%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL294-3 : TPTP v3.4.2. Released v2.3.0.
% 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 13:47:52 EDT 2009
% Result : Unsatisfiable 3.5s
% Output : Refutation 3.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 61 ( 5 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/LCL294-3.tptp',unknown),
[] ).
cnf(153271952,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/LCL294-3.tptp',unknown),
[] ).
cnf(153248952,plain,
( theorem(A)
| ~ axiom(A) ),
inference(rewrite,[status(thm)],[rule_1]),
[] ).
fof(axiom_1_3,plain,
! [A,B] : axiom(implies(A,or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),
[] ).
cnf(153221920,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(161239920,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[153248952,153221920]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),
[] ).
cnf(153242400,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(161325072,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[161239920,153242400,theory(equality)]),
[] ).
cnf(161714704,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[153271952,161325072]),
[] ).
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/LCL294-3.tptp',unknown),
[] ).
cnf(153229704,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(161247488,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[153248952,153229704]),
[] ).
cnf(212565672,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[161714704,161247488]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),
[] ).
cnf(153217672,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(161091648,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[153248952,153217672]),
[] ).
cnf(161105344,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[153271952,161091648]),
[] ).
cnf(161924064,plain,
( ~ theorem(or(A,A))
| theorem(B)
| ~ theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[161105344,153271952]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),
[] ).
cnf(153225688,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(161131184,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[153248952,153225688]),
[] ).
cnf(161146416,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[153271952,161131184]),
[] ).
cnf(161296288,plain,
theorem(or(not(or(A,A)),A)),
inference(paramodulation,[status(thm)],[161091648,153242400,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/LCL294-3.tptp',unknown),
[] ).
cnf(153280160,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(161386880,plain,
theorem(or(and(A,A),not(A))),
inference(paramodulation,[status(thm)],[161296288,153280160,theory(equality)]),
[] ).
cnf(162609976,plain,
theorem(or(not(A),and(A,A))),
inference(resolution,[status(thm)],[161146416,161386880]),
[] ).
cnf(163163128,plain,
theorem(implies(A,and(A,A))),
inference(paramodulation,[status(thm)],[162609976,153242400,theory(equality)]),
[] ).
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/LCL294-3.tptp',unknown),
[] ).
cnf(153284200,plain,
$equal(and(implies(A,B),implies(B,A)),equivalent(A,B)),
inference(rewrite,[status(thm)],[equivalent_defn]),
[] ).
cnf(163280144,plain,
theorem(implies(implies(A,A),equivalent(A,A))),
inference(paramodulation,[status(thm)],[163163128,153284200,theory(equality)]),
[] ).
cnf(166756920,plain,
theorem(implies(or(not(A),A),equivalent(A,A))),
inference(paramodulation,[status(thm)],[163280144,153242400,theory(equality)]),
[] ).
cnf(222315112,plain,
theorem(equivalent(A,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[212565672,161924064,166756920]),
[] ).
fof(prove_this,plain,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),
[] ).
cnf(153288904,plain,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(162796032,plain,
~ theorem(equivalent(implies(p,q),implies(p,q))),
inference(paramodulation,[status(thm)],[153288904,153242400,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[222315112,162796032]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153271952,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153248952,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153221920,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(161239920,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[153248952,153221920]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153242400,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(161325072,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[161239920,153242400,theory(equality)]),[]).
%
% cnf(161714704,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[153271952,161325072]),[]).
%
% 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/LCL294-3.tptp',unknown),[]).
%
% cnf(153229704,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(161247488,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[153248952,153229704]),[]).
%
% cnf(212565672,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[161714704,161247488]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153217672,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(161091648,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[153248952,153217672]),[]).
%
% cnf(161105344,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[153271952,161091648]),[]).
%
% cnf(161924064,plain,(~theorem(or(A,A))|theorem(B)|~theorem(implies(A,B))),inference(resolution,[status(thm)],[161105344,153271952]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153225688,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(161131184,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[153248952,153225688]),[]).
%
% cnf(161146416,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[153271952,161131184]),[]).
%
% cnf(161296288,plain,(theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[161091648,153242400,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/LCL294-3.tptp',unknown),[]).
%
% cnf(153280160,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(161386880,plain,(theorem(or(and(A,A),not(A)))),inference(paramodulation,[status(thm)],[161296288,153280160,theory(equality)]),[]).
%
% cnf(162609976,plain,(theorem(or(not(A),and(A,A)))),inference(resolution,[status(thm)],[161146416,161386880]),[]).
%
% cnf(163163128,plain,(theorem(implies(A,and(A,A)))),inference(paramodulation,[status(thm)],[162609976,153242400,theory(equality)]),[]).
%
% fof(equivalent_defn,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153284200,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),inference(rewrite,[status(thm)],[equivalent_defn]),[]).
%
% cnf(163280144,plain,(theorem(implies(implies(A,A),equivalent(A,A)))),inference(paramodulation,[status(thm)],[163163128,153284200,theory(equality)]),[]).
%
% cnf(166756920,plain,(theorem(implies(or(not(A),A),equivalent(A,A)))),inference(paramodulation,[status(thm)],[163280144,153242400,theory(equality)]),[]).
%
% cnf(222315112,plain,(theorem(equivalent(A,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[212565672,161924064,166756920]),[]).
%
% fof(prove_this,plain,(~theorem(equivalent(implies(p,q),or(not(p),q)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL294-3.tptp',unknown),[]).
%
% cnf(153288904,plain,(~theorem(equivalent(implies(p,q),or(not(p),q)))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(162796032,plain,(~theorem(equivalent(implies(p,q),implies(p,q)))),inference(paramodulation,[status(thm)],[153288904,153242400,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[222315112,162796032]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------