%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS013-1 : TPTP v3.4.2. Released v2.0.0.
% 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 13:24:45 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 17 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 45 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clause_6,plain,
! [A] :
( t(A,u1r1(A))
| ~ t2least(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157925464,plain,
( t(A,u1r1(A))
| ~ t2least(A) ),
inference(rewrite,[status(thm)],[clause_6]),
[] ).
fof(clause_3,plain,
! [A] :
( t2least(A)
| ~ c(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157895744,plain,
( t2least(A)
| ~ c(A) ),
inference(rewrite,[status(thm)],[clause_3]),
[] ).
fof(clause_29,plain,
! [A] :
( f(A)
| r(A,u6r1(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158142912,plain,
( f(A)
| r(A,u6r1(A)) ),
inference(rewrite,[status(thm)],[clause_29]),
[] ).
fof(clause_2,plain,
~ f(exist),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157888520,plain,
~ f(exist),
inference(rewrite,[status(thm)],[clause_2]),
[] ).
cnf(168793744,plain,
r(exist,u6r1(exist)),
inference(resolution,[status(thm)],[158142912,157888520]),
[] ).
fof(clause_16,plain,
! [A,B] :
( c(A)
| ~ e(B)
| ~ r(B,A)
| ~ s2least(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158023152,plain,
( c(A)
| ~ e(B)
| ~ r(B,A)
| ~ s2least(A) ),
inference(rewrite,[status(thm)],[clause_16]),
[] ).
fof(clause_1,plain,
e(exist),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157882920,plain,
e(exist),
inference(rewrite,[status(thm)],[clause_1]),
[] ).
cnf(168761128,plain,
( c(A)
| ~ r(exist,A)
| ~ s2least(A) ),
inference(resolution,[status(thm)],[158023152,157882920]),
[] ).
fof(clause_26,plain,
! [A,B,C] :
( s2least(A)
| equalish(B,C)
| ~ s(A,B)
| ~ s(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158109288,plain,
( s2least(A)
| equalish(B,C)
| ~ s(A,B)
| ~ s(A,C) ),
inference(rewrite,[status(thm)],[clause_26]),
[] ).
fof(clause_33,plain,
! [A] :
( s1most(A)
| s(A,u7r2(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158175376,plain,
( s1most(A)
| s(A,u7r2(A)) ),
inference(rewrite,[status(thm)],[clause_33]),
[] ).
fof(clause_28,plain,
! [A] :
( f(A)
| ~ s1most(u6r1(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158133368,plain,
( f(A)
| ~ s1most(u6r1(A)) ),
inference(rewrite,[status(thm)],[clause_28]),
[] ).
cnf(168778600,plain,
~ s1most(u6r1(exist)),
inference(resolution,[status(thm)],[158133368,157888520]),
[] ).
cnf(168821584,plain,
s(u6r1(exist),u7r2(u6r1(exist))),
inference(resolution,[status(thm)],[158175376,168778600]),
[] ).
cnf(168981664,plain,
( s2least(u6r1(exist))
| equalish(u7r2(u6r1(exist)),A)
| ~ s(u6r1(exist),A) ),
inference(resolution,[status(thm)],[158109288,168821584]),
[] ).
fof(clause_32,plain,
! [A] :
( s1most(A)
| s(A,u7r1(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158170760,plain,
( s1most(A)
| s(A,u7r1(A)) ),
inference(rewrite,[status(thm)],[clause_32]),
[] ).
cnf(168808128,plain,
s(u6r1(exist),u7r1(u6r1(exist))),
inference(resolution,[status(thm)],[158170760,168778600]),
[] ).
cnf(169004976,plain,
( s2least(u6r1(exist))
| equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) ),
inference(resolution,[status(thm)],[168981664,168808128]),
[] ).
fof(clause_31,plain,
! [A] :
( s1most(A)
| ~ equalish(u7r2(A),u7r1(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158161200,plain,
( s1most(A)
| ~ equalish(u7r2(A),u7r1(A)) ),
inference(rewrite,[status(thm)],[clause_31]),
[] ).
cnf(168840792,plain,
~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))),
inference(resolution,[status(thm)],[158161200,168778600]),
[] ).
cnf(169046312,plain,
s2least(u6r1(exist)),
inference(resolution,[status(thm)],[169004976,168840792]),
[] ).
cnf(169126936,plain,
c(u6r1(exist)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168793744,168761128,169046312]),
[] ).
