TSTP Solution File: SET016-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET016-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:23:46 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(unordered_pair_1,plain,
! [A,B] : member(A,unordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166069304,plain,
member(A,unordered_pair(A,B)),
inference(rewrite,[status(thm)],[unordered_pair_1]),
[] ).
fof(unordered_pair_3,plain,
! [A,B,C] :
( ~ member(A,unordered_pair(B,C))
| $equal(B,A)
| $equal(C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166080208,plain,
( ~ member(A,unordered_pair(B,C))
| $equal(B,A)
| $equal(C,A) ),
inference(rewrite,[status(thm)],[unordered_pair_3]),
[] ).
fof(ordered_pair,plain,
! [A,B] : $equal(unordered_pair(singleton_set(A),unordered_pair(A,B)),ordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166089192,plain,
$equal(unordered_pair(singleton_set(A),unordered_pair(A,B)),ordered_pair(A,B)),
inference(rewrite,[status(thm)],[ordered_pair]),
[] ).
cnf(174007632,plain,
( ~ member(A,ordered_pair(B,C))
| $equal(singleton_set(B),A)
| $equal(unordered_pair(B,C),A) ),
inference(paramodulation,[status(thm)],[166080208,166089192,theory(equality)]),
[] ).
fof(equal_ordered_pairs,plain,
$equal(ordered_pair(m2,r2),ordered_pair(m1,r1)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166093168,plain,
$equal(ordered_pair(m2,r2),ordered_pair(m1,r1)),
inference(rewrite,[status(thm)],[equal_ordered_pairs]),
[] ).
cnf(174076576,plain,
( ~ member(A,ordered_pair(m2,r2))
| $equal(singleton_set(m1),A)
| $equal(unordered_pair(m1,r1),A) ),
inference(paramodulation,[status(thm)],[174007632,166093168,theory(equality)]),
[] ).
cnf(174162232,plain,
( ~ member(A,unordered_pair(singleton_set(m2),unordered_pair(m2,r2)))
| $equal(singleton_set(m1),A)
| $equal(unordered_pair(m1,r1),A) ),
inference(paramodulation,[status(thm)],[174076576,166089192,theory(equality)]),
[] ).
cnf(174183168,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| $equal(unordered_pair(m1,r1),singleton_set(m2)) ),
inference(resolution,[status(thm)],[174162232,166069304]),
[] ).
fof(singleton_2,plain,
! [A,B] :
( ~ member(A,singleton_set(B))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166065184,plain,
( ~ member(A,singleton_set(B))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[singleton_2]),
[] ).
fof(prove_first_components_equal,plain,
~ $equal(m2,m1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166097952,plain,
~ $equal(m2,m1),
inference(rewrite,[status(thm)],[prove_first_components_equal]),
[] ).
cnf(173902232,plain,
~ member(m1,singleton_set(m2)),
inference(resolution,[status(thm)],[166065184,166097952]),
[] ).
cnf(174252880,plain,
$equal(singleton_set(m1),singleton_set(m2)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[166069304,174183168,173902232,theory(equality)]),
[] ).
fof(singleton_1,plain,
! [A] : member(A,singleton_set(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),
[] ).
cnf(166055280,plain,
member(A,singleton_set(A)),
inference(rewrite,[status(thm)],[singleton_1]),
[] ).
cnf(174369664,plain,
member(m1,singleton_set(m2)),
inference(paramodulation,[status(thm)],[174252880,166055280,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[174369664,173902232]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pair_1,plain,(member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166069304,plain,(member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair_1]),[]).
%
% fof(unordered_pair_3,plain,(~member(A,unordered_pair(B,C))|$equal(B,A)|$equal(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166080208,plain,(~member(A,unordered_pair(B,C))|$equal(B,A)|$equal(C,A)),inference(rewrite,[status(thm)],[unordered_pair_3]),[]).
%
% fof(ordered_pair,plain,($equal(unordered_pair(singleton_set(A),unordered_pair(A,B)),ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166089192,plain,($equal(unordered_pair(singleton_set(A),unordered_pair(A,B)),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
%
% cnf(174007632,plain,(~member(A,ordered_pair(B,C))|$equal(singleton_set(B),A)|$equal(unordered_pair(B,C),A)),inference(paramodulation,[status(thm)],[166080208,166089192,theory(equality)]),[]).
%
% fof(equal_ordered_pairs,plain,($equal(ordered_pair(m2,r2),ordered_pair(m1,r1))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166093168,plain,($equal(ordered_pair(m2,r2),ordered_pair(m1,r1))),inference(rewrite,[status(thm)],[equal_ordered_pairs]),[]).
%
% cnf(174076576,plain,(~member(A,ordered_pair(m2,r2))|$equal(singleton_set(m1),A)|$equal(unordered_pair(m1,r1),A)),inference(paramodulation,[status(thm)],[174007632,166093168,theory(equality)]),[]).
%
% cnf(174162232,plain,(~member(A,unordered_pair(singleton_set(m2),unordered_pair(m2,r2)))|$equal(singleton_set(m1),A)|$equal(unordered_pair(m1,r1),A)),inference(paramodulation,[status(thm)],[174076576,166089192,theory(equality)]),[]).
%
% cnf(174183168,plain,($equal(singleton_set(m1),singleton_set(m2))|$equal(unordered_pair(m1,r1),singleton_set(m2))),inference(resolution,[status(thm)],[174162232,166069304]),[]).
%
% fof(singleton_2,plain,(~member(A,singleton_set(B))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166065184,plain,(~member(A,singleton_set(B))|$equal(B,A)),inference(rewrite,[status(thm)],[singleton_2]),[]).
%
% fof(prove_first_components_equal,plain,(~$equal(m2,m1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166097952,plain,(~$equal(m2,m1)),inference(rewrite,[status(thm)],[prove_first_components_equal]),[]).
%
% cnf(173902232,plain,(~member(m1,singleton_set(m2))),inference(resolution,[status(thm)],[166065184,166097952]),[]).
%
% cnf(174252880,plain,($equal(singleton_set(m1),singleton_set(m2))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[166069304,174183168,173902232,theory(equality)]),[]).
%
% fof(singleton_1,plain,(member(A,singleton_set(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET016-1.tptp',unknown),[]).
%
% cnf(166055280,plain,(member(A,singleton_set(A))),inference(rewrite,[status(thm)],[singleton_1]),[]).
%
% cnf(174369664,plain,(member(m1,singleton_set(m2))),inference(paramodulation,[status(thm)],[174252880,166055280,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[174369664,173902232]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------