%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL064-3 : TPTP v3.4.2. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 11:33:37 EDT 2009
% Result : Unsatisfiable 0.5s
% Output : Refutation 0.5s
% 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/COL064-3.tptp',unknown),
[] ).
cnf(162015264,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))),b)),apply(apply(b,b),t)),x),y),z),apply(apply(z,x),y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-3.tptp',unknown),
[] ).
cnf(162024728,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)),x),y),z),apply(apply(z,x),y)),
inference(rewrite,[status(thm)],[prove_v_combinator]),
[] ).
cnf(170450656,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(apply(apply(b,b),t),x)),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[162024728,162015264,theory(equality)]),
[] ).
cnf(174458016,plain,
~ $equal(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[170450656,162015264,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/COL064-3.tptp',unknown),
[] ).
cnf(162019464,plain,
$equal(apply(apply(t,A),B),apply(B,A)),
inference(rewrite,[status(thm)],[t_definition]),
[] ).
cnf(180703800,plain,
~ $equal(apply(apply(apply(apply(b,apply(apply(apply(b,b),t),x)),apply(apply(b,b),t)),y),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[174458016,162019464,theory(equality)]),
[] ).
cnf(185095720,plain,
~ $equal(apply(apply(apply(apply(apply(b,b),t),x),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[180703800,162015264,theory(equality)]),
[] ).
cnf(185485112,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)],[185095720,162015264,theory(equality)]),
[] ).
cnf(185740320,plain,
~ $equal(apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[185485112,162015264,theory(equality)]),
[] ).
cnf(185790504,plain,
~ $equal(apply(apply(apply(apply(apply(b,b),t),y),z),x),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[185740320,162019464,theory(equality)]),
[] ).
cnf(186113720,plain,
~ $equal(apply(apply(apply(b,apply(t,y)),z),x),apply(apply(z,x),y)),
inference(paramodulation,[status(thm)],[185790504,162015264,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[162015264,186113720,162019464,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-3.tptp',unknown),[]).
%
% cnf(162015264,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))),b)),apply(apply(b,b),t)),x),y),z),apply(apply(z,x),y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-3.tptp',unknown),[]).
%
% cnf(162024728,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)),x),y),z),apply(apply(z,x),y))),inference(rewrite,[status(thm)],[prove_v_combinator]),[]).
%
% cnf(170450656,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(apply(apply(b,b),t),x)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[162024728,162015264,theory(equality)]),[]).
%
% cnf(174458016,plain,(~$equal(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[170450656,162015264,theory(equality)]),[]).
%
% fof(t_definition,plain,($equal(apply(apply(t,A),B),apply(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-3.tptp',unknown),[]).
%
% cnf(162019464,plain,($equal(apply(apply(t,A),B),apply(B,A))),inference(rewrite,[status(thm)],[t_definition]),[]).
%
% cnf(180703800,plain,(~$equal(apply(apply(apply(apply(b,apply(apply(apply(b,b),t),x)),apply(apply(b,b),t)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[174458016,162019464,theory(equality)]),[]).
%
% cnf(185095720,plain,(~$equal(apply(apply(apply(apply(apply(b,b),t),x),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[180703800,162015264,theory(equality)]),[]).
%
% cnf(185485112,plain,(~$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)],[185095720,162015264,theory(equality)]),[]).
%
% cnf(185740320,plain,(~$equal(apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[185485112,162015264,theory(equality)]),[]).
%
% cnf(185790504,plain,(~$equal(apply(apply(apply(apply(apply(b,b),t),y),z),x),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[185740320,162019464,theory(equality)]),[]).
%
% cnf(186113720,plain,(~$equal(apply(apply(apply(b,apply(t,y)),z),x),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[185790504,162015264,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[162015264,186113720,162019464,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------