TSTP Solution File: LCL023-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL023-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 13:40:05 EDT 2009
% Result : Unsatisfiable 7.7s
% Output : Refutation 7.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL023-1.tptp',unknown),
[] ).
cnf(170819488,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(yql,plain,
! [A,B,C] : is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL023-1.tptp',unknown),
[] ).
cnf(170824344,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(rewrite,[status(thm)],[yql]),
[] ).
cnf(178607872,plain,
( ~ is_a_theorem(equivalent(A,B))
| is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C))) ),
inference(resolution,[status(thm)],[170819488,170824344]),
[] ).
cnf(178718736,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(equivalent(C,B))
| is_a_theorem(equivalent(A,C)) ),
inference(resolution,[status(thm)],[178607872,170819488]),
[] ).
cnf(178866648,plain,
( ~ is_a_theorem(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))))
| is_a_theorem(equivalent(equivalent(B,C),A)) ),
inference(resolution,[status(thm)],[178718736,170824344]),
[] ).
cnf(178878368,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolution,[status(thm)],[178718736,170824344]),
[] ).
cnf(178992648,plain,
is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),equivalent(equivalent(A,B),C))),
inference(resolution,[status(thm)],[178878368,178607872]),
[] ).
cnf(179079704,plain,
( ~ is_a_theorem(equivalent(D,equivalent(equivalent(A,B),C)))
| is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),D)) ),
inference(resolution,[status(thm)],[178992648,178718736]),
[] ).
cnf(178974320,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[178878368,170819488]),
[] ).
cnf(178627504,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(D,C),equivalent(B,D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[170819488,170824344]),
[] ).
cnf(180230800,plain,
is_a_theorem(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),equivalent(A,B))),
inference(resolution,[status(thm)],[178627504,178992648]),
[] ).
cnf(181330792,plain,
is_a_theorem(equivalent(A,A)),
inference(resolution,[status(thm)],[178974320,180230800]),
[] ).
cnf(181378528,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(A,B))),
inference(resolution,[status(thm)],[178607872,181330792]),
[] ).
cnf(181397528,plain,
( ~ is_a_theorem(equivalent(B,A))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[170819488,181378528]),
[] ).
cnf(181283032,plain,
( ~ is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[170819488,180230800]),
[] ).
cnf(181243696,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B)))),
inference(resolution,[status(thm)],[178866648,178992648]),
[] ).
cnf(181884216,plain,
is_a_theorem(equivalent(equivalent(equivalent(B,A),B),A)),
inference(resolution,[status(thm)],[181283032,181243696]),
[] ).
cnf(182076168,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B))),
inference(resolution,[status(thm)],[181397528,181884216]),
[] ).
cnf(182551272,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B)),
inference(resolution,[status(thm)],[179079704,182076168]),
[] ).
cnf(182853760,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(equivalent(C,equivalent(C,A)),B))),
inference(resolution,[status(thm)],[178607872,182551272]),
[] ).
cnf(199919176,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C))),
inference(resolution,[status(thm)],[178866648,182853760]),
[] ).
cnf(178997232,plain,
( ~ is_a_theorem(equivalent(C,equivalent(A,B)))
| is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolution,[status(thm)],[178878368,178718736]),
[] ).
fof(prove_ec_2,plain,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL023-1.tptp',unknown),
[] ).
cnf(170828560,plain,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
inference(rewrite,[status(thm)],[prove_ec_2]),
[] ).
cnf(180597344,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(resolution,[status(thm)],[178997232,170828560]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[199919176,180597344,181397528]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 8 seconds
% START OF PROOF SEQUENCE
% fof(condensed_detachment,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL023-1.tptp',unknown),[]).
%
% cnf(170819488,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(yql,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL023-1.tptp',unknown),[]).
%
% cnf(170824344,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C))))),inference(rewrite,[status(thm)],[yql]),[]).
%
% cnf(178607872,plain,(~is_a_theorem(equivalent(A,B))|is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))),inference(resolution,[status(thm)],[170819488,170824344]),[]).
%
% cnf(178718736,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(equivalent(C,B))|is_a_theorem(equivalent(A,C))),inference(resolution,[status(thm)],[178607872,170819488]),[]).
%
% cnf(178866648,plain,(~is_a_theorem(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))))|is_a_theorem(equivalent(equivalent(B,C),A))),inference(resolution,[status(thm)],[178718736,170824344]),[]).
%
% cnf(178878368,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B)))),inference(resolution,[status(thm)],[178718736,170824344]),[]).
%
% cnf(178992648,plain,(is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),equivalent(equivalent(A,B),C)))),inference(resolution,[status(thm)],[178878368,178607872]),[]).
%
% cnf(179079704,plain,(~is_a_theorem(equivalent(D,equivalent(equivalent(A,B),C)))|is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),D))),inference(resolution,[status(thm)],[178992648,178718736]),[]).
%
% cnf(178974320,plain,(~is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[178878368,170819488]),[]).
%
% cnf(178627504,plain,(~is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(D,C),equivalent(B,D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[170819488,170824344]),[]).
%
% cnf(180230800,plain,(is_a_theorem(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),equivalent(A,B)))),inference(resolution,[status(thm)],[178627504,178992648]),[]).
%
% cnf(181330792,plain,(is_a_theorem(equivalent(A,A))),inference(resolution,[status(thm)],[178974320,180230800]),[]).
%
% cnf(181378528,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(A,B)))),inference(resolution,[status(thm)],[178607872,181330792]),[]).
%
% cnf(181397528,plain,(~is_a_theorem(equivalent(B,A))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[170819488,181378528]),[]).
%
% cnf(181283032,plain,(~is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[170819488,180230800]),[]).
%
% cnf(181243696,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B))))),inference(resolution,[status(thm)],[178866648,178992648]),[]).
%
% cnf(181884216,plain,(is_a_theorem(equivalent(equivalent(equivalent(B,A),B),A))),inference(resolution,[status(thm)],[181283032,181243696]),[]).
%
% cnf(182076168,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B)))),inference(resolution,[status(thm)],[181397528,181884216]),[]).
%
% cnf(182551272,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B))),inference(resolution,[status(thm)],[179079704,182076168]),[]).
%
% cnf(182853760,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(equivalent(C,equivalent(C,A)),B)))),inference(resolution,[status(thm)],[178607872,182551272]),[]).
%
% cnf(199919176,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C)))),inference(resolution,[status(thm)],[178866648,182853760]),[]).
%
% cnf(178997232,plain,(~is_a_theorem(equivalent(C,equivalent(A,B)))|is_a_theorem(equivalent(equivalent(A,B),C))),inference(resolution,[status(thm)],[178878368,178718736]),[]).
%
% fof(prove_ec_2,plain,(~is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL023-1.tptp',unknown),[]).
%
% cnf(170828560,plain,(~is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c)))),inference(rewrite,[status(thm)],[prove_ec_2]),[]).
%
% cnf(180597344,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),inference(resolution,[status(thm)],[178997232,170828560]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[199919176,180597344,181397528]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------