TSTP Solution File: SET096+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET096+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:39:06 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 9 unt; 0 def)
% Number of atoms : 171 ( 55 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 63 ~; 69 |; 28 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 79 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
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(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,Y] :
( subclass(X,singleton(Y))
=> ( X = null_class
| singleton(Y) = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] :
( subclass(X,singleton(Y))
=> ( X = null_class
| singleton(Y) = 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(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(f56,plain,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
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(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,Y] :
( subclass(X,singleton(Y))
& X != null_class
& singleton(Y) != X ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f192,plain,
( subclass(sk0_7,singleton(sk0_8))
& sk0_7 != null_class
& singleton(sk0_8) != sk0_7 ),
inference(skolemization,[status(esa)],[f191]) ).
fof(f193,plain,
subclass(sk0_7,singleton(sk0_8)),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
sk0_7 != null_class,
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f195,plain,
singleton(sk0_8) != sk0_7,
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f196,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f204,plain,
( spl0_0
<=> singleton(sk0_8) = sk0_7 ),
introduced(split_symbol_definition) ).
fof(f205,plain,
( singleton(sk0_8) = sk0_7
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( spl0_1
<=> subclass(singleton(sk0_8),sk0_7) ),
introduced(split_symbol_definition) ).
fof(f209,plain,
( ~ subclass(singleton(sk0_8),sk0_7)
| spl0_1 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( singleton(sk0_8) = sk0_7
| ~ subclass(singleton(sk0_8),sk0_7) ),
inference(resolution,[status(thm)],[f58,f193]) ).
fof(f211,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f210,f204,f207]) ).
fof(f250,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| X0 = X2
| ~ subclass(X3,unordered_pair(X1,X2))
| ~ member(X0,X3) ),
inference(resolution,[status(thm)],[f62,f50]) ).
fof(f262,plain,
! [X0,X1,X2] :
( X0 = X1
| X0 = X1
| ~ subclass(X2,singleton(X1))
| ~ member(X0,X2) ),
inference(paramodulation,[status(thm)],[f66,f250]) ).
fof(f263,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ subclass(X2,singleton(X1))
| ~ member(X0,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f262]) ).
fof(f265,plain,
! [X0] :
( X0 = sk0_8
| ~ member(X0,sk0_7) ),
inference(resolution,[status(thm)],[f263,f193]) ).
fof(f266,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f263,f196]) ).
fof(f267,plain,
( spl0_6
<=> sk0_5(sk0_7) = sk0_8 ),
introduced(split_symbol_definition) ).
fof(f268,plain,
( sk0_5(sk0_7) = sk0_8
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( spl0_7
<=> sk0_7 = null_class ),
introduced(split_symbol_definition) ).
fof(f271,plain,
( sk0_7 = null_class
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( sk0_5(sk0_7) = sk0_8
| sk0_7 = null_class ),
inference(resolution,[status(thm)],[f265,f184]) ).
fof(f274,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f273,f267,f270]) ).
fof(f287,plain,
( spl0_10
<=> member(sk0_8,sk0_7) ),
introduced(split_symbol_definition) ).
fof(f290,plain,
( sk0_7 = null_class
| member(sk0_8,sk0_7)
| ~ spl0_6 ),
inference(paramodulation,[status(thm)],[f268,f184]) ).
fof(f291,plain,
( spl0_7
| spl0_10
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f290,f270,f287,f267]) ).
fof(f292,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f194]) ).
fof(f293,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f598,plain,
! [X0,X1] :
( sk0_0(X0,singleton(X1)) = X1
| subclass(singleton(X1),X0) ),
inference(resolution,[status(thm)],[f266,f51]) ).
fof(f609,plain,
( sk0_0(sk0_7,singleton(sk0_8)) = sk0_8
| spl0_1 ),
inference(resolution,[status(thm)],[f598,f209]) ).
fof(f953,plain,
( subclass(singleton(sk0_8),sk0_7)
| ~ member(sk0_8,sk0_7)
| spl0_1 ),
inference(paramodulation,[status(thm)],[f609,f52]) ).
fof(f954,plain,
( spl0_1
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f953,f207,f287]) ).
fof(f991,plain,
( sk0_7 != sk0_7
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f205,f195]) ).
fof(f992,plain,
( $false
| ~ spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f991]) ).
fof(f993,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f994,plain,
$false,
inference(sat_refutation,[status(thm)],[f211,f274,f291,f293,f954,f993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET096+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:39:17 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.21/0.39 % Refutation found
% 0.21/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.41 % Elapsed time: 0.057351 seconds
% 0.21/0.41 % CPU time: 0.321130 seconds
% 0.21/0.41 % Total memory used: 63.783 MB
% 0.21/0.41 % Net memory used: 63.558 MB
%------------------------------------------------------------------------------