TSTP Solution File: COL042-9 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL042-9 : TPTP v3.4.2. Released v2.1.0.
% 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 11:32:22 EDT 2009
% Result : Unsatisfiable 555.2s
% Output : Refutation 555.2s
% 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 : 7 ( 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/COL042-9.tptp',unknown),
[] ).
cnf(144439472,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/COL042-9.tptp',unknown),
[] ).
cnf(144456808,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(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),strong_fixed_point),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-9.tptp',unknown),
[] ).
cnf(144448056,plain,
$equal(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),strong_fixed_point),
inference(rewrite,[status(thm)],[strong_fixed_point]),
[] ).
cnf(152289280,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),fixed_pt)),
inference(paramodulation,[status(thm)],[144456808,144448056,theory(equality)]),
[] ).
cnf(152635544,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt))),
inference(paramodulation,[status(thm)],[152289280,144439472,theory(equality)]),
[] ).
cnf(153889264,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt)))),
inference(paramodulation,[status(thm)],[152635544,144439472,theory(equality)]),
[] ).
cnf(156056160,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)],[153889264,144439472,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/COL042-9.tptp',unknown),
[] ).
cnf(144443672,plain,
$equal(apply(apply(w1,A),B),apply(apply(B,A),A)),
inference(rewrite,[status(thm)],[w1_definition]),
[] ).
cnf(156954224,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)],[156056160,144443672,theory(equality)]),
[] ).
cnf(157205416,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)],[156954224,144439472,theory(equality)]),
[] ).
cnf(157265816,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)],[157205416,144443672,theory(equality)]),
[] ).
cnf(162728736,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)],[157265816,144443672,theory(equality)]),
[] ).
cnf(211494720,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)],[162728736,144439472,theory(equality)]),
[] ).
cnf(298734832,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)],[211494720,144439472,theory(equality)]),
[] ).
cnf(315043160,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)],[298734832,144443672,theory(equality)]),
[] ).
cnf(315164720,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)],[315043160,144439472,theory(equality)]),
[] ).
cnf(315324000,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)],[315164720,144443672,theory(equality)]),
[] ).
cnf(315423784,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)],[315324000,144439472,theory(equality)]),
[] ).
cnf(316047224,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(apply(apply(b,b),b),fixed_pt))))),
inference(paramodulation,[status(thm)],[315423784,144439472,theory(equality)]),
[] ).
cnf(338188272,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt)))),
inference(paramodulation,[status(thm)],[316047224,144439472,theory(equality)]),
[] ).
cnf(527825520,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),fixed_pt))),
inference(paramodulation,[status(thm)],[338188272,144439472,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[144439472,527825520,144448056,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 556 seconds
% START OF PROOF SEQUENCE
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-9.tptp',unknown),[]).
%
% cnf(144439472,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/COL042-9.tptp',unknown),[]).
%
% cnf(144456808,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(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),strong_fixed_point)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-9.tptp',unknown),[]).
%
% cnf(144448056,plain,($equal(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),strong_fixed_point)),inference(rewrite,[status(thm)],[strong_fixed_point]),[]).
%
% cnf(152289280,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),fixed_pt))),inference(paramodulation,[status(thm)],[144456808,144448056,theory(equality)]),[]).
%
% cnf(152635544,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt)))),inference(paramodulation,[status(thm)],[152289280,144439472,theory(equality)]),[]).
%
% cnf(153889264,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt))))),inference(paramodulation,[status(thm)],[152635544,144439472,theory(equality)]),[]).
%
% cnf(156056160,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),inference(paramodulation,[status(thm)],[153889264,144439472,theory(equality)]),[]).
%
% fof(w1_definition,plain,($equal(apply(apply(w1,A),B),apply(apply(B,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-9.tptp',unknown),[]).
%
% cnf(144443672,plain,($equal(apply(apply(w1,A),B),apply(apply(B,A),A))),inference(rewrite,[status(thm)],[w1_definition]),[]).
%
% cnf(156954224,plain,(~$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)],[156056160,144443672,theory(equality)]),[]).
%
% cnf(157205416,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),inference(paramodulation,[status(thm)],[156954224,144439472,theory(equality)]),[]).
%
% cnf(157265816,plain,(~$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)],[157205416,144443672,theory(equality)]),[]).
%
% cnf(162728736,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,apply(b,fixed_pt)),w1),apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[157265816,144443672,theory(equality)]),[]).
%
% cnf(211494720,plain,(~$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)],[162728736,144439472,theory(equality)]),[]).
%
% cnf(298734832,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))))),inference(paramodulation,[status(thm)],[211494720,144439472,theory(equality)]),[]).
%
% cnf(315043160,plain,(~$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)],[298734832,144443672,theory(equality)]),[]).
%
% cnf(315164720,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1)))),inference(paramodulation,[status(thm)],[315043160,144439472,theory(equality)]),[]).
%
% cnf(315324000,plain,(~$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)],[315164720,144443672,theory(equality)]),[]).
%
% cnf(315423784,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))))),inference(paramodulation,[status(thm)],[315324000,144439472,theory(equality)]),[]).
%
% cnf(316047224,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt)))))),inference(paramodulation,[status(thm)],[315423784,144439472,theory(equality)]),[]).
%
% cnf(338188272,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt))))),inference(paramodulation,[status(thm)],[316047224,144439472,theory(equality)]),[]).
%
% cnf(527825520,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),fixed_pt)))),inference(paramodulation,[status(thm)],[338188272,144439472,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[144439472,527825520,144448056,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------