%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET016+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:08:52 PM UTC 2026
% Result : Theorem 3.20s 0.80s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 99 ( 35 unt; 0 def)
% Number of atoms : 229 ( 81 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 205 ( 75 ~; 90 |; 32 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 155 ( 143 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,X,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
<=> ( member(V,Y)
& member(U,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : ~ member(X,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [W,X,Y,Z] :
( ( member(W,universal_class)
& ordered_pair(W,X) = ordered_pair(Y,Z) )
=> W = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [W,X,Y,Z] :
( ( member(W,universal_class)
& ordered_pair(W,X) = ordered_pair(Y,Z) )
=> W = Y ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,Y)
| ~ member(U,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ! [X,Y] :
( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ( ~ member(sK0_skl(Y,X),Y)
& member(sK0_skl(Y,X),X) )
| subclass(X,Y) )
& ! [X,Y] :
( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl(Y,X))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(f62,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,plain,
! [X0,X1,X2] :
( X0 != X2
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f65,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f66,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f67,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f68,plain,
! [U,V,X,Y] :
( ( ~ member(V,Y)
| ~ member(U,X)
| member(ordered_pair(U,V),cross_product(X,Y)) )
& ( ( member(V,Y)
& member(U,X) )
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f69,plain,
( ! [U,V,X,Y] :
( ~ member(V,Y)
| ~ member(U,X)
| member(ordered_pair(U,V),cross_product(X,Y)) )
& ! [U,V,X,Y] :
( ( member(V,Y)
& member(U,X) )
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f96,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(thm)],[f16]) ).
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(f183,plain,
! [X0] :
( member(sK5_skl(X0),universal_class)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
! [X0] :
( member(sK5_skl(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f191,plain,
? [W,X,Y,Z] :
( W != Y
& member(W,universal_class)
& ordered_pair(W,X) = ordered_pair(Y,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
? [W,Y] :
( W != Y
& member(W,universal_class)
& ? [X,Z] : ordered_pair(W,X) = ordered_pair(Y,Z) ),
inference(miniscoping,[status(thm)],[f191]) ).
fof(f193,plain,
( sK7_skl != sK8_skl
& member(sK7_skl,universal_class)
& ordered_pair(sK7_skl,sK9_skl) = ordered_pair(sK8_skl,sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl,sK10_skl]),skolemize(W,sK7_skl),skolemize(Y,sK8_skl),skolemize(X,sK9_skl),skolemize(Z,sK10_skl)],[f192]) ).
fof(f194,plain,
ordered_pair(sK7_skl,sK9_skl) = ordered_pair(sK8_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f195,plain,
member(sK7_skl,universal_class),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f196,plain,
sK7_skl != sK8_skl,
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f199,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f200,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f64]) ).
fof(f204,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f53,f50]) ).
fof(f209,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f66,f65]) ).
fof(f221,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f222,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f221]) ).
fof(f232,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f66,f199]) ).
fof(f233,plain,
! [X0] :
( sK5_skl(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f184,f222]) ).
fof(f244,plain,
! [X0,X1] :
( ~ member(singleton(X0),universal_class)
| member(singleton(X0),ordered_pair(X0,X1)) ),
inference(paramodulation,[status(thm)],[f67,f199]) ).
fof(f245,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,singleton(X2))
| X0 = singleton(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(paramodulation,[status(thm)],[f67,f62]) ).
fof(f249,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f244,f209]) ).
fof(f251,plain,
member(singleton(sK8_skl),ordered_pair(sK7_skl,sK9_skl)),
inference(paramodulation,[status(thm)],[f194,f249]) ).
fof(f266,plain,
! [X0,X1] :
( member(sK8_skl,X0)
| ~ member(ordered_pair(sK7_skl,sK9_skl),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f194,f70]) ).
fof(f270,plain,
! [X0,X1] :
( ~ member(sK10_skl,X1)
| ~ member(sK8_skl,X0)
| member(ordered_pair(sK7_skl,sK9_skl),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f194,f72]) ).
fof(f271,plain,
! [X0,X1] :
( ~ member(sK9_skl,X1)
| ~ member(sK7_skl,X0)
| member(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f266,f72]) ).
fof(f285,plain,
! [X0,X1] :
( member(sK9_skl,X1)
| ~ member(sK10_skl,X1)
| ~ member(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f270,f71]) ).
fof(f288,plain,
! [X0,X1] :
( ~ member(sK10_skl,X1)
| member(sK9_skl,universal_class)
| ~ member(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f285,f204]) ).
fof(f375,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class)
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f233,f183]) ).
fof(f377,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f233,f184]) ).
fof(f378,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f375]) ).
fof(f380,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f377]) ).
fof(f384,plain,
! [X0] :
( ~ member(sK7_skl,X0)
| member(sK8_skl,X0)
| singleton(sK9_skl) = null_class ),
inference(resolution,[status(thm)],[f378,f271]) ).
fof(f554,plain,
( ~ member(sK7_skl,universal_class)
| member(sK8_skl,singleton(sK7_skl))
| singleton(sK9_skl) = null_class ),
inference(resolution,[status(thm)],[f384,f232]) ).
fof(f563,plain,
( member(sK8_skl,singleton(sK7_skl))
| singleton(sK9_skl) = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f195]) ).
fof(f570,plain,
( sK8_skl = sK7_skl
| singleton(sK9_skl) = null_class ),
inference(resolution,[status(thm)],[f563,f222]) ).
fof(f571,plain,
singleton(sK9_skl) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f570,f196]) ).
fof(f580,plain,
( ~ member(sK9_skl,universal_class)
| member(sK9_skl,null_class) ),
inference(paramodulation,[status(thm)],[f571,f232]) ).
