TSTP Solution File: LCL066-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL066-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 13:41:03 EDT 2009
% Result : Unsatisfiable 2.5s
% Output : Refutation 2.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 27 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 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 : 91 ( 20 sgn 9 !; 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/LCL066-1.tptp',unknown),
[] ).
cnf(168663672,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/LCL066-1.tptp',unknown),
[] ).
cnf(168643024,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_18,plain,
! [A,B] : is_a_theorem(implies(A,implies(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL066-1.tptp',unknown),
[] ).
cnf(168647808,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(rewrite,[status(thm)],[cn_18]),
[] ).
cnf(176426776,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[168643024,168647808]),
[] ).
cnf(176670232,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolution,[status(thm)],[176426776,168647808]),
[] ).
cnf(176889792,plain,
( ~ is_a_theorem(implies(implies(A,implies(B,implies(C,B))),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[176670232,168643024]),
[] ).
fof(cn_35,plain,
! [A,B,C] : is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL066-1.tptp',unknown),
[] ).
cnf(168651952,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_35]),
[] ).
cnf(187850120,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[176889792,168651952]),
[] ).
cnf(188391688,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(A,implies(C,B))) ),
inference(resolution,[status(thm)],[168643024,187850120]),
[] ).
fof(cn_49,plain,
! [A,B] : is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL066-1.tptp',unknown),
[] ).
cnf(168655856,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(rewrite,[status(thm)],[cn_49]),
[] ).
cnf(176589816,plain,
( ~ is_a_theorem(implies(not(A),not(B)))
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[168643024,168655856]),
[] ).
cnf(176638040,plain,
( ~ is_a_theorem(implies(implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[168643024,168651952]),
[] ).
cnf(176618640,plain,
( ~ is_a_theorem(implies(A,implies(B,C)))
| is_a_theorem(implies(implies(A,B),implies(A,C))) ),
inference(resolution,[status(thm)],[168643024,168651952]),
[] ).
cnf(176446168,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[168643024,168647808]),
[] ).
cnf(177362640,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolution,[status(thm)],[176446168,168651952]),
[] ).
cnf(177466456,plain,
is_a_theorem(implies(A,A)),
inference(resolution,[status(thm)],[177362640,176446168]),
[] ).
cnf(177484872,plain,
is_a_theorem(implies(B,implies(A,A))),
inference(resolution,[status(thm)],[177466456,176426776]),
[] ).
cnf(177572416,plain,
( ~ is_a_theorem(implies(implies(B,implies(A,A)),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[177484872,168643024]),
[] ).
cnf(177505648,plain,
( ~ is_a_theorem(implies(implies(A,A),B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[177466456,168643024]),
[] ).
cnf(179777824,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolution,[status(thm)],[177505648,168651952]),
[] ).
cnf(188136400,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolution,[status(thm)],[177572416,179777824]),
[] ).
cnf(188332176,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolution,[status(thm)],[176426776,188136400]),
[] ).
cnf(189347000,plain,
is_a_theorem(implies(implies(A,implies(implies(C,C),B)),implies(A,B))),
inference(resolution,[status(thm)],[176618640,188332176]),
[] ).
cnf(193054088,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolution,[status(thm)],[176638040,189347000]),
[] ).
cnf(193595320,plain,
( ~ is_a_theorem(implies(A,implies(A,B)))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[168643024,193054088]),
[] ).
cnf(176732728,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolution,[status(thm)],[176426776,168655856]),
[] ).
cnf(187963536,plain,
is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[176618640,176732728]),
[] ).
cnf(200834456,plain,
is_a_theorem(implies(not(B),implies(B,A))),
inference(resolution,[status(thm)],[176446168,187963536]),
[] ).
cnf(201469440,plain,
( ~ is_a_theorem(implies(implies(not(C),implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[168643024,200834456]),
[] ).
cnf(201772616,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolution,[status(thm)],[201469440,187963536]),
[] ).
cnf(202361072,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolution,[status(thm)],[193595320,201772616]),
[] ).
cnf(202581400,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolution,[status(thm)],[176589816,202361072]),
[] ).
cnf(204008048,plain,
is_a_theorem(implies(A,implies(B,not(not(A))))),
inference(resolution,[status(thm)],[188391688,202581400]),
[] ).
cnf(210477680,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,not(not(B)))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[168643024,204008048]),
[] ).
cnf(212161848,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(resolution,[status(thm)],[210477680,187963536]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[168663672,212161848]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 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/LCL066-1.tptp',unknown),[]).
%
% cnf(168663672,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/LCL066-1.tptp',unknown),[]).
%
% cnf(168643024,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_18,plain,(is_a_theorem(implies(A,implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL066-1.tptp',unknown),[]).
