TSTP Solution File: LCL069-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL069-1 : TPTP v3.4.2. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 13:41:06 EDT 2009
% Result : Unsatisfiable 269.4s
% Output : Refutation 269.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 26 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 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 : 109 ( 32 sgn 11 !; 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/LCL069-1.tptp',unknown),
[] ).
cnf(152433240,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/LCL069-1.tptp',unknown),
[] ).
cnf(152412488,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/LCL069-1.tptp',unknown),
[] ).
cnf(152421504,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(rewrite,[status(thm)],[cn_37]),
[] ).
cnf(160431288,plain,
( ~ is_a_theorem(implies(implies(A,B),C))
| is_a_theorem(implies(not(A),C)) ),
inference(resolution,[status(thm)],[152412488,152421504]),
[] ).
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/LCL069-1.tptp',unknown),
[] ).
cnf(152417344,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(rewrite,[status(thm)],[cn_19]),
[] ).
cnf(160224696,plain,
( ~ is_a_theorem(implies(implies(A,B),C))
| is_a_theorem(implies(B,C)) ),
inference(resolution,[status(thm)],[152412488,152417344]),
[] ).
cnf(160560240,plain,
is_a_theorem(implies(A,implies(C,A))),
inference(resolution,[status(thm)],[160224696,152417344]),
[] ).
cnf(161883256,plain,
is_a_theorem(implies(not(A),implies(D,implies(A,B)))),
inference(resolution,[status(thm)],[160431288,160560240]),
[] ).
cnf(162860752,plain,
( ~ is_a_theorem(implies(implies(not(A),implies(D,implies(A,B))),E))
| is_a_theorem(E) ),
inference(resolution,[status(thm)],[161883256,152412488]),
[] ).
fof(cn_59,plain,
! [A,B,C] : is_a_theorem(implies(implies(not(A),B),implies(implies(C,B),implies(implies(A,C),B)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL069-1.tptp',unknown),
[] ).
cnf(152425416,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(C,B),implies(implies(A,C),B)))),
inference(rewrite,[status(thm)],[cn_59]),
[] ).
cnf(160480592,plain,
( ~ is_a_theorem(implies(not(A),B))
| is_a_theorem(implies(implies(C,B),implies(implies(A,C),B))) ),
inference(resolution,[status(thm)],[152412488,152425416]),
[] ).
cnf(161962768,plain,
is_a_theorem(implies(not(implies(B,C)),implies(C,A))),
inference(resolution,[status(thm)],[160431288,152417344]),
[] ).
cnf(170765552,plain,
is_a_theorem(implies(implies(A,implies(D,B)),implies(implies(implies(C,D),A),implies(D,B)))),
inference(resolution,[status(thm)],[160480592,161962768]),
[] ).
cnf(241985200,plain,
is_a_theorem(implies(implies(implies(E,D),not(A)),implies(D,implies(A,B)))),
inference(resolution,[status(thm)],[162860752,170765552]),
[] ).
cnf(682448464,plain,
( ~ is_a_theorem(implies(implies(E,D),not(A)))
| is_a_theorem(implies(D,implies(A,B))) ),
inference(resolution,[status(thm)],[152412488,241985200]),
[] ).
cnf(160244112,plain,
( ~ is_a_theorem(implies(implies(implies(implies(B,C),D),implies(C,D)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[152412488,152417344]),
[] ).
cnf(160631816,plain,
( ~ is_a_theorem(implies(implies(A,implies(C,A)),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[160560240,152412488]),
[] ).
cnf(162696472,plain,
is_a_theorem(implies(implies(D,implies(B,not(C))),implies(implies(C,D),implies(B,not(C))))),
inference(resolution,[status(thm)],[160631816,152425416]),
[] ).
cnf(175333096,plain,
is_a_theorem(implies(implies(D,implies(implies(A,B),not(D))),implies(B,not(D)))),
inference(resolution,[status(thm)],[160244112,162696472]),
[] ).
cnf(178814712,plain,
( ~ is_a_theorem(implies(D,implies(implies(A,B),not(D))))
| is_a_theorem(implies(B,not(D))) ),
inference(resolution,[status(thm)],[152412488,175333096]),
[] ).
cnf(163416112,plain,
( ~ is_a_theorem(implies(implies(not(implies(B,C)),implies(C,A)),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[161962768,152412488]),
[] ).
cnf(175414872,plain,
is_a_theorem(implies(implies(D,not(implies(A,B))),implies(B,not(D)))),
inference(resolution,[status(thm)],[163416112,162696472]),
[] ).
