TSTP Solution File: SET018-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET018-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:23:58 EDT 2009
% Result : Unsatisfiable 72.2s
% Output : Refutation 72.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 27 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 20 ~; 68 |; 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 : 33 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET018-1.tptp',unknown),
[] ).
cnf(161027384,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/SET018-1.tptp',unknown),
[] ).
cnf(161036368,plain,
$equal(unordered_pair(singleton_set(A),unordered_pair(A,B)),ordered_pair(A,B)),
inference(rewrite,[status(thm)],[ordered_pair]),
[] ).
cnf(168956296,plain,
( ~ member(A,ordered_pair(B,C))
| $equal(singleton_set(B),A)
| $equal(unordered_pair(B,C),A) ),
inference(paramodulation,[status(thm)],[161027384,161036368,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/SET018-1.tptp',unknown),
[] ).
cnf(161040344,plain,
$equal(ordered_pair(m2,r2),ordered_pair(m1,r1)),
inference(rewrite,[status(thm)],[equal_ordered_pairs]),
[] ).
cnf(169025240,plain,
( ~ member(A,ordered_pair(m2,r2))
| $equal(singleton_set(m1),A)
| $equal(unordered_pair(m1,r1),A) ),
inference(paramodulation,[status(thm)],[168956296,161040344,theory(equality)]),
[] ).
cnf(169114960,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)],[169025240,161036368,theory(equality)]),
[] ).
fof(unordered_pair_1,plain,
! [A,B] : member(A,unordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),
[] ).
cnf(161016480,plain,
member(A,unordered_pair(A,B)),
inference(rewrite,[status(thm)],[unordered_pair_1]),
[] ).
cnf(169135928,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| $equal(unordered_pair(m1,r1),singleton_set(m2)) ),
inference(resolution,[status(thm)],[169114960,161016480]),
[] ).
cnf(169194944,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| member(m1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[169135928,161016480,theory(equality)]),
[] ).
fof(singleton_1,plain,
! [A] : member(A,singleton_set(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),
[] ).
cnf(161002456,plain,
member(A,singleton_set(A)),
inference(rewrite,[status(thm)],[singleton_1]),
[] ).
cnf(169483792,plain,
member(m1,singleton_set(m2)),
inference(paramodulation,[status(thm)],[169194944,161002456,theory(equality)]),
[] ).
fof(singleton_2,plain,
! [A,B] :
( ~ member(A,singleton_set(B))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),
[] ).
cnf(161012360,plain,
( ~ member(A,singleton_set(B))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[singleton_2]),
[] ).
cnf(169497352,plain,
$equal(m2,m1),
inference(resolution,[status(thm)],[169483792,161012360]),
[] ).
cnf(169527576,plain,
$equal(ordered_pair(m2,r2),ordered_pair(m2,r1)),
inference(paramodulation,[status(thm)],[169497352,161040344,theory(equality)]),
[] ).
cnf(169592768,plain,
$equal(unordered_pair(singleton_set(m2),unordered_pair(m2,r1)),ordered_pair(m2,r2)),
inference(paramodulation,[status(thm)],[169527576,161036368,theory(equality)]),
[] ).
fof(unordered_pair_2,plain,
! [A,B] : member(A,unordered_pair(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),
[] ).
cnf(161020296,plain,
member(A,unordered_pair(B,A)),
inference(rewrite,[status(thm)],[unordered_pair_2]),
[] ).
cnf(170207824,plain,
member(unordered_pair(m2,r1),ordered_pair(m2,r2)),
inference(paramodulation,[status(thm)],[169592768,161020296,theory(equality)]),
[] ).
cnf(170478136,plain,
( $equal(singleton_set(m2),unordered_pair(m2,r1))
| $equal(unordered_pair(m2,r2),unordered_pair(m2,r1)) ),
inference(resolution,[status(thm)],[170207824,168956296]),
[] ).
