%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU257+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:53:52 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 117 ( 56 ~; 54 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 12 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(dt_k2_wellord1,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_restriction(A,B)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160583832,plain,
( ~ relation(A)
| relation(relation_restriction(A,B)) ),
inference(rewrite,[status(thm)],[dt_k2_wellord1]),
[] ).
fof(t32_wellord1,plain,
( relation(b)
& well_ordering(b)
& ~ well_ordering(relation_restriction(b,a)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160719888,plain,
relation(b),
inference(rewrite,[status(thm)],[t32_wellord1]),
[] ).
cnf(173913488,plain,
relation(relation_restriction(b,A)),
inference(resolution,[status(thm)],[160583832,160719888]),
[] ).
fof(d4_wellord1,plain,
! [A] :
( ( well_ordering(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ antisymmetric(A)
| ~ connected(A)
| ~ well_founded_relation(A)
| ~ relation(A) )
& ( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) )
& ( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) )
& ( connected(A)
| ~ well_ordering(A)
| ~ relation(A) )
& ( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) )
& ( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160552840,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(160711200,plain,
well_ordering(b),
inference(rewrite,[status(thm)],[t32_wellord1]),
[] ).
cnf(173891680,plain,
transitive(b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160552840,160711200]),
[] ).
fof(t24_wellord1,plain,
! [B,A] :
( ~ relation(B)
| ~ transitive(B)
| transitive(relation_restriction(B,A)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160626824,plain,
( ~ relation(B)
| ~ transitive(B)
| transitive(relation_restriction(B,A)) ),
inference(rewrite,[status(thm)],[t24_wellord1]),
[] ).
cnf(173940920,plain,
transitive(relation_restriction(b,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173891680,160626824,160719888]),
[] ).
cnf(160523664,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(173867152,plain,
well_founded_relation(b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160523664,160711200]),
[] ).
fof(t31_wellord1,plain,
! [B,A] :
( ~ relation(B)
| ~ well_founded_relation(B)
| well_founded_relation(relation_restriction(B,A)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160650848,plain,
( ~ relation(B)
| ~ well_founded_relation(B)
| well_founded_relation(relation_restriction(B,A)) ),
inference(rewrite,[status(thm)],[t31_wellord1]),
[] ).
cnf(173956344,plain,
well_founded_relation(relation_restriction(b,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173867152,160650848,160719888]),
[] ).
cnf(160544432,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(173883504,plain,
antisymmetric(b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160544432,160711200]),
[] ).
fof(t25_wellord1,plain,
! [B,A] :
( ~ relation(B)
| ~ antisymmetric(B)
| antisymmetric(relation_restriction(B,A)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160640816,plain,
( ~ relation(B)
| ~ antisymmetric(B)
| antisymmetric(relation_restriction(B,A)) ),
inference(rewrite,[status(thm)],[t25_wellord1]),
[] ).
cnf(173948632,plain,
antisymmetric(relation_restriction(b,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173883504,160640816,160719888]),
[] ).
cnf(160536080,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(173875328,plain,
connected(b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160536080,160711200]),
[] ).
fof(t23_wellord1,plain,
! [B,A] :
( ~ relation(B)
| ~ connected(B)
| connected(relation_restriction(B,A)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160616792,plain,
( ~ relation(B)
| ~ connected(B)
| connected(relation_restriction(B,A)) ),
inference(rewrite,[status(thm)],[t23_wellord1]),
[] ).
cnf(173933208,plain,
connected(relation_restriction(b,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173875328,160616792,160719888]),
[] ).
cnf(160515056,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(173859000,plain,
reflexive(b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160515056,160711200]),
[] ).
fof(t22_wellord1,plain,
! [B,A] :
( ~ relation(B)
| ~ reflexive(B)
| reflexive(relation_restriction(B,A)) ),
file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),
[] ).
cnf(160606824,plain,
( ~ relation(B)
| ~ reflexive(B)
| reflexive(relation_restriction(B,A)) ),
inference(rewrite,[status(thm)],[t22_wellord1]),
[] ).
cnf(173925496,plain,
reflexive(relation_restriction(b,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173859000,160606824,160719888]),
[] ).
cnf(160568040,plain,
( well_ordering(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ antisymmetric(A)
| ~ connected(A)
| ~ well_founded_relation(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(160699248,plain,
~ well_ordering(relation_restriction(b,a)),
inference(rewrite,[status(thm)],[t32_wellord1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[173913488,173940920,173956344,173948632,173933208,173925496,160568040,160699248]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(dt_k2_wellord1,plain,(~relation(A)|relation(relation_restriction(A,B))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160583832,plain,(~relation(A)|relation(relation_restriction(A,B))),inference(rewrite,[status(thm)],[dt_k2_wellord1]),[]).