cnf(169136248,plain,
t2least(u6r1(exist)),
inference(resolution,[status(thm)],[157895744,169126936]),
[] ).
cnf(169151176,plain,
t(u6r1(exist),u1r1(u6r1(exist))),
inference(resolution,[status(thm)],[157925464,169136248]),
[] ).
fof(clause_9,plain,
! [A] :
( t1most(A)
| ~ d(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157955224,plain,
( t1most(A)
| ~ d(A) ),
inference(rewrite,[status(thm)],[clause_9]),
[] ).
fof(clause_15,plain,
! [A,B] :
( d(A)
| ~ e(B)
| ~ r(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(158014104,plain,
( d(A)
| ~ e(B)
| ~ r(B,A) ),
inference(rewrite,[status(thm)],[clause_15]),
[] ).
cnf(168749064,plain,
( d(A)
| ~ r(exist,A) ),
inference(resolution,[status(thm)],[158014104,157882920]),
[] ).
cnf(168864256,plain,
d(u6r1(exist)),
inference(resolution,[status(thm)],[168749064,168793744]),
[] ).
cnf(168895352,plain,
t1most(u6r1(exist)),
inference(resolution,[status(thm)],[157955224,168864256]),
[] ).
fof(clause_11,plain,
! [A,B,C] :
( equalish(A,B)
| ~ t1most(C)
| ~ t(C,A)
| ~ t(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157976896,plain,
( equalish(A,B)
| ~ t1most(C)
| ~ t(C,A)
| ~ t(C,B) ),
inference(rewrite,[status(thm)],[clause_11]),
[] ).
fof(clause_7,plain,
! [A] :
( t(A,u1r2(A))
| ~ t2least(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157931792,plain,
( t(A,u1r2(A))
| ~ t2least(A) ),
inference(rewrite,[status(thm)],[clause_7]),
[] ).
cnf(169168624,plain,
t(u6r1(exist),u1r2(u6r1(exist))),
inference(resolution,[status(thm)],[157931792,169136248]),
[] ).
cnf(169199856,plain,
( equalish(u1r2(u6r1(exist)),A)
| ~ t(u6r1(exist),A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168895352,157976896,169168624]),
[] ).
fof(clause_5,plain,
! [A] :
( ~ t2least(A)
| ~ equalish(u1r2(A),u1r1(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),
[] ).
cnf(157914136,plain,
( ~ t2least(A)
| ~ equalish(u1r2(A),u1r1(A)) ),
inference(rewrite,[status(thm)],[clause_5]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[169151176,169136248,169199856,157914136]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(clause_6,plain,(t(A,u1r1(A))|~t2least(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157925464,plain,(t(A,u1r1(A))|~t2least(A)),inference(rewrite,[status(thm)],[clause_6]),[]).
%
% fof(clause_3,plain,(t2least(A)|~c(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157895744,plain,(t2least(A)|~c(A)),inference(rewrite,[status(thm)],[clause_3]),[]).
%
% fof(clause_29,plain,(f(A)|r(A,u6r1(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158142912,plain,(f(A)|r(A,u6r1(A))),inference(rewrite,[status(thm)],[clause_29]),[]).
%
% fof(clause_2,plain,(~f(exist)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157888520,plain,(~f(exist)),inference(rewrite,[status(thm)],[clause_2]),[]).
%
% cnf(168793744,plain,(r(exist,u6r1(exist))),inference(resolution,[status(thm)],[158142912,157888520]),[]).
%
% fof(clause_16,plain,(c(A)|~e(B)|~r(B,A)|~s2least(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158023152,plain,(c(A)|~e(B)|~r(B,A)|~s2least(A)),inference(rewrite,[status(thm)],[clause_16]),[]).
%
% fof(clause_1,plain,(e(exist)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157882920,plain,(e(exist)),inference(rewrite,[status(thm)],[clause_1]),[]).
%
% cnf(168761128,plain,(c(A)|~r(exist,A)|~s2least(A)),inference(resolution,[status(thm)],[158023152,157882920]),[]).
%
% fof(clause_26,plain,(s2least(A)|equalish(B,C)|~s(A,B)|~s(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158109288,plain,(s2least(A)|equalish(B,C)|~s(A,B)|~s(A,C)),inference(rewrite,[status(thm)],[clause_26]),[]).
%
% fof(clause_33,plain,(s1most(A)|s(A,u7r2(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158175376,plain,(s1most(A)|s(A,u7r2(A))),inference(rewrite,[status(thm)],[clause_33]),[]).
