TSTP Solution File: LCL056-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL056-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 13:40:51 EDT 2009
% Result : Unsatisfiable 449.4s
% Output : Refutation 449.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 37 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 136 ( 39 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_39,plain,
~ is_a_theorem(implies(not(not(a)),a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),
[] ).
cnf(150558920,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(rewrite,[status(thm)],[prove_cn_39]),
[] ).
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/LCL056-1.tptp',unknown),
[] ).
cnf(150538544,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_1,plain,
! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),
[] ).
cnf(150543368,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_1]),
[] ).
cnf(158547560,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(implies(B,C),implies(A,C))) ),
inference(resolution,[status(thm)],[150538544,150543368]),
[] ).
fof(cn_2,plain,
! [A] : is_a_theorem(implies(implies(not(A),A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),
[] ).
cnf(150547328,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(rewrite,[status(thm)],[cn_2]),
[] ).
cnf(158325272,plain,
( ~ is_a_theorem(implies(not(A),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[150538544,150547328]),
[] ).
fof(cn_3,plain,
! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),
[] ).
cnf(150551240,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(rewrite,[status(thm)],[cn_3]),
[] ).
cnf(158374344,plain,
( ~ is_a_theorem(implies(implies(B,implies(not(B),C)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[150538544,150551240]),
[] ).
cnf(159585296,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolution,[status(thm)],[158374344,150543368]),
[] ).
cnf(164552600,plain,
( ~ is_a_theorem(implies(implies(not(A),B),C))
| is_a_theorem(implies(A,C)) ),
inference(resolution,[status(thm)],[159585296,150538544]),
[] ).
cnf(158344760,plain,
( ~ is_a_theorem(implies(implies(implies(not(B),B),B),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[150538544,150547328]),
[] ).
cnf(164602592,plain,
is_a_theorem(implies(A,A)),
inference(resolution,[status(thm)],[159585296,158344760]),
[] ).
cnf(158355024,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(not(A),B)) ),
inference(resolution,[status(thm)],[150538544,150551240]),
[] ).
cnf(164939952,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolution,[status(thm)],[164602592,158355024]),
[] ).
cnf(165445272,plain,
is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C))),
inference(resolution,[status(thm)],[164939952,158547560]),
[] ).
cnf(168747160,plain,
is_a_theorem(implies(A,implies(not(implies(C,C)),B))),
inference(resolution,[status(thm)],[164552600,165445272]),
[] ).
cnf(168853320,plain,
is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B))),
inference(resolution,[status(thm)],[158547560,168747160]),
[] ).
cnf(173381336,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolution,[status(thm)],[158344760,168853320]),
[] ).
cnf(173897936,plain,
is_a_theorem(implies(implies(implies(C,C),B),implies(A,B))),
inference(resolution,[status(thm)],[158547560,173381336]),
[] ).
cnf(174292608,plain,
( ~ is_a_theorem(implies(implies(implies(implies(D,D),C),implies(B,C)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[150538544,173897936]),
[] ).
cnf(161030080,plain,
is_a_theorem(implies(implies(implies(implies(C,D),implies(B,D)),A),implies(implies(B,C),A))),
inference(resolution,[status(thm)],[158547560,150543368]),
[] ).
cnf(181919168,plain,
is_a_theorem(implies(implies(C,B),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[174292608,161030080]),
[] ).
cnf(182385976,plain,
is_a_theorem(implies(A,implies(C,implies(not(A),B)))),
inference(resolution,[status(thm)],[164552600,181919168]),
[] ).
cnf(183459904,plain,
is_a_theorem(implies(implies(implies(D,implies(not(A),C)),B),implies(A,B))),
inference(resolution,[status(thm)],[158547560,182385976]),
[] ).
cnf(217242280,plain,
( ~ is_a_theorem(implies(implies(D,implies(not(A),C)),B))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[150538544,183459904]),
[] ).
cnf(181521208,plain,
( ~ is_a_theorem(implies(implies(implies(C,D),implies(B,D)),A))
| is_a_theorem(implies(implies(B,C),A)) ),
inference(resolution,[status(thm)],[150538544,161030080]),
[] ).
cnf(174273560,plain,
( ~ is_a_theorem(implies(implies(C,C),B))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[150538544,173897936]),
[] ).
cnf(159227128,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolution,[status(thm)],[158344760,150543368]),
[] ).
cnf(174470808,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolution,[status(thm)],[174273560,159227128]),
[] ).
cnf(174950352,plain,
is_a_theorem(implies(implies(implies(implies(not(C),C),C),B),implies(A,B))),
inference(resolution,[status(thm)],[158547560,174470808]),
[] ).
cnf(194505152,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolution,[status(thm)],[181521208,174950352]),
[] ).
cnf(255251040,plain,
is_a_theorem(implies(A,implies(C,implies(B,A)))),
inference(resolution,[status(thm)],[217242280,194505152]),
[] ).
cnf(255894104,plain,
( ~ is_a_theorem(implies(implies(B,implies(D,implies(C,B))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[150538544,255251040]),
[] ).
