%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:09:17 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 98 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 87 ( 30 ~; 33 |; 19 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 42 !; 4 ?)
% 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(f16,axiom,
! [X] : ~ member(X,null_class),
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(f45,axiom,
! [Y] :
( member(Y,universal_class)
=> singleton(member_of(singleton(Y))) = singleton(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
! [X,U] :
( ( X = singleton(U)
& member(U,universal_class) )
=> member_of(X) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ! [X,U] :
( ( X = singleton(U)
& member(U,universal_class) )
=> member_of(X) = U ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f63,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(f64,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)],[f63]) ).
fof(f66,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f70,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f100,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f185,plain,
! [X] :
( ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) )
| X = null_class ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f186,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))],[f185]) ).
fof(f188,plain,
! [X0] :
( member(sK5_skl(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f197,plain,
! [Y] :
( singleton(member_of(singleton(Y))) = singleton(Y)
| ~ member(Y,universal_class) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f198,plain,
! [X0] :
( singleton(member_of(singleton(X0))) = singleton(X0)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f201,plain,
? [X,U] :
( member_of(X) != U
& X = singleton(U)
& member(U,universal_class) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f202,plain,
( member_of(sK7_skl) != sK8_skl
& sK7_skl = singleton(sK8_skl)
& member(sK8_skl,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(X,sK7_skl),skolemize(U,sK8_skl)],[f201]) ).
fof(f203,plain,
member(sK8_skl,universal_class),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
sK7_skl = singleton(sK8_skl),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f205,plain,
member_of(sK7_skl) != sK8_skl,
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f208,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f217,plain,
( singleton(member_of(sK7_skl)) = singleton(sK8_skl)
| ~ member(sK8_skl,universal_class) ),
inference(paramodulation,[status(thm)],[f204,f198]) ).
fof(f218,plain,
( singleton(member_of(sK7_skl)) = sK7_skl
| ~ member(sK8_skl,universal_class) ),
inference(forward_demodulation,[status(thm)],[f204,f217]) ).
fof(f219,plain,
singleton(member_of(sK7_skl)) = sK7_skl,
inference(forward_subsumption_resolution,[status(thm)],[f218,f203]) ).
fof(f251,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f70,f66]) ).
fof(f252,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f251]) ).
fof(f255,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f70,f208]) ).
fof(f258,plain,
! [X0] :
( X0 = member_of(sK7_skl)
| ~ member(X0,sK7_skl) ),
inference(paramodulation,[status(thm)],[f219,f252]) ).
fof(f260,plain,
! [X0] :
( X0 = sK8_skl
| ~ member(X0,sK7_skl) ),
inference(paramodulation,[status(thm)],[f204,f252]) ).
fof(f269,plain,
( sK5_skl(sK7_skl) = sK8_skl
| sK7_skl = null_class ),
inference(resolution,[status(thm)],[f188,f260]) ).
fof(f304,plain,
( sK7_skl = null_class
| member(sK8_skl,sK7_skl)
| sK7_skl = null_class ),
inference(paramodulation,[status(thm)],[f269,f188]) ).
fof(f306,plain,
( member(sK8_skl,sK7_skl)
| sK7_skl = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f304]) ).
fof(f307,plain,
( sK8_skl = member_of(sK7_skl)
| sK7_skl = null_class ),
inference(resolution,[status(thm)],[f306,f258]) ).
fof(f309,plain,
sK7_skl = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f307,f205]) ).
fof(f333,plain,
null_class = singleton(sK8_skl),
inference(backward_demodulation,[status(thm)],[f309,f204]) ).
fof(f646,plain,
( ~ member(sK8_skl,universal_class)
| member(sK8_skl,null_class) ),
inference(paramodulation,[status(thm)],[f333,f255]) ).
fof(f649,plain,
~ member(sK8_skl,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f646,f100]) ).
fof(f652,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f649,f203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:46:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.065473 seconds
% 0.13/0.43 % CPU time: 0.255603 seconds
% 0.13/0.43 % Total memory used: 95.079 MB
% 0.13/0.43 % Net memory used: 94.806 MB
%------------------------------------------------------------------------------