TSTP Solution File: LCL178-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL178-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 13:44:59 EDT 2009
% Result : Unsatisfiable 3.8s
% Output : Refutation 3.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 22 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 5 sgn 13 !; 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/LCL178-3.tptp',unknown),
[] ).
cnf(144000840,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/LCL178-3.tptp',unknown),
[] ).
cnf(143982024,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/LCL178-3.tptp',unknown),
[] ).
cnf(143955224,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(152093888,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[143982024,143955224]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),
[] ).
cnf(143975568,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(152221264,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[152093888,143975568,theory(equality)]),
[] ).
cnf(152516408,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[144000840,152221264]),
[] ).
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/LCL178-3.tptp',unknown),
[] ).
cnf(143962936,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(152109440,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[143982024,143962936]),
[] ).
cnf(199028144,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[152516408,152109440]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),
[] ).
cnf(143951032,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(151793624,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[143982024,143951032]),
[] ).
cnf(151807240,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[144000840,151793624]),
[] ).
cnf(214986968,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[199028144,151807240]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),
[] ).
cnf(143958952,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(152101512,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[143982024,143958952]),
[] ).
cnf(152547648,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[144000840,152101512]),
[] ).
fof(prove_this,plain,
~ theorem(implies(p,not(not(p)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),
[] ).
cnf(144009648,plain,
~ theorem(implies(p,not(not(p)))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(152189168,plain,
~ theorem(or(not(p),not(not(p)))),
inference(paramodulation,[status(thm)],[144009648,143975568,theory(equality)]),
[] ).
cnf(154639184,plain,
~ theorem(or(not(not(p)),not(p))),
inference(resolution,[status(thm)],[152547648,152189168]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[214986968,154639184]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(144000840,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(143982024,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(143955224,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(152093888,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[143982024,143955224]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(143975568,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(152221264,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[152093888,143975568,theory(equality)]),[]).
%
% cnf(152516408,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[144000840,152221264]),[]).
%
% 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/LCL178-3.tptp',unknown),[]).
%
% cnf(143962936,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(152109440,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[143982024,143962936]),[]).
%
% cnf(199028144,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[152516408,152109440]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(143951032,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(151793624,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[143982024,143951032]),[]).
%
% cnf(151807240,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[144000840,151793624]),[]).
%
% cnf(214986968,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[199028144,151807240]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(143958952,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(152101512,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[143982024,143958952]),[]).
%
% cnf(152547648,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[144000840,152101512]),[]).
%
% fof(prove_this,plain,(~theorem(implies(p,not(not(p))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL178-3.tptp',unknown),[]).
%
% cnf(144009648,plain,(~theorem(implies(p,not(not(p))))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(152189168,plain,(~theorem(or(not(p),not(not(p))))),inference(paramodulation,[status(thm)],[144009648,143975568,theory(equality)]),[]).
%
% cnf(154639184,plain,(~theorem(or(not(not(p)),not(p)))),inference(resolution,[status(thm)],[152547648,152189168]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[214986968,154639184]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------