TSTP Solution File: LCL098-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL098-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 13:42:05 EDT 2009
% Result : Unsatisfiable 347.2s
% Output : Refutation 347.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_lg_4,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL098-1.tptp',unknown),
[] ).
cnf(146993672,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(rewrite,[status(thm)],[prove_lg_4]),
[] ).
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/LCL098-1.tptp',unknown),
[] ).
cnf(146979888,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(lg_3,plain,
! [A,B,C,D,E] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E),E)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL098-1.tptp',unknown),
[] ).
cnf(146984976,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E),E)),
inference(rewrite,[status(thm)],[lg_3]),
[] ).
cnf(154774552,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),E),equivalent(equivalent(C,D),E)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[146979888,146984976]),
[] ).
cnf(155816632,plain,
is_a_theorem(equivalent(equivalent(equivalent(B,D),A),equivalent(equivalent(C,D),equivalent(equivalent(B,C),A)))),
inference(resolution,[status(thm)],[154774552,146984976]),
[] ).
cnf(157036336,plain,
is_a_theorem(equivalent(equivalent(E,D),equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),E),equivalent(equivalent(B,C),D)))),
inference(resolution,[status(thm)],[154774552,155816632]),
[] ).
cnf(157147664,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(F,E),equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),F),equivalent(equivalent(C,D),E))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[146979888,157036336]),
[] ).
cnf(154794248,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),E),equivalent(equivalent(C,D),E)),F),F),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[146979888,146984976]),
[] ).
cnf(157199504,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(F,G),equivalent(F,H)),equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)),equivalent(equivalent(G,H),E))),
inference(resolution,[status(thm)],[154794248,157036336]),
[] ).
cnf(236200928,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),A),E),equivalent(equivalent(equivalent(B,D),A),equivalent(equivalent(C,D),E)))),
inference(resolution,[status(thm)],[157147664,157199504]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[146993672,236200928]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 348 seconds
% START OF PROOF SEQUENCE
% fof(prove_lg_4,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL098-1.tptp',unknown),[]).
%
% cnf(146993672,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),inference(rewrite,[status(thm)],[prove_lg_4]),[]).
%
% 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/LCL098-1.tptp',unknown),[]).
%
% cnf(146979888,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(lg_3,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E),E))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL098-1.tptp',unknown),[]).
%
% cnf(146984976,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E),E))),inference(rewrite,[status(thm)],[lg_3]),[]).
%
% cnf(154774552,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),E),equivalent(equivalent(C,D),E)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[146979888,146984976]),[]).
%
% cnf(155816632,plain,(is_a_theorem(equivalent(equivalent(equivalent(B,D),A),equivalent(equivalent(C,D),equivalent(equivalent(B,C),A))))),inference(resolution,[status(thm)],[154774552,146984976]),[]).
%
% cnf(157036336,plain,(is_a_theorem(equivalent(equivalent(E,D),equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),E),equivalent(equivalent(B,C),D))))),inference(resolution,[status(thm)],[154774552,155816632]),[]).
%
% cnf(157147664,plain,(~is_a_theorem(equivalent(equivalent(equivalent(F,E),equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),F),equivalent(equivalent(C,D),E))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[146979888,157036336]),[]).
%
% cnf(154794248,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),E),equivalent(equivalent(C,D),E)),F),F),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[146979888,146984976]),[]).
%
% cnf(157199504,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(F,G),equivalent(F,H)),equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)),equivalent(equivalent(G,H),E)))),inference(resolution,[status(thm)],[154794248,157036336]),[]).
%
% cnf(236200928,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),A),E),equivalent(equivalent(equivalent(B,D),A),equivalent(equivalent(C,D),E))))),inference(resolution,[status(thm)],[157147664,157199504]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[146993672,236200928]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------