%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET102+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 : n014.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 02:09:21 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 38 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 37 ( 16 ~; 13 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 33 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f44,conjecture,
! [X,Y] : member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] : member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
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(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(f67,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f191,plain,
? [X,Y] : ~ member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
~ member(unordered_pair(sK7_skl,singleton(sK8_skl)),ordered_pair(sK7_skl,sK8_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(X,sK7_skl),skolemize(Y,sK8_skl)],[f191]) ).
fof(f193,plain,
~ member(unordered_pair(sK7_skl,singleton(sK8_skl)),ordered_pair(sK7_skl,sK8_skl)),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f197,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f64]) ).
fof(f213,plain,
! [X0,X1] :
( ~ member(unordered_pair(X0,singleton(X1)),universal_class)
| member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)) ),
inference(paramodulation,[status(thm)],[f67,f197]) ).
fof(f219,plain,
! [X0,X1] : member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f213,f65]) ).
fof(f222,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f193,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET102+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 04:52:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.061331 seconds
% 0.14/0.43 % CPU time: 0.143835 seconds
% 0.14/0.43 % Total memory used: 104.418 MB
% 0.14/0.43 % Net memory used: 104.338 MB
%------------------------------------------------------------------------------