TSTP Solution File: LCL072-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL072-1 : 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 13:41:10 EDT 2009
% Result : Unsatisfiable 213.8s
% Output : Refutation 213.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 27 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 30 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_3,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),
[] ).
cnf(162600672,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(rewrite,[status(thm)],[prove_cn_3]),
[] ).
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),
[] ).
cnf(162579784,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_37,plain,
! [A,B,C] : is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),
[] ).
cnf(162588800,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(rewrite,[status(thm)],[cn_37]),
[] ).
cnf(170472256,plain,
( ~ is_a_theorem(implies(implies(A,B),C))
| is_a_theorem(implies(not(A),C)) ),
inference(resolution,[status(thm)],[162579784,162588800]),
[] ).
fof(cn_19,plain,
! [A,B,C] : is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),
[] ).
cnf(162584640,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(rewrite,[status(thm)],[cn_19]),
[] ).
cnf(170391472,plain,
( ~ is_a_theorem(implies(implies(A,B),C))
| is_a_theorem(implies(B,C)) ),
inference(resolution,[status(thm)],[162579784,162584640]),
[] ).
cnf(170689800,plain,
is_a_theorem(implies(A,implies(C,A))),
inference(resolution,[status(thm)],[170391472,162584640]),
[] ).
cnf(171949872,plain,
is_a_theorem(implies(not(A),implies(D,implies(A,B)))),
inference(resolution,[status(thm)],[170472256,170689800]),
[] ).
cnf(173200304,plain,
( ~ is_a_theorem(implies(implies(not(A),implies(D,implies(A,B))),E))
| is_a_theorem(E) ),
inference(resolution,[status(thm)],[171949872,162579784]),
[] ).
cnf(170410888,plain,
( ~ is_a_theorem(implies(implies(implies(implies(B,C),D),implies(C,D)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,162584640]),
[] ).
cnf(170491576,plain,
( ~ is_a_theorem(implies(implies(implies(implies(B,C),D),implies(not(B),D)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,162588800]),
[] ).
fof(cn_60,plain,
! [A,B,C,D] : is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C))))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),
[] ).
cnf(162592816,plain,
is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C))))),
inference(rewrite,[status(thm)],[cn_60]),
[] ).
cnf(182289520,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(D,C),implies(implies(A,D),C)))),
inference(resolution,[status(thm)],[170491576,162592816]),
[] ).
cnf(195653968,plain,
is_a_theorem(implies(implies(D,implies(B,C)),implies(implies(implies(A,B),D),implies(B,C)))),
inference(resolution,[status(thm)],[170410888,182289520]),
[] ).
cnf(294256896,plain,
is_a_theorem(implies(implies(implies(E,D),not(A)),implies(D,implies(A,B)))),
inference(resolution,[status(thm)],[173200304,195653968]),
[] ).
cnf(312884168,plain,
( ~ is_a_theorem(implies(implies(E,D),not(A)))
| is_a_theorem(implies(D,implies(A,B))) ),
inference(resolution,[status(thm)],[162579784,294256896]),
[] ).
cnf(294114320,plain,
is_a_theorem(implies(implies(implies(D,B),implies(implies(A,B),C)),implies(B,C))),
inference(resolution,[status(thm)],[170410888,195653968]),
[] ).
cnf(356257568,plain,
is_a_theorem(implies(B,B)),
inference(resolution,[status(thm)],[170410888,294114320]),
[] ).
cnf(357359648,plain,
( ~ is_a_theorem(implies(implies(C,C),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,356257568]),
[] ).
cnf(356194960,plain,
( ~ is_a_theorem(implies(implies(D,B),implies(implies(A,B),C)))
| is_a_theorem(implies(B,C)) ),
inference(resolution,[status(thm)],[162579784,294114320]),
[] ).
cnf(356949912,plain,
is_a_theorem(implies(not(B),implies(B,C))),
inference(resolution,[status(thm)],[356194960,294256896]),
[] ).
cnf(359709032,plain,
( ~ is_a_theorem(implies(implies(not(C),implies(C,D)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,356949912]),
[] ).
cnf(175415648,plain,
is_a_theorem(implies(implies(implies(A,not(C)),B),implies(implies(D,B),implies(implies(C,D),B)))),
inference(resolution,[status(thm)],[170410888,162592816]),
[] ).
cnf(194825704,plain,
is_a_theorem(implies(implies(D,implies(B,not(C))),implies(implies(C,D),implies(B,not(C))))),
inference(resolution,[status(thm)],[170410888,175415648]),
[] ).