cnf(257406152,plain,
is_a_theorem(implies(C,implies(A,implies(B,A)))),
inference(resolution,[status(thm)],[255894104,194505152]),
[] ).
cnf(257533392,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolution,[status(thm)],[158325272,257406152]),
[] ).
cnf(258309192,plain,
is_a_theorem(implies(implies(implies(C,A),B),implies(A,B))),
inference(resolution,[status(thm)],[158547560,257533392]),
[] ).
cnf(267462072,plain,
( ~ is_a_theorem(implies(implies(C,A),B))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[150538544,258309192]),
[] ).
cnf(161040200,plain,
( ~ is_a_theorem(implies(A,implies(not(B),B)))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[158547560,158344760]),
[] ).
cnf(254846560,plain,
( ~ is_a_theorem(implies(A,implies(not(B),B)))
| is_a_theorem(implies(C,implies(A,B))) ),
inference(resolution,[status(thm)],[150538544,194505152]),
[] ).
cnf(255408384,plain,
is_a_theorem(implies(B,implies(implies(implies(implies(not(C),C),C),A),A))),
inference(resolution,[status(thm)],[254846560,174950352]),
[] ).
cnf(666955280,plain,
is_a_theorem(implies(implies(implies(implies(not(B),B),B),A),A)),
inference(resolution,[status(thm)],[158325272,255408384]),
[] ).
cnf(669678656,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))),
inference(resolution,[status(thm)],[181521208,666955280]),
[] ).
cnf(671005872,plain,
is_a_theorem(implies(implies(not(A),implies(not(A),A)),A)),
inference(resolution,[status(thm)],[161040200,669678656]),
[] ).
cnf(673011320,plain,
( ~ is_a_theorem(implies(implies(implies(not(B),implies(not(B),B)),B),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[150538544,671005872]),
[] ).
cnf(164571800,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[159585296,150538544]),
[] ).
cnf(181901672,plain,
is_a_theorem(implies(implies(C,not(A)),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[164571800,161030080]),
[] ).
cnf(184741024,plain,
is_a_theorem(implies(implies(implies(B,implies(D,C)),A),implies(implies(D,not(B)),A))),
inference(resolution,[status(thm)],[158547560,181901672]),
[] ).
cnf(674635616,plain,
is_a_theorem(implies(implies(not(A),not(not(A))),A)),
inference(resolution,[status(thm)],[673011320,184741024]),
[] ).
cnf(675224008,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolution,[status(thm)],[267462072,674635616]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[150558920,675224008]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 449 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_39,plain,(~is_a_theorem(implies(not(not(a)),a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),[]).
%
% cnf(150558920,plain,(~is_a_theorem(implies(not(not(a)),a))),inference(rewrite,[status(thm)],[prove_cn_39]),[]).
%
% 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/LCL056-1.tptp',unknown),[]).
%
% cnf(150538544,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_1,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),[]).
%
% cnf(150543368,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
%
% cnf(158547560,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[150538544,150543368]),[]).
%
% fof(cn_2,plain,(is_a_theorem(implies(implies(not(A),A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),[]).
%
% cnf(150547328,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn_2]),[]).
%
% cnf(158325272,plain,(~is_a_theorem(implies(not(A),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[150538544,150547328]),[]).
%
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL056-1.tptp',unknown),[]).
%
% cnf(150551240,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
%
% cnf(158374344,plain,(~is_a_theorem(implies(implies(B,implies(not(B),C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[150538544,150551240]),[]).
%
% cnf(159585296,plain,(is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C)))),inference(resolution,[status(thm)],[158374344,150543368]),[]).
%
% cnf(164552600,plain,(~is_a_theorem(implies(implies(not(A),B),C))|is_a_theorem(implies(A,C))),inference(resolution,[status(thm)],[159585296,150538544]),[]).
%
% cnf(158344760,plain,(~is_a_theorem(implies(implies(implies(not(B),B),B),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[150538544,150547328]),[]).
%
% cnf(164602592,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[159585296,158344760]),[]).
%
% cnf(158355024,plain,(~is_a_theorem(A)|is_a_theorem(implies(not(A),B))),inference(resolution,[status(thm)],[150538544,150551240]),[]).
%
% cnf(164939952,plain,(is_a_theorem(implies(not(implies(A,A)),B))),inference(resolution,[status(thm)],[164602592,158355024]),[]).
%
% cnf(165445272,plain,(is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C)))),inference(resolution,[status(thm)],[164939952,158547560]),[]).
%
% cnf(168747160,plain,(is_a_theorem(implies(A,implies(not(implies(C,C)),B)))),inference(resolution,[status(thm)],[164552600,165445272]),[]).
%
% cnf(168853320,plain,(is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B)))),inference(resolution,[status(thm)],[158547560,168747160]),[]).
%
% cnf(173381336,plain,(is_a_theorem(implies(A,implies(B,B)))),inference(resolution,[status(thm)],[158344760,168853320]),[]).
%
% cnf(173897936,plain,(is_a_theorem(implies(implies(implies(C,C),B),implies(A,B)))),inference(resolution,[status(thm)],[158547560,173381336]),[]).
