%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL066-3 : TPTP v3.4.2. Bugfixed v1.2.0.
% 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 11:33:53 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(q_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),
[] ).
cnf(160423608,plain,
$equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
inference(rewrite,[status(thm)],[q_definition]),
[] ).
fof(prove_p_combinator,plain,
~ $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(x,y),apply(apply(x,y),z))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),
[] ).
cnf(160437120,plain,
~ $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(x,y),apply(apply(x,y),z))),
inference(rewrite,[status(thm)],[prove_p_combinator]),
[] ).
fof(b_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),
[] ).
cnf(160419360,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
cnf(168288624,plain,
~ $equal(apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z),apply(apply(x,y),apply(apply(x,y),z))),
inference(paramodulation,[status(thm)],[160437120,160419360,theory(equality)]),
[] ).
fof(w_definition,plain,
! [A,B] : $equal(apply(apply(w,A),B),apply(apply(A,B),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),
[] ).
cnf(160427696,plain,
$equal(apply(apply(w,A),B),apply(apply(A,B),B)),
inference(rewrite,[status(thm)],[w_definition]),
[] ).
cnf(168792000,plain,
~ $equal(apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z),apply(apply(x,y),apply(apply(x,y),z))),
inference(paramodulation,[status(thm)],[168288624,160427696,theory(equality)]),
[] ).
cnf(170956640,plain,
~ $equal(apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z),apply(apply(x,y),apply(apply(x,y),z))),
inference(paramodulation,[status(thm)],[168792000,160423608,theory(equality)]),
[] ).
cnf(175757024,plain,
~ $equal(apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z),apply(apply(x,y),apply(apply(x,y),z))),
inference(paramodulation,[status(thm)],[170956640,160423608,theory(equality)]),
[] ).
cnf(177834224,plain,
~ $equal(apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z),apply(apply(x,y),apply(apply(x,y),z))),
inference(paramodulation,[status(thm)],[175757024,160423608,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[160423608,177834224,160423608,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(q_definition,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),[]).
%
% cnf(160423608,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),inference(rewrite,[status(thm)],[q_definition]),[]).
%
% fof(prove_p_combinator,plain,(~$equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(x,y),apply(apply(x,y),z)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),[]).
%
% cnf(160437120,plain,(~$equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(x,y),apply(apply(x,y),z)))),inference(rewrite,[status(thm)],[prove_p_combinator]),[]).
%
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),[]).
%
% cnf(160419360,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% cnf(168288624,plain,(~$equal(apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z),apply(apply(x,y),apply(apply(x,y),z)))),inference(paramodulation,[status(thm)],[160437120,160419360,theory(equality)]),[]).
%
% fof(w_definition,plain,($equal(apply(apply(w,A),B),apply(apply(A,B),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-3.tptp',unknown),[]).
%
% cnf(160427696,plain,($equal(apply(apply(w,A),B),apply(apply(A,B),B))),inference(rewrite,[status(thm)],[w_definition]),[]).
%
% cnf(168792000,plain,(~$equal(apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z),apply(apply(x,y),apply(apply(x,y),z)))),inference(paramodulation,[status(thm)],[168288624,160427696,theory(equality)]),[]).
%
% cnf(170956640,plain,(~$equal(apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z),apply(apply(x,y),apply(apply(x,y),z)))),inference(paramodulation,[status(thm)],[168792000,160423608,theory(equality)]),[]).
%
% cnf(175757024,plain,(~$equal(apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z),apply(apply(x,y),apply(apply(x,y),z)))),inference(paramodulation,[status(thm)],[170956640,160423608,theory(equality)]),[]).
%
% cnf(177834224,plain,(~$equal(apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z),apply(apply(x,y),apply(apply(x,y),z)))),inference(paramodulation,[status(thm)],[175757024,160423608,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[160423608,177834224,160423608,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------