TSTP Solution File: LCL296-3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL296-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 13:47:54 EDT 2009
% Result : Unsatisfiable 79.9s
% Output : Refutation 79.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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 : 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 : 67 ( 8 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/LCL296-3.tptp',unknown),
[] ).
cnf(142246408,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/LCL296-3.tptp',unknown),
[] ).
cnf(142223408,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/LCL296-3.tptp',unknown),
[] ).
cnf(142196376,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(150133048,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[142223408,142196376]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),
[] ).
cnf(142216856,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(150210480,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[150133048,142216856,theory(equality)]),
[] ).
cnf(150605824,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[142246408,150210480]),
[] ).
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/LCL296-3.tptp',unknown),
[] ).
cnf(142204160,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(150115832,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[142223408,142204160]),
[] ).
cnf(195392256,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[150605824,150115832]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),
[] ).
cnf(142192128,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(150066008,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[142223408,142192128]),
[] ).
cnf(150079688,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[142246408,150066008]),
[] ).
cnf(214280184,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[195392256,150079688]),
[] ).
cnf(214915752,plain,
theorem(implies(A,A)),
inference(paramodulation,[status(thm)],[214280184,142216856,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/LCL296-3.tptp',unknown),
[] ).
cnf(142200144,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(150105536,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[142223408,142200144]),
[] ).
cnf(150655664,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[142246408,150105536]),
[] ).
cnf(150177512,plain,
theorem(or(not(or(A,A)),A)),
inference(paramodulation,[status(thm)],[150066008,142216856,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/LCL296-3.tptp',unknown),
[] ).
cnf(142254616,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(150268232,plain,
theorem(or(and(A,A),not(A))),
inference(paramodulation,[status(thm)],[150177512,142254616,theory(equality)]),
[] ).
cnf(152555944,plain,
theorem(or(not(A),and(A,A))),
inference(resolution,[status(thm)],[150655664,150268232]),
[] ).
cnf(152984240,plain,
theorem(implies(A,and(A,A))),
inference(paramodulation,[status(thm)],[152555944,142216856,theory(equality)]),
[] ).
cnf(153044328,plain,
( theorem(and(A,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[152984240,142246408]),
[] ).
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/LCL296-3.tptp',unknown),
[] ).
cnf(142258656,plain,
$equal(and(implies(A,B),implies(B,A)),equivalent(A,B)),
inference(rewrite,[status(thm)],[equivalent_defn]),
[] ).
cnf(154070496,plain,
( theorem(equivalent(A,A))
| ~ theorem(implies(A,A)) ),
inference(paramodulation,[status(thm)],[153044328,142258656,theory(equality)]),
[] ).
cnf(215208184,plain,
theorem(equivalent(A,A)),
inference(resolution,[status(thm)],[214915752,154070496]),
[] ).
cnf(150523216,plain,
( theorem(or(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[142246408,150133048]),
[] ).
cnf(152566328,plain,
( theorem(or(B,A))
| ~ theorem(B) ),
inference(resolution,[status(thm)],[150655664,150523216]),
[] ).
cnf(215231640,plain,
theorem(or(equivalent(A,A),B)),
inference(resolution,[status(thm)],[215208184,152566328]),
[] ).
fof(prove_this,plain,
~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),
[] ).
cnf(142263368,plain,
~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(156141056,plain,
~ theorem(equivalent(implies(p,not(q)),implies(p,not(q)))),
inference(paramodulation,[status(thm)],[142263368,142216856,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[215231640,156141056,150079688]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 79 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142246408,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142223408,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142196376,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(150133048,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[142223408,142196376]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142216856,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(150210480,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[150133048,142216856,theory(equality)]),[]).
%
% cnf(150605824,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[142246408,150210480]),[]).
%
% 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/LCL296-3.tptp',unknown),[]).
%
% cnf(142204160,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(150115832,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[142223408,142204160]),[]).
%
% cnf(195392256,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[150605824,150115832]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142192128,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(150066008,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[142223408,142192128]),[]).
%
% cnf(150079688,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[142246408,150066008]),[]).
%
% cnf(214280184,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[195392256,150079688]),[]).
%
% cnf(214915752,plain,(theorem(implies(A,A))),inference(paramodulation,[status(thm)],[214280184,142216856,theory(equality)]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142200144,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(150105536,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[142223408,142200144]),[]).
%
% cnf(150655664,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[142246408,150105536]),[]).
%
% cnf(150177512,plain,(theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[150066008,142216856,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/LCL296-3.tptp',unknown),[]).
%
% cnf(142254616,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(150268232,plain,(theorem(or(and(A,A),not(A)))),inference(paramodulation,[status(thm)],[150177512,142254616,theory(equality)]),[]).
%
% cnf(152555944,plain,(theorem(or(not(A),and(A,A)))),inference(resolution,[status(thm)],[150655664,150268232]),[]).
%
% cnf(152984240,plain,(theorem(implies(A,and(A,A)))),inference(paramodulation,[status(thm)],[152555944,142216856,theory(equality)]),[]).
%
% cnf(153044328,plain,(theorem(and(A,A))|~theorem(A)),inference(resolution,[status(thm)],[152984240,142246408]),[]).
%
% fof(equivalent_defn,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142258656,plain,($equal(and(implies(A,B),implies(B,A)),equivalent(A,B))),inference(rewrite,[status(thm)],[equivalent_defn]),[]).
%
% cnf(154070496,plain,(theorem(equivalent(A,A))|~theorem(implies(A,A))),inference(paramodulation,[status(thm)],[153044328,142258656,theory(equality)]),[]).
%
% cnf(215208184,plain,(theorem(equivalent(A,A))),inference(resolution,[status(thm)],[214915752,154070496]),[]).
%
% cnf(150523216,plain,(theorem(or(B,A))|~theorem(A)),inference(resolution,[status(thm)],[142246408,150133048]),[]).
%
% cnf(152566328,plain,(theorem(or(B,A))|~theorem(B)),inference(resolution,[status(thm)],[150655664,150523216]),[]).
%
% cnf(215231640,plain,(theorem(or(equivalent(A,A),B))),inference(resolution,[status(thm)],[215208184,152566328]),[]).
%
% fof(prove_this,plain,(~theorem(equivalent(implies(p,not(q)),or(not(p),not(q))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL296-3.tptp',unknown),[]).
%
% cnf(142263368,plain,(~theorem(equivalent(implies(p,not(q)),or(not(p),not(q))))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(156141056,plain,(~theorem(equivalent(implies(p,not(q)),implies(p,not(q))))),inference(paramodulation,[status(thm)],[142263368,142216856,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[215231640,156141056,150079688]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------