cnf(225705928,plain,
( $equal(unordered_pair(m2,r2),unordered_pair(m2,r1))
| member(r1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[170478136,161020296,theory(equality)]),
[] ).
fof(prove_second_components_equal,plain,
~ $equal(r2,r1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),
[] ).
cnf(161045128,plain,
~ $equal(r2,r1),
inference(rewrite,[status(thm)],[prove_second_components_equal]),
[] ).
cnf(168854288,plain,
~ member(r1,singleton_set(r2)),
inference(resolution,[status(thm)],[161012360,161045128]),
[] ).
cnf(169152104,plain,
( $equal(singleton_set(m1),unordered_pair(m2,r2))
| $equal(unordered_pair(m1,r1),unordered_pair(m2,r2)) ),
inference(resolution,[status(thm)],[169114960,161020296]),
[] ).
cnf(171558280,plain,
( $equal(unordered_pair(m1,r1),unordered_pair(m2,r2))
| member(r2,singleton_set(m1)) ),
inference(paramodulation,[status(thm)],[169152104,161020296,theory(equality)]),
[] ).
cnf(179061352,plain,
( $equal(unordered_pair(m1,r1),unordered_pair(m2,r2))
| $equal(m1,r2) ),
inference(resolution,[status(thm)],[171558280,161012360]),
[] ).
cnf(179095400,plain,
( member(r2,singleton_set(m1))
| member(r1,unordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[171558280,161020296,theory(equality)]),
[] ).
cnf(168921504,plain,
( ~ member(r1,unordered_pair(A,r2))
| $equal(A,r1) ),
inference(resolution,[status(thm)],[161027384,161045128]),
[] ).
cnf(179363888,plain,
( member(r2,singleton_set(m1))
| $equal(m2,r1) ),
inference(resolution,[status(thm)],[179095400,168921504]),
[] ).
cnf(179464528,plain,
( $equal(m2,r1)
| $equal(m1,r2) ),
inference(resolution,[status(thm)],[179363888,161012360]),
[] ).
cnf(179895240,plain,
( $equal(m2,r1)
| $equal(m2,r2) ),
inference(paramodulation,[status(thm)],[179464528,169497352,theory(equality)]),
[] ).
cnf(180108072,plain,
( $equal(m2,r2)
| member(m1,singleton_set(r1)) ),
inference(paramodulation,[status(thm)],[179895240,169483792,theory(equality)]),
[] ).
cnf(181796832,plain,
( $equal(m2,r2)
| $equal(r1,m1) ),
inference(resolution,[status(thm)],[180108072,161012360]),
[] ).
cnf(182260520,plain,
( $equal(r1,m1)
| member(m1,singleton_set(r2)) ),
inference(paramodulation,[status(thm)],[181796832,169483792,theory(equality)]),
[] ).
cnf(183529888,plain,
( $equal(r1,m1)
| $equal(r2,m1) ),
inference(resolution,[status(thm)],[182260520,161012360]),
[] ).
cnf(210384088,plain,
( $equal(unordered_pair(r1,r1),unordered_pair(m2,r2))
| $equal(m1,r2) ),
inference(paramodulation,[status(thm)],[179061352,183529888,theory(equality)]),
[] ).
cnf(412628944,plain,
( $equal(m1,r2)
| member(r2,unordered_pair(r1,r1)) ),
inference(paramodulation,[status(thm)],[210384088,161020296,theory(equality)]),
[] ).
cnf(414842520,plain,
( $equal(m1,r2)
| $equal(r1,r2) ),
inference(resolution,[status(thm)],[412628944,161027384]),
[] ).
cnf(171544448,plain,
( $equal(unordered_pair(m1,r1),unordered_pair(m2,r2))
| member(m2,singleton_set(m1)) ),
inference(paramodulation,[status(thm)],[169152104,161016480,theory(equality)]),
[] ).
cnf(175707560,plain,
( member(m2,singleton_set(m1))
| member(r1,unordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[171544448,161020296,theory(equality)]),
[] ).
