TSTP Solution File: SET821-2 by Faust---1.0

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%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET821-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 15:38:03 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   31 (  14 unt;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   42 (  17   ~;  25   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   54 (   8 sgn  17   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
    ! [A] :
      ( c_in(v_c,A,tc_intdef_oint)
      | ~ c_in(v_b,A,tc_intdef_oint)
      | c_in(v_a,A,tc_intdef_oint) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(171062560,plain,
    ( c_in(v_c,A,tc_intdef_oint)
    | ~ c_in(v_b,A,tc_intdef_oint)
    | c_in(v_a,A,tc_intdef_oint) ),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

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/SET821-2.tptp',unknown),
    [] ).

cnf(171026592,plain,
    c_in(A,c_insert(A,B,C),C),
    inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),
    [] ).

cnf(184216336,plain,
    ( c_in(v_c,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
    | c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint) ),
    inference(resolution,[status(thm)],[171062560,171026592]),
    [] ).

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/SET821-2.tptp',unknown),
    [] ).

cnf(171042392,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]),
    [] ).

cnf(184988720,plain,
    ( c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
    | c_in(v_c,A,tc_intdef_oint)
    | $equal(v_b,v_c) ),
    inference(resolution,[status(thm)],[184216336,171042392]),
    [] ).

fof(cls_conjecture_1,plain,
    c_less(v_b,v_c,tc_intdef_oint),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(171055344,plain,
    c_less(v_b,v_c,tc_intdef_oint),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

cnf(186668152,plain,
    ( c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
    | c_in(v_c,A,tc_intdef_oint)
    | c_less(v_c,v_c,tc_intdef_oint) ),
    inference(paramodulation,[status(thm)],[184988720,171055344,theory(equality)]),
    [] ).

fof(cls_Orderings_Oorder__less__irrefl__iff1_0,plain,
    ! [A,B] :
      ( ~ class_orderings_oorder(A)
      | ~ c_less(B,B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(170999880,plain,
    ( ~ class_orderings_oorder(A)
    | ~ c_less(B,B,A) ),
    inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__irrefl__iff1_0]),
    [] ).

fof(clsarity_IntDef__Oint_31,plain,
    class_orderings_oorder(tc_intdef_oint),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(171067416,plain,
    class_orderings_oorder(tc_intdef_oint),
    inference(rewrite,[status(thm)],[clsarity_IntDef__Oint_31]),
    [] ).

cnf(184144672,plain,
    ~ c_less(A,A,tc_intdef_oint),
    inference(resolution,[status(thm)],[170999880,171067416]),
    [] ).

cnf(190718808,plain,
    ( c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
    | c_in(v_c,A,tc_intdef_oint) ),
    inference(resolution,[status(thm)],[186668152,184144672]),
    [] ).

cnf(190887128,plain,
    ( c_in(v_c,A,tc_intdef_oint)
    | c_in(v_a,A,tc_intdef_oint)
    | $equal(v_b,v_a) ),
    inference(resolution,[status(thm)],[190718808,171042392]),
    [] ).

fof(cls_conjecture_0,plain,
    c_less(v_a,v_b,tc_intdef_oint),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(171047136,plain,
    c_less(v_a,v_b,tc_intdef_oint),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

cnf(191111784,plain,
    ( c_in(v_c,A,tc_intdef_oint)
    | c_in(v_a,A,tc_intdef_oint)
    | c_less(v_b,v_b,tc_intdef_oint) ),
    inference(paramodulation,[status(thm)],[190887128,171047136,theory(equality)]),
    [] ).

cnf(191130656,plain,
    ( c_in(v_c,A,tc_intdef_oint)
    | c_in(v_a,A,tc_intdef_oint) ),
    inference(resolution,[status(thm)],[191111784,184144672]),
    [] ).

fof(cls_Set_OComplD__dest_0,plain,
    ! [A,B,C] :
      ( ~ c_in(A,B,C)
      | ~ c_in(A,c_uminus(B,tc_set(C)),C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(171006728,plain,
    ( ~ c_in(A,B,C)
    | ~ c_in(A,c_uminus(B,tc_set(C)),C) ),
    inference(rewrite,[status(thm)],[cls_Set_OComplD__dest_0]),
    [] ).

cnf(184189344,plain,
    ~ c_in(A,c_uminus(c_insert(A,C,B),tc_set(B)),B),
    inference(resolution,[status(thm)],[171006728,171026592]),
    [] ).

cnf(191288904,plain,
    c_in(v_a,c_uminus(c_insert(v_c,A,tc_intdef_oint),tc_set(tc_intdef_oint)),tc_intdef_oint),
    inference(resolution,[status(thm)],[191130656,184189344]),
    [] ).

fof(cls_Set_OinsertCI_0,plain,
    ! [A,B,C,D] :
      ( ~ c_in(A,B,C)
      | c_in(A,c_insert(D,B,C),C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
    [] ).