cnf(360262328,plain,
is_a_theorem(implies(implies(D,not(B)),implies(B,not(D)))),
inference(resolution,[status(thm)],[359709032,194825704]),
[] ).
cnf(370513528,plain,
is_a_theorem(implies(C,not(not(C)))),
inference(resolution,[status(thm)],[357359648,360262328]),
[] ).
cnf(376300120,plain,
( ~ is_a_theorem(implies(implies(D,not(not(D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,370513528]),
[] ).
cnf(170778528,plain,
( ~ is_a_theorem(implies(implies(A,implies(C,A)),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[170689800,162579784]),
[] ).
cnf(204141184,plain,
is_a_theorem(implies(implies(D,not(D)),implies(B,not(D)))),
inference(resolution,[status(thm)],[170778528,194825704]),
[] ).
cnf(204640640,plain,
( ~ is_a_theorem(implies(implies(implies(E,not(E)),implies(C,not(E))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,204141184]),
[] ).
cnf(205059840,plain,
is_a_theorem(implies(implies(D,implies(D,not(D))),implies(B,not(D)))),
inference(resolution,[status(thm)],[204640640,194825704]),
[] ).
cnf(206436592,plain,
( ~ is_a_theorem(implies(implies(implies(E,implies(E,not(E))),implies(C,not(E))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,205059840]),
[] ).
cnf(356798000,plain,
is_a_theorem(implies(implies(C,not(C)),not(C))),
inference(resolution,[status(thm)],[206436592,294114320]),
[] ).
cnf(360480752,plain,
( ~ is_a_theorem(implies(implies(implies(D,not(D)),not(D)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162579784,356798000]),
[] ).
cnf(361082248,plain,
is_a_theorem(implies(implies(D,not(C)),implies(implies(C,D),not(C)))),
inference(resolution,[status(thm)],[360480752,175415648]),
[] ).
cnf(621319272,plain,
is_a_theorem(implies(implies(not(C),C),not(not(C)))),
inference(resolution,[status(thm)],[376300120,361082248]),
[] ).
cnf(629328240,plain,
is_a_theorem(implies(C,implies(not(C),A))),
inference(resolution,[status(thm)],[312884168,621319272]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162600672,629328240]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 213 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_3,plain,(~is_a_theorem(implies(a,implies(not(a),b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),[]).
%
% cnf(162600672,plain,(~is_a_theorem(implies(a,implies(not(a),b)))),inference(rewrite,[status(thm)],[prove_cn_3]),[]).
%
% fof(condensed_detachment,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),[]).
%
% cnf(162579784,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_37,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),[]).
%
% cnf(162588800,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C)))),inference(rewrite,[status(thm)],[cn_37]),[]).
%
% cnf(170472256,plain,(~is_a_theorem(implies(implies(A,B),C))|is_a_theorem(implies(not(A),C))),inference(resolution,[status(thm)],[162579784,162588800]),[]).
%
% fof(cn_19,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),[]).
%
% cnf(162584640,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(B,C)))),inference(rewrite,[status(thm)],[cn_19]),[]).
%
% cnf(170391472,plain,(~is_a_theorem(implies(implies(A,B),C))|is_a_theorem(implies(B,C))),inference(resolution,[status(thm)],[162579784,162584640]),[]).
%
% cnf(170689800,plain,(is_a_theorem(implies(A,implies(C,A)))),inference(resolution,[status(thm)],[170391472,162584640]),[]).
%
% cnf(171949872,plain,(is_a_theorem(implies(not(A),implies(D,implies(A,B))))),inference(resolution,[status(thm)],[170472256,170689800]),[]).
%
% cnf(173200304,plain,(~is_a_theorem(implies(implies(not(A),implies(D,implies(A,B))),E))|is_a_theorem(E)),inference(resolution,[status(thm)],[171949872,162579784]),[]).
%
% cnf(170410888,plain,(~is_a_theorem(implies(implies(implies(implies(B,C),D),implies(C,D)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,162584640]),[]).
%
% cnf(170491576,plain,(~is_a_theorem(implies(implies(implies(implies(B,C),D),implies(not(B),D)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,162588800]),[]).
%
% fof(cn_60,plain,(is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C)))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL072-1.tptp',unknown),[]).
%
% cnf(162592816,plain,(is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C)))))),inference(rewrite,[status(thm)],[cn_60]),[]).
