TSTP Solution File: LCL239-3 by Faust---1.0

View Problem - 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
% 
%------------------------------------------------------------------------------