TSTP Solution File: SET098+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET098+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:39:07 EDT 2024
% Result : Theorem 14.21s 2.19s
% Output : CNFRefutation 14.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 10 unt; 0 def)
% Number of atoms : 223 ( 42 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 254 ( 101 ~; 101 |; 42 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 144 ( 133 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(X,Y)
& subclass(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( member(Z,intersection(X,Y))
<=> ( member(Z,X)
& member(Z,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( member(Z,universal_class)
& ~ member(Z,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( X != null_class
=> ? [U] :
( member(U,universal_class)
& member(U,X)
& disjoint(U,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X] :
( X = null_class
| ? [Y] : singleton(Y) = X
| ? [V] :
( member(V,X)
& ? [W] :
( member(W,intersection(complement(singleton(V)),X))
& member(W,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X] :
( X = null_class
| ? [Y] : singleton(Y) = X
| ? [V] :
( member(V,X)
& ? [W] :
( member(W,intersection(complement(singleton(V)),X))
& member(W,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( ~ member(U,X)
| member(U,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ( member(sk0_0(Y,X),X)
& ~ member(sk0_0(Y,X),Y) ) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f53,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f54,plain,
! [X,Y] :
( ( X != Y
| ( subclass(X,Y)
& subclass(Y,X) ) )
& ( X = Y
| ~ subclass(X,Y)
| ~ subclass(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
( ! [X,Y] :
( X != Y
| ( subclass(X,Y)
& subclass(Y,X) ) )
& ! [X,Y] :
( X = Y
| ~ subclass(X,Y)
| ~ subclass(Y,X) ) ),
inference(miniscoping,[status(esa)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f59,plain,
! [U,X,Y] :
( ( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f60,plain,
( ! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ! [U,X,Y] :
( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f66,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f85,plain,
! [X,Y,Z] :
( ( ~ member(Z,intersection(X,Y))
| ( member(Z,X)
& member(Z,Y) ) )
& ( member(Z,intersection(X,Y))
| ~ member(Z,X)
| ~ member(Z,Y) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f86,plain,
( ! [X,Y,Z] :
( ~ member(Z,intersection(X,Y))
| ( member(Z,X)
& member(Z,Y) ) )
& ! [X,Y,Z] :
( member(Z,intersection(X,Y))
| ~ member(Z,X)
| ~ member(Z,Y) ) ),
inference(miniscoping,[status(esa)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f89,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f90,plain,
! [X,Z] :
( ( ~ member(Z,complement(X))
| ( member(Z,universal_class)
& ~ member(Z,X) ) )
& ( member(Z,complement(X))
| ~ member(Z,universal_class)
| member(Z,X) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f91,plain,
( ! [X,Z] :
( ~ member(Z,complement(X))
| ( member(Z,universal_class)
& ~ member(Z,X) ) )
& ! [X,Z] :
( member(Z,complement(X))
| ~ member(Z,universal_class)
| member(Z,X) ) ),
inference(miniscoping,[status(esa)],[f90]) ).
fof(f94,plain,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f181,plain,
! [X] :
( X = null_class
| ? [U] :
( member(U,universal_class)
& member(U,X)
& disjoint(U,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f41]) ).
fof(f182,plain,
! [X] :
( X = null_class
| ( member(sk0_5(X),universal_class)
& member(sk0_5(X),X)
& disjoint(sk0_5(X),X) ) ),
inference(skolemization,[status(esa)],[f181]) ).
fof(f184,plain,
! [X0] :
( X0 = null_class
| member(sk0_5(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f182]) ).
fof(f191,plain,
? [X] :
( X != null_class
& ! [Y] : singleton(Y) != X
& ! [V] :
( ~ member(V,X)
| ! [W] :
( ~ member(W,intersection(complement(singleton(V)),X))
| ~ member(W,X) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f192,plain,
( sk0_7 != null_class
& ! [Y] : singleton(Y) != sk0_7
& ! [V] :
( ~ member(V,sk0_7)
| ! [W] :
( ~ member(W,intersection(complement(singleton(V)),sk0_7))
| ~ member(W,sk0_7) ) ) ),
inference(skolemization,[status(esa)],[f191]) ).
fof(f193,plain,
sk0_7 != null_class,
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
! [X0] : singleton(X0) != sk0_7,
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f195,plain,
! [X0,X1] :
( ~ member(X0,sk0_7)
| ~ member(X1,intersection(complement(singleton(X0)),sk0_7))
| ~ member(X1,sk0_7) ),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f202,plain,
! [X0,X1] :
( ~ member(X0,sk0_7)
| ~ member(X1,intersection(complement(singleton(X0)),sk0_7)) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f88]) ).
