%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL268-3 : 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 13:47:39 EDT 2009
% Result : Unsatisfiable 6.1s
% Output : Refutation 6.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 10 |; 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 58 ( 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/LCL268-3.tptp',unknown),
[] ).
cnf(158020488,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/LCL268-3.tptp',unknown),
[] ).
cnf(158001608,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/LCL268-3.tptp',unknown),
[] ).
cnf(157974704,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(165872360,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[158001608,157974704]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),
[] ).
cnf(157995088,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(166198992,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[165872360,157995088,theory(equality)]),
[] ).
cnf(166618880,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[158020488,166198992]),
[] ).
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/LCL268-3.tptp',unknown),
[] ).
cnf(157982456,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(166125664,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[158001608,157982456]),
[] ).
cnf(224303256,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[166618880,166125664]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),
[] ).
cnf(157970488,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(166117984,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[158001608,157970488]),
[] ).
cnf(166554880,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[158020488,166117984]),
[] ).
cnf(266100856,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[224303256,166554880]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),
[] ).
cnf(157978472,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(165932680,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[158001608,157978472]),
[] ).
cnf(166676792,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[158020488,165932680]),
[] ).
cnf(166239232,plain,
theorem(or(not(or(A,A)),A)),
inference(paramodulation,[status(thm)],[166117984,157995088,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/LCL268-3.tptp',unknown),
[] ).
cnf(158028664,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(166324536,plain,
theorem(or(and(A,A),not(A))),
inference(paramodulation,[status(thm)],[166239232,158028664,theory(equality)]),
[] ).
cnf(169890512,plain,
theorem(or(not(A),and(A,A))),
inference(resolution,[status(thm)],[166676792,166324536]),
[] ).
cnf(170634752,plain,
theorem(implies(A,and(A,A))),
inference(paramodulation,[status(thm)],[169890512,157995088,theory(equality)]),
[] ).
cnf(170699608,plain,
( theorem(and(A,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[170634752,158020488]),
[] ).
fof(prove_this,plain,
~ theorem(equivalent(p,p)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),
[] ).
cnf(158037264,plain,
~ theorem(equivalent(p,p)),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
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/LCL268-3.tptp',unknown),
[] ).
cnf(158032672,plain,
$equal(and(implies(A,B),implies(B,A)),equivalent(A,B)),
inference(rewrite,[status(thm)],[equivalent_defn]),
[] ).
cnf(166155696,plain,
~ theorem(and(implies(p,p),implies(p,p))),
inference(paramodulation,[status(thm)],[158037264,158032672,theory(equality)]),
[] ).
cnf(171340240,plain,
~ theorem(implies(p,p)),
inference(resolution,[status(thm)],[170699608,166155696]),
[] ).
cnf(171810472,plain,
~ theorem(or(not(p),p)),
inference(paramodulation,[status(thm)],[171340240,157995088,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[266100856,171810472]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(158020488,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(158001608,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(157974704,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(165872360,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[158001608,157974704]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(157995088,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(166198992,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[165872360,157995088,theory(equality)]),[]).
%
% cnf(166618880,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[158020488,166198992]),[]).
%
% 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/LCL268-3.tptp',unknown),[]).
%
% cnf(157982456,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(166125664,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[158001608,157982456]),[]).
%
% cnf(224303256,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[166618880,166125664]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(157970488,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(166117984,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[158001608,157970488]),[]).
%
% cnf(166554880,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[158020488,166117984]),[]).
%
% cnf(266100856,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[224303256,166554880]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(157978472,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(165932680,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[158001608,157978472]),[]).
%
% cnf(166676792,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[158020488,165932680]),[]).
%
% cnf(166239232,plain,(theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[166117984,157995088,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/LCL268-3.tptp',unknown),[]).
%
% cnf(158028664,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(166324536,plain,(theorem(or(and(A,A),not(A)))),inference(paramodulation,[status(thm)],[166239232,158028664,theory(equality)]),[]).
%
% cnf(169890512,plain,(theorem(or(not(A),and(A,A)))),inference(resolution,[status(thm)],[166676792,166324536]),[]).
%
% cnf(170634752,plain,(theorem(implies(A,and(A,A)))),inference(paramodulation,[status(thm)],[169890512,157995088,theory(equality)]),[]).
%
% cnf(170699608,plain,(theorem(and(A,A))|~theorem(A)),inference(resolution,[status(thm)],[170634752,158020488]),[]).
%
% fof(prove_this,plain,(~theorem(equivalent(p,p))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(158037264,plain,(~theorem(equivalent(p,p))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% fof(equivalent_defn,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL268-3.tptp',unknown),[]).
%
% cnf(158032672,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),inference(rewrite,[status(thm)],[equivalent_defn]),[]).
%
% cnf(166155696,plain,(~theorem(and(implies(p,p),implies(p,p)))),inference(paramodulation,[status(thm)],[158037264,158032672,theory(equality)]),[]).
%
% cnf(171340240,plain,(~theorem(implies(p,p))),inference(resolution,[status(thm)],[170699608,166155696]),[]).
%
% cnf(171810472,plain,(~theorem(or(not(p),p))),inference(paramodulation,[status(thm)],[171340240,157995088,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[266100856,171810472]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------