%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL032-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 11:32:02 EDT 2009
% Result : Unsatisfiable 3.0s
% Output : Refutation 3.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 5 !; 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/COL032-1.tptp',unknown),
[] ).
cnf(159700872,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/COL032-1.tptp',unknown),
[] ).
cnf(159696024,plain,
$equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
inference(rewrite,[status(thm)],[q_definition]),
[] ).
cnf(167549504,plain,
~ $equal(apply(f(apply(apply(q,A),B)),apply(B,apply(A,f(apply(apply(q,A),B))))),apply(apply(apply(q,A),B),f(apply(apply(q,A),B)))),
inference(paramodulation,[status(thm)],[159700872,159696024,theory(equality)]),
[] ).
cnf(168389768,plain,
~ $equal(apply(f(apply(apply(q,A),B)),apply(B,apply(A,f(apply(apply(q,A),B))))),apply(B,apply(A,f(apply(apply(q,A),B))))),
inference(paramodulation,[status(thm)],[167549504,159696024,theory(equality)]),
[] ).
cnf(170652640,plain,
~ $equal(apply(apply(apply(q,B),f(apply(apply(q,A),B))),apply(A,f(apply(apply(q,A),B)))),apply(B,apply(A,f(apply(apply(q,A),B))))),
inference(paramodulation,[status(thm)],[168389768,159696024,theory(equality)]),
[] ).
fof(m_definition,plain,
! [A] : $equal(apply(m,A),apply(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL032-1.tptp',unknown),
[] ).
cnf(159691976,plain,
$equal(apply(m,A),apply(A,A)),
inference(rewrite,[status(thm)],[m_definition]),
[] ).
cnf(188995184,plain,
~ $equal(apply(m,apply(apply(q,A),f(apply(apply(q,apply(q,A)),A)))),apply(A,apply(apply(q,A),f(apply(apply(q,apply(q,A)),A))))),
inference(paramodulation,[status(thm)],[170652640,159691976,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(equality_resolution,[status(thm)],[188995184]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(f(A),apply(A,f(A))),apply(A,f(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL032-1.tptp',unknown),[]).
%
% cnf(159700872,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/COL032-1.tptp',unknown),[]).
%
% cnf(159696024,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),inference(rewrite,[status(thm)],[q_definition]),[]).
%
% cnf(167549504,plain,(~$equal(apply(f(apply(apply(q,A),B)),apply(B,apply(A,f(apply(apply(q,A),B))))),apply(apply(apply(q,A),B),f(apply(apply(q,A),B))))),inference(paramodulation,[status(thm)],[159700872,159696024,theory(equality)]),[]).
%
% cnf(168389768,plain,(~$equal(apply(f(apply(apply(q,A),B)),apply(B,apply(A,f(apply(apply(q,A),B))))),apply(B,apply(A,f(apply(apply(q,A),B)))))),inference(paramodulation,[status(thm)],[167549504,159696024,theory(equality)]),[]).
%
% cnf(170652640,plain,(~$equal(apply(apply(apply(q,B),f(apply(apply(q,A),B))),apply(A,f(apply(apply(q,A),B)))),apply(B,apply(A,f(apply(apply(q,A),B)))))),inference(paramodulation,[status(thm)],[168389768,159696024,theory(equality)]),[]).
%
% fof(m_definition,plain,($equal(apply(m,A),apply(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL032-1.tptp',unknown),[]).
%
% cnf(159691976,plain,($equal(apply(m,A),apply(A,A))),inference(rewrite,[status(thm)],[m_definition]),[]).
%
% cnf(188995184,plain,(~$equal(apply(m,apply(apply(q,A),f(apply(apply(q,apply(q,A)),A)))),apply(A,apply(apply(q,A),f(apply(apply(q,apply(q,A)),A)))))),inference(paramodulation,[status(thm)],[170652640,159691976,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[188995184]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------