%
% cnf(174292608,plain,(~is_a_theorem(implies(implies(implies(implies(D,D),C),implies(B,C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[150538544,173897936]),[]).
%
% cnf(161030080,plain,(is_a_theorem(implies(implies(implies(implies(C,D),implies(B,D)),A),implies(implies(B,C),A)))),inference(resolution,[status(thm)],[158547560,150543368]),[]).
%
% cnf(181919168,plain,(is_a_theorem(implies(implies(C,B),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[174292608,161030080]),[]).
%
% cnf(182385976,plain,(is_a_theorem(implies(A,implies(C,implies(not(A),B))))),inference(resolution,[status(thm)],[164552600,181919168]),[]).
%
% cnf(183459904,plain,(is_a_theorem(implies(implies(implies(D,implies(not(A),C)),B),implies(A,B)))),inference(resolution,[status(thm)],[158547560,182385976]),[]).
%
% cnf(217242280,plain,(~is_a_theorem(implies(implies(D,implies(not(A),C)),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[150538544,183459904]),[]).
%
% cnf(181521208,plain,(~is_a_theorem(implies(implies(implies(C,D),implies(B,D)),A))|is_a_theorem(implies(implies(B,C),A))),inference(resolution,[status(thm)],[150538544,161030080]),[]).
%
% cnf(174273560,plain,(~is_a_theorem(implies(implies(C,C),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[150538544,173897936]),[]).
%
% cnf(159227128,plain,(is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B)))),inference(resolution,[status(thm)],[158344760,150543368]),[]).
%
% cnf(174470808,plain,(is_a_theorem(implies(A,implies(implies(not(B),B),B)))),inference(resolution,[status(thm)],[174273560,159227128]),[]).
%
% cnf(174950352,plain,(is_a_theorem(implies(implies(implies(implies(not(C),C),C),B),implies(A,B)))),inference(resolution,[status(thm)],[158547560,174470808]),[]).
%
% cnf(194505152,plain,(is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B))))),inference(resolution,[status(thm)],[181521208,174950352]),[]).
%
% cnf(255251040,plain,(is_a_theorem(implies(A,implies(C,implies(B,A))))),inference(resolution,[status(thm)],[217242280,194505152]),[]).
%
% cnf(255894104,plain,(~is_a_theorem(implies(implies(B,implies(D,implies(C,B))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[150538544,255251040]),[]).
%
% cnf(257406152,plain,(is_a_theorem(implies(C,implies(A,implies(B,A))))),inference(resolution,[status(thm)],[255894104,194505152]),[]).
%
% cnf(257533392,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(resolution,[status(thm)],[158325272,257406152]),[]).
%
% cnf(258309192,plain,(is_a_theorem(implies(implies(implies(C,A),B),implies(A,B)))),inference(resolution,[status(thm)],[158547560,257533392]),[]).
%
% cnf(267462072,plain,(~is_a_theorem(implies(implies(C,A),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[150538544,258309192]),[]).
%
% cnf(161040200,plain,(~is_a_theorem(implies(A,implies(not(B),B)))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[158547560,158344760]),[]).
%
% cnf(254846560,plain,(~is_a_theorem(implies(A,implies(not(B),B)))|is_a_theorem(implies(C,implies(A,B)))),inference(resolution,[status(thm)],[150538544,194505152]),[]).
%
% cnf(255408384,plain,(is_a_theorem(implies(B,implies(implies(implies(implies(not(C),C),C),A),A)))),inference(resolution,[status(thm)],[254846560,174950352]),[]).
%
% cnf(666955280,plain,(is_a_theorem(implies(implies(implies(implies(not(B),B),B),A),A))),inference(resolution,[status(thm)],[158325272,255408384]),[]).
%
% cnf(669678656,plain,(is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B)))),inference(resolution,[status(thm)],[181521208,666955280]),[]).
%
% cnf(671005872,plain,(is_a_theorem(implies(implies(not(A),implies(not(A),A)),A))),inference(resolution,[status(thm)],[161040200,669678656]),[]).
%
% cnf(673011320,plain,(~is_a_theorem(implies(implies(implies(not(B),implies(not(B),B)),B),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[150538544,671005872]),[]).
%
% cnf(164571800,plain,(~is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[159585296,150538544]),[]).
%
% cnf(181901672,plain,(is_a_theorem(implies(implies(C,not(A)),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[164571800,161030080]),[]).
%
% cnf(184741024,plain,(is_a_theorem(implies(implies(implies(B,implies(D,C)),A),implies(implies(D,not(B)),A)))),inference(resolution,[status(thm)],[158547560,181901672]),[]).
%
% cnf(674635616,plain,(is_a_theorem(implies(implies(not(A),not(not(A))),A))),inference(resolution,[status(thm)],[673011320,184741024]),[]).
%
% cnf(675224008,plain,(is_a_theorem(implies(not(not(A)),A))),inference(resolution,[status(thm)],[267462072,674635616]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[150558920,675224008]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------