TSTP Solution File: LCL013-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL013-1 : 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 @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:39:50 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 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 : 27 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(xgf,plain,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL013-1.tptp',unknown),
[] ).
cnf(172887080,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))),
inference(rewrite,[status(thm)],[xgf]),
[] ).
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/LCL013-1.tptp',unknown),
[] ).
cnf(172882224,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
cnf(180701824,plain,
( ~ is_a_theorem(equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[172882224,172887080]),
[] ).
fof(prove_um,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL013-1.tptp',unknown),
[] ).
cnf(172891328,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
inference(rewrite,[status(thm)],[prove_um]),
[] ).
cnf(180719576,plain,
~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a))))),
inference(resolution,[status(thm)],[180701824,172891328]),
[] ).
cnf(180775920,plain,
( ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a))))))
| ~ is_a_theorem(A) ),
inference(resolution,[status(thm)],[172882224,180719576]),
[] ).
cnf(180850312,plain,
~ is_a_theorem(equivalent(equivalent(D,equivalent(equivalent(E,equivalent(D,F)),equivalent(F,E))),equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))))),
inference(resolution,[status(thm)],[180775920,172887080]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[172887080,180850312]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(xgf,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL013-1.tptp',unknown),[]).
%
% cnf(172887080,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))))),inference(rewrite,[status(thm)],[xgf]),[]).
%
% 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/LCL013-1.tptp',unknown),[]).
%
% cnf(172882224,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% cnf(180701824,plain,(~is_a_theorem(equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[172882224,172887080]),[]).
%
% fof(prove_um,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL013-1.tptp',unknown),[]).
%
% cnf(172891328,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a))))),inference(rewrite,[status(thm)],[prove_um]),[]).
%
% cnf(180719576,plain,(~is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))))),inference(resolution,[status(thm)],[180701824,172891328]),[]).
%
% cnf(180775920,plain,(~is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a))))))|~is_a_theorem(A)),inference(resolution,[status(thm)],[172882224,180719576]),[]).
%
% cnf(180850312,plain,(~is_a_theorem(equivalent(equivalent(D,equivalent(equivalent(E,equivalent(D,F)),equivalent(F,E))),equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a))))))),inference(resolution,[status(thm)],[180775920,172887080]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[172887080,180850312]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------