TSTP Solution File: SET510-6 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET510-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 20:39:46 EDT 2024
% Result : Unsatisfiable 0.21s 0.45s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 111 ( 18 unt; 0 def)
% Number of atoms : 254 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 257 ( 114 ~; 133 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 89 !; 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(f7,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| X = Y ),
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(f9,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
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(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(f47,axiom,
! [X] :
( ~ inductive(X)
| member(null_class,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
member(omega,universal_class),
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,
singleton(universal_class) != null_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(f121,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
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(f124,plain,
! [X] :
( ~ member(X,universal_class)
| ! [Y] : member(X,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f125,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f128,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f129,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
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(f169,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f172,plain,
inductive(omega),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f174,plain,
member(omega,universal_class),
inference(cnf_transformation,[status(esa)],[f52]) ).
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,
singleton(universal_class) != null_class,
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f250,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f129,f128]) ).
fof(f252,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ),
inference(resolution,[status(thm)],[f121,f118]) ).
fof(f254,plain,
! [X0] :
( universal_class = X0
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(resolution,[status(thm)],[f252,f117]) ).
fof(f279,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
fof(f280,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f279]) ).
fof(f281,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f129,f125]) ).
fof(f355,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f280,f188]) ).
fof(f399,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| X1 = null_class ),
inference(paramodulation,[status(thm)],[f189,f142]) ).
fof(f413,plain,
( spl0_18
<=> universal_class = universal_class ),
introduced(split_symbol_definition) ).
fof(f430,plain,
regular(singleton(universal_class)) = universal_class,
inference(resolution,[status(thm)],[f355,f245]) ).
fof(f446,plain,
( spl0_25
<=> inductive(null_class) ),
introduced(split_symbol_definition) ).
fof(f448,plain,
( ~ inductive(null_class)
| spl0_25 ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f453,plain,
( spl0_26
<=> member(null_class,universal_class) ),
introduced(split_symbol_definition) ).
fof(f454,plain,
( member(null_class,universal_class)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f468,plain,
( spl0_29
<=> singleton(universal_class) = null_class ),
introduced(split_symbol_definition) ).
fof(f469,plain,
( singleton(universal_class) = null_class
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( spl0_30
<=> intersection(singleton(universal_class),universal_class) = null_class ),
introduced(split_symbol_definition) ).
fof(f472,plain,
( intersection(singleton(universal_class),universal_class) = null_class
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( singleton(universal_class) = null_class
| intersection(singleton(universal_class),universal_class) = null_class ),
inference(paramodulation,[status(thm)],[f430,f189]) ).
fof(f475,plain,
( spl0_29
| spl0_30 ),
inference(split_clause,[status(thm)],[f474,f468,f471]) ).
fof(f476,plain,
( spl0_31
<=> member(universal_class,singleton(universal_class)) ),
introduced(split_symbol_definition) ).
fof(f477,plain,
( member(universal_class,singleton(universal_class))
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( singleton(universal_class) = null_class
| member(universal_class,singleton(universal_class)) ),
inference(paramodulation,[status(thm)],[f430,f188]) ).
fof(f480,plain,
( spl0_29
| spl0_31 ),
inference(split_clause,[status(thm)],[f479,f468,f476]) ).
fof(f481,plain,
( $false
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f245]) ).
fof(f482,plain,
~ spl0_29,
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f541,plain,
( spl0_41
<=> member(universal_class,null_class) ),
introduced(split_symbol_definition) ).
fof(f542,plain,
( member(universal_class,null_class)
| ~ spl0_41 ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f559,plain,
! [X0] :
( ~ member(X0,null_class)
| member(X0,singleton(universal_class))
| ~ spl0_30 ),
inference(paramodulation,[status(thm)],[f472,f142]) ).
fof(f569,plain,
( spl0_46
<=> universal_class = singleton(universal_class) ),
introduced(split_symbol_definition) ).
fof(f570,plain,
( universal_class = singleton(universal_class)
| ~ spl0_46 ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f571,plain,
( universal_class != singleton(universal_class)
| spl0_46 ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f574,plain,
! [X0] :
( ~ member(X0,null_class)
| X0 = universal_class
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f559,f280]) ).
fof(f583,plain,
( spl0_48
<=> null_class = universal_class ),
introduced(split_symbol_definition) ).
fof(f584,plain,
( null_class = universal_class
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( null_class = universal_class
| ~ inductive(null_class)
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f574,f169]) ).
fof(f587,plain,
( spl0_48
| ~ spl0_25
| ~ spl0_30 ),
inference(split_clause,[status(thm)],[f586,f583,f446,f471]) ).
fof(f599,plain,
( universal_class != null_class
| ~ spl0_46 ),
inference(backward_demodulation,[status(thm)],[f570,f245]) ).
fof(f604,plain,
( spl0_50
<=> member(universal_class,universal_class) ),
introduced(split_symbol_definition) ).
fof(f605,plain,
( member(universal_class,universal_class)
| ~ spl0_50 ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f606,plain,
( ~ member(universal_class,universal_class)
| spl0_50 ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f627,plain,
( $false
| ~ spl0_46
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f599]) ).
fof(f628,plain,
( ~ spl0_46
| ~ spl0_48 ),
inference(contradiction_clause,[status(thm)],[f627]) ).
