',unknown),[]).
%
% cnf(157607864,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_Set_OUnionE_1,plain,(~c_in(A,c_union(B,C),C)|c_in(A,c_main_ounione__1(A,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),[]).
%
% cnf(157596672,plain,(~c_in(A,c_union(B,C),C)|c_in(A,c_main_ounione__1(A,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OUnionE_1]),[]).
%
% cnf(168424264,plain,(~c_lessequals(c_main_ounione__1(A,D,B),C,tc_set(B))|c_in(A,C,B)|~c_in(A,c_union(D,B),B)),inference(resolution,[status(thm)],[157607864,157596672]),[]).
%
% fof(cls_Set_OUnionE_0,plain,(~c_in(A,c_union(B,C),C)|c_in(c_main_ounione__1(A,B,C),B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),[]).
%
% cnf(157588144,plain,(~c_in(A,c_union(B,C),C)|c_in(c_main_ounione__1(A,B,C),B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OUnionE_0]),[]).
%
% fof(cls_conjecture_4,plain,(c_lessequals(A,v_m,tc_set(tc_set(t_a)))|~c_in(A,v_y,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET842-2.tptp',unknown),[]).
%
% cnf(157581512,plain,(c_lessequals(A,v_m,tc_set(tc_set(t_a)))|~c_in(A,v_y,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(168244136,plain,(~c_in(A,c_union(v_y,tc_set(t_a)),tc_set(t_a))|c_lessequals(c_main_ounione__1(A,v_y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[157588144,157581512]),[]).
%
% cnf(170699624,plain,(c_in(A,v_m,tc_set(t_a))|~c_in(A,c_union(v_y,tc_set(t_a)),tc_set(t_a))),inference(resolution,[status(thm)],[168424264,168244136]),[]).
%
% 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/SET842-2.tptp',unknown),[]).
%
% cnf(157624288,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(168076656,plain,(~c_in(c_main_osubseti__1(c_union(v_y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))),inference(resolution,[status(thm)],[157624288,157574784]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[168045976,170699624,168076656]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------