TSTP Solution File: LCL239-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL239-3 : 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 13:47:16 EDT 2009
% Result : Unsatisfiable 7.2s
% Output : Refutation 7.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 24 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 5 sgn 15 !; 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/LCL239-3.tptp',unknown),
[] ).
cnf(152706456,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/LCL239-3.tptp',unknown),
[] ).
cnf(152687608,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/LCL239-3.tptp',unknown),
[] ).
cnf(152660736,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(160516056,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[152687608,152660736]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),
[] ).
cnf(152681120,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(160672432,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[160516056,152681120,theory(equality)]),
[] ).
cnf(161125176,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[152706456,160672432]),
[] ).
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/LCL239-3.tptp',unknown),
[] ).
cnf(152668488,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(160596504,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[152687608,152668488]),
[] ).
cnf(206366328,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[161125176,160596504]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),
[] ).
cnf(152656552,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(160508136,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[152687608,152656552]),
[] ).
cnf(160529456,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[152706456,160508136]),
[] ).
cnf(230244336,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[206366328,160529456]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),
[] ).
cnf(152664504,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(160588784,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[152687608,152664504]),
[] ).
cnf(161174920,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[152706456,160588784]),
[] ).
cnf(230755240,plain,
theorem(or(A,not(A))),
inference(resolution,[status(thm)],[230244336,161174920]),
[] ).
cnf(161284912,plain,
( theorem(A)
| ~ theorem(or(not(B),A))
| ~ theorem(B) ),
inference(paramodulation,[status(thm)],[152706456,152681120,theory(equality)]),
[] ).
cnf(231598280,plain,
( theorem(not(not(A)))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[230755240,161284912]),
[] ).
fof(prove_this,plain,
~ theorem(not(and(p,not(p)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),
[] ).
cnf(152719272,plain,
~ theorem(not(and(p,not(p)))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
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/LCL239-3.tptp',unknown),
[] ).
cnf(152714600,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(160737528,plain,
~ theorem(not(not(or(not(p),not(not(p)))))),
inference(paramodulation,[status(thm)],[152719272,152714600,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[230755240,231598280,160737528]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152706456,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152687608,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152660736,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(160516056,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[152687608,152660736]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152681120,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(160672432,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[160516056,152681120,theory(equality)]),[]).
%
% cnf(161125176,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[152706456,160672432]),[]).
%
% 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/LCL239-3.tptp',unknown),[]).
%
% cnf(152668488,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(160596504,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[152687608,152668488]),[]).
%
% cnf(206366328,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[161125176,160596504]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152656552,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(160508136,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[152687608,152656552]),[]).
%
% cnf(160529456,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[152706456,160508136]),[]).
%
% cnf(230244336,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[206366328,160529456]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152664504,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(160588784,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[152687608,152664504]),[]).
%
% cnf(161174920,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[152706456,160588784]),[]).
%
% cnf(230755240,plain,(theorem(or(A,not(A)))),inference(resolution,[status(thm)],[230244336,161174920]),[]).
%
% cnf(161284912,plain,(theorem(A)|~theorem(or(not(B),A))|~theorem(B)),inference(paramodulation,[status(thm)],[152706456,152681120,theory(equality)]),[]).
%
% cnf(231598280,plain,(theorem(not(not(A)))|~theorem(A)),inference(resolution,[status(thm)],[230755240,161284912]),[]).
%
% fof(prove_this,plain,(~theorem(not(and(p,not(p))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152719272,plain,(~theorem(not(and(p,not(p))))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% fof(and_defn,plain,($equal(not(or(not(A),not(B))),and(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL239-3.tptp',unknown),[]).
%
% cnf(152714600,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(160737528,plain,(~theorem(not(not(or(not(p),not(not(p))))))),inference(paramodulation,[status(thm)],[152719272,152714600,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[230755240,231598280,160737528]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------