cnf(176238328,plain,
( member(m2,singleton_set(m1))
| $equal(m2,r1) ),
inference(resolution,[status(thm)],[175707560,168921504]),
[] ).
cnf(176337096,plain,
( member(m2,singleton_set(m1))
| member(m1,singleton_set(r1)) ),
inference(paramodulation,[status(thm)],[176238328,169483792,theory(equality)]),
[] ).
cnf(176781944,plain,
( member(m2,singleton_set(m1))
| $equal(r1,m1) ),
inference(resolution,[status(thm)],[176337096,161012360]),
[] ).
cnf(169203512,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| member(r1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[169135928,161020296,theory(equality)]),
[] ).
cnf(169641488,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| $equal(m2,r1) ),
inference(resolution,[status(thm)],[169203512,161012360]),
[] ).
cnf(169771664,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| $equal(unordered_pair(m1,r1),singleton_set(r1)) ),
inference(paramodulation,[status(thm)],[169641488,169135928,theory(equality)]),
[] ).
cnf(171298272,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| $equal(singleton_set(r1),singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[169771664,169135928,theory(equality)]),
[] ).
cnf(176958032,plain,
( member(m2,singleton_set(m1))
| $equal(singleton_set(r1),singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[176781944,171298272,theory(equality)]),
[] ).
cnf(177549240,plain,
( $equal(singleton_set(r1),singleton_set(m2))
| $equal(m1,m2) ),
inference(resolution,[status(thm)],[176958032,161012360]),
[] ).
cnf(177717560,plain,
( $equal(m1,m2)
| ~ member(A,singleton_set(r1))
| $equal(m2,A) ),
inference(paramodulation,[status(thm)],[177549240,161012360,theory(equality)]),
[] ).
cnf(169703872,plain,
( $equal(singleton_set(m1),singleton_set(m2))
| member(m1,singleton_set(r1)) ),
inference(paramodulation,[status(thm)],[169641488,169483792,theory(equality)]),
[] ).
cnf(169976968,plain,
( member(m1,singleton_set(r1))
| ~ member(A,singleton_set(m2))
| $equal(m1,A) ),
inference(paramodulation,[status(thm)],[169703872,161012360,theory(equality)]),
[] ).
cnf(174233752,plain,
( member(m1,singleton_set(r1))
| $equal(m1,m2) ),
inference(resolution,[status(thm)],[169976968,161002456]),
[] ).
cnf(271047864,plain,
$equal(m1,m2),
inference(resolution,[status(thm)],[177717560,174233752]),
[] ).
cnf(416170944,plain,
( $equal(r1,r2)
| $equal(r2,m2) ),
inference(paramodulation,[status(thm)],[414842520,271047864,theory(equality)]),
[] ).
cnf(417666552,plain,
$equal(r2,m2),
inference(paramodulation,[status(thm)],[416170944,161045128,theory(equality)]),
[] ).
cnf(171566064,plain,
( $equal(singleton_set(m1),unordered_pair(m2,r2))
| member(r1,unordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[169152104,161020296,theory(equality)]),
[] ).
cnf(199287872,plain,
( $equal(singleton_set(m1),unordered_pair(m2,r2))
| $equal(m2,r1) ),
inference(resolution,[status(thm)],[171566064,168921504]),
[] ).
cnf(228752152,plain,
( $equal(m2,r1)
| ~ member(r1,singleton_set(m1)) ),
inference(paramodulation,[status(thm)],[199287872,168921504,theory(equality)]),
[] ).
cnf(183551464,plain,
( $equal(r1,m1)
| member(m2,singleton_set(r2)) ),
inference(paramodulation,[status(thm)],[182260520,169497352,theory(equality)]),
[] ).
cnf(185925176,plain,
( member(m2,singleton_set(r2))
| member(r1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[183551464,169483792,theory(equality)]),
[] ).