cnf(176388408,plain,
( ~ is_a_theorem(implies(D,not(implies(A,B))))
| is_a_theorem(implies(B,not(D))) ),
inference(resolution,[status(thm)],[152412488,175414872]),
[] ).
cnf(175305440,plain,
is_a_theorem(implies(implies(D,not(D)),implies(B,not(D)))),
inference(resolution,[status(thm)],[160631816,162696472]),
[] ).
cnf(175663864,plain,
( ~ is_a_theorem(implies(implies(implies(E,not(E)),implies(C,not(E))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[152412488,175305440]),
[] ).
cnf(175196952,plain,
( ~ is_a_theorem(implies(D,implies(B,not(C))))
| is_a_theorem(implies(implies(C,D),implies(B,not(C)))) ),
inference(resolution,[status(thm)],[152412488,162696472]),
[] ).
cnf(176617464,plain,
is_a_theorem(implies(implies(C,implies(C,not(implies(D,B)))),implies(B,not(C)))),
inference(resolution,[status(thm)],[175196952,175414872]),
[] ).
cnf(189913944,plain,
is_a_theorem(implies(D,not(implies(implies(E,D),not(implies(E,D)))))),
inference(resolution,[status(thm)],[175663864,176617464]),
[] ).
cnf(192698224,plain,
is_a_theorem(implies(not(implies(F,B)),not(B))),
inference(resolution,[status(thm)],[176388408,189913944]),
[] ).
cnf(196091240,plain,
is_a_theorem(implies(implies(A,not(C)),implies(implies(implies(G,C),A),not(C)))),
inference(resolution,[status(thm)],[160480592,192698224]),
[] ).
cnf(262999888,plain,
is_a_theorem(implies(not(A),implies(implies(implies(G,C),A),not(C)))),
inference(resolution,[status(thm)],[160431288,196091240]),
[] ).
cnf(264286088,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolution,[status(thm)],[178814712,262999888]),
[] ).
cnf(265087696,plain,
( ~ is_a_theorem(implies(implies(B,not(not(B))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[152412488,264286088]),
[] ).
cnf(266669112,plain,
is_a_theorem(implies(implies(implies(F,not(A)),A),not(not(A)))),
inference(resolution,[status(thm)],[265087696,196091240]),
[] ).
cnf(683774776,plain,
is_a_theorem(implies(C,implies(not(C),A))),
inference(resolution,[status(thm)],[682448464,266669112]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[152433240,683774776]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 268 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/LCL069-1.tptp',unknown),[]).
%
% cnf(152433240,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/LCL069-1.tptp',unknown),[]).
%
% cnf(152412488,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/LCL069-1.tptp',unknown),[]).
%
% cnf(152421504,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C)))),inference(rewrite,[status(thm)],[cn_37]),[]).
%
% cnf(160431288,plain,(~is_a_theorem(implies(implies(A,B),C))|is_a_theorem(implies(not(A),C))),inference(resolution,[status(thm)],[152412488,152421504]),[]).
%
% 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/LCL069-1.tptp',unknown),[]).
%
% cnf(152417344,plain,(is_a_theorem(implies(implies(implies(A,B),C),implies(B,C)))),inference(rewrite,[status(thm)],[cn_19]),[]).
%
% cnf(160224696,plain,(~is_a_theorem(implies(implies(A,B),C))|is_a_theorem(implies(B,C))),inference(resolution,[status(thm)],[152412488,152417344]),[]).
%
% cnf(160560240,plain,(is_a_theorem(implies(A,implies(C,A)))),inference(resolution,[status(thm)],[160224696,152417344]),[]).
%
% cnf(161883256,plain,(is_a_theorem(implies(not(A),implies(D,implies(A,B))))),inference(resolution,[status(thm)],[160431288,160560240]),[]).
%
% cnf(162860752,plain,(~is_a_theorem(implies(implies(not(A),implies(D,implies(A,B))),E))|is_a_theorem(E)),inference(resolution,[status(thm)],[161883256,152412488]),[]).
%
% fof(cn_59,plain,(is_a_theorem(implies(implies(not(A),B),implies(implies(C,B),implies(implies(A,C),B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL069-1.tptp',unknown),[]).
%
% cnf(152425416,plain,(is_a_theorem(implies(implies(not(A),B),implies(implies(C,B),implies(implies(A,C),B))))),inference(rewrite,[status(thm)],[cn_59]),[]).
%
% cnf(160480592,plain,(~is_a_theorem(implies(not(A),B))|is_a_theorem(implies(implies(C,B),implies(implies(A,C),B)))),inference(resolution,[status(thm)],[152412488,152425416]),[]).