fof(f203,plain,
! [X0,X1] :
( ~ member(X0,complement(singleton(X1)))
| ~ member(X0,sk0_7)
| ~ member(X1,sk0_7) ),
inference(resolution,[status(thm)],[f89,f202]) ).
fof(f204,plain,
! [X0,X1] :
( ~ member(X0,sk0_7)
| ~ member(X1,sk0_7)
| ~ member(X0,universal_class)
| member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f203,f94]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( ~ subclass(intersection(X0,X1),X2)
| member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1) ),
inference(resolution,[status(thm)],[f50,f89]) ).
fof(f270,plain,
! [X0,X1] :
( subclass(X0,singleton(X1))
| ~ member(sk0_0(singleton(X1),X0),sk0_7)
| ~ member(X1,sk0_7)
| ~ member(sk0_0(singleton(X1),X0),universal_class) ),
inference(resolution,[status(thm)],[f52,f204]) ).
fof(f300,plain,
! [X0,X1,X2] :
( member(X0,universal_class)
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(resolution,[status(thm)],[f207,f53]) ).
fof(f317,plain,
! [X0,X1,X2] :
( member(sk0_0(X0,X1),universal_class)
| ~ member(sk0_0(X0,X1),X2)
| subclass(X1,X0) ),
inference(resolution,[status(thm)],[f300,f51]) ).
fof(f345,plain,
! [X0,X1] :
( subclass(X0,singleton(X1))
| ~ member(sk0_0(singleton(X1),X0),sk0_7)
| ~ member(X1,sk0_7) ),
inference(backward_subsumption_resolution,[status(thm)],[f270,f317]) ).
fof(f368,plain,
! [X0] :
( subclass(sk0_7,singleton(X0))
| ~ member(X0,sk0_7)
| subclass(sk0_7,singleton(X0)) ),
inference(resolution,[status(thm)],[f345,f51]) ).
fof(f369,plain,
! [X0] :
( subclass(sk0_7,singleton(X0))
| ~ member(X0,sk0_7) ),
inference(duplicate_literals_removal,[status(esa)],[f368]) ).
fof(f373,plain,
! [X0] :
( ~ member(X0,sk0_7)
| singleton(X0) = sk0_7
| ~ subclass(singleton(X0),sk0_7) ),
inference(resolution,[status(thm)],[f369,f58]) ).
fof(f374,plain,
! [X0] :
( ~ member(X0,sk0_7)
| ~ subclass(singleton(X0),sk0_7) ),
inference(forward_subsumption_resolution,[status(thm)],[f373,f194]) ).
fof(f554,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f555,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f554]) ).
fof(f558,plain,
! [X0,X1] :
( sk0_0(X0,singleton(X1)) = X1
| subclass(singleton(X1),X0) ),
inference(resolution,[status(thm)],[f555,f51]) ).
fof(f654,plain,
( spl0_31
<=> sk0_7 = null_class ),
introduced(split_symbol_definition) ).
fof(f655,plain,
( sk0_7 = null_class
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f727,plain,
( $false
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f655,f193]) ).
fof(f728,plain,
~ spl0_31,
inference(contradiction_clause,[status(thm)],[f727]) ).
fof(f729,plain,
( spl0_43
<=> member(sk0_5(sk0_7),sk0_7) ),
introduced(split_symbol_definition) ).
fof(f730,plain,
( member(sk0_5(sk0_7),sk0_7)
| ~ spl0_43 ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f731,plain,
( ~ member(sk0_5(sk0_7),sk0_7)
| spl0_43 ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f740,plain,
( sk0_7 = null_class
| spl0_43 ),
inference(resolution,[status(thm)],[f731,f184]) ).
fof(f741,plain,
( spl0_31
| spl0_43 ),
inference(split_clause,[status(thm)],[f740,f654,f729]) ).
fof(f9321,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
inference(paramodulation,[status(thm)],[f558,f52]) ).
fof(f9322,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f9321]) ).
fof(f9323,plain,
! [X0] : ~ member(X0,sk0_7),
inference(backward_subsumption_resolution,[status(thm)],[f374,f9322]) ).
fof(f9324,plain,
( $false
| ~ spl0_43 ),
inference(backward_subsumption_resolution,[status(thm)],[f730,f9323]) ).
fof(f9325,plain,
~ spl0_43,
inference(contradiction_clause,[status(thm)],[f9324]) ).
fof(f9326,plain,
$false,
inference(sat_refutation,[status(thm)],[f728,f741,f9325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET098+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n004.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Apr 29 21:31:03 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 14.21/2.19 % Refutation found
% 14.21/2.19 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.21/2.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.61/2.21 % Elapsed time: 1.842071 seconds
% 14.61/2.21 % CPU time: 14.433911 seconds
% 14.61/2.21 % Total memory used: 174.454 MB
% 14.61/2.21 % Net memory used: 164.917 MB
%------------------------------------------------------------------------------