%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL035-1 : TPTP v3.4.2. Released v1.0.0.
% 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 11:32:07 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_fixed_point,plain,
! [A] : ~ $equal(apply(f(A),apply(A,f(A))),apply(A,f(A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),
[] ).
cnf(166723008,plain,
~ $equal(apply(f(A),apply(A,f(A))),apply(A,f(A))),
inference(rewrite,[status(thm)],[prove_fixed_point]),
[] ).
fof(q_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),
[] ).
cnf(166714080,plain,
$equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
inference(rewrite,[status(thm)],[q_definition]),
[] ).
cnf(174688768,plain,
~ $equal(apply(apply(apply(q,A),f(A)),f(A)),apply(A,f(A))),
inference(paramodulation,[status(thm)],[166723008,166714080,theory(equality)]),
[] ).
fof(w_definition,plain,
! [A,B] : $equal(apply(apply(w,A),B),apply(apply(A,B),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),
[] ).
cnf(166710168,plain,
$equal(apply(apply(w,A),B),apply(apply(A,B),B)),
inference(rewrite,[status(thm)],[w_definition]),
[] ).
cnf(174836784,plain,
~ $equal(apply(apply(w,apply(q,A)),f(A)),apply(A,f(A))),
inference(paramodulation,[status(thm)],[174688768,166710168,theory(equality)]),
[] ).
cnf(175103296,plain,
~ $equal(apply(apply(apply(apply(q,q),w),A),f(A)),apply(A,f(A))),
inference(paramodulation,[status(thm)],[174836784,166714080,theory(equality)]),
[] ).
fof(l_definition,plain,
! [A,B] : $equal(apply(apply(l,A),B),apply(A,apply(B,B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),
[] ).
cnf(166706032,plain,
$equal(apply(apply(l,A),B),apply(A,apply(B,B))),
inference(rewrite,[status(thm)],[l_definition]),
[] ).
cnf(175261248,plain,
~ $equal(apply(apply(apply(l,apply(apply(q,q),w)),A),f(apply(A,A))),apply(apply(A,A),f(apply(A,A)))),
inference(paramodulation,[status(thm)],[175103296,166706032,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(equality_resolution,[status(thm)],[175261248]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(f(A),apply(A,f(A))),apply(A,f(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),[]).
%
% cnf(166723008,plain,(~$equal(apply(f(A),apply(A,f(A))),apply(A,f(A)))),inference(rewrite,[status(thm)],[prove_fixed_point]),[]).
%
% fof(q_definition,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),[]).
%
% cnf(166714080,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),inference(rewrite,[status(thm)],[q_definition]),[]).
%
% cnf(174688768,plain,(~$equal(apply(apply(apply(q,A),f(A)),f(A)),apply(A,f(A)))),inference(paramodulation,[status(thm)],[166723008,166714080,theory(equality)]),[]).
%
% fof(w_definition,plain,($equal(apply(apply(w,A),B),apply(apply(A,B),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),[]).
%
% cnf(166710168,plain,($equal(apply(apply(w,A),B),apply(apply(A,B),B))),inference(rewrite,[status(thm)],[w_definition]),[]).
%
% cnf(174836784,plain,(~$equal(apply(apply(w,apply(q,A)),f(A)),apply(A,f(A)))),inference(paramodulation,[status(thm)],[174688768,166710168,theory(equality)]),[]).
%
% cnf(175103296,plain,(~$equal(apply(apply(apply(apply(q,q),w),A),f(A)),apply(A,f(A)))),inference(paramodulation,[status(thm)],[174836784,166714080,theory(equality)]),[]).
%
% fof(l_definition,plain,($equal(apply(apply(l,A),B),apply(A,apply(B,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL035-1.tptp',unknown),[]).
%
% cnf(166706032,plain,($equal(apply(apply(l,A),B),apply(A,apply(B,B)))),inference(rewrite,[status(thm)],[l_definition]),[]).
%
% cnf(175261248,plain,(~$equal(apply(apply(apply(l,apply(apply(q,q),w)),A),f(apply(A,A))),apply(apply(A,A),f(apply(A,A))))),inference(paramodulation,[status(thm)],[175103296,166706032,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[175261248]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------