TSTP Solution File: GRP168-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP168-2 : 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 12:30:37 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (  14 unt;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   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   :   18 (   0 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associativity,plain,
    ! [A,B,C] : $equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),
    [] ).

cnf(149038072,plain,
    $equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C)),
    inference(rewrite,[status(thm)],[associativity]),
    [] ).

fof(prove_p01b,plain,
    ~ $equal(greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(a,c))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),
    [] ).

cnf(149158488,plain,
    ~ $equal(greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(a,c))),
    inference(rewrite,[status(thm)],[prove_p01b]),
    [] ).

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/GRP168-2.tptp',unknown),
    [] ).

cnf(149094512,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(157128240,plain,
    ~ $equal(multiply(inverse(c),greatest_lower_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),multiply(a,c))),
    inference(paramodulation,[status(thm)],[149158488,149094512,theory(equality)]),
    [] ).

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/GRP168-2.tptp',unknown),
    [] ).

cnf(149145568,plain,
    $equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
    inference(rewrite,[status(thm)],[monotony_glb2]),
    [] ).

cnf(157244824,plain,
    ~ $equal(multiply(inverse(c),multiply(greatest_lower_bound(a,b),c)),multiply(inverse(c),multiply(a,c))),
    inference(paramodulation,[status(thm)],[157128240,149145568,theory(equality)]),
    [] ).

cnf(157365320,plain,
    ~ $equal(multiply(inverse(c),multiply(greatest_lower_bound(a,b),c)),multiply(multiply(inverse(c),a),c)),
    inference(paramodulation,[status(thm)],[157244824,149038072,theory(equality)]),
    [] ).

fof(p01b_1,plain,
    $equal(greatest_lower_bound(a,b),a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),
    [] ).

cnf(149153312,plain,
    $equal(greatest_lower_bound(a,b),a),
    inference(rewrite,[status(thm)],[p01b_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[149038072,157365320,149153312,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(associativity,plain,($equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),[]).
% 
% cnf(149038072,plain,($equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C))),inference(rewrite,[status(thm)],[associativity]),[]).
% 
% fof(prove_p01b,plain,(~$equal(greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(a,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),[]).
% 
% cnf(149158488,plain,(~$equal(greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(a,c)))),inference(rewrite,[status(thm)],[prove_p01b]),[]).
% 
% fof(monotony_glb1,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),[]).
% 
% cnf(149094512,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_glb1]),[]).
% 
% cnf(157128240,plain,(~$equal(multiply(inverse(c),greatest_lower_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),multiply(a,c)))),inference(paramodulation,[status(thm)],[149158488,149094512,theory(equality)]),[]).
% 
% fof(monotony_glb2,plain,($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/GRP168-2.tptp',unknown),[]).
% 
% cnf(149145568,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_glb2]),[]).
% 
% cnf(157244824,plain,(~$equal(multiply(inverse(c),multiply(greatest_lower_bound(a,b),c)),multiply(inverse(c),multiply(a,c)))),inference(paramodulation,[status(thm)],[157128240,149145568,theory(equality)]),[]).
% 
% cnf(157365320,plain,(~$equal(multiply(inverse(c),multiply(greatest_lower_bound(a,b),c)),multiply(multiply(inverse(c),a),c))),inference(paramodulation,[status(thm)],[157244824,149038072,theory(equality)]),[]).
% 
% fof(p01b_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-2.tptp',unknown),[]).
% 
% cnf(149153312,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[p01b_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[149038072,157365320,149153312,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------