%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL061-2 : TPTP v3.4.2. Bugfixed v1.2.0.
% 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 11:33:12 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t_definition,plain,
! [A,B] : $equal(apply(apply(t,A),B),apply(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL061-2.tptp',unknown),
[] ).
cnf(171074608,plain,
$equal(apply(apply(t,A),B),apply(B,A)),
inference(rewrite,[status(thm)],[t_definition]),
[] ).
fof(prove_q1_combinator,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL061-2.tptp',unknown),
[] ).
cnf(171079792,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y))),
inference(rewrite,[status(thm)],[prove_q1_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/COL061-2.tptp',unknown),
[] ).
cnf(171070408,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
cnf(179274376,plain,
~ $equal(apply(apply(apply(apply(t,t),apply(apply(apply(b,b),b),x)),y),z),apply(x,apply(z,y))),
inference(paramodulation,[status(thm)],[171079792,171070408,theory(equality)]),
[] ).
cnf(180513304,plain,
~ $equal(apply(apply(apply(apply(apply(apply(b,b),b),x),t),y),z),apply(x,apply(z,y))),
inference(paramodulation,[status(thm)],[179274376,171074608,theory(equality)]),
[] ).
cnf(182627304,plain,
~ $equal(apply(apply(apply(apply(b,apply(b,x)),t),y),z),apply(x,apply(z,y))),
inference(paramodulation,[status(thm)],[180513304,171070408,theory(equality)]),
[] ).
cnf(183300448,plain,
~ $equal(apply(apply(apply(b,x),apply(t,y)),z),apply(x,apply(z,y))),
inference(paramodulation,[status(thm)],[182627304,171070408,theory(equality)]),
[] ).
cnf(183467104,plain,
~ $equal(apply(x,apply(apply(t,y),z)),apply(x,apply(z,y))),
inference(paramodulation,[status(thm)],[183300448,171070408,theory(equality)]),
[] ).
cnf(183495800,plain,
~ $equal(apply(apply(t,apply(apply(t,y),z)),x),apply(x,apply(z,y))),
inference(paramodulation,[status(thm)],[183467104,171074608,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171074608,183495800,171074608,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t_definition,plain,($equal(apply(apply(t,A),B),apply(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL061-2.tptp',unknown),[]).
%
% cnf(171074608,plain,($equal(apply(apply(t,A),B),apply(B,A))),inference(rewrite,[status(thm)],[t_definition]),[]).
%
% fof(prove_q1_combinator,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL061-2.tptp',unknown),[]).
%
% cnf(171079792,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y)))),inference(rewrite,[status(thm)],[prove_q1_combinator]),[]).
%
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL061-2.tptp',unknown),[]).
%
% cnf(171070408,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% cnf(179274376,plain,(~$equal(apply(apply(apply(apply(t,t),apply(apply(apply(b,b),b),x)),y),z),apply(x,apply(z,y)))),inference(paramodulation,[status(thm)],[171079792,171070408,theory(equality)]),[]).
%
% cnf(180513304,plain,(~$equal(apply(apply(apply(apply(apply(apply(b,b),b),x),t),y),z),apply(x,apply(z,y)))),inference(paramodulation,[status(thm)],[179274376,171074608,theory(equality)]),[]).
%
% cnf(182627304,plain,(~$equal(apply(apply(apply(apply(b,apply(b,x)),t),y),z),apply(x,apply(z,y)))),inference(paramodulation,[status(thm)],[180513304,171070408,theory(equality)]),[]).
%
% cnf(183300448,plain,(~$equal(apply(apply(apply(b,x),apply(t,y)),z),apply(x,apply(z,y)))),inference(paramodulation,[status(thm)],[182627304,171070408,theory(equality)]),[]).
%
% cnf(183467104,plain,(~$equal(apply(x,apply(apply(t,y),z)),apply(x,apply(z,y)))),inference(paramodulation,[status(thm)],[183300448,171070408,theory(equality)]),[]).
%
% cnf(183495800,plain,(~$equal(apply(apply(t,apply(apply(t,y),z)),x),apply(x,apply(z,y)))),inference(paramodulation,[status(thm)],[183467104,171074608,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171074608,183495800,171074608,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------