TSTP Solution File: SET839-2 by Faust---1.0

View Problem - 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
% 
%------------------------------------------------------------------------------