TSTP Solution File: SET025-9 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET025-9 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:24:38 EDT 2009
% Result : Unsatisfiable 5.7s
% Output : Refutation 5.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 9 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(universal_set,plain,
! [A] :
( member(A,universal_set)
| ~ little_set(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(145953048,plain,
( member(A,universal_set)
| ~ little_set(A) ),
inference(rewrite,[status(thm)],[universal_set]),
[] ).
fof(non_ordered_pair4,plain,
! [A,B] : little_set(non_ordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(145382456,plain,
little_set(non_ordered_pair(A,B)),
inference(rewrite,[status(thm)],[non_ordered_pair4]),
[] ).
cnf(165364800,plain,
member(non_ordered_pair(A,B),universal_set),
inference(resolution,[status(thm)],[145953048,145382456]),
[] ).
fof(ordered_pair,plain,
! [A,B] : $equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(145287896,plain,
$equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B)),
inference(rewrite,[status(thm)],[ordered_pair]),
[] ).
cnf(166919080,plain,
member(ordered_pair(A,B),universal_set),
inference(paramodulation,[status(thm)],[165364800,145287896,theory(equality)]),
[] ).
fof(a2,plain,
! [A,B] :
( ~ member(A,B)
| little_set(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(145291888,plain,
( ~ member(A,B)
| little_set(A) ),
inference(rewrite,[status(thm)],[a2]),
[] ).
cnf(168210136,plain,
little_set(ordered_pair(A,B)),
inference(resolution,[status(thm)],[166919080,145291888]),
[] ).
fof(ordered_pair_predicate3,plain,
! [A] :
( ~ ordered_pair_predicate(A)
| $equal(ordered_pair(f2(A),f3(A)),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(145426824,plain,
( ~ ordered_pair_predicate(A)
| $equal(ordered_pair(f2(A),f3(A)),A) ),
inference(rewrite,[status(thm)],[ordered_pair_predicate3]),
[] ).
fof(an_ordered_pair_predicate,plain,
ordered_pair_predicate(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(145284464,plain,
ordered_pair_predicate(a),
inference(rewrite,[status(thm)],[an_ordered_pair_predicate]),
[] ).
cnf(156588752,plain,
$equal(ordered_pair(f2(a),f3(a)),a),
inference(resolution,[status(thm)],[145426824,145284464]),
[] ).
fof(prove_predicate_is_small,plain,
~ little_set(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),
[] ).
cnf(146965312,plain,
~ little_set(a),
inference(rewrite,[status(thm)],[prove_predicate_is_small]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168210136,156588752,146965312,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 5 seconds
% START OF PROOF SEQUENCE
% fof(universal_set,plain,(member(A,universal_set)|~little_set(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(145953048,plain,(member(A,universal_set)|~little_set(A)),inference(rewrite,[status(thm)],[universal_set]),[]).
%
% fof(non_ordered_pair4,plain,(little_set(non_ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(145382456,plain,(little_set(non_ordered_pair(A,B))),inference(rewrite,[status(thm)],[non_ordered_pair4]),[]).
%
% cnf(165364800,plain,(member(non_ordered_pair(A,B),universal_set)),inference(resolution,[status(thm)],[145953048,145382456]),[]).
%
% fof(ordered_pair,plain,($equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(145287896,plain,($equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
%
% cnf(166919080,plain,(member(ordered_pair(A,B),universal_set)),inference(paramodulation,[status(thm)],[165364800,145287896,theory(equality)]),[]).
%
% fof(a2,plain,(~member(A,B)|little_set(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(145291888,plain,(~member(A,B)|little_set(A)),inference(rewrite,[status(thm)],[a2]),[]).
%
% cnf(168210136,plain,(little_set(ordered_pair(A,B))),inference(resolution,[status(thm)],[166919080,145291888]),[]).
%
% fof(ordered_pair_predicate3,plain,(~ordered_pair_predicate(A)|$equal(ordered_pair(f2(A),f3(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(145426824,plain,(~ordered_pair_predicate(A)|$equal(ordered_pair(f2(A),f3(A)),A)),inference(rewrite,[status(thm)],[ordered_pair_predicate3]),[]).
%
% fof(an_ordered_pair_predicate,plain,(ordered_pair_predicate(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(145284464,plain,(ordered_pair_predicate(a)),inference(rewrite,[status(thm)],[an_ordered_pair_predicate]),[]).
%
% cnf(156588752,plain,($equal(ordered_pair(f2(a),f3(a)),a)),inference(resolution,[status(thm)],[145426824,145284464]),[]).
%
% fof(prove_predicate_is_small,plain,(~little_set(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-9.tptp',unknown),[]).
%
% cnf(146965312,plain,(~little_set(a)),inference(rewrite,[status(thm)],[prove_predicate_is_small]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168210136,156588752,146965312,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------