TSTP Solution File: LCL044-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL044-1 : 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 13:40:33 EDT 2009
% Result : Unsatisfiable 7.0s
% Output : Refutation 7.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_40,plain,
~ is_a_theorem(implies(a,not(not(a)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),
[] ).
cnf(147582008,plain,
~ is_a_theorem(implies(a,not(not(a)))),
inference(rewrite,[status(thm)],[prove_cn_40]),
[] ).
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/LCL044-1.tptp',unknown),
[] ).
cnf(147553856,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/LCL044-1.tptp',unknown),
[] ).
cnf(147562616,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(rewrite,[status(thm)],[cn_18]),
[] ).
cnf(155359648,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[147553856,147562616]),
[] ).
fof(cn_54,plain,
! [A,B] : is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),
[] ).
cnf(147578384,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B))),
inference(rewrite,[status(thm)],[cn_54]),
[] ).
cnf(155550760,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(implies(not(A),B),B)) ),
inference(resolution,[status(thm)],[147553856,147578384]),
[] ).
fof(cn_3,plain,
! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),
[] ).
cnf(147558608,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(rewrite,[status(thm)],[cn_3]),
[] ).
cnf(155495488,plain,
( ~ is_a_theorem(implies(implies(B,implies(not(B),C)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[147553856,147558608]),
[] ).
fof(cn_21,plain,
! [A,B,C] : is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),
[] ).
cnf(147566504,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(rewrite,[status(thm)],[cn_21]),
[] ).
cnf(160029912,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolution,[status(thm)],[155495488,147566504]),
[] ).
cnf(161645672,plain,
is_a_theorem(implies(implies(not(not(A)),implies(A,B)),implies(A,B))),
inference(resolution,[status(thm)],[155550760,160029912]),
[] ).
cnf(222410784,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolution,[status(thm)],[155359648,161645672]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[147582008,222410784]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_40,plain,(~is_a_theorem(implies(a,not(not(a))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),[]).
%
% cnf(147582008,plain,(~is_a_theorem(implies(a,not(not(a))))),inference(rewrite,[status(thm)],[prove_cn_40]),[]).
%
% 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/LCL044-1.tptp',unknown),[]).
%
% cnf(147553856,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/LCL044-1.tptp',unknown),[]).
%
% cnf(147562616,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[cn_18]),[]).
%
% cnf(155359648,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[147553856,147562616]),[]).
%
% fof(cn_54,plain,(is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),[]).
%
% cnf(147578384,plain,(is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B)))),inference(rewrite,[status(thm)],[cn_54]),[]).
%
% cnf(155550760,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(not(A),B),B))),inference(resolution,[status(thm)],[147553856,147578384]),[]).
%
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),[]).
%
% cnf(147558608,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
%
% cnf(155495488,plain,(~is_a_theorem(implies(implies(B,implies(not(B),C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[147553856,147558608]),[]).
%
% fof(cn_21,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL044-1.tptp',unknown),[]).
%
% cnf(147566504,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C))))),inference(rewrite,[status(thm)],[cn_21]),[]).
%
% cnf(160029912,plain,(is_a_theorem(implies(not(A),implies(A,B)))),inference(resolution,[status(thm)],[155495488,147566504]),[]).
%
% cnf(161645672,plain,(is_a_theorem(implies(implies(not(not(A)),implies(A,B)),implies(A,B)))),inference(resolution,[status(thm)],[155550760,160029912]),[]).
%
% cnf(222410784,plain,(is_a_theorem(implies(A,not(not(A))))),inference(resolution,[status(thm)],[155359648,161645672]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[147582008,222410784]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------