TSTP Solution File: NUM159-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM159-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:24:34 EDT 2023
% Result : Unsatisfiable 127.02s 16.37s
% Output : CNFRefutation 127.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 20 unt; 0 def)
% Number of atoms : 128 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 114 ( 49 ~; 65 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 122 (; 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( X != Y
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f163,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f165,plain,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f167,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f189,plain,
! [Z,Y] :
( ! [X] : ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f189]) ).
fof(f192,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f193,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f194,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f322,plain,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
inference(cnf_transformation,[status(esa)],[f138]) ).
fof(f347,plain,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
inference(cnf_transformation,[status(esa)],[f159]) ).
fof(f348,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f165]) ).
fof(f773,plain,
! [X0,X1,X2] :
( member(X0,complement(X1))
| member(X0,X1)
| ~ subclass(X2,universal_class)
| ~ member(X0,X2) ),
inference(resolution,[status(thm)],[f193,f161]) ).
fof(f774,plain,
! [X0,X1,X2] :
( member(X0,complement(X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f773,f164]) ).
fof(f904,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f162,f192]) ).
fof(f913,plain,
! [X0,X1,X2] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),complement(X2))
| member(not_subclass_element(X0,X1),X2) ),
inference(resolution,[status(thm)],[f162,f774]) ).
fof(f928,plain,
! [X0,X1,X2] :
( subclass(X0,X1)
| ~ subclass(X2,X1)
| ~ member(not_subclass_element(X0,X1),X2) ),
inference(resolution,[status(thm)],[f163,f161]) ).
fof(f1087,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f190,f162]) ).
fof(f2093,plain,
! [X0,X1,X2] :
( subclass(complement(X0),X1)
| ~ subclass(X2,X0)
| ~ member(not_subclass_element(complement(X0),X1),X2) ),
inference(resolution,[status(thm)],[f904,f161]) ).
fof(f2306,plain,
! [X0,X1,X2,X3] :
( subclass(complement(X0),X1)
| ~ subclass(X2,X0)
| ~ subclass(X3,X2)
| ~ member(not_subclass_element(complement(X0),X1),X3) ),
inference(resolution,[status(thm)],[f2093,f161]) ).
fof(f4451,plain,
! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| subclass(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[f913,f904]) ).
fof(f4452,plain,
! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f4451]) ).
fof(f4455,plain,
! [X0,X1] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) ),
inference(resolution,[status(thm)],[f913,f163]) ).
fof(f4456,plain,
! [X0,X1] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f4455]) ).
fof(f4668,plain,
! [X0,X1,X2] :
( subclass(complement(X0),complement(X1))
| subclass(complement(X0),complement(X1))
| ~ subclass(X2,X0)
| ~ subclass(X1,X2) ),
inference(resolution,[status(thm)],[f4456,f2306]) ).
fof(f4669,plain,
! [X0,X1,X2] :
( subclass(complement(X0),complement(X1))
| ~ subclass(X2,X0)
| ~ subclass(X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f4668]) ).
fof(f4670,plain,
! [X0,X1] :
( subclass(complement(X0),complement(X1))
| subclass(complement(X0),complement(X1))
| ~ subclass(X1,X0) ),
inference(resolution,[status(thm)],[f4456,f2093]) ).
fof(f4671,plain,
! [X0,X1] :
( subclass(complement(X0),complement(X1))
| ~ subclass(X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f4670]) ).
fof(f4691,plain,
! [X0,X1] :
( subclass(X0,complement(complement(X1)))
| ~ member(not_subclass_element(X0,complement(complement(X1))),X1) ),
inference(resolution,[status(thm)],[f4456,f192]) ).
fof(f4862,plain,
! [X0] :
( subclass(complement(complement(X0)),X0)
| subclass(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f4452,f163]) ).
fof(f4863,plain,
! [X0] : subclass(complement(complement(X0)),X0),
inference(duplicate_literals_removal,[status(esa)],[f4862]) ).
fof(f4976,plain,
! [X0] : subclass(complement(X0),complement(complement(complement(X0)))),
inference(resolution,[status(thm)],[f4863,f4671]) ).
fof(f4977,plain,
! [X0] :
( ~ subclass(X0,complement(complement(X0)))
| X0 = complement(complement(X0)) ),
inference(resolution,[status(thm)],[f4863,f167]) ).
fof(f5117,plain,
! [X0,X1] :
( subclass(complement(complement(complement(complement(X0)))),complement(X1))
| ~ subclass(X1,complement(X0)) ),
inference(resolution,[status(thm)],[f4976,f4669]) ).
fof(f7862,plain,
! [X0] :
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[f4691,f162]) ).
fof(f7863,plain,
! [X0] : subclass(X0,complement(complement(X0))),
inference(duplicate_literals_removal,[status(esa)],[f7862]) ).
fof(f7905,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f4977,f7863]) ).
fof(f8207,plain,
! [X0,X1] : complement(intersection(X0,complement(X1))) = union(complement(X0),X1),
inference(paramodulation,[status(thm)],[f7905,f194]) ).
fof(f9737,plain,
! [X0,X1] :
( subclass(complement(complement(X0)),complement(X1))
| ~ subclass(X1,complement(X0)) ),
inference(forward_demodulation,[status(thm)],[f7905,f5117]) ).
fof(f9738,plain,
! [X0,X1] :
( subclass(X0,complement(X1))
| ~ subclass(X1,complement(X0)) ),
inference(forward_demodulation,[status(thm)],[f7905,f9737]) ).
fof(f64283,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X2) ),
inference(resolution,[status(thm)],[f1087,f928]) ).
fof(f64284,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f64283]) ).
fof(f66133,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(resolution,[status(thm)],[f64284,f348]) ).
fof(f66174,plain,
! [X0,X1] : subclass(X0,complement(intersection(X1,complement(X0)))),
inference(resolution,[status(thm)],[f66133,f9738]) ).
fof(f66175,plain,
! [X0,X1] : subclass(X0,union(complement(X1),X0)),
inference(forward_demodulation,[status(thm)],[f8207,f66174]) ).
fof(f66560,plain,
! [X0,X1] : subclass(X0,union(X1,X0)),
inference(paramodulation,[status(thm)],[f7905,f66175]) ).
fof(f66655,plain,
subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
inference(paramodulation,[status(thm)],[f322,f66560]) ).
fof(f66656,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f66655,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM159-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:48:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 127.02/16.37 % Refutation found
% 127.02/16.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 127.02/16.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 127.81/16.51 % Elapsed time: 16.149862 seconds
% 127.81/16.51 % CPU time: 127.710855 seconds
% 127.81/16.51 % Memory used: 429.073 MB
%------------------------------------------------------------------------------