%
% cnf(161962768,plain,(is_a_theorem(implies(not(implies(B,C)),implies(C,A)))),inference(resolution,[status(thm)],[160431288,152417344]),[]).
%
% cnf(170765552,plain,(is_a_theorem(implies(implies(A,implies(D,B)),implies(implies(implies(C,D),A),implies(D,B))))),inference(resolution,[status(thm)],[160480592,161962768]),[]).
%
% cnf(241985200,plain,(is_a_theorem(implies(implies(implies(E,D),not(A)),implies(D,implies(A,B))))),inference(resolution,[status(thm)],[162860752,170765552]),[]).
%
% cnf(682448464,plain,(~is_a_theorem(implies(implies(E,D),not(A)))|is_a_theorem(implies(D,implies(A,B)))),inference(resolution,[status(thm)],[152412488,241985200]),[]).
%
% cnf(160244112,plain,(~is_a_theorem(implies(implies(implies(implies(B,C),D),implies(C,D)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[152412488,152417344]),[]).
%
% cnf(160631816,plain,(~is_a_theorem(implies(implies(A,implies(C,A)),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[160560240,152412488]),[]).
%
% cnf(162696472,plain,(is_a_theorem(implies(implies(D,implies(B,not(C))),implies(implies(C,D),implies(B,not(C)))))),inference(resolution,[status(thm)],[160631816,152425416]),[]).
%
% cnf(175333096,plain,(is_a_theorem(implies(implies(D,implies(implies(A,B),not(D))),implies(B,not(D))))),inference(resolution,[status(thm)],[160244112,162696472]),[]).
%
% cnf(178814712,plain,(~is_a_theorem(implies(D,implies(implies(A,B),not(D))))|is_a_theorem(implies(B,not(D)))),inference(resolution,[status(thm)],[152412488,175333096]),[]).
%
% cnf(163416112,plain,(~is_a_theorem(implies(implies(not(implies(B,C)),implies(C,A)),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[161962768,152412488]),[]).
%
% cnf(175414872,plain,(is_a_theorem(implies(implies(D,not(implies(A,B))),implies(B,not(D))))),inference(resolution,[status(thm)],[163416112,162696472]),[]).
%
% cnf(176388408,plain,(~is_a_theorem(implies(D,not(implies(A,B))))|is_a_theorem(implies(B,not(D)))),inference(resolution,[status(thm)],[152412488,175414872]),[]).
%
% cnf(175305440,plain,(is_a_theorem(implies(implies(D,not(D)),implies(B,not(D))))),inference(resolution,[status(thm)],[160631816,162696472]),[]).
%
% cnf(175663864,plain,(~is_a_theorem(implies(implies(implies(E,not(E)),implies(C,not(E))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[152412488,175305440]),[]).
%
% cnf(175196952,plain,(~is_a_theorem(implies(D,implies(B,not(C))))|is_a_theorem(implies(implies(C,D),implies(B,not(C))))),inference(resolution,[status(thm)],[152412488,162696472]),[]).
%
% cnf(176617464,plain,(is_a_theorem(implies(implies(C,implies(C,not(implies(D,B)))),implies(B,not(C))))),inference(resolution,[status(thm)],[175196952,175414872]),[]).
%
% cnf(189913944,plain,(is_a_theorem(implies(D,not(implies(implies(E,D),not(implies(E,D))))))),inference(resolution,[status(thm)],[175663864,176617464]),[]).
%
% cnf(192698224,plain,(is_a_theorem(implies(not(implies(F,B)),not(B)))),inference(resolution,[status(thm)],[176388408,189913944]),[]).
%
% cnf(196091240,plain,(is_a_theorem(implies(implies(A,not(C)),implies(implies(implies(G,C),A),not(C))))),inference(resolution,[status(thm)],[160480592,192698224]),[]).
%
% cnf(262999888,plain,(is_a_theorem(implies(not(A),implies(implies(implies(G,C),A),not(C))))),inference(resolution,[status(thm)],[160431288,196091240]),[]).
%
% cnf(264286088,plain,(is_a_theorem(implies(A,not(not(A))))),inference(resolution,[status(thm)],[178814712,262999888]),[]).
%
% cnf(265087696,plain,(~is_a_theorem(implies(implies(B,not(not(B))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[152412488,264286088]),[]).
%
% cnf(266669112,plain,(is_a_theorem(implies(implies(implies(F,not(A)),A),not(not(A))))),inference(resolution,[status(thm)],[265087696,196091240]),[]).
%
% cnf(683774776,plain,(is_a_theorem(implies(C,implies(not(C),A)))),inference(resolution,[status(thm)],[682448464,266669112]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[152433240,683774776]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------