%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL117-2 : 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 11:35:15 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_0,plain,
c_in(c_pair(v_z,v_w,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),
[] ).
cnf(145789464,plain,
c_in(c_pair(v_z,v_w,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
fof(cls_conjecture_2,plain,
c_in(c_pair(v_ya,v_y_ha,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),
[] ).
cnf(145797736,plain,
c_in(c_pair(v_ya,v_y_ha,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
fof(cls_Comb_Oparcontract_Ointros__4_0,plain,
! [A,B,C,D] :
( ~ c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
| ~ c_in(c_pair(C,D,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,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(D,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),
[] ).
cnf(145849968,plain,
( ~ c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
| ~ c_in(c_pair(C,D,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,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(D,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
inference(rewrite,[status(thm)],[cls_Comb_Oparcontract_Ointros__4_0]),
[] ).
fof(cls_conjecture_1,plain,
c_in(c_pair(v_x,v_x_h,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),
[] ).
cnf(145793776,plain,
c_in(c_pair(v_x,v_x_h,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(161731160,plain,
( ~ c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
| c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,A),c_comb_ocomb_oop_a_d_d(v_x_h,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
inference(resolution,[status(thm)],[145849968,145793776]),
[] ).
cnf(161755264,plain,
c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_x_h,v_w),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(resolution,[status(thm)],[161731160,145789464]),
[] ).
fof(cls_conjecture_3,plain,
! [A] :
( ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,v_x_h),v_y_ha),v_w),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
| ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_ya,v_z)),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),
[] ).
cnf(145808888,plain,
( ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,v_x_h),v_y_ha),v_w),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))
| ~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_ya,v_z)),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
fof(cls_Comb_Oparcontract_Ointros__3_0,plain,
! [A,B,C] : c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,A),B),C),c_comb_ocomb_oop_a_d_d(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_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),
[] ).
cnf(145817736,plain,
c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,A),B),C),c_comb_ocomb_oop_a_d_d(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_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(rewrite,[status(thm)],[cls_Comb_Oparcontract_Ointros__3_0]),
[] ).
cnf(162486608,plain,
~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_ya,v_z)),c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x_h,v_w),c_comb_ocomb_oop_a_d_d(v_y_ha,v_w)),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(resolution,[status(thm)],[145808888,145817736]),
[] ).
cnf(162746648,plain,
~ c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_ya,v_z),c_comb_ocomb_oop_a_d_d(v_y_ha,v_w),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[161755264,145849968,162486608]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[145789464,145797736,162746648,145849968]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_0,plain,(c_in(c_pair(v_z,v_w,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),[]).
%
% cnf(145789464,plain,(c_in(c_pair(v_z,v_w,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(c_pair(v_ya,v_y_ha,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),[]).
%
% cnf(145797736,plain,(c_in(c_pair(v_ya,v_y_ha,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% fof(cls_Comb_Oparcontract_Ointros__4_0,plain,(~c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|~c_in(c_pair(C,D,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,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(D,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),[]).
%
% cnf(145849968,plain,(~c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|~c_in(c_pair(C,D,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,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(D,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_Comb_Oparcontract_Ointros__4_0]),[]).
%
% fof(cls_conjecture_1,plain,(c_in(c_pair(v_x,v_x_h,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),[]).
%
% cnf(145793776,plain,(c_in(c_pair(v_x,v_x_h,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(161731160,plain,(~c_in(c_pair(A,B,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,A),c_comb_ocomb_oop_a_d_d(v_x_h,B),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[145849968,145793776]),[]).
%
% cnf(161755264,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_x_h,v_w),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[161731160,145789464]),[]).
%
% fof(cls_conjecture_3,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,v_x_h),v_y_ha),v_w),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|~c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_ya,v_z)),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),[]).
%
% cnf(145808888,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,v_x_h),v_y_ha),v_w),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))|~c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_ya,v_z)),A,tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% fof(cls_Comb_Oparcontract_Ointros__3_0,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,A),B),C),c_comb_ocomb_oop_a_d_d(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_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL117-2.tptp',unknown),[]).
%
% cnf(145817736,plain,(c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_os,A),B),C),c_comb_ocomb_oop_a_d_d(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_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(rewrite,[status(thm)],[cls_Comb_Oparcontract_Ointros__3_0]),[]).
%
% cnf(162486608,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x,v_z),c_comb_ocomb_oop_a_d_d(v_ya,v_z)),c_comb_ocomb_oop_a_d_d(c_comb_ocomb_oop_a_d_d(v_x_h,v_w),c_comb_ocomb_oop_a_d_d(v_y_ha,v_w)),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(resolution,[status(thm)],[145808888,145817736]),[]).
%
% cnf(162746648,plain,(~c_in(c_pair(c_comb_ocomb_oop_a_d_d(v_ya,v_z),c_comb_ocomb_oop_a_d_d(v_y_ha,v_w),tc_comb_ocomb,tc_comb_ocomb),c_comb_oparcontract,tc_prod(tc_comb_ocomb,tc_comb_ocomb))),inference(forward_subsumption_resolution__resolution,[status(thm)],[161755264,145849968,162486608]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[145789464,145797736,162746648,145849968]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------