cnf(230112792,plain,
( ~ member(r1,singleton_set(m1))
| member(r1,singleton_set(m2)) ),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,228752152,185925176,theory(equality)]),
[] ).
cnf(419503336,plain,
~ member(r1,singleton_set(m1)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,417666552,230112792,theory(equality)]),
[] ).
cnf(175682536,plain,
( $equal(unordered_pair(m1,r1),unordered_pair(m2,r2))
| $equal(m1,m2) ),
inference(resolution,[status(thm)],[171544448,161012360]),
[] ).
cnf(169230296,plain,
( $equal(unordered_pair(m1,r1),singleton_set(m2))
| ~ member(A,singleton_set(m2))
| $equal(m1,A) ),
inference(paramodulation,[status(thm)],[169135928,161012360,theory(equality)]),
[] ).
cnf(173551320,plain,
( $equal(unordered_pair(m1,r1),singleton_set(m2))
| $equal(m1,m2) ),
inference(resolution,[status(thm)],[169230296,161002456]),
[] ).
cnf(173720384,plain,
( $equal(unordered_pair(m2,r1),singleton_set(m2))
| $equal(m1,m2) ),
inference(paramodulation,[status(thm)],[173551320,169497352,theory(equality)]),
[] ).
cnf(174010576,plain,
( $equal(m1,m2)
| $equal(unordered_pair(m1,r1),unordered_pair(m2,r1)) ),
inference(paramodulation,[status(thm)],[173720384,173551320,theory(equality)]),
[] ).
cnf(202115632,plain,
( $equal(m1,m2)
| $equal(unordered_pair(m2,r2),unordered_pair(m2,r1)) ),
inference(paramodulation,[status(thm)],[175682536,174010576,theory(equality)]),
[] ).
cnf(425795920,plain,
$equal(unordered_pair(m2,r2),unordered_pair(m2,r1)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[225705928,419503336,202115632,theory(equality)]),
[] ).
cnf(478292824,plain,
member(r1,unordered_pair(m2,r2)),
inference(paramodulation,[status(thm)],[425795920,161020296,theory(equality)]),
[] ).
cnf(418213008,plain,
member(m1,singleton_set(r2)),
inference(paramodulation,[status(thm)],[417666552,169483792,theory(equality)]),
[] ).
cnf(420900080,plain,
member(m2,singleton_set(r2)),
inference(paramodulation,[status(thm)],[418213008,169497352,theory(equality)]),
[] ).
cnf(181808976,plain,
( $equal(m2,r2)
| member(m2,singleton_set(r1)) ),
inference(paramodulation,[status(thm)],[180108072,169497352,theory(equality)]),
[] ).
cnf(182952728,plain,
( $equal(m2,r2)
| $equal(r1,m2) ),
inference(resolution,[status(thm)],[181808976,161012360]),
[] ).
cnf(183282784,plain,
( $equal(r1,m2)
| member(m1,singleton_set(r2)) ),
inference(paramodulation,[status(thm)],[182952728,169483792,theory(equality)]),
[] ).
cnf(173930576,plain,
( $equal(r1,m2)
| member(m2,singleton_set(r2)) ),
inference(paramodulation,[status(thm)],[183282784,169497352,theory(equality)]),
[] ).
cnf(229982168,plain,
( ~ member(r1,singleton_set(m1))
| $equal(r1,m2) ),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,228752152,173930576,theory(equality)]),
[] ).
cnf(231316208,plain,
( ~ member(r1,unordered_pair(m2,r2))
| $equal(r1,m2) ),
inference(paramodulation,[status(thm)],[229982168,199287872,theory(equality)]),
[] ).
cnf(424076264,plain,
~ member(r1,unordered_pair(m2,r2)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,420900080,231316208,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[478292824,424076264]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 71 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pair_3,plain,(~member(A,unordered_pair(B,C))|$equal(B,A)|$equal(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161027384,plain,(~member(A,unordered_pair(B,C))|$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/SET018-1.tptp',unknown),[]).
