TSTP Solution File: SEU244+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU244+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:53:30 EDT 2009
% Result : Theorem 0.4s
% Output : Refutation 0.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 282 ( 124 ~; 135 |; 23 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t8_wellord1,plain,
( ( relation(a)
| ~ well_orders(a,relation_field(a)) )
& ( well_orders(a,relation_field(a))
| ~ well_orders(a,relation_field(a)) )
& ( ~ well_ordering(a)
| ~ well_orders(a,relation_field(a)) )
& ( relation(a)
| well_ordering(a) )
& ( well_orders(a,relation_field(a))
| well_ordering(a) )
& ( ~ well_ordering(a)
| well_ordering(a) )
& ( relation(a)
| relation(a) )
& ( well_orders(a,relation_field(a))
| relation(a) )
& ( ~ well_ordering(a)
| relation(a) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(153228960,plain,
( well_orders(a,relation_field(a))
| relation(a) ),
inference(rewrite,[status(thm)],[t8_wellord1]),
[] ).
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/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(152854952,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(153239272,plain,
( well_orders(a,relation_field(a))
| well_ordering(a) ),
inference(rewrite,[status(thm)],[t8_wellord1]),
[] ).
cnf(172178472,plain,
( connected(a)
| well_orders(a,relation_field(a)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152854952,153239272]),
[] ).
cnf(153234312,plain,
relation(a),
inference(rewrite,[status(thm)],[t8_wellord1]),
[] ).
fof(d5_wellord1,plain,
! [A,B] :
( ( well_orders(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_well_founded_in(A,B)
| ~ relation(A) )
& ( is_transitive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) )
& ( is_antisymmetric_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) )
& ( is_connected_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) )
& ( is_well_founded_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) )
& ( is_reflexive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(153019592,plain,
( is_connected_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d5_wellord1]),
[] ).
fof(d14_relat_2,plain,
! [A] :
( ( connected(A)
| ~ is_connected_in(A,relation_field(A))
| ~ relation(A) )
& ( ~ connected(A)
| is_connected_in(A,relation_field(A))
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(152906632,plain,
( connected(A)
| ~ is_connected_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d14_relat_2]),
[] ).
cnf(171920944,plain,
( connected(a)
| ~ is_connected_in(a,relation_field(a)) ),
inference(resolution,[status(thm)],[152906632,153234312]),
[] ).
cnf(172611056,plain,
connected(a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172178472,153234312,153019592,171920944]),
[] ).
cnf(152962824,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(172189184,plain,
( antisymmetric(a)
| well_orders(a,relation_field(a)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152962824,153239272]),
[] ).
cnf(153032408,plain,
( is_antisymmetric_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d5_wellord1]),
[] ).
fof(d12_relat_2,plain,
! [A] :
( ( antisymmetric(A)
| ~ is_antisymmetric_in(A,relation_field(A))
| ~ relation(A) )
& ( ~ antisymmetric(A)
| is_antisymmetric_in(A,relation_field(A))
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(152885320,plain,
( antisymmetric(A)
| ~ is_antisymmetric_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d12_relat_2]),
[] ).
cnf(171892848,plain,
( antisymmetric(a)
| ~ is_antisymmetric_in(a,relation_field(a)) ),
inference(resolution,[status(thm)],[152885320,153234312]),
[] ).
cnf(172736672,plain,
antisymmetric(a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172189184,153234312,153032408,171892848]),
[] ).
fof(d9_relat_2,plain,
! [A] :
( ( reflexive(A)
| ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A) )
& ( ~ reflexive(A)
| is_reflexive_in(A,relation_field(A))
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(153087504,plain,
( reflexive(A)
| ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d9_relat_2]),
[] ).
cnf(153002200,plain,
( is_reflexive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d5_wellord1]),
[] ).
cnf(172355408,plain,
( is_reflexive_in(a,relation_field(a))
| well_ordering(a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153002200,153239272]),
[] ).
cnf(153080552,plain,
( ~ reflexive(A)
| is_reflexive_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d9_relat_2]),
[] ).
cnf(152936016,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(171824432,plain,
( reflexive(a)
| ~ well_ordering(a) ),
inference(resolution,[status(thm)],[152936016,153234312]),
[] ).
cnf(172897632,plain,
is_reflexive_in(a,relation_field(a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172355408,153234312,153080552,171824432]),
[] ).
