TSTP Solution File: COL104-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL104-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 11:34:41 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_Comb_Ocontract_OAp2_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(C,A),c_comb_ocomb_oop_a_d_d(C,B),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/COL104-2.tptp',unknown),
[] ).
cnf(161709592,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(C,A),c_comb_ocomb_oop_a_d_d(C,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
inference(rewrite,[status(thm)],[cls_Comb_Ocontract_OAp2_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/COL104-2.tptp',unknown),
[] ).
cnf(161664888,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(174800288,plain,
c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,v_y),c_comb_ocomb_oop_a_d_d(A,v_za),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(resolution,[status(thm)],[161709592,161664888]),
[] ).
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/COL104-2.tptp',unknown),
[] ).
cnf(161719624,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]),
[] ).
cnf(175467504,plain,
c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,v_y),c_comb_ocomb_oop_a_d_d(A,v_za),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)],[174800288,161719624]),
[] ).
fof(cls_conjecture_2,plain,
c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_y),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/COL104-2.tptp',unknown),
[] ).
cnf(161669192,plain,
c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_y),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/COL104-2.tptp',unknown),
[] ).
cnf(161727688,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_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_za),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/COL104-2.tptp',unknown),
[] ).
cnf(161674304,plain,
~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_za),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(177656648,plain,
( ~ c_in(c_pair(A,c_comb_ocomb_oop_a_d_d(v_z,v_za),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_z,v_x),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)],[161727688,161674304]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[175467504,161669192,177656648]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Comb_Ocontract_OAp2_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(C,A),c_comb_ocomb_oop_a_d_d(C,B),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/COL104-2.tptp',unknown),[]).
%
% cnf(161709592,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(C,A),c_comb_ocomb_oop_a_d_d(C,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_Comb_Ocontract_OAp2_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/COL104-2.tptp',unknown),[]).
%
% cnf(161664888,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(174800288,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,v_y),c_comb_ocomb_oop_a_d_d(A,v_za),tc_comb_ocomb,tc_comb_ocomb),c_comb_ocontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[161709592,161664888]),[]).
%
% 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/COL104-2.tptp',unknown),[]).
%
% cnf(161719624,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]),[]).
%
% cnf(175467504,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(A,v_y),c_comb_ocomb_oop_a_d_d(A,v_za),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)],[174800288,161719624]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_y),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/COL104-2.tptp',unknown),[]).
%
% cnf(161669192,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_y),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/COL104-2.tptp',unknown),[]).
%
% cnf(161727688,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_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_za),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/COL104-2.tptp',unknown),[]).
%
% cnf(161674304,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_z,v_x),c_comb_ocomb_oop_a_d_d(v_z,v_za),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(177656648,plain,(~c_in(c_pair(A,c_comb_ocomb_oop_a_d_d(v_z,v_za),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_z,v_x),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)],[161727688,161674304]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[175467504,161669192,177656648]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------