TSTP Solution File: GRP170-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP170-2 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.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 12:30:45 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  18 unt;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    7 (   7   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(monotony_glb2,plain,
    ! [A,C,B] : $equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
    [] ).

cnf(158406744,plain,
    $equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
    inference(rewrite,[status(thm)],[monotony_glb2]),
    [] ).

fof(prove_p03b,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
    [] ).

cnf(158288896,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
    inference(rewrite,[status(thm)],[prove_p03b]),
    [] ).

fof(p03b_1,plain,
    $equal(greatest_lower_bound(a,b),a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
    [] ).

cnf(158414488,plain,
    $equal(greatest_lower_bound(a,b),a),
    inference(rewrite,[status(thm)],[p03b_1]),
    [] ).

cnf(166258392,plain,
    ~ $equal(greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,d)),multiply(a,c)),
    inference(paramodulation,[status(thm)],[158288896,158414488,theory(equality)]),
    [] ).

cnf(166602184,plain,
    ~ $equal(greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(b,d)),multiply(a,c)),
    inference(paramodulation,[status(thm)],[166258392,158406744,theory(equality)]),
    [] ).

fof(associativity_of_glb,plain,
    ! [A,B,C] : $equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
    [] ).

cnf(158324880,plain,
    $equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C))),
    inference(rewrite,[status(thm)],[associativity_of_glb]),
    [] ).

cnf(168743464,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),multiply(b,d))),multiply(a,c)),
    inference(paramodulation,[status(thm)],[166602184,158324880,theory(equality)]),
    [] ).

fof(monotony_glb1,plain,
    ! [A,B,C] : $equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
    [] ).

cnf(158355688,plain,
    $equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C))),
    inference(rewrite,[status(thm)],[monotony_glb1]),
    [] ).

cnf(174853936,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))),multiply(a,c)),
    inference(paramodulation,[status(thm)],[168743464,158355688,theory(equality)]),
    [] ).

fof(p03b_2,plain,
    $equal(greatest_lower_bound(c,d),c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
    [] ).

cnf(158418464,plain,
    $equal(greatest_lower_bound(c,d),c),
    inference(rewrite,[status(thm)],[p03b_2]),
    [] ).

cnf(175744672,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c)),
    inference(paramodulation,[status(thm)],[174853936,158418464,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158406744,175744672,158414488,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(monotony_glb2,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
% 
% cnf(158406744,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_glb2]),[]).
% 
% fof(prove_p03b,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
% 
% cnf(158288896,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c))),inference(rewrite,[status(thm)],[prove_p03b]),[]).
% 
% fof(p03b_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
% 
% cnf(158414488,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[p03b_1]),[]).
% 
% cnf(166258392,plain,(~$equal(greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,d)),multiply(a,c))),inference(paramodulation,[status(thm)],[158288896,158414488,theory(equality)]),[]).
% 
% cnf(166602184,plain,(~$equal(greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(b,d)),multiply(a,c))),inference(paramodulation,[status(thm)],[166258392,158406744,theory(equality)]),[]).
% 
% fof(associativity_of_glb,plain,($equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
% 
% cnf(158324880,plain,($equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[associativity_of_glb]),[]).
% 
% cnf(168743464,plain,(~$equal(greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),multiply(b,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[166602184,158324880,theory(equality)]),[]).
% 
% fof(monotony_glb1,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
% 
% cnf(158355688,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_glb1]),[]).
% 
% cnf(174853936,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[168743464,158355688,theory(equality)]),[]).
% 
% fof(p03b_2,plain,($equal(greatest_lower_bound(c,d),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
% 
% cnf(158418464,plain,($equal(greatest_lower_bound(c,d),c)),inference(rewrite,[status(thm)],[p03b_2]),[]).
% 
% cnf(175744672,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c))),inference(paramodulation,[status(thm)],[174853936,158418464,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158406744,175744672,158414488,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------