%
% fof(clause_28,plain,(f(A)|~s1most(u6r1(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158133368,plain,(f(A)|~s1most(u6r1(A))),inference(rewrite,[status(thm)],[clause_28]),[]).
%
% cnf(168778600,plain,(~s1most(u6r1(exist))),inference(resolution,[status(thm)],[158133368,157888520]),[]).
%
% cnf(168821584,plain,(s(u6r1(exist),u7r2(u6r1(exist)))),inference(resolution,[status(thm)],[158175376,168778600]),[]).
%
% cnf(168981664,plain,(s2least(u6r1(exist))|equalish(u7r2(u6r1(exist)),A)|~s(u6r1(exist),A)),inference(resolution,[status(thm)],[158109288,168821584]),[]).
%
% fof(clause_32,plain,(s1most(A)|s(A,u7r1(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158170760,plain,(s1most(A)|s(A,u7r1(A))),inference(rewrite,[status(thm)],[clause_32]),[]).
%
% cnf(168808128,plain,(s(u6r1(exist),u7r1(u6r1(exist)))),inference(resolution,[status(thm)],[158170760,168778600]),[]).
%
% cnf(169004976,plain,(s2least(u6r1(exist))|equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))),inference(resolution,[status(thm)],[168981664,168808128]),[]).
%
% fof(clause_31,plain,(s1most(A)|~equalish(u7r2(A),u7r1(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158161200,plain,(s1most(A)|~equalish(u7r2(A),u7r1(A))),inference(rewrite,[status(thm)],[clause_31]),[]).
%
% cnf(168840792,plain,(~equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))),inference(resolution,[status(thm)],[158161200,168778600]),[]).
%
% cnf(169046312,plain,(s2least(u6r1(exist))),inference(resolution,[status(thm)],[169004976,168840792]),[]).
%
% cnf(169126936,plain,(c(u6r1(exist))),inference(forward_subsumption_resolution__resolution,[status(thm)],[168793744,168761128,169046312]),[]).
%
% cnf(169136248,plain,(t2least(u6r1(exist))),inference(resolution,[status(thm)],[157895744,169126936]),[]).
%
% cnf(169151176,plain,(t(u6r1(exist),u1r1(u6r1(exist)))),inference(resolution,[status(thm)],[157925464,169136248]),[]).
%
% fof(clause_9,plain,(t1most(A)|~d(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157955224,plain,(t1most(A)|~d(A)),inference(rewrite,[status(thm)],[clause_9]),[]).
%
% fof(clause_15,plain,(d(A)|~e(B)|~r(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(158014104,plain,(d(A)|~e(B)|~r(B,A)),inference(rewrite,[status(thm)],[clause_15]),[]).
%
% cnf(168749064,plain,(d(A)|~r(exist,A)),inference(resolution,[status(thm)],[158014104,157882920]),[]).
%
% cnf(168864256,plain,(d(u6r1(exist))),inference(resolution,[status(thm)],[168749064,168793744]),[]).
%
% cnf(168895352,plain,(t1most(u6r1(exist))),inference(resolution,[status(thm)],[157955224,168864256]),[]).
%
% fof(clause_11,plain,(equalish(A,B)|~t1most(C)|~t(C,A)|~t(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157976896,plain,(equalish(A,B)|~t1most(C)|~t(C,A)|~t(C,B)),inference(rewrite,[status(thm)],[clause_11]),[]).
%
% fof(clause_7,plain,(t(A,u1r2(A))|~t2least(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157931792,plain,(t(A,u1r2(A))|~t2least(A)),inference(rewrite,[status(thm)],[clause_7]),[]).
%
% cnf(169168624,plain,(t(u6r1(exist),u1r2(u6r1(exist)))),inference(resolution,[status(thm)],[157931792,169136248]),[]).
%
% cnf(169199856,plain,(equalish(u1r2(u6r1(exist)),A)|~t(u6r1(exist),A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168895352,157976896,169168624]),[]).
%
% fof(clause_5,plain,(~t2least(A)|~equalish(u1r2(A),u1r1(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS013-1.tptp',unknown),[]).
%
% cnf(157914136,plain,(~t2least(A)|~equalish(u1r2(A),u1r1(A))),inference(rewrite,[status(thm)],[clause_5]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[169151176,169136248,169199856,157914136]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------