%
% cnf(168647808,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[cn_18]),[]).
%
% cnf(176426776,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[168643024,168647808]),[]).
%
% cnf(176670232,plain,(is_a_theorem(implies(A,implies(B,implies(C,B))))),inference(resolution,[status(thm)],[176426776,168647808]),[]).
%
% cnf(176889792,plain,(~is_a_theorem(implies(implies(A,implies(B,implies(C,B))),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[176670232,168643024]),[]).
%
% fof(cn_35,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL066-1.tptp',unknown),[]).
%
% cnf(168651952,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),inference(rewrite,[status(thm)],[cn_35]),[]).
%
% cnf(187850120,plain,(is_a_theorem(implies(implies(A,B),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[176889792,168651952]),[]).
%
% cnf(188391688,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(A,implies(C,B)))),inference(resolution,[status(thm)],[168643024,187850120]),[]).
%
% fof(cn_49,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL066-1.tptp',unknown),[]).
%
% cnf(168655856,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),inference(rewrite,[status(thm)],[cn_49]),[]).
%
% cnf(176589816,plain,(~is_a_theorem(implies(not(A),not(B)))|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[168643024,168655856]),[]).
%
% cnf(176638040,plain,(~is_a_theorem(implies(implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[168643024,168651952]),[]).
%
% cnf(176618640,plain,(~is_a_theorem(implies(A,implies(B,C)))|is_a_theorem(implies(implies(A,B),implies(A,C)))),inference(resolution,[status(thm)],[168643024,168651952]),[]).
%
% cnf(176446168,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[168643024,168647808]),[]).
%
% cnf(177362640,plain,(is_a_theorem(implies(implies(A,B),implies(A,A)))),inference(resolution,[status(thm)],[176446168,168651952]),[]).
%
% cnf(177466456,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[177362640,176446168]),[]).
%
% cnf(177484872,plain,(is_a_theorem(implies(B,implies(A,A)))),inference(resolution,[status(thm)],[177466456,176426776]),[]).
%
% cnf(177572416,plain,(~is_a_theorem(implies(implies(B,implies(A,A)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[177484872,168643024]),[]).
%
% cnf(177505648,plain,(~is_a_theorem(implies(implies(A,A),B))|is_a_theorem(B)),inference(resolution,[status(thm)],[177466456,168643024]),[]).
%
% cnf(179777824,plain,(is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B)))),inference(resolution,[status(thm)],[177505648,168651952]),[]).
%
% cnf(188136400,plain,(is_a_theorem(implies(implies(implies(A,A),B),B))),inference(resolution,[status(thm)],[177572416,179777824]),[]).
%
% cnf(188332176,plain,(is_a_theorem(implies(A,implies(implies(implies(B,B),C),C)))),inference(resolution,[status(thm)],[176426776,188136400]),[]).
%
% cnf(189347000,plain,(is_a_theorem(implies(implies(A,implies(implies(C,C),B)),implies(A,B)))),inference(resolution,[status(thm)],[176618640,188332176]),[]).
%
% cnf(193054088,plain,(is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))),inference(resolution,[status(thm)],[176638040,189347000]),[]).
%
% cnf(193595320,plain,(~is_a_theorem(implies(A,implies(A,B)))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[168643024,193054088]),[]).
%
% cnf(176732728,plain,(is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B))))),inference(resolution,[status(thm)],[176426776,168655856]),[]).
%
% cnf(187963536,plain,(is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[176618640,176732728]),[]).
%
% cnf(200834456,plain,(is_a_theorem(implies(not(B),implies(B,A)))),inference(resolution,[status(thm)],[176446168,187963536]),[]).
%
% cnf(201469440,plain,(~is_a_theorem(implies(implies(not(C),implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[168643024,200834456]),[]).
%
% cnf(201772616,plain,(is_a_theorem(implies(not(not(A)),implies(B,A)))),inference(resolution,[status(thm)],[201469440,187963536]),[]).
%
% cnf(202361072,plain,(is_a_theorem(implies(not(not(A)),A))),inference(resolution,[status(thm)],[193595320,201772616]),[]).
%
% cnf(202581400,plain,(is_a_theorem(implies(A,not(not(A))))),inference(resolution,[status(thm)],[176589816,202361072]),[]).
%
% cnf(204008048,plain,(is_a_theorem(implies(A,implies(B,not(not(A)))))),inference(resolution,[status(thm)],[188391688,202581400]),[]).
%
% cnf(210477680,plain,(~is_a_theorem(implies(implies(B,implies(C,not(not(B)))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[168643024,204008048]),[]).
%
% cnf(212161848,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(resolution,[status(thm)],[210477680,187963536]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[168663672,212161848]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------