TSTP Solution File: COM007+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COM007+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:36:32 EDT 2009

% Result   : Theorem 0.5s
% Output   : Refutation 0.5s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   42 (  16 unt;   0 def)
%            Number of atoms       :   80 (   0 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   78 (  40   ~;  36   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :   42 (   0 sgn  16   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(substitution,plain,
    ! [A,B,C] :
      ( ~ equalish(A,B)
      | ~ reflexive_rewrite(B,C)
      | reflexive_rewrite(A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140626528,plain,
    ( ~ equalish(A,B)
    | ~ reflexive_rewrite(B,C)
    | reflexive_rewrite(A,C) ),
    inference(rewrite,[status(thm)],[substitution]),
    [] ).

fof(assumption,plain,
    ( reflexive_rewrite(a,b)
    & reflexive_rewrite(a,c) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140588888,plain,
    reflexive_rewrite(a,c),
    inference(rewrite,[status(thm)],[assumption]),
    [] ).

cnf(148513904,plain,
    ( ~ equalish(A,a)
    | reflexive_rewrite(A,c) ),
    inference(resolution,[status(thm)],[140626528,140588888]),
    [] ).

fof(goal_ax,plain,
    ! [A] :
      ( ~ reflexive_rewrite(b,A)
      | ~ reflexive_rewrite(c,A)
      | goal ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140604320,plain,
    ( ~ reflexive_rewrite(b,A)
    | ~ reflexive_rewrite(c,A)
    | goal ),
    inference(rewrite,[status(thm)],[goal_ax]),
    [] ).

fof(goal_to_be_proved,plain,
    ~ goal,
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140702712,plain,
    ~ goal,
    inference(rewrite,[status(thm)],[goal_to_be_proved]),
    [] ).

cnf(148480928,plain,
    ( ~ reflexive_rewrite(b,A)
    | ~ reflexive_rewrite(c,A) ),
    inference(resolution,[status(thm)],[140604320,140702712]),
    [] ).

fof(equalish_in_reflexive_rewrite,plain,
    ! [A,B] :
      ( ~ equalish(A,B)
      | reflexive_rewrite(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140631464,plain,
    ( ~ equalish(A,B)
    | reflexive_rewrite(A,B) ),
    inference(rewrite,[status(thm)],[equalish_in_reflexive_rewrite]),
    [] ).

fof(reflexivity,plain,
    ! [A] : equalish(A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140609168,plain,
    equalish(A,A),
    inference(rewrite,[status(thm)],[reflexivity]),
    [] ).

cnf(148550528,plain,
    reflexive_rewrite(A,A),
    inference(resolution,[status(thm)],[140631464,140609168]),
    [] ).

cnf(148599552,plain,
    ~ reflexive_rewrite(b,c),
    inference(resolution,[status(thm)],[148480928,148550528]),
    [] ).

cnf(149500848,plain,
    ~ equalish(b,a),
    inference(resolution,[status(thm)],[148513904,148599552]),
    [] ).

fof(equalish_or_rewrite,plain,
    ! [A,B] :
      ( ~ reflexive_rewrite(A,B)
      | equalish(A,B)
      | rewrite(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140645120,plain,
    ( ~ reflexive_rewrite(A,B)
    | equalish(A,B)
    | rewrite(A,B) ),
    inference(rewrite,[status(thm)],[equalish_or_rewrite]),
    [] ).

cnf(140596344,plain,
    reflexive_rewrite(a,b),
    inference(rewrite,[status(thm)],[assumption]),
    [] ).

cnf(148530720,plain,
    ( equalish(a,b)
    | rewrite(a,b) ),
    inference(resolution,[status(thm)],[140645120,140596344]),
    [] ).

fof(symmtery,plain,
    ! [A,B] :
      ( ~ equalish(A,B)
      | equalish(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140615784,plain,
    ( ~ equalish(A,B)
    | equalish(B,A) ),
    inference(rewrite,[status(thm)],[symmtery]),
    [] ).

cnf(149011920,plain,
    ( rewrite(a,b)
    | equalish(b,a) ),
    inference(resolution,[status(thm)],[148530720,140615784]),
    [] ).

