%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN138-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 16:54:27 EDT 2009
% Result : Unsatisfiable 4.7s
% Output : Refutation 4.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 43 ( 22 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 38 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 7 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_127,plain,
! [A,B,C,D] :
( k2(A,B)
| ~ m1(C,B,A)
| ~ k1(D)
| ~ k2(D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(171602488,plain,
( k2(A,B)
| ~ m1(C,B,A)
| ~ k1(D)
| ~ k2(D,B) ),
inference(rewrite,[status(thm)],[rule_127]),
[] ).
fof(rule_001,plain,
! [A,B] :
( k1(A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(170267880,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/SYN138-1.tptp',unknown),
[] ).
cnf(170078040,plain,
n0(d,e),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(183484760,plain,
k1(e),
inference(resolution,[status(thm)],[170267880,170078040]),
[] ).
cnf(183851624,plain,
( k2(A,B)
| ~ m1(C,B,A)
| ~ k2(e,B) ),
inference(resolution,[status(thm)],[171602488,183484760]),
[] ).
fof(rule_130,plain,
( k2(e,e)
| ~ l1(e,e) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(171650896,plain,
( k2(e,e)
| ~ l1(e,e) ),
inference(rewrite,[status(thm)],[rule_130]),
[] ).
fof(rule_002,plain,
! [A,B] :
( l1(A,A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(170281336,plain,
( l1(A,A)
| ~ n0(B,A) ),
inference(rewrite,[status(thm)],[rule_002]),
[] ).
cnf(183495416,plain,
l1(e,e),
inference(resolution,[status(thm)],[170281336,170078040]),
[] ).
cnf(185270880,plain,
k2(e,e),
inference(resolution,[status(thm)],[171650896,183495416]),
[] ).
cnf(185591824,plain,
( k2(A,e)
| ~ m1(B,e,A) ),
inference(resolution,[status(thm)],[183851624,185270880]),
[] ).
fof(rule_021,plain,
! [A,B] :
( m1(A,B,A)
| ~ l0(A)
| ~ k0(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(170500488,plain,
( m1(A,B,A)
| ~ l0(A)
| ~ k0(B) ),
inference(rewrite,[status(thm)],[rule_021]),
[] ).
fof(axiom_24,plain,
l0(c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(170197040,plain,
l0(c),
inference(rewrite,[status(thm)],[axiom_24]),
[] ).
cnf(190638712,plain,
( m1(c,A,c)
| ~ k0(A) ),
inference(resolution,[status(thm)],[170500488,170197040]),
[] ).
fof(axiom_28,plain,
k0(e),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(170213176,plain,
k0(e),
inference(rewrite,[status(thm)],[axiom_28]),
[] ).
cnf(190719800,plain,
m1(c,e,c),
inference(resolution,[status(thm)],[190638712,170213176]),
[] ).
cnf(259194400,plain,
k2(c,e),
inference(resolution,[status(thm)],[185591824,190719800]),
[] ).
fof(rule_097,plain,
! [A] :
( q1(A,A,A)
| ~ s0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(171331760,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/SYN138-1.tptp',unknown),
[] ).
cnf(170059568,plain,
s0(d),
inference(rewrite,[status(thm)],[axiom_1]),
[] ).
cnf(172479240,plain,
q1(d,d,d),
inference(resolution,[status(thm)],[171331760,170059568]),
[] ).
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/SYN138-1.tptp',unknown),
[] ).
cnf(171562672,plain,
( r1(A)
| ~ q0(A,B)
| ~ q1(d,B,d) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,170059568]),
[] ).
fof(axiom_17,plain,
! [A] : q0(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(170162904,plain,
q0(A,d),
inference(rewrite,[status(thm)],[axiom_17]),
[] ).
cnf(184382672,plain,
r1(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172479240,171562672,170162904]),
[] ).
fof(rule_188,plain,
! [A] :
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(172459344,plain,
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
inference(rewrite,[status(thm)],[rule_188]),
[] ).
cnf(187825352,plain,
r2(c),
inference(forward_subsumption_resolution__resolution,[status(thm)],[184382672,170197040,172459344]),
[] ).