cnf(171022496,plain,
    ( ~ c_in(A,B,C)
    | c_in(A,c_insert(D,B,C),C) ),
    inference(rewrite,[status(thm)],[cls_Set_OinsertCI_0]),
    [] ).

cnf(184168272,plain,
    c_in(A,c_insert(C,c_insert(A,D,B),B),B),
    inference(resolution,[status(thm)],[171022496,171026592]),
    [] ).

cnf(184353696,plain,
    ~ c_in(A,c_uminus(c_insert(C,c_insert(A,D,B),B),tc_set(B)),B),
    inference(resolution,[status(thm)],[171006728,184168272]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[191288904,184353696]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,(c_in(v_c,A,tc_intdef_oint)|~c_in(v_b,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171062560,plain,(c_in(v_c,A,tc_intdef_oint)|~c_in(v_b,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% fof(cls_Set_OinsertCI_1,plain,(c_in(A,c_insert(A,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171026592,plain,(c_in(A,c_insert(A,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),[]).
% 
% cnf(184216336,plain,(c_in(v_c,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)),inference(resolution,[status(thm)],[171062560,171026592]),[]).
% 
% fof(cls_Set_OinsertE_0,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171042392,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),inference(rewrite,[status(thm)],[cls_Set_OinsertE_0]),[]).
% 
% cnf(184988720,plain,(c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_c,A,tc_intdef_oint)|$equal(v_b,v_c)),inference(resolution,[status(thm)],[184216336,171042392]),[]).
% 
% fof(cls_conjecture_1,plain,(c_less(v_b,v_c,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171055344,plain,(c_less(v_b,v_c,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% cnf(186668152,plain,(c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_c,A,tc_intdef_oint)|c_less(v_c,v_c,tc_intdef_oint)),inference(paramodulation,[status(thm)],[184988720,171055344,theory(equality)]),[]).
% 
% fof(cls_Orderings_Oorder__less__irrefl__iff1_0,plain,(~class_orderings_oorder(A)|~c_less(B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(170999880,plain,(~class_orderings_oorder(A)|~c_less(B,B,A)),inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__irrefl__iff1_0]),[]).
% 
% fof(clsarity_IntDef__Oint_31,plain,(class_orderings_oorder(tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171067416,plain,(class_orderings_oorder(tc_intdef_oint)),inference(rewrite,[status(thm)],[clsarity_IntDef__Oint_31]),[]).
% 
% cnf(184144672,plain,(~c_less(A,A,tc_intdef_oint)),inference(resolution,[status(thm)],[170999880,171067416]),[]).
% 
% cnf(190718808,plain,(c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_c,A,tc_intdef_oint)),inference(resolution,[status(thm)],[186668152,184144672]),[]).
% 
% cnf(190887128,plain,(c_in(v_c,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)|$equal(v_b,v_a)),inference(resolution,[status(thm)],[190718808,171042392]),[]).
% 
% fof(cls_conjecture_0,plain,(c_less(v_a,v_b,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171047136,plain,(c_less(v_a,v_b,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% cnf(191111784,plain,(c_in(v_c,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)|c_less(v_b,v_b,tc_intdef_oint)),inference(paramodulation,[status(thm)],[190887128,171047136,theory(equality)]),[]).
% 
% cnf(191130656,plain,(c_in(v_c,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)),inference(resolution,[status(thm)],[191111784,184144672]),[]).
% 
% fof(cls_Set_OComplD__dest_0,plain,(~c_in(A,B,C)|~c_in(A,c_uminus(B,tc_set(C)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171006728,plain,(~c_in(A,B,C)|~c_in(A,c_uminus(B,tc_set(C)),C)),inference(rewrite,[status(thm)],[cls_Set_OComplD__dest_0]),[]).
% 
% cnf(184189344,plain,(~c_in(A,c_uminus(c_insert(A,C,B),tc_set(B)),B)),inference(resolution,[status(thm)],[171006728,171026592]),[]).
% 
% cnf(191288904,plain,(c_in(v_a,c_uminus(c_insert(v_c,A,tc_intdef_oint),tc_set(tc_intdef_oint)),tc_intdef_oint)),inference(resolution,[status(thm)],[191130656,184189344]),[]).
% 
% fof(cls_Set_OinsertCI_0,plain,(~c_in(A,B,C)|c_in(A,c_insert(D,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
% 
% cnf(171022496,plain,(~c_in(A,B,C)|c_in(A,c_insert(D,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_0]),[]).
% 
% cnf(184168272,plain,(c_in(A,c_insert(C,c_insert(A,D,B),B),B)),inference(resolution,[status(thm)],[171022496,171026592]),[]).
% 
% cnf(184353696,plain,(~c_in(A,c_uminus(c_insert(C,c_insert(A,D,B),B),tc_set(B)),B)),inference(resolution,[status(thm)],[171006728,184168272]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[191288904,184353696]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------