%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET014-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 9 unt; 2 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 25 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Xs,Ys] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [Element,Superset] :
( member(Element,Superset)
| ! [Subset] :
( ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X,Ys] :
( member(X,Ys)
| ! [Xs] :
( member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f54,plain,
subset(as,cs),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
subset(bs,cs),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
~ subset(union(as,bs),cs),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f57,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,as) ),
inference(resolution,[status(thm)],[f54,f27]) ).
fof(f58,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,bs) ),
inference(resolution,[status(thm)],[f55,f27]) ).
fof(f73,plain,
! [X0,X1,X2] :
( member(member_of_1_not_of_2(union(X0,X1),X2),X1)
| member(member_of_1_not_of_2(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f28,f37]) ).
fof(f75,plain,
( member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as) ),
inference(resolution,[status(thm)],[f73,f56]) ).
fof(f80,definition,
( sQ0_spl
<=> member(member_of_1_not_of_2(union(as,bs),cs),as) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| member(member_of_1_not_of_2(union(as,bs),cs),as) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> member(member_of_1_not_of_2(union(as,bs),cs),bs) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| member(member_of_1_not_of_2(union(as,bs),cs),bs) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f80,f83]) ).
fof(f98,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(X0,cs),as)
| subset(X0,cs) ),
inference(resolution,[status(thm)],[f29,f57]) ).
fof(f181,plain,
( ~ sQ0_spl
| subset(union(as,bs),cs) ),
inference(resolution,[status(thm)],[f98,f81]) ).
fof(f184,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f56]) ).
fof(f185,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f190,plain,
( ~ sQ1_spl
| member(member_of_1_not_of_2(union(as,bs),cs),cs) ),
inference(resolution,[status(thm)],[f84,f58]) ).
fof(f192,plain,
( ~ sQ1_spl
| subset(union(as,bs),cs) ),
inference(resolution,[status(thm)],[f190,f29]) ).
fof(f193,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f56]) ).
fof(f194,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f195,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f185,f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET014-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:41:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.45 % Refutation found
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.47 % Elapsed time: 0.094394 seconds
% 0.10/0.47 % CPU time: 0.500998 seconds
% 0.10/0.47 % Total memory used: 24.102 MB
% 0.10/0.47 % Net memory used: 23.008 MB
%------------------------------------------------------------------------------