TSTP Solution File: LCL297-3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL297-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 13:47:55 EDT 2009
% Result : Unsatisfiable 32.3s
% Output : Refutation 32.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 32 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 7 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_2,plain,
! [A,B] :
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151629504,plain,
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
inference(rewrite,[status(thm)],[rule_2]),
[] ).
fof(rule_1,plain,
! [A] :
( theorem(A)
| ~ axiom(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151606504,plain,
( theorem(A)
| ~ axiom(A) ),
inference(rewrite,[status(thm)],[rule_1]),
[] ).
fof(axiom_1_5,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151587256,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(159500512,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[151606504,151587256]),
[] ).
cnf(159519840,plain,
( theorem(or(B,or(A,C)))
| ~ theorem(or(A,or(B,C))) ),
inference(resolution,[status(thm)],[151629504,159500512]),
[] ).
fof(axiom_1_3,plain,
! [A,B] : axiom(implies(A,or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151579472,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(159549176,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[151606504,151579472]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151599952,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(159626608,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[159549176,151599952,theory(equality)]),
[] ).
cnf(172921792,plain,
theorem(or(A,or(not(B),B))),
inference(resolution,[status(thm)],[159519840,159626608]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151575224,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(159449032,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[151606504,151575224]),
[] ).
cnf(159462760,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[151629504,159449032]),
[] ).
cnf(174109464,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[172921792,159462760]),
[] ).
cnf(174453968,plain,
theorem(implies(A,A)),
inference(paramodulation,[status(thm)],[174109464,151599952,theory(equality)]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151583240,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(159488600,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[151606504,151583240]),
[] ).
cnf(160071960,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[151629504,159488600]),
[] ).
cnf(159939512,plain,
( theorem(or(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[151629504,159549176]),
[] ).
cnf(162154160,plain,
( theorem(or(B,A))
| ~ theorem(B) ),
inference(resolution,[status(thm)],[160071960,159939512]),
[] ).
cnf(174514376,plain,
theorem(or(implies(A,A),B)),
inference(resolution,[status(thm)],[174453968,162154160]),
[] ).
cnf(159597728,plain,
theorem(or(not(or(A,A)),A)),
inference(paramodulation,[status(thm)],[159449032,151599952,theory(equality)]),
[] ).
fof(and_defn,plain,
! [A,B] : $equal(not(or(not(A),not(B))),and(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151637712,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(159688424,plain,
theorem(or(and(A,A),not(A))),
inference(paramodulation,[status(thm)],[159597728,151637712,theory(equality)]),
[] ).
cnf(162143712,plain,
theorem(or(not(A),and(A,A))),
inference(resolution,[status(thm)],[160071960,159688424]),
[] ).
cnf(162576864,plain,
theorem(implies(A,and(A,A))),
inference(paramodulation,[status(thm)],[162143712,151599952,theory(equality)]),
[] ).
cnf(162641040,plain,
( theorem(and(A,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[162576864,151629504]),
[] ).
cnf(163172256,plain,
( theorem(and(A,A))
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[162641040,159462760]),
[] ).
fof(equivalent_defn,plain,
! [A,B] : $equal(and(implies(A,B),implies(B,A)),equivalent(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151641752,plain,
$equal(and(implies(A,B),implies(B,A)),equivalent(A,B)),
inference(rewrite,[status(thm)],[equivalent_defn]),
[] ).
cnf(206901824,plain,
theorem(equivalent(A,A)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174514376,163172256,151641752,theory(equality)]),
[] ).
fof(prove_this,plain,
~ theorem(equivalent(not(implies(p,not(q))),and(p,q))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),
[] ).
cnf(151646456,plain,
~ theorem(equivalent(not(implies(p,not(q))),and(p,q))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(162005112,plain,
~ theorem(equivalent(not(or(not(p),not(q))),and(p,q))),
inference(paramodulation,[status(thm)],[151646456,151599952,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[206901824,162005112,151637712,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 31 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151629504,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151606504,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_5,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151587256,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(159500512,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[151606504,151587256]),[]).
%
% cnf(159519840,plain,(theorem(or(B,or(A,C)))|~theorem(or(A,or(B,C)))),inference(resolution,[status(thm)],[151629504,159500512]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151579472,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(159549176,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[151606504,151579472]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151599952,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(159626608,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[159549176,151599952,theory(equality)]),[]).
%
% cnf(172921792,plain,(theorem(or(A,or(not(B),B)))),inference(resolution,[status(thm)],[159519840,159626608]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151575224,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(159449032,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[151606504,151575224]),[]).
%
% cnf(159462760,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[151629504,159449032]),[]).
%
% cnf(174109464,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[172921792,159462760]),[]).
%
% cnf(174453968,plain,(theorem(implies(A,A))),inference(paramodulation,[status(thm)],[174109464,151599952,theory(equality)]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151583240,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(159488600,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[151606504,151583240]),[]).
%
% cnf(160071960,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[151629504,159488600]),[]).
%
% cnf(159939512,plain,(theorem(or(B,A))|~theorem(A)),inference(resolution,[status(thm)],[151629504,159549176]),[]).
%
% cnf(162154160,plain,(theorem(or(B,A))|~theorem(B)),inference(resolution,[status(thm)],[160071960,159939512]),[]).
%
% cnf(174514376,plain,(theorem(or(implies(A,A),B))),inference(resolution,[status(thm)],[174453968,162154160]),[]).
%
% cnf(159597728,plain,(theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[159449032,151599952,theory(equality)]),[]).
%
% fof(and_defn,plain,($equal(not(or(not(A),not(B))),and(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151637712,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(159688424,plain,(theorem(or(and(A,A),not(A)))),inference(paramodulation,[status(thm)],[159597728,151637712,theory(equality)]),[]).
%
% cnf(162143712,plain,(theorem(or(not(A),and(A,A)))),inference(resolution,[status(thm)],[160071960,159688424]),[]).
%
% cnf(162576864,plain,(theorem(implies(A,and(A,A)))),inference(paramodulation,[status(thm)],[162143712,151599952,theory(equality)]),[]).
%
% cnf(162641040,plain,(theorem(and(A,A))|~theorem(A)),inference(resolution,[status(thm)],[162576864,151629504]),[]).
%
% cnf(163172256,plain,(theorem(and(A,A))|~theorem(or(A,A))),inference(resolution,[status(thm)],[162641040,159462760]),[]).
%
% fof(equivalent_defn,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151641752,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),inference(rewrite,[status(thm)],[equivalent_defn]),[]).
%
% cnf(206901824,plain,(theorem(equivalent(A,A))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174514376,163172256,151641752,theory(equality)]),[]).
%
% fof(prove_this,plain,(~theorem(equivalent(not(implies(p,not(q))),and(p,q)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL297-3.tptp',unknown),[]).
%
% cnf(151646456,plain,(~theorem(equivalent(not(implies(p,not(q))),and(p,q)))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(162005112,plain,(~theorem(equivalent(not(or(not(p),not(q))),and(p,q)))),inference(paramodulation,[status(thm)],[151646456,151599952,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[206901824,162005112,151637712,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------