%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL123-2 : 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 11:35:34 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 28 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 37 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_7,plain,
! [A,B,C] :
( c_in(c_pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163162072,plain,
( c_in(c_pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_7]),
[] ).
fof(cls_conjecture_1,plain,
c_in(c_pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163094352,plain,
c_in(c_pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(186879360,plain,
( c_in(c_pair(A,v_xa(v_y,v_z,A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_y,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[163162072,163094352]),
[] ).
fof(cls_conjecture_4,plain,
! [A] :
( c_in(c_pair(v_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163118424,plain,
( c_in(c_pair(v_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
fof(cls_conjecture_2,plain,
c_in(c_pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163102656,plain,
c_in(c_pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(187218872,plain,
c_in(c_pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[163118424,163102656]),
[] ).
cnf(196359760,plain,
c_in(c_pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[186879360,187218872]),
[] ).
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/COL123-2.tptp',unknown),
[] ).
cnf(163081400,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_conjecture_3,plain,
! [A] :
( c_in(c_pair(A,v_xaa(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163108488,plain,
( c_in(c_pair(A,v_xaa(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
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/COL123-2.tptp',unknown),
[] ).
cnf(163089656,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_6,plain,
! [A,B,C] :
( c_in(c_pair(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163154152,plain,
( c_in(c_pair(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_6]),
[] ).
cnf(186838192,plain,
( c_in(c_pair(v_z,v_xa(v_y,v_z,A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_y,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[163154152,163094352]),
[] ).
cnf(191161152,plain,
c_in(c_pair(v_z,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[186838192,187218872]),
[] ).
fof(cls_conjecture_5,plain,
! [A] :
( ~ c_in(c_pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_xb,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),
[] ).
cnf(163124240,plain,
( ~ c_in(c_pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_xb,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_5]),
[] ).
cnf(191566040,plain,
~ c_in(c_pair(v_xb,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[191161152,163124240]),
[] ).
cnf(198022008,plain,
( ~ c_in(c_pair(A,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_xb,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[163089656,191566040]),
[] ).
cnf(199419976,plain,
~ c_in(c_pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[163102656,163108488,198022008]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[196359760,163081400,199419976]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_7,plain,(c_in(c_pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163162072,plain,(c_in(c_pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_7]),[]).
%
% fof(cls_conjecture_1,plain,(c_in(c_pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163094352,plain,(c_in(c_pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(186879360,plain,(c_in(c_pair(A,v_xa(v_y,v_z,A),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(v_y,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[163162072,163094352]),[]).
%
% fof(cls_conjecture_4,plain,(c_in(c_pair(v_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163118424,plain,(c_in(c_pair(v_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(c_pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163102656,plain,(c_in(c_pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(187218872,plain,(c_in(c_pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[163118424,163102656]),[]).
%
% cnf(196359760,plain,(c_in(c_pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[186879360,187218872]),[]).
%
% 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/COL123-2.tptp',unknown),[]).
%
% cnf(163081400,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_conjecture_3,plain,(c_in(c_pair(A,v_xaa(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163108488,plain,(c_in(c_pair(A,v_xaa(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% 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/COL123-2.tptp',unknown),[]).
%
% cnf(163089656,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_6,plain,(c_in(c_pair(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163154152,plain,(c_in(c_pair(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_6]),[]).
%
% cnf(186838192,plain,(c_in(c_pair(v_z,v_xa(v_y,v_z,A),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(v_y,A,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[163154152,163094352]),[]).
%
% cnf(191161152,plain,(c_in(c_pair(v_z,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[186838192,187218872]),[]).
%
% fof(cls_conjecture_5,plain,(~c_in(c_pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(v_xb,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL123-2.tptp',unknown),[]).
%
% cnf(163124240,plain,(~c_in(c_pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(v_xb,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_5]),[]).
%
% cnf(191566040,plain,(~c_in(c_pair(v_xb,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[191161152,163124240]),[]).
%
% cnf(198022008,plain,(~c_in(c_pair(A,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_xb,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[163089656,191566040]),[]).
%
% cnf(199419976,plain,(~c_in(c_pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[163102656,163108488,198022008]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[196359760,163081400,199419976]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------