%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET079+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 : n005.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 02:09:14 PM UTC 2026
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 43 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 40 ( 16 ~; 12 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 24 !; 1 ?)
% 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(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(f63,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ member(X0,universal_class)
| 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(f96,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(thm)],[f16]) ).
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(f197,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f274,plain,
! [X0] : member(sK7_skl,unordered_pair(sK7_skl,X0)),
inference(resolution,[status(thm)],[f197,f193]) ).
fof(f318,plain,
member(sK7_skl,singleton(sK7_skl)),
inference(paramodulation,[status(thm)],[f66,f274]) ).
fof(f326,plain,
member(sK7_skl,null_class),
inference(forward_demodulation,[status(thm)],[f194,f318]) ).
fof(f327,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f326,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 21 04:49:47 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.19/0.43 % Drodi V4.1.1
% 0.19/0.46 % Refutation found
% 0.19/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.50 % Elapsed time: 0.086622 seconds
% 0.19/0.50 % CPU time: 0.167194 seconds
% 0.19/0.50 % Total memory used: 40.160 MB
% 0.19/0.50 % Net memory used: 40.083 MB
%------------------------------------------------------------------------------