fof(f583,plain,
! [X0] : member(null_class,ordered_pair(sK9_skl,X0)),
inference(paramodulation,[status(thm)],[f571,f249]) ).
fof(f584,plain,
! [X0] : ordered_pair(X0,sK9_skl) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)),
inference(paramodulation,[status(thm)],[f571,f67]) ).
fof(f589,plain,
member(null_class,universal_class),
inference(paramodulation,[status(thm)],[f571,f209]) ).
fof(f590,plain,
~ member(sK9_skl,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f580,f96]) ).
fof(f591,plain,
! [X0,X1] :
( ~ member(sK10_skl,X1)
| ~ member(sK8_skl,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f288,f590]) ).
fof(f619,plain,
! [X0] :
( singleton(sK10_skl) = null_class
| ~ member(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f591,f380]) ).
fof(f704,plain,
ordered_pair(null_class,sK9_skl) = unordered_pair(singleton(null_class),singleton(null_class)),
inference(paramodulation,[status(thm)],[f66,f584]) ).
fof(f709,plain,
ordered_pair(null_class,sK9_skl) = singleton(singleton(null_class)),
inference(forward_demodulation,[status(thm)],[f66,f704]) ).
fof(f727,plain,
! [X0] :
( X0 = singleton(null_class)
| ~ member(X0,ordered_pair(null_class,sK9_skl)) ),
inference(paramodulation,[status(thm)],[f709,f222]) ).
fof(f1607,plain,
( singleton(sK8_skl) = unordered_pair(sK7_skl,singleton(sK9_skl))
| singleton(sK8_skl) = singleton(sK7_skl) ),
inference(resolution,[status(thm)],[f245,f251]) ).
fof(f1617,plain,
( singleton(sK8_skl) = unordered_pair(sK7_skl,null_class)
| singleton(sK8_skl) = singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f571,f1607]) ).
fof(f1733,plain,
( singleton(sK8_skl) = singleton(sK7_skl)
| ~ member(null_class,universal_class)
| member(null_class,singleton(sK8_skl)) ),
inference(paramodulation,[status(thm)],[f1617,f200]) ).
fof(f1737,plain,
( singleton(sK8_skl) = singleton(sK7_skl)
| member(null_class,singleton(sK8_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1733,f589]) ).
fof(f1834,plain,
( null_class = sK8_skl
| singleton(sK8_skl) = singleton(sK7_skl) ),
inference(resolution,[status(thm)],[f1737,f222]) ).
fof(f1890,plain,
! [X0] :
( null_class = sK8_skl
| X0 = sK8_skl
| ~ member(X0,singleton(sK7_skl)) ),
inference(paramodulation,[status(thm)],[f1834,f222]) ).
fof(f1978,plain,
( ~ member(sK7_skl,universal_class)
| null_class = sK8_skl
| sK7_skl = sK8_skl ),
inference(resolution,[status(thm)],[f1890,f232]) ).
fof(f1983,plain,
( ~ member(sK7_skl,universal_class)
| null_class = sK8_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f1978,f196]) ).
fof(f2086,plain,
! [X0] :
( singleton(sK10_skl) = null_class
| ~ member(null_class,X0) ),
inference(backward_demodulation,[status(thm)],[f2094,f619]) ).
fof(f2092,plain,
ordered_pair(sK7_skl,sK9_skl) = ordered_pair(null_class,sK10_skl),
inference(backward_demodulation,[status(thm)],[f2094,f194]) ).
fof(f2093,plain,
sK7_skl != null_class,
inference(backward_demodulation,[status(thm)],[f2094,f196]) ).
fof(f2094,plain,
null_class = sK8_skl,
inference(forward_subsumption_resolution,[status(thm)],[f1983,f195]) ).
fof(f2125,plain,
member(singleton(sK7_skl),ordered_pair(null_class,sK10_skl)),
inference(paramodulation,[status(thm)],[f2092,f249]) ).
fof(f2328,plain,
singleton(sK10_skl) = null_class,
inference(resolution,[status(thm)],[f2086,f583]) ).
fof(f2408,plain,
! [X0] : ordered_pair(X0,sK10_skl) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)),
inference(paramodulation,[status(thm)],[f2328,f67]) ).
fof(f2433,plain,
! [X0] : ordered_pair(X0,sK10_skl) = ordered_pair(X0,sK9_skl),
inference(forward_demodulation,[status(thm)],[f584,f2408]) ).
fof(f2954,plain,
member(singleton(sK7_skl),ordered_pair(null_class,sK9_skl)),
inference(forward_demodulation,[status(thm)],[f2433,f2125]) ).
fof(f2955,plain,
singleton(sK7_skl) = singleton(null_class),
inference(resolution,[status(thm)],[f2954,f727]) ).
fof(f3008,plain,
( ~ member(sK7_skl,universal_class)
| member(sK7_skl,singleton(null_class)) ),
inference(paramodulation,[status(thm)],[f2955,f232]) ).
fof(f3050,plain,
member(sK7_skl,singleton(null_class)),
inference(forward_subsumption_resolution,[status(thm)],[f3008,f195]) ).
fof(f3069,plain,
sK7_skl = null_class,
inference(resolution,[status(thm)],[f3050,f222]) ).
fof(f3070,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3069,f2093]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET016+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 04:42:37 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 3.20/0.80 % Refutation found
% 3.20/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.20/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.20/0.82 % Elapsed time: 0.524927 seconds
% 3.20/0.82 % CPU time: 3.553300 seconds
% 3.20/0.82 % Total memory used: 160.600 MB
% 3.20/0.82 % Net memory used: 153.810 MB
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