%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET020+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 : n002.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 02:08:55 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 51 ( 30 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 12 |; 15 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y] :
( ( member(Y,universal_class)
& member(X,universal_class) )
=> ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f73,plain,
! [X,Y] :
( ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X )
| ~ member(Y,universal_class)
| ~ member(X,universal_class) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f74,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f191,plain,
? [U,V,X] :
( ( second(X) != V
| first(X) != U )
& X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
( ( second(sK9_skl) != sK8_skl
| first(sK9_skl) != sK7_skl )
& sK9_skl = ordered_pair(sK7_skl,sK8_skl)
& member(sK8_skl,universal_class)
& member(sK7_skl,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(U,sK7_skl),skolemize(V,sK8_skl),skolemize(X,sK9_skl)],[f191]) ).
fof(f193,plain,
member(sK7_skl,universal_class),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
member(sK8_skl,universal_class),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,plain,
sK9_skl = ordered_pair(sK7_skl,sK8_skl),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f196,plain,
( second(sK9_skl) != sK8_skl
| first(sK9_skl) != sK7_skl ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f203,plain,
! [X0] :
( first(ordered_pair(X0,sK8_skl)) = X0
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f74,f194]) ).
fof(f206,plain,
first(ordered_pair(sK7_skl,sK8_skl)) = sK7_skl,
inference(resolution,[status(thm)],[f203,f193]) ).
fof(f207,plain,
first(sK9_skl) = sK7_skl,
inference(forward_demodulation,[status(thm)],[f195,f206]) ).
fof(f208,plain,
! [X0] :
( second(ordered_pair(X0,sK8_skl)) = sK8_skl
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f75,f194]) ).
fof(f214,plain,
( second(sK9_skl) != sK8_skl
| sK7_skl != sK7_skl ),
inference(backward_demodulation,[status(thm)],[f207,f196]) ).
fof(f215,plain,
second(sK9_skl) != sK8_skl,
inference(trivial_equality_resolution,[status(thm)],[f214]) ).
fof(f217,plain,
second(ordered_pair(sK7_skl,sK8_skl)) = sK8_skl,
inference(resolution,[status(thm)],[f208,f193]) ).
fof(f218,plain,
second(sK9_skl) = sK8_skl,
inference(forward_demodulation,[status(thm)],[f195,f217]) ).
fof(f219,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f218,f215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:45:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.062869 seconds
% 0.11/0.45 % CPU time: 0.169044 seconds
% 0.11/0.45 % Total memory used: 101.292 MB
% 0.11/0.45 % Net memory used: 101.211 MB
%------------------------------------------------------------------------------