cnf(149583888,plain,
    rewrite(a,b),
    inference(resolution,[status(thm)],[149500848,149011920]),
    [] ).

cnf(148541056,plain,
    ( ~ equalish(A,a)
    | reflexive_rewrite(A,b) ),
    inference(resolution,[status(thm)],[140626528,140596344]),
    [] ).

cnf(148586720,plain,
    ~ reflexive_rewrite(c,b),
    inference(resolution,[status(thm)],[148480928,148550528]),
    [] ).

cnf(149610696,plain,
    ~ equalish(c,a),
    inference(resolution,[status(thm)],[148541056,148586720]),
    [] ).

cnf(148493608,plain,
    ( equalish(a,c)
    | rewrite(a,c) ),
    inference(resolution,[status(thm)],[140645120,140588888]),
    [] ).

cnf(148939792,plain,
    ( rewrite(a,c)
    | equalish(c,a) ),
    inference(resolution,[status(thm)],[148493608,140615784]),
    [] ).

cnf(149665160,plain,
    rewrite(a,c),
    inference(resolution,[status(thm)],[149610696,148939792]),
    [] ).

fof(rewrite_diamond,plain,
    ! [C,A,B] :
      ( ( rewrite(C,d(A,B,C))
        | ~ rewrite(A,B)
        | ~ rewrite(A,C) )
      & ( rewrite(B,d(A,B,C))
        | ~ rewrite(A,B)
        | ~ rewrite(A,C) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140663840,plain,
    ( rewrite(B,d(A,B,C))
    | ~ rewrite(A,B)
    | ~ rewrite(A,C) ),
    inference(rewrite,[status(thm)],[rewrite_diamond]),
    [] ).

cnf(151899736,plain,
    ( rewrite(b,d(a,b,A))
    | ~ rewrite(a,A) ),
    inference(resolution,[status(thm)],[140663840,149583888]),
    [] ).

cnf(155908512,plain,
    rewrite(b,d(a,b,c)),
    inference(resolution,[status(thm)],[151899736,149665160]),
    [] ).

fof(rewrite_in_reflexive_rewrite,plain,
    ! [A,B] :
      ( ~ rewrite(A,B)
      | reflexive_rewrite(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
    [] ).

cnf(140637744,plain,
    ( ~ rewrite(A,B)
    | reflexive_rewrite(A,B) ),
    inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),
    [] ).

cnf(148637680,plain,
    ( ~ reflexive_rewrite(c,A)
    | ~ rewrite(b,A) ),
    inference(resolution,[status(thm)],[148480928,140637744]),
    [] ).

cnf(148791816,plain,
    ( ~ rewrite(b,A)
    | ~ rewrite(c,A) ),
    inference(resolution,[status(thm)],[148637680,140637744]),
    [] ).

cnf(156282824,plain,
    ~ rewrite(c,d(a,b,c)),
    inference(resolution,[status(thm)],[155908512,148791816]),
    [] ).