fof(rule_231,plain,
! [A,B] :
( m3(A,B,A)
| ~ r2(A)
| ~ k2(c,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(173051096,plain,
( m3(A,B,A)
| ~ r2(A)
| ~ k2(c,B) ),
inference(rewrite,[status(thm)],[rule_231]),
[] ).
fof(prove_this,plain,
~ m3(c,e,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),
[] ).
cnf(174443840,plain,
~ m3(c,e,c),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(193057664,plain,
~ k2(c,e),
inference(forward_subsumption_resolution__resolution,[status(thm)],[187825352,173051096,174443840]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[259194400,193057664]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 seconds
% START OF PROOF SEQUENCE
% fof(rule_127,plain,(k2(A,B)|~m1(C,B,A)|~k1(D)|~k2(D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(171602488,plain,(k2(A,B)|~m1(C,B,A)|~k1(D)|~k2(D,B)),inference(rewrite,[status(thm)],[rule_127]),[]).
%
% fof(rule_001,plain,(k1(A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(170267880,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/SYN138-1.tptp',unknown),[]).
%
% cnf(170078040,plain,(n0(d,e)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(183484760,plain,(k1(e)),inference(resolution,[status(thm)],[170267880,170078040]),[]).
%
% cnf(183851624,plain,(k2(A,B)|~m1(C,B,A)|~k2(e,B)),inference(resolution,[status(thm)],[171602488,183484760]),[]).
%
% fof(rule_130,plain,(k2(e,e)|~l1(e,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(171650896,plain,(k2(e,e)|~l1(e,e)),inference(rewrite,[status(thm)],[rule_130]),[]).
%
% fof(rule_002,plain,(l1(A,A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(170281336,plain,(l1(A,A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_002]),[]).
%
% cnf(183495416,plain,(l1(e,e)),inference(resolution,[status(thm)],[170281336,170078040]),[]).
%
% cnf(185270880,plain,(k2(e,e)),inference(resolution,[status(thm)],[171650896,183495416]),[]).
%
% cnf(185591824,plain,(k2(A,e)|~m1(B,e,A)),inference(resolution,[status(thm)],[183851624,185270880]),[]).
%
% fof(rule_021,plain,(m1(A,B,A)|~l0(A)|~k0(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(170500488,plain,(m1(A,B,A)|~l0(A)|~k0(B)),inference(rewrite,[status(thm)],[rule_021]),[]).
%
% fof(axiom_24,plain,(l0(c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(170197040,plain,(l0(c)),inference(rewrite,[status(thm)],[axiom_24]),[]).
%
% cnf(190638712,plain,(m1(c,A,c)|~k0(A)),inference(resolution,[status(thm)],[170500488,170197040]),[]).
%
% fof(axiom_28,plain,(k0(e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(170213176,plain,(k0(e)),inference(rewrite,[status(thm)],[axiom_28]),[]).
%
% cnf(190719800,plain,(m1(c,e,c)),inference(resolution,[status(thm)],[190638712,170213176]),[]).
%
% cnf(259194400,plain,(k2(c,e)),inference(resolution,[status(thm)],[185591824,190719800]),[]).
%
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(171331760,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/SYN138-1.tptp',unknown),[]).
%
% cnf(170059568,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
%
% cnf(172479240,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[171331760,170059568]),[]).
%
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(171562672,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,170059568]),[]).
%
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(170162904,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
%
% cnf(184382672,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172479240,171562672,170162904]),[]).
%
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(172459344,plain,(r2(A)|~r1(A)|~l0(A)),inference(rewrite,[status(thm)],[rule_188]),[]).
%
% cnf(187825352,plain,(r2(c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[184382672,170197040,172459344]),[]).
%
% fof(rule_231,plain,(m3(A,B,A)|~r2(A)|~k2(c,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(173051096,plain,(m3(A,B,A)|~r2(A)|~k2(c,B)),inference(rewrite,[status(thm)],[rule_231]),[]).
%
% fof(prove_this,plain,(~m3(c,e,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN138-1.tptp',unknown),[]).
%
% cnf(174443840,plain,(~m3(c,e,c)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(193057664,plain,(~k2(c,e)),inference(forward_subsumption_resolution__resolution,[status(thm)],[187825352,173051096,174443840]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[259194400,193057664]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------