%
% cnf(182289520,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(implies(D,C),implies(implies(A,D),C))))),inference(resolution,[status(thm)],[170491576,162592816]),[]).
%
% cnf(195653968,plain,(is_a_theorem(implies(implies(D,implies(B,C)),implies(implies(implies(A,B),D),implies(B,C))))),inference(resolution,[status(thm)],[170410888,182289520]),[]).
%
% cnf(294256896,plain,(is_a_theorem(implies(implies(implies(E,D),not(A)),implies(D,implies(A,B))))),inference(resolution,[status(thm)],[173200304,195653968]),[]).
%
% cnf(312884168,plain,(~is_a_theorem(implies(implies(E,D),not(A)))|is_a_theorem(implies(D,implies(A,B)))),inference(resolution,[status(thm)],[162579784,294256896]),[]).
%
% cnf(294114320,plain,(is_a_theorem(implies(implies(implies(D,B),implies(implies(A,B),C)),implies(B,C)))),inference(resolution,[status(thm)],[170410888,195653968]),[]).
%
% cnf(356257568,plain,(is_a_theorem(implies(B,B))),inference(resolution,[status(thm)],[170410888,294114320]),[]).
%
% cnf(357359648,plain,(~is_a_theorem(implies(implies(C,C),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,356257568]),[]).
%
% cnf(356194960,plain,(~is_a_theorem(implies(implies(D,B),implies(implies(A,B),C)))|is_a_theorem(implies(B,C))),inference(resolution,[status(thm)],[162579784,294114320]),[]).
%
% cnf(356949912,plain,(is_a_theorem(implies(not(B),implies(B,C)))),inference(resolution,[status(thm)],[356194960,294256896]),[]).
%
% cnf(359709032,plain,(~is_a_theorem(implies(implies(not(C),implies(C,D)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,356949912]),[]).
%
% cnf(175415648,plain,(is_a_theorem(implies(implies(implies(A,not(C)),B),implies(implies(D,B),implies(implies(C,D),B))))),inference(resolution,[status(thm)],[170410888,162592816]),[]).
%
% cnf(194825704,plain,(is_a_theorem(implies(implies(D,implies(B,not(C))),implies(implies(C,D),implies(B,not(C)))))),inference(resolution,[status(thm)],[170410888,175415648]),[]).
%
% cnf(360262328,plain,(is_a_theorem(implies(implies(D,not(B)),implies(B,not(D))))),inference(resolution,[status(thm)],[359709032,194825704]),[]).
%
% cnf(370513528,plain,(is_a_theorem(implies(C,not(not(C))))),inference(resolution,[status(thm)],[357359648,360262328]),[]).
%
% cnf(376300120,plain,(~is_a_theorem(implies(implies(D,not(not(D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,370513528]),[]).
%
% cnf(170778528,plain,(~is_a_theorem(implies(implies(A,implies(C,A)),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[170689800,162579784]),[]).
%
% cnf(204141184,plain,(is_a_theorem(implies(implies(D,not(D)),implies(B,not(D))))),inference(resolution,[status(thm)],[170778528,194825704]),[]).
%
% cnf(204640640,plain,(~is_a_theorem(implies(implies(implies(E,not(E)),implies(C,not(E))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,204141184]),[]).
%
% cnf(205059840,plain,(is_a_theorem(implies(implies(D,implies(D,not(D))),implies(B,not(D))))),inference(resolution,[status(thm)],[204640640,194825704]),[]).
%
% cnf(206436592,plain,(~is_a_theorem(implies(implies(implies(E,implies(E,not(E))),implies(C,not(E))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,205059840]),[]).
%
% cnf(356798000,plain,(is_a_theorem(implies(implies(C,not(C)),not(C)))),inference(resolution,[status(thm)],[206436592,294114320]),[]).
%
% cnf(360480752,plain,(~is_a_theorem(implies(implies(implies(D,not(D)),not(D)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162579784,356798000]),[]).
%
% cnf(361082248,plain,(is_a_theorem(implies(implies(D,not(C)),implies(implies(C,D),not(C))))),inference(resolution,[status(thm)],[360480752,175415648]),[]).
%
% cnf(621319272,plain,(is_a_theorem(implies(implies(not(C),C),not(not(C))))),inference(resolution,[status(thm)],[376300120,361082248]),[]).
%
% cnf(629328240,plain,(is_a_theorem(implies(C,implies(not(C),A)))),inference(resolution,[status(thm)],[312884168,621319272]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162600672,629328240]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------