%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN161-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 17:02:17 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 67 ( 32 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 127 ( 67 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 92 ( 27 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_126,plain,
! [A,B,C] :
( s1(A)
| ~ q0(A,B)
| ~ s1(C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(161660760,plain,
( s1(A)
| ~ q0(A,B)
| ~ s1(C) ),
inference(rewrite,[status(thm)],[rule_126]),
[] ).
fof(rule_125,plain,
! [A] :
( s1(A)
| ~ p0(A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(161648616,plain,
( s1(A)
| ~ p0(A,A) ),
inference(rewrite,[status(thm)],[rule_125]),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160221384,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
cnf(174157280,plain,
s1(b),
inference(resolution,[status(thm)],[161648616,160221384]),
[] ).
cnf(174411752,plain,
( s1(A)
| ~ q0(A,B) ),
inference(resolution,[status(thm)],[161660760,174157280]),
[] ).
fof(axiom_29,plain,
q0(d,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160297960,plain,
q0(d,b),
inference(rewrite,[status(thm)],[axiom_29]),
[] ).
cnf(174759952,plain,
s1(d),
inference(resolution,[status(thm)],[174411752,160297960]),
[] ).
fof(rule_133,plain,
! [A,B,C,D] :
( l2(A,A)
| ~ p0(B,B)
| ~ s1(C)
| ~ m0(D,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(161769704,plain,
( l2(A,A)
| ~ p0(B,B)
| ~ s1(C)
| ~ m0(D,C,A) ),
inference(rewrite,[status(thm)],[rule_133]),
[] ).
cnf(174331952,plain,
( l2(A,A)
| ~ s1(B)
| ~ m0(C,B,A) ),
inference(resolution,[status(thm)],[161769704,160221384]),
[] ).
fof(axiom_4,plain,
m0(e,d,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160162968,plain,
m0(e,d,a),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
cnf(183608416,plain,
l2(a,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174759952,174331952,160162968]),
[] ).
fof(rule_097,plain,
! [A] :
( q1(A,A,A)
| ~ s0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(161405528,plain,
( q1(A,A,A)
| ~ s0(A) ),
inference(rewrite,[status(thm)],[rule_097]),
[] ).
fof(axiom_1,plain,
s0(d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160133336,plain,
s0(d),
inference(rewrite,[status(thm)],[axiom_1]),
[] ).
cnf(162553008,plain,
q1(d,d,d),
inference(resolution,[status(thm)],[161405528,160133336]),
[] ).
fof(rule_124,plain,
! [A,B] :
( r1(A)
| ~ q0(A,B)
| ~ s0(d)
| ~ q1(d,B,d) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(161636440,plain,
( r1(A)
| ~ q0(A,B)
| ~ q1(d,B,d) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,160133336]),
[] ).
fof(axiom_17,plain,
! [A] : q0(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160236672,plain,
q0(A,d),
inference(rewrite,[status(thm)],[axiom_17]),
[] ).
cnf(180599984,plain,
r1(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162553008,161636440,160236672]),
[] ).
fof(rule_258,plain,
! [A,B,C] :
( q3(A,A)
| ~ r2(A)
| ~ s1(B)
| ~ l2(C,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(163485232,plain,
( q3(A,A)
| ~ r2(A)
| ~ s1(B)
| ~ l2(C,C) ),
inference(rewrite,[status(thm)],[rule_258]),
[] ).
cnf(174463792,plain,
( q3(A,A)
| ~ r2(A)
| ~ l2(B,B) ),
inference(resolution,[status(thm)],[163485232,174157280]),
[] ).
fof(rule_298,plain,
! [A,B,C,D] :
( r4(A)
| ~ n3(A)
| ~ q3(B,C)
| ~ p0(D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(164054304,plain,
( r4(A)
| ~ n3(A)
| ~ q3(B,C)
| ~ p0(D,A) ),
inference(rewrite,[status(thm)],[rule_298]),
[] ).
cnf(174267328,plain,
( r4(A)
| ~ n3(A)
| ~ q3(B,C) ),
inference(resolution,[status(thm)],[164054304,160221384]),
[] ).
fof(rule_240,plain,
! [A,B,C] :
( n3(A)
| ~ p2(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(163240904,plain,
( n3(A)
| ~ p2(B,C,A) ),
inference(rewrite,[status(thm)],[rule_240]),
[] ).
fof(rule_159,plain,
! [A] :
( p2(A,A,A)
| ~ k1(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(162133440,plain,
( p2(A,A,A)
| ~ k1(A) ),
inference(rewrite,[status(thm)],[rule_159]),
[] ).