cnf(172931224,plain,
reflexive(a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153087504,172897632]),
[] ).
cnf(152974008,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(172199896,plain,
( transitive(a)
| well_orders(a,relation_field(a)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152974008,153239272]),
[] ).
cnf(152854352,plain,
( is_transitive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d5_wellord1]),
[] ).
fof(d16_relat_2,plain,
! [A] :
( ( transitive(A)
| ~ is_transitive_in(A,relation_field(A))
| ~ relation(A) )
& ( ~ transitive(A)
| is_transitive_in(A,relation_field(A))
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(152927888,plain,
( transitive(A)
| ~ is_transitive_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d16_relat_2]),
[] ).
cnf(171949008,plain,
( transitive(a)
| ~ is_transitive_in(a,relation_field(a)) ),
inference(resolution,[status(thm)],[152927888,153234312]),
[] ).
cnf(172831696,plain,
transitive(a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172199896,153234312,152854352,171949008]),
[] ).
fof(t5_wellord1,plain,
! [A] :
( ( well_founded_relation(A)
| ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A) )
& ( ~ well_founded_relation(A)
| is_well_founded_in(A,relation_field(A))
| ~ relation(A) ) ),
file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),
[] ).
cnf(153116040,plain,
( well_founded_relation(A)
| ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[t5_wellord1]),
[] ).
cnf(153010960,plain,
( is_well_founded_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d5_wellord1]),
[] ).
cnf(172462312,plain,
( is_well_founded_in(a,relation_field(a))
| well_ordering(a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153010960,153239272]),
[] ).
cnf(153109176,plain,
( ~ well_founded_relation(A)
| is_well_founded_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[t5_wellord1]),
[] ).
cnf(152948808,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d4_wellord1]),
[] ).
cnf(171834400,plain,
( well_founded_relation(a)
| ~ well_ordering(a) ),
inference(resolution,[status(thm)],[152948808,153234312]),
[] ).
cnf(172975032,plain,
is_well_founded_in(a,relation_field(a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172462312,153234312,153109176,171834400]),
[] ).
cnf(173003088,plain,
well_founded_relation(a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153116040,172975032]),
[] ).
cnf(152919024,plain,
( ~ transitive(A)
| is_transitive_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d16_relat_2]),
[] ).
cnf(172318136,plain,
( is_transitive_in(a,relation_field(a))
| well_orders(a,relation_field(a)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152919024,172199896]),
[] ).
cnf(152897752,plain,
( ~ connected(A)
| is_connected_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d14_relat_2]),
[] ).
cnf(172275000,plain,
( is_connected_in(a,relation_field(a))
| well_orders(a,relation_field(a)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152897752,172178472]),
[] ).
cnf(153060808,plain,
( well_orders(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_well_founded_in(A,B)
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d5_wellord1]),
[] ).
cnf(152872152,plain,
( ~ antisymmetric(A)
| is_antisymmetric_in(A,relation_field(A))
| ~ relation(A) ),
inference(rewrite,[status(thm)],[d12_relat_2]),
[] ).
cnf(176378704,plain,
( well_orders(A,relation_field(A))
| ~ is_reflexive_in(A,relation_field(A))
| ~ is_transitive_in(A,relation_field(A))
| ~ is_connected_in(A,relation_field(A))
| ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A)
| ~ antisymmetric(A) ),
inference(resolution,[status(thm)],[153060808,152872152]),
[] ).
cnf(171854464,plain,
( antisymmetric(a)
| ~ well_ordering(a) ),
inference(resolution,[status(thm)],[152962824,153234312]),
[] ).
cnf(176383904,plain,
well_orders(a,relation_field(a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153239272,153228960,172318136,172275000,172897632,172975032,176378704,171854464]),
[] ).
cnf(153244608,plain,
( ~ well_ordering(a)
| ~ well_orders(a,relation_field(a)) ),
inference(rewrite,[status(thm)],[t8_wellord1]),
[] ).
cnf(152989432,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(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[172611056,172736672,172931224,153234312,172831696,173003088,176383904,153244608,152989432]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(t8_wellord1,plain,(((relation(a)|~well_orders(a,relation_field(a)))&(well_orders(a,relation_field(a))|~well_orders(a,relation_field(a)))&(~well_ordering(a)|~well_orders(a,relation_field(a)))&(relation(a)|well_ordering(a))&(well_orders(a,relation_field(a))|well_ordering(a))&(~well_ordering(a)|well_ordering(a))&(relation(a)|relation(a))&(well_orders(a,relation_field(a))|relation(a))&(~well_ordering(a)|relation(a)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(153228960,plain,(well_orders(a,relation_field(a))|relation(a)),inference(rewrite,[status(thm)],[t8_wellord1]),[]).
