TSTP Solution File: COL121-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL121-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 11:35:28 EDT 2009
% Result : Unsatisfiable 2.7s
% Output : Refutation 2.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 67 ( 38 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_4,plain,
! [A] :
( c_in(c_pair(v_ya,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_y,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/COL121-2.tptp',unknown),
[] ).
cnf(147139304,plain,
( c_in(c_pair(v_ya,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_y,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_4]),
[] ).
fof(cls_conjecture_3,plain,
c_in(c_pair(v_y,v_xaa,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/COL121-2.tptp',unknown),
[] ).
cnf(147129232,plain,
c_in(c_pair(v_y,v_xaa,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(168335608,plain,
c_in(c_pair(v_ya,v_x(v_xaa),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[147139304,147129232]),
[] ).
fof(cls_conjecture_2,plain,
c_in(c_pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),
[] ).
cnf(147124992,plain,
c_in(c_pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
fof(cls_conjecture_0,plain,
c_comb_odiamond(v_r,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),
[] ).
cnf(147008360,plain,
c_comb_odiamond(v_r,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
fof(cls_Comb_Odiamond__strip__lemmaE_1,plain,
! [A,B,C,D,E] :
( ~ c_comb_odiamond(A,B)
| ~ c_in(c_pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))
| c_in(c_pair(E,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),A,tc_prod(B,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),
[] ).
cnf(147097096,plain,
( ~ c_comb_odiamond(A,B)
| ~ c_in(c_pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))
| c_in(c_pair(E,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),A,tc_prod(B,B)) ),
inference(rewrite,[status(thm)],[cls_Comb_Odiamond__strip__lemmaE_1]),
[] ).
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/COL121-2.tptp',unknown),
[] ).
cnf(147103480,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_5,plain,
! [A] :
( c_in(c_pair(A,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_y,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/COL121-2.tptp',unknown),
[] ).
cnf(147145352,plain,
( c_in(c_pair(A,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_y,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]),
[] ).
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/COL121-2.tptp',unknown),
[] ).
cnf(147111488,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_Comb_Odiamond__strip__lemmaE_0,plain,
! [A,B,C,D,E] :
( ~ c_comb_odiamond(A,B)
| ~ c_in(c_pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))
| c_in(c_pair(D,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),
[] ).
cnf(147064688,plain,
( ~ c_comb_odiamond(A,B)
| ~ c_in(c_pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))
| c_in(c_pair(D,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B)) ),
inference(rewrite,[status(thm)],[cls_Comb_Odiamond__strip__lemmaE_0]),
[] ).
fof(cls_conjecture_6,plain,
! [A] :
( ~ c_in(c_pair(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_z,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/COL121-2.tptp',unknown),
[] ).
cnf(147150840,plain,
( ~ c_in(c_pair(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_z,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_6]),
[] ).
cnf(174310104,plain,
( ~ c_in(c_pair(A,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(A,B,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_xaa,c_comb_odiamond__strip__lemmae__1(v_r,B,v_z,t_a),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)],[147008360,147064688,147150840]),
[] ).
cnf(185708848,plain,
( ~ c_in(c_pair(v_y,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_xaa,c_comb_odiamond__strip__lemmae__1(v_r,v_x(A),v_z,t_a),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)],[147124992,147139304,174310104]),
[] ).
cnf(186241960,plain,
~ c_in(c_pair(v_xaa,c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[147129232,185708848]),
[] ).
cnf(186379192,plain,
( ~ c_in(c_pair(A,c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_pair(v_xaa,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[147111488,186241960]),
[] ).
cnf(186669720,plain,
~ c_in(c_pair(v_x(v_xaa),c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),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)],[147129232,147145352,186379192]),
[] ).
cnf(186750656,plain,
~ c_in(c_pair(v_x(v_xaa),c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[147103480,186669720]),
[] ).
cnf(187787176,plain,
( ~ c_in(c_pair(A,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_pair(A,v_x(v_xaa),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)],[147008360,147097096,186750656]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[168335608,147124992,187787176]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_4,plain,(c_in(c_pair(v_ya,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_y,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/COL121-2.tptp',unknown),[]).
