TSTP Solution File: SET287-6 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET287-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:34:23 EDT 2023
% Result : Unsatisfiable 3.75s 0.89s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 18 unt; 0 def)
% Number of atoms : 163 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 136 ( 60 ~; 72 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 149 (; 149 !; 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(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(f21,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,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(f113,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
domain_of(intersection(complement(y),x)) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f119,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f122,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f142,plain,
! [Z,X] :
( ! [Y] : ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f142]) ).
fof(f144,plain,
! [Z,Y] :
( ! [X] : ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f144]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f153,plain,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f189,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f246,plain,
subclass(x,y),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f247,plain,
domain_of(intersection(complement(y),x)) != null_class,
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f252,plain,
! [X0] :
( ~ member(X0,x)
| member(X0,y) ),
inference(resolution,[status(thm)],[f116,f246]) ).
fof(f253,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[f116,f119]) ).
fof(f264,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f117,f145]) ).
fof(f265,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f117,f143]) ).
fof(f266,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f117,f147]) ).
fof(f269,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(resolution,[status(thm)],[f117,f253]) ).
fof(f927,plain,
! [X0] :
( subclass(complement(universal_class),X0)
| subclass(complement(universal_class),X0) ),
inference(resolution,[status(thm)],[f269,f266]) ).
fof(f928,plain,
! [X0] : subclass(complement(universal_class),X0),
inference(duplicate_literals_removal,[status(esa)],[f927]) ).
fof(f946,plain,
! [X0] :
( ~ subclass(X0,complement(universal_class))
| complement(universal_class) = X0 ),
inference(resolution,[status(thm)],[f928,f122]) ).
fof(f955,plain,
! [X0,X1] :
( subclass(intersection(X0,x),X1)
| member(not_subclass_element(intersection(X0,x),X1),y) ),
inference(resolution,[status(thm)],[f264,f252]) ).
fof(f962,plain,
! [X0,X1,X2] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ),
inference(resolution,[status(thm)],[f265,f147]) ).
fof(f1278,plain,
! [X0] :
( subclass(intersection(complement(y),x),X0)
| subclass(intersection(complement(y),x),X0) ),
inference(resolution,[status(thm)],[f962,f955]) ).
fof(f1279,plain,
! [X0] : subclass(intersection(complement(y),x),X0),
inference(duplicate_literals_removal,[status(esa)],[f1278]) ).
fof(f1323,plain,
complement(universal_class) = intersection(complement(y),x),
inference(resolution,[status(thm)],[f1279,f946]) ).
fof(f1352,plain,
domain_of(complement(universal_class)) != null_class,
inference(backward_demodulation,[status(thm)],[f1323,f247]) ).
fof(f1605,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f189,f145]) ).
fof(f1615,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f189,f147]) ).
fof(f1895,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,restrict(X1,X2,X3))
| member(X0,cross_product(X2,X3)) ),
inference(paramodulation,[status(thm)],[f151,f145]) ).
fof(f1896,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,restrict(X1,X2,X3))
| member(X0,X1) ),
inference(paramodulation,[status(thm)],[f151,f143]) ).
fof(f2238,plain,
( spl0_26
<=> null_class = null_class ),
introduced(split_symbol_definition) ).
fof(f2240,plain,
( null_class != null_class
| spl0_26 ),
inference(component_clause,[status(thm)],[f2238]) ).
fof(f2287,plain,
! [X0] :
( restrict(X0,singleton(regular(domain_of(X0))),universal_class) != null_class
| domain_of(X0) = null_class ),
inference(resolution,[status(thm)],[f153,f189]) ).
fof(f2663,plain,
! [X0,X1,X2] :
( member(regular(restrict(X0,X1,X2)),cross_product(X1,X2))
| restrict(X0,X1,X2) = null_class ),
inference(resolution,[status(thm)],[f1895,f189]) ).
fof(f2865,plain,
! [X0,X1,X2] :
( member(regular(restrict(X0,X1,X2)),X0)
| restrict(X0,X1,X2) = null_class ),
inference(resolution,[status(thm)],[f1896,f189]) ).
fof(f3001,plain,
! [X0,X1,X2,X3,X4] :
( restrict(restrict(X0,X1,X2),X3,X4) = null_class
| member(regular(restrict(restrict(X0,X1,X2),X3,X4)),X0) ),
inference(resolution,[status(thm)],[f2865,f1896]) ).
fof(f3002,plain,
! [X0,X1,X2,X3,X4] :
( restrict(restrict(X0,X1,X2),X3,X4) = null_class
| member(regular(restrict(restrict(X0,X1,X2),X3,X4)),cross_product(X1,X2)) ),
inference(resolution,[status(thm)],[f2865,f1895]) ).
fof(f3537,plain,
( spl0_74
<=> intersection(complement(y),x) = null_class ),
introduced(split_symbol_definition) ).
fof(f3538,plain,
( intersection(complement(y),x) = null_class
| ~ spl0_74 ),
inference(component_clause,[status(thm)],[f3537]) ).
fof(f3542,plain,
( spl0_75
<=> member(regular(complement(universal_class)),x) ),
introduced(split_symbol_definition) ).
fof(f3543,plain,
( member(regular(complement(universal_class)),x)
| ~ spl0_75 ),
inference(component_clause,[status(thm)],[f3542]) ).
fof(f3545,plain,
( intersection(complement(y),x) = null_class
| member(regular(complement(universal_class)),x) ),
inference(paramodulation,[status(thm)],[f1323,f1605]) ).
fof(f3546,plain,
( spl0_74
| spl0_75 ),
inference(split_clause,[status(thm)],[f3545,f3537,f3542]) ).
