TSTP Solution File: COL044-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL044-1 : 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 11:32:25 EDT 2009
% Result : Unsatisfiable 2.3s
% Output : Refutation 2.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 23 ( 0 sgn 7 !; 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/COL044-1.tptp',unknown),
[] ).
cnf(151991064,plain,
~ $equal(apply(f(A),apply(A,f(A))),apply(A,f(A))),
inference(rewrite,[status(thm)],[prove_fixed_point]),
[] ).
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/COL044-1.tptp',unknown),
[] ).
cnf(151982096,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
cnf(159840808,plain,
~ $equal(apply(apply(apply(b,f(A)),A),f(A)),apply(A,f(A))),
inference(paramodulation,[status(thm)],[151991064,151982096,theory(equality)]),
[] ).
fof(n_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL044-1.tptp',unknown),
[] ).
cnf(151986280,plain,
$equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C)),
inference(rewrite,[status(thm)],[n_definition]),
[] ).
cnf(160063864,plain,
~ $equal(apply(apply(apply(n,b),A),f(A)),apply(A,f(A))),
inference(paramodulation,[status(thm)],[159840808,151986280,theory(equality)]),
[] ).
cnf(160134752,plain,
~ $equal(apply(apply(apply(apply(b,apply(n,b)),A),B),f(apply(A,B))),apply(apply(A,B),f(apply(A,B)))),
inference(paramodulation,[status(thm)],[160063864,151982096,theory(equality)]),
[] ).
cnf(160980368,plain,
~ $equal(apply(apply(apply(apply(apply(b,apply(b,apply(n,b))),B),C),A),f(apply(apply(B,C),A))),apply(apply(apply(B,C),A),f(apply(apply(B,C),A)))),
inference(paramodulation,[status(thm)],[160134752,151982096,theory(equality)]),
[] ).
cnf(170629552,plain,
~ $equal(apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),B),A),f(apply(apply(A,B),A))),apply(apply(apply(A,B),A),f(apply(apply(A,B),A)))),
inference(paramodulation,[status(thm)],[160980368,151986280,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(equality_resolution,[status(thm)],[170629552]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(f(A),apply(A,f(A))),apply(A,f(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL044-1.tptp',unknown),[]).
%
% cnf(151991064,plain,(~$equal(apply(f(A),apply(A,f(A))),apply(A,f(A)))),inference(rewrite,[status(thm)],[prove_fixed_point]),[]).
%
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL044-1.tptp',unknown),[]).
%
% cnf(151982096,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% cnf(159840808,plain,(~$equal(apply(apply(apply(b,f(A)),A),f(A)),apply(A,f(A)))),inference(paramodulation,[status(thm)],[151991064,151982096,theory(equality)]),[]).
%
% fof(n_definition,plain,($equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL044-1.tptp',unknown),[]).
%
% cnf(151986280,plain,($equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C))),inference(rewrite,[status(thm)],[n_definition]),[]).
%
% cnf(160063864,plain,(~$equal(apply(apply(apply(n,b),A),f(A)),apply(A,f(A)))),inference(paramodulation,[status(thm)],[159840808,151986280,theory(equality)]),[]).
%
% cnf(160134752,plain,(~$equal(apply(apply(apply(apply(b,apply(n,b)),A),B),f(apply(A,B))),apply(apply(A,B),f(apply(A,B))))),inference(paramodulation,[status(thm)],[160063864,151982096,theory(equality)]),[]).
%
% cnf(160980368,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(b,apply(n,b))),B),C),A),f(apply(apply(B,C),A))),apply(apply(apply(B,C),A),f(apply(apply(B,C),A))))),inference(paramodulation,[status(thm)],[160134752,151982096,theory(equality)]),[]).
%
% cnf(170629552,plain,(~$equal(apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),B),A),f(apply(apply(A,B),A))),apply(apply(apply(A,B),A),f(apply(apply(A,B),A))))),inference(paramodulation,[status(thm)],[160980368,151986280,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[170629552]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------