TSTP Solution File: LCL212-3 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL212-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 13:46:28 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   26 (  17 unt;   0 def)
%            Number of atoms       :   37 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  13   ~;  11   |;   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   43 (  11 sgn  10   !;   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/LCL212-3.tptp',unknown),
    [] ).

cnf(160369648,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/LCL212-3.tptp',unknown),
    [] ).

cnf(160350800,plain,
    ( theorem(A)
    | ~ axiom(A) ),
    inference(rewrite,[status(thm)],[rule_1]),
    [] ).

fof(axiom_1_4,plain,
    ! [A,B] : axiom(implies(or(A,B),or(B,A))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
    [] ).

cnf(160327600,plain,
    axiom(implies(or(A,B),or(B,A))),
    inference(rewrite,[status(thm)],[axiom_1_4]),
    [] ).

cnf(168276328,plain,
    theorem(implies(or(A,B),or(B,A))),
    inference(resolution,[status(thm)],[160350800,160327600]),
    [] ).

cnf(168629072,plain,
    ( theorem(or(B,A))
    | ~ theorem(or(A,B)) ),
    inference(resolution,[status(thm)],[160369648,168276328]),
    [] ).

fof(axiom_1_3,plain,
    ! [A,B] : axiom(implies(A,or(B,A))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
    [] ).

cnf(160323872,plain,
    axiom(implies(A,or(B,A))),
    inference(rewrite,[status(thm)],[axiom_1_3]),
    [] ).

cnf(168175328,plain,
    theorem(implies(A,or(B,A))),
    inference(resolution,[status(thm)],[160350800,160323872]),
    [] ).

cnf(168507000,plain,
    ( theorem(or(B,A))
    | ~ theorem(A) ),
    inference(resolution,[status(thm)],[160369648,168175328]),
    [] ).

cnf(170158184,plain,
    ( theorem(or(B,A))
    | ~ theorem(B) ),
    inference(resolution,[status(thm)],[168629072,168507000]),
    [] ).

fof(implies_definition,plain,
    ! [A,B] : $equal(or(not(A),B),implies(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
    [] ).

cnf(160344312,plain,
    $equal(or(not(A),B),implies(A,B)),
    inference(rewrite,[status(thm)],[implies_definition]),
    [] ).

cnf(168338544,plain,
    theorem(implies(A,implies(B,A))),
    inference(paramodulation,[status(thm)],[168175328,160344312,theory(equality)]),
    [] ).

cnf(168530640,plain,
    ( theorem(implies(B,A))
    | ~ theorem(A) ),
    inference(resolution,[status(thm)],[160369648,168338544]),
    [] ).

cnf(169081264,plain,
    theorem(implies(A,implies(B,implies(C,B)))),
    inference(resolution,[status(thm)],[168530640,168338544]),
    [] ).

cnf(170753584,plain,
    theorem(or(implies(B,implies(C,implies(D,C))),A)),
    inference(resolution,[status(thm)],[170158184,169081264]),
    [] ).

fof(prove_this,plain,
    ~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
    [] ).

cnf(160378560,plain,
    ~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
    inference(rewrite,[status(thm)],[prove_this]),
    [] ).

fof(axiom_1_2,plain,
    ! [A] : axiom(implies(or(A,A),A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
    [] ).

cnf(160319648,plain,
    axiom(implies(or(A,A),A)),
    inference(rewrite,[status(thm)],[axiom_1_2]),
    [] ).

cnf(168167408,plain,
    theorem(implies(or(A,A),A)),
    inference(resolution,[status(thm)],[160350800,160319648]),
    [] ).

cnf(168188728,plain,
    ( theorem(A)
    | ~ theorem(or(A,A)) ),
    inference(resolution,[status(thm)],[160369648,168167408]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[170753584,160378560,168188728]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 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/LCL212-3.tptp',unknown),[]).
% 
% cnf(160369648,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/LCL212-3.tptp',unknown),[]).
% 
% cnf(160350800,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
% 
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
% 
% cnf(160327600,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
% 
% cnf(168276328,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[160350800,160327600]),[]).
% 
% cnf(168629072,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[160369648,168276328]),[]).
% 
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
% 
% cnf(160323872,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
% 
% cnf(168175328,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[160350800,160323872]),[]).
% 
% cnf(168507000,plain,(theorem(or(B,A))|~theorem(A)),inference(resolution,[status(thm)],[160369648,168175328]),[]).
% 
% cnf(170158184,plain,(theorem(or(B,A))|~theorem(B)),inference(resolution,[status(thm)],[168629072,168507000]),[]).
% 
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
% 
% cnf(160344312,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
% 
% cnf(168338544,plain,(theorem(implies(A,implies(B,A)))),inference(paramodulation,[status(thm)],[168175328,160344312,theory(equality)]),[]).
% 
% cnf(168530640,plain,(theorem(implies(B,A))|~theorem(A)),inference(resolution,[status(thm)],[160369648,168338544]),[]).
% 
% cnf(169081264,plain,(theorem(implies(A,implies(B,implies(C,B))))),inference(resolution,[status(thm)],[168530640,168338544]),[]).
% 
% cnf(170753584,plain,(theorem(or(implies(B,implies(C,implies(D,C))),A))),inference(resolution,[status(thm)],[170158184,169081264]),[]).
% 
% fof(prove_this,plain,(~theorem(implies(not(p),implies(q,implies(implies(p,q),q))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
% 
% cnf(160378560,plain,(~theorem(implies(not(p),implies(q,implies(implies(p,q),q))))),inference(rewrite,[status(thm)],[prove_this]),[]).
% 
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
% 
% cnf(160319648,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
% 
% cnf(168167408,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[160350800,160319648]),[]).
% 
% cnf(168188728,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[160369648,168167408]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[170753584,160378560,168188728]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------