%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET014-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:08:50 PM UTC 2026
% Result : Unsatisfiable 180.11s 23.21s
% Output : CNFRefutation 180.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 77 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( little_set(X)
| ~ member(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [Z,X,Y] :
( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [Z,X] :
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] : union(X,Y) = complement(intersection(complement(X),complement(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [X,Y] :
( member(f17(X,Y),X)
| subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [X,Y] :
( ~ member(f17(X,Y),Y)
| subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f142,hypothesis,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,hypothesis,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,plain,
! [X] :
( little_set(X)
| ! [Y] : ~ member(X,Y) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f146,plain,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f182,plain,
! [Z,Y] :
( ~ member(Z,Y)
| ! [X] :
( ~ member(Z,X)
| member(Z,intersection(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f185,plain,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f186,plain,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f229,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subset(X,Y) ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f230,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
! [X0,X1] :
( member(f17(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f232,plain,
! [X0,X1] :
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f322,plain,
subset(as,cs),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f323,plain,
subset(bs,cs),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f324,plain,
~ subset(union(as,bs),cs),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f330,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,as) ),
inference(resolution,[status(thm)],[f322,f230]) ).
fof(f331,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,bs) ),
inference(resolution,[status(thm)],[f323,f230]) ).
fof(f382,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(complement(X1),complement(X2)))
| ~ member(X0,union(X1,X2)) ),
inference(paramodulation,[status(thm)],[f186,f184]) ).
fof(f1613,plain,
member(f17(union(as,bs),cs),union(as,bs)),
inference(resolution,[status(thm)],[f231,f324]) ).
fof(f1615,plain,
~ member(f17(union(as,bs),cs),cs),
inference(resolution,[status(thm)],[f232,f324]) ).
fof(f1617,plain,
~ member(f17(union(as,bs),cs),as),
inference(resolution,[status(thm)],[f1615,f330]) ).
fof(f1618,plain,
~ member(f17(union(as,bs),cs),intersection(complement(as),complement(bs))),
inference(resolution,[status(thm)],[f1613,f382]) ).
fof(f2034,plain,
( ~ member(f17(union(as,bs),cs),complement(bs))
| ~ member(f17(union(as,bs),cs),complement(as)) ),
inference(resolution,[status(thm)],[f1618,f183]) ).
fof(f2035,plain,
( member(f17(union(as,bs),cs),bs)
| ~ little_set(f17(union(as,bs),cs))
| ~ member(f17(union(as,bs),cs),complement(as)) ),
inference(resolution,[status(thm)],[f2034,f185]) ).
fof(f2036,plain,
( member(f17(union(as,bs),cs),bs)
| ~ member(f17(union(as,bs),cs),complement(as)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2035,f146]) ).
fof(f2086,plain,
( member(f17(union(as,bs),cs),as)
| ~ little_set(f17(union(as,bs),cs))
| member(f17(union(as,bs),cs),bs) ),
inference(resolution,[status(thm)],[f2036,f185]) ).
fof(f2087,plain,
( ~ little_set(f17(union(as,bs),cs))
| member(f17(union(as,bs),cs),bs) ),
inference(forward_subsumption_resolution,[status(thm)],[f2086,f1617]) ).
fof(f2088,plain,
( member(f17(union(as,bs),cs),cs)
| ~ little_set(f17(union(as,bs),cs)) ),
inference(resolution,[status(thm)],[f2087,f331]) ).
fof(f2089,plain,
~ little_set(f17(union(as,bs),cs)),
inference(forward_subsumption_resolution,[status(thm)],[f2088,f1615]) ).
fof(f2092,plain,
! [X0] : ~ member(f17(union(as,bs),cs),X0),
inference(resolution,[status(thm)],[f2089,f146]) ).
fof(f2145,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1613,f2092]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.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
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 04:41:50 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 180.11/23.21 % Refutation found
% 180.11/23.21 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 180.11/23.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 183.17/24.42 % Elapsed time: 23.845041 seconds
% 183.17/24.42 % CPU time: 176.398348 seconds
% 183.17/24.42 % Total memory used: 961.116 MB
% 183.17/24.42 % Net memory used: 893.662 MB
%------------------------------------------------------------------------------