TSTP Solution File: GRP168-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP168-1 : 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 12:30:35 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/GRP168-1.tptp',unknown),
[] ).
cnf(164631544,plain,
$equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C)),
inference(rewrite,[status(thm)],[associativity]),
[] ).
fof(prove_p01a,plain,
~ $equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),
[] ).
cnf(164751960,plain,
~ $equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c))),
inference(rewrite,[status(thm)],[prove_p01a]),
[] ).
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/GRP168-1.tptp',unknown),
[] ).
cnf(164684192,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(172719304,plain,
~ $equal(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),multiply(b,c))),
inference(paramodulation,[status(thm)],[164751960,164684192,theory(equality)]),
[] ).
fof(monotony_lub2,plain,
! [A,C,B] : $equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),
[] ).
cnf(164717192,plain,
$equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C)),
inference(rewrite,[status(thm)],[monotony_lub2]),
[] ).
cnf(172835880,plain,
~ $equal(multiply(inverse(c),multiply(least_upper_bound(a,b),c)),multiply(inverse(c),multiply(b,c))),
inference(paramodulation,[status(thm)],[172719304,164717192,theory(equality)]),
[] ).
cnf(172957192,plain,
~ $equal(multiply(inverse(c),multiply(least_upper_bound(a,b),c)),multiply(multiply(inverse(c),b),c)),
inference(paramodulation,[status(thm)],[172835880,164631544,theory(equality)]),
[] ).
fof(p01a_1,plain,
$equal(least_upper_bound(a,b),b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),
[] ).
cnf(164746784,plain,
$equal(least_upper_bound(a,b),b),
inference(rewrite,[status(thm)],[p01a_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164631544,172957192,164746784,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(associativity,plain,($equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),[]).
%
% cnf(164631544,plain,($equal(multiply(A,multiply(B,C)),multiply(multiply(A,B),C))),inference(rewrite,[status(thm)],[associativity]),[]).
%
% fof(prove_p01a,plain,(~$equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),[]).
%
% cnf(164751960,plain,(~$equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c)))),inference(rewrite,[status(thm)],[prove_p01a]),[]).
%
% fof(monotony_lub1,plain,($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/GRP168-1.tptp',unknown),[]).
%
% cnf(164684192,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_lub1]),[]).
%
% cnf(172719304,plain,(~$equal(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),multiply(b,c)))),inference(paramodulation,[status(thm)],[164751960,164684192,theory(equality)]),[]).
%
% fof(monotony_lub2,plain,($equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),[]).
%
% cnf(164717192,plain,($equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_lub2]),[]).
%
% cnf(172835880,plain,(~$equal(multiply(inverse(c),multiply(least_upper_bound(a,b),c)),multiply(inverse(c),multiply(b,c)))),inference(paramodulation,[status(thm)],[172719304,164717192,theory(equality)]),[]).
%
% cnf(172957192,plain,(~$equal(multiply(inverse(c),multiply(least_upper_bound(a,b),c)),multiply(multiply(inverse(c),b),c))),inference(paramodulation,[status(thm)],[172835880,164631544,theory(equality)]),[]).
%
% fof(p01a_1,plain,($equal(least_upper_bound(a,b),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP168-1.tptp',unknown),[]).
%
% cnf(164746784,plain,($equal(least_upper_bound(a,b),b)),inference(rewrite,[status(thm)],[p01a_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164631544,172957192,164746784,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------