%
% cnf(161036368,plain,($equal(unordered_pair(singleton_set(A),unordered_pair(A,B)),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
%
% cnf(168956296,plain,(~member(A,ordered_pair(B,C))|$equal(singleton_set(B),A)|$equal(unordered_pair(B,C),A)),inference(paramodulation,[status(thm)],[161027384,161036368,theory(equality)]),[]).
%
% fof(equal_ordered_pairs,plain,($equal(ordered_pair(m2,r2),ordered_pair(m1,r1))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161040344,plain,($equal(ordered_pair(m2,r2),ordered_pair(m1,r1))),inference(rewrite,[status(thm)],[equal_ordered_pairs]),[]).
%
% cnf(169025240,plain,(~member(A,ordered_pair(m2,r2))|$equal(singleton_set(m1),A)|$equal(unordered_pair(m1,r1),A)),inference(paramodulation,[status(thm)],[168956296,161040344,theory(equality)]),[]).
%
% cnf(169114960,plain,(~member(A,unordered_pair(singleton_set(m2),unordered_pair(m2,r2)))|$equal(singleton_set(m1),A)|$equal(unordered_pair(m1,r1),A)),inference(paramodulation,[status(thm)],[169025240,161036368,theory(equality)]),[]).
%
% fof(unordered_pair_1,plain,(member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161016480,plain,(member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair_1]),[]).
%
% cnf(169135928,plain,($equal(singleton_set(m1),singleton_set(m2))|$equal(unordered_pair(m1,r1),singleton_set(m2))),inference(resolution,[status(thm)],[169114960,161016480]),[]).
%
% cnf(169194944,plain,($equal(singleton_set(m1),singleton_set(m2))|member(m1,singleton_set(m2))),inference(paramodulation,[status(thm)],[169135928,161016480,theory(equality)]),[]).
%
% fof(singleton_1,plain,(member(A,singleton_set(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161002456,plain,(member(A,singleton_set(A))),inference(rewrite,[status(thm)],[singleton_1]),[]).
%
% cnf(169483792,plain,(member(m1,singleton_set(m2))),inference(paramodulation,[status(thm)],[169194944,161002456,theory(equality)]),[]).
%
% fof(singleton_2,plain,(~member(A,singleton_set(B))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161012360,plain,(~member(A,singleton_set(B))|$equal(B,A)),inference(rewrite,[status(thm)],[singleton_2]),[]).
%
% cnf(169497352,plain,($equal(m2,m1)),inference(resolution,[status(thm)],[169483792,161012360]),[]).
%
% cnf(169527576,plain,($equal(ordered_pair(m2,r2),ordered_pair(m2,r1))),inference(paramodulation,[status(thm)],[169497352,161040344,theory(equality)]),[]).
%
% cnf(169592768,plain,($equal(unordered_pair(singleton_set(m2),unordered_pair(m2,r1)),ordered_pair(m2,r2))),inference(paramodulation,[status(thm)],[169527576,161036368,theory(equality)]),[]).
%
% fof(unordered_pair_2,plain,(member(A,unordered_pair(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161020296,plain,(member(A,unordered_pair(B,A))),inference(rewrite,[status(thm)],[unordered_pair_2]),[]).
%
% cnf(170207824,plain,(member(unordered_pair(m2,r1),ordered_pair(m2,r2))),inference(paramodulation,[status(thm)],[169592768,161020296,theory(equality)]),[]).
%
% cnf(170478136,plain,($equal(singleton_set(m2),unordered_pair(m2,r1))|$equal(unordered_pair(m2,r2),unordered_pair(m2,r1))),inference(resolution,[status(thm)],[170207824,168956296]),[]).
%
% cnf(225705928,plain,($equal(unordered_pair(m2,r2),unordered_pair(m2,r1))|member(r1,singleton_set(m2))),inference(paramodulation,[status(thm)],[170478136,161020296,theory(equality)]),[]).
