TSTP Solution File: SET838-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET838-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:39:00 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
! [A] :
( $equal(v_g(v_f(v_xa(A))),v_xa(A))
| ~ $equal(v_g(v_f(A)),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
[] ).
cnf(145616072,plain,
( $equal(v_g(v_f(v_xa(A))),v_xa(A))
| ~ $equal(v_g(v_f(A)),A) ),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
fof(cls_conjecture_0,plain,
$equal(v_f(v_g(v_x)),v_x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
[] ).
cnf(145604688,plain,
$equal(v_f(v_g(v_x)),v_x),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(161456000,plain,
$equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x))),
inference(paramodulation,[status(thm)],[145616072,145604688,theory(equality)]),
[] ).
fof(cls_conjecture_1,plain,
! [A] :
( $equal(v_x,A)
| ~ $equal(v_f(v_g(A)),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
[] ).
cnf(145610352,plain,
( $equal(v_x,A)
| ~ $equal(v_f(v_g(A)),A) ),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(161623968,plain,
$equal(v_x,v_f(v_xa(v_g(v_x)))),
inference(paramodulation,[status(thm)],[161456000,145610352,theory(equality)]),
[] ).
cnf(161862208,plain,
$equal(v_g(v_x),v_xa(v_g(v_x))),
inference(paramodulation,[status(thm)],[161623968,161456000,theory(equality)]),
[] ).
cnf(161927536,plain,
$equal(v_x,v_f(v_xa(v_xa(v_g(v_x))))),
inference(paramodulation,[status(thm)],[161862208,161623968,theory(equality)]),
[] ).
cnf(162431776,plain,
$equal(v_g(v_x),v_xa(v_xa(v_g(v_x)))),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161927536,145616072,theory(equality)]),
[] ).
fof(cls_conjecture_3,plain,
! [A] :
( ~ $equal(v_xa(A),A)
| ~ $equal(v_g(v_f(A)),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
[] ).
cnf(145622544,plain,
( ~ $equal(v_xa(A),A)
| ~ $equal(v_g(v_f(A)),A) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161862208,162431776,145622544,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,($equal(v_g(v_f(v_xa(A))),v_xa(A))|~$equal(v_g(v_f(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
%
% cnf(145616072,plain,($equal(v_g(v_f(v_xa(A))),v_xa(A))|~$equal(v_g(v_f(A)),A)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% fof(cls_conjecture_0,plain,($equal(v_f(v_g(v_x)),v_x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
%
% cnf(145604688,plain,($equal(v_f(v_g(v_x)),v_x)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(161456000,plain,($equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x)))),inference(paramodulation,[status(thm)],[145616072,145604688,theory(equality)]),[]).
%
% fof(cls_conjecture_1,plain,($equal(v_x,A)|~$equal(v_f(v_g(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
%
% cnf(145610352,plain,($equal(v_x,A)|~$equal(v_f(v_g(A)),A)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(161623968,plain,($equal(v_x,v_f(v_xa(v_g(v_x))))),inference(paramodulation,[status(thm)],[161456000,145610352,theory(equality)]),[]).
%
% cnf(161862208,plain,($equal(v_g(v_x),v_xa(v_g(v_x)))),inference(paramodulation,[status(thm)],[161623968,161456000,theory(equality)]),[]).
%
% cnf(161927536,plain,($equal(v_x,v_f(v_xa(v_xa(v_g(v_x)))))),inference(paramodulation,[status(thm)],[161862208,161623968,theory(equality)]),[]).
%
% cnf(162431776,plain,($equal(v_g(v_x),v_xa(v_xa(v_g(v_x))))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161927536,145616072,theory(equality)]),[]).
%
% fof(cls_conjecture_3,plain,(~$equal(v_xa(A),A)|~$equal(v_g(v_f(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
%
% cnf(145622544,plain,(~$equal(v_xa(A),A)|~$equal(v_g(v_f(A)),A)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161862208,162431776,145622544,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------