%
% 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/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(152854952,plain,(connected(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(153239272,plain,(well_orders(a,relation_field(a))|well_ordering(a)),inference(rewrite,[status(thm)],[t8_wellord1]),[]).
%
% cnf(172178472,plain,(connected(a)|well_orders(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152854952,153239272]),[]).
%
% cnf(153234312,plain,(relation(a)),inference(rewrite,[status(thm)],[t8_wellord1]),[]).
%
% fof(d5_wellord1,plain,(((well_orders(A,B)|~is_reflexive_in(A,B)|~is_transitive_in(A,B)|~is_antisymmetric_in(A,B)|~is_connected_in(A,B)|~is_well_founded_in(A,B)|~relation(A))&(is_transitive_in(A,B)|~well_orders(A,B)|~relation(A))&(is_antisymmetric_in(A,B)|~well_orders(A,B)|~relation(A))&(is_connected_in(A,B)|~well_orders(A,B)|~relation(A))&(is_well_founded_in(A,B)|~well_orders(A,B)|~relation(A))&(is_reflexive_in(A,B)|~well_orders(A,B)|~relation(A)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(153019592,plain,(is_connected_in(A,B)|~well_orders(A,B)|~relation(A)),inference(rewrite,[status(thm)],[d5_wellord1]),[]).
%
% fof(d14_relat_2,plain,(((connected(A)|~is_connected_in(A,relation_field(A))|~relation(A))&(~connected(A)|is_connected_in(A,relation_field(A))|~relation(A)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(152906632,plain,(connected(A)|~is_connected_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d14_relat_2]),[]).
%
% cnf(171920944,plain,(connected(a)|~is_connected_in(a,relation_field(a))),inference(resolution,[status(thm)],[152906632,153234312]),[]).
%
% cnf(172611056,plain,(connected(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172178472,153234312,153019592,171920944]),[]).
%
% cnf(152962824,plain,(antisymmetric(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(172189184,plain,(antisymmetric(a)|well_orders(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152962824,153239272]),[]).
%
% cnf(153032408,plain,(is_antisymmetric_in(A,B)|~well_orders(A,B)|~relation(A)),inference(rewrite,[status(thm)],[d5_wellord1]),[]).
%
% fof(d12_relat_2,plain,(((antisymmetric(A)|~is_antisymmetric_in(A,relation_field(A))|~relation(A))&(~antisymmetric(A)|is_antisymmetric_in(A,relation_field(A))|~relation(A)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(152885320,plain,(antisymmetric(A)|~is_antisymmetric_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d12_relat_2]),[]).
%
% cnf(171892848,plain,(antisymmetric(a)|~is_antisymmetric_in(a,relation_field(a))),inference(resolution,[status(thm)],[152885320,153234312]),[]).
%
% cnf(172736672,plain,(antisymmetric(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172189184,153234312,153032408,171892848]),[]).
%
% fof(d9_relat_2,plain,(((reflexive(A)|~is_reflexive_in(A,relation_field(A))|~relation(A))&(~reflexive(A)|is_reflexive_in(A,relation_field(A))|~relation(A)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(153087504,plain,(reflexive(A)|~is_reflexive_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d9_relat_2]),[]).
%
% cnf(153002200,plain,(is_reflexive_in(A,B)|~well_orders(A,B)|~relation(A)),inference(rewrite,[status(thm)],[d5_wellord1]),[]).
%
% cnf(172355408,plain,(is_reflexive_in(a,relation_field(a))|well_ordering(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153002200,153239272]),[]).
%
% cnf(153080552,plain,(~reflexive(A)|is_reflexive_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d9_relat_2]),[]).
%
% cnf(152936016,plain,(reflexive(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(171824432,plain,(reflexive(a)|~well_ordering(a)),inference(resolution,[status(thm)],[152936016,153234312]),[]).
%
% cnf(172897632,plain,(is_reflexive_in(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[172355408,153234312,153080552,171824432]),[]).
%
% cnf(172931224,plain,(reflexive(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153087504,172897632]),[]).