%
% fof(prove_second_components_equal,plain,(~$equal(r2,r1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET018-1.tptp',unknown),[]).
%
% cnf(161045128,plain,(~$equal(r2,r1)),inference(rewrite,[status(thm)],[prove_second_components_equal]),[]).
%
% cnf(168854288,plain,(~member(r1,singleton_set(r2))),inference(resolution,[status(thm)],[161012360,161045128]),[]).
%
% cnf(169152104,plain,($equal(singleton_set(m1),unordered_pair(m2,r2))|$equal(unordered_pair(m1,r1),unordered_pair(m2,r2))),inference(resolution,[status(thm)],[169114960,161020296]),[]).
%
% cnf(171558280,plain,($equal(unordered_pair(m1,r1),unordered_pair(m2,r2))|member(r2,singleton_set(m1))),inference(paramodulation,[status(thm)],[169152104,161020296,theory(equality)]),[]).
%
% cnf(179061352,plain,($equal(unordered_pair(m1,r1),unordered_pair(m2,r2))|$equal(m1,r2)),inference(resolution,[status(thm)],[171558280,161012360]),[]).
%
% cnf(179095400,plain,(member(r2,singleton_set(m1))|member(r1,unordered_pair(m2,r2))),inference(paramodulation,[status(thm)],[171558280,161020296,theory(equality)]),[]).
%
% cnf(168921504,plain,(~member(r1,unordered_pair(A,r2))|$equal(A,r1)),inference(resolution,[status(thm)],[161027384,161045128]),[]).
%
% cnf(179363888,plain,(member(r2,singleton_set(m1))|$equal(m2,r1)),inference(resolution,[status(thm)],[179095400,168921504]),[]).
%
% cnf(179464528,plain,($equal(m2,r1)|$equal(m1,r2)),inference(resolution,[status(thm)],[179363888,161012360]),[]).
%
% cnf(179895240,plain,($equal(m2,r1)|$equal(m2,r2)),inference(paramodulation,[status(thm)],[179464528,169497352,theory(equality)]),[]).
%
% cnf(180108072,plain,($equal(m2,r2)|member(m1,singleton_set(r1))),inference(paramodulation,[status(thm)],[179895240,169483792,theory(equality)]),[]).
%
% cnf(181796832,plain,($equal(m2,r2)|$equal(r1,m1)),inference(resolution,[status(thm)],[180108072,161012360]),[]).
%
% cnf(182260520,plain,($equal(r1,m1)|member(m1,singleton_set(r2))),inference(paramodulation,[status(thm)],[181796832,169483792,theory(equality)]),[]).
%
% cnf(183529888,plain,($equal(r1,m1)|$equal(r2,m1)),inference(resolution,[status(thm)],[182260520,161012360]),[]).
%
% cnf(210384088,plain,($equal(unordered_pair(r1,r1),unordered_pair(m2,r2))|$equal(m1,r2)),inference(paramodulation,[status(thm)],[179061352,183529888,theory(equality)]),[]).
%
% cnf(412628944,plain,($equal(m1,r2)|member(r2,unordered_pair(r1,r1))),inference(paramodulation,[status(thm)],[210384088,161020296,theory(equality)]),[]).
%
% cnf(414842520,plain,($equal(m1,r2)|$equal(r1,r2)),inference(resolution,[status(thm)],[412628944,161027384]),[]).
%
% cnf(171544448,plain,($equal(unordered_pair(m1,r1),unordered_pair(m2,r2))|member(m2,singleton_set(m1))),inference(paramodulation,[status(thm)],[169152104,161016480,theory(equality)]),[]).
%
% cnf(175707560,plain,(member(m2,singleton_set(m1))|member(r1,unordered_pair(m2,r2))),inference(paramodulation,[status(thm)],[171544448,161020296,theory(equality)]),[]).