%
% fof(t32_wellord1,plain,((relation(b)&well_ordering(b)&~well_ordering(relation_restriction(b,a)))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160719888,plain,(relation(b)),inference(rewrite,[status(thm)],[t32_wellord1]),[]).
%
% cnf(173913488,plain,(relation(relation_restriction(b,A))),inference(resolution,[status(thm)],[160583832,160719888]),[]).
%
% fof(d4_wellord1,plain,(((well_ordering(A)|~reflexive(A)|~transitive(A)|~antisymmetric(A)|~connected(A)|~well_founded_relation(A)|~relation(A))&(transitive(A)|~well_ordering(A)|~relation(A))&(antisymmetric(A)|~well_ordering(A)|~relation(A))&(connected(A)|~well_ordering(A)|~relation(A))&(well_founded_relation(A)|~well_ordering(A)|~relation(A))&(reflexive(A)|~well_ordering(A)|~relation(A)))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160552840,plain,(transitive(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(160711200,plain,(well_ordering(b)),inference(rewrite,[status(thm)],[t32_wellord1]),[]).
%
% cnf(173891680,plain,(transitive(b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160552840,160711200]),[]).
%
% fof(t24_wellord1,plain,(~relation(B)|~transitive(B)|transitive(relation_restriction(B,A))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160626824,plain,(~relation(B)|~transitive(B)|transitive(relation_restriction(B,A))),inference(rewrite,[status(thm)],[t24_wellord1]),[]).
%
% cnf(173940920,plain,(transitive(relation_restriction(b,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173891680,160626824,160719888]),[]).
%
% cnf(160523664,plain,(well_founded_relation(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(173867152,plain,(well_founded_relation(b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160523664,160711200]),[]).
%
% fof(t31_wellord1,plain,(~relation(B)|~well_founded_relation(B)|well_founded_relation(relation_restriction(B,A))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160650848,plain,(~relation(B)|~well_founded_relation(B)|well_founded_relation(relation_restriction(B,A))),inference(rewrite,[status(thm)],[t31_wellord1]),[]).
%
% cnf(173956344,plain,(well_founded_relation(relation_restriction(b,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173867152,160650848,160719888]),[]).
%
% cnf(160544432,plain,(antisymmetric(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(173883504,plain,(antisymmetric(b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160544432,160711200]),[]).
%
% fof(t25_wellord1,plain,(~relation(B)|~antisymmetric(B)|antisymmetric(relation_restriction(B,A))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160640816,plain,(~relation(B)|~antisymmetric(B)|antisymmetric(relation_restriction(B,A))),inference(rewrite,[status(thm)],[t25_wellord1]),[]).
%
% cnf(173948632,plain,(antisymmetric(relation_restriction(b,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173883504,160640816,160719888]),[]).
%
% cnf(160536080,plain,(connected(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(173875328,plain,(connected(b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160536080,160711200]),[]).
%
% fof(t23_wellord1,plain,(~relation(B)|~connected(B)|connected(relation_restriction(B,A))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160616792,plain,(~relation(B)|~connected(B)|connected(relation_restriction(B,A))),inference(rewrite,[status(thm)],[t23_wellord1]),[]).
%
% cnf(173933208,plain,(connected(relation_restriction(b,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173875328,160616792,160719888]),[]).
%
% cnf(160515056,plain,(reflexive(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(173859000,plain,(reflexive(b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160719888,160515056,160711200]),[]).
%
% fof(t22_wellord1,plain,(~relation(B)|~reflexive(B)|reflexive(relation_restriction(B,A))),file('/tmp/SystemOnTPTP15891/SEU257+1.p',unknown),[]).
%
% cnf(160606824,plain,(~relation(B)|~reflexive(B)|reflexive(relation_restriction(B,A))),inference(rewrite,[status(thm)],[t22_wellord1]),[]).
%
% cnf(173925496,plain,(reflexive(relation_restriction(b,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173859000,160606824,160719888]),[]).
%
% cnf(160568040,plain,(well_ordering(A)|~reflexive(A)|~transitive(A)|~antisymmetric(A)|~connected(A)|~well_founded_relation(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(160699248,plain,(~well_ordering(relation_restriction(b,a))),inference(rewrite,[status(thm)],[t32_wellord1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[173913488,173940920,173956344,173948632,173933208,173925496,160568040,160699248]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------