fof(rule_001,plain,
! [A,B] :
( k1(A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160341648,plain,
( k1(A)
| ~ n0(B,A) ),
inference(rewrite,[status(thm)],[rule_001]),
[] ).
fof(axiom_3,plain,
n0(d,e),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160151808,plain,
n0(d,e),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(173576960,plain,
k1(e),
inference(resolution,[status(thm)],[160341648,160151808]),
[] ).
cnf(173714088,plain,
p2(e,e,e),
inference(resolution,[status(thm)],[162133440,173576960]),
[] ).
fof(rule_165,plain,
! [A,B,C] :
( p2(A,A,A)
| ~ q1(B,C,B)
| ~ p2(B,B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(162239400,plain,
( p2(A,A,A)
| ~ q1(B,C,B)
| ~ p2(B,B,C) ),
inference(rewrite,[status(thm)],[rule_165]),
[] ).
fof(rule_107,plain,
! [A] :
( q1(e,A,A)
| ~ m0(A,d,A)
| ~ m0(e,d,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160244152,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).
cnf(161501920,plain,
q1(e,A,A),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,160244152]),
[] ).
cnf(176328912,plain,
p2(A,A,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173714088,162239400,161501920]),
[] ).
cnf(176989536,plain,
n3(A),
inference(resolution,[status(thm)],[163240904,176328912]),
[] ).
cnf(179351720,plain,
( r4(A)
| ~ q3(B,C) ),
inference(resolution,[status(thm)],[174267328,176989536]),
[] ).
fof(rule_314,plain,
! [A] :
( n5(A,A)
| ~ r4(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(164274352,plain,
( n5(A,A)
| ~ r4(A) ),
inference(rewrite,[status(thm)],[rule_314]),
[] ).
fof(prove_this,plain,
! [A] : ~ n5(c,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(164517608,plain,
~ n5(c,A),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(176392256,plain,
~ r4(c),
inference(resolution,[status(thm)],[164274352,164517608]),
[] ).
cnf(179386376,plain,
~ q3(A,B),
inference(resolution,[status(thm)],[179351720,176392256]),
[] ).
cnf(180061576,plain,
( ~ r2(A)
| ~ l2(B,B) ),
inference(resolution,[status(thm)],[174463792,179386376]),
[] ).
fof(rule_188,plain,
! [A] :
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(162533112,plain,
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
inference(rewrite,[status(thm)],[rule_188]),
[] ).
fof(axiom_20,plain,
l0(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),
[] ).
cnf(160248512,plain,
l0(a),
inference(rewrite,[status(thm)],[axiom_20]),
[] ).
cnf(173145760,plain,
( r2(a)
| ~ r1(a) ),
inference(resolution,[status(thm)],[162533112,160248512]),
[] ).
cnf(180081008,plain,
( ~ l2(A,A)
| ~ r1(a) ),
inference(resolution,[status(thm)],[180061576,173145760]),
[] ).
cnf(180741440,plain,
~ l2(A,A),
inference(resolution,[status(thm)],[180599984,180081008]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[183608416,180741440]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(rule_126,plain,(s1(A)|~q0(A,B)|~s1(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(161660760,plain,(s1(A)|~q0(A,B)|~s1(C)),inference(rewrite,[status(thm)],[rule_126]),[]).
%
% fof(rule_125,plain,(s1(A)|~p0(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(161648616,plain,(s1(A)|~p0(A,A)),inference(rewrite,[status(thm)],[rule_125]),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160221384,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(174157280,plain,(s1(b)),inference(resolution,[status(thm)],[161648616,160221384]),[]).
%
% cnf(174411752,plain,(s1(A)|~q0(A,B)),inference(resolution,[status(thm)],[161660760,174157280]),[]).
%
% fof(axiom_29,plain,(q0(d,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160297960,plain,(q0(d,b)),inference(rewrite,[status(thm)],[axiom_29]),[]).
%
% cnf(174759952,plain,(s1(d)),inference(resolution,[status(thm)],[174411752,160297960]),[]).
%
% fof(rule_133,plain,(l2(A,A)|~p0(B,B)|~s1(C)|~m0(D,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(161769704,plain,(l2(A,A)|~p0(B,B)|~s1(C)|~m0(D,C,A)),inference(rewrite,[status(thm)],[rule_133]),[]).
%
% cnf(174331952,plain,(l2(A,A)|~s1(B)|~m0(C,B,A)),inference(resolution,[status(thm)],[161769704,160221384]),[]).
