%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:10:08 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 58 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 25 ~; 16 |; 15 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 35 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( ( member(B,D)
& member(B,C) )
=> not_equal(intersection(C,D),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( ( member(B,D)
& member(B,C) )
=> not_equal(intersection(C,D),empty_set) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
( ! [B,C] :
( B = C
| not_equal(B,C) )
& ! [B,C] :
( B != C
| ~ not_equal(B,C) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f32,plain,
? [B,C,D] :
( ~ not_equal(intersection(C,D),empty_set)
& member(B,D)
& member(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
? [C,D] :
( ~ not_equal(intersection(C,D),empty_set)
& ? [B] :
( member(B,D)
& member(B,C) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ~ not_equal(intersection(sK2_skl,sK3_skl),empty_set)
& member(sK4_skl,sK3_skl)
& member(sK4_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(C,sK2_skl),skolemize(D,sK3_skl),skolemize(B,sK4_skl)],[f33]) ).
fof(f35,plain,
member(sK4_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
member(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
~ not_equal(intersection(sK2_skl,sK3_skl),empty_set),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
intersection(sK2_skl,sK3_skl) = empty_set,
inference(resolution,[status(thm)],[f25,f37]) ).
fof(f54,plain,
! [X0] :
( ~ member(X0,sK3_skl)
| ~ member(X0,sK2_skl)
| member(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f39,f13]) ).
fof(f57,plain,
! [X0] :
( ~ member(X0,sK3_skl)
| ~ member(X0,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f14]) ).
fof(f66,plain,
~ member(sK4_skl,sK2_skl),
inference(resolution,[status(thm)],[f57,f36]) ).
fof(f68,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f66,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:30:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.045981 seconds
% 0.14/0.41 % CPU time: 0.136704 seconds
% 0.14/0.41 % Total memory used: 101.535 MB
% 0.14/0.41 % Net memory used: 101.121 MB
%------------------------------------------------------------------------------