TSTP Solution File: COL064-5 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL064-5 : TPTP v3.4.2. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 11:33:41 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 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(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/COL064-5.tptp',unknown),
[] ).
cnf(164485960,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
fof(prove_v_combinator,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),b))),t),x),y),z),apply(apply(z,x),y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-5.tptp',unknown),
[] ).
cnf(164495424,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),b))),t),x),y),z),apply(apply(z,x),y)),
inference(rewrite,[status(thm)],[prove_v_combinator]),
[] ).
cnf(172949512,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),b)),apply(t,x)),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[164495424,164485960,theory(equality)]),
[] ).
cnf(177687904,plain,
~ $equal(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),b),apply(t,x))),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[172949512,164485960,theory(equality)]),
[] ).
fof(t_definition,plain,
! [A,B] : $equal(apply(apply(t,A),B),apply(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-5.tptp',unknown),
[] ).
cnf(164490160,plain,
$equal(apply(apply(t,A),B),apply(B,A)),
inference(rewrite,[status(thm)],[t_definition]),
[] ).
cnf(185091528,plain,
~ $equal(apply(apply(apply(apply(apply(apply(b,b),b),apply(t,x)),apply(apply(b,b),t)),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[177687904,164490160,theory(equality)]),
[] ).
cnf(189064904,plain,
~ $equal(apply(apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[185091528,164485960,theory(equality)]),
[] ).
cnf(189437088,plain,
~ $equal(apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[189064904,164485960,theory(equality)]),
[] ).
cnf(189771336,plain,
~ $equal(apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[189437088,164485960,theory(equality)]),
[] ).
cnf(189846608,plain,
~ $equal(apply(apply(apply(apply(apply(b,b),t),y),z),x),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[189771336,164490160,theory(equality)]),
[] ).
cnf(190165600,plain,
~ $equal(apply(apply(apply(b,apply(t,y)),z),x),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[189846608,164485960,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164485960,190165600,164490160,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-5.tptp',unknown),[]).
%
% cnf(164485960,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% fof(prove_v_combinator,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),b))),t),x),y),z),apply(apply(z,x),y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-5.tptp',unknown),[]).
%
% cnf(164495424,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),b))),t),x),y),z),apply(apply(z,x),y))),inference(rewrite,[status(thm)],[prove_v_combinator]),[]).
%
% cnf(172949512,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),b)),apply(t,x)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[164495424,164485960,theory(equality)]),[]).
%
% cnf(177687904,plain,(~$equal(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),b),apply(t,x))),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[172949512,164485960,theory(equality)]),[]).
%
% fof(t_definition,plain,($equal(apply(apply(t,A),B),apply(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-5.tptp',unknown),[]).
%
% cnf(164490160,plain,($equal(apply(apply(t,A),B),apply(B,A))),inference(rewrite,[status(thm)],[t_definition]),[]).
%
% cnf(185091528,plain,(~$equal(apply(apply(apply(apply(apply(apply(b,b),b),apply(t,x)),apply(apply(b,b),t)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[177687904,164490160,theory(equality)]),[]).
%
% cnf(189064904,plain,(~$equal(apply(apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[185091528,164485960,theory(equality)]),[]).
%
% cnf(189437088,plain,(~$equal(apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[189064904,164485960,theory(equality)]),[]).
%
% cnf(189771336,plain,(~$equal(apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[189437088,164485960,theory(equality)]),[]).
%
% cnf(189846608,plain,(~$equal(apply(apply(apply(apply(apply(b,b),t),y),z),x),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[189771336,164490160,theory(equality)]),[]).
%
% cnf(190165600,plain,(~$equal(apply(apply(apply(b,apply(t,y)),z),x),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[189846608,164485960,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164485960,190165600,164490160,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------