cnf(140689384,plain,
    ( rewrite(C,d(A,B,C))
    | ~ rewrite(A,B)
    | ~ rewrite(A,C) ),
    inference(rewrite,[status(thm)],[rewrite_diamond]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[149583888,149665160,156282824,140689384]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(substitution,plain,(~equalish(A,B)|~reflexive_rewrite(B,C)|reflexive_rewrite(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140626528,plain,(~equalish(A,B)|~reflexive_rewrite(B,C)|reflexive_rewrite(A,C)),inference(rewrite,[status(thm)],[substitution]),[]).
% 
% fof(assumption,plain,((reflexive_rewrite(a,b)&reflexive_rewrite(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140588888,plain,(reflexive_rewrite(a,c)),inference(rewrite,[status(thm)],[assumption]),[]).
% 
% cnf(148513904,plain,(~equalish(A,a)|reflexive_rewrite(A,c)),inference(resolution,[status(thm)],[140626528,140588888]),[]).
% 
% fof(goal_ax,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140604320,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),inference(rewrite,[status(thm)],[goal_ax]),[]).
% 
% fof(goal_to_be_proved,plain,(~goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140702712,plain,(~goal),inference(rewrite,[status(thm)],[goal_to_be_proved]),[]).
% 
% cnf(148480928,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)),inference(resolution,[status(thm)],[140604320,140702712]),[]).
% 
% fof(equalish_in_reflexive_rewrite,plain,(~equalish(A,B)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140631464,plain,(~equalish(A,B)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[equalish_in_reflexive_rewrite]),[]).
% 
% fof(reflexivity,plain,(equalish(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140609168,plain,(equalish(A,A)),inference(rewrite,[status(thm)],[reflexivity]),[]).
% 
% cnf(148550528,plain,(reflexive_rewrite(A,A)),inference(resolution,[status(thm)],[140631464,140609168]),[]).
% 
% cnf(148599552,plain,(~reflexive_rewrite(b,c)),inference(resolution,[status(thm)],[148480928,148550528]),[]).
% 
% cnf(149500848,plain,(~equalish(b,a)),inference(resolution,[status(thm)],[148513904,148599552]),[]).
% 
% fof(equalish_or_rewrite,plain,(~reflexive_rewrite(A,B)|equalish(A,B)|rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140645120,plain,(~reflexive_rewrite(A,B)|equalish(A,B)|rewrite(A,B)),inference(rewrite,[status(thm)],[equalish_or_rewrite]),[]).
% 
% cnf(140596344,plain,(reflexive_rewrite(a,b)),inference(rewrite,[status(thm)],[assumption]),[]).
% 
% cnf(148530720,plain,(equalish(a,b)|rewrite(a,b)),inference(resolution,[status(thm)],[140645120,140596344]),[]).
% 
% fof(symmtery,plain,(~equalish(A,B)|equalish(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140615784,plain,(~equalish(A,B)|equalish(B,A)),inference(rewrite,[status(thm)],[symmtery]),[]).
% 
% cnf(149011920,plain,(rewrite(a,b)|equalish(b,a)),inference(resolution,[status(thm)],[148530720,140615784]),[]).
% 
% cnf(149583888,plain,(rewrite(a,b)),inference(resolution,[status(thm)],[149500848,149011920]),[]).
% 
% cnf(148541056,plain,(~equalish(A,a)|reflexive_rewrite(A,b)),inference(resolution,[status(thm)],[140626528,140596344]),[]).
% 
% cnf(148586720,plain,(~reflexive_rewrite(c,b)),inference(resolution,[status(thm)],[148480928,148550528]),[]).
% 
% cnf(149610696,plain,(~equalish(c,a)),inference(resolution,[status(thm)],[148541056,148586720]),[]).
% 
% cnf(148493608,plain,(equalish(a,c)|rewrite(a,c)),inference(resolution,[status(thm)],[140645120,140588888]),[]).
% 
% cnf(148939792,plain,(rewrite(a,c)|equalish(c,a)),inference(resolution,[status(thm)],[148493608,140615784]),[]).
% 
% cnf(149665160,plain,(rewrite(a,c)),inference(resolution,[status(thm)],[149610696,148939792]),[]).
% 
% fof(rewrite_diamond,plain,(((rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C))&(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140663840,plain,(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
% 
% cnf(151899736,plain,(rewrite(b,d(a,b,A))|~rewrite(a,A)),inference(resolution,[status(thm)],[140663840,149583888]),[]).
% 
% cnf(155908512,plain,(rewrite(b,d(a,b,c))),inference(resolution,[status(thm)],[151899736,149665160]),[]).
% 
% fof(rewrite_in_reflexive_rewrite,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
% 
% cnf(140637744,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),[]).
% 
% cnf(148637680,plain,(~reflexive_rewrite(c,A)|~rewrite(b,A)),inference(resolution,[status(thm)],[148480928,140637744]),[]).
% 
% cnf(148791816,plain,(~rewrite(b,A)|~rewrite(c,A)),inference(resolution,[status(thm)],[148637680,140637744]),[]).
% 
% cnf(156282824,plain,(~rewrite(c,d(a,b,c))),inference(resolution,[status(thm)],[155908512,148791816]),[]).
% 
% cnf(140689384,plain,(rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[149583888,149665160,156282824,140689384]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------