%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS003-1 : 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 13:24:31 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clause_11,plain,
! [A,B,C] :
( equalish(A,B)
| ~ s1most(C)
| ~ s(C,A)
| ~ s(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169405064,plain,
( equalish(A,B)
| ~ s1most(C)
| ~ s(C,A)
| ~ s(C,B) ),
inference(rewrite,[status(thm)],[clause_11]),
[] ).
fof(clause_9,plain,
! [A] :
( s1most(A)
| ~ d(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169388312,plain,
( s1most(A)
| ~ d(A) ),
inference(rewrite,[status(thm)],[clause_9]),
[] ).
fof(clause_16,plain,
! [A] :
( d(A)
| ~ f(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169432864,plain,
( d(A)
| ~ f(A) ),
inference(rewrite,[status(thm)],[clause_16]),
[] ).
fof(clause_2,plain,
f(exist),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169328560,plain,
f(exist),
inference(rewrite,[status(thm)],[clause_2]),
[] ).
cnf(179910864,plain,
d(exist),
inference(resolution,[status(thm)],[169432864,169328560]),
[] ).
cnf(179927192,plain,
s1most(exist),
inference(resolution,[status(thm)],[169388312,179910864]),
[] ).
cnf(179991424,plain,
( equalish(A,B)
| ~ s(exist,A)
| ~ s(exist,B) ),
inference(resolution,[status(thm)],[169405064,179927192]),
[] ).
fof(clause_6,plain,
! [A] :
( s(A,u1r1(A))
| ~ s2least(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169359608,plain,
( s(A,u1r1(A))
| ~ s2least(A) ),
inference(rewrite,[status(thm)],[clause_6]),
[] ).
fof(clause_3,plain,
! [A] :
( s2least(A)
| ~ c(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169335312,plain,
( s2least(A)
| ~ c(A) ),
inference(rewrite,[status(thm)],[clause_3]),
[] ).
fof(clause_15,plain,
! [A] :
( c(A)
| ~ e(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169427776,plain,
( c(A)
| ~ e(A) ),
inference(rewrite,[status(thm)],[clause_15]),
[] ).
fof(clause_1,plain,
e(exist),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169323448,plain,
e(exist),
inference(rewrite,[status(thm)],[clause_1]),
[] ).
cnf(179902792,plain,
c(exist),
inference(resolution,[status(thm)],[169427776,169323448]),
[] ).
cnf(179919016,plain,
s2least(exist),
inference(resolution,[status(thm)],[169335312,179902792]),
[] ).
cnf(179945936,plain,
s(exist,u1r1(exist)),
inference(resolution,[status(thm)],[169359608,179919016]),
[] ).
cnf(180028192,plain,
( equalish(A,u1r1(exist))
| ~ s(exist,A) ),
inference(resolution,[status(thm)],[179991424,179945936]),
[] ).
fof(clause_7,plain,
! [A] :
( s(A,u1r2(A))
| ~ s2least(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169369544,plain,
( s(A,u1r2(A))
| ~ s2least(A) ),
inference(rewrite,[status(thm)],[clause_7]),
[] ).
cnf(179958936,plain,
s(exist,u1r2(exist)),
inference(resolution,[status(thm)],[169369544,179919016]),
[] ).
cnf(180042144,plain,
equalish(u1r2(exist),u1r1(exist)),
inference(resolution,[status(thm)],[180028192,179958936]),
[] ).
fof(clause_5,plain,
! [A] :
( ~ s2least(A)
| ~ equalish(u1r2(A),u1r1(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),
[] ).
cnf(169352848,plain,
( ~ s2least(A)
| ~ equalish(u1r2(A),u1r1(A)) ),
inference(rewrite,[status(thm)],[clause_5]),
[] ).
cnf(179974128,plain,
~ equalish(u1r2(exist),u1r1(exist)),
inference(resolution,[status(thm)],[169352848,179919016]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[180042144,179974128]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(clause_11,plain,(equalish(A,B)|~s1most(C)|~s(C,A)|~s(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169405064,plain,(equalish(A,B)|~s1most(C)|~s(C,A)|~s(C,B)),inference(rewrite,[status(thm)],[clause_11]),[]).
%
% fof(clause_9,plain,(s1most(A)|~d(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169388312,plain,(s1most(A)|~d(A)),inference(rewrite,[status(thm)],[clause_9]),[]).
%
% fof(clause_16,plain,(d(A)|~f(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169432864,plain,(d(A)|~f(A)),inference(rewrite,[status(thm)],[clause_16]),[]).
%
% fof(clause_2,plain,(f(exist)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169328560,plain,(f(exist)),inference(rewrite,[status(thm)],[clause_2]),[]).
%
% cnf(179910864,plain,(d(exist)),inference(resolution,[status(thm)],[169432864,169328560]),[]).
%
% cnf(179927192,plain,(s1most(exist)),inference(resolution,[status(thm)],[169388312,179910864]),[]).
%
% cnf(179991424,plain,(equalish(A,B)|~s(exist,A)|~s(exist,B)),inference(resolution,[status(thm)],[169405064,179927192]),[]).
%
% fof(clause_6,plain,(s(A,u1r1(A))|~s2least(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169359608,plain,(s(A,u1r1(A))|~s2least(A)),inference(rewrite,[status(thm)],[clause_6]),[]).
%
% fof(clause_3,plain,(s2least(A)|~c(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169335312,plain,(s2least(A)|~c(A)),inference(rewrite,[status(thm)],[clause_3]),[]).
%
% fof(clause_15,plain,(c(A)|~e(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169427776,plain,(c(A)|~e(A)),inference(rewrite,[status(thm)],[clause_15]),[]).
%
% fof(clause_1,plain,(e(exist)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169323448,plain,(e(exist)),inference(rewrite,[status(thm)],[clause_1]),[]).
%
% cnf(179902792,plain,(c(exist)),inference(resolution,[status(thm)],[169427776,169323448]),[]).
%
% cnf(179919016,plain,(s2least(exist)),inference(resolution,[status(thm)],[169335312,179902792]),[]).
%
% cnf(179945936,plain,(s(exist,u1r1(exist))),inference(resolution,[status(thm)],[169359608,179919016]),[]).
%
% cnf(180028192,plain,(equalish(A,u1r1(exist))|~s(exist,A)),inference(resolution,[status(thm)],[179991424,179945936]),[]).
%
% fof(clause_7,plain,(s(A,u1r2(A))|~s2least(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169369544,plain,(s(A,u1r2(A))|~s2least(A)),inference(rewrite,[status(thm)],[clause_7]),[]).
%
% cnf(179958936,plain,(s(exist,u1r2(exist))),inference(resolution,[status(thm)],[169369544,179919016]),[]).
%
% cnf(180042144,plain,(equalish(u1r2(exist),u1r1(exist))),inference(resolution,[status(thm)],[180028192,179958936]),[]).
%
% fof(clause_5,plain,(~s2least(A)|~equalish(u1r2(A),u1r1(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS003-1.tptp',unknown),[]).
%
% cnf(169352848,plain,(~s2least(A)|~equalish(u1r2(A),u1r1(A))),inference(rewrite,[status(thm)],[clause_5]),[]).
%
% cnf(179974128,plain,(~equalish(u1r2(exist),u1r1(exist))),inference(resolution,[status(thm)],[169352848,179919016]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[180042144,179974128]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------