TSTP Solution File: COL102-2 by Faust---1.0

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%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL102-2 : 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 @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:34:34 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   16 (   9 unt;   0 def)
%            Number of atoms       :   25 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   21 (  12   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-4 aty)
%            Number of variables   :   25 (   0 sgn  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Transitive__Closure_Or__into__rtrancl_0,plain,
    ! [A,B,C] :
      ( ~ c_in(A,B,tc_prod(C,C))
      | c_in(A,c_transitive__closure_ortrancl(B,C),tc_prod(C,C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),
    [] ).

cnf(172438856,plain,
    ( ~ c_in(A,B,tc_prod(C,C))
    | c_in(A,c_transitive__closure_ortrancl(B,C),tc_prod(C,C)) ),
    inference(rewrite,[status(thm)],[cls_Transitive__Closure_Or__into__rtrancl_0]),
    [] ).

fof(cls_Comb_Ocontract_OAp1_0,plain,
    ! [A,B,C] :
      ( ~ c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
      | c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,C),c_comb_ocomb_oop_a_d_d(B,C),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),
    [] ).

cnf(172428824,plain,
    ( ~ c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
    | c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,C),c_comb_ocomb_oop_a_d_d(B,C),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
    inference(rewrite,[status(thm)],[cls_Comb_Ocontract_OAp1_0]),
    [] ).

fof(cls_conjecture_1,plain,
    c_in(c_pair(v_y,v_za,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),
    [] ).

cnf(172384120,plain,
    c_in(c_pair(v_y,v_za,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

cnf(185519520,plain,
    c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_y,A),c_comb_ocomb_oop_a_d_d(v_za,A),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    inference(resolution,[status(thm)],[172428824,172384120]),
    [] ).

cnf(185636888,plain,
    c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_y,A),c_comb_ocomb_oop_a_d_d(v_za,A),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    inference(resolution,[status(thm)],[172438856,185519520]),
    [] ).

fof(cls_conjecture_2,plain,
    c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_y,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),
    [] ).

cnf(172388424,plain,
    c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_y,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

fof(cls_Transitive__Closure_Ortrancl__trans_0,plain,
    ! [A,B,C,D,E] :
      ( ~ c_in(c_pair(A,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))
      | ~ c_in(c_pair(E,A,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))
      | c_in(c_pair(E,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),
    [] ).

cnf(172446920,plain,
    ( ~ c_in(c_pair(A,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))
    | ~ c_in(c_pair(E,A,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))
    | c_in(c_pair(E,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C)) ),
    inference(rewrite,[status(thm)],[cls_Transitive__Closure_Ortrancl__trans_0]),
    [] ).

fof(cls_conjecture_3,plain,
    ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_za,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),
    [] ).

cnf(172393536,plain,
    ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_za,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
    inference(rewrite,[status(thm)],[cls_conjecture_3]),
    [] ).

cnf(188060936,plain,
    ( ~ c_in(c_pair(A,c_comb_ocomb_oop_a_d_d(v_za,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))
    | ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),A,tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
    inference(resolution,[status(thm)],[172446920,172393536]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[185636888,172388424,188060936]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Transitive__Closure_Or__into__rtrancl_0,plain,(~c_in(A,B,tc_prod(C,C))|c_in(A,c_transitive__closure_ortrancl(B,C),tc_prod(C,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),[]).
% 
% cnf(172438856,plain,(~c_in(A,B,tc_prod(C,C))|c_in(A,c_transitive__closure_ortrancl(B,C),tc_prod(C,C))),inference(rewrite,[status(thm)],[cls_Transitive__Closure_Or__into__rtrancl_0]),[]).
% 
% fof(cls_Comb_Ocontract_OAp1_0,plain,(~c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,C),c_comb_ocomb_oop_a_d_d(B,C),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),[]).
% 
% cnf(172428824,plain,(~c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,C),c_comb_ocomb_oop_a_d_d(B,C),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_Comb_Ocontract_OAp1_0]),[]).
% 
% fof(cls_conjecture_1,plain,(c_in(c_pair(v_y,v_za,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),[]).
% 
% cnf(172384120,plain,(c_in(c_pair(v_y,v_za,tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% cnf(185519520,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_y,A),c_comb_ocomb_oop_a_d_d(v_za,A),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[172428824,172384120]),[]).
% 
% cnf(185636888,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_y,A),c_comb_ocomb_oop_a_d_d(v_za,A),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[172438856,185519520]),[]).
% 
% fof(cls_conjecture_2,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_y,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),[]).
% 
% cnf(172388424,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_y,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% fof(cls_Transitive__Closure_Ortrancl__trans_0,plain,(~c_in(c_pair(A,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))|~c_in(c_pair(E,A,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))|c_in(c_pair(E,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),[]).
% 
% cnf(172446920,plain,(~c_in(c_pair(A,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))|~c_in(c_pair(E,A,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))|c_in(c_pair(E,B,C,C),c_transitive__closure_ortrancl(D,C),tc_prod(C,C))),inference(rewrite,[status(thm)],[cls_Transitive__Closure_Ortrancl__trans_0]),[]).
% 
% fof(cls_conjecture_3,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_za,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL102-2.tptp',unknown),[]).
% 
% cnf(172393536,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_za,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
% 
% cnf(188060936,plain,(~c_in(c_pair(A,c_comb_ocomb_oop_a_d_d(v_za,v_z),tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))|~c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),A,tc_comb_ocomb,tc_comb_ocomb),c_transitive__closure_ortrancl(c_comb_ocontract,tc_comb_ocomb),tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[172446920,172393536]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[185636888,172388424,188060936]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------