TSTP Solution File: LCL022-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL022-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 13:40:03 EDT 2009
% Result : Unsatisfiable 1.4s
% Output : Refutation 1.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 : 52 ( 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/LCL022-1.tptp',unknown),
[] ).
cnf(146130440,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/LCL022-1.tptp',unknown),
[] ).
cnf(146135296,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(rewrite,[status(thm)],[yql]),
[] ).
cnf(153918824,plain,
( ~ is_a_theorem(equivalent(A,B))
| is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C))) ),
inference(resolution,[status(thm)],[146130440,146135296]),
[] ).
cnf(154082104,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(equivalent(C,B))
| is_a_theorem(equivalent(A,C)) ),
inference(resolution,[status(thm)],[153918824,146130440]),
[] ).
cnf(154228632,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolution,[status(thm)],[154082104,146135296]),
[] ).
cnf(154324600,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[154228632,146130440]),
[] ).
cnf(153938456,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)],[146130440,146135296]),
[] ).
cnf(154347016,plain,
is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),equivalent(equivalent(A,B),C))),
inference(resolution,[status(thm)],[154228632,153918824]),
[] ).
cnf(154526816,plain,
is_a_theorem(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),equivalent(A,B))),
inference(resolution,[status(thm)],[153938456,154347016]),
[] ).
cnf(156032896,plain,
is_a_theorem(equivalent(A,A)),
inference(resolution,[status(thm)],[154324600,154526816]),
[] ).
cnf(156080344,plain,
( ~ is_a_theorem(equivalent(B,A))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[156032896,154082104]),
[] ).
cnf(156445560,plain,
( ~ is_a_theorem(equivalent(B,A))
| is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C))) ),
inference(resolution,[status(thm)],[156080344,153918824]),
[] ).
cnf(156075096,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(A,B))),
inference(resolution,[status(thm)],[156032896,153918824]),
[] ).
cnf(156148336,plain,
( ~ is_a_theorem(equivalent(C,equivalent(A,B)))
| is_a_theorem(equivalent(equivalent(B,A),C)) ),
inference(resolution,[status(thm)],[156075096,154082104]),
[] ).
cnf(157970976,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(resolution,[status(thm)],[156148336,154526816]),
[] ).
cnf(163560704,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(C,B)),equivalent(equivalent(equivalent(D,C),equivalent(B,D)),A))),
inference(resolution,[status(thm)],[156445560,157970976]),
[] ).
cnf(155128368,plain,
( ~ is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[154526816,146130440]),
[] ).
fof(prove_ec_1,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL022-1.tptp',unknown),
[] ).
cnf(146139512,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
inference(rewrite,[status(thm)],[prove_ec_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[163560704,155128368,146139512]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 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/LCL022-1.tptp',unknown),[]).
%
% cnf(146130440,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/LCL022-1.tptp',unknown),[]).
%
% cnf(146135296,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C))))),inference(rewrite,[status(thm)],[yql]),[]).
%
% cnf(153918824,plain,(~is_a_theorem(equivalent(A,B))|is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))),inference(resolution,[status(thm)],[146130440,146135296]),[]).
%
% cnf(154082104,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(equivalent(C,B))|is_a_theorem(equivalent(A,C))),inference(resolution,[status(thm)],[153918824,146130440]),[]).
%
% cnf(154228632,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B)))),inference(resolution,[status(thm)],[154082104,146135296]),[]).
%
% cnf(154324600,plain,(~is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[154228632,146130440]),[]).
%
% cnf(153938456,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)],[146130440,146135296]),[]).
%
% cnf(154347016,plain,(is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),equivalent(equivalent(A,B),C)))),inference(resolution,[status(thm)],[154228632,153918824]),[]).
%
% cnf(154526816,plain,(is_a_theorem(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),equivalent(A,B)))),inference(resolution,[status(thm)],[153938456,154347016]),[]).
%
% cnf(156032896,plain,(is_a_theorem(equivalent(A,A))),inference(resolution,[status(thm)],[154324600,154526816]),[]).
%
% cnf(156080344,plain,(~is_a_theorem(equivalent(B,A))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[156032896,154082104]),[]).
%
% cnf(156445560,plain,(~is_a_theorem(equivalent(B,A))|is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))),inference(resolution,[status(thm)],[156080344,153918824]),[]).
%
% cnf(156075096,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(A,B)))),inference(resolution,[status(thm)],[156032896,153918824]),[]).
%
% cnf(156148336,plain,(~is_a_theorem(equivalent(C,equivalent(A,B)))|is_a_theorem(equivalent(equivalent(B,A),C))),inference(resolution,[status(thm)],[156075096,154082104]),[]).
%
% cnf(157970976,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(equivalent(C,B),equivalent(A,C))))),inference(resolution,[status(thm)],[156148336,154526816]),[]).
%
% cnf(163560704,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(C,B)),equivalent(equivalent(equivalent(D,C),equivalent(B,D)),A)))),inference(resolution,[status(thm)],[156445560,157970976]),[]).
%
% cnf(155128368,plain,(~is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[154526816,146130440]),[]).
%
% fof(prove_ec_1,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL022-1.tptp',unknown),[]).
%
% cnf(146139512,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c)))),inference(rewrite,[status(thm)],[prove_ec_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163560704,155128368,146139512]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------