%
% fof(axiom_4,plain,(m0(e,d,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160162968,plain,(m0(e,d,a)),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% cnf(183608416,plain,(l2(a,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174759952,174331952,160162968]),[]).
%
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(161405528,plain,(q1(A,A,A)|~s0(A)),inference(rewrite,[status(thm)],[rule_097]),[]).
%
% fof(axiom_1,plain,(s0(d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160133336,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
%
% cnf(162553008,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[161405528,160133336]),[]).
%
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(161636440,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,160133336]),[]).
%
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160236672,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
%
% cnf(180599984,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162553008,161636440,160236672]),[]).
%
% fof(rule_258,plain,(q3(A,A)|~r2(A)|~s1(B)|~l2(C,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(163485232,plain,(q3(A,A)|~r2(A)|~s1(B)|~l2(C,C)),inference(rewrite,[status(thm)],[rule_258]),[]).
%
% cnf(174463792,plain,(q3(A,A)|~r2(A)|~l2(B,B)),inference(resolution,[status(thm)],[163485232,174157280]),[]).
%
% fof(rule_298,plain,(r4(A)|~n3(A)|~q3(B,C)|~p0(D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(164054304,plain,(r4(A)|~n3(A)|~q3(B,C)|~p0(D,A)),inference(rewrite,[status(thm)],[rule_298]),[]).
%
% cnf(174267328,plain,(r4(A)|~n3(A)|~q3(B,C)),inference(resolution,[status(thm)],[164054304,160221384]),[]).
%
% fof(rule_240,plain,(n3(A)|~p2(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(163240904,plain,(n3(A)|~p2(B,C,A)),inference(rewrite,[status(thm)],[rule_240]),[]).
%
% fof(rule_159,plain,(p2(A,A,A)|~k1(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(162133440,plain,(p2(A,A,A)|~k1(A)),inference(rewrite,[status(thm)],[rule_159]),[]).
%
% fof(rule_001,plain,(k1(A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160341648,plain,(k1(A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_001]),[]).
%
% fof(axiom_3,plain,(n0(d,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160151808,plain,(n0(d,e)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(173576960,plain,(k1(e)),inference(resolution,[status(thm)],[160341648,160151808]),[]).
%
% cnf(173714088,plain,(p2(e,e,e)),inference(resolution,[status(thm)],[162133440,173576960]),[]).
%
% fof(rule_165,plain,(p2(A,A,A)|~q1(B,C,B)|~p2(B,B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(162239400,plain,(p2(A,A,A)|~q1(B,C,B)|~p2(B,B,C)),inference(rewrite,[status(thm)],[rule_165]),[]).
%
% fof(rule_107,plain,(q1(e,A,A)|~m0(A,d,A)|~m0(e,d,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160244152,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(161501920,plain,(q1(e,A,A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,160244152]),[]).
%
% cnf(176328912,plain,(p2(A,A,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173714088,162239400,161501920]),[]).
%
% cnf(176989536,plain,(n3(A)),inference(resolution,[status(thm)],[163240904,176328912]),[]).
%
% cnf(179351720,plain,(r4(A)|~q3(B,C)),inference(resolution,[status(thm)],[174267328,176989536]),[]).
%
% fof(rule_314,plain,(n5(A,A)|~r4(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(164274352,plain,(n5(A,A)|~r4(A)),inference(rewrite,[status(thm)],[rule_314]),[]).
%
% fof(prove_this,plain,(~n5(c,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(164517608,plain,(~n5(c,A)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(176392256,plain,(~r4(c)),inference(resolution,[status(thm)],[164274352,164517608]),[]).
%
% cnf(179386376,plain,(~q3(A,B)),inference(resolution,[status(thm)],[179351720,176392256]),[]).
%
% cnf(180061576,plain,(~r2(A)|~l2(B,B)),inference(resolution,[status(thm)],[174463792,179386376]),[]).
%
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(162533112,plain,(r2(A)|~r1(A)|~l0(A)),inference(rewrite,[status(thm)],[rule_188]),[]).
%
% fof(axiom_20,plain,(l0(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN161-1.tptp',unknown),[]).
%
% cnf(160248512,plain,(l0(a)),inference(rewrite,[status(thm)],[axiom_20]),[]).
%
% cnf(173145760,plain,(r2(a)|~r1(a)),inference(resolution,[status(thm)],[162533112,160248512]),[]).
%
% cnf(180081008,plain,(~l2(A,A)|~r1(a)),inference(resolution,[status(thm)],[180061576,173145760]),[]).
%
% cnf(180741440,plain,(~l2(A,A)),inference(resolution,[status(thm)],[180599984,180081008]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[183608416,180741440]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------