TSTP Solution File: SEU275+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU275+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:54:23 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 60 ( 28 ~; 26 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 14 ( 4 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t5_wellord2,plain,
! [A] : antisymmetric(inclusion_relation(A)),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166476024,plain,
antisymmetric(inclusion_relation(A)),
inference(rewrite,[status(thm)],[t5_wellord2]),
[] ).
fof(t4_wellord2,plain,
! [A] :
( ~ ordinal(A)
| connected(inclusion_relation(A)) ),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166471864,plain,
( ~ ordinal(A)
| connected(inclusion_relation(A)) ),
inference(rewrite,[status(thm)],[t4_wellord2]),
[] ).
fof(t7_wellord2,plain,
( ordinal(a)
& ~ well_ordering(inclusion_relation(a)) ),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166530768,plain,
ordinal(a),
inference(rewrite,[status(thm)],[t7_wellord2]),
[] ).
cnf(177105472,plain,
connected(inclusion_relation(a)),
inference(resolution,[status(thm)],[166471864,166530768]),
[] ).
fof(t2_wellord2,plain,
! [A] : reflexive(inclusion_relation(A)),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166457000,plain,
reflexive(inclusion_relation(A)),
inference(rewrite,[status(thm)],[t2_wellord2]),
[] ).
fof(dt_k1_wellord2,plain,
! [A] : relation(inclusion_relation(A)),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166424472,plain,
relation(inclusion_relation(A)),
inference(rewrite,[status(thm)],[dt_k1_wellord2]),
[] ).
fof(t3_wellord2,plain,
! [A] : transitive(inclusion_relation(A)),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166465216,plain,
transitive(inclusion_relation(A)),
inference(rewrite,[status(thm)],[t3_wellord2]),
[] ).
fof(t6_wellord2,plain,
! [A] :
( ~ ordinal(A)
| well_founded_relation(inclusion_relation(A)) ),
file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166330240,plain,
( ~ ordinal(A)
| well_founded_relation(inclusion_relation(A)) ),
inference(rewrite,[status(thm)],[t6_wellord2]),
[] ).
cnf(177117352,plain,
well_founded_relation(inclusion_relation(a)),
inference(resolution,[status(thm)],[166330240,166530768]),
[] ).
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/SystemOnTPTP22630/SEU275+1.p',unknown),
[] ).
cnf(166419456,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(166523072,plain,
~ well_ordering(inclusion_relation(a)),
inference(rewrite,[status(thm)],[t7_wellord2]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[166476024,177105472,166457000,166424472,166465216,177117352,166419456,166523072]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t5_wellord2,plain,(antisymmetric(inclusion_relation(A))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166476024,plain,(antisymmetric(inclusion_relation(A))),inference(rewrite,[status(thm)],[t5_wellord2]),[]).
%
% fof(t4_wellord2,plain,(~ordinal(A)|connected(inclusion_relation(A))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166471864,plain,(~ordinal(A)|connected(inclusion_relation(A))),inference(rewrite,[status(thm)],[t4_wellord2]),[]).
%
% fof(t7_wellord2,plain,((ordinal(a)&~well_ordering(inclusion_relation(a)))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166530768,plain,(ordinal(a)),inference(rewrite,[status(thm)],[t7_wellord2]),[]).
%
% cnf(177105472,plain,(connected(inclusion_relation(a))),inference(resolution,[status(thm)],[166471864,166530768]),[]).
%
% fof(t2_wellord2,plain,(reflexive(inclusion_relation(A))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166457000,plain,(reflexive(inclusion_relation(A))),inference(rewrite,[status(thm)],[t2_wellord2]),[]).
%
% fof(dt_k1_wellord2,plain,(relation(inclusion_relation(A))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166424472,plain,(relation(inclusion_relation(A))),inference(rewrite,[status(thm)],[dt_k1_wellord2]),[]).
%
% fof(t3_wellord2,plain,(transitive(inclusion_relation(A))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166465216,plain,(transitive(inclusion_relation(A))),inference(rewrite,[status(thm)],[t3_wellord2]),[]).
%
% fof(t6_wellord2,plain,(~ordinal(A)|well_founded_relation(inclusion_relation(A))),file('/tmp/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166330240,plain,(~ordinal(A)|well_founded_relation(inclusion_relation(A))),inference(rewrite,[status(thm)],[t6_wellord2]),[]).
%
% cnf(177117352,plain,(well_founded_relation(inclusion_relation(a))),inference(resolution,[status(thm)],[166330240,166530768]),[]).
%
% 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/SystemOnTPTP22630/SEU275+1.p',unknown),[]).
%
% cnf(166419456,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(166523072,plain,(~well_ordering(inclusion_relation(a))),inference(rewrite,[status(thm)],[t7_wellord2]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[166476024,177105472,166457000,166424472,166465216,177117352,166419456,166523072]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------