TSTP Solution File: LCL397-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL397-1 : TPTP v3.4.2. Released v2.3.0.
% 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 13:49:11 EDT 2009
% Result : Unsatisfiable 1.2s
% Output : Refutation 1.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 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 : 47 ( 12 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_63,plain,
~ is_a_theorem(implies(x,implies(y,y))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),
[] ).
cnf(162389920,plain,
~ is_a_theorem(implies(x,implies(y,y))),
inference(rewrite,[status(thm)],[prove_cn_63]),
[] ).
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/LCL397-1.tptp',unknown),
[] ).
cnf(162369416,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_2,plain,
! [A] : is_a_theorem(implies(implies(not(A),A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),
[] ).
cnf(162378264,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(rewrite,[status(thm)],[cn_2]),
[] ).
cnf(170180488,plain,
( ~ is_a_theorem(implies(implies(implies(not(B),B),B),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162369416,162378264]),
[] ).
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/LCL397-1.tptp',unknown),
[] ).
cnf(162374272,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_1]),
[] ).
cnf(170385536,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(implies(B,C),implies(A,C))) ),
inference(resolution,[status(thm)],[162369416,162374272]),
[] ).
fof(cn_3,plain,
! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),
[] ).
cnf(162382240,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(rewrite,[status(thm)],[cn_3]),
[] ).
cnf(170319560,plain,
( ~ is_a_theorem(implies(implies(B,implies(not(B),C)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162369416,162382240]),
[] ).
cnf(171479856,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolution,[status(thm)],[170319560,162374272]),
[] ).
cnf(176058456,plain,
( ~ is_a_theorem(implies(implies(not(A),B),C))
| is_a_theorem(implies(A,C)) ),
inference(resolution,[status(thm)],[171479856,162369416]),
[] ).
cnf(176129312,plain,
is_a_theorem(implies(A,A)),
inference(resolution,[status(thm)],[171479856,170180488]),
[] ).
cnf(170296248,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(not(A),B)) ),
inference(resolution,[status(thm)],[162369416,162382240]),
[] ).
cnf(176454056,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolution,[status(thm)],[176129312,170296248]),
[] ).
cnf(176901920,plain,
is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C))),
inference(resolution,[status(thm)],[176454056,170385536]),
[] ).
cnf(180287720,plain,
is_a_theorem(implies(A,implies(not(implies(C,C)),B))),
inference(resolution,[status(thm)],[176058456,176901920]),
[] ).
cnf(180389232,plain,
is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B))),
inference(resolution,[status(thm)],[170385536,180287720]),
[] ).
cnf(192309496,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolution,[status(thm)],[170180488,180389232]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162389920,192309496]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_63,plain,(~is_a_theorem(implies(x,implies(y,y)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),[]).
%
% cnf(162389920,plain,(~is_a_theorem(implies(x,implies(y,y)))),inference(rewrite,[status(thm)],[prove_cn_63]),[]).
%
% 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/LCL397-1.tptp',unknown),[]).
%
% cnf(162369416,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_2,plain,(is_a_theorem(implies(implies(not(A),A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),[]).
%
% cnf(162378264,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn_2]),[]).
%
% cnf(170180488,plain,(~is_a_theorem(implies(implies(implies(not(B),B),B),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162369416,162378264]),[]).
%
% 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/LCL397-1.tptp',unknown),[]).
%
% cnf(162374272,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
%
% cnf(170385536,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[162369416,162374272]),[]).
%
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),[]).
%
% cnf(162382240,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
%
% cnf(170319560,plain,(~is_a_theorem(implies(implies(B,implies(not(B),C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162369416,162382240]),[]).
%
% cnf(171479856,plain,(is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C)))),inference(resolution,[status(thm)],[170319560,162374272]),[]).
%
% cnf(176058456,plain,(~is_a_theorem(implies(implies(not(A),B),C))|is_a_theorem(implies(A,C))),inference(resolution,[status(thm)],[171479856,162369416]),[]).
%
% cnf(176129312,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[171479856,170180488]),[]).
%
% cnf(170296248,plain,(~is_a_theorem(A)|is_a_theorem(implies(not(A),B))),inference(resolution,[status(thm)],[162369416,162382240]),[]).
%
% cnf(176454056,plain,(is_a_theorem(implies(not(implies(A,A)),B))),inference(resolution,[status(thm)],[176129312,170296248]),[]).
%
% cnf(176901920,plain,(is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C)))),inference(resolution,[status(thm)],[176454056,170385536]),[]).
%
% cnf(180287720,plain,(is_a_theorem(implies(A,implies(not(implies(C,C)),B)))),inference(resolution,[status(thm)],[176058456,176901920]),[]).
%
% cnf(180389232,plain,(is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B)))),inference(resolution,[status(thm)],[170385536,180287720]),[]).
%
% cnf(192309496,plain,(is_a_theorem(implies(A,implies(B,B)))),inference(resolution,[status(thm)],[170180488,180389232]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162389920,192309496]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------