%
% cnf(176238328,plain,(member(m2,singleton_set(m1))|$equal(m2,r1)),inference(resolution,[status(thm)],[175707560,168921504]),[]).
%
% cnf(176337096,plain,(member(m2,singleton_set(m1))|member(m1,singleton_set(r1))),inference(paramodulation,[status(thm)],[176238328,169483792,theory(equality)]),[]).
%
% cnf(176781944,plain,(member(m2,singleton_set(m1))|$equal(r1,m1)),inference(resolution,[status(thm)],[176337096,161012360]),[]).
%
% cnf(169203512,plain,($equal(singleton_set(m1),singleton_set(m2))|member(r1,singleton_set(m2))),inference(paramodulation,[status(thm)],[169135928,161020296,theory(equality)]),[]).
%
% cnf(169641488,plain,($equal(singleton_set(m1),singleton_set(m2))|$equal(m2,r1)),inference(resolution,[status(thm)],[169203512,161012360]),[]).
%
% cnf(169771664,plain,($equal(singleton_set(m1),singleton_set(m2))|$equal(unordered_pair(m1,r1),singleton_set(r1))),inference(paramodulation,[status(thm)],[169641488,169135928,theory(equality)]),[]).
%
% cnf(171298272,plain,($equal(singleton_set(m1),singleton_set(m2))|$equal(singleton_set(r1),singleton_set(m2))),inference(paramodulation,[status(thm)],[169771664,169135928,theory(equality)]),[]).
%
% cnf(176958032,plain,(member(m2,singleton_set(m1))|$equal(singleton_set(r1),singleton_set(m2))),inference(paramodulation,[status(thm)],[176781944,171298272,theory(equality)]),[]).
%
% cnf(177549240,plain,($equal(singleton_set(r1),singleton_set(m2))|$equal(m1,m2)),inference(resolution,[status(thm)],[176958032,161012360]),[]).
%
% cnf(177717560,plain,($equal(m1,m2)|~member(A,singleton_set(r1))|$equal(m2,A)),inference(paramodulation,[status(thm)],[177549240,161012360,theory(equality)]),[]).
%
% cnf(169703872,plain,($equal(singleton_set(m1),singleton_set(m2))|member(m1,singleton_set(r1))),inference(paramodulation,[status(thm)],[169641488,169483792,theory(equality)]),[]).
%
% cnf(169976968,plain,(member(m1,singleton_set(r1))|~member(A,singleton_set(m2))|$equal(m1,A)),inference(paramodulation,[status(thm)],[169703872,161012360,theory(equality)]),[]).
%
% cnf(174233752,plain,(member(m1,singleton_set(r1))|$equal(m1,m2)),inference(resolution,[status(thm)],[169976968,161002456]),[]).
%
% cnf(271047864,plain,($equal(m1,m2)),inference(resolution,[status(thm)],[177717560,174233752]),[]).
%
% cnf(416170944,plain,($equal(r1,r2)|$equal(r2,m2)),inference(paramodulation,[status(thm)],[414842520,271047864,theory(equality)]),[]).
%
% cnf(417666552,plain,($equal(r2,m2)),inference(paramodulation,[status(thm)],[416170944,161045128,theory(equality)]),[]).
%
% cnf(171566064,plain,($equal(singleton_set(m1),unordered_pair(m2,r2))|member(r1,unordered_pair(m2,r2))),inference(paramodulation,[status(thm)],[169152104,161020296,theory(equality)]),[]).
%
% cnf(199287872,plain,($equal(singleton_set(m1),unordered_pair(m2,r2))|$equal(m2,r1)),inference(resolution,[status(thm)],[171566064,168921504]),[]).
%
% cnf(228752152,plain,($equal(m2,r1)|~member(r1,singleton_set(m1))),inference(paramodulation,[status(thm)],[199287872,168921504,theory(equality)]),[]).
%
% cnf(183551464,plain,($equal(r1,m1)|member(m2,singleton_set(r2))),inference(paramodulation,[status(thm)],[182260520,169497352,theory(equality)]),[]).
