TSTP Solution File: GRP159-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP159-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.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 12:29:59 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    :   20 (  20 unt;   0 def)
%            Number of atoms       :   20 (   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;   3 con; 0-2 aty)
%            Number of variables   :   24 (   1 sgn  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(lub_absorbtion,plain,
    ! [A,B] : $equal(least_upper_bound(A,greatest_lower_bound(A,B)),A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
    [] ).

cnf(158595400,plain,
    $equal(least_upper_bound(A,greatest_lower_bound(A,B)),A),
    inference(rewrite,[status(thm)],[lub_absorbtion]),
    [] ).

fof(prove_ax_mono2c,plain,
    ~ $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
    [] ).

cnf(158674480,plain,
    ~ $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)),
    inference(rewrite,[status(thm)],[prove_ax_mono2c]),
    [] ).

fof(monotony_lub1,plain,
    ! [A,B,C] : $equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
    [] ).

cnf(158607056,plain,
    $equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C))),
    inference(rewrite,[status(thm)],[monotony_lub1]),
    [] ).

cnf(166542456,plain,
    ~ $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)),
    inference(paramodulation,[status(thm)],[158674480,158607056,theory(equality)]),
    [] ).

fof(symmetry_of_lub,plain,
    ! [B,A] : $equal(least_upper_bound(B,A),least_upper_bound(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
    [] ).

cnf(158571992,plain,
    $equal(least_upper_bound(B,A),least_upper_bound(A,B)),
    inference(rewrite,[status(thm)],[symmetry_of_lub]),
    [] ).

cnf(166613728,plain,
    ~ $equal(multiply(c,least_upper_bound(b,a)),multiply(c,b)),
    inference(paramodulation,[status(thm)],[166542456,158571992,theory(equality)]),
    [] ).

fof(ax_mono2c_1,plain,
    $equal(greatest_lower_bound(a,b),a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
    [] ).

cnf(158669648,plain,
    $equal(greatest_lower_bound(a,b),a),
    inference(rewrite,[status(thm)],[ax_mono2c_1]),
    [] ).

cnf(166662840,plain,
    ~ $equal(multiply(c,least_upper_bound(b,greatest_lower_bound(a,b))),multiply(c,b)),
    inference(paramodulation,[status(thm)],[166613728,158669648,theory(equality)]),
    [] ).

fof(symmetry_of_glb,plain,
    ! [B,A] : $equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
    [] ).

cnf(158563216,plain,
    $equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B)),
    inference(rewrite,[status(thm)],[symmetry_of_glb]),
    [] ).

cnf(166866696,plain,
    ~ $equal(multiply(c,least_upper_bound(b,greatest_lower_bound(b,a))),multiply(c,b)),
    inference(paramodulation,[status(thm)],[166662840,158563216,theory(equality)]),
    [] ).

cnf(167027088,plain,
    ~ $equal(least_upper_bound(multiply(c,b),multiply(c,greatest_lower_bound(b,a))),multiply(c,b)),
    inference(paramodulation,[status(thm)],[166866696,158607056,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/GRP159-1.tptp',unknown),
    [] ).

cnf(158610848,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(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158595400,167027088,158610848,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(lub_absorbtion,plain,($equal(least_upper_bound(A,greatest_lower_bound(A,B)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
% 
% cnf(158595400,plain,($equal(least_upper_bound(A,greatest_lower_bound(A,B)),A)),inference(rewrite,[status(thm)],[lub_absorbtion]),[]).
% 
% fof(prove_ax_mono2c,plain,(~$equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
% 
% cnf(158674480,plain,(~$equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b))),inference(rewrite,[status(thm)],[prove_ax_mono2c]),[]).
% 
% fof(monotony_lub1,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
% 
% cnf(158607056,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_lub1]),[]).
% 
% cnf(166542456,plain,(~$equal(multiply(c,least_upper_bound(a,b)),multiply(c,b))),inference(paramodulation,[status(thm)],[158674480,158607056,theory(equality)]),[]).
% 
% fof(symmetry_of_lub,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
% 
% cnf(158571992,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_lub]),[]).
% 
% cnf(166613728,plain,(~$equal(multiply(c,least_upper_bound(b,a)),multiply(c,b))),inference(paramodulation,[status(thm)],[166542456,158571992,theory(equality)]),[]).
% 
% fof(ax_mono2c_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
% 
% cnf(158669648,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[ax_mono2c_1]),[]).
% 
% cnf(166662840,plain,(~$equal(multiply(c,least_upper_bound(b,greatest_lower_bound(a,b))),multiply(c,b))),inference(paramodulation,[status(thm)],[166613728,158669648,theory(equality)]),[]).
% 
% fof(symmetry_of_glb,plain,($equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
% 
% cnf(158563216,plain,($equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_glb]),[]).
% 
% cnf(166866696,plain,(~$equal(multiply(c,least_upper_bound(b,greatest_lower_bound(b,a))),multiply(c,b))),inference(paramodulation,[status(thm)],[166662840,158563216,theory(equality)]),[]).
% 
% cnf(167027088,plain,(~$equal(least_upper_bound(multiply(c,b),multiply(c,greatest_lower_bound(b,a))),multiply(c,b))),inference(paramodulation,[status(thm)],[166866696,158607056,theory(equality)]),[]).
% 
% fof(monotony_glb1,plain,($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/GRP159-1.tptp',unknown),[]).
% 
% cnf(158610848,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_glb1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158595400,167027088,158610848,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------