%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL042-6 : TPTP v3.4.2. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 11:32:18 EDT 2009
% Result : Unsatisfiable 514.4s
% Output : Refutation 514.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 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 : 5 ( 5 usr; 4 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/COL042-6.tptp',unknown),
[] ).
cnf(142865808,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
fof(prove_strong_fixed_point,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),
[] ).
cnf(142883144,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
inference(rewrite,[status(thm)],[prove_strong_fixed_point]),
[] ).
fof(strong_fixed_point,plain,
$equal(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),strong_fixed_point),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),
[] ).
cnf(142874392,plain,
$equal(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),strong_fixed_point),
inference(rewrite,[status(thm)],[strong_fixed_point]),
[] ).
cnf(150715592,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),fixed_pt)),
inference(paramodulation,[status(thm)],[142883144,142874392,theory(equality)]),
[] ).
cnf(151197120,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b),apply(b,fixed_pt))),
inference(paramodulation,[status(thm)],[150715592,142865808,theory(equality)]),
[] ).
cnf(152786120,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,fixed_pt)))),
inference(paramodulation,[status(thm)],[151197120,142865808,theory(equality)]),
[] ).
cnf(155178208,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))),
inference(paramodulation,[status(thm)],[152786120,142865808,theory(equality)]),
[] ).
fof(w1_definition,plain,
! [A,B] : $equal(apply(apply(w1,A),B),apply(apply(B,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),
[] ).
cnf(142870008,plain,
$equal(apply(apply(w1,A),B),apply(apply(B,A),A)),
inference(rewrite,[status(thm)],[w1_definition]),
[] ).
cnf(155258904,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1)),
inference(paramodulation,[status(thm)],[155178208,142870008,theory(equality)]),
[] ).
cnf(155328920,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)),
inference(paramodulation,[status(thm)],[155258904,142865808,theory(equality)]),
[] ).
cnf(155397520,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramodulation,[status(thm)],[155328920,142870008,theory(equality)]),
[] ).
cnf(160508352,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,apply(b,fixed_pt)),w1),apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramodulation,[status(thm)],[155397520,142870008,theory(equality)]),
[] ).
cnf(207554280,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,fixed_pt),apply(w1,apply(apply(b,apply(b,fixed_pt)),w1))),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramodulation,[status(thm)],[160508352,142865808,theory(equality)]),
[] ).
cnf(288966296,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),
inference(paramodulation,[status(thm)],[207554280,142865808,theory(equality)]),
[] ).
cnf(308783280,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
inference(paramodulation,[status(thm)],[288966296,142870008,theory(equality)]),
[] ).
cnf(308904864,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1))),
inference(paramodulation,[status(thm)],[308783280,142865808,theory(equality)]),
[] ).
cnf(309060016,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),
inference(paramodulation,[status(thm)],[308904864,142870008,theory(equality)]),
[] ).
cnf(309172112,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),
inference(paramodulation,[status(thm)],[309060016,142865808,theory(equality)]),
[] ).
cnf(309763328,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,fixed_pt))))),
inference(paramodulation,[status(thm)],[309172112,142865808,theory(equality)]),
[] ).
cnf(335896312,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b),apply(b,fixed_pt)))),
inference(paramodulation,[status(thm)],[309763328,142865808,theory(equality)]),
[] ).
cnf(524330744,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),fixed_pt))),
inference(paramodulation,[status(thm)],[335896312,142865808,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[142865808,524330744,142874392,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 512 seconds
% START OF PROOF SEQUENCE
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),[]).
%
% cnf(142865808,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% fof(prove_strong_fixed_point,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),[]).
%
% cnf(142883144,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt))),inference(rewrite,[status(thm)],[prove_strong_fixed_point]),[]).
%
% fof(strong_fixed_point,plain,($equal(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),strong_fixed_point)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),[]).
%
% cnf(142874392,plain,($equal(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),strong_fixed_point)),inference(rewrite,[status(thm)],[strong_fixed_point]),[]).
%
% cnf(150715592,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),fixed_pt))),inference(paramodulation,[status(thm)],[142883144,142874392,theory(equality)]),[]).
%
% cnf(151197120,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b),apply(b,fixed_pt)))),inference(paramodulation,[status(thm)],[150715592,142865808,theory(equality)]),[]).
%
% cnf(152786120,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,fixed_pt))))),inference(paramodulation,[status(thm)],[151197120,142865808,theory(equality)]),[]).
%
% cnf(155178208,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),inference(paramodulation,[status(thm)],[152786120,142865808,theory(equality)]),[]).
%
% fof(w1_definition,plain,($equal(apply(apply(w1,A),B),apply(apply(B,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-6.tptp',unknown),[]).
%
% cnf(142870008,plain,($equal(apply(apply(w1,A),B),apply(apply(B,A),A))),inference(rewrite,[status(thm)],[w1_definition]),[]).
%
% cnf(155258904,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1))),inference(paramodulation,[status(thm)],[155178208,142870008,theory(equality)]),[]).
%
% cnf(155328920,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),inference(paramodulation,[status(thm)],[155258904,142865808,theory(equality)]),[]).
%
% cnf(155397520,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[155328920,142870008,theory(equality)]),[]).
%
% cnf(160508352,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,apply(b,fixed_pt)),w1),apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[155397520,142870008,theory(equality)]),[]).
%
% cnf(207554280,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,fixed_pt),apply(w1,apply(apply(b,apply(b,fixed_pt)),w1))),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[160508352,142865808,theory(equality)]),[]).
%
% cnf(288966296,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))))),inference(paramodulation,[status(thm)],[207554280,142865808,theory(equality)]),[]).
%
% cnf(308783280,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)))),inference(paramodulation,[status(thm)],[288966296,142870008,theory(equality)]),[]).
%
% cnf(308904864,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1)))),inference(paramodulation,[status(thm)],[308783280,142865808,theory(equality)]),[]).
%
% cnf(309060016,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))))),inference(paramodulation,[status(thm)],[308904864,142870008,theory(equality)]),[]).
%
% cnf(309172112,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))))),inference(paramodulation,[status(thm)],[309060016,142865808,theory(equality)]),[]).
%
% cnf(309763328,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,fixed_pt)))))),inference(paramodulation,[status(thm)],[309172112,142865808,theory(equality)]),[]).
%
% cnf(335896312,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b),apply(b,fixed_pt))))),inference(paramodulation,[status(thm)],[309763328,142865808,theory(equality)]),[]).
%
% cnf(524330744,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),fixed_pt)))),inference(paramodulation,[status(thm)],[335896312,142865808,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[142865808,524330744,142874392,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------