TSTP Solution File: LCL287-3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL287-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 13:47:47 EDT 2009
% Result : Unsatisfiable 7.4s
% Output : Refutation 7.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 28 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 19 |; 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 : 62 ( 3 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/LCL287-3.tptp',unknown),
[] ).
cnf(155185680,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/LCL287-3.tptp',unknown),
[] ).
cnf(155162680,plain,
( theorem(A)
| ~ axiom(A) ),
inference(rewrite,[status(thm)],[rule_1]),
[] ).
cnf(163191136,plain,
( theorem(A)
| ~ theorem(B)
| ~ axiom(implies(B,A)) ),
inference(resolution,[status(thm)],[155185680,155162680]),
[] ).
cnf(163202064,plain,
( theorem(A)
| ~ axiom(implies(B,A))
| ~ axiom(B) ),
inference(resolution,[status(thm)],[163191136,155162680]),
[] ).
cnf(164451312,plain,
( theorem(A)
| ~ theorem(B)
| ~ axiom(implies(C,implies(B,A)))
| ~ axiom(C) ),
inference(resolution,[status(thm)],[155185680,163202064]),
[] ).
fof(axiom_1_6,plain,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),
[] ).
cnf(155151472,plain,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(rewrite,[status(thm)],[axiom_1_6]),
[] ).
cnf(167023712,plain,
( theorem(or(C,B))
| ~ theorem(or(C,A))
| ~ axiom(implies(A,B)) ),
inference(resolution,[status(thm)],[164451312,155151472]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),
[] ).
cnf(155131400,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(167263384,plain,
( theorem(or(B,A))
| ~ theorem(or(B,or(A,A))) ),
inference(resolution,[status(thm)],[167023712,155131400]),
[] ).
fof(axiom_1_3,plain,
! [A,B] : axiom(implies(A,or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),
[] ).
cnf(155135648,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(163228048,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[155162680,155135648]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),
[] ).
cnf(155156128,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(173661664,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[163228048,155156128,theory(equality)]),
[] ).
cnf(251852704,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[167263384,173661664]),
[] ).
cnf(252905040,plain,
theorem(implies(A,A)),
inference(paramodulation,[status(thm)],[251852704,155156128,theory(equality)]),
[] ).
cnf(163005256,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[155162680,155131400]),
[] ).
cnf(173625448,plain,
theorem(or(not(or(A,A)),A)),
inference(paramodulation,[status(thm)],[163005256,155156128,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/LCL287-3.tptp',unknown),
[] ).
cnf(155139416,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(163404544,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[163191136,155139416]),
[] ).
cnf(174988456,plain,
theorem(or(A,not(or(A,A)))),
inference(resolution,[status(thm)],[173625448,163404544]),
[] ).
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/LCL287-3.tptp',unknown),
[] ).
cnf(155193888,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(175983624,plain,
theorem(or(not(A),and(A,A))),
inference(paramodulation,[status(thm)],[174988456,155193888,theory(equality)]),
[] ).
cnf(176496104,plain,
theorem(implies(A,and(A,A))),
inference(paramodulation,[status(thm)],[175983624,155156128,theory(equality)]),
[] ).
cnf(176557680,plain,
( theorem(and(A,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[176496104,155185680]),
[] ).
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/LCL287-3.tptp',unknown),
[] ).
cnf(155197928,plain,
$equal(and(implies(A,B),implies(B,A)),equivalent(A,B)),
inference(rewrite,[status(thm)],[equivalent_defn]),
[] ).
cnf(177175336,plain,
( theorem(equivalent(A,A))
| ~ theorem(implies(A,A)) ),
inference(paramodulation,[status(thm)],[176557680,155197928,theory(equality)]),
[] ).
cnf(253255912,plain,
theorem(equivalent(A,A)),
inference(resolution,[status(thm)],[252905040,177175336]),
[] ).
fof(prove_this,plain,
~ theorem(equivalent(and(p,q),not(or(not(p),not(q))))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),
[] ).
cnf(155202640,plain,
~ theorem(equivalent(and(p,q),not(or(not(p),not(q))))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(174583768,plain,
~ theorem(equivalent(and(p,q),and(p,q))),
inference(paramodulation,[status(thm)],[155202640,155193888,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[253255912,174583768]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 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/LCL287-3.tptp',unknown),[]).
%
% cnf(155185680,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/LCL287-3.tptp',unknown),[]).
%
% cnf(155162680,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% cnf(163191136,plain,(theorem(A)|~theorem(B)|~axiom(implies(B,A))),inference(resolution,[status(thm)],[155185680,155162680]),[]).
%
% cnf(163202064,plain,(theorem(A)|~axiom(implies(B,A))|~axiom(B)),inference(resolution,[status(thm)],[163191136,155162680]),[]).
%
% cnf(164451312,plain,(theorem(A)|~theorem(B)|~axiom(implies(C,implies(B,A)))|~axiom(C)),inference(resolution,[status(thm)],[155185680,163202064]),[]).
%
% fof(axiom_1_6,plain,(axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155151472,plain,(axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))),inference(rewrite,[status(thm)],[axiom_1_6]),[]).
%
% cnf(167023712,plain,(theorem(or(C,B))|~theorem(or(C,A))|~axiom(implies(A,B))),inference(resolution,[status(thm)],[164451312,155151472]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155131400,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(167263384,plain,(theorem(or(B,A))|~theorem(or(B,or(A,A)))),inference(resolution,[status(thm)],[167023712,155131400]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155135648,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(163228048,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[155162680,155135648]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155156128,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(173661664,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[163228048,155156128,theory(equality)]),[]).
%
% cnf(251852704,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[167263384,173661664]),[]).
%
% cnf(252905040,plain,(theorem(implies(A,A))),inference(paramodulation,[status(thm)],[251852704,155156128,theory(equality)]),[]).
%
% cnf(163005256,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[155162680,155131400]),[]).
%
% cnf(173625448,plain,(theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[163005256,155156128,theory(equality)]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155139416,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(163404544,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[163191136,155139416]),[]).
%
% cnf(174988456,plain,(theorem(or(A,not(or(A,A))))),inference(resolution,[status(thm)],[173625448,163404544]),[]).
%
% fof(and_defn,plain,($equal(not(or(not(A),not(B))),and(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155193888,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(175983624,plain,(theorem(or(not(A),and(A,A)))),inference(paramodulation,[status(thm)],[174988456,155193888,theory(equality)]),[]).
%
% cnf(176496104,plain,(theorem(implies(A,and(A,A)))),inference(paramodulation,[status(thm)],[175983624,155156128,theory(equality)]),[]).
%
% cnf(176557680,plain,(theorem(and(A,A))|~theorem(A)),inference(resolution,[status(thm)],[176496104,155185680]),[]).
%
% fof(equivalent_defn,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155197928,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),inference(rewrite,[status(thm)],[equivalent_defn]),[]).
%
% cnf(177175336,plain,(theorem(equivalent(A,A))|~theorem(implies(A,A))),inference(paramodulation,[status(thm)],[176557680,155197928,theory(equality)]),[]).
%
% cnf(253255912,plain,(theorem(equivalent(A,A))),inference(resolution,[status(thm)],[252905040,177175336]),[]).
%
% fof(prove_this,plain,(~theorem(equivalent(and(p,q),not(or(not(p),not(q)))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL287-3.tptp',unknown),[]).
%
% cnf(155202640,plain,(~theorem(equivalent(and(p,q),not(or(not(p),not(q)))))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(174583768,plain,(~theorem(equivalent(and(p,q),and(p,q)))),inference(paramodulation,[status(thm)],[155202640,155193888,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[253255912,174583768]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------