%
% cnf(147139304,plain,(c_in(c_pair(v_ya,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_y,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_4]),[]).
%
% fof(cls_conjecture_3,plain,(c_in(c_pair(v_y,v_xaa,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/COL121-2.tptp',unknown),[]).
%
% cnf(147129232,plain,(c_in(c_pair(v_y,v_xaa,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(168335608,plain,(c_in(c_pair(v_ya,v_x(v_xaa),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[147139304,147129232]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(c_pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),[]).
%
% cnf(147124992,plain,(c_in(c_pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% fof(cls_conjecture_0,plain,(c_comb_odiamond(v_r,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),[]).
%
% cnf(147008360,plain,(c_comb_odiamond(v_r,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% fof(cls_Comb_Odiamond__strip__lemmaE_1,plain,(~c_comb_odiamond(A,B)|~c_in(c_pair(C,D,B,B),A,tc_prod(B,B))|~c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))|c_in(c_pair(E,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),A,tc_prod(B,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),[]).
%
% cnf(147097096,plain,(~c_comb_odiamond(A,B)|~c_in(c_pair(C,D,B,B),A,tc_prod(B,B))|~c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))|c_in(c_pair(E,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),A,tc_prod(B,B))),inference(rewrite,[status(thm)],[cls_Comb_Odiamond__strip__lemmaE_1]),[]).
%
% 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/COL121-2.tptp',unknown),[]).
%
% cnf(147103480,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_5,plain,(c_in(c_pair(A,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_y,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/COL121-2.tptp',unknown),[]).
%
% cnf(147145352,plain,(c_in(c_pair(A,v_x(A),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_y,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]),[]).
%
% 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/COL121-2.tptp',unknown),[]).
%
% cnf(147111488,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_Comb_Odiamond__strip__lemmaE_0,plain,(~c_comb_odiamond(A,B)|~c_in(c_pair(C,D,B,B),A,tc_prod(B,B))|~c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))|c_in(c_pair(D,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL121-2.tptp',unknown),[]).
%
% cnf(147064688,plain,(~c_comb_odiamond(A,B)|~c_in(c_pair(C,D,B,B),A,tc_prod(B,B))|~c_in(c_pair(C,E,B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))|c_in(c_pair(D,c_comb_odiamond__strip__lemmae__1(A,E,D,B),B,B),c_transitive__closure_ortrancl(A,B),tc_prod(B,B))),inference(rewrite,[status(thm)],[cls_Comb_Odiamond__strip__lemmaE_0]),[]).
%
% fof(cls_conjecture_6,plain,(~c_in(c_pair(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_z,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/COL121-2.tptp',unknown),[]).
%
% cnf(147150840,plain,(~c_in(c_pair(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_z,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_6]),[]).
%
% cnf(174310104,plain,(~c_in(c_pair(A,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(A,B,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_xaa,c_comb_odiamond__strip__lemmae__1(v_r,B,v_z,t_a),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)],[147008360,147064688,147150840]),[]).
%
% cnf(185708848,plain,(~c_in(c_pair(v_y,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_xaa,c_comb_odiamond__strip__lemmae__1(v_r,v_x(A),v_z,t_a),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)],[147124992,147139304,174310104]),[]).
%
% cnf(186241960,plain,(~c_in(c_pair(v_xaa,c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[147129232,185708848]),[]).
%
% cnf(186379192,plain,(~c_in(c_pair(A,c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_xaa,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[147111488,186241960]),[]).
%
% cnf(186669720,plain,(~c_in(c_pair(v_x(v_xaa),c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),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)],[147129232,147145352,186379192]),[]).
%
% cnf(186750656,plain,(~c_in(c_pair(v_x(v_xaa),c_comb_odiamond__strip__lemmae__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))),inference(resolution,[status(thm)],[147103480,186669720]),[]).
%
% cnf(187787176,plain,(~c_in(c_pair(A,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_pair(A,v_x(v_xaa),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)],[147008360,147097096,186750656]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[168335608,147124992,187787176]),[]).
%
% END OF PROOF SEQUENCE
%
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