TSTP Solution File: SET822-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET822-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.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 15:38:13 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  11 unt;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   22 (  13   ~;   9   |;   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   :   35 (   5 sgn  13   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_1,plain,
    ! [A,B] :
      ( ~ c_in(v_f(A),B,tc_intdef_oint)
      | c_in(v_x(A,B),B,tc_intdef_oint) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
    [] ).

cnf(150384752,plain,
    ( ~ c_in(v_f(A),B,tc_intdef_oint)
    | c_in(v_x(A,B),B,tc_intdef_oint) ),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

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/SET822-2.tptp',unknown),
    [] ).

cnf(150355960,plain,
    c_in(A,c_insert(A,B,C),C),
    inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),
    [] ).

cnf(163487504,plain,
    c_in(v_x(A,c_insert(v_f(A),B,tc_intdef_oint)),c_insert(v_f(A),B,tc_intdef_oint),tc_intdef_oint),
    inference(resolution,[status(thm)],[150384752,150355960]),
    [] ).

fof(cls_Set_OinsertE_0,plain,
    ! [A,B,C,D] :
      ( ~ c_in(A,c_insert(B,C,D),D)
      | c_in(A,C,D)
      | $equal(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
    [] ).

cnf(150370016,plain,
    ( ~ c_in(A,c_insert(B,C,D),D)
    | c_in(A,C,D)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[cls_Set_OinsertE_0]),
    [] ).

fof(cls_Set_OemptyE_0,plain,
    ! [A,B] : ~ c_in(A,c_emptyset,B),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
    [] ).

cnf(150350976,plain,
    ~ c_in(A,c_emptyset,B),
    inference(rewrite,[status(thm)],[cls_Set_OemptyE_0]),
    [] ).

cnf(163452624,plain,
    ( ~ c_in(A,c_insert(B,c_emptyset,C),C)
    | $equal(B,A) ),
    inference(resolution,[status(thm)],[150370016,150350976]),
    [] ).

cnf(163702344,plain,
    $equal(v_f(A),v_x(A,c_insert(v_f(A),c_emptyset,tc_intdef_oint))),
    inference(resolution,[status(thm)],[163487504,163452624]),
    [] ).

fof(cls_conjecture_2,plain,
    ! [A,B] :
      ( ~ c_in(v_f(A),B,tc_intdef_oint)
      | ~ v_p(v_x(A,B)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
    [] ).

cnf(150389744,plain,
    ( ~ c_in(v_f(A),B,tc_intdef_oint)
    | ~ v_p(v_x(A,B)) ),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

cnf(163474544,plain,
    ~ v_p(v_x(A,c_insert(v_f(A),B,tc_intdef_oint))),
    inference(resolution,[status(thm)],[150389744,150355960]),
    [] ).

cnf(163797408,plain,
    ~ v_p(v_f(A)),
    inference(paramodulation,[status(thm)],[163702344,163474544,theory(equality)]),
    [] ).

fof(cls_conjecture_0,plain,
    v_p(v_f(v_b)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
    [] ).

cnf(150378936,plain,
    v_p(v_f(v_b)),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[163797408,150378936]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_1,plain,(~c_in(v_f(A),B,tc_intdef_oint)|c_in(v_x(A,B),B,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
% 
% cnf(150384752,plain,(~c_in(v_f(A),B,tc_intdef_oint)|c_in(v_x(A,B),B,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% fof(cls_Set_OinsertCI_1,plain,(c_in(A,c_insert(A,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
% 
% cnf(150355960,plain,(c_in(A,c_insert(A,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),[]).
% 
% cnf(163487504,plain,(c_in(v_x(A,c_insert(v_f(A),B,tc_intdef_oint)),c_insert(v_f(A),B,tc_intdef_oint),tc_intdef_oint)),inference(resolution,[status(thm)],[150384752,150355960]),[]).
% 
% fof(cls_Set_OinsertE_0,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
% 
% cnf(150370016,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),inference(rewrite,[status(thm)],[cls_Set_OinsertE_0]),[]).
% 
% fof(cls_Set_OemptyE_0,plain,(~c_in(A,c_emptyset,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
% 
% cnf(150350976,plain,(~c_in(A,c_emptyset,B)),inference(rewrite,[status(thm)],[cls_Set_OemptyE_0]),[]).
% 
% cnf(163452624,plain,(~c_in(A,c_insert(B,c_emptyset,C),C)|$equal(B,A)),inference(resolution,[status(thm)],[150370016,150350976]),[]).
% 
% cnf(163702344,plain,($equal(v_f(A),v_x(A,c_insert(v_f(A),c_emptyset,tc_intdef_oint)))),inference(resolution,[status(thm)],[163487504,163452624]),[]).
% 
% fof(cls_conjecture_2,plain,(~c_in(v_f(A),B,tc_intdef_oint)|~v_p(v_x(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
% 
% cnf(150389744,plain,(~c_in(v_f(A),B,tc_intdef_oint)|~v_p(v_x(A,B))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% cnf(163474544,plain,(~v_p(v_x(A,c_insert(v_f(A),B,tc_intdef_oint)))),inference(resolution,[status(thm)],[150389744,150355960]),[]).
% 
% cnf(163797408,plain,(~v_p(v_f(A))),inference(paramodulation,[status(thm)],[163702344,163474544,theory(equality)]),[]).
% 
% fof(cls_conjecture_0,plain,(v_p(v_f(v_b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
% 
% cnf(150378936,plain,(v_p(v_f(v_b))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[163797408,150378936]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------