%
% cnf(152974008,plain,(transitive(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(172199896,plain,(transitive(a)|well_orders(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152974008,153239272]),[]).
%
% cnf(152854352,plain,(is_transitive_in(A,B)|~well_orders(A,B)|~relation(A)),inference(rewrite,[status(thm)],[d5_wellord1]),[]).
%
% fof(d16_relat_2,plain,(((transitive(A)|~is_transitive_in(A,relation_field(A))|~relation(A))&(~transitive(A)|is_transitive_in(A,relation_field(A))|~relation(A)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(152927888,plain,(transitive(A)|~is_transitive_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d16_relat_2]),[]).
%
% cnf(171949008,plain,(transitive(a)|~is_transitive_in(a,relation_field(a))),inference(resolution,[status(thm)],[152927888,153234312]),[]).
%
% cnf(172831696,plain,(transitive(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172199896,153234312,152854352,171949008]),[]).
%
% fof(t5_wellord1,plain,(((well_founded_relation(A)|~is_well_founded_in(A,relation_field(A))|~relation(A))&(~well_founded_relation(A)|is_well_founded_in(A,relation_field(A))|~relation(A)))),file('/tmp/SystemOnTPTP16054/SEU244+1.p',unknown),[]).
%
% cnf(153116040,plain,(well_founded_relation(A)|~is_well_founded_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[t5_wellord1]),[]).
%
% cnf(153010960,plain,(is_well_founded_in(A,B)|~well_orders(A,B)|~relation(A)),inference(rewrite,[status(thm)],[d5_wellord1]),[]).
%
% cnf(172462312,plain,(is_well_founded_in(a,relation_field(a))|well_ordering(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153010960,153239272]),[]).
%
% cnf(153109176,plain,(~well_founded_relation(A)|is_well_founded_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[t5_wellord1]),[]).
%
% cnf(152948808,plain,(well_founded_relation(A)|~well_ordering(A)|~relation(A)),inference(rewrite,[status(thm)],[d4_wellord1]),[]).
%
% cnf(171834400,plain,(well_founded_relation(a)|~well_ordering(a)),inference(resolution,[status(thm)],[152948808,153234312]),[]).
%
% cnf(172975032,plain,(is_well_founded_in(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[172462312,153234312,153109176,171834400]),[]).
%
% cnf(173003088,plain,(well_founded_relation(a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153234312,153116040,172975032]),[]).
%
% cnf(152919024,plain,(~transitive(A)|is_transitive_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d16_relat_2]),[]).
%
% cnf(172318136,plain,(is_transitive_in(a,relation_field(a))|well_orders(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152919024,172199896]),[]).
%
% cnf(152897752,plain,(~connected(A)|is_connected_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d14_relat_2]),[]).
%
% cnf(172275000,plain,(is_connected_in(a,relation_field(a))|well_orders(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153228960,152897752,172178472]),[]).
%
% cnf(153060808,plain,(well_orders(A,B)|~is_reflexive_in(A,B)|~is_transitive_in(A,B)|~is_antisymmetric_in(A,B)|~is_connected_in(A,B)|~is_well_founded_in(A,B)|~relation(A)),inference(rewrite,[status(thm)],[d5_wellord1]),[]).
%
% cnf(152872152,plain,(~antisymmetric(A)|is_antisymmetric_in(A,relation_field(A))|~relation(A)),inference(rewrite,[status(thm)],[d12_relat_2]),[]).
%
% cnf(176378704,plain,(well_orders(A,relation_field(A))|~is_reflexive_in(A,relation_field(A))|~is_transitive_in(A,relation_field(A))|~is_connected_in(A,relation_field(A))|~is_well_founded_in(A,relation_field(A))|~relation(A)|~antisymmetric(A)),inference(resolution,[status(thm)],[153060808,152872152]),[]).
%
% cnf(171854464,plain,(antisymmetric(a)|~well_ordering(a)),inference(resolution,[status(thm)],[152962824,153234312]),[]).
%
% cnf(176383904,plain,(well_orders(a,relation_field(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153239272,153228960,172318136,172275000,172897632,172975032,176378704,171854464]),[]).
%
% cnf(153244608,plain,(~well_ordering(a)|~well_orders(a,relation_field(a))),inference(rewrite,[status(thm)],[t8_wellord1]),[]).
%
% cnf(152989432,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(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172611056,172736672,172931224,153234312,172831696,173003088,176383904,153244608,152989432]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------