TSTP Solution File: COM007+2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COM007+2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 11:36:35 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (  12 unt;   0 def)
%            Number of atoms       :   62 (   0 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   60 (  30   ~;  28   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :   28 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(equal_or_rewrite,plain,
    ! [A,B] :
      ( ~ reflexive_rewrite(A,B)
      | $equal(B,A)
      | rewrite(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
    [] ).

cnf(150221504,plain,
    ( ~ reflexive_rewrite(A,B)
    | $equal(B,A)
    | rewrite(A,B) ),
    inference(rewrite,[status(thm)],[equal_or_rewrite]),
    [] ).

fof(assumption,plain,
    ( reflexive_rewrite(a,b)
    & reflexive_rewrite(a,c) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
    [] ).

cnf(150181504,plain,
    reflexive_rewrite(a,b),
    inference(rewrite,[status(thm)],[assumption]),
    [] ).

cnf(158087728,plain,
    ( $equal(b,a)
    | rewrite(a,b) ),
    inference(resolution,[status(thm)],[150221504,150181504]),
    [] ).

cnf(150174048,plain,
    reflexive_rewrite(a,c),
    inference(rewrite,[status(thm)],[assumption]),
    [] ).

cnf(158378592,plain,
    ( rewrite(a,b)
    | reflexive_rewrite(b,c) ),
    inference(paramodulation,[status(thm)],[158087728,150174048,theory(equality)]),
    [] ).

fof(goal_ax,plain,
    ! [A] :
      ( ~ reflexive_rewrite(b,A)
      | ~ reflexive_rewrite(c,A)
      | goal ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
    [] ).

cnf(150189480,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+2.tptp',unknown),
    [] ).

cnf(150271768,plain,
    ~ goal,
    inference(rewrite,[status(thm)],[goal_to_be_proved]),
    [] ).

cnf(158058096,plain,
    ( ~ reflexive_rewrite(b,A)
    | ~ reflexive_rewrite(c,A) ),
    inference(resolution,[status(thm)],[150189480,150271768]),
    [] ).

fof(equal_in_reflexive_rewrite,plain,
    ! [B,A] :
      ( ~ $equal(B,A)
      | reflexive_rewrite(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
    [] ).

cnf(150203416,plain,
    ( ~ $equal(B,A)
    | reflexive_rewrite(A,B) ),
    inference(rewrite,[status(thm)],[equal_in_reflexive_rewrite]),
    [] ).

cnf(158111360,plain,
    reflexive_rewrite(A,A),
    inference(equality_resolution,[status(thm)],[150203416]),
    [] ).

cnf(158141816,plain,
    ~ reflexive_rewrite(b,c),
    inference(resolution,[status(thm)],[158058096,158111360]),
    [] ).

cnf(158447096,plain,
    rewrite(a,b),
    inference(resolution,[status(thm)],[158378592,158141816]),
    [] ).

cnf(158073192,plain,
    ( $equal(c,a)
    | rewrite(a,c) ),
    inference(resolution,[status(thm)],[150221504,150174048]),
    [] ).

cnf(158348424,plain,
    ( rewrite(a,c)
    | reflexive_rewrite(c,b) ),
    inference(paramodulation,[status(thm)],[158073192,150181504,theory(equality)]),
    [] ).

cnf(158128984,plain,
    ~ reflexive_rewrite(c,b),
    inference(resolution,[status(thm)],[158058096,158111360]),
    [] ).

cnf(158410712,plain,
    rewrite(a,c),
    inference(resolution,[status(thm)],[158348424,158128984]),
    [] ).

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+2.tptp',unknown),
    [] ).

cnf(150258440,plain,
    ( rewrite(C,d(A,B,C))
    | ~ rewrite(A,B)
    | ~ rewrite(A,C) ),
    inference(rewrite,[status(thm)],[rewrite_diamond]),
    [] ).

cnf(150240232,plain,
    ( rewrite(B,d(A,B,C))
    | ~ rewrite(A,B)
    | ~ rewrite(A,C) ),
    inference(rewrite,[status(thm)],[rewrite_diamond]),
    [] ).

cnf(158502496,plain,
    ( rewrite(c,d(a,c,A))
    | ~ rewrite(a,A) ),
    inference(resolution,[status(thm)],[150240232,158410712]),
    [] ).

cnf(159075944,plain,
    rewrite(c,d(a,c,b)),
    inference(resolution,[status(thm)],[158502496,158447096]),
    [] ).