fof(f679,plain,
! [X0] :
( ~ member(universal_class,X0)
| member(universal_class,intersection(X0,singleton(universal_class)))
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f145,f477]) ).
fof(f683,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[f169,f172]) ).
fof(f771,plain,
! [X0] :
( member(not_subclass_element(universal_class,X0),universal_class)
| universal_class = X0 ),
inference(resolution,[status(thm)],[f116,f252]) ).
fof(f832,plain,
( member(universal_class,intersection(singleton(universal_class),singleton(universal_class)))
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f679,f477]) ).
fof(f1122,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[f115,f118]) ).
fof(f1124,plain,
! [X0] :
( ~ member(universal_class,X0)
| spl0_50 ),
inference(resolution,[status(thm)],[f1122,f606]) ).
fof(f1149,plain,
( universal_class = universal_class
| universal_class = universal_class ),
inference(resolution,[status(thm)],[f771,f254]) ).
fof(f1150,plain,
spl0_18,
inference(split_clause,[status(thm)],[f1149,f413]) ).
fof(f1162,plain,
( $false
| spl0_50
| ~ spl0_31 ),
inference(backward_subsumption_resolution,[status(thm)],[f832,f1124]) ).
fof(f1163,plain,
( spl0_50
| ~ spl0_31 ),
inference(contradiction_clause,[status(thm)],[f1162]) ).
fof(f1176,plain,
! [X0] :
( ~ member(universal_class,X0)
| member(universal_class,intersection(X0,universal_class))
| ~ spl0_50 ),
inference(resolution,[status(thm)],[f605,f145]) ).
fof(f1198,plain,
( ~ member(universal_class,singleton(universal_class))
| member(universal_class,null_class)
| ~ spl0_50
| ~ spl0_30 ),
inference(paramodulation,[status(thm)],[f472,f1176]) ).
fof(f1199,plain,
( ~ spl0_31
| spl0_41
| ~ spl0_50
| ~ spl0_30 ),
inference(split_clause,[status(thm)],[f1198,f476,f541,f604,f471]) ).
fof(f1201,plain,
! [X0] :
( member(universal_class,X0)
| X0 = null_class
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f542,f399]) ).
fof(f1212,plain,
! [X0] :
( singleton(X0) = null_class
| universal_class = X0
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f1201,f280]) ).
fof(f1274,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,null_class)
| universal_class = X0
| ~ spl0_41 ),
inference(paramodulation,[status(thm)],[f1212,f281]) ).
fof(f1275,plain,
! [X0] :
( ~ member(X0,universal_class)
| universal_class = X0
| ~ spl0_30
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[status(thm)],[f1274,f574]) ).
fof(f1324,plain,
! [X0] :
( universal_class = singleton(X0)
| ~ spl0_30
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f1275,f250]) ).
fof(f1325,plain,
( universal_class = omega
| ~ spl0_30
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f1275,f174]) ).
fof(f1326,plain,
( universal_class = null_class
| ~ spl0_30
| ~ spl0_41
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f1275,f454]) ).
fof(f1339,plain,
( inductive(universal_class)
| ~ spl0_30
| ~ spl0_41 ),
inference(backward_demodulation,[status(thm)],[f1325,f172]) ).
fof(f1384,plain,
( ~ inductive(universal_class)
| ~ spl0_30
| ~ spl0_41
| ~ spl0_26
| spl0_25 ),
inference(backward_demodulation,[status(thm)],[f1326,f448]) ).
fof(f1392,plain,
( $false
| ~ spl0_30
| ~ spl0_41
| ~ spl0_26
| spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f1384,f1339]) ).
fof(f1393,plain,
( ~ spl0_30
| ~ spl0_41
| ~ spl0_26
| spl0_25 ),
inference(contradiction_clause,[status(thm)],[f1392]) ).
fof(f1394,plain,
( member(null_class,universal_class)
| ~ spl0_30
| ~ spl0_41 ),
inference(backward_demodulation,[status(thm)],[f1325,f683]) ).
fof(f1395,plain,
( spl0_26
| ~ spl0_30
| ~ spl0_41 ),
inference(split_clause,[status(thm)],[f1394,f453,f471,f541]) ).
fof(f1681,plain,
( universal_class != universal_class
| ~ spl0_30
| ~ spl0_41
| spl0_46 ),
inference(backward_demodulation,[status(thm)],[f1324,f571]) ).
fof(f1682,plain,
( $false
| ~ spl0_30
| ~ spl0_41
| spl0_46 ),
inference(trivial_equality_resolution,[status(esa)],[f1681]) ).
fof(f1683,plain,
( ~ spl0_30
| ~ spl0_41
| spl0_46 ),
inference(contradiction_clause,[status(thm)],[f1682]) ).
fof(f1684,plain,
$false,
inference(sat_refutation,[status(thm)],[f475,f480,f482,f587,f628,f1150,f1163,f1199,f1393,f1395,f1683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : SET510-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Apr 29 22:04:17 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 0.21/0.45 % Refutation found
% 0.21/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.47 % Elapsed time: 0.097934 seconds
% 0.21/0.47 % CPU time: 0.630191 seconds
% 0.21/0.47 % Total memory used: 71.596 MB
% 0.21/0.47 % Net memory used: 71.057 MB
%------------------------------------------------------------------------------