TSTP Solution File: COL064-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL064-2 : TPTP v3.4.2. Bugfixed v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.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 11:33:36 EDT 2009

% Result   : Unsatisfiable 0.5s
% Output   : Refutation 0.5s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   15 (  15 unt;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   10 (  10   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(b_definition,plain,
    ! [A,B,C] : $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-2.tptp',unknown),
    [] ).

cnf(160298192,plain,
    $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
    inference(rewrite,[status(thm)],[b_definition]),
    [] ).

fof(prove_v_combinator,plain,
    ~ $equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z),apply(apply(z,x),y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-2.tptp',unknown),
    [] ).

cnf(160307656,plain,
    ~ $equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z),apply(apply(z,x),y)),
    inference(rewrite,[status(thm)],[prove_v_combinator]),
    [] ).

cnf(168693136,plain,
    ~ $equal(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[160307656,160298192,theory(equality)]),
    [] ).

fof(t_definition,plain,
    ! [A,B] : $equal(apply(apply(t,A),B),apply(B,A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-2.tptp',unknown),
    [] ).

cnf(160302392,plain,
    $equal(apply(apply(t,A),B),apply(B,A)),
    inference(rewrite,[status(thm)],[t_definition]),
    [] ).

cnf(172287528,plain,
    ~ $equal(apply(apply(apply(apply(apply(apply(b,b),apply(apply(b,b),t)),x),apply(apply(b,b),t)),y),z),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[168693136,160302392,theory(equality)]),
    [] ).

cnf(178401912,plain,
    ~ $equal(apply(apply(apply(apply(b,apply(apply(apply(b,b),t),x)),apply(apply(b,b),t)),y),z),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[172287528,160298192,theory(equality)]),
    [] ).

cnf(182882184,plain,
    ~ $equal(apply(apply(apply(apply(apply(b,b),t),x),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[178401912,160298192,theory(equality)]),
    [] ).

cnf(183236392,plain,
    ~ $equal(apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[182882184,160298192,theory(equality)]),
    [] ).

cnf(183505624,plain,
    ~ $equal(apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[183236392,160298192,theory(equality)]),
    [] ).

cnf(183555792,plain,
    ~ $equal(apply(apply(apply(apply(apply(b,b),t),y),z),x),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[183505624,160302392,theory(equality)]),
    [] ).

cnf(183879024,plain,
    ~ $equal(apply(apply(apply(b,apply(t,y)),z),x),apply(apply(z,x),y)),
    inference(paramodulation,[status(thm)],[183555792,160298192,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[160298192,183879024,160302392,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-2.tptp',unknown),[]).
% 
% cnf(160298192,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
% 
% fof(prove_v_combinator,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z),apply(apply(z,x),y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-2.tptp',unknown),[]).
% 
% cnf(160307656,plain,(~$equal(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z),apply(apply(z,x),y))),inference(rewrite,[status(thm)],[prove_v_combinator]),[]).
% 
% cnf(168693136,plain,(~$equal(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[160307656,160298192,theory(equality)]),[]).
% 
% fof(t_definition,plain,($equal(apply(apply(t,A),B),apply(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL064-2.tptp',unknown),[]).
% 
% cnf(160302392,plain,($equal(apply(apply(t,A),B),apply(B,A))),inference(rewrite,[status(thm)],[t_definition]),[]).
% 
% cnf(172287528,plain,(~$equal(apply(apply(apply(apply(apply(apply(b,b),apply(apply(b,b),t)),x),apply(apply(b,b),t)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[168693136,160302392,theory(equality)]),[]).
% 
% cnf(178401912,plain,(~$equal(apply(apply(apply(apply(b,apply(apply(apply(b,b),t),x)),apply(apply(b,b),t)),y),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[172287528,160298192,theory(equality)]),[]).
% 
% cnf(182882184,plain,(~$equal(apply(apply(apply(apply(apply(b,b),t),x),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[178401912,160298192,theory(equality)]),[]).
% 
% cnf(183236392,plain,(~$equal(apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[182882184,160298192,theory(equality)]),[]).
% 
% cnf(183505624,plain,(~$equal(apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[183236392,160298192,theory(equality)]),[]).
% 
% cnf(183555792,plain,(~$equal(apply(apply(apply(apply(apply(b,b),t),y),z),x),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[183505624,160302392,theory(equality)]),[]).
% 
% cnf(183879024,plain,(~$equal(apply(apply(apply(b,apply(t,y)),z),x),apply(apply(z,x),y))),inference(paramodulation,[status(thm)],[183555792,160298192,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[160298192,183879024,160302392,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------