TSTP Solution File: SET511-6 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET511-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 : Tue Apr 30 20:39:47 EDT 2024
% Result : Unsatisfiable 95.67s 12.41s
% Output : CNFRefutation 96.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 21 unt; 0 def)
% Number of atoms : 135 ( 56 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 127 ( 58 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( restrict(X,singleton(Z),universal_class) != null_class
| ~ member(Z,domain_of(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( X = null_class
| member(regular(X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( X = null_class
| intersection(X,regular(X)) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f122,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,unordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f129,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f130,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f141,plain,
! [Z,X] :
( ! [Y] : ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f152,plain,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f188,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f189,plain,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f245,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f251,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
fof(f252,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f251]) ).
fof(f755,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f188,f252]) ).
fof(f757,plain,
! [X0,X1] :
( X0 = null_class
| ~ subclass(X0,X1)
| member(regular(X0),X1) ),
inference(resolution,[status(thm)],[f188,f115]) ).
fof(f766,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f795,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f142,f116]) ).
fof(f1463,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,regular(X1))
| member(X0,null_class)
| X1 = null_class ),
inference(paramodulation,[status(thm)],[f189,f145]) ).
fof(f6106,plain,
! [X0,X1] :
( X0 = null_class
| ~ subclass(X0,complement(X1))
| ~ member(regular(X0),X1) ),
inference(resolution,[status(thm)],[f757,f146]) ).
fof(f6270,plain,
! [X0] :
( complement(X0) = null_class
| complement(X0) = null_class
| ~ subclass(complement(X0),X0) ),
inference(resolution,[status(thm)],[f766,f757]) ).
fof(f6271,plain,
! [X0] :
( complement(X0) = null_class
| ~ subclass(complement(X0),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f6270]) ).
fof(f6296,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f6271,f118]) ).
fof(f16145,plain,
! [X0,X1] :
( X0 = null_class
| ~ subclass(X0,complement(X1))
| X0 = null_class
| ~ subclass(X0,X1) ),
inference(resolution,[status(thm)],[f6106,f757]) ).
fof(f16146,plain,
! [X0,X1] :
( X0 = null_class
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f16145]) ).
fof(f19020,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class)
| ~ subclass(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f6296,f16146]) ).
fof(f19021,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f19020,f118]) ).
fof(f20777,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f795,f117]) ).
fof(f20778,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(esa)],[f20777]) ).
fof(f21246,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(resolution,[status(thm)],[f20778,f19021]) ).
fof(f21281,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(paramodulation,[status(thm)],[f150,f21246]) ).
fof(f21423,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(resolution,[status(thm)],[f21281,f152]) ).
fof(f21453,plain,
domain_of(null_class) = null_class,
inference(resolution,[status(thm)],[f21423,f188]) ).
fof(f21607,plain,
! [X0] : ~ member(X0,null_class),
inference(backward_demodulation,[status(thm)],[f21453,f21423]) ).
fof(f26905,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,regular(X1))
| X1 = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f1463,f21607]) ).
fof(f26932,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| ~ member(X0,X1)
| singleton(X1) = null_class
| singleton(X1) = null_class ),
inference(paramodulation,[status(thm)],[f755,f26905]) ).
fof(f26933,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| ~ member(X0,X1)
| singleton(X1) = null_class ),
inference(duplicate_literals_removal,[status(esa)],[f26932]) ).
fof(f27709,plain,
! [X0] :
( ~ member(regular(singleton(X0)),X0)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f26933,f188]) ).
fof(f27710,plain,
! [X0] :
( ~ member(regular(singleton(X0)),X0)
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(esa)],[f27709]) ).
fof(f27724,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ subclass(singleton(X0),X0) ),
inference(resolution,[status(thm)],[f27710,f757]) ).
fof(f27725,plain,
! [X0] :
( singleton(X0) = null_class
| ~ subclass(singleton(X0),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f27724]) ).
fof(f27779,plain,
singleton(universal_class) = null_class,
inference(resolution,[status(thm)],[f27725,f118]) ).
fof(f27797,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,universal_class),
inference(paramodulation,[status(thm)],[f27779,f130]) ).
fof(f44770,plain,
ordered_pair(x,universal_class) != ordered_pair(x,universal_class),
inference(backward_demodulation,[status(thm)],[f27797,f245]) ).
fof(f44771,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f44770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET511-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.17/0.32 % Computer : n002.cluster.edu
% 0.17/0.32 % Model : x86_64 x86_64
% 0.17/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.32 % Memory : 8042.1875MB
% 0.17/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.32 % CPULimit : 300
% 0.17/0.32 % WCLimit : 300
% 0.17/0.32 % DateTime : Mon Apr 29 22:01:24 EDT 2024
% 0.17/0.32 % CPUTime :
% 0.17/0.33 % Drodi V3.6.0
% 95.67/12.41 % Refutation found
% 95.67/12.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 95.67/12.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 96.47/12.53 % Elapsed time: 12.192750 seconds
% 96.47/12.53 % CPU time: 96.407254 seconds
% 96.47/12.53 % Total memory used: 509.128 MB
% 96.47/12.53 % Net memory used: 491.562 MB
%------------------------------------------------------------------------------