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+2.tptp',unknown),
    [] ).

cnf(150210032,plain,
    ( ~ rewrite(A,B)
    | reflexive_rewrite(A,B) ),
    inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),
    [] ).

cnf(158183224,plain,
    ( ~ reflexive_rewrite(c,A)
    | ~ rewrite(b,A) ),
    inference(resolution,[status(thm)],[158058096,150210032]),
    [] ).

cnf(158300224,plain,
    ( ~ rewrite(b,A)
    | ~ rewrite(c,A) ),
    inference(resolution,[status(thm)],[158183224,150210032]),
    [] ).

cnf(159280720,plain,
    ~ rewrite(b,d(a,c,b)),
    inference(resolution,[status(thm)],[159075944,158300224]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[158447096,158410712,150258440,159280720]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(equal_or_rewrite,plain,(~reflexive_rewrite(A,B)|$equal(B,A)|rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
% 
% cnf(150221504,plain,(~reflexive_rewrite(A,B)|$equal(B,A)|rewrite(A,B)),inference(rewrite,[status(thm)],[equal_or_rewrite]),[]).
% 
% fof(assumption,plain,((reflexive_rewrite(a,b)&reflexive_rewrite(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
% 
% cnf(150181504,plain,(reflexive_rewrite(a,b)),inference(rewrite,[status(thm)],[assumption]),[]).
% 
% cnf(158087728,plain,($equal(b,a)|rewrite(a,b)),inference(resolution,[status(thm)],[150221504,150181504]),[]).
% 
% cnf(150174048,plain,(reflexive_rewrite(a,c)),inference(rewrite,[status(thm)],[assumption]),[]).
% 
% cnf(158378592,plain,(rewrite(a,b)|reflexive_rewrite(b,c)),inference(paramodulation,[status(thm)],[158087728,150174048,theory(equality)]),[]).
% 
% fof(goal_ax,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
% 
% cnf(150189480,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),inference(rewrite,[status(thm)],[goal_ax]),[]).
% 
% fof(goal_to_be_proved,plain,(~goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
% 
% cnf(150271768,plain,(~goal),inference(rewrite,[status(thm)],[goal_to_be_proved]),[]).
% 
% cnf(158058096,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)),inference(resolution,[status(thm)],[150189480,150271768]),[]).
% 
% fof(equal_in_reflexive_rewrite,plain,(~$equal(B,A)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
% 
% cnf(150203416,plain,(~$equal(B,A)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[equal_in_reflexive_rewrite]),[]).
% 
% cnf(158111360,plain,(reflexive_rewrite(A,A)),inference(equality_resolution,[status(thm)],[150203416]),[]).
% 
% cnf(158141816,plain,(~reflexive_rewrite(b,c)),inference(resolution,[status(thm)],[158058096,158111360]),[]).
% 
% cnf(158447096,plain,(rewrite(a,b)),inference(resolution,[status(thm)],[158378592,158141816]),[]).
% 
% cnf(158073192,plain,($equal(c,a)|rewrite(a,c)),inference(resolution,[status(thm)],[150221504,150174048]),[]).
% 
% cnf(158348424,plain,(rewrite(a,c)|reflexive_rewrite(c,b)),inference(paramodulation,[status(thm)],[158073192,150181504,theory(equality)]),[]).
% 
% cnf(158128984,plain,(~reflexive_rewrite(c,b)),inference(resolution,[status(thm)],[158058096,158111360]),[]).
% 
% cnf(158410712,plain,(rewrite(a,c)),inference(resolution,[status(thm)],[158348424,158128984]),[]).
% 
% 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+2.tptp',unknown),[]).
% 
% cnf(150258440,plain,(rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
% 
% cnf(150240232,plain,(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
% 
% cnf(158502496,plain,(rewrite(c,d(a,c,A))|~rewrite(a,A)),inference(resolution,[status(thm)],[150240232,158410712]),[]).
% 
% cnf(159075944,plain,(rewrite(c,d(a,c,b))),inference(resolution,[status(thm)],[158502496,158447096]),[]).
% 
% fof(rewrite_in_reflexive_rewrite,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
% 
% cnf(150210032,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),[]).
% 
% cnf(158183224,plain,(~reflexive_rewrite(c,A)|~rewrite(b,A)),inference(resolution,[status(thm)],[158058096,150210032]),[]).
% 
% cnf(158300224,plain,(~rewrite(b,A)|~rewrite(c,A)),inference(resolution,[status(thm)],[158183224,150210032]),[]).
% 
% cnf(159280720,plain,(~rewrite(b,d(a,c,b))),inference(resolution,[status(thm)],[159075944,158300224]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[158447096,158410712,150258440,159280720]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------