%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:15 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 9 unt; 4 def)
% Number of atoms : 97 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 92 ( 36 ~; 33 |; 15 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
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] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X] :
( ~ member(X,universal_class)
=> singleton(X) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X] :
( ~ member(X,universal_class)
=> singleton(X) = null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f59,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f60,plain,
( ! [U,X,Y] :
( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ! [U,X,Y] :
( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f66,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f181,plain,
! [X] :
( ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) )
| X = null_class ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f182,plain,
! [X] :
( ( disjoint(sK5_skl(X),X)
& member(sK5_skl(X),X)
& member(sK5_skl(X),universal_class) )
| X = null_class ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(U,sK5_skl(X))],[f181]) ).
fof(f184,plain,
! [X0] :
( member(sK5_skl(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f191,plain,
? [X] :
( singleton(X) != null_class
& ~ member(X,universal_class) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
( singleton(sK7_skl) != null_class
& ~ member(sK7_skl,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X,sK7_skl)],[f191]) ).
fof(f193,plain,
~ member(sK7_skl,universal_class),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
singleton(sK7_skl) != null_class,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f227,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f61]) ).
fof(f229,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f230,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f229]) ).
fof(f242,plain,
! [X0] :
( singleton(X0) = null_class
| sK5_skl(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f230,f184]) ).
fof(f429,plain,
! [X0] : ~ member(sK7_skl,singleton(X0)),
inference(resolution,[status(thm)],[f227,f193]) ).
fof(f452,plain,
( sK5_skl(singleton(sK7_skl)) = sK7_skl
| null_class != null_class ),
inference(paramodulation,[status(thm)],[f242,f194]) ).
fof(f472,definition,
( sQ20_spl
<=> null_class = null_class ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ20_spl
| null_class != null_class ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,definition,
( sQ21_spl
<=> sK5_skl(singleton(sK7_skl)) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ21_spl
| sK5_skl(singleton(sK7_skl)) = sK7_skl ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f452,f472,f475]) ).
fof(f490,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f474]) ).
fof(f491,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f503,plain,
( ~ sQ21_spl
| member(sK7_skl,singleton(sK7_skl))
| singleton(sK7_skl) = null_class ),
inference(paramodulation,[status(thm)],[f476,f184]) ).
fof(f505,definition,
( sQ25_spl
<=> singleton(sK7_skl) = null_class ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ25_spl
| singleton(sK7_skl) = null_class ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f509,definition,
( sQ26_spl
<=> member(sK7_skl,singleton(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ26_spl
| member(sK7_skl,singleton(sK7_skl)) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( ~ sQ21_spl
| sQ26_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f503,f505,f509,f475]) ).
fof(f517,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f194]) ).
fof(f518,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f429]) ).
fof(f520,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f521,plain,
$false,
inference(sat_refutation,[status(thm)],[f478,f491,f512,f518,f520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:50:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.049765 seconds
% 0.09/0.42 % CPU time: 0.137911 seconds
% 0.09/0.42 % Total memory used: 56.186 MB
% 0.09/0.42 % Net memory used: 56.103 MB
%------------------------------------------------------------------------------