%
% cnf(185925176,plain,(member(m2,singleton_set(r2))|member(r1,singleton_set(m2))),inference(paramodulation,[status(thm)],[183551464,169483792,theory(equality)]),[]).
%
% cnf(230112792,plain,(~member(r1,singleton_set(m1))|member(r1,singleton_set(m2))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,228752152,185925176,theory(equality)]),[]).
%
% cnf(419503336,plain,(~member(r1,singleton_set(m1))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,417666552,230112792,theory(equality)]),[]).
%
% cnf(175682536,plain,($equal(unordered_pair(m1,r1),unordered_pair(m2,r2))|$equal(m1,m2)),inference(resolution,[status(thm)],[171544448,161012360]),[]).
%
% cnf(169230296,plain,($equal(unordered_pair(m1,r1),singleton_set(m2))|~member(A,singleton_set(m2))|$equal(m1,A)),inference(paramodulation,[status(thm)],[169135928,161012360,theory(equality)]),[]).
%
% cnf(173551320,plain,($equal(unordered_pair(m1,r1),singleton_set(m2))|$equal(m1,m2)),inference(resolution,[status(thm)],[169230296,161002456]),[]).
%
% cnf(173720384,plain,($equal(unordered_pair(m2,r1),singleton_set(m2))|$equal(m1,m2)),inference(paramodulation,[status(thm)],[173551320,169497352,theory(equality)]),[]).
%
% cnf(174010576,plain,($equal(m1,m2)|$equal(unordered_pair(m1,r1),unordered_pair(m2,r1))),inference(paramodulation,[status(thm)],[173720384,173551320,theory(equality)]),[]).
%
% cnf(202115632,plain,($equal(m1,m2)|$equal(unordered_pair(m2,r2),unordered_pair(m2,r1))),inference(paramodulation,[status(thm)],[175682536,174010576,theory(equality)]),[]).
%
% cnf(425795920,plain,($equal(unordered_pair(m2,r2),unordered_pair(m2,r1))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[225705928,419503336,202115632,theory(equality)]),[]).
%
% cnf(478292824,plain,(member(r1,unordered_pair(m2,r2))),inference(paramodulation,[status(thm)],[425795920,161020296,theory(equality)]),[]).
%
% cnf(418213008,plain,(member(m1,singleton_set(r2))),inference(paramodulation,[status(thm)],[417666552,169483792,theory(equality)]),[]).
%
% cnf(420900080,plain,(member(m2,singleton_set(r2))),inference(paramodulation,[status(thm)],[418213008,169497352,theory(equality)]),[]).
%
% cnf(181808976,plain,($equal(m2,r2)|member(m2,singleton_set(r1))),inference(paramodulation,[status(thm)],[180108072,169497352,theory(equality)]),[]).
%
% cnf(182952728,plain,($equal(m2,r2)|$equal(r1,m2)),inference(resolution,[status(thm)],[181808976,161012360]),[]).
%
% cnf(183282784,plain,($equal(r1,m2)|member(m1,singleton_set(r2))),inference(paramodulation,[status(thm)],[182952728,169483792,theory(equality)]),[]).
%
% cnf(173930576,plain,($equal(r1,m2)|member(m2,singleton_set(r2))),inference(paramodulation,[status(thm)],[183282784,169497352,theory(equality)]),[]).
%
% cnf(229982168,plain,(~member(r1,singleton_set(m1))|$equal(r1,m2)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,228752152,173930576,theory(equality)]),[]).
%
% cnf(231316208,plain,(~member(r1,unordered_pair(m2,r2))|$equal(r1,m2)),inference(paramodulation,[status(thm)],[229982168,199287872,theory(equality)]),[]).
%
% cnf(424076264,plain,(~member(r1,unordered_pair(m2,r2))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168854288,420900080,231316208,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[478292824,424076264]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------