fof(f3550,plain,
( complement(universal_class) = null_class
| ~ spl0_74 ),
inference(forward_demodulation,[status(thm)],[f1323,f3538]) ).
fof(f3602,plain,
( domain_of(null_class) != null_class
| ~ spl0_74 ),
inference(backward_demodulation,[status(thm)],[f3550,f1352]) ).
fof(f4538,plain,
! [X0,X1,X2,X3,X4] :
( restrict(restrict(complement(X0),X1,X2),X3,X4) = null_class
| ~ member(regular(restrict(restrict(complement(X0),X1,X2),X3,X4)),X0) ),
inference(resolution,[status(thm)],[f3001,f147]) ).
fof(f5536,plain,
! [X0,X1,X2,X3] :
( restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1) = null_class
| restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1) = null_class ),
inference(resolution,[status(thm)],[f4538,f2663]) ).
fof(f5537,plain,
! [X0,X1,X2,X3] : restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1) = null_class,
inference(duplicate_literals_removal,[status(esa)],[f5536]) ).
fof(f5556,plain,
! [X0,X1,X2,X3,X4,X5] :
( restrict(restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1),X4,X5) = null_class
| member(regular(restrict(null_class,X4,X5)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f5537,f3002]) ).
fof(f5557,plain,
! [X0,X1,X2,X3] :
( restrict(null_class,X0,X1) = null_class
| member(regular(restrict(null_class,X0,X1)),cross_product(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f5537,f5556]) ).
fof(f5560,plain,
! [X0,X1,X2,X3,X4,X5] :
( restrict(restrict(restrict(complement(cross_product(X0,X1)),X2,X3),X0,X1),X4,X5) = null_class
| member(regular(restrict(null_class,X4,X5)),restrict(complement(cross_product(X0,X1)),X2,X3)) ),
inference(paramodulation,[status(thm)],[f5537,f3001]) ).
fof(f5561,plain,
! [X0,X1,X2,X3,X4,X5] :
( restrict(null_class,X0,X1) = null_class
| member(regular(restrict(null_class,X0,X1)),restrict(complement(cross_product(X2,X3)),X4,X5)) ),
inference(forward_demodulation,[status(thm)],[f5537,f5560]) ).
fof(f5653,plain,
! [X0,X1,X2,X3] :
( restrict(null_class,X0,X1) = null_class
| member(regular(restrict(null_class,X0,X1)),complement(cross_product(X2,X3))) ),
inference(resolution,[status(thm)],[f5561,f1896]) ).
fof(f5662,plain,
! [X0,X1,X2,X3] :
( restrict(null_class,X0,X1) = null_class
| ~ member(regular(restrict(null_class,X0,X1)),cross_product(X2,X3)) ),
inference(resolution,[status(thm)],[f5653,f147]) ).
fof(f5663,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f5662,f5557]) ).
fof(f5697,plain,
domain_of(null_class) = null_class,
inference(resolution,[status(thm)],[f5663,f2287]) ).
fof(f5703,plain,
( spl0_127
<=> domain_of(null_class) = null_class ),
introduced(split_symbol_definition) ).
fof(f5704,plain,
( domain_of(null_class) = null_class
| ~ spl0_127 ),
inference(component_clause,[status(thm)],[f5703]) ).
fof(f5706,plain,
( null_class != null_class
| domain_of(null_class) = null_class ),
inference(paramodulation,[status(thm)],[f5663,f2287]) ).
fof(f5707,plain,
( ~ spl0_26
| spl0_127 ),
inference(split_clause,[status(thm)],[f5706,f2238,f5703]) ).
fof(f5864,plain,
( member(regular(complement(universal_class)),universal_class)
| ~ spl0_75 ),
inference(resolution,[status(thm)],[f3543,f253]) ).
fof(f6010,plain,
( complement(universal_class) = null_class
| ~ spl0_75 ),
inference(resolution,[status(thm)],[f5864,f1615]) ).
fof(f6049,plain,
( domain_of(null_class) != null_class
| ~ spl0_75 ),
inference(backward_demodulation,[status(thm)],[f6010,f1352]) ).
fof(f6690,plain,
( $false
| ~ spl0_74 ),
inference(forward_subsumption_resolution,[status(thm)],[f5697,f3602]) ).
fof(f6691,plain,
~ spl0_74,
inference(contradiction_clause,[status(thm)],[f6690]) ).
fof(f7229,plain,
( null_class != null_class
| ~ spl0_127
| ~ spl0_75 ),
inference(forward_demodulation,[status(thm)],[f5704,f6049]) ).
fof(f7230,plain,
( $false
| ~ spl0_127
| ~ spl0_75 ),
inference(trivial_equality_resolution,[status(esa)],[f7229]) ).
fof(f7231,plain,
( ~ spl0_127
| ~ spl0_75 ),
inference(contradiction_clause,[status(thm)],[f7230]) ).
fof(f7238,plain,
( $false
| spl0_26 ),
inference(trivial_equality_resolution,[status(esa)],[f2240]) ).
fof(f7239,plain,
spl0_26,
inference(contradiction_clause,[status(thm)],[f7238]) ).
fof(f7240,plain,
$false,
inference(sat_refutation,[status(thm)],[f3546,f5707,f6691,f7231,f7239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET287-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue May 30 10:14:12 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.34 % Drodi V3.5.1
% 3.75/0.89 % Refutation found
% 3.75/0.89 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.75/0.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.75/0.92 % Elapsed time: 0.585293 seconds
% 3.75/0.92 % CPU time: 4.133341 seconds
% 3.75/0.92 % Memory used: 